arxiv:2008.02280v1 [astro-ph.ga] 5 aug 2020 · mnras 000,1{27(2020) preprint 7 august 2020 compiled...

MNRAS 000 1ndash27 (2020) Preprint 5 January 2021 Compiled using MNRAS LATEX style file v30

Chemo-kinematics of the Gaia RR Lyrae the halo and the disc

Giuliano Iorio123 and Vasily Belokurov3dagger1Physics and Astronomy Department Galileo Galilei University of Padova Vicolo dellrsquoOsservatorio 3 Indash35122 Padova Italy2INFN - Padova Via Marzolo 8 Indash35131 Padova Italy3Institute of Astronomy University of Cambridge Madingley Road Cambridge CB3 0HA UK

Accepted XXX Received YYY in original form ZZZ

ABSTRACTWe present the results of a multi-component kinematic model of a large sample of RR Lyraedetected by Gaia By imposing a four-fold symmetry and employing Gaia proper motionswe are able to infer the behaviour of the velocity ellipsoid between asymp 3 and asymp 30 kpc fromthe centre of the Galaxy We detect the presence of two distinct components a dominant non-rotating halo-like population and amuch smaller rotating disc-like populationWe demonstratethat the halo RR Lyrae can be described as a superposition of an isotropic and radially-biasedparts The radially-biased portion of the halo is characterised by a high orbital anisotropy120573 asymp 09 and contributes between 50 and 80 of the halo RR Lyrae at 5 lt 119877(kpc)lt 25 Inline with previous studies we interpret this high-120573 component as the debris cloud of the ancientmassive merger also known as the Gaia Sausage (GS) whose orbital extrema we constrainThe lightcurve properties of the RR Lyrae support the kinematic decomposition the GS starsare more metal-rich and boast higher fractions of Oosterhoff Type 1 and high amplitude shortperiod (HASP) variables compared to the isotropic halo component The metallicityHASPmaps reveal that the inner 10 kpc of the halo is likely inhabited by the RR Lyrae born in-situThe mean azimuthal speed and the velocity dispersion of the disc RR Lyrae out to 119877 asymp 30 kpcare consistent with the behaviour of a young and metal-rich thin disc stellar population

Key words stars variables RR Lyrae ndash Galaxy kinematics and dynamics ndash Galaxy stellarcontent ndash Galaxy halo ndash Galaxy disc

1 INTRODUCTION

The simple and convenient picture in which the Galaxy is made upof clear-cut structural blocks largely independent yet arranged towork in concert is falling apart before our eyes The harbinger ofthis paradigm shift is the mushrooming of dualities ndash today everypiece of the Milky Way has acquired a sidekick there are two discslsquothinrsquo and lsquothickrsquo (or more precisely 120572-poor and 120572-rich see Gilmoreamp Reid 1983 Fuhrmann 1998 Bensby et al 2003 Haywood 2008Bovy et al 2012 Hayden et al 2015) the accreted halo must bedistinguished from the one built in-situ (eg Searle amp Zinn 1978Helmi et al 1999 Brook et al 2003 Venn et al 2004 Bell et al2008 Nissen amp Schuster 2010 Bonaca et al 2017 Gallart et al2019 Belokurov et al 2020a) and the bulge is really a bar orperhaps several (Blitz amp Spergel 1991 Binney et al 1997 Zoccaliet al 2003 McWilliam amp Zoccali 2010 Robin et al 2012 Nesset al 2013 Wegg amp Gerhard 2013 Bensby et al 2013)

Thanks to the ESArsquos Gaia space observatory (Gaia Collabo-ration et al 2016) we are reminded that in fact the Galaxy is anevolving and interconnected system where components may inter-

giulianoiorioastrogmailcomdagger vasilyastcamacuk

act and can profoundly affect each other For instance it is nowclear that the last significant merger that formed the bulk of thestellar halo (Deason et al 2013 Belokurov et al 2018b Haywoodet al 2018 Helmi et al 2018 Mackereth et al 2019a Fattahi et al2019) may be connected to a series of metamorphoses occurringin the young Milky Way This early accretion event revealed by theunprecedented astrometry from Gaia not only dictates the struc-ture of the inner stellar halo (Deason et al 2018 Myeong et al2018ab Koppelman et al 2018 Lancaster et al 2019 Iorio amp Be-lokurov 2019 Simion et al 2019 Bird et al 2019) but appears tobe contemporaneous with the demise of the thick disc emergenceof the in-situ halo and the formation of the bar (Di Matteo et al2019 Fantin et al 2019 Belokurov et al 2020a Grand et al 2020Bonaca et al 2020 Fragkoudi et al 2020 Sit amp Ness 2020) Thesetumultuous transmutations are not exclusive to the Galaxyrsquos youthndash signs have been uncovered of the ongoing interactions quakingthe Galactic plane (Minchev et al 2009 Widrow et al 2012 Xuet al 2015) including pieces of evidence procured recently usingtheGaiaData Release 2 (see Antoja et al 2018 Laporte et al 2019Bland-Hawthorn et al 2019) Even today it is easy to start in the discand end up in the halo (Michel-Dansac et al 2011 Price-Whelanet al 2015 Goacutemez et al 2016 Jean-Baptiste et al 2017 Laporteet al 2018 de Boer et al 2018)

copy 2020 The Authors

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2 G Iorio and V Belokurov

In this time of confusion reliable distance and agemetallicityindicators are essential to building a coherent picture of the MilkyWay For decades pulsating horizontal branch stars known as RRLyrae (RRL hereafter) have been trusted upon to help us chart theGalaxy (eg Kinman et al 1966 Oort amp Plaut 1975 Saha 1985Hartwick 1987 Catelan 2009 Pietrukowicz et al 2015) Usingpainstakingly-assembled spectroscopic samples it has been estab-lished that RRL metallicities span a wide range but the stars appearpredominantly metal-poor while the analysis of the Galactic Glob-ular clusters revealed prevalence for old ages (Preston 1959 Butler1975 Sandage 1982 Suntzeff et al 1991 Lee et al 1994 Clemen-tini et al 1995 Clement et al 2001) Note that in the field RRLare sufficiently rare therefore no large spectroscopic datasets arecurrently available However an approximate metallicity estimatecan be gauged from the properties of the lightcurve alone (Sandage1982 Carney et al 1992 Nemec et al 1994 Jurcsik amp Kovacs1996 Nemec et al 2013)

In the last two decades wide-area multi-epoch surveys havebrought in a rich harvest of variable stars in general and RRL inparticular (eg Sesar et al 2007 Soszyński et al 2009 Drake et al2013 Soszyński et al 2014 Torrealba et al 2015 Sesar et al 2017)Typically old and metal-poor RRL have long served as a tried andtrue tracer of the Galactic halo and its sub-structures (eg Vivaset al 2001 Morrison et al 2009 Watkins et al 2009 Sesar et al2013 Simion et al 2014 Mateu et al 2018 Hernitschek et al2018) Gaia the first truly all-sky variability census in the opticalhas further improved our understanding of the MilkyWay RRL notonly by filling in the gaps left behind by the previous generationsof surveys but also by providing high-quality proper motions forthe bulk of the RRL it sees The Gaia data has thus enabled a newprecise characterisation of the Galactic halo density field (eg Iorioet al 2018 Wegg et al 2019 Iorio amp Belokurov 2019) and helpedto discover halo sub-structures previously not seen (Belokurov et al2017 Koposov et al 2019 Belokurov et al 2019 Torrealba et al2019)

While it is true that RRL are being used primarily to trace thefossil record of the Milky Way assembly it was always known thatin the field a relatively small number of metal-rich examples exist(Kukarkin 1949 Preston 1959 Smith 1984 Layden 1994 Walkeramp Terndrup 1991 Deacutekaacuteny et al 2018 Chadid et al 2017 Fabrizioet al 2019 Zinn et al 2020) Based on their kinematics thesemetal-rich RRL were assigned to the Galactic disc(s) (Layden 1995a)Given the enormous number of available red giant progenitorsmetal-rich RRL in the disc were estimated to form between 200and 800 times less often compared to their old and metal-poor halocounterparts (Taam et al 1976 Layden 1995b)While the formationchannel has not yet been identified these early studies as well as thesubsequent follow-up conjectured that the progenitors of metal-richRRL ought to be old ie gt 10Gyr (eg Mateu amp Vivas 2018) Thepresence of likely old metal-rich RRL has been confirmed also inmetal-rich Globular Clusters (eg NGC 6338 and NGC 6441 seePritzl et al 2000) however they have periods that are significantlylarger with respect to field metal-rich RRL The main obstacle tothe production of a metal-rich RRL is its temperature on the HBwith higher envelope opacities these stars tend to sit too far to thered from the instability strip (eg Dorman 1992) Therefore beforearriving onto the HB metal-rich RRL progenitors are required toundergo copious levels of mass-loss asymp 05M or more which maywell be beyond what is physically possible

Most recently the conundrum of metal-rich RRL has beengiven a new lease of life Marsakov et al (2018) demonstrated thatwhile plenty of the local metal-rich RRL likely belong to the thick

disc (and thus can be as old as asymp10 Gyr) a substantial fractiondisplays the kinematics of the younger portion of the thin disc Anage of only few Gyrs would be very difficult to reconcile with theconventional scenarios of the RRL formation Note that if extrememass loss can be invoked ie in excess of 1 M then even young(gt 1 Gyr) progenitors can produce metal-rich RRL (see Bono et al1997ab) In a follow-up study Marsakov et al (2019) estimatedthe masses of the metal-rich thin disc RRL and found them to be oforder of 05minus06M thus confirming the need formass loss beyondthe typically accepted values Finally Zinn et al (2020) and Prudilet al (2020) combined RRL with available spectroscopy with theGaia DR2 astrometry to confirm the existence of metal-rich RRLstars with the orbital properties typical of the Galactic thin discWith these most recent observations in hand it remains to be seenif metal-rich RRL can actually be easily accommodated within thecurrent stellar evolution theory Comparing the structural propertiesof themetal-rich andmetal-poorRRLChadid et al (2017) concludethat it can not

What is hard to achieve via single stellar evolution channelscan (sometimes) be effortlessly done with binary stars Indeed anobject has been discovered that nimbly mimics the classic RR Lyraebehaviour ie lives on the instability strip and pulsates with thesame kind of lightcurve yet it is not an RR Lyrae at least notin the conventional meaning of the term (Pietrzyński et al 2012)This star designatedBinaryEvolution Pulsator (BEP) is a low-mass(026119872) remnant of mass transfer in a binary systemwith a periodofasymp 15 daysAs the follow-up theoreticalwork demonstrates binaryevolution can lead to a broad range ofBEPmasses and in some caseseven involve a stripped starwith a helium-burning core (Karczmareket al 2017) These impostors would be indistinguishable from theclassic RR Lyrae but have an age of only 4-5 Gyr Only one suchobject has been found so far but searches for RR Lyrae in binarysystems are ongoing (eg Prudil et al 2019b Kervella et al 2019)

This work aims to exploit the unprecedented all-sky coverageof Gaia to study the chemo-kinematics of the halo and the discof the Milky Way as traced by RRL stars The paper is organisedas follows Section 2 presents the construction of a clean sampleof Gaia RRL stars and gives the details of the methods we use toestimate physical quantities like distance metallicity and transversevelocity Section 3 describes the machinery employed to performthe kinematic decomposition of the Galactic components Thenwe discuss the properties of the individual components the haloin Section 4 and the disc in Section 5 In Section 6 we discusspossible biases affecting the results and finally we summarise themain conclusions

2 THE SAMPLE

We use the whole catalogue of stars classified as RRL in GaiaDR2 (Gaia Collaboration et al 2018a) combining the SOS(Specific Object Study Clementini et al 2019) RRL cataloguewith the stars classified as RRL in the general variability tablevari_classifier_result (Holl et al 2018) following the proce-dure described in Iorio amp Belokurov (2019) The initial combinedcatalogue contains 228853 stars (asymp 77 RRab asymp 21 RRc andasymp 2 RRd)

21 Distance and velocities estimate

One of the key ingredients of this analysis is the distance from theSun 119863 of each star Once the heliocentric distance is known

MNRAS 000 1ndash27 (2020)

Chemo-kinematics of the Gaia RR Lyrae 3

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Figure 1 Distances and transverse velocities for stars in the Gclean catalogue (see Section 22) Top panels show density distributions in the plane of relativeerror (absolute value) and heliocentric distance Bottom panels give distributions of the heliocentric distance and the components of the apparent (sky-projected)tangential velocity Note that this plot also shows stars with 119863 gt 40 kpc that are eliminated in the final Gclean catalogue

we estimate the Galactocentric coordinates and using the observedproper motion calculate the velocities 119881ℓ (along the Galactic lon-gitude ℓ) and 119881119887 (along the Galactic latitude)Galactic parametersWe set a left-handed Galactocentric frame ofreference similar to the one defined in Iorio et al (2018) here 119909119910119911indicate theCartesian coordinates 119877 is the cylindrical radius 119903 is thespherical radius and 120601 represent the azimuthal and zenithal angleIn this coordinate system the Sun is located at 119909 = 119877 = 813plusmn03kpc (Gravity Collaboration et al 2018) and 119911 = 0 kpc (see Io-rio et al 2018) In order to correct the observed stellar veloc-ity for Sunrsquos motion we adopt 119881lsr = 238 plusmn 9 km sminus1 (Schoumln-rich 2012) for the local standard of rest (lsr) and (119880 119881 119882) =(minus1110plusmn123 1224plusmn205 725plusmn063) km sminus1 (Schoumlnrich et al2010) for the Sunrsquos proper motion with respect to the lsr (assum-ing the Galactocentric frame of reference defined above) The finalcorrecting vector is

119881corr = (minus1110 plusmn 123 25024 plusmn 923 725 plusmn 063) (1)

In order to take into account all of the uncertainties in theestimate of the physical parameters of interest we use aMonte-Carlosamplingmethod (105 realisations) following the steps i) correctionof Gaia 119866 magnitudes for the dust reddening 119894119894) estimate of themetallicity 119894119894119894) estimate of the absolute magnitude119872G 119894119907) estimateof the distance and the Galactocentric coordinates 119907) estimate ofthe velocities Where not specified we sample the value of a givenparameter 119883 = plusmn 120575119883 drawing variates from a normal distributioncentred on and with a standard deviation 120575119883

Magnitude correction for dust reddening We correct the ob-

served 119866obs magnitude as

119866 = 119866obs minus 119896G119864 (119861 minus119881) (2)

where 119864 (119861 minus 119881) and its error 120575E(BminusV) = 016 times 119864 (119861 minus 119881) comesfrom Schlegel et al (1998) The factor 119896G is obtained by applyingEquation 1 of Gaia Collaboration et al (2018b) iteratively if thestar has an estimate of the Gaia color 119861119875 minus 119877119875 otherwise weassume 119896G = 227 plusmn 030 (Iorio amp Belokurov 2019) For the starsin the SOS catalogue the adopted 119866obs is the SOS table entryint_average_g and the color 119861119875minus119877119875 is the difference between thecolumns int_average_bp and int_average_rp For the otherstarswe use the values reported in the generalGaia source catalogue(phot_g_mean_mag phot_bp_mean_mag phot_rp_mean_mag)We notice a small offset (asymp 003 for 119866obs and asymp 002 for 119861119875 minus 119877119875)between the SOS and general Gaia values hence we correct thelatter We use the values from the SOS catalogue as standard fortwo reasons they are estimated directly from the lightcurves (robustagainst outliers see Clementini et al 2019) and the magnitude-metallicity relation we use (see below) has been calibrated on these119866 values (see Muraveva et al 2018) After the offset correction thedifferences between the SOS and Gaia observed magnitudes canbe treated as another source of random errors on the estimate of119866 For most of the stars in the sample (gt 98 ) the magnitude ofthis error is 01 representing a negligible amount in the errorbudget of the final distance estimate (see below) We decided to notconsider the errors on 119866obs thus the error on 119866 comes only fromthe uncertainties on 119896G or 119864 (119861 minus119881)Metallicity estimate It is well known that the metallicities of RRLcorrelate with their lightcurve properties (eg Jurcsik amp Kovacs



1000100 [deg]

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eg]

Gclean catalogue N = 72973

0 20 40R [kpc]

010203040

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Figure 2Galactic (top panel) and Galactocentric cylindrical (bottom panel)star count maps for objects in the Gclean catalogue (see Section 22)

1996 Smolec 2005 Nemec et al 2013 Hajdu et al 2018) Twoof the most used properties are the period (fundamental period 119875for RRab stars first overtone period 1198751o for RRc stars) and thephase difference between the third and the first harmonics Φ31 ofthe lightcurve decomposition Although the SOS catalogue alreadyreports an estimate of the metallicity based on the Nemec et al 2013relations (see Clementini et al 2019) we decide to use instead alinear relation calibrated directly on the Gaia 119875 (or 1198751o) and Φ31parameters (see eg Jurcsik amp Kovacs 1996) For the RRab starswe cross-match the SOS catalogue with the spectroscopic sampleof Layden (1994) finding 84 stars in common and deriving thefollowing relation

[FeH]RRab =(minus168 plusmn 005) + (minus508 plusmn 05) times (119875 minus 06)+ (068 plusmn 011) times (Φ31 minus 20)

(3)

with an intrinsic scatter 120575 [FeH] = 031 plusmn 003 Concerning theRRc following Nemec et al (2013) we use the RRc stars in knownGlobular Clusters as classified by Gaia Collaboration et al (2018d)then we assign to each of them the metallicity reported for theGlobular Clusters in Harris (1996)1 Using this method we obtainthe following metallicity relation

[FeH]RRc =(minus126 plusmn 003) + (minus939 plusmn 066) times (1198751o minus 03)+ (029 plusmn 005) times (Φ31 minus 35)

(4)

with an intrinsic scatter 120575 [FeH] = 016plusmn003We sample themetal-licity distribution for each star drawing from both the 119875 (or 1198751o) andΦ31 distributions considering their errors and from the posterior ofthe model parameters (taking into account their correlation) In casethe star has not a period estimate andorΦ31 these values are drawnfrom their overall 2D distribution considering the whole Gaia SOScatalogue After this step we end up with 105 [FeH] realisations

1 httpvizieru-strasbgfrviz-binVizieR-source=VII

202

for each star Further information on the metallicity estimate can befound in the Appendix AAbsolute magnitude The absolute magnitudes are estimated usingthe 119872G minus [FeH] relation described in Muraveva et al (2018)We sample the absolute magnitude distribution for each star usingthe [FeH] realisations (see above) and drawing the 119872G minus [FeH]relation parameters (taking into account the intrinsic scatter) usingthe errors reported by Muraveva et al (2018)Distance estimateWe produce 105 realisations of the heliocentricdistance using the familiar equation

log(119863kpc

)=119866 minus 119872G5

minus 2 (5)

Then the heliocentric distance and the observed Galactic coordi-nates (ℓ 119887 taken without their associated uncertainties) are used toobtain realisations of the Galactocentric Cartesian cylindrical andspherical coordinates (119909119910119911119877119903120601) taking into account the errorson the Galactic parameters Finally we use the mean and the stan-dard deviation of the final realisations to obtain the fiducial valueand errors on the Galactic coordinates for each starVelocity estimate We estimate the physical velocities from theobserved proper motions as

119881ℓ = 119870`ℓ119863 +119881ℓ119881b = 119870`119887119863 +119881b

(6)

where 119870 asymp 474 is the conversion factor from mas kpc yrminus1 tokm sminus1 119881ℓ and 119881b represent the projection of the Sun velocity(Equation 1) in the tangential plane at the position of the star Thesetwo values are estimated by applying the projection matrix definedin EquationA2 in Iorio et al (2019) to the correcting vector in Equa-tion 1We draw 105 realisations for each star taking into account the119863 samples the errors and the covariances of the proper motionsand the errors on 119881corr Then we estimate the mean value thestandard deviation and the covariance between 119881ℓ and 119881b We usethese values to perform our kinematic analysis (see Section 3)

22 Cleaning

In order to study the global properties of the (large-scale) Galacticcomponents we clean the RRL sample by removing the stars be-longing to the most obvious compact structures (Globular Clustersand dwarf galaxies including the Magellanic Clouds) as well asvarious artefacts and contaminants This procedure is similar to thecleaning process described in Iorio amp Belokurov (2019) especiallywith regards to the cull of known Galactic sub-structures Concern-ing the artefacts and contaminants we employ a slightly differentscheme in order to both maintain as many stars at low latitudes aspossible and have more robust quality cuts In particular we focuson removing stars that could have biased astrometric solutions orunreliable photometry

Artefacts and contaminants Holl et al (2018) Clementini et al(2019) and Rimoldini et al (2019) found that in certain regions(the bulge and the area close to the Galactic plane) the presence ofartefacts and spurious contaminants in the Gaiarsquos RRL cataloguescan be quite significant The contaminants in these crowded fieldsare predominantly eclipsing binaries and blended sources with aminute number of spurious defections due to misclassified vari-able stars (Holl et al 2018) To remove the majority of the likelycontaminants we apply the following selection cuts

bull 119877119880119882119864lt12



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Figure 3 Top results of the double-component fit for the RRLs in the Gclean sample (see Table 1) Maximum-a-posteriori (MAP) values are shown incylindrical coordinates Bottom mixed 1 and 2 component results (results from the double-component fit if ΔBIC gt 10 otherwise from the single-componentfit see text for details) Left column shows the fraction of the rotating component middle panels give the azimuthal velocity of the rotating component whileright column presents the anisotropy of the halo-like component

bull 10+ 0015times (119861119875minus 119877119875)2 lt 119861119877119864 lt 13+ 006times (119861119875minus 119877119875)2bull 119864 (119861 minus119881)lt08

The renormalised_unit_weight_error (119877119880119882119864) is ex-pected to be around one for sources whose astrometric measure-ments are well-represented by the single-star five-parameter modelas described in Lindegren et al (2018) Therefore the above 119877119880119882119864cut eliminates unresolved stellar binaries (see eg Belokurov et al2020b) as well as blends and galaxies (see eg Koposov et al 2017)The phot_bp_rp_excess_factor 119861119877119864 represents the ratio be-tween the combined flux in the Gaia 119861119875 and 119877119875 bands and the fluxin the 119866 band and thus by design is large for blended sources (seeEvans et al 2018) Following Lindegren et al (2018) we removestars with 119861119877119864 larger or lower than limits that are functions of theobserved colors (Equation C2 in Lindegren et al 2018) Finally weremove stars in regions with high reddening 119864 (119861 minus 119881) (accordingto Schlegel et al 1998) for which the dust extinction correction islikely unreliable After these cuts our RRL sample contains 115774RRL starsGlobular clusters and dwarf satellites We consider all globularclusters (GCs) from the Harris (1996) catalogue2 and all dwarfgalaxies (dWs) from the catalogue published as part of the Pythonmodule galstream3 (Mateu et al 2018) We select all stars withintwice the truncation radius of a GC if this information is presentotherwise we use 10 times the half-light radius For the dWs wetake 15 times the half-light radius Amongst the selected objects weremove only the stars in the heliocentric distance range 119863GCdWs plusmn025 times 119863GCdWs The chosen interval should be large enough tosafely take into account the spread due to the uncertainty in the RRLdistance estimate (see Section 21 and Figure 1) This procedureremoves 1350 stars

2 httpphyswwwmcmasterca~harrisDatabaseshtml3 httpsgithubcomcmateugalstreams

Sagittarius dwarf In order to exclude the core of the Sagittariusdwarf we select all stars with |minus Sgr | lt 9 and |Λminus ΛSgr | lt 50where and Λ are the latitude and longitude in the coordinatesystem aligned with the Sagittarius stream as defined in Belokurovet al (2014)4 and Sgr = 424 and ΛSgr = minus155 represent theposition of the Sagittarius dwarf Then among the selected objectswe get rid of all stars with a proper motion relative to Sagittariuslower than 2mas yrminus1 considering the dwarfrsquos proper motion fromGaia Collaboration et al (2018d) The stars in the tails have beenremoved considering all the objects within | minus Sag | lt 11 andwith proper motions (in the system aligned with the Sgr stream)within 15 mas yrminus1 from the proper motions tracks of the Sgrstream (D Erkal private communication the tracks are consistentwith the ones showed in Ramos et al 2020) The cuts of the coreand tails of the Sgr dwarf remove 7233 starsMagellanic CloudsWe apply the same selection cuts as those usedin Iorio amp Belokurov (2019) thus removing 14987 stars (11934 forthe LMC and 3053 for the SMC)Cross-match with other catalogues In order to identify possi-ble classification mistakes and other contaminants we cross-matchthe catalogue scrubbed of substructures and artefacts (as describedabove) with the 119878119868119872119861119860119863 astronomical database (Wenger et al2000) the 119862119878119878 periodic variable table5 (Drake et al 2017) andthe 119860119878119860119878-1198781198736 catalogue of variable stars (Jayasinghe et al 20182019ab) We remove all stars that have not been classified asRRLyr CandidateRRLyr HB Star Candidate_HB UNKNOWNV V in 119878119894119898119887119886119889 (1015 stars) RRab RRc or RRd in 119862119878119878 (655stars) or 119860119878119860119878-119878119873 (11963 stars) Analysing these data we found a

4 Actually we use a slightly different pole for the Sagittarius stream with120572 = 30363 (Right Ascension) and 120575 = 5958 (declination)5 httpvizieru-strasbgfrviz-binVizieR-3-source=J

ApJS2139table3amp6 httpsasas-snosueduvariables



00 02 04 06 08 10qMAP halo

10 2

10 1

100

NN

tot

rotating component selectionhalo component selection

Figure 4Distribution of the RRLmaximum-a-posteriori probability (MAPsee Section 31) of belonging to the non-rotating (halo) kinematic compo-nent from the double component fit described in Section 33 The redo-hatched and the green x-hatched regions indicate the 119902MAPhalo cuts usedto select the halo and the rotating (disc-like) subsample respectively

low level of contamination (stars not classified as RRL in the cross-matched catalogue 3) considering 119878119894119898119887119886119889 and 119862119878119878 while thelevel of contamination considering 119860119878119860119878-119878119873 is ten times larger(asymp 27) However as most of the contaminants are classified asUNKNOWN (asymp 20) in 119860119878119860119878-119878119873 these objects could suffer frompoor lightcurve sampling Another significant contaminant classis eclipsing binaries mostly W Ursae Majoris variables (WUMaasymp 5) for which the lightcurve could bemisclassified as an RRc In-deed among the stars classified as WUma in 119860119878119860119878-119878119873 about 80are classified as RRc in the Gaia SOS catalogue Not consideringthe dominant sources of contamination discussed above the numberof unwanted interlopers estimated from 119860119878119860119878-119878119873 is similar to thatobtained with 119878119894119898119887119886119889 and119862119878119878 Comparing the RRL classificationfor the stars in common between the Gaia SOS catalogue and theGaia general variability catalogue we decided to remove all starsthat have been classified as RRd (2941 stars) in at least one of thetwo catalogues In total these cuts remove 15633 starsDistance cutGiven the significant increase in velocity uncertaintiesat large distance we decide to limit the extent of our sample towithin40 kpc from the Galactic centre This cut removes 4057 stars

The final cleaned catalogue contains 72 973 stars (Gclean cat-alogue) We also produce a very conservative catalogue consideringonly the stars that have been classified as RRab in both Gaia SOSand 119860119878119860119878-119878119873 (17 570 stars SA catalogue) we also require thatthey have complete Gaia lightcurve information (period and Φ31)In the rest of the paper we will compare the results of the analysis ofthe two catalogues to investigate potential biases due to artefacts andcontaminants that went unnoticed The distributions of heliocentricdistances and of the transverse velocities in the Gclean catalogue areshown in the bottom panel of Figure 1 (displaying the sample beforethe distance cut)Most of the stars are locatedwithin 20-25 kpc fromthe Sun but there are still hundreds of stars out to approximately40 kpc beyond this radius the number of objects in the cataloguedecreases abruptly (these objects are not present in the final Gcleancatalogue) The relative distance and velocities uncertainties areshown in the top panels of Figure 1 four sequences are clear inthe left-hand panel The vertical sequence located around 8-10 kpcis due to the stars in highly-extincted regions where the uncertain-ties on the reddening dominate the error budget (see Section 21)The higher horizontal sequence (120575119863119863 asymp 012) comprises of

the stars without the period estimate The other two sequences aredue to stars without Φ31 estimate (120575119863119863 asymp 011) and to starsin the SOS catalogue with complete information (period and Φ31120575119863119863 asymp 010) Overall most of the stars have distance errorsslightly larger than 10 while the relative errors on velocities canreach substantial values (up to 50 minus 100) The errors reportedin Figure 1 are random errors based on the Monte-Carlo analy-sis (Section 21) however we also analyse the possible systematiceffects due to the assumptions made when information about theperiod andor when Φ31 andor the Gaia colors is not available(Section 21) For most of the cases the systematic shift is sub-dominant (relative errorasymp 5) with respect to the random errorsHence we do not include a systematic component in the uncertain-ties used in the kinematic analysis Based on the error properties ofthe catalogue we expect that our analysis (Section 3) is able to givereliable constraints on the kinematic parameters within 20-30 kpcfrom the Galactic centre while the quality of the results progres-sively degrades at large radii The distribution of the stars on thesky and in the Galactocentric 119877 |119911 | plane are shown in the left-handcolumn of Figure 2

3 THE METHOD

This work aims to study the kinematics of the RRL stars in theGaia dataset Such an analysis is however hampered by the lack ofline-of-sight (los) velocity measurements for most of the stars in ourfinal catalogue ndash indeed only 266 out of more than 70 000 stars haveGaia radial velocity Relying on cross-matches with other spectro-scopic catalogue such as 119877119860119881119864 (Kunder et al 2017) 119860119875119874119866119864119864(Majewski et al 2017) or 119871119860119872119874119878119879 (Cui et al 2012) would reducethe number of objects as well as the radial extent and sky coverage ofthe catalogue Moreover the periodic radial expansioncontractionof the RRL surface layers if not taken into account can bias theradial velocity measurements by up to 40minus 70 km sminus1 (see eg Liu1991 Drake et al 2013)

The lack of the los velocities makes it impossible to estimatethe full 3D velocity information on a star-by-star basis Howeversince stars at different celestial coordinates and different heliocen-tric distances have distinct projections onto the 3DGalactic velocityspace it is possible to estimate the velocity moments (mean valuesand standard deviations) of the intrinsic 3D velocity ellipsoid us-ing the proper motions of a group of stars taken together under theassumptions of symmetry (see eg Dehnen amp Binney 1998 Schoumln-rich et al 2012 Schoumlnrich amp Dehnen 2018 Wegg et al 2019)In practice we consider two possibilities and assume that propermotions of stars i) at the same 119877 and |119911 | (cylindrical symmetry) orii) the same 119903 (spherical symmetry) sample the same 3D velocitydistribution

31 Kinematic fit

In what followswe implement the ensemble velocity moment modelfollowing and extending the method described inWegg et al (2019)(W19 hereafter) In this section we briefly summarise the methodfurther details can be found in the original W19 paper The basicassumption is that the intrinsic velocity distribution of stars in agiven Galactic volume at given Galactocentric coordinates (egspherical or cylindrical) is a multivariate normal 119891 (119933) = N

(Σ

)

where is the Gaussian centroid and Σ is the covariance matrix orvelocity dispersion tensor This distribution can be projected ontothe heliocentric sky coordinates 119933sky = (119881los 119881ℓ 119881119887) appliyng the



1000100 [deg]

500

50

b [d

eg]

Halo N = 49914

1000100 [deg]

500

50

b [d

eg]

Rotating N = 3126

1000100 [deg]

500

50

b [d

eg]

Unclassified N = 20353

0 20 40R [kpc]

0

10

20

30

40

|z| [

kpc]

0 20 40R [kpc]

0

10

20

30

40|z

| [kp

c]

0 20 40R [kpc]

0

10

20

30

40

|z| [

kpc]

Figure 5 Three RRL groups Same as Figure 2 but for the stars in the Gclean catalogue (Section 22) belonging to the halo sub-sample (left) rotating disc-likesubsample (centre) and stars that satisfy neither of the above criteria (right) see Section 33 for details The color-map is the same as that shown in Figure 2

00 02 04 06 08 10qMAP halo anisotropic

10 2

10 1

100

NN

tot

Figure 6Distribution of the RRLmaximum-a-posteriori probability (MAPsee Section 31) of belonging to the (radially) anisotropic kinematic compo-nent as inferred from the double component fit described in Section 33

rotation matrix R (different for each sky position) satisfying119933sky =R119933 The projected distribution is still a Gaussian and therefore itcan be easily analytically marginalised over the unknown term119881losFinally the likelihood for a given star located at given distance andposition on the sky to have velocities 119933perp = (119881ℓ 119881119887) is given by

L = N(perpΛperp + S

) (7)

where

bull perp = Rperp and Rperp is the rotation matrix R without the 1strow related to the los velocity (2 times 3 matrix see Appendix B)

bull Λperp is the projected covariance matrix Λ = R120506Rᵀ without the1st row and the 1st column related to the los velocity (2times2matrix)

bull S is a 2x2 matrix of the119881ℓ 119881119887 measurement errors and covari-ance (see Section 21)

In order to estimate the velocity moments we consider the totallikelihood as the product of the likelihoods (Equation 7) of all starsin a given Galactic volume bin The method described so far fol-lows point by point what has been done in W19 We add a furthergeneralisation considering the intrinsic velocity distribution as acomposition of multiple multivariate normal distributions There-fore the likelihood for a single star becomes

Lmulti =sum119894

119891119894N(119894perpΛ119894perp + S119894

)=sum119894

119891119894L119894 (8)

where the component weights 119891 sum up to 1 Using Equation 8we can apply a Gaussian Mixture Model to the intrinsic velocitydistribution fitting only the observed tangential velocities Startingform Equation 8 it is possible to define for each star the a-posteriorlikelihood of belonging to the 119894th component as

119902119894 =119891119894L119894

Lmulti (9)

The stochastic variables 119902 (and their uncertainties) allow us to de-compose the stars into different kinematic populations using a quan-titative ldquometric For a given sample of stars (see Section 32) weretrieve the properties (119933120506) (3+6 parameters) of the kinematiccomponents and their weights adopting a Monte Carlo MarkovChain (MCMC) to sample the posterior distributions generatedby the product of all likelihoods defined in Equation 8 In prac-tice the posterior distributions have been sampled using the affine-invariant ensemble sampler MCMC method implemented in thePython module emcee7 (Foreman-Mackey et al 2013) We used50 walkers evolved for 50000 steps after 5000 burn-in steps Weevaluate the convergence of the chains by analysing the trace plots

7 httpsemceereadthedocsioenstable



Figure 7 Properties of the radially-anisotropic halo component (see Section 41) relative fraction of the radial component over the total (top) its anisotropy(middle) and the position of the peak of the double-horn profile assumed for the distribution of the radial velocity (bottom see Section 4) Left (right) panelsshow the results of the model applied to spherical (cylindrical) Voronoi bins (see Section 32 and Section 4) The large yellow data-points give the medianof the a-posteriori distribution while the error-bars indicate its 16th and 84th percentile the small-red points show the Maximum-a-Posteriori (MAP) of theposteriors X-axis represents the median of the spherical radial distribution while the errorbars indicate the median value of the errors on the radius of thestars in each bin the grey bands show the 1120590 and 2120590 interval from a Gaussian Process (GP) interpolation We interpolate the symmetrised version of thedata points with a GP process data-points show the middle values between the 16th and 84th percentile while the vertical error-bars are half of the 16th-84thpercentile distance the blue band shows the 1120590 interval of the posterior obtained using the SA (SOS+119860119878119860119878-119878119873 ) catalogue (see Section 22) The circularlines indicate the spherical radii of 5810152025 kpc

and estimating the autocorrelation time 120591 119891 8 (see eg Goodman ampWeare 2010) In particular we check that for all of our fits andparameters the number of steps is larger than 50120591 119891 ie the num-ber is sufficient to significantly reduce the sampling variance of theMCMC run All kinematics models have been run and analysedusing the Python module Poe9

In the next Sections we exploit this method to separate theRRL sample into two distinct kinematic components a non-rotating(or weakly rotating) halo-like population and a population with alarge azimuthal velocity Subsequently the same method is appliedagain to separate kinematically the halo into an anisotropic and anisotropic populations The choice of binning in the given coordinatesystem (spherical or cylindrical) the number of Gaussian compo-

8 An useful note about autocorrelation analysis and convergence can befound at httpsemceereadthedocsioenstabletutorialsautocorr9 httpsgitlabcomiogiulpoegit

nents and the prior distributions of their parameters are describedin the following Sections

32 Binning strategy

Each of our kinematic analyses is applied to stars grouped in binsof Galactic 119903 or 119877 |119911 | assuming spherical or cylindrical symmetrycorrespondingly In each of these bins the intrinsic distribution ofvelocities is considered constant In order to have approximately thesame Poisson signal-to-noise ratio (

radic119873stars) in each bin we compute

a Voronoi tessellation of the 119877 |119911 | plane making use of the vorbinPython package (Cappellari amp Copin 2003)10 When assigningstars to bins in spherical 119903 we select the bin edges so that each bincontains 119873stars objects If the outermost bin remains with a numberof stars lower than 119873stars we merge it with the adjacent bin In the

10 httpswww-astrophysicsoxacuk~mxcsoftware

binning



Figure 8 Same as Figure 7 but for the azimuthal velocity for the radially-anisotropic (left-hand panel) and the isotropic (right-hand panel) components

rest of the paper we identify the coordinates of a given bin (119877 |119911 | or119903) as themedian of the coordinate of the stars in the bin we associateto these values an error that is themedian of the corresponding errorsof the stars Although we do not take account explicitly of the errorson 119877|119911 | and 119903 in the kinematic fit the velocities 119881ℓ and 119881119887 alreadyincorporate the errors on distance (Section 21) In practice wedo not allow stars to belong to more than one bin even if this isconsistent with their Galactic coordinate errors This choice doesnot represent a serious issue in our analysis but at large radii wherethe errors are larger the kinematic parameters obtained with our fitare likely correlated in adjacent bins

33 Kinematic separation

In order to separate the non-rotating halo from a component with ahigh azimuthal velocity we set up a double-component fit

bull 1st component (halo-like) spherical frame-of-reference norotation (119881120601 = 0) anisotropic velocity dispersion tensor (we fit thethe radial 120590r and tangential 120590t = 120590120601 = 120590 velocity dispersion)

bull 2nd component (rotating) spherical frame of referenceisotropic velocity dispersion tensor

In both cases the centroids along 119881r and 119881 are set to 0 We assumethat the velocity ellipsoids are aligned in spherical coordinates fix-ing to 0 the diagonal terms of the velocity dispersion tensor (seeeg Evans et al 2018) Table 1 summarises the model parametersand their prior distributions In particular we set non-exchangeablepriors for the velocity centroids and velocity dispersions to breaklabelling degeneracy (switching between models in the MCMC

Prior distributionshalo rotating

119881120601 120575 (0) N(100 200) [50infin]119881r = 119881 120575 (0)120590r N(150 200) [0infin] N(0 20) [0infin]120590t N(100 200) [0infin]120588r120601 = 120588r = 120588120601 120575 (0)119891 U(0 1)

Table 1 Prior distributions for the parameters of the double-component fitnon-rotating halorotating components (Section 33) Both components aremultivariate normals defined in aGalactocentric spherical frame of reference(see Section 21) The parameters are from the top to the bottom centroidsof the normal distribution velocity dispersions (assuming 120590t = 120590120601 = 120590

and 120590r = 120590t for the isotropic component) covariance terms of the velocitydispersion tensor weight of one of the component (see Equation 8) Theused distributions are Dirac Delta 120575 normal N( 120590x) where is thecentroid and 120590x the standard deviation uniform U(119909low 119909up) where 119909lowand 119909up represent the distribution limits The squared bracket indicate thedistribution boundary ie the prior probability is 0 outside the given range Ifthe brackets are not present the boundary is set to [minusinfininfin] All the velocitycentroids and velocity dispersions are in unit of km sminus1 Considering theparameters drawn from Dirac Delta as fixed in the fit the total number offree parameters is 5

chains) and improve model identifiability11 In order to detect pos-sible overfitting due to the double-component assumption we alsorun a single-component fit considering only the halo model sum-marised in Table 1 The significance of the more complex double

11 see httpsmc-stanorgusersdocumentation

case-studiesidentifying_mixture_modelshtml for usefulnotes on identifiability of Bayesian Mixture Models



component fit is analysed with the Bayesian Information Criterion(BIC) using the maximum-a-posteriori (MAP) of the likelihoodLMAP

BIC = 119896 ln 119899 minus 2 lnLMAP (10)

where 119896 is the number of free parameters and 119899 is the data samplesize The model with the lowest BIC is preferred in particular weconsider significant the results of the two component fit where theBIC difference (ΔBIC) is larger than 10 In order to apply the fitwe separate the whole sample (72973 stars) into 692 cylindrical119877 |119911 | bins with an average Poisson signal-to-noise ratio of 10 (seeSection 32) The fit is applied separately in each bin

Figure 3 presents the maps of the kinematic properties of thetwo principal components the halo and the disc in cylindrical 119877and |119911 | The two rows give the same information but the bottomrow shows the results of the double-component fit only if there is asignificant improvement as indicated by the Bayesian InformationCriterion ΔBIC gt 10 otherwise it reverts to the results of a single-component fit The first column shows the map of the fractionalcontribution of the rotating component While there are some hintsof rotating parts of the halo at high |119911 | in the top panel as demon-strated by the bottom panel these are not significant enough Thebulk of the rotating component sits at |119911 | lt 5 kpc across a widerange of 119877 and closer to the Sun its vertical extent is clearly limitedto a couple of kpc at most The second column presents the map ofthe azimuthal velocity 119881120601 as a function of 119877 and |119911 | Again someVoronoi cells at high |119911 | may have the kinematics consistent with aslow rotation however ΔBIC criterion renders them not significantenough Therefore in the bottom row these high |119911 | cells are emptyand the bulk of the 119881120601 map is limited to low vertical heights wherethe rotation velocity is in excess of119881120601 gt 200 kmsminus1 across the entirerange of 119877 Two single bins at high 119911 with 119877 asymp 10minus 15 kpc survivethe BIC cut they show an azimuthal rotation of asymp 50 km sminus1 Starsin these bins are likely related to the rotating halo structure foundin the unclassified sample and discussed in Section 61 Finally thethird column displays the behaviour of the halo velocity anisotropy120573 as mapped by RRL Except for a small region near the centre ofthe Milky Way and a few cells at high |119911 | where the motion appearsnearly isotropic the rest of the halo exhibits strong radial anisotropywith 06 lt 120573 lt 09

Figure 4 shows the distribution of the posterior probabilityof belonging to the non-rotating (halo) component for the stars inour sample Going from 119902MAPhalo = 1 to 119902MAPhalo = 0 thedistribution can be divided in three regions a clear peak around119902MAPhalo = 1 these are the RRL that do not exhibit any significantrotation and thus can be confidently assigned to the halo a decreas-ing trend in the number fraction ranging from 119902MAPhalo asymp 09 to119902MAPhalo asymp 05 finally a region with an increasing number frac-tion from 119902MAPhalo asymp 05 to 119902MAPhalo = 0 The latter region islikely populated by the stars with disc-like kinematics (closer to 0 is119902MAPhalo more robust is the association with the rotating compo-nent) while the second region is composed of stars that do not fallsquarely into one of the two groups Setting this latter undeterminedgroup aside for now we focus on the stars that can be classified ashalo or disc with certainty We select the halo and disc-like stars byapplying the following cuts

halo 119902MAPhalo gt 09 amp 11990216thhalo gt 05rotatingdisc minus like 119902MAPhalo lt 03 amp 11990284thhalo lt 05

amp |119911 | lt 5 kpc amp ΔBIC gt 10(11)

where 11990216thhalo and 11990284thhalo are the 16th and 84th percentile of

the a-posteriori 119902halo distribution The selection cut for the halois straightforward (see Fig 4) the additional cut on the 16th per-centile has been added to conservatively remove stars with poorlyconstrained 119902halo The 119902MAPhalo cut for the disc-like component issomehow arbitrary but we find it the best compromise between alarge enough number of stars (to have good statistics) and to be con-servative enough to target the stars that are more ldquopurely associatedwith the rotating component The other conditions has been addedto focus on the disc-like flattened structure (119911 cut) and to removeportion of the Galaxy volumewhere the presence of two-componentis not statistically significant (BIC cut)

Of the total 72973 RRL in our sample 49914 (or asymp 68)are classified as halo 3126 (or asymp 4) as disc while the remaining19993 (asymp 28) are unclassified Figure 5 shows the distributionof the three kinematic groups on the sky in Galactic coordinates(top row) and in cylindrical 119877 |119911 | (bottom row) The halo stars (firstcolumn) span a wide range of Galactic latitudes but mostly residein a centrally concentrated slightly flattened structure limited by119877 lt 30 kpc and |119911 | lt 20 kpc The middle panels of Figure 5 clearlyshow that the rotating component has a disc-like spatial distributionand extends to R asymp 30 kpc (see also the bottom panels of Figure 3)Interestingly a similarly-extended and highly flattened distributionwas already detected previously in the sample of candidate-RRLstars selected in the first Gaia data release (Iorio et al 2018)

Finally the shape of the unclassified portion of our sample(third column) resembles a superposition of the disc and the haloalbeit more concentrated to the centre most of the stars are at119877 lt 10 kpc and |119911 | lt 5 kpc Additionally at higher |119911 | there areseveral lumps and lobes likely corresponding to parts of the VirgoOverdensity and the Hercules Aquila Cloud (eg Vivas et al 2001Vivas amp Zinn 2006 Belokurov et al 2007 Jurić et al 2008 Simionet al 2014 2019)

Our kinematic decomposition unambiguously demonstratesthe presence of a disc-like population amongst the Gaia RRL Ac-cording to the left panel of Figure 3 this rapidly rotating populationcontributes from asymp 30 (outer disc) to up to asymp 50 minus 60 (innerdisc) of the RRL with |119911 | lt 1 kpc We also see clear signs of theRRL disc flaring beyond 15 kpc (see first two panels in the bot-tom row of the Figure) This is unsurprising as the restoring forceweakens with distance from the Galactic centre (see eg Bacchiniet al 2019) Additionally the Milky Way disc at these distances iswithstanding periodic bombardment by the Sgr dwarf (eg Laporteet al 2018 2019) The structure of the outer disc as traced by RRLis consistent with the recent measurements of the Galactic disc flare(eg Loacutepez-Corredoira ampMolgoacute 2014 Deacutekaacuteny et al 2019 Thomaset al 2019 Skowron et al 2019) In what follows we consider thehalo and the disc RRL sub-samples selected using criteria listed inEquation 11 separately

4 THE HALO RR LYRAE

As convincingly demonstrated by Lancaster et al (2019) the kine-matic properties of the Galactic stellar halo can not be adequatelydescribed with a single Gaussian This is because the inner asymp 30kpc are inundated with the debris from the Gaia Sausage event (seeeg Belokurov et al 2018b Myeong et al 2018b) also known asGaia Enceladus (see eg Helmi et al 2018 Koppelman et al 2020but see also Evans 2020) producing a striking bimodal signaturein the radial velocity space Lancaster et al (2019) devise a flexiblekinematic model to faithfully reproduce the behaviour of an ensem-ble of stars on nearly radial orbits (see also Necib et al 2019 for a



0 10 20 30r [kpc]

0

50

100

150

200

250

[km

s]

r MEDIANr MAP

t MEDIANt MAP

0 10 20 30r [kpc]

00

02

04

06

08

10

12

= 09MEDIANMAPSA cat 1

0 10 20 30r [kpc]

60

40

20

0

20

40

60

V [k

ms

]

V = 0 kmsGP 1GP 2

Figure 9 Same as Figure 7 but for the anisotropy (middle panel) and the azimuthal velocity (right-hand panel) estimated in the single-component fit of thehalo catalogue (see Section 4) The left-hand panel shows the radial and tangential velocity dispersion

Prior distributionshalo-anisotropic halo-isotropic

119881120601 N(0 100) N(0 100)119881r = 119881 120575 (0)119871rdagger N(0 300) [0infin] 120575 (0)120590r N(150 100) [0infin] N(100 20) [0infin]120590t N(50 50) [0infin]120588r120601 = 120588r = 120588120601 120575 (0)119891 U(0 1)

Table 2 Same as Table 1 but for the double component fit halo-anisotropichalo-isotropic components daggerThe halo-anisotropic componentis a superposition of two multivariate normals (with same normalisation)offset from each other in 119881r space by 2119871r (see Section 4) The total numberof free parameters is 7

similar idea) We use the halo model developed by Lancaster et al(2019) and Necib et al (2019) to describe the kinematics of the halosub-sample (see Section 33) More precisely the model is the mix-ture of two components isotropic and anisotropic both of whichcan rotate ie have non-zero mean 119881120601 The model its parametersand their prior distributions are summarised in Table 2 The priordistributions of the anisotropic component reflect our knowledge ofthe radially-anisotropic nature of the halo Moreover they are setup to help the convergence of the chain and the model identifia-bility as discussed in Section 33 By testing on the mock datasetwe ensure that the chosen priors are not preventing the selection ofisotropic (120590r = 120590t) or tangentially-anisotropic models (120590r lt 120590t) ormodels with simple Gaussian distribution along 119881r (119871r asymp 0) Thistwo-component model with 7 free parameters is applied to the halosub-sample (49914 stars) twice once in bins of 119903 and again in binsof 119877 and |119911 | (see Section 32) In the first case we use 41 bins withan average Poisson signal-to-ratio of 35 in the second case the binsare 203 with an average signal-to-ratio of 15 Parameters of bothcomponents are allowed to vary from bin to bin For comparisonwe also model the RRL kinematics in the halo sub-sample with asingle anisotropic multivariate normal with 4 free parameters 119881120601(prior N(0 100)) 120590r 120590120601 120590 (prior N(0 200) [0infin])

Note that in our analysis we do not attempt to distinguishbetween the bulge and the halo RR Lyrae This is because many ofthe classical bulge formation channels are not very different fromthose of the stellar halo especially when both accreted and in-situhalo components are considered (see eg Kormendy amp Kennicutt2004 Athanassoula 2005) Historically quite often the term ldquobulgeis used to refer simply to the innermost region of the Milky Way

In that case the Galactic bar and the discs would be included (seeeg Barbuy et al 2018) However we do not believe that theseadditional in-situ populations contribute significantly to the datasetwe are working with This is because our sample is highly depletedin the inner low |119911 | portion of the Galaxy where the RR Lyraedistribution is at its densest and the most complex ie 119877 lt 2 kpcFor example we do not have any stars with 119877 lt 1 kpc there areonly sim2700 (sim200) stars in the main (SA) sample with 119877 lt 2 kpc

41 Kinematic trends in the halo

For stars in the halo sub-sample Figure 6 shows the distribution ofthe posterior probability of membership in either of the two com-ponents As evidenced in the Figure the anisotropic component isdominant in this particular dataset Figure 7 presents the propertiesof the anisotropic halo population Given the high values of 120573 dis-played in the middle row of the Figure we identify this componentwith the Gaia Sausage debris (see Iorio amp Belokurov 2019 for dis-cussion of the GS as traced by the RRL) It is important to note thatin some cases the median and the maximum-a-posteriori (MAP)points in Figure 7 show large differences because the posterior dis-tribution is bimodal In those cases the median results are closerto the minimum that has been sampled more while the error-barsdo not correspond to the classical Gaussian 1120590 errors but rather thedistance between the two minima sampled by the MCMC Despitethe large uncertainties due to the bimodal distribution the MAPand the median estimates indicate similar behaviour if we considerthe MAP the fraction of the radial component remains high but119871r drops to 0 if we consider the median 119871r asymp 50 km sminus1 butthe fraction drops to small values Therefore both the MAP andmedian indicate a transition between the strong radially anisotropiccomponent and the rest of the stellar halo

The top row of Figure 7 gives the contribution of the stars inthe radially-dominated portion of the halo as a function of 119903 Thisfraction is at its lowest (asymp 20) near the Galactic centre Outside of119877 = 3 kpc stars on nearly-radial orbits contribute between 50 and80 Beyond 119877 = 20 kpc this fraction becomes highly uncertainFrom the right panel in the top row it appears that the contribu-tion of the radially-biased debris falls slightly faster with |119911 | asexpected if the debris cloud is flattened vertically The middle rowof Figure 7 presents the behaviour of the velocity anisotropy 120573 withGalactocentric radius 119877 (left) and 119877 and |119911 | (right) Note that in themodel with two 119881r humps anisotropy 120573 can increase i) when radialvelocity dispersion dominates or ii) when the velocity separation



between the two humps 2119871119903 increases For stars in the radial com-ponent 120573 is relatively low at 120573 asymp 03 in the inner 3 kpc but growsquickly to 120573 = 09 at 5 kpc and stays flat out to 20 kpc Finallythe bottom panel of the Figure shows the radial velocity separation119871119903 It reaches maximum 119871119903 asymp 270 kmsminus1 around 3 lt 119877 lt 5 kpcfrom the Galactic centre and then drops to 119871119903 asymp 0 kmsminus1 around30 kpc The trend of 119871119903 as a function of 119877 looks very similar to theprojection of a high-eccentricity orbit onto the phase-space (119881119903 119877)Along such an orbit the highest radial velocity is reached just beforethe pericentre crossing where it quickly drops to zero The orbitalradial velocity decreases more slowly towards the apocentre whereit also reaches zero As judged by the bottom row of Figure 7 thepericentre of the GS progenitor (in its final stages of disruption)ought to be around 2 lt 119877 lt 3 kpc while its apocentre somewherebetween 119877 = 20 kpc and 119877 = 30 kpc

In Figure 7 as well as in several subsequent Figures we com-pare the kinematic properties of theGaiaDR2RRL sample (Gclean)with those obtained for a more restrictive set of RRL ie that pro-duced by cross-matching the objects reported in the Gaia SOS andby the 119860119878119860119878-119878119873 variability survey (SA catalogue shown as lightlilac filled contour) The SA catalogue does not only suffer lowerrate of contamination it contains only bona fide RRab stars withperiod information and therefore muchmore robust (and unbiased)distance estimates This more trustworthy RRL dataset comes at aprice the size of the SA sample is asymp 5 times smaller compared tothe Gclean catalogue and the sampled distances are reduced by themagnitude limit (119881 asymp 17) of the 119860119878119860119878-119878119873 dataset Reassuringlyhowever the differences between the kinematic properties of theradially-biased halo component inferred with the Gclean and theSA data are minimal as demonstrated in the left column of Figure 7The only clear distinction worth mentioning is the blow-up of the119871119903 confidence interval shown in the bottom left panel Beyond 15kpc the SA-based 119871119903 uncertainty explodes due to the lack of distantRR Lyrae in this sample

Figure 8 is concerned with the mean azimuthal velocity ofeach of the two halo components Mean 119881120601 is shown for the radial(top) and the isotropic (bottom) portions of the model applied to thehalo sample For theGS-dominated radially-biased halo component119881120601 is slightly prograde (asymp 15 kmsminus1) within the Solar circle andbecomes slightly retrograde (asymp minus15 kmsminus1) outside of 10 kpc Notethat net rotation is particularly affected by hidden distance biases(as discussed in eg Schoumlnrich et al 2011) and is driven by over-or under- correcting for the Solar reflex motion (see Section 62)The mean azimuthal velocity of the radially-biased component ofthe halo plays an important role in reconstructing the details of theGS merger As discussed in Belokurov et al (2018b) the Sausageprogenitor galaxy did not necessarily have to arrive to theMilkyWayhead-on Instead the dwarf could start the approach with plenty ofangularmomentumwhich it then lost as it coalesced and disrupted inthe Galaxyrsquos potential The idea that dynamical friction could causethe orbit of a massive satellite to radialise instead of circularisingwas first proposed in Amorisco (2017) A clearer picture of theazimuthal velocity behavior is given by the SA dataset which ismuch less susceptible to distance errors and as a consequence to119881120601 biases The SA probability contours show that the net rotation ofthe radially-biased halo component remains very slightly prograde(at the level of asymp 15 kmsminus1) throughout the Galactocentric distancerange probed Such slight prograde spin is in agreement with anumber of recent studies (see Deason et al 2017 Tian et al 2019Wegg et al 2019 Belokurov et al 2020a) Note that this low-amplitude prograde rotation can only be claimed with some degreeof confidence at distances 119877 lt 10 kpc ie the region containing a

larger portion of RRL in our sample Further out in the halo the netazimuthal velocity is consistent with zero (see also Bird et al 2020Naidu et al 2020) For the isotropic halo component both Gcleanand SA datasets indicate a slight retrograde net rotation (asymp minus20kmsminus1) at least in the inner Galaxy

Figure 9 offers a view of the Galactic stellar halo as describedby a single Gaussian component12 It is not surprising to see thebehaviour which appears to be consistent with an average betweenthe strongly radial and isotropic components shown in the previousFigures Between 5 and 25 kpc the velocity anisotropy is high075 lt 120573 lt 09 only slightly lower than that shown in the top leftpanel of Figure 8 Similarly the superposition of slightly progradeand slightly retrograde populations yields amean azimuthal velocityconsistentwith zero (as previously reported eg bySmith et al 2009)as measured for the SA sample (see filled pale lilac contours in theright panel of the Figure) The Gclean dataset gives a retrogradebias of minus10 kmsminus1 Remember however that a portion of the halowas excised and is now a part of the lsquounclassifiedrsquo subset Theselsquounclassifiedrsquo RRL ought to be considered to give the final answeras to the net rotation of the halo (see Section 61)

42 Stellar population trends in the halo

Belokurov et al (2018b) used 119878119863119878119878+Gaia DR1 data to establish atight link between the velocity anisotropy and the metallicity in thelocal stellar halo They show that the highest values of 120573 asymp 09 areachieved by stars with metallicity minus17 lt[FeH]lt minus12 while atlower metallicities the anisotropy drops to 02 lt 120573 lt 04 Using asuite of zoom-in simulations of the MW halo formation the preva-lence in the Solar neighborhood of comparatively metal-rich halostars on highly eccentric orbits is interpreted by Belokurov et al(2018b) as evidence for an ancient head-on collision with a rela-tivelymassive dwarf galaxy In this picture the lower-anisotropy andlower-metallicity halo component is contributed via the accretionof multiple smaller Galactic sub-systems Note that strong trendsbetween orbital and chemical properties in the Galactic stellar halohad been detected well before the arrival of the Gaia data (see egEggen et al 1962ChibaampBeers 2000 Ivezić et al 2008Bond et al2010 Carollo et al 2010)Most recently such chemo-kinematic cor-relations have been observed in glorious detail in multiple studiesthat used the GDR2 astrometry (eg Myeong et al 2018a Deasonet al 2018 Lancaster et al 2019 Conroy et al 2019 Das et al2020 Bird et al 2020 Feuillet et al 2020) Consequently in thelast couple of years a consensus has emerged based on the numer-ical simulations of stellar halo formation and chemical evolutionmodels that the bulk of the local stellar halo debris is contributedby a single old and massive (and therefore relatively metal-rich)merger (see Haywood et al 2018 Helmi et al 2018 Mackerethet al 2019a Fattahi et al 2019 Bignone et al 2019 Bonaca et al2020 Renaud et al 2020 Elias et al 2020 Grand et al 2020)

Figure 10 explores the connection between the RR Lyrae kine-matics and their metallicity (estimated from the lightcurve shapesee Section 21 and Appendix A) Both the top and the bottom rowuse the sample of halo stars contained in the SOS catalogue ofGaiaDR2 RRL In the top row we present the metallicity maps obtainedusing our [FeH] calibration presented in Equations 3 and 4 Thebottom row uses the metallicity estimates reported as part of the

12 The fit parameters and their prior distributions are the same of theanisotropic halo component summarised in Table 2 but with 119871r sim 120575 (0) The total number of free parameter is 3



Figure 10 Cylindrical maps showing the distributions of the median metallicity estimated in this work (top see Section 21 and Appendix A) and reported inthe SOS catalogue (bottom) respectively Left-hand panels show the metallicity maps for the stars in the radially-biased halo component (23734 stars) whilethe middle panels show the stars in the isotropic halo component (7767 stars) The right-hand panels show the difference between the radial and the isotropiccomponent maps The stars in this map are subsamples of the halo component (see Section 4) belonging to the SOS catalogue and with an a-posteriori MAPlikelihood of belonging to the anisotropic or isotropic component larger than 07 (see Figure 6) The Voronoi-tesselation has been obtained using the isotropichalo sample with a target Poisson signal-to-noise equals to 10 The bins in which the number of stars is lower than 50 are excluded from the maps (see eg thewhite bins in the left-hand and right-hand panels)

SOS catalogue While the two rows display different absolute meanvalues of [FeH] in the halo (due to different calibrations used) therelative metallicity changes as a function of 119877 and |119911 | and betweenthe two halo components look very similar The left column of Fig-ure 10 shows the metallicity distribution in the radially-biased halocomponent As discussed above the bulk of this halo population haslikely been contributed by the Gaia Sausage merger Both top andbottom panels reveal a slightly flattened ellipsoidal structure whosemetallicity is elevated compared to the rest of the halo This [FeH]pattern extends out to 119877 asymp 30 kpc and |119911 | asymp 20 kpc No significantmetallicity gradient is observed in the radial direction although theinner 2-3 kpc do appear to be more metal-rich However given thebehaviour of 119871119903 shown in Figure 7 we conjecture that very littleGaia Sausage debris reaches the inner core of the Galaxy (see Sec-tion 41 for discussion) In the vertical direction there are hints ofa metallicity gradient where [FeH] decreases with increasing |119911 |

The behaviour of [FeH] in the isotropic halo component isgiven in the middle column of Figure 10 The most striking featurein the metallicity distribution of the isotropic component is the com-pact spheroidal structure with 119877 lt 10 kpc whose mean metallicityexceeds that of the radially-anisotropic component (and hence thatof the Gaia Sausage) Beyond 119877 asymp 10 kpc no strong large-scalemetallicity gradient is discernible [FeH] does change apprecia-bly and stays at levels slightly lower than those achieved by theGS debris at similar spatial coordinates To contrast the metallicitytrends of the two halo components the right column of the Figureshows the difference of the left and middle metallicity distributions

This differential picture highlights dramatically the shape of the GSdebris cloud whose mean metallicity sits some 02 dex above thetypical halo [FeH] value Even more metal-rich is the inner 10 kpcThis inner halo structure - which also appears flattened in the verti-cal direction - exhibits the highest mean metallicity in the inner 30kpc of the halo at least 02 dex higher than the radially-biased GS

The position of an RRL on the period-amplitude plane con-tains non-trivial information about its birth environment In theMilky Way halo globular clusters show a well-defined lsquoOosterhoffdichotomyrsquo (Oosterhoff 1939 1944) where RRL in clusters of Oost-erhoff Type I (OoI) have a shorter mean period compared to thosein GCs of Oosterhoff Type II (OoII) The lsquoOosterhoff dichotomyrsquois not present in the dwarf spheroidals observed today around theMilky Way that appear to contain mixtures of Oosterhoff types butnot in arbitrary proportions (eg Catelan 2004 2009) Thus therelative fraction of RRL of each Oosterhoff type can be used to de-cipher the contribution of disrupted satellite systems to the Galacticstellar halo (see eg Miceli et al 2008 Zinn et al 2014) Finally theso-called High Amplitude Short Period (HASP) RRL can be foundacross the Milky Way but are rather rare amongst its satellites Thisallowed Stetson et al (2014) and Fiorentino et al (2015) to put con-straints on the contribution of dwarf galaxies of different massesto the Galactic stellar halo Most recently Belokurov et al (2018a)used RRL tagging according to their type (OoI OoII or HASP)to lsquounmixrsquo the Milky Way halo Taking advantage of the wide-areaRRL catalogue provided as part of the Catalina Real-Time TransientSurvey (Drake et al 2013 2014 2017) they show that the fraction



Figure 11 Same as Figure 10 but for the Oosterhoff Type 1 (OoI top panels) and the High Amplitude Short Period (HASP bottom panels) fractions SeeSection 42 and Belokurov et al (2018a)

of OoI RRL changes coherently and dramatically as a function ofGalactocentric distance They also demonstrate that in the MilkyWay dwarf spheroidal satellites the OoI fraction increases withdwarfrsquos mass Using a suite of Cosmological zoom-in simulationsBelokurov et al (2018a) conjecture that the radial evolution in theRR Lyrae mixture is driven by a change in the fractional contribu-tion of satellites of different masses More precisely they interpretthe peak in the OoI fraction within 119877 asymp 30 kpc as evidence that theMilky Wayrsquos inner halo is dominated by the debris of a single mas-sive galaxy accreted some 8-11 Gyr ago This picture is confirmedby the change in the HASP RRL at 10 lt 119877(kpc)lt 30 Howeverinwards of 119877 asymp 10 kpc the HASP fraction grows further to levelssignificantly higher than those displayed in the most massive MWsatellites such as LMC SMC and Sgr making the very core of thehalo unlike any satellite on orbit around the Galaxy today Notethat the Oosterhoff and HASP classes are used here simply as away to select particular regions on the period-amplitude plane Theexact position on this so called Bailey diagram has remained a use-ful RR Lyrae diagnostic tool for decades but is only now startingto be investigated thoroughly with the help of the Gaia data andhigh-resolution spectroscopy (see eg Fabrizio et al 2019)

Figure 11 follows the ideas discussed in Belokurov et al(2018a) and tracks the fraction of OoI type (top) and HASP (bot-tom) RRL as a function of 119877 and |119911 | in both radially-biased (left)and isotropic (middle) halo components Additionally the differ-ence between the two maps is shown in the right column of theFigure As the Figure demonstrates the OoI and HASP fractionsin the radially-biased halo component are higher compared to theisotropic halo population In comparison the RRL in the inner asymp 10kpc show slightly lower OoI contribution yet the HASP fractionis higher These trends in the period-amplitude of halo RRL arefully consistent with those presented in Belokurov et al (2018a)

and support the picture in which the RRL on highly eccentric or-bits originate from a single massive and relatively metal-rich dwarfgalaxy Given its lower metallicity lower fraction of OoI and HASPRRL the isotropic population could be a superposition of tidaldebris from multiple smaller sub-systems

As Figures 7 10 and 11 reveal the inner 5-10 kpc of theGalactic stellar halo look starkly distinct from both the metal-richerradially-biased Gaia Sausage debris cloud and the metal-poorerisotropic halo Belokurov et al (2018a) suggested that a third kindof accretion event is required to explain the RRL properties in theinner Milky Way This hypothesis however must be revisited inlight of the Gaia data Thanks to the Gaia DR1 and DR2 astrom-etry we now have a better understanding of the composition ofthe Galactic stellar halo within the Solar radius In particular therenow exist several lines of evidence that perhaps as much as asymp 50of the nearby halo could be formed in situ The earliest evidencefor such a dichotomy in the stellar halo could be found in Nissenamp Schuster (2010) who identified two distinct halo sequences inthe 120572-[FeH] abundance plane Using Gaia DR1 astrometry com-plemented with 119860119875119874119866119864119864 and 119877119860119881119864 spectroscopy Bonaca et al(2017) showed that approximately half of the stars on halo-like or-bits passing through the Solar neighborhood are more metal-richthan [FeH]= minus1 and were likely born in-situ Gaia Collaborationet al (2018b) used Gaia DR2 data to build a colour-magnitude dia-gram of nearby stars with high tangential velocities and showed thatthe Main Sequence of the kinematically-selected halo population isstrongly bimodal Subsequently Haywood et al (2018) Di Matteoet al (2019) and Gallart et al (2019) used Gaia DR2 to investigatethe behaviour of the stars residing in the blue and red halo sequencesuncovered by Gaia Collaboration et al (2018b) All three studiesagreed that the blue sequence is provided by the accreted tidal debriswhile the stars in the red sequence were likely formed in-situ Both



0 5 10 15 20 25R [kpc]

0

100

200

300

400

V [k

ms

]

V = 230 kmsAblimit+20 (Cepheids)SA cat 1

0 5 10 15 20 25R [kpc]

0

20

40

60

80

100

120

[km

s]

Sharma+20 10 GyrSharma+20 2 Gyr

GP 1GP 2

00

05

10

15

20

25

30

|z| [

kpc]

Figure 12 Azimuthal velocity and velocity dispersion (assuming isotropy) obtained for the sample of rotating stars (see Section 5) Y-axis gives the medianof the a-posteriori distribution of the azimuthal velocity while the errorbars indicate its 16th and 84th percentile X-axis shows the median of the cylindricalradial distribution while the error-bars indicate the median value of the errors on the cylindrical radius of the stars in the given bin Vertical black dashed linesmark 5 kpc radius roughly corresponding to the region where the presence of the bar may be important The horizontal dashed line in the left panel indicates119881120601 = 230 km sminus1 Grey bands show the 1120590 and 2120590 intervals from the Gaussian Process interpolation as described in Figure 7 Blue band shows the 1120590interval of the posterior obtained using the SA (SOS+119860119878119878119860119878119873 ) catalogue (see text) The blue SA band explodes around 119877 asymp 12 kpc due to a particular binwhere most of stars have been classified as the background The magenta line in the left-hand panel shows the azimuthal velocity measured by Ablimit et al(2020) using a sample of Cepheids The blue and orange lines in the right-hand panel show the median of the combination of the vertical and radial velocitydispersion model predictions by Sharma et al (2020) Here we assumed [FeH]=minus10 (see Figure 14) 119911 = 05 kpc and stellar age 119905 = 2 Gyr (orange line) and119905 = 10 Gyr (blue line) see text in Section 5 for further information

Di Matteo et al (2019) and Gallart et al (2019) point out that thestars in the in-situ component had likely formed before the accretionof Gaia Sausage and were heated up onto halo orbits as a result ofthe merger It remains somewhat unclear however where the thickdisc stops and the in-situ halo starts

Belokurov et al (2020a) used the catalogue of stellar orbitalproperties and accurate ages produced by Sanders amp Das (2018) toisolate the halo component they dubbed the lsquoSplashrsquo Splash con-tains stars with high metallicities minus07 lt [119865119890119867] lt minus02 andlow-angular momentum (or retrograde) motion Importantly its az-imuthal velocity distribution does not appear to be an extension ofthe thick discrsquos ndash it stands out as a distinct kinematic component(see also Amarante et al 2020) The age distribution of the Splashpopulation shows a sharp drop around 95 Gyr in agreement withprevious estimates described above Belokurov et al (2020a) usedAuriga (Grand et al 2017) and Latte (Wetzel et al 2016) numeri-cal simulations of Milky Way-like galaxy formation to gain furtherinsight into the Splash formation They demonstrate that a Splash-like population is ubiquitous in both simulation suites and indeedcorresponds to the ancient Milky Way disc stars lsquosplashedrsquo up ontothe halo-like orbits (as conjectured by eg Bonaca et al 2017 DiMatteo et al 2019 Gallart et al 2019) Most recently Grand et al(2020) provided a detailed study of the effects of the Gaia Sausage-like accretion events on the nascent Milky Way They show thatthe propensity to Splash formation can be used to place constraintson the properties of the Gaia Sausage accretion event for exam-ple the mass ratio of the satellite and the host Additionally theydemonstrate that in many instances in their suite the accretion isgas-rich and leads to a star-burst event in the central Milky Way In-terestingly as pointed out by Belokurov et al (2020a) recent obser-vations of intermediate-redshift galaxies reveal that star-formationcan originate in the gas outflows associated with profuse AGN orstar-formation activity (see Maiolino et al 2017 Gallagher et al2019 Veilleux et al 2020) thus raising a question of whether the

MilkyWayrsquos Splash could also originate in the gas outflow (see alsoYu et al 2020)

While the earlier studies of the Galactic in-situ halo had beenlimited to the Solar neighborhood (Nissenamp Schuster 2010 Bonacaet al 2017 Haywood et al 2018 DiMatteo et al 2019 Gallart et al2019) Belokurov et al (2020a) provide the first analysis of the over-all spatial extent of this structure Using a selection of spectroscopicdatasets they show that the Splash does not extend much beyond119877 asymp 15 kpc and |119911 | asymp 10 kpc Compare the picture in which theSplash looks like a miniature halo - or perhaps a blown-up bulge -(see red contours in Figures 11 and 13 in Belokurov et al 2020a)and the RRL stellar population maps presented here in Figures 10and 11 There is a very clear correspondence between themetal-richand HASP-enhanced portion of the (mostly) isotropic halo popu-lation and the Splash We therefore conjecture that the inner asymp10kpc of the Galactic halo RRL distribution is pervaded by the in-situ halo population The in-situ halo RRL are metal-rich and havelower mean OoI fraction compared toGaia Sausage and possess thehighest mean HASP fraction amongst all halo components

5 THE DISC RR LYRAE

As described in Section 33 a small but significant fraction of theGDR2 RRL (just under 5) are classified as belonging to a rotatingcomponent based on their kinematics Figures 3 and 5 demonstratethat the stars in the rotating sample are heavily biased towards lowGalactic latitude |119887 | and small height |119911 | and thus likely represent aMilky Way disc population Here we provide a detailed discussionof the properties of this intriguing specimen

In order to take into account possibile residual contaminantsand outliers in the sample of rotating RRL (see Section 33) we seta double component fit (see eg Hogg et al 2010)

bull 1st component (disc-like) cylindrical frame-of-reference



Prior distributionsdisc background

119881120601 N(0 400) [0infin]119881R = 119881z 120575 (0)120590 = 120590R = 120590z = 120590120601 N(0 200) [0infin]120588Rz = 120588R120601 = 120588z120601 120575 (0)119881ℓ 120575 ( 〈119881ℓstars 〉)119881119887 120575 ( 〈119881119887stars 〉)120590ℓ C(0 500) [0infin]120590119887 C(0 500) [0infin]120588ℓ119887 U(minus1 1)119891 U(0 1)

Table 3 Same as Table 1 but for the parameters of the double component fitrotating-discbackground The rotating-disc component is a 3D multivariatenormal distribution defined in aGalactocentric cylindrical frame of reference(see Section 21) with parameters centroids (119881120601 119881R119881z) isotropic velocitydispersion 120590 and correlation terms of the velocity dispersion tensor 120588 Thebackground is modelled as 2D multivariate normal in the observed velocityspace The parameters are the centroids (119881ℓ 119881119887) which are fixed to theaverage values of the observed velocity distribution of the stars in eachbin the velocity dispersions (120590ℓ 120590119887) and the velocity correlation (120588ℓ119887)C(119909c 119897) indicates the Chaucy distribution centred in 119909c and with scale 119897The total number of free parameters is 6

isotropic velocity dispersion tensor azimuthal velocity as the onlystreaming motion (119881R = 119881z = 0)

bull 2nd component (background) observed velocity space(119881ℓ 119881119887) the centroid is fixed to the median of the observed velocitydistribution the velocity dispersion and the velocity covariance arefree parameters

Table 3 summarises the model parameters and their prior distribu-tions the number of free parameters is 6

We apply the fit to the subsample of 3126 rotating RRL (seeSection 33 and Equation 11) grouped in 60 cylindrical Voronoi-cells (see Section 32) with an average Poisson signal-to-noise ofasymp 7 For each region in the 119877 |119911 | plane our kinematicmodel providesan estimate of the rotational velocity as well as the properties of thevelocity ellipsoid and an estimate of the background level After ouranalysis we found a low level of contaminating background (asymp 12of stars have 119902bkg gt 07) confirming that our subsample is a quiteclean view of the rotating disc-like RRL population

Figure 12 shows the mean azimuthal velocity (left) and veloc-ity dispersion (right) as a function of the Galactocentric cylindricalradius 119877 The colour of the symbols represents their height abovethe plane |119911 | The left panel of the Figure displays a well-behavedrotation curve traced by RRL starting around 119881120601 asymp 100 kmsminus1 atdistances of 2-3 kpc from the centre of the Galaxy it quickly risesto 119881120601 asymp 230 kmsminus1 at 119877 asymp 5 kpc and then stays relatively flat at5 lt 119877(kpc)lt 25 Note that such high rotational velocities are char-acteristic of the thin disc population of the Milky Way Overplottedon top of our measurements is the magenta line representing the az-imuthal velocity curve of the thin disc Cepheids recently reported byAblimit et al (2020) and consistent with the kinematics of other thindisc tracers (eg Red Giants Eilers et al 2019 Loacutepez-Corredoiraamp Molgoacute 2014) In the range of Galactocentric distances sampledby both the Cepheids and the RRL their azimuthal velocities are incomplete agreement thus vanquishing any remaining doubt aboutthe nature of the fast-rotating RRL

Stars in the Galactic disc are exposed to a variety of processeswhich can change their kinematics with time Repeated interac-tions with non-axisymmetric structures such as the spiral arms thebar and the Giant Molecular Clouds (with additional likely mi-

Figure 13 Stellar population properties of the rotating disc-like componentin cylindrical coordinates Top panel gives the median of the metallicitymiddle panel shows the fraction of OoI type RR Lyrae while the bottompanel presents the fraction of HASP stars Thesemaps use a subsample of thedisc catalogue (see Section 5) obtained considering only objects belongingto the SOS catalogue (1841 stars) Each bin contains at least ten stars Themetallicities shown in this figure have been estimated through Equations 3and 4 (see Appendix A)

nor contribution from in-falling dark matter substructure) result inthe increase of the stellar velocity dispersion more pronouncedfor older stars often described as Age Velocity dispersion Rela-tion or AVR (see eg Stroumlmberg 1946 Spitzer amp Schwarzschild1951 Barbanis amp Woltjer 1967 Wielen 1977 Lacey 1984 Sell-wood amp Carlberg 1984 Carlberg amp Sellwood 1985 Carlberg 1987Velazquez amp White 1999 Haumlnninen amp Flynn 2002 Aumer amp Bin-ney 2009 Martig et al 2014 Grand et al 2016 Moetazedian ampJust 2016 Aumer et al 2016 Mackereth et al 2019b Ting amp Rix2019 Frankel et al 2020) Most recently Sharma et al (2020) useda compilation of spectroscopic datasets and Gaia DR2 astrometryto study the dependence of radial and vertical velocity dispersionsfor stars with 3 lt 119877(kpc)lt 20 They use a combination of stellartracers Main Sequence Turn-Off stars and Red Giant Branch starswhose ages are calculated using spectro-photometric models cali-brated with asteroseismology Sharma et al (2020) demonstrate thatthe stellar velocity dispersions are controlled by four independentvariables angular momentum age metallicity and vertical heightMoreover they show that the joint dependence of the dispersion onthese variables is described by a separable functional form

The right panel of Figure 12 compares the RRL velocity dis-persions (under the assumption of isotropy) to the median betweenradial and vertical dispersion approximations obtained by Sharmaet al (2020) Here we have fixed other model parameters to the val-ues most appropriate for our dataset ie [FeH]=-1 and |119911 | = 05First thing to note is that the shape of the radial dispersion curvetraced by the Gaia RRL matches remarkably well the behaviourreported by Sharma et al (2020) for the disc dwarfs and giantsSecondly the RRL velocity dispersion at the Solar radius is strik-ingly low around asymp 20 kmsminus1 Overall both the shape and thenormalisation of the RRL velocity dispersion agree well with that



4 2 0[FeH]

00

05

10

pdf

Dekany+18Med=-148Med=-099HaloDisc

04 06 08 10P [day]

0

2

4

pdf

Med=058Med=052HaloDisc

0 2 4 631 [rad]

00

02

04

06

pdf


4 2 0[FeH]SOS

000

025

050

075

100

pdf


02 03 04 05P1o [day]

0

5

10

pdf


00 05 10 15AMP [mag]

00

05

10

15

20

pdf


Figure 14 Lightcurve properties of a subsample of SOS stars in the Gclean catalogue (see Section 22) belonging to the halo (red see Section 4) and the disccomponents (blue see Section 5) From top-left to bottom-right the panels show the metallicity estimated in this work (see Section 21 and Appendix A) theperiod of the RRab stars the lightcurve phase difference Φ31 (see Section 21) the metallicity from Gaia SOS the period of the RRc stars and the lightcurveamplitude in theGaia 119866 band The vertical dashed lines give medians of the distributions Green curves in the left-hand panels show the best Gaussian MixtureModels of the photometric metallicity distribution of the sample of disc RRLs in Deacutekaacuteny et al (2018) Only stars that have estimates of both the period andthe lightcurve phase difference have been considered for this plot (24598 and 1146 stars from the halo and disc sample respectively)

predicted for a stellar population of 2 Gyr in age (orange curve) Incomparison an older age of 10 Gyr would yield a dispersion almosttwice as large (blue curve) Given the high azimuthal velocity andlow velocity dispersion as demonstrated in Figure 12 for both theGclean and SA catalogues we conclude that our sample of rotatingRRL is dominated by a relatively young thin disc population Notethat as a check we also perform a more detailed analysis obtainingan age estimate by fitting the velocity dispersions with the median(radial and vertical) model prediction from Sharma et al (2020)considering all stars in the disc-like subsample and their propertiesand errors ([FeH] 119877 119911 119881120601 and 120590 from the kinematic fit) Thisyields an age distribution consistent with a young disc populationthe peak is at asymp 2Gyr and the wings extend from very young ages(lt 1 Gyr) to 5-7 Gyr

Our findings are in agreement with those reported in the liter-ature recently (eg Marsakov et al 2018 Zinn et al 2020 Prudilet al 2020) that demonstrate the presence in the Solar neighbor-hood of RRL with thin disc kinematics and chemistry For the firsttime however we are able to map out the kinematics of the discRRL across a wide range of Galactocentric 119877 and show that theirvelocity dispersion behaviour is clearly inconsistent with that of anold population Moreover as demonstrated in the bottom row ofFigure 3 beyond 119877 asymp 20 kpc we detect prominent flare in the spa-tial distribution of the disc RRL (compare to eg Loacutepez-Corredoiraamp Molgoacute 2014 Thomas et al 2019) Note that the increase of themean Galactic height with 119877 detected here is gentler comparedto the above studies thus also pointing at a younger age of theseRRL in agreement with the maps presented in Cantat-Gaudin et al(2020) Figure 13 zooms in on the rotating disc-like componentand shows the properties of its stellar population (inferred from theRRL lightcurve shapes) as a function of cylindrical coordinates

From top to bottom the panels show metallicity (top) OoI fraction(middle) and HASP fraction (bottom) Across the three panels thedisc RR Lyrae show consistent behaviour their metallicity OoI andHASP fractions remain high for |119911 | lt 1 kpc For 3 lt 119877(kpc)lt 15radial behaviour shows no trends but in the very inner Galaxymetallicity and HASP fractions drop Similarly there appears to bea decrease in metallicity and HASP fraction in the outer parts of thedisc beyond 119877 = 15 kpc The apparent central ldquoholerdquo in the discRRL population is consistent with the radial offset of the metal-richcomponent presented in Deacutekaacuteny et al (2018) and in Prudil et al(2020) The central depression can also be an indication of radialmigration for the disc RRL population (see eg Beraldo e Silva et al2020) However for our sample we can not rule out that some of thechange in the inner 3 kpc at low |119911 | is driven by the cleaning criteriaapplied (eg extinction cut) or increasing contamination from othercomponents (bulgebar thick disc) The synchronous change in theRRLmetallicity and the HASP fraction points to the fact that HASPobjects are simply the high tail of the RR Lyrae [FeH] distribution

Finally let us contrast the lightcurve shapes of the halo and thedisc RRL Figure 14 presents the distributions of metallicity period119875 amplitude and phase difference 12060131 for the halo (red) and the disc(blue) samples We give two [FeH] distributions computed usingtwo different calibrations the top left panel of the Figure relieson the metallicity estimated using Equations 3 and 4 while thebottom left panel employs [FeH] values reported by Gaiarsquos SOSIrrespective of the calibration used the metallicities attained by thedisc RRL are significantly higher than those in the halo The [FeH]distribution of the rotating population exhibits a long tail towardslow metallicities but the peak (and the median) value is higherby 05 (08) dex depending on the calibration used Given that theRRL metallicities are computed using only the period and phase



difference we expect that both 119875 and 12060131 distributions should showclear differenceswhen the halo and the disc RRL are compared Thisis indeed the case as revealed by the middle column and the top rightpanel of Figure 14 The main difference is in the period distributionthe disc RRL have a shorter period on average There is also a slightprevalence of lower values of 12060131 while the amplitude distributionsare not distinguishable This behavior is in happy agreement withthe properties of the disc RRL populations gleaned from smallerlocal samples (see eg Marsakov et al 2018 Zinn et al 2020 Prudilet al 2020)

6 DISCUSSION AND CONCLUSIONS

61 The unclassified stars

So far we have left out a substantial asymp 25 of the total RR Lyraedataset as ldquounclassifiedrdquo Note that according to our definition anysample of stars with intermediate properties ie a population thatdoes show either a strong prograde rotation (disc) or a zero meanazimuthal velocity (halo) would be deemed unclassified Here weattempt to investigate the presence of any coherent chemo-kinematictrends amongst these leftover stars According to Figure 5 the bulkof this unclassified population gravitates to the centre of the MilkyWay and sits close to the plane of the disc

Figure 15 presents the results of the kinematic modelling13of the hitherto unclassified RRL stars The left panel of the Figureshows the mean azimuthal velocity as a function of Galactocentric119877 with the colour-coding corresponding to |119911 | Two main groups areimmediately apparent First between 1 and 10 kpc from the MilkyWayrsquos centre at low heights there exists a population of RRL rotat-ing with speeds lagging behind the thin disc by some asymp 50 kmsminus1which we attribute to the thick disc population It is interesting tonote that a hint of the presence of a population with thick-disc likekinematics is already shown in Figure 12 approximately at the Sunpositionwe can identify a clear vertical gradient of the azimuthal ve-locity In particular the119881120601 of the point with |119911 | asymp 2 kpc is consistentwith the thick-disc velocities shown in Figure 15

Additionally beyond 119877 gt 10 kpc and |119911 | gt 10 kpc above theplane another barely rotating population is discernible - most likelybelonging to the halo There is also a small number of bins thatdisplay kinematical properties in between the thick disc and thehalo Interestingly the halo portion of the unclassified RRL exhibithigh orbital anisotropy 120573 asymp 08 as evidenced in the middle panel ofFigure 15 This would imply that much of this halo substructure isattributable to theGaiaSausage This is in agreementwith the earlierclaims of Simion et al (2019) who connect the Virgo Overdensityand the Hercules Aquila Cloud to the same merger event In fact inFigure 5 traces of both the VOD and the HAC are visible amongstthe unclassified RRL stars Note that assigning the slowly-rotatingportions of the halo to the GS debris cloud would increase thenet angular momentum of this radially-biased halo component Thebins dominated by the thick disc stars have 120573 asymp 0 with a mildincrease with radius 119877 It is curious to see that the slowly rotatingRRL population is limited to 119877 lt 12 kpc as has been seen in manyprevious studies (eg Bovy et al 2012 Hayden et al 2015 Bland-Hawthorn et al 2019 Grady et al 2020) supporting the picturewhere rather than just thick this is an inner old disc of the Galaxy


The right panel of Figure 15 presents the metallicity distribu-tions of the halo (unfilled magenta) thick disc (unfilled blue) andintermediate 119907120601 (green dashed) populations amongst the previouslyunclassified RRL These can be compared to the halo (filled lightred) and thin disc (filled light blue) [FeH] distributions Reassur-ingly the bits of halo substructure with slight prograde motion havethe [FeH] distribution indistinguishable from the that of the halorsquossample The thick disc displays metallicities that are on averagelower than the thin discrsquos but not as low as in the halo Based onthe chemo-kinematic trends amongst the lsquounclassifiedrsquo stars weconclude that the majority asymp 70 belong to the Milky Wayrsquos thickdisc while the remaining asymp 30 are part of the halo substructurewhich displays the prevalence for prograde motion and high orbitalanisotropy

62 Tests and caveats

The results of this work rely on a number of assumptions In thissection we quantify the impact of some of the possible systemat-ics repeating the analysis of the halo and the disc kinematics (seeSection 31 Section 4 and Section 5)

One of the principal ingredients of our modelling is the dis-tance estimate for the RRL stars in our sample We investigate therole of a potential distance bias using the SOS metallicity estimateinstead of the one presented in this paper in Equation 3 and Equa-tion 4 (see Appendix A) Moreover we test the effect of assuming aconstant absolute magnitude 119872G = 064 plusmn 024 (see Appendix A)in Equation 5 We are happy to report that all main conclusionsof our analysis remain unchanged The radial profile of the fittedhalo and disc properties are all within 1120590 of our fiducial results andwe do not find any significant systematic differences between theoutcomes

The separation of the halo and disc component relies on aselection cut basedmainly on the a-posteriori likelihood to belong tothe non-rotating halo component (see Sectionlsquo33)We do not repeatthe kinematic analysis for different 119902halo-thresholds but looking atFigure 15 the result of such an experiment is easily extrapolatedIncreasing the value of the disc 119902halo-cut we include more andmore of thick disc stars (that are larger in number) lowering therotational velocity increasing the velocity dispersion and loweringthe metallicity This does not change our conclusions but just hidesthe subdominant thin-disc-like component under a large number ofstars belonging to a different kinematic component

Part of the halo analysis relies on splitting the stars into spheri-cal bins however the inner stellar halo is known to be flattened (seeeg Deason et al 2011 Xue et al 2015 Das amp Binney 2016 Iorioet al 2018 Iorio amp Belokurov 2019) We repeat the kinematic fitof the halo subsample using elliptical bins instead tuned on the el-lipsoidal shape described in Iorio amp Belokurov (2019) Comparingthe outcomes of the spherical and elliptical analysis we do not findany significant differences Moreover we perform an alternativeanalysis binning the volume in cylindrical coordinates so that theresults are independent on the assumption of spherical or ellipti-cal symmetry (but still dependent on the azimuthal symmetry seebelow) The results of the cylindrical analysis are qualitatively inagreement with the 1D radial profile obtained assuming sphericalsymmetry (see Figure 7 and Figure 8)

We test the assumption of the four-fold symmetry repeating ouranalysis considering only stars located in a given Galactic quadrantie we select stars based on their Galactic azimuthal angle Wedo not detect any significant difference or systematic offset in thefitted halo and disc parameters (within 1120590 of our fiducial results)



Halo structure

Mid-velocity

Thick disc

Figure 15 Chemo-kinematic analysis of the unclassified subsample (see Section 33 and Figure 5) Left rotational velocity as function of the cylindricalradius the grey bands show the GP-interpolation of the rotational velocities obtained for the rotating disc-like component (see Figure 12) Centre anisotropyparameter as a function of the cylindrical radius The color map in the left and middle panels indicates the median value of the absolute value of 119911 the points andthe error bars indicate the median values the 16th and 84th percentile correspondingly of the a-posteriori distribution obtained for each bin Right metallicitydistribution for the SOS stars in the unclassified subsample the unfilled blue histogram contains the unclassified stars with thick-disc like kinematics the unfilledmagenta histogram shows the distribution for unclassified stars with halo like kinematics while the unfilled dashed-green histogram contains unclassified starsin bins with intermediate azimuthal velocity (asymp 100 km sminus1) As comparison the blue and red filled histograms show the metallicity distribution of the starsbelonging to the the halo-like and disc-like components (see Section 33 and Figure 14) The metallicities shown in this figure have been estimated throughEquations 3 and 4 (see Appendix A)

except for the azimuthal velocity of the radial component of thehalo (see Section 41) This parameter shows a significant offsetdepending on the considered quadrants in the Galactic semi-planenot containing the Sun (90 lt Φ lt 270) the average azimuthalvelocity is negative (119881120601rad asymp minus25 km sminus1) while in the otherportion of the Galaxy 119881120601rad is just slightly higher than 0 except inthe innermost part where it rises up to 30 minus 40 km sminus1 The finalvelocity profile showed in Figure 8 is approximately the weightedmean (there are more stars in the quadrants closer to the Sun) of the119881120601rad profiles obtained considering the four different quadrantsAlthough we cannot exclude the presence of real asymmetries orhidden halo subcomponents it is more likely that this difference isdriven by the distance biases present (see eg Schoumlnrich et al 20112012) Indeed the velocity offset is dependent on the distance fromthe Sun with more distant quadrants showing a larger deviationfrom 119881120601rad = 0 Curiously the velocity offset is not present in theisotropic component however 119881120601iso is in general less constrainedIn that case the random errors are likely dominating the error budgetreducing the effect of the systematic offset

The results for the thin disc are obtained assuming isotropyhence we repeat the fit leaving the three components of the velocityellipsoid free (120590R 120590z 120590120601) We also model the non-diagonal termsof the correlation matrix as nuisance parameters The results areconsistent with those shown in Figure 12 in particular the threevelocity dispersions agree within the errors confirming that ourassumption of isotropy is supported by the data However we doexpect a certain degree on anisotropy in the disc (120590R gt 120590z see egSharma et al 2020 Gaia Collaboration et al 2018c) The reasonwhy we do not detect the velocity dispersion anisotropy in our datais unclear It is possible that we are introducing some selection biasin the kinematic decomposition (Section 33) as we force the rotat-ing component to be isotropic It could also be that the differencesare washed out by the noise in our data and by the limitation of ouranalysis In particular most of the stars in the rotating subsamplehave small 119911 (see Figure 5) hence 119881119887 is almost directly mapping119881z while the other two velocity components are harder to constrainDespite this possible issue about the velocity dispersion the model

parameters of the rotating component (azimuthal velocity and ve-locity dispersion see Section 5) are relatively insensitive to anyof the tested variations therefore the association of this componentwith the kinematic thin disc is robust

Concerning the chemical analysis it is important to stress that itis based on photometric metallicities (see Appendix A) As alreadynoted by Clementini et al (2019) and Cacciari et al (2005) suchphotometric estimates are not suited to describe individual metal-licities but rather the average metal abundance of a populationMoreover as shown in Figure 14 the photometric metallicity candiffer significantly between different calibrations Most of our anal-ysis is based on the comparison between metallicity distributionsof groups of stars (see Figure 10 and Figure 14) hence the resultsshould be robust despite the limitation imposed by the use of pho-tometric metallicities Concerning the rotating disc-like componentit is evident that the metallicity is on average higher with respect tothe halo However given the uncertainty of the photometric metal-licities it is hard to constrain the real average metallicity of thispopulation As discussed in Appendix A we notice that our pho-tometric estimate seems to underestimate high metallicities on thecontrary the metal abundance reported in the SOS catalogue tendsto overpopulate the high metallicity end of the [FeH] distributionTherefore we conjecture that the true average value is somewherebetween our estimate ([FeH]asymp minus1) and the higher value estimatedin the SOS catalogue ([FeH]asymp minus04) Interesting we notice thatthe high resolution spectroscopic datasample of field RRL fromMagurno et al (2018) shows a clear metal-rich component rangingbetween [FeH]asymp minus05 and [FeH]asymp 02 in the metallicity distribu-tion (see Figure 12 in Fabrizio et al 2019 and FigureA2 inAppendixA)

Recently Beraldo e Silva et al (2020) pointed out that ourcomparison with the Sharma et al (2020) models could be biasedtoward younger age because our sample is kinematically selectedHowever we stress that the Sharma et al (2020) models take intoaccount the kinematics through the vertical angular momentumparameter 119871z Indeed at a given age they predict smaller velocitydispersions for larger 119871z this is an expectation of the model not an



effect of a selection bias It is important to note that in our case wecan associate 119871z = 119881120601119877 to each star in a bin (see Fig 13) so theselection on 119881120601 (selecting small 119902halo) as well on 119911 (see Eq 11)are not introducing any bias since they are both parameters of theSharma et al (2020) models and the only free parameters of ouranalysis is the population age

Beraldo e Silva et al (2020) conclude that the presence of apopulation of old RRL in the thin disc can be easily accommodateconsidering an early co-formation of thin and thick discs This cansurely be the case but we stress once again that the progenitors ofmetal-rich RRL ([FeH]gt minus1) need a significant mass loss to reachthe instability strip regardless of their age

63 The bulgebar

The closest the stars in our sample get to the Galactic centre isasymp 13 kpc Combined with the restriction on the dust reddeningwhich eliminates low latitudes this implies that the Milky Wayrsquosbar and bulge are mostly excluded from our study As of todayOGLE (eg Soszyński et al 2014) and VVV (Deacutekaacuteny et al 2013)surveys provide much better view of the RR Lyrae properties in theheart of our Galaxy The structure and the metallicity distribution ofthe bulge region as traced byRRLyrae appear complex and puzzlingand agreement is yet to be reached as to the exact interplay of distinctGalactic components here (Pietrukowicz et al 2015 Kunder et al2016 Deacutekaacuteny et al 2018 Prudil et al 2019ac Kunder et al 2020Du et al 2020) The bulge tangled mess might well have reachedinto our sample for stars with distances 119877 lt 4 kpc from the Galacticcentre but their numbers are low and their (potential) contributiondoes not change any of the conclusions reported here

64 Conclusions

We use Gaia DR2 proper motions to identify individual Galacticcomponents amongst RRL pulsating horizontal branch stars usu-ally assumed to be mostly old and metal-poor Following the ideasrecently highlighted in Wegg et al (2019) we assume four-foldsymmetry to extract the properties of the 3D velocity ellipsoid asa function of Galactocentric distance 119877 and height |119911 | The GaiaDR2 RRL catalogue is dominated by stars with halo kinematics(asymp 70) ie those with little prograde rotation Some asymp 5 of theRR Lyrae have fast azimuthal velocities 119907120601 asymp 220 minus 230 kmsminus1while the remaining asymp 25 are unclassified ie have kinematicproperties intermediate between the halo and the thin disc We fur-ther demonstrate that the halo sample contains at least three distinctsub-populations The unclassified sample is dominated by the thickdisc stars with a small addition of a mildly prograde halo debris

Between 50and 80of the haloRRL starswith 5 lt 119877(kpc)lt25 belong to the radially biased (120573 asymp 09) non-rotating (or perhapsslowly rotating) structure known as the Gaia Sausage left behindby an ancient merger with a massive dwarf galaxy (see eg Deasonet al 2013 Belokurov et al 2018b Haywood et al 2018 Deasonet al 2018 Helmi et al 2018 Mackereth et al 2019a Lancasteret al 2019 Fattahi et al 2019) The remainder of the halo is muchmore isotropic and probably contains a mixture of stars accretedfrom lower-mass satellites The Gaia Sausage component exhibitslittle angular momentum and a strong bimodality in the radial ve-locity (see Lancaster et al 2019 Necib et al 2019) We model theradial velocity distribution of the Gaia Sausage with two Gaussiansseparated by 2119871119903 and show that the amplitude of the radial velocityseparation is a strong function of the Galactocentric distance 119877 119871119903

peaks around 3 lt 119877(kpc)lt 5 the distance we conjecture whichmarks the location of the pericentre of the GS while its apocentreis close to 119877 asymp 25 kpc where 119871119903 drops to 0 kmsminus1 The GS debris isdistinct from the rest of the halo not only kinematically but also interms of the lightcurve shapes of the constituent RRL Compared tothe isotropic halo the GS RRL boast a higher fraction of OosterhoffType 1 objects Beyond 119877 asymp 10 kpc theGS stars aremoremetal-richthan the isotropic halo and additionally exhibit a higher fraction ofthe HASP RRL (in agreement with eg Belokurov et al 2018a)supporting the massive merger scenario However within 10 kpcthere exists a subset of the isotropic halo RRL whose metallicityand HASP fraction is even higher than those in the GS We conjec-ture that these inner metal-rich and HASP-rich RRL were born insitu (representing the population previously seen in eg Nissen ampSchuster 2010 Bonaca et al 2017 Haywood et al 2018 Di Matteoet al 2019 Gallart et al 2019 Belokurov et al 2020a)

We are not the first to detect RRL stars with disc kinematics(see Kukarkin 1949 Preston 1959 Taam et al 1976 Layden 19941995ab Mateu amp Vivas 2018 Marsakov et al 2018 2019 Prudilet al 2020 Zinn et al 2020) Note however that these previousstudies have been mostly limited to the Solar neighborhood Herefor the first time we map out the kinematics of the disc RRL overthe entire extent of the disc ie 3 lt 119877(kpc)lt 30 The RRL with thefastest azimuthal speeds in our sample follow closely the thin discbehaviour both in terms of their rotation curve and the evolution ofthe velocity dispersion Using the recent models of the velocity dis-persion obtained for conventional thin disc tracers such as MS andRGB stars by Sharma et al (2020) we place strong constraints onthe typical age of the thin disc RR Lyrae The thin disc traced by theGaiaRRL is very cold and can not be more than asymp 5Gyr old More-over we demonstrate that the thin disc RRL ought to be significantlymore metal-rich compared to their halo counterparts in agreementwith the earlier studies mentioned above The thick disc RRL arealso detected as part of our study These stars do not rotate as fastand hence are placed in the ldquounclassifiedrdquo category Careful exam-ination of these stars with intermediate kinematic properties revealthat in bulk they are denizens of the thick disc Their lightcurveshapes indicate that they only slightly more metal-rich comparedto the halo Curiously the kinematically-selected thick disc RRLdo not tend to reach beyond 10-12 kpc from the Galactic centre inagreement with the theories of the thick disc formation

We draw attention to the fact that the existence of young andmetal-rich RRL stars in the thin disc can not be easily reconciledwith the predictions of the accepted single-star evolutionary modelmetal-rich young progenitors require un-physically high mass lossPerhaps instead we have discovered an army of RR Lyrae impostors(akin to BEPs) produced via mass transfer in binary systems

ACKNOWLEDGEMENTS

The authors thank the anonymous referee for suggestions that helpedto improve the manuscript We are grateful to Maacutercio CatelanGisella Clementini Alessandro Savino and Leandro Beraldo e Silvafor the thoughtful comments they supplied on the earlier version ofthe manuscript We thank Jason Sanders GyuChul Meyong Eu-gene Vasiliev Wyn Evans and the other members of the CambridgeStreams group for the stimulating discussions at the early stage ofthis work We thank Iulia Simion for useful discussions and the forher help in the cross-match of the Liu+20 dataset with Gaia RRLyrae We thank Yang Huang for sharing the Liu+20 dataset GIwish to thank Nicola Giacobbo for inspiring discussions During



his period in UK GI was supported by the Royal Society New-ton International Fellowship VB is grateful to Natagravelia Mora-Sitjagravefor the careful proof-reading of the manuscript This work hasmade use of data from the European Space Agency (ESA) missionGaia (httpswwwcosmosesaintgaia) processed by theGaia Data Processing and Analysis Consortium (DPAC httpswwwcosmosesaintwebgaiadpacconsortium) Fundingfor the DPAC has been provided by national institutions in partic-ular the institutions participating in the Gaia Multilateral Agree-ment The research has made use of the NASAIPAC ExtragalacticDatabase (NED)which is operated by the Jet Propulsion LaboratoryCalifornia Institute of Technology under contract with the NationalAeronautics and Space Administration

DATA AVAILABILITY

The data underlying this article are available in Zenodo at httpdoiorg105281zenodo3972287

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Vivas A K Zinn R 2006 AJ 132 714Vivas A K et al 2001 ApJ 554 L33Walker A R Terndrup D M 1991 ApJ 378 119Watkins L L et al 2009 MNRAS 398 1757Wegg C Gerhard O 2013 MNRAS 435 1874Wegg C Gerhard O Bieth M 2019 MNRAS 485 3296Wenger M et al 2000 AampAS 143 9Wetzel A R Hopkins P F Kim J-h Faucher-Giguegravere C-A Kereš DQuataert E 2016 ApJ 827 L23

Widrow L M Gardner S Yanny B Dodelson S Chen H-Y 2012 ApJ750 L41

Wielen R 1977 AampA 60 263Xu Y Newberg H J Carlin J L Liu C Deng L Li J Schoumlnrich RYanny B 2015 ApJ 801 105

Xue X-X Rix H-W Ma Z Morrison H Bovy J Sesar B Janesh W2015 ApJ 809 144

Yu S et al 2020 MNRAS 494 1539Zinn R West M J 1984 ApJS 55 45

Zinn R Horowitz B Vivas A K Baltay C Ellman N Hadjiyska ERabinowitz D Miller L 2014 ApJ 781 22

Zinn R Chen X Layden A C Casetti-Dinescu D I 2020 MNRAS 4922161

Zoccali M et al 2003 AampA 399 931de Boer T J L Belokurov V Koposov S E 2018 MNRAS 473 647



APPENDIX A PHOTOMETRIC METALLICITYESTIMATE

Most of the stars in the SOSGaia catalogue have photometricmetal-licities (Clementini et al 2019) estimated through the non-linearrelation by Nemec et al (2013) The Nemec et al (2013) relationhas been fitted to a small sample of stars and it does not seem togeneralise well enough on larger sample In particular it assigns toa group of RRL with intermediate-large periods and largeΦ31 highmetallicities ([119865119890119867] amp minus05) that are likely artefacts (see eg FigA2) Moreover the relation is based on the Kepler magnitude bandand a number of auxiliary relations have to be used to translatethe Φ31 from the original band to the Gaia one (Clementini et al2019) additionally the value ofΦ31 can change if we use a differentnumber of harmonics to decompose the light curve For all thesereasons we decide to find a relation based solely on the light curveproperties reported in the Gaia SOS catalogue For the purpose ofour analysis we cross-matched the subsample of RRab stars withcomplete SOS light curve information in our Gclean catalogue (seeSec 2) with different spectroscopic sample of RRab stars with spec-troscopic metallicity estimate Layden (1994) (84 stars) Marsakovet al (2018) (76 stars) Nemec et al (2013) (21 stars) Zinn et al(2020) (149 stars mostly based on the sample by Dambis et al 2013containing also the 84 stars in Layden 1994) Concerning the RRcstars we followNemec et al (2013) considering the RRL in globularclusters (50 stars) assigning them the metallicity of the cluster theybelong We use the catalog ofGaia objected associated with Globu-lar Clusters in Gaia Collaboration et al (2018d) while the GlobularCluster metallicity are taken from Harris (1996) We consider theold Harris (1996) compilation because the metallicities are reportedin the Zinn amp West (1984) metallicity scale instead of the Carrettaet al (2009) scale used in the more recent Harris (2010) catalogueThe Zinn ampWest (1984) scale is the same metallicity scale of spec-troscopic catalogs and the absolute magnitude-metallicity relationused in this work has been calibrated on this same scale (Muravevaet al 2018)

We perform a large number of tests using both linear (eg Ju-rcsik amp Kovacs 1996 Smolec 2005) and non linear relations (egNemec et al 2013) and investigating different combinations of lightcurve and stellar properties Initially we evaluate the feature rele-vance through a random forest regression of the metallicity usingthe scikit-learn python module (Pedregosa et al 2011) In prac-tice we consider as feature the period 119875 (fundamental period forRRab and first overtone period for RRc) the phase difference be-tween the third or second light curve harmonics with respect to thefundamental one the amplitude the ratio between the amplitude ofthird or second light curve harmonics with respect to the fundamen-tal one and the stellar color In order to check possible biases andartefacts we also add the number of Gaia observations the mean 119866magnitude and the 119877119880119882119864 to the group of features For both RRaband RRc samples the most relevant feature is by far the period 119875followed by the phase difference Φ31 We do not use the randomforest method to estimate the metallicity since our training sampleis relatively small and considering the large number of parametersinvolved it is very likely to produce a significant variance or overfitproblem Instead we fit the relations using a Bayesian approach tak-ing into account the uncertainties of all the used features In eachtested relation we consider also the presence of an intrinsic scatterWe sample the posterior of the relation parameters exploiting theHamiltonian MCMC technique making use of the python modulePYMC3 (Salvatier et al 2016) The performance of the various rela-tions are analysed considering 119894) fit residuals 119894119894) comparison with

02 04 06 08P [day]

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Figure A1 Best fit linear relation [119865119890119867 ] prop 119886 times 119875 + 119887 times Φ31 for RRab(top panel) and RRc stars (bottom panel) The spectroscopic metallicities arefrom Layden (1994) and Harris (1996) for RRab and RRc stars respectivelyPeriods and phase difference Φ31 values are from the SOS Gaia catalogueThe solid black lines show the median of the posterior distributions ofthe relations while the gray lines are randomly sampled from the samedistributions The black dashed lines indicate the intrinsic scatter The bestfit relations are given in Equations 3 and 4

metallicities of RRL stars in Globular clusters (association with GCfrom Gaia Collaboration et al 2018d metallicites estimate fromHarris 1996) 119894119894119894) comparison with the spectroscopic metallicitiesof the RRL stars in the solar neighboursthe halo and the bulge takenfrom the crossmatchwith theMagurno et al (2018) Liu et al (2020)and Savino et al (2020) samples (see Fig A2) 119894119907) comparison ofthe distance moduli derived using the 119872119866 minus [119865119890119867] relation byMuraveva et al (2018) with the distance moduli of the MagellanicClouds14 We conclude that the optimal fit both for RRab and RRcstars is obtained with a linear relation with 119875 and Φ31 very littleimprovements can be obtained using non-linearity or adding param-eters to the relation As already noted by Jurcsik amp Kovacs (1996)Smolec (2005) Nemec et al (2011) the major issue is a moderatesystematic trend of the residuals as a function of the spectroscopicmetallicities the relation tends to overestimate (underestimate) themetallicity at the metal-poor (metal-rich) end Anyhow this prob-lem is present with the same significance also with more complexmodels This is likely due to the lack of calibrators at both ends ofthe metallicity distribution Among the various samples of RRabthe results of the fit are very similar except for the Nemec samplebut it contains a small number of stars covering a narrower range ofmetallicites with respect to the other samples Therefore we adoptas final relations (Equation 3 and 4) the linear relation in 119875 andΦ31 obtained with the Layden (1994) sample (for RRab stars) Thischoice is motivated by the fact that it is not a collection of differentcatalogues and it reports a metallicities uncertainty for each starFig A1 shows the best-fit relations The metallicity interval of thefit training set ranges from -251 to 008 for the RRabs stars andfrom -237 to -055 for the RRc stars Only a very small portion(mostly RRc stars) of our Gclean sample (see Sec 22) has metal-licities extrapolated outside these ranges 396 at the metal-poor tail

14 We used the median of the distance moduli estimates taken from NED(NASAIPACExtragalactic Database httpnedipaccaltechedu)



(93 RRab 303 RRc 295 in the halo subsample 6 in the disc sub-sample) 105 at the metal-rich end (26 RRab 79 RRc 15 in the halosubsample 42 in the disc subsample) These numbers are smallenough to have negligible effects on our outcomes as confirmed bythe results obtained with the SA sample (see eg Fig 12 and Fig7) that contains only 03 of stars with extrapolated metallicitiesMoreover the fit procedure ldquonaturally assigns larger errors to ex-trapolated metallicities and the implemented linear function limitsuncontrolled behaviour outside the range of calibrators

Compared to the photometric metallicities reported in theGaiaSOS catalogue our estimate perform better both on estimating theabsolute magnitude of the stars in the Magellanic Clouds (usingthe 119872119866 minus [119865119890119867] relation by Muraveva et al 2018) and com-pared to the RRL sample of spectroscopic metallicity obtained bySavino et al (2020) Liu et al (2020) and Magurno et al (2018)Fig A2 shows that the distribution of SOS photometric metallici-ties significantly differs from the spectroscopic ones in both shapeand centroid position (see also Hajdu 2019) In particular con-sidering the bulge sample the SOS distribution peaks at a verymetal-rich value of [119865119890119867] asymp minus05 while the peak of the spectro-scopic metallicity is [119865119890119867] asymp minus15 The photometric metallicityestimated with our relation shows a more similar distribution witha coincident but narrower peak The narrow distribution of the pho-tometric metallicities is due to the already discussed problem ofoverestimatingunderestimating the metallicities at the edge of thedistribution Considering the Liu et al (2020) sample our metallic-ity distribution is slightly offset from the spectroscopic distributionbut overall the distribution widths are very similar On the contrarythe SOS distribution is much more spread containing a significantnumber of metal-rich stars ([119865119890119867] gt minus1) The peak of the distri-bution of our photometric metallicities is consistent with the peakof the high resolution spectroscopic metallicities in Magurno et al(2018) but in this case the differences in the tails are more signifi-cant For the same sample the SOS photometric metallicities coverthe same range of the spectroscopic metallicities but their distribu-tion is much flatter without a clear peak and with an over-abundanceof very metal-rich stars

Finally we test that the use of the constant absolute magni-tude 119872119866 = 064 plusmn 025 for both RRab and RRc stars (see egIorio amp Belokurov 2019) is a good approximation when light curveproperties are not availableThe associated error 120575119872119866 = 025 is arobust and conservative estimate that can absorb both random andsystematic uncertainties (eg RRL type metallicity) giving a erroron heliocentrinc distance of about 13

APPENDIX B ROTATION MATRIX

The rotation matrix R to pass from velocities in Spherical 119933sph =(119881r 119881 119881120601) or Cylindrical 119933cyl = (119881R 119881z 119881120601) Galactocentriccoordinates to the velocities in the observed frame of reference119933sky = (119881los 119881ℓ 119881119887) can be obtained with the matrix product

R = Rc middot Rssphcyl (B1)

where Rc is the rotation matrix to pass from the Galactic cartesianvelocities 119933car = (119881x 119881y 119881z) to the the observed velocities whileRssph and Rscyl are the rotation matrix to pass from Galacticcartesian velocities to Galactic spherical and cylidrincal velocities

4 2 0[FeH]

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Savino+20 spectThis work photGaia SOS phot

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Figure A2 Comparison between the distribution of photometric (this workblueGaia SOS orange) and spectroscopic (dashed-black) metallicity valuesfor two samples of RRL Top panel cross-match between the bulge RRLsample in Savino et al (2020) and Gaia SOS with lightcurve information(212 stars) Middle panel cross-match between the RRL sample (mostly inthe halo) from Liu et al (2020) and Gaia SOS with lightcurve information(3153 stars) Bottom panel cross-match between the RRL sample (localfield) from Magurno et al (2018) and the Gaia SOS with lightcurve infor-mation (64 stars) Vertical lines indicate the median of each distribution

respectively The matrix Rc is defined as

Rc =cos 119887 cos ℓ cos 119887 sin ℓ sin 119887minus sin ℓ cos ℓ 0

minus sin 119887 cos ℓ minus sin 119887 sin ℓ cos 119887

(B2)

while the matrices Rs are defined as

Rssph =Γ cos cos 120601 minusΓ sin cos 120601 minusΓ sin 120601cos sin 120601 minus sin sin 120601 minus cos sin cos 0

(B3)

and

Rscyl =Γ cos 120601 0 minusΓ sin 120601sin 120601 0 minus cos 1206010 1 0

(B4)



The factor Γ is equal to 1 for a right-handed Galactocentric frame ofreference or to -1 for a left-handedGalactocentric frame of reference(as the one used in this work) The angular coordinates and 120601 arethe zenithal and azimuthal angle respectively while 119887 and ℓ are theGalactic sky coordinates (see Sec 21)



This paper has been typeset from a TEXLATEX file prepared by the author


1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae

6 Discussion and Conclusions



63 The bulgebar

64 Conclusions

A Photometric metallicity estimate

B Rotation Matrix


In this time of confusion reliable distance and agemetallicityindicators are essential to building a coherent picture of the MilkyWay For decades pulsating horizontal branch stars known as RRLyrae (RRL hereafter) have been trusted upon to help us chart theGalaxy (eg Kinman et al 1966 Oort amp Plaut 1975 Saha 1985Hartwick 1987 Catelan 2009 Pietrukowicz et al 2015) Usingpainstakingly-assembled spectroscopic samples it has been estab-lished that RRL metallicities span a wide range but the stars appearpredominantly metal-poor while the analysis of the Galactic Glob-ular clusters revealed prevalence for old ages (Preston 1959 Butler1975 Sandage 1982 Suntzeff et al 1991 Lee et al 1994 Clemen-tini et al 1995 Clement et al 2001) Note that in the field RRLare sufficiently rare therefore no large spectroscopic datasets arecurrently available However an approximate metallicity estimatecan be gauged from the properties of the lightcurve alone (Sandage1982 Carney et al 1992 Nemec et al 1994 Jurcsik amp Kovacs1996 Nemec et al 2013)

In the last two decades wide-area multi-epoch surveys havebrought in a rich harvest of variable stars in general and RRL inparticular (eg Sesar et al 2007 Soszyński et al 2009 Drake et al2013 Soszyński et al 2014 Torrealba et al 2015 Sesar et al 2017)Typically old and metal-poor RRL have long served as a tried andtrue tracer of the Galactic halo and its sub-structures (eg Vivaset al 2001 Morrison et al 2009 Watkins et al 2009 Sesar et al2013 Simion et al 2014 Mateu et al 2018 Hernitschek et al2018) Gaia the first truly all-sky variability census in the opticalhas further improved our understanding of the MilkyWay RRL notonly by filling in the gaps left behind by the previous generationsof surveys but also by providing high-quality proper motions forthe bulk of the RRL it sees The Gaia data has thus enabled a newprecise characterisation of the Galactic halo density field (eg Iorioet al 2018 Wegg et al 2019 Iorio amp Belokurov 2019) and helpedto discover halo sub-structures previously not seen (Belokurov et al2017 Koposov et al 2019 Belokurov et al 2019 Torrealba et al2019)

While it is true that RRL are being used primarily to trace thefossil record of the Milky Way assembly it was always known thatin the field a relatively small number of metal-rich examples exist(Kukarkin 1949 Preston 1959 Smith 1984 Layden 1994 Walkeramp Terndrup 1991 Deacutekaacuteny et al 2018 Chadid et al 2017 Fabrizioet al 2019 Zinn et al 2020) Based on their kinematics thesemetal-rich RRL were assigned to the Galactic disc(s) (Layden 1995a)Given the enormous number of available red giant progenitorsmetal-rich RRL in the disc were estimated to form between 200and 800 times less often compared to their old and metal-poor halocounterparts (Taam et al 1976 Layden 1995b)While the formationchannel has not yet been identified these early studies as well as thesubsequent follow-up conjectured that the progenitors of metal-richRRL ought to be old ie gt 10Gyr (eg Mateu amp Vivas 2018) Thepresence of likely old metal-rich RRL has been confirmed also inmetal-rich Globular Clusters (eg NGC 6338 and NGC 6441 seePritzl et al 2000) however they have periods that are significantlylarger with respect to field metal-rich RRL The main obstacle tothe production of a metal-rich RRL is its temperature on the HBwith higher envelope opacities these stars tend to sit too far to thered from the instability strip (eg Dorman 1992) Therefore beforearriving onto the HB metal-rich RRL progenitors are required toundergo copious levels of mass-loss asymp 05M or more which maywell be beyond what is physically possible

Most recently the conundrum of metal-rich RRL has beengiven a new lease of life Marsakov et al (2018) demonstrated thatwhile plenty of the local metal-rich RRL likely belong to the thick

disc (and thus can be as old as asymp10 Gyr) a substantial fractiondisplays the kinematics of the younger portion of the thin disc Anage of only few Gyrs would be very difficult to reconcile with theconventional scenarios of the RRL formation Note that if extrememass loss can be invoked ie in excess of 1 M then even young(gt 1 Gyr) progenitors can produce metal-rich RRL (see Bono et al1997ab) In a follow-up study Marsakov et al (2019) estimatedthe masses of the metal-rich thin disc RRL and found them to be oforder of 05minus06M thus confirming the need formass loss beyondthe typically accepted values Finally Zinn et al (2020) and Prudilet al (2020) combined RRL with available spectroscopy with theGaia DR2 astrometry to confirm the existence of metal-rich RRLstars with the orbital properties typical of the Galactic thin discWith these most recent observations in hand it remains to be seenif metal-rich RRL can actually be easily accommodated within thecurrent stellar evolution theory Comparing the structural propertiesof themetal-rich andmetal-poorRRLChadid et al (2017) concludethat it can not

What is hard to achieve via single stellar evolution channelscan (sometimes) be effortlessly done with binary stars Indeed anobject has been discovered that nimbly mimics the classic RR Lyraebehaviour ie lives on the instability strip and pulsates with thesame kind of lightcurve yet it is not an RR Lyrae at least notin the conventional meaning of the term (Pietrzyński et al 2012)This star designatedBinaryEvolution Pulsator (BEP) is a low-mass(026119872) remnant of mass transfer in a binary systemwith a periodofasymp 15 daysAs the follow-up theoreticalwork demonstrates binaryevolution can lead to a broad range ofBEPmasses and in some caseseven involve a stripped starwith a helium-burning core (Karczmareket al 2017) These impostors would be indistinguishable from theclassic RR Lyrae but have an age of only 4-5 Gyr Only one suchobject has been found so far but searches for RR Lyrae in binarysystems are ongoing (eg Prudil et al 2019b Kervella et al 2019)

This work aims to exploit the unprecedented all-sky coverageof Gaia to study the chemo-kinematics of the halo and the discof the Milky Way as traced by RRL stars The paper is organisedas follows Section 2 presents the construction of a clean sampleof Gaia RRL stars and gives the details of the methods we use toestimate physical quantities like distance metallicity and transversevelocity Section 3 describes the machinery employed to performthe kinematic decomposition of the Galactic components Thenwe discuss the properties of the individual components the haloin Section 4 and the disc in Section 5 In Section 6 we discusspossible biases affecting the results and finally we summarise themain conclusions

2 THE SAMPLE

We use the whole catalogue of stars classified as RRL in GaiaDR2 (Gaia Collaboration et al 2018a) combining the SOS(Specific Object Study Clementini et al 2019) RRL cataloguewith the stars classified as RRL in the general variability tablevari_classifier_result (Holl et al 2018) following the proce-dure described in Iorio amp Belokurov (2019) The initial combinedcatalogue contains 228853 stars (asymp 77 RRab asymp 21 RRc andasymp 2 RRd)


One of the key ingredients of this analysis is the distance from theSun 119863 of each star Once the heliocentric distance is known



20 40D [kpc]

010

015

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025

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VV

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119866 = 119866obs minus 119896G119864 (119861 minus119881) (2)




1000100 [deg]

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kpc]

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log(119863kpc

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119881ℓ = 119870`ℓ119863 +119881ℓ119881b = 119870`119887119863 +119881b

(6)


22 Cleaning



bull 119877119880119882119864lt12



0 25R [kpc]

0

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0

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0

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kpc]

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0001020304050607

f rot

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0001020304050607

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00 02 04 06 08 10qMAP halo

10 2

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3 THE METHOD



31 Kinematic fit


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1000100 [deg]

500

50

b [d

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1000100 [deg]

500

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b [d

eg]

Rotating N = 3126

1000100 [deg]

500

50

b [d

eg]


0 20 40R [kpc]

0

10

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|z| [

kpc]

0 20 40R [kpc]

0

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0 20 40R [kpc]

0

10

20

30

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|z| [

kpc]



10 2

10 1

100

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) (7)

where





Lmulti =sum119894

119891119894N(119894perpΛ119894perp + S119894

)=sum119894

119891119894L119894 (8)


119902119894 =119891119894L119894

Lmulti (9)










32 Binning strategy





binning































4 THE HALO RR LYRAE




0 10 20 30r [kpc]

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[km

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r MEDIANr MAP

t MEDIANt MAP

0 10 20 30r [kpc]

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0 5 10 15 20 25R [kpc]

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0 5 10 15 20 25R [kpc]

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[km

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GP 1GP 2

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Halo structure

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63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

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(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix


20 40D [kpc]

010

015

020

025

DD

0 20 40D [kpc]

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VV

0 20 40D [kpc]

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b0 20 40

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101

102

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119866 = 119866obs minus 119896G119864 (119861 minus119881) (2)




1000100 [deg]

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010203040

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0102030405060

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(3)



(4)



202


log(119863kpc

)=119866 minus 119872G5

minus 2 (5)


119881ℓ = 119870`ℓ119863 +119881ℓ119881b = 119870`119887119863 +119881b

(6)


22 Cleaning



bull 119877119880119882119864lt12



0 25R [kpc]

0

20

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0 25R [kpc]

0

20

40

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0 25R [kpc]

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00 02 04 06 08 10qMAP halo

10 2

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3 THE METHOD



31 Kinematic fit


(Σ

)




1000100 [deg]

500

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1000100 [deg]

500

50

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Rotating N = 3126

1000100 [deg]

500

50

b [d

eg]


0 20 40R [kpc]

0

10

20

30

40

|z| [

kpc]

0 20 40R [kpc]

0

10

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0 20 40R [kpc]

0

10

20

30

40

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kpc]



10 2

10 1

100

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) (7)

where





Lmulti =sum119894

119891119894N(119894perpΛ119894perp + S119894

)=sum119894

119891119894L119894 (8)


119902119894 =119891119894L119894

Lmulti (9)










32 Binning strategy





binning































4 THE HALO RR LYRAE




0 10 20 30r [kpc]

0

50

100

150

200

250

[km

s]

r MEDIANr MAP

t MEDIANt MAP

0 10 20 30r [kpc]

00

02

04

06

08

10

12


0 10 20 30r [kpc]

60

40

20

0

20

40

60

V [k

ms

]

V = 0 kmsGP 1GP 2






































0 5 10 15 20 25R [kpc]

0

100

200

300

400

V [k

ms

]


0 5 10 15 20 25R [kpc]

0

20

40

60

80

100

120

[km

s]


GP 1GP 2

00

05

10

15

20

25

30

|z| [

kpc]






5 THE DISC RR LYRAE




















4 2 0[FeH]

00

05

10

pdf


04 06 08 10P [day]

0

2

4

pdf


0 2 4 631 [rad]

00

02

04

06

pdf


4 2 0[FeH]SOS

000

025

050

075

100

pdf


02 03 04 05P1o [day]

0

5

10

pdf


00 05 10 15AMP [mag]

00

05

10

15

20

pdf

























Halo structure

Mid-velocity

Thick disc











63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix


1000100 [deg]

50

0

50

b [d

eg]


0 20 40R [kpc]

010203040

|z| [

kpc]

0102030405060

Nst

ar




(3)



(4)



202


log(119863kpc

)=119866 minus 119872G5

minus 2 (5)


119881ℓ = 119870`ℓ119863 +119881ℓ119881b = 119870`119887119863 +119881b

(6)


22 Cleaning



bull 119877119880119882119864lt12



0 25R [kpc]

0

20

40

z [kp

c]

0 25R [kpc]

0

20

40

z [kp

c]

0 25R [kpc]

0

20

40

z [kp

c]

0 25R [kpc]

0

20

40

z [kp

c]

0 25R [kpc]

0

20

40z [

kpc]

0 25R [kpc]

0

20

40

z [kp

c]

0001020304050607

f rot

MAP

0001020304050607

f rot

MAP

050100150200250300

VM

AP [k

ms

]

050100150200250300

VM

AP [k

ms

]

000015030045060075090

halo

MAP

000015030045060075090

halo

MAP










00 02 04 06 08 10qMAP halo

10 2

10 1

100

NN

tot






3 THE METHOD



31 Kinematic fit


(Σ

)




1000100 [deg]

500

50

b [d

eg]

Halo N = 49914

1000100 [deg]

500

50

b [d

eg]

Rotating N = 3126

1000100 [deg]

500

50

b [d

eg]


0 20 40R [kpc]

0

10

20

30

40

|z| [

kpc]

0 20 40R [kpc]

0

10

20

30

40|z

| [kp

c]

0 20 40R [kpc]

0

10

20

30

40

|z| [

kpc]



10 2

10 1

100

NN

tot




) (7)

where





Lmulti =sum119894

119891119894N(119894perpΛ119894perp + S119894

)=sum119894

119891119894L119894 (8)


119902119894 =119891119894L119894

Lmulti (9)










32 Binning strategy





binning































4 THE HALO RR LYRAE




0 10 20 30r [kpc]

0

50

100

150

200

250

[km

s]

r MEDIANr MAP

t MEDIANt MAP

0 10 20 30r [kpc]

00

02

04

06

08

10

12


0 10 20 30r [kpc]

60

40

20

0

20

40

60

V [k

ms

]

V = 0 kmsGP 1GP 2






































0 5 10 15 20 25R [kpc]

0

100

200

300

400

V [k

ms

]


0 5 10 15 20 25R [kpc]

0

20

40

60

80

100

120

[km

s]


GP 1GP 2

00

05

10

15

20

25

30

|z| [

kpc]






5 THE DISC RR LYRAE




















4 2 0[FeH]

00

05

10

pdf


04 06 08 10P [day]

0

2

4

pdf


0 2 4 631 [rad]

00

02

04

06

pdf


4 2 0[FeH]SOS

000

025

050

075

100

pdf


02 03 04 05P1o [day]

0

5

10

pdf


00 05 10 15AMP [mag]

00

05

10

15

20

pdf

























Halo structure

Mid-velocity

Thick disc











63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix


0 25R [kpc]

0

20

40

z [kp

c]

0 25R [kpc]

0

20

40

z [kp

c]

0 25R [kpc]

0

20

40

z [kp

c]

0 25R [kpc]

0

20

40

z [kp

c]

0 25R [kpc]

0

20

40z [

kpc]

0 25R [kpc]

0

20

40

z [kp

c]

0001020304050607

f rot

MAP

0001020304050607

f rot

MAP

050100150200250300

VM

AP [k

ms

]

050100150200250300

VM

AP [k

ms

]

000015030045060075090

halo

MAP

000015030045060075090

halo

MAP










00 02 04 06 08 10qMAP halo

10 2

10 1

100

NN

tot






3 THE METHOD



31 Kinematic fit


(Σ

)




1000100 [deg]

500

50

b [d

eg]

Halo N = 49914

1000100 [deg]

500

50

b [d

eg]

Rotating N = 3126

1000100 [deg]

500

50

b [d

eg]


0 20 40R [kpc]

0

10

20

30

40

|z| [

kpc]

0 20 40R [kpc]

0

10

20

30

40|z

| [kp

c]

0 20 40R [kpc]

0

10

20

30

40

|z| [

kpc]



10 2

10 1

100

NN

tot




) (7)

where





Lmulti =sum119894

119891119894N(119894perpΛ119894perp + S119894

)=sum119894

119891119894L119894 (8)


119902119894 =119891119894L119894

Lmulti (9)










32 Binning strategy





binning































4 THE HALO RR LYRAE




0 10 20 30r [kpc]

0

50

100

150

200

250

[km

s]

r MEDIANr MAP

t MEDIANt MAP

0 10 20 30r [kpc]

00

02

04

06

08

10

12


0 10 20 30r [kpc]

60

40

20

0

20

40

60

V [k

ms

]

V = 0 kmsGP 1GP 2






































0 5 10 15 20 25R [kpc]

0

100

200

300

400

V [k

ms

]


0 5 10 15 20 25R [kpc]

0

20

40

60

80

100

120

[km

s]


GP 1GP 2

00

05

10

15

20

25

30

|z| [

kpc]






5 THE DISC RR LYRAE




















4 2 0[FeH]

00

05

10

pdf


04 06 08 10P [day]

0

2

4

pdf


0 2 4 631 [rad]

00

02

04

06

pdf


4 2 0[FeH]SOS

000

025

050

075

100

pdf


02 03 04 05P1o [day]

0

5

10

pdf


00 05 10 15AMP [mag]

00

05

10

15

20

pdf

























Halo structure

Mid-velocity

Thick disc











63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix


00 02 04 06 08 10qMAP halo

10 2

10 1

100

NN

tot






3 THE METHOD



31 Kinematic fit


(Σ

)




1000100 [deg]

500

50

b [d

eg]

Halo N = 49914

1000100 [deg]

500

50

b [d

eg]

Rotating N = 3126

1000100 [deg]

500

50

b [d

eg]


0 20 40R [kpc]

0

10

20

30

40

|z| [

kpc]

0 20 40R [kpc]

0

10

20

30

40|z

| [kp

c]

0 20 40R [kpc]

0

10

20

30

40

|z| [

kpc]



10 2

10 1

100

NN

tot




) (7)

where





Lmulti =sum119894

119891119894N(119894perpΛ119894perp + S119894

)=sum119894

119891119894L119894 (8)


119902119894 =119891119894L119894

Lmulti (9)










32 Binning strategy





binning































4 THE HALO RR LYRAE




0 10 20 30r [kpc]

0

50

100

150

200

250

[km

s]

r MEDIANr MAP

t MEDIANt MAP

0 10 20 30r [kpc]

00

02

04

06

08

10

12


0 10 20 30r [kpc]

60

40

20

0

20

40

60

V [k

ms

]

V = 0 kmsGP 1GP 2






































0 5 10 15 20 25R [kpc]

0

100

200

300

400

V [k

ms

]


0 5 10 15 20 25R [kpc]

0

20

40

60

80

100

120

[km

s]


GP 1GP 2

00

05

10

15

20

25

30

|z| [

kpc]






5 THE DISC RR LYRAE




















4 2 0[FeH]

00

05

10

pdf


04 06 08 10P [day]

0

2

4

pdf


0 2 4 631 [rad]

00

02

04

06

pdf


4 2 0[FeH]SOS

000

025

050

075

100

pdf


02 03 04 05P1o [day]

0

5

10

pdf


00 05 10 15AMP [mag]

00

05

10

15

20

pdf

























Halo structure

Mid-velocity

Thick disc











63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix


1000100 [deg]

500

50

b [d

eg]

Halo N = 49914

1000100 [deg]

500

50

b [d

eg]

Rotating N = 3126

1000100 [deg]

500

50

b [d

eg]


0 20 40R [kpc]

0

10

20

30

40

|z| [

kpc]

0 20 40R [kpc]

0

10

20

30

40|z

| [kp

c]

0 20 40R [kpc]

0

10

20

30

40

|z| [

kpc]



10 2

10 1

100

NN

tot




) (7)

where





Lmulti =sum119894

119891119894N(119894perpΛ119894perp + S119894

)=sum119894

119891119894L119894 (8)


119902119894 =119891119894L119894

Lmulti (9)










32 Binning strategy





binning































4 THE HALO RR LYRAE




0 10 20 30r [kpc]

0

50

100

150

200

250

[km

s]

r MEDIANr MAP

t MEDIANt MAP

0 10 20 30r [kpc]

00

02

04

06

08

10

12


0 10 20 30r [kpc]

60

40

20

0

20

40

60

V [k

ms

]

V = 0 kmsGP 1GP 2






































0 5 10 15 20 25R [kpc]

0

100

200

300

400

V [k

ms

]


0 5 10 15 20 25R [kpc]

0

20

40

60

80

100

120

[km

s]


GP 1GP 2

00

05

10

15

20

25

30

|z| [

kpc]






5 THE DISC RR LYRAE




















4 2 0[FeH]

00

05

10

pdf


04 06 08 10P [day]

0

2

4

pdf


0 2 4 631 [rad]

00

02

04

06

pdf


4 2 0[FeH]SOS

000

025

050

075

100

pdf


02 03 04 05P1o [day]

0

5

10

pdf


00 05 10 15AMP [mag]

00

05

10

15

20

pdf

























Halo structure

Mid-velocity

Thick disc











63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix







32 Binning strategy





binning































4 THE HALO RR LYRAE




0 10 20 30r [kpc]

0

50

100

150

200

250

[km

s]

r MEDIANr MAP

t MEDIANt MAP

0 10 20 30r [kpc]

00

02

04

06

08

10

12


0 10 20 30r [kpc]

60

40

20

0

20

40

60

V [k

ms

]

V = 0 kmsGP 1GP 2






































0 5 10 15 20 25R [kpc]

0

100

200

300

400

V [k

ms

]


0 5 10 15 20 25R [kpc]

0

20

40

60

80

100

120

[km

s]


GP 1GP 2

00

05

10

15

20

25

30

|z| [

kpc]






5 THE DISC RR LYRAE




















4 2 0[FeH]

00

05

10

pdf


04 06 08 10P [day]

0

2

4

pdf


0 2 4 631 [rad]

00

02

04

06

pdf


4 2 0[FeH]SOS

000

025

050

075

100

pdf


02 03 04 05P1o [day]

0

5

10

pdf


00 05 10 15AMP [mag]

00

05

10

15

20

pdf

























Halo structure

Mid-velocity

Thick disc











63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix






























4 THE HALO RR LYRAE




0 10 20 30r [kpc]

0

50

100

150

200

250

[km

s]

r MEDIANr MAP

t MEDIANt MAP

0 10 20 30r [kpc]

00

02

04

06

08

10

12


0 10 20 30r [kpc]

60

40

20

0

20

40

60

V [k

ms

]

V = 0 kmsGP 1GP 2






































0 5 10 15 20 25R [kpc]

0

100

200

300

400

V [k

ms

]


0 5 10 15 20 25R [kpc]

0

20

40

60

80

100

120

[km

s]


GP 1GP 2

00

05

10

15

20

25

30

|z| [

kpc]






5 THE DISC RR LYRAE




















4 2 0[FeH]

00

05

10

pdf


04 06 08 10P [day]

0

2

4

pdf


0 2 4 631 [rad]

00

02

04

06

pdf


4 2 0[FeH]SOS

000

025

050

075

100

pdf


02 03 04 05P1o [day]

0

5

10

pdf


00 05 10 15AMP [mag]

00

05

10

15

20

pdf

























Halo structure

Mid-velocity

Thick disc











63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix


0 10 20 30r [kpc]

0

50

100

150

200

250

[km

s]

r MEDIANr MAP

t MEDIANt MAP

0 10 20 30r [kpc]

00

02

04

06

08

10

12


0 10 20 30r [kpc]

60

40

20

0

20

40

60

V [k

ms

]

V = 0 kmsGP 1GP 2






































0 5 10 15 20 25R [kpc]

0

100

200

300

400

V [k

ms

]


0 5 10 15 20 25R [kpc]

0

20

40

60

80

100

120

[km

s]


GP 1GP 2

00

05

10

15

20

25

30

|z| [

kpc]






5 THE DISC RR LYRAE




















4 2 0[FeH]

00

05

10

pdf


04 06 08 10P [day]

0

2

4

pdf


0 2 4 631 [rad]

00

02

04

06

pdf


4 2 0[FeH]SOS

000

025

050

075

100

pdf


02 03 04 05P1o [day]

0

5

10

pdf


00 05 10 15AMP [mag]

00

05

10

15

20

pdf

























Halo structure

Mid-velocity

Thick disc











63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix



























0 5 10 15 20 25R [kpc]

0

100

200

300

400

V [k

ms

]


0 5 10 15 20 25R [kpc]

0

20

40

60

80

100

120

[km

s]


GP 1GP 2

00

05

10

15

20

25

30

|z| [

kpc]






5 THE DISC RR LYRAE




















4 2 0[FeH]

00

05

10

pdf


04 06 08 10P [day]

0

2

4

pdf


0 2 4 631 [rad]

00

02

04

06

pdf


4 2 0[FeH]SOS

000

025

050

075

100

pdf


02 03 04 05P1o [day]

0

5

10

pdf


00 05 10 15AMP [mag]

00

05

10

15

20

pdf

























Halo structure

Mid-velocity

Thick disc











63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix
















4 2 0[FeH]

00

05

10

pdf


04 06 08 10P [day]

0

2

4

pdf


0 2 4 631 [rad]

00

02

04

06

pdf


4 2 0[FeH]SOS

000

025

050

075

100

pdf


02 03 04 05P1o [day]

0

5

10

pdf


00 05 10 15AMP [mag]

00

05

10

15

20

pdf

























Halo structure

Mid-velocity

Thick disc











63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix


















Halo structure

Mid-velocity

Thick disc











63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix




63 The bulgebar


64 Conclusions






ACKNOWLEDGEMENTS





DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix



DATA AVAILABILITY


REFERENCES





















































































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix























































02 04 06 08P [day]

2

0

[Fe

H] -

b(31

-06

)

RRab

025 030 035 040 045P1o [day]

3

2

1

[Fe

H] -

b(31

-03

)

RRc

15

20

25

31

3

4

31













4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix









4 2 0[FeH]

00

05

10

15

20

pdf


3 2 1 0 1[FeH]

00

05

10

pdf


2 0[FeH]

00

05

10

15

pdf






(B2)



(B3)

and


(B4)








1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix







1 Introduction

2 The sample


22 Cleaning

3 The Method

31 Kinematic fit

32 Binning strategy


4 The halo RR Lyrae



5 The disc RR Lyrae




63 The bulgebar

64 Conclusions


B Rotation Matrix

arxiv:2008.02280v1 [astro-ph.ga] 5 aug 2020 · mnras 000,1{27(2020) preprint 7 august 2020 compiled...

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