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Chasing Ghosts in the Galactic Halo
L. Aguilar, A. Brown & H. VelázquezInst. de Astronomía, UNAM (México)
& Leiden Observatory (Netherlands)
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The punch line ...
When looking for something,sometimes what you get,is not what you thought you would see.
Issues: Observational errors,selection effects,background.
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Outline
Why search ?How to search ?
The promise of GaiaThis work:
Questions of backgroundQuestions of samplingQuestions of accuracy
Expected resultsThe future
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Why search?
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Why search?Current cosmological models envisage the formation of large luminous galaxies as a long process of merging of smaller structures.This process must have left an imprint on halos of galaxies like ours, where long dynamical time scales preserve remnants of old mergers.By probing the structure of our galaxy´s halo, we do “in situ” cosmology.
www.iap.fr
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Why search?We actually see evidence of structure in our galactic halo
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Why search?We actually see evidence of structure in our galactic halo
The Sagittarius dwarf spheroidal galaxy (Ibata, Gilmore & Irwin, 1994)
Ibata, Wyse and Sword
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Why search?We actually see evidence of structure in our galactic halo
The tidal disruption of Palomar 5 (Odenkirchen et al., 2002)
Oderkirchen et al. (MPIA) & SDSS collaboration (2002)
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Why search?We actually see evidence of structure in our galactic halo
Groups in the velocity space of a solar neighborhood halo sample (Helmi et al., 2002)
Helmi et al. Nat. 402, 53 (2002)
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Why search?We actually see evidence of structure in our galactic halo
and many more ...
Eggen (1965),Lynden-Bell (1976),Rodgers and Paltoglou (1984),Ratnatunga and Freeman (1985),Dionidis and Beers (1989),Arnold and Gilmore (1992),Majewski, Munn and Hawley (1996),Ibata et al. (2003),Martin et al. (2004), ...
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How to search?
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How to search?Spatial information from photometry
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How to search?Spatial information from photometry
Large scale photometric surveys (SDSS, 2MASS).
Newberg et al. ApJ, 569, 245 (2002)Polar plot of g* vs. R.A.0.1 < (g*-r*) < 0.3 MV ~ +4.2
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How to search?Search in E vs L and Lz space
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How to search?Search in E vs L and Lz space
A steady state potential preserves E,a spherical potential preserves L,an axisymmetric potential preserves Lz
Helmi and de Zeeuw, MNRAS, 319, 657 (2000)Space of conserved quantitiesSimulations: Multipolar code, fixed galactic
potential, 105 particle King model satellites, 12 Gyrs time span,simulated Gaia errors.
Initial conditions
Final frame
But where is the galactic background?
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How to search?Use N-body simulations to look for clues
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How to search?Use N-body simulations to look for clues
N-body simulations can reveal characteristics of the debris that can be used to devise a search method
Johnston, Hernquist and Bolte, ApJ, 465, 278 (1996)Great Circle Cell Count MethodSimulations: Self-consistent field code, fixed
spherical galactic potential, 104 particle Plummer model satellites, 10 Gyrs time span.
Sky projections
Arc on the sky vs. radial velocity
Fiducial case
Effect of decreasing velocity dispersion ↓Effect of increasing central density ↓
But it’s a spherical halo!
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The promise of Gaia
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The promise of GaiaThe Gaia Mission
A stereoscopic census of our Galaxy:
Magnitude limit: 20-21 magCompletness: 20 magNumber of objects: 26 million to V=15 250 million to V=18 1,000 million to V=20Astrometric accuracy: 4 μarcsec at V=10 10 μarcsec at V=15 200 μarcsec at V=20Photometry: 4 broad band to V=20 11 medium band to V=20Radial velocities: 1-10 km/s at V=16-17Observing program: On-board and unbiasedExpected launch year: 2011Space agency: ESA
ESA and Medialab
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The promise of GaiaThe Gaia Mission
10 μarcsec ⇒10% accuracy in distances at 10 kpc 10 μarcsec/yr ⇒ 1 km/s accuracy at 20 kpc
ESA and Medialab
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This work
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This workWhat sets this work apart?
Realistic modeling of galactic background
We address sampling issues
Realistic modeling of the observational errors
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This workKey ingredients
Realistic modeling of the dynamical process of satellite destruction:
Mass model of the Galaxy with non-spherical haloN-body simulation with self-gravity and large number
of particles
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Mass model of the Galaxy
Bulge: Spherical Hernquist
Mb = 1.4 × 1010 Mo Md = 5.6 × 1010 Mo vh = 186 km/sa = 630 pc Rd = 3.5 kpc Rc = 12 kpc β -1 = 700 pc qh = 0.8
0 50 100 150
0
50
100
150
200
250
Halo:
Disk:Double exponential
LogarithmicBulge Disk Halo
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Mass model of satellites
King models:N = 106
M = 2.8 × 107 Mo and 5.6 × 107 Mo
rt = 3.15 kpc
c = 0.9
A50l Perigalactico 1
-5
0
5
x-5
0
5
y
-5
0
5
z
-5
0
5
x
M. Mateo, 1998, ARA&A, 36, 435
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N-body simulations
Simulation specs:Code: Tree (Dubinski)Runs: 5CPU per run: 4 daysTime span: 10 GyrsEnergy error < 0.1%Computer: 32 processor Beowulf “La Granja”
1:
2:
3:
4:
5:
Run Satellite Peri (kpc) Apo θ1 High mass 8.75 105 30o
2 High mass 7 60 45o
3 Low mass 7 80 60o
4 Low mass 40 60 25o
5 Low mass 3.5 55 45o
Orthogonal projections of 5 runs
“La Granja”
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This workKey ingredients
Realistic modeling of the dynamical process of satellite destruction:
Mass model of the Galaxy with non-spherical haloN-body simulation with self-gravity and large number
of particles
Realistic modeling of galactic background: Luminosity model of the Galaxy
Efficient Monte Carlo realization
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Luminosity model of the Galaxy3 components:
Bulge ∝ (rB2 + r2)-5/2 rB = 0.38 kpc
Disk ∝ exp[- ( (R-Ro)/RD + |z|/zD] Ro = 8.5 kpc RD = 3.5 kpc zD = 0.2 kpc
Halo ∝ 1/(rH7/2 + r´7/2) r´ = (R2 + (z/q´)2)1/2 rH = 1 kpc q´ = 0.8
0.1 1
0.1
1
R (kpc)
0.1 1
0.1
1
z (kpc)
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Efficient Monte Carlo realizationLuminosity function:
We first calculate the weighted luminosity function for a survey limited to V=20 (Gaia)
-5 0 5 10 15MV
0
2
4
6
8
log
!(M
V)
(sta
rs/k
pc
3)
Intrinsic luminosity function
Expected number of stars in survey
Vlim = 20.0
104
105
106
107
108
109
# s
tars
in
su
rve
y
Integrated over the whole galaxy, the weightedluminosity function results in ~1.5 × 109 stars!
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Efficient Monte Carlo realizationThen for each individual star:
Choose Mv from weighted luminosity functionChoose spectral type from Hess diagramCompute maximum visible distance dmaxGenerate random position within sun-centered sphere of radius dmax using Von Neumann rejection techniqueAssign galactic component from local relative densities
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Efficient Monte Carlo realizationThen for each individual star:
Choose Mv from weighted luminosity functionChoose spectral type from Hess diagramCompute maximum visible distance dmaxGenerate random position within sun-centered sphere of radius dmax using Von Neumann rejection techniqueAssign galactic component from local relative densities
We have avoided the galactic plane:
-90o < l < +90o and -5o < b < +5o
This reduces the number of stars to be generated to 3.1 × 108 stars.
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Efficient Monte Carlo realizationThen for each individual star:
Choose Mv from weighted luminosity functionChoose spectral type from Hess diagramCompute maximum visible distance dmaxGenerate random position within sun-centered sphere of radius dmax using Von Neumann rejection techniqueAssign galactic component from local relative densities
We have avoided the galactic plane:
-90o < l < +90o and -5o < b < +5o
This reduces the number of stars to be generated to 3.1 × 108 stars.
Our simulated survey contains every single one of those!
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This workKey ingredients
Realistic modeling of the dynamical process of satellite destruction:
Mass model of the Galaxy with non-spherical haloN-body simulation with self-gravity and large number
of particles
Realistic modeling of galactic background: Luminosity model of the Galaxy
Efficient Monte Carlo realization
Realistic modeling of Gaia errors: Simulate dependency on apparent magnitude, color and ecliptic latitude
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Simulating Gaia astrometry
We need to add kinematics to our Galaxy model
Bulge: Non-rotating Isotropic velocity dispersionDisk: Rotating Velocity ellipsoids for each spectral typeHalo: Rotating Single velocity ellipsoid
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Simulating Gaia astrometry
We need to add kinematics to our Galaxy model
Bulge: Non-rotating Isotropic velocity dispersionDisk: Rotating Velocity ellipsoids for each spectral typeHalo: Rotating Single velocity ellipsoid
Component vrot σ (km/s)
Bulge 0 110
Disk 220 Sp. Type σR σθ σz O 10 9 6 B 10 9 6 A 20 9 9 F 27 17 17 G 32 17 15 K 35 20 16 M 31 23 16
Halo 35 135 105 90
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Simulating Gaia astrometry
We also need to add photometric information to our simulated satellites
Assume all stars on a single isochrone (Girardi et al. 2000): Low metallicity
Age corresponds to simulation snapshot
Assume power law mass function: ξ(m) ∝ m-1.5
Get Mv and (V - I) from assumed isochrone
Girardi et al. A&AS 141, 371 (2000)
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Simulating Gaia astrometry
We can now simulate the astrometry and its errors
Convert phase space information to astrometric observables: proper motion,parallax and radial velocity
Add astrometric errors as a function of Gaia G magnitude, (V - I) color andecliptic latitude
Add radial velocity errors as a function of apparent magnitude
5 10 15 20V
0
50
100
150
200
!"!"#
as)
5 10 15 20V
0
50
100
150
200
!"!"#
as)
a
-50 0 50# (degrees)
0
10
20
30
40
50
60
!"!"#
as)
-50 0 50# (degrees)
0
10
20
30
40
50
60
!"!"#
as)
17.5 < V < 18.0
b
-50 0 50# (degrees)
0
10
20
30
40
50
60
!#$* (#
as/y
r)
-50 0 50# (degrees)
0
10
20
30
40
50
60
!#$* (#
as/y
r)
17.5 < V < 18.0
c
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This workKey ingredients
Realistic modeling of the dynamical process of satellite destruction:
Mass model of the Galaxy with non-spherical haloN-body simulation with self-gravity and large number
of particles
Realistic modeling of galactic background: Luminosity model of the Galaxy
Efficient Monte Carlo realization
Realistic modeling of Gaia errors: Simulate dependency on apparent magnitude, color and ecliptic latitude
Realistic modeling of sampling limitations and bias: Variation in probing of satellite luminosity function along streamer
Proper matching of star counts for background and satellite
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Variation in depth of probing of streamer
A dissolving satellite is spread along a streamer with varying distance to the observer.
Sun
Simulation #1
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Variation in depth of probing of streamer
A dissolving satellite is spread along a streamer with varying distance to the observer.
Sun
And this results in stars that are always seen,others that are seen sometimesand other that are never seen Faintest star seen at closest distance
Faintest star seen at largest distance
Brighter
Simulation #1
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Variation in depth of probing of streamer
Given an assumed isochrone, metallicity and mass function for the satellite, we can compute the fraction of stars visible along the streamer
Histogram: Distribution of distances to observer (right vertical axis)
Simulation #110 Gyr isochrone, Z=0.004, ξ ∝ m-1.5
Black line: Visible fraction of simulated satellite stars (left vertical axis)
Overall fraction of visible stars: 0.0025!
Red line: Visible fraction of simulated satellite stars, eliminating those that are never seen
Overall fraction of visible stars: 0.01!
It is clear that the answer is to simulate a tracer bright population only.
But how to choose a proper luminosity cut-off ?
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Proper matching of star counts for background and satellite
Given a dwarf galaxy with an assumed luminosity function and simulated orbit, we can compute the fraction of stars brighter than a given absolute magnitude, that will visible by Gaia.
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Proper matching of star counts for background and satellite
Given a dwarf galaxy with an assumed luminosity function and simulated orbit, we can compute the fraction of stars brighter than a given absolute magnitude, that will visible by Gaia.
The answer obviously depends on the total luminosity of the dwarf galaxy.
Mv = -17
-15
-13
-11
As we dim the faint luminosity cut-off, more stars become visible, until we reach the total number that can be seen given the Gaia apparent magnitude limit.
Fainter
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Given a simulated satellite we can compute the number of particles that will be seen if we assume that all are brighter than a given absolute magnitude.
Proper matching of star counts for background and satellite
Given a dwarf galaxy with an assumed luminosity function and simulated orbit, we can compute the fraction of stars brighter than a given absolute magnitude, that will visible by Gaia.
The answer obviously depends on the total luminosity of the dwarf galaxy.
Mv = -17
-15
-13
-11
As we dim the faint luminosity cut-off, more stars become visible, until we reach the total number that can be seen given the Gaia apparent magnitude limit.
Fainter
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Proper matching of star counts for background and satellite
Given a dwarf galaxy with an assumed luminosity function and simulated orbit, we can compute the fraction of stars brighter than a given absolute magnitude, that will visible by Gaia.
The answer obviously depends on the total luminosity of the dwarf galaxy.
Mv = -17
-15
-13
-11
As we dim the faint luminosity cut-off, more stars become visible, until we reach the total number that can be seen given the Gaia apparent magnitude limit.
Given a simulated satellite we can compute the number of particles that will be seen if we assume that all are brighter than a given absolute magnitude.
The point where these two curves intersect defines the correct number of particles that should be considered. Fainter
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Proper matching of star counts for background and satellite
For a Mv = -15 dwarf galaxy, a 106 particle simulation results in 3×105 that should be considered (30%).
This wastes precious simulated particles, but ensures the correct inclusion of the varying depth of sampling along the orbit and the proper matching of satellite and galactic background.
-15
Fainter
Mass vs luminosity for Local Group dwarfs
M. Mateo, 1998, ARA&A, 36, 435
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Expected results
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Gauging the galactic background problem
Mollwide projection on the sky of runs 1 and 5
Excluded region
Star counts on an equal area projection on the sky of two simulated satellites
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Gauging the galactic background problem
Mollwide projection on the sky of runs 1 and 5
Same as above but with inclusion of galactic background
Excluded region
Excluded region
Star counts on an equal area projection on the sky of two simulated satellites
Adding the proper galactic background swamps all but the densest parts of the remnant
Using photometric information to isolate particular sets of stars will greatly help the identification of remnants on the sky
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Galaxy data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Satellite data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Combined data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
The E vs Lz diagramGalaxy Satellites combined
These figures show error-free data
Despite the background, the three satellites are clearly visible
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Galaxy data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Satellite data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Combined data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
Galaxy data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Satellite data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Combined data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
The E vs Lz diagramGalaxy Satellites combined
These figures show error-free data
Despite the background, the three satellites are clearly visible
These figures show data with errors
The satellites are smeared over a large region, but are still seen
Notice that errors produce caustic-like structures, with several emanating from each satellite
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Galaxy data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Satellite data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Combined data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
Galaxy data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Satellite data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Combined data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
Galaxy data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Satellite data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5Combined data
-2 -1 0 1 2Lz [104 kpc km/s]
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
E [10
5 (
km
/s)2
]
-2 -1 0 1 2
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
The E vs Lz diagramGalaxy Satellites combined
These figures show error-free data
Despite the background, the three satellites are clearly visible
These figures show data with errors
The satellites are smeared over a large region, but are still seen
These figures show high quality dataRestricting to a high quality sample improves the detection.
V < 15, ϖ/σϖ > 5
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The d vs vr diagram
0 20 40 60 80 100Distance (kpc)
-400
-200
0
200
400
Vr (k
m/s
)
0 20 40 60 80 100
-400
-200
0
200
400
0 10 20 30 40 50Distance (kpc)
-400
-200
0
200
400
Vr (k
m/s
)
0 10 20 30 40 50
-400
-200
0
200
400
0 20 40 60 80 100Distance (kpc)
-400
-200
0
200
400
Vr (k
m/s
)
0 20 40 60 80 100
-400
-200
0
200
400
Similar searches can be made in other diagrams, like distance vs radial velocity
In all cases, the conclusion is that the picture becomes quite fuzzy, and high quality data must be used
The use of photometry to restrict the sample to particular stellar populations will be very important
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Why the huge spread?
This figure illustrates the effect of 3σ errors in the astrometry and radial velocity for a particular star in the E-Lz
plane.
Parallax error
Proper motion error
Radial velocity error
The largest spread is due to the parallax error, which produces the caustic-like structures in this diagram.
After the parallax, the radial velocity and the proper motion errors in turn, have decreasing effects. The errors are correlated and it is necessary to propagate them from observables to derived quantities.
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Why the huge spread?
Parallax error
Proper motion error
Radial velocity error
Notice that the parallax error, if severe enough, may not even allow us to determine whether the star is rotating or counterotating around the Galaxy. negative
spin
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Slices in the E vs Lz diagram
Another approach is to take slices in the E vs Lz diagram and plot the resulting histograms
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Slices in the E vs Lz diagram
Another approach is to take slices in the E vs Lz diagram and plot the resulting histograms
with errors
error free
Full sample
The satellites, wich are clarely visible in the error-free data, are completely swamped out by the errors
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Slices in the E vs Lz diagram
Another approach is to take slices in the E vs Lz diagram and plot the resulting histograms
with errors
error free
High quality sample
Using the high quality sample (V<15, ϖ/σϖ >5) recovers the signal for the satellites, but it will be difficult to isolate them based on dynamics alone.
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Slices in the E vs Lz diagram
Another approach is to take slices in the E vs Lz diagram and plot the resulting histograms
High quality sample
Full sample
with errors
error free
In this case we fare better, since most of disk stars are left behind.The E-Lz technique is a good starting point, but it needs to be complemented with further criteria
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The future
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Things to do
Improve Gaia astrometry modelModel improvements
Search techniquesTry global diagnostics of substructure: entropyContrast enhancement techniques: unsharp maskingSimulate restricted searches: “pencil beams”
AstronomyUse a “cosmological halo” with remnants in various stages of relaxation and diverse stellar populations
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Basic Lessons
The Gaia database will be a treasure of information about our Galaxy, but extracting knowledge from it won’t be straightforward.
We have to be clever
Use a “holisitc” approachDevise search strategies that employ as much of Gaia information at once, don’t throw away useful information.
Learn to live in observable spaceAs much as it is possible, we should conduct our studies directly in the space of observables. Models have infinite signal to noise ratio, observations don’t.
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End of the story!(at least for now)
MNRAS (2005) 359, 1287