the asteroseismic analysis of the pulsating sdb feige 48 revisited v. van grootel, s. charpinet, g....

The asteroseismic analysis of the The asteroseismic analysis of the

pulsating sdB Feige 48pulsating sdB Feige 48revisitedrevisited

V. Van GrootelV. Van Grootel, S. Charpinet, G. Fontaine, S. Charpinet, G. Fontaine

P. Brassard, E.M. Green and P. ChayerP. Brassard, E.M. Green and P. Chayer

ContentsContents1.1. Method and objectives for an asteroseismological Method and objectives for an asteroseismological

analysis. Introduction of the rotation of the staranalysis. Introduction of the rotation of the star

2.2. About Feige 48: spectroscopy, close binary system and About Feige 48: spectroscopy, close binary system and first asteroseismic analysis (Charpinet et al., 2005)first asteroseismic analysis (Charpinet et al., 2005)

3.3. Results from re-analysis with rotation :Results from re-analysis with rotation :

• Search for the optimal model with solid rotationSearch for the optimal model with solid rotation• Period fit and mode identificationPeriod fit and mode identification• Comparison with Charpinet et al. (2005)Comparison with Charpinet et al. (2005)• Consistency with Han’s simulations (2003) and Stellar Evolution TheoryConsistency with Han’s simulations (2003) and Stellar Evolution Theory• Comments about the period of rotationComments about the period of rotation

4.4. Testing the hypothesis of a fast core rotationTesting the hypothesis of a fast core rotation

5.5. Room for improvement and conclusionsRoom for improvement and conclusions

26/07/2007New asteroseismic analysis of Feige 48

1. Asteroseismological analysis :1. Asteroseismological analysis :Method and ObjectivesMethod and Objectives

Forward approachForward approach : fit theoretical periods with : fit theoretical periods with all observed periods simultaneouslyall observed periods simultaneously• Internal structure calculation from TInternal structure calculation from Teffeff, log , log gg, log q(H) (here after, , log q(H) (here after,

lqh) and Mlqh) and Mtottot

• Calculation of the adiabatic and non-adiabatic pulsations + Calculation of the adiabatic and non-adiabatic pulsations + rotational splitting calculation (see next slide)rotational splitting calculation (see next slide)

• Double-optimisation scheme to find the best fit(s)Double-optimisation scheme to find the best fit(s)

SS² = ² = ΣΣ (P (Pobsobs – P – Pthth)²)²

A-posteriori A-posteriori mode identification (mode identification (k, lk, l, , mm). For ). For l:l: independent test from multi-colour photometryindependent test from multi-colour photometry

New asteroseismic analysis of Feige 48 26/07/2007

Introduction of the star rotationIntroduction of the star rotation

Ω(r) rotation, 1st order Perturbative Theory:Ω(r) rotation, 1st order Perturbative Theory:


wherewhere andand Dziembowski’s variables are givenDziembowski’s variables are given

by pulsation codes. For each theoretical (adiabatic) period by pulsation codes. For each theoretical (adiabatic) period mm = 0, = 0, calculation of the multiplets for a given Ω(r) (solid, fast core or calculation of the multiplets for a given Ω(r) (solid, fast core or

linear rotation)linear rotation). . Advantage :Advantage : All observed periods can be used for analysis, no need for assumptions about All observed periods can be used for analysis, no need for assumptions about mm = 0 modes = 0 modes

2. What is known so far 2. What is known so far about Feige 48about Feige 48


Feige 48 : SpectroscopyFeige 48 : Spectroscopy

Koen et al., 1998Koen et al., 1998• TTeffeff = 28,900 ± 300 K = 28,900 ± 300 K

• log log gg = 5.45 ± 0.05 = 5.45 ± 0.05 Heber et al., 2000, Keck/HIRESHeber et al., 2000, Keck/HIRES

• TTeffeff = 29,500 ± 300 K = 29,500 ± 300 K

• log log gg = 5.50 ± 0.05 = 5.50 ± 0.05

+ + VV sin sin ii ≤ 5 km s ≤ 5 km s-1-1

Charpinet et al., 2005, MMTCharpinet et al., 2005, MMT• TTeffeff = 29,580 ± 370 K = 29,580 ± 370 K

• log log gg = 5.480 ± 0.046 = 5.480 ± 0.046


Feige 48 : a close binary systemFeige 48 : a close binary system S. O’Toole et al., 2004: S. O’Toole et al., 2004: Detection of a companion to the Detection of a companion to the

pulsating sdB Feige 48. pulsating sdB Feige 48. HST/STIS, FUSE archivesHST/STIS, FUSE archives• Velocity semi-amplitude KVelocity semi-amplitude KsdB sdB = 28.0 ± 0.2 km s= 28.0 ± 0.2 km s-1-1

• Orbital period of 0.376 ± 0.003 d (Orbital period of 0.376 ± 0.003 d ( 9.024 ± 0.072h) 9.024 ± 0.072h)

• The unseen companion is a white dwarf with ≥ 0.46 MThe unseen companion is a white dwarf with ≥ 0.46 Mss

• Orbital inclination Orbital inclination ii ≤ 11.4° ≤ 11.4°


Feige 48 : time-series photometryFeige 48 : time-series photometry CFHT, six nights in June 1998. Resolution of CFHT, six nights in June 1998. Resolution of ~ 2.18 µHz~ 2.18 µHz 9 periods detected:9 periods detected:

Mean spacing: <Mean spacing: <ΔνΔν> ~ 28.2 µHz, > ~ 28.2 µHz, σ(Δν) σ(Δν) = 2.48 µHz= 2.48 µHz

SpacingSpacing of of

52.9 µHz with 52.9 µHz with ff11

(Δm=2) !!!(Δm=2) !!!


Feige 48 : first asteroseismic analysisFeige 48 : first asteroseismic analysisCharpinet et al., A&A 343, 251-269, 2005Charpinet et al., A&A 343, 251-269, 2005

Assumption of 4 Assumption of 4 mm = 0 modes, no rotation included = 0 modes, no rotation included Only degrees Only degrees l l ≤ 2≤ 2 Structural parameters obtained:Structural parameters obtained:

TTeffeff = 29 580 = 29 580 ± 370 K (fixed)± 370 K (fixed), log , log gg = 5.4365 = 5.4365 ± 0.0060± 0.0060, ,

lqh = -2.97 lqh = -2.97 ± 0.09 and± 0.09 and M Mtottot = 0.460 = 0.460 ± 0.008± 0.008 Ms Ms

Period fit : Period fit : <dp/p> ~ 0.005%, <dp> ~ 0.018s, close <dp/p> ~ 0.005%, <dp> ~ 0.018s, close to the accuracy of the observationsto the accuracy of the observations ! !

Derived inclination Derived inclination ii ≤ 10.4 ± 1.7°, very good ≤ 10.4 ± 1.7°, very good agreement with O’Toole et al.agreement with O’Toole et al.


First Asteroseismic analysis:First Asteroseismic analysis:Mode IdentificationMode Identification


3. New asteroseismological 3. New asteroseismological analysis with rotationanalysis with rotation

26/07/2007New asteroseismic analysis of Feige 48

Search for the optimal model with Search for the optimal model with solid rotationsolid rotation

Solid Rotation: hypothesisSolid Rotation: hypothesis No assumption about No assumption about mm = 0 modes (used all 9 periods); still = 0 modes (used all 9 periods); still

only degrees only degrees l l ≤ 2; no ≤ 2; no a-priori a-priori constraint on identificationconstraint on identification Optimisation on 4 parameters : log Optimisation on 4 parameters : log gg, lqh, M, lqh, Mtottot and P and Protrot

Several models* can fit the 9 periods, the preferred one is:Several models* can fit the 9 periods, the preferred one is:TTeffeff = 29 580 = 29 580 ± 370 K (still fixed)± 370 K (still fixed), log , log gg = 5.4622 = 5.4622 ± 0.0060± 0.0060, ,

lqh = -2.58 lqh = -2.58 ± 0.09 and± 0.09 and M Mtottot = 0.519 = 0.519 ± 0.008± 0.008 Ms Ms Solid rotation PSolid rotation Protrot = 32 500s ± 2200s = 32 500s ± 2200s 9.028 ± 0.61h 9.028 ± 0.61h

ExcellentExcellent agreement with orbital period determined agreement with orbital period determined independently from velocities variations (Pindependently from velocities variations (Porb orb = 9.024 ± = 9.024 ± 0.072h).0.072h).

Period fit : Period fit : SS² ~ 0.60 ² ~ 0.60 <dp/p> ~ 0.06%, <dp> ~ 0.22s<dp/p> ~ 0.06%, <dp> ~ 0.22sNew asteroseismic analysis of Feige 48 26/07/2007

Analysis with solid rotation:Analysis with solid rotation:Mode IdentificationMode Identification

Space parameters mapsSpace parameters maps

Left : lqh and MLeft : lqh and Mtottot fixed; right : T fixed; right : Teffeff and log and log g g fixedfixed


log log gg

TeffTeff lqhlqh

MtotMtot

Comparison with Charpinet et al., 2005Comparison with Charpinet et al., 2005

About model parameters:About model parameters:• New surface gravity log New surface gravity log gg closer to spectroscopy closer to spectroscopy• Total mass relatively high (MTotal mass relatively high (Mtottot ~ 0.52 M ~ 0.52 Mss) but ) but possiblepossible according to according to

Han’s simulations (2003)Han’s simulations (2003)• H-envelope slightly thicker, still completely consistent with Stellar H-envelope slightly thicker, still completely consistent with Stellar

Evolution TheoryEvolution Theory

About period fit and mode identification:About period fit and mode identification:• The difference is about the The difference is about the mm = 0 modes in the doublet (343-346s) = 0 modes in the doublet (343-346s)

and the triplet (374-378-383s). The identification “and the triplet (374-378-383s). The identification “m m = -1, = -1, m m = -2” is = -2” is maybe unexpected, but the intrinsic amplitudes are never knownmaybe unexpected, but the intrinsic amplitudes are never known

• Forcing Charpinet’s model + solid rotation : Forcing Charpinet’s model + solid rotation : SS² ~ 2.6 (4x poorer). No ² ~ 2.6 (4x poorer). No convergence to a Rotation Period of ~ 32 500s (rather ~ 29 500s) convergence to a Rotation Period of ~ 32 500s (rather ~ 29 500s)


Conclusion : Charpinet’s model is not given up, but there is also hints in favor of a higher Conclusion : Charpinet’s model is not given up, but there is also hints in favor of a higher mass modelmass model

Consistency with Han’s simulations Consistency with Han’s simulations and EHB Stellar Evolution Theoryand EHB Stellar Evolution Theory


Comparison with Charpinet et al., 2005Comparison with Charpinet et al., 2005

S² S² ~ 0.6~ 0.6

log g ~ 5.46 log g ~ 5.46

MMtot tot ~ 0.52 M~ 0.52 Mss

PProtrot ~ 32,500s ~ 32,500s

S² S² ~ 0.9~ 0.9

log g ~ 5.45 log g ~ 5.45


PProtrot ~ 30,500s ~ 30,500s

S² S² ~ 2.6~ 2.6

log g ~ 5.435 log g ~ 5.435


PProtrot ~ 29,500s ~ 29,500s

SuggestionSuggestion : time-series spectroscopy observations : time-series spectroscopy observations could give (needed) hints about could give (needed) hints about mm

Comments about the period of solid Comments about the period of solid rotation rotation (= 9.028 (= 9.028 ± 0.61h)± 0.61h)

Fitting all 9 periods independently is impossible (very poor Fitting all 9 periods independently is impossible (very poor SS² ² and no convincing models) and no convincing models) → not a slow rotator→ not a slow rotator

The smallest The smallest ΔΔff is 8.82 µHz ( is 8.82 µHz ( P Protrot~1.2 days at the ~1.2 days at the slowestslowest), ), but again convincing models don’t exist at this ratebut again convincing models don’t exist at this rate

Even without knowing the orbital period, ~ 9.5h is the only Even without knowing the orbital period, ~ 9.5h is the only acceptable rate for the rotation period acceptable rate for the rotation period

Conclusion :Conclusion :

Orbital period = Rotation periodOrbital period = Rotation period (even if lower accuracy for P(even if lower accuracy for Protrot))

→ → Confirmation of the Confirmation of the reasonable assumption of a reasonable assumption of a

tidally locked system tidally locked system

New asteroseismic analysis of Feige 48

4. Testing the hypothesis of 4. Testing the hypothesis of a fast core rotationa fast core rotation


4. Testing a fast core rotation4. Testing a fast core rotation (Kawaler et al. ApJ 621, 432-444, 2005)(Kawaler et al. ApJ 621, 432-444, 2005)

Reminder : only degrees Reminder : only degrees ll ≤ 2 for this star ≤ 2 for this star → ideal to test the hypothesis of a fast core → ideal to test the hypothesis of a fast core

Surface rotation fixed at the optimal value of Surface rotation fixed at the optimal value of 32,500s. Core rotation was varied from 500 to 32,500s. Core rotation was varied from 500 to 32,500s, by steps of 500s. For each core period, 32,500s, by steps of 500s. For each core period, computing merit function computing merit function SS²²

Transition fixed at 0.3 R* (following Kawaler et Transition fixed at 0.3 R* (following Kawaler et al., 2005)al., 2005)


Testing a fast core rotationTesting a fast core rotation


log S²log S²

Core rotation (sec)Core rotation (sec)

Surface fixed at 32,500sSurface fixed at 32,500s

Conclusions and room for improvementConclusions and room for improvement

We determined an « alternative » convincing model for We determined an « alternative » convincing model for Feige 48 by adding the rotation as a free parameter. This Feige 48 by adding the rotation as a free parameter. This rotation is found to be solid with a period of rotation is found to be solid with a period of ~ 9.028h ~ 9.028h (equals to orbital period), which confirms that the system is (equals to orbital period), which confirms that the system is tidally locked. A fast core rotation can be excluded for this tidally locked. A fast core rotation can be excluded for this star.star.

Room for improvement: Room for improvement: • Better observations (more pulsations modes Better observations (more pulsations modes andand better resolution) better resolution)

are needed to confirm/reject the results (and choose between the are needed to confirm/reject the results (and choose between the models…)models…)

• Multi-colour photometry to confirm degrees Multi-colour photometry to confirm degrees l l (particularly (particularly ll = 0 or 2 = 0 or 2 for 352s mode)for 352s mode)

• Ultimate test: time-series spectroscopy to confirm/reject the Ultimate test: time-series spectroscopy to confirm/reject the ll and and mm values inferredvalues inferred

Thank you for your attention !Thank you for your attention !New asteroseismic analysis of Feige 48 26/07/2007

Testing a fast core rotationTesting a fast core rotation

Apparently slight differential rotation: best Apparently slight differential rotation: best SS² ² obtained for Pobtained for Pcorecore ~ 29,500s (and P~ 29,500s (and Psurfsurf = 32,500s) = 32,500s)

BUT not significant:BUT not significant:• gg and and ff-modes are very sensitive to a fast core rotation, while -modes are very sensitive to a fast core rotation, while

most p-modes are not (except « marginal » ones)most p-modes are not (except « marginal » ones)

• The triplet 374-378-382s, identified as the The triplet 374-378-382s, identified as the gg-mode « -mode « ll = 2, = 2, kk = 1 », shows Δ = 1 », shows Δf f of 29.5µHz and 31.2µHz, above the mean of 29.5µHz and 31.2µHz, above the mean spacing of 28.2µHz. This is better reproduced with a fast spacing of 28.2µHz. This is better reproduced with a fast core rotation. But these higher Δcore rotation. But these higher Δf f are not significant with a are not significant with a resolution of 2.17µHz !resolution of 2.17µHz !


Conclusion : a fast core rotation is impossible for Feige 48, which has Conclusion : a fast core rotation is impossible for Feige 48, which has probably a solid rotation !probably a solid rotation !

the asteroseismic analysis of the pulsating sdb feige 48 revisited v. van grootel, s. charpinet, g....

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