1. The asteroseismic analysis of the pulsating sdB Feige 48 revisited V. Van Grootel, S. Charpinet, G. Fontaine P. Brassard, E.M. Green and P. Chayer

2. Contents 1. Method and objectives for an asteroseismological analysis. Introduction of the rotation of the star 2. About Feige 48: spectroscopy, close binary system and first asteroseismic analysis (Charpinet et al., 2005) 3. 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. Testing the hypothesis of a fast core rotation 5. Room for improvement and conclusions 26/07/2007 New asteroseismic analysis of Feige 48

3. 1. Asteroseismological analysis : Method and Objectives Forward approach : fit theoretical periods with all observed periods simultaneously Forward approach : fit theoretical periods with all observed periods simultaneously Internal structure calculation from T eff, log g, log q(H) (here after, lqh) and M totInternal structure calculation from T eff, log g, log q(H) (here after, lqh) and M tot Calculation of the adiabatic and non-adiabatic pulsations + rotational splitting calculation (see next slide)Calculation of the adiabatic and non-adiabatic pulsations + rotational splitting calculation (see next slide) Double-optimisation scheme to find the best fit(s)Double-optimisation scheme to find the best fit(s) S² = Σ (P obs – P th )² A-posteriori mode identification (k, l, m). For l: independent test from multi-colour photometry A-posteriori mode identification (k, l, m). For l: independent test from multi-colour photometry New asteroseismic analysis of Feige 48 26/07/2007

4. Introduction of the star rotation Ω(r) rotation, 1st order Perturbative Theory: Ω(r) rotation, 1st order Perturbative Theory: New asteroseismic analysis of Feige 48 26/07/2007 whereand Dziembowski’s variables are given by pulsation codes. For each theoretical (adiabatic) period m = 0, calculation of the multiplets for a given Ω(r) (solid, fast core or linear rotation). Advantage : by pulsation codes. For each theoretical (adiabatic) period m = 0, calculation of the multiplets for a given Ω(r) (solid, fast core or linear rotation). Advantage : All observed periods can be used for analysis, no need for assumptions about m = 0 modes

5. 2. What is known so far about Feige 48 New asteroseismic analysis of Feige 4826/07/2007

6. Feige 48 : Spectroscopy Koen et al., 1998 Koen et al., 1998 T eff = 28,900 ± 300 KT eff = 28,900 ± 300 K log g = 5.45 ± 0.05log g = 5.45 ± 0.05 Heber et al., 2000, Keck/HIRES Heber et al., 2000, Keck/HIRES T eff = 29,500 ± 300 KT eff = 29,500 ± 300 K log g = 5.50 ± 0.05log g = 5.50 ± 0.05 + V sin i ≤ 5 km s -1 + V sin i ≤ 5 km s -1 Charpinet et al., 2005, MMT Charpinet et al., 2005, MMT T eff = 29,580 ± 370 KT eff = 29,580 ± 370 K log g = 5.480 ± 0.046log g = 5.480 ± 0.046 New asteroseismic analysis of Feige 48 26/07/2007

7. Feige 48 : a close binary system S. O’Toole et al., 2004: Detection of a companion to the pulsating sdB Feige 48. HST/STIS, FUSE archives S. O’Toole et al., 2004: Detection of a companion to the pulsating sdB Feige 48. HST/STIS, FUSE archives Velocity semi-amplitude K sdB = 28.0 ± 0.2 km s -1Velocity semi-amplitude K sdB = 28.0 ± 0.2 km s -1 Orbital period of 0.376 ± 0.003 d (  9.024 ± 0.072h)Orbital period of 0.376 ± 0.003 d (  9.024 ± 0.072h) The unseen companion is a white dwarf with ≥ 0.46 M sThe unseen companion is a white dwarf with ≥ 0.46 M s Orbital inclination i ≤ 11.4°Orbital inclination i ≤ 11.4° New asteroseismic analysis of Feige 4826/07/2007

8. Feige 48 : time-series photometry CFHT, six nights in June 1998. Resolution of ~ 2.18 µHz CFHT, six nights in June 1998. Resolution of ~ 2.18 µHz 9 periods detected: 9 periods detected: Mean spacing: ~ 28.2 µHz, σ(Δν) = 2.48 µHz Mean spacing: ~ 28.2 µHz, σ(Δν) = 2.48 µHz Spacing of 52.9 µHz with f 1 (Δm=2) !!! New asteroseismic analysis of Feige 4826/07/2007

9. Feige 48 : first asteroseismic analysis Charpinet et al., A&A 343, 251-269, 2005 Assumption of 4 m = 0 modes, no rotation included Assumption of 4 m = 0 modes, no rotation included Only degrees l ≤ 2 Only degrees l ≤ 2 Structural parameters obtained: Structural parameters obtained: T eff = 29 580 ± 370 K (fixed), log g = 5.4365 ± 0.0060, T eff = 29 580 ± 370 K (fixed), log g = 5.4365 ± 0.0060, lqh = -2.97 ± 0.09 and M tot = 0.460 ± 0.008 Ms lqh = -2.97 ± 0.09 and M tot = 0.460 ± 0.008 Ms Period fit : ~ 0.005%, ~ 0.018s, close to the accuracy of the observations ! Period fit : ~ 0.005%, ~ 0.018s, close to the accuracy of the observations ! Derived inclination i ≤ 10.4 ± 1.7°, very good agreement with O’Toole et al. Derived inclination i ≤ 10.4 ± 1.7°, very good agreement with O’Toole et al. New asteroseismic analysis of Feige 4826/07/2007

10. First Asteroseismic analysis: Mode Identification New asteroseismic analysis of Feige 4826/07/2007

11. 3. New asteroseismological analysis with rotation 26/07/2007New asteroseismic analysis of Feige 48

12. Search for the optimal model with solid rotation Solid Rotation: hypothesis Solid Rotation: hypothesis No assumption about m = 0 modes (used all 9 periods); still only degrees l ≤ 2; no a-priori constraint on identification No assumption about m = 0 modes (used all 9 periods); still only degrees l ≤ 2; no a-priori constraint on identification Optimisation on 4 parameters : log g, lqh, M tot and P rot Optimisation on 4 parameters : log g, lqh, M tot and P rot Several models* can fit the 9 periods, the preferred one is: Several models* can fit the 9 periods, the preferred one is: T eff = 29 580 ± 370 K (still fixed), log g = 5.4622 ± 0.0060, lqh = -2.58 ± 0.09 and M tot = 0.519 ± 0.008 Ms Solid rotation P rot = 32 500s ± 2200s  9.028 ± 0.61h Excellent agreement with orbital period determined independently from velocities variations (P orb = 9.024 ± 0.072h). Solid rotation P rot = 32 500s ± 2200s  9.028 ± 0.61h Excellent agreement with orbital period determined independently from velocities variations (P orb = 9.024 ± 0.072h). Period fit : S² ~ 0.60  ~ 0.06%, ~ 0.22s Period fit : S² ~ 0.60  ~ 0.06%, ~ 0.22s New asteroseismic analysis of Feige 4826/07/2007

13. Analysis with solid rotation: Mode Identification

14. Space parameters maps Left : lqh and M tot fixed; right : T eff and log g fixed Left : lqh and M tot fixed; right : T eff and log g fixed New asteroseismic analysis of Feige 4826/07/2007 log g Teff lqh Mtot

15. Comparison with Charpinet et al., 2005 About model parameters: About model parameters: New surface gravity log g closer to spectroscopyNew surface gravity log g closer to spectroscopy Total mass relatively high (M tot ~ 0.52 M s ) but possible according to Han’s simulations (2003)Total mass relatively high (M tot ~ 0.52 M s ) but possible according to Han’s simulations (2003) H-envelope slightly thicker, still completely consistent with Stellar Evolution TheoryH-envelope slightly thicker, still completely consistent with Stellar Evolution Theory About period fit and mode identification: About period fit and mode identification: The difference is about the m = 0 modes in the doublet (343-346s) and the triplet (374-378-383s). The identification “m = -1, m = -2” is maybe unexpected, but the intrinsic amplitudes are never knownThe difference is about the m = 0 modes in the doublet (343-346s) and the triplet (374-378-383s). The identification “m = -1, m = -2” is maybe unexpected, but the intrinsic amplitudes are never known Forcing Charpinet’s model + solid rotation : S² ~ 2.6 (4x poorer). No convergence to a Rotation Period of ~ 32 500s (rather ~ 29 500s)Forcing Charpinet’s model + solid rotation : S² ~ 2.6 (4x poorer). No convergence to a Rotation Period of ~ 32 500s (rather ~ 29 500s) New asteroseismic analysis of Feige 4826/07/2007 Conclusion : Charpinet’s model is not given up, but there is also hints in favor of a higher mass model

16. Consistency with Han’s simulations and EHB Stellar Evolution Theory New asteroseismic analysis of Feige 4826/07/2007

17. Comparison with Charpinet et al., 2005 S² ~ 0.6 log g ~ 5.46 M tot ~ 0.52 M s P rot ~ 32,500s S² ~ 0.9 log g ~ 5.45 M tot ~ 0.49 M s P rot ~ 30,500s S² ~ 2.6 log g ~ 5.435 M tot ~ 0.46 M s P rot ~ 29,500s Suggestion : time-series spectroscopy observations could give (needed) hints about m

18. Comments about the period of solid rotation (= 9.028 ± 0.61h) Fitting all 9 periods independently is impossible (very poor S² and no convincing models) → not a slow rotator Fitting all 9 periods independently is impossible (very poor S² and no convincing models) → not a slow rotator The smallest Δf is 8.82 µHz (  P rot ~1.2 days at the slowest), but again convincing models don’t exist at this rate The smallest Δf is 8.82 µHz (  P rot ~1.2 days at the slowest), but again convincing models don’t exist at this rate Even without knowing the orbital period, ~ 9.5h is the only acceptable rate for the rotation period Even without knowing the orbital period, ~ 9.5h is the only acceptable rate for the rotation period Conclusion : Orbital period = Rotation period (even if lower accuracy for P rot ) → Confirmation of the reasonable assumption of a tidally locked system New asteroseismic analysis of Feige 48

19. 4. Testing the hypothesis of a fast core rotation New asteroseismic analysis of Feige 4826/07/2007

20. 4. Testing a fast core rotation (Kawaler et al. ApJ 621, 432-444, 2005) Reminder : only degrees l ≤ 2 for this star → ideal to test the hypothesis of a fast core Reminder : only degrees l ≤ 2 for this star → ideal to test the hypothesis of a fast core Surface rotation fixed at the optimal value of 32,500s. Core rotation was varied from 500 to 32,500s, by steps of 500s. For each core period, computing merit function S² Surface rotation fixed at the optimal value of 32,500s. Core rotation was varied from 500 to 32,500s, by steps of 500s. For each core period, computing merit function S² Transition fixed at 0.3 R* (following Kawaler et al., 2005) Transition fixed at 0.3 R* (following Kawaler et al., 2005) New asteroseismic analysis of Feige 4826/07/2007

21. Testing a fast core rotation New asteroseismic analysis of Feige 4826/07/2007 log S² Core rotation (sec) Surface fixed at 32,500s

22. Conclusions and room for improvement We determined an « alternative » convincing model for Feige 48 by adding the rotation as a free parameter. This rotation is found to be solid with a period of ~ 9.028h (equals to orbital period), which confirms that the system is tidally locked. A fast core rotation can be excluded for this star. We determined an « alternative » convincing model for Feige 48 by adding the rotation as a free parameter. This rotation is found to be solid with a period of ~ 9.028h (equals to orbital period), which confirms that the system is tidally locked. A fast core rotation can be excluded for this star. Room for improvement: Room for improvement: Better observations (more pulsations modes and better resolution) are needed to confirm/reject the results (and choose between the models…)Better observations (more pulsations modes and better resolution) are needed to confirm/reject the results (and choose between the models…) Multi-colour photometry to confirm degrees l (particularly l = 0 or 2 for 352s mode)Multi-colour photometry to confirm degrees l (particularly l = 0 or 2 for 352s mode) Ultimate test: time-series spectroscopy to confirm/reject the l and m values inferredUltimate test: time-series spectroscopy to confirm/reject the l and m values inferred Thank you for your attention ! New asteroseismic analysis of Feige 4826/07/2007

23. Testing a fast core rotation Apparently slight differential rotation: best S² obtained for P core ~ 29,500s (and P surf = 32,500s) Apparently slight differential rotation: best S² obtained for P core ~ 29,500s (and P surf = 32,500s) BUT not significant: BUT not significant: g and f-modes are very sensitive to a fast core rotation, while most p-modes are not (except « marginal » ones)g and f-modes are very sensitive to a fast core rotation, while most p-modes are not (except « marginal » ones) The triplet 374-378-382s, identified as the g-mode « l = 2, k = 1 », shows Δf of 29.5µHz and 31.2µHz, above the mean spacing of 28.2µHz. This is better reproduced with a fast core rotation. But these higher Δf are not significant with a resolution of 2.17µHz !The triplet 374-378-382s, identified as the g-mode « l = 2, k = 1 », shows Δf of 29.5µHz and 31.2µHz, above the mean spacing of 28.2µHz. This is better reproduced with a fast core rotation. But these higher Δf are not significant with a resolution of 2.17µHz ! New asteroseismic analysis of Feige 4826/07/2007 Conclusion : a fast core rotation is impossible for Feige 48, which has probably a solid rotation !