Asteroseismology of evolved stars: from hot B subdwarfs to white dwarfs

1. AG2014 – Splinter B 24 September 2014 Asteroseismology of evolved stars:from hot B subdwarfs to white dwarfs Valerie Van Grootel Université de Liège, FNRS Research Associate Main collaborators: S. Charpinet (IRAP Toulouse) G. Fontaine (U. Montréal) S.K. Randall (ESO) P. Brassard (U. Montréal) M.A. Dupret (U. Liège) E.M. Green (U. Arizona)

2. Evolved stars Asteroseismology HR Diagram of pulsating stars • Hot B subdwarf (sdB) stars extreme horizontal branch (EHB) stars • White dwarf pulsators: • GW Vir (atm. He/C/O) • DBV (atm. He) • DQV (atm. C-rich) • DAV (atm. H) = 80% of WDs

3. Hot B subdwarfs Asteroseismology Focus: Origin of hot B subdwarfs

4. log q log (1-M(r)/M*) H-richenvelope Envelope He mantle Core He/C/O core Hot B subdwarfs • Hot (Teff 20 000 - 40 000 K) and compact stars (log g  5.2 - 6.2) • belonging to the Extreme Horizontal Branch (EHB) • He-burning to C+O (I), radiative He mantle (II) and very thin H-rich envelope (III) • Lifetime of ~ 108 ans (100 Myr) on EHB, then evolve to white dwarfs without AGB phase • ~50% of sdBs reside in binary systems, generally in close orbits (Porb 10 d) 2 classes of pulsators: > Short periods (P ~ 80 - 600 s), A  1%, p-modes (envelope) > Long periods (P ~ 45 min - 3 h), A  0.1%, g-modes (mantle). Space observations! > K-mechanism for pulsation driving (Fe accumulation in envelope) M* ~ 0.5 Ms Menv < 0.005 Ms

5. The formation of sdB stars How such stars form is a long standing problem • For sdB in binaries (~50%) • For single sdB stars (~50%) 2 main scenarios: • Single star evolution: • enhanced mass loss at tip of RGB, at He-burning ignition (He-flash) • mechanism quite unclear (cf later) • The merger scenario: • Two low mass He white dwarfs merge to form a He core burning sdB star • in the red giant phase: Common envelope ejection (CEE), stable mass transfer by Roche lobe overflow (RLOF)  The red giant lose its envelope at tip of RGB, when He-burning ignites (He-flash)  Remains the stripped core of the former red giant, which is the sdB star, with a close stellar companion

6. Common envelopeevolution (close binary sdB systems) CEE: sdB + MS star or white dwarf

7. Stable Roche lobe overflow (widebinary sdB systems) RLOF: sdB + MS star (later than F-G)

8. Single sdBs: single star evolution or He-white dwarfsmergers mergers Envelope ejection at tip of RGB or

9. The formation of sdB stars • Single star evolution (“almost impossible”): Mass range in 0.40 - 0.43  M*/Ms  0.52 • (Dorman et al. 1993) • Binary star evolution: numerical simulations on binary population synthesis (Han et al. 2002, 2003) Figures from Han et al. (2003) RLOF (Roche Lobe overflow) This is the theoretical mass distribution we want to test by eclipsing/reflecting binaries and by asteroseismology Weighted mean distribution for binary evolution: (including selection effects) CE (commonenvelope) 0.30  M*/Ms  0.70 peak ~ 0.46 Ms (CE, RLOF) high masses (mergers) mergers

10. > Example: PG 1336-018, pulsating sdB + dM eclipsing binary (a unique case!) • Light curve modeling (Vuckovic et al. 2007): • M  0.466  0.006 Ms, R  0.15  0.01 Rs, • and log g  5.77  0.06 • Seismic analysis (Van Grootel et al. 2013): M  0.471  0.006 Ms, R  0.1474  0.0009 Rs, and log g  5.775  0.007  Our asteroseismic method is sound and free of significant systematic effects The method for sdB asteroseismology • Search the stellar model(s) whose theoretical periods best fit all the observed ones, in order to minimize • Optimization codes (based on Genetic Algorithms) to find the minima of S2 • External constraints: Teff, log g from spectroscopy • Results: global parameters (mass, radius), internal structure (envelope & core mass,…) Figure from Vuckovic et al. (2007)

11. Available samples of sdBs with known masses I. The asteroseismic sample 15 sdB stars modeled by asteroseismology (we took the most recent value in case of several analyses)

12. Available samples II. The extended sample (sdB + WD or dM star) Light curve modeling + spectroscopy  mass of the sdB component Need uncertainties to build a mass distribution  7 sdB stars retained in this subsample Extended sample: 15+7  22 sdB stars with accurate mass estimates • 11 (apparently) single stars • 11 in binaries (including 4 pulsators)

13. Building the mass distributions Binning the distribution in the form of an histogram (bin width    0.024 Ms) Extended sample: (white) Mean mass: 0.470 Ms Median mass: 0.471 Ms Range of 68.3% of stars: 0.439-0.501 Ms Asteroseismic sample: (shaded) Mean mass: 0.470 Ms Median mass: 0.470 Ms Range of 68.3% of stars: 0.441-0.499 Ms No detectable significant differences between distributions (especially between singles and binaries)

14. Comparison with theoretical distributions • A word of caution: still small number statistics (need ~30 stars for a significant sample) • Distribution strongly peaked near 0.47 Ms • No differences between sub­samples (eg, binaries vs single sdB stars) • It seems to have a deficit of high mass sdB stars, i.e. from the merger channel. Especially, the single sdBs distribution ≠ merger distribution.

15. Comparison with theoretical distributions The single sdBs distribution ≠ merger channel distribution Han et al. 2003 Single sdB stars can not be explained only in terms of binary evolution via merger channel merger channel Moreover, Geier & Heber (2012): 105 single or in wide binaries sdB stars: all are slow rotators (Vsin i < 10 km s-1) (the majority of) sdB stars are post-RGB stars

16. sdB stars are (in majority) post-RGB stars, and even post He-flash stars MS mass of sdB progenitors: 0.7 – 1.8 Ms (e.g. Castellani et al. 2000) So: the red giant has expelled almost all its envelope and has reached the minimum mass for He-flash • At the He-flash: rather unlikely that these 2 events occur simultaneously • Alternative: “hot flash”, after having left the RGB (before tip), in the contraction phase (Castellani&Castellani 1993; D’Cruz et al. 1996)

17. Extreme mass loss on RGB If this scenario holds true, the red giant has experienced extreme mass loss on RGB (Red Giant Branch) What could cause extreme mass loss on RGB ? • For binary stars: ok, thanks to stellar companion • For single stars, it’s more difficult: • Internal rotation => mixing of He => enhanced mass loss on RGB (Sweigart 1997) • Dynamical interactions: Substellar companions (Soker 1998) Indeed, planets and brown dwarfs are discovered around sdB stars: In short orbits: • 5 planets (Charpinet et al. 2011, Silvotti et al. 2014) • At least 2 BDs (Geier et al. 2011, 2012, Schaffenroth et al. 2014)

18. A consistent scenario Figure from Kempton 2011, Nature, 480, 460 • Former close-in giant planets/BDs were deeply engulfed in the red giant envelope • The planets’ volatile layers were removed and only the dense cores survived and migrated where they are now seen • The star probably left RGB when envelope was too thin to sustain H-burning shell and experienced a delayed He-flash (or, less likely, He-flash at tip of RGB) • Planets/BDs are responsible of strong mass loss and kinetic energy loss of the star along the RGB • As a bonus: this scenario explains why “single” sdB stars are all slow rotators

19. Conclusions • No significant differences between distributions of various samples (asteroseismic, light curve modeling, single, binaries, etc.) • Single star evolution scenario does exist; importance of the merger scenario? (single stars with presumably fast rotation) • A consistent scenario to form “single” sdB stars: delayed He-flasher + strong mass loss on RGB due to planets/brown dwarfs? But: • Currently only 22 objects: 11 single stars and 11 in binaries • Among  2000 known sdB, ~100 pulsators are now known • Both light curve modeling and asteroseismology are a challenge (accurate spectroscopic and photometric observations, stellar models, etc.)

20. White Dwarfs Asteroseismology Focus: instability strip of DA white dwarf pulsators (i.e. ZZ Ceti pulsators)

21. White dwarfs Late stages of evolution of ~97% of stars in the Universe DA (H-rich atmosphere): ~80%; DB (no/little H atmosphere): ~20% of WDs • 4 types of g-mode pulsators along the cooling sequence: • GW Vir stars (He/C/O atmospheres) Teff~ 120,000 K, discovered in 1979 • V777 Her stars (He-atmosphere), 1982Teff~ 25,000 K • Hot DQ stars (C-rich/He atmosphere) Teff~ 20,000 K, discovered in 2007 • ZZ Ceti stars (H-atmosphere, DA) Teff~ 12,000 K, discovered in 1968 • Most numerous (~200 known including SDSS+Kepler) From Saio (2012), LIAC40 proceedings

22. Pulsating DA white dwarfs Excitation mechanism of ZZ Ceti stars • Don Winget (1981): • H recombination around Teff~12,000 K •  envelope opacity increase • strangle the flow of radiation • modes instabilities • Pulsations are destabilized at the base of the convection zone • (details: e.g. Van Grootel et al. 2012) “convective driving” log q log (1-M(r)/M*) Pulsations are driven when the convection zone is sufficiently deep and developed

23. Pulsating DA white dwarfs Empirical ZZ Ceti instability strip (classic view)  Observed pulsator ; O non-variable DA white dwarf • Typical mass range: 0.5-1.1 Ms • Multiperiodic pulsators, observed period range: 100-1500 s (g-modes) • Reliable atmospheric parameters: work of Bergeron et al., Gianninas et al., here with ML2/α=0.6 • (most probably) a pure strip • log g/Teff correlation (with a more pronounced slope for red edge): the lower log g, the lower edge Teff Figure from Fontaine & Brassard (2008)

24. Pulsating DA white dwarfs Empirical ZZ Ceti instability strip (2014 view) non variable (<10mmag); pulsator • Hermes et al. (2012, 2013a,b): • 5 Extremely-Low-Mass pulsators 0.15 Ms 0.20 Ms • Hermes et al. (2013c): • 1 ultra-massive pulsator This is the observed instability strip we want to theoretically reproduce 1.2 Ms

25. The theoretical instability strip • Evolutionary DA White Dwarf Models

26. -4.0 -2.0 log q log (1-M(r)/M*) - H envelope Envelope He mantle Core C/O core 0 Evolutionary DA models • A standard DA white dwarf structure model (C/O core) “onion-like” stratification Base of the atmosphere • Evolutionary tracks computed for 0.4Ms to 1.2Ms (0.1Ms step) • from Teff35,000 K to 2,000 K (~150 models) • with ML2 version (a1,b2,c16);   1 (iel  Hp)

27. Evolutionary DA models Base of the atmosphere Detailed modeling of the superficial layers Superficial convection zone Our evolutionary models have the same T stratification as the complete (1D) model atmospheres ”feedback” of the convection on the global atmosphere structure • Standard grey atmosphere • Detailed atmosphere

28. -4.0 -2.0 -2.0 log q log (1-M(r)/M*) log q log (1-M(r)/M*) - - H envelope H envelope Envelope Envelope He mantle He core Core Core C core 0 0 Evolutionary DA models • Extremely Low Mass (ELM) DA white dwarf: • H envelope on top of He core ELM white dwarfs come from stars that never experienced any He-flash, because of extreme mass loss on RGB (from binary interactions or due to high Z) • 2 kinds of evolutionary tracks computed here: • Standard C core models, but for 0.125Ms and 0.15-0.4Ms (steps 0.05Ms) • Pure He core/H envelope models, for the same masses, thick envelopes Instability strip location in Teff-log g plane insensitive to detailed core composition and envelope thickness

29. The theoretical instability strip • Evolutionary DA White Dwarf Models • Time-Dependent Convection (TDC) Approach

30. The Time-Dependent Convection approach For a standard 0.6Ms DA model: • Teff~ 12,000 K: convective turnover timescale conv  (pulsation periods)  convection adapts quasi-instantaneously to the pulsations • Teff~ 11,000 K: conv ≈ NEED full Time-Dependent Convection (TDC) • Frozen convection (FC), i.e. conv  :NEVER justified in the ZZ Ceti Teff regime (FC is the usual assumption to study the theoretical instability strip)  1500 s  100 s

31. Full development in Grigahcène et al.(2005), following the theory of M. Gabriel (1974,1996), based on ideas of Unno et al. (1967) • The Liege nonadiabatic pulsation code MAD(Dupret 2002) is the only one to implement convenient TDC treatment • The timescales of pulsations and convection are both taken into account • Perturbation of the convective flux taken into account here: • Built within the mixing-length theory (MLT), with the adopted perturbation of the mixing-length: • if   conv (instantaneous adaption): • if   conv (frozen convection): The Time-Dependent Convection theory

32. The theoretical instability strip • Evolutionary DA White Dwarf Models • Time-Dependent Convection (TDC) Approach • Results

33. Results: computing the theoretical instability strip • We applied the MAD code to all evolutionary sequences • “normal” CO-core DA models, 0.4 – 1.2Ms, log q(H)=-4.0 • ELM, C-core models: 0.125-0.4 Ms, log q(H)=-4.0 • ELM, He-core models: 0.125-0.4 Ms, log q(H)=-2.0 • 0.17Ms, He-core models, “thin” envelope log q(H)=-3.7 with ML2/  1, detailed atmospheric modeling, and TDC treatment • We computed the degree l1 in the range 10-7000 s (p- and g-modes) • For the red edge (long-standing problem): based on the idea of Hansen, Winget & Kawaler (1985): red edge arises when th ~ Pcrit α (l(l+1))-0.5 (th : thermal timescale at the base of the convection zone), which means the mode is no longer reflected back by star’s atmosphere

34. Empirical ZZ Ceti instability strip (2014 view) pulsator non variable (<10mmag); • Spectroscopic estimates: • ELM white dwarfs: D. Koester models (Brown et al. 2012) • UHM white dwarf: Gianninas et al. (2011) • Standard ZZ Ceti: P. Bergeron et al. • But all ML2/α=0.6 0.15 Ms 0.20 Ms (must be consistent) + standard ZZCeti: spectroscopic observations gathered during several cycles of pulsations 1.2 Ms

35. Theoretical instability strip (g-modes l=1) non variable (<10mmag); pulsator TDC blue edge Red edge 0.15 Ms • Narrower strip at low masses • (larger slope for the red edge) • Structure models: ML2/  1 0.20 Ms Model atmospheres: ML2/  0.6  Convective efficiency increases with depth? 1.2 Ms (consistent with hydrodynamical simulations; Ludwig et al. 1994, Tremblay & Ludwig 2011) NB: evolutionary and atmospheric MLT calibrations are dependent

36. Theoretical instability strip (g-modes l=1) Is the whole ZZ Ceti instability strip pure? YES • Need only small fine-tuning • J2228 is a little bit tricky • Consistency between ML calibrations atmospheres  structure models • Spectra must cover a few pulsational cycles ! 0.15 Ms 0.20 Ms BUT • Are all ELM pure H (DA) white dwarfs or with traces of He ? 1.2 Ms

37. Qualitative fit to the observed periods of the ELM pulsators SDSS J1840+6423 Teff~ 9140±170 K, logg ~ 6.16±0.06 He-core model, log q(H)=-2.0 SDSS J1518+0658 Teff~ 9810±320 K, logg ~ 6.66±0.06 He-core model, log q(H)=4.0 and -2.0 • SDSS J1112+1117 • Teff~ 9400±490 K, logg ~ 5.99±0.12 • He-core model, log q(H)=-2.0 Adiabatic properties are sensitive to exact interior structure

38. Conclusion and prospects

39. Conclusion and Prospects Conclusions: • Excellent agreement between theoretical and observed instability strip: • Blue edge, TDC approach • Red edge, by energy leakage through the atmosphere • ELM pulsators are low mass equivalent to standard ZZ Ceti pulsators excited by convective driving •  such pulsators exist from 0.15 to 1.2 Ms (log g = 5 – 9 !) • Is ML2/α=1.0 the good flavor for convection inside white dwarfs? Related to spectroscopic calibration (here ML2/α=0.6) and 3D hydrodynamical simulations (Tremblay et al. 2011,2012, 2014) Prospects: • Is the ZZ Ceti instability strip pure? Traces of He in ELM white dwarfs? • Instability strip with structure models including 3D atmospheres? • Asteroseismology of ELM/standard/massive ZZ Ceti pulsators • internal structure & fundamental parameters • age • understanding of matter under extreme conditions

40. Supp slides

41. (the majority of) sdB stars are post-RGB stars, and even post He-flash stars • What does it imply ? The star has removed all but a small fraction of its envelope and has reached the minimum mass to trigger He-flash • at tip of RGB, as a classic RGB-tip flasher ? (classic way for HB stars) -> It’s rather unlikely that the 2 events occur at the same time ! • an alternative (old and somewhat forgotten) idea: • Hot He-flashers (Castellani&Castellani 1993; D’Cruz et al. 1996) • i.e., stars that experience a delayed He-flash during contraction, at higher Teff, after leaving the RGB before tip • (H-burning shell stops due to strong mass loss on RGB) • D’Cruz et al. (1996) showed that such stars populate the EHB, with similar (core) masses

42. Another hint: Horizontal branch/EHB morphology • There is a gap between EHB and classic blue HB (BHB) Green et al. (2008) Size of dots related to He abundance This suggests something “different” for the formation of EHB and classic HB stars