1. Subdwarf B stars from He white dwarf mergers Haili Hu

2. Subdwarf B stars from various formation channels Haili Hu

3. March 4, 2016March 4, 2016March 4, 2016 subdwarf B stars  Extreme Horizontal Branch (Heber 86, Dorman et al 93)  He-burning core (~0.5 M  )  Very thin, inert H-envelope (<0.02 M  )  40-70% found in binaries (e.g. Allard et al 1994, Maxted et al 2001, Morales-Rueda et al 2006)  L/L  White dwarf <-------  L/L  (K) T eff (K)  tip sdB Haili Hu, Stellar Mergers Lorentz Workshop

4. sdB formation channels  Common-envelope ejection  close binary (Han et al 2002)  Stable Roche lobe overflow  wide binary (Mengel et al 1976) For single sdB stars:  Double helium white dwarf merger (Webbink 1984)  Enhanced mass loss on RGB (d’Cruz 1996)  CE merger of RGB + low mass companion (Soker 1998, Politano et al. 2008) March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop

5. sdB formation channels  Common-envelope ejection  close binary (Han et al 2002) subchannels: Helium flash or non-degenerate ignition  Stable Roche lobe overflow  wide binary (Mengel et al 1976) subchannels: Helium flash or non-degenerate ignition For single sdB stars:  Double helium white dwarf merger (Webbink 1984)  Enhanced mass loss on RGB (d’Cruz 1996)  CE merger of RGB + low mass companion (Soker 1998, Politano et al. 2008) subchannels: Helium flash or non-degenerate ignition March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop

6. sdB formation channels  Common-envelope ejection  close binary (Han et al 2002) subchannels: Helium flash or non-degenerate ignition  Stable Roche lobe overflow  wide binary (Mengel et al 1976) subchannels: Helium flash or non-degenerate ignition For single sdB stars:  Double helium white dwarf merger (Webbink 1984)  Enhanced mass loss on RGB (d’Cruz 1996)  CE merger of RGB + low mass companion (Soker 1998, Politano et al. 2008) subchannels: Helium flash or non-degenerate ignition M  0.4-0.5 M  March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop

7. sdB formation channels  Common-envelope ejection  close binary (Han et al 2002) subchannels: Helium flash or non-degenerate ignition  Stable Roche lobe overflow  wide binary (Mengel et al 1976) subchannels: Helium flash or non-degenerate ignition For single sdB stars:  Double helium white dwarf merger (Webbink 1984)  Enhanced mass loss on RGB (d’Cruz 1996)  CE merger of RGB + low mass companion (Soker 1998, Politano et al. 2008) subchannels: Helium flash or non-degenerate ignition M  0.4-0.5 M  March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop M  0.3-0.8 M 

8. sdB formation channels  Common-envelope ejection  close binary (Han et al 2002) subchannels: Helium flash or non-degenerate ignition  Stable Roche lobe overflow  wide binary (Mengel et al 1976) subchannels: Helium flash or non-degenerate ignition For single sdB stars:  Double helium white dwarf merger (Webbink 1984)  Enhanced mass loss on RGB (d’Cruz 1996)  CE merger of RGB + low mass companion (Soker 1998, Politano et al. 2008) subchannels: Helium flash or non-degenerate ignition M  0.4-0.5 M  March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop M  0.3-0.8 M  M  0.4-0.7 M 

9. Han et al 2003 March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop

10. Fontaine et al 2008 March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop

11. Asteroseismology  Goal: Better understanding of stellar structure and evolution through study of stellar pulsations  Principle: Use waves (gravity and sound) to infer what cannot be seen directly March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop

12. March 4, 2016March 4, 2016March 4, 2016 Why do stars pulsate? Excitation mechanisms:  opacity/kappa-mechanism (white dwarfs, massive MS stars, sdB stars)  convective motions in outer layers (Sun, red giants)  dynamic tides (close binaries) Haili Hu, Stellar Mergers Lorentz Workshop

13. March 4, 2016March 4, 2016March 4, 2016 How to descibe the oscillations? Easy in 1D groundtonefirst overtonesecond overtone oscillation modesnodes Haili Hu, Stellar Mergers Lorentz Workshop

14. March 4, 2016March 4, 2016March 4, 2016 But a star has 3d oscillations!  Instead of nodes: node lines on the surface, and node surfaces in the star  Wave numbers l, m on the surface  Radial wave number n in the star  Each mode (n, l, m) oscillates with its own eigenfrequency its own eigenfrequency Haili Hu, Stellar Mergers Lorentz Workshop

15. March 4, 2016March 4, 2016March 4, 2016 But a star has 3d oscillations!  Instead of nodes: node lines on the surface, and node surfaces in the star  Wave numbers l, m on the surface  Radial wave number n in the star  Each mode (n, l, m) oscillates with its own eigenfrequency its own eigenfrequency Haili Hu, Stellar Mergers Lorentz Workshop

16. March 4, 2016March 4, 2016March 4, 2016 l = 3 m = 0 l = 3 m = 2 l = 3 m = 3 Blue : moves towards us Red : moves away from us Haili Hu, Stellar Mergers Lorentz Workshop

17. March 4, 2016March 4, 2016March 4, 2016 How to observe pulsations?  photometry  spectroscopy ©C. Schrijvers l=m=7l=m=10 Haili Hu, Stellar Mergers Lorentz Workshop

18. HR diagram of pulsators  Many classes of pulsators during various evolutionary phases: main sequence starsmain sequence stars red giantsred giants white dwarfswhite dwarfs subdwarf B starssubdwarf B stars March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop Figure from Christensen-Dalsgaard (2004)

19. March 4, 2016March 4, 2016March 4, 2016 Asteroseismology of sdB stars  V361 Hya / EC 14026 stars (Kilkenny et al 96) : short-periods (80-600 s)short-periods (80-600 s) p-mode pulsationsp-mode pulsations  V1093 Her / PG 1716 / Betsy stars (Green et al 03): long-periods (30 min-2 hr)long-periods (30 min-2 hr) g-mode pulsationsg-mode pulsations  Both driven by  -mechanism related to the Iron Opacity Bump (Charpinet et al 97, Fontaine etal 03) Figure from Christensen-Dalsgaard (2004) Haili Hu, Stellar Mergers Lorentz Workshop

20. March 4, 2016March 4, 2016March 4, 2016 Observations:  42 short-period pulsators  31 long-period pulsators  3 hybrid pulsators Theory:  Seismic solutions for 12 short-period pulsators (Fontaine et al 08, and references therein) and references therein) Figure from Fontaine et al (2008) Haili Hu, Stellar Mergers Lorentz Workshop Asteroseismology of sdB stars

21.  Current solutions all based on post-He flash sdB models  However, structure of a post-non-degenerate and post-merger sdB model are different  Differing interior structure gives different oscillation signature (frequencies, mode degree, excitation)  We focused on differences between post-flash and post-non-degenerate sdB stars March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop Asteroseismology of sdB stars

22. Constructing stellar models with:  Stellar evolution code STARS (Eggleton 71) Computing pulsation properties with:  Adiabatic oscillation code OSC (Scuflaire et al 07)  Non-adiabatic oscillation code MAD (Dupret 01) March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop Method

23. March 4, 2016March 4, 2016March 4, 2016 Helium flash vs non-degenerate ignition H-envelope lost when core is above minimum for He-ignition, but below the tip of the RGB  M zams < ~2 M  : He-flash  M zams > ~2 M  : Non-degenerate He-ignition Hu et al 2007 Haili Hu, Stellar Mergers Lorentz Workshop

24. March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop  ULTRACAM / VLT lightcurves (May 18, 2005)  P = 2.4 hr Vuckovic et al 2007 PG 1336-018 / NY Vir: a post-CE, eclipsing, pulsating sdB binary

25. pre-CE phase of NY Vir At onset of mass transfer: or: Model assumptions: Z = 0.02 Reimer’s mass loss (η = 0.4) M 2 = 0.12 M  P i (d) M ZAMS (M  ) M core = M core,tip M core = M core,min March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop Hu et al 2007

26. Results: The CE phase   -formalism (Webbink 1984) :   -formalism (Nelemans et al 2000, 2005) : where M giant, R giant, M remnant and E bind,env follow from evolution calculations, a f and M 2 from orbital light curve solution  ~1.5 0 <  < 1 March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop

27. Results: The CE parameter  for NY Vir M  Assuming M remnant = M sdB and M 2 = 0.12 M  March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop Hu et al 2007

28. Results: The CE parameter  for NY Vir M  Assuming M remnant = M sdB and M 2 = 0.12 M  March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop Hu et al 2007

29. March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop NY Vir  From orbital lightcurve solution (Vuckovic et al 2007) and asteroseismology (Charpinet et al 2008): M-dwarf 0.12 M  sdB 0.47 M 

30. March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop Helium flash vs non-degenerate ignition Hu et al 2008

31. March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop Helium flash vs non-degenerate ignition Comparison between two models with same log g and T eff Hu et al 2008

32. March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop M2M2 (i)Allow unstable frequencies of non-degenerate model to be matched to any frequency of post-flash model (ii) Assume mode identification: allow matching only to modes with same l - value (iii) Assume log g & T eff known: i.e. allow matching only to modes with ~same log g & T eff (iv) Allow matching only to unstable modes Helium flash vs non-degenerate ignition

33. March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop He-flash vs non-degenerate models  M zams = 1.50 M   At RGB tip:  M core = 0.465 M 

34. March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop He-flash vs non-degenerate models  M zams = 3.00 M   At RGB tip:  M core = 0.450 M 

35.  Thus seismic difference between post-flash (M zams ~2 M  ) sdB stars  Also true for sdB stars from He WD mergers? March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop Helium flash vs non-degenerate ignition

36. How to model a He WD merger  Approach so far: Accretion of He on a He white dwarf (Iben 1990, Saio & Jeffery 2000, Han et al 2002)Accretion of He on a He white dwarf (Iben 1990, Saio & Jeffery 2000, Han et al 2002)  Maybe ok for following subsequent evolution  NOT ok for comparing seismic properties  Besides global structure parameters (M *, R *, T eff ), we need detailed information on core composition, chemical stratifications, mass of H- envelope, … March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop

37. Approach (future work)  SPH simulation of WD merger product (or use entropy sorting algorithm?) (Rosswog)  Import merger product into 1D stellar evolution code (Glebbeek)  Evolve product further  Compute pulsational properties (frequencies, excitation, mode degree)  Compare observables: log g, T eff, f, l March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop

38. Approach (future work)  SPH simulation of WD merger product (or use entropy sorting algorithm?) (Rosswog)  Import merger product into 1D stellar evolution code (Glebbeek)  Evolve product further  Compute pulsational properties (frequencies, excitation, mode degree)  Compare observables: log g, T eff, f, l March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop

39. Difficulties/Problems  How much H is left on merger remnant? i.e. how much H is burned during merger?  How to deal with He flash? Numerical problem in the Eggleton code  And many other issues discussed these weeks March 4, 2016March 4, 2016March 4, 2016Haili Hu, Stellar Mergers Lorentz Workshop