1. GD 358: The Case for Oblique Pulsation and Temperature Change Mike Montgomery (UT-Austin, DARC), J. L. Provencal, A. Kanaan, A. S. Mukadam, S. E. Thompson, J. Dalessio, H. L. Shipman, D. E. Winget, S. O. Kepler, & D. Koester (DARC = Delaware Asteroseismic Research Center)

2. A couple of recent developments… Gabriel Montgomery, born Dec. 23 rd, 2009 Mari Kleinman, born Feb. 25 th, 2010

3. GD358 First single white dwarf to show evidence of a large change in T eff (seen in WZ SGe systems) - accretion? First white dwarf to show evidence of oblique pulsation (seen in roAp stars) - magnetic field? Both questions can be addressed with non- linear light curve fits

4. Need a mechanism for producing non-linearities –convection zone is most likely candidate –can change thickness by » 10 during pulsations

5. ) Assumes all the nonlinearity is caused by the convection zone Hybrid Approach Montgomery (2005) based on work of Brickhill (1992), Wu & Goldreich (1998), and Ising & Koester (2001) linear region (small amplitude) nonlinear convection zone (larger amplitude)

6. N » 90 for DAVs (T eff » 12000 K) N » 23 for DBVs ( T eff » 25000 K) F ph ´ photospheric flux, F b ´ flux at base of convection zone Depth of convection zone is very temperature dependent!

7. It is certainly present… bolometric: Passband X: Compared to T 90 (or T 23 ) dependence of τ, this nonlinearity is negligible What about T 4 nonlinearity?

8. Brief review of linear pulsations white dwarfs are non-radial gravity mode (g-mode) pulsators temperature variations l=1, m=0 l=1, m=1

9. Nonlinear pulsations l=1, m=0 (traveling wave) pole equator

10. Nonlinear pulsations l=1, m=1 (standing wave) pole equator

11. Limb darkening and conversion of flux from bolometric to observed passband variations is done using model atmospheres of D. Koester fairly linear

12. Observations: Kleinman –1988 Dominant period: 615.15 s Nonlinear light curve fitting of pulsations of G29-38 For nearly mono-periodic pulsators, the fits are straightforward (from Montgomery 2005)

13. l=1, m=1 τ 0 = 150.1 sec N=95.0 θ i = 65.5 deg Amp= 0.259 Res = 0.160 We derive convection zone parameters as well as constraints on l and m

14. Normally, GD358 looks like this… (May 2006)

15. However, it looked like this during the “whoopsie” or “sforzando” (Aug 1996)

17. So what is GD 358 normally like?

18. GD358 during the May 2006 WET Run

19. Simultaneous fit 29 high S/N runs: linear fit (12 periodicities – 36 parameters)

20. Simultaneously fit 29 high S/N runs: nonlinear fit (only 3 additional parameters)

21. Period (s) ell m 422.561 1 1 423.898 1 463.376 1 1 464.209 1 0 465.034 1 571.735 1 1 574.162 1 0 575.933 1 699.684 1 0 810.291 1 0 852.502 1 0 962.38510 ¿ 0 ~ 586 § 20 sec µ i ~ 47.5 § 2.5 degrees

22. The difference in τ 0 implies that GD 358 was ~ 3000 K hotter during the “sforzando” Is there any other corroborating evidence? Normal state: “sforzando”:

23. Yes, there is… There were separate measurements of its relative brightness (which Judi dug out) before and after this event McDonald Mt. Suhora

24. Theoretical vs observed τ 0 as a function of T eff

25. Back to the 2006 WET run… oblique pulsation?

26. Example of precession/oblique pulsations m=1m=0

27. Could this be oblique pulsation? Need exactly evenly spaced triplets in the FT The phases of the members of the triplet have to “line up”: The amplitudes of the modes need to follow a given relation

28. Pre-whitening by 2 sets of equally spaced triplets

29. For each triplet Now lets fit the amplitudes…

30. Amplitudes

31. The amplitudes fit very well: “98% significance level”

32. Pre-whitening by complete solution

33. Conclusions The nonlinearities in GD358’s light curve can be understood as originating in its convection zone Compared to 2006, GD358 had a much thinner convection zone during the “sforzando” (1996) about 3000 K hotter The oblique pulsator model provides an excellent match to the 6 peaks around k=12 (~575 sec): –frequencies –phases –amplitudes This provides important constraints on the physics of convection in white dwarf stars Thanks!