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)

A couple of recent developments…

Gabriel Montgomery, born Dec. 23rd, 2009

Mari Kleinman, born Feb. 25th, 2010

GD358

• First single white dwarf to show evidence of a large change in Teff

(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

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

) 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)

N » 90 for DAVs (Teff » 12000 K)

N » 23 for DBVs ( Teff » 25000 K)

Fph ´ photospheric flux, Fb ´ flux at base of convection zone

Depth of convection zone is very temperature dependent!

Fph =Fb +τ c

dFphdt

τ c ≡ thermal response timescale of CZ

~ τ 0 (Teff /T0 )−N

Observations:Kleinman –1988

Dominant period: 615.15 s

Nonlinear light curvefitting of pulsations of

G29-38

For nearly mono-periodic pulsators, the fits are straightforward (from Montgomery 2005)

l=1, m=1τ0= 150.1 secN=95.0θi= 65.5 degAmp= 0.259Res = 0.160

We derive convection zone parameters as well as constraints on l and m

Normally, GD358 looks like this…(May 2006)

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

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

So what is GD 358 normally like?

τ 0 à 50sec

θi ~52±5degrees

GD358 during the May 2006 WET Run

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

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

Period (s) ell m422.561 1 1

423.898 1 -1

463.376 1 1

464.209 1 0

465.034 1 -1

571.735 1 1

574.162 1 0

575.933 1 -1

699.684 1 0

810.291 1 0

852.502 1 0

962.385 1 0

¿0 ~ 586 § 20 sec

µi ~ 47.5 § 2.5 degrees

The difference in τ0 implies that GD 358 was ~ 3000 K hotter during the “sforzando”

Is there any other corroborating evidence?

τ 0 à 50sec

θi ~52±5degrees

τ 0 ~ 590sec

θ i ~ 47.5 ± 2.5degreesNormal state:

“sforzando”:

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

McDonaldMt. Suhora

Theoretical vs observed τ0 as a function of Teff

Back to the 2006 WET run…oblique pulsation?

Example of precession/oblique pulsations

m=1 m=0

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

ΔΦ =0 for m = 0

ΔΦ = π for | m |= 1

Pre-whitening by 2 sets of equally spaced triplets

For each triplet

Now lets fit the amplitudes…

ΔΦ / 2π ~ 0.5 ⇒ m = 1 modes

ΔΦ ≡2Φ0 − (Φ+ + Φ− )

Amplitudes

Amplitudes

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

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!

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