Period Stability in Two Pulsating White DwarfsD. J. Sullivan & P. Chote (now at University of Warwick)

School of Chemical and Physical Sciences, Victoria University of Wellington, NZ

Introduction

The two primary temperature regimes where isolated cooling white dwarfs (WDs)

are observed to pulsate are Teff ∼ 12, 000 K for the H atmosphere (DAV) WDs, and

Teff ∼ 25, 000 K for the He atmosphere (DBV) WDs. The pulsations are driven in a

subsurface partial ionization zone of the dominant surface chemical element, have

periods between ∼ 102− 103 s, and are composed of nonradial gravity modes (which

explains the time scales for these dense objects). Given the compact nature of WDs,

it is not surprising that many of the pulsators feature relatively stable periods. Since

the evolutionary contraction for both the DAV and DBV WDs has essentially halted,

theoretical models predict small increases in the periods of these pulsators due to

evolutionary cooling: ∼ 10−13 ss−1 for the DBVs and ∼ 10−15 ss−1 for the DAVs [1]. P

values have been published for 2 DAV WDs – G 117B15A [2] and ZZ Ceti [3].

In the hot WDs including down to the DBV cooling region (∼ 25,000 K), theory pre-

dicts neutrino creation in the WD core via the plasmon process; the resulting escaping

energy flux is expected to provide a cooling mechanism that exceeds that of the sur-

face photon flux [4]. So, in principle, a detected pulsation cooling rate in a DBV WD,

in combination with suitable models, can be used to identify this theoretical neutrino

flux. Neutrino cooling in the cooler DAV WDs (∼ 12,000 K) has become negigible,

but a detected cooling rate in these objects can be used to constrain the mass of

the hypothetical axion particle. We present observational data (some published and

some unpublished) that demonstrate the period stability of a DAV and a DBV WD and

comment on the implications.

The southern hydrogen atmosphere DAV WD L19−2

L19−2 (alternatively MY Aps) was identified as a WD variable in 1977 and then mon-

itored extensively from SAAO using time-series photometery techniques [5]. The

combined data set covered a period ∼5 years and among other things demonstrated

that the two dominant periodicities were stable at the ∼ 10−14 ss−14 level. In 1995 a

Whole Earth Telescope (WET) campaign [6,7] observed L19−2 using three southern

observatories over a period ∼ 9 days. An amplitude discrete Fourier transform (DFT)

of the WET run xcov12 is displayed in the Fig. 1 (blue lines). The red lines correspond

to prewhitening by selected frequencies. Following this WET run, time-series photom-

etry was regularly obtained from Mt John Observatory in NZ until 2015. Overall we

have access to a combined data set covering an interval of four decades. The phase

stability of the dominant pulsation in L19−2 (192 s) is demonstrated in Fig. 2, which

plots the results of cycle counting (Observed minus Calculated) applied to the data.

A real P value will appear in the data as a quadratic term. The blue line corresponds

to a least squares parabolic fit and yields the apparent P value given in the figure.

Subtracting a proper motion contribution yields a P value of ≈ 2 × 10−15 ss−1. These

P measurements have been used to place constraints on the mass of the hypotheti-

cal axion particle [8]. An O−C analysis of frequency f7 (133 s) yielded a smaller but

consistent P value. Journal articles are in preparation [9].

The southern helium atmosphere DBV WD EC 20058−5234

This object (alternatively QU Tel) was identified in 1994 as a variable He atmosphere

WD by undertaking spectroscopy and time-series photometry at SAAO [10]. In 1997 a

WET run (xcov15) monitored the object using four southern observatories over an ∼ 8

day interval [11]. A DFT of the WET data set is given in Fig. 3. Following the WET

run, the object was regularly monitored from Mt John Observatory (and eventually

from Chile) with the aim of identifying a possible P due to evolutionary cooling, and

thereby potentially obtain evidence of the predicted core neutrino flux. A stability

analysis using the O−C cycle counting technique of four of the pulsation periods is

depicted in Fig. 4. This analysis uses only the xcov15 data combined with the Mt

John data; a more complete analysis using all available observations can be found

in reference [12]. It is clear the observed O−C variations will mask any evolutionary

cooling effects: a detection of the neutrino cooling flux in not possible with this object.

A satisfactory model to explain the observed well characterised variations awaits.

Fig 4: The results (red points) of an O−C cycle counting analysis of 4 frequencies in the DBV QU

Tel. The expected cooling induced parabolic trends in the O−C measurements for dP/dt values of

1&5 × 10−13 ss−1 are plotted for the f8 (257 s) mode. The observed variations mask any such trends.

References

[1] Bradley, P. A. 1996, ApJ, 468, 350 [2] Kepler, S. O. et al. 2005, ApJ 634:1311

[3] Mukadam, A. S. et al. ApJ, 2013, 771:17 [4] Winget D. E. et al. 2004, ApJL, 602, L109

[5] O’Donoghue, D. E. & Warner, B. 1987, MNRAS, 736, L39 [6] Nather, et al. 1990, ApJ, 361, 309

[7] Sullivan, D. J. 1998, Balt. Astron., 7, 159 [8] Corsico, A. H. et al. 2016, JCAP, 7, 36

[9] Sullivan D. J. et al., Chote & Sullivan (in prep.) [10] Koen, C. et al. 1995, MNRAS, 277, 913

[11] Sullivan, D. J. et al. 2008, MNRAS, 387, 137 [12] Dalessio, J. et al. 2013, ApJ 765:5

Fig 1: The Discrete Fourier transform (DFT) of the 1995 WET run (xcov12) on the WD L19−2 (blue

lines). The red lines correspond to prewhitening using 5 frequencies. The y axis uses millimodulation

units (1 mma = 0.1% modulation). The dashed lines show the 10−3 significance level using the False

Alarm Probability (FAP) methodology.

Fig 2: The red points show the result of applying the O−C cycle counting method to the dominant

periodicity in L19−2 (192 s). The solid blue line is a least squares parabolic fit and yields the apparent P

value given in the figure. The dashed red line indicates the proper motion contribution to P.

Fig 3: The DFT of the 1997 WET run (blue lines) on the DBV WD EC 20058−5234. The red lines result

from prewhitening by 10 frequencies. Modulation amplitudes are plotted in mma (1 mma = 0.1%) units,

and the 10−3 FAP peak threshhold is indicated by the dashed lines.Contact: Denis.Sullivan@vuw.ac.nz, paul@chote.net