A SECOND CASE OF OUTBURSTS IN A PULSATING WHITE DWARF OBSERVED BY KEPLER

The outburst events shown in the top panel of Figure 2 confirm a new phenomenon observed in pulsating white dwarfs. Only one other pulsating white dwarf displays similar recurring behavior: The cool DAV KIC 4552982 (WD J1916+3938), observed for nearly 2.5 years in the original Kepler mission (Bell et al. 2015).

That DAV has very similar 3D atmospheric parameters to PG 1149+057—${T}_{\mathrm{eff}}$ = 10,860 ± 120 K and $\mathrm{log}\;g$ = 8.16 ± 0.06—and it also has a very similar pulsation spectrum. The only other reminiscent event seen in a pulsating white dwarf occurred during monitoring of the cool variable DB (helium-atmosphere) white dwarf GD 358, which in 1996 underwent a dramatic change in excited frequencies accompanied by a rapid increase in fractional amplitude, its sforzando (Montgomery et al. 2010).

The outbursts in KIC 4552982 increase its mean flux by between 2% and 17%, last 4–25 hr, and recur on an average every 2.7 days (Bell et al. 2015). Everything about the outbursts in PG 1149+057 is scaled up by roughly a factor of three. The outbursts here increase the quiescent flux by between 5%–45%, have durations on average of 14.5 hr (ranging from 9.3–36.4 hr), and recur on a timescale between 3.5 and 11.5 days, on average every 8 days. These rough timescales were determined by eye, noting when the point-to-point scatter rose and fell to the quiescent values. With so few events, an autocorrelation function reveals only that most events last more than 12 hr. There does not appear to be any periodicity to the outbursts. Each outburst requires an increase in energy from quiescence of roughly ${10}^{34}$ erg, found by integrating the mean equivalent duration of the outbursts of 24.8 minutes.

We see convincing evidence that the pulsations persist on the white dwarf during the outburst, and actually change properties relative to those excited in quiescence. It is important to note that if these outbursts came from a contaminating source the pulsation amplitudes would decrease as a result of flux dilution. That the pulsation amplitudes actually increase proves that the outbursts are on the white dwarf.

The bottom panel of Figure 2 shows Fourier transforms (FTs) of the entire light curve, differentiated by data in and out of outburst. Both datasets have peaks in the FT above the respective 3σ significance threshold, which was determined by randomly shuffling the fluxes for each point in the light curve and computing the highest peak in the entire resultant FT for 10,000 random permutations (see Hermes et al. 2015).

Figure 2 shows that the pulsations in outburst have shorter periods and higher amplitudes than those in quiescence; the unweighted mean period before, during, and after the seventh outburst goes from 1083.3 s to 919.7 s to 1072.7 s, respectively. If the flux increase during the outbursts are due to an increase in the average effective temperature of the star, the formalism of Wu & Goldreich (1999) predicts that the surface amplitudes of the modes should increase, with the enhancement being greater for shorter-period modes. The 1000 s modes are expected to have growth times of order days (Goldreich & Wu 1999a).

Smoothing the light curve by 3000 s, over several pulsation cycles, the outbursts increase the mean flux by up to 14%, which would require a global 750 K temperature increase from the quiescent effective temperature of 11,060 K. The pulsations induce even more dramatic, localized temperature excursions.

Figure 4 explores the light curve surrounding and during the seventh observed outburst, between Days 46–56 from the start of K2 monitoring, using an equal amount of data before and after the outburst. An FT of each subset clearly shows that pulsations are excited to significant amplitudes, even during the outburst.

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Many of the significant signals in outburst are not present in quiescence, especially the mode at 949.3 ± 0.8 μHz (1053.4 ± 0.8 s), which decreases in amplitude the longer we monitor it after outburst. Many modes appear to eventually return at roughly the same period after the outburst. However, the amplitude evolution of these pulsations holds key insight.

In essentially all cases in Figure 4, the amplitudes shown in the subset immediately after the outburst are lower than the pre-outburst subset. There are more data in this post-outburst subset, and we can clearly see many modes growing after the outburst. We explore this amplitude evolution using a running FT, shown in Figure 5. We have computed this diagram by taking an FT across a sliding 3-day window, stepped every hour with 0.05 μHz frequency resolution.

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This time-dependent FT demonstrates that the outburst has depleted considerable pulsation energy. The apparent resetting of amplitudes offers the unprecedented opportunity to actually measure the linear growth rates of pulsation modes in a white dwarf, although that is outside the scope of this Letter.

Finally, the bottom right panel of Figure 4 shows the relatively stable group of three symmetric signals centered at 2425.0 μHz (the $m=\pm 1$ components are visible in this short subset but not the central component). This pulsation triplet arises from rotation of the white dwarf (Pesnell 1985), from which we measure an ${\ell }=1$ frequency splitting of roughly 4.7 μHz, which corresponds to a rotation period of roughly 1.2 days in the asymptotic limit. We reserve a full period determination and detailed asteroseismic analysis of the many pulsations in PG 1149+057 for a future publication.

We consider various timescales in white dwarfs to explore different underlying mechanisms for the outbursts.

White dwarfs have very short dynamical timescales, roughly a few seconds. While this is a global estimate, we expect all processes which are not in hydrostatic equilibrium to locally occur on this or an even shorter timescale. The timescales for the duration and recurrence of the outbursts are clearly much longer than this. This likely rules out magnetic reconnection events as responsible for the outbursts, since the rise times of magnetic flares occur at roughly the dynamical timescale, and the rise times of the outbursts here are of order hours.

On the other hand, thermal processes can occur on longer timescales. To explore this more quantitatively, we have computed a theoretical white dwarf envelope appropriate to this star (11,000 K, $\mathrm{log}\;g$ = 8.0, ML2/α = 1.0) using the Warsaw–New Jersey stellar envelope code (Pamyatnykh 1999). We find that the thermal timescale corresponding to the average duration of the outbursts, 14.5 hr, occurs at a depth of ${10}^{-11.5}$ of the star by mass, placing it slightly deeper but near the base of the convection zone.

We note that the recurrence timescale of roughly 8 days is mapped to a deeper layer, the outer 10⁻¹⁰ of the star by mass. It is possible that processes at these depths play a role in the outbursts. However, the recurrence timescale probably rules out runaway thermonuclear events as the source of the temporary brightness increases, since the equilibrium temperature in this region is below 10⁶ K, significantly too low for nuclear burning.

An occasional deposition of asteroids onto the surface of the white dwarf could contribute the energy required to match the brightness increases, and we now have compelling evidence that disrupted planetesimals frequently pollute the atmospheres of white dwarfs (e.g., Koester et al. 2014). However, this pollution causes metal absorption, which we can rule out from spectroscopy (Voss et al. 2006).

Since the only two known outbursting white dwarfs have very similar effective temperatures and pulsation spectra, it is logical to suspect a connection between the events and the pulsations and the deep convection zone that drives them, especially since we have demonstrated here that the pulsations change before, during, and after outbursts.

We consider a model where the outbursts represent a temporary, rapid reassignment of kinetic energy away from pulsations. It is possible to transfer energy between pulsation modes through resonant mode coupling (Dziembowski 1982), which has previously been invoked to explain the amplitude evolution of δ Scuti stars in the Kepler mission (Breger & Montgomery 2014). We note that there is still considerable kinetic energy in the modes which are damped in radiative regions of the star as well as from turbulent dissipation in the convection zone.

A theoretical framework exists for parametric instability via mode coupling of white dwarf pulsations, in which energy is rapidly channelled from an observed, overstable parent mode to damped daughter modes (Wu & Goldreich 2001). It is possible that the energy of a mode (or multiple modes) grows linearly until it reaches a critical threshold, after which it enters a nonlinear regime and rapidly transfers its energy to resonant daughter modes, or a cascade of resonant daughter modes. These daughter modes may be quickly damped by turbulence in the convection zone and thus deposit their newfound energy there. However, more detailed energetics calculations are required to determine if there is sufficient energy in one (or even multiple) modes to power the observed luminosity increases during outburst.

We present confirmation of a new phenomenon in pulsating white dwarfs by analyzing the second case of outbursts in a cool DAV observed by the Kepler spacecraft, PG 1149+057. We suggest that these outbursts are connected with the pulsations, perhaps as a result of nonlinear mode coupling.

Still, exciting questions remain. Why have we not previously seen outbursts in extensively studied cool DAVs, such as GD 154 and G29-38 (Pfeiffer et al. 1996; Kleinman et al. 1998)? How do the horizontal surface velocities change from quiescence to outburst (e.g., Van Kerkwijk et al. 2000)? If resonant mode coupling of pulsations is responsible, what mechanism triggers the outburst? Are the outbursts responsible for the eventual cessation of pulsations and the empirical red edge of the DAV instability strip?

Theory can reasonably reproduce the onset of pulsations observed at the blue edge of the DAV instability strip (Brickhill 1991b; Wu & Goldreich 1999). However, there is still not a clear picture for the red edge where pulsations shut down, which is observed empirically to occur at roughly 10,500 K for a canonical 0.6 ${M}_{\odot }$ white dwarf (Gianninas et al. 2014). Current non-adiabatic calculations predict a much cooler red edge, below 6000 K (Van Grootel et al. 2012).

Hansen et al. (1985) proposed that longer-period modes would not be reflected off the surface, setting a condition for the red edge. Subsequently, Brickhill (1991b) and Goldreich & Wu (1999b) suggested that turbulent viscosity in the convection zone may damp the longest-period modes and thus define the red edge. However, neither theory provides a complete picture. Perhaps this newly discovered outburst phenomena plays some role in shutting down pulsations in cool DAVs.

Long-timescale monitoring is necessary to catch and constrain future outbursts from cool pulsating white dwarfs, and it is a testament to the utility of the Kepler instrument to non-planetary science that these events were first discovered thanks to its unblinking gaze. Fortunately, the extended Kepler mission continues its tour of new K2 fields along the ecliptic every three months, offering the possibility to survey additional cool DAVs in the coming years. We look forward to future theoretical and observational constraints to this unexpected phenomenon.