http://jjherm.es J.J. Hermes Hubble Fellow University of North Carolina at Chapel Hill Rogue waves from parametric resonance in pulsating white dwarfs 

Rogue waves from parametric resonance in pulsating white dwarfs Key takeaway: outbursts are not rare in coolest pulsating WDs - only requirement seems to be high mode density for coupling - expression of energy transfer via nonlinear mode coupling 

A Visual Guide to Outbursts in Pulsating White Dwarfs Quiescent pulsations (All outburstersdominant >800 s) PG 1149+057: Hermes et al. 2015b recurrence time: chaotic; days to weeks duration: 2-20 hr excess energy: 1033-34 erg 15% flux increase: 700 K Teff increase 

(3-day sliding window) A Visual Guide to Outbursts in Pulsating White Dwarfs PG 1149+057: Hermes et al. 2015b pulsations are affected by the outbursts 

A Visual Guide to Outbursts in Pulsating White Dwarfs Keaton Bell 2017 (PhD thesis) outbursts seen in at least 13 DAVs (this is not a rare phenomenon!) none of the outbursts in pulsating WDs are periodic; appear chaotic each color is a different DAV 

He P.I. zone (30-20 kK) H P.I. zone (13-10 kK) DBV aka V477 Her DAV aka ZZ Ceti a step back: pulsating white dwarfs in the HR diagram 

1000 s 200 s 500 s 125 s white dwarfs: g-modes, not all modes are observed excited model: 11,245 K, 0.632 M¤ , 10-4.12 MH /MWD (Romero et al. 2012) l=1 l=2 n=5 n=10 n>20 n>35 

n l=1 l=2 l=1 l=2 

n l=1 l=2 l=1 l=2 

Spectroscopy Yields Effective Temperatures and Masses SDSS 4.2m SOAR Telescope our workhorse we have obtained and analyzed SOAR spectra of 62 of the first 65 DAVs observed by K2 so far: first 27 at k2wd.org WDs Evolve (Cool) à Blue: Observed by Kepler Open: Ground-based fits via Pier-Emmanuel Tremblay 

Outbursting DAVs are Among the Coolest DAVs Blue: Observed by Kepler Red: Outbursting DAV Open: Ground-based more than 50% of DAVs from 11,200-10,600 K show outbursts in ~70 days of K2 monitoring 

Outbursting DAVs are Among the Coolest DAVs Blue: Observed by Kepler Red: Outbursting DAV Open: Ground-based GD 1212 friendly bet: Josh Fuchs (formerly UNC) thought GD 1212 should pulsate based on his fits to SOAR spectra of DAVs 

GD 1212, Hermes et al. 2014a data from the 9-day K2 engineering test run V=13.3 mag 

GD 1212: The Brightest Outbursting White Dwarf Quiescent pulsations (1135.2 s, 856.9 s, …) In Outburst (864.1 s, 846.4 s, …) GD 1212: Hermes et al. 2018, in prep. >60 days between outbursts! K2 Campaign 12 

GD 1212: The Brightest Outbursting White Dwarf Quiescent pulsations (1135.2 s, 856.9 s, …) In Outburst (864.1 s, 846.4 s, …) GD 1212: Hermes et al. 2018, in prep. >60 days between outbursts! K2 Campaign 12 

GD 1212: K2 Campaign 12 GD 1212: The Brightest Outbursting White Dwarf GD 1212: Hermes et al. 2018, in prep. 

13/65 (20% of) DAVs with Kepler Data Show Outbursts Blue: Observed by Kepler Red: Outbursting DAV Open: Ground-based we expect all non-magnetic white dwarfs to pulsate at the appropriate temperature, and it appears most (all?) outburst at some point, too outbursts are likely a new phase of stellar evolution uncovered by Kepler/K2 

150 s 1000 s white dwarfs cool: longer-period (higher-radial-order) pulsations driven and mode density rapidly increases 

Coming Soon: NASA/TESS will observe all bright WDs every 2 min 815 WDs in Cycle 1 accepted for 2-min monitoring ~70 I < 16 mag white dwarfs per sector 

Should Other Pulsating Stars Show Outbursts? DBVs (He-atmosphere WDs) have very similar structures to DAVs, and thus similar mode densities so far 7 DBVs observed by Kepler: none show outbursts (but so far none with dominant periods >1000 s) See poster by Zach Vanderbosch 

l=1 l=2 Adiabatic Model: 11,245 K, 0.632 M¤ , 10-4.12 MH /MWD Observed: 11,060(170) K, 0.64(0.03) M¤ (Romero et al. 2012) (Gianninas et al. 2011) Mode Coupling via Parametric Resonance à Driving exceeds damping Radiative damping ß outbursts are likely “limit cycles arising from sufficiently resonant 3-mode couplings between overstable parent modes and pairs of radiatively damped daughter modes” Jing Luan & Goldreich 2018 

à Driving Radiative damping ß l=1 l=2 Adiabatic Model: 11,245 K, 0.632 M¤ , 10-4.12 MH /MWD Observed: 11,060(170) K, 0.64(0.03) M¤ (Romero et al. 2012) (Gianninas et al. 2011) Mode Coupling via Parametric Resonance ωp = 897.7 µHz (l=1, m=0, n=24) 

Wu & Goldreich (2001) predicted nonlinear mode coupling could transfer energy into damped modes in the cool DAVs ωp = 897.7 µHz (l=1, m=0, n=24) ωd1 = 435.9 µHz (l=2, m=0, n=88) l=1 l=2 ωd2 = 461.9 µHz (l=1, m=0, n=48) Adiabatic Model: 11,245 K, 0.632 M¤ , 10-4.12 MH /MWD Observed: 11,060(170) K, 0.64(0.03) M¤ (Romero et al. 2012) (Gianninas et al. 2011) Mode Coupling via Parametric Resonance ωd1 + ωd2 = ωp + δω Limit cycle if: δω < γd (typical 1/γd < 1 day) 

ωp = 897.7 µHz (l=1, m=0, n=24) ωd1 = 435.9 µHz (l=2, m=0, n=88) l=1 l=2 ωd2 = 461.9 µHz (l=1, m=0, n=48) Adiabatic Model: 11,245 K, 0.632 M¤ , 10-4.12 MH /MWD Observed: 11,060(170) K, 0.64(0.03) M¤ (Romero et al. 2012) (Gianninas et al. 2011) Mode Coupling via Parametric Resonance Wu & Goldreich 2001 ωd1 + ωd2 = ωp + δω Limit cycle if: δω < γd (typical 1/γd < 1 day) 

Key Takeaways: Outbursts in the Coolest Pulsating WDs Blue: Observed by Kepler Red: Outbursting DAV Open: Ground-based - outbursts are not rare in coolest pulsating WDs - this is a common (universal?) phase of stellar evolution! - only requirement seems to be high mode density for coupling - nonlinear resonances expressed as outbursts are very likely responsible for the cessation of pulsations at the red edge of the DAV instability strip 

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Should Other Pulsating Stars Show Outbursts? the well-studied DBV GD 358 showed pulsation changes and got ~20-30% brighter during 2006 WET run for just one day nicknamed the ‘sforzando’ or often the ‘whoopsie’ GD 358: Montgomery et al. 2010 

WET, and KASC4 Boulder (7/2011 so SIX YEARS AGO!) He P.I. zone (30-20 kK) H P.I. zone (13-10 kK) Fontaine & Brassard 2008 N2 Ll 2 DAV Propagation Diagram Core Surface p-modes σ2 > Ll 2, N2 convection zone log σ2 (s-2) g-modes σ2 < Ll 2, N2 

oDAV1 10860 K 0.70 M¤ oDAV2 11060 K 0.64 M¤ oDAV3 10570 K 0.56 M¤ oDAV4 11190 K 0.62 M¤ oDAV5 10850 K 0.53 M¤ 3rd & 4th: Bell et al. 2016, ApJ, arXiv: 1607.01392 

(3-day sliding window) As seen in other bright oDAV, outbursts affect pulsations! oDAV4, Kp = 16.7 mag 

1000 s 500 s 360 s 1400 s oDAV1 10860 K 0.70 M¤ oDAV2 11060 K 0.64 M¤ oDAV3 10570 K 0.56 M¤ oDAV4 11190 K 0.62 M¤ oDAV5 10850 K 0.53 M¤ 800 s 3rd & 4th: Bell et al. 2016, ApJ, arXiv: 1607.01392