Fuchs, Stephen Fanale U. Warwick: Boris Gaensicke, Roberto Raddi, N. P. Gentile Fusillo, P.-E. Tremblay, Paul Chote U. Texas: Keaton J. Bell, Mike Montgomery, Don Winget, Zach Vanderbosch + Steve Kawaler, Agnes Bischoff-Kim, Judi Provencal, S.O. Kepler, Alejandra Romero Rumblings in the Stellar Graveyard: White Dwarf Pulsations with K2 and TESS
the range of WD envelope masses • Empirically constrain the efficiency of convection in WDs • Witness nonlinear mode coupling • Measure the endpoints of angular momentum evolution • Test for radial differential rotation All without extremely detailed asteroseismic fits
6 pulsating WDs (just two >3 months) K2 through Campaign 10: >1000 white dwarf candidates observed 35 more pulsating WDs K2 has given us hundreds of candidate pulsating white dwarfs to observe
hot DAV: 1. Small number of independent modes observed 2. Best model hinges on mode identification 3. Hidden free parameters (core profile, layer masses), with 8+ degrees of freedom e.g., WD0111+0018, 6 hr ground-based data e.g., WD0111+0018, 78.7-d K2 data Hermes et al. 2013 Hermes et al. 2017, in prep.
hot DAV: 1. Small number of independent modes observed 2. Best model hinges on mode identification 3. Hidden free parameters (core profile, layer masses), with 8+ degrees of freedom e.g., WD0111+0018, 6 hr ground-based data e.g., WD0111+0018, 78.7-d K2 data Hermes et al. 2013 Hermes et al. 2017, in prep.
to edge of DAV instability strip (We will address purity by the end of K2) Hermes et al. 2017, k2wd.org Josh Fuchs et al. 2017, in prep. Stay tuned: Recent UNC Ph.D. Josh Fuchs is exploring strip with minimal systematics (same instrument, methods, models) Empirical edges by Tremblay+ 2015
frequencies) Histogram of eigenperiods (again, no combination frequencies) 0 5 10 15 20 25 30 50 100 150 200 250 300 350 400 450 500 0 5 10 15 20 25 30 50 100 150 200 250 300 350 400 450 Clemens et al. 2017, in prep. Insights from the Aggregated Periods of DAVs Mode Amplitude (ppt) N Mode Period (s) Mode Period (s)
frequencies, mostly Kepler/K2) 0 1 2 3 4 5 6 7 8 50 100 150 200 250 300 350 400 450 Clemens et al. 2017, in prep. Insights from the Aggregated Periods of DAVs n = 1 l = 1 n = 2 l = 1 n = 3 l = 1 Kepler makes mode identification relatively trivial Mode Period (s) N n=1 n=2 n=3 n=4
100 150 200 250 300 350 400 450 l=1 hDAV periods, observed 0 1 2 3 4 5 6 7 8 50 100 150 200 250 300 350 400 450 l=1 random MH simulation Clemens et al. 2017, in prep. Romero et al. 2012 Comparing to a random distribution of models with thick (10-4 MH /M ★ ) to thin (10-10 MH /M ★ ) hydrogen layer masses, using spectroscopic Teff & masses Insights from the Aggregated Periods of DAVs
within the same DAV show very different linewidths Many of the broadened modes appear relatively Lorentzian in shape (Absolutely no way to have made these measurements before Kepler) Hermes et al. 2017, in prep.
rather than driving important for broadening; phase incoherence Broadened modes: bounded by the base of the convection zone! Mike Montgomery et al. 2017, in prep.
et al. 2017, in prep. 0.4 0.6 0.8 1.0 1.2 1.4 ↵ 0.675 0.700 0.725 0.750 0.775 0.800 0.825 0.850 Fraction Correct 0 200 400 600 800 1000 1200 1400 Period (s) 0 1 2 3 4 5 6 HWHM (µHz) ML2/↵ = 0.6 0 200 400 600 800 1000 1200 1400 Period (s) 0 1 2 3 4 5 6 HWHM (µHz) ML2/↵ = 0.9 Given spectroscopic Teff /log(g), we can calculate the critical period for a mode reflecting off the base of the convection zone This empirically constrains ML2/α
5 days: 885.243(0.057) µHz Last 5 days: 888.285(0.067) µHz Some longer-period modes appear to change very quickly in frequency: Nonlinear mode coupling appears to be the only way the star can transfer that much energy so quickly!
al. 2017 We see outbursts in 6 of the 27 DAVs observed through Campaign 8 These are aperiodic brightenings causing up to 15% mean flux increases (>750 K Teff increases) Pulsations persist in outburst, and are consistent with the star having a thinner convection zone
al. 2017 We see outbursts in 6 of the 27 DAVs observed through Campaign 8 These are aperiodic brightenings causing up to 15% mean flux increases (>750 K Teff increases) Pulsations persist in outburst, and are consistent with the star having a thinner convection zone
4 6 8 10 N Kepler & K2 Kawaler (2015) Kepler & K2 have doubled the number of white dwarfs with measured internal rotation periods using asteroseismology Hermes et al. 2017, in prep. None of the stars here are currently in binaries: Representative of single-star evolution Rotation Rates Usually Fall Readily from K2 Data 0.5 d 1 d 2 d 4 d
0.7 0.8 0.9 WD Mass (M⊙ ) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 ZAMS Progenitor Mass (M⊙ ) 1 10 100 White Dwarf Rotation Period (hr) 0 2 4 6 8 10 N Kepler & K2 Kawaler (2015) 1 d 2 d 4 d Hermes et al. 2017, in prep. We Can Finally Probe WD Rotation as a Function of Mass The fastest-rotating pulsating white dwarf (1.13 hr) is also the most massive (0.87 M¤ ) – descended from a single 4.0 M¤ ZAMS progenitor Hermes et al. 2017c, ApJL, 841, L2; arXiv: 1704.08690
ZAMS) These WDs rotate at 0.5-2.2 d (WD Prot : 35 ± 28 hr) Link emerging between higher WD mass and faster rotation 1 10 100 0 1 2 3 4 N 1.7 2.0 M ZAMS WD Prot = 1.48 ± 0.94 d 1 10 100 0 1 2 3 4 N 2.0 2.5 M ZAMS WD Prot = 1.35 ± 0.74 d 1 10 100 0 1 2 3 4 N 2.5 3.0 M ZAMS WD Prot = 1.32 ± 1.04 d 1 10 100 White Dwarf Rotation Period (hr) 0 1 2 3 4 N 3.5 4.0 M ZAMS WD Prot = 0.17 ± 0.15 d We Can Finally Probe WD Rotation as a Function of Mass
Hermes et al. 2017a l=1 modes n (n) n=2 n=3 n=4 n=5 n=6 Frequency splittings and overtone spacings behave in concert: Modes trapped to different depths Early hints: rigid rotation Period spacing difference (s)
core: 10.1±0.9hr PG 0112+104: Hermes et al. 2017a 10.17404 hr surface spot rotation period The Most Evolved Test of Radial Differential Rotation Using l=1 and l=2 modes we measure a rotation period of 10.1±0.9 hr in PG 0112+104 (better asteroseismic modeling will improve this uncertainty)
dwarfs provide opportunity to: • Establish the range of WD envelope masses § Most have canonically thick (10-4 MH /M ★ ) hydrogen envelopes • Empirically constrain the efficiency of convection in WDs § ML2/α > 0.8 from mode linewidths bounded by base of convection zone • Witness nonlinear mode coupling § Outbursts (and frequency changes) on day-week timescales • Measure the endpoints of angular momentum evolution § Endpoints of 1.7-3.0 M¤ stars rotate at 35 ± 28 hr, but >3.0 M¤ faster • Test for radial differential rotation § White dwarfs appear to rotate rigidly, but more tests on the way! All of these constraints significantly improve by observing more pulsating WDs with K2 and TESS!
ZAMS) These WDs rotate at 0.5-2.2 d (WD Prot : 35 ± 28 hr) Link emerging between higher WD mass and faster rotation 1 10 100 0 1 2 3 4 N 1.7 2.0 M ZAMS WD Prot = 1.48 ± 0.94 d 1 10 100 0 1 2 3 4 N 2.0 2.5 M ZAMS WD Prot = 1.35 ± 0.74 d 1 10 100 0 1 2 3 4 N 2.5 3.0 M ZAMS WD Prot = 1.32 ± 1.04 d 1 10 100 White Dwarf Rotation Period (hr) 0 1 2 3 4 N 3.5 4.0 M ZAMS WD Prot = 0.17 ± 0.15 d We Can Finally Probe WD Rotation as a Function of Mass