h/t: Mike Montgomery, Agnes Bischoff-Kim, Keaton Bell, Don Winget, Steve Kawaler,! Bart Dunlap, Chris Clemens, S. O. Kepler, Barbara Castanheira, Boris Gänsicke,! Paul Chote, Tom Marsh, Tom Barclay, Fergal Mullally, Detlev Koester JJ Hermes
Ll 2# Propagation/Diagram# Core Surface p-modes σ2*>*Ll 2,*N2 g-modes σ2*<*Ll 2,*N2 convection! zone log*σ2*(s:2) A ‘typical’ white dwarf electron degenerate! C/O core! (r = 8500 km) non-degerate! He layer! (260 km) non-degerate H layer! (30 km)
2# Propagation/Diagram# Core Surface p-modes σ2*>*Ll 2,*N2 g-modes σ2*<*Ll 2,*N2 convection! zone log*σ2*(s:2) A ‘typical’ white dwarf electron degenerate! C/O core! (8500 km thick) non-degerate! He layer! (260 km) non-degerate H layer! (30 km) DA: Broad hydrogen Balmer lines Fractional*Mass*Depth:2
• Most*WDs*≈* 0.6*M!2 • Pulsate*at*onset*of*H* partial*ionization*zone* (DAVs,*aka*ZZ*Cetis)2 The observed pulsating white dwarf stars lie in three strips in the H-R diagram, a in Figure 3. The pulsating pre-white dwarf PG 1159 stars, the DOVs, around 7 170,000 K have the highest number of detected modes. The first class of pulsating 5.5 5.0 4.5 Planetary Nebula Main sequence DOV DBV DAV 4.0 3.5 3.0 log [T eff (K)] 4 2 0 –2 –4 log (L/L ) Figure 3 A 13-Gyr isochrone with z = 0.019 from Marigo et al. (2007), on which we have drawn the obs locations of the instability strips, following the nonadiabatic calculations of C´ orsico, Althaus & M Annu. Rev. Astro. Astrophys. 2008.46:157-199. Downloade by University of Texas - Austin on 01/28/09. The Astrophysical Journal, 730:128 (23pp), 2011 April 1 Tremblay, Bergeron, & Gianninas Winget & Kepler 2008 Tremblay+ 2011 One*DBV*in*original* mission*(Østensen+*2011,* Bischoff:Kim+*2014)
Figure 4. Prewhitening sequence for the 213 s feature. Figure 5. Prewhitening sequence for the 274 s feature. White Dwarf Rotation from the Ground Giammichele+/2013# • ZZ/Ceti/itself://P rot (≈(1.7(d. prewhitened: prewhitened: prewhitened: prewhitened:
not exactly 0.5. If we adopt the Ck,l values of the model from Romero et al. (2012) discussed in Section 4.2, we obtain a rotation rate of 3.5 ± 0.2 d. To best reflect the systematic uncertainties, we adopt a rotation rate of 3.5 ± 0.5 d. Notably, the small but significant deviations in the observed fre- quency splittings provide additional asteroseismic information, es- pecially useful for constraining which modes are trapped by com- position transition zones (Brassard et al. 1992). The shorter-period g modes have lower radial order, and these splittings are observed to have values of 1.97 µHz for f1 , 1.77 µHz for f2 , 2.03 µHz for f3 and 1.94 µHz for f4 . This value is in agreement with previous rotation frequencies found in ZZ Ceti stars. Fontaine & Brassard (2008) give an overview on pulsating WDs and provide the asteroseismic rotation rates of seven ZZ Ceti stars, spanning from 9 to 55 h, i.e. 0.4 to 2.3 d. In the case of non-pulsating WDs, the sharp NLTE core of the Hα line in their spectra has been used in many studies to measure the projected rotation velocities of the stars (Heber, Napiwotzki & Reid 1997; Koester et al. 1998; Karl et al. 2005). In all cases, the same conclusion was drawn: isolated WDs are generally slow rotators. 5 CONCLUSION We report on the discovery of the second ZZ Ceti in the Kepler field: KIC 11911480. It was discovered using colour selections from the Kepler-INT Survey and confirmed with ground-based time series photometry from the RATS-Kepler survey. Follow-up Kepler short- cadence observations during Q12 and Q16 are analysed: five inde- • Kp /=*18.1*mag*DAV2 • 6*months*Kepler*data2 • Clean*rotational* spli\ings:* 2P rot (=(3.5(±(0.5(days. • 0.57*±*0.06*M! *WD:* 2~1.5*M! *(F)*progenitor2 Web Formulas ⌫ = m(1 Ck,` )⌦ l. 4.3 Rotation rate We see what appears to be multiplet splitting of some modes, which is a direct manifestation of the star’s rotation rate (Fig. 5). In the limit of slow rotation, the difference between the frequency of one mode of indices l, k, m (σk,lm ) and the frequency in the non-rotating case (σk,l ) is: σk,l,m − σk,l = m(1 − Ck,l ) (1) where Ck,l comes from the Coriolis force term in the momentum equation and is the rotation frequency (Winget et al. 1991; Vau- clair 1997). Note that this equation is the classical first-order ex- pansion. In the asymptotic limit for g modes, Ck,l only depends on the degree of the mode: Ck,l ≃ 1 l(l+1) . When a pulsating WD ro- tates, each mode of degree l can be split into 2l+1 components. We see splitting into three components in several modes in the power spectrum of KIC 11911480 (see Fig. 5), which likely corre- sponds to an ℓ = 1 mode in those cases, leading to Ck,l ≃ 0.5. The frequency spacing between the split components of the modes is quite consistent, 1.93 ± 0.10 µHz, suggesting these modes are all of the same spherical degree. This corresponds to a rotation rate of 3.0 ± 0.2 d. However, f1 − f4 (with periods from 172.9 to 324.5s) are likely low-radial-order and far from the asymptotic limit, so their Ck,l values should not be identical, and are not exactly 0.5. If we adopt the Ck,l values of the model from Romero et al. (2012) discussed in Section 4.2, we obtain a rotation rate of 3.5 ± 0.2 d. To best reflect the systematic uncertainties, we adopt a rotation rate of 3.5 ± 0.5 d. White Dwarf Rotation Made Easy with Kepler
Evolution of the average core rotational period as a function of Boundary Cond’s: Angular Momentum Transport Cantiello+/2014# Core Rotation Surface! Rotation WD$rotation$constrains$ RGB$core1envelope$ coupling7
et al.: The instab Fig. 2. Structure of the envelope of our representative evolving 0.6 M DA white dwarf. The ordinate gives the fractional mass depth in loga rithmic units. The small dots define “isocontours” of opacity, and som Surface Core Base(of( convection(zone( deepens(as(WD(cools. Van/Grootel+/2012#
1.— Representative sections of the Kepler light curve of KIC 4552982 in units of days since the start of observations. The top p shows the full Q11 light curve. The one-month shaded region in the top panel is expanded in the middle panel. The one-week sh region in the middle panel is expanded in the bottom panel. The solid line is the light curve smoothed with a 30-minute window. point-to-point scatter dominates the pulsation amplitudes in the light curve, so pulsations are not apparent to the eye. The dram increases in brightness are discussed in detail in Section 3. to medium-resolution spectra for the white dwarf and fit the Balmer line profiles to models to determine its val- tion rate. We summarize our findings and conclud Section 5. KIC/4552982:/Bell+/2015,/in/review# 3 months: 1 month: 1 week:
1.— Representative sections of the Kepler light curve of KIC 4552982 in units of days since the start of observations. The top p shows the full Q11 light curve. The one-month shaded region in the top panel is expanded in the middle panel. The one-week sh region in the middle panel is expanded in the bottom panel. The solid line is the light curve smoothed with a 30-minute window. point-to-point scatter dominates the pulsation amplitudes in the light curve, so pulsations are not apparent to the eye. The dram increases in brightness are discussed in detail in Section 3. to medium-resolution spectra for the white dwarf and fit the Balmer line profiles to models to determine its val- tion rate. We summarize our findings and conclud Section 5. KIC/4552982:/Bell+/2015,/in/review# 3 months: 1 month: 1 week: e measured equivalent durations of the 186 outbursts at were recorded without interruption from gaps in the ta is displayed in Figure 4 and the continua used for e example outbursts are the dashed lines in Figure 3. e median outburst equivalent duration is 6.8 minutes he corresponding outburst is displayed in the second nel of Figure 3). Since the Kepler point-to-point scat- is 1.8% for this target, we are limited to detecting ly large outbursts by eye and so are undoubtedly in-
1.— Representative sections of the Kepler light curve of KIC 4552982 in units of days since the start of observations. The top p shows the full Q11 light curve. The one-month shaded region in the top panel is expanded in the middle panel. The one-week sh region in the middle panel is expanded in the bottom panel. The solid line is the light curve smoothed with a 30-minute window. point-to-point scatter dominates the pulsation amplitudes in the light curve, so pulsations are not apparent to the eye. The dram increases in brightness are discussed in detail in Section 3. to medium-resolution spectra for the white dwarf and fit the Balmer line profiles to models to determine its val- tion rate. We summarize our findings and conclud Section 5. KIC/4552982:/Bell+/2015,/submi^ed# 3 months: 1 month: 1 week: e measured equivalent durations of the 186 outbursts at were recorded without interruption from gaps in the ta is displayed in Figure 4 and the continua used for e example outbursts are the dashed lines in Figure 3. e median outburst equivalent duration is 6.8 minutes he corresponding outburst is displayed in the second nel of Figure 3). Since the Kepler point-to-point scat- is 1.8% for this target, we are limited to detecting ly large outbursts by eye and so are undoubtedly in- Broad power bands reminiscent of stochastic driving
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