Download Asteroseismology of Kepler ZZ Ceti Stars with Fully Evolutionary

20th European White Dwarf Workshop
ASP Conference Series, Vol. 509
Tremblay, Gänsicke, and Marsh, eds.
c 2017 Astronomical Society of the Pacific
Asteroseismology of Kepler ZZ Ceti Stars with Fully
Evolutionary Models
A. D. Romero,1 A. H. Córsico,2,3 B. G. Castanheira,4 F. C. De Gerónimo,2,3
S. O. Kepler,1 L. G. Althaus,2,3 D. Koester,5 A. Kawka,6 A. Gianninas,7 and
C. Bonato1
1
Departamento de Astronomia, Universidade Federal do Rio Grande do Sul,
Av. Bento Goncalves 9500, Porto Alegre 91501-970, RS, Brazil
alejandra.romero@ ufrgs.br
2
Grupo de Evolución Estelar y Pulsaciones, Facultad de Ciencias
Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del
Bosque s/n, 1900 La Plata, Argentina
3 Instituto
de Astrofísica La Plata, CONICET-UNLP, Argentina
4 Department
of Astronomy and McDonald Observatory, University of Texas at
Austin, Austin, TX 78712, USA
5 Institut
für Theoretische Physik und Astrophysik, Universität Kiel, 24098 Kiel,
Germany
6 Astronomický
ústav, Akademie vĕd C̆eské republiky, Fric̆ova 298, CZ-251 65
Ondr̆ejov, Czech Republic
7 Homer
L. Dodge Department of Physics and Astronomy, University of
Oklahoma, 440 W. Brooks St., Norman, OK 73019, USA
Abstract.
Recently the Kepler spacecraft observed ZZ Ceti stars giving the opportunity to study their variability for long baselines. We present a study of pulsational properties of two ZZ Ceti stars observed with the Kepler spacecraft: GD 1212
and SDSS J113655.17+040952.6, based on a grid of full evolutionary models of DA
white dwarf stars, characterized by detailed and consistent inner chemical profiles.
For J113655.17+040952 we found values of gravity and effective temperature in good
agreement with spectroscopy. For GD 1212 the asteroseismological fits show a stellar mass higher than the spectroscopic value, but in agreement with the determinations
from photometry coupled with parallax.
1.
Introduction
ZZ Ceti (or DAV) variable stars constitute the most populous class of pulsating white
dwarfs (WDs). They are otherwise normal DA (H-rich atmospheres) WDs located in
a narrow instability strip with effective temperatures between 10 500 K and 12 500 K
(e.g. Winget & Kepler 2008; Fontaine & Brassard 2008; Althaus et al. 2010a) that
show luminosity variations of up to 0.30 mag caused by nonradial g-mode pulsations
269
270
Romero et al.
of low degree (ℓ ≤ 2) and periods between 70 and 1500 s. Because of their pulsating nature, we can use asteroseismology to study these objects. Two main approaches
have been adopted for WD asteroseismology: one employing static stellar models with
parametrized chemical profiles; and the other —the one we adopt in this work— employing fully evolutionary models resulting from the complete evolution of the progenitor stars. This last approach involves the most detailed and updated input physics,
in particular regarding the predictions of the full evolutionary history for the internal
chemical structure from the stellar core to the surface (Romero et al. 2012, 2013).
Recently, several ZZ Cetis were observed with the Kepler spacecraft field, thus
opening a new avenue for WD asteroseismology based on observations from space. In
this work, we focus on two objects: GD 1212 and SDSS J113655.17+040952.6. GD
1212 (T eff = 10 970 ± 170 K, log g = 8.03 ± 0.05) was observed for a total of 264.5
h using the Kepler (K2) spacecraft in two-wheel mode (Hermes et al. 2014). This
star shows 19 independent pulsation modes, with periods ranging from 828 to 1221
s. SDSS J113655.17+040952.6 (i.e. J1136+0409, T eff = 12 330 ± 260 K, log g =
7.99 ± 0.06 ) was discovered by Pyrzas et al. (2015) and observed in detail by Hermes
et al. (2015). This is the first known DAV variable WD in a post common envelope
binary system. From the analysis of the light curve, Hermes et al. (2015) found 12
pulsation frequencies, 6 of them being components of rotational triplets (ℓ = 1), and
several harmonics. Thus, only 5 frequencies are identified as independent, with three
of them the m = 0 component of an ℓ = 1 triplet.
10
9
-log(MH/M*)
8
7
6
5
4
Romero et al. (2012)
Romero et al. (2013)
3
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
M*/Msun
1
1.05
Figure 1. Basic grid of DA WD evolutionary sequences in the M∗ /M⊙ vs
− log(MH /M∗ ) plane. Each circle corresponds to a sequence of models representative of WD stars characterized by a given stellar mass and hydrogen envelope mass.
Hollow circles correspond to the evolutionary sequences computed in Romero et
al. (2012), while filled circles correspond to sequences computed in Romero et al.
(2013). The green thick line connects the sequences with the maximum values for
the thickness of the hydrogen envelope, predicted by evolutionary computations.
Asteroseismology of Kepler ZZ Ceti Stars
2.
271
The Models
We carry out a complete and detailed asteroseismological analysis of J1136+0904 and
GD 1212 by employing evolutionary DA WD models computed using the LPCODE
code (Althaus et al. 2005, Romero et al. 2015) and presented in Romero et al. (2012,
2013). These models are the result of full evolutionary calculations of the progenitor
stars, from the ZAMS, through the hydrogen and helium central burning stages, thermal
pulses, the planetary nebula phase and finally the white dwarf cooling sequences. The
adiabatic pulsation periods of nonradial g-modes for our complete set of DA WD models were computed using the adiabatic version of the LP-PUL pulsation code described
in Córsico & Althaus (2006), coupled with the LPCODE evolutionary code. The white
dwarf sequences have stellar masses from 0.52 to 1.05 M⊙ , corresponding to C/O core
WDs. For each sequence, several hydrogen envelope masses have been computed. A
basic grid is shown in Fig. 1 in the M∗ /M⊙ vs. − log(MH /M∗ ) plane. Note that the maximum value of the hydrogen envelope (thick green line) shows a strong dependence on
the stellar mass. This upper limit for the hydrogen envelope mass is set by the onset of
residual hydrogen burning.
3.
Results and Discussion
For our target stars we searched for an asteroseismological representative model that
best matches the observed periods. To this end, we seek for the theoretical model that
minimize the quality function given by:
v
u
t N
X [Πth − Πobs ]2 × wi
i
k
S =
(1)
PN
i=1 wi
i=1
where N is the number of observed modes and wi is the observed amplitude.
J1136+0409 has 5 frequencies identified as independent, being three of them the
m = 0 component of an ℓ = 1 triplet. In our seismological fits we fix the ℓ = 1
values for those modes. A list of observed periods, pulsation amplitudes and harmonic
degrees are shown in the first three columns of Table 1. Our results are shown in Fig. 2,
which shows the projection of the inverse of the quality function S on the T eff − M∗ /M⊙
plane. We show the spectroscopic values from Hermes et al. (2015) as a blue open
circle. As can be seen from this figure, we have a family of minima around ∼ 0.57M⊙
and 12 000 K. The parameters characterizing the best fit model for J1136+0904 are:
M∗ = (0.57 ± 0.023)M⊙ , T eff = 12060 ± 210 K, MH /M⊙ = 10−5 , MHe /M⊙ = 2 × 10−2 ,
XC = 0.301 and XO = 0.696. We also computed the rotation coefficients Ckℓ and used
the identified triplets to derive a consistent rotation period of 2.6 h.
GD 1212 has a much richer pulsation spectra than J1136+0409, with 19 independent pulsation modes detected with periods between 828.2 and 1220.8 s (Hermes et al.
2015), consistent with a red edge ZZ Ceti pulsator. Using the period spacing for ℓ = 1
modes of ∆Π = 41.5 ± 2.5 s determined by Hermes et al. (2015) and the spectroscopic
effective temperature, we estimated the stellar mass by comparing this value to the theoretical asymptotic period spacing. As a result, we obtained M∗ = (0.770 ± 0.067)M⊙ .
Then, we performed an asteroseismological fit using two independent codes: LPCODE
and WDEC. The results are listed in Table 2. From the fits with LPCODE we obtained
solutions characterized by a high stellar mass of ∼ 0.878M⊙ , 15-20% higher than the
272
Romero et al.
Table 1. Observed periods of J1136+0409 to be employed as input of our asteroseismological analysis with the ℓ value fixed for three modes, according to Hermes
et al. (2015). The theoretical periods with their corresponding harmonic degree and
radial order for our best fit model, are listed in the last three columns.
Πobs
i
279.443
181.283
162.231
344.407
201.782
Ai (ppt)
2.272
1.841
1.213
0.775
0.519
ℓ
1
1
1
-
ΠTheo
i
277.9
185.2
161.1
344.2
195.9
ℓ
1
1
1
1
2
k
3
2
1
5
4
Figure 2. Projection on the effective temperature vs. stellar mass plane of the
inverse of the quality function S for J1136+0409. The open circle indicates the
stellar mass and effective temperature values obtained from spectroscopy by Hermes
et al. (2015).
spectroscopic value. This is shown in the left panel of Fig. 3, where we depict the
projection on the T eff − M∗ /M⊙ plane of the inverse of the quality function S for GD
1212. The solutions show T eff around 11 200 and 11 600 K. All possible solutions are
characterized by thick hydrogen envelopes. The best fit model obtained with WDEC
also shows a high mass of 0.815M⊙ .
Because of the discrepancy between the spectroscopic and the seismological masses
we decided to re-compute the atmospheric parameters. Fitting the spectra of GD 1212
from Kawka et al. (2004) and Gianninas et al. (2011) we computed the values of log g
and T eff using the atmosphere models from Koester (2010), Gianninas et al. (2011) and
Kawka & Vennes (2012). For the photometric determinations we consider ugriz from
SDSS, BVIJHK photometry and Galex, combined with the paralax 62.7 ± 1.7 mas from
Subasavage et al. (2009). The results are depicted in the right panel of Fig. 3. Note
273
Asteroseismology of Kepler ZZ Ceti Stars
that photometry and non-3D-corrected spectroscopy leads to a higher stellar mass determination, closer to our asteroseismological values (green squares). In particular, the
solution obtained with WDEC is in excellent agreement with the photometric values.
1
Spec+1D
Spec+3D
Phot+paralax
0.9
M*/Msun
0.8
LPCODE
WDEC
0.7
0.6
0.5
10750
11000
11250 11500
Teff [K]
11750
12000
Figure 3.
Left: Projection on the effective temperature vs. stellar mass plane of
the inverse of the quality function S for GD 1212. Open circles indicate the values
obtained from spectroscopy (Gianninas et al. 2011), with 3D convection correction
from Tremblay et al. (2013) (via Hermes et al. 2014) and from photometry (Giammichele et al. 2012). Right: Determinations of the atmospheric parameters from
different techniques. The black box corresponds to the range of stellar mass and
effective temperature from spectroscopic determinations. The red box corresponds
to the spectroscopic values after applying the 3D convection correction. The blue
box shows our results from photometry. Green squares show the position of our
asteroseismological solutions with the LPCODE and WDEC codes.
Table 2.
List of parameters characterizing the best fit models obtained for GD
1212 using the LPCODE and WDEC codes. Also, we list the spectroscopic values
from Hermes et al. (2014).
Hermes et al. (2014)
M∗ = 0.619 ± 0.03M⊙
T eff = 10970 ± 170 K
LPCODE
M∗ = 0.877M⊙
T eff = 11613 K
MH /M⊙ = 7.4 − 3.5 × 10−6
MHe /M⊙ = 2 × 10−2
XC = 0.367, XO = 0.611
S = 3.6 s
WDEC
M∗ = 0.815M⊙
T eff = 11100 K
MH /M⊙ = 10−4
MHe /M⊙ = 10−2
XC = XO = 0.5
S = 4.5 s
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4.
Romero et al.
Conclusion
In the case of J1136+0409, we found a seismological mass of 0.570M⊙ and T eff =
12060 K, in good agreement with the spectroscopic determinations.
For GD 1212, the seismological analysis points to a high mass solution, 15-20%
higher than the spectroscopic mass from Hermes et al. (2014). However, non-3D corrected spectroscopy and photometry coupled with parallax also point to a high stellar
mass ∼ 0.8M⊙ , in better agreement with the asteroseismological determinations. Additional spectroscopic observations, including the IR, and a better determination of the
period spectra of GD 1212 might help to solve the discrepancy in stellar mass found for
this star, and also to constrain the structure and seismological properties of DA white
dwarfs.
Acknowledgments. Partial financial support from this research comes from CNPq
and PRONEX-FAPERGS/CNPq (Brazil). DK received support from programme Science without Borders, MCIT/MEC-Brazil. Part of this work was supported by AGENCIA through the Programa de Modernización Tecnológica BID 1728/OC-AR and the
PIP 112-200801-00940 grant from CONICET. AK acknowledges support from the
Czech Science Foundation (15-15943S). AG gratefully acknowledges the support of
the NSF under grant AST-1312678, and NASA under grant NNX14AF65G. A.G. gratefully acknowledges the support of the NSF under grant AST-1312678, and NASA grant
NNX144AF65G.
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