61 research outputs found
Mode Identification from Combination Frequency Amplitudes in ZZ Ceti Stars
The lightcurves of variable DA stars are usually multi-periodic and
non-sinusoidal, so that their Fourier transforms show peaks at eigenfrequencies
of the pulsation modes and at sums and differences of these frequencies. These
combination frequencies provide extra information about the pulsations, both
physical and geometrical, that is lost unless they are analyzed. Several
theories provide a context for this analysis by predicting combination
frequency amplitudes. In these theories, the combination frequencies arise from
nonlinear mixing of oscillation modes in the outer layers of the white dwarf,
so their analysis cannot yield direct information on the global structure of
the star as eigenmodes provide. However, their sensitivity to mode geometry
does make them a useful tool for identifying the spherical degree of the modes
that mix to produce them. In this paper, we analyze data from eight hot,
low-amplitude DAV white dwarfs and measure the amplitudes of combination
frequencies present. By comparing these amplitudes to the predictions of the
theory of Goldreich & Wu, we have verified that the theory is crudely
consistent with the measurements. We have also investigated to what extent the
combination frequencies can be used to measure the spherical degree (ell) of
the modes that produce them. We find that modes with ell > 2 are easily
identifiable as high ell based on their combination frequencies alone.
Distinguishing between ell=1 and 2 is also possible using harmonics. These
results will be useful for conducting seismological analysis of large ensembles
of ZZ Ceti stars, such as those being discovered using the Sloan Digital Sky
Survey. Because this method relies only on photometry at optical wavelengths,
it can be applied to faint stars using 4 m class telescopes.Comment: 73 pages, 22 figures, accepted in the Ap
Gravity-Modes in ZZ Ceti Stars: I.Quasiadiabatic Analysis of Overstability
We analyze the stability of g-modes in variable white dwarfs with hydrogen
envelopes. In these stars, the radiative layer contributes to mode damping
because its opacity decreases upon compression and the amplitude of the
Lagrangian pressure perturbation increases outward. The overlying convective
envelope is the seat of mode excitation because it acts as an insulating
blanket with respect to the perturbed flux that enters it from below. A crucial
point is that the convective motions respond to the instantaneous pulsational
state. Driving exceeds damping by as much as a factor of two provided
, where is the radian frequency of the mode and
with being the thermal time constant
evaluated at the base of the convective envelope. As a white dwarf cools, its
convection zone deepens, and modes of lower frequency become overstable.
However, the deeper convection zone impedes the passage of flux perturbations
from the base of the convection zone to the photosphere. Thus the photometric
variation of a mode with constant velocity amplitude decreases. These factors
account for the observed trend that longer period modes are found in cooler
DAVs. The linear growth time, ranging from hours for the longest period
observed modes ( minutes) to thousands of years for those of
shortest period ( minutes), probably sets the time-scale for
variations of mode amplitude and phase. This is consistent with observations
showing that longer period modes are more variable than shorter period ones.
Our investigation confirms many results obtained by Brickhill in his pioneering
studies of ZZ Cetis.Comment: 26 pages, including 5 figures, uses aaspp4.sty, submitted to Ap
High Resolution Spectroscopy of the Pulsating White Dwarf G29-38
We present the analysis of time-resolved, high resolution spectra of the cool
white dwarf pulsator, G29-38. From measuring the Doppler shifts of the H-alpha
core, we detect velocity changes as large as 16.5 km/s and conclude that they
are due to the horizontal motions associated with the g-mode pulsations on the
star. We detect seven pulsation modes from the velocity time-series and
identify the same modes in the flux variations. We discuss the properties of
these modes and use the advantage of having both velocity and flux measurements
of the pulsations to test the convective driving theory proposed for DAV stars.
Our data show limited agreement with the expected relationships between the
amplitude and phases of the velocity and flux modes. Unexpectedly, the velocity
curve shows evidence for harmonic distortion, in the form of a peak in the
Fourier transform whose frequency is the exact sum of the two largest
frequencies. Combination frequencies are a characteristic feature of the
Fourier transforms of light curves of G29-38, but before now have not been
detected in the velocities, nor does published theory predict that they should
exist. We compare our velocity combination frequency to combination frequencies
found in the analysis of light curves of G29-38, and discuss what might account
for the existence of velocity combinations with the properties we observe.
We also use our high-resolution spectra to determine if either rotation or
pulsation can explain the truncated shape observed for the DAV star's line
core. We are able to eliminate both mechanisms: the average spectrum does not
fit the rotationally broadened model and the time-series of spectra provides
proof that the pulsations do not significantly truncate the line.Comment: 24 pages, 9 figures, Accepted for publication in ApJ (June
The Peculiar Pulsations of PY Vul
The pulsating white dwarf star PY Vul (G~185-32) exhibits pulsation modes
with peculiar properties that set it apart from other variable stars in the ZZ
Ceti (DAV) class. These peculiarities include a low total pulsation amplitude,
a mode with bizarre amplitudes in the ultraviolet, and a mode harmonic that
exceeds the amplitude of its fundamental. Here, we present optical, time series
spectroscopy of PY Vul acquired with the Keck II LRIS spectrograph. Our
analysis has revealed that the mode with unusual UV amplitudes also has
distinguishing characteristics in the optical. Comparison of its line profile
variations to models suggests that this mode has a spherical degree of four. We
show that all the other peculiarities in this star are accounted for by a
dominant pulsation mode of l=4, and propose this hypothesis as a solution to
the mysteries of PY Vul.Comment: 30 pages, 14 figures, Accepted for publication in Ap
Prospects for Measuring Differential Rotation in White Dwarfs Through Asteroseismology
We examine the potential of asteroseismology for exploring the internal
rotation of white dwarf stars. Data from global observing campaigns have
revealed a wealth of frequencies, some of which show the signature of
rotational splitting. Tools developed for helioseismology to use many solar
p-mode frequencies for inversion of the rotation rate with depth are adapted to
the case of more limited numbers of modes of low degree. We find that the small
number of available modes in white dwarfs, coupled with the similarity between
the rotational-splitting kernels of the modes, renders direct inversion
unstable. Accordingly, we adopt what we consider to be plausible functional
forms for the differential rotation profile; this is sufficiently restrictive
to enable us to carry out a useful calibration. We show examples of this
technique for PG 1159 stars and pulsating DB white dwarfs. Published frequency
splittings for white dwarfs are currently not accurate enough for meaningful
inversions; reanalysis of existing data can provide splittings of sufficient
accuracy when the frequencies of individual peaks are extracted via
least-squares fitting or multipeak decompositions. We find that when mode
trapping is evident in the period spacing of g modes, the measured splittings
can constrain dOmega/dr.Comment: 26 pages, 20 postscript figures. Accepted for publication in The
Astrophysical Journa
Re-defining the Empirical ZZ Ceti Instability Strip
We use the new ZZ Ceti stars (hydrogen atmosphere white dwarf variables;
DAVs) discovered within the Sloan Digital Sky Survey (Mukadam et al. 2004) to
re-define the empirical ZZ Ceti instability strip. This is the first time since
the discovery of white dwarf variables in 1968 that we have a homogeneous set
of spectra acquired using the same instrument on the same telescope, and with
consistent data reductions, for a statistically significant sample of ZZ Ceti
stars. The homogeneity of the spectra reduces the scatter in the spectroscopic
temperatures and we find a narrow instability strip of width ~950K, from
10850--11800K. We question the purity of the DAV instability strip as we find
several non-variables within. We present our best fit for the red edge and our
constraint for the blue edge of the instability strip, determined using a
statistical approach.Comment: 14 pages, 5 pages, ApJ paper, accepte
Pulsational Mapping of Calcium Across the Surface of a White Dwarf
We constrain the distribution of calcium across the surface of the white
dwarf star G29-38 by combining time series spectroscopy from Gemini-North with
global time series photometry from the Whole Earth Telescope. G29-38 is
actively accreting metals from a known debris disk. Since the metals sink
significantly faster than they mix across the surface, any inhomogeneity in the
accretion process will appear as an inhomogeneity of the metals on the surface
of the star. We measure the flux amplitudes and the calcium equivalent width
amplitudes for two large pulsations excited on G29-38 in 2008. The ratio of
these amplitudes best fits a model for polar accretion of calcium and rules out
equatorial accretion.Comment: Accepted to the Astrophysical Journal. 16 pages, 10 figures
The pulsating DA white dwarf star EC 14012-1446: results from four epochs of time-resolved photometry
The pulsating DA white dwarfs are the coolest degenerate stars that undergo
self-driven oscillations. Understanding their interior structure will help to
understand the previous evolution of the star. To this end, we report the
analysis of more than 200 h of time-resolved CCD photometry of the pulsating DA
white dwarf star EC 14012-1446 acquired during four observing epochs in three
different years, including a coordinated three-site campaign. A total of 19
independent frequencies in the star's light variations together with 148
combination signals up to fifth order could be detected. We are unable to
obtain the period spacing of the normal modes and therefore a mass estimate of
the star, but we infer a fairly short rotation period of 0.61 +/- 0.03 d,
assuming the rotationally split modes are l=1. The pulsation modes of the star
undergo amplitude and frequency variations, in the sense that modes with higher
radial overtone show more pronounced variability and that amplitude changes are
always accompanied by frequency variations. Most of the second-order
combination frequencies detected have amplitudes that are a function of their
parent mode amplitudes, but we found a few cases of possible resonantly excited
modes. We point out the complications in the analysis and interpretation of
data sets of pulsating white dwarfs that are affected by combination
frequencies of the form f_A+f_B-f_C intruding into the frequency range of the
independent modes.Comment: 14 pages, 6 figures, 6 tables. MNRAS, in pres
The Everchanging Pulsating White Dwarf GD358
We report 323 hours of nearly uninterrupted time series photometric
observations of the DBV star GD 358 acquired with the Whole Earth Telescope
(WET) during May 23rd to June 8th, 2000. We acquired more than 232 000
independent measurements. We also report on 48 hours of time-series photometric
observations in Aug 1996. We detected the non-radial g-modes consistent with
degree l=1 and radial order 8 to 20 and their linear combinations up to 6th
order.We also detect, for the first time, a high amplitude l=2 mode, with a
period of 796s. In the 2000 WET data, the largest amplitude modes are similar
to those detected with the WET observations of 1990 and 1994, but the highest
combination order previously detected was 4th order. At one point during the
1996 observations, most of the pulsation energy was transferred into the radial
order k=8 mode, which displayed a sinusoidal pulse shape in spite of the large
amplitude. The multiplet structure of the individual modes changes from year to
year, and during the 2000 observations only the k=9 mode displays clear normal
triplet structure. Even though the pulsation amplitudes change on timescales of
days and years, the eigenfrequencies remain essentially the same, showing the
stellar structure is not changing on any dynamical timescale.Comment: 34 pages, 14 figures, WET data, accepted to A&
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