Search for p-mode oscillations in DA white dwarfs with VLT-ULTRACAM. I. Upper limits to the p-modes

Abstract

The main goal of this project is to search for p-mode oscillations in a selected sample of DA white dwarfs near the blue edge of the DAV (g-mode) instability strip, where the p-modes should be excited following theoretical models. A set of high quality time-series data on nine targets has been obtained in 3 photometric bands (Sloan u', g', r') using ULTRACAM at the VLT with a typical time resolution of a few tens of ms. Such high resolution is required because theory predicts very short periods, of the order of a second, for the p-modes in white dwarfs. The data have been analyzed using Fourier transform and correlation analysis methods. Results: P-modes have not been detected in any of our targets. The upper limits obtained for the pulsation amplitude, typically less than 0.1%, are the smallest limits reported in the literature. The Nyquist frequencies are large enough to fully cover the frequency range of interest for the p-modes. For the brightest target of our sample, G 185-32, a p-mode oscillation with a relative amplitude of 5x10**(-4) would have been easily detected, as shown by a simple simulation. For G 185-32 we note an excess of power below ~2 Hz in all the three nights of observation, which might be due in principle to tens of low-amplitude close modes. However, neither correlation analysis nor Fourier transform of the amplitude spectrum show significant results. We also checked the possibility that the p-modes have a very short lifetime, shorter than the observing runs, by dividing each run in several subsets and analyzing these subsets independently. The amplitude spectra show only a few peaks with S/N ratio higher than 4 sigma but the same peaks are not detected in different subsets, as we would expect, and we do not see any indication of frequency spacing. As a secondary result of this project, ... (see the paper) Comment: 7 pages, 6 figures, Astronomy & Astrophysics in press

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arXiv:1011.4392v1 [astro-ph.SR] 19 Nov 2010
Astronomy & Astrophysics manuscript no. 15334s
November 22, 2010
c ? ESO 2010
Search for p-mode oscillations in DA white dwarfs with
VLT-ULTRACAM
I. Upper limits to the p-modes⋆
R. Silvotti1, G. Fontaine2, M. Pavlov3, T. R. Marsh4, V. S. Dhillon5, S. P. Littlefair5, F. Getman6
1INAF–Osservatorio Astronomico di Torino, strada dell’Osservatorio 20, 10025 Pino Torinese, Italy
e-mail: silvotti@oato.inaf.it
2D´ epartement de Physique, Universit´ e de Montr´ eal, C.P. 6128, Succ. Centre-Ville, Montr´ eal, Qu´ ebec H3C 3J7, Canada
e-mail: fontaine@astro.umontreal.ca
3Sternberg Astronomical Institute, Universitatskij Prospect 13, Moscow, Russia
e-mail: pav@sai.msu.ru
4Department of Physics, University of Warwick, Coventry CV4 7AL, UK
e-mail: t.r.marsh@warwick.ac.uk
5Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK
e-mail: vik.dhillon@sheffield.ac.uk; s.littlefair@sheffield.ac.uk
6INAF–Osservatorio Astronomico di Capodimonte, via Moiariello 16, 80131 Napoli, Italy
e-mail: tig@oacn.inaf.it
Received .... 2010 / Accepted .....
ABSTRACT
Aims. The main goal of this project is to search for p-mode oscillations in a selected sample of DA white dwarfs near the blue edge
of the DAV (g-mode) instability strip, where the p-modes should be excited following theoretical models.
Methods. A set of high quality time-series data on nine targets has been obtained in 3 photometric bands (Sloan u’, g’, r’) using
ULTRACAM at the VLT with a typical time resolution of a few tens of ms. Such high resolution is required because theory predicts
very short periods, of the order of a second, for the p-modes in white dwarfs. The data have been analyzed using Fourier transform
and correlation analysis methods.
Results. P-modes have not been detected in any of our targets. The upper limits obtained for the pulsation amplitude, typically less
than 0.1%, are the smallest limits reported in the literature. The Nyquist frequencies are large enough to fully cover the frequency
range of interest for the p-modes. For the brightest target of our sample, G 185-32, a p-mode oscillation with a relative amplitude
of 5×10−4would have been easily detected, as shown by a simple simulation. For G 185-32 we note an excess of power below ∼2
Hz in all the three nights of observation, which might be due in principle to tens of low-amplitude close modes. However, neither
correlation analysis nor Fourier transform of the amplitude spectrum show significant results. We also checked the possibility that the
p-modes have a very short lifetime,shorter than the observing runs, by dividing each run inseveral subsets and analyzing these subsets
independently. The amplitude spectra show only a few peaks with S/N ratio higher than 4 σ but the same peaks are not detected in
different subsets, as we would expect, and we do not see any indication of frequency spacing.
As a secondary result of this project, the detection of a new g-mode DAV pulsator near the blue edge of the ZZ Ceti instability strip
was claimed (Silvotti et al. 2006) and will be described in detail in a forthcoming paper (Silvotti et al. 2010, paper II).
Key words. stars: white dwarfs – stars: oscillations
1. Introduction
From the first detection of a pulsating white dwarf (Landolt
1968), the number of known white dwarf pulsators has grown
to the current number of almost two hundred, divided into three
(plus perhaps one) distinct groups along the WD cooling se-
quence (see Fontaine & Brassard 2008 and Winget & Kepler
2008 for recent reviews). All the pulsation periods detected so
far in white dwarfs, with values between about 2 and 35 min,
can be explained in terms of nonradial gravity mode (g-mode)
oscillations. These oscillations are well reproduced by adiabatic
and nonadiabatic theoretical models and white dwarf asteroseis-
Send offprint requests to: R. Silvotti
⋆Based on observations obtained at the ESO Paranal Observatory
(programme 075.D-0371).
mologyis capable of producingaccurate measurementsof mass,
rotation period, thickness of the external layers of hydrogen or
helium. An exhaustive review on white dwarf asteroseismology
is given by Fontaine et al. (2010).
However, the same theory predicts that also acoustic modes
(p-modes) could be excited in white dwarfs. These acoustic
modes are mostly sensitive to the structure of the inner core
(whereas the g-modes probe mainly the envelope)and have very
short periods, roughly between 0.1 and 10 seconds. Radial (p-
mode) oscillations in white dwarfs are predicted since a long
time (see Ostriker 1971 for a review of the early adiabatic work)
and the first quasi-adiabatic or nonadiabatic theoretical stud-
ies have shown that some of these modes should be excited
(Vauclair 1971, Cox et al. 1980). Using realistic atmospheric
compositions for DA white dwarfs, computations have shown

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2 R. Silvotti et al.: Search for p-mode oscillations in DA white dwarfs. I) Upper limits to the p-modes
that the blue edge of the radial instability strip lies at effective
temperatures slightly higher than for nonradial pulsations (Saio
et al. 1983, Starrfield et al. 1983) and a similar situation occurs
forDB whitedwarfs(Kawaler1993).ForbothDAandDB white
dwarfs, the maximum growth rates are obtained for high over-
tone modes, with periods of a few tenths of second, with a lower
limit near0.1s, set bytheatmosphericacousticcutoff(Saioet al.
1983,Hansen et al. 1985).For periodsshorter than this limit, the
reflective boundary condition at the surface is no longer valid.
Therefore the best period range to search for p-modes in white
dwarfs should be between ∼0.1 and about 1 s, with longer peri-
ods up to about 12 s (where the fundamental radial mode falls),
that should have a lower observability due to their lower growth
rates. The best DA white dwarf candidates should be those near
the DAV (or ZZ Ceti) g-mode instability strip and close to the
radial blue edge, as the growth rates become smaller moving to
the red.
From the observational side, high frequency p-mode pulsa-
tions have neverbeen detectedin white dwarfs.Robinson(1984)
reports the results on 19 DA white dwarfs (including 6 DAVs):
five of them were observed with a photoelectric photometer at
the 2.l m McDonald telescope using a time resolution of 0.05
or 0.1 s; the other 14 stars were observed in previous surveys
with smaller telescopes. The typical upper limits obtained were
1-2×10−3(relative amplitude) with a Nyquist limit between 5
and 10 Hz.
Kawaler et al. (1994), with the High Speed Photometer
aboard the HST, observed two DB white dwarfs with a time res-
olution of 10 ms: the DBV pulsator GD 358 and PG 0112+104,
a stable DB white dwarf with a slightly higher effective temper-
ature.
Our new attempt is focused on a sample of nine DA white
dwarfs near the blue edge of the DAV instability strip. The com-
bination of the large aperture of the VLT with the unique char-
acteristics of ULTRACAM (high speed and high efficiency in
3 bands simultaneously) provides an ideal research tool for this
project.
2. Targets, observations and data reduction
Most of the targets selected (six of them) are close to the blue
edge of the DAV (g-mode)instability strip, according to theoret-
ical expectations. Two of them, G 185-32and L 19-2,are known
DAV pulsators. A third DAV pulsator, GD 133, has been dis-
covered during our VLT run (Silvotti et al. 2006; 2010, paper
II). The other three targets lie in a larger range of effective tem-
peratures, in order to check whether the p-mode instability strip
might be shifted with respect to the expectations.
All the observations were performed in May 2005, when
ULTRACAM was mounted for the first time at the visitor focus
of the VLT UT3 (Melipal). ULTRACAM1(Dhillon et al. 2007)
is a portable ultrafast 3-CCD camera that can reach a maximum
speed of 300 frames per second in three photometric bands at
the same time, selected among the u’g’r’i’z’ filters of the Sloan
Digital Sky Survey (SDSS) photometric system.
All the targets were observed using the SDSS filters u′, g′
and r′during single runs with duration between 15 and 69 min-
utes. Only the brightest target, G 185-32, was observed in three
independent runs in order to push down as much as possible the
detection limit. We used exposure times between 9 and 376 ms,
dependingonmagnitudeandskyconditions.Furtherdetails con-
cerning targets and observations are given in Table 1.
1http://www.vikdhillon.staff.shef.ac.uk/ultracam/
Near each target, at an angular distance between 1.1 and
1.9 arcmin, we observed also a reference star in order to remove
the spurious effects introduced by variable sky conditions.
Data reduction was carried out using the ULTRACAM
pipeline (see Littlefair et al. 2008 for details). After bias and
flat field correction, we performed aperture photometry and we
computeddifferential photometrydividingthe target’s counts by
the counts of the stable star. Finally we applied the barycentric
correction to the times. In Fig. 1 the light curves of the nine tar-
gets are shown in a wide band obtained summing the g′and r′
counts. This “white light” has a higher S/N ratio and for this
reason it has been used in the first part of our analysis.
2.1. Sky stability on short time scales using a 8m class
telescope
In all our runs we see sky variations on time scales up to tens of
minutes that can reach amplitudes of 10% and even more. In our
best runs on HS 1443+2934 and L 19-2 these variations have
much smaller intensities (few thousandths) and the flux remains
constant within ∼3% during the whole observation. Our data al-
low to test the sky stability also on much shorter time scales,
down to tenths of seconds. An example is given in Fig. 2, where
we see that the variability on time scales from seconds to tens of
seconds resembles that of the typical transparency variations on
longer time scales (minutes to hours). These variations are co-
herent at angular distances of 1-2 arcmin, as we see comparing
target and reference star’s light curves. However, at higher fre-
quencies (>∼1 Hz), the spatial coherence is lost, as shown in the
small panels of Fig. 2.
3. Search for periodicities
Fig. 3shows the amplitudespectraof theelevenrunsin theg′+r′
band. The only significant peak at about 3.3 Hz in the spectrum
of HS 1253+1033 is a false detection which appears also in the
spectrum of the reference star alone. These amplitude spectra
were calculated using the flux ratios (target’s counts divided by
stable star’s counts). However, we have seen in Sect. 2.1 that
differential photometry is useful only at frequencies lower than
about 1 Hz (see Fig. 2 and Fig. 4). For this reason we calculated
also the amplitude spectra of the eleven runs using only the tar-
get’s counts. Again we did not detected any significant peak in
any of the spectra. Negative results were found also when using
the data of the single u′, g′and r′photometric bands.
Looking at Fig. 3, we note an excess of power below
∼2 Hz in all the three nights of observation on G 185-32,
the brightest target of our sample. This excess, which is only
marginally present in three other targets (L 19-2, GD 133 and
HS 1443+2934),couldbeduein principletotens ofclose modes
with low amplitude. However, when we look in detail to the
low frequency part of the spectra, we see that the low-amplitude
peaks are different from night to night, contrary to what we
wouldexpect(Fig.4).Totest thishypothesisingreaterdepth,we
can use one of the properties of the p-modes: the high-overtone
modes should be almost equally spaced in frequency(a constant
spacing is expected when the adiabatic sound speed is constant
in a star with an homogeneous composition). An almost con-
stant frequency spacing would be easily detected using correla-
tion analysis or through Fourier transform (FT) of the amplitude
spectrum(orFT2).Forall ourtargetswehaveusedbothmethods
without detecting any significant peak. An example is given in
Fig. 5, where FT2and autocorrelation function of G 185-32 are

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R. Silvotti et al.: Search for p-mode oscillations in DA white dwarfs. I) Upper limits to the p-modes3
Fig.1. Light curves of the eleven VLT runs in a wide photometric band obtained summing the g′and r′counts. The target’s counts
are divided by the counts of the stable star.
shown and compared with those of a synthetic run containing a
set of 20 equally spaced frequencies between 1.265 and 2.5 Hz
with same amplitude. (see caption of Fig. 5 for more details).
With relative amplitudesequal to 2×10−4, no synthetic sinusoids
are detected in the amplitude spectrum. With larger amplitudes
of 4×10−4(6×10−4), 8 out of 20 (20/20) sinusoids are found.
With 4×10−4(6×10−4) a significant peak is found also from cor-
relation analysis at 6 σ (17 σ), while FT2is less sensitive.
Another possibility that we have considered is that the p-
modes are not seen because of short life times. With life times
shorter than the observing runs, their amplitude in the Fourier
spectrum would be reduced due to phase incoherence and they
could escape detection. In order to verify also this possibility,
we have divided each run in a number of subruns of at least
14 s each and calculated the amplitude spectrum of each sub-
set. Then, an automated procedure has found all the peaks with
an amplitude higher than 3 times the local noise. The local noise
has been determined by fitting each amplitude spectrum with a
(smooth) cubic spline; an example of cubic spline interpolation
is shown in Fig. 5 (2ndcolumn). This procedure has been re-
peated for different size of the subsets, starting from 1,344 data
points and increasing the size by a factor of ∼2 at each itera-
tion. The results for the three runs on G 185-32 are illustrated
in Fig. 6. We see from this plot that only a few peaks with S/N
ratio higher than 4 σ are found but, also in this case, the same
peaks are not detected in different subsets, as we would expect.
Moreover,fromautocorrelationanalysiswedonotobtainanyin-
dication of frequencyspacing in these subsets. We conclude that

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4 R. Silvotti et al.: Search for p-mode oscillations in DA white dwarfs. I) Upper limits to the p-modes
Fig.2. Sky intensity fluctuations on time scales from tenths to tens of seconds (u′, g′and r′photometric bands). A section of the
light curve of G 185-32 (18 May 2005), with a duration of 1 min, is represented in the upper panels, while the reference star is
shown in the central panels. The average counts of each integration (8.8 ms) are reported. The lower panels show the intensity ratio
(target’s counts divided by reference star’s counts). This figure shows that on time scales longer than about 1 s it is essential to
have a reference star in order to reduce the sky fluctuations. However, for shorter time scales, the light curves of the target and the
reference star are not coherentanymore,as we can see from the small panels representinga short section (only 2 s) of the same light
curves. Note that the u′band has a different vertical scale in all panels.
also the possibility that the p-modes have very short life times is
not supported by our observations. This conclusion is valid for
all the targets of our sample.
4. Summary
We have not detected any significant peak in the amplitudespec-
tra of nine DA white dwarfs near the DAV instability strip in the
range of frequencies expected for the p-modes. The upper limits
that we have obtained for the pulsation amplitudes are reported
in Table 1, together with the main characteristics of the stars ob-
served. Thanks to the high efficiency of the VLT-ULTRACAM
system, our results move down the detection limit for the p-
modes in DA white dwarfs to less than 0.1% for most of our
targets. These limits are lower by a factor of about 2-3 (at same
magnitude level) respect to previous findings (Robinson 1984)
and the Nyquist frequencies are much larger,coveringthe whole
range of frequencies expected for the p-modes. For G 185-32,
the brightest target of our sample, an apparentexcess of poweris
seen below ∼2 Hz in all the three nights of observation but none
of our analysis allows us to deduce that this apparent excess of
power is indicative of the presence of p-modes. As shown by a
simple simulation, a peak with a relative amplitude of 6×10−4
(3×10−4) in the frequency range 1-3 Hz (3-10 Hz) would have
been easily detected in the amplitude spectrum of G 185-32.
In our analysis we have considered various possibilities that
could hide the p-modes (low amplitudes, very short life times)
and applied various techniques that can help to bring the signal
outofthenoise.Usingoneofthepropertiesofthehighovertones
p-modes, that should be almost equally spaced in frequency, we
have searched for a constant frequency spacing through corre-
lation analysis and Fourier transform of the amplitude spectrum
(FT2), without finding significant results. Then we have divided
each data set into several subsets of varying length and analyzed
each subset independently, again without finding any trace of
excited modes with very short life times.
Our results do not necessarily mean that the p-modes in DA
white dwarfs stars are not excited at all. As the p-modes act

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R. Silvotti et al.: Search for p-mode oscillations in DA white dwarfs. I) Upper limits to the p-modes5
Fig.3. Fourier amplitude spectra of the light curves of Fig. 1. For G 185-32 the high frequency tail, from 14.5 Hz to the Nyquist
frequencyat about 46.7 Hz, is not shown in this plot and does not contain any significant peak. The ordinate is in relative amplitude
× 1000, which is equivalent to milli-modulation amplitude units (mma, 1 mma=0.1%=1000 ppm). For two stars, WD 1338-0023
and HS 1253+1033, a different vertical scale has been used. The peak near 3.3 Hz in the spectrum of HS 1253+1033 is a false
detection (see text for details).
mainly in the vertical direction, and vertical motions are limited
by the huge gravity, a very low amplitude, below our detection
limit, would not be surprising. We will examine in a subsequent
publication with the help of detailed models how this can come
about. The upper limits reported in this paper can help to con-
strain the nonadiabatic models of the DA white dwarfs, which
have large uncertainties because of the convection.
Acknowledgements. ULTRACAM is supported by STFC grant PP/D002370/1.
S.P.L. acknowledges the support of an RCUK Fellowship and STFC grant
PP/E001777/1. G.F. acknowledges the contribution of the Canada Research
Chair Program. A first observational search for p-mode pulsations in DA white
dwarfs started in 2003, based on two observing runs at the SAO 6 m telescope
using the MANIA instrument. Because of bad weather conditions, both the ob-
serving runs did not produced useful data. R.S. and M.P. wish to thank Grigory
M. Beskin, Sergey V. Karpov and Vladimir L. Plokhotnichenko for the collabo-
ration to the observations and for their kind hospitality at the 6 m SAO telescope
in June 2004. Finally we thank the referee, Susan E. Thompson, for a careful
reading of the manuscript and for useful suggestions.
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