Mode Identification from Combination Frequency Amplitudes in ZZ Ceti Stars

Abstract

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.

73 pages, 22 figures, accepted in the ApJ

References in corpus (11)

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• On the Purity of the ZZ Ceti Instability Strip: Discovery of More Pulsating DA White Dwarfs on the Basis of Optical Spectroscopy
• Combination Frequencies in the Fourier Spectra of White Dwarfs
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• A CCD Time-Series Photometer
• Surface motion in the pulsating DA white dwarf G 29-38
• Mode identification from time-resolved spectroscopy of the pulsating white dwarf G 29-38
• Mode identification of Pulsating White Dwarfs using the HST
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• Empirical Determination of Convection Parameters in White Dwarfs I : Whole Earth Telescope Observations of EC14012-1446
• 2006 Whole Earth Telescope Observations of GD358: A New Look at the Prototype DBV
• Discovery of a ZZ Ceti in the Kepler Mission Field
• TESS first look at evolved compact pulsators: Known ZZ Ceti stars of the southern ecliptic hemisphere as seen by TESS
• Whole Earth Telescope observations of the hot helium atmosphere pulsating white dwarf EC 20058-5234
• A New Timescale for Period Change in the Pulsating DA White Dwarf WD 0111+0018
• A Non-Radial Oscillation Model for Pulsar State Switching
• New Pulsating White Dwarfs in Cataclysmic Variables
• Pulsational Mapping of Calcium Across the Surface of a White Dwarf
• Deciphering the Pulsations of G 29-38 with Optical Time Series Spectroscopy
• The pulsating DA white dwarf star EC 14012-1446: results from four epochs of time-resolved photometry
• Kepler and TESS Observations of PG 1159-035
• ZZ Ceti stars of the southern ecliptic hemisphere re-observed by TESS
• Mode identification in the high-amplitude δ Scuti star V2367 Cyg
• Seismic test of the mass-radius relationship of hydrogen-atmospheric white dwarf stars