Mode Identification from Combination Frequency Amplitudes in ZZ Ceti Stars

Abstract

The lightcurves of variable DA stars are usually multi-periodic and nonsinusoidal, 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 and 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 (ℓ) of the modes that produce them. We find that modes with ℓ > 2 are easily identifiable as high ℓ based on their combination frequencies alone. Distinguishing between ℓ = 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 four-meter class telescopes.

Toward ensemble asteroseismology of ZZ Ceti stars with fully evolutionary models

“… a Bognár & Paparó (2010), b Yeates et al (2005), c Bischoff‐Kim (2009), d Vauclair et al (2000), e Voss et al (2006), f Pakštienė et al (2011), g Bognár et al (2009), h Bradley (1995). …”

First Kepler results on compact pulsators - III. Subdwarf B stars with V1093 Her and hybrid (DW Lyn) type pulsations

“…Typically, a key to discerning interior conditions of stars is the association of frequencies with pulsation modes. It is possible that the asymptotic approach, as has been applied to KIC010670103, or possible combination frequencies, as has been done for ZZ Ceti stars (Yeates et al 2005), may be useful for determining modes. Such constraints could be very useful for distinguishing between various models and between various modelling methods, and help with mismatches between observed and theoretical period distributions.…”

White Dwarf Period Tables I. Pulsators with hydrogen-dominated atmospheres

“…• Identifiers: the first column shows the star's identifier in WD (J)HHMM±DDM(M) format, while the second column shows another identifier used in the literature or can be used to identify the object in the SIMBAD database (Wenger et al 2000). The identifiers in parentheses are not recognized by SIMBAD, but used in the literature.…”