2007ApJ...654.1087F

We examine in this paper the nature of the intriguing small-frequency spacings that have been reported in the pulsation spectra of rapidly pulsating hot B subdwarf stars. It has been said that these mysterious and puzzling spacings should not be present if current models of these stars and their pulsations are any guide to reality. They lead to highly accurate fits to observed frequency data and have been suggested to contain valuable (but still encoded) information about the inner structure of sdB stars. The empirical relation that leads to such high-accuracy fits involves a zero-point frequency, two small-frequency spacings (a factor of 15-30 smaller than the so-called large-frequency spacing for acoustic modes in the asymptotic regime), and two sets of integers, all optimized to best match the observed frequencies. After investigating its true nature, we have to report that this empirical relation contains, in fact, no physical information and is a purely numerical artifact. In particular, we show that the two best-fit frequency spacings used in the proposed relation correspond basically to the largest common denominators between the real frequency spacings in the observed sequence: one acting on a coarse scale and the other on a finer scale. As common denominators, the numerical values of these spacings depend sensitively on the signal-to-noise ratio (S/N) of the observations and cannot therefore represent intrinsic properties of a pulsating star. We suggest that, for the time being, progress on the front of the asteroseismology of sdB stars might still best be done with the help of physical models such as those pioneered by Brassard et al.