White dwarf stars as strange quark matter detectors - II

Abstract

We study the properties of the non-radial pulsations of strange dwarf stars. These objects are white dwarfs (WDs) with a compact core made up of strange quark matter (SQM). We show that the SQM core compresses the surrounding normal matter strongly enough to give rise to the occurrence of a sharp peak in the Brunt-Väisälä frequency. This, in turn, allows for the existence of a completely new resonant cavity for gravity (g-) modes, which is absent in standard WDs. We study the cases in which the mass of the SQM core is 10-2, 10-3, 10-4 and 10-5 of the total stellar mass, which have been added to a 0.525 M⊙ WD model adequate to account for the period structure of the DAV G117B15A, showing that this new resonant cavity is present for such a large range of core mass fractions. Due to the extremely short wavelength of g-modes in the new resonant cavity, we treat oscillations there with an asymptotic analysis up to an intermediate, evanescent zone (located at ≈10 per cent of the stellar radius). At such a point, we consider the asymptotic treatment as a boundary condition for a self-consistent numerical calculation of the g-mode spectrum of oscillations. In particular, we consider dipolar oscillations, which are currently identified with the observed oscillations in standard WDs. We find a very distinctive signal for the presence of a SQM core inside a WD: the difference of periods between two consecutive modes is far shorter than it is in standard WDs due to the oscillations in the new resonant cavity, being even shorter than a second. This confirms previous expectations based on very simplified calculations. Our calculations indicate that, while the period spacing between consecutive modes is a smooth function of the period, the square of the amplitude of the modes near the SQM core is a strongly varying function. While some modes will have large amplitude there, and thus large kinetic energy, others will have far lower energy. Then, if (as usual) we assume that the excited modes are those with low kinetic energy, we expect a very particular spectrum of dipolar oscillations of WDs with SQM cores. The spectrum should be characterized by several well-detached sets of a very large number of evenly (in period) spaced modes. This should be considered as a clearly distinctive, observable signature of the presence of SQM inside WDs.