Nonradial oscillation modes of compact stars with a crust

Oscillation modes of isolated compact stars can, in principle, be a fingerprint of the equation of state (EoS) of dense matter. We study the non-radial high-frequency $l=2$ spheroidal modes of neutron stars and strange quark stars, adopting a two-component model (core and crust) for these two types of stars. Using perturbed fluid equations in the relativistic Cowling approximation, we explore the effect of a strangelet or hadronic crust on the oscillation modes of strange stars. The results differ from the case of neutron stars with a crust. In comparison to fluid-only configurations, we find that a solid crust on top of a neutron star increases the $p$-mode frequency slightly with little effect on the $f$-mode frequency, whereas for strange stars, a strangelet crust on top of a quark core significantly increases the $f$-mode frequency with little effect on the $p$-mode frequency.

Figure 1

Mass-radius relation for homogeneous quark stars described by the EoS [Eq. (1)] with $B=48.34\mathrm{MeV}/{\mathrm{fm}}^3\left({\mu }_{\mathrm{crit}}=300\mathrm{MeV}\right)$ and $B=55.61\mathrm{MeV}/{\mathrm{fm}}^3\left({\mu }_{\mathrm{crit}}=310\mathrm{MeV}\right)$. The interaction parameter $a_4=0.7$ and $m_s=100\mathrm{MeV}$. Measured limits on the mass of PSR J1614-$2230\left(1.97\pm 0.04M_{\odot }\right)$ and PSR J0348-$0432\left(2.01\pm 0.04M_{\odot }\right)$ are shown.

Figure 2

Mass-radius curves for bare strange, hadronic, and hybrid stars based on the EoS discussed in the text. The values of $B$ and $a_4$ are varied to obtain configurations of bare/hybrid stars of varying maximum mass.

Figure 3

The $f$-mode frequencies for a hadronic star for SLy EoS with and without a solid BPS crust, compared with the GM1 and NL3 EoS.

Figure 4

The $f$-mode frequencies for a single-component (core only) strange quark star compared to the case with a strangelet crust. A large upward shift of 150–200 Hz occurs upon the addition of a strangelet crust.

Figure 5

The $p$-mode frequencies for a hadronic star for SLy EoS with and without a solid BPS crust. The acoustic wave speed is affected by the shear modulus of the crust, which implies that $p$-mode frequencies are slightly higher than the homogeneous case.

Figure 6

The $p$-mode frequencies for a single-component (core only) strange quark star compared to the case with a strangelet crust. The mode frequencies show very little change upon addition of the strangelet crust.