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Register a new userDecoupling of superfluid and normal modes in pulsating neutron stars
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We show that equations governing pulsations of superfluid neutron stars can be splitted into two sets of weakly coupled equations, one describing the superfluid modes and another one -- the normal modes. The coupling parameter s is small, |s| ~ 0.01-0.05, for realistic equations of state. Already an approximation s=0 is sufficient to calculate the pulsation spectrum within the accuracy of a few percents. Our results indicate, in particular, that emission of gravitational waves from superfluid pulsation modes is suppressed in comparison to that from normal modes. The proposed approach allows to drastically simplify modeling of pulsations of superfluid neutron stars.
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We study the effects of finite stellar temperatures on the oscillations of superfluid neutron stars. The importance of these effects is illustrated with a simple example of a radially pulsating general relativistic star. Two main effects are taken into account: (i) temperature dependence of the entrainment matrix and (ii) the variation of the size of superfluid region with temperature. Four models are considered, which include either one or both of these two effects. Pulsation spectra are calculated for these models, and asymptotes for eigenfrequencies at temperatures close to critical temperature of neutron superfluidity, are derived. It is demonstrated that models that allow for the temperature effect (ii) but disregard the effect (i), yield unrealistic results. Eigenfunctions for the normal- and superfluid-type pulsations are analyzed. It is shown that superfluid pulsation modes practically do not appear at the neutron-star surface and, therefore, can hardly be observed by measuring the modulation of the electromagnetic radiation from the star. The e-folding times for damping of pulsations due to the shear viscosity and nonequilibrium modified Urca processes are calculated and their asymptotes at temperatures close to the neutron critical temperature, are obtained. It is demonstrated that superfluid pulsation modes are damped by 1--3 orders of magnitude faster than normal modes.
We study non-radial oscillations of neutron stars with superfluid baryons, in a general relativistic framework, including finite temperature effects. Using a perturbative approach, we derive the equations describing stellar oscillations, which we solve by numerical integration, employing different models of nucleon superfluidity, and determining frequencies and gravitational damping times of the quasi-normal modes. As expected by previous results, we find two classes of modes, associated to superfluid and non-superfluid degrees of freedom, respectively. We study the temperature dependence of the modes, finding that at specific values of the temperature, the frequencies of the two classes of quasi-normal modes show avoided crossings, and their damping times become comparable. We also show that, when the temperature is not close to the avoided crossings, the frequencies of the modes can be accurately computed by neglecting the coupling between normal and superfluid degrees of freedom. Our results have potential implications on the gravitational wave emission from neutron stars.
We analyse the oscillations of general relativistic superfluid hyperon stars, following the approach suggested by Gusakov & Kantor and Gusakov et al. and generalizing it to the nucleon-hyperon matter. We show that the equations governing the oscillations can be split into two weakly coupled systems with the coupling parameters $s_{rm e}$, $s_{rm mu}$, and $s_{rm str}$. The approximation $s_{rm e} = s_{rm mu} = s_{rm str} = 0$ (decoupling approximation) allows one to drastically simplify the calculations of stellar oscillation spectra. An efficiency of the presented scheme is illustrated by the calculation of sound speeds in the nucleon-hyperon matter composed of neutrons (n), protons (p), electrons (e), muons ($mu$), as well as $rm Lambda$, ${rm Xi}^-$, and ${rm Xi}^0$-hyperons. However, the gravity oscillation modes (g-modes) cannot be treated within this approach, and we discuss them separately. For the first time we study the composition g-modes in superfluid hyperon stars with the $rm npemuLambda$ core and show that there are two types of g-modes (`muonic and `$Lambda$--hyperonic) in such stars. We also calculate the g-mode spectrum and find out that the eigenfrequencies $ u$ of the superfluid g-modes can be exceptionally large (up to $ u approx 742~{rm Hz}$ for a considered stellar model).
For the first time nonradial oscillations of superfluid nonrotating stars are self-consistently studied at finite stellar temperatures. We apply a realistic equation of state and realistic density dependent model of critical temperature of neutron and proton superfluidity. In particular, we discuss three-layer configurations of a star with no neutron superfluidity at the centre and in the outer region of the core but with superfluid intermediate region. We show, that oscillation spectra contain a set of modes whose frequencies can be very sensitive to temperature variations. Fast temporal evolution of the pulsation spectrum in the course of neutron star cooling is also analysed.
We demonstrate a possibility of existence of a peculiar temperature-dependent composition $g$-modes in superfluid neutron stars. We calculate the Brunt-V$ddot{rm a}$is$ddot{rm a}$l$ddot{rm a}$ frequency for these modes, as well as their eigenfrequencies. The latter turn out to be rather large, up to $sim 500$ Hz for a chosen model of a neutron star. This result indicates, in particular, that use of the barotropic equation of state may be not a good approximation for calculation of inertial modes even in most rapidly rotating superfluid neutron stars.
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