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Register a new userRelativistic tidal properties of superfluid neutron stars
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We investigate the tidal deformability of a superfluid neutron star. We calculate the equilibrium structure in the general relativistic two-fluid formalism with entrainment effect where we take neutron superfluid as one fluid and the other fluid is comprised of protons and electrons, making it a charge neutral fluid. We use a relativistic mean field model for the equation of state of matter where the interaction between baryons is mediated by the exchange $sigma$, $omega$ and $rho$ mesons. Then, we study the linear, static $l=2$ perturbation on the star to compute the electric-type Love number following Hinderers prescription.
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We explore in a parameterized manner a very large range of physically plausible equations of state (EOSs) for compact stars for matter that is either purely hadronic or that exhibits a phase transition. In particular, we produce two classes of EOSs with and without phase transitions, each containing one million EOSs. We then impose constraints on the maximum mass, ($M < 2.16 M_{odot}$), and on the dimensionless tidal deformability ($tilde{Lambda} <800$) deduced from GW170817, together with recent suggestions of lower limits on $tilde{Lambda}$. Exploiting more than $10^9$ equilibrium models for each class of EOSs, we produce distribution functions of all the stellar properties and determine, among other quantities, the radius that is statistically most probable for any value of the stellar mass. In this way, we deduce that the radius of a purely hadronic neutron star with a representative mass of $1.4,M_{odot}$ is constrained to be $12.00!<!R_{1.4}/{rm km}!<!13.45$ at a $2$-$sigma$ confidence level, with a most likely value of $bar{R}_{1.4}=12.39,{rm km}$; similarly, the smallest dimensionless tidal deformability is $tilde{Lambda}_{1.4}!>!375$, again at a $2$-$sigma$ level. On the other hand, because EOSs with a phase transition allow for very compact stars on the so-called `twin-star branch, small radii are possible with such EOSs although not probable, i.e. $8.53!<!R_{1.4}/{rm km}!<!13.74$ and $bar{R}_{1.4}=13.06,{rm km}$ at a $2$-$sigma$ level, with $tilde{Lambda}_{1.4}!>!35.5$ at a $3$-$sigma$ level. Finally, since these EOSs exhibit upper limits on $tilde{Lambda}$, the detection of a binary with total mass of $3.4,M_{odot}$ and $tilde{Lambda}_{1.7}!>!461$ can rule out twin-star solutions.
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 study the effect of superfluidity on the tidal response of a neutron star in a general relativistic framework. In this work, we take a dual-layer approach where the superfluid matter is confined in the core of the star. Then, the superfluid core is encapsulated with an envelope of ordinary matter fluid which acts effectively as the low-density crustal region of the star. In the core, the matter content is described by a two-fluid model where only the neutrons are taken as superfluid and the other fluid consists of protons and electrons making it charge neutral. We calculate the values of various tidal love numbers of a neutron star and discuss how they are affected due to the presence of entrainment between the two fluids in the core. We also emphasize that more than one tidal parameter is necessary to probe superfluidity with the gravitational wave from the binary inspiral.
We analyze damping of oscillations of general relativistic superfluid neutron stars. To this aim we extend the method of decoupling of superfluid and normal oscillation modes first suggested in [Gusakov & Kantor PRD 83, 081304(R) (2011)]. All calculations are made self-consistently within the finite temperature superfluid hydrodynamics. The general analytic formulas are derived for damping times due to the shear and bulk viscosities. These formulas describe both normal and superfluid neutron stars and are valid for oscillation modes of arbitrary multipolarity. We show that: (i) use of the ordinary one-fluid hydrodynamics is a good approximation, for most of the stellar temperatures, if one is interested in calculation of the damping times of normal f-modes; (ii) for radial and p-modes such an approximation is poor; (iii) the temperature dependence of damping times undergoes a set of rapid changes associated with resonance coupling of neighboring oscillation modes. The latter effect can substantially accelerate viscous damping of normal modes in certain stages of neutron-star thermal evolution.
In the late inspiral phase, gravitational waves from binary neutron star mergers carry the imprint of the equation of state due to the tidally deformed structure of the components. If the stars contain solid crusts, then their shear modulus can affect the deformability of the star and, thereby, modify the emitted signal. Here, we investigate the effect of realistic equations of state (EOSs) of the crustal matter, with a realistic model for the shear modulus of the stellar crust in a fully general relativistic framework. This allows us to systematically study the deviations that are expected from fluid models. In particular, we use unified EOSs, both relativistic and non-relativistic, in our calculations. We find that realistic EOSs of crusts cause a small correction, of $sim 1%$, in the second Love number. This correction will likely be subdominant to the statistical error expected in LIGO-Virgo observations at their respective advanced design sensitivities, but rival that error in third generation detectors. For completeness, we also study the effect of crustal shear on the magnetic-type Love number and find it to be much smaller.
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