Gravitational wave emission from a magnetically deformed non-barotropic neutron star

Abstract

A strong candidate for a source of gravitational waves is a highly magnetized, rapidly rotating neutron star (magnetar) deformed by internal magnetic stresses. We calculate the mass quadrupole moment by perturbing a zeroth‐order hydrostatic equilibrium by an axisymmetric magnetic field with a linked poloidal–toroidal structure. In this work, we do not require the model star to obey a barotropic equation of state (as a realistic neutron star is not barotropic), allowing us to explore the hydromagnetic equilibria with fewer constraints. We derive the relation between the ratio of poloidal to total field energy Λ and ellipticity ε, and briefly compare our results to those obtained using the barotropic assumption. Then, we present some examples of how our results can be applied to astrophysical contexts. First, we show how our formulae, in conjunction with current gravitational wave (non‐)detections of the Crab pulsar and the Cassiopeia A central compact object (Cas A CCO), can be used to constrain the strength of the internal toroidal fields of those objects. We find that, for the Crab pulsar (whose canonical equatorial dipole field strength, inferred from spin‐down, is 4 × 108 T) to emit detectable gravitational radiation, the neutron star must have a strong toroidal field component, with maximum internal toroidal field strength Btm= 7 × 1012 T; for gravitational waves to be detected from the Cas A CCO at 300 Hz, Btm∼ 1013 T, whereas detection at 100 Hz would require Btm∼ 1014 T. Using our results, we also show how the gravitational wave signal emitted by a magnetar immediately after its birth (assuming it is born rapidly rotating, with Λ≲ 0.2) makes such a newborn magnetar a stronger candidate for gravitational wave detection than, for example, an SGR giant flare.

Stably stratified magnetized stars in general relativity

“…By using a relation h e ν = const., which is satisfied for nonmagnetized "isentropic" spherical stars, we also show for isentropic stars with no meridional flow that basic equations of Ref. [23], (75), (94), (95), and (100) -(103), become equivalent to our basic equations, (56), and (74) -(79) (but note some differences in notation and definition of physical quantities, e.g., theirL corresponds to our L). Here, it should be emphasized that the parameterC associated with the strength of the meridional flow does not appear in the equations of Ref.…”

“…However, at the moment, no definite conclusion has been obtained. A reason that non-stratified magnetized stars are employed for the stability analyses in general relativity is that no model of stratified magnetized stars have been constructed, although in the framework of Newtonian dynamics, magnetized stars with stable stratification due to composition gradients have been obtained [56][57][58].…”

Gravitational radiation from neutron stars deformed by crustal Hall drift

“…We present the results of the numerical magneto-thermal simulation by Viganò et al (2012) and Geppert & Viganò (2014) in Section 2.1, we recap the essentials of the density perturbation calculation in a non-barotropic star (Mastrano et al 2011(Mastrano et al , 2015 in Section 2.2, and we discuss the importance of the magnetic dipole moment and how it is calculated in Section 2.3.…”

“…We begin by decomposing the magnetic field into its poloidal and toroidal components and express it in dimensionless spherical polar coordinates (r, θ, φ), such that the stellar surface is located at r = 1 (Chandrasekhar 1956;Mastrano et al 2011;Mastrano & Melatos 2012;Mastrano et al 2013), viz.…”

“…The zeroth-order density profile ρ(r) is chosen to be that of an n = 1 polytropic star [unlike, e.g., Mastrano et al (2011) and Mastrano et al (2015)]…”