Incompressible analytical models for spinning-down pulsars

Abstract

We study a class of Newtonian models for the deformations of non-magnetized neutron stars during their spin-down. The models have all an analytical solution, and thus allow to understand easily the dependence of the strain on the star's main physical quantities, such as radius, mass and crust thickness. In the first "historical" model the star is assumed to be comprised of a fluid core and an elastic crust with the same density. We compare the response of stars with different masses and equations of state to a decreasing centrifugal force, finding smaller deformations for heavier stars: the strain angle is peaked at the equator and turns out to be a decreasing function of the mass.We introduce a second, more refined, model in which the core and the crust have different densities and the gravitational potential of the deformed body is self-consistently accounted for. Also in this case the strain angle is a decreasing function of the stellar mass, but its maximum value is at the poles and is always larger than the corresponding one in the one-density model by a factor of two. Finally, within the present analytic approach, it is possible to estimate easily the impact of the Cowling approximation: neglecting the perturbations of the gravitational potential, the strain angle is 40% of the one obtained with the complete model.

Revisiting neutron starquakes caused by spin-down

“…Up to this point, the model is identical to that of Franco et al (2000). However, as recently done by Giliberti et al (2019), we allow for different densities in the two domains, ρ s in the elastic, solid crust, and ρ f = ρ s (1 + ∆ ρ) in the fluid core, which will be seen to make an important difference.…”

“…when they are not, i. e., in the Cowling approximation. In both equations, P and Q are functions whose precise form is unimportant for the present argument, and we have neglected higherorder terms in t and β (q and χ 2 , in the notation of Giliberti et al 2019), both of which are assumed to be small. From our equations ( 62) and ( 63), we see that the rigidity parameter depends on the fractional difference between the displacements for a purely fluid star ( β = 0) and a star with an elastic crust ( β 0),…”

“…Recently, Giliberti et al (2020) calculated numerically the centrifugal deformation of a (Newtonian) polytropic star with different adiabatic indices and confirmed that, although the value of the adiabatic index has some effect on the deformations, the strain accumulated between successive glitches of the Vela pul-sar is in all cases much too small to break the crust; therefore, if starquakes are invoked to trigger glitches, the crust must always remain close to the breaking strain. The same authors (Giliberti et al 2019) calculated analytically the centrifugal deformation for a star with uniform, but possibly different densities in the fluid core and the elastic crust. Among other things, they analyzed the effect of the Cowling approximation (neglecting perturbations of the gravitational potential; Cowling 1941) for the case of equal densities in the crust and the core, finding that the displacements with this approximation are ≈ 2/5 of those for the exact solution.…”

“…In the present paper, we consider the same simple model as Giliberti et al (2019), namely a Newtonian star with uniform, but possibly different densities in the fluid core and the solid crust. 1 In order not to overcomplicate this already quite difficult problem, we apply the Cowling approximation, neglecting the gravitational potential perturbations in our calculations, but making an approximate correction for it at the end.…”

Constraining mechanism associated with fast radio burst and glitch from SGR J1935

“…A large b is conductive to produce large glitches. Crustquake model of NSs have been developed recently (Giliberti et al 2019(Giliberti et al , 2020Rencoret, Aguilera-Gómez, & Reisenegger 2021), which got challenged compared with observations. Previously, Baym & Pines found that, crustquakes of NSs encountered difficulty in explaining the frequent and large glitches (∆ν/ν ∼ 10 −6 ) in the Vela pulsar, unless the Vela pulsar is a lightest NS and glitch of size ∼ 10 −6 is an extremely unusual event (Baym & Pines 1971).…”