Starquakes in millisecond pulsars and gravitational waves emission

Abstract

So far, only transient Gravitational waves (GWs) produced by catastrophic events of extra-galactic origin have been detected. However, it is generally believed that there should be also continuous sources of GWs within our galaxy, such as accreting neutron stars (NSs), that could in principle be detected in the next near future. In fact, in these objects, centrifugal forces can be so strong to break the neutron star crust (causing a starquake), thus producing a quadrupole moment responsible for the continuous emission of GWs. At equilibrium, the angular momentum gained by accretion and the one lost via GWs emission should balance each other, stopping the stellar spin-up. We hereinafter investigate the above physical picture within the framework of a Newtonian model describing compressible, non-magnetized and self-gravitating NSs. In particular, we calculate the rotational frequency need to break the stellar crust of an accreting pulsar and we estimate the upper limit for the ellipticity due to this event. We find that the maximum starquake-induced ellipticity ranges from 10−9 to 10−5, depending on the stellar mass and its equation of state. The corresponding equilibrium frequency that we calculate is in good agreement with observations and, for all the scenarios, it is below the higher NS frequency observed of 716.36 Hz. Finally, we also discuss possible observational constraints on the ellipticity upper limit of accreting pulsars.

Early Evolution of a Newborn Magnetar with Strong Precession Motion in GRB 180620A

“…It found that τ sd is longer than τ p by a factor of 4.21, indicating that the decreases of Ω p is faster than Ω s . Note that ǫ depends on the deformation of a newborn magnetar, which is mainly induced by its magnetic field and starquake (Mastrano et al 2018;Giliberti & Cambiotti 2022). The change of the magnetic field can be ignored in the early stage since its decay timescale is relatively long, and the deformation induced by the magnetic field can be regarded as a constant in the early stage (Turolla et al 2015).…”

Gravitational-wave evolution of newborn magnetars with different deformed structure

“…It is worth noting that the value of σ max is very uncertain. Reference [14] adopted a larger breaking strain σ max = 10 −1 , and found that the breaking frequency is in the range 200 − 600 Hz for a typical M = 1.4M of NS, while σ max = 10 −5 is adopted by [48], and found that the fracture frequency would be about two orders of magnitude smaller than that of 200 − 600 Hz. It means that the crust of the neutron star will be fractured when we change the frequency a little bit (a few Hz).…”

“…To date, many deformation mechanisms that enable an isolated system to emit GWs have been proposed in the literature [13][14][15][16][17][18][19]. Magnetars are generally believed to have strong magnetic fields [20][21][22][23][24][25][26], and the magnetic stress is too large for the magnetar to maintain a longlasting spherical structure [27].…”

“…Afterwards, they applied it to the relativity case, and found that the maximum deformation that can support the crust of neutron star is two orders lower than the Newtonian case [31]. On the other hand, strong centrifugal forces in such magnetars can also break the NS's crust to result in starquakes, and form an asymmetric structure of the star [14]. Moreover, magnetars can be born in the core collapse of a massive star [32][33][34] or from the merger of binary stars [35][36][37][38].…”

“…The evolution of inclination angle is also considered in their study, which found that the magnetic axis is orthogonal to the axis of rotation immediately after the birth of the star, which causes the accretion column to produce time-varying quadrupoles and GW radiation [39]. In previous studies, several magnetar deformation mechanisms were even adopted to power the GW signals, but the authors did not consider simultaneously the contributions of all possible deformation mechanisms [13][14][15][16][17][18][19].…”