Starquakes in millisecond pulsars and gravitational waves emission

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 NS 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.