Sco X-1 as a continuous gravitational waves source: modelling the secular evolution using MESA

We study the prospects for detecting continuous gravitational waves (GWs) from Sco X-1 and evaluate the most likely waveform and progenitor parameters. We model the spin of the neutron star by the accretion torque and the gravitational-wave torque, considering two mechanisms for generating the non-axisymmetry responsible for the latter: magnetic mountains and crustal breakage deformation. Both torques are intertwined with the binary evolution, which we trace from the formation of the NS in a binary system with a main-sequence companion. We do this with MESA, starting from a set of initial binary configurations. At current sensitivity, a magnetic ellipticity of $\varepsilon\gtrsim 10^{-6}$ is necessary for detection. The highest frequency at which we have detectable signals increases with the accretion efficiency $\eta$, and it can be as high as 360Hz. At 3G (Cosmic Explorer/Einstein telescope) sensitivity, less deformed Sco X-1 NSs, with ellipticities as small as $6\cdot 10^{-9}$, are detectable, but the waveform highly depends on the binary system: the highest frequency of detectable signals spans the very broad range 600-1700Hz, strongly depending on $\eta$ and mass of the progenitor donor star $M^d$. If $\eta\leq$30%, the crust does not break. For $\eta\in$[40%,60%] only progenitors with $M^d\geq[1.1,1.5]M_{\odot}$ present crustal breakage, while if $\eta\geq$70% all crusts break. In some systems, the crust breaks during their Sco X-1 phase. If Sco X-1 were one of those systems, it would be emitting a very loud GW signal sweeping from O(1000)Hz down to torque-balance frequencies in $\approx 150000[\varepsilon /10^{-5}]^{-2/5}$ years. We estimate the current detection probability for this signal to be under 1%; this probability increases substantially - to around 41% - with 3G detectors.