Detectability of continuous gravitational waves from isolated neutron stars in the Milky Way. The population synthesis approach

Aims. We estimate the number of pulsars, detectable as continuous gravitational wave sources with the current and future gravitational-wave detectors, assuming a simple phenomenological model of evolving non-axisymmetry of the rotating neutron star. Methods. We employ a numerical model of the Galactic neutron star population, with the properties established by comparison with radio observations of isolated Galactic pulsars. We generate an arbitrarily large synthetic population of neutron stars and evolve their period, magnetic field, and position in space. We use a gravitational wave emission model based on exponentially decaying ellipticity - a non-axisymmetry of the star, with no assumption of the origin of a given ellipticity. We calculate the expected signal in a given detector for a 1 year observations and assume a detection criterion of the signal-to-noise ratio of 11.4 - comparable to a targeted continous wave search. We analyze the population detectable separately in each detector: Advanced LIGO, Advanced Virgo, and the planned Einstein Telescope. In the calculation of the expected signal we neglect signals frequency change due to the source spindown and the Earth motion with respect to the Solar barycentre. Results. With conservative values for the neutron stars evolution: supernova rate once per 100 years, initial ellipticity $\epsilon_{0}$ = 1e-5 with no decay of the ellipticity $\eta$ = $t_\rm{hub}$ = 1e4 Myr, the expected number of detected neutron stars is below one: 0.15 (based on a simulation of 10 M stars) for the Advanced LIGO detector. A broader study of the parameter space ($\epsilon_{0}$ , $\eta$) is presented. With the planned sensitivity for the Einstein Telescope, and assuming the same ellipiticity model, the expected detection number is: 26.4 pulsars during a 1-year long observing run.