Targeted search for the stochastic gravitational-wave background from the galactic millisecond pulsar population

The millisecond pulsars, old-recycled objects spinning with high frequency $\mathcal{O}$ (kHz) sustaining the deformation from their spherical shape, may emit gravitational waves (GW). These are one of the potential candidates contributing to the anisotropic stochastic gravitational-wave background (SGWB) observable in the ground-based GW detectors. Here, we present the results from a likelihood-based targeted search for the SGWB due to millisecond pulsars in the Milky Way, by analyzing the data from the first three observing runs of Advanced LIGO and Advanced Virgo detector. We assume that the shape of SGWB power spectra and the sky distribution is known \textit{a priori} from the population synthesis model. The information of the ensemble source properties, i.e., the in-band number of pulsars, $N_{\textrm{obs}}$ and the averaged ellipticity, $\mu_\epsilon$ is encoded in the maximum likelihood statistic. We do not find significant evidence for the SGWB signal from the considered source population. The best Bayesian upper limit with $95\%$ confidence for the parameters are $N_{\textrm{obs}}\leq8.8\times10^{4}$ and $\mu_\epsilon\leq1.4\times10^{-6}$, which is comparable to the bounds on mean ellipticity with the GW observations of the individual pulsars. Finally, we show that for the plausible case of $N_{\textrm{obs}}=40,000$, with the one year of observations, the one-sigma sensitivity on $\mu_\epsilon$ might reach $1.5\times10^{-7}$ and $4.1\times10^{-8}$ for the second-generation detector network having A+ sensitivity and third-generation detector network, respectively.