Quark deconfinement in neutron star cores: The effects of spin-down

We study the role of spin-down in driving quark deconfinement in the high density core of isolated neutron stars. Assuming spin-down to be solely due to magnetic braking, we obtain typical timescales to quark deconfinement for neutron stars that are born with Keplerian frequencies. Employing different equations of state (EOS), we determine the minimum and maximum neutron star masses that will allow for deconfinement via spin-down only. We find that the time to reach deconfinement is strongly dependent on the magnetic field and that this time is least for EOS that support the largest minimum mass at zero spin, unless rotational effects on stellar structure are large. For a fiducial critical density of $5\rho_0$ for the transition to the quark phase ($\rho_0=2.5\times10^{14}$g/cm$^3$ is the saturation density of nuclear matter), we find that neutron stars lighter than $1.5M_{\odot}$ cannot reach a deconfined phase. Depending on the EOS, neutron stars of more than $1.5M_{\odot}$ can enter a quark phase only if they are spinning faster than about 3 milliseconds as observed now, whereas larger spin periods imply that they are either already quark stars or will never become one.