Note on fast spinning neutron stars with unified equations of states

For the propose of confronting updated pulsar observations with developed neutron star equation of states (EoSs), we employ four unified EoSs for both the core and the crust, namely BCPM, BSk20, BSk21, Shen-TM1, as well as two non-unified EoSs widely used in the literature, i.e. APR and GM1 EoS, which are commonly matched with the Negele-Vautherin and the Baym-Pethick-Sutherland crust EoS. All the core EoSs satisfy the recent observational constraints of the two massive pulsars whose masses are precisely measured. We show that the NS mass-equatorial radius relations are slightly affected by the smoothness at the core-crust matching interface. Moreover, the uncertainties in the crust EoS and the matching interface bring insignificant changes, even at maximally rotating (Keplerian) configurations. We also find that for all four unified EoSs, rotation can increase the star's gravitational mass up to $18\%-19\%$ and the equatorial radius by $29\%-36\%$, which are consistent with the previous calculations using non-unified EoSs. For stars as heavy as 1.4 M$_{\odot}$, the radius increase is more pronounced, reaching $41\%-43\%$, i.e. $5-6$ km. Moreover, by confronting the results using unified EoSs, which give the correct empirical values at saturation density, with two controversial determinations of the radius for the fast rotator 4U 1608-52, we address that a small radius may be better justified for this source.