Upgraded Giant Metrewave Radio Telescope timing of NGC 1851A: a possible millisecond pulsar-neutron star system

(abridged) In this work we present the results of one year of upgraded Giant Metrewave Radio Telescope timing measurements of PSR~J0514$-$4002A, a 4.99-ms pulsar in a 18.8-day, eccentric ($e \, =\, 0.89$) orbit with a massive companion located in the globular cluster NGC~1851. Combining these data with earlier Green Bank Telescope data, we greatly improve the precision of the rate of advance of periastron, $\dot{\omega} \, = \, 0.0129592(16)\, \deg \, \rm yr^{-1}$ which, assuming the validity of general relativity, results in a much refined measurement of the total mass of the binary, $M_{\rm tot} \, = \, 2.4730(6) \, M_{\odot}$. Additionally, we measure the Einstein delay parameter, $\gamma\,, = \, 0.0216(9) \, \rm s$. Furthermore, we measure the proper motion of the system ($\mu_{\alpha} \, = \, 5.19(22)$ and $\mu_{\delta} = -0.56(25)\rm~mas ~ yr^{-1}$), which is not only important for analyzing its motion in the cluster, but is also essential for a proper interpretation of $\gamma$, given the latter parameter's correlation with the variation of the projected semi-major axis. The measurements of $\gamma$ and the proper motion enable a separation of the system component masses: we obtain a pulsar mass of $M_{p} \, = \, 1.25^{+0.05}_{-0.06} \, M_{\odot}$ and a companion mass of $M_{c} \, = \, 1.22^{+0.06}_{-0.05} \, M_{\odot}$. This raises the possibility that the companion is also a neutron star. Searches for radio pulsations from the companion have thus far been unsuccessful, hence we cannot confirm the latter hypothesis. The low mass of this millisecond pulsar - one of the lowest ever measured for such objects - clearly indicates that the recycling process can be achieved with a relatively small amount of mass transfer.