Discovery and Timing of Four $\gamma$-ray Millisecond Pulsars

We discovered four millisecond pulsars (MSPs) in searches of 80 $\gamma$-ray sources conducted from 2015 to 2017 with the Murriyang radio telescope of the Parkes Observatory. We provide an overview of the survey and focus on the results of a follow-up pulsar timing campaign. Using Fermi Large Area Telescope data, we have detected $\gamma$-ray pulsations from all four pulsars, and by combining radio and $\gamma$-ray data we obtain improved timing solutions. We also provide flux density distributions for the radio pulsars and flux-calibrated and phase-aligned radio and $\gamma$-ray pulse profiles. Some of the pulsars may be suitable for radio pulsar timing array experiments. PSR J0646-5455, PSR J1803-4719, and PSR J2045-6837 are in typical, nearly circular white dwarf binaries with residual eccentricities proportional to their binary periods. PSR J1833-3840 is a black widow pulsar with the longest known period, Pb = 0.9 d, and a very soft radio spectrum. PSR J0646-5455 has a strong, Vela-like $\gamma$-ray pulse profile and is suitable for inclusion in the $\gamma$-ray Pulsar Timing Array (GPTA). Despite this, it is possibly one of the lowest-efficiency $\gamma$-ray MSPs known. Indeed, all four new $\gamma$-ray MSPs have lower-than-average efficiency, a potential indication of bias in earlier searches. Finally, we retrospectively evaluate the efficiency of this survey: while only four new MSPs were directly discovered, subsequent campaigns have found pulsars in a further 19 of our targets, an excellent 30% efficiency.