Decade-long Timing Study of the Black Widow Millisecond Pulsar J1544+4937

Results from 11 yr of radio timing for the eclipsing black widow millisecond pulsar (MSP) binary J1544+4937 is presented in this paper. We report a phase-connected timing model for this MSP, using observations with the Giant Metrewave Radio Telescope (GMRT) at multiple frequencies and with the Green Bank Telescope. This is the longest-duration timing study of any galactic-field MSP with the GMRT. While extending the timing baseline from the existing 1.5 yr to about a decade we report the first detection for a significant value of proper motion (mu (T) similar to 10.14(5) mas yr(-1)) for this pulsar. Temporal variations of dispersion measure (Delta DM similar to 10(-3) pc cm(-3)) manifested by significant determination of first-, second-, and third-order dispersion measure (DM) derivatives are observed along the line of sight to the pulsar. We also noticed frequency-dependent DM variations of the order of 10(-3) pc cm(-3), which could arise due to spatial electron density variations in the interstellar medium. This study has revealed a secular variation of the orbital period for this MSP for the first time. We investigated possible causes and propose that variation in the gravitational quadrupole moment of the companion could be responsible for the observed temporal changes in the orbital period.