Shapiro Delay of Pulsar J1640$+$2224

Pulsar J1640$+$2224 is a binary millisecond pulsar with a white dwarf companion and is being used in pulsar timing arrays being used in experiments to detect gravitational waves. A previous study of the system's Shapiro Delay by L\"{o}hmer et al, 2005 constrained the companion mass to m2 $=$0.15$+$0.08 -0.05 Msolar which would imply an unprecedentedly low pulsar mass. We improved their result by analyzing pulsar timing data from four different radio telescopes: the Effelsberg 100m radio telescope in Germany, the Westerbork Synthesis Radio Telescope in the Netherlands, the Nan\c{c}ay radio telescope in France, and the Lovell radio telescope at Jodrell Bank in the United Kingdom. Our study constrains the companion mass to m2$=$0.28$+$0.35 -0.03 Msolar and the pulsar mass to m1$=$1.51$+$3.30 -0.22 Msolar. The relatively wide orbit in which this pulsar resides (period $\sim$ 6 months) complicates this analysis as it introduces covariances with the Earth's motion. Continued monitoring should therefore allow further improvements to this mass measurement.