Orbital Parameters of the PSR B1620-26 Triple System

Previous timing data for PSR~B1620$-$26 were consistent with a second companion mass $m_2$ anywhere in the range $\sim10^{-3}-1\,M_\odot$, i.e., from a Jupiter-type planet to a star. We present the latest timing parameters for the system, including a significant change in the projected semi-major axis of the inner binary, a marginal detection of the fourth time derivative of the pulse frequency, and the pulsar proper motion (which is in agreement with published values for the proper motion of M4), and use them to further constrain the mass $m_2$ and the orbital parameters. Using the observed value of $\stackrel{\ldots.}{f}$, we obtain a one-parameter family of solutions, all with $m_2 \lo 10^{-2}\,M_\odot$, i.e., excluding stellar masses. Varying $\stackrel{\ldots.}{f}$ within its formal $1\sigma$ error bar does not affect the mass range significantly. However, if we vary $\stackrel{\ldots.}{f}$ within a $4\sigma$ error bar, we find that stellar-mass solutions are still possible. We also calculate the predicted rate of change of the projected semi-major axis of the inner binary and show that it agrees with the measured value.