LISA, binary stars, and the mass of the graviton

We extend and improve earlier estimates of the ability of the proposed LISA (Laser Interferometer Space Antenna) gravitational wave detector to place upper bounds on the graviton mass $m_g$ by comparing the arrival times of gravitational and electromagnetic signals from binary star systems. We show that the best possible limit on $m_g$ obtainable this way is $\sim 50$ times better than the current limit set by solar system measurements. Among currently known, well-understood binaries, 4U1820-30 is the best for this purpose; LISA observations of 4U1820-30 should yield a limit $\approx 3-4$ times better than the present solar system bound. AM CVn-type binaries offer the prospect of improving the limit by a factor of $10,$ if such systems can be better understood by the time of the LISA mission. We briefly discuss the likelihood that radio and optical searches during the next decade will yield binaries that more closely approach the best possible case.