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In this work, analyzing the propagation of electromagnetic waves in the fieldof gravitational waves, we show the presence and significance of the so calledsurfing effect for pulsar timing measurements. It is shown that, due to thetransverse nature of gravitational waves, the surfing effect leads to enormouspulsar timing residuals if the speed of gravitational waves is smaller thanspeed of light. This fact allows to place significant constraints on parameter$\epsilon$, which characterizes the relative deviation of the speed ofgravitational waves from the speed of light. We show that the existingconstraints from pulsar timing measurements already place stringent limits on$\epsilon$ and consequently on the mass of graviton $m_g$. These limits on$m_g$ are three orders of magnitude stronger than the current constraints fromSolar System tests. The current constraints also allow to rule out massivegravitons as possible candidates for cold dark matter in galactic halo. In thenear future, the gravitational wave background from extragalactic super massiveblack hole binaries, along with the expected sub-microsecond pulsar timingaccuracy, will allow to achieve constrains of $\epsilon\lesssim 0.4\%$ andpossibly stronger.

Limits on the speed of gravitational waves from pulsar timing