Limits on the speed of gravitational waves from pulsar timing

In this work, analyzing the propagation of electromagnetic waves in the field of gravitational waves, we show the presence and significance of the so-called surfing effect for pulsar timing measurements. It is shown that, due to the transverse nature of gravitational waves, the surfing effect leads to enormous pulsar timing residuals if the speed of gravitational waves is smaller than the speed of light. This fact allows one to place significant constraints on parameter $ϵ$, which characterizes the relative deviation of the speed of gravitational waves from the speed of light. We show that the existing constraints from pulsar timing measurements already place stringent limits on $ϵ$ and consequently on the mass of the graviton $m_g$. The limits on $m_g\lesssim 8.5\times {10}^{-24}$ are 2 orders of magnitude stronger than the current constraints from Solar System tests. The current constraints also allow one to rule out massive gravitons as possible candidates for cold dark matter in the galactic halo. In the near future, the gravitational wave background from extragalactic super massive black hole binaries, along with the expected submicrosecond pulsar timing accuracy, will allow one to achieve constraints of $ϵ\lesssim 0.4\%$ and possibly stronger.

Figure 1

The illustration of the resonance effect, present for $ϵ\ne 0$. The graphs show integrand in expression (22). For the case $ϵ\ne 0$ the integrand sharply peaks at angle $\mu \approx (1-ϵ)$ (solid red line), while for the case $ϵ=0$ the effect is absent (dashed blue line). In the case of $ϵ\ne 0$, the gravitational waves travelling at an angle $\cos \theta \approx (1-ϵ)$ to the line of sight are the predominant contributors to the surfing effect. The figure on the left shows the integrand for the whole region of $\mu$, while the figure on the right zooms into the region around the resonance.

Figure 2

The upper limit on strain amplitude $h_c$ and velocity parameter $ϵ$ for gravitational waves, achievable by pulsar timing residual measurements with precision $R_{\mathrm{rms}}=0.1\mu \sec$ and time of observation $T_{\mathrm{obs}}=10\mathrm{yr}$. The shaded area shows the region that can be probed or ruled out by pulsar timing observations. The horizontal lines show the strain $h_c$, at $f=(10\mathrm{yr}{)}^{-1}$, for some viable sources of gravitational waves.