Constraints from the time lag between gravitational waves and gamma rays: Implications of GW170817 and GRB 170817A

The Laser Interferometer Gravitational-Wave Observatory (LIGO) has recently discovered gravitational waves (GWs) from its first neutron star-neutron star merger at a distance of ∼40 Mpc from the Earth. The associated electromagnetic (EM) detection of the event, including the short gamma-ray burst within Δt∼2 s after the GW arrival, can be used to test various aspects of sources physics and GW propagation. Using GW170817 as the first GW-EM example, we show that this event provides a stringent direct test that GWs travel at the speed of light. The gravitational potential of the Milky Way provides a potential source of Shapiro time delay difference between the arrival of photons and GWs, and we demonstrate that the nearly coincident detection of the GW and EM signals can yield strong limits on anomalous gravitational time delay, through updating the previous limits taking into account details of Milky Way's gravitational potential. Finally, we also obtain an intriguing limit on the size of the prompt emission region of GRB 170817A, and discuss implications for the emission mechanism of short gamma-ray bursts.