Pulsar acceleration shifts from nearby supernova explosion

We show that when a supernova explodes, a nearby pulsar signal goes through a very specific change. The observed period first changes smoothly, then is followed by a sudden change in the time derivative. A stable millisecond pulsar can allow us to measure such an effect. This may improve our measurement of the total energy released in neutrinos and also the orientation of the supernova-pulsar system.

Figure 1

Spacetime diagram showing the relative distances between the SN and Earth, $r_e$, and SN and pulsar, $r_p$. The red line represents the neutrino null shell. Above this line, we are in Schwarzschild metric $f$; below this line, we are in Schwarzschild metric $i$. The two blue lines represent the photon trajectories that we receive from the pulsar right before and after we see the SN explosion.

Figure 2

General geometry of the three objects, where $b$ is the impact parameter of the photons from pulsar to Earth.

Figure 3

Spacetime diagram showing the pulsar at $\theta \approx \pi$ with the same color code as Fig. 1. The two photons are right before the first change and right after the second change of $\dot{w_e}$.

Figure 4

From left to right, the pulse arrival time shift and its first and second derivatives. The arrival time shift is the direct observable, its first derivative is simply Eq. (14), while second derivatives highlights the discontinuity—the most distinctive feature of our effect. From top to bottom, $\theta =0.8\pi$, $0.5\pi$, $0.3\pi$. The distance to supernova $r_p$ and the neutrino shell mass (its effective Schwarzschild radius) $\delta M$ are used to make all quantities dimensionless.