Galactic Shapiro Delay to the Crab Pulsar and limit on Einstein's Equivalence Principle Violation

TL;DR

This paper calculates the galactic Shapiro delay to the Crab pulsar considering dark and baryonic matter, and sets new limits on Einstein's equivalence principle violation using pulsar observations.

Contribution

It provides a detailed calculation of the galactic Shapiro delay including dark matter, and establishes tighter constraints on EEP violation parameters from pulsar data.

Findings

Total galactic Shapiro delay is approximately 3.84 days.

Limits on EEP violation parameter Δγ are <2.41×10⁻¹⁵ from nano-shots.

Limits on Δγ are <1.54×10⁻⁹ from optical-radio time differences.

Abstract

We calculate the total galactic Shapiro delay to the Crab pulsar by including the contributions from the dark matter as well as baryonic matter along the line of sight. The total delay due to dark matter potential is about 3.4 days. For baryonic matter, we included the contributions from both the bulge and the disk, which are approximately 0.12 and 0.32 days respectively. The total delay from all the matter distribution is therefore 3.84 days. We also calculate the limit on violations of Einstein's equivalence principle by using observations of "nano-shot" giant pulses from the Crab pulsar with time-delay $<0.4$~ns as well as using time differences between radio and optical photons observed from this pulsar. Using the former, we obtain a limit on violation of Einstein's equivalence principle in terms of the PPN parameter $\Delta \gamma < 2.41\times 10^{-15}$. From the time-difference between simultaneous optical and radio observations, we get $\Delta \gamma < 1.54\times 10^{-9}$. We also point out differences in our calculation of Shapiro delay and that from two recent papers (arXiv:1612.00717 and arXiv:1608.07657), which used the same observations to obtain a corresponding limit on $\Delta \gamma$.