Test of Weak Equivalence Principle with the multi-band timing of the Crab Pulsar

Abstract

Weak Equivalent Principle (WEP) can be tested through the parameterized post-Newtonian parameter $\gamma$, representing the space curvature produced by unit rest mass. The parameter $\gamma$ in turn has been constrained by comparing the arrival times of photons originating in distant transient events, such as gamma-ray bursts, fast radio bursts as well as giant pulses of pulsars. Those measurements normally correspond to an individual burst event with very limited energy bands and signal-to-noise ratio (S/N). In this letter, the discrepancy in the pulse arrival times of the Crab Pulsar between different energy bands is obtained by the phase difference between corresponding pulse profiles. This allows us to compare the pulse arrival times at the largest energy band differences, between radio and optical, radio and X-ray, radio and gamma-ray respectively. As the pulse profiles are generated by phase-folding thousands of individual pulses, the time discrepancies between two energy bands are actually measured from thousands of events at each energy band, which corresponds to much higher S/N. The upper limit of the $\gamma$ discrepancy set by such an extensively-observed and well-modeled source is as follows: ${\gamma }_{radio}-{\gamma }_{\gamma -ray}<3.28\times 10^{-9}$ at the energy difference of $E_{\gamma -ray}/E_{radio}\sim 10^{13}$, ${\gamma }_{radio}-{\gamma }_{X-ray}<4.01\times 10^{-9}$ at the energy difference of $E_{X-ray}/E_{radio}\sim 10^9$, ${\gamma }_{radio}-{\gamma }_{optical}<2.63\times 10^{-9}$ at $E_{optical}/E_{radio}\sim 10^5$, and ${\gamma }_{optical}-{\gamma }_{\gamma -ray}<3.03\times 10^{-10}$ at $E_{\gamma -ray}/E_{optical}\sim 10^8$. This actually measures the arrival times of freely-falling photons in the gravitational field of the Milky Way with the largest amount of events and with data of the highest S/N, which tests WEP at the energy band differences that has never been reached before.

5 pages. Accepted for publication in ApJ

References in corpus (5)

• The Confrontation between General Relativity and Experiment
• TEMPO2, a new pulsar timing package. I: Overview
• A Precise Proper Motion for the Crab Pulsar, and the Difficulty of Testing Spin-Kick Alignment for Young Neutron Stars
• Simultaneous Absolute Timing of the Crab Pulsar at Radio and Optical Wavelengths
• Testing Einstein's weak equivalence principle with a 0.4-nanosecond giant pulse of the Crab pulsar

Cited by in corpus (5)

• Multimessenger tests of the weak equivalence principle from GW170817 and its electromagnetic counterparts
• Precision Test of the Weak Equivalence Principle from Gamma-Ray Burst Polarization
• Constraints on Equivalence Principle Violation from Gamma Ray Bursts
• Constraining Einstein's Equivalence Principle With Multi-Wavelength Observations of Polarized Blazars
• Constraining Einstein's Equivalence Principle With Multi-Wavelength Polarized astrophysical Sources