Modulation of pulse profile as a signal for phase transitions in a pulsar core

TL;DR

This paper models how phase transition-induced density fluctuations in a pulsar's core can cause observable pulse profile modulations, providing a potential method to study internal phase transitions through pulsar timing analysis.

Contribution

It introduces a detailed numerical and analytical framework to connect pulsar pulse modifications with internal phase transition dynamics and density fluctuations.

Findings

Specific pulse modulation patterns are observable over large time periods.

Pulse modulations decay as density fluctuations relax, indicating phase transition dynamics.

Off-diagonal moments of inertia vanish as fluctuations fade, distinguishing transient effects from intrinsic wobbling.

Abstract

We calculate detailed modification of pulses from a pulsar arising from the effects of phase transition induced density fluctuations on the pulsar moment of inertia. We represent general statistical density fluctuations using a simple model where the initial moment of inertia tensor of the pulsar (taken to be diagonal here) is assumed to get random additional contributions for each of its component which are taken to be Gaussian distributed with certain width characterized by the strength of density fluctuations $\epsilon$. Using sample values of $\epsilon$, (and the pulsar deformation parameter $\eta$) we numerically calculate detailed pulse modifications by solving Euler's equations for the rotational dynamics of the pulsar. We also give analytical estimates which can be used for arbitrary values of $\epsilon$ and $\eta$. We show that there are very specific patterns in the perturbed pulses which are observable in terms of modulations of pulses over large time periods. In view of the fact that density fluctuations fade away eventually leading to a uniform phase in the interior of pulsar, the off-diagonal components of MI tensor also vanish eventually. Thus, the modification of pulses due to induced wobbling (from the off-diagonal MI components) will also die away eventually. This allows one to distinguish these transient pulse modulations from the effects of any wobbling originally present. Further, the decay of these modulations in time directly relates to relaxation of density fluctuations in the pulsar giving valuable information about the nature of phase transition occurring inside the pulsar.