Relativistic ocean $r$-modes during type-I X-ray bursts

TL;DR

This paper models relativistic effects on ocean $r$-modes in neutron stars during X-ray bursts, showing these effects significantly reduce predicted mode frequencies and drifts, aligning better with observations.

Contribution

It introduces a relativistic model of ocean $r$-modes that accounts for frame-dragging and gravitational redshift, improving agreement with observed burst oscillation frequencies.

Findings

Relativistic effects decrease mode frequency by up to 30%.

Frequency drift predictions are reduced by up to 20%.

Mode frequencies are brought closer to observed values (~2 Hz).

Abstract

Accreting neutron stars (NS) can exhibit high frequency modulations in their lightcurves during thermonuclear X-ray bursts, known as burst oscillations. These frequencies can be offset from the NS spin frequency by several Hz (where known independently) and can drift by 1-3 Hz. One plausible explanation is that a wave is present in the bursting ocean, the rotating frame frequency of which is the offset. The frequency of the wave should decrease (in the rotating frame) as the burst cools hence explaining the drift. A strong candidate is a buoyant $r$-mode. To date, models that calculated the frequency of this mode taking into account the radial structure neglected relativistic effects and predicted rotating frame frequencies of $\sim$ 4 Hz and frequency drifts of > 5 Hz; too large to be consistent with observations. We present a calculation that includes frame-dragging and gravitational redshift that reduces the rotating frame frequency by up to 30 % and frequency drift by up to 20 %. Updating previous models for the ocean cooling in the aftermath of the burst to a model more representative of detailed calculations of thermonuclear X-ray bursts reduces the frequency of the mode still further. This model, combined with relativistic effects, can reduce the rotating frequency of the mode to $\sim$ 2 Hz and frequency drift to $\sim$ 2 Hz, which is closer to the observed values.