Fireballs' Whispers of Their Central Engine: Relativistic Filtering of Afterglow QPOs

TL;DR

This paper demonstrates that relativistic effects significantly influence the observed quasi-periodic oscillations in gamma-ray burst afterglows, affecting interpretations of the central engine's intrinsic variability.

Contribution

It reveals how relativistic propagation acts as a frequency-dependent filter, challenging previous assumptions about direct correlations between observed and intrinsic oscillation frequencies.

Findings

Relativistic propagation modifies observed QPO frequencies.

Equal-arrival-time surface integration acts as a low-pass filter.

Deceleration causes an apparent frequency drift in observations.

Abstract

Quasi-periodic oscillations (QPOs) in gamma-ray bursts (GRBs) afterglows have been suggested as probes of the central engine. Such interpretations generally assume that the observed modulation frequency directly corresponds to an intrinsic oscillation frequency of the source. We show that this assumption is not generally valid and that interpreting such features without accounting for relativistic propagation may lead to misleading inferences about the engine nature. We show that relativistic propagation effects - most importantly integration over equal-arrival-time surfaces - act as a frequency-dependent filter that can significantly modify or suppress intrinsic variability. In the constant-$\Gamma$ case, the angular kernel acts as a stationary low-pass filter that suppresses high-frequency variability without altering its frequency, whereas Blandford-McKee deceleration renders the filter time-dependent and manifests observationally as an apparent frequency drift.