On the response of the Einstein Telescope to Doppler anisotropies

TL;DR

This paper investigates how the Einstein Telescope detects Doppler anisotropies in the stochastic gravitational wave background, especially when the background's frequency dependence is complex, providing new formulas and analysis for such scenarios.

Contribution

It introduces a general response function for the Einstein Telescope to Doppler anisotropies without assuming factorizability or small effects, applicable to various background models.

Findings

Derived response functions for non-factorizable Doppler anisotropies.

Analyzed signal-to-noise ratios for different background profiles.

Provided formulas valid for any relative velocity between frames.

Abstract

We study the response function of the Einstein Telescope to kinematic Doppler anisotropies, which represent one of the guaranteed properties of the stochastic gravitational wave background. If the frequency dependence of the stochastic background changes slope within the detector frequency band, the Doppler anisotropic contribution to the signal can not be factorized in a part depending on frequency, and a part depending on direction. For the first time, we study the detector response function to Doppler anisotropies without making any factorizable Ansatz. Moreover, we do not assume that kinematic effects are small, and we derive general formulas valid for any relative velocity among frames. We apply our findings to three well-motivated examples of background profiles: power-law, broken power-law, and models with a resonance motivated by primordial black hole scenarios. We derive the signal-to-noise ratio associated with an optimal estimator for the detection of non-factorizable kinematic anisotropies, and we study it for representative examples.