Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Detection of Gravitational Wave modes in third generation detectors

Massimo Tinto, Sanjeev Dhurandhar, Harshit Raj

Abstract

We investigate the detectability of Gravitational Wave (GW) modes (emitted by black-holes and neutron stars) by third generation, ground-based gravitational wave detectors planned to be operational in the next decade. Our analysis focuses on the Cosmic Explorer and Einstein Telescope projects, which are expected to have arm lengths of tens of kilometers and to experience the amplification of a gravitational wave signal at their Full-Spectral Range (FSR) frequencies. We find that both projects will also observe with good Signal-to-Noise ratio (SNR) the elusive {\it w-modes}, which are expected to be emitted at these frequencies by spinning neutron stars.

Detection of Gravitational Wave modes in third generation detectors

Abstract

We investigate the detectability of Gravitational Wave (GW) modes (emitted by black-holes and neutron stars) by third generation, ground-based gravitational wave detectors planned to be operational in the next decade. Our analysis focuses on the Cosmic Explorer and Einstein Telescope projects, which are expected to have arm lengths of tens of kilometers and to experience the amplification of a gravitational wave signal at their Full-Spectral Range (FSR) frequencies. We find that both projects will also observe with good Signal-to-Noise ratio (SNR) the elusive {\it w-modes}, which are expected to be emitted at these frequencies by spinning neutron stars.
Paper Structure (7 sections, 26 equations, 4 figures)

This paper contains 7 sections, 26 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Response of a Fabry-Pérot Interferometer to a Gravitational Wave Signal
  3. Approximate analytical expression of the SNR of a GW mode
  4. The general expression for the SNR
  5. The band-width of the GW mode
  6. The amplitude and SNR of the GW mode
  7. Concluding Remarks and Summary

Figures (4)

  • Figure 1: The two coordinate systems associated with the interferometer and the GW signal. They are related through the Euler angles ($\theta, \phi, \psi$). See text for a complete description of the geometry.
  • Figure 2: Strain sensitivities of the Cosmic Explorer (CE) and Einstein Telescope (ET) projects. The CE project envisions an arm length of $40$ km, while current sensitivity studies for ET have been considering arm lengths ranging from $10$ to $20$ km. Here we have assumed an ET arm length of $20$ km, which results in a FSR frequency of $7.5$ kHz.
  • Figure 3: Magnified view of the CE (40 Km) and ET (20 Km) sensitivity curve highlighting the flatness of the response in the free spectral range (FSR) region.
  • Figure 4: Fig. (a) shows $|\tilde{h}(\omega)|^2$ as a function of $\omega$ with $A = 1$ and $\lambda = 10$. As seen from Eq. (\ref{['eq:time_domain_power']}) the height of the peak is $\sim 1/4 \lambda = 0.0025$. In Fig (b) a zoomed version of figure (a) is shown in the vicinity of the peak and it further displays the FWHM $\simeq 2 \lambda = 20$ rad/sec. which corresponds to about 3 Hz.