All-sky analysis of astrochronometric signals induced by gravitational waves

Abstract

We introduce a unified formalism to describe both timing and astrometric perturbations induced on astrophysical point sources by gravitational waves using a complex spin field on the sphere. This allows the use of spin-weighted spherical harmonics to analyse "astrochronometric" observables. This approach simplifies the interpretation and simulation of anisotropies induced in the observables by gravitational waves. It also allows a simplified derivation of angular cross-spectra of the observables and their relationship with generalised Hellings-Downs correlation functions. The spin-weighted formalism also allows an explicit connection between correlation components and the spin of gravitational wave polarisations and any presence of chirality. We also calculate expected signal-to-noise ratios for observables to compare the utility of timing and deflection observables.

Constraining the stochastic gravitational wave background with photometric surveys

“…We note that the most commonly analyzed signals are spin-0 scalar signals, (e.g., CMB temperature map, galaxy counts) and spin-2 tensor signals, (e.g., CMB polarization, weak lensing distortion map). The GW-induced astrometric deflection is a spin-1 vector signal, and will be decomposed with vector spherical harmonics as [33,35,36,47,50] (dn…”

“…If the SNR is sufficiently large, this method can in principle become a probe for modified gravity theories, as is discussed in Refs. [33][34][35][36]. Just as this method complements PTAs in the frequency domain, it would also cross-check the non-GR effect with the timing residual measurements.…”

“…Several authors have investigated the potential of this method, both from a theoretical perspective [30,[33][34][35][36] and in close connection with specific surveys [27][28][29]. In Ref.…”