Relativistic imprints on dispersion measure space distortions
Abstract
We investigate the threedimensional clustering of sources emitting electromagnetic pulses traveling through cold electron plasma, whose radial distance is inferred from their dispersion measure. As a distance indicator, dispersion measure is systematically affected by inhomogeneities in the electron density along the line of sight and special and general relativistic effects, similar to the case of redshift surveys. We present analytic expressions for the correlation function of fast radio bursts (FRBs), and for the galaxyFRB crosscorrelation function, in the presence of these dispersion measurespace distortions. We find that the even multipoles of these correlations are primarily dominated by nonlocal contributions (e.g. the electron density fluctuations integrated along the line of sight), while the dipole also receives a significant contribution from the Doppler effect, one of the major relativistic effects. A large number of FRBs, $\mathcal{O}(10^{5}\sim10^{6})$, expected to be observed in the Square Kilometre Array, would be enough to measure the even multipoles at very high significance, ${\rm S}/{\rm N} \approx 100$, and perhaps to make a first detection of the dipole (${\rm S}/{\rm N} \approx 10$) in the FRB correlation function and FRBgalaxy cross correlation function. This measurement could open a new window to study and test cosmological models.
 Publication:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.06049
 arXiv:
 arXiv:2404.06049
 Bibcode:
 2024arXiv240406049S
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 16 pages, 10 figures