Dispersion Distance and the Matter Distribution of the Universe in Dispersion Space

We propose that “standard pings,” brief broadband radio impulses, can be used to study the three-dimensional clustering of matter in the Universe even in the absence of redshift information. The dispersion of radio waves as they travel through the intervening plasma can, like redshift, be used as a cosmological distance measure. Because of inhomogeneities in the electron density along the line of sight, dispersion is an imperfect proxy for radial distance and we show that this leads to calculable dispersion-space distortions in the apparent clustering of sources. Fast radio bursts (FRBs) are a new class of radio transients that are the prototypical standard ping and, due to their high observed dispersion, have been interpreted as originating at cosmological distances. The rate of fast radio bursts has been estimated to be several thousand over the whole sky per day and, if cosmological, the sources of these events should trace the large-scale structure of the Universe. We calculate the dispersion-space power spectra for a simple model where electrons and FRBs are biased tracers of the large-scale structure of the Universe, and we show that the clustering signal could be measured using as few as 10 000 events. Such a survey is in line with what may be achieved with upcoming wide-field radio telescopes.

Figure 1

(Top) Comoving density of sources in a toy model, as described in the text. Normalization is such that the survey has a total of 10 000 FRB events. (Bottom) Resulting coefficient $A(\chi )$ as given in Eq. (14).

Figure 2

Terms in the dispersion-space cross-correlation angular power spectrum. All terms are evaluated at $\overline{\chi }=2000\mathrm{Mpc}/h$ and $\chi -{\chi }^{\prime }=10\mathrm{Mpc}/h$, except the lowest most local term curve, which is for $\chi -{\chi }^{\prime }=50\mathrm{Mpc}/h$. While the other two terms are highly insensitive to the separation of the radial slices, the local term drops rapidly with separation.

Figure 3

Sensitivity of a survey with 10 000 dispersion measures distributed uniformly over half of the sky. Plotted is the cross-correlation power spectrum weighted averaged over all pairs of radial bins. Weights are chosen to maximize signal to noise at $\ell =100$ for the $b_f=1.3$ case.