Extracting local velocity from cosmic dipole using simulations

Abstract Our velocity with respect to the cosmic frame of rest leads to a dipole in the number count distribution of galaxies. The dipole depends on the source spectrum, which is usually assumed to be a power law, S ( ν ) ∝ ν - α and on the flux dependence of the number density of sources. The latter is also generally assumed to be a power law, parametrised with exponent x . The velocity can be extracted from the observed dipole once the two parameters x and α are known. The standard procedure uses the mean value of α and the parameter x is inferred by fitting the cumulative number count, dN / d Ω(> S * ) ∝ S * -x , near the flux density limit S * of the survey. Here, we introduce a simulation procedure to extract the velocity which directly uses the α values of each source rather than their mean and does not rely on the functional form of the cumulative number count near the flux density limit S * . We apply this to the quasar sample in CatWISE2020 data and find that the final results differ from the standard procedure by approximately one sigma.