Probing the cosmological principle using the slope of log N-log S relationship for quasars

We study the dipole signal in the slope x of the log N–log S relationship for quasars using the CatWISE2020 catalog of infrared sources. Here N is the number of sources with flux density greater than S. The slope is extracted by using a maximized log-likelihood method as well as Bayesian analysis. We obtain the value x = 1.579 ± 0.001 for a quasar sample of 1355352 sources. We extract the dipole signal in this parameter by employing χ ² minimization, assuming a sky model of x up to the quadrupole term. We find that the dipole amplitude |D| is 0.005 ± 0.002 and dipole direction (l, b) in Galactic coordinate system equal to (201.50° ± 27.87°, -29.37° ± 19.86°). The direction of dipole anisotropy is found to be very close to the hemispherical power asymmetry (l, b)=(221°,-27°) in the Cosmic Microwave Background (CMB). The dipole signal is also extracted using Bayesian analysis and found to be in good agreement with that obtained using χ ² minimization. We also obtain a signal of quadrupole anisotropy which is found to be correlated with the ecliptic poles and can be attributed to ecliptic bias.