The Cosmic Dipole’s Troublesome Factor of 2

In this paper, we show that the reported excess in the matter cosmological dipole relative to the cosmic microwave background dipole is primarily a result of errors in the procedures used to extract the dipole from observations of radio galaxies and quasars. The basis of all the work done to date is a formula given by Ellis and Baldwin (EB) in their 1984 paper. The main issue is that this formula is only valid when applied to a collection of galaxies isotropic in the source rest frame whereas, in practice, it is being applied to collections obtained using a uniform flux cutoff in the observer frame. The result is a collection that is not isotropic in the source frame and so violates the conditions required for the validity of the EB result. We rst provide a qualitative description of the source of this excess and then develop a new formula that can be applied to the observer frame data set. Analysis with this new formula eliminates about 80% of the reported dipole discrepancy in the quasar case. In the radio galaxy case, the corrected analysis of the published results removes only about 30% of the discrepancy but we then go on to show that the remaining large discrepancy between the radio galaxy and CMB dipoles is a consequence of a flux cutoff that is set too low. After an upward adjustment of the cutoff , the predicted dipole in the radio galaxy case is the same as the quasar dipole prediction.