Wising up to CatWISE: using simulation-based inference to interpret the ecliptic bias and confirm the cosmic dipole excess

Abstract

We apply Simulation-Based Inference ('SBI') to the cosmic dipole problem for the first time, measuring the distribution of quasar counts over the sky in the CatWISE2020 ('CatWISE') sample. We show that the quadrupole anisotropy in CatWISE can be attributed to the correlation between WISE's scanning law and photometric uncertainty in the $W1$ and $W2$ magnitudes, inducing an Eddington bias which varies with sky position. After explicitly modelling this with SBI, we use a neural likelihood estimator to find the posterior distribution for CatWISE's dipole, confirming the presence of a dipole twice as large as the CMB expectation but more seriously misaligned with the CMB direction ($\approx 3 \sigma$). We also use our learned likelihood to infer the Bayesian evidence, learning that models which increase the scale of CatWISE's photometric errors are most favoured. This is strong evidence that the sample's errors are underestimated or that there is an additional, unresolved systematic producing the same effect as Eddington bias. While our results indicate that the cosmic dipole excess is a persistent issue for $\Lambda$CDM, we showcase that SBI can untangle the subtle and complex systematic issues affecting any sample derived from real astronomical data.