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

TL;DR

The paper addresses a persistent cosmic dipole tension by forward-modeling CatWISE counts with Simulation-Based Inference (SBI) to jointly capture the cosmic dipole and an ecliptic bias arising from WISE photometric uncertainties. Using neural likelihood and neural posterior estimators, the authors infer a dipole amplitude around $\hat{v}_{\text{obs}} \approx 2$ in units of the CMB velocity $v_{\text{CMB}}$, with a direction offset of about $3\sigma$ from the CMB direction, and find Bayesian evidence strongly favoring models that include extra photometric error ($\eta_{\text{extra}}$). They demonstrate that the ecliptic trend can be reproduced by the forward model, supporting an Eddington-bias interpretation or an additional systematic, rather than a simple linear correction. The results imply a persistent dipole excess beyond $\Lambda$CDM expectations and showcase SBI as a principled approach to disentangle complex, instrument-induced systematics in astronomical data, with broad applicability to upcoming surveys.

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 ($\approx 3 σ$). 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 $Λ$CDM, we showcase that SBI can untangle the subtle and complex systematic issues affecting any sample derived from real astronomical data.

Figures (10)

• Figure 1: Visual indication of the relationship between coverage and photometric error. A higher coverage implies a lower error. Left: Median coverage per pixel for CatWISE in the $W1$ photometric band. Right: Median photometric uncertainty (percentage error) per pixel for CatWISE in the $W1$ band.
• Figure 2: The spectral indices determined from our simulation (CatSIM) and the empirical data (CatWISE). The dashed grey histogram indicates the true indices in the simulated sample, while the solid red histogram indicates what an observer would measure after noise has been added to the photometric magnitudes. The blue histogram indicates the distribution of $\alpha$ from the actual CatWISE dataset. In the top panel, we zoom in on the peak of all three histograms to highlight the difference between the simulated and empirical indices.
• Figure 3: Relationship between coverage, magnitude and median error in the W1 band. In each coverage-magnitude bin, we compute the median photometric error across all real CatWISE samples made from the deeper catalogue ($W1 < 17.0$ and $W1 - W2 > 0.5$). Top: without the northern ecliptic pole mask. Bottom: with the northern ecliptic pole mask.
• Figure 4: Comparing the real CatWISE data to the outputs of our simulation. Left: The real CatWISE2020 sample (smoothed with a moving average) as similar to that in secrest2021 except for minor modifications to the mask. Right: Example of a CatSIM sample (smoothed) generated from one function call. The particular arguments passed to the function are the median parameters from Fig. \ref{['fig:free_gauss_err_corner']}, which includes an observer velocity of $v_{\text{obs.}} \approx 740\,$km s$^{-1}$. In this sense, the plot is also a posterior predictive check for that model.
• Figure 5: The inferred posterior distribution for our fiducial model: 'free dipole, extra error, Gaussian'. This assumes a dipole with free parameters and an $\eta_{\text{extra}}$ term which increases the width of CatWISE's photometric error distribution (assumed to be Gaussian). A $1 \sigma$ credible interval is indicated by the dashed lines and titles of the 1D marginals. Meanwhile, $1 \sigma$ and $2 \sigma$ intervals are shown by the filled contours in the 2D marginals.