Isotropy Test with Quasars Using Method of Smoothed Residuals

TL;DR

This work tests statistical isotropy of the CatWISE quasar distribution by constructing smoothed spherical density fields and evaluating extreme-value statistics $Q_{\max}$, $Q_{\min}$, and $T_{\max}$ across smoothing scales $\delta$. By comparing to $N_{\rm real}=10^5$ isotropic mocks (with an increased $3\times10^6$ samples at $\delta=\pi/6$), the authors quantify the significance of large-scale anisotropies and systematically remove known systematics via CMB dipole and ecliptic corrections, and even an anomalous dipole proposed in Secrest2021. The key finding is a strong, scale-dependent dipole-like under-density in the southern sky; after removing both CMB- and ecliptic-related signals, a residual under-density persists with $p\approx 0.0018$ at $\delta=\pi/6$, implying either a localized structure or unaccounted systematics. Overall, the method provides a robust, model-independent framework for isolating and characterizing large-scale anisotropies in sparse sky maps, with implications for tests of isotropy and potential local structures in quasar catalogs, and it motivates follow-up investigations with redshift information and independent surveys.

Abstract

To assess the significance and scale dependence of anomalous large scale modes in the CatWISE quasar data, we generate smoothed number density fields on the sphere and study their extreme values -- maximum, minimum, maximum antipodal difference. By comparing these summary statistics to those obtained from random isotropic realisations of the data, we determine the statistical significance of large scale modes as a function of smoothing scale. We perform our analysis using five different versions of the data -- the original quasar map, the maps after separately subtracting the ecliptic bias and the CMB dipole, the map obtained after subtracting both, and the map after subtracting the ecliptic bias and anomalous dipole inferred in \cite{Secrest2021}. We find that the ecliptic-corrected, CMB dipole-removed map exhibits large scale modes that are in tension with random realisations of the data (p-values $p \lesssim 10^{-4}$), over a wide range of smoothing scales $π/8 \leq δ\leq π/2$. The most prominent feature in the data is an under-density in the southern galactic plane at $(b,\ell) = (-31^\circ,78^\circ)$, which reaches its highest statistical significance when smoothed on scales $δ= π/6$ ($p = 1.2 \times 10^{-6}$). Notably, the minima statistics align with the maximum antipodal difference statistics, whereas the maxima do not. This suggests that the observed dipole-like behavior in the data is primarily driven by the under-density in the southern sky. The ecliptic corrected, anomalous dipole subtracted map reduces the significance of any residual anisotropic features, but an under-density in the south sky persists with p-value $p =0.0018$.

Figures (8)

• Figure 1: [Left panel] CatWISE quasar data binned into a $N_{\rm side} = 64$ HEALPix map, unsmoothed and mean subtracted. [Middle panel] The same data as in the left panel, but now smoothed using a tophat filter of area 1 steradian. [Right panel] The $W1$ coverage map, also smoothed with a 1 steradian tophat.
• Figure 2: Results from the real-space analysis of the full data density map. Top Left: The smoothed density map of the quasar distribution from the CatWISE catalog. The gray regions represent masked areas in the map. Top Right: The angular correlation function, $\zeta(\theta)$, where $\theta$ is in radians. The shape is predominantly quadrupolar but is modulated by a dipole. Bottom Rows: The distributions of $Q_{\rm max}$, $Q_{\rm min}$ and $T_{\rm max}$ from $10^{5}$ isotropic realisations are shown (blue histograms) alongside the corresponding values of the same statistics measured from the data (vertical red dashed lines). Results are presented for two smoothing scales: $\delta = \pi/2$ (middle row) and $\delta = \pi/4$ (bottom row).
• Figure 3: Results from the real-space analysis of the CMB dipole-removed density map. Top Left: The smoothed density map of the quasar distribution from the CatWISE catalog. The gray regions represent masked areas in the map. Top Right: The angular correlation function, $\zeta(\theta)$, where $\theta$ is in radians. The shape is now predominantly quadrupolar. Bottom Rows: The distributions of $Q_{\rm max}$, $Q_{\rm min}$ and $T_{\rm max}$ from $10^{5}$ isotropic realisations are shown (blue histograms) alongside the corresponding values of the same statistics measured from the data (vertical red dashed lines). Results are presented for two smoothing scales: $\delta = \pi/2$ (middle row) and $\delta = \pi/4$ (bottom row).
• Figure 4: Results from the real-space analysis of the ecliptic-corrected density map. Top Left: The smoothed density map of the quasar distribution from the CatWISE catalog. The gray regions represent masked areas in the map. Top Right: The angular correlation function, $\zeta(\theta)$, where $\theta$ is in radians. The shape is predominantly dipolar. Bottom Rows: The distributions of $Q_{\rm max}$, $Q_{\rm min}$ and $T_{\rm max}$ from $10^{5}$ isotropic realisations are shown (blue histograms) alongside the corresponding values of the same statistics measured from the data (vertical red dashed lines). Results are presented for two smoothing scales: $\delta = \pi/2$ (middle row) and $\delta = \pi/4$ (bottom row).
• Figure 5: Results from the real-space analysis of the CMB dipole-removed and ecliptic-corrected density map. Top Left: The smoothed density map of the quasar distribution from the CatWISE catalog. The gray regions represent masked areas in the map. Top Right: The angular correlation function, $\zeta(\theta)$, where $\theta$ is in radians. Bottom Rows: The distributions of $Q_{\rm max}$, $Q_{\rm min}$ and $T_{\rm max}$ from $10^{5}$ isotropic realisations are shown (blue histograms) alongside the corresponding values of the same statistics measured from the data (vertical red dashed lines). Results are presented for two smoothing scales: $\delta = \pi/2$ (middle row) and $\delta = \pi/4$ (bottom row).