The kinematic cosmic dipole beyond Ellis and Baldwin

TL;DR

The paper tackles the cosmic dipole anomaly by generalizing the Ellis & Baldwin kinematic dipole formula beyond power-law spectra and luminosity functions. It develops monochromatic and photometric derivations that yield effective coefficients $x_eff$ and $alpha_eff$ and shows how the EB expression is recovered in the appropriate limits. Applying the framework to CatWISE quasars and AKARI QSONG spectra indicates that the dipole amplitude persists and remains about a factor of two above the kinematic expectation, with $alpha_eff$ broadly consistent with power-law estimates. These results provide a robust, survey-ready framework for interpreting future large-scale dipole measurements and highlight the importance of spectral information in photometric surveys.

Abstract

The cosmic dipole anomaly, currently detected at a significance exceeding 5$σ$ in several independent survey poses a significant challenge to the standard model of cosmology. The Ellis & Baldwin formula provides a theoretical link between the intrinsic dipole anisotropy in the sky distribution of extragalactic light sources and the observer's velocity relative to the cosmic rest frame, under the assumptions that the sources follow a power-law luminosity function and exhibit power-law spectral energy distributions. In this work, we demonstrate that this relation can be generalized to arbitrary luminosity distributions and spectral profiles. We derive the corresponding expression for the effective spectral index and apply it to a sample of quasars observed in the W1 band of the CatWISE survey. We show that the anomalous cosmic dipole persists beyond the power-law assumption. These results provide a more general and robust framework to interpret measurements of the cosmic dipole in future large-scale surveys.

Figures (3)

• Figure 1: (a) The frame moving with the observer, (b) the rest frame, in which the observer has a velocity $\mathbf{v}$. For the sake of simplicity, we assume that the $z$ axis is parallel to the movement of this observer.
• Figure 2: Comparison of the spectral index $\alpha$ obtained with different methods, for 41 quasar's spectra. The black dashed line corresponds to the identity. The two red dots with a high deviation between their calculated $\alpha_{\rm eff}$ and the two other method corresponds to the two quasars with the lowest mean spectral flux density.
• Figure 3: Example of a spectrum for a quasar (PG2112+059, located at $(272.101907, 64.128918)$, in galactic coordinates) given by AKARI, with the spectral indexes $\alpha_{\rm mag}$ obtained using the $W1-W2$ method, and $\alpha_{\rm eff}$ using a direct integration of the spectra using \ref{['eq:alpha_eff']}. These spectral indexes are plotted as pure power laws $S_\nu\propto\nu^{-\alpha}$.