Clues from $\mathcal{Q}$--A null test designed for line intensity mapping cross-correlation studies

TL;DR

This paper introduces a new diagnostic statistic, al, for validating assumptions in cross-correlation based auto-spectrum estimation in line-intensity mapping, enhancing robustness against systematics.

Contribution

The al statistic is a novel, data-driven null test that assesses the validity of key assumptions in cross-spectrum auto-spectrum reconstruction using multiple spectral lines.

Findings

al reliably identifies regimes where assumptions hold

Deviations in al indicate violations of linear bias or correlation assumptions

Validated through analytic models and simulations across various redshifts and configurations

Abstract

Estimating the auto power spectrum of cosmological tracers from line-intensity mapping (LIM) data is often limited by instrumental noise, residual foregrounds, and systematics. Cross-power spectra between multiple lines offer a robust alternative, mitigating noise bias and systematics. However, inferring the auto spectrum from cross-correlations relies on two key assumptions: that all tracers are linearly biased with respect to the matter density field, and that they are strongly mutually correlated. In this work, we introduce a new diagnostic statistic, \(\mathcal{Q}\), which serves as a data-driven null test of these assumptions. Constructed from combinations of cross-spectra between four distinct spectral lines, \(\mathcal{Q}\) identifies regimes where cross-spectrum-based auto-spectrum reconstruction is unbiased. We validate its behavior using both analytic toy models and simulations of LIM observables, including star formation lines ([CII], [NII], [CI],[OIII]) and the 21-cm signal. We explore a range of redshifts and instrumental configurations, incorporating noise from representative surveys. Our results demonstrate that the criterion \( \mathcal{Q} \approx 1 \) reliably selects the modes where cross-spectrum estimators are valid, while significant deviations are an indicator that the key assumptions have been violated. The \( \mathcal{Q} \) diagnostic thus provides a simple yet powerful data-driven consistency check for multi-tracer LIM analyses.