Thermal Sunyaev-Zel'dovich cross-correlations with unWISE galaxies: disentangling radio contamination, dust properties, and electron pressure

Technical Summary: Thermal Sunyaev-Zel'dovich Cross-Correlations with unWISE Galaxies

Problem Statement
Cross-correlations between the thermal Sunyaev-Zel'dovich (tSZ) effect and galaxy surveys offer a sensitive probe of hot gas in low-mass halos, a regime critical for understanding baryonic feedback and the missing-baryon problem. However, on the small angular scales ($\ell > 1000$) where halo-pressure modeling is most informative, these measurements are highly susceptible to residual foreground contamination. Specifically, the Cosmic Infrared Background (CIB) and radio emission correlated with the galaxy sample can mimic or bias the frequency dependence of the tSZ signal. Previous analyses using component-separated maps (e.g., NILC) have struggled to isolate the true low-redshift tSZ signal, sometimes resulting in physically implausible negative galaxy-tSZ cross-correlations at small scales. The challenge lies in disentangling these components without relying on map-level deprojection methods that may leave residual correlations.

Methodology
The authors analyze the cross-correlation of two low-redshift unWISE galaxy samples (Low-z, $\langle z \rangle \approx 0.14$; Mid-z, $\langle z \rangle \approx 0.23$) with Planck PR4 and ACT DR6 microwave temperature sky maps directly in harmonic space.

1. Signal Modeling: The galaxy-temperature cross-spectrum is modeled as a linear superposition of astrophysical components with distinct Spectral Energy Distributions (SEDs): tSZ, CIB amplitude, CIB spectral variation (CIB-$\delta\beta$), and radio emission. The frequency dependence is encoded in band-averaged response coefficients, while scale dependence is carried by the component cross-spectra.
2. Component Separation Strategy:
   • Model Selection: Using the nine Planck frequency bands, the authors perform Bayesian model selection to determine the necessary foreground components. They compare recipes including tSZ, radio, CIB-amplitude, and CIB-$\delta\beta$.
   • Application to High-Resolution Data: Once the optimal recipe is selected using Planck, it is applied to the ACT+Planck coadded maps (90, 150, 220 GHz) to recover small-scale signals up to $\ell \simeq 6000$.
3. Halo Model Analysis: The cleaned tSZ $\times$ unWISE spectra are interpreted using a Halo Occupation Distribution (HOD) model calibrated to the galaxy clustering and a two-parameter Generalized NFW (GNFW) electron pressure profile.

Key Results

• Necessity of Radio Modeling: Model selection using Planck data strongly favors a three-component model (tSZ + Radio + CIB-amplitude) over models omitting radio contamination. The preference is significant at $9.5\sigma$ for the Low-z sample and $11\sigma$ for the Mid-z sample. A four-component model including CIB-$\delta\beta$ provides a better fit but is disfavored by the Bayesian Information Criterion (BIC), indicating overfitting.
• Spectral Indices: The best-fit effective radio spectral indices are $\beta_r = -2.18 \pm 0.24$ (Low-z) and $\beta_r = -2.62 \pm 0.26$ (Mid-z). These values suggest a preference for free-free emission in Low-z galaxies and synchrotron radiation in Mid-z galaxies. The CIB parameters are constrained to $\beta_0 \approx 1.4-1.8$ and $T_0 \approx 22-28$ K.
• Resolution of Negative Correlations: In recipes omitting the radio component (or using standard NILC maps), the recovered galaxy-tSZ cross-spectrum becomes suppressed or spuriously negative at $\ell > 2000$. The inclusion of the radio term in the cleaning recipe removes this artifact, yielding a physically positive cross-correlation consistent with a standard halo model up to $\ell \simeq 6000$.
• Halo Model Constraints: The cleaned spectra are well-described by a GNFW pressure profile. The inferred pressure normalization ($P_0$) and outer-slope parameter ($\beta_{GNFW}$) are lower than those found in cluster samples (e.g., Melin & Pratt 2023), implying lower central pressure and more extended profiles for the $\sim 10^{13} M_\odot$ halos traced by unWISE. This is consistent with stronger feedback effects in lower-mass halos.

Significance and Claims
The paper concludes that radio contamination separation is not a subdominant correction but a crucial, necessary component for interpreting small-scale tSZ $\times$ galaxy measurements. The authors claim that:

1. Radio Bias: Failure to explicitly model radio emission leads to a misinterpretation of the tSZ signal, potentially resulting in negative correlations that contradict physical expectations.
2. Limitations of NILC: While NILC maps effectively deproject CIB, they may not fully account for radio contamination correlated with the galaxy sample. Consequently, agreement with CIB-deprojected NILC results should not be taken as evidence that a signal is free from radio-induced bias, particularly for low-mass, low-redshift populations.
3. Methodological Framework: The study demonstrates that direct harmonic-space component separation, guided by multi-frequency model selection, is a robust method for isolating the tSZ signal from complex foregrounds in galaxy cross-correlations.

The authors note that their analysis is limited by the three-band coverage of ACT, which restricts component separation to three components and necessitates fixing spectral parameters derived from Planck. They suggest that future observatories with broader frequency coverage (e.g., Simons Observatory) will allow for more independent constraints on these spectral parameters.