Robustness of pairwise kinematic Sunyaev-Zel'dovich effect to optical-cluster-selection bias

Technical Summary: Robustness of Pairwise Kinematic Sunyaev–Zel'dovich Effect to Optical-Cluster-Selection Bias

Problem Statement
The pairwise kinematic Sunyaev–Zel'dovich (kSZ) effect serves as a critical tracer for cosmic growth and baryon distribution, measuring the relative motion of galaxy clusters and the amount of gas within them. However, interpreting the cosmological information derived from kSZ measurements requires a rigorous understanding of systematic effects, particularly optical-cluster-selection bias. In optical surveys, cluster identification relies on mass proxies such as richness ($\lambda$), which is a weighted sum of member galaxy counts. Line-of-sight structures can contribute to both the optical observable (richness) and the cosmological signal, inducing a correlation between these quantities at a fixed cluster mass. If unmodeled, this selection bias can lead to systematic errors in halo mass estimation and affect inferred cosmological parameters, potentially contributing to tensions observed between results from the Dark Energy Survey (DES-Y1) and Planck. While this bias is a known systematic for weak lensing and cluster abundance, its impact on pairwise kSZ signals, pairwise velocities, and optical depth ($\tau$) has not yet been quantified.

Methodology
To investigate this bias, the authors utilized hydrodynamical simulations from the Magneticum project (Box2), which includes comprehensive physical processes such as radiative cooling, star formation, and active galactic nucleus (AGN) feedback, essential for modeling the intracluster medium (ICM). The study focused on a $5\times5$ deg$^2$ light cone with a depth of $z < 2.1$, specifically analyzing the redshift range $z=0.2-0.6$ to match DES results.

The methodology involved the following steps:

1. Alternative Richness Construction: Mimicking the optical selection process, the authors implemented a "cylindrical count" method. They defined cylindrical volumes along the line of sight centered on cluster positions, with apertures approximating the cluster size ($R_{200m}$) and depths corresponding to photometric redshift uncertainties (ranging from 40 to 100 comoving Mpc). Galaxy counts within these cylinders served as an alternative richness proxy.
2. Galaxy Selection Criteria: A wide range of galaxy-selection criteria was applied based on stellar mass, average stellar age, and specific star formation rate (sSFR). These criteria were tuned to produce Mass-Richness ($M-\lambda$) relations consistent with DES-Y1 observations.
3. Signal Measurement: The authors measured the pairwise kSZ effect, pairwise velocity ($v_{12}$), and optical depth ($\tau$) on the mock data. The pairwise kSZ signal was estimated using the estimator from Ferreira et al. (1999), while optical depth was derived by fitting a linear regression between the kSZ temperature decrement and pairwise velocity in fine mass bins.
4. Bias Estimation: To quantify the selection bias, the authors compared the signals from the richness-selected sample ($\lambda \ge 5$) against a "reconstructed" unbiased signal. The reconstructed signal was generated by selecting halos purely by mass and weighting them to match the mass probability distribution function (PDF) of the richness-selected sample. The bias was calculated as the ratio between the richness-selected signal and the reconstructed signal.

Key Results
The study examined a broad parameter space of galaxy-selection criteria and cylindrical depths. The primary findings are:

• No Significant Bias: Within the current uncertainty limits, the authors found no significant bias on the pairwise kSZ signals, pairwise velocities, or optical depth when comparing optically selected clusters to mass-selected halos.
• Quantitative Constraints: The biases for the pairwise kSZ signal, pairwise velocity, and optical depth were found to be consistent with unity (no bias) within $1\sigma$. Specifically, the results indicate no significant bias above the levels of approximately 19%, 11%, and 9%, respectively. The median uncertainty levels across the tested galaxy selections were approximately 16% for the kSZ signal, 10% for pairwise velocity, and 8% for optical depth.
• Contrast with Weak Lensing: Unlike weak lensing, where optical-selection bias is known to introduce considerable systematic errors, the pairwise kSZ estimator appears robust against these effects. The authors attribute this to the complex projection effects of peculiar velocities and the non-linear relationship between the projected kSZ signal and mass along the line of sight.

Significance and Claims
The paper claims that its results pave the way for confident interpretation of upcoming pairwise kSZ measurements, particularly those utilizing optical cluster samples cross-matched with large spectroscopic surveys like the Dark Energy Spectroscopic Instrument (DESI). The authors assert that at the current level of statistical precision (where detections have reached $\sim 5\sigma$ to $9\sigma$), optical-selection bias does not play a dominant role in systematic errors for pairwise kSZ analyses.

The study emphasizes that while the current findings are robust within the simulation constraints, achieving tighter cosmological constraints will require larger simulation volumes with comparable resolution to improve statistical power. The authors conclude that their framework supports the use of optically selected clusters for kSZ cosmology, provided that the selection bias is understood to be negligible within current uncertainty margins. They note that future work may require more sophisticated models to quantitatively estimate biases in finer mass bins and to investigate multi-observable probes.