PSZ2 G126.57+51.61: High-Redshift Galaxy Cluster

• PSZ2 G126.57+51.61 is a high-redshift (z=0.815) galaxy cluster serving as a key cosmological probe via Sunyaev–Zeldovich effect detection.
• It is characterized through matched multi-filter techniques and GNFW profile assumptions to derive robust mass estimates and structural properties.
• Its multi-wavelength identification, including optical, X-ray, and infrared cross-matching, underpins its inclusion in high-purity cosmological samples.

PSZ2 G126.57+51.61 is a galaxy cluster confirmed in the Second Planck Catalogue of Sunyaev–Zeldovich Sources (PSZ2), notable for its high redshift and its role as a cosmological probe. Identified via its “G” Galactic coordinates (longitude 126.57°, latitude +51.61°), it serves as a representative example of the robust, multi-wavelength cluster detection methodology and subsequent astrophysical characterization implemented by the Planck collaboration. Its significance is accentuated by the spectroscopic confirmation of its redshift at $z=0.815$, and its selection as part of the cosmological sample within PSZ2, making it a critical datapoint for studies of cluster evolution and cosmological parameter constraints.

1. Detection Methodology and Catalogue Inclusion

PSZ2 G126.57+51.61 was detected in the Planck full-mission data, which mapped 83.6% of the sky for Sunyaev–Zeldovich (SZ) sources (Collaboration et al., 2015). Three independent detection algorithms—MMF1, MMF3 (matched multi-filter), and the Bayesian PowellSnakes (PwS)—were employed, with the “union” catalogue incorporating all candidates identified by at least one of these methods. PSZ2 G126.57+51.61 is robustly confirmed in this sample and also typically appears in the “intersection” high-purity subsample.

Catalogue construction involves validation against external datasets through positional, SZ signal, and, where available, redshift consistency checks. Cross-identification is performed with X-ray (e.g., MCXC catalogue), optical (e.g., redMaPPer, SDSS), infrared (WISE), and other SZ catalogues, ensuring robustness in counterpart assignment.

2. Physical Characterization and Mass Estimation

For PSZ2 G126.57+51.61, the Planck team measures the spherically-integrated Compton parameter (“integrated Compton-y”) as

$$Y_{5R_{500}} = \hat{y}_0 \times \int_{\theta < 5\times\theta_{500}} \tau_{\theta_s}(r)\ dr$$

where $\hat{y}_0$ is the central Compton parameter estimate, $\tau_{\theta_s}(r)$ represents the assumed universal pressure profile (typically Generalized Navarro-Frenk-White, GNFW), and $\theta_{500}$ is the angular radius corresponding to a density contrast of 500 relative to the critical density.

The total SZ mass proxy $M_\text{SZ}$ is derived by intersecting the two-dimensional $(Y, \theta)$ likelihood with an externally calibrated $Y_{500}$–$M_{500}$ scaling relation, following

$Y_{500} \propto M_{500}^{\alpha}$

with $\alpha \approx 1$ (logarithmic scale). Priors on pressure profile shape and scaling relations from earlier Planck studies are incorporated. When redshift information is available from optical or other wavelengths, $M_\text{SZ}$ and $\theta_{500}$ are refined as functions of $z$, and catalogue entries include $M_\text{SZ}(z)$ arrays for interpolation at the precise counterpart redshift.

3. Multi-Wavelength Counterpart Identification

A layered multi-wavelength search confirms PSZ2 G126.57+51.61. The process includes:

• Positional merging with PSZ1 within 5 arcmin
• Cross-matching with X-ray catalogues (MCXC), verifying $L_{500}$ within $r_{500}$ and the $L_X$–$M_{500}$ scaling relation
• Automated and targeted optical identification (e.g., redMaPPer, SDSS), measuring optical richness ($\lambda$) and obtaining redshift when possible
• Infrared confirmation via AllWISE, searching for galaxy overdensities at 3.4 μm and 4.6 μm
• Comparison with higher-resolution SZ datasets (SPT, ACT), leveraging independent mass and scale information

The spectroscopic redshift for PSZ2 G126.57+51.61, $z = 0.815$, was precisely measured using the ADAM spectrograph at the Sayan Observatory, enabled by identification of the 4000 Å break in the brightest cluster galaxy. Infrared imaging (WISE, convolved with a $\beta$-model profile corresponding to $\approx180$ kpc at $z\simeq0.8$) further validates the cluster as a surface brightness enhancement (Burenin et al., 2018).

4. Statistical Validation: Completeness and Purity

The completeness of the PSZ2 sample is modeled via Monte Carlo injections of simulated clusters into real Planck maps, sampling a wide array of pressure profiles (e.g., cosmo-OWLS). An analytic error-function (ERF) model reinforces the findings. Purity is quantified by noise-only simulations and neural-network quality assessments (parameter $Q_\text{NEURAL}$), flagging potential foreground contamination. The catalogue achieves a lower purity bound of 83%. For PSZ2 G126.57+51.61, the high Galactic latitude (b $= +$51.61°) implies low infrared contamination and optimal selection function reliability.

5. Context within Cosmological Studies

PSZ2 G126.57+51.61 is singled out as the only high-redshift ($z > 0.7$) cluster from the cosmological sample of PSZ2 confirmed in this program (Burenin et al., 2018). This sample prioritizes high-SZ-significance and likely higher mass objects for cosmological analysis. The identification of this cluster nearly doubles the number of confirmed PSZ2 clusters at $z \approx 0.8$ and enhances the reliability of galaxy cluster number counts at high redshift.

High-redshift SZ clusters are critical for the calibration of the evolution of the cluster mass function, constraining cosmological parameters (e.g., $\Omega_m$, $\sigma_8$), and tracing structure formation. The spectroscopically precise $z = 0.815$ measurement tightens the constraints on theoretical models by yielding an empirically verified abundance at this epoch.

6. Comparison with External Cluster Surveys

The Planck SZ selection function is nearly mass-limited and largely independent of redshift, in contrast to X-ray selected samples (e.g., MCXC, ROSAT All-Sky Survey) which are flux-limited. Planck detects clusters—such as PSZ2 G126.57+51.61—that may be under-luminous in X-rays, possibly due to non-cool-core or dynamically disturbed conditions. This selection ameliorates biases inherent in X-ray surveys and complements higher-resolution SZ datasets (SPT, ACT), which explore alternative angular scales and redshift regimes.

Comparison of multi-wavelength properties (SZ, X-ray, optical, IR) ensures consistency in mass–observable scaling relations and enables cross-catalogue validation.

7. Significance, Systematics, and Future Outlook

Many PSZ2 clusters, including PSZ2 G126.57+51.61, probe the lower mass regime near the detection threshold, expanding the catalog for studies of cluster population evolution and cosmological analysis. The cluster’s location at high Galactic latitude minimizes foreground systematics. While not explicitly confirmed as X-ray under-luminous, its inclusion in systematic studies demonstrates SZ selection’s utility in uncovering clusters potentially missed by X-ray surveys.

A plausible implication is that continued multi-wavelength follow-up and spectroscopic campaigns for SZ-selected samples will further refine cosmological constraints and improve understanding of cluster astrophysics. The accurate measurement of $z=0.815$ and robust multi-wavelength identification of PSZ2 G126.57+51.61 exemplify the synergy between CMB-based SZ selection and targeted optical/IR follow-up, cementing the role of such clusters in constraining models of cosmic structure formation.

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Property	Measurement / Method	Source
SZ Detection	MMF1, MMF3, PwS	PSZ2 (Collaboration et al., 2015)
Spectroscopic Redshift	$z=0.815$	ADAM/Sayan Obs (Burenin et al., 2018)
Completeness Lower Limit	83%	PSZ2 (Collaboration et al., 2015)
Multi-wavelength Counterparts	Optical, IR, X-ray, SZ	PSZ2, WISE, MCXC

PSZ2 G126.57+51.61 remains a key object for both astrophysical and cosmological research, exemplifying the advances afforded by cross-survey, multi-wavelength detection and characterization protocols.