Galaxy Cluster Detection and Dynamical Analysis in the VIPERS High-Redshift Spectroscopic Survey

We present a dynamical analysis of galaxy clusters identified in the VIPERS spectroscopic survey within the redshift range 0.5 <= z <= 1.2. Cluster candidates were first detected as overdense regions in redshift space through the Finger-of-God (FoG) effect, and cluster membership was assigned using the GalWeight technique within the FoG-GalWeight methodology developed by our team. For each cluster, we derived the virial radius (R200), velocity dispersion (sigma200), and virial mass (M200) using the virial mass estimator. We identified ten VIPERS clusters spanning a mass range of 0.59 x 10^14 <= M200/(h^-1 Msun) <= 4.32 x 10^14 and velocity dispersions of 360 <= sigma200 <= 900 km s^-1. We cross-matched the VIPERS clusters with published catalogs and found at least one matching system for each cluster, offering external validation for our detections. We investigated the velocity dispersion-mass relation for these systems and obtained log(sigma200) = (2.73 +/- 0.06) + (0.36 +/- 0.18) log(M200), with an intrinsic scatter of sigma_int = 0.04 +/- 0.07. The derived relation is consistent with theoretical predictions from N-body and hydrodynamical simulations, confirming the reliability of the FoG-GalWeight methodology and the robustness of the virial mass estimator. Our findings demonstrate that the velocity dispersion can serve as a reliable and direct proxy for cluster mass, even at high redshift, without requiring additional dynamical mass modeling.

💡 Research Summary

This paper presents a comprehensive dynamical study of galaxy clusters identified in the VIMOS Public Extragalactic Redshift Survey (VIPERS) within the redshift interval 0.5 ≤ z ≤ 1.2. The authors develop and apply a fully spectroscopic detection pipeline that couples the Finger‑of‑God (FoG) effect with the GalWeight membership algorithm – a methodology they refer to as FoG‑GalWeight.

The dataset consists of the second public data release (PDR‑2) of VIPERS, containing ~90 000 galaxies with high‑confidence spectroscopic redshifts (quality flag ≥ 2) and a typical redshift error σ_z ≈ 0.00054(1+z). The survey covers two fields (W1 and W4) spanning ~24 deg² and a comoving volume of ≈5 × 10⁷ h⁻³ Mpc³.

Cluster detection proceeds in four steps. First, a local density ρ_cy is computed for each galaxy inside a cylindrical volume of radius 1 h⁻¹ Mpc and height 3000 km s⁻¹ (the typical FoG length). Galaxies are ranked by ρ_cy and any region containing at least seven galaxies within ±1500 km s⁻¹ is flagged as a candidate overdensity. Second, a binary‑tree algorithm together with a two‑dimensional Adaptive Kernel Method (2D AKM) locates the spatial centre (α_c, δ_c), while a one‑dimensional AKM yields the mean redshift z_c. Third, the GalWeight technique is applied to all galaxies within a projected radius of 8 h⁻¹ Mpc and a velocity window of ±3000 km s⁻¹. GalWeight assigns dynamical weights in projected phase space (R_p, v_pec) and separates true members from foreground/background interlopers with >98 % accuracy, as demonstrated in previous simulation tests.

With membership established, the authors compute dynamical quantities using the classic virial mass estimator:

M_VT = (3π/N) Σ_i v_pec,i² / (G Σ_{i<j} 1/R_ij).

Because the virial theorem strictly applies only within the virialized region, they apply a surface‑pressure correction S(r) derived under the assumption of an NFW density profile and isotropic orbits. The corrected mass is M_VTC = M_VT