The velocity dispersion function of red galaxies in four Hubble Frontier Fields galaxy clusters

Abstract

We present a detailed study of the stellar kinematic properties of red member galaxies in the cores of four strong lensing galaxy clusters at intermediate redshift included in the the Hubble Frontier Fields programme: Abell 2744 ($z=0.307$), Abell S1063 ($z=0.346$), MACS J0416.1$-$2403 ($z=0.397$), and MACS J1149.6$+$2223 ($z=0.542$). We focussed on a sample of 723 red cluster members in the four clusters and we measured their structural parameters using MORPHOFIT for all Hubble Frontier Fields bands. Taking advantage of deep (3.1h to 17h of exposure) integral-field spectroscopy from MUSE on the Very Large Telescope, we tested a pipeline based on the public spectral fitting code pPXF to systematically measure the line-of-sight stellar velocity dispersion $σ$ of cluster members with a spectral $S/N\geq 10$, with a statistical uncertainty consistently below 5%. The resulting catalogue contains 213 measured $σ$ values across the four clusters. We calibrated the Fundamental Plane relation in the rest-frame $r$ band for the early-type cluster members, selected from their colour and morphology, finding compatible parameters both across the clusters, and noting hints of zero-point evolution with redshift. Finally, we used the calibrated Fundamental Plane relations to assign a velocity dispersion value to all 723 red cluster members and studied the velocity dispersion function for each cluster, down to $\log σ\, \mathrm{[km \, s^{-1}] = 1.5}$. A Schechter-function fit of the velocity functions suggests compatible parameters: a positive $α$ slope with values in the range $0.55-1.60$, and $\logσ^*\, [\mathrm{km\,s^{-1}}]$ between $2.18$ and $2.47$. Compared to previous works, we extend the systematic study of the central velocity dispersion of cluster galaxies to lower-$σ$ regimes.

Figures (12)

• Figure 1: RGB images of the cores of the four clusters from HFF photometry. Red, green, and blue channels are obtained by combining the filters F105W + F125W + F140W + F160W, F606W + F814W, and F435W, respectively. We show the FoV of the MUSE observations with red contours, and we mark all the cluster members for which we have measured a velocity dispersion value with green circles. Finally, we showcase the region intersection of all HFF bands for each cluster with cyan contours.
• Figure 2: Line-of-sight velocity dispersion fit with pPXF and main spectral absorption features contributing to the measurement. We choose the cluster member ID 82063 of M0416 (R.A.$=64.0401169$, Dec.=$-24.0659218$, $S/N=133$). We shade the regions masked as potentially affected by issues with the subtraction of sky features and emission lines. We note that the mask in the spectral region around $4200 \, \mathrm{\AA}$ is intended to avoid the effects of the adaptive-optics laser emission used for some MUSE exposures of M0416, and as such is not adopted for the other three clusters. We show the observed spectrum in black, the best-fit in red, and the fit-measured spectral residuals in green. We mark the main absorption lines with red vertical dashed lines.
• Figure 3: Relative increase of the value of the $S/N$ of the spectra of cluster member galaxies when weighting with their surface brightness in the HST F814W band. We compare $S/N$ of the spectrum extracted within an aperture of $1.5"$ from the galaxy centre of light from the weighted MUSE cubes with the $S/N$ of the spectrum extracted for the same galaxy within an aperture of $0.8"$ directly from the (non-weighted) MUSE cube.
• Figure 4: Velocity dispersion values of the cluster members from weighted spectra ($\sigma_w$) compared with the velocity dispersion within the effective radius ($\sigma_e$). The weighted spectrum was extracted within an aperture of $1.5"$ from the galaxy centre of light from the MUSE cubes weighted with the HST F814W surface brightness.
• Figure 5: Distribution around the FP relations of the galaxies used for the calibration for the four clusters. The FP relations are shown on the plot diagonal. The values of $\alpha$, $\beta$, and $\gamma$ for the four clusters are reported in Table \ref{['tabfp']}.