Spectroscopic Characterization of redMaPPer Galaxy Clusters with DESI

TL;DR

This study uses DESI spectroscopy to quantify projection effects in redMaPPer optical clusters, modeling the line-of-sight velocity distribution with a two-component Gaussian to separate true cluster members from projections and defining a spectroscopic richness $\lambda_{spec}$ to compare with the photometric richness $\lambda$. It finds a clear richness dependence of projection effects, and first robust evidence that projections increase with redshift by about $\sim$25% from $z\sim0.1$ to $z\sim0.2$, with fainter galaxies contributing more to projections. The authors show that the stacked cluster velocity dispersion scales with spectroscopic richness as $\sigma_{cl} \propto \lambda_{spec}^{k}$ with $k \approx 0.36$–$0.37$, implying a near-linear $\lambda_{spec}$–halo mass relation, and they quantify the richness bias $b_\lambda$ due to projection. These results highlight the importance of representative spectroscopy to calibrate optical cluster observables, especially for LSST-era surveys, and motivate targeted spectroscopic follow-up to tightly constrain mass proxies and cosmological inferences.

Abstract

Optical galaxy cluster identification algorithms such as redMaPPer promise to enable an array of astrophysical and cosmological studies, but suffer from biases whereby galaxies in front of and behind a galaxy cluster are mistakenly associated with the primary cluster halo. These projection effects caused by irreducible photometric redshift uncertainty must be quantified to facilitate the use of optical cluster catalogues. We present measurements of galaxy cluster projection effects and velocity dispersion using spectroscopy from the Dark Energy Spectroscopic Instrument (DESI). Our findings are as follows: we confirm that the fraction of redMaPPer putative member galaxies mistakenly associated with cluster haloes is richness dependent, being more than twice as large at low richness than high richness; we present the first spectroscopic evidence of an increase in projection effects with increasing redshift, by as much as 25 per cent from $z\sim0.1$ to $z\sim0.2$; moreover, we find qualitative evidence for luminosity dependence in projection effects, with fainter galaxies being more commonly far behind clusters than their bright counterparts; finally we fit the scaling relation between measured mean spectroscopic richness and velocity dispersion, finding an implied linear scaling between spectroscopic richness and halo mass. We discuss further directions for the application of spectroscopic datasets to improve use of optically selected clusters to test cosmological models.

Figures (16)

• Figure 1: Luminosity distribution of redMaPPer cluster galaxies, inferred assuming redMaPPer photometric redshifts and $i$-band magnitudes. The upper left, middle, and right panels illustrate redMaPPer member galaxies for clusters with photometric redshifts satisfying $\mathop{\mathrm{\textit{z}_{\lambda}\xspace}}\nolimits>0$, $0.08 \leq \mathop{\mathrm{\textit{z}_{\lambda}\xspace}}\nolimits \leq0.12$, and $0.18 \leq \mathop{\mathrm{\textit{z}_{\lambda}\xspace}}\nolimits \leq 0.22$, respectively. The red curve corresponds to the SDSS DR9 spectroscopy used to construct the redMaPPer catalogue; the blue curve corresponds to spectra used in this work that were not used by redMaPPer (i.e., DESI DR2 and SDSS DR17 exclusive of data in DR9); the purple combines the spectroscopic data represented by the blue and red curves. Lower panels indicate the fraction of galaxies with spectroscopic redshifts, where the horizontal line indicates the sample mean. For the analysis in this work, we adopt lower luminosity limits of $0.2\mathop{\mathrm{\textit{L}^*\xspace}}\limits$ at $z\sim 0.1$ and $0.4\mathop{\mathrm{\textit{L}^*\xspace}}\limits$ at $z\sim0.2$; for details on this choice see § \ref{['sec:data']}. The grey shading indicates regions of selection-parameter space not used in this work. This figure illustrates that new spectroscopic observations improve cluster galaxy coverage, enabling the measurements in this work.
• Figure 2: Line-of-sight velocity distribution of redMaPPer cluster galaxies for the samples used in this analysis. This distribution exhibits evidence of multiple contributing components, representing true cluster halo members and galaxies in projection, respectively. The galaxies in projection can in principle be attributed to multiple failure modes dominated by photometric redshift uncertainty, and including blending, etc. Modeling this distribution enables both calibration of redMaPPer richness and direct use of stacked cluster velocity dispersion for cosmological studies.
• Figure 3: Line-of-sight velocity distribution of redMaPPer galaxy clusters for the fiducial samples at $z \sim0.1$ and $z\sim0.2$, respectively. A double Gaussian model is fit to the data, where the component representing galaxies in projection is constrained jointly with all richness bins. The galaxies in projection exhibit mean redshift on the far side of their respective host clusters and asymmetry in their distribution, with a surplus (shortage) of data observed relative to the model at the extreme end on the far (near) side of the cluster, discussed further in § \ref{['sec:results']}. Outlying galaxies with $|\frac{\Delta z}{1+z}|>0.1$ are excluded from the samples used in this analysis. This model is used to quantify the degree of richness- and redshift- dependence in the projected galaxy fraction parameter $\mathop{\mathrm{\textit{f}_{\text{proj}}}}\limits$, as shown in Figure \ref{['fig:fproj_vs_lambda']}.
• Figure 4: Dependence of projection effects on redMaPPer richness ($x$-axis) and redshift. Shown in the top panel is the value of the model parameter $\mathop{\mathrm{\textit{f}_{\text{proj}}}}\limits$ encoding the amplitude of projection effects. $\langle \mathop{\mathrm{\textit{f}_{\text{proj}}}}\limits \rangle$ is the mean fraction of putative redMaPPer galaxies whose line-of-sight velocities indicate that these galaxies are not true cluster halo members. The bottom panel illustrates the richness bias $b_\lambda$ derived from the probability of each individual cluster galaxy being in projection according to our model. The shape and relative amplitudes of the Gaussian mixture model components attributed to projection effects can vary for different samples; $\mathop{\mathrm{\textit{f}_{\text{proj}}}}\limits$ summarizes the total amplitude of projection effects. This figure illustrates the redshift and richness dependence of projection effects. Small $x$-axis offsets have been introduced to reduce overlap between points.
• Figure 5: Mean redMaPPer membership probability as a function of richness. Circular markers indicate all members, whereas non-circular markers indicate the subsets with spectroscopic data, as specified in the left legend. On average, $\mathop{\mathrm{\textit{p}_{\text{mem}}}}\limits$ decreases as redshift increases from $z\sim0.1$ to $z\sim0.2$. This effect is observed in the photometric sample and in the subsamples with representative spectroscopy from SDSS and DESI. The decrease in mean $\mathop{\mathrm{\textit{p}_{\text{mem}}}}\limits$ as redshift increases counteracts the increase in the projection fraction of redMaPPer galaxies. Taking both of these effects into account, richness bias improves from $z\sim0.1$ to $z\sim0.2$. Determining how richness bias scales fully with redshift, however, depends on spectroscopic measurement of $\mathop{\mathrm{\textit{f}_{\text{proj}}}}\limits$ at all redshifts.