# On the statistics of proto-cluster candidates detected in the Planck all-sky survey

## TL;DR

This study analyzes the statistical nature of proto-cluster candidates detected by Planck, showing most are due to Poisson fluctuations of high-redshift dusty proto-clusters rather than individual bound galaxy clumps, aiding understanding of large-scale structure evolution.

## Contribution

The paper demonstrates through simulations that Planck's proto-cluster candidates are primarily Poisson fluctuations, not individual clusters, refining interpretations of all-sky sub-millimeter surveys.

## Key findings

- Planck proto-clusters are mainly Poisson fluctuations of high-z dusty proto-clusters.
- Simulations reproduce the statistical properties of Planck detections.
- Redshift distribution peaks at 1.5 to 3, informing high-z structure evolution.

## Abstract

Observational investigations of the abundance of massive precursors of local galaxy clusters ("proto-clusters") allow us to test the growth of density perturbations, to constrain cosmological parameters that control it, to test the theory of non-linear collapse and how the galaxy formation takes place in dense environments. The Planck collaboration has recently published a catalogue of >~ 2000 cold extra-galactic sub-millimeter sources, i.e. with colours indicative of z >~ 2, almost all of which appear to be over-densities of star-forming galaxies. They are thus considered as proto-cluster candidates. Their number densities (or their flux densities) are far in excess of expectations from the standard scenario for the evolution of large-scale structure. Simulations based on a physically motivated galaxy evolution model show that essentially all cold peaks brighter than S_{545GHz} = 500 mJy found in Planck maps after having removed the Galactic dust emission can be interpreted as positive Poisson fluctuations of the number of high-z dusty proto-clusters within the same Planck beam, rather then being individual clumps of physically bound galaxies. This conclusion does not change if an empirical fit to the luminosity function of dusty galaxies is used instead of the physical model. The simulations accurately reproduce the statistic of the Planck detections and yield distributions of sizes and ellipticities in qualitative agreement with observations. The redshift distribution of the brightest proto-clusters contributing to the cold peaks has a broad maximum at 1.5 <~ z <~ 3. Therefore follow-up of Planck proto-cluster candidates will provide key information on the high-z evolution of large scale structure.