Mapping with Probability – The Fortunate Isles Anthony Smith, Andrew Hopkins, Dick Hunstead

Galaxy Clusters Morphology-Density SFR-Density Mass Tracers Galaxy Cluster Abell 1689 (Hubble)

Detecting Clusters - Tricks Colour Clustering, Miller et al BCG Colour-Redshift, Koester et al not so good for finding things you don’t expect

Detecting Clusters – Geometry (1) Smoothing Different scales, and filters, give different answers

Detecting Clusters - Geometry (2) Minimal Spanning Tree (Barrow, Bhavsar & Sonoda 1985) Delaunay Tessellation Field Estimator (van de Weygaert & Schaap 2007)

Probability Smoothing Smoothing on many scales (no filter) Take Maximum Values

Scale Selection Smoothing on many scales Remember Scales that admit Maximum Probabilities

Probability and Scale Maps Probability Map (P) Comparison with Average Scale Map (S) Comparison with Surrounding Locations P – S Equal weighting of both Probability map for density threshold, scale map for substructure

Structure Identification Probability Map finds Islands Scale Map finds Banks Set threshold in P - S Bank Island

Adaptive Contouring

Application to Sloan DR7 Spectroscopic Survey, all galaxies with r < (~ ), median redshift ~ 0.1 Use galaxies as an adaptive grid Sample scales 0.25 – 1 h -1 Mpc in steps of 0.05 Line-of-sight Redshift radius 50 h -1 Mpc Threshold in Probability minus Scale of 0.5 Minimum Membership of 4

Scaling Redshift Radii 100 h -1 Mpc Relative Galaxy Density z < 0.1 z > h -1 Mpc50 h -1 Mpc Line-of-Sight

Running it for Real Catalogue contains 3475 clusters < z < 0.22 Mean cluster radius 0.65 h -1 Mpc Raising the P – S threshold in the < z < 0.05 redshift slice

Sky Positions (0.05 < z < 0.075)

Occupation Values Low Occupation Value; Filamentary High Occupation Value; Clustery Occupation Value01 Number

Scale Distribution Berlind et al Yoon et al Radius (h -1 Mpc) Us Radius (h -1 Mpc) r

3D Visualisation Clusters from < z < h -1 Mpc

Summary Have designed and implemented a multi- scale structure identification algorithm Minimal assumptions made about cluster properties Identified ~3500 clusters in the Sloan Digital Sky Survey to z = 0.22 Positions and Scale distribution are consistent with previous studies

Further Work Comparisons with other catalogues Quantify cluster properties; refine occupation statistic Examine intracluster galaxy populations Use photometric data Extend to larger scales