\n\n\nUnlike a standard FoF this algorithm percolates in angular space.\n\nThe angular distance in radians between two galaxies (*D*) is calculated as shown in the figure on the right. Where $\\alpha\"$ and $\\delta\"$ correspond to right ascension and declination, respectively.\n\nFor two galaxies in a given redshift bin to be considered friends (*i.e.* linked) they must satisfy the following condition:\n\n $D$ \n\nwhere $D_{friend}(z)\"$ is the transverse linking length in radians for a given redshift bin.\n\n### Redshift Binning\n\nThis section is only relevant for `fof_mode=dynamic`.\n\nThe first task the code performs is to bin all of the input galaxies by redshift. This is used to calculate $dn\\/dz\"$ where $dn\"$ is the number of galaxies in a given bin and $dz\"$ is the bin width. Each galaxy is only counted once for this calculation, thus for photometric data the peak photometric redshift value of the galaxy is used.\n\n> NOTE: If a predefined $N(z)\"$ is provided, then these values are used for the $dn\\/dz\"$ calculation.\n\nThe differential comoving volume as a function of redshift, $dV\\/dz\"$ , and the angular diameter distance, $d_A\"$ , are then calculated for each bin using the values of $H_0\"$ , $\\Omega_M\"$ and $\\Omega_\\Lambda\"$ provided.\n\nFinally the angular linking length, $R_{friend}(z)\"$ , for each bin is defined as:\n\n $R_{friend}(z)$ \n\nwhere $r_{ref}\"$ is:\n\n $r_{ref}$ \n\n $z_{ref}\"$ is the specified reference redshift and $R_0\"$ is the input transverse linking parameter. This calculation ensures that:\n\n $R_{friend}(z_{ref})$ \n\nand that for bins with less galaxies (*e.g.* at higher redshifts when selection effects have a stronger impact) the value of $R_{friend}(z_{ref})\"$ will increase, while for bins with more galaxies the value of $R_{friend}(z_{ref})\"$ will decrease. This produces $N_{gal}\"$ values that are more redshift independent.\n\n### Line-of-Sight Linking\n\n

\n\n**• Spectroscopic Data**\n\nIn the spectroscopic mode the line-of-sight linking length is calculated as follows:\n\n $z_{friend}$ \n\nFor two galaxies to be friends they must satisfy:\n\n $|z_1$ \n\nIn this sense the percolation is performed in 3 dimensions.\n\n**• Photometric Data**\n\n

\n\nIn the photometric mode a galaxy is allocated to a redshift bin if it satisfies the following:\n\n $|z_{gal}$ \n\nIn this case $z_0\"$ is a factor that determines how much the galaxies smear along the line-of-sight.\n\nIn this mode percolation is performed in 2 dimensions for each redshift bin independently. As galaxies can exist in multiple bins it is possible to form \"proto-clusters\" in different bins with similar members.\n\nWhen the percolation has finished for all of the bins proto-clusters with common members are merged to form the final detections.\n\n### Cluster properties\n\n**• Centre**\n\nThe cluster centre (*RA, Dec, z*) is calculated as the median of the galaxy members. The errors are calculated as the standard error on the median (*i.e.* $\\sigma$ ).\n\n**• Richness**\n\nThe cluster richness is calculated a the number of member galaxies.\n\n**• Singal-to-Noise**\n\nThe cluster singal-to-noise ratio is calculated as follows:\n\n $SNR$ \n\nwhere $A\"$ is the cluster area and $Bg\"$ is the background level at the cluster redshift. Unless an $N(z)\"$ is provided, the code simply takes the number of objects at the cluster redshift divided by the catalogue area as $Bg\"$ .\n\n**• Radius**\n\nThe cluster radius, $r_{cls}\"$ , is calculated as the distance from the cluster center to the position of the farthest member in the units specified.\n\n**• Area**\n\nThe cluster area is calculated as:\n\n $\\pi$ \n\nin the units specified.\n\n### Optimisation\n\n**• k-d Tree**\n\nThe code make us of an angular [*k-d* Tree](https://en.wikipedia.org/wiki/K-d_tree) (implemented by Luca Tornatore) to reduce the number of calculations required.\n\n**• Union-Find**\n\nThe code also makes use of a [union-find data structure](https://en.wikipedia.org/wiki/Disjoint-set_data_structure) (implemented by Stefano Sartor) to speed up the processes of merging proto-clusters.\n\n**• OpenMP**\n\n[OpenMP](https://en.wikipedia.org/wiki/OpenMP) is used to perform the redshift bin percolations in parallel.\n\n**• Splitting**\n\nThe `cat_split.cpp` code can be used to divide large data sets into overlapping pieces that can be processed individually. The `cat_merge.cpp` code can then reassemble the full catalogue using the results with little to no loss of information.\n","has_starred","hub_user","immutable_tags_settings",{"_75":11,"_76":77},"enabled","rules",[78],".*","is_automated","permissions",{"_82":21,"_83":11,"_84":11},"read","write","admin","user","storage_size",644886946,"orgData","recentTags",[91],{"_92":44,"_93":94,"_95":96,"_97":98,"_99":100,"_50":118,"_119":94,"_120":33,"_121":56,"_57":122,"_123":124,"_125":109,"_126":118,"_127":66,"_128":21},"content_type","creator",2161295,"full_size",322737126,"id",102729540,"images",[101],{"_102":103,"_104":105,"_106":107,"_108":109,"_110":111,"_112":113,"_114":107,"_115":-5,"_116":96,"_63":66,"_117":-5},"architecture","amd64","digest","sha256:32f840746993af0c6ac5da156d0119491607fbc0ace18bec29f0193952937354","features","","last_pulled","2026-10-08T16:47:32.235125396Z","last_pushed","2020-08-28T08:05:21Z","os","linux","os_features","os_version","size","variant","2020-08-28T08:05:20.630172Z","last_updater","last_updater_username","media_type","latest","repository",9153987,"tag_last_pulled","tag_last_pushed","tag_status","v2","sbxKitMetadata","isPotentialSpam","isHubSbxKitsEnabled","showSbxLogoOverride","sbxTrademarkText","displaySecurityMetadata","tagAttestations","tagsHaveAttestations",[],"selectedTag","attestationsUrl","routes/_layout.r.$namespace.$reponame.tags",{"_38":142,"_149":150,"_136":159,"_160":11},{"_40":143,"_42":144,"_45":46,"_47":48,"_49":11,"_50":51,"_52":53,"_54":145,"_57":35,"_32":33,"_58":59,"_60":44,"_61":62,"_63":64,"_65":66,"_67":-5,"_68":62,"_69":70,"_71":11,"_72":33,"_73":146,"_79":11,"_80":148,"_85":33,"_86":87},[],[44],[56],{"_75":11,"_76":147},[78],{"_82":21,"_83":11,"_84":11},"tags",{"_151":64,"_152":-5,"_153":-5,"_154":155},"count","next","previous","results",[156],{"_92":44,"_93":94,"_95":96,"_97":98,"_99":157,"_50":118,"_119":94,"_120":33,"_121":56,"_57":122,"_123":124,"_125":109,"_126":118,"_127":66,"_128":21},[158],{"_102":103,"_104":105,"_106":107,"_108":109,"_110":111,"_112":113,"_114":107,"_115":-5,"_116":96,"_63":66,"_117":-5},[],"canDeleteTags","actionData","errors"]

sfarrens/sfof

Tags for sfarrens/sfof