John Phillips edited Data Section.tex  over 9 years ago

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In selecting our sample, we initially adhere closely to the procudure of I14. We select a sample of hosts in the magnitude range $-23 \lt r \lt -20$ and within a redshift range of $0.002 \lt z \lt 0.05$. A host is considered isolated if there are no brighter objects within 500 kpc on the sky in projection and within 1500 km/s in velocity space. Only isolated hosts are retained, reducing the number of sources to 22780 isolated hosts. From there we identified satellites around each host. Galaxies meet the criteria for being counted as satellites if their magnitudes lie in the range $r_{host} + 1 < r_{sat} < -16$, their projected distance from the host lies between 20 kpc and 150 kpc, and their velocity offset from the host lies in the range $\rm 25 \, km/s < |v_{sat} - v{host}| < 300 \,km/s \times exp(-(d_{proj}/300 \, kpc)^{0.8})$ This velocity bound is taken from I14, and is designed to reduce the contamination from interlopers in the satellite sample. Since our interest is on pairs of satellites, we focus on hosts with two or more satellites. Our sample contains 427 such hosts, with 965 assosiated satellites. Satellites within 150 kpc are of priniciple interest to us, however we will also consider ``outer" satellites, satellites located at projected distances between 150 kpc and 350 kpc and otherwise subject to the same selection criteria. This sample will constitute our ``fiducial" sample.  We will be interested in investigating how our results change when we change how our sample is selected. To this end, we will introduce two more isolation schemes. The first we term our ``annular" sample: a galaxy in the host magnitude range is considered isolated if it has no other galaxies in the host magnitude range within 350 kpc in projection and 1000 km/s in velocity space, and at most one other galaxy in the host magnitude range between 350 kpc and 1 Mpc in projection and 1000 km/s in velocity space. We also define the ``group" sample, we select galaxies that have no brighter objects within 1 Mpc and 1000 km/s but have at least three neighbors in the host magnitude range within 1 Mpc and 1000 km/s. In each case, satellites are selected identially to the fiducial case. The annular selection method yields 116 hosts and 245 satellites, and the group selection method gives 170 hosts with 413 satellites. \subsection{llllll}