John Phillips edited Data Section.tex  over 9 years ago

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We draw our obseravational data from Data Release 7 (DR7) of the Sloan Digital Sky Survay (SDSS), making use of derived data products from the NYU Value-Added Galactic Catalog (VAGC). The magnitudes from the NYU VAGC that we use have been k-corrected to z = 0.1 using the code Kcorrect. Additionally, we restrict ourselves to regions of SDSS where the spectroscopic completeness parameter FGOTMAIN exceeds 0.7. We also reject all galaxies with velocity errors greater than 25 km/s.  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 associated  satellites. \subsection{Corotation signal}  In this subsection, we investigate pairs of satellite pairs located diametrically opposite their host for signals of corotation. To facilitate this, we will introduce the parameter $\alpha$, defined as the angle between the line extending from one satellite through the host and the position vector of the second satellite. This definition is sketched in Figure \ref{fig:corot}.  We first focus on the corotation signal at small alpha, $\alpha$,  where for the duration of this paper we will refer to a satellite pair as ``corotating" if they have opposite-signed velocity offsets relative to the hosts and their associated $\alpha$ is greater than $90^{\circ}$, or they have same-signed velocity offsets relative to the hosts and their associated $\alpha$ is less than 90\degree ; otherwise, they are deemed counter-rotating. Figure \ref{fig:zoom} shows the fraction of satellite pairs that are corotating as a function of $\alpha$ for $\alpha \lt 45^{\circ}$. At $alpha \gt 45^{\circ}$, the signal is consistent with the sample being divided equally between co-rotating and counterrotating, i.e. a corotation fraction of 0.5, as is what would be expected in the absense of any corotating structure. At small $\alpha$, the corotation signal increases to $\gt 1 \sigma$ above 0.5, potentially indicating a relative overabundance of co-rotating pairs versus counter-rotating ones. Viewed in this way, the data would seem to indicate the presense of coherently rotating scrutures that can only be detected at small $\alpha$. However, viewed a different way the picture becomes less clear. Figure \ref{fig:full} shows the corotating fraction of satellite pairs over the full domain of $\alpha$. It no longer seems to be the case that the data is described as being consistent with a flat line at 0.5 over most of the domain and an increase at small alpha. Rather, it seems to be the case that the spike at $\alpha \sim 10^{\circ}$ is consistent with seemingly random noise present in the data, and that the data is potentially consistent with a flat line. The remainder of this paper will examine the argument that the spike at small alpha is significant, and indicative of ubiquitous coherent corotation in satellite populations (of the kind seemingly seen in M31) by comparing the data to statistical models of satellite kinematics.