# How to find out if a galaxy is in a specific cluster

I am trying to find out how to find out if a certain galaxy is located inside a cluster. For the famous ones this is quite easy (sometimes even on wikipedia!), but I haven't been able to do it for some less-known galaxies. I have tried to look them up on Simbad, but I couldn't find it written down anywhere (even for the ones I know to be in clusters). Also generic "googling" has not helped me. Do you have any suggestions?

• By "in" do you mean "currently present within the boundaries of" or "gravitationally bound to"? The former is fairly straightforward, the latter is more difficult since it requires a determination of the peculiar velocity of the galaxy with respect to the cluster and a mass estimate of the cluster. Oct 16 '16 at 12:39
• Or do you just mean whether it's an optical coincidence?? Oct 16 '16 at 16:40

You want to use NED (NASA Extragalactic Database) rather than SIMBAD, since the former has more galaxy- and cluster-specific information.

I'm going to assume you have a reasonably accurate position for your galaxy as well as its redshift (in km/s). The basic idea is to identify candidate galaxy clusters which are close enough to your galaxy on the sky and in redshift so that the galaxy could potentially be a member of one of them.

1. Determine what angular radius $R$ corresponds to 1 or 2 megaparsecs at the redshift of your galaxy (e.g., using Ned Wright's Cosmology Calculator)

2. Do a search in NED for Galaxy Clusters within R of the coordinates of your galaxy. If your galaxy has a name, you can skip the coordinate lookup and use the "Near name" search form; if you only have coordinates, there's a "Near position" search form.

A. Put the estimated angular radius $R$ (converted to arc minutes) in the "Search Radius" box;

B. Set the "Selection in Redshift" form to "Between" and give it lower and upper limits of $V_{\rm gal} - 2000$ and $V_{\rm gal} + 2000$ in km/s, where $V_{\rm gal}$ is the redshift (in km/s) of your galaxy;

C. Under "Selection by Object Type", select "Galaxy Clusters" in the "Classified Extragalactic Objects" list.

That should give you a list of galaxy clusters within the specified radius of your galaxy which are at a similar redshift. Note that the same cluster may come up multiple times under different names (i.e., from different cluster catalogs), but it should be clear from the coordinates and the redshifts which are the same clusters.

Now the question is whether your galaxy is plausibly a member of a given candidate cluster or not. Ideally you should find some measurement of each cluster's velocity dispersion $\sigma$; if the galaxy's redshift isn't within $\pm 3 \sigma$ of the cluster's redshift $V_{\rm cluster}$, then you can ignore that cluster, since it's very unlikely that a galaxy with that relative velocity with respect to the cluster is actually gravitationally bound to the cluster.

You can't really do better than a probabilistic assessment: roughly how likely it is that the galaxy is a member of a given cluster. Galaxies which are members of a cluster are more likely to be close to the center (on the sky); member galaxies closer to the center can have a higher range of relative velocities, while member galaxies further away should have velocities closer to the cluster redshift.

A quick example: Is NGC 4889 ($V_{\rm gal} = 6495$ km/s) a member of a cluster? At its redshift, 1 Mpc = 33 arc minutes; if we search on NED for galaxy clusters within 33 arcmin of NGC 4889 with redshift limits of 4500-8500 km/s, we get 6 results, 4 of which are just the Coma Cluster in different catalogs, with $V_{\rm cluster} \sim 6900$ km/s. Since the various distances ("Separ. arcmin") translate to $\sim$ 100-300 kpc from the cluster center, and since the Coma cluster has a velocity dispersion of $\sim$ 1000 km/s and the difference between NGC 4889 and the cluster is only $\sim$ 400 km/s, it's a very good bet that this galaxy is a member of the Coma Cluster. (It's actually one of the two cD galaxies in the cluster center.)

First: You can use all galaxies in the line of sight of the cluster to construct their color-magnitude diagram. Those galaxies on the Red Sequence are more likely to be in the cluster (not always true).

Second: You should be able to determine their redshift, and compare with the mean cluster redshift. To be able to make cut, see next step.

Third: You should run some algorithms in order to see whether the redshifts/velocities you have are within the clusters mean velocity dispersion (usually in the clustercentric-velocity space), as used in these papers for example: https://arxiv.org/pdf/1601.06080.pdf