The velocity dispersion and structure of the Perseus cluster

Prof. Mark Birkinshaw

Outline

The purpose of this module is to use recent astronomical data from the Updated Zwicky catalogue of Falco et al. (1999; PASP 111, 438) to identify galaxies associated with the Perseus cluster, and then to use the positions and redshifts of those galaxies to calculate the mass of the cluster.

If time and enthusiasm permit, the data can be used to examine also


Method

A file of galaxy positions and velocities that contains the locations and redshifts of galaxies within 1.5 hours of right ascension of NGC1275 (a galaxy near the centre of the Perseus cluster) has been prepared and saved on disk. This catalogue is derived from the Updated Zwicky Catalogue (UZC), and therefore only goes to a relatively shallow magnitude limit. Additional lists of Perseus cluster galaxies can be found elsewhere and used to augment the UZC if desired.

The file contains a list of galaxy positions (in J2000 coordinates, right ascension and declination, hhmmss.2, +/-ddmmss), Zwicky magnitudes, redshift and redshift error (in km/s), spectral type (absorption or emission: A/E), the UZC class (0,1,2,3 or 4; see Falco et al.), the number of UZC neighbours, the Zwicky name of the galaxy, a code for the type of spectrum used (F/Z; see Falco et al.), a reference code (also in Falco et al.), any other name for the galaxy, a code showing whether the object is a multiple galaxy (*), and an indication if the NASA Extragalactic Database (NED) thinks the galaxy is in a pair, triple or group (P/T/G). The columns are marked with a short descriptive header.

The redshift of a galaxy is affected by the expansion of the Universe, and the motion of that galaxy in the potential well of the cluster as a whole. In that case, the virial theorem (see this brief description or the longer discussion in Peebles, P.J.E., 1990, Physical Cosmology , Princeton University Press) can be used to calculate the mass of the cluster.

There are three main ingredients to the calculation. First, the Perseus cluster must be identified (it lies near RA 03:30:00, Dec +41:30:00, cz 5300 km/s), and the galaxies which are potential members of the cluster extracted.

Second, the velocity dispersion of galaxies in the cluster must be found. This can be done using the method of Danese, L., De Zotti, G. & Di Tullio, G, 1980 Astronomy and Astrophysics 82, 322 , a method that has the advantage of returning an error on the dispersion. The same calculation also finds the redshift of the centre of mass of the cluster (with an error).

The third part of the calculation is to estimate the gravitational effective radius of the cluster. This can be done in a number of ways: one is to assume that each galaxy has the same mass-to-light ratio and use the galaxy brightnesses (using, say, the Zwicky magnitudes) as a measure of their masses and then to use the galaxy positions and estimated masses to calculate the effective radius.

Finally, the effective radius and the velocity dispersion can be combined to produce an estimate for the mass (and an error on that estimate).

A number of alternative methods for computing masses from this type of data have been discussed (e.g., Bahcall, J.N. & Tremaine, S., 1981, Astrophysical Journal, 244, 805 or Heisler, J, Tremaine, S. & Bahcall, J.N., 1985, Astrophysical Journal, 298, 8 ) and it is clear that the mass estimates that are derived may depend strongly on substructure within the cluster and the choice of galaxies with measured velocities (e.g., for the Coma cluster: Colless, M. & Dunn, A.M., 1996, Astrophysical Journal, 458, 435 ). An exploration of these issues is difficult, but a brief discussion could be given of their effect on the simple mass estimate that you derive.

Finally, if you follow up on the references to substructure in clusters, or X-ray emission from clusters, or the influence of cluster gas on radio sources and sources in the Perseus cluster, or the radial distribution of galaxy types in clusters (via searches on the Perseus cluster on NED , or via bibliography searches on the NASA Astrophysics Data System , or using the data available on-line in various places), you will be able to enrich the project by applying your results to some contemporary astrophysics problems. I should warn you, however, that this part of the project is likely to be tough and time-consuming, and is only for enthusiasts.


Further information

I have placed on this WWW site, the results of a simple NED search for all objects which that database believes are associated with the Perseus cluster (Abell 426).

Some related references that might be of interest (and which can be found via the NASA Astrophysics Data System ) are

although only small sections of the latter two papers are likely to be useful to you. Many more (346 at the latest count) references on the Perseus cluster and its properties can be found using NED and the ADS.


Mark Birkinshaw