F. D. A. Hartwick

Peer reviewed: NoNRC publication: Ye

We construct models describing the velocity field in the infall regions of clusters of galaxies. In all models the velocity field is the superposition of a radial systematic component that is assumed to be spherically symmetric and a "noise" component of random nature. The latter accounts for the combined effects of small-scale substructure and observational errors. The effect of the noise term is to smear out the caustic envelopes searched for by previous groups, resulting in models that resemble the observations quite well. When the systematic component is known, the infall velocity and the mass profile of the infall region of the clusters can be determined. Given a particular model, it is possible to calculate the distribution function f(cz, θ, m) at all points in the observable (cz, θ, m) phase space outside the virialized region. It is demonstrated, on simulated data, that the use of a maximum likelihood estimator enables identification of the correct model, even at realistic noise levels. To minimize systematic effects caused by deviations from spherical infall, observations from a number of clusters should be used when applying the method to a real data set. Combining data from different clusters is a straightforward procedure. In the models the mass-to-light ratio is allowed to vary freely with radius. Furthermore, the models do not require any knowledge of the virial region. Rather, such knowledge can be used to test the models' ability to produce realistic results by comparing the mass estimated by the models at small radii to the mass estimates obtained for the inner region using the virial theorem. As a corollary we show how distance information of the quality obtained using the Tully-Fisher relation enhances the likelihood signal. Such distance information might be used in the future either to strengthen the results for this type of model or to allow more advanced models to be used (e.g., models breaking the assumption of spherical symmetry). The method relies on observations of redshifts of galaxies at large angular separations from the centers of the clusters. Currently, such data exist only for Coma, to which we apply the method as an example. The estimated mass at r = 2.5 h^-1 Mpc falls in the range 1.1-2.4 × 10¹⁵ h^-1 M_☉, depending on the model and on the level of the noise term. We find r_turn to be of the order of 10 h^-1 Mpc, a result that is rather robust against changes in the model and subdivision of the data in various ways. We find 0.6<Ω^0.6₀/b^0.75b is the bias parameter, when using the luminosity profile adopted in the models. Interpreting this result, one must recall that the luminosity function of Coma is not well known in the infall region, and that ideally the method should be used on several clusters simultaneously to minimize the effects of deviations from the spherical model. The method provides a promising way of measuring the infall velocities in the outer regions of clusters. However, a robust determination of cluster properties must await future redshift observations of galaxies in the outer regions of a number of clusters.

Results of a blind test of photometric redshift predictions against spectroscopic galaxy redshifts obtained in the Hubble Deep Field with the Keck Telescope are presented. The best photometric redshift schemes predict spectroscopic redshifts with a redshift accuracy of |Delta-z|<0.1 for more than 68 percent of sources and with |Delta-z|<0.3 for 100 percent, when single-feature spectroscopic redshifts are removed from consideration. This test shows that photometric redshift schemes work well at least when the photometric data are of high quality and when the sources are at moderate redshifts.Comment: 14 pp., accepted for publication in A

We construct models describing the velocity field in the infall regions of clusters. The velocity field is the superposition of a systematic component and a "noise" component accounting for the effects of small scale substructure and observational errors. This procedure results in models which resemble the observations (redshifts and angular separations of galaxies surrounding clusters) quite well. We demonstrate, on simulated data, that it is possible to estimate correctly the parameters of the systematic velocity component, knowledge of which allows determination of the mass profile of a cluster. To avoid systematic effects when analyzing real data, observations from a number of clusters should be combined. In the absence of sufficient data on other clusters we illustrate the method by applying it only to the Coma cluster. This results in mass estimates near the virial radius as well as at the turn around radius.

Results of a blind test of photometric redshift predictions against spectroscopic galaxy redshifts obtained in the Hubble Deep Field with the Keck Telescope are presented. The best photometric redshift schemes predict spectroscopic redshifts with a redshift accuracy of |Delta-z|<0.1 for more than 68 percent of sources and with |Delta-z|<0.3 for 100 percent, when single-feature spectroscopic redshifts are removed from consideration. This test shows that photometric redshift schemes work well at least when the photometric data are of high quality and when the sources are at moderate redshifts.

Photometric redshifts have been determined for the galaxies in the Hubble Deep Field. The resulting redshift distribution shows two peaks: one at z ~ 0.6 and one at z ~ 2.2. Luminosity functions derived from the redshifts show strong luminosity evolution as a function of redshift. This evolution is consistent with the Babul & Rees scenario wherein massive galaxies form stars at high redshift while star formation in dwarf galaxies is delayed until after z = 1.

Photometric redshifts have been determined for the galaxies in the Hubble Deep Field. The resulting redshift distribution shows two peaks: one at z~0.6 and one at z~2.2. Luminosity functions derived from the redshifts show strong luminosity evolution as a function of redshift. This evolution is consistent with the Babul & Rees (1992) scenario wherein massive galaxies form stars at high redshift while star formation in dwarf galaxies is delayed until after z=1.