7.1.2 The Cluster Properties of HydraI and Coma

Table  lists key cluster properties of HydraI and Coma, namely the Abell richness, the cluster velocity dispersion, the intracluster gas temperature, and the mean projected galaxy density. They all indicate that Coma is substantially (a factor 2-3) more massive than HydraI. In addition the table gives the fraction of spiral galaxies. Hydra has more spiral galaxies than Coma, which is in agreement with Coma being more massive than HydraI - this is the so-called morphology-density relation (Dressler 1980a, Postman & Geller 1984).

Given the above differences, it is interesting to investigate whether there is a difference in the global scaling relations (e.g. the FP and the ${ {\rm Mg}_2}$-$\sigma$ relation) between the two clusters.

The mean projected galaxy densities ${{< \hspace{-3pt} \mu_{\rm gal} \hspace{-3pt}>}}$ given in Table  have been calculated as follows. For the Coma cluster, Kent & Gunn (1982) have counted the number of galaxies brighter than $V = 16\hbox{$.\!\!^{\rm m}$ }5$ and within $33\hbox{$.\mkern-4mu^\prime$ }6$ from the cluster center. They find this number to be 221 galaxies. This is after subtracting an estimated number of 5 background galaxies. They use a background galaxy density from the literature of 10 galaxies/deg². The above-mentioned projected radius corresponds to 1.35 Mpc at the Coma distance. The above-mentioned magnitude limit (i.e. $V = 16\hbox{$.\!\!^{\rm m}$ }5$) corresponds to ${M_{\rm r_T}}= -19\hbox{$.\!\!^{\rm m}$ }5$, where we have used a typical E/S0 galaxy color of $(r-V) = -0\hbox{$.\!\!^{\rm m}$ }2$.

For HydraI, ${M_{\rm r_T}}= -19\hbox{$.\!\!^{\rm m}$ }5$ corresponds to ${m_{\rm r_T}}= 15\hbox{$.\!\!^{\rm m}$ }1$. For the 64 E and S0 galaxies in our HydraI photometry sample, we find the relation ${m_{\rm r_T}}= V_{25} - 0.75$ (rms = 0.32) when comparing with the V₂₅ isophotal magnitudes given in the catalog of Richter (1989). The above magnitude limit therefore corresponds to $V_{25} = 15\hbox{$.\!\!^{\rm m}$ }85$. Note, that this is just a bit fainter than the completeness limit of the Richter catalog, which is $V_{25} = 15\hbox{$.\!\!^{\rm m}$ }65$. The metric projected center distance of 1.35 Mpc corresponds to $57\hbox{$.\mkern-4mu^\prime$ }4$ at the distance of HydraI. Within this radius, the Richter catalog has 114 galaxies brighter than $V_{25} = 15\hbox{$.\!\!^{\rm m}$ }85$. Richter estimates the fraction of background galaxies to be 0.15 for galaxies brighter than $V_{25} = 15\hbox{$.\!\!^{\rm m}$ }85$. This is based on the galaxies that has spectroscopy. It is not clear what a representative outer radius for this spectroscopy sample is, but if we use $57\hbox{$.\mkern-4mu^\prime$ }4$, the implied background galaxy density is 6 galaxies/deg² for $V_{25} \le 15\hbox{$.\!\!^{\rm m}$ }85$. When simply subtracting $0.15\cdot114$ as the estimated number of background galaxies, we are left with 97 galaxies.

The mean projected galaxy density for $r \le 1.35$ Mpc and ${M_{\rm r_T}}\le -19\hbox{$.\!\!^{\rm m}$ }5$ comes out to 39 galaxies/Mpc² for Coma and 17 galaxies/Mpc² for HydraI.

The fraction of spiral galaxies given in Table  has been calculated as follows. In the Coma catalog of Dressler (1980b) there are 25 spiral galaxies within the area that our Coma sample covers and to the completeness limit of our Coma sample, ${M_{\rm r_T}}= -20\hbox{$.\!\!^{\rm m}$ }75$. Since we have 105 E+S0 galaxies in our 93% complete Coma sample brighter than ${M_{\rm r_T}}= -20\hbox{$.\!\!^{\rm m}$ }75$, the spiral fraction is 25/(25+113) = 18%. In the HydraI catalog of Richter (1989) there are 20 spiral galaxies and 49 E+S0 galaxies within $1\hbox{$.\!\!^\circ$ }5$ from the center and brighter than ${M_{\rm r_T}}= -20\hbox{$.\!\!^{\rm m}$ }75$. This gives a spiral fraction of 20/(20+49) = 29%. Note, that the galaxies in the two catalogs are classified by two different persons, and might therefore not be quite comparable.

 

Table: Cluster Properties of HydraI and Coma

	HydraI	Coma	References
Abell richness$^{\rm a}$	39	106	Abell, Corwin, & Olowin (1989)
${\sigma_{\rm cl}}$ [km/s]$^{\rm b}$	608-39+58	1010-44+51	Zabludoff et al. (1990)
$T_{\rm gas}$ [keV]$^{\rm c}$	$3.9\pm0.2$	$8.3\pm0.6$	David et al. (1993)
${{< \hspace{-3pt} \mu_{\rm gal} \hspace{-3pt}>}}$ [galaxies/Mpc2]$^{\rm d}$	17	39	Richter (1989); Kent & Gunn (1982)
Spiral fraction$^{\rm e}$	29%	18%	Richter (1989); Dressler (1980b)

 

Notes: $^{\rm a}$ Abell richness is the number of galaxies in the magnitude range m₃ to m₃+2, where m₃ is the magnitude of the third brightest galaxy in the cluster. The numbers from Abell et al. (1989) have been corrected for background galaxies on a statistical basis. $^{\rm b}$  ${\sigma_{\rm cl}}$ is the line-of-sight velocity dispersion of the cluster, in the rest frame of the cluster. $^{\rm c}$  $T_{\rm gas}$ is the intracluster gas temperature derived from X-ray observations. $^{\rm d}$  ${{< \hspace{-3pt} \mu_{\rm gal} \hspace{-3pt}>}}$ is the mean projected galaxy density for galaxies brighter than ${M_{\rm r_T}}= -19\hbox{$.\!\!^{\rm m}$ }5$ and within a projected radius of 1.35 Mpc from the cluster center, cf. the text. Here and below $H_0 = 50\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$ is assumed. The densities have been corrected for background galaxies on a statistical basis. $^{\rm e}$ The spiral fraction is the fraction of spiral galaxies. The numbers given refer to galaxies brighter than ${M_{\rm r_T}}= -20\hbox{$.\!\!^{\rm m}$ }75$ and within $\approx$ 1.9 Mpc from the cluster center, cf. the text.