5 Kinematics of the CVn I cloud

The sample of 34 possible members of the CVn I cloud, which are marked in Table 2 in bold print, are characterized by a mean distance ${ < D >} = 4.1 \pm 0.2$ Mpc and a mean radial velocity ${< V_{\rm LG} >} = 286 \pm 9$ km s^-1. The ratio of these quantities yields $H(CVn~I) = 70 \pm 4$ km s^-1 Mpc^-1as the local value of the Hubble constant, which agrees well with its global value, $H_0 = 69 \pm 4$ (random) $\pm 6$ (systematic) km s^-1 Mpc^-1 (Ferrarese et al. 2000). In other words, within the uncertainties the CVn I cloud as a whole is at rest with respect to the global cosmic flow within random errors.

As a dynamical system, the CVn I cloud has the following integrated parameters: a radial velocity dispersion $\sigma_{\rm v} = 50$ km s^-1, a mean projected linear radius ${< R_{\rm p} >} = 760$ kpc, a mean harmonic projected radius ${< R_{\rm H} >} = 635$ kpc, and an integrated luminosity of $L_B = 2.15\times 10^{10}~ L_{\odot}$. Considering the CVn I cloud to be in dynamical equilibrium and applying the virial relation (Limber & Mathews 1960)

$$M_{\rm vir} = 3\pi N \cdot(N-1)^{-1} \cdot G^{-1} \cdot \sigma^2_{\rm v} \cdot R_{\rm H},$$

where G is the gravitational constant and N is the number of group members, we obtain the virial mass estimate

$$M_{\rm vir} = 3.6\times 10^{12} ~M_{\odot}$$

and the virial mass-to-total luminosity ratio of 167  $M_{\odot}/L_{\odot}$. Because half of the total luminosity of the CVn I cloud is emitted by its brightest galaxy, NGC 4736, we may consider formally the remaining cloud members as companions to NGC 4736. Under these assumptions, the orbital mass estimator is

$$M_{\rm orb} = (32/3\pi)\cdot G^{-1}\cdot (1- 2e^2/3)^{-1} <R_{\rm p}\cdot \Delta V^2_{\rm r} >,$$

where e is the eccentricity of the Keplerian orbit, and R_i and $\Delta V_i$are the projected linear distance and radial velocity of a companion with respect to NGC 4736. Adopting a mean eccentricity e=0.7, we derive $M_{\rm orb} = 1.9\times 10^{12}~ M_{\odot}$ and $M_{\rm orb}/L_{B} = 88$  $M_{\odot}/L_{\odot}$. Both estimates are in satisfactory agreement with the mass-to-luminosity ratio, $M_{\rm vir}/L_{B} = 93$  $M_{\odot}/L_{\odot}$ obtained by Tully (1987) for 22 members of the CVn I cloud.

Based on the present (incomplete) data on galaxy distances, we may establish that the CVn I cloud extends in depth some 2.5-3.5 Mpc, namely, from $D_{\min} = 2.5$ Mpc to $D_{\max} = 5$ Mpc (via the TRGB method) or even to 6 Mpc via the less reliable distance estimates from the brightest stars. In the projection onto the sky the most distant CVn I members are situated at $R_{\rm p} \sim 1.4$ Mpc from the center. Hence, the CVn I cloud is a system slightly elongated in space along the line of sight.

It should be emphasized that such an extended complex of galaxies with a low velocity dispersion (only 50 km s^-1!) has not yet reached the virialized state. The "crossing time'' of the CVn I cloud defined as $T_{\rm cross} = {< R_{\rm p}>}/ \sigma_{\rm v}$ is 15 Gyr, comparable to the cosmic expansion time. Consequently, the derived estimates of the virial/orbital mass should be used with great caution.

What is the dynamical state of the CVn I cloud? Is it a semi-virialized system or a structure taking part in the free Hubble flow? Figure 6 presents the distribution of galaxies in the CVn I region according to their distances and radial velocities.

Figure 6: Velocity-distance relation for galaxies in the CVn I region. The galaxies with accurate distance estimates are indicated by filled circles, The most luminous of them are shown as filled squares. The galaxies with distances estimated via the brightest stars are marked by crosses. The straight line corresponds to the Hubble constant $H_{\rm o} = 71$ km s-1 Mpc-1. Position of the CVn I centroid is shown as an open box with sides equal to 1-$\sigma$ errors of the mean distance and velocity.

Here the galaxies with accurate distance estimates are shown by filled circles, and the galaxies with distances known only via the brightest stars are indicated by crosses. Four luminous galaxies with M_B < -18 mag are shown by filled squares. The straight line that passes the foreground objects KK 230, DDO 187, and UGC 8508, and the background galaxies UGCA 290, NGC 4258, and NGC 5194/95, fits a Hubble constant H = 71 km s^-1 Mpc^-1. The CVn I centroid position is indicated by an open box whose sides correspond to the 1-$\sigma$ errors of the mean distance and velocity. From the data we conclude that the peculiar velocity of the centroid of the CVn I cloud does not exceed the error of its determination, $\sim$20 km s^-1. This result seems to be not trivial, because of the existence of the Virgo-centric flow (Kraan-Korteweg 1986) can generate significant deviations from the pure Hubble flow on a scale of $\sim$5 Mpc.

The behavior of the members of the CVn I cloud in Fig. 6 reveals an interesting feature: all the galaxies at the front of the cloud are situated above the Hubble regression line. That may be caused by the differential motion of the peripheral galaxies towards the cloud center at a velocity of $\sim$65 km s^-1. In the case of spherical symmetry, a similar motion of more distant cloud members towards its center (i.e., towards us) is expected (Tonry et al. 2000). Unfortunately, the distances to galaxies at the back of the cloud are known so far only with large errors, and the suspected "back-flow'' effect turns out to be very noisy. But we believe that more accurate distance measurements for a dozen galaxies on the back of the cloud can easily clarify whether the backflow effect exists or not.

Thus, returning to the question about the dynamical state of the CVn I cloud, we suggest that the complex of predominantly irregular galaxies shows some signs of deviation from the free Hubble expansion. But it seems to be very far from the virialized state. Presumably evolving systems like the CVn I cloud, UMa cloud, and the Cancer cluster are a common feature of the large scale structure of the universe.

It should also be noted that in the CVn I region there are some galaxies (UGC 7131, NGC 4150, KK 127, and UGC 7949) with radial velocities of 100-350 km s^-1, but with distance estimates in the range of (10-20) Mpc. These objects tend to be concentrated on the southern side of the cloud, closer to the Virgo cluster. These galaxies may belong to the Virgo cluster outskirts, and their low radial velocities may be caused by large peculiar motions with respect to the Virgo core.