4 Results

4.1 The distribution of radial velocities

In Fig. 1 we plot the spatial distribution of the measured stars in three different velocity bins in order to check for the presence large scale motions, such as rotation, or clustering of stars in large substructures of different kinematics. Unfortunately, the distribution of the points, dictated by the geometry of the spectral masks, precludes a finer analysis, but a visual inspection of the graph reveals no evidence of clumping of stars with similar velocities, nor of rotation along the axis defined by the observational technique.

We can safely proceed, therefore, to draw histograms and estimate velocity dispersions. Figure 2 presents velocity histograms of the single stars in Table 1 with two different bin sizes, and two different origins to check for sampling effect. The top two panels are for a binning of 11 km s^-1 (corresponding to our estimate for the mean random error in the velocities) and the lower two for a binning of twice this error. The multiple peaks of the first plot disappear when the bins are shifted by 5 km s^-1 (half a step), indicating that they are artifacts of the small number statistics. This is confirmed in the lower panel where shifting the sampling by half a step (11 km s^-1) does not change the distribution in any significant way. The hypothesis of a Gaussian distribution is valid, based on $\chi^2$ tests performed to the distribution.

We conclude that there is no evidence for statistically significant peaks in the radial velocity distribution of the cluster. Thus, we can use all the data to estimate the velocity dispersion of the cluster. After correction for measurement (internal) errors and zero point errors (from the [O I] Auroral line), the radial velocity dispersion of 48 single stars in the cluster is 32 km s^-1. This is much larger that the value expected if the cluster is virialised with a total mass equal to the photometric mass and also much larger than our combined errors ( $\sigma_{\rm {tot}}\sim 15$ km s^-1).

Figure 2: Distribution of radial velocities for two bin sizes of corresponding to the typical measurement error (11 km s-1, top panels) and twice that error (bottom panels). The histograms are shifted by half a bin between the left and the right panels to illustrate features due to sampling statistics.

4.2 Binaries

Spectroscopic binaries are very difficult to detect in a single observation, specially single-lined ones. Clearly, therefore, the number of binary candidates listed in Table 1 is only a lower limit. This is consistent with the fact that studies of young open clusters indicate 30% to be a typical percentage of binaries detected in these systems (Garmany et al. 1980; Levato et al. 1991) to be compared to 13% in our sample.

Our data alone, therefore, can only be used to determine a lower-limit to the effect of binaries in the observed velocity dispersion of NGC 2070. An upper limit can be obtained using the Montecarlo simulations of Bosch & Meza (1998). Assuming that all the stars in the cluster are binaries with their center of mass at rest within the cluster the models predict a velocity dispersion of $\sigma_{\rm {bin}} \sim 35$ km s^-1. This must be compared with our observed dispersion of 46.5 km s^-1 including the 55 stars of Table 1 (corrected for observational errors). If we exclude star #1024 with a radial velocity of 510 km s^-1 which may not be a member of the cluster, the dispersion is reduced to 36.5 km s^-1. This result is consistent, within the uncertainties, with the hypothesis that most of our observed velocity dispersion for the cluster is due to binary motions. A (very uncertain) lower limit for the virial motions of the stars in the cluster potential is thus, $\sigma_{\rm {vir}}=\sqrt{36.5^2 - 35^2}\sim 10$ km s^-1.

For comparison purposes we can estimate the expected velocity dispersion assuming the cluster is virialised and the total mass is equal to the upper photometric mass limit from Paper III. From the density distribution derived in the same paper, we estimate a core radius of 0.5 pc which yields $\sigma_{\rm {phot}}=18$ km s^-1.

4.3 Mass segregation

In Paper II, using only the stars with spectroscopy, we found that the most massive stars in NGC 2070 were preferentially found closer to the center of the cluster. This was interpreted as tentative evidence in favor of the existence of mass segregation, as was originally advocated by Malumuth & Heap (1995). This conclusion was somewhat weakened in Paper III which presented a detailed analysis of the IMF in several rings around the cluster center. The IMF was found to have the Salpeter slope almost everywhere with the exception of the very core where, combining intermediate mass HST data from Hunter et al. (1995) with our high mass end data, we found marginal evidence for flattening. The most important "mass segregation" was found in a "ring" 6 pc away from the cluster center, again weakening the idea that closer to the center we would find the major relative concentration of massive stars. We should point out in the context that, because of the strong density gradient, the half-mass ratio of the cluster is very small. This explains the large concentration of high mass stars in the central parsec of the cluster found by Massey & Hunter (1998).

The two-body relaxation time for NGC 2070 is about two orders of magnitude larger than the age of the stars. Therefore, if mass segregation is indeed present it must be primordial (Bonnel & Davies 1998; Elmegreen 2000). In either case, dynamical or primordial, we expect to see a difference in the velocity dispersion of the stars as a function of mass in the sense of it being lower for more massive stars. Moreover, if mass segregation has a dynamical origin, we expect to see energy equipartition between stars of different masses (Spitzer 1969).

We can test these hypotheses by splitting the observed non-binary stars into two equal groups of 24 objects according to their masses as indicated by their spectral types (Table 1). The result is presented in Table 2.

 

 

Table 2: Mass segregation.

Mass range	Mean mass	Velocity dispersion
>23.5 $M_\odot$	49.6 $M_\odot$	27.8 km s-1
<23.5 $M_\odot$	19.4 $M_\odot$	36.7 km s-1

The Fischer F-test on both distributions gives a value of F=1.6 corresponding to a probability of 27% that both samples are drawn from the same parent distribution. Thus, there is tentative, but not conclusive, evidence that the massive stars have a lower dispersion. The ratio of mean energy (M²) between the two mass bins is $\sim$ $1.5 \pm 0.1$, significantly different from the equipartition ratio, r=1. So if the mass segregation is indeed present, it is most likely not due to two-body relaxation. We remark, however, that our radial velocity data samples very sparsely the inner 10 pc of the cluster, where we concentrated our photometric study, and which contains most of the cluster mass.