5 U, V, W, and metallicity

5.1 Kinematics of stars with planets

There are only a few studies in the literature on the kinematics of planet host stars (Gonzalez 1999; Reid 2002; Barbieri & Gratton 2002). None of them, however, has made use of a completely unbiased sample to compare planet and non-planet host stars. To fill this gap, we have analyzed the spatial velocities distributions and velocity dispersions for the subsample of extra-solar planet host stars that are included in the CORALIE sample, and have compared this results with space velocities for $\sim$1000 dwarfs that make part of the CORALIE survey (Udry et al. 2000) and have precise radial-velocity measurements. We have restricted the planet sample to only those planets belonging to the CORALIE sample in order to minimize the biases when trying to compare planet and non-planet host stars.

The U, V, and W velocities were computed using CORALIE radial velocities, as well as coordinates and proper motions from Hipparcos (ESA 1997). The convention used is so that U, V and W are positive in the direction of the galactic center, the galactic rotation, and the north galactic pole, respectively. We have then corrected the velocities with respect to the Solar motion relative to the LSR adopting ( $U_{{\rm LSR}}$, $V_{{\rm LSR}}$, $W_{{\rm LSR}}$)$_{\odot}$ = (10,6,6) km s^-1 (e.g. Gonzalez 1999).

In Fig. 9 we plot the classical $U_{{\rm LSR}}$- $V_{{\rm LSR}}$, $U_{{\rm LSR}}$- $W_{{\rm LSR}}$, and $V_{{\rm LSR}}$- $W_{{\rm LSR}}$ diagrams (left plots) for planet hosts (dots) and non-planet hosts (small points), as well as the cumulative functions of $U_{{\rm LSR}}$, $V_{{\rm LSR}}$ and $W_{{\rm LSR}}$ (right plots) for the two samples. As we can see, there is no major difference between the two groups of points. This is supported in all cases by a Kormogorov-Smirnov test. The only special feature to mention in this plot is that the $W_{{\rm LSR}}$ velocity seems to have a greater dispersion for non-planet hosts than for planet hosts (this can be seen from the cumulative functions of $W_{{\rm LSR}}$ for the two samples).

As discussed by Raboud et al. (1998) - see also review by Grenon (2000) - Galactic dynamic models imply that stars coming from the inner disk and influenced by the Galactic bar should present a lower dispersion in $W_{{\rm LSR}}$ and a higher $U_{{\rm LSR}}$. Although the former of these two trends is suggested by our data, the higher $U_{{\rm LSR}}$ observed for the planet hosts (with respect to the other CORALIE sample stars) is not significant (see also Table 3).

Figure 9: Left: $U_{{\rm LSR}}$- $V_{{\rm LSR}}$, $U_{{\rm LSR}}$- $W_{{\rm LSR}}$, and $V_{{\rm LSR}}$- $W_{{\rm LSR}}$ diagrams for planet hosts (filled dots) and stars in the CORALIE sample (see text for more details). Right: cumulative functions of $U_{{\rm LSR}}$, $V_{{\rm LSR}}$, and $W_{{\rm LSR}}$ for the two samples (planet hosts are the filled line, and the CORALIE sample is denoted by the dotted line).

 

 

Table 3: Average space velocities and their dispersions.

Velocities (km s-1)	Planet hosts	CORALIE sample
$<U_{{\rm LSR}}>$	3.2 $\pm$ 6.0	-2.5 $\pm$ 1.2
$<V_{{\rm LSR}}>$	-17.2 $\pm$ 3.9	-18.3 $\pm$ 0.8
$<W_{{\rm LSR}}>$	-1.6 $\pm$ 2.2	-2.6 $\pm$ 0.6
$\sigma(U_{{\rm LSR}})$	37.9 $\pm$ 4.3	37.9 $\pm$ 0.9
$\sigma(V_{{\rm LSR}})$	24.5 $\pm$ 2.8	25.4 $\pm$ 0.6
$\sigma(W_{{\rm LSR}})$	13.8 $\pm$ 1.6	18.9 $\pm$ 0.4

Here we use $\sigma/\sqrt{N-1}$ for the errors in < $U_{{\rm LSR}}$>, < $V_{{\rm LSR}}$>, and < $W_{{\rm LSR}}$>, and $\sigma/\sqrt{2~N-1}$ for the errors in $\sigma(U_{{\rm LSR}})$, $\sigma(V_{{\rm LSR}})$,
and  $\sigma(W_{{\rm LSR}})$; N equals 990 for the CORALIE sample, and 41 for the planet sample.

In Table 3 we list the mean $U_{{\rm LSR}}$, $V_{{\rm LSR}}$, and $W_{{\rm LSR}}$ velocities and their dispersions for the two groups of stars analyzed. As we can see, besides the lower dispersion in W $_{{\rm LSR}}$ for the planet host sample, the two groups do not seem to differ considerably. The mean total space velocity for planet and non-planet hosts (42.2 $\pm$ 4.4 km s^-1 and 45.6 $\pm$ 0.8 km s^-1, respectively), and their dispersions (27.7 $\pm$ 3.1 km s^-1 and 26.4 $\pm$ 0.6 km s^-1) also do not show any special trend.

Figure 10: Right: metallicity as a function of the space velocities for planet and non-planet hosts. Left: cumulative functions for the two samples but dividing the stars in metal rich ([Fe/H] > 0.0 - right panels) and metal poor ([Fe/H] $\leq$ 0.0 - left panels). Symbols as in Fig. 9.

5.2 Kinematics vs. [Fe/H]

In Fig. 10 we further compare the metallicity as a function of the space velocities for the same two samples described above. In the right panels we plot [Fe/H] as a function of $U_{{\rm LSR}}$, $V_{{\rm LSR}}$, and $W_{{\rm LSR}}$, and in the left plots we have the cumulative functions for $U_{{\rm LSR}}$, $V_{{\rm LSR}}$, and $W_{{\rm LSR}}$ as in Fig. 9, but this time separating the stars with [Fe/H] higher than solar (right panel) and lower than solar (left panel). Again, no statistically significant conclusions can be drawn. Stars with planets seem to occupy basically the metal-rich envelope of the $U_{{\rm LSR}}$, $V_{{\rm LSR}}$, and $W_{{\rm LSR}}$ vs. [Fe/H] plots.

In a few words, within the statistical significance of our sample, we can say that for a given metallicity interval, the space velocity distribution of the planet host stars are basically the same as the one found for the whole planet search sample.