4 Space velocity and galactocentric orbit

As shown below, the parameters of the runaway motion and galactocentric orbit of GRO J1655-40 are essentially the same for distances in the range of 0.9-3.2 kpc. The tangential velocity is

$$V_{\rm t} = (25 \pm 3)~ D_{{\rm kpc}}~ {\rm km} ~ {\rm s}^{-1},$$ (2)

where $D_{{\rm kpc}}$ is the distance in kpc. The radial velocity with respect to the Sun is -142.4 $\pm$ 1.5 km s^-1 (Orosz & Bailyn 1997; Shahbaz et al. 1999).

Using values of the position, distance, proper motion and radial velocity, the Galactic orbit of GRO J1655-40 can be computed using a Galactic gravitational potential model (Johnston et al. 1995). The velocity components U, V, and W directed to the Galactic centre, rotation direction, and north Galactic pole are derived using Johnson & Soderblom (1987)'s equations of transformation, and assuming the sun moves ($U_{\odot}$,$V_{\odot}$,$W_{\odot}$) = (9, 12, 7) km s^-1relative to the local standard of rest (lsr) (Mihalas & Binney 1981). Two different orbits were computed for two extreme values of the distance: for D = 0.9 kpc we obtain (U,V,W) = ( $-133\pm2, 27\pm2, 1\pm3$) and for D = 3.2 kpc, (U,V,W) = ( $-121\pm18, -33\pm8, 3\pm8$). These two sets of values are rather different from the mean values that characterize the kinematics of stars that belong to the halo, and the thin and thick disk of the Galaxy (Chiba & Beers 2000). The runaway velocities $V_{{\rm run}}$ were computed for the two possible extreme distances of 0.9 kpc and 3.2 kpc (see Table 1), after subtracting the Galactic differential rotation given by the model for the corresponding position of the source in the Galactic disk.

 

 

Table 1: Parameters of the runaway motion and galactocentric orbit of GRO J1655-40, for two extreme values of the distance. $V_{{\rm run}}$ is the runaway velocity in three dimensions after correction for differential Galactic rotation. e is the eccentricity of the galactocentric orbit, $Z_{{\rm max}}$ is the maximal height above the Galactic plane, and $r_{{\rm max}}$ and $r_{{\rm min}}$ are the maximal and minimal galactocentric distances. The runaway linear momentum p and kinetic energy $T_{{\rm kin}}$ of the binary system are computed according to the masses given in the text.

D [kpc]	0.9	3.2
$V_{{\rm run}}$ [km s-1]	130	93
e	0.39	0.29
$z_{{\rm max}}$ [kpc]	0.05	0.15
$r_{{\rm max}}$ [kpc]	13.8	7.2
$r_{{\rm min}}$ [kpc]	6.0	3.9
p [$M_{\odot}$ km s-1]	430	637
$T_{{\rm kin}}$ [erg]	5.6 $\times 10^{47}$	5.9 $\times 10^{47}$

The runaway linear momentum p and kinetic energy $T_{{\rm kin}}$ were computed assuming $M_{{\rm BH}}$ = 5.4 $\pm$ 0.3 $M_{\odot}$ and M_* = 1.45 $\pm$ 0.3 $M_{\odot}$ for a distance D = 3.2 kpc (Beer & Podsiadlowski 2002), and $M_{{\rm BH}}$ = 3.2 $M_{\odot}$ and M_* = 0.1 $M_{\odot}$ for a distance D = 0.9 kpc (Beer & Podsiadlowski, private communication).

The parameters of the runaway motion and galactocentric orbit of GRO J1655-40 are given in Table 1. In Fig. 2 are represented the Galactocentric orbits. For a given Galactic potential the orbital parameters do not change as a function of time. The selection of different Galactic potentials from the current models introduce a scatter in the values of the orbital parameters smaller than 10%. In fact, the errors in the parameters listed in Table 1 are largely dominated by the uncertainty in the distance. For the range of distances 0.9-3.2 kpc, the galactocentric orbit is highly eccentric (e = 0.29-0.39), the source always moves within a maximum height of 150 pc from the Galactic plane, and since the minimum perigalactic distance is 3.9 kpc it never reaches the Galactic bulge.

Clearly, GRO J1655-40 does not move in a halo orbit as XTE J1118+480 (Mirabel et al. 2001). GRO J1655-40 must have been born in the Galactic plane at a galactocentric distance $\geq$3.8 kpc. The runaway linear momentum and kinetic energy of the binary system are comparable to those of solitary neutron stars and millisecond pulsars (Toscano et al. 1999).