6 Kinematics

6.1 Radial velocities and proper motions

Radial velocities of the slowly rotating programme stars were derived from the lineshift of metal lines. For the rapidly rotating stars only the Balmer and He I lines could be used. Radial velocities obtained this way were then corrected to heliocentric values and the results are listed in Table 6. The error of the velocities estimated from the scatter of the velocities derived from individual lines is about 3-11 km $\rm {s^{-1}}$. Our measurements agree to within error limits with previous estimates (see Table 6).

Proper motions were taken from literature and are listed in Table 5.

 

 

Table 5: Data of proper motion. The position angle is counted positive east of north.

Name	$\mu$ (mas/y)	Position angle $^\circ$	Reference
PG 0122+214	3.4 $\pm$ 2.3	234 $\pm$ 71	1
PG 1533+467	16.8 $\pm$ 3.6	326 $\pm$ 0	1
PG 1610+239	8.1 $\pm$ 4.0	150 $\pm$ 16	1
PG 2219+094	6.2 $\pm$ 3.6	194 $\pm$ 47	1
BD-15$^\circ$115	9.0 $\pm$ 2.7	92 $\pm$ 10	2
PHL 346	8.9 $\pm$ 3.1	144 $\pm$ 20	3

References: (1) Thejll et al. (1997); (2) Perryman et al. (1997); (3) Tycho-2 catalog, Høg et al. (2000).

 

 

Table 6: Physical and kinematic parameters of the programme stars. Five stars have been analysed previously. The results of these analyses from literature are given for comparison. The errors of the evolutionary times are formal errors introduced by the errors in ${T_{\rm eff}}$ and $\log {g}$.

Name	${T_{\rm eff}}$	${\log(\frac{g}{\rm cm~s^{-2}})}$	$v_{\rm rad}$	$v_{\rm e}$	M	d	z	$T_{\rm flight}$	${T_{\rm evol}}$
	K		km s-1	km s-1	$M_{\odot}$	kpc	kpc	Myr	Myr
PG 0122+214	18300	3.86	$26\pm 5$	290	6.7	9.6	6.2	$51 \pm 24$	$35 \pm 6$
PG 1511+367	16100	4.15	$102\pm 11$	300:	4.8	3.8	3.2	24:	$34 \pm 7$
PG 1533+467	18100	4.00	$33\pm 6$	440	6.0	3.0	2.4	$20 \pm 4$	$33 \pm 5$
PG 1610+239	15500	3.72	$91\pm10$	130	5.8	8.4	5.9	>62	$54 \pm 10$
PHL 159	18500	3.59	$88\pm 3$	320:	8.0	5.3	3.2	31:	$28 \pm 2$
PG 2219+094	19500	3.58	$-24\pm9$	220	8.7	9.8	6.1	$43 \pm 22$	$27 \pm 2$
(1)	17900	3.60	-7	-	7.5	-	-	67	41
BD-15$^\circ$115	20100	3.81	$93\pm 4$	410	8.0	4.9	4.8	$30 \pm 5$	$26 \pm 4$
(2)	19500	3.50	94	-	10.0	-	-	47	20
HS 1914+7139	17600	3.90	-	330:	6.2	14.9	6.0	91:$^\star$	39 $\pm$ 6
(3)	18000	3.75	-39	-	6.5-10.0	16-18.4	-	-	-
PHL 346	20700	3.58	$63\pm4$	350	9.9	8.7	7.4	$27 \pm 7$	$19 \pm 2$
(4)	22600	3.60	$66\pm10$	-	13.0	-	8.7	-	11
SB 357	19700	3.90	$58\pm 10$	230:	7.4	7.9	7.8	61:	$26 \pm 4$
(2)	19000	3.70	54	-	8	-	9.0	64	25

$\parbox{160mm}{{References}: (1) Rolleston et~al. (\cite{roha99}); ... ... et~al. (\cite{hemo95}).\\ : Uncertain due to the lack of proper motion data.}$

6.2 Times-of-flight and ejection velocities

The times-of-flight, which the stars need to reach their current halo positions from the galactic disk, were calculated with the program ORBIT6 developed by Odenkirchen & Brosche (1992). This numerical code calculates the orbit of a test body in the Galactic potential of Allen & Santillan (1991). The complete set of cylindrical coordinates is integrated and positions and velocities are calculated in equidistant time steps. The input for this program version are equatorial coordinates, distance d from the sun, heliocentric radial velocities and observed absolute proper motions. Values for proper motions are given in Table 5. The proper motions for PHL 159, PG 1511+467, SB 357 and HS 1914+7139 were set to zero, because no measurements are available. We followed the orbits backwards in time (time steps of 0.01-0.1 Myr). The time of passage through the galactic disk (= change of sign in z-position relative to the disk) defines the time-of-flight $T_{\rm flight}$. The velocity at the time of first crossing of the galactic plane is regarded as the ejection velocity $v_{\rm e}$and is also calculated by the program ORBIT6.

Results for all parameters of the programme stars (effective temperature, gravity, radial velocity, ejection velocity, mass, distance, age and time-of-flight) are summarised in Table 6. For the origin of the stars (see next section) the ages ( ${T_{\rm evol}}$) and the times-of-flight ( $T_{\rm flight}$) are important. We improved $T_{\rm flight}$ for BD-15$^\circ$115 and PHL 346 for which proper motion measurements have become available recently. For BD-15$^\circ$115 we derive a somewhat lower $T_{\rm flight}$ than Conlon et al. (1992) and find $T_{\rm flight}$ to be consistent with ${T_{\rm evol}}$ to within our error limits. For PHL 346 we confirm that $T_{\rm flight}$ is slightly larger than ${T_{\rm evol}}$, but given the error limits this is insignificant.

For PG 2219+094 we find $T_{\rm flight}$ and ${T_{\rm evol}}$ to be lower than derived by Rolleston et al. (1999) and $T_{\rm flight}$ to be consistent with ${T_{\rm evol}}$. For PG 1610+239 the time-of-flight is poorly constrained and only a lower limit could be determined which is consistent with the estimate of the evolutionary time.