3 Radial velocities

   
3.1 Zero-point errors

The problems with the calibration lamps may introduce systematic differences between the zero points of each mask. We have used the radial velocity of the [O I] 5577 Å Auroral line, whenever possible, to test for this effect.

The straightforward approach would be to add algebraically the radial velocity of the sky line to the velocity of each star. Unfortunately, however, the problems with the calibration lamps described above imply that several spectra have unreliable wavelength calibration in the region of [O I].

For most spectra the formal (measurement) error in the position of the sky line is $\sim$6.6 km s^-1. The mean radial velocity of the [O I] lines with reliable calibrations is -6.5 km s^-1 with a dispersion of 12.9 km s^-1. Thus, while we cannot correct the individual velocities for systematic zero point errors, the radial velocity dispersion must be corrected by this effect by subtracting quadratically the [O I] dispersion $\sigma_{[O {\sc i}]}=\sqrt{12.9^2 - 6.6^2}=10.9$ km s^-1.

3.2 Velocity determination

As mentioned above, the resolution of our combination of dispersion grating and camera yields 1.3 Å per pixel. For 2-pixel sampling this corresponds to a spectral resolution of about 165 km s^-1 at 4750 Å. The ultimate limit attainable in the precision of Doppler shifts is dominated by the photon noise in the spectrum (Brown 1990). The uncertainty in the measured radial velocity for the case of a single line of width w and depth d, measured in units of the continuum intensity $I_{\rm {c}}$, is given by

$$\delta v_{\rm {rms}} = \frac{c \, w}{\lambda \, d \, (N_w \, I_{\rm {c}})^{1/2}}$$ (1)

where N_w is the number of samples across the width of the line, c is the speed of light, and $\lambda$ is the central wavelength of the line. For typical lines measured in our stars ( $\lambda = 4500$ Å, w=7 Å, N_w=6, d=0.2, and $I_{\rm {c}} = 2 \times 10^4$), we obtain $\delta v_{\rm {rms}} = 15$ km s^-1. This is smaller than the velocity dispersion expected if the cluster is virialised and the total mass is close to our photometric estimate. However, the signatures of expanding stellar atmospheres and binaries may be much stronger than the virial motions. Thus, it is very important to constrain these effects with the data at hand before embarking in a high spectral resolution survey of the kinematics of the cluster.

At our resolution the Balmer lines cannot be used to measure radial velocities because they are severely contaminated by nebular emission. Therefore, we have restricted our analysis to stars with well exposed HeI and HeII absorption lines. In order to have an indication of the presence of atmospheric motions we have only considered stars with at least three He lines detected. This further restricts our sample to 97 spectra, several of which correspond to the same star.

The centroids of the lines were determined from Gaussian fits using the package ngauss within IRAF. The fitting errors were used as weights to calculate the (weighted) mean velocity of each star. A conservative $\kappa-\sigma$ filter was used to reject stars with suspected internal (atmospheric) motions. Thus, all stars with a dispersion of more than 25 km s^-1 between the measured lines were rejected. The final list is presented in Table 1 that gives, for each star, the Parker number, the spectral type from Paper II, position in arcsec from the cluster center, assumed to be R136 (Selman et al. 1999a), the weighted average radial velocity, and the weighted error. A number of stars appear to be binaries on the basis of showing double peaked lines (stars # 1024, 1369 and 1938), asymmetric line profiles (# 222, 613, and 1191), or different radial velocities for the He I and He II lines (# 1998). These stars tend to have larger internal errors as can be seen in the second part of Table 1.

 

 

Table 1: Stellar radial velocities.

Star id.	Sp.Type	$\Delta\alpha('')$	$\Delta\delta('')$	$\langle V_{\rm r} \rangle$	$\sigma_{\rm {int}}$
15	O8.5 V	-107	107	234.9	14.0
32	O9 IV	-102	72	272.1	09.5
124	O8.5 V	-76	25	287.5	06.9
316	O6.5 V	-50	-164	265.9	09.5
541	O7.5 V	-29	-65	252.6	07.1
649	O8-9 V	-20	-106	323.7	09.4
713	O5 V	-15	-53	308.7	11.8
747	O6-8 V	-13	-142	364.3	22.8
791	O5 V	-09	141	310.7	08.8
805	O5-6 V	-08	-38	292.1	09.4
863	O6.5 V	-04	-03	308.0	06.5
871	O4 V((f*))	-04	-44	290.3	06.5
901	O3 V((f*))	-02	26	276.2	08.7
905	O9-B0 V	-02	61	198.2	16.3
975	O6-7 V((f))	02	-27	325.5	05.9
1022	O5: V	04	-139	320.6	07.2
1063	O6-7 V	06	108	267.0	16.5
1109	O9 V	09	-167	229.7	05.9
1139	B0 V	11	36	225.5	09.5
1163	O4 If:	12	-72	274.1	11.3
1247	B0.5 IV	17	91	333.0	11.6
1283	O6 V:((f*))	19	-09	352.2	06.7
1339	B0-0.2 IV	23	-60	265.5	12.0
1389	B1: V::	27	70	292.6	06.1
1419	B0-0.2 III-I	31	98	259.0	10.0
1459	O9.5 II	34	145	272.7	14.3
1460	B0-2 V	34	172	282.7	21.0
1468	O9.5 V	36	16	321.0	13.3
1500	B0.2 III	39	40	275.2	09.0
1531	O6 V((f))	43	-25	308.0	09.0
1553	O7 V	47	-09	321.5	07.3
1563	O7.5 II-III(f)	47	-04	271.6	06.9
1584	B0-1 V	50	-02	320.8	23.1
1604	B1 V	55	85	360.2	17.6
1614	O5-6 V((f))	56	09	291.2	06.6
1618	B0-0.2 III	56	128	270.1	07.6
1619	O8 III(f)	56	102	357.8	20.0
1643	O5 V	60	128	279.0	06.6
1661	B1 III	62	124	322.7	07.5
1685	B0.5-0.7 III-I	66	161	291.8	11.6
1729	B1 II-III	71	80	283.2	17.3
1737	B1.5 III	71	139	339.1	05.7
1969	B0.7 IV	113	74	329.6	12.7
1987	B2 I	120	-113	294.8	05.0
10001	O4 V			246.1	14.7
10003	B1-1.5 V			279.9	06.9
Suspected Binaries
222	O9.5-B0 V	-62	143	198.9	26.4
613	O8.5 V	-23	-154	203.2	13.7
1024	O9-B0 V	05	-110	510.7	27.9
1191	B0.2-1 III-V	13	-30	345.7	28.8
1369	O8.5 V	26	-09	318.1	78.5
1938	O7.5 V	107	134	350.0	18.0
1988	B0.5 V	121	-22	300.0	18.0

Figure 1: Spatial distribution of stellar radial velocities. Two stars are missing, as they fall out of the photometry area.