3 Data analysis

3.1 Cluster size

To know how much of HM1 has been covered by our photometry, we used the Digitized Sky Survey plates produced by the STScI that include the cluster and its surroundings. After taking a 15 ${\hbox {$^\prime $ }}$ radius area centred approximately on star 1, we calibrated the stellar magnitudes inside it and computed the stellar density down to $V \approx 16$ mag. We then adjusted the counts using a bidimensional Gaussian to obtain a density profile by means of which we settled the cluster angular radius at the point where the stellar density merges into the background level. In this way we found a cluster radius of 3 ${\hbox {$^\prime $ }}$, represented by the circle in Fig. 1, which is of the same order as the one found by HM77, 4 ${\hbox {$^\prime $ }}$. Thus, our photometry properly covers the cluster centre and part of its surroundings.

3.1.1 Cluster analysis

Figure 4: The two-colour diagram. Symbols are: filled circles for likely members (the WR-stars are shown as open circles); triangles for probable members; small open squares for non-members; crosses are stars for which no membership could be estimated. The dashed line represents the Schmidt- Kaler's (1982) ZAMS, displaced by EB-V=1.75 from its normal intrinsic location (solid line). The arrows show the path of the reddening for O- and late B-type stars

The two-colour diagram in Fig. 4 shows that the HM1 stars are affected by a combination of increasing foreground absorption followed by intense differential reddening inside the cluster. Proper motions of six of our stars (1, 2, 4, 5, 7 and 10) are reported in the Hipparcos/Tycho Catalogues. Only the WR star LSS 4065 (star 1) has a parallax measure, but its error is so huge that nothing relevant concluded.

By means of a star-by-star comparison of the star locations in all the photometric diagrams (Figs. 4 and 5) simultaneously, we confirm most of the members stated in previous works and included several new ones. There are five stars: 16, (26), (32), 39 and (52), located above the path of the reddening for an O-type star in Fig. 4 as if they had U excess. In particular, stars 16 and (26) resemble Be-type stars due to their displacement to the red side of the cluster sequence in the colour-magnitude diagrams (Fig. 5). Although stars 20 and 24 were found to be likely members by HM77 and TAH82, after our analysis, star 20 remains a probable member but star 24 becomes a definite foreground star in view of its location in Fig. 4. As was mentioned above, six stars have proper motions. Although this is clearly too small a number to derive independent membership assessment, we want to mention that the mean proper motion for the suspected members 1, 2 and 10 ( $\overline{\mu_{\alpha} \cos\delta} = -4.4 \pm 2.1({\rm s.d.})$ mas yr^-1, $\overline{\mu_{\delta}} = -4.3 \pm 2.3({\rm s.d.})$ mas yr^-1) do not contradict the results based on photometry, while the proper motions of suspected non-members (4, 5 and 7) differ significantly from the mean cluster motion.

We explored the possibility of having a "clean'' version of the lower main sequence of HM1 using a comparison field ( $7{\hbox{$^\prime$ }}\times 7{\hbox{$^\prime$ }}$) located 15$^\prime$ north of it (Fig. 6a) with a method already described in Vázquez et al. (1997). As it would prove useless to repeat it here, we will directly comment on the result of its application as seen in Fig. 6b, the HM1 V vs. B-V diagram after the subtraction of field stars. It is apparent from this figure that too many stars remain to the left of the main sequence while a few others are on the right side of the cluster sequence, a location usually reserved for pre-main sequence stars (compare Figs. 6b and 5a). However, these two facts are not reliable results, since our reference frame for field stars does not seem to represent the field star population against which the cluster is projected, as there are fewer field stars in the comparison frame than in the cluster itself.

Figure 5: a) The V vs. B-V diagram. The Schmidt-Kaler's (1982) ZAMS, adapted to the distance modulus found in Sect. 3.4, is shown by a solid line. The two WR and the stars 16 and (26) that may be Be-type stars are indicated. Symbols as in Fig. 4; b) this is the V vs. U-Bdiagram. Symbols and lines as in Fig. 4

Figure 6: a) The V vs. B-V diagram of the comparison field stars; b) The V vs. B-V diagram of Fig. 5 a) after subtracting the field stars

   

Table 4: Magnitudes and intrinsic colours of members and probable members in HM1

#	VO	(B-V)0	EB-V	(U-B)0	EU-B	(V-I)0	EV-I	MV	EV-I/EB-V	Com.
1	5.30	-0.20	1.68			-0.29	2.43	-7.30	1.44	lm *
4	5.44	-0.33	1.82	-1.20	1.57	-0.29	2.57	-7.16	1.41	lm
5	5.53	-0.33	1.83	-1.20	1.66	-0.29	2.61	-7.07	1.42	lm
9	5.30	-0.20	1.84			-0.29	2.93	-7.30	1.59	lm *
10	6.38	-0.32	1.85	-1.14	1.49	-0.29	2.33	-6.22	1.26	lm
11	6.68	-0.30	1.77	-1.05	1.43	-0.29	2.61	-5.92	1.47	lm
13	6.89	-0.32	1.78	-1.14	1.52	-0.29	2.59	-5.71	1.46	lm
14	6.68	-0.31	1.84	-1.15	1.50	-0.29		-5.92		lm
16	6.94	-0.31	1.86	-1.14	1.51	-0.29	2.31	-5.66	1.24	lm
20	6.32	-0.33	2.07	-1.20	1.71	-0.29	3.08	-6.28	1.48	pm
24	7.53	-0.31	1.76	-1.10	1.43	-0.29	2.18	-5.07	1.24	lm
25	8.22	-0.28	1.57	-0.99	1.25	-0.29	2.30	-4.38	1.47	pm
26	6.53	-0.33	2.09	-1.20	1.72	-0.29	2.60	-6.07	1.25	lm
32	7.53	-0.36	1.86	-1.31	1.51	-0.29	2.08	-5.07	1.12	lm
35	7.98	-0.30	1.79	-1.08	1.45	-0.29	2.23	-4.62	1.25	lm
37	8.03	-0.31	1.84	-1.11	1.50	-0.29	2.28	-4.57	1.24	lm
47	8.19	-0.29	1.88	-1.05	1.53	-0.29	2.37	-4.41	1.26	lm
52	7.86	-0.33	2.06	-1.20	1.69	-0.29		-4.74		lm
54	8.96	-0.26	1.73	-0.95	1.40	-0.29	2.56	-3.64	1.48	lm
55	8.33	-0.31	1.93	-1.14	1.58	-0.29	2.48	-4.27	1.29	lm
57	7.75	-0.34	2.12	-1.24	1.75	-0.29	3.06	-4.85	1.44	lm
65	8.09	-0.34	2.08	-1.24	1.71	-0.29	2.56	-4.51	1.23	lm
67	9.71	-0.24	1.59	-0.86	1.27	-0.25	1.90	-2.88	1.19	pm
69	9.28	-0.29	1.73	-1.05	1.40	-0.29	2.19	-3.32	1.26	lm
70	8.60	-0.31	1.94	-1.13	1.59	-0.29	2.84	-4.00	1.46	lm
76	9.11	-0.28	1.83	-1.00	1.48	-0.29	2.64	-3.49	1.44	lm
81	9.29	-0.27	1.80	-0.97	1.46	-0.29	2.66	-3.31	1.48	lm
87	9.28	-0.30	1.81	-1.05	1.47	-0.29	2.25	-3.32	1.24	lm
95	8.38	-0.33	2.11	-1.20	1.74	-0.29	2.72	-4.22	1.29	lm
96	8.39	-0.35	2.11	-1.26	1.74	-0.29	2.58	-4.21	1.23	lm
104	9.50	-0.28	1.79	-1.02	1.45	-0.29	2.27	-3.10	1.27	lm
105	9.25	-0.25	1.87	-0.91	1.52	-0.27	2.40	-3.35	1.28	lm
120	10.02	-0.26	1.72	-0.95	1.38	-0.29	2.34	-2.58	1.37	lm
123	9.71	-0.25	1.83	-0.89	1.48	-0.27	2.35	-2.89	1.29	lm
126	9.60	-0.30	1.87	-1.07	1.52	-0.29	2.52	-3.00	1.35	lm
128	9.67	-0.31	1.85	-1.13	1.50	-0.29	2.47	-2.93	1.34	lm
130	9.86	-0.23	1.80	-0.85	1.45	-0.25	2.34	-2.74	1.30	lm
132	9.55	-0.25	1.89	-0.91	1.54	-0.28	2.87	-3.05	1.51	lm
154	10.04	-0.23	1.83	-0.85	1.49	-0.24	1.82	-2.56	0.99	pm
162	11.10	-0.18	1.53	-0.62	1.22	-0.17	2.12	-1.50	1.39	pm
180	10.20	-0.28	1.84	-1.00	1.50	-0.29	2.37	-2.40	1.29	lm
186	10.79	-0.18	1.67	-0.63	1.34	-0.18	2.16	-1.81	1.29	pm
193	10.75	-0.03	1.70	-0.83	1.37	-0.02		-1.85		lm
205	9.95	-0.29	1.96	-1.03	1.60	-0.29	2.42	-2.65	1.24	lm
207	11.07	-0.17	1.63	-0.61	1.30	-0.17	3.04	-1.53	1.87	pm
213	10.40	-0.17	1.84		1.49	-0.17	2.35	-2.20	1.28	pm
216	10.42	-0.23	1.84	-0.80	1.50	-0.24	2.15	-2.18	1.17	lm
229	10.57	-0.13	1.84		1.49	-0.11	2.66	-2.03	1.45	pm
244	10.33	-0.20	1.94	-0.67	1.59	-0.19	2.94	-2.27	1.51	pm
247	11.21	-0.20	1.68	-0.69	1.35	-0.20	2.40	-1.39	1.43	pm
252	10.70	-0.21	1.84		1.49	-0.21	2.34	-1.90	1.27	pm
303	11.09	-0.16	1.84		1.49	-0.15	2.42	-1.51	1.31	pm
324	11.18	-0.08	1.84		1.49	-0.06	2.38	-1.42	1.29	pm
359	11.33	-0.04	1.84		1.49	-0.02	2.67	-1.27	1.45	pm
362	11.35	-0.18	1.84		1.49	-0.18	2.67	-1.25	1.45	pm
371	11.38	-0.11	1.84		1.49	-0.09	2.78	-1.22	1.51	pm
384	11.42	-0.03	1.84		1.49	-0.02	2.31	-1.18	1.26	pm
389	11.45	-0.09	1.84		1.49	-0.08	2.23	-1.15	1.21	pm
398	11.48	-0.18	1.84		1.49	-0.17	2.32	-1.12	1.26	pm
405	11.52	-0.08	1.84		1.49	-0.07	2.51	-1.08	1.36	pm
410	11.54	-0.12	1.84		1.49	-0.11	2.59	-1.06	1.41	pm
414	11.56	-0.13	1.84		1.49	-0.12	2.28	-1.04	1.24	pm
416	11.56	-0.19	1.84		1.49	-0.19	2.41	-1.04	1.31	pm
468	11.78	-0.18	1.84		1.49	-0.18	2.83	-0.82	1.54	pm
470	11.79	-0.10	1.84		1.49	-0.09	2.33	-0.81	1.27	pm
477	11.80	-0.11	1.84		1.49	-0.10	2.34	-0.80	1.27	pm
504	11.91	-0.15	1.84		1.49	-0.14	2.60	-0.69	1.41	pm
506	11.92	-0.18	1.84		1.49	-0.18	2.47	-0.68	1.34	pm
509	11.93	-0.01	1.84		1.49	0.00	2.51	-0.67	1.37	pm
511	11.94	-0.00	1.84		1.49	0.01	2.78	-0.66	1.51	pm
512	11.94	-0.17	1.84		1.49	-0.17	2.28	-0.66	1.24	pm
518	11.95	-0.00	1.84		1.49	0.01	2.59	-0.65	1.41	pm
519	11.95	-0.12	1.84		1.49	-0.11	2.69	-0.65	1.46	pm
520	11.96	-0.09	1.84		1.49	-0.07	2.18	-0.64	1.19	pm
537	12.01	-0.16	1.84		1.49	-0.15	2.31	-0.59	1.26	pm

Note: Star numbers in the first column are from the present work.

Com:

lm = likely member;

lm * = likely member with intrinsic (B-V)₀ colours from Lundström & Stenholm (1984);

pm = probable member.

Intrinsic colours of stars with unique reddening solution in Fig. 4 (WR stars excluded) were estimated with the colour excess relation E_U-B / E_B-V = 0.72 + 0.05 $\times E_{B-V}$ following the procedure explained in Vázquez & Feinstein (1991a) and assuming their luminosity is class V. Mean excesses $\overline{E_{B-V}} = 1.84\pm 0.07 ({\rm s.d.})$ and $\overline{E_{U-B}} = 1.49\pm 0.07 ({\rm s.d.})$were derived from likely members but, if we include also probable members with U-B, we obtain $\overline{E_{B-V}} = 1.83 \pm 0.2 ({\rm s.d.})$ and $\overline{E_{U-B}} = 1.49\pm 0.2 ({\rm s.d.})$; in both cases these values are close to E_B-V =1.85 found by HM77. These mean values were used to correct the observed colours of probable members. For the two WR-stars we used (B-V)₀= -0.22 from Lundström & Stenholm (1984) to obtain their colour excesses. Intrinsic UBV colours and colour excesses of likely and probable members are listed in Cols. 3-6 in Table 4.

3.2 The reddening law and the interstellar medium towards HM1

3.2.1 Photometry

The way absorption changes with distance in this zone is outlined in the interstellar extinction maps constructed by Neckel & Klare (1980). They suggest a rapidly increasing absorption pattern, reaching up to 2 mag in the first kiloparsec from the Sun.

Figure 7 shows the B-V vs. V-I diagram together with the intrinsic lines for stars of luminosities V and III from Cousins (1978). In terms of the reddening law (i.e., the ratio of visual to selective absorption, R = A_V/E_B-V), this figure shows a real star-to-star variation of R. Cluster members lie between two extreme R-values: one of them corresponds to the normal excess relation, E_V-I/E_B-V = 1.244, R = 3.1 (Dean et al. 1978), and the other to a higher one, E_V-I /E_B-V = 1.47 or $R \approx 3.7$. Judging by the increasing spread from V-I > 1.5 and B-V > 1.0 seen in Fig. 7, we do not rule out that part of the interstellar material in front of HM1 is also producing anomalous extinction.

The individual E_V-I excesses can be used to compute the E_V-I/E_B-V ratio in order to analyse the spatial distribution of R across the cluster. Intrinsic (V-I)₀ colours of normal stars were obtained with the relation of B-V and V-I from Cousins (1978). Individual E_V-I and E_V-I/E_B-V number ratios are listed in Cols. 8 and 10 in Table 4.

The distribution of the R-values is depicted in Fig. 8. It shows that stars with high R-values tend to lie on the cluster's southwest side, while normal R-value stars are more concentrated in the cluster centre. Since the R-value varies between the two extremes mentioned above we adopted a mean value $\overline{R} = 3.3$ to obtain reddening-free V₀ magnitudes for likely and probable members. The two WR stars were treated differently (see Sect. 3.4).

3.2.2 Polarimetry

The polarimetric information in Table 3 shows that stars 5, 8, 15, 19 and (29) have not only large relative fitting errors, $\varepsilon_{\rm P}/P_{\max}$, but also $\lambda_{\max}$ values smaller than the average ones for the interstellar medium, 0.545 $\mu$m (Serkowski et al. 1975). An extreme case is the foreground star 15 that seems to shows anomalous polarisation in the U and B bands. However, in this case we suspect that a companion, star (66), at 6 ${\hbox{$^{\prime\prime}$ }}$ is distorting our observations. Since we assume that polarisation is strictly due to the interstellar medium, if the relative fitting errors are larger than 0.1, as is the case for stars 8, 15, 19 and (44), intrinsic polarisation should be suspected. We are aware, however, that some peculiar stellar envelopes may sometimes reproduce a wavelength dependence similar to the interstellar medium (Orsatti et al. 1998), yielding $\varepsilon_{\rm P}/P_{\max} < 0.1$.

Figure 7: The B-V vs. V-I diagram. Symbols as in Fig. 4. The solid lines represent the intrinsic location of stars of luminosity V and III from Cousins (1978). The path of the reddening line for R = 3.1 and R=3.7 is also shown

Figure 8: The spatial distribution of polarisation vectors in the zone of HM1. The 1% polarisation is indicated. Grey filled circles denote members having anomalous EV-I/EB-V ratios. Black filled circles indicate members with normal EV-I/EB-V ratios. Open circles are foreground stars. The small $5^{\circ } \times 5^{\circ }$ box shows the distribution of polarisation vectors around HM1, taken from Klare & Neckel (1977)

Figure 8 shows the spatial distribution of the polarisation vectors in the HM1 area. The small panel inside this figure shows the distribution of the polarisation vectors from Klare & Neckel (1977) in an area ( $5^{\circ } \times 5^{\circ }$) centred in the cluster. The polarisation patterns in both figures suggest the presence of several dust components producing different amounts of polarisation. Notice the handful of cluster members on the cluster south-west side that appear highly polarised.

Following Whittet & van Breda (1978), the mean R-value in terms of polarimetry is given by:

$$R = \left( 5.6 \pm 0.3 \right) \times \lambda_{\max}.$$

If we do not take into account stars with anomalous fittings, we find a mean value $\overline{\lambda_{\max}} = 0.57\pm 0.11~\mu$m (close to Serkowski et al. 1975, value) and $\overline{R} = 3.2 \pm 0.7$(s.d.) that agrees with the R average adopted from photometry alone. On the other hand, the assessment of the polarisation efficiency of the interstellar material when it is produced by a normal size-particle distribution can be performed by inspecting the relationship between the polarisation percentage and the visual absorption, which should not surpass the upper limit given by Serkowski et al. (1975):

$$P_{\max} \approx 3 \times R \times E_{B-V},$$

although they found an average $P_{\max} = 5.03 \times E_{B-V}$ in the Galaxy. The $P_{\max}/ E_{B-V}$ ratio depends mainly on the alignment efficiency and the intensity of the magnetic field but it also depends on the depolarisation produced when the star-light passes through dust clouds having different magnetic field orientations.

In Fig. 9 we show the $P_{\max}$ vs. E_B-V plot (star 15 excluded) along with the upper limit from Serkowski et al. (1975). The E_B-V values of foreground stars were estimated assuming they are of late B- or A-types and luminosity class V. The probable colour excess of star 17, without CCD photometry, was computed from the HM77 data. We distinguish three stellar groups in this figure: one of them corresponds to members with high polarisation values, $P > 4\%$, (3, 6, 12, 13, 16 and 20), located on the south-west side of the cluster (except star 6); the other is constituted by members in the centre of the cluster having $P < 4\%$, and the third one made up of foreground stars with $P < 4\%$. The typical polarisation observed for foreground stars implies a contribution of 1.5 to 2.6% produced by nearby interstellar material (not far from this region, Feinstein et al. 2000 found a similar foreground contribution in the cluster Trumpler 27). We notice also that the members at the southwest side of the cluster, bearing the highest polarisation values, are surrounded (in projection) by foreground stars 4, 7, 17, (29) and (44). We would like to point out that finding cluster members with $P > 4\%$ that show, on the average, high E_V-I/E_B-V ratios ( $R \geq 3.5$) and members with $P < 4\%$ that have normal E_V-I/E_B-V ratios (R = 3.1) is just a matter of chance and it does not reflect any physical connection between polarisation and absorption. In fact, the high polarisation values of stars 3, 12, 13, 16 and 20 are likely to be produced by a nearby small dust cloud instead of being produced somewhere in the proximity of the cluster itself. For instance, foreground star 7, which is close to this group, has a polarisation of 3.26% (the highest among foreground stars), probably due to its location on the northern edge of this cloud where it is partially covered by the cloud. The cloud only becomes apparent through its polarimetric effects, as no hints of increasing absorption for stars 3, 12, 13, 16 and 20 relative to other members is evident in Figs. 4 and 9. Indeed, Fig. 9 confirms that whatever the polarisation state of cluster members, the reddening across HM1 remains approximately the same (from 1.6 to 2.0). Probably, another small nearby cloud is also covering star 6, north of the HM1 centre.

Figure 9: The $P_{\max}$ vs. E(B-V) diagram. The solid line is the upper limit given by Serkowski et al. (1975). The two dotted lines provide the EB-V limits within which cluster stars are mainly distributed. Bars indicate polarisation errors

Figure 10: The absorption-free colour-magnitude diagram of HM1. The ZAMS is superposed to V0-MV= 12.6. The dashed lines are the isochrones of Schaller et al. (1992). The number shown is the $\log (age)$. The location of star 35 is indicated. Symbols as in Fig. 4

3.3 Distance and age

Figure 10 shows the Schmidt-Kaler's (1982) ZAMS fitted to a distance modulus of $V_0-M_V = 12.6 \pm 0.2$ (error by inspection). The early ZAMS fittings (HM77 or TAH82) were performed using a few stars distributed along the vertical part of the main sequence, which makes their estimates uncertain; now, however, we have the advantage that our photometry is two magnitudes lower than in any earlier investigation. Had the distance modulus been obtained with the six stars with spectroscopy and the Schmidt-Kaler's relation of spectral types and absolute magnitudes instead, we would have found distinct values according to the luminosity class adopted ranging from $\overline{V_0-M_V} = 11.7\pm 0.4$ (LC V) to $\overline{V_0-M_V} = 12.9 \pm 0.5$ (LC I). Since the magnitude spread in this last procedure introduces severe uncertainties in the distance modulus (large deviations can be produced by binarity or stellar duplicity), we adopt V₀-M_V = 12.6, from the ZAMS superposition, that corresponds to a distance d = 3.3 kpc. Although our distance is larger than the one found by HM77 (2.9 kpc), it still is in the range from 2.9 to 3.9 kpc determined by TAH82, confirming that HM1 belongs to the internal spiral arm-II, beyond the Sagittarius arm.

To determine the age of HM1, we superposed the cluster sequence to the isochrones from Schaller et al. (1992) evolutionary models computed with solar metallicity, mass loss and overshooting. The best isochrone fitting that corresponds to an age of 2-4 Myr is shown in Fig. 10. With such an age, there is no chance that star 35 is a cluster member because it is 30-40 Myr old, judging from the closest isochorone. TAH82 assumed it is a red super-giant cluster, probably an early product of a non-coeval star formation process. However, this assertion is not confirmed by our photometry since neither clues of age spread among massive stars nor the presence of faint stars lying well above the cluster main sequence are observed in our diagrams (however, this last statement reveals our inability to adequately subtract field stars instead of confirming a definite lack of contraction-phase stars). Notwithstanding, star 35 shows strong colour anomalies (its U-B colour is too blue when compared to its B-V=2.59 and V-I = 3.47), a fact deserving further observations.

Figure 11: The colour difference method for stars 1, 2, 3 and 6

3.4 Some especial stars in HM1

From Lundström & Stenholm (1984) we know that the two WN7-type stars 1 (LSS 4065) and 3 (LSS 4064) are conspicuous cluster members that have different absolute magnitudes despite their similar spectral types. Later on, both stars were classified as WN7+(abs?) (see Crowther et al. 1995) and very recently LSS 4065 was re-classified WN8-A (Walborn & Fitzpatrick 2000). This star, with a polarisation value comparable to the foreground stars, is placed in the centre of HM1; LSS 4064, on the contrary, is placed in the south-west and shows the highest polarisation (6.04%) found in our survey. On the basis of a normal absorption law, TAH82 pointed out these two WR-type stars show infrared excess caused by free-free emission in their winds when compared to model fluxes. In particular, TAH82 suggest that LSS 4064 has a depression in its spectral energy distribution shortwards of $\lambda_V$ (see their Fig. 4) suggesting, in adition, that a better agreement with the 40000 K Kurucz's (1979) model would be achieved for LSS 4064 if a colour excess E_B-V = 1.99 is adopted instead of 1.87. However, firstly, the colour excess adopted by TAH82 is correct (the intrinsic colour (B-V)₀ for a WN7-type star is -0.22 from Lundström & Stenholm 1984) and, secondly, we have found that the reddening law is anomalous in the location of LSS 4064. So, the probable near IR excess may have another explanation: Fig. 11 shows the colour-difference method applied to the two Of and the two WR stars combining our UBVRI and JHKL data from TAH82 along with the van der Hulst curve # 15 and intrinsic colour from Johnson (1968). This figure shows that only star 3 (LSS 4064) shows clear hints of having infrared excess and that, in view of our findings of Sect. 3.3, it is very probably produced by the intracluster material and not in its own wind, as suggested by TAH82.

We computed the reddening-free magnitudes of these two WR stars using the R-values according to their locations, obtaining the same absolute magnitude M_V = -7.3. Although they compare fairly well with the absolute magnitude of the WR-star WN7+abs, HD 93162 (Crowther et al. 1995), -7.2, they still are a bit far from the average given in Table 10 of Crowther et al. (1995), M_V = -6.7, and of the average given by Lundström & Stenholm (1984), -6.5. However, Vacca & Torres-Dodgen (1990) found absolute magnitudes of -7.3 for stars LSS 4064 and -6.7 for LSS 4065 though assuming that HM1 is located at a distance of 2800 pc and that the R-value in the cluster remains not only invariable but also normal.

Star 2 (LSS 4067), an O4If+ (Walborn & Fitzpatrick 2000) and star 6, an O5f, show high values for their E_V-I/E_B-V ratios as well. Their $P_{\max}$ values are low for star 2 (it has a companion, star (14), at $1.3{\hbox{$^{\prime\prime}$ }}$ with V = 12.77) and high in the case of star 6.

 

 

Table 5: The luminosity and initial mass functions

MV	$\log{\cal M}$	N	$\log N$
-8,-7	1.98, 1.80	4	0.60
-7,-6	1.80, 1.62	3	0.48
-6,-5	1.62, 1.43	6	0.78
-5,-4	1.43, 1.26	10	1.00
-4,-3	1.26, 1.08	10	1.00
-3,-2	1.08, 0.90	12	1.08
-2,-1	0.90, 0.72	18	1.26
-1,0	0.72, 0.54	12	1.08
	MV = -1	$\gamma =$	$0.12\pm0.02$
	MV = -3	$\gamma =$	$0.13\pm0.04$
	MV = -1	x=	$0.67\pm0.10$
	MV = -3	x =	$0.73\pm0.21$

Figure 12: The initial mass function. The solid and dotted lines are the least squares fitting to MV = -3 and -1 respectively