Annu. Rev. Astron. Astrophys. 1994. 32: 227-275
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2. DISTRIBUTION OF INDIVIDUAL OB STARS

2.1. Overview

Massive stars are, for the most part, located in stellar associations born in giant molecular clouds; a powerful enough birth event would be called a "starburst." Initially these stars are surrounded by the dense molecular gas cloud and surrounded by the commonly associated dust. These ensembles will radiate strongly in the IR and radio regions due to the heating of dust and gas excitation, but might be completely hidden optically (e.g. W51 in our Galaxy). After some time, the molecular clouds are dissociated and the dust is dissipated by the radiation and stellar winds from the O stars within, and the region becomes visible as an optical H II or giant H II (GH II) region (e.g. 30 Doradus). The appearance of the spiral arms of galaxies in the visible is primarily determined by the distributions of the H II and GH II regions within them. For the nearer galaxies, the individual stars may be investigated, but for more distant ones, only the integrated properties of the association as it affects the excited gas (and dust) can be studied.

Actual counts of massive stars in associations can be used directly to give estimates of the slope of the IMF, along with the related upper and lower mass limits Mupper and Mlower. We consider these parameters for a group of associations in our Galaxy and the Magellanic Clouds in Section 2.2. Tn more distant GH II regions and starburst galaxies (Section 5), we turn to indirect methods used to confront the questions of "How many?" and "What kinds of massive stars are present?". In such distant galaxies, we make use of the integrated spectra and of global properties, such as their far-infrared (FIR) luminosities, and their optical and UV imaging. For indirect methods, we examine the use of 30 Doradus as a fundamental calibrator.

2.2 Direct Star Counts/Census

Pioneering efforts to elucidate the numbers and types of massive stars in various environments have been made primarily by Massey and associates, using both photometry and spectroscopy. As Massey (1985) has shown, even the unreddened U BV colors for the hottest stars are degenerate, i.e. one cannot distinguish between the hottest and coolest O type stars on the basis of their photometry alone, as is commonly done with luminosity functions, Massey and his associates' homogeneous approach to the determination of the IMF for various associations of the Galaxy and Magellanic Clouds assures us that their comparisons among various stellar groupings ought to be consistent with each other.

2.2.1 PROCEDURE     One first acquires deep CCD U BV frames of the relevant stellar associations. Accurate photometry (to 0.02 mag) must be accomplished, and color-color plots used to estimate the extinction and identify the bluest stars. The U BV colors are used to determine the brightness of the stars but spectra suitable for classification are needed to determine the effective temperature, Teff, of all stars earlier in type than BlV or so. Obtaining spectra is a time-consuming effort requiring large telescopes; the photometry can be done on modest ones.

Distances of the associations by classic spectroscopic parallax methods are obtained for the Galactic clusters; for the Magellanic Clouds, the standard distances are used. MV and spectral type (or unreddened color) are converted to Mbol and Teff using a calibration procedure. These "observed" parameters for the association stars are plotted on a "theoretical" HR diagram with evolutionary tracks. Finally, one counts the numbers of stars in each mass interval along the track, and plots the values as a function of mass. The slope of this relationship is referred to as Gamma, defined in the equation

Equation 1   (1)

where f(M) is the fractional number of stars per unit mass interval M, A is a scaling constant, and the Salpeter value for Gamma is -1.35. By the above procedure, one is essentially measuring the slope of the Present Day Mass Function (PDMF). An important assumption is that this number is identical to the slope of the IMF; in other words, stellar deaths can be ignored. This is reasonable for the very youngest O associations, and one can, if necessary, account for the already highly evolved W-R stars that are present in some of the regions studied. A further typical assumption is that the spread in formation time is of the order of, or less than, the evolution time, which seems reasonable for O associations (but see Section 2.2.2). Finally, one ignores the binary membership. Unless the binary fraction, typically considered to be 40% for hot stars (Garmany et al 1980), is different from place to place, this assumption is also not unreasonable in the context of seeking similarities and differences in the numbers and types of massive stars in various environments.

2.2.2 MASSIVE STAR CENSUS IN O-ASSOCATIONS In Table 1 (adapted from Conti 1994), we summarize the statistics for ten associations in the Galaxy and Magellanic Clouds, along with those for the solar vicinity. They have been grouped by galaxy abundance, thus sampling the composition of the environment out of which these stars formed.

Table 1. Massive star statistics for various regions

Association -Gamma # > 60 Msun Galaxy References

Field < Rsun 1.3 Milky Way Garmany et al 1982
Field > Rsun 2.1 Garmany et al 1982
Cyg OB2 1.0 7 Massey & Thompson 1991
Car OB1 1.3 7 Massey & Johnson 1993
Ser OB1 1.1 1 Hillenbrand et al 1993
LH9 1.6 0 LMC Parker et al 1992
LH10 1.1 4 Parker et al 1992
LH58 1.7 0 Garmany et al 1993
LH117 1.8 2 Massey et al 1989a
LH118 1.8 0 Massey et al 1989a
30 Dor 1.4 21 Parker 1992
NGC 346 1.8 3 SMC Massey et al 1989b

The two entries for the solar vicinity were obtained by a method similar to the others but the models used were older and the numbers not quite comparable; the values are just noted for completeness. The authors of the various papers cited suggest that Gamma has been determined to an accuracy of ± 0.2 in each association. If there is a dependence on metal abundance, Z, which, given the uncertainties, is by no means clear, then Gamma gets shallower as the metal abundance increases. This is in opposition to the prevailing view (Shields & Tinsley 1976) that Gamma becomes steeper with increasing abundance.

The entries in Table 1 also give a quantitative indication of Mupper for the most massive objects by listing the actual numbers of stars with masses larger than 60 Msun as inferred from the Mbol and Teff. We obtained this by inspection of the HR diagrams plotted in the various papers cited. The values, which are more or less proportional to the total numbers of stars in each region, range farther upward in mass to somewhere between 80 to 100 Msun this is a reasonable estimate of Mupper for starburst modeling purposes (see also Section 3.4). There is no dependence of either the numbers of massive stars or the Mupper on the galaxy environment, or on metallicity Z.

It has been suggested from indirect arguments that the Mlower, limit in some starburst regions might be significantly larger than the canonical 0.1 Msun found near the Sun, and more like a few Msun (e.g. M82 - Rieke 1991, McLeod et al 1993). Is there any direct evidence for this? Among well-studied energetic GH II regions, 30 Dor would be the place to look. However, Parker's (1992) survey was complete only to an apparent magnitude corresponding to a few Msun, i.e. just where it begins to get interesting. Despite the (crowding) difficulties, a deeper CCD photometric survey of 30 for needs to be made to investigate its Mlower limit and this issue in general.

In their study of NGC 6611 = Ser OB1, Hillenbrand et al (1993) have gone sufficiently deep in their CCD survey to be able to say something about the stellar population at 3-7 Msun. Remarkably, they find that these stars are above the main sequence, in the pre-main sequence phase. Furthermore, the ages of these still contracting stars are a few × 105 years, appreciably less than the turn-off time of the upper main sequence, which is a few × 106 years! Thus in this association, the presence of (at least) 13 O stars has not inhibited further star formation of lower mass stars. Whether ten or one hundred times that many O stars would inhibit subsequent lower mass star formation remains problematic.

Hillenbrand et al (1993) also call attention to several luminous stars that sit well to the right of the main body of massive stars in NGC 6611. They argue that these stars are indeed cluster members, which must have formed before most of the rest. Eye examination of the rest of the associations referenced above also invariably reveals a few stars in similar, advanced, evolutionary stages. Hillenbrand et al suggest star formation might proceed much like "popcorn" when it is heated; a few kernels "pop" before the main body, and a few more lag behind.

2.2.3 LUMINOSITY FUNCTIONS Massey (1985) noted that using only photometry, it is difficult to distinguish among the most massive stars employing luminosity functions alone. In particular. Massey et al (1989b) show that had they taken only their U BV photometry for the analysis of NGC 346, they would have found Gamma to be -2.5, instead of the -1.8 value listed in Table 1. Hill et al (1994) have derived Gamma for 14 OB associations in the Magellanic Clouds using CCD photometry. They too find no difference in this parameter between the LMC and SMC, thus no dependence on Z. While their mean values of Gamma are somewhat larger than those listed in Table 1 (and probably for the reason mentioned above), this distinction is probably not significant. Their uncertainties in Gamma are also larger than those found by Massey and associates with their techniques.

Massey et al (1986) have done CCD photometry of several associations in M31. Using plots and evolution tracks similar to those discussed above, they obtained the curious result (shown in their Figures 31 and 32) that there are no stars in the luminous associations OB78 and OB48 more massive than 40 Msun, although both have W-R stars present. This inference is probably faulty as it is based on photometry only. Thus the use of luminosity functions for massive stars must be treated with caution, as both the derived Gamma and the Mupper might be suspect. For luminous stars of M31 and other Local Group galaxies, spectra are difficult but not impossible to obtain on the largest telescopes, especially - with multiple slit instrumentation.

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