This cluster lies at a distance of ^320 pc ((m-M)0 = 7.5 magnitudes) in the Perseus Molecular Cloud. Originally catalogued by Dreyer, the cluster has 40-50 members detectable at optical wavelengths, and the brightest star o Persei (type B5) is surrounded by a prominent reflection nebula (Figure 9.15). Herbig's [H8] spectroscopic observations of strong Ha emission in 16 stars within this region confirmed the presence of a young cluster. Infrared scans [S8] reveal a moderate to large population of optically-invisible sources, embedded in what is presumably the remnants of the parent molecular cloud [K6]. The general characteristics point to a young age for the system - initially estimated as between 5 and 20 Myr [S8]. More recent studies [H9], [L6], [L7] find that most of the stars have ages between 1 and 5 Myr.

Lada and Lada [L2] surveyed the central 0.1 square degree of this cluster, reaching limiting magnitudes of 16.5, 15.5 and 14.5 in the /, H and K passbands. These observations cover most of the cluster core, but not the outer regions; the cluster has a diameter of ~30 arcmin (~3 parsecs). Of the 600+ sources detected in the [L2] survey, most are concentrated in a relatively small region south of o Persei, where the source density rises to ^250 stars pc-2. The contamination from background and foreground stars is estimated through observations of control fields, offset by 1° from the cluster centre. The resulting K-band luminosity function (Figure 9.16) has a broad peak at MK ~ 4.5, or K = 11.5, well above the limiting magnitude of the survey. As in studies of other young clusters, the brighter source

Figure 9.15. An R-band image of the cluster IC 348. The field is 10 arcmin square. (Courtesy of Palomar Observatory/STScI.)

Figure 9.16. (a) K-band source counts towards IC 348. The dotted histogram shows the likely contribution from background/foreground sources [L2]; (b) the K-band luminosity function (histogram) matched against predictions based on a log-normal mass function (open triangles) and a truncated mass function (open squares - from [L3]).

Figure 9.16. (a) K-band source counts towards IC 348. The dotted histogram shows the likely contribution from background/foreground sources [L2]; (b) the K-band luminosity function (histogram) matched against predictions based on a log-normal mass function (open triangles) and a truncated mass function (open squares - from [L3]).

counts follow a near-power law distribution with magnitude, index 0.38 at K and 0.32 at J. This is much steeper than those measured for either intermediate-age open clusters or field stars at similar magnitudes and reflects a compression of the mass-luminosity relationship: a smaller interval in L spans a larger range in M.

Rather than attempting a direct transformation of $(MK) to ^(M), [L2] and [L3] invert the analysis, using computer simulations to predict $(MK) given ^(M) and a star-formation history. Starting with a Miller-Scalo log-normal mass function, pre-main sequence tracks from [D2] are used to estimate (L, Teff) as a function of (mass, age). Transforming to MK via temperature-dependent bolometric corrections, the resulting KLFs are compared to the observed luminosity function. The star-count data match models where star formation has progressed at a relatively uniform rate over the last 5-10 Myr [L4]; single-burst (coeval) star-formation models produce luminosity functions which are either too narrow or fail to match the observed slope of the source counts at bright magnitudes. Recent spectroscopic analysis of cluster members [L6], [L7] has refined these timescales: as indicated above, the majority of the cluster stars prove to be younger than —3 Myr. Results favour a mass function matching the Miller-Scalo formulation to —0.2 M0, but are better represented by a power law 0.3 < a < 0.8 at lower masses.

The Orion Nebula Cluster

This is the young star cluster surrounding 0X Ori - the four O-type stars of the Trapezium that ionise the Orion nebula. Lying at a distance of 470 ± 70 pc [G1], the Orion Nebula Cluster (ONC) is one of the most prominent of a series of active star-forming regions in the Orion OB association [G2]. Immediately behind the cluster lies the L1640 molecular cloud whose very substantial density leads to extinctions of Av > 80 magnitudes, effectively eliminating any contribution by background stars to even near-infrared source counts. The ONC itself is parsecs in diameter, and lies primarily within the low gas-density region excavated by winds from the Trapezium stars (the overall morphology of the area is described by Zuckerman [Z3]). Proper-motion studies [J1] show that the overwhelming majority of stars within ~20 arcmin of the Trapezium are cluster members, simplifying source-count analysis. The star density rises to ^20,000 stars pc~3 in the central ^0.3 parsecs.

The Orion complex has been the subject of numerous spectroscopic and photometric investigations of both the stellar and gaseous content (see [G2] and [H10] for summaries), including recent high-resolution Hubble Space Telescope imaging [P5] which provides direct observations of the 'silhouettes' of circumstellar disks ('proplyds' - Figure 3.19, in colour section) around a number of cluster stars. The cluster was an early target of infrared observations [A4]; the relatively narrow KLF has been modelled as a single burst of star formation, aged 106 years, with a Miller-Scalo mass function [L2].

The most detailed study of the ONC, however, was undertaken at optical wavelengths. Hillenbrand [H10] compiled V, I photometry for 1,600 of the 3,500 sources identified within the central 5 pc of the cluster, as well as spectroscopy for more than 980 of the brighter stars. While the photometric sample includes only 40% of the complete population, the spatial distribution of the observed sources is similar to the complete sample, and there is no evidence for significant differences between the constituent stars in the two datasets. Thus, the optically-selected sample is probably a fair subset of the population in the ONC cluster.

Hillenbrand's estimate of the ONC mass function is derived using the star-by-star approach. Effective temperatures are estimated from the spectral types, while Mboi is derived from the photometry allowing each star to be placed on the H-R diagram. Comparison with theoretical evolutionary tracks (Figure 9.17) give the age and mass of each star; and the mass function and star-formation history follow by combining those individual results. As in the star-count analyses, age and mass calibrations rest entirely upon the theoretical models, and choosing a different set of models, or different transformations from the observational to theoretical plane, can lead to different conclusions. Restricting analysis to the lower main sequence stars plotted in Figure 9.17, comparison with either the [D2] or the more recent [D6] tracks indicates that the average age of ONC members is somewhat less than 1 Myr, but with an overall spread in age of at least 2 Myr.

Initial analysis of these data led to the derivation of a log-normal mass function, peaking at ^0.3 M0, similar to the results for IC 348 shown in Figure 9.16. There

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