Wavelength log X (|xm)

Figure 4.4 Spectral energy distribution of the Class 0 source L1448/mm in Perseus.

4.1.3 Cluster Luminosity Functions

The spectral classification scheme is a convenient means to gauge the evolutionary status of cluster stars that are inaccessible to more direct observation. A complementary tool of equal importance is the cluster luminosity function. Here one counts up the number of stars AN that have luminosities in the range L* to L* + AL*, where L* itself spans the range of observed values. We recall from Chapter 1 that pre-main-sequence stars have luminosities that evolve during contraction, at rates that are highly mass-dependent. Since any sufficiently young cluster contains a large fraction of such objects, the form of AN(L*) changes with time until most members have settled onto the main sequence. The potential value of the luminosity function as an evolutionary probe is thus apparent, but observers have not yet taken full advantage of this technique.

The main impediment has been the practical difficulty of obtaining bolometric luminosities for large numbers of embedded stars. The satellite observations used at long wavelengths have so far lacked the high spatial resolution required to sample the crowded fields in dense clusters. Consequently, the most complete luminosity functions at present are those in a single near-infrared wavelength, usually the K band. Figure 4.5 shows the K luminosity function for 90 stars in the central region (L1688 cloud) of the p Ophiuchi complex. Note that the falloff in the population for mK > 10 simply reflects the incompleteness of observations at this magnitude. Subsequent observations have found the population to increase down to at least mK = 14. At this faint level and beyond, the membership of the numerous sources in the vicinity is less secure.

Measurements at other wavelengths have allowed the determination of bolometric luminosities for about 50 of the p Ophiuchi stars in L1688. Figure 4.6 displays the currently known bolometric luminosity function. Also shown here is the distribution of sources among the spectral classes. Once again, the decline in the population at the highest luminosities is real, but that at low Lboi is not, and is being pushed back by more sensitive surveys. We will return to the physical interpretation of luminosity functions later in this chapter and again in Chapter 12, when we revisit cluster evolution from a more theoretical perspective.

Figure 4.5 Luminosity function in the K band for 90 stars in the L1688 region of p Ophiuchi.

Apparent Magnitude mK

Figure 4.5 Luminosity function in the K band for 90 stars in the L1688 region of p Ophiuchi.

I 1 I 1 I 1 p Ophiuchi

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