L

+1 +2 Luminosity log

Figure 4.13 Bolometric luminosity functions for (a) Taurus-Auriga and (b) Chamaeleon I. The dashed curve is the initial luminosity function, defined here as the relative number of field stars per logarithmic unit of Lbol (see § 4.5.1.). Shading indicates different infrared classes, as explained in panel (a).

torically, it was the discovery of this main-sequence turnon in the equivalent color-magnitude diagram that enabled M. Walker in 1956 to demonstrate unambiguously the existence of the pre-main-sequence phase. Through spectroscopic analysis, Walker then confirmed that the youngest low-mass members were the recently identified T Tauri class. Note that the contraction time from the birthline to the ZAMS for a 3 Mq star is 2 x 106 yr. This figure represents the time in the past when visible stars first began to emerge from the front face of the Mon OB1 cloud. Clearly, this process is continuing today.

4.2.3 Association Luminosity Functions

The bolometric luminosity functions of T associations, like those for embedded clusters, are another potentially valuable diagnostic and less plagued in this case by incompleteness of the sample. Figure 4.13a shows the luminosity function for 130 stars in Taurus-Auriga. Here, as in Figure 4.6, we have subdivided the members by their near-infrared class. The peak near Lbol ~ 1 Lq is real, since the limiting luminosity of the survey is closer to 0.1 Lq.

Figure 4.13b displays the same data for 62 stars in Chamaeleon I. The existence of a maximum in this case is more problematic. In addition, the absence of Class III objects simply reflects the selection criteria for membership, which included the detection of a near-infrared excess. For both associations, the luminosity functions have more stars than the respective HR diagrams, which require spectroscopic analysis to establish Teff.

How are we to gauge the significance of Figure 4.13? It is instructive to compare these results with the theoretical luminosity distribution of field stars as they first appear on the ZAMS. This so-called initial luminosity function, denoted ^ (Lbol), is shown by the dashed curves in Figure 4.13. As described in § 4.5 below, we obtain the function by combining stellar luminosities with main-sequence lifetimes. In both Taurus-Auriga and Chamaeleon I, ^ (Lboi) matches rather well the observed falloff at high luminosity. For Taurus, however, the data display a steeper decline near 1 Lq. Figure 4.6 shows that the same is true for the embedded p Ophiuchi cluster. Another difference from the smooth field-star curve is the maximum in the Taurus-Auriga luminosity function. Both these characteristics are in accord with theoretical expectations (Chapter 12). The "initial" luminosity function is in fact only reached gradually in a cluster or association, as pre-main-sequence members contract and cool.

4.2.4 Intermediate-Mass Objects

We have seen how the discovery of a T association generally begins with an objective prism search for emission-line objects. Included in this category are the rarer Herbig Ae and Be stars, which are often picked out through the same technique. Most intermediate-mass stars, however, are even closer to the ZAMS and lack prominent emission lines. On the other hand, their contraction times are so short that such stars are frequently still illuminating nearby molecular gas. Groups of young, intermediate-mass stars are therefore conspicuous on optical photographs by the reflection nebulae accompanying them. These appear as fuzzy patches that are bluer in color than their host stars, since the reflection of visible light from dust grains is more efficient at shorter wavelengths. We call such stellar groups R associations.

Because intermediate-mass stars lack both the brilliance of more massive objects and the large numbers of T Tauri stars, R associations have not received a great deal of scrutiny. The

Table 4.1 The Nearest R Associations

Name

Distance

B stars

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