Early Phases

For an object that is not fusing hydrogen, both L* and Teff change with time. Correspondingly, its representative point moves in the HR diagram. The fact that most stars are observed to be on the main sequence reflects the longevity of the hydrogen-burning phase, during which L* and Teff change only slightly. Younger objects are more distended, with central temperatures that are too low for maintaining the fusion reaction. Nevertheless, these pre-main-sequence stars are relatively luminous. Since they are also detectable at visible wavelengths, their properties are well studied.

What supplies the star's luminosity during this early phase? The answer is the compressive work of gravity, which slowly squeezes the object to higher density. The local rate of energy loss from this process is zero at the center and increases monotonically outward. Thus, as illustrated in Figure 1.17, Lint across an arbitrary mass shell within a pre-main-sequence star is less than L*. The surface radiation now causes a net drain of energy, leading to steady contraction and to continuous alteration of both L* and Teff.

Determining pre-main-sequence tracks in the HR diagram for different stellar masses is an important aspect of star formation theory. Anticipating later results, Figure 1.15 shows the evolutionary track for a star of 1 M0. The star first appears as an optically visible object on a curve called the birthline. As it then contracts, the star begins to descend a nearly vertical path. During this time, L* is so high that energy is transported outward not by radiation but by thermal convection, i. e., the mechanical motion of buoyant gas. By the time the star's path turns sharply upward and to the left, energy is partially transported by radiation, as well. After 3 x 107 yr, the star joins the main sequence.

Pre-Main-Sequence Star

Pre-Main-Sequence Star

"int

Figure 1.17 Energy transport in a pre-main-sequence star. In this case, there is no nuclear-burning region. The luminosity Lint mono-tonically increases from zero at the center to Lt at the surface.

Stars of other mass traverse analogous paths in the HR diagram but at very different rates. Less massive objects tend to have lower surface temperatures. According to equation (1.5), their values of L* are also smaller for a given surface area, resulting in slower contraction. To quantify the rate, we first note that the sum of a star's thermal and gravitational energies is a negative quantity that is about GM*/R* in absolute value. The object radiates away an appreciable portion of this energy over the Kelvin-Helmholtz time:

1 Rn

1 La

The significance of tKH is that the star shrinks by about a factor of two over this interval, starting from any point during its pre-main-sequence phase. Notice that tKH gets longer as the contraction proceeds. Thus, equation (1.6) also provides an approximate measure of the total time needed for a star to contract to its main-sequence values of M*, R*, and L*.

Figure 1.18 displays pre-main-sequence tracks over a wide range of masses. All tracks descend from the birthline, which intersects the main sequence near 8 M0. Higher-mass stars exhibit no optically visible pre-main-sequence phase, but first appear on the main sequence itself. If we imagine a group of stars all beginning contraction on the birthline at t = 0, their subsequent positions in the diagram at any fixed time would fall along a sequence of smooth curves. Figure 1.18 also shows a set of such pre-main-sequence isochrones. The reader should verify that the pattern of isochrones is consistent with the slower evolution of less massive objects and with the continual slowing of contraction at any fixed mass.

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