Differences in Structure

High- and low-mass stars have very different internal structures (Fig. 25.5). Above about 1.2 M0, the CNO cycles dominate the energy production (Fig. 25.2). The nuclear energy generation rate e strongly depends on T, this dependence is expressed by eT or v (Fig. 25.3). This means that the luminosity L is rapidly built near the center. In turn, the thermal gradient Vrad (5.32) which depends on the ratio Lr/Mr is large. In stars with masses above ~ 1.2 M0, Vrad is larger than the adiabatic gradient Vad (about 2/5). Thus, when the CNO cycles dominate (at first it is just the CN cycle), the criterion for convective instability (5.54) is satisfied. This is why stars more massive than about 1.2 M0 have a convective core. The size of the convec-tive core determines the mass fraction which participates in the nuclear burning, the cores cover larger mass fractions in more massive stars. Stars with M < 1.2 M0 burn hydrogen by the pp chains, with a milder dependence on T (Fig. 25.2) and thus show no convective cores, their deep interior being fully radiative.

The outer structures of low- and high-mass stars are also very different (Fig. 25.5). For Teff < 7500 K which corresponds to stellar masses M < 1.4 M0, the opacities k in the stellar envelopes are large as illustrated by Fig. 8.4, because hydrogen and other elements are partially ionized and provide numerous transitions. Larger k values imply larger Vrad (5.32) and thus convection. This is why stars with M < 1.4 M0 have external convective envelopes, which extend deeper for lower masses. Details on the internal structure of a 1 M0 are given below (Sect. 25.3). Below about 0.4 M0, the opacities are large enough everywhere to make the stars fully convective.

Fig. 25.5 Schematic structure of the Sun and a star of 9 [email protected] on the main sequence with indications of T and q. Cloudy regions indicate convection. The percentages indicate the fraction of the total energy produced
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