18-4 Protostars evolve into main-sequence stars

Evolutionary tracks in Figure 18-10 show how a protostar matures into a star as its gases contract. The details of this evolution depend on the star’s mass. To follow these details, you should keep in mind the basic principle that a star’s luminosity, radius, and surface temperature are intimately related. The luminosity, which is the total energy output per second, depends on how hot and how large the star is. Specifically, the luminosity is proportional to the square of a star’s radius and to the fourth power of its surface temperature (see Section 17-6).

A One-Solar-Mass Protostar

For a protostar with the same mass as our Sun (1 M_⊙), the outer layers are relatively cool and quite opaque (for the same reasons that the Sun’s photosphere is opaque; see the discussion at the end of Section 16-5). Due to frequent scattering or absorption, light does not pass easily through an opaque material. This means that energy released from the shrinking inner layers in the form of radiation cannot easily reach the protostar’s surface. Instead, energy flows outward by the slower and less effective method of convection. The result is that for a contracting 1-M_⊙ protostar, the surface temperature stays roughly constant, the luminosity decreases as the radius decreases, and the protostar’s evolutionary track initially moves downward on the H-R diagram in Figure 18-10.

Although its surface temperature changes relatively little, the internal temperature of the shrinking protostar increases. After a time, the interior becomes more ionized, which makes it less opaque. Energy is then conveyed outward by radiation in the interior and by convection in the opaque outer layers, just as in the present-day Sun (see Section 16-2, especially Figure 16-4). This makes it easier for energy to escape from the protostar, so the luminosity—the rate at which energy is emitted from the protostar’s surface—increases. As a result, the evolutionary track for a 1-M_⊙ protostar in Figure 18-10 bends upward (higher luminosity) and to the left (higher surface temperature, caused by the increased energy flow).

In time, the 1-M_⊙ protostar’s interior temperature reaches a few million kelvins, hot enough for thermonuclear reactions to begin converting hydrogen into helium. As we saw in Section 16-1 and Box 16-1, these reactions release enormous amounts of energy. Eventually, these reactions provide enough heat and internal pressure to stop the star’s gravitational contraction, and hydrostatic equilibrium is reached. The protostar’s evolutionary track has now led it to the main sequence, and the protostar has become a full-fledged main-sequence star.

In summary, energy transport is initially dominated by convection as a 1-M_⊙ protostar shrinks and dims. Next, the protostar transports more energy through radiation and its surface temperature increases. Finally, temperatures near the protostar’s center climb high enough to cause thermonuclear reactions, and a star is born.

High-Mass and Low-Mass Protostars

Figure 18-12: Main-Sequence Stars of Different Masses Stellar models show that when a protostar evolves into a main-sequence star, its internal structure depends on its mass. Note: The three stars shown here are not drawn to scale. Compared with a 1-M_⊙ main-sequence star like that shown in (b), a 6-M_⊙ main-sequence star like that in (a) has more than 4 times the radius, and a 0.2-M_⊙ main-sequence star like that in (c) has only one-third the radius.

More massive protostars evolve a bit differently. If its mass is more than about 4 M_⊙, a protostar contracts and heats more rapidly, and hydrogen fusion begins quite early. As a result, the luminosity quickly stabilizes at nearly its final value, while the surface temperature continues to increase as the star shrinks. Thus, the evolutionary tracks of massive protostars traverse the H-R diagram roughly horizontally (signifying approximately constant luminosity) in the direction from right to left (from low to high surface temperature). You can see this most easily for the 9-M_⊙ and 15-M_⊙ evolutionary tracks in Figure 18-10.

Greater mass means greater pressure and temperature in the interior, which means that a massive star has an even larger temperature difference between its core and its outer layers than the Sun. This difference causes convection deep in the interior of a massive star (Figure 18-12). By contrast, a massive star’s outer layers are of such low density that energy flows through them more easily by radiation than by convection. Therefore, main-sequence stars with masses more than about 4 M_⊙ have convective interiors but radiative outer layers (Figure 18-12a). By contrast, less massive main-sequence stars such as the Sun have radiative interiors and convective outer layers (Figure 18-12b).

The internal structure is also different for main-sequence stars of very low mass. When such a star forms from a protostar, the interior temperature is never high enough to fully ionize the interior. The interior remains too opaque for radiation to flow efficiently, so energy is transported by convection throughout the volume of the star (Figure 18-12c).

Arriving on the Main Sequence

The main sequence represents stars in which thermonuclear reactions are converting hydrogen into helium, and all of the protostar evolutionary tracks in Figure 18-10 end on the main sequence. For most stars, these thermonuclear reactions are part of a stable situation. For example, our Sun will remain on or very near the main sequence with a roughly constant temperature and luminosity, quietly fusing hydrogen into helium at its core, for a total of some 10¹⁰ years. The point along the main sequence where each evolutionary track ends depends on the star’s mass. The most massive stars are the most luminous and their evolutionary tracks end at the upper left of the main sequence, while the least massive stars are the least luminous and their evolutionary tracks end at the lower right of the main sequence. That a main-sequence star’s luminosity is greater for increasing mass should be familiar because this relationship is just the mass-luminosity relation (recall the Cosmic Connections figure in Section 17-9).

The theory of how protostars evolve helps explain why the main sequence has both an upper mass limit and a lower mass limit. As we saw in Section 17-5, protostars less massive than about 0.08 M_⊙ can never develop the necessary pressure and temperature to start hydrogen fusion in their cores. Instead, such “failed stars” end up as brown dwarfs, which shine faintly by Kelvin-Helmholtz contraction (see Figure 17-13).

Protostars with masses greater than about 200 solar masses also do not become main-sequence stars. Such a protostar rapidly becomes very luminous, resulting in tremendous internal pressures. This pressure is so great that it overwhelms the effects of gravity, expelling the outer layers into space and disrupting the star. Main-sequence stars therefore have masses between about 0.08 and 200 M_⊙, although the high-mass stars are extremely rare.