Figure 2.6 Bipolar outflow from the protostar in an object called HH-30. A disc (edge on) is also apparent. The scale bar is 1000 AU long. (Reproduced by permission of C Burrow, AURA/STScI ID Team, ESA)

where the disc is also apparent edge on. Why these outflows are so tightly collimated is not well understood, but the magnetic field of the protostar or of the disc itself, acting on electrically charged particles in the flow, might be important. Bipolar outflow would have carried off only a small proportion of the rotational angular momentum of the proto-Sun. But this is not the whole outflow, particularly in the strong T Tauri phase (Section 2.1.3), when a significant proportion of the proto-Sun's angular momentum could have been carried off.

How does the distribution of angular momentum cast light on the initial mass of the disc? If the initial disc mass were only about 1% of the solar mass M0 (the MMSN) the angular momentum transfer would be weak, to the extent that it would be difficult to explain the necessary loss of angular momentum by the proto-Sun. At the other extreme, an initial disc mass comparable with M0 is considerably more than is necessary and requires a huge proportion of disc mass to be lost to space. Therefore, many astronomers favour an intermediate value, a few times the MMSN. This will be adopted implicitly in Section 2.2.

Question 2.4

(b) Use equation (2.1) to calculate the magnitude of the average orbital angular momentum of the Earth, and then use equation (2.2) to calculate the magnitude of the average orbital angular momenta of Jupiter and Neptune.

2.2.2 The Evaporation and Condensation of Dust in the Solar Nebula

In nebular theories the formation of planets and other bodies occurs in a number of stages, the first of which is the evaporation of some of the initial complement of the dust in the solar nebula.

Evaporation of dust

You have seen (Section 2.1.3) that the proto-Sun only begins to increase greatly in temperature when it becomes dense enough to be opaque to its own radiation. The disc never becomes as dense as the proto-Sun and therefore the tendency for its temperature to rise as it contracts is more strongly moderated. Nevertheless the disc does rise in temperature, particularly in its inner regions where it is denser and thus more opaque, and where infall to the proto-Sun has caused greater frictional heating.

□ What additional source of energy heats the inner disc more than the outer disc? This is the proto-Sun when it becomes luminous.

In the inner disc, out to perhaps 1 AU, the calculated temperatures exceed about 2000 K, high enough to evaporate practically all of the dust in the disc - only those substances with very high sublimation temperatures escape evaporation. In sublimation, a substance goes directly from solid to gas, as does carbon dioxide ice (dry ice) at the Earth's surface. It occurs when the pressure is too low to sustain a liquid, and in the disc the pressures are well below his threshold. Above the sublimation temperature the substance is a gas, and below it, a solid. For any particular substance the sublimation temperature depends on the pressure: the higher the pressure, the higher the sublimation temperature. The value of the sublimation temperature for a particular substance at a given pressure is one measure of the volatility of the substance. The most volatile substances, such as hydrogen (H2) and helium (He), have extremely low sublimation temperatures, whereas substances such as corundum (Al2O3) have extremely high sublimation temperatures, and are said to be refractory. With increasing distance from the proto-Sun the disc temperature decreases, and therefore increasingly more volatile substances avoid sublimation. Beyond the order of 10 AU even quite volatile substances escape sublimation, such as water ice.

Condensation of dust

So far the disc has evolved in completely the wrong direction to make planets - it has gained gas at the expense of solid material! However, at some point the contraction of the disc slows. Moreover, the luminosity of the proto-Sun declines as it contracts, its surface area decreasing greatly whilst its surface temperature increases only slightly. (In contrast, the protosolar core temperature is increasing enormously, because of the lower rate of energy transfer across the outer layers of the proto-Sun.) Heat generation within the disc also declines, and so the disc temperatures begin to fall as it continues to emit IR radiation. At some point fresh dust begins to condense, its composition depending on the composition of the gas and on the local temperature. Because of the low pressures, solids rather than liquids appeared.

Table 2.3 gives the condensation temperatures of representative substances (these are also the sublimation temperatures). The pressure for the data is 100 Pa, 0.1% of the atmospheric pressure at the Earth's surface. This is a theoretical value for the total gas pressure in the disc. The temperature at which a substance condenses will depend not only on this total pressure but also on the proportion of the disc accounted for by the substance, which determines its contribution to the total pressure, i.e. the partial pressure. It is the partial pressure that determines, albeit rather weakly, the condensation temperature of a substance. Also, the pressure might have been rather lower than 100 Pa, though the condensation temperatures are only slightly lower even at 10 Pa.

Table 2.3 A condensation sequence of some substances at 100 Pa nebular pressure



Chemical formula

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