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Figure 2.12 One way in which the Moon could have formed from a grazing embryo impact on the Earth. Note the decreasing scale from frame to frame - the Earth (the larger object) is about the same size in all frames. (Reproduced by permission of A G W Cameron)

Figure 2.12 One way in which the Moon could have formed from a grazing embryo impact on the Earth. Note the decreasing scale from frame to frame - the Earth (the larger object) is about the same size in all frames. (Reproduced by permission of A G W Cameron)

mass in the neighbourhood of Jupiter is less than in the neighbourhood of the terrestrial planets. Figure 2.9 therefore indicates that, in the models, as the heliocentric distance increases, planetary embryos not only become more massive, but also become fewer in number. In other words, the 'feeding zone' of each embryo covers a wider annular strip of the disc. Consequently, embryo masses of order 1026kg are typical in the models for the Jovian region, i.e. of order 10 times the Earth's final mass!

At greater heliocentric distances it also takes longer to form the embryos from planetesimals, about 0.5 Ma at 4-5 AU, and even longer further out. However, the time required is shorter for smaller planetesimals, and so if there is a trend whereby the greater the heliocentric distance, the smaller the planetesimals, then this would partly offset the increasing embryo formation times. In any case, many planetesimals are left over after the embryos have formed, enabling the embryos to grow.

The embryos are so few and far between beyond the ice line that embryo collisions are very rare, and so the slow embryo-to-final-planet phase that operates in the terrestrial region does not occur. Instead the embryos are massive enough to act as kernels that gravitationally capture large quantities of the considerable mass of gas that still dominates the solar nebula. □ Which two substances made up nearly all of the mass of this gas? Hydrogen (as H2) and helium (as He) together accounted for about 98% of the mass of the nebula, and for nearly all of the gas component. At first, the rate of capture of gas by the kernels is low, and it is estimated that it takes several times the kernel formation time for the capture of a mass of gas equal to the initial kernel mass. At this point, the capture rate is much higher and it is rising rapidly with further mass increase - there is a runaway.

As nebular gas is captured it undergoes self-compression, to yield an envelope with an average density that grows as its mass increases. As well as gas, the growing giants also capture a small but significant proportion of the surviving planetesimals, which still account for nearly 2% of the mass of the nebula. These icy-rocky bodies partially or wholly dissolve in the envelope, particularly in its later, denser stages. Icy materials dissolve more readily than rocky materials, so some preferential accretion of rocky materials onto the kernel might occur. On the other hand, convection in the envelope opposes core growth, so the further central concentration of icy-rocky materials might be slight. The (runaway) capture of gas is halted by the T Tauri phase of the proto-Sun, when the high radiation and particle fluxes sweep the remaining nebular gas into interstellar space.

We can thus account for the presence of giants in the outer Solar System. However, some critical timing is seen to be essential when we look at the differences between the giants, notably the decrease in mass with increasing heliocentric distance (item 8 in Table 2.1). In the models outlined so far, the key to understanding this trend is the increasing time it takes to reach the runaway stage with increasing heliocentric distance. If the T Tauri phase occurs after the onset of runaway at Jupiter and Saturn, but before it starts at Uranus and Neptune, then we can account qualitatively for the lower masses of Uranus and Neptune. This truncation of gas capture by Uranus and Neptune also explains their smaller proportion of hydrogen and helium; Chapter 5 presents incontrovertible evidence for this. Figure 2.13 is one possible time line for the formation of the giant planets. Again, this is illustrative, not definitive. As in Figure 2.10, the end of the T Tauri phase is around the time marked 'nebula rapidly disappearing'. □ What would have been the consequence of a much later T Tauri phase? If the T Tauri phase had been much later, then all the giants would now be more massive than Jupiter.

After the T Tauri phase the giants must have captured further icy-rocky planetesimals. These will have added only very slightly to the total mass, but could have significantly enriched the envelopes in icy and rocky materials.

Non-zero axial inclinations of the giants could readily result from the off centre accumulation of mass - the same sort of explanation that can account for the axial inclinations of the terrestrial planets. But Saturn has a rather large inclination, 26.7°, and the planet is far too massive for off centre accumulation to be the cause. Instead, the explanation probably lies in the rate of Saturn's axial precession being equal to the rate of regression of the nodes of Neptune's orbit.

Jupiter

Disc kernel Jupiter Uranus as in nearly nearly nearly

Figure 2.3(a) complete complete complete

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