On the origin and initial temperature of Jupiter and Saturn

Abstract

A two-stage growth of the giant planets, Jupiter and Saturn, is considered, which is different from the model of contraction of large gaseous protoplanets. In the first stage, within a time of ∼3 × 10 7 years in Jupiter's zone and ∼2 × 10 8 years in Saturn's zone, a nucleus forms from condensed (solid) material having the mass, ∼10 28 g, necessary for the beginning of acceleration. The second stage may gravitating body, and a relatively slow accretion begins until the mass of the planet reaches ∼10 m ⊕. Then a rapid accretion begins with the critical radius less than the radius of the Hill lobe, so that the classical formulae for the rate of accretion may be applied. At a mass m > m 1 ≈ 50 m ⊕ accretion proceeds slower than it would according to these formulae. When the planet sweeps out all the gas from its nearest zone of feeding ( m = m 2 ≈ 130 m ⊕), the width of the exhausted zone being ∼ built1 3 of the whole zone of the planet) growth is provided the slow diffusion of gas from the rest of the zone (time scale increases to 10 5−10 6 years and more). The process is terminated by the dissipation of the remnants of gas. In Saturn's zone m 1 > m 2 ≈ 30 m ⊕. The initial mass of the gas in Jupiter's zone is estimated. Before the beginning of the rapid accretion about 90% of the gas should have been lost from the solar system, and in the planet's zone less than two Jupiter masses remain. The highest temperature of Jupiter's surface, ≈5000°K, is reached at the stage of rapid accretion, m < 100 m ⊕, when the luminosity of the planet reaches 3 × 10 −3 L ⊙. This favors an effective heating of the inner parts of the accretionary disk and the dissipation of gas from the disk. The accretion of Saturn produced a temperature rise up to 2000−2400° K (at m ≈ 20−25 m ⊕) and a luminosity up to 10 −4 L ⊙.