R

where S(R) [kgm~2] and T(R) are the column density and temperature of the disk at radius R, R0 is a reference radius, often taken as 1 AU (the orbit of Earth) or 10 AU (orbit of Saturn), and the indices p and q describe the radial fall-off of the density and temperature, respectively. Estimates of and p can be obtained by studying the distribution of mass within the Solar system. If we smear the augmented masses of the planets over annuli extending half way to the nearest planet (e.g., Saturn would be smeared from 7.5 to 15 AU) we p q obtain p ~ 3/2 (with an uncertainty of at least ±1/2) and £(Rq) ~ 50kgm~2 at R0 = 10 AU. This is the total (gas plus dust) surface density. The dust surface density is about 100 times smaller. The temperature of a blackbody in radiative equilibrium with sunlight is described by (2) with T(R0 = 10) = 88 K and q = 0.5.

The values of disk parameters so derived are not particularly accurate, given the uncertainties in computing augmented masses from current masses and given the likelihood that the orbits of the planets were not always where we now find them. Still, the above give a reasonable starting guess for the structure of the disk. It is natural to think that observations of disks around young stars should provide independent constraints on likely disk parameters. Unfortunately, most existing data generally lack angular resolution high enough for the disk spatial parameters to be directly measured. Instead, the disk parameters are inferred from measurements of the spectral energy distribution using models in which the number of free parameters is larger than the number of observational constraints. Assuming p = 3/2, measurements give mean values q = 0.6 ± 0.1 and T(10 AU) = 45 ± 21 K [4], which fit well with the nominal values. The dust mass inferred from disk observations averages Md = 4 x 10~3 M0 ( [4]; from 67 classical T-Tauri stars, likely analogs of the young Sun). The dust mass is really a lower limit to the mass in solids: particles much larger than the millimeter wavelengths of observation contribute little to the measured radiation and go undetected. Augmented to cosmic composition, the implied average disk mass is ~0.4M0. This is substantially larger than MMSN but the scatter in disk masses is large, as are the uncertainties, and there are presumably observational biases against the measurement of lower disk masses.

Constraints on Disk Timescales and Environment

The most important observational constraints on timescales in the protoplan-etary disk are provided by measurements of the products of radioactive decay of short-lived elements in meteorites. The latter are rocks derived by shattering collisions amongst the asteroids and delivered to Earth by gravitational scattering after their orbits become planet-crossing. Minerals in many meteorites incorporate the decay products of short-lived nuclei, showing that the minerals formed on timescales comparable to the half-lives of the decaying elements. The quintessential example is provided by 26Al, which ^-decays into 26Mg with a half-life t1/2 = 0.7 Myr [90]. When 26Mg is found incorporated within the mineral structure of a meteorite, we may conclude that 26Al was originally present. To be captured in abundance, 26Al must have been incorporated into the meteorites within a few half-lives of its formation. Element formation occurs naturally in the explosion of massive stars as supernovae, but the significance of 26Al has sometimes been questioned because it can be also formed by spallation reactions with particles accelerated to energies >MeV [91]. Such particles might have been emitted by the magnetically super-active young sun. Recent measurements of 60Ni, which is produced by the decay of 60Fe with a half-life of 1.5 Myr [116], do not suffer this ambiguity because there is no route to its production through spallation. We conclude with confidence that macroscopic solid bodies formed in the asteroid belt on timescales of a few Myr.

Other timescale constraints come from observations of circumstellar matter in disks around nearby Solar-mass stars. These observations show that circumstellar gas has a lifetime that is less than 10 Myr [10,161] and potentially just a few Myr. Dust emission from stars also declines rapidly with age (Fig. 3). The initial decline is probably due to growth into particles that are much larger than the wavelength of observation (typically ~1mm). There is evidence for thermal excess above the emission from the stellar photospheres in stars as old as ^0.5 Gyr, and this dust is probably produced in recent times by collisions among unseen bodies in the circumstellar disks, or released by unseen comets. The general decline in the dustiness of nearby stars is occasionally punctuated by objects with surprising dust emission excess. This could be showing that the stars are, for some reason, intrinsically more dusty than others of similar age. An alternative explanation is that the dust has been

Fig. 3. Dust emission from nearby stars at 24¡m wavelength expressed as a ratio to the flux density expected from the photosphere alone. Values >1 indicate excess emission, most likely from circumstellar dust heated by starlight. The emission generally declines with stellar age, but, at any given age, there is a range of thermal excesses, with occasional dramatic spikes, as at Z Lep and HD 79108. The solid curve shows a 1/(time) dependence. Ages of the stars are estimated from cluster membership and from models of their spectra, and are accurate to about a factor of two. One interpretation of the spikes is that dust is impulsively created by collisions between massive bodies. Figure reproduced from [131]

Fig. 3. Dust emission from nearby stars at 24¡m wavelength expressed as a ratio to the flux density expected from the photosphere alone. Values >1 indicate excess emission, most likely from circumstellar dust heated by starlight. The emission generally declines with stellar age, but, at any given age, there is a range of thermal excesses, with occasional dramatic spikes, as at Z Lep and HD 79108. The solid curve shows a 1/(time) dependence. Ages of the stars are estimated from cluster membership and from models of their spectra, and are accurate to about a factor of two. One interpretation of the spikes is that dust is impulsively created by collisions between massive bodies. Figure reproduced from [131]

recently created, perhaps by impact and shattering of massive planetesimals in the unseen circumstellar disks [131].

Two pieces of evidence suggest that the Sun formed in a star cluster.

First, some of the short-lived radionuclides (notably 60Fe) must have been produced, in an exploding star, only shortly before their incorporation into minerals and meteorite parent bodies (asteroids), otherwise, they would have already decayed to insignificance. Supernovae are very rare (the galactic rate is only ^one per 50 years) and typically distant so that the likelihood of having one occur nearly simultaneously with the formation of solid bodies in the disk is small. The simplest interpretation is that the Sun was part of a cluster of stars in which nearby high mass members exploded upon reaching the ends of their stable main-sequence lifetimes. An estimate of the cluster population can be made based on the dual requirements that the cluster must have been populated enough to contain a massive star capable of reaching supernova status but yet not so populated that gravitational perturbations would have noticably disturbed the orbits of the planets. A cluster containing ~2000±1100 stars seems capable of meeting both conditions [2].

Second, the truncated outer edge of the classical Kuiper belt and the excited dynamical structure of the belt in general suggests to some that the pro-toplanetary disk might have been tidally truncated by a passing star [66,114]. Numerical simulations show that to truncate or seriously disturb the disk down to radius r [AU] implies a stellar impact parameter ^3 r. The classical belt ends near 50 AU, requiring a Solar mass star to pass ~150AU from the Sun. In its current environment, the sun and stars are separated by ~1pc (200,000 AU), and the probability of two stars passing within 150 AU in the 4.6 Gyr age is negligible. Again, a plausible inference is that the mean distance between the Sun and nearby stars was once much smaller: the Sun was in a cluster.

2.2 The Three Domains

It is useful to consider the Solar system as divided into three domains, based on the compositions, masses, and radial distances of its constituents. These are as follows:

The Domain of the Terrestrial Planets

The primary objects are Mercury, Venus, Earth, and Mars, but the asteroids in the main-belt between Mars and Jupiter are also included (the largest asteroid is (1) Ceres; see Table 1). These objects are all distinguished by refractory (non-volatile) compositions dominated by metals [principally iron (Fe) and nickel (Ni)] and compounds of silicon (Si), oxygen (O), magnesium (Mg), and aluminium (Al). The bulk densities are high (p = 3930 kg m-3 for Mars up to 5515 kg m-3 for Earth, the latter slightly enhanced by self-compression due to gravity), reflecting the lack of volatiles. Densities of many

Table 1. Terrestrial Planets

Object

Mass/M®

Radius/fi®

P [kg m 3 ]

a [AU]

e

i [deg]

Mercury

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