3. Solar System Formation and Early Evolution: the First 100 Million Years

The solar system, as we know it today, is about 4.5 billion years old. It is widely believed that it was essentially completed 100 million years after the formation of the Sun, which itself took less than 1 million years, although the exact chronology remains highly uncertain. For instance: which, of the giant planets or the terrestrial planets, formed first, and how? How did they acquire their mass? What was the early evolution of the “primitive solar nebula” (solar nebula for short)? What is its relation with the circumstellar disks that are ubiquitous around young low-mass stars today? Is it possible to define a “time zero” (t ₀), the epoch of the formation of the solar system? Is the solar system exceptional or common? This astronomical chapter focuses on the early stages, which determine in large part the subsequent evolution of the proto-solar system. This evolution is logarithmic, being very fast initially, then gradually slowing down. The chapter is thus divided in three parts: (1) The first million years: the stellar era. The dominant phase is the formation of the Sun in a stellar cluster, via accretion of material from a circumstellar disk, itself fed by a progressively vanishing circumstellar envelope. (2) The first 10 million years: the disk era. The dominant phase is the evolution and progressive disappearance of circumstellar disks around evolved young stars; planets will start to form at this stage. Important constraints on the solar nebula and on planet formation are drawn from the most primitive objects in the solar system, i.e., meteorites. (3) The first 100 million years: the “telluric” era. This phase is dominated by terrestrial (rocky) planet formation and differentiation, and the appearance of oceans and atmospheres.     

Internal waves in a rotating stratified spherical shell: asymptotic solutions

Summary. Small amplitude oscillations of a rotating, density-stratified fluid bounded by a spherical shell are examined. No restrictions are placed on the thickness of the shell. The internal mode spectrum is examined in the complete rotation-stratification parameter range including the regime that is appropriate for a plausible stratification distribution in the Earth's fluid core. A mathematical model is derived in terms of an eigenvalue PDE of mixed type. The existence of oscillatory solutions is exhibited in the limits of no rotation and no stratification. The frequency spectrum is extended asymptotically away from these limiting cases. A reduction in the complexity of the PDE for modes oscillating at the inertial frequency is exploited. A variational formulation is constructed in which the stratification parameter is treated as an eigenvalue of the system for fixed wave frequency. The spectral information is again extended asymptotically away from these 'accessible' points. Although the PDE reduces to Laplace's tidal equations (LTE) only under stringent parameter restrictions, it is observed that aspects of the behaviour of low frequency LTE modes are reproduced in the general model.     

An investigation of sand–dust storm events and land surface characteristics in China using NOAA NDVI data

Observations from 560 weather stations in China show that sand–dust storms occur most frequently in April in north China. The region consists of Sub-dry Mid Temperate, Dry Mid Temperate, Sub-dry South Temperate and Dry South Temperate Zones and much of the land surface is desert or semi-desert: it is relatively dry with minimal rainfall and a high annual mean temperature. In most regions of China, the annual mean frequency of sand–dust events decreased sharply between 1980 and 1997 and then increased from 1997 to 2000. Statistical analyses demonstrate that the frequency of sand–dust storms correlates highly with wind speed, which in turn is strongly related to land surface features; on the other hand, a significant correlation between storm events and other atmospheric quantities such as precipitation and temperature was not observed. Accordingly, land surface cover characteristics (vegetation, snowfall and soil texture) may play a significant role in determining the occurrence of sand–dust storms in China. Analysis of Normalized Difference Vegetation Index derived from National Oceanic and Atmospheric Administration and Empirical Orthogonal Function show that since 1995 surface vegetation cover in large areas of Northern China has significantly deteriorated. Moreover, a high correlation is shown to exist among the annual occurrence of sand–dust storms, surface vegetation cover and snowfall. This suggests that the deterioration of surface vegetation cover may strongly influence the occurrence of sand–dust storms in China. Soils with coarse and medium textures are found to be more associated with sand–dust storms than other soils.     

Molecular Gas and Dust in the Massive Star Forming Region S 233 IR

The massive star forming region S 233 IR is observed in the molecular lines CO J = 2-1, 3-2, NH3 (1,1), (2,2) and the 870#m dust continuum. Four submillimeter continuum sources, labelled SMM 1-4, are revealed in the 870μm dust emission. The main core, SMM1, is found to be associated with a deeply embedded near infrared cluster in the northeast; while the weaker source SMM2 coincides with a more evolved cluster in the southwest. The best fit spectral energy distribution of SMM1 gives an emissivity of β = 1.6, and temperatures of 32 K and 92 K for the cold- and hot-dust components. An SMM1 core mass of 246 M⊙ and a total mass of 445 M⊙ are estimated from the 870μm dust continuum emission.SMM1 is found to have a temperature gradient decreasing from inside out, indicative of the presence of interior heating sources. The total outflow gas mass as traced by the CO J = 3-2 emission is estimated to be 35 M⊙. Low velocity outflows are also found in the NH3 (1,1) emission. The non-thermal dominant NH3 line width as well as the substantial core mass suggest that the SMM1 core is a “turbulent,massive dense core”, in the process of forming a group or a cluster of stars. The much higher star formation efficiency found in the southwest cluster supports the suggestion that this cluster is more evolved than the northeast one. Large near infrared photometric variations found in the source PCS-IR93, a previously found highly polarized nebulosity, indicate an underlying star showing the FU Orionis type of behavior.     

On the mixing rules for astrophysical inhomogeneous grains

We present the computation of effective refractive coefficients for inhomogeneous two-component grains with three kinds of inclusions with   m _incl= 3.0 + 4.0i, 2.0 + 1.0i, 2.5 + 0.0001i  and a matrix with   m_m = 1.33 + 0.01i  for 11 volume fractions of inclusions from 0 to 50 per cent and wavelengths  λ= 0.5  , 1.0, 2.0 and 5.0 μm. The coefficients of extinction for these grains have been computed using a discrete dipole approximation. Computation of the extinction by the same method for grains composed of a matrix material with randomly embedded inclusions has been carried out for different volume fractions of inclusions. A comparison of extinction coefficients obtained for both models of grain material allows one to choose the best mixing rule for a mixture. In cases of inclusions with   m _incl= 2.0 + 1.0i  and 2.5 + 0.0001i the best fit for the whole wavelength range and volume fractions of inclusions from 0 to 50 per cent has been obtained for the Lichtenecker mixing rule. In the case of   m _incl= 3.0 + 4.0i  the fit for the whole wavelength range and volume fractions of inclusions from 0 to 50 per cent is not very significant but the best fit has been obtained for the Hanai rule. For volume fractions of inclusions from 0 to 15 per cent a very good fit has been obtained for the whole wavelength range for Rayleigh and Maxwell-Garnett mixing rules.