Chapter 2
Formation and Composition of Refractory Grains

It has been calculated that the formation of grains in the interstellar medium would require time-scales far in excess of the destruction time-scale. For this reason, it is to the cool outer atmospheres of red stars that we must look for the origin of interstellar dust. Formation in the circumstellar region is still poorly understood.

A process of homogeneous nucleation and condensation of refractory atoms, forms dust grains. This process requires very cool temperatures and very high densities in a gas. Formation is unlikely to occur except in some special environments. The dust is primarily formed in the exospheres of stars in the cool, red-giant phase of their evolution, but a small fraction is also formed in the circumstellar shells around super-giants, novae, planetary nebulae and in the ejecta of supernovae. These appear to be the only places cool enough and dense enough for particles to condense out spontaneously. Formation takes two forms, condensation and nucleation.

2.1 Condensation

Condensation and growth from the gas phase will occur when the energy barrier caused by opposing partial and vapour pressures of the condensing particles has been overcome. To this end there has to be a supersaturation of the condensing species to allow the partial pressure to significantly exceed the vapour pressure and allow condensation. Salpeter (1977) showed that the phase transition for graphite grains in a carbon-rich gas will occur at around 2000K for a wide range of gas pressures. While in a gas of normal cosmic abundances condensation is expected to transpire between 1000K and 1500K.

2.2 Homogeneous Nucleation

Homogeneous nucleation: The growth of microcrystals from an initially pure gas that under-goes cooling. There is no gaseous 'monomer' (gas molecules or atoms) formed during nucleation, the , and ions are held together by coulomb forces. The details of the dust growth under astrophysical conditions are not well understood.

2.3 Composition

The chemical composition and size of interstellar dust has been inferred by theoretical interpretation of observations and laboratory experiments. UV observations of diffuse-cloud dust (dust not in molecular clouds) reveals that there are three populations of dust.

1. Large grains of in radius, these prove to be the major cause of the blocking of starlight in the visual.
2. Small carbonaceous grains are particles less than in radius. These were found to produce a strong absorption feature at about (Stecher, 1965).
3. There is also an independent population of very small grains in size, composed of silicate type particles.

The large grains form in cool red giants where the atmosphere is dominated more by oxygen than carbon. Most of the carbon is therefore likely to be contained in carbon monoxide molecules , while the free oxygen molecules are able to condense to form metallic oxides such as and or silicates such as . On ejection from the star, by radiation pressure or supernova explosion, the grains become centres for the growth of ice mantles. These mantles result from abundant atomic species such as oxygen, carbon, nitrogen and sulphur. In the final stage of dust evolution, the population of very small grains accretes to these icy mantles to form pre-cometary dust grains.

The small grains also form in the atmospheres of cool red giants, but in atmospheres with an excess of carbon. The small percentage of oxygen present will be locked in carbon monoxide molecules, allowing the carbon to form Hydrogenated Amorphous Carbonate grains.

2.4 Propagation Processes

Grains formed in circumstellar shells propagate away from the star through the relatively gentle process of outward radiation pressure. In this process, the grains couple with the gas through gas-grain collisions and drive mass loss. The radiation pressure is counter acted by gas-drag. Thus, the net effect determines the terminal velocity of the grains and the grain growth in the circumstellar shell. The upper limit on the size of a dust grain, and hence an estimate of this terminal velocity, can be calculated by appreciating that the radiation force acting on a newly-formed dust grain must be able to over come gravity and thus push the grain out into interstellar space.

The flux of radiant energy at distance D from a star with luminosity is given by . Since , then the flux of radiant momentum, or (radiation pressure) is given by:

.    EQ.16

Assuming the effective cross-section for radiation pressure is equal to the geometric cross section,

,    EQ.17

the radiation force is then:

,    EQ.18

where is the grain radius, is the radiation pressure efficiency factor, is the stellar luminosity , D is the distance away from the star and c is the speed of light. The radiation pressure efficiency factor is determined by the absorption and scattering efficiency factors, & respectively and the scattering asymmetry factor g through:

,    EQ.19

The parameter g is a measure of the forward or backward scattering properties of the grain and therefore, in part, determines the effectiveness of the coupling between the stellar radiation scattered by the grains and their outward motion.

Inward gravitational force on a dust grain for a star of mass is given by:

,    EQ.20

where allows for the fact that the dust carries with it the gas, so the effective mass of a dust grain is increased by this amount. For dust to be ejected into interstellar space it is required that:

,    EQ.21

therefore:

,    EQ.22

Radiation pressure can accelerate a grain with to a terminal velocity given by:

    EQ.23

With such a large velocity, it is easy to see why dust grains do not stay in the vicinity of their formation.

2.5 The Destruction of Grains by Protostellar Nebulae and Star Formation

Matter from the interstellar medium goes to form new stars, at a rate only slightly greater than that at which old stars return matter to the interstellar medium, . The grains that are used in star formation have little chance of surviving the process, while reprocessed grains will eventually be re-ejected by the star. The processes which go to form stars are complex and many, and it is also unknown how much additional interstellar material comes close enough to a young star for the star to super-heat and in some cases evaporate it. Estimates put a value on this additional material at marginally greater than the final mass of the star. This super-heated material is eventually expelled from the protostellar nebula and new grains may from in it.