Table of Contents

1. Introduction
2. Theory of Stellar Dust Production
3. Project Goals, Figure 1
4. Modelling Stellar Spectra, compositions, optical depth, scaling, Figure 2
5. Observations, Figure 3, Figure 4, Figure 5
6. Preliminary Results, Figure 6
7. References, Acknowledgements, and Figure Captions

Theory of Stellar Dust Production
All stars have some sort of stellar wind where material from their surfaces is ejected outward driven by radiative pressure. In the case of the sun, the total amount of material is very small and is composed mostly of ionized hydrogen (protons) and electrons. In late-type giant stars, typically larger and cooler than the sun, this wind can contain many particles, not just hydrogen, but heavier elements as well.

As material leaves the surface, two forces act upon it. Radiation pressure pushes the material outward while gravity tries to pull it back in. Since both of these forces decrease as r^-2, the velocity of particles is more or less constant as a function of radius. [Gilman, 72] The radiative temperature and the particle density both fall off as functions of r^-2. If conditions are correct -- the particle density is high enough for frequent collisions, yet the temperature is low enough for inelastic low-energy collisions (about 800K) -- at a certain radius from the star, the atoms and simple molecules start to coalesce into into aggregations. These are the beginnings of dust grains. This dust then continues outward still driven by radiative pressure cooling further and growing larger. At some point the particle density becomes low enough that the grains will not become significantly larger.

Project goals
Theoretical work on dust grain synthesis and populations abounds, but observations have thus far not allowed a good statistical understanding of dust creation. The ultimate aim of our study is to create just such a statistical base so that trends can be seen. Just as Hertzsprung and Russel created a useful diagram upon which different types of stars and their evolution can be traced, an analogous diagram can be created for dust. However there is no experimental proof of such a construction. [Fig 1.] Different tracks represent different types of dusty atmospheres (differing in composition and density profile).

Many models of these dust grains have been presented. It is thought that most stellar dust grains are a few tenths of a micron across and composed of various materials. Some have a core of one material (silicon-carbide, for instance) and a mantle of another (such as ice), as if different materials were able to coalesce at different radii.

Modelling Stellar Spectra
The most common models for stellar dust have cores which are composed of "astronomical" silicates and amorphous carbons. They can be recognized by their spectral signatures [Fig 2]. Other composition models exist as well (Indeed there are several types of silicates and carbon models to choose from. One of the side-goals of this project is to determine which models have the best observational support.)

Since the dust is assumed to be created symmetrically around the star, light from the central star must pass through the dust in order to reach us independent of our line of sight on the system. (Note that more complicated geometries have been modelled by other groups.) In doing so, the dust grains absorb some of the radiation and re-emit it at different wavelengths. Depending on the type and quantity of dust, we see different types of output spectra. Thus in theory, by observing the spectrum, you can tell everything there is to know about the dust.

However, since all we can detect of the star and dust system is a spectrum, a bolometric flux and perhaps a distance, one would think that there would be too many free parameters for us to determine anything with any confidence. For instance, the spectrum given off by the dust would depend on the "input" spectrum of the star itself.

But, because of the phenomena of scaling, the properties of the central star turn out to be largely irrelevant. In terms of source spectrum, the photospheric emission can be closely modelled as a black body of a temperature around 2500K. Fluctuation up and down do not affect the system very much. The radius at which the dust forms (the inner edge of the dust cloud) depends on temperature, and temperature depends on luminosity and surface temperature. Since dust will form at a given temperature, a hotter star or more luminous star will simply have an inner dust radius farther out than that of a cooler star. Furthermore, its density scale will be larger than that of the cool star. So, while there is proportionally more energy in the large star, there is also more dust being produced to absorb it and to the outside observer, both stars' spectra look identical to an overall bolometric flux.

Factors that matter in the observed spectrum:	Factors which do not matter for the observed spectrum:
€ Grain Composition	× Stellar Luminosity
€ Total Optical Depth	× System Dimensions
€ Dust Density Profile	× Density Scale Height.

Given the freedom from many parameters, a program was devised by Zeljko Ivezic and Nathan Netzer to calculate a theoretical observed spectrum for a certain set of input parameters (composition, optical depth, density profile). With this FORTRAN code, a large library of model stars can be produced covering a large range of optical depth and several different chemical compositions.

Observations
The models are only half the project. On the observational side, this project would not have been possible without decades of laborious data collection by hoards of astronomers (both amateur and professional) concerning late type dusty stars. Major contributions of data came from a number of sources:

• The IRAS satellite mission of 1984 brought in the largest and most internally consistent set of data from 245,889 sources 5425 of which are believed to be late-type stars. [Fig 3] Observations were made at 12, 25, 60, and 100 microns as well as in a continuous "low resolution spectrum" (LRS) between 7 and 23 microns. From the general shape of this LRS spectrum an "LRS number" was assigned to the source. LRS 2n and 3n sources (eg 24) showed characteristics of silicate dust (2n being optically thin, 3n optically thick). 1n and 4n sources showed carbonaceous characteristics.
• Revised Air Force Infrared Sky Survey (RAFGL) (May 1984) with fluxes at 4.2, 11, 20, and 27 microns
• 2-Micron Sky Survey (2-mu) (July, 1979) with photometry in the V (0.55µ), I(0.90µ), and K(2.2µ) bands.
• Fouque, et al. (1993) with fluxes at 1.25, 1.60, 2.2, 3.0 and 4.0 microns.
• The Catalogue of Variable Stars (CVS) compiled between 1985 and 1988 with fluxes either in B or V bands (0.44 and 0.55 microns) at both maximum and minimum. (Since many of these dust-producing stars are variable in nature, this data provided a great check on the reality of the other data).
• Future data from the ISO and SIRTF missions will augment the current set.

,

Once the best fit was found, the optical depth and grain composition, as well as input observations of number and source of data points, relative errors and so forth, are extracted and catalogued.[Fig 4], [Fig 5]

Preliminary Results
Though it is still far too soon to make any sweeping conclusions about dust or the effectiveness of the program, it already appears that Superfit can fit observed data to models with a fair degree of accuracy (Fig 4,5). Presumably the poorer fits are a symptom of not having enough models and, with more models to choose among, the fits would look better.

Furthermore we can see from Fig 6 that our initial method of estimating optical depth correlates fairly well with the numbers chosen by Superfit. Most sources fall within less than an order of magnitude of the predicted values. The original estimates derive from looking at the IRAS fluxes at 12 and 60 microns and the LRS number (to estimate composition).

Acknowledgements

None of this work would have been possible without the generous support of the University of Kentucky Center for Computational Science and its director Dr. John Connolly. My advisor, Dr. Moshe Elitzur and Dr. Zeljko Ivezic of the University of Kentucky were the originators of the project and produced most of the actual science.

References

Netzer and Elitzur, "The Dynamics of Stellar Outflows Dominated by Interaction of Dust and Radiation" ApJ 410, 701-713, 1993 June 20

[I&E 95, I]: Ivezic and Elitzur, "IR Emission and Dynamics of Outflows in Late-type stars", ApJ 445: 415-432 1995 May 20.

[I&E 95, II]: Ivezic and Elitzur, "Infrared Classification of Young Stellar Objects", Proc. ESO Workshop on the Role of Dust in the Formation of Stars, Sept `95. In press.

[I&E 95, III]: Ivezic and Elitzur, "Infrared Classification of Young Stellar Objects", Proc. ESO Workshop on the Role of Dust in the Formation of Stars, Sept `95. In press.

Draine, B. T. And Lee, H. M. 1984, ApJ, 285,89.

Simpson, J.P. 1991, ApJ, 368, 570.

[Gilman, 72] Gilman, "On the coupling of grains to the gas in circumstellar envelopes", ApJ 178: 423-426 Dec 1, 1972.

Captions for Figures

Figure 1 An example of stellar dust evolution tracks plotted on a color-color diagram. These are preliminary model results for power-law dust density distributions (power given). The solid lines represent amorphous carbon dust while the dashed lines are silicates. Symbols indicate changing optical depth from the Rayleigh-Jeans point (squares=0.001, circles=0.1, crosses=.03). [Ivezic and Elitzur, 95] What is not known is the speed of evolution along these tracks.

Figure 2 Theoretical absorption curves of several types of dust grains. Notice that most of the interesting details lie in the range from 8 to 20 microns, the range covered by the Low Resolution Spectrometer on the IRAS spacecraft. Of special note here are the curves for astronomical silicates (Sil) and amorphous carbon (am.C). [I&E 95, I], data adapted from Draine and Lee (1984) and Simpson (1991).

Figure 3 A mapping of the IRAS sources into the color color plane. Groupings are illustrated. A smaller region of this data is used in Fig. 1. [I&E 95, III].

Figure 4: Superfit output of four stars believed to have astronomical silicate dusts in their atmospheres. The program compiles the data and chooses the best fit from its model catalogues (illustrated here in each case). Relevant data is printed alongside each plot.

Figure 5: More Superfit output for four amorphous carbon dust stars, as above covering a range of optical depths.

Figure 6. Preliminary fitting results for 150 LRS 2n stars (optically thin silicates).