Size distribution of dust grains: A problem of self-similarity

Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e.g., diffusion-limited growth discussed by Sander (1986), who applied the theory of fractal geometry to the classification of non-equilibrium growth processes. He received D=2.4 for diffusion-limited aggregation in 3d-space

Dust in the wind: Crystalline silicates, corundum and periclase in PG 2112+059

We have determined the mineralogical composition of dust in the Broad Absorption Line (BAL) quasar PG 2112+059 using mid-infrared spectroscopy obtained with the Spitzer Space Telescope. From spectral fitting of the solid state features, we find evidence for Mg-rich amorphous silicates with olivine stoichiometry, as well as the first detection of corundum (Al_2O_3) and periclase (MgO) in quasars. This mixed composition provides the first direct evidence for a clumpy density structure of the grain forming region. The silicates in total encompass 56.5% of the identified dust mass, while corundum takes up 38 wt.%. Depending on the choice of continuum, a range of mass fractions is observed for periclase ranging from 2.7% in the most conservative case to 9% in a less constrained continuum. In addition, we identify a feature at 11.2 micron as the crystalline silicate forsterite, with only a minor contribution from polycyclic aromatic hydrocarbons. The 5% crystalline silicate fraction requires high temperatures such as those found in the immediate quasar environment in order to counteract rapid destruction from cosmic rays.Comment: 2 figure

Where Are The M Dwarf Disks Older Than 10 Million Years?

We present 11.7-micron observations of nine late-type dwarfs obtained at the Keck I 10-meter telescope in December 2002 and April 2003. Our targets were selected for their youth or apparent IRAS 12-micron excess. For all nine sources, excess infrared emission is not detected. We find that stellar wind drag can dominate the circumstellar grain removal and plausibly explain the dearth of M Dwarf systems older than 10 Myr with currently detected infrared excesses. We predict M dwarfs possess fractional infrared excess on the order of L_{IR}/L_{*}\sim10^{-6} and this may be detectable with future efforts.Comment: 24 pages, 2 figures, accepted to Ap

FU Orionis - The MIDI/VLTI Perspective

We present the first mid-infrared interferometric measurements of FU Orionis. We clearly resolve structures that are best explained with an optically thick accretion disk. A simple accretion disk model fits the observed SED and visibilities reasonably well and does not require the presence of any additional structure such as a dusty envelope. The inclination and also the position angle of the disk can be constrained from the multibaseline interferometric observations. Our disk model is in general agreement with most published near-infrared interferometric measurements. From the shape and strength of the 8-13 micrometer spectrum the dust composition of the accretion disk is derived for the first time. We conclude that most dust particles are amorphous and already much larger than those typically observed in the ISM. Although the high accretion rate of the system provides both, high temperatures out to large radii and an effective transport mechanism to distribute crystalline grains, we do not see any evidence for crystalline silicates neither in the total spectrum nor in the correlated flux spectra from the inner disk regions. Possible reasons for this non-detection are mentioned. All results are discussed in context with other high-spatial resolution observations of FU Ori and other FU Ori objects. We also address the question whether FU Ori is in a younger evolutionary stage than a classical TTauri star.Comment: 41 pages (aastex style), 11 figures, 8 tables, accepted by Ap

The Truncated Disk of CoKu Tau/4

We present a model of a dusty disk with an inner hole which accounts for the Spitzer Space Telescope Infrared Spectrograph observations of the low-mass pre-main sequence star CoKu Tau/4. We have modeled the mid-IR spectrum (between 8 and 25 mic) as arising from the inner wall of a disk. Our model disk has an evacuated inner zone of radius ~ 10 AU, with a dusty inner ``wall'', of half-height ~ 2 AU, that is illuminated at normal incidence by the central star. The radiative equilibrium temperature decreases from the inner disk edge outward through the optically-thick disk; this temperature gradient is responsible for the emission of the silicate bands at 10 and 20 mic. The observed spectrum is consistent with being produced by Fe-Mg amorphous glassy olivine and/or pyroxene, with no evidence of a crystalline component. The mid-infrared spectrum of CoKu Tau/4 is reminiscent of that of the much older star TW Hya, where it has been suggested that the significant clearing of its inner disk is due to planet formation. However, no inner disk remains in CoKu Tau/4, consistent with the star being a weak-emission (non-accreting) T Tauri star. The relative youth of CoKu Tau/4 (~ 1 Myr) may indicate much more rapid planet formation than typically assumed.Comment: 32 pages, 9 figures, accepted in Ap

Tracing the development of dust around evolved stars: The case of 47 Tuc

We observed mid-infrared (7.5-22 mum) spectra of AGB stars in the globular cluster 47 Tuc with the Spitzer telescope and find significant dust features of various types. Comparison of the characteristics of the dust spectra with the location of the stars in a logP-K-diagram shows that dust mineralogy and position on the AGB are related. A 13 mum feature is seen in spectra of low luminosity AGB stars. More luminous AGB stars show a broad feature at 11.5 mum. The spectra of the most luminous stars are dominated by the amorphous silicate bending vibration centered at 9.7 mum. For 47 Tuc AGB stars, we conclude that early on the AGB dust consisting primarily of Mg-, Al- and Fe oxides is formed. With further AGB evolution amorphous silicates become the dominant species.Comment: 2 figures, accepted for publication in ApJ Letter

Born Again Protoplanetary Disk Around Mira B

The Mira AB system is a nearby (~107 pc) example of a wind accreting binary star system. In this class of system, the wind from a mass-losing red giant star (Mira A) is accreted onto a companion (Mira B), as indicated by an accretion shock signature in spectra at ultraviolet and X-ray wavelengths. Using novel imaging techniques, we report the detection of emission at mid-infrared wavelengths between 9.7 and 18.3 $\mu$m from the vicinity of Mira B but with a peak at a radial position about 10 AU closer to the primary Mira A. We interpret the mid-infrared emission as the edge of an optically-thick accretion disk heated by Mira A. The discovery of this new class of accretion disk fed by M-giant mass loss implies a potential population of young planetary systems in white-dwarf binaries which has been little explored, despite being relatively common in the solar neighborhood.Comment: Accepted for Ap

2-Dust : a Dust Radiative Transfer Code for an Axisymmetric System

We have developed a general purpose dust radiative transfer code for an axisymmetric system, 2-Dust, motivated by the recent increasing availability of high-resolution images of circumstellar dust shells at various wavelengths. This code solves the equation of radiative transfer following the principle of long characteristic in a 2-D polar grid while considering a 3-D radiation field at each grid point. A solution is sought through an iterative scheme in which self-consistency of the solution is achieved by requiring a global luminosity constancy throughout the shell. The dust opacities are calculated through Mie theory from the given size distribution and optical properties of the dust grains. The main focus of the code is to obtain insights on (1) the global energetics of dust grains in the shell (2) the 2-D projected morphologies that are strongly dependent on the mixed effects of the axisymmetric dust distribution and inclination angle of the shell. Here, test models are presented with discussion of the results. The code can be supplied with a user-defined density distribution function, and thus, is applicable to a variety of dusty astronomical objects possessing the axisymmetric geometry.Comment: To be published in ApJ, April 2003 issue; 13 pages, 4 tables, 17 figures, 5-page appendix (no figures for the main text included in this preprint). For the complete preprint and code distribution, contact the author

Signatures of Planets in Spatially Unresolved Disks

Main sequence stars are commonly surrounded by debris disks, composed of cold dust continuously replenished by a reservoir of undetected dust-producing planetesimals. In a planetary system with a belt of planetesimals (like the Solar System's Kuiper Belt) and one or more interior giant planets, the trapping of dust particles in the mean motion resonances with the planets can create structure in the dust disk, as the particles accumulate at certain semimajor axes. Sufficiently massive planets may also scatter and eject dust particles out of a planetary system, creating a dust depleted region inside the orbit of the planet. In anticipation of future observations of spatially unresolved debris disks with the Spitzer Space Telescope, we are interested in studying how the structure carved by planets affects the shape of the disk's spectral energy distribution (SED), and consequently if the SED can be used to infer the presence of planets. We numerically calculate the equilibrium spatial density distributions and SEDs of dust disks originated by a belt of planetesimals in the presence of interior giant planets in different planetary configurations, and for a representative sample of chemical compositions. The dynamical models are necessary to estimate the enhancement of particles near the mean motion resonances with the planets, and to determine how many particles drift inside the planet's orbit. Based on the SEDs and predicted $\it{Spitzer}$ colors we discuss what types of planetary systems can be distinguishable from one another and the main parameter degeneracies in the model SEDs.Comment: 40 pages (pre-print form), including 16 figures. Published in ApJ 200

Dust in the Local Interstellar Wind

The gas-to-dust mass ratios found for interstellar dust within the Solar System, versus values determined astronomically for the cloud around the Solar System, suggest that large and small interstellar grains have separate histories, and that large interstellar grains preferentially detected by spacecraft are not formed exclusively by mass exchange with nearby interstellar gas. Observations by the Ulysses and Galileo satellites of the mass spectrum and flux rate of interstellar dust within the heliosphere are combined with information about the density, composition, and relative flow speed and direction of interstellar gas in the cloud surrounding the solar system to derive an in situ value for the gas-to-dust mass ratio, $R_{g/d} = 94^{+46}_{-38}$. Hubble observations of the cloud surrounding the solar system yield a gas-to-dust mass ratio of Rg/d=551+61-251 when B-star reference abundances are assumed. The exclusion of small dust grains from the heliosheath and heliosphere regions are modeled, increasing the discrepancy between interstellar and in situ observations. The shock destruction of interstellar grains is considered, and comparisons are made with interplanetary and presolar dust grains.Comment: 87 pages, 9 figures, 6 tables, accepted for publication in Astrophysical Journal. Uses AASTe