Formulation of Non-steady-state Dust Formation Process in Astrophysical Environments

The non-steady-state formation of small clusters and the growth of grains accompanied by chemical reactions are formulated under the consideration that the collision of key gas species (key molecule) controls the kinetics of dust formation process. The formula allows us to evaluate the size distribution and condensation efficiency of dust formed in astrophysical environments. We apply the formulation to the formation of C and MgSiO3 grains in the ejecta of supernovae, as an example, to investigate how the non-steady effect influences the formation process, condensation efficiency f_{con}, and average radius a_{ave} of newly formed grains in comparison with the results calculated with the steady-state nucleation rate. We show that the steady-state nucleation rate is a good approximation if the collision timescale of key molecule tau_{coll} is much smaller than the timescale tau_{sat} with which the supersaturation ratio increases; otherwise the effect of the non-steady state becomes remarkable, leading to a lower f_{con} and a larger a_{ave}. Examining the results of calculations, we reveal that the steady-state nucleation rate is applicable if the cooling gas satisfies Lambda = tau_{sat}/tau_{coll} > 30 during the formation of dust, and find that f_{con} and a_{ave} are uniquely determined by Lambda_{on} at the onset time t_{on} of dust formation. The approximation formulae for f_{con} and a_{ave} as a function of Lambda_{on} could be useful in estimating the mass and typical size of newly formed grains from observed or model-predicted physical properties not only in supernova ejecta but also in mass-loss winds from evolved stars.Comment: 44 pages, 10 figures, 1 table, accepted for publication in Ap

Dust formation and mass loss around intermediate-mass AGB stars with initial metallicity Zini≤10−4Z_{\rm ini} \leq 10^{-4} in the early Universe I: Effect of surface opacity on the stellar evolution and dust-driven wind

Dust formation and resulting mass loss around Asymptotic Giant Branch (AGB) stars with initial metallicity in the range of $0 \leq Z_{\rm ini} \leq 10^{-4}$ and initial mass $2\leq M_{\rm ini}/M_{\odot} \leq 5$ are explored by the hydrodynamical calculations of dust-driven wind (DDW) along the AGB evolutionary tracks. We employ the MESA code to simulate the evolution of stars, assuming an empirical mass-loss rate in the post-main sequence phase, and considering the three types of low-temperature opacities (scaled-solar, CO-enhanced, and CNO-enhanced opacities) to elucidate the effect on the stellar evolution and the DDW. We find that the treatment of low-temperature opacity strongly affects the dust formation and resulting DDW; in the carbon-rich AGB phase, the maximum $\dot{M}$ of $M_{\rm ini} \geq$ 3 $M_{\odot}$ star with the CO-enhanced opacity is at least one order of magnitude smaller than that with the CNO-enhanced opacity. A wide range of stellar parameters being covered, a necessary condition for driving efficient DDW with $\dot{M} \ge 10^{-6}$ $M_{\odot}$ yr$^{-1}$ is expressed as the effective temperature $T_{\rm eff} \lesssim 3850$ K and $\log(\delta_{\rm C}L/\kappa_{\rm R} M) \gtrsim 10.43\log T_{\rm eff}-32.33$ with the carbon excess $\delta_{\rm C}$ defined as $\epsilon_{\rm C} - \epsilon_{\rm O}$ and the Rosseland mean opacity $\kappa_{\rm R}$ in units of cm$^2$g$^{-1}$ in the surface layer, and the stellar mass (luminosity) $M$ $(L)$ in solar units. The derived fitting formulae of gas and dust mass-loss rates in terms of input stellar parameters could be useful for investigating the dust yield from AGB stars in the early Universe being consistent with the stellar evolution calculations.Comment: 26 pages, 7 figures, 4 tables, accepted for publication in MNRA

Alfv\'en wave-driven wind from RGB and AGB stars

We develop a magnetohydrodynamical model of Alfv\'en wave-driven wind in open magnetic flux tubes piercing the stellar surface of Red Giant Branch (RGB) and Asymptotic Giant Branch (AGB) stars, and investigate the physical properties of the winds. The model simulations are carried out along the evolutionary tracks of stars with initial mass in the range of 1.5 to 3.0 $M_{\odot}$ and initial metallicity $Z_{\rm ini}$=0.02. The surface magnetic field strength being set to be 1G, we find that the wind during the evolution of star can be classified into the following four types; the first is the wind with the velocity higher than 80 km s$^{-1}$ in the RGB and early AGB (E-AGB) phases; the second is the wind with outflow velocity less than 10 km s$^{-1}$ seen around the tip of RGB or in the E-AGB phase; the third is the unstable wind in the E-AGB and thermally pulsing AGB (TP-AGB) phases; the fourth is the stable massive and slow wind with the mass-loss rate higher than 10$^{-7} M_{\odot}$ yr$^{-1}$ and the outflow velocity lower than 20 km s$^{-1}$ in the TP-AGB phase. The mass-loss rates in the first and second types of wind are two or three orders of magnitude lower than the values evaluated by an empirical formula. The presence of massive and slow wind of the fourth type suggests the possibility that the massive outflow observed in TP-AGB stars could be attributed to the Alfv\'en wave-driven wind.Comment: 17 pages, 15 figures, accepted for publication in Ap

Modeling Porous Dust Grains with Ballistic Aggregates. II. Light Scattering Properties

We study the light scattering properties of random ballistic aggregates constructed in Shen et al. (Paper I). Using the discrete-dipole-approximation, we compute the scattering phase function and linear polarization for random aggregates with various sizes and porosities, and with two different compositions: 100% silicate and 50% silicate-50% graphite. We investigate the dependence of light scattering properties on wavelength, cluster size and porosity using these aggregate models. We find that while the shape of the phase function depends mainly on the size parameter of the aggregates, the linear polarization depends on both the size parameter and the porosity of the aggregates, with increasing degree of polarization as the porosity increases. Contrary to previous studies, we argue that monomer size has negligible effects on the light scattering properties of ballistic aggregates, as long as the constituent monomer is smaller than the incident wavelength up to 2*pi*a_0/lambda\sim 1.6 where a_0 is the monomer radius. Previous claims for such monomer size effects are in fact the combined effects of size parameter and porosity. Finally, we present aggregate models that can reproduce the phase function and polarization of scattered light from the AU Mic debris disk and from cometary dust, including the negative polarization observed for comets at scattering angles 160<theta<180 deg. These aggregates have moderate porosities, P\sim 0.6, and are of sub-micron-size for the debris disk case, or micron-size for the comet case.Comment: Submitted to ApJ. Scattering properties can be downloaded at http://www.astro.princeton.edu/~draine/SDJ2009.html Target geometries are at http://www.astro.princeton.edu/~draine/agglom.htm

On the formation and processing of carbon and nitrogen compounds in carbonaceous chondrites

On the basis of chemical kinetic consideration, we examine processing of carbon and nitrogen compounds that leads to the linear relation between the logarithmic contents of C and N in carbonaceous chondrites : log N=a log C-b, found by A. SHIMOYAMA et al. (Chem. Lett., 10,2013,1987), where a>1 and b are constants. It is shown that the linear relation results from dissociation of organic polymer in the grains before accretion to parent body-sized objects by radiation that penetrates through the grains such as cosmic ray. Condensation of volatile molecules composed of C and N is also examined as a possible process to form precursors of organic compounds in carbonaceous chondrites. From an analysis of a model thermodynamic system, it is conjectured that this process can also realize the linear relation under certain conditions

Dust Production Factories in the Early Universe: Formation of Carbon Grains in Red-supergiant Winds of Very Massive Population III Stars

We investigate the formation of dust in a stellar wind during the red-supergiant (RSG) phase of a very massive Population III star with the zero-age main sequence mass of 500 M_sun. We show that, in a carbon-rich wind with a constant velocity, carbon grains can form with a lognormal-like size distribution, and that all of the carbon available for dust formation finally condense into dust for wide ranges of the mass-loss rate ((0.1-3)x10^{-3} M_sun yr^{-1}) and wind velocity (1-100 km s^{-1}). We also find that the acceleration of the wind driven by newly formed dust suppresses the grain growth but still allows more than half of gas-phase carbon to be finally locked up in dust grains. These results indicate that at most 1.7 M_sun of carbon grains can form in total during the RSG phase of 500 M_sun Population III stars. Such a high dust yield could place very massive primordial stars as important sources of dust at the very early epoch of the universe if the initial mass function of Population III stars was top-heavy. We also briefly discuss a new formation scenario of carbon-rich ultra-metal-poor stars considering the feedback from very massive Population III stars.Comment: 1 table, 4 figures, accepted for publication in the ApJ Letter

A model for the infrared dust emission from forming galaxies

In the early epoch of galaxy evolution, dust is only supplied by supernovae (SNe). With the aid of a new physical model of dust production by SNe developed by Nozawa et al. (2003) (N03), we constructed a model of dust emission from forming galaxies on the basis of the theoretical framework of Takeuchi et al. (2003) (T03). N03 showed that the produced dust species depends strongly on the mixing within SNe. We treated both unmixed and mixed cases and calculated the infrared (IR) spectral energy distribution (SED) of forming galaxies for both cases. Our model SED is less luminous than the SED of T03 model by a factor of 2-3. The difference is due to our improved treatment of UV photon absorption cross section, as well as different grain size and species newly adopted in this work. The SED for the unmixed case is found to have an enhanced near to mid-IR (N-MIR) continuum radiation in its early phase of the evolution (age < 10^{7.25} yr) compared with that for the mixed case. The strong N--MIR continuum is due to the emission from Si grains, which only exist in the species of the unmixed dust production. We also calculated the IR extinction curves for forming galaxies. Then we calculated the SED of a local starbursting dwarf galaxy SBS 0335-052. Our present model SED naturally reproduced the strong N--MIR continuum and the lack of cold FIR emission of SBS 0335-052. We found that only the SED of unmixed case can reproduce the NIR continuum of this galaxy. We then made a prediction for the SED of another typical star-forming dwarf, I Zw 18. We also presented the evolution of the SED of LBGs. Finally, we discussed the possibility of observing forming galaxies at z > 5.Comment: MNRAS, in press. 18 pages, 15 figures. Abstract abridge

Supernova dust for the extinction law in a young infrared galaxy at z = 1

We apply the supernova(SN) extinction curves to reproduce the observed properties of SST J1604+4304 which is a young infrared (IR) galaxy at z = 1. The SN extinction curves used in this work were obtained from models of unmixed ejecta of type II supernovae(SNe II) for the Salpeter initial mass function (IMF) with a mass range from 8 to 30 M_sun or 8 to 40 M_sun. The effect of dust distributions on the attenuation of starlight is investigated by performing the chi-square fitting method against various dust distributions. These are the commonly used uniform dust screen, the clumpy dust screen, and the internal dust geometry. We add to these geometries three scattering properties, namely, no-scattering, isotropic scattering, and forward-only scattering. Judging from the chi-square values, we find that the uniform screen models with any scattering property provide good approximations to the real dust geometry. Internal dust is inefficient to attenuate starlight and thus cannot be the dominant source of the extinction. We show that the SN extinction curves reproduce the data of SST J1604+4304 comparable to or better than the Calzetti extinction curve. The Milky Way extinction curve is not in satisfactory agreement with the data unless several dusty clumps are in the line of sight. This trend may be explained by the abundance of SN-origin dust in these galaxies; SN dust is the most abundant in the young IR galaxy at z = 1, abundant in local starbursts, and less abundant in the Galaxy. If dust in SST J1604+4304 is dominated by SN dust, the dust production rate is about 0.1 M_sun per SN.Comment: 12 pages, 8 figures, 1 tabl