DOI: 10.5281/zenodo.13743507
title: Geometry and Opacity Data for Fractal Aggregates

description: In a previous version of this archive, geometry data and tables of opacity calculations were given that could be used to calculate the radiative pressure and absorption on fractal dust grains under Asymptotic Giant Branch (AGB) conditions (with a peak stellar wavelength of ~ 1 micron) for aggregates containing up to 256 primary particles.  Because the focus of that work was on radiative pressure from a stellar spectrum peaking at approximately 1 micron, these data only covered the wavelength range from 0.3 to 30 microns.  In this updated archive the wavelength range of the data has been expanded to allow calculation of the emission of the grains at longer wavelengths.  Data are calculated for three common dust materials:  forsterite, (Mg2SiO4), olivine, (Mg_(2x)Fe_(2(1-x))SiO4) with x=0.5, and 'astronomical silicate' (B.T. Draine and H.M. Lee, Optical Properties of Interstellar Graphite and Silicate Grains, Astrophysical Journal, 1984).  In this updated version the range of aggregate sizes (number of primary particles in the aggregate) of some of these materials has also been increased from a maximum of 256 to 1024 constituent particles. Example fractal aggregates were generated using the Diffusion Limited Aggregation (DLA) code as described in Wozniak M., Onofri F.R.A., Barbosa S., Yon J., Mroczka J., Comparison of methods to derive morphological parameters of multi-fractal samples of particle aggregates from TEM images, Journal of Aerosol Science 47: 12–26 (2012) and Onofri F.R.A., M. Wozniak, S. Barbosa, On the Optical Characterization of Nanoparticle and their Aggregates in Plasma Systems, Contributions to Plasma Physics 51(2-3):228-236 (2011).  Aggregates were generated with a constant prefactor, kf=1.3, and two fractal dimensions (Df), representing open, porous (Df=1.8) aggregates and more compact (Df=2.8) aggregates. The geometry files were produced with the DLA software.  An example run using this software is shown for aggregates with 256 primary particles and a fractal dimension of 2.8 in the file 'dla_example.png' For the fractal dimension=1.8 data, the number of primary particles in the aggregate, N, was increased up to 1024 from the previous maximum of 256 for all three dust materials investigated.  In addition, the data for MgFeSiO4 with a fractal dimension of 2.8 was increased from 256 to 1024.  As in the previous archive, 12 instances of each aggregate size were generated with primary particles having a radius of 0.5.  These geometry data are given in:aggregates_kf1.3_df1.8.zip  -->  Geometry for a prefactor of 1.3 and fractal dimension 1.8aggregates_kf1.3_df2.8.zip  -->  Geometry for a prefactor of 1.3 and fractal dimension 2.8 An example file name for an aggregate is 'N_00000032_Agg_00000008.dat'  where the first number is the number of primary particles in the aggregate (N=32) and the second number is the instance number (e.g. 8 of 12).  The radius of each primary particle in an aggregate is 0.5.  The geometry files have 4 columns:  the x, y and z coordinates of each primary particle followed by the primary particle radius.  In each zip file there is also a pdf document that describes the geometry data and shows an image of each geometry file.

 These geometry data were then used to calculate the opacity of the aggregates using the Multiple Sphere T-Matrix code (MSTM v 3.0) developed by Daniel Mackowski (D.W. Mackowski, M.I. Mishchenko,  A multiple sphere T-matrix Fortran code for use on parallel computer clusters, Journal of Quantitative Spectroscopy and Radiative Transfer, Volume 112, Issue 13, 2011).  Data were generated using the first 10 instances of each aggregate size, and the geometry data were appropriately scaled to calculate the opacity data for primary particle radii ranging from  0.001 - 1.0 microns.  As noted earlier, an earlier version of this archive was focused on radiative pressure on these aggregates and only covered the spectrum of a typical AGB star (0.3 to 30 microns wavelength).  In this updated version this wavelength range has been increased to the longer wavelength limits of the optical data.  By default, MSTM calculations are made along the z-axis of the geometry data.  Additional calculations were made along the x and y axes for each aggregate.   Therefore the final data set is the average of 30 values (10 instances each in the x,y,z directions). The opacity data files are given in:

astronomical_silicate_df1.8.zip --> astronomical silicate aggregates with fractal dimension 1.8astronomical_silicate_df2.8.zip --> astronomical silicate aggregates with fractal dimension 2.8forsterite_df1.8.zip --> forsterite aggregates with fractal dimension 1.8forsterite_df2.8.zip --> forsterite aggregates with fractal dimension 2.8olivine_df1.8.zip --> olivine aggregates with fractal dimension 1.8olivine_df2.8.zip --> olivine aggregates with fractal dimension 2.8

In the previous version of this archive, only the table files with the averages of the 10 instances were provided.  In this updated version each of the individual opacity files used to create these tables is now also provided.  These opacity files are numbered similar to the geometry files.  For example, the opacity calculations for N=32, instance=5, angle=3 is given by 'opacity_results_N000032_I05_A03_file.dat.'  Each file begins with a short header describing the data.  For example, the astronomical silicate header for this N=32, instance=5, angle=3 file is:

############################################################################################## Number of primary particles in aggregate:        32 # Geometry Instance Number:                5 # Geometry File Name:                    N_00000032_Agg_00000005.dat # Rotation Angles:                      90.000    90.000     0.000 # Number of radius values:                30 # Minimum and maximum radius values in microns:        1.00000e-003  1.00000e+000 # Number of wavelength values:                92 # Minimum and maximum wavelength values in microns:    3.00000e-001  1.00000e+004 #############################################################################################

Afterwards the columns list the line number, the primary particle radius (microns), the wavelength (microns), the extinction efficiency factor, the absorption efficiency factor, the scattering absorption efficiency factor,  the asymmetry factor and the radiation pressure efficiency factor.  These efficiency factors are based on the effective radius of the aggregate described later in this document.

Within each of these zipped folders is a file that contains the averages of these individual opacity files.  For example 'astronomical_silicate_df1.8.dat' is the averaged data for the astronomical silicate aggregates with a fractal dimension 1.8.  As in the previous archive, the first lines of these table files are a header starting with the '#' character describing the table and the source of the optical data used. After the header, the first line of data in the table has the following nine values giving the range for the data table and number of samples in N, (aggregate size), primary particle radius (microns) and wavelength (microns).  These are:  Minimum aggregate size  Maximum aggregate size  Number of Aggregate samples  Primary Particle Minimum Radius (microns)  Primary Particle Maximum Radius (microns)  Number of Primary Particle radii samples  Wavelength minimum (microns)  Wavelength maximum (microns)  Number of Wavelength samples  Subsequent lines contain 13 columns.  These columns give the efficiency factors and asymmetry factor for aggregates.  These efficiency factors are based on the effective radius of the aggregate given by:             a_eff = a_primary*N^(1/3)where a_primary is the primary particle radius and N is the number of primary particles in the aggregate. For example, the absorption opacity of an aggregate would then be = pi*a_eff^2 * Q_abs.The values in each column are:  Column 1:   Primary particle radius in microns  Column 2:   Wavelength in microns  Column 3:   Number of primary particles in aggregate  Column 4:   Mean Q_ext, mean extinction efficiency factor  Column 5:   Standard Deviation of Mean Q_ext   Column 6:   Mean Q_abs, mean absorption efficiency factor  Column 7:   Standard Deviation of Mean Q_abs  Column 8:   Mean Q_sca, mean scattering efficiency factor  Column 9:   Standard Deviation of mean Q_sca  Column 10:  Mean g_cos, mean asymmetry factor  Column 11:  Standard Deviation of mean asymmetry factor  Column 12:  Mean Q_pr, mean radiation pressure efficiency factor  Column 13:  Standard Deviation of mean