DOI: 10.5281/zenodo.13743508
title: Geometry and Opacity Data for Fractal Aggregates

description:  

The tables in this data set may be used to calculate the radiative pressure 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.  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).

 

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'

 

The number of primary particles in the aggregate, N, was sampled up to 256.  In each case 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 1.8

aggregates_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).

 

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 and covering the spectrum of a typical AGB star (0.3 to 30 microns wavelength).  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:

astronomical_silicate_df1.8 --> astronomical silicate aggregates with fractal dimension 1.8

astronomical_silicate_df2.8 --> astronomical silicate aggregates with fractal dimension 2.8

forsterite_df1.8 --> forsterite aggregates with fractal dimension 1.8

forsterite_df2.8 --> forsterite aggregates with fractal dimension 2.8

olivine_df1.8 --> olivine aggregates with fractal dimension 1.8

olivine_df2.8 --> olivine aggregates with fractal dimension 2.8

 

The first lines of the files give 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 six 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