DOI: 10.5281/zenodo.7340108
title: A three-dimensional Galactic extinction model

description: <strong>Overview</strong> A large-scale three-dimensional model of Galactic extinction is presented based on the Galactic dust distribution model of Drimmel & Spergel (2001). The extinction A<sub>V</sub> to any point within the Galactic disk can be quickly deduced using a set of three-dimensional Cartesian grids. Extinctions from the model are compared to empirical extinction measures, including lines-of-sight in and near the Galactic plane using optical and NIR extinction measures; in particular we show how extinction can be derived from NIR color-magnitude diagrams in the Galactic plane to a distance of 8 kiloparsec. Please cite Drimmel, Cabrera-Lavers, and López-Corredoira (2003) when using this model. The provided tarball includes the contribution to the extinction from different Galactic components in binary format. Code to read and use this data is included in the mwdust package. <strong>Instructions for use of the extinction grids (from the original README)</strong> <pre>The data-for.tar.gz file contains a suite of three-dimensional cartesian grids of the extinction in V band. Each grid corresponds to one of three structural components of the dust model (disk, spiral arms, local Orion arm). Local and "global" grids provide different levels of detail, or resolution. The local grids are centered on the Sun, the large scale grids cover the entire Galaxy, excepting that of the local Orion arm. For all grids the z=0 plane corresponds to the Galactic Plane. For the local grids the x-axis points toward the Galactic center. The conversion from Galactic coordinates (l,b,d) to cartesian heliocentric coordinates are: x = d cosb cosl y = d cosb sinl z = d sinb + Z_sun with Z_sun = 0.015 kpc. Using the convention that array indices start at 0 (as in IDL), the grid coordinates (i,j,k) are given by i = x / \Delta x + (n_x - 1)/2 j = y / \Delta y + (n_y - 1)/2 k = z / \Delta z + (n_z - 1)/2 where the dimensions of the grid are (n_x, n_y, n_z) and the grid spacing is (\Delta x, \Delta y, \Delta z), where \Delta x = \Delta y for all the grids. The table below lists these parameters for each of the grids. The above formulas will be convenient for any 3-D interpolation routine that requires grid coordinates for the points to be interpolated. Note that for FORTRAN +1 should be added to the above grid coordinates to conform with the convention that array indices start with the number 1. For the large scale grids galactocentric coordinates are more convenient. Using the same axis directions the same conversions from (l,b,d) to cartesian coordinates above will still apply with the exception of the x-coordinate, which is now x = d cosb cosl + X_sun with X_sun = -8 kpc. For the grids avdisk and avspir the same conversions to (i,j,k) can be used, however the grid avori only covers part of the Galactic disk, so that i = x/ \Delta x + 2.5(n_x - 1) Care should be taken not to extrapolate beyond the boundaries of the large-scale grids, but a working approximation for points beyond the grid boundaries is to use a point farthest from the Sun *along the line-of-sight* that is on the boundary of the large-scale grid. In most directions this is equivalent to the total Galactic extinction. Grid parameters: grid component \Delta x \Delta z n_x n_y n_z ---------------------------------------------------------------------------- large-scale: avgrid all 0.2 0.02 151 151 51 avdisk disk 0.2 0.02 151 151 51 avspir spiral arms 0.2 0.02 151 151 51 avori Orion arm 0.05 0.02 76 151 51 local: avloc all 0.02 0.02 101 201 51 avdloc disk 0.05 0.02 31 31 51 avori2 Orion arm 0.02 0.02 101 201 51 ---------------------------------------------------------------------------- Rescaling factors: The rescaling factors are based on the residuals between the COBE FIR observations and the predictions of the dust distribution model. For this reason the rescaling factors are rooted to the COBE data structure; for each COBE pixel there is an associated rescaling factor. This introduces some complication in the retrieval of the rescaling factors for any arbitrary direction as the COBE sky maps use a nonstandard projection and pixel ordering scheme. (See http://space.gsfc.nasa.gov/astro/cobe/skymap_info.html for a brief introduction and Appendix G of the COBE Guest Investigator Software (CGIS) Software User's Guide (version 2.2), retrievable at ftp://rosette.gsfc.nasa.gov/pub/cobe-gi/doc/, for further details.) The rescaling factors for each COBE pixel are contained in a binary file in unformatted FORTRAN format, rf_allsky.dat. This file contains arrays that specify: the COBE pixel number, the structural component to be rescaled (i.e. the component with a rescaling factor not equal to 1), the Galactic longitude and latitude of each pixel, and the rescaling factor to be applied. (See the example FORTRAN code below.) The second integer array specifies the component to be rescaled is an integer array with a value of 1, 2 or 3, corresponding to the disk, spiral and local arm components respectively. There are a total of 393216 pixels. To access these rescaling factors the user must find the pixel that coincides with the direction of interest. For this task there are at least three options: 1) Write a routine that searches through the list of longitudes and latitudes for the nearest pixel. 2) Work within the UIDL environment which provides an efficient means, via CGIS IDL code, to retrieve the pixel number nearest a given direction. The UIDL package with instructions for installation can be found at http://space.gsfc.nasa.gov/astro/cobe/cgis.html. The code findext.pro in this directory is an example of such a routine. 3) Use stand alone CGIS code (standard FORTRAN) to retrieve the pixel number for a given direction. This code can be down loaded via anonymous ftp from ftp://rosette.gsfc.nasa.gov/pub/cobe-gi/. The relevant files are aacgis_for.txt and cgis-for.tar, the latter containing the FORTRAN library with makefiles. The code ll2pix.for queries for longitude, latitude, coordinate system and resolution level to return a pixel number. The resolution level corresponding to the FIR data, and hence the rescaling factors, is level 9. See the FORTRAN code Av3_FEB03.f as an example. Once the correct COBE pixel index is found for the desired direction, use the first array to discern to which component the rescaling factor should be applied to. For example, using the array nomenclature in the example FORTRAN code below, if for pixel J the the NCOMP(J) value is 2, then the extinction should be AV = AVDISK + RF(J)*AVSPIR + AVORI, where AVDISK, AVSPIR and AVORI correspond to the interpolated values from these three-dimensional arrays. The user is also cautioned that in directions where extragalactic sources contribute significantly to the FIR flux the derived rescaling factors will be erroneous. This includes the Andromeda Galaxy, M33, the LMC and SMC. There are also nearby regions within the Galaxy that have anomalous emission due to warm dust that are not described by the model, especially the rho Ophiucus and Orion regions. Finally, the nuclear disk in the Galactic center (|l| &lt; 3 deg) is not described by the model. The rescaling factors in these directions also should not be used. Algorithm: Using the three-dimensional extinction grids a value for the extinction A_i due to each of the components i of the dust distribution can be found for any point in the Galactic disk via interpolation. Together with the appropriate rescaling factor a final estimate of the extinction is arrived at: A(l,b,r) = \sum f_i(l,b) A_i(l,b,r) To summarize, an algorithm for arriving at an extinction A_v for a point in the Galaxy (l,b,r) is outlined below: 1) Find the COBE pixel coinciding to (l,b). 2) Recover the rescaling factor f_i and component i to be rescaled from the rf_allsky.dat file. (Set f=1 for the other components.) 3) Determine the grid coordinates: (l,b,r) ----&gt; (x,y,z) -----&gt; (i,j,k) 4) Interpolate from appropriate grids to find A_i(l,b,r) for each component. 5) Sum over the components (above equation) to arrive at A(l,b,r). </pre>