A three-dimensional Galactic extinction model

Overview

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_V 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.

Instructions for use of the extinction grids (from the original README)

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| < 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) ----> (x,y,z) -----> (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).