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 AV 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).