Program: POTENTIAL
Purpose: Program to calculate the 2-dim gravitational potential
map of a 2-dim image. This is evaluating the integral
given as Eq. 2-3 in the book Galactic Dynamics by
Binney and Tremaine.
Category: ANALYSIS, CALCULATION
File: potential.c
Author: M.G.R. Vogelaar
Roelof Bottema (algorithm and documentation).
Keywords:
INSET= Give set, subsets:
Maximum number of subsets is 1024.
Input map for which you want to calculate the potential.
BOX1= Region for potential field: [entire subset]
Region in the input map for which you want to calculate
the potential.
BOX2= Region to include in calculation: [entire subset]
The region of the input map which you want to include in
the calculation of the potential.
OUTSET= Give output set (, subsets):
Output set and subset(s) for the result. The number of
output subsets is the same as the number of input
subsets.
Also, the size and attributes (header items)
of the output map are equal to that of the input map.
Description: Program to calculate the 2-dim gravitational potential map
of a 2-dim image. This is evaluating the integral given
as Eq. 2-3 Galactic Dynamics by Binney and Tremaine. The
integral is replaced by a sum over the pixel values in
the image of INSET=
rho(p)
Pot(P) = -G * SUM ---------- dx dy dz
| p - P |
P, and p are vector positions, rho(p) is the space density
at position p. For the present application, rho(p) * dz
is replaced by the (surface density) value at pixel p.
dx and dy are pixel sizes which are taken to be equal to
1.0 and the distance |p-P| is measured in pixels.
Furthermore the constant -G is replaced with 1.0.
To calculate the physical value for the potential in
some units, you have to multiply the value of Pot
with a certain constant. Then you have to know your
pixel size in length units and actual value of the surface
density. In addition the gravitational constant G has to
be included. Since everybody uses his or her own units
we leave this calculation to the user........
Blanks or undefined values in the input map are replaced
with zeros. Positions outside BOX1 in the output map are
filled up with blanks.
Notes: For large regions the calculation may take a while,
which gives you the opportunity to have a cup of coffee.
Example: Calculate the 2-dim potential which would result for a
photometric image of a galaxy. You first have to do a
proper sky subtraction and interpolation over any
irregularities or foreground stars. Project the image
to face on. Then use POTENTIAL.
Updates: Jun 14, 2001: VOG, Document created.