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ccdpot - potential of an infinitesimally thin disk

**ccdpot**
[parameter=value]

Computes the potential in the plane of an
infinitesimally thin disk. The method used here is VERY slow, since it evaluates
the integral exactly as given in Eq. 2-3 of e.g. *Galactic Dynamics* by Binney
and Tremaine (1987, 2008). The integral is replaced by a sum over the pixel
values of the input image of

Sigma(p)
Pot(P) = -Gravc * SUM ---------- dx dy
| p - P |

P, and p are vector positions, Sigma(p)
is the surface density at position
p. dx and dy are pixel sizes and the distance |p-P| is measured in pixels.

A faster way is to use FFT’s, as described by Hockney & Eastwood (1978),
and implemented in MIRIAD’s potfft program.

The following parameters
are recognized in any order if the keyword is also given:
**in=**
- Input image
file, in
*image(5NEMO)*
format. No default.
**out=**
- Output image file. No default.
**gravc=**
- Gravitional constant. Normally taken as 1, but this allows you to
more easily convert to your own units already. See also
*units(5NEMO)*
. Default:
1
**report=***N*
- Give a rolling percentage progress report every
*N* pixels computed.
Default: 0 (meaning no progress report)
**nbench=1**
- Set this to how often
the integral is computed, in order for fast versions (small maps) to get
accurate timings on fast machines. [Default: 1]

As an example, if
units are 1e10Msun and kpc, Gravc = 43007.1 (see *units(1NEMO)*
, the potential

potential(GIPSY), potfft(MIRIAD), rotcurves(1NEMO)
, units(1NEMO)
,
image(5NEMO)

Since for each of the N^2 pixels, all other N^2 pixels
will be interrogated, this algorithm is O(N^4). In practice you will find
it to be more like O(N^5). The code precomputes a kernel, which is simplified
if we can assume the pixel size in X and Y are the same. If not, the program
will currently probably compute it terribly wrong.

Peter Teuben
(loosely based on Roelof Bottema’s POTENTIAL code)

26-Jul-02` ` ` ` V0.1 Created to check potfft PJT
22-oct-02` ` ` ` V0.2 correct kernel at (0,0)` ` ` ` PJT
28-feb-03` ` ` ` V0.3 added gravc=` ` ` ` PJT
17-mar-2021` ` ` ` V0.6

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