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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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