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snapfour - fourier analyze a snapshot
snapfour in=snapshot_file
[parameters=values...]
snapfour computes a number of requested
fourier (cos and sin) coefficients in a user determined part of the snapshot
By default the snapshot is divided in a set of concentric cylindrical rings,
and a fourier analysis is done in cylindrical coordinates.
The observable
quantity f is fitted as
f(r,theta) = sum_{cmi..}{A(r)cos(cmi*theta) + sum_{smi..}{B(r)sin(smi*theta)
where x, y as well as f r = sqrt(x*x+y*y) , theta=atan2(y,x)
can be any arbitrary bodytrans(3NEMO)
expression using the xvar, yvar
and fvar keywords. The least squares is done using normalized equations,
which are known for roundoff problem in case a large number of coefficients
or points are used.
Optionally the cos (A) and sin (B) coefficients can
be transformed into an amplitude (C) and phase (P), see amode= below.
The
following parameters are recognized in any order if the keyword is also
given:
- in=in_file
- Input data file, must be in standard snapshot(5NEMO)
format [No default].
- radii=rmin,r1,..,rmax
- Radii of the rings (but see xvar
and yvar below) within which the fourier coefficients are computed. [Default:
0:2:0.2].
- cos=cm1,cm2,..
- Set of integers for which the cosine amplitudes need
to be computed. [Default: 0:4].
- sin=sm1,sm2,..
- Set of integers for which the
sine amplitudes need to be computed. [Default: 1:4].
- xvar=x-variable
- X-variable
which is used to compute the radius and angle used in the fourier decomposition.
[Default: x].
- yvar=y-variable
- Y-variable which is used to compute the radius
and angle used in the fourier decomposition. [Default: y].
- fvar=f-variable
- Fourier-variable which is the variable used in in the fourier decomposition.
[Default: vy].
- weight=w-variable
- Weight-variable which is the weight applied
to the observable. [Default: 1].
- amode=t|f
- Logical; if true it displays the
sin and cos terms, if false, the amplitudes and phases (in degrees). [Default:
t]
- times=t1,t2,...
- Times to select for analysis. [Default: all].
% mkexpdisk disk1 10000
% snapfour disk1 amode=f > tab1
% tabplot tab1 1 4,3,6,8,10 line=1,1 color=2,3,4,5 ycoord=0
% tabplot tab1 1 5:11:2 line=1,1 color=2,3,4,5 ycoord=0
Another case is that of an inclined disk that first needs to be rectified,
but preserving the position angle of the major axis. Lets assume the $pa
and $inc are known. Unlike for kinematic observations (see e.g. rotcur(1NEMO)
)
we don’t care which side of the disk is the near side. The rectify operation
to get the galaxy back to a "face-on" view depends if you disk is truely
3D or (as is normally observed) a sky-projected inclined disk. For the former
case we then get:
% snaprotate disk1 disk2 theta=-$pa,-$inc,$pa order=zyz
% snapfour disk2 ...
and for the latter case
% snaprotate disk1 - theta=-$pa order=z |\
snapscale - - rscale="1/cosd($inc),1,0" |\
snaprotate - disk2 theta=$pa order=z
% snapfour disk2 ...
bodytyrans(1NEMO)
, orbfour(1NEMO)
, snapshot(5NEMO)
Binney, J.J. &
Spergel, D. (1982) ApJ 253, 308.
Peter Teuben
~/src/nbody/reduc snapfour.c
3-dec-90 V1.0: written PJT
17-feb-92 V1.1: added weight= PJT
10-nov-93 V1.2: added times= pjt