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## Name

ellipse - ellipse (de)projection properties

## Synopsis

ellipse [parameter=value]

## Description

ellipse de-projects ellipses, and computes the intrinsic properties, and vice versa. It also computes kinematic properties, assuming flow is along the ellipses, such as the kinematic minor axis (the major axis cannot be defined, since the flow-velocity along the ellipse is not defined with this routine.

Apart from giving the eccentricity of the ellipse ("bar") in the disk, and the inclination of the disk, the two angles in this routine are theta and phi, of which only one needs to be given.

For some input parameters an array is allowed to create an output table, which can then be easily plotted.

## Parameters

The following parameters are recognized in any order if the keyword is also given:
ba=
Axis ratio of bar. An array is allowed, in nemoinp(1NEMO) notation. No default.
inc=
Inclination of disk in which the ellipse ("bar") is located. An array is allowed. No default.
phi=
Angle between bar and disk in sky plane. An array is allowed. Either phi or theta (not both) are required. It determines if projection (theta given) or deprojection (phi given) is done.
theta=
Angle between bar and disk in galax plane. Again an array is allowed.
a=
Length of the bar (currently only projected) bar. If this option is used, the stick formulae (ba=0) will be applied, and errors can be computed using dphi=.
dba=
Error term in b/a. Useful if you want to compute errors in (de)projected parameters using nsim=
dphi=
Error term in phi.
nsim=
Number of monte carlo to perform to compute an error term. 
seed=
Seed for random number generator. 

## Examples

Here for a set of apparent position angles w.r.t. line of notes, and given apparent b/a and inc, the intrinsic b/a, angle between bar and line of nodes and the (sky plane) kinematic major axis (assumed perpendicular to the kinematic minor axis) are computed:
```% ellipse 0.3 45 20:30:2
De-projecting ellipse:
b/a inc phi    b/a’    theta   phi_kin
0.3 45 20    0.376558 29.4085 -46.4712
0.3 45 22    0.368488 31.9773 -45.7525
0.3 45 24    0.360246 34.4675 -44.8267
0.3 45 26    0.351921 36.8805 -43.7464
0.3 45 28    0.343591 39.2183 -42.5507
0.3 45 30    0.335325 41.4834 -41.2693
```

and here a plot that shows how the axis ratio of a 0.5 bar changes as the bar angle changes, for fixed inclincation of 20 degrees:

```   %  ellipse 0.5 1:89:1 20 | tabplot - 2 4 line=1,1
```

Here is an example of creating a bar in a disk, and viewing the sky projection. The example is taken from NGC 253 (see also rotcur(5NEMO) ):

```# disk
r_d=2
pa_d=230
inc_d=76
# bar
a_b=1
b_b=0.25
pa_b=18

# create bar and disk
mkconfig - 361 ring \$a_b | snapscale - - rscale=\$b_b,1,0 | snaprotate - bar0
\$pa_b,\$inc_d,\$pa_d zyz
mkconfig - 361 ring \$r_d | snaprotate - disk0 \$inc_d,\$pa_d yz
# add, and plot the two ellipses
snapadd disk0,bar0 - | snapplot -
```

## Caveats

For the stick formulae (a= used) only projection is done.

```Skillman et al. A&A 198, 33 (1988), p39.
Arnaboldi et al. 1995AJ....110..199A Kinematics of the Ionized Gas in NGC 253

```

## Files

src/orbit/misc    ellipse.c

Peter Teuben

## Update History

```fall-1986    V0.0 formulae derived for Skillman et al paper    PJT