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## Name

twspeed - calculate the pattern speed of a stellar system using the Tremaine-Weinberg method

## Synopsis

twspeed vel=ccd-velocity den=ccd-density [parameter=value]

## Description

twspeed calculates the pattern speed of a stellar system using Tremaine & Weinberg’s method (1984ApJ...282L...5T). For this a line parallel but offset to the line of nodes of a galaxy must have information on intensity and radial velocity.

twspeed assumes the line of nodes is along the X-axis, the galaxy center and position angle are keywords but not implemented yet?

In the following (x,y) are defined along the major and minor axis of the galaxy resp., and pspeed will then compute the numerical sums

```        V(y) =  SUM ( vel(x,y) * den(x,y)) / SUM ( den(x,y) )
X(y) =  SUM ( x * den(x,y)) / SUM ( den(x,y) )
```
where the summation is along x. This will result in a correlation
```    V = Omega * SIN(inc) * X
```
The output will be a table which can be inspected for signal and noise, and fed into a least squared fitter, such as tablsqfit(1NEMO) or tabnllsqfit(1NEMO) .

## Parameters

The following parameters are recognized in any order if the keyword is also given:
vel=vel-file
input file, must be the radial velocity in image(5NEMO) format [no default].
den=int-file
input file, must be the intensity in image(5NEMO) format [no default].
xin=int-file
input mean position image (optional)
pa=
*** Position Angle of disk [90]
inc=
*** Inclincation of the disk [0]
center=
*** Center of galaxy (map-center) []
step=
Slit width in pixels [1]
window=
Window functions (0=none, ..) [0]

## Examples

Here is an example creating a rotating bar at pattern speed 1, inclining it by 30 degrees,and measuring a pattern speed of 0.5 (omega*sin(inc)):
```% mkdisk disk1 10000 harmonic mass=1
% snapscale disk1 disk2 rscale=1,0.5,0 vscale=0
% snapspin disk2 disk3 omega=1
% snaprotate disk3 disk4 30 x
% snapgrid disk4 ccd4-den moment=0
% snapgrid disk4 ccd4-vel moment=-1
% twspeed ccd4-vel ccd4-den > ccd4.tab
% tabnllsqfit ccd4.tab

Fitting a+bx:
a= -5.11039e-05 0.000116198
b= -0.499963 0.00931362

```

snapslit(1NEMO) , snaprotate(1NEMO) , tabnllsqfit(1NEMO) , tablsqfit(1NEMO) , snapshot(5NEMO) , image(5NEMO)

Peter Teuben

## Files

```~/src/pjt/image      twspeed.c
```

## Update History

```17-Aug-87    Original created as pspeed (though never made it into NEMO)    PJT
18-nov-03    1.0: documented the new twspeed version     PJT
22-apr-04    1.1: changed order of keywords      PJT
```