5.2.3 Extragalactic velocity field

In this example we shall make a velocity field of a a particle representation of a disk galaxy, with stars on circular orbits in centrifugal balance with a fixed background potential.

For disk-stars on circular orbits the program mkdisk is useful^5.9:

   21% mkdisk out=disk1 potname=expdisk potpars=0,1,0.5 rmax=2 mass=1

In this the mass of the disk was set to non-zero, in order to assign a finite emission to each star later on. If you would plot it's configuration with a program like snapplot, you would see not only a more-or-less constant surface density but also that the disk is infinitely thin (snapplot yvar=z). Also the particles are indeed on circular orbits (snapplot xvar=r yvar=vt), and there is no velocity dispersion (snapplot xvar=r yvar=vr).

Viewed from the positive Z axis (the default with snapplot xvar=x yvar=y) we would see no radial velocities in the disk; in order to get a realistic looking velocity field, we would have to rotate the model around a line of nodes (say the X axis) using snaprotate:

    22% snaprotate in=disk1 out=disk1.r theta=60 order=x

To plot the radial velocity the program snapplot is used by assigning a different symbol (psize=) to different radial velocities:

    23% snapplot in=disk1.r psize=0.1*vz

To simulate a true observation we shall use the program snapgrid to grid the discrete snapshot data (x,y,z,vx,vy,vz) from the file disk1.r onto a CCD-like device: a rectangular pixel array (matrix), with a value (brightness, velocity etc.) associated with each pixel. Since we are interested in the radial velocity field the zero-th and first order moment maps need to be obtained, and divided to get a radial velocity field: $$\left< v \right> = - { \int{I(z) V_z(z) dz } \over {\int{I(z) dz}} } \eqno(1)$$ Here $I(z)$ and $V_z(z)$ are the intensity and radial velocity along the line of sight. Note the extra $-$ sign, to conform to the astronomical convention that positive velocity means negative vz if viewed from the positive Z axis. In NEMO the denominator and numerator in eq. (1) are evaluated as follows:

    24% snapgrid in=disk1.r out=mom0 moment=0 zvar=-vz evar=m
    25% snapgrid in=disk1.r out=mom1 moment=1 zvar=-vz evar=m

Since the data will be noisy, it is best to smooth the data a bit. Smoothing must however be done before the maps are divided (why?). Since the default pixel size is 4/64=0.0625 a Gaussian beam with a FWHM of 0.15 is used to convolve the data. We would use the programs ccdsmooth and ccdmath in the following order:

   26% ccdsmooth in=mom0 out=mom0s gauss=0.15
   27% ccdsmooth in=mom1 out=mom1s gauss=0.15
   28% ccdmath in=mom0s,mom1s out=disk1.vel fie=%2/%1

The final output file, disk1.vel, now contains the radial velocity field map at an inclination of $60^o$. It can be displayed with programs like ccdplot and ds. ccdplot is a NEMO program, capable of plotting contours as well as greyscale (if given the right graphics device driver). ds is general purpose image display program and displays a map in color on a sun workstation (for this, ds must have been installed to understand the NEMO file format).

Figure: Velocity field of a galactic disk

You can also convert the NEMO image file to a FITS file. A FITS file is a true astronomical standard, which can be read into any other image processing package (ds can also read FITS files) (AIPS, IRAF, MIDAS, Miriad). Creating it can be done as follows:

    29% ccdfits in=velfie out=fits1