Radio Views of a Spiral Galaxy
Joachim Köppen Kiel Sep 2017

### Some brief explanations

This Monte Carlo simulation computes how the rotating gas disk in a spiral galaxy is observed by a (radio) telescope which makes images of the object, but also takes spectra, from which the radial velocity of each pixel is measured. The simulation shows how an object which is arbitrarily oriented in the sky appears to the observer and what information one can extract from images and spectral data.

How it works: the simulation picks at random a gas element in the disk, according to the prescribed geometry, and follows what happens to a photon emitted by the element. Since depending on the radial scale the inner parts are brighter, these elements are picked more often, thus they produce more photons. According to the rotation speed, each emitted photon receives its velocity components. Then, the position and velocities are recomputed according to the specified rotation angles, and the photon appears in the observer's X-Y-plane - but with randomly deviations which correspond to the finite spatial resolution of the telescope - and with a radial velocity which comes from the Z-component of the velocity. This process is carried out as many times as the displayed plot or image has become sufficiently stable, so that the user can stop the simulation.

Galaxy properties:
• inner radius is inner boundary of the gas disk.
• outer radius is outer boundary of the gas disk.
• radial scale: the surface brightness of the gas disk is assumed to decrease exponentially with distance from the centre, with this scalelength. A constant brightness disk has a very large radial scale, say 1000 kpc.
• thickness is the thickness of the disk (at the moment the brightness does not vary with height above the galactic plane).
• rotation speed: the disk gas is assumed to be rotating about the galactic centre with this speed, which does not vary with distance from the centre.
• velocity dispersion: takes into account the random motions of the gas clouds in the disk.
• inclinationX..: the angles with which the galaxy is turned around each of the three axes. The Z-axis stands at right angles to the screen.
• antenna HPBW: the observed data are smoothed in the two spatial directions by a gaussian function with this FWHM, representing the finite resolution of the antenna beam
Simulation display:
• photons per step is the number of photons created in each simulation step between two displays of the data. Choose a small value (10) to see how a plot is built up; take a high value (1000) when you're too impatient to see the final result in a histogram.
• photons now displays the number of photons created for the current plot.
• no. of bins is the number of bins in the histogram, and the number of pixels in X and Y direction in the intensity and vrad maps. The maximum number is 100.
• fly dirt plot: each photon is plotted as a small red dot at the chosen abscissa and ordinate.
• histogram: plots the relative number of photons in each bin of the abscissa.
• intensity map: plots the relative number of occurrences of each pixel of the chosen abscissa and ordinate. These numbers are coded by colour, with black=0 and red=maximum value, according to the colour band shown at the right. The scaling is linear or logarithmic. A plot of X and Y represents an image of the galaxy, with these numbers showing the intensity of the pixels.
• Vrad colour map: when chosen to display the X and Y coordinates it shows pixels with positive radial velocity (receeding) in shades of red, and pixels with negative radial velocity (approaching) in blue.
• X = and Y = : the abscissa and ordinate of the plot can be chosen from these parameters:
• X, Y: the coordinates with respect to the centre of the image
• distance from centre
• Set range: when this radio button is clicked, the plotting limits are taken from the associated fields (min, max)
• start: to begin the simulation
• stop: to halt the simulation
• resume: to continue with the simulation
• clear: to wipe the plot
• Mouse position: displays the coordinates of the present position of the mouse. In the false colour maps, it also shows the actual number as well as the relative number of photons in the pixel.

Galaxy properties
disk thickness [kpc]
rotation speed [km/s]
velocity dispersion [km/s]

inclinationY [°]
inclinationZ [°]

antenna HPBW [kpc]
Simulation display
photons/step
photons now
no. of bins

X-axis =
Set range: ...
Y-axis =
Set range: ...

Mouse position: