Solid Body Rotation

The previous section has of course in no way tested the rotational aspects of the program. Since this is one of the main motivating factors for writing this program it is especially important to test this section. The ASTRA program is capable of modelling any required type of rotation, something that can only be done with a 2-D (or 3-D) model. However, there is one specific type of rotation that can be modelled with the STEN program, namely solid body rotation. This is possible because solid body rotation can be viewed as simply a change in the frame of reference. In other words, the usual frame of reference used is of course a stationary one relative to the centre of the cloud. It is however possible to switch to a reference frame that rotates around the centre of the cloud. This means that the sections of the program that are solving the radiative transfer equations inside the cloud during the lambda iteration process are unaffected and it is only the output routine that needs changing. The actual change is very simple involving only the addition or subtraction of a constant velocity to the line profile for each line of sight used in the gridded convolution for the beam. Solid body rotation [l] $\includegraphics[scale=0.6]{solidrot.eps}$ This is demonstrated in figure 5.29 which shows a cloud rotating as a solid body with the outer edge at

km s $^{-1}$ . The line profile for a line of sight at a distance

from the centre is then shifted by $v \cos \theta$ km s $^{-1}$ . This method was first implemented by Buckley [7] and the example output produced by his model will be used to test the rotational aspects of the ASTRA program. Figure 5.30 shows the line profiles produced by his model. The dashed lines are the line profiles for a non-rotating cloud and the solid lines are for a cloud rotating around its central axis (perpendicular to the telescope). The line profiles are shown for various different offset positions along the axis of the cloud that is perpendicular to the rotating axis^5.3.

$\includegraphics[scale=0.9]{buksn1.eps}$ $\includegraphics[scale=0.9]{buksn2.eps}$ $\includegraphics[scale=0.9]{buksn3.eps}$ $\includegraphics[scale=0.9]{buksn4.eps}$ $\includegraphics[scale=0.9]{buksn5.eps}$

$\includegraphics[scale=0.9]{bukbsn1.eps}$ $\includegraphics[scale=0.9]{bukbsn2.eps}$ $\includegraphics[scale=0.9]{bukbsn3.eps}$ $\includegraphics[scale=0.9]{bukbsn4.eps}$ $\includegraphics[scale=0.9]{bukbsn5.eps}$

Line profiles for HCO+ $4\rightarrow 3$ (left column) and CS $5 \rightarrow 4$ (right column) for a non-rotating cloud (dashed lines) and a cloud rotating as a solid body (solid lines) at a speed of $\Omega =30$ km s $^{-1}$ pc $^{-1}$ . The rows represent output at offsets of (from the top down) -20 $^{\prime \prime}$ , -10 $^{\prime \prime}$ , 0 $^{\prime \prime}$ , 10 $^{\prime \prime}$ & 20 $^{\prime \prime}$ for a JCMT type telescope (ie. beamsize of 13.6 $^{\prime \prime}$ for HCO+ and 20.0 $^{\prime \prime}$ for CS.

The model in figure 5.30 can now be reproduced using the ASTRA program. The results for this are shown in figure 5.31. It is immediately clear that the agreement between the two models is extremely good with the only discrepancy being the aforementioned intensity differences. The line shapes are almost identical for all positions in the cloud. This result completes the testing of the geometry section since in order for the program to be able to reproduce these results the geometry subroutine must be working correctly. This conclusion is especially valid since Buckley produced his solid body rotation line profiles using a completely independent method thus removing the possibility of common errors between the two programs.