Required number of disks/cylinders

Same model as upper left diagram in figure 6.18 except with only 30 cylinders and 30 disks (ie. half the number of rings).  [r] Before starting the modelling there is one additional point that needs to be considered, namely finding a balance between the amount of detail and accuracy a model should have and the length of time the computer takes to run a model. In the modelling done so far the model cloud has been simulated using a 60x60 cylinder/disk model which, whilst virtually eliminating the possibility of insufficient rings causing features in the line profiles, has the disadvantage of causing rather long run times to solve the model cloud. This has not been much of a problem in the previous sections as they have generally involved solving the cloud once and then producing many outputs for different resolutions or different transitions. These do not involve solving the cloud again and so the large number of rings does not carry a large penalty in time. However, the next sections will need to solve many different types of cloud in order to test different models. It will therefore be sensible to use a smaller number of cylinders and disks, at least initially, to test the different models.

To demonstrate that this can be done without making too large a difference in the output, the model presented in figure 6.18 will be re-calculated using only 30 cylinders and 30 disks. Note that this means there is effectively twice the resolution across the cyinders as there is across the disks since there need to be twice the number of disks as cylinders for an equal distribution in both directions. This has been relatively unimportant so far, since the slices for the position velocity diagrams have been across the cylinders and all the rotational velocity change is across the cylinders. The time taken to solve the model cloud then reduces from around 4 hours to just 25 minutes. A strategy would be to investigate a large parameter space with this more crude model and then investigate the promising regions of the parameter space with the more accurate model.

Previously the rotating disk has required large numbers of lines of sight to simulate the beam in the cloud due to the rapid velocity changes in the centre of the cloud (as discussed in the text around figure 6.6). Since there are probably no large velocity changes in this cloud far fewer lines of sight will be needed. In the modelling presented in the next few sections, unless overwise stated, the models presented use 30x30 cylinders and disks and $nodd=21$ (ie. 441 lines of sight) for the beam simulation. However, during the searching through the parameter space 20x20 cylinder/disk models were used to indicate the general parameters that fit best. Such a model runs through the lambda iteration routine in just $4\frac{1}{2}$ minutes. With $nodd=15$ (225 lines of sight) for this rapid testing a spectra is generated every 3-4 seconds.