A Subjective Test Using the Dust Model

Since the dust modelling program described in section 4.10 has the same geometry routine in it as ASTRA it provides another way of testing the geometry section. Since the output is visual it maybe provides a more convincing test than the previous pages of numbers and equations. The idea is to take one simple cloud shape and view it from various different angles to see if the output changes as expected. The shape used will be two spherically symmetric, optically thin clouds of uniform density and temperature situated on top of each other within the cylindrical boundaries of the model shape. This is shown in figure 5.7.

  

Dust emission from two uniform spherically symmetric clouds tilted towards the observer at $0^{\circ }$, $15^{\circ }$, $30^{\circ }$, $45^{\circ }$, $60^{\circ }$, $75^{\circ }$ & $90^{\circ }$.

Dust emission from two uniform spherically symmetric clouds rotated at $30^{\circ }$, $60^{\circ }$ & $90^{\circ }$ and then tilted towards the observer at $60^{\circ }$ (see text for more information).

Figure 5.5 shows this cloud at a increasing tilt angles ranging from $0^{\circ }$ to $90^{\circ }$. The grey scaling in each diagram runs from 0 intensity for pure white to the maximum intensity in that particular diagram for pure black. This explains the changes in intensity that are seen in the examples where overlapping takes place. Since the clouds have a uniform distribution of material, in those diagrams where the edges of the clouds do not overlap, the edges of the cloud (where the lines of sight travel through less material) are fainter than the centre of the cloud (where the path length and hence intensity are at a maximum). In those diagrams where the clouds overlap the longest path lengths are generally in the overlapping region so the intensity will be at a maximum there causing the non-overlapping sections to be assigned a fainter grey value - even though the intensity is the same there as in previous diagrams.

Two spherical clouds within the model boundaries  [l]

Figure 5.6 shows the cloud rotated 30, 60 and 90 degrees and then tilted at $60^{\circ }$ towards the observer. Note that the rotation is performed before the tilt (as explained in section 4.8.1) and therefore, when the cloud is rotated through $90^{\circ }$, the tilt is in fact now simply a rotation of the cylinder around its axis of symmetry and therefore has no effect - hence why the third diagram in figure 5.6 appears to have only a rotation. Referring to figure 4.20 may help clarify these diagrams with both tilt and rotation. The main use for having the program rotate is to enable the output to be used in comparison with real observations that may also be rotated (although in retrospect it may be easier to simply manipulate the tilted diagrams to get the required rotation).

Although this is not a numerically accurate test of the geometry subroutine it is certainly a good subjective test which clearly shows that the ability to rotate the cloud and view it from any desired angle works as intended. The numerical values returned for the peak intensities in each diagram also show that as expected for an optically thin cloud the intensities double where the clouds overlap.