Effects of the Viewing Angle of the Disk

All the position velocity diagrams presented so far have been for edge on disks and thus all the conclusions about the observability of this model object rely on the object being edge on from the Earth's point of view. In reality of course these objects will be arranged at random inclinations relative to the Earth. Figure 6.19 therefore shows the C$^{18}$O $3 \rightarrow 2$ transition tilted in 15$^\circ$steps. The problem is in distinguishing between the radial infall which produces the bulge that can be seen in the later diagrams - which appear almost identical to the non-rotating test cloud in figure 6.9 (the self absorption dip in figure 6.9 is due to this being for $^{13}$CO which has a higher optical depth than the C$^{18}$O transition presented here). The signature for rotation is the asymmetry in the position velocity diagram which is due to the direction of motion of the gas being equal and opposite on opposite sides of the cloud in the plane of the sky (unlike infall which is equal and opposite along the line of sight which gives symmetrical position velocity diagrams). It can therefore be seen that the JCMT has difficulty detecting the rotation when the cloud is at angles of more than about 30$^\circ$ and is unable to detect rotation at angles above about 45$^\circ$. This means that any survey using this method to search for rotating disks would miss about half of them. This situation would of course improve somewhat for larger telescopes but is a fundamental restriction on this type of search for rotation. Disks that are face on can only be detected via the reduction in peak line intensity as shown in figures 6.2 & 6.3 which is only possible if a very accurate prediction the line intensity for a non-rotating cloud can be made.

 

15$^\circ$ 30$^\circ$

45$^\circ$ 60$^\circ$

75$^\circ$ 90$^\circ$

Position velocity diagrams for C$^{18}$O at a variety of disk viewing angles. The disk is angled at $15^{\circ }$ (top left), $30^{\circ }$ (top right), $45^{\circ }$ (middle left), $60^{\circ }$ (middle right), $75^{\circ }$ (bottom left) and $90^{\circ }$ (bottom right). The edge on disk diagram has previously been presented as the top right diagram of figure 6.12. See text for details.