Fig. 4 shows six graphs. The top left graph gives the variation of the deduced edge-on optical depth of the galaxy as we observe it from different angles. From this graph one can see that the variation of the deduced optical depth from different points of view is no more than 6% different than the mean value of the optical depth. Furthermore, a comparison with Fig. 3, which shows the real value of the optical depth, reveals that there is no systematic error in the derived value. The deviations are equally distributed around , which is what we would have without the spiral structure. The variation is of the same order of magnitude regardless of the pitch angle. The top right graph in Fig. 4 presents the deduced central luminosity of the disk. This graph shows that the variation of the inferred central luminosity of the stellar disk is very small and it is weakly dependent on the pitch angle. In the middle left graph of Fig. 4 the derived scalelength of the dust is presented. The variation of the derived value is about 5% for the 10-degree pitch angle and goes up to 17% for the 30-degree pitch angle. The increase of the variation with increasing pitch angle is expected, because for large pitch angles the spiral arms are loosely wound, thus causing the galaxy to be less axisymmetric. As a result, from some points of view the dust seems to be more concentrated to the center of the galaxy and from other points of view more extended.
In the middle right graph of Fig. 4, that shows the scalelength of the stars, it is evident that the same effect occurs for the stars as well. Certain points of view give the impression of a more centrally condensed disk, while others of an extended disk. The fact that we have taken the stellar and the dust spiral structure to be in phase (i.e. the dust spiral arms are neither trailing nor leading the stellar spiral arms) causes the deduced scalelengths of the dust and the stars to also vary in phase. The case of a phase difference is examined below.
The bottom left and bottom right graphs of Fig. 4 show the variation of the scaleheight of the dust and the stars respectively. The variation of both scaleheights is negligible. This is an attribute of the formula we used for our artificial galaxy. Since the spiral variation we added to the exponential disks is not a function of z it is expected that in the z direction our artificial galaxy behaves exactly as the exponential model.
There are indications (van der Kruit & Searle 1981; Wainscoat et al. 1989) that the dust arms are not located exactly on the stellar arms. Thus, we re-created the edge-on images, but this time the stellar spiral arms were set to lead the dust arms by 30 degrees. We then fitted the new images with the exponential model and the deduced parameters are shown in Fig. 5. As in Fig. 4, the top left graph of Fig. 5 shows the optical depth as a function of position angle. A comparison of this graph with the corresponding graph in Fig. 4 reveals that the variation of the values derived from the new set of images is significantly larger. The origin of this effect is the fact that the dust is either in front of the stars (for some position angles) or behind the stars (for other position angles). A strong dependence on the pitch angle is also evident. Note, however, that the mean of all the derived values is unaffected. The same effect can be seen on the top right graph of Fig. 5, where the derived central luminosity of the disk is plotted. The variation of the central luminosity is again larger than in the previous case, but the mean value is equal to the true one.
In the middle left graph of Fig. 5 we show the scalelength of the dust as a function of the position angle. The variation of the derived dust scalelength can differ as much as 25% for a galaxy with pitch angle equal to 30 degrees. But again the mean value for all position angles is identical to the one we used to create the images. In the middle right graph one can see that the scalelength of the stars also varies as much as 30%,but the mean of all the derived values is the correct one.
The left and right bottom graphs show the variation of the scaleheights of the dust and the stars, which is about 10% for the worst case of a 30-degree pitch angle and is practically zero for a galaxy with more tight arms.
The most important conclusion of all the graphs is that the derived values of all quantities tend to distribute equally around the real value we used to create the artificial images.
© European Southern Observatory (ESO) 2000
Online publication: December 8, 1999