As outlined in the
methodology section of this report,
a computer program was written to visualize galactic orientation.
In the program, each galaxy is simulated using a three-dimensional
cylinder.
The side of each cylinder is drawn in blue. The top and bottom of each cylinder is shown in gray, with a red "bulls-eye" at the centre.
Each cylinder is rotated by a random amount about two perpendicular
axes that are orthogonal to the main axis of the cylinder. The
two axes are called alpha and beta. A third axis
of rotation along the main axis of the cylinder is ignored due
to symmetry.
Rotation about alpha and beta for each of one hundred
simulated galaxies was plotted to verify a random distribution.
The result is shown in the scatter plot to the left.
The plot demonstrates that the simulation program's random
number generator produced an even distribution of rotation pairs,
and that simulated galaxies are randomly oriented.
The
computer program converts the internal three-dimensional representation
of each simulated galaxy into a two-dimension image, similar to
a photograph of a real galaxy that might be taken from an earth-bound
telescope.
The amount of rotation about alpha and beta cannot be recovered directly from such an image. Instead, it is possible to measure the apparent rotation about the larger of alpha and beta as projected onto the image plane.
These values were measured for one hundred simulated galaxies with random orientation using a Java application and plotted in bins of ten degrees.
See the Java Applet version of this application, pre-loaded with results from the simulation experiment. By clicking and dragging the mouse in the applet, the user can determine the major axis of apparent rotation as projected on the image plane. By moving the scrollbar, the user can set the apparent rotation about this axis.
Face-on galaxies have an apparent rotation of 0 degrees. Edge-on
galaxies have an apparent rotation of 90 degrees. Assuming that
galaxies have a random orientation with respect to the earth,
the results of this experiment predict that an earth bound observer
should see more edge-on galaxies than face-on galaxies in any
random sample. The reason is that there are many combinations
of alpha and beta rotations that lead to galaxies that appear
to be edge-on when viewed from earth. In contrast, face-on galaxies
are constrained to those exhibiting zero rotation about both the
alpha and beta axes. This result is vividly illustrated in the
plot. Although this plot does not closely resemble a sine
distribution, it is consistent with the expectation of seeing
more galaxies in an edge-on orientation, and may be an artifact
introduced by the random number sequence.
Each
of the one hundred simulated galaxies is shown in the figure to
the left, grouped according to orientation bin. The first bin
group contains simulated galaxies with an apparent rotation between
80 and 90 degrees. The second bin group contains simulated galaxies
with an apparent rotation between 70 and 79 degrees, and so on.
The final bin group in the bottom right hand corner of the figure
are simulated galaxies with an apparent rotation between 0 and
9 degrees.
From the bin groupings, it is clear that more edge-on galaxies should be visible from the earth than face-on galaxies, even though they are randomly oriented.
In the figure, notice that no blue "sides" are seen in the face-on galaxies. Comparatively more blue can be seen in galaxies tending towards the edge-on corner of the figure. In estimating the ellipse used in determining apparent rotation, the gray portion of the cylinder is fit to an ellipse. This ellipse is then used in determining apparent rotation. The side has been coloured blue to avoid any confusion.
In the simulation, ellipse fitting is relatively accurate, since the boundary between the disc surface and the cylinder side is well defined.
It should be apparent that using the method outlined here to fit ellipses and determine the apparent rotation using real galaxy images introduces the possibility of error in measuring the apparent ellipse, particularly for edge-on galaxies. That is, uncertainty in ellipse fitting due to difficulties in differentiating identifying the top , side, and midplane of the galactic disk using real galaxy images has the potential to lead to underestimated apparent rotation for galaxies tending toward an edge-on orientation.
Each of the images in the simulation, along with the measured apparent rotation value, is indicated in table below. The table is sorted by apparent rotation value, listing face on galaxies first. Alternatively, use the GalacticEllipseApplet and select the appropriate simulated galaxy to verify the result shown.
