DM Lab: Making Rotation Curves

Making Rotation Curves

Optical rotation curves, like the one used in the Dark Matter Lab (figure 1), are created using long slit spectra.

What is a long slit spectra?
When you take an image with an optical telescope, the information has to fit on the two dimensions of your CCD chip. When we want to split the image into various colors to examine some of the properties of an astronomical object (like it's velocity, mass, or composition), we pass the light through a diffraction grating. The result is a spectra.

A spectra

One of the two dimensions of the CCD chip spans across the different colors. That leaves one dimension of the CCD chip to represent some other information. We let that axis represent a spatial dimension. It is along our slit. Cutting a pretty image of a galaxy down to one dimension so that we can spread the light of that dimension out looks something like this:

Slit over galaxy

The result of all this is our long slit spectra.

What information can we glean from a long slit spectra?
The Doppler Effect causes light emitted from an object moving away from us to be red shifted, and light from an object moving towards us to be blue shifted.

These shifts show up on our long slit spectra:

Doppler Shifted Lines

The bright spots represent emission lines. This would work just as well for absorption lines. Emission lines tend to come from gas clouds of ionized hydrogen (sometimes called HII). Higher up on the slit, they are red-shifted. Lower down, they are blue-shifted.

We can measure the degree that each line is shifted and relate that to a velocity. When we take data points all the way out to large radii, we've almost created figure 1.

What's left?
Doppler shifting only works in the line of sight direction. That means we are only seeing the component of motion towards or away from us. Thus, we need to multiply the velocity we've found by some trigonometric factor (sine or cosine of something) and we've found figure 1. This is left as an exercise for the student.

Figure 1 of the Dark Matter lab was taken from Courteau, S. 1997, Astronomical Journal, 114, 2402. Look it up at ADS.