If you ask people to picture in their head what a galaxy looks like, as long as they don't immediately picture a chocolate bar they'll often think of something like this:
This is an image of M101, the 'Pinwheel galaxy', taken with the Hubble Space Telescope (HST). The blue colour in the spiral arms comes from clumps of young stars being formed there, whilst the redder, central region is probably harbouring a supermassive black hole. Although spiral galaxies are undoubtedly very interesting objects, the galaxies that I work with tend to look a little bit different.
Below is an HST image of NGC 1399, an elliptical galaxy I've studied in some detail:
Not quite as impressive! Elliptical galaxies often just look like smears or blobs, without any of the impressive structure you see in spiral galaxies. You typically don't see any young, blue regions which implies that ellipticals form stars at a lower rate than spirals do.
Incidentally, you may just be able to see a line of blue specks running from bottom to top of the image- this is just an artefact from stitching together a number of separate exposures to make one big image, and isn't a real astronomical phenomenon!
Galaxies are made of stars
Stars are the building blocks of galaxies. They are always in motion around the centre of the galaxy they reside in, just like the Earth is always in motion around the Sun. If they weren't, they'd all quickly get pulled together by gravity and end up in the very centre in a big heap. In our own Milky Way galaxy we can track the motion of stars as they move across the sky, but galaxies outside the local group are too far away to make out individual stars, let alone track individual orbits. These galaxies often just appear like smooth patches of light on the sky (like NGC 1399 above). So how do we measure the movements (or "kinematics") of these stars? It turns out we can study the spectra of these objects.
Using an instrument called a spectrograph, we can split up the light we receive from a galaxy (essentially with something like a prism) to make a spectrum. An example of a spectrum from my own observations of the very centre of NGC 1399 is here:
Each of those dips is caused by a certain molecule, which absorbs photons in the atmosphere of the stars in the galaxy. Due to something called the Doppler effect, if most of the stars in a galaxy are moving towards us then these lines are shifted in wavelength to the 'blue' (i.e shorter wavelengths). If the stars are mostly moving away from us, these lines are shifted to the red (longer wavelengths). Since we know the wavelengths of these absorption lines in the lab here on Earth, we can measure the velocity of the stars in a galaxy by measuring the magnitude of this shift in the absorption lines.
Note that this 'redshift' and 'blueshift' is very similar to the cosmological redshift that you may have heard of. Cosmological redshifts are caused by the fact that the universe is expanding, meaning that all the galaxies in the sky appear to be moving away from us. Consequently, their entire spectrum is shifted to the red. This is a bulk motion affecting all the stars in a certain galaxy. The kinematic resdshift and blueshifts I'm talking about above are local properties within a galaxy, caused by its rotation.
Mapping these motions
If we measure these shifts at lots of different points in a galaxy, we can build up a two dimensional image of how the stars are orbiting.
The top image is of an elliptical galaxy called NGC 1277, taken from the Sloan Digital Sky Survey. On the bottom is a map I've made of the stellar velocities in this galaxy. Each pixel corresponds to a spectrum, and the colour of the pixel refers to the shift in that spectrum with respect to the lab values. Blue regions are coming towards us and red regions are moving away. We can see that the stars in NGC 1277 are rotating at around 300 kilometres per second at the largest radii. For reference, the Sun is moving around the centre of the Milky Way at around 220 km/s.
It turns out that there are other things we can learn about a galaxy's kinematics from its spectrum- the width of the absorption lines is also dependent on how the stars are moving. If all the stars are moving more or less together, then the absorption lines we measure will be narrow. If, however, the stellar orbits are more random and jumbled up, the absorption lines will be broader. Measuring this width tells us about something called the velocity 'dispersion' in a galaxy.
Here's a plot of the velocity dispersion in the centre of NGC 1399. (Note the scale of the colour bar should be in km/s, and the x and y axes are in pixels when they should be in arcseconds. I'll update with a better plot when I have time!)
The scale of this map roughly corresponds to the central bright blob in the HST image above. A similar plot of the velocities in this galaxy shows the stars are only rotating at around 30-40 km/s- far less than in NGC 1277.
So elliptical galaxies seem to fall into two categories: 'fast rotators' such as NGC 1277 (speeds of hundreds of kilometres per second) and 'slow rotators' such as NGC 1399 (smaller rotation speeds, large amounts of random motion). Fast rotators vastly outnumber slow rotators. It seems that only the most massive galaxies ever fall into this second category.
This idea of elliptical galaxies belonging to two families of 'kinematic morphology' has only been proven pretty recently, in the late 2000s by the SAURON and ATLAS3D teams. Much work is still being done to understand why some galaxies but not all turn into slow rotators (since we think all ellipticals are born rotating quickly), and whether the split between these two kinematic types exists further back in the universe's history. Big surveys (such as MANGA and SAMI) aim to make kinematic maps like the ones above for thousands of nearby galaxies- it's a very active area of research!