When trying to identify structure in the sky, astronomers are faced with the problem of distance; we see the sky as two-dimensional, and can’t tell between a faint object nearby and a bright one further away. Sure, there are a few objects whose special properties make their distance uniquely calculable – Type Ia Supernovae, for example, always have the same intrinsic luminosity, and Cepheid Variable stars pulsate slower if they are intrinsically brighter. These are called Standard Candles, and they are very rare. Moreover, they cannot tell us whether objects that appear close to them in the sky are in fact nearby in space.
The most accurate solution, of course, lies in spectroscopy. Take light from any source, disperse it through a prism, note absorption lines, see how much they are offset from the same absorption lines in light in a laboratory on Earth, and plug that shift into the redshift equation:
The catch, as usual, is that spectroscopy is expensive. The signal-to-noise of a spectrometer decreases with increasing spectral resolution, and you want high resolution to correctly identify spectral lines. If you’re looking at a galaxy with millions of (resolved) stars, or a cluster with hundreds of galaxies, you can only hope to have spectroscopy for a handful of the members.
Sample Hertzsprung-Russell diagram, courtesy Chandra team.
Thankfully, we know a couple things about the structures we are interested in. In the case of galaxies, we know that if you were to plot the luminosity against the temperature – and temperature is related to colour, thanks to Wien’s law – we always end up with a scatterplot that looks more or less the same. The pattern is called a Hertzsprung-Russell (HR) diagram.
This works because star populations within a galaxy evolve together. So if you plot the magnitudes and colours of everything in a region of sky, those belonging to the same galaxy with form an HR diagram. You decide how close a given star needs to be to the most clear lines to be considered part of the galaxy, and chuck out the rest. Sounds shoddy, but it works.
The galaxy CMD features are shown here for nine clusters. Image from Li et al, ApJ 749 150.
You can plot a similar colour-magnitude diagram for a set of galaxies. That ends up giving you a red sequence of old, quiescent, ellipticals, a green valley of quiescent spirals and a blue cloud of star-forming spirals. The red sequence, as it turns out, will consist mostly of galaxies within the same cluster because, like stars in a single galaxy, these guys have lived in a similar environment and have similar star-formation and merger histories that leave them with similar shapes and colours. Again, there will be some scatter in the relation. How much scatter you think is acceptable.. is pretty arbitrary. And there could still be outliers.
The way to check for contaminants from one method is to approach the same problem from another angle. And a pretty cool other angle out there merges the principles of spectroscopy and CMD selection, and that is photometric redshift.
Photo-z takes in photometry of your object in multiple bands; more is usually better, but the improvement is usually limited after 7-10 bands. It compares these points to various Spectral Energy Distribution (SED) templates, each corresponding to a model of galaxy evolution. Based on the agreement between the observed and template SED, each template – and the redshift corresponding to it – is given a probability. The output of a photo-z code is then a probability distribution function (PDF) of redshifts for the galaxy based on its input colours. You can choose to deal with either the best-fit redshift value, or the marginalized value, which is the sum of the products of each possible redshift and the probability of the galaxy being at that redshift.
The key value-add over spectroscopy is that the spectral resolution is very low – you measure an entire band of wavelengths in a single filter – and the redshift estimate comes from fitting a few points on the SED to those of a model. There are many, many ways of coming up with the template SEDs, of deciding which one(s) best describe the observed photometry, modeling errors, etc. I’ll share notes on EAZY, which I’ve been working with, in a future post.