Lecture 2/4 : Nothing Will Come Of Nothing

Second post from my lecture course on galaxy evolution. This one covers two major practical techniques : optical photometry (measuring brightness and other parameters) and HI spectroscopy (measuring the gas content from radio telescopes). For the full details see the complete transcript of the 90 minute lecture.

In this much shorter post I'll skip the gritty equations and just summarise the major methods, their uncertainties, and why the subjective aspect isn't as bad as you might think. This post is focused on methodology rather than galaxy evolutionary theory.


Optical photometry

There are several major parameters we can get very easily that can tell us some important information : brightness, colour, and size. There's no end to how difficult we can make these measurements, if we want to get sophisticated, so here's the most basic approach possible.

When we have an optical image of our galaxy, we can define an aperture around it in using specialised software. This is much like drawing a polygon in standard drawing programs. Unlike ordinary jpeg or png images though, we can manipulate the displayed data range in more complex ways so as to reveal fainter features. This often involves a lot of interacting with the data, trying out different ranges to see what works best. When we think we can see the faintest emission, we draw our aperture.

Aperture photometry using the popular ds9 software.

You can see in the example there are also some boxes with dashed outlines. These are what we have decided is background noise, while the circle with the red strikethrough is a masked region. When we get the software to make the measurement, it will sum up all the emission within the green ellipse, excluding any present within the mask. Then it will estimate the average background value using the boxes and subtract this. We keep the boxes close to the target galaxy as the background level can vary in complex ways (in this example it's about as flat as it ever gets), so we need similar values to what would be present at the location of the galaxy itself.

From this simple procedure we can directly measure the apparent brightness of the galaxy and also its angular diameter. If we know the galaxy's distance, we can easily convert these to absolute magnitude (i.e. how much energy the galaxy is emitting, or its stellar mass) and physical size.

Unlike images from a smartphone, in astronomy we save the data from different wavelengths separately. The image above uses one wavelength range, but if we want to measure the galaxy's colour we have to repeat the procedure using another wavelength range. Colour is defined as the difference of the measurements in the two wavebands (usually only slightly different from each other).

You might wonder if the subjective size of the aperture is a problem. For brightness this isn't really a big deal. As long as our data quality is high, then it doesn't really matter if we make the aperture too big : the sum of the noise beyond the edge of the galaxy will be close to zero. It's a lot more important when it comes to measuring size, but more on that shortly.

The above is an ideal case. In reality we often have to deal with bright foreground stars, clouds of dust in our own Galaxy, the difficulties of defining where interacting galaxies end, and instrumental effects that can make the noise look really weird. Some of these effects we can mitigate, but if they're too bad we have to admit defeat and discard those observations from our analysis.

Example of a problematic foreground star.

Example of faint dust clouds (left) which cause galaxies to appear redder than they really are, which we can correct for, and much thicker clouds (right) which can completely hide background galaxies and prevent any measurements at all.

The same patch of sky viewed through two filters, one of which cause horrendous fringing.

We can also get the morphology of the galaxy by inspection of the images. Sometimes a classification will already be available in existing catalogues. If not, we have to decide for ourselves. This is really just a judgement call. We can check if the galaxy has specific features but there's no (good) automatic solution to this.

The photometric measurements of a single galaxy are usually incredibly boring. But if we have a large sample we can already start to do very useful science. For example, we can construct a luminosity function, which shows the distribution of galaxies of given (absolute) luminosities.

Distribution functions are a lot like histograms, except with many bins.

This shows three examples of a particular function (called a Schecter function, which is often used as it's a good fit to real data), each with a slightly different slope of the faint end (α). In all cases, there are clearly far more galaxies of low luminosity than there are bright galaxies. Indeed, above a certain threshold the number drops very rapidly. The slope of the linear, faint-end part is controversial. Cosmological simulations have predicted it should be a lot steeper than is observed : that is, there should be more faint galaxies than we actually detect. This boring-looking graph reveals one the biggest problems in modern cosmology !

We can also plot a colour-magnitude diagram like we saw last time. The key, take-home message from this post is that it's not so much about what data we have, it's all about what comparisons we make. Having a bunch of data, even really good data, means diddly-squat by itself. But divide the sample cleverly and trends can be revealed that can tell us what galaxies are up to.

This example shows galaxies in the Virgo cluster. LTGs are blue squares whereas ETGs are small triangles. LTGs which are strongly deficient in gas (more later) are green blobs. The paints quite a convincing picture of gas loss driving morphology evolution, where the lack of gas from a LTG prevents further star formation and eventually transforms it in an ETG, slowly moving up the colour-magnitude diagram.

The by-eye methods described are not the only ones available. It is possible to be much more objective, it's just more difficult. The aperture photometry gives us the total amount of light coming from a galaxy, but if we divide it into smaller regions we can construct a surface brightness profile. This shows how the amount of light emitted per unit area varies radially throughout the galaxy.

Examples of typical surface brightness profiles.

Different types of galaxy have different shapes of profile, so this is one way to supplement our subjective judgement on morphology with something more rigorous and quantifiable. Surface brightness profiles sound like a fantastic improvement on aperture photometry, but they have limitations besides being harder to construct. They are impractical for large galaxy samples, still involve some amount of subjective decision-making, and there are many galaxies for which they simply can't be done : those which are very small or have weird morphologies, for example. So aperture photometry still has an important role to play.

The shape of the surface brightness profiles hints at the final issue for optical data - deciding on a measurement of the galaxy's size. There are different conventions adopted, not all of which are appropriate for every galaxy. We could measure the size at some fixed surface brightness level (the isophotal radius, e.g. the Holmberg radius), or we could find some particular part of the profile (e.g. where it begins to drop rapidly), or extrapolate it further based on the best-fit function. One popular measure is the half-light radius, also known as the effective radius. This is the radius enclosing half of the galaxy's light. Because the profile can be very much steeper in the centre, the effective radius can be much smaller than the isophotal radius. For example the effective radius of the Milky Way is estimated at around 3.6 kpc, whereas the isophotal value is more like 15 kpc.


Measuring the atomic gas

Virtually all problems in extragalactic science revolve around star formation. We know that gaseous clouds can collapse under their own gravity, but almost all the details of this are controversial. The rate of collapse is affected by the chemistry of the gas, which determines how quickly it radiates away heat that would otherwise exert an outward pressure. Chemistry is affected by star formation, with massive stars converting light elements into heavier ones. And the gas itself can be in different phases : hot, ionised gas (with temperatures > 1 million Kelvin and emitting X-rays), warm neutral atomic gas (at 10,000 K) and cold molecular gas (typically, say, ~500 K).

Atomic hydrogen gas (HI, pronounced H one) is sometimes described as the reservoir of fuel for star formation, though the current thinking is that the gas has to cool to molecular densities before it can form stars. The atomic gas is probably only involved more indirectly, though it still has a role to play. But observationally, the atomic gas has a number of advantages : it's easier to measure and usually more massive and extended compared to the molecular gas.

NGC 628 from the optical SDSS and the HI survey THINGS.

In some cases we can map the HI directly (shown in red in the above figure), just like making an optical map. Unlike the optical images we can also directly measure the line of sight velocity of the gas, allowing us to construct a rotation curve. This shows how fast the galaxy is rotating at different points. The disagreement between the theoretical prediction, based on the mass of the visible stars and gas, and the observed shape of the curve is one of the most important discoveries in radio astronomy, and is one of the main reasons we infer the presence of dark matter.

Pretty much all galaxies show curves like this. Unless the galaxies are actually exploding, the only way to explain these flat rotation curves is the presence of a substantial amount of undetected mass.

Unfortunately we cannot usually map the structure of the gas to this level of precision : that requires the galaxy be quite close and/or we use an interferometer, a linked array of radio telescopes that's extremely powerful but also highly complex. Most HI measurements come from single-dish telescopes, which don't have great resolution but are much, much easier to use - and also hundreds of times more sensitive. What we typically get from such a telescope is a spectrum. This shows the brightness of the HI (from the whole galaxy) as a function of velocity. The shape and size of this spectrum tell us about the mass of gas and how quickly it's rotating.

A classic HI spectral profile.

Here, the central velocity (about 1,000 km/s) indicates the systemic velocity of the galaxy. We can use Hubble's Law to estimate its distance based on this. We see that emission is detected over the velocity range ~800 - 1,200 km/s, giving us an indication of the rotation speed (it would be half this line width, after we correct for the galaxy's orientation with respect to us).

This examples shows a very distinct double-horn (a.k.a. "Batman") profile, typical of spiral galaxies (deviations from this can indicate the galaxy might be interacting with something). If you look back to the rotation curve figure, you see it's mainly flat, with most of the gas moving at a single velocity relative to us. Of course, since the galaxy is rotating, about half the gas is moving away from us and half is moving towards us. Hence we get these two brighter "horns" representing the majority of gas at this single rotation velocity on different sides of the galaxy respective to us.

The total area under the curve can be measured, and that gives us the total HI flux. It's not that dissimilar to the optical measurements : we choose which part of the spectrum to measure, and the software does the integration and background subtraction for us. And once we've got the flux, we can convert it into HI mass if we know the distance.

As mentioned, the line width has to be corrected for the viewing angle to get the rotation. If we assume the galaxy is actually circular it becomes easy to calculate this - we just have to measure its major and minor axial diameter from the optical data.


Finding gas

Modern HI surveys typically map large areas of the sky, but at low resolution. Somehow we have to turn data like this :

https://www.youtube.com/watch?time_continue=1&amp=&v=XmpGTGkaFg4

... into a nice catalogue of galaxies. The animation shows a series of slices through a data set. Each elongated bright blob is the HI component of a galaxy.

I won't cover the extraction procedures in detail, but it boils down to someone going through frame by frame (or rather, channel by channel) and deciding where they think the HI is present. This is obviously imperfect. The observer might find something that looks real but isn't, or miss real sources. Fortunately, afterwards we can do simple follow-up observations to quickly confirm or disprove the candidate sources in a nice objective way. And this leads to two key parameters of our HI catalogue :

Completeness is defined as the fraction of real sources present that are in your catalogue. If you should somehow find all of them then your catalogue is 100% complete.

Reliability is defined as the fraction of sources in your catalogue which are real. If all your sources are real then your catalogue is 100% reliable, but it would be very unlikely to also be 100% complete.

Why reliability is easy to measure through repeat observations, completeness is much, much more difficult - but more on that next time. Knowing these parameters can be useful in everyday life : think about what someone really means if they say a procedure is 90% reliable !


Putting it all together

With all this optical and radio data, and knowing some basic statistical parameters to check, we can do quite a lot. We have stellar mas, colour, size, morphology, gas mass, and rotation speed. We can also get HI deficiency alluded to earlier. Studies on large numbers of galaxies have revealed that in the field, knowing the size and morphology of a galaxy enables a fairly accurate prediction of its HI mass. By comparing the actual mass of a galaxy with its prediction, we can work out if it has more or less gas than expected. Typically, galaxies in clusters have significantly less gas - by a factor 10 or more - than comparable field galaxies. This deficiency measurement gives us another parameter we can use to divide up our sample.

We'd also like to have the total dynamical mass of a galaxy. The rotation curves indicate how much dark matter is present, but we can also get a crude estimate of this from the line width. For this we need to know the radius of the HI, which we can't measure directly. Fortunately all those field galaxy studies have found that the HI is typically extended by around a factor of 1.7 compared to the optical size of a galaxy, so that gives us something reasonable to work with. Not perfect, but decent.

Let's finish off with two take-home messages :

• Comparisons are king. It's nice to have really good data, but far more important to have a good sample and clever ways to divide it. Sometimes we can see nice dramatic examples of galaxies undergoing change, but to work out whether this is important overall we need good statistical data.
• The procedures we use are often messy. They aren't black-and-white cases where we can ever be truly certain about our precision, and some where objective measurements are actually inferior to subjective judgements. But this subjectivity is limited : you can't really accidentally measure colours so badly that you don't see a red or blue sequence.

In the next two posts we'll look at the importance of statistics and subjective/objective measurements in a lot more detail.