Tracing the baryons in star forming galaxies

Galaxies are big. Our own Milky Way contains about fifty billion solar masses of stars, and another ten billion of interstellar gas, roughly speaking. The average star is maybe half a solar mass, so crudely speaking, that’s one hundred billion stars. Give or take. For comparison, the population of the Earth has not quite reached eight billion humans. So if you gave each one of us our own personal starship, in order to visit every star in the Galaxy, each one of us would have to visit a dozen stars. Give or take. I’m getting old, so I call dibs on Proxima Centauri through Procyon.

Figure 1 shows a picture of NGC 628, a relatively nearby spiral galaxy. What you see here is mostly stars, along with some interstellar dust and ionized gas. In addition to those components, there are also stellar remnants left behind by dead stars (mostly white dwarfs, some neutron stars, and the occasional black hole). In the space between the stars resides colder forms of interstellar gas, including both atomic gas (individual atoms in space) and molecular gas (the cold, dense material from which new stars form). How much is there of each component?

The bulk of the normal mass (excluding dark matter) in big spiral galaxies like the Milky Way is stars and their remnants. But there is also diffuse material in the vast interstellar medium – the ample space between the stars. This includes dust and several distinct phases of gas – molecular, atomic, and ionized (plasma). The dust and plasma are easy to see, but don’t add up to much – a mere millions of solar masses each for the whole Milky Way. The atomic and molecular gas add up to a lot more, but cannot be seen optically.

Atomic gas can be traced by 21 cm emission from the spin-flip transition of atomic hydrogen using radio telescopes. This is commonly referred to with the spectroscopic notation “HI”. The HI mass – the mass of atomic hydrogen – is usually the second largest mass component in spirals, after stars. In dwarf galaxies, the atomic gas often outweighs the stars (Fig. 2).

Stars and atomic (HI) gas are the big two. When it comes to star forming galaxies, more massive spirals are usually star dominated while less massive dwarfs are usually dominated by atomic gas. But what about molecular gas?

Molecular gas is important to the star formation process. It is the densest (a very relative term!) material in the interstellar medium, the place where cold gas can condense into the nuggets that sometimes form stars. How much of this necessary ingredient is there?

The bulk of the mass of molecular gas is in molecular hydrogen, H₂. Spectroscopically, H₂ is a really boring molecule. It has no transitions in wavelength regimes that are readily accessible to observation. So, unlike atomic hydrogen, which brazenly announces its presence throughout the universe via the 21 cm line, molecular hydrogen is nigh-on invisible.

So we use proxies. The most commonly employed proxy for tracing molecular gas mass is carbon monoxide. CO is one of many molecules that accompany the much more abundance molecular hydrogen, and CO produces emission features that are more readily accessible observationally in the mm wavelength range. That has made it the tracer of choice.

CO is far from an ideal tracer of mass. Carbon and oxygen are both trace elements compared to hydrogen, so the correspondence between CO emission and molecular gas mass depends on the relative abundance of both. If that sounds dodgy, it gets worse. It also depends on the interstellar radiation field, the opacity thereto (molecular gas is inevitably associated with dense clumps of dust that shield it from the ambient radiation), and the spatial overlap of the two components – CO and H₂ thrive in similar but not identical regions of space. Hence, converting the observed intensity of CO into a molecular hydrogen mass is a highly sensitive procedure that we typically bypass by assuming it is a universal constant.

It’s astronomy. We do what we can.

People have obsessed long and hard about the CO-to-H2 conversion, so we do have a reasonable idea what it is. While many debates can be had over the details, we have a decent idea of what the molecular gas mass is in some galaxies, at least to a first approximation. Molecular gas is usually outweighed by atomic gas, but sometimes it is comparable. So we’d like to keep track of it for the mass budget.

Obtaining CO observations is expensive, and often impossible: there are a lot of star forming galaxies where it simply isn’t detected. So we presume there is molecular gas there – that’s where the stars form, but we can’t always see it. So it would be handy to have another proxy besides CO.

Atomic gas is a lousy proxy for molecular gas. The mass of one hardly correlates with the other (Fig. 3). The two phases coexist in a complex and ever-changing variable quasi-equilibrium, with the amount of each at any given moment subject to change so that a snapshot of many galaxies provides a big mess.

Fortunately, the molecular gas mass correlates better with other properties – notably star formation. This makes sense, because stars form from molecular gas. So in some appropriately averaged sense, one follows the other. Star formation can be traced in a variety of ways, like the Balmer emission in Fig. 1. We can see the stars forming and infer the amount of molecular gas required to fuel that star formation even if we can’t detect the gas directly (Fig. 4).

I’ve done a lot of work on low surface brightness galaxies, a class of objects that have proven particularly difficult to detect in CO. They have low dust contents, low oxygen abundances, relatively hard interstellar radiation fields – all factors that mitigate against CO. Yet we do see them forming stars, sometimes just one O star at a time, and we know how much molecular gas it takes to do that. So we can use star formation as a proxy for molecular gas mass. This is probably no worse than using CO, and perhaps even better – or would be, if we didn’t have to rely on CO to calibrate it in the first place.

Accurate tracers of star formation are also somewhat expensive to obtain. There are situations in which we need an estimate for the molecular gas mass where we don’t have either CO or a measurement of the star formation rate. So… we need a proxy for the proxy. Fortunately, that is provided by the stellar mass.

The stellar mass of a star-forming galaxy correlates with both its molecular gas mass and its star formation rate (Figs. 3 and 4). This is not surprising. It takes molecules to form stars, and it takes star formation to build up stellar mass. Indeed, the stellar mass is the time-integral of the star formation rate, so a correlation between the two (as seen in the left panel of Fig. 4) is mathematically guaranteed.

This brings us to the seven percent solution. Going through all the calibration steps, the molecular gas mass is, on average, about 7% of the stellar mass (the red lines in Figs. 3 and 4). The uncertainties in this are considerable. I’ve tried to work this out previously, and typically came up with numbers in the 5 – 10% range. So it seems to be in there somewhere.

This is adequate for some purposes, but not for others. One thing I want it for is to keep track of the total mass budget of baryons in galaxies so that we can calibrate the Baryonic Tully-Fisher relation. For this purpose it is adequate since molecular gas ranks behind both stars and atomic gas in the mass budget of almost every rotating galaxy. If it is 5% or 10% instead of 7%, this is a difference of a few percent of something that is itself typically < 10% of the total, and often less. A few percent of a few percent is a good working definition of negligible – especially in astronomy.

On top of all that, we also have to keep track of the stuff that isn’t hydrogen – helium and everything else in the periodic table, which astronomers often refer to collectively as “metals.” This makes for all sorts of partially-deserved jokes – oxygen isn’t a metal! but it is number 3 in cosmic abundance after hydrogen and helium. Like many anachronisms, the practice has good historical precedent. Early efforts to measure the abundances of the chemical elements in stars first gave results for iron. As other elements were probed, their abundances followed a pattern that scaled pretty well with the abundance of iron relative to hydrogen. So once again we have a proxy – this time, the iron abundance being a stand-in for that of everything else. Hence the persistence of the terminology – the metallicity of a star is a shorthand for the fraction of its mass that is not hydrogen and helium.

And that fraction is small. We usually write the mass fractions of hydrogen, helium, and everything else (metals) as

X + Y + Z = 1

where X is the fraction of mass in hydrogen, Y that in helium, and Z is everything else. For the sun, Lodders gives X = 0.7389, Y = 0.2463, and Z = 0.0148. Do I believe all those significant digits? No. Is there a good reason for them to be there? Yes. So without delving into those details, let’s just note that the universe is about 3 parts hydrogen, one part helium, with a sprinkling of everything else. Everything else being all the elements in the periodic table that aren’t hydrogen or helium – all the carbon and nitrogen and oxygen and silicon and magnesium and noble gases and actual metals – these all add up to about 1.5% of the mass of the sun, which is typical of nearby stars. So you can see why they’re all just metals to many astronomers.

For the mass of gas in galaxies, we need to correct what we measure in hydrogen for the presence of helium and metals. We measure the mass of atomic hydrogen using the 21 cm line, but that’s just the hydrogen. There is a corresponding amount of helium and metals that goes along with it. So we estimate the mass fraction in hydrogen, X, and use divide by that to get the total mass: M_gas = M_HI/X. We do the same for molecular gas, etc.

There are measurements of the metallicities of entire galaxies, but – you guessed it – this isn’t observationally cheap, and isn’t always available. So we need another proxy. Luckily for us, it turns out that once again there is a pretty good correlation of metallicity with stellar mass: galaxies with lots of stars have made lots of supernovae that have processed lots of material into metals. Most of it is still hydrogen, so this is a very subtle effect: 1/X = 1.34 for the tiniest dwarf, going up to about 1.4 for a galaxy like the Milky Way. Still, we know this happens, so we can account for it, at least in a statistical way.

For those who are curious about the details, or want the actual formulae to use, please refer to this AAS research note. Next time, I hope to discuss an application for all this.