Tracing the baryons in star forming galaxies

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?

ngc628_final
Fig 1. The spiral galaxy NGC 628. The continuum light of stars in contrasted by dark dust lanes and highlighted by pink pinpoints of Balmer line emission. These are regions of interstellar gas illuminated by the UV emission of short-lived, massive O stars. Not visible here is the interstellar atomic and molecular gas from which stars form.

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).

MgMst
Fig 2. Gas mass vs. stellar mass for galaxies in the SPARC database (blue) and an independent sample selected from SDSS (grey) by Bradford. The line is the line of equality where gas mass and stellar mass are equal. The red point is the Milky Way. Like other bright spirals, it is more stars than gas. Among lower mass dwarf galaxies, the reverse is commonly true: those in the field have more gas than stars.

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.

LCOMHIMst
Fig 3. The mass in molecular hydrogen gas as a function of atomic hydrogen (left) and stellar mass (right) from xGASS. The dotted line is the line of equality; molecular gas is usually outweighed by both atomic gas and stars. The red line at right is where the molecular gas mass is 7% of the stellar mass.

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).

MH2SFRMst
Fig 4. The current star formation rate (left) and molecular gas mass (right) as a function of stellar mass. The grey and black points are from xGASS, with the black points being those where the current star formation rate is within a factor of two of the past average (i.e., the stellar mass divided by the age of the universe). Blue points are low surface brightness galaxies. These extend the relation at left to much lower mass, but are generally not detected in CO. The molecular gas at right (open squares) is inferred by the amount required to sustain the observed star formation.

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: Mgas = MHI/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.

The Star Forming Main Sequence – Dwarf Style

The Star Forming Main Sequence – Dwarf Style

A subject of long-standing interest in extragalactic astronomy is how stars form in galaxies. Some galaxies are “red and dead” – most of their stars formed long ago, and have evolved as stars will: the massive stars live bright but short lives, leaving the less massive ones to linger longer, producing relatively little light until they swell up to become red giants as they too near the end of their lives. Other galaxies, including our own Milky Way, made some stars in the ancient past and are still actively forming stars today. So what’s the difference?

The difference between star forming galaxies and those that are red and dead turns out to be both simple and complicated. For one, star forming galaxies have a supply of cold gas in their interstellar media, the fuel from which stars form. Dead galaxies have very little in the way of cold gas. So that’s simple: star forming galaxies have the fuel to make stars, dead galaxies don’t. But why that difference? That’s a more complicated question I’m not going to begin to touch in this post.

One can see current star formation in galaxies in a variety of ways. These usually relate to the ultraviolet (UV) photons produced by short-lived stars. Only O stars are hot enough to produce the ionizing radiation that powers the emission of HII (pronounced `H-two’) regions – regions of ionized gas that are like cosmic neon lights. O stars power HII regions but live less than 10 million years. That’s a blink of the eye on the cosmic timescale, so if you see HII regions, you know stars have formed recently enough that the short-lived O stars are still around.

f549_1_small
The dwarf LSB galaxy F549-1 and companion. The pink knots are HII regions detected in the light of H-alpha, the first emission line in the Balmer sequence of hydrogen. HII regions are ionized by short-lived O-stars, serving as cosmic shingles that shout “Hey! We’re forming stars here!”

Measuring the intensity of the Hα Balmer line emission provides a proxy for the number of UV photons that ionize the gas, which in turn basically counts the number of O stars that produce the ionizing radiation. This number, divided by the short life-spans of O stars, measures the current star formation rate (SFR).

There are many uncertainties in the calibration of this SFR: how many UV photons do O stars emit? Over what time span? How many of these ionizing photons are converted into Hα, and how many are absorbed by dust or manage to escape into intergalactic space? For every O star that comes and goes, how many smaller stars are born along with it? This latter question is especially pernicious, as most stellar mass resides in small stars. The O stars are only the tip of the iceberg; we are using the tip to extrapolate the size of the entire iceberg.

Astronomers have obsessed over these and related questions for a long time. See, for example, the review by Kennicutt & Evans. Suffice it to say we have a surprisingly decent handle on it, and yet the systematic uncertainties remain substantial. Different methods give the same answer to within an order of magnitude, but often differ by a factor of a few. The difference is often in the mass spectrum of stars that is assumed, but even rationalizing that to the same scale, the same data can be interpreted to give different answers, based on how much UV we estimate to be absorbed by dust.

In addition to the current SFR, one can also measure the stellar mass. This follows from the total luminosity measured from starlight. Many of the same concerns apply, but are somewhat less severe because more of the iceberg is being measured. For a long time we weren’t sure we could do better than a factor of two, but this work has advanced to the point where the integrated stellar masses of galaxies can be estimated to ~20% accuracy.

A diagram that has become popular in the last decade or so is the so-called star forming main sequence. This name is made in analogy with the main sequence of stars, the physics of which is well understood. Whether this is an appropriate analogy is debatable, but the terminology seems to have stuck. In the case of galaxies, the main sequence of star forming galaxies is a plot of star formation rate against stellar mass.

The star forming main sequence is shown in the graph below. It is constructed from data from the SINGS survey (red points) and our own work on dwarf low surface brightness (LSB) galaxies (blue points). Each point represents one galaxy. Its stellar mass is determined by adding up the light emitted by all the stars, while the SFR is estimated from the Hα emission that traces the ionizing UV radiation of the O stars.

SFMSannotated.001
The star formation rate measured as a function of stellar mass for star forming galaxies, the “star forming main sequence” (from McGaugh, Schombert, & Lelli 2017). Each point represents one galaxy. Star formation is rapid in the most luminous spirals, which contain tens of thousands of O stars. In contrast, some dwarf galaxies contain only a single HII region that is so faint that it may be ionized by a single O star.

The data show a nice correlation, albeit with plenty of intrinsic scatter. This is hardly surprising, as the two axes are not physically independent. They are measuring different quantities that trace the same underlying property: star formation over different time scales. The y-axis is a measure of the quasi-instantaneous star formation rate; the x-axis is the SFR integrated over the age of the galaxy.

Since the stellar mass is the time integral of the SFR, one expects the slope of the star forming main sequence (SFMS) to be one. This is illustrated by the diagonal line marked “Hubble time.” A galaxy forming stars at a constant rate for the age of the universe will fall on this line.

The data for LSB galaxies scatter about a line with slope unity. The best-fit line has a normalization a bit less than that of a constant SFR for a Hubble time. This might mean that the galaxies are somewhat younger than the universe (a little must be true, but need not be much), have a slowly declining SFR (an exponential decline with an e-folding time of a Hubble time works well), or it could just be an error in the calibration of one or both axes. The systematic errors discussed above are easily large enough to account for the difference.

To first order, the SFR in LSB galaxies is constant when averaged over billions of years. On the millions of years timescale appropriate to O stars, the instantaneous SFR bounces up and down. Looks pretty stochastic: galaxies form stars at a steady average rate that varies up and down on short timescales.

Short-term fluctuations in the SFR explain the data with current SFR higher than the past average. These are the points that stray into the gray region of the plot, which becomes increasingly forbidden towards the top left. This is because galaxies that form stars so fast for too long will build up their entire stellar mass in the blink of a cosmic eye. This is illustrated by the lines marked as 0.1 and 0.01 of a Hubble time. A galaxy above these lines would make all their stars in < 2 Gyr; it would have had to be born yesterday. No galaxies reside in this part of the diagram. Those that approach it are called “starbursts:” they’re forming stars at a high specific rate (relative to their mass) but this is presumably a brief-lived phenomenon.

Note that the most massive of the SINGS galaxies all fall below the extrapolation of the line fit to the LSB galaxies (dotted line). The are forming a lot of stars in an absolute sense, simply because they are giant galaxies. But the current SFR is lower than the past average, as if they were winding down. This “quenching” seems to be a mass-dependent phenomenon: more massive galaxies evolve faster, burning through their gas supply before dwarfs do. Red and dead galaxies have already completed this process; the massive spirals of today are weary giants that may join the red and dead galaxy population in the future.

One consequence of mass-dependent quenching is that it skews attempts to fit relations to the SFMS. There are very many such attempts in the literature; these usually have a slope less than one. The dashed line in the plot above gives one specific example. There are many others.

If one looks only at the most massive SINGS galaxies, the slope is indeed shallower than one. Selection effects bias galaxy catalogs strongly in favor of the biggest and brightest, so most work has been done on massive galaxies with M* > 1010 M. That only covers the top one tenth of the area of this graph. If that’s what you’ve got to work with, you get a shallow slope like the dashed line.

The dashed line does a lousy job of extrapolating to low mass. This is obvious from the dwarf galaxy data. It is also obvious from the simple mathematical considerations outlined above. Low mass galaxies could only fall on the dashed line if they were born yesterday. Otherwise, their high specific star formation rates would over-produce their observed stellar mass.

Despite this simple physical limit, fits to the SFMS that stray into the forbidden zone are ubiquitous in the literature. In addition to selection effects, I suspect the calibrations of both SFR and stellar mass are in part to blame. Galaxies will stray into the forbidden zone if the stellar mass is underestimated or the SFR is overestimated, or some combination of the two. Probably both are going on at some level. I suspect the larger problem is in the SFR. In particular, it appears that many measurements of the SFR have been over-corrected for the effects of dust. Such a correction certainly has to be made, but since extinction corrections are exponential, it is easy to over-do. Indeed, I suspect this is why the dashed line overshoots even the bright galaxies from SINGS.

This brings us back to the terminology of the main sequence. Among stars, the main sequence is defined by low mass stars that evolve slowly. There is a turn-off point, and an associated mass, where stars transition from the main sequence to the sub giant branch. They then ascend the red giant branch as they evolve.

If we project this terminology onto galaxies, the main sequence should be defined by the low mass dwarfs. These are nowhere near to exhausting their gas supplies, so can continue to form stars far into the future. They establish a star forming main sequence of slope unity because that’s what the math says they must do.

Most of the literature on this subject refers to massive star forming galaxies. These are not the main sequence. They are the turn-off population. Massive spirals are near to exhausting their gas supply. Star formation is winding down as the fuel runs out.

Red and dead galaxies are the next stage, once star formation has stopped entirely. I suppose these are the red giants in this strained analogy to individual stars. That is appropriate insofar as most of the light from red and dead galaxies is produced by red giant stars. But is this really they right way to think about it? Or are we letting our terminology get the best of us?