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.

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.

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?

9 thoughts on “The Star Forming Main Sequence – Dwarf Style

  1. I’d love to hear what you think about the work of Alexander Deur on gravity in some future post.

    He claims to reproduce MOND, extend that result to clusters, make a new finding regarding elliptical galaxies related to gravity, and explain all or much of dark energy, by using a graviton model of gravity that derives these effects largely by graviton self-interaction. He describes it as just GR, but authors of the leading textbooks on GR would consider the effects he describes as contrary to it.

    He does using mathematics analogous to QCD (which is his primary speciality in physics) and using static approximation of gravitons as spin-0 scalars (on the theory that average tensor contributions from flux and kinetic energy in weak fields are much smaller than first order effects captured with self-interacting scalar gravitons).

    The trouble is that his day job has limited him to half a dozen or so papers comparing this theory to the data at only a back of napkin level, and he’s gotten little attention in the field since he’s an outsider.

    But, at face value, it is probably the most plausible and viable quantum gravity way to derive MOND-like effects that I’ve seen and in principal ought to require only the gravitational coupling constant with even the MOND acceleration and cosmological constant being emergent quantities.

    A number of blog posts discussing his work and with links to it can be found here: https://dispatchesfromturtleisland.blogspot.com/search?q=Deur&max-results=20&by-date=true


  2. Interesting.

    My knee jerk reaction is no way. It is true that deviations from isotropy as structure develops can lead to the inference of Lambda; we’ve been down that rabbit hole and it seems hard to have an affect of the needed size. Similarly in galaxies: there are many claims to reproduce MOND-like behavior but few to hold water.

    However, knee-jerk reactions are often unfair. After doing a bit of reading, all I can say quickly is that I’ll have to do more reading, and think about it more in my copious spare time. The work of Deur looks more solid than the knee would jerk.

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  3. Yes, the external field effect is almost certainly important. My back of the envelope calculation puts it at 0.15 a0, about the same as the internal field “should” be for their assumed stellar mass. The uncertainties are … large.


  4. A poster over at Backreaction at 2:34 PM, December 15, 2018 (https://www.blogger.com/comment.g?blogID=22973357&postID=2131424387676000750) raises very important points with regard to the spiral structure of the outer arms of galaxies. He points out that if galaxies more or less obeyed Newtonian dynamics, the outermost stars would not form the spiral structures, seen in most galaxies, but would be “smeared out” over time. I’ve actually mused about that very thing myself and assumed whatever mechanism is behind the gravitational effect attributed to Dark Matter was the source of such structure. He then points out that MOND is more compatible with spiral structures since a homogenous distribution of Dark Matter particles, circulating in a halo about the galaxy, would be unlikely to give rise to concentrations of stars as seen in the spiral arms.

    My question is: does MOND successfully predict spiral structures in the outer reaches of galaxies? If that’s the case it certainly would be another feather in MOND’s cap, and another problem for the DM paradigm to explain. But perhaps the issue is more complicated and the existence of spiral arms is not decisive for either paradigm.


  5. Yes. This is what I pointed out over 20 years ago in section 3.3 of https://xxx.lanl.gov/abs/astro-ph/9801102 – spiral structure makes a lot more sense in MOND than in dark matter, especially in regions of low surface brightness (the outskirts of bright galaxies, and throughout LSB galaxies). See also the work of Tiret & Combes, who performed numerical simulations of structure in galaxies, e.g., https://arxiv.org/abs/0803.2631

    This test is not decisive because we don’t understand spiral structure well enough conventionally to say what it cannot do. This is a recurring problem with testing the dark matter hypothesis. There is no null hypothesis so solid that it can be contradicted in a way that can’t be fudged. That is, we have seen many contradictions to our expectations for dark matter, but we are always free to refashion those expectations to match the data. That pretty much sums up the history of the subject.


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