Space and Time – Part II

NOTE:  this is a repost of an entry from my blogger account.

Well that was a long hiatus. Between pushing out a paper, TA-ing two classes, and getting distracted with fiction writing, this blog went way on the back burner for a couple of months.

I was frankly surprised and flabbergasted by the degree of interest my first post got. I just play an astrobiology type on the internet, I’m really just a molecular biologist with a hobby. I got a number of interesting pointers to recent research, a lot of interesting questions, and spoke to a number of very interesting people actually working in the field of astrobiology! As a result, I’m putting the next topic (our own solar system and its history) on hold for a little bit and going a little more in depth into our solar system’s cosmological position in space and time. The more I look into this, the more clear it becomes to me that we are utterly typical in terms of where and when you’d expect a complex biosphere to form – on a coarse scale, at least. Some interesting questions still arise about the sort of star we find ourselves around.

Anyway, in my last post I mentioned a recent study (Sobral 2012, which looked at star formation rates across cosmological time using proxy measurements, finding a precipitous decline in star formation rates for many gigayears. I can do better than this – I think I can put some rough numbers on our star, planet, and biosphere’s relative position in time and how typical it is drawing from multiple sources.

Numerous publications for decades at this point have performed similar measurements of star formation rate over time, and all those with sufficient detail reveal one, simple, important fact: the rate of star formation per unit mass in the universe as a whole is decaying exponentially, and has been for most of the history of the universe. I could point to a number of publications for this, but for the purposes of this post I will use Yuskel, 2008 ( This group collated a number of datasets and fit an equation to the star formation rate going all the way back to when the universe was less than a billion years old. I’ve reproduced a figure from Horuchi, 2010 ( which while not actually being ABOUT star formation rates takes the fit from Yuskel and compares it to multiple data sets, supporting its validity:

Figure from Horuchi, 2010.  Plots star formation rate on the Y axis and redshift on a log scale on the X, which is related in a complicated way to actual age of the universe (see the top of the graph).

There’s a couple of things going on here. Firstly, note that the star formation rate is given in terms of something called Z – the redshift. Astronomers love talking about their observations in terms of the redshift of what they observe because it is directly observable and related to both distance and age of what you are looking at, as well as the size of the universe when the light was emitted.  You look and you see something that should be radiating at wavelength X instead radiating at wavelength X*(1+Z), indicating it was emitted when the size of the universe was 1/(1+z) as big as today and the light has stretched with the expansion.  That observation is generally incontestable.  But to turn that observation into a distance or time you need to start messing around with cosmological models which, although they have been converging to a pretty tight focus in recent years, are still open to refinement and change. It’s generally better to keep your data in the raw observational form as a result.

Secondly, note the FORM of the equation of best fit. Since around Z = 1, corresponding to more than eight billion years ago, the star formation rate has been cratering in a very consistent way. As the universe has expanded over that timeframe, star formation rate has very closely tracked [size of the universe]^-3.4th. The plateau of steady high star formation rates lasted only about 3 or 4 gigayears, long before our Sun formed. This represents huge bursts of star formation from young galaxies and giant ellipticals that formed and burned out young.

If I want to get an idea of the total number of stars that have been born and will ever be born, I need to turn this function of star formation rate at a given Z (expressed in solar masses formed per comoving cubic megaparsec per year so as to normalize for the expansion of the universe) into a function of star formation rate at a given absolute time, project it forward with reasonable assumptions, and integrate. Here is a graph of Z with respect to T from the best modern cosmological models, with epochs in which the expansion of the universe behaves very differently indicated by color:

redshift Redshift changes with time very differently when the universe is matter-dominated (blue line), has a roughly even amount of matter and dark energy (red line), and when it is dark-energy-dominated (green line). Whatever the case, I can use the relationship between redshift and time to turn the graph of star formation rate across redshift into star formation rate over time for the history of the universe so far:


The red circle represents the formation of the Sun, and the end of the black line the present day at t = 13.82 gigayears. As you can see, the vast vast majority of star formation occurred before our Sun was born.

How to project this plot forward into the future in order to determine how many stars will ever live? I have made two executive decisions. Firstly, I have decided to simply project the exponential decay that has been occurring since Z=1 forward into the future, for reasons that I will get to later. Secondly, I have decided to break with a slavish devotion to the redshift numbers of the far future, once the universe has turned completely dark-energy dominated. Instead, I will keep the same function of Z with T and therefore the same function of star formation over time that has held since approximately Z=1, because I fail to see how simply increasing the distance between galaxy clusters more and more rapidly as will happen once the universe is dark energy dominated will change star formation rates within the clusters. It doesn’t make a huge difference, going one way or the other changes the final numbers by less than five percent.

Anyways, after much obsessive faffing around with these equations in matlab to deal with the above set of assumptions, I projected star formation rates forward into the future to get the following graph. The red circle continues to represent the formation of the Sun, and the blue dot the present day:


The decline is striking.  Star formation is a phenomenon of the early universe, a temporary phase not something that goes on stably.

By integrating this curve forward, we can get an idea of where the Sun lays in the final star-order of the universe. I have normalized the graph to the (finite) number of stars that will ever exist when you integrate out to infinity:


In short, we find that the Sun was born when ~79% of stars that will ever exist already existed, and at the present moment ~90% of all stars that will ever exist already exist. Thus, the sun is a relative but by no means extreme latecomer to the universe, and despite existing near the beginning of an apparently open-ended universe its time of formation is not terribly special.

The universe is full to bursting with hydrogen and helium, only the tiniest fraction having been converted into heavy elements by being consumed in stars. Naively one might assume that all this gas would eventually condense down into stars one day. Recent results in astrophysics are suggesting reasons, however, that this probably won’t happen – reasons for my continued use of the exponential decay of the universal star formation rate in my above analysis, as processes happening today continue. In my last post, I mentioned the life histories of various types of galaxies and how they suggested that star formation might be closer to finishing than starting. I feel compelled to go into a little bit more detail here, speaking more in terms of what happens to all the gas that could form stars but doesn’t using recent astrophysical results.

When you look out into the universe, the vast vast majority of elliptical type galaxies are very red due to the age of their stars and are not forming stars, whether they have an internal reservoir of gas within their dark matter halo or not – see for a discussion on this. Big spirals are mostly forming stars at a steady clip, with only a few tapering down and turning ‘green’ or eventually ‘red’ from their initial ‘blue’ status. Recently, a project called GalaxyZoo which has automated and crowdsourced the analysis of huge numbers of new galaxies observed in the Sloan Digital Sky Survey has taken a very quantitative look at star formation across galaxy types in the universe, and come up with some striking conclusions:

These studies were able to get more information than the instantaneous rate of star formation, and look back along the history of the galaxies by looking at light of different frequencies – huge stars that don’t live long make lots of ultraviolet, stars like our Sun peak in the green light, while long lived stars peak in the red. They were able to see that among elliptical galaxies, the tiny fraction that are star-forming mostly show evidence of recently being involved in mergers, and that all those that are red and green colored show spectral patterns indicative of very rapid shutdown of star formation, faster than can be accounted for by star formation eating up available gas. They call this fast star-formation shutdown ‘quenching’. Something about their formation, either primordially or via mergers of spirals, puts their gas into forms that cannot form stars. The prime suspect is the initiation of regular energetic outbursts from their large central black holes, heating the gas and rendering it too turbulent.

This actually dovetails interestingly with another problem in astrophysics: the ‘cooling paradox’. As I mentioned, about 90% of the baryonic mass of the universe is in the form of X-ray hot gas clouds blanketing entire galaxy clusters (largely outside the dark matter halos of individual galaxies). This gas is ridiculously thin and immensely hot, and radiating energy rapidly in the X-rays. It turns out that when you figure out how much mass is in these gas clouds and how much energy they are radiating in the X-rays, they should cool and sink down to the centers of the clusters on a timescale of gigayears, probably turning into cool gas flows onto the large galaxies at the centers of these clusters. But they don’t. Looking back in time across the universe they are at more or less the same temperature now as they always have been and never seem to cool despite the fact that they are radiating energy. In recent years, for various reasons (images of turbulence in the gas, calculations of the available energy) the prime suspect for the energy source keeping these gas clouds energized has become supermassive black hole jets.

Anyways, as for spiral galaxies, they were able to model the distribution they saw (most of which are forming stars at a steady rate, some of which are tapering off, and some of which are red and dead) as a mixture of populations. One population is forming stars at a steady slowly decreasing rate, much like ours. Another is quenching on a much slower timescale than ellipticals, indicative of a cut-off of gas inflow into their star-forming discs and star formation then slowly depleting their reservoir of gas over a 1-2 gigayear timescale, likely caused by events in their immediate galactic neighborhood disrupting the inflows of cool gas within their dark matter halos onto their star forming discs.

All of this suggests to me that the decline in star formation rate seen across the cosmological past represents larger and larger fractions of galaxies quenching along with spirals merging into ellipticals with slow decreases in star formation rates within individual galaxies, and that the numbers I produced above have at least some semblance of validity.  I can’t, of course, rule out the possibility that galaxy quenching is a temporary or cyclical phenomenon  on very long timescales, or that there’s some special subset of galaxies that will never quench and will use up all their gas.  But these numbers are a good start.


These numbers are, however, numbers about STARS and the Sun’s position in star-order.  And as vital as stars are for life, we don’t live on a star.  We live on a terrestrial planet.  And this makes a difference.

The huge bolus of star formation early in the universe consisted of many low-metallicity stars at the starts of spiral galaxies and the fast star formation bursts of elliptical galaxies.  Many of these stars are probably not suitable for the creation of terrestrial planets and thus biospheres-as-we-know-them.  In order to get a handle on Earth’s position in planet-order we need to normalize this.  I am utterly unprepared to do this rigorously since the astronomical community as a whole hasn’t got a good handle on planet formation – if there’s one incontrovertible takeaway from the Kepler mission, this is it.  I can, however, pull up some numbers  that are better than nothing and layer them on top of my star formation numbers and see what comes out.

I will be taking data from a paper (Behroozi & Peeples, 2015: that made the rounds last year suggesting that Earth came in the 8th percentile of terrestrial planets (that is, 92% come after us).  Their conclusion is extremely suspect because it includes the assumption that ALL gas within galactic dark matter halos will eventually form stars.  However, the authors include a nice set of metallicity normalizations that they apply to the early universe that I will take in its entirety, as it is far too complicated for someone like me who doesn’t study cosmology professionally to critique.

In this work, all stars are assumed to form terrestrial planets with a power-law dependence on metallicity and a sharp metallicity cutoff for ‘gas planet’ formation is assumed.  I will use both these functions, on the chance that either of them is relevant – again, nobody really understands planet formation.  I find myself suspecting that the latter is more relevant due to some talks I’ve seen on solar system structure and planet formation modeling, but I really don’t know.

This work finds that using a power law metallicity dependence, the Earth is younger than ~83% of currently existing planets, and that with a sharp metallicity cutoff our planetary system is younger than ~64% of currently existing systems (both of these numbers shamelessly scraped from graphs).  Now I apply an almost certainly oversimplified and wrong assumption:  that the fraction of star systems that have been planet-forming has been constant since the formation of the Sun, on the theory that the pollution of heavy elements is more or less complete because most short-lived stars that will ever be born have already died.  Applying these numbers, I estimate the following positions of the Earth and by extension our biosphere in planet-order:

Under the power-law metallicity assumption, Earth shows up as younger than 72% of planetary systems that will exist.

Under a sharp metallicity-cutoff assumption, Earth shows up as younger than 51% of planetary systems that will exist.  

In the words of the first person I showed these calculations to, these numbers are very interesting in that they are very boring.  We find ourselves in an unremarkable position in terms of planet-formation order. We are not early and other explanations for the so-called Fermi pardox must be invoked.  Any errors my simplifying assumptions produce will slightly increase these percentages but not by much.

Wow this post has gotten long.  I still have some thoughts on other large-scale considerations about our position in space and time – namely why we find ourselves around a star as large and relatively short-lived as the Sun (larger than most stars) and not, say, 30 billion years into the lifespan of a small star born at the same time as the Sun but with a 40 billion year lifetime.  I will save that for another revisit to this topic.  Stay tuned for my original intent, talking about our own solar system.

Space and Time – Part I

NOTE:  This is a repost from my original site at blogger.

Those of an anthropic bent have often made much of the fact that we are only 13.7 billion years into what is apparently an open-ended universe that will expand at an accelerating rate forever. The era of the stars will last a trillion years; why do we find ourselves at this early date if we assume we are a ‘typical’ example of an intelligent observer? In particular, this has lent support to lines of argument that perhaps the answer to the ‘great silence’ and lack of astronomical evidence for intelligence or its products in the universe is that we are simply the first. This notion requires, however, that we are actually early in the universe when it comes to the origin of biospheres and by extension intelligent systems. It has become clear recently that this is not the case.

The clearest research I can find illustrating this is the work of Sobral et al, illustrated here via a paper on arxiv and here via a summary article. To simplify what was done, these scientists performed a survey of a large fraction of the sky looking for the emission lines put out by emission nebulae, clouds of gas which glow like neon lights excited by the ultraviolet light of huge, short-lived stars. The amount of line emission from a galaxy is thus a rough proxy for the rate of star formation – the greater the rate of star formation, the larger the number of large stars exciting interstellar gas into emission nebulae. The authors use redshift of the known hydrogen emission lines to determine the distance to each instance of emission, and performed corrections to deal with the known expansion rate of the universe. The results were striking. Per unit mass of the universe, the current rate of star formation is less than 1/30 of the peak rate they measured 11 gigayears ago. It has been constantly declining over the history of the universe at a precipitous rate. Indeed, their preferred model to which they fit the trend converges towards a finite quantity of stars formed as you integrate total star formation into the future to infinity, with the total number of stars that will ever be born only being 5% larger than the number of stars that have been born at this time.

In summary, 95% of all stars that will ever exist, already exist. The smallest longest-lived stars will shine for a trillion years, but for most of their history almost no new stars will have formed.

At first this seems to reverse the initial conclusion that we came early, suggesting we are instead latecomers. This is not true, however, when you consider where and when stars of different types can form and the fact that different galaxies have very different histories. Most galaxies formed via gravitational collapse from cool gas clouds and smaller precursor galaxies quite a long time ago, with a wide variety of properties. Dwarf galaxies have low masses, and their early bursts of star formation lead to energetic stars with strong stellar winds and lots of ultraviolet light which eventually go supernova. Their energetic lives and even more energetic deaths appear to usually blast star-forming gases out of their galaxies’ weak gravity or render it too hot to re-collapse into new star-forming regions, quashing their star formation early. Giant elliptical galaxies, containing many trillions of stars apiece and dominating the cores of galactic clusters, have ample gravity but form with nearly no angular momentum. As such, most of their cool gas falls straight into their centers, producing an enormous burst of low-heavy-element star formation that uses most of the gas. The remaining gas is again either blasted into intergalactic space or rendered too hot to recollapse and accrete by a combination of the action of energetic young stars and the infall of gas onto the central black hole producing incredibly energetic outbursts.   (It should be noted that a full 90% of the non-dark-matter mass of the universe appears to be in the form of very thin X-ray-hot plasma clouds surrounding large galaxy clusters, unlikely to condense to the point of star formation via understood processes.) Thus, most dwarf galaxies and giant elliptical galaxies contributed to the early star formation of the universe but are producing few or no stars today, have very low levels of heavy element rich stars, and are unlikely to make many more going into the future.

Spiral galaxies are different. Their distinguishing feature is the way they accreted – namely with a large amount of angular momentum. This allows large amounts of their cool gas to remain spread out away from their centers. This moderates the rate of star formation, preventing the huge pulses of star formation and black hole activation that exhausts star-forming gas and prevents gas inflow in giant ellipticals. At the same time, their greater mass than dwarf galaxies ensures that the modest rate of star formation they do undergo does not blast nearly as much matter out of their gravitational pull. Some does leave over time, and their rate of inflow of fresh cool gas does apparently decrease over time – there are spiral galaxies that do seem to have shut down star formation. But on the whole a spiral is a place that maintains a modest rate of star formation for gigayears, while heavy elements get more and more enriched over time. These galaxies thus dominate the star production in the later eras of the universe, and dominate the population of stars produced with large amounts of heavy elements needed to produce planets like ours. They do settle down slowly over time, and eventually all spirals will either run out of gas or merge with each other to form giant ellipticals, but for a long time they remain a class apart.

Considering this, we’re just about where we would expect a planet like ours (and thus a biosphere-as-we-know-it) to exist in space and on a coarse scale in time. Let’s look closer at our galaxy now. Our galaxy is generally agreed to be about 12 billion years old based on the ages of globular clusters, with a few interloper stars here and there that are older and would’ve come from an era before the galaxy was one coherent object. It will continue forming stars for about another 5 gigayears, at which point it will undergo a merger with the Andromeda galaxy, the nearest large spiral galaxy. This merger will most likely put an end to star formation in the combined resultant galaxy, which will probably wind up as a large elliptical after one final exuberant starburst. Our solar system formed about 4.5 gigayears ago, putting its formation pretty much halfway along the productive lifetime of the galaxy (and probably something like 2/3 of the way along its complement of stars produced, since spirals DO settle down with age, though more of its later stars will be metal-rich).

On a stellar and planetary scale, we once again find ourselves where and when we would expect your average complex biosphere to be. Large stars die fast – star brightness goes up with the 3.5th power of star mass, and thus star lifetime goes down with the 2.5th power of mass. A 2 solar mass star would be 11 times as bright as the sun and only live about 2 billion years – a time along the evolution of life on Earth before photosynthesis had managed to oxygenate the air and in which the majority of life on earth (but not all – see an upcoming post) could be described as “algae”. Furthermore, although smaller stars are much more common than larger stars (the Sun is actually larger than over 80% of stars in the universe) stars smaller than about 0.5 solar masses (and thus 0.08 solar luminosities) are usually ‘flare stars’ – possessing very strong convoluted magnetic fields and periodically putting out flares and X-ray bursts that would frequently strip away the ozone and possibly even the atmosphere of an earthlike planet.

All stars also slowly brighten as they age – the sun is currently about 30% brighter than it was when it formed, and it will wind up about twice as bright as its initial value just before it becomes a red giant. Depending on whose models of climate sensitivity you use, the Earth’s biosphere probably has somewhere between 250 million years and 2 billion years before the oceans boil and we become a second Venus. Thus, we find ourselves in the latter third-to-twentieth of the history of Earth’s biosphere (consistent with complex life taking time to evolve).

Together, all this puts our solar system – and by extension our biosphere – pretty much right where we would expect to find it in space, and right in the middle of where one would expect to find it in time. Once again, as observers we are not special. We do not find ourselves in the unexpectedly early universe, ruling out one explanation for the Fermi paradox sometimes put forward – that we do not see evidence for intelligence in the universe because we simply find ourselves as the first intelligent system to evolve. This would be tenable if there was reason to think that we were right at the beginning of the time in which star systems in stable galaxies with lots of heavy elements could have birthed complex biospheres. Instead we are utterly average, implying that the lack of obvious intelligence in the universe must be resolved either via the genesis of intelligent systems being exceedingly rare or intelligent systems simply not spreading through the universe or becoming astronomically visible for one reason or another.

In my next post, I will look at the history of life on Earth, the distinction between simple and complex biospheres, and the evidence for or against other biospheres elsewhere in our own solar system.

What’s all this about?

NOTE:  This is a repost from my original site at blogger.

This blog is to be a repository for the thoughts and analysis I’ve accrued over the years on the topic of astrobiology, and the place of life and intelligence in the universe.  All my life I’ve been pulled to the very large and the very small.  Life has always struck me as the single most interesting thing on Earth, with its incredibly fine structure and vast, amazing history and fantastic abilities.  At the same time, the vast majority of what exists is NOT on Earth.  Going up in size from human-scale by the same number of orders of magnitude as you go down through to get to a hydrogen atom, you get just about to Venus at its closest approach to Earth – or one billionth the distance to the nearest star.  The large is much larger than the small is small.  On top of this, we now know that the universe as we know it is much older than life on Earth.  And we know so little of the vast majority of the universe.

There’s a strong tendency towards specialization in the sciences.  These days, there pretty much has to be for anybody to get anywhere.  Much of the great foundational work of physics was done on tabletops, and the law of gravitation was derived from data on the motions of the planets taken without the benefit of so much as a telescope.  All the low-hanging fruit has been picked.  To continue to further knowledge of the universe, huge instruments and vast energies are put to bear in astronomy and physics.  Biology is arguably a bit different, but the very complexity that makes living systems so successful and so fascinating to study means that there is so much to study that any one person is often only looking at a very small problem.

This has distinct drawbacks.  The universe does not care for our abstract labels of fields and disciplines – it simply is, at all scales simultaneously at all times and in all places.  When people focus narrowly on their subject of interest, it can prevent them from realizing the implications of their findings on problems usually considered a different field.

It is one of my hopes to try to bridge some gaps between biology and astronomy here.  I very nearly double-majored in biology and astronomy in college; the only thing that prevented this (leading to an astronomy minor) was a bad attitude towards calculus.  As is, I am a graduate student studying basic cell biology at a major research university, who nonetheless keeps in touch with a number of astronomer friends and keeps up with the field as much as possible.  I quite often find that what I hear and read about has strong implications for questions of life elsewhere in the universe, but see so few of these implications actually get publicly discussed. All kinds of information shedding light on our position in space and time, the origins of life, the habitability of large chunks of the universe, the course that biospheres take, and the possible trajectories of intelligences seem to me to be out there unremarked.

It is another of my hopes to try, as much as is humanly possible, to take a step back from the usual narratives about extraterrestrial life and instead focus from something closer to first principles.  What we actually have observed and have not, what we can observe and what we cannot, and what this leaves open, likely, or unlikely.  In my study of the history of the ideas of extraterrestrial life and extraterrestrial intelligence, all too often these take a back seat to popular narratives of the day.  In the 16th century the notion that the Earth moved in a similar way to the planets gained currency and lead to the suppositions that they might be made of similar stuff and that the planets might even be inhabited.  The hot question was, of course, if their inhabitants would be Christians and their relationship with God given the anthropocentric biblical creation stories.  In the late 19th and early 20th century, Lowell’s illusory canals on Mars were advanced as evidence for a Martian socialist utopia.  In the 1970s, Carl Sagan waxed philosophical on the notion that contacting old civilizations might teach us how to save ourselves from nuclear warfare.  Today, many people focus on the Fermi paradox – the apparent contradiction that since much of the universe is quite old, extraterrestrials experiencing continuing technological progress and growth should have colonized and remade it in their image long ago and yet we see no evidence of this.  I move that all of these notions have a similar root – inflating the hot concerns and topics of the day to cosmic significance and letting them obscure the actual, scientific questions that can be asked and answered.

Life and intelligence in the universe is a topic worth careful consideration, from as many angles as possible.  Let’s get started.