Supernovae and cosmological measurements

Hello everyone, thank you for reading. Today I will tell you about another path dying stars can take and a particular important use that comes out of this. That path – a supernova explosion – is a rare, yet fascinating event. There are no people alive today who have seen a supernova with a naked eye, but that only adds to the interest, as you will see later. The important use I referred to is the possibility of measuring immense distances in the Universe utilizing a subgroup of supernovae as a kind of ruler.

The reason for me choosing a seemingly double topic, as well as a rather specific one, is twofold. First of all, it serves as an example of how everything in the Universe is interconnected in one way or another, and how we can employ the physical processes beyond our control to act as tools in the research of the cosmos. The second reason is much more simplistic – I will be giving a talk on this subject in a couple of weeks, so this article is a perfect opportunity to practise the key points I need to address.

Let us begin our journey with some historical perspective. For ages people have been observing the stars. They noticed that most stars look “fixed” to the firmament, whereas others aren’t. Among those “loose stars” were planets, whose motion was regular; some were comets that appeared in the sky, had a tail, moved around for a while and finally disappeared; still others were called “novae”, that is, “new stars”, that appeared very rarely, quickly became bright and then dimmed very slowly, taking decades if not centuries to fade into invisibility. Finally, some were similar to “novae”, but were bright enough to be visible in daytime and dimmed to being barely visible over the course of a few hundred days.

A very long time later than these observations were made, people started observing novae and supernovae and discovering new ones. It was rather difficult to detect supernovae, because there have been only 2 known ones happening in our Galaxy in the past four hundred years (although theory predicts approximately 4 per century). Novae are difficult to detect because although they are periodic, they light up once every thousand or ten thousand years and human civilisation hasn’t been around for that long yet. In any case, an understanding of the processes behind these objects formed, albeit slowly. Novae are now known to be caused by sudden onsets of thermonuclear burning on surfaces of white dwarfs that accrete matter from companion stars in binary systems. Supernovae, on the other hand, are explosions of stars.

When detailed observations of supernovae started some 30 years ago, it was quickly discovered that supernovae can be broadly classified into two groups. The Type I supernovae have no hydrogen lines in their spectra (which mean that there is no hydrogen in the explosion), while Type II supernovae have hydrogen. Later on it was noticed that such classification is not representative of the physics behind the explosions and the classification was expanded: Type Ia supernovae are ones with no hydrogen lines, weak helium lines and strong silicon lines and represent an explosion called a thermonuclear supernova; Types Ib and Ic are supernovae with no hydrogen lines, but also lack silicon lines and have helium lines (stronger in Ic than in Ib); they represent the same mechanism as Type II supernovae, except the progenitor stars are very heavy.

The two physical mechanisms behind supernova explosions are these. In a core-collapse supernova, a massive star burns chemical elements in its core until it reaches iron and is unable to go any further. The star’s core then collapses (hence the name) very suddenly and rapidly, and the outer layers are blown away in the resulting shock. The other process that may also lead to a supernova explosion is a sudden onset of thermonuclear burning inside a white dwarf, caused by accretion of matter from a companion star in a binary system. As you can see, the two kinds of supernovae are fundamentally different. While both are interesting, I will concentrate on the Type Ia supernovae, because this is the sub-group I mentioned above which is used in cosmological distance calculations.

In order to understand why Type Ia supernovae can be used in cosmology, we need to understand the necessity of “standard rulers” or objects that can help us determine distance. In the everyday world, we can usually measure things directly – with a ruler, or by walking. Longer distances, e.g. to the other planets, can be calculated knowing their movement in the sky and the laws of physics that govern it. When we go further, to the stars, this becomes more difficult. We don’t have rulers that stretch for light-years; we cannot send signal to stars and hope for an echo, because the echo would be too faint to detect and would take years, if not millennia, to reach us. As a result, a variety of indirect distance measurement methods can be employed. Nearby stars can be identified by measuring their parallax – that is, the angle by which a star moves in the sky over the course of a year with respect to the background of more distant stars. This apparent motion comes about because the Earth revolves around the Sun, so our position changes with respect to the background. The closer the star in question is to us, the more movement we will see, although even for the nearest stars, this movement is less that one arcsecond. A unit of measurement, the parsec, is related to this method: one parsec (or parallax second) is the distance at which an object would have a parallax of one arcsecond when viewed from Earth.

Parallax can only help us so much though. A good way of determining distances within our galaxy is the Doppler shift method. When an object is approaching us, all features in its spectrum will be moved to shorter wavelengths, i.e. toward the “blue end” of the spectrum; conversely, when an object is moving away, it will be red-shifted. Knowing the intrinsic spectrum of some object (for example, hydrogen, which is by far the most abundant element in the Universe) allows us to determine its speed. Knowing the speed and some geometry allows us to place the object somewhere in the galaxy. Distances to nearby galaxies can be identified if a particular type of variable stars, the Cepheids, is present in it. Cepheids have a very strict relation between their total luminosity and the period of variability. So knowing this period it is easy to identify the star’s total luminosity and comparing it with the observed magnitude allows us to calculate the distance to it. There are similar methods for larger distances; some are very precise, some are very imprecise, but they all act as aides when determining cosmic distances.

Together, such objects are called “Standard rulers”. A subset of them that have nearly identical luminosities (or luminosities dependent on a single parameter only) are called “Standard candles”. Type Ia supernovae happen to be such standard candles, and are the candles that extend further into the depths of space than anything else. In order to understand the reason for them being standard candles and the precision of measurements taken with them, we have to learn more about the physics behind these explosions.

Type Ia supernovae occur in binary star systems that contain at least one white dwarf star. A white dwarf is a dead star, its structure only kept by the so-called degeneracy pressure (i.e. quantum effects) of electrons. This star may capture material from its companion and thus slowly grow in size. Once a white dwarf’s mass exceeds the Chandrasekhar limit, approximately 1.4 Solar masses, degeneracy pressure cannot hold again the gravitational attraction and the star starts evolving. The nature of this evolution depends on many parameters – the density profiles within the star, the type of elements that are accreted from the companion and so on. Resolving this issue is not aided by the fact that there is considerable debate over the nature of the companion star. Theoretical modelling seems to favour a doubly-degenerate system, that is, a system of two white dwarfs; however observations shows a grand total of zero such systems in our Galaxy or nearby ones, and a singly-degenerate system of a white dwarf and a main sequence or red giant star is preferred. The next problem regarding the progenitor system is its properties at the onset of the explosion. In doubly-degenerate scenarios, the white dwarf accretes mass very quickly, so it may grow significantly larger than the Chandrasekhar mass before exploding. In singly-degenerate scenarios, the situation is much more complex and explosion can start while the white dwarf is anywhere between 1.1 to 1.7 Solar masses.

If it looks like there are many problems with our understanding of the progenitor system, it’s even worse when we consider the explosion process itself. The explosion is a case of thermonuclear burning of carbon and oxygen (two main components of the white dwarf) and possibly some helium captured from the companion, converting them to heavier elements – neon, magnesium and so on, until finally most of the star’s mass is converted into iron, nickel and cobalt (the latter two later decay back into iron). The explosion is very rapid – it takes only a few seconds from the moment thermonuclear burning starts somewhere in the star until the entire star is engulfed in flames. At least we think so – no one has observed a Type Ia supernova explosion in real time yet. The explosion is also very powerful – the whole star is completely destroyed in the process. The rest of the process is left to theory and computer modelling of the problem, which itself suffers from several problems. First of all, the length scale of the models has to be extremely huge – there are important processes of every size ranging from flame front less than a millimetre wide through turbulent flows a few hundred meters long to the whole star a few thousand kilometres across and even the ejecta, which can be several hundred thousand kilometres long. Such a wide range of lengths cannot be resolved even with modern supercomputers, so scientists have to resort to using partial solutions and stitch them together to get meaningful results. Secondly, a similar problem exists with time scales – although the explosion itself takes only a few seconds, the various thermonuclear processes in the ejecta last for several hundred days and have to be considered. In this case it is easier to use partial solutions, but even so it is not a rigorous approach. A third problem is the way of relating simulation results to observable properties of the explosion – there is no unique way to do that.

Yet another, and possibly the most fundamental, problem is choosing among the ways the explosion can occur. Without going into detail, the possibilities include prompt detonation (the burning front proceeds faster than sound from the onset), delayed detonation (burning starts slower than sound and becomes supersonic later), pure deflagration (burning is slower than sound all the time) or pulsed detonation (burning moves subsonically for a while, then the star contracts a little starting another, supersonic, burning front); each one of those models is different depending on whether burning starts in the centre of the star, slightly off-centre or close to the surface; there are other parameters which can be changed as well, producing a myriad different models. While some of them, such as pure deflagration, are considered unlikely to be correct, there is still a large amount of uncertainty related to the nature of the explosion.

Although there are so many problems related to the physics of supernova explosions, their observations are a gold mine for cosmologists. All Type Ia supernovae have very similar absolute brightnesses at maximum light. The shapes of their light curves (a light curve is a function of brightness over time) are also very similar. In 1992, a guy named Phillips noticed that the light curve similarity can be translated into a correlation parameter, namely the decline in brightness over the first 15 days after maximum light, which can then be applied to correct the absolute brightness and produce a nearly perfect correlation. With such a correction, all Type Ia supernova light curves become pretty much identical and so they can be said to be standard candles.
This realisation ushered a new era in cosmological observations. Having such a precise standard candle available made it possible to test the very geometry of the Universe, as well as some of its other fundamental properties. There have been some standard rulers known from earlier, but they were either difficult to detect or were imprecise. The geometry estimation rests on comparison of distance to the supernova obtained from two measurements. The first one is the simple Hubble’s law: the further away the object is from us, the faster it is moving away and therefore has a higher redshift. A mathematical model of cosmology relates the distance of the object to its redshift in more rigorous terms. The second measurement is the aforementioned brightness of the supernova. Since the absolute brightness is known and apparent brightness decreases the further the object is from us, it is possible to calculate the distance to that object. This distance is also related to some parameters in cosmological models. Among such parameters are the deceleration parameter (a measure of how quickly the Universal expansion is slowing down), the relative densities of matter, radiation and dark energy (also called the cosmological constant) and others. Since different parameters are most important at different distances from us, it is possible to estimate the values of these parameters if we have a set of standard candles at distances ranging from the Galactical to the very edge of the observable Universe.

It turns out that we do. The Supernova cosmology project, started in 1997, currently contains more than a thousand records of Type Ia supernovae the occured outside of our own Galaxy. As soon as the first data sets began to appear, scientists all over the world started checking the models of cosmology. Although the initial results were inconclusive, mostly due to the limited information available and the large uncertainties related to it, it took less than a year for the first significant conclusion to be made. It is still the most groundbreaking result to come out of supernova observations. It turns out that the farthest supernovae are dimmer than they should be if the Universe’s expansion was gradually slowing down. This realisation led to a development of a new cosmological theory, the Concordance (Lambda-CDM) model, which posits the Universe as dominated by a mysterious dark energy which causes the expansion to accelerate rather than slow down.

Obviously, there are problems with this part of the whole picture as well. Any cosmological model rests upon numerous assumptions, some of them more fundamental than others. Most measurements that we can take of distant objects are indirect in one way or another. In addition, since light does not travel infinitely fast, the images we see of distant objects represent them as they were a long time in the past. These three limitations lead to a number of potential problems. One – we do not know if Type Ia supernovae had the same absolute brightness those billion years ago. Two – we cannot be certain that we accounted for all possible sources of light absorption in the way between distant supernovae and us. And finally three – even if the calculated distance is correct, we do not know if the interpretation of accelerating Universal expansion is the best way of explaining this result. These problems can be reformulated into assumptions and then tested, but this is extremely difficult. We cannot go back in time and check how Type Ia supernovae really looked “back then” or what possible unknown sources of absorption could have been there. We also cannot look at the Universe from outside and understand its geometry, because there is no “outside”. There are methods of checking all that, but they are, once again, indirect and difficult to make. Very recently there have been detailed studies of spectra of supernovae and comparison of nearby and distant ones, with somewhat surprising results that the spectra actually differ a little. Scientists do not yet know how this difference in spectra would reflect in the absolute brightness, but some relationship should definitely exist. There have also been tests proposed of more fundamental assumptions of cosmological theories, such as the Copernican principle, but they rely on long term measurements and it will take decades until first meaningful results are obtained.

Knowing the amount of problems related to Type Ia supernovae it may be difficult to understand why we still use them as standard candles. The reason is twofold: as I mentioned above, Ia supernovae are the standard candles that extend the furthest into the Universe; in addition, most of the problems of the theoretical understanding of the physics behind the explosion are only marginally significant to their cosmological use. Furthermore, it is usually the case in science that theories are used without having first proven them beyond reasonable doubt, as proving theories is quite often very difficult.

All of this information was probably quite overwhelming, but I hope that I was able to show at least a small glimpse of how many things in science and exploration of the Universe are interconnected and interdependent. While writing, I realised that I should tell a lot of introduction before delving into the main subject area, which increased the length of this article, but hopefully did not get you completely lost. Thank you for reading.