S3C4: The Sun - Syllab

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a) The nature of stars

The first three chapters of this third series centred on our Pale Blue Dot – a reference to a photograph taken in 1990 by the Voyager 1 space probe that also served as title for the excellent namesake book by Carl Sagan [Pale Blue Dot] – and from those it should be strikingly clear that our star, the Sun, played a central role in the emergence of life and still does in its sustenance.

And so, it is time to stare at it, figuratively of course, to understand how it came to be, its inner workings, its impact on the planets orbiting around it, and its future. First things first, what exactly is a star and what type of star is our Sun?

Stars are large astronomical objects held together by the gravitational forces of their own material, which is mostly hydrogen and helium in the form of plasma, the most abundant state of matter in the universe, as previously mentioned in S1 Section 2.e. When I write large, I mean really large in the context of the human scale though not in the context of the universe.

If we except dead, degenerate stars such as white dwarfs and neutron stars that have experienced gravitational collapse – we will revert to this in section c) – the radius of stars varies from about 30,000km at the low end for red dwarfs, less than a tenth of the Sun’s 695,700 kms, and red supergiants such as Betelgeuse at the top end recording a radius of about 700 times that of the Sun. However, size is not the primary variable used to classify stars (according to the MK system); instead stars are assigned a letter and Roman numeral based on their spectral class and luminosity class.

The spectral signature of a star reflects its ionization state and thus, indirectly, the temperature of its outer shell called the photosphere. The hottest stars belong to the O class with temperatures in excess of 30,000 K, the Sun belongs to the intermediary G class with a temperature of nearly 5,800 K in its photosphere, and the lowest rung is class M with temperatures averaging around 3,000 K. As for the luminosity, it is indirectly deduced from the spectral lines: the stars with large surfaces and therefore large radii emit more light so their luminosity is inversely correlated with their surface gravity and therefore the pressure near the surface, and in turn this can be detected through the thickness of the spectral lines (narrower lines means lower pressure). The Sun luminosity falls under class V, the bottom rank among main-sequence stars, and class I is the domain of supergiants – there is even a class 0 or Ia+ for hypergiants. White dwarfs have been affixed the number VII but they are not really stars, at least not any longer, because their core doesn’t experience nuclear fusion. In between, class VI consists of subdwarfs, stars with much less luminosity on account of their low metallicity (not enriched by elements heavier than helium) or because they are in a late stage of their life cycle and have lost their outer hydrogen layers; those are respectively called red and blue subdwarfs.

Lastly, just as all the planets rotate upon themselves, so does the Sun, although it takes a leisurely 25 days to rotate, at the equator. It is necessary to mention the equator because the rotation at its pole is different, it is in excess of 33 days. How is that possible? Simply because the sun is not a solid. This also means the differential in rotation rate and angular momentum will create turbulences within the Sun, which will contribute to the creation of its magnetic field.

b) Sun power

Clearly, it is time to look into the inner structure and working of the Sun. Over 98% of the Sun consists of the two lightest elements: it is about 75% hydrogen and just under 24% helium. As we’ll see in the next section, because it is not a first-generation star, it is enriched by what is called metals in astronomy, a category that encompasses all elements other than hydrogen and helium. In the case of the Sun, and other stars as well, the other elements of note are oxygen, neon, carbon and iron.

At the current stage in its life-cycle, almost all of the Sun power is generated by the thermonuclear fusion of hydrogen into helium through a reaction called proton-proton chain. This is a multi-stage process involving 4 hydrogen atoms with a simple nucleus consisting of only one proton and ending with a helium-4 atom with a nucleus comprising 2 protons and 2 neutrons. To get there, two protons fuse to create deuterium (hydrogen-2) with one proton and one neutron, this is essentially β⁺ decay and the conversion from proton to neutron is accompanied by the emission of a positron and an electron neutrino – something we have seen in S1 Section 7.c – with the positron being annihilated with an electron. Both these steps liberate energy, as does the next one, the fusion of the deuterium nucleus (called deuteron) with another hydrogen atom (i.e. a proton) forming helium-3 and emitting a gamma ray, a radiation with an extremely high photon energy. The final step sees two of those helium-3 fuse to create one atom of helium-4 and 2 freed up protons. I have enclosed the Wikipedia link for this process in the last section for those keen on diving deeper into the physics of it.

The energy to mass yield doesn’t appear to be very high, only 0.7%, but since approximately 600 MT of hydrogen is fused every second, this still translates into a staggering power of ~3.8×10²⁶ watts – frankly this order of magnitude is impossible to wrap our head around, as the entire electricity consumption on Earth in 2022 was about 24,400 terawatt-hour which is equal to 24,400TWh/8,760h per year = 2.78×10¹² watts or less than 1 / 100,000,000,000,000 (1 divided by one hundred trillion) of the Sun’s output. The proton-proton chain is complemented by the CNO cycle where the three letters stand for Carbon, Nitrogen and Oxygen and those three elements only play a catalytic role, it too starts with protons and ends up with helium-4. For the time being, it accounts for less than 1% of our star’s energy production but it does increase as time goes by or at higher temperatures so that it is expected to be the main source of energy for stars with temperature above 17×10⁶ K, which is around 4 times higher than our Sun’s.

Almost all of this energy is produced in what we call the solar core, extending up to a quarter of its radius, and some of it is being transferred outward through thermal radiation, to a layer called the radiative zone starting from the core up to 70% of the radius (starting from the centre). The temperature between the inner and outer boundary of this area drops by a multiple of about 3.5 times, quite significant yet insufficient for heat convection to play a significant role. Not so in the next layer, the convective zone, which extends almost all the way to the surface and sees a drop in temperature from about 2 million kelvins to 5,700K; this 350-fold reduction in temperature is coupled with a dramatically reduced density from 200 kg/m³ down to 0.2 g/m³ at the photosphere, the beginning of the stellar atmosphere – this is about a sixth of the sea-level density of Earth’s atmosphere. The difference in behaviours between the convective and radiative zones creates a transition layer called tachocline where a dynamo effect takes place that could be at the origin of most of the Sun’s magnetic field.

The photosphere constitutes the lowest layer of the stellar atmosphere and the surface that we see. This is because in deeper layers there are too many ionized hydrogen atoms (H^–) to absorb or reemit photons in the visible spectrum of light. The effective temperature of the photosphere is just under 5800K and reaches its lowest level of 4100K at the boundary with the chromosphere which is characterized by a sharp drop in density, a spectral emission dominated by wavelength corresponding to the colour red (it is called H-alpha and is the result of an electron in an hydrogen atom moving down from the third to the second lowest energy level), and a rising temperature gradient, reaching in excess of 30,000K with the next layer called the transition region. The name is fitting because although it is only 200km thick (or thin in the context of the Sun) a couple of important shifts take place: firstly, as heat increases the helium loses an increasing proportion of its electrons and this state of ionization greatly reduces the thermal radiation so that temperature skyrockets up to nearly 1 million K in the upper part, and secondly magnetic forces become the main drivers of motion instead of pressure. The last layer of the stellar atmosphere proper is the intensely hot corona, in the case of our Sun it reaches in excess of 10 million kelvin though there is no solid hypothesis to confidently explain the physical process behind this. What we call the solar wind is a flow of plasma exiting the corona and crossing outside of the heliosphere into interstellar space; these particles have so much energy they are able to escape the star’s gravitational pull. As for the heliosphere, it is both the extent of the Sun’s magnetosphere and the volume of space under the influence of solar wind, so it extends well past the last planets of the solar system and provides a first line of defence by deflecting certain types of cosmic radiations.

Non-living doesn’t mean boring.

c) The life cycle of stars

As stated earlier, the type of reaction dominating the core of a star is partly a function of the stage it is at within its lifecycle, which does not mean it is absolutely correlated with its age because said lifecycle will vary depending on how big and how hot the star is. This is where the stellar classification comes in handy.

The dominant theory regarding the formation of the Sun 4.6 billion years ago is that an existing cloud of particles, mostly hydrogen and helium, would have been compressed by the shock wave emanating from a supernova, essentially the dying of another star. At the centre, the region with highest density would have drawn matter inward under the effect of increasing gravity to the point where, under extremely high pressure and temperature the helium began to fuse, thus entering what is called its main sequence.

Most stars in the known universe are class V (five) and on this main sequence, a technical term corresponding to the plotting of stars depending on their colour index and their absolute magnitude, which is a measure of their luminosity on an inverse logarithmic scale. This is neatly illustrated in Figure 2 that also shows the horizontal branches followed by other classes of stars.

Figure 2: Hertzsprung–Russell diagram

Credit: Richard Powell (CC BY-SA 2.5)

During this period that already lasted a few billion years and will continue for another few, hydrogen fusion will continue to power the Sun with the inward gravitational pull being kept in check by the thermal pressure. Eventually, stars in this stage will run out of hydrogen fuel and move off the main sequence on one of the horizontal branches shown in Figure 2; the larger they are the faster they will exhaust their fuel, thus there is a dramatic difference in the lifespan of stars depending on their mass. For the Sun, we are looking at about 12 billion years, so it is middle-aged and we still have an estimated 7 billion years to go, whereas it is only 11 million years for a star with 10 solar masses (millions, not billions!) and thousands of billions of years for one with a tenth of the mass of the Sun – which means none of these smaller stars has died yet since the universe is thought to be just under 13.8 billion years old.

Back to our Sun and fast forward a few eons to the end of the main sequence when the core is now containing helium with the last bit of hydrogen surrounding it. As fusion in the core tapers out, the thermal pressure becomes insufficient to prevent gravitational collapse of the core, which increases the temperature and permits hydrogen fusion to take place via the CNO cycle but this time in the shell around the core, thereby causing an expansion of the star and an increase in its luminosity. This transition period is called the Subgiant phase and in the case of the Sun, the expansion is expected to be pursued as part of the red-giant-branch (RGB) phase, fed by an increasingly massive and dense helium core, which translates into higher temperature and therefore rate of hydrogen fusion. Stars walking that path are said to be ascending the RGB; such a stellar expression, isn’t it?

By the end of this RGB phase, in an estimated 7.6 billion years, Earth will be engulfed by the Sun as it extends up to 1.2 AU radius (1 AU or Astronomical Unit is the average distance separating the Earth from the Sun, being approx. 149.6 million kms).

Eventually, an RGB will reach what is dubbed “the tip of the red-giant branch”, at which point its luminosity would be 2000 to 2500 times as elevated as that of the Sun currently, and for stars with a mass in between 0.8 and 2.0 times that of the sun, the helium core will undergo nuclear fusion when temperature reaches around 100 million kelvin. This will trigger a runaway reaction called helium flash lasting only a few minutes. Such reaction relies on the triple-alpha process which starts with three helium-4 atoms and ends with one carbon-12 atom and some gamma emission. At its peak, the energy output will be 100 billion times what it was on the main branch; in fact this is so intense that for a few seconds the rate will be comparable to that of our entire Milky Way galaxy, though from the outside nothing so dramatic will be observed as most of the energy allows the core to temporarily come out of degeneracy.

Degeneracy is a rather complex mechanism so, to keep it short, think that at some stage gravitational pressure becomes so great the electrons with low energy states are forced to fill upper energy states because the others are already occupied. Being physically compressed, there comes a point where their kinetic energy prevents further collapse – this is electron degeneracy pressure. However, in case where this threshold is overcome, electrons combine with protons to form neutrons. This results in much more compact atoms and therefore much higher gravitational pressure leading to another gravitational collapse to form neutron stars. Above a certain threshold, the Tolman–Oppenheimer–Volkoff limit, even the neutron degeneracy pressure mediated by the strong force may be insufficient to prevent a final gravitational collapse into what we call a black hole. The state of matter inside such an astronomical entity is an open question.

Our Sun, however, is not massive enough to make it to the neutron star stage, let alone turning into a black hole. Instead, after the helium flash it will continue its progression along the horizontal branch until the helium core is exhausted, at which point its core would mostly consist of carbon and oxygen and would be powered by helium and hydrogen fusion in two distinct layers around the core, processes also called helium and hydrogen burning. This phase is called the asymptotic giant branch (AGB) and is characterised by a luminosity reaching thousands of time that of the Sun currently. A series of thermal pulses will then occur as follows: helium in the shell is burned until exhausted, then hydrogen burning in the outer shell will partially replenish the amount of helium which will start burning again in a flash, causing an expansion and cooling of the star. This will create a temporary interruption to the hydrogen burn which ends up reigniting on the back of the temperature provided by the helium burn. And the cycle repeats. Four of those cycles are predicted for the Sun before, on the back of those temperature shifts and the strong convection they create, a significant amount of the star’s mass ends up being lost in the form of stellar wind. In the final stage, the Sun will shed its non-core envelope, ejecting ionized gas carrying some of the heavier chemical elements manufactured within the star during its lifetime. What will be left is an extremely dense core made mostly of electron degenerate matter called a white dwarf. The white colour is the result of the radiation of trapped heat and, in the case of our Sun, this core would occupy less than the volume of the Earth.

d) Stellar nucleosynthesis

During the course of this chapter, we have alluded a couple of times to the genesis of heavy elements, a process called stellar nucleosynthesis.

If the theory is correct, the first instance of this process occurred as part of the original Big Bang, with deuterium, helium-3, helium-4 and lithium-7 all being created within the first 3 minutes or so. The sequence involves the creation of photons, then electrons and positrons, then neutrons and protons and from there atoms fused to produce deuterium, then helium-3 and helium-4, the latter combining with unstable hydrogen-3 (tritium) to produce lithium-7.

These initial ingredients then coalesced into planets or stars and, within stars, various fusion processes have been taking place to produce further elements, as we have just seen in the previous section. We covered hydrogen burning and helium burning but, in stars significantly more massive than the Sun, other types of fusion can also take place, the first of which is carbon burning.

The conditions required for carbon fusion to take place include temperatures approaching half a billion kelvin and extremely high pressure (in the order of several million tons per cubic metre). The coming together of two carbon-12 atoms results in magnesium-24 which mainly decays into neon-20 + helium-4.

With this neon now available and an even greater temperature, the absorption of gamma rays by neon-20 leads to their disintegration into oxygen-16 + helium-4 and this helium-4 then fuses with some neon-20 to produce magnesium-24 while emitting a gamma ray. This magnesium-24 then fuses with helium-4 to produce silicon-28, a process also accompanied by a gamma ray emission.

Once carbon then neon are exhausted, the fusion process stops and as the core further contracts, the pressure and temperature become sufficiently elevated – we are talking around 2 billion kelvin and north of 3 billion tons per cubic metre here – the oxygen burn starts. The two main reactions are 2 oxygen-16 creating one silicon-28 and one helium-4 or one sulfur-32 plus a gamma ray. This stage lasts anywhere from a few days to a handful of years, mostly as a function of mass.

The last sequence of nuclear fusion is silicon burning and follows the Alpha process which sees the incremental fusing of helium-4 atoms with intermediary products. For silicon burning, it starts with silicon-28 which yields sulphur-32, then we have argon-36, calcium-40, titanium-44, chromium-48 , iron-52 and Nickel-56. The Nickel-56 eventually decays to iron-56 by way of cobalt-56, and as stated in S1 Section 7.b, this is the terminus for stellar cores. In certain cases, the alpha process can start all the way with carbon-12 atoms with intermediary steps being oxygen-16, neon-20 and magnesium-24.

These heavier elements are being contributed to interstellar space, and some are even being formed when stars explode, what we call a supernova. Supernovae are a topic unto itself so for purpose of closing this section, I will only mention the two main types of supernovae: Ia and II. A type Ia supernova is the result of a white dwarf accreting mass from a binary companion star and this will ignite carbon fusion resulting in a runaway thermonuclear reaction liberating sufficient energy to overthrow the gravitational pressure and blow up the star. Different story for Type II which is the result of the explosion of a massive star following the gravitational collapse of the core. The freeing up of energy stemming from this collapse and subsequent rebound creates a shock wave that blows the star apart with the core remnants forming a neutron star and perhaps even a black hole depending on the leftover mass.

e) Trivia – Solar eclipses

From time immemorial the Sun seems to have been an astronomical object of wonder for modern humans who ascribed powers of life and death to it, which in many ways it does have. In fact, in many cultures it was not perceived as an astronomical object as such but as the incarnation of a deity, the Sun God. The best-known examples are arguably Ra in Ancient Egypt and Inti in the Incan empire, though that is because those two civilizations have been a particular source of fascination and it would be safe to wager the Sun had a central place in the mythology of most tribes. Central but not at the centre, this particular spot was reserved for Earth for the simple reason that this is where we live, one more example of anthropocentrism and, to be fair, an understandable one since the Sun does appear to be rising over and setting under the horizon and suggesting the Earth travelled around this luminescent body opened as many issues as it solved, including why the stars in the sky did not appear to move (the distances involved and the size of the cosmos went beyond the imagination of the time) and why the Earth’s rotation was not throwing us off our feet (the concept of gravity was not even close from being developed).

Whether a deity or not, when the Sun disappeared it generally caused the ringing of alarm bells, even as it eventually reappeared a handful of minutes later, or even if it had only been partially masked by the Moon. Such an extraordinary occurrence had to signify something, the behaviour of celestial objects either had to be the expression of displeasure by the god or one of the gods, or the portent of an important event in the near future, an omen. And so it had to be taken seriously and sacrifices or other types of offering were called for.

An interesting aspect of the occurrence of a solar eclipse, and even more so for total eclipses, is that since they are so infrequent at a given location, it is possible to date many documents making references to them. By deduction, it is also possible to date other events that have a clear chronological relationship with these eclipses.

The Sun and the Moon both travel across our sky, however their path is not aligned so they only occasionally occupy the same coordinates with the Moon effectively shielding an observer from the Sun’s rays. It so happens that the ratio between the Sun’s diameter and that of the Moon is identical to the ratio between the distance from the Sun to Earth and from the Moon to Earth: 400. Accordingly, provided the alignment is perfect, the magnitude of the eclipse might be a perfect 1. In fact, these ratios are averages because the orbit of the Moon around Earth and of the Earth around the Sun are elliptical so if an eclipse occurs close to the Moon’s perigee (closest point of the orbit) then the magnitude can be above 1 – the orbit of the Earth around the Sun plays a lesser role in the change in ratio because the Moon orbit eccentricity is 0.0549 and the Earth’s is a well-behaved 0.0167.

In cases of total eclipse, it is possible to observe the solar corona, which is otherwise too faint compared to the photosphere to be distinguished properly. Amazingly, these unusual conditions allowed for scientific discoveries or the testing of hypotheses regarding light. Helium was discovered during the solar eclipse of 18 August 1868 and that of 29 May 1919 saw the carrying out of the Eddington experiment which confirmed the value of the gravitational deflection exerted by the Sun on starlight passing near it, what we call the bending of light. Mind-bending.

a) The nature of stars

b) Sun power

c) The life cycle of stars

d) Stellar nucleosynthesis

e) Trivia – Solar eclipses

f) Further reading (S3C4)