Stars

“Every atom of our bodies has been part of a star, and every informed person should know something of how the stars evolve.”

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I gave the book three stars on goodreads. At times it’s a bit too popular-science-y for me, and I think the level of coverage is a little bit lower than that of some of the other physics books in the ‘A Very Brief Introduction‘ series by Oxford University Press, but on the other hand it did teach me some new things and explained some other things I knew about but did not fully understand before and I’m well aware that it can be really hard to strike the right balance when writing books like these. I don’t like it when authors employ analogies instead of equations to explain stuff, but on the other hand I’ve seen some of the relevant equations before, e.g. in the context of IAS lectures, so I was okay with skipping some of the math because I know how the math here can really blow up in your face fast – and it’s not like this book has no math or equations, but I think it’s the kind of math most people should be able to deal with. It’s a decent introduction to the topic, and I must admit I have yet really to be significantly disappointed in a book from the physics part of this OUP series – they’re good books, readable and interesting.

Below I have added some quotes and observations from the book, as well as some relevant links to material or people covered in the book. Some of the links below I have also added previously when covering other books in the physics series, but I do not really care about that as I try to cover each book separately; the two main ideas behind adding links of this kind are: 1) to remind me which topics (…which I was unable to cover in detail in the post using quotes, because there’s too much stuff to cover in the book for that to make sense…) were covered in the book, and: 2) to give people who might be interested in reading the book an idea of which topics are covered therein; if I neglected to add relevant links simply because such topics were also covered in other books I’ve covered here, the link collection would not accomplish what I’d like it to accomplish. The link collection was gathered while I was reading the book (I was bookmarking relevant wiki articles along the way while reading the book), whereas the quotes included in the post were only added to the post after I had finished adding the links from the link collection; I am well aware that some topics covered in the quotes of the book are also covered in the link collection, but I didn’t care enough about this ‘double coverage of topics’ to remove those links that refer to material also covered in my quotes in this post from the link collection.

I think the part of the book coverage related to finding good quotes to include in this post was harder than it has been in the context of some of the other physics books I’ve covered recently, because the author goes into quite some detail explaining some specific dynamics of star evolution which are not easy to boil down to a short quote which is still meaningful to people who do not know the context. The fact that he does go into those details was of course part of the reason why I liked the book.

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“[W]e cannot consider heat energy in isolation from the other large energy store that the Sun has – gravity. Clearly, gravity is an energy source, since if it were not for the resistance of gas pressure, it would make all the Sun’s gas move inwards at high speed. So heat and gravity are both potential sources of energy, and must be related by the need to keep the Sun in equilibrium. As the Sun tries to cool down, energy must be swapped between these two forms to keep the Sun in balance […] the heat energy inside the Sun is not enough to spread all of its contents out over space and destroy it as an identifiable object. The Sun is gravitationally bound – its heat energy is significant, but cannot supply enough energy to loosen gravity’s grip, and unbind the Sun. This means that when pressure balances gravity for any system (as in the Sun), the total heat energy T is always slightly less than that needed (V) to disperse it. In fact, it turns out to be exactly half of what would be needed for this dispersal, so that 2T + V = 0, or V = −2 T. The quantities T and V have opposite signs, because energy has to be supplied to overcome gravity, that is, you have to use T to try to cancel some of V. […] you need to supply energy to a star in order to overcome its gravity and disperse all of its gas to infinity. In line with this, the star’s total energy (thermal plus gravitational) is E = T + V = −T, that is, the total energy is minus its thermal energy, and so is itself negative. That is, a star is a gravitationally bound object. Whenever the system changes slowly enough that pressure always balances gravity, these two energies always have to be in this 1:2 ratio. […] This reasoning shows that cooling, shrinking, and heating up all go together, that is, as the Sun tries to cool down, its interior heats up. […] Because E = –T, when the star loses energy (by radiating), making its total energy E more negative, the thermal energy T gets more positive, that is, losing energy makes the star heat up. […] This result, that stars heat up when they try to cool, is central to understanding why stars evolve.”

“[T]he whole of chemistry is simply the science of electromagnetic interaction of atoms with each other. Specifically, chemistry is what happens when electrons stick atoms together to make molecules. The electrons doing the sticking are the outer ones, those furthest from the nucleus. The physical rules governing the arrangement of electrons around the nucleus mean that atoms divide into families characterized by their outer electron configurations. Since the outer electrons specify the chemical properties of the elements, these families have similar chemistry. This is the origin of the periodic table of the elements. In this sense, chemistry is just a specialized branch of physics. […] atoms can combine, or react, in many different ways. A chemical reaction means that the electrons sticking atoms together are rearranging themselves. When this happens, electromagnetic energy may be released, […] or an energy supply may be needed […] Just as we measured gravitational binding energy as the amount of energy needed to disperse a body against the force of its own gravity, molecules have electromagnetic binding energies measured by the energies of the orbiting electrons holding them together. […] changes of electronic binding only produce chemical energy yields, which are far too small to power stars. […] Converting hydrogen into helium is about 15 million times more effective than burning oil. This is because strong nuclear forces are so much more powerful than electromagnetic forces.”

“[T]here are two chains of reactions which can convert hydrogen to helium. The rate at which they occur is in both cases quite sensitive to the gas density, varying as its square, but extremely sensitive to the gas temperature […] If the temperature is below a certain threshold value, the total energy output from hydrogen burning is completely negligible. If the temperature rises only slightly above this threshold, the energy output becomes enormous. It becomes so enormous that the effect of all this energy hitting the gas in the star’s centre is life-threatening to it. […] energy is related to mass. So being hit by energy is like being hit by mass: luminous energy exerts a pressure. For a luminosity above a certain limiting value related to the star’s mass, the pressure will blow it apart. […] The central temperature of the Sun, and stars like it, must be almost precisely at the threshold value. It is this temperature sensitivity which fixes the Sun’s central temperature at the value of ten million degrees […] All stars burning hydrogen in their centres must have temperatures close to this value. […] central temperature [is] roughly proportional to the ratio of mass to radius [and this means that] the radius of a hydrogen-burning star is approximately proportional to its mass […] You might wonder how the star ‘knows’ that its radius is supposed to have this value. This is simple: if the radius is too large, the star’s central temperature is too low to produce any nuclear luminosity at all. […] the star will shrink in an attempt to provide the luminosity from its gravitational binding energy. But this shrinking is just what it needs to adjust the temperature in its centre to the right value to start hydrogen burning and produce exactly the right luminosity. Similarly, if the star’s radius is slightly too small, its nuclear luminosity will grow very rapidly. This increases the radiation pressure, and forces the star to expand, again back to the right radius and so the right luminosity. These simple arguments show that the star’s structure is self-adjusting, and therefore extremely stable […] The basis of this stability is the sensitivity of the nuclear luminosity to temperature and so radius, which controls it like a thermostat.”

“Hydrogen burning produces a dense and growing ball of helium at the star’s centre. […] the star has a weight problem to solve – the helium ball feels its own weight, and that of all the rest of the star as well. A similar effect led to the ignition of hydrogen in the first place […] we can see what happens as the core mass grows. Let’s imagine that the core mass has doubled. Then the core radius also doubles, and its volume grows by a factor 2 × 2 × 2 = 8. This is a bigger factor than the mass growth, so the density is 2/(2 × 2 × 2) = 1/4 of its original value. We end with the surprising result that as the helium core mass grows in time, its central number density drops. […] Because pressure is proportional to density, the central pressure of the core drops also […] Since the density of the hydrogen envelope does not change over time, […] the helium core becomes less and less able to cope with its weight problem as its mass increases. […] The end result is that once the helium core contains more than about 10% of the star’s mass, its pressure is too low to support the weight of the star, and things have to change drastically. […] massive stars have much shorter main-sequence lifetimes, decreasing like the inverse square of their masses […] A star near the minimum main-sequence mass of one-tenth of the Sun’s has an unimaginably long lifetime of almost 10¹³ years, nearly a thousand times the Sun’s. All low-mass stars are still in the first flush of youth. This is the fundamental fact of stellar life: massive stars have short lives, and low-mass stars live almost forever – certainly far longer than the current age of the Universe.”

“We have met all three […] timescales [see links below – US] for the Sun. The nuclear time is ten billion years, the thermal timescale is thirty million years, and the dynamical one […] just half an hour. […] Each timescale says how long the star takes to react to changes of the given type. The dynamical time tells us that if we mess up the hydrostatic balance between pressure and weight, the star will react by moving its mass around for a few dynamical times (in the Sun’s case, a few hours) and then settle down to a new state in which pressure and weight are in balance. And because this time is so short compared with the thermal time, the stellar material will not have lost or gained any significant amount of heat, but simply carried this around […] although the star quickly finds a new hydrostatic equilibrium, this will not correspond to thermal equilibrium, where heat moves smoothly outwards through the star at precisely the rate determined by the nuclear reactions deep in the centre. Instead, some bits of the star will be too cool to pass all this heat on outwards, and some will be too hot to absorb much of it. Over a thermal timescale (a few tens of millions of years in the Sun), the cool parts will absorb the extra heat they need from the stellar radiation field, and the hot parts rid themselves of the excess they have, until we again reach a new state of thermal equilibrium. Finally, the nuclear timescale tells us the time over which the star synthesizes new chemical elements, radiating the released energy into space.”

“[S]tars can end their lives in just one of three possible ways: white dwarf, neutron star, or black hole.”

“Stars live a long time, but must eventually die. Their stores of nuclear energy are finite, so they cannot shine forever. […] they are forced onwards through a succession of evolutionary states because the virial theorem connects gravity with thermodynamics and prevents them from cooling down. So main-sequence dwarfs inexorably become red giants, and then supergiants. What breaks this chain? Its crucial link is that the pressure supporting a star depends on how hot it is. This link would snap if the star was instead held up by a pressure which did not care about its heat content. Finally freed from the demand to stay hot to support itself, a star like this would slowly cool down and die. This would be an endpoint for stellar evolution. […] Electron degeneracy pressure does not depend on temperature, only density. […] one possible endpoint of stellar evolution arises when a star is so compressed that electron degeneracy is its main form of pressure. […] [Once] the star is a supergiant […] a lot of its mass is in a hugely extended envelope, several hundred times the Sun’s radius. Because of this vast size, the gravity tying the envelope to the core is very weak. […] Even quite small outward forces can easily overcome this feeble pull and liberate mass from the envelope, so a lot of the star’s mass is blown out into space. Eventually, almost the entire remaining envelope is ejected as a roughly spherical cloud of gas. The core quickly exhausts the thin shell of nuclear-burning material on its surface. Now gravity makes the core contract in on itself and become denser, increasing the electron degeneracy pressure further. The core ends as an extremely compact star, with a radius similar to the Earth’s, but a mass similar to the Sun, supported by this pressure. This is a white dwarf. […] Even though its surface is at least initially hot, its small surface means that it is faint. […] White dwarfs cannot start nuclear reactions, so eventually they must cool down and become dark, cold, dead objects. But before this happens, they still glow from the heat energy left over from their earlier evolution, slowly getting fainter. Astronomers observe many white dwarfs in the sky, suggesting that this is how a large fraction of all stars end their lives. […] Stars with an initial mass more than about seven times the Sun’s cannot end as white dwarfs.”

“In many ways, a neutron star is a vastly more compact version of a white dwarf, with the fundamental difference that its pressure arises from degenerate neutrons, not degenerate electrons. One can show that the ratio of the two stellar radii, with white dwarfs about one thousand times bigger than the 10 kilometres of a neutron star, is actually just the ratio of neutron to electron mass.”

“Most massive stars are not isolated, but part of a binary system […]. If one is a normal star, and the other a neutron star, and the binary is not very wide, there are ways for gas to fall from the normal star on to the neutron star. […] Accretion on to very compact objects like neutron stars almost always occurs through a disc, since the gas that falls in always has some rotation. […] a star’s luminosity cannot be bigger than the Eddington limit. At this limit, the pressure of the radiation balances the star’s gravity at its surface, so any more luminosity blows matter off the star. The same sort of limit must apply to accretion: if this tries to make too high a luminosity, radiation pressure will tend to blow away the rest of the gas that is trying to fall in, and so reduce the luminosity until it is below the limit. […] a neutron star is only 10 kilometres in radius, compared with the 700,000 kilometres of the Sun. This can only happen if this very small surface gets very hot. The surface of a healthily accreting neutron star reaches about 10 million degrees, compared with the 6,000 or so of the Sun. […] The radiation from such intensely hot surfaces comes out at much shorter wavelengths than the visible emission from the Sun – the surfaces of a neutron star and its accretion disc emit photons that are much more energetic than those of visible light. Accreting neutron stars and black holes make X-rays.”

“[S]tar formation […] is harder to understand than any other part of stellar evolution. So we use our knowledge of the later stages of stellar evolution to help us understand star formation. Working backwards in this way is a very common procedure in astronomy […] We know much less about how stars form than we do about any later part of their evolution. […] The cyclic nature of star formation, with stars being born from matter chemically enriched by earlier generations, and expelling still more processed material into space as they die, defines a cosmic epoch – the epoch of stars. The end of this epoch will arrive only when the stars have turned all the normal matter of the Universe into iron, and left it locked in dead remnants such as black holes.”

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Stellar evolution.
Gustav Kirchhoff.
Robert Bunsen.
Joseph von Fraunhofer.
Spectrograph.
Absorption spectroscopy.
Emission spectrum.
Doppler effect.
Parallax.
Stellar luminosity.
Cecilia Payne-Gaposchkin.
Ejnar Hertzsprung/Henry Norris Russell/Hertzsprung–Russell diagram.
Red giant.
White dwarf (featured article).
Main sequence (featured article).
Gravity/Electrostatics/Strong nuclear force.
Pressure/Boyle’s law/Charles’s law.
Hermann von Helmholtz.
William Thomson (Kelvin).
Gravitational binding energy.
Thermal energy/Gravitational energy.
Virial theorem.
Kelvin-Helmholtz time scale.
Chemical energy/Bond-dissociation energy.
Nuclear binding energy.
Nuclear fusion.
Heisenberg’s uncertainty principle.
Quantum tunnelling.
Pauli exclusion principle.
Eddington limit.
Convection.
Electron degeneracy pressure.
Nuclear timescale.
Number density.
Dynamical timescale/free-fall time.
Hydrostatic equilibrium/Thermal equilibrium.
Core collapse.
Hertzsprung gap.
Supergiant star.
Chandrasekhar limit.
Core-collapse supernova (‘good article’).
Crab Nebula.
Stellar nucleosynthesis.
Neutron star.
Schwarzschild radius.
Black hole (‘good article’).
Roy Kerr.
Pulsar.
Jocelyn Bell.
Anthony Hewish.
Accretion/Accretion disk.
X-ray binary.
Binary star evolution.
SS 433.
Gamma ray burst.
Hubble’s law/Hubble time.
Cosmic distance ladder/Standard candle/Cepheid variable.
Star formation.
Pillars of Creation.
Jeans instability.
Initial mass function.