Knowledge in a Nutshell: Astrophysics

Chapter 12 Stellar Evolution

The biggest driver of stellar evolution is the mass of the star. This determines the core temperature via the conversion of gravitational potential energy into thermal energy, and this in turn sharply determines the luminosity of the star. There are three basic relationships, or equations, for stellar evolution. These equations use the Sun as a unit of measurement, so M is the star’s mass in multiples of our Sun’s mass and L is the star’s luminosity in multiples of the Sun’s luminosity. The Sun’s mass is MSun=2×1030 kg (M=1.0) and LSun=4×1026 watts (L=1.0). The temperature (T) is the star’s surface temperature. For the Sun, a typical ‘yellow’ star, T=5770 K.

The first equation describes how the luminosity of a star depends on its surface temperature and radius:

The second equation relates the luminosity of a star to its mass and takes into account that objects within the different mass groups – dwarf star, main sequence star, massive star – behave somewhat differently as their sources of internal energy change:

This final equation relates the available mass of the star in nuclear fuel to the luminosity of the star to give an estimate of the star’s lifetime as it burns hydrogen to helium on the Main Sequence (MS):

The bright star Betelgeuse has a mass of 20 MSun (M=20) and a surface temperature of T=3,500 K. From Equation 1, its radius R is about 1,100 RSuns. Equation 3 its estimated life as a main sequence star is six million years. These properties make this star a red supergiant.

The Main Sequence (MS) lifetime is the longest evolutionary phase that a star experiences during which time it is fusing the most abundant element: hydrogen. Eventually it ‘evolves off’ the MS as it approaches its end of life. Our Sun arrived on the MS about 4.5 billion years ago and so, with an MS lifespan of 12 billion years, it has another 7.5 billion years to go before hydrogen fusion becomes fuel-starved and our Sun evolves dramatically. For red dwarf stars like Proxima Centauri, with masses of 0.12 MSun, this MS time can be 6 trillion years. For massive stars like Rigel, with M=19 MSun, the MS time can be as short as 6 million years. Exactly what happens to a star as it evolves off the Main Sequence depends entirely upon its mass.

Brown Dwarf Stars (0.08 to 0.3 MSun)

These stars have insufficient mass to fuse hydrogen into helium. Because of their low mass, the only support they have against gravitational collapse is via electrostatic repulsion between constituent ions and atoms. This is the same ‘solid body’ force that keeps the atoms in the chair you are sitting on from collapsing into a dense ball of nuclear matter. This inter-atomic, electrostatic repulsion limits their sizes to about that of Jupiter, so their evolution is similar to the evolution of massive, gas-rich planets like Jupiter. As these objects cool, they undergo gravitational contraction to still smaller radii over time. Initially, these ‘failed stars’ may be held up by simple thermal ‘heat’ pressure but very quickly the core of the object under its high pressure becomes what is called a degenerate plasma. Electrons are forced out from their atoms and become a new type of gas whose properties are limited by quantum mechanics. At most two electrons (with opposite spins) can be in the same energy/momentum quantum state. If a plasma reaches the point in pressure and density where all the electron quantum states are completely filled, no further density change can occur. Under these degeneracy conditions, even gravitational collapse cannot overcome the quantum rigidity of this electron plasma and so the object ceases to contract forever. From this time onwards, the object steadily gives up its internal thermal energy and evolves over the course of trillions of years into a solid, cold object at near absolute zero.

Main Sequence Stars (0.4 to 2 Msun)

These stars span the spectral classes from red dwarf M-type stars to very hot A-type stars. The evolution of these stars is extremely complex because as hydrogen fuels become insufficient to prevent gravitational collapse, other nuclear fuels step in as the core temperature increases to alter the progress of evolution. Also, the primary source of energy generation can move temporarily from the core to fuel-rich zones surrounding the core. This also changes the structure and size of the star. The stars in this mass range represent the vast majority of the stars in the Milky Way and evolve in roughly the same way, though the details depend very sensitively on the mass of the star.

When the abundance of hydrogen fuel in the core is depleted by about 20 per cent, the star has already grown slightly in luminosity and size because the steady collapse of the core heats it up and so the fusion reactions run more vigorously. This causes the star to slowly expand. Eventually, the region surrounding the core reaches the triggering temperature for fusion and, from this time forward, hydrogen ‘shell burning’ starts to produce more energy than the core so the star begins to expand rapidly and its outer layers cool. The star has now become an evolving red giant, and will steadily grow in radius and luminosity as its surface temperature remains roughly constant. Meanwhile, these reactions continue to shower the core region with inert helium ‘ash’, which is a by-product of hydrogen fusion. The massive ash core increases in temperature through gravitational collapse until it is possible for three helium nuclei to fuse into a carbon nucleus, a process called the triple-alpha reaction.

For stars in this mass range, the triple-alpha reaction is triggered in a core of matter that is being held up by electron degeneracy pressure. Such a gas does not behave the same way as ordinary gases because instead of the pressure increasing as it is heated, the pressure remains exactly the same as the core heats up. The triple-alpha reaction is triggered literally in a flash, but all this does is to remove the degeneracy effect so the core can temporarily behave as a normal gas. Nevertheless, this has little effect on the star as a whole. With helium burning in the core and hydrogen burning in the shell region, the star has reached its largest size as a red giant. From now on, as the helium is depleted in the core, and with no further fusion sources available to it, the core returns to a degenerate state and the star dramatically contracts in size. Eventually, it will lose its outer layers as a planetary nebula, with only its dense hot degenerate, carbon-rich core left behind as a dim ‘white dwarf’ no larger than our Earth.

Massive Stars (3 MSun to 50 MSun)

These stars are classified as O- and B-type stars and have far more dramatic evolutionary histories. Like the lower-mass stars, they too will deplete their hydrogen fuel reserves, expanding and cooling to become red giants, but by the time core temperatures reach the triple-alpha ignition temperature of about 300 million K, their core regions are not degenerate. The helium burning phase occurs far more gently and the star expands to become a red supergiant. As helium ash is converted to carbon in the core, the shell-burning region also contributes to expanding the star. These stars can be so vast that they would occupy the entire solar system out to the orbit of Neptune.

As the helium ash becomes steadily depleted from conversion into carbon, the core collapses and heats, allowing carbon to be fused into a steadily increasing list of heavier elements thanks to the availability and growing abundances of helium nuclei, and other lower-mass nuclei which can now participate in fusion reactions. With each change, the core grows hotter and the shell-burning layers outside the nucleus become more complex. In fact, the interior becomes a multi-shelled energy production environment with the hydrogen-burning shell being the farthest from the core, followed by a helium-burning shell, a carbon-burning shell and so on. With each change, the star temporarily decreases in luminosity while its surface temperature increases slightly. Then, as the new shell-burning reaction takes over, it again rises back into the domain of the red supergiant. Eventually, as the availability of new nuclei to fuse diminishes, the reactions reach a critical point for the most massive stars.

For the low end of this mass range, the amount of material in the core is comparable to the mass of our Sun. At the same time that the nuclear reactions have been producing gamma-rays that heat the interior, they also produce neutrinos, which escape from the interior within minutes and do not contribute to providing internal pressure. By the time the temperatures become high enough so that iron nuclei become abundant fusion by-products, continued core collapse no longer increases the core energy but instead becomes a mechanism for fragmenting the iron nuclei by gamma-ray interactions. This process, like the neutrino emission, causes substantial energy to be lost from the core and so gravitational collapse begins and overcomes the restraining pressure. As the core region becomes denser and denser within a few minutes of infall, the enormous luminosity of neutrinos becomes suddenly trapped by the dramatic increase in density to near-nuclear levels. This happens so suddenly that this pressure spike causes the star to explode as a ‘Type-II’ supernova. Meanwhile, the ‘equal and opposite force’ causes the core to become compressed.

Lower-mass stars in this range, those with masses between 10 and 30 MSun, leave behind neutron stars. Below 10 MSun they become white dwarfs. But above 30 MSun not even the degeneracy pressure provided by neutrons (quarks) can prevent further collapse, so the supernova remnants continue to collapse until they become black holes (see page 134). This rearrangement happens literally within a few minutes after the star detonates.

The out-flowing plasma is incredibly dense and turbulent. Computer models show that in the brief seconds that this nuclear plasma exists, it creates nearly all the elements in the periodic table. Earlier studies were concerned that this enriched material would recollapse and never be mixed with the interstellar medium. However, modern calculations show that the neutrino pressure is more than sufficient to detonate the star, allowing enormous quantities of matter to reach escape velocity. The most important added factor that made the calculations predict a full detonation of the star was contributed by the electroweak theory developed by physicists Steven Weinberg, Abdus Salam and Howard Georgi in the late 1960s. It was known that the luminosity and energy loss by pre-supernova stars through neutrino emission was gargantuan and of the order of five times the luminosity of our Sun. But neutrinos hardly interact at all with matter so they were unable to deliver this energy to take part in the detonation of the star. What electroweak theory predicted is that there should be a neutral, weak interaction between neutrinos and matter. This turned out to be the missing ingredient. When it was added to the dynamics of the collapsing supernova core, as the density of matter approached nuclear densities, the neutral weak interaction delivered a sudden pulse of new energy and pressure that countered the collapse. But its pressure was so great that it almost instantly pushed the infalling matter outwards with enough energy to cause detonation and the ejection of tens of solar masses of matter into interstellar space.

Neutron Stars

Under high-enough pressure, electrons in a dense plasma can be forced to react with protons to form neutrons. At densities approaching nuclear matter, 1014 g/cc, this material forms neutronized matter consisting of about 5 per cent protons and electrons with 95 per cent as pure neutrons. Like the white dwarfs supported by electron degeneracy pressure, neutrons also produce a quantum degeneracy pressure that stabilizes the object against further collapse. Unlike electron degeneracy pressure mediated by the electromagnetic force, the neutron degeneracy pressure involves the strong nuclear force and the object stabilizes at a size that is 1,000 times smaller than a white dwarf, or about 20 km (12½ miles) across. The object has conserved angular momentum following the supernova explosion and can be rotating hundreds of times a second. The crust is a thin 1 m (3 ft) layer of dense plasma and magnetic fields, which can emit pulses of radio, optical and X-ray energy detectable by astronomers as ‘pulsar’ emission.

The Discovery of Pulsars

Jocelyn Bell Burnell is an Irish astrophysicist who discovered the first pulsar in 1967 as a piece of ‘scruff’ on her data recorder, which had a pulse interval of 1.5 seconds. The radio source was called B1919+21, or also ‘Little Green Man-1’ due to its seemingly artificial nature. Later called a ‘pulsar’, this discovery opened the door on investigating neutron stars and their environments. She was awarded the 2018 Special Breakthrough Prize in Physics but donated the $3 million award ‘to fund women, under-represented ethnic minority and refugee students to become physics researchers’.

Only 5 per cent of the star’s mass consists of electrons and protons, which form a crust less than 2 km (1¼ miles) thick. This crust is subject to ‘starquakes’, which can be observed from Earth as glitches in pulsar radio signals.

There may be as many as 100 million neutron stars in the Milky Way. Only 2,000 are known, primarily because these spinning objects produce pulses of radio radiation that is detectable if aimed directly towards our planet where it can be detected by Earth-based receivers and are therefore called pulsars.

Black holes

The most massive stable neutron star has a theoretical mass of 3.0 MSun and could be produced by a star with under 20 MSun if most of its mass is lost during the supernova phase. For stars leaving behind remnant masses greater than this, the object cannot be stabilized by neutron degeneracy pressure and continues to collapse to become a black hole. These objects have such intense gravitational fields light cannot escape from them and hence would be black to a distant observer. They also distort the geometry of space and time in their vicinity, leading to many complicated effects. Black holes were predicted by Albert Einstein’s 1915 theory of general relativity, and their properties are completely defined by three numbers: mass (M), angular momentum (L), charge (Q). If they are not spinning so that L=0, they are called Schwarzschild black holes and for them their critical radius, called the event horizon, is given by the simple formula R = 2.9 M km, where M is in MSun units. For a remnant the mass of our sun, its event horizon would be at a distance of only 2.9 km (1¾ miles) from its centre.

In almost all cases for young supernovae, the black hole will be at least temporarily surrounded by an accretion disk, that is, a collection of material brought together by the influence of gravity and forming a disk around the black hole. If the black hole is part of a binary star system, this disk can also be formed over time by accreting material from the nearby star. The emission from this disk makes it a very strong X-ray source. These can be distinguished from accretion disks that may form around neutron stars by the energy of the X-rays. Black hole disks are at higher temperature and can produce higher energy (or ‘hard’) X-rays than is the case for neutron stars, which produce lower energy (or ‘soft’) X-rays.

Currently there are 18 known stellar-massed black holes. The closest is V616 Monocerotis with a mass of 11 MSun, located 3,500 light years from the Sun. Estimates suggest that millions of black holes may exist in our Milky Way, but are currently not being ‘fed’ by the accreting interstellar matter necessary to make them detectable.

Hyperstars ( > 50 MSun)

The relationship between mass and lifetime undergoes a huge change for stars with masses above 100 MSun. Within less than 1 million years, the star exhausts its hydrogen and during the next million years or so reaches the point where a supernova explosion takes place. This timescale is so rapid that these stars are almost always found inside or close by the giant molecular clouds out of which they formed. The star may be deeply embedded in the cloud and not even visible at optical wavelengths but can be detected as an intense ultra-luminous infrared ‘star’. If it has broken out of its cloud, it is accompanied by a vast HII region.

Hyperstars continue, and amplify, the trend found in the most massive O-type stars (M=20 MSun). The amount of light emitted by their surfaces is so intense that the pressure of radiation is capable of pushing back at the incoming material. The outer layers of hydrogen have been ejected by the radiation pressure producing intense stellar winds. These stars are known as Wolf–Rayet stars, and their surfaces are rich in helium and carbon convected to the surface from the interior shell-burning zones. Surface temperatures exceed 100,000 K. As powerful ultraviolet sources, they ionize huge volumes of the interstellar medium, provided they are not too embedded in dense cloud material. About 500 of these stars have been found in our own galaxy, and they are among the easiest stars to identify in other galaxies. Wolf–Rayet galaxies have so many of these stars that the light from the galaxy looks like that of a normal WR star.

What remains behind after a hyperstar’s supernova depends on its mass. Below about 150 MSun, their cores collapse to black holes within a rapidly expanding supernova shell. Between about 150 and 250 MSun, a powerful instability occurs in the oxygen-fusing core. The gamma-ray photons are energetic and numerous enough to produce matter–antimatter pairs. This ultimately leads to a detonation that completely destroys the core of the star, leaving nothing behind as a remnant. For masses more than about 250 MSun, the matter–antimatter pair-production instability is not energetic enough to destroy the core. Instead, we end up with another phenomenon: gamma-ray bursts.

As the core region implodes, some may be in a state of rapid rotation so that leading up to the explosion event the core resembles a central core surrounded by a rotating disk of matter. The density of this matter is at near-nuclear densities. When the core collapse event occurs, a massive black hole forms within milliseconds, and the rotating disk of matter acts to ‘focus’ (collimate) a powerful jet of particles along the poles of the rotating disk. This pair of beams blasts through the dense plasma within the body of the star and erupts at the star’s surface, producing a powerful pulse or ‘burst’ of gamma-ray light. The beams may erupt in two opposite directions. If Earth is along the axis of one of these beams, spacecraft will detect a burst of gamma-ray light even when the source is billions of light years distant. Astronomers believe that this is the most likely mechanism for producing the gamma-ray bursts (GRBs) that have been detected all across the sky, since they were first discovered by the Vela military reconnaisance satellites in the 1960s. GRBs are detected among the most distant galaxies in our visible universe, and appear about once every day. Some calculations suggest that up to half the explosion energy can be converted into beams of gamma-rays.

Hyperstars can have masses up to 300 MSun and are very rare within spiral and irregular galaxies in which star formation can take place. At a distance of 2 billion light years, GRB 030329 is the closest GRB detected. The closest potential GRB hyperstar is R136a1 with a mass estimated at 315 MSun. It is located in the Tarantula Nebula in the Large Magellanic Cloud about 160,000 light years from the Sun. This ‘front row seat’ on the evolution of a potential GRB progenitor would be of some concern if Earth were located along the rotation axis of R136a1, which fortunately it is not. The GRB beam that will some day travel along this axis and into the depths of the universe would be capable of ionizing the atmosphere of Earth even at this distance, causing the instant extinction of life on Earth.

Key Points

• The mass of a star determines how it will evolve, how long this process will take, and the luminosity of the star.

• The lowest-mass stars, called Brown Dwarfs, have masses between 0.08 and 0.3 times the sun’s mass and fuse hydrogen into helium so slowly that they can sustain this process for trillions of years.

• Stars like our sun evolve to become white dwarfs and planetary nebula within tens of billions of years.

• Stars with higher masses become supernovae and leave behind neutron stars or black holes depending on whether their masses are below or above about 20 solar masses.

• The most massive stars with upwards of 100 solar masses evolve in only a few million years into supernovae, which can produce gamma ray bursts visible for billions of light years across the universe.