Chapter 13

This chapter was copied with permission from Nick Strobel’s Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version. This chapter has been edited for content. Paragraphs that have been altered from the original text are denoted in green font.

Lives and Deaths of Stars

This chapter covers: stellar development (all nine stages) and stellar remnants (white dwarfs, neutron stars, black holes).

13.1 Introduction

Stars live for a very long time compared to human lifetimes. Your great, great grandparents saw the same stars as you will see tonight (if it’s clear). Our lifetimes are measured in years. Star lifetimes are measured in millions of years. Even though star timescales are enormous, it is possible to know how stars are born, live, and die. This chapter covers the stages a star will go through in its life and how it was figured out. The last part of the chapter will cover the remains of stars, white dwarfs, neutron stars, and the Hollywood favorite: black holes. The vocabulary terms are in boldface.

13.2 Stellar Development

The development of individual stars over their lifetimes is often compared to human stages of development: stars are born, they live for a certain amount of time, and they die. Astronomers refer to this development as stellar evolution. The word “evolution” has a connotation from biology of a population gradually turning into something else over very long periods of time; however, this is not the case in stellar astronomy. The first thing to keep in mind is that while the millions or billions of years that comprise stellar lifetimes seem like very long periods of time compared to the lifetimes of living organisms on Earth, these are not extraordinary periods of time in astronomy. The most important thing to have in mind for this chapter is that the word evolution in this context simply means the changes an individual star experiences as it proceeds along its life track, much the same way an individual human “evolves” from an infant to an adult to an elderly person in the last stage of his or her life. Stellar evolution is in no way related to biological evolution, and does not imply the same sort of process taking place within populations of stars. It is important to remember this as you proceed through the rest of this textbook, and especially if you decide to go further in your study of astronomy. You will encounter the word evolution many times in modern astronomy, but it is always in the context of an individual object changing as a result of aging or undergoing an event, such as an interaction with another object. With this in mind, the more common term stellar evolution will be used instead of stellar development for the rest of this chapter. 

In the previous chapter you found that mass was an important quantity for determining what stars are like. In fact, all of the other aspects of a star such as its luminosity, temperature, size, density, etc., can be explained using the fundamental property of a star: its mass. There is also a slight dependence of the luminosity, temperature, size, etc. on the composition of the star, but because stars are all mostly hydrogen and helium, the star’s mass is the important quantity.

13.2.1 Mass Dependence

The stages a star will go through and how long it will last in each stage also depend on the mass (with just little bit of dependence on composition). Massive stars evolve quicker than light stars. In the previous chapter, the relationship between the luminosity and mass was explained using basic principles of how compressed gases behave. Slight increases in mass produce large increases in the luminosities of stars.

Stars shine because of nuclear fusion reactions in their core. The more luminous they are, the more reactions are taking place in their cores. Massive stars live shorter lives than the common small stars because even though they have a larger amount of hydrogen for nuclear reactions, their rate of consuming their fuel is very much greater. The massive stars are analogous to the big, gas-guzzling automobiles with big gas tanks of a few decades ago and the small stars are analogous to the small economy automobiles of today that are frugal with their gasoline.

It is a simple calculation to find out how long something can continue consuming fuel. The lifetime = amount of fuel/consumption rate. If your car has a full 15-gallon gas tank and it consumes 2 gallons/hour on the highway, then your car can travel for 15 gallons/(2 gallons/hour) = 7.5 hours. Stars are the same way. The amount of fuel for nuclear fusion is proportional to the total mass of the star when it first started producing energy from nuclear reactions, so the amount of fuel = k × initial mass. The consumption rate is simply the star’s luminosity, so the star will live as a main sequence star for an amount of time = k × initial mass/luminosity. If the star masses and luminosity are in units relative to the Sun, then the star’s lifetime = mass/luminosity × 1010 years. Recall that the Sun’s will live for ten billion (1010) years before it runs out of hydrogen in its core.

In order to remain stable via hydrostatic equilibrium, a star’s luminosity increases with mass as (the star’s mass)p. The value of the exponent p varies between 3 and 4. For the rare massive stars (M* > 30 Msun), p = 3 and for the more common low-mass stars (M* < 10 Msun), p = 4. You can use the mass-luminosity relation to find the star’s lifetime in terms of just its initial mass. The lifetime = mass/luminosity × 1010 years is simply = (star’s mass)/[(star’s mass)p] × 1010 years = 1/(star’s mass)p-1 × 1010 years. Remember that the star’s mass is in solar masses.

How do you do that?

A 5 solar mass star has only five times more hydrogen fuel than the Sun, but (the star’s luminosity)/(the Sun’s luminosity) = (5/1)4= 625! Its lifetime = 1/(5/1)(4-1) × 1010 years = (1/125) × 1010 years = 8.0 × 107 years.

Some representative lifetimes for other stars are given in the table below. Stars that have fewer elements heavier than helium in them compared to other stars, will have slightly shorter lifetimes than those given in the table.

star mass (solar masses) time (years) Spectral type
60 3 million O3
30 11 million O7
10 32 million B4
3 370 million A5
1.5 3 billion F5
1 10 billion G2 (Sun)
0.1 1000’s billions M7

13.2.2 The Basic Scheme

All stars follow the same basic series of steps in their lives: Gas Cloud to Main Sequence to Red Giant to (Planetary Nebula or Supernova) to Remnant. How long a star lasts in each stage, whether a planetary nebula forms or a spectacular supernova occurs, and what type of remnant will form depends on the initial mass of the star.


Evolution of stars depends on their mass (at start of fusion only)*

*with a tiny bit of dependence on chemical composition

What follows is a description of each of these stages.

13.2.2.1 Stage 1: Giant Molecular Cloud

A giant molecular cloud is a large, dense gas cloud (with dust) that is cold enough for molecules to form. Thousands of giant molecular clouds exist in the disk part of our galaxy. Each giant molecular cloud has 100,000’s to a few million solar masses of material.

Orion Nebula and its location
AAO source

One nearby example is the Orion Molecular Cloud Complex that stretches from the belt of the Orion constellation to his sword of which the Orion Nebula is a part. The Orion Complex is about 1340 light years away, several hundred light years across, and has enough material to form many tens of thousands of suns. The giant molecular clouds have dust in them to shield the densest parts of them from the harsh radiation of nearby stars so that molecules can form in them. Therefore, they are very dark and very cold with a temperature of only about 10 K. In addition to the most common molecule, molecular hydrogen, over 80 other molecules have been discovered in the clouds from simple ones like carbon monoxide to complex organic molecules such as methanol and acetone. Radio telescopes are used to observe these very dark, cold clouds. The clouds are dense relative to the rest of the gas between the stars but are still much less dense than the atmosphere of a planet. Typical cloud densities are 100 to 1000 molecules per cubic centimeter while each cubic centimeter of the air you breath has about 2.5 × 1019 molecules—a molecular cloud is tens to hundreds of times “emptier” than the best vacuum chambers we have on Earth!

In the parts of a giant molecular cloud where very hot stars (O and B-type) have formed, the hydrogen gas surrounding them can be made to glow in the visible band to make what is called a H II region. The Orion Nebula is an example of this. It is the fuzzy patch you can see in the sword part of the Orion constellation. It is a bubble about 26 light years across that has burst out of one side of the Orion Complex.

formation of the Orion Nebula in the Orion Complex

The nebula is lit up by the fluorescence of the hydrogen gas around a O-type star in the Trapezium cluster of four stars at the heart of the nebula. The O-type star is so hot that it produces a large amount of ultraviolet light. The ultraviolet light ionizes the surrounding hydrogen gas. When the electrons recombine with the hydrogen nuclei, they produce visible light. Several still-forming stars are seen close to the Trapezium stars. They appear as oblong blobs in the figure below with their long axis pointed toward the hot Trapezium stars. If you select the image, an expanded view of the Trapezium cluster will appear in another window. Both images are from the Hubble Space Telescope (courtesy of Space Telescope Science Institute).

HST view of Trapezium

H II regions mark sites of star formation because they are formed by hot, young stars. Recall from the table at the beginning of the chapter that O-type stars live just a few million years, a very short time for a star! They do not live long enough to move out from where they were formed. Behind the visible part of the Orion Nebula is a much denser region of gas and dust that is cool enough for molecules to form. Several hundred stars are now forming inside the Orion Nebula.

Fragments of giant molecular clouds with tens to hundreds of solar masses of material a piece will start collapsing for some reason all at about the same time. Possible trigger mechanisms could be a shock wave from the explosion of a nearby massive star at its death or from the passage of the cloud through regions of more intense gravity as found in the spiral arms of spiral galaxies. These shock waves compress the gas clouds enough for them to gravitationally collapse. Gas clouds may start to collapse without any outside force if they are cool enough and massive enough to spontaneously collapse. Whatever the reason, the result is the same: gas clumps compress to become protostars.

13.2.2.2 Stage 2: Protostar

As a gas clump collapses it heats up because the gas particles run into each other. The energy the gas particles had from falling under the force of gravity gets converted to heat energy. The gas clump becomes warm enough to produce a lot of infrared and microwave radiation. At this stage the warm clump is called a protostar. The gas clump forms a disk with the protostar in the center. Other material in the disk may coalesce to form another star or planets.

A protostar will reach a temperature of 2000 to 3000 K, hot enough to glow a dull red with most of its energy in the infrared. The cocoon of gas and dust surrounding them blocks the visible light. The surrounding dust warms up enough to produce copious amounts of infrared and the cooler dust further out glows with microwave energy. This longer wavelength electromagnetic radiation can pass through the dust. The infrared telescopes are able to observe the protostars themselves and their cocoons in dust clouds in our galaxy while the microwave telescopes probe the surrounding regions. The power of infrared detectors is illustrated in the images below. The part of the nebula above and to the right of the Trapezium stars is actually forming many stars. They can only be seen in the infrared image on the right side of the figure. If you select the figure, an expanded view will appear in another window. Both images are from the Hubble Space Telescope (courtesy of Space Telescope Science Institute).

HST view of OMC1 in IR

The low-mass protostars (those up to about 5 solar masses) are initially much more luminous than the main sequence star they will become because of their large surface area. As these low-mass protostars collapse, they decrease in luminosity while staying at roughly a constant surface temperature. A star remains in the protostar stage for only a short time, so it is hard to catch many stars in that stage of their life. More massive protostars collapse quicker than less massive ones. Fusion starts in the core and the outward pressure from those reactions stops the core from collapsing any further. But material from the surrounding cloud continues to fall onto the protostar. Most of the energy produced by the protostar is from the gravitational collapse of the cloud material.

Young stars are social—fragmentation of the giant molecular cloud produces protostars that form at about the same time. Stars are observed to be born in clusters. Other corroborating evidence for this is that there are no isolated young stars. This observation is important because a valuable test of the stellar evolution models is the comparison of the models with star clusters. That analysis is based on the assumption that the stars in the clusters used to validate the models all formed at about the same time.

evaporating protostars

The Hubble Space Telescope has directly observed protostars in the Orion Nebula and the Eagle Nebula (in the Serpens constellation). The protostars it has observed have been prematurely exposed. The intense radiation from nearby hot O or B-type stars has evaporated the dust and driven away the gas around the smaller still-forming stars. In more than one case in the Orion Nebula, all of the gas has been blown away to leave just the dark dust disk with the protostar in the center. One example of a totally exposed dust disk seen almost face-on is shown in the figure above. It is the black spot to the right of the prominent cocoon nebula around the protostar at the center. The teardrop-shaped cocoon nebula around the center protostar is oriented toward the Trapezium stars to the right of the figure above. The evaporation of the dark, dense fingers of dust and gas in the Eagle Nebula was captured in the famous “gas pillars” picture on the right side of the figure below. Selecting the figure will bring up an expanded view of the Hubble Space Telescope image in another window (courtesy of Space Telescope Science Institute). Note that the tiniest fingers you see sticking out of the sides of the pillars are larger than our entire solar system!

Eagle Nebula from ground and space

AAO imageHST image

A nice interactive showing how the iconic “Pillars of Creation” image from HST was created from putting together various filter images is the The Pillars of Creation interactive from NOVA’s Origins series that was broadcast on PBS (selecting the link will bring it up in another window).

Another beautiful example from the Hubble Space Telescope is the huge panoramic image of the Carina Nebula released by the Space Telescope Science Institute in mid-2007. This nebula has at least a dozen stars that are 50 to 100 times the mass of the Sun and plenty of Bok globules, pillars, jets from forming stars. For this one you need to sample various parts of the image available from the link.

13.2.2.3 Stage 3: T-Tauri

The young star will produce strong winds in the T-Tauri stage, named after the prototype star in the constellation Taurus. These strong winds eject much of the surrounding cocoon gas and dust. The winds are constrained to flow preferentially along the rotation axes by the disk of dust and gas. With most of the cocoon gas blown away, the forming star itself becomes visible to the outside for the first time. The HST images below show jets shooting out from three young stars. The disk around one star is seen in the top left frame. Select the image to get an enlarged view in another window. The scale in the bottom left corner of each frame represents 150 billion kilometers, or 1,000 times the distance between Earth and the Sun (over twelve times Pluto’s entire orbit; courtesy of Space Telescope Science Institute).

Jets from young stars

13.2.2.4 Stage 4: Main Sequence

Eventually the star becomes stable because hydrostatic equilibrium has been established. The star settles down to spend about 90% of its life as a main sequence star. It is fusing hydrogen to form helium in the core.

Stars initially begin their lives near other stars in a cluster. After a few orbits around the galactic center, gravitational tugs from other stars in the galaxy cause the stars in the cluster to wander away from their cluster and live their lives alone or with perhaps one or two companions. The Pleiades are a young cluster of stars easily visible in the shoulder of the Taurus (the Bull) constellation during the winter months. They are about 80 million years old (compare that to our Sun which is 4,600 million = 4.6 billion years old!). The gas and dust around the stars may be residual material from their formation or simply interstellar clouds the cluster is passing through.

the Pleiades

A star remains at a given spectral type during the entire main sequence stage—the main sequence is not an evolutionary sequence. For example, a F-type star formed as a F-type star and will remain a F-type star during the entire main sequence stage. Only if the star has a very close companion may a change occur if gas is transferred between the stars in the system. The main sequence star does slowly increase in luminosity with only a slight change in its surface temperature as the helium builds up in its core. Our Sun’s luminosity is now about 30% more than when it formed.

star birth stages

13.2.2.5 Stage 5: Subgiant, Red Giant, Supergiant

All through the long main sequence stage, the relentless compression of gravity is balanced by the outward pressure from the nuclear fusion reactions in the core. Eventually the hydrogen in the core is all converted to helium and the nuclear reactions stop. Gravity takes over and the core shrinks. The layers outside the core collapse too, the ones closer to the center collapse quicker than the ones near the surface. As the layers collapses, the gas compresses and heats up.

Eventually, the layer just outside the core called the “shell layer” gets hot and dense enough for fusion to start. The fusion in the layer just outside the core is called shell burning. This fusion is very rapid because the shell layer is still compressing and increasing in temperature. The luminosity of the star increases from its main sequence value. The gas envelope surrounding the core puffs outward under the action of the extra outward pressure. As the star begins to expand it becomes a subgiant and then a red giant.

The Sun becomes a red giant

At the bloated out surface, the increased amount of energy is spread out over a larger area so each square centimeter will be cooler. The surface will have a red color because it is so cool and it will be much further from the center than during the main sequence. Despite its cooler surface temperature, the red giant is very luminous because of its huge surface area. When the Sun becomes a red giant, Mercury and Venus will be swallowed up by the Sun and perhaps the Earth will too. Even if the Earth is not swallowed up, conditions on its surface will become impossible for life to exist. The Sun’s increased luminosity will heat the Earth’s surface so much that the water oceans and atmosphere will evaporate away. Massive main sequence stars will expand much further to become supergiants. Betelgeuse, the bright red star in the top left corner of the Orion constellation, is an example of a supergiant star. If placed at the center of our solar system, all of the planets out to Jupiter would be inside Betelgeuse. A few supergiants are even larger than Betelgeuse!

Betelgeuse and its locationHST image

Red giants can have strong “winds” that dispel more mass than all of the stellar winds that occurred during the long main sequence stage. However, most of the star’s mass will be lost in the “last gasp” stage (planetary nebula or supernova) described below. All through the star’s life after it first started nuclear reactions, it has been losing mass as it converted some mass to energy and other mass was lost in the winds. This means that even though a red giant is large in terms of linear size, it is less massive than the main sequence star it came from. A red giant has the extremes in temperature and density: its surface is cold and very low density, while its core is very hot and extremely dense.

13.2.2.6 Stage 6: Core fusion

If the star is massive enough, gravity can compress the core enough to create high enough temperatures, 100 million K, to start fusing helium, or temperatures of billions of Kelvin to fuse heavier elements if it is repeating this stage. In low mass stars (like the Sun), the onset of helium fusion can be very rapid, producing a burst of energy called a helium flash. Eventually the reaction rate settles down. Fusion in the core during this stage releases more energy/second than the core fusion of the main sequence stage, so the star is bigger, but stable! Hydrostatic equilibrium is restored until the core fuel runs out.

Stars entering and leaving this stage can create conditions in their interiors that trap their radiated energy in their outer layers. The outward thermal pressure increases enough to expand the outer layers of the star. The trapped energy is able to escape when the outer layers are expanded and the thermal pressure drops. Gravity takes over and the star shrinks, but it shrinks beyond the equilibrium point. The energy becomes trapped again and the cycle continues.

In ordinary stars hydrostatic equilibrium works to dampen (diminish) the pulsations. But stars entering and leaving stage 6 can briefly (in terms of star lifetimes!) create conditions where the pressure and gravity are out of sync and the pulsations continue for a time. The larger, more luminous stars will pulsate with longer periods than the smaller, fainter stars because gravity takes longer to pull the more extended outer layers of the larger stars back. The period-luminosity relation can be used to determine the distances of these luminous stars from the inverse square law of light brightness. Stars of this type are called Cepheid variables, a very important kind of star for setting the scale of the universe, discussed in the Milky Way chapter.

NGC 3603 captures star life cycle

This picture of NGC 3603 from the Hubble Space Telescope (courtesy of Space Telescope Science Institute) captures the life cycle of stars in a single view. From lower right to upper left you see: dark clouds and a giant gaseous pillar with embryo stars at the tip to circumstellar disks around young stars to main sequence stars in a cluster at center to a supergiant with a ring and bipolar outflow at upper left of center near the end of the life cycle.

13.2.2.7 Stage 7: Red Giant or Supergiant

When the core fuel runs out again, the core resumes its collapse. If the star is massive enough, it will repeat stage 5. The number of times a star can cycle through stages 5 to 6 to 7 depends on the mass of the star. Each time through the cycle, the star creates new heavier elements in its core (stage 6) from the ash of fusion reactions in the previous cycle. This creation of heavier elements from lighter elements is called stellar nucleosynthesis. For the most massive stars, this continues up to the production of iron in the core. Stars like our Sun will synthesize elements only up to carbon and oxygen in their cores. Each repeat of stages 5 to 6 to 7 occurs over a shorter time period than the previous repeat. Carbon fusion occurs at about 600 million K, Neon fusion occurs at about 1.2 billion K, Oxygen fusion occurs at about 1.5 billion K, and Silicon fusion occurs at about 2.7 billion K.

red giant core is made of layers of heavier material

Up to the production of iron in the most massive stars, the nuclear fusion process is able to create extra energy from the fusion of lighter nuclei. But the fusion of iron nuclei absorbs energy. The core of the massive stars implodes and the density gets so great that protons and electrons are combined to form neutrons + neutrinos and the outer layers are ejected in a huge supernova explosion. The more common low-mass stars will have a gentler death, forming a planetary nebula.

13.2.2.8 Stage 8: Planetary Nebula or Supernova

In this next-to-last stage of a star’s life, the outer layers are ejected as the core shrinks to its most compact state. A large amount of mass is lost at this stage as the outer layers are returned to the interstellar medium. For the common low-mass stars (those with masses of 0.08 to about 6 or 7 times the mass of the Sun during their main sequence stage), the increased number of photons flowing outward from the star’s hot, compressed core will push on the carbon and silicon grains that have formed in the star’s cool outer layers to eject the outer layers and form a planetary nebula. The ultraviolet from the hot exposed core, called a white dwarf, causes the gases to fluoresce. Most noticeable is the red emission from the excited hydrogen and nitrogen, the green emission from doubly-ionized oxygen, and the blue emission from excited helium. Planetary nebulae can be distinguished from H II regions by their compact shape and strong emission lines of doubly-ionized oxygen (that give them their green color), doubly-ionized neon, and singly-ionized helium. (The image of the Ring Nebula on the left is courtesy of Palomar Observatory.)

Ring Nebula and Helix Nebula
AAO image

Planetary nebula get their name because some looked like round, green planets in early telescopes. They are now known to be entirely different than the planets and are about one or more light years across (much larger than our solar system!). Originally, we thought planetary nebulae were simple expanding spherical shells that look like rings on the sky because when you look along the edge of the expanding spherical shell, you look through more material than when you look toward the center of the shell. The round soap bubbles you made as a child (or still do!) look like rings for the same reason. Indeed, many of the planetary nebulae first seen, like the Ring Nebula in Lyra and the Helix Nebula in Aquarius look like rings.

how a spherical bubble looks like a ring

More complete surveys of the planetary nebulae, high-resolution images from the Hubble Space Telescope, and careful analysis of the various parts of the planetary nebulae have shown that planetary nebulae have much more complex structures. Many have bipolar outflows like the Dumbbell Nebula, Hourglass Nebula, and Eskimo Nebula whose different orientations of their poles with our line of sight cause the differences in their appearance as seen from the Earth. These nebula probably have equatorial rings or disks of material ejected during the red giant phase that force the material to flow perpendicular to the rings/disks. The two rings of the Hourglass Nebula (see the picture below) are centered along the star’s poles that are oriented around 60° to our line of sight. The upper ring is around the pole that is coming towards us and the lower ring is around the pole that is oriented away from us. There is evidence that the Ring Nebula in Lyra is similar to the Hourglass Nebula except that we are viewing it from right along the pole, so just one ring is seen. Also, the Helix Nebula is probably two disks oriented perpendicular to each other.

Dumbbell Nebula and Cat's Eye Nebula
Dumbbell imageCat’s Eye image

Companion stars may also be affecting the shapes and may explain why some, like Hourglass Nebula, have the central white dwarf not centered. Complex ones like the Cat’s Eye Nebula seem to show that the star ejected its layers in a series of spherical pulses separated by about 1500 years. There are also jets of high-speed gas and shockwaves of gases of different speeds running into each other. While we have just some rough ideas of the causes of their shapes, we certainly can marvel at their beauty!

HST view of Hourglass Nebula and Eskimo Nebula
Hourglass imageEskimo image

High-resolution images of planetary nebulae show complex structures in the expanding nebula. The picture below is a detailed view of the Helix Nebula from the Hubble Space Telescope. The expanding gas from the planetary nebula gas ejection runs into gas and dust dispersed in the red giant winds. As it passes the slower moving red giant wind material, the gas shapes the denser blobs into comet-like shapes. Although they are called “comet knots”, they are not to be confused with real comets in our solar system. Each of these blobs is over twice the size of our entire solar system!

HST view of Helix Nebula

Further explanation of the causes of the sometimes bizarre shapes of the planetary nebula is available at Bruce Balick’s homepage.

The rare high-mass stars (those with masses of about 8 to 50 times the Sun’s mass during their main sequence stage) will go the explosive supernova route. When a massive star’s iron core implodes, the protons and electrons fuse together to form neutrons and neutrinos. The core, once the size of the Earth, becomes a very stiff neutron star about the size of a small town in less than a second. The infalling outer layers hit the core and heat up to billions of degrees from the impact. Enough of the huge number of neutrinos produced when the core collapses interact with the gas in outer layers, helping to heat it up. During the supernova outburst, elements heavier than iron are produced as free neutrons produced in the explosion rapidly combine with heavy nuclei to produce heavier and very rare nuclei like gold, platinum, uranium among others. This happens in about the first 15 minutes of the supernova. The most massive stars may also produce very powerful bursts of gamma-rays that stream out in jets at the poles of the stars at the moment their cores collapse to form a black hole (source of the long gamma-ray bursts—we see only the jets pointed towards us).

The superheated gas is blasted into space carrying a lot of the heavy elements produced in the stellar nucleosynthesis process. This explosion is a supernova. As the expanding gas crashes into the surrounding interstellar gas at thousands of kilometers/second, the shock wave heats up the interstellar gas to very high temperatures and it glows. Strong emission lines of neutral oxygen and ionized sulfur distinguish their spectra from planetary nebulae and H II regions. Also, the ratio of the strengths of the individual doubly-ionized oxygen is that expected from shock-wave heating. Planetary nebulae and H II regions are lit up by the action of ultraviolet light on the gas, while supernova glow from shock-wave heating. The gas from supernova explosions also has strong radio emission with a non-thermal continuous spectrum that is produced by electrons spiraling around magnetic field lines. Gas from recent explosions (within a few thousand years ago) are visible with X-ray telescopes as well.

Crab Nebula

A famous supernova remnant is the Crab Nebula above. Chinese astronomers recorded the explosion on July 4, 1054 and the Anasazi Indians painted at least one picture of it. The Vela supernova (in the constellation Vela; figure below) occurred long before the Crab Nebula so it is much more spread out. Different parts of the expanding gas have run into regions of the interstellar medium of different densities. For that reason and also because there is turbulence in the expanding supernova gas, the remnant seen today is wispy strands of glowing gas.

Vela supernova remnant

The neutrinos formed when the neutron core is created fly away from the stiff core, carrying most of the energy (over 99%) from the core collapse away with them. Some energy (less than1%) goes into driving the gas envelope outward. The rest of the energy (less than only 0.01%) goes into making the supernova as bright as 1011 Suns (as bright as an entire galaxy)! When a supernova occurred in a satellite galaxy of the Milky Way at the beginning of 1987 (called SN1987a), the Kamiokande neutrino detector in Japan detected a huge burst of neutrinos from the direction of the satellite galaxy. This provided confirmation of the supernova models. The images below show the star before it went supernova (right frame and arrow) and after the explosion (left frame)

SN1987A before and after the explosion

Recent views of SN1987a from the Hubble Space Telescope (below) shows the material from the supernova explosion itself expanding outward at over 9.5 million kilometers per hour preferentially into two lobes that are roughly aligned with the bright central ring. The central bright ring and two outer rings are from material ejected by the star before its death. Does this image remind you of the Hourglass Nebula above?

HST view of SN1987A ten years later

Supernovae are very rare—about one every hundred years in any given galaxy—because the stars that produce them are rare. However, there are billions of galaxies in the universe, so simple probability says that there should be a few supernovae happening somewhere in the universe during a year and that is what is seen! Because supernovae are so luminous and the energy is concentrated in a small area, they stand out and can be seen from hundreds of millions of light years away.

The bright gas nebula of a planetary nebula or supernova does not last long, only a few tens of thousands of years. As the nebula expands, it cools and dims. The processed material becomes part of the interstellar medium in the galaxy.

star death stages

13.2.2.9 Stage 9: Core Remnant

What remains after the outer layers are thrown off depends on the mass of the core. The core remnants are described fully in the next section. Here a brief description of each type of core remnant will be given. If the core has a mass less than 1.4 solar masses, it will shrink down to a white dwarf the size of the Earth. The electrons in the compressed gas bump right against each other to form a strange sort of gas called a degenerate gas. The electrons prevent further collapse of the core.

If the core has a mass between 1.4 and 3 solar masses, the neutrons will bump up against each other to form a degenerate gas in a neutron star about the size of small city. The neutrons prevent further collapse of the core. Nothing can prevent the highest mass cores (greater than 3 solar masses) from collapsing to a point. On the way to total collapse, it may momentarily create a neutron star and the resulting supernova rebound explosion and powerful bursts of gamma-rays in bipolar jets (probably the source of the long gamma-ray burst objects). Gravity finally wins. Nothing holds it up. The gravity around the collapsed core becomes so great that Newton’s law of gravity becomes inadequate and the gravity must be described by the more powerful theory of General Relativity developed by Albert Einstein. This will be discussed further below.

The supercompact point mass is called a black hole because the escape velocity around the point mass is greater than the speed of light. Since the speed of light is the fastest that any radiation or any other information can travel, the region is totally black. The distance at which the escape velocity equals the speed of light is called the event horizon because no information of events occurring inside the event horizon can get to the outside. The radius of the event horizon in kilometers = 3 × core mass in solar masses.

13.2.3 Stellar Nucleosynthesis

Hydrogen and helium and some lithium, boron, and beryllium were created when the universe was created. All of the rest of the elements of the universe were produced by the stars in nuclear fusion reactions. These reactions created the heavier elements from fusing together lighter elements in the central regions of the stars. When the outer layers of a star are thrown back into space, the processed material can be incorporated into gas clouds that will later form stars and planets. The material that formed our solar system incorporated some of the remains of previous stars. All of the atoms on the Earth except hydrogen and most of the helium are recycled material—they were not created on the Earth. They were created in the stars.

The use of the word “created” here is different than what is normally meant by scientists. In chemical reactions, different atoms or combinations of atoms are said to be produced or created when a reaction takes place. For example, in the Earth section of the planets chapter, I said that oxygen was produced in the photosynthesis process of plants. That oxygen then goes into the air and you breathe it in. To be more correct I should have said that the oxygen atoms were moved or broken off from one set of compounds [carbon dioxide (CO2) and water (H2O)] to form a molecule of two oxygen atoms bound together (O2) and a molecule of carbohydrate made of carbon atoms, hydrogen atoms, and oxygen atoms (C6H12O6). Each atom is rearranged or re-used. It was much simpler to say that oxygen was “created” as a by-product of the photosynthesis process. I hope you did not mind. In defense I want you to know that practically everyone, except for the astronomer researching stellar evolution, uses this loose meaning of “creation.”

However, now that you know about stellar nucleosynthesis, I need to be more careful about what is being created from scratch and what is being re-used. Except for the hydrogen and most of the helium atoms, all of the materials around you, in the food you eat and drink, in the air you breathe, in your muscles and bones, in the paper and ink or toner of this book (or computer screen you are reading), everything (!) are made of atoms that were created in the stars. Those atoms are rearranged to produce the vast variety of things around and in you. In the cores of stars and in supernova explosions, new atoms are manufactured from nuclear fusion reactions. You will find out where the hydrogen and most of the helium atoms came from in the cosmology chapter.

The atoms heavier than helium up to the iron and nickel atoms were made in the cores of stars (the process that creates iron also creates a smaller amount of nickel too). The lowest mass stars can only synthesize helium. Stars around the mass of our Sun can synthesize helium, carbon, and oxygen. Massive stars (M* > 8 solar masses) can synthesize helium, carbon, oxygen, neon, magnesium, silicon, sulfur, argon, calcium, titanium, chromium, and iron (and nickel). Elements heavier than iron are made in supernova explosions from the rapid combination of the abundant neutrons with heavy nuclei. Massive red giants are also able to make small amounts of elements heavier than iron (up to mercury and lead) through a slower combination of neutrons with heavy nuclei, but supernova probably generate the majority of elements heavier than iron and nickel (and certainly those heavier than lead up to uranium). The synthesized elements are dispersed into the interstellar medium during the planetary nebula or supernova stage (with supernova being the best way to distribute the heavy elements far and wide). These elements will be later incorporated into giant molecular clouds and eventually become part of future stars and planets (and life forms?)

Although the particulars of various nucleosynthesis processes are beyond the scope of this website, it is important to note a couple of things:

  1. The stellar nucleosynthesis theory correctly predicts the observed abundances of all of the naturally-occurring heavy elements seen on the Earth, meteorites, Sun, other stars, interstellar clouds—everywhere in the universe. (In the cosmology chapter you will see where the hydrogen and most of the helium came from.) We understand now why some elements like carbon, oxygen, silicon, and iron are common and the heaviest elements like gold, mercury, and uranium are so rare.
  2. In order to create a terrestrial planet like the Earth (and life on such a planet), enough of the heavy elements have to be created in previous generations of stars and then concentrated in the interstellar clouds to collect into sizable chunks around forming stars. There is necessarily a “lag” between the beginning of the universe and the beginning of life.

Sections Review

Vocabulary

  • black hole
  • event horizon
  • giant molecular cloud
  • helium flash
  • main sequence
  • neutron star
  • planetary nebula
  • protostar
  • red giant
  • shell burning
  • stellar evolution
  • stellar nucleosynthesis
  • subgiant
  • supergiant
  • supernova
  • T-Tauri
  • white dwarf
  1. Star main sequence lifetime = [star’s mass / star’s luminosity] × 1010 years.
  2. Star main sequence lifetime = 1010 / (star’s mass)(p – 1), where p = 3 for stars more massive than 30 solar masses and p = 4 for stars less massive than 10 solar masses.

Review Questions 1

  1. What fundamental property of stars determines their evolution?
  2. Why do massive stars last for a short time as main sequence stars but low-mass stars last a long time in the main sequence stage?
  3. How can you detect protostars if the surrounding gas and dust blocks visible light?
  4. How do T-Tauri stars get rid of the surrounding gas and dust from which they formed?
  5. What is happening in the core of a main sequence star and why is it so stable?
  6. What happens to a main sequence star that has stopped fusing hydrogen in its core?
  7. Are all red giants or supergiants very massive stars? Why are red giants so big and red? What is going on inside the giants?
  8. What is the evolution sequence for stars around the mass of our Sun? How long is the Sun’s main sequence lifetime?
  9. What is the evolution sequence for high-mass stars? How long is the main sequence lifetime of an O7 star?
  10. In which stage is most of a star’s mass lost?
  11. How is a planetary nebula formed? What is formed at the center of the planetary nebula? Which main sequence stars will eventually form planetary nebulae?
  12. What happens in a supernova explosion? Which main sequence stars will eventually go supernova?
  13. How can you distinguish planetary nebulae and supernovae from each other and from ordinary H II regions?
  14. About how often does a supernova occur in a typical galaxy? Why is it better to look for supernovae in other galaxies?
  15. How does the concept of stellar nucleosynthesis explain where all of the elements on the Earth came from?
  16. Why is iron the limit for stellar nucleosynthesis in red giants? Where did heavier elements than iron come from?

13.2.4 Confirmation of Stellar Evolution Models

Even the shortest-lived massive stars last longer than the entire span of human history, so how can astronomers test the predictions of their stellar evolution models? In science the sole judge of scientific truth is experiments or observation. Regardless of how nice or beautiful a scientific theory may appear, if it does not make accurate testable predictions, it is invalid. When color-magnitude (H-R) diagrams for star clusters are constructed, there is a convincing confirmation of our stellar evolution models.

What is nice about clusters is that differences in the stars can be explained in terms of only one variable: mass. Stars in a cluster all form at about the same time, so age differences is not a factor in our analysis. The stars form from the same gas cloud, so their chemical composition is the same and all of them are at about the same distance from us (relative to their huge distance from us), so any differences in apparent brightness are due to luminosity differences. More luminous main sequence stars are more massive than dimmer main sequence stars.

Comparison of the theories with reality is easy since you need to only consider how mass affects the cluster stars’ evolution. The predictions from the stellar evolution models as to what the characteristics of the stars in different clusters should be are compared with reality. Star formation and stellar evolution models are confirmed by observations of real clusters. By observing clusters of different ages, you can piece together how a star will form, live, and die.

young cluster history

old cluster history

13.2.5 Finding the Ages of Clusters

Cluster color-magnitude diagrams change with age. More massive stars evolve quicker than low-mass stars. The hot, luminous main sequence stars will die before the cool, dim main sequence stars. This means that an old cluster will have only the low-mass stars still on the main sequence, but a young cluster will have both high and low-mass stars on the main sequence.

The most massive star still on the main sequence tells us the age of the cluster. That point on the main sequence is called the main sequence turnoff. All stars in a cluster are assumed to have formed at about the same time (observations of current star formation do show that stars form in batches). Stars slightly more massive than the turnoff point have already evolved “away” from main sequence. The main sequence turnoff is analogous to a candle burning—a candle that has been lit longer will be shorter than an identical candle lit more recently.

candle analogy for main sequence turnoff

The age of the cluster equals the lifetime of the stars with masses at the main sequence turnoff.

  1. For the common lower mass stars (< 10 solar masses), age of the cluster = (1010) / (MST mass3) years. Use solar masses!
  2. For the rare massive stars (> 30 solar masses), age of the cluster = (1010) / (MST mass2) years.

The most accurate age for a cluster is found from fitting the entire cluster HR diagram (main sequence, sub-giant, red giant, and horizontal branch) to a stellar evolution model of a specific age and chemical composition.

The American Astronomical Society and the Astronomical Society of the Pacific published a beautifully-illustrated guide for teachers, students, and the public called An Ancient Universe: How Astronomers Know the Vast Scale of Cosmic Time. (PDF document: 800 kB in size!) This guide for Teachers, Students and the Public was written by a subcommittee of the American Astronomical Society’s Astronomy Education Board. This is a local copy from the AAS Education Board.

Vocabulary

  • main sequence turnoff

Review Questions 2

  1. How do cluster H-R diagrams confirm the stellar evolution models?
  2. How can you use a cluster’s H-R diagram to find the age of the cluster? 
  3. What assumptions are made in the age-dating method of the main sequence turnoff?
  4. How do you know that a cluster with a MST of 3 solar masses is younger than a cluster with a MST of 2.8 solar masses and older than a cluster with a MST of 3.2 solar masses?

13.3 Stellar Remnants

All that is left of the star after the outer layers are ejected to space is the core remnant. The core’s gas is super-compressed by gravity to form a strange type of gas made of “degenerate matter.” It is important to remember that what happens to the core depends on the mass of the core, rather than the original mass of the main sequence star from which it came, because the only thing left for gravity to really compress is the core.

13.3.1 Degenerate matter

When gas become super-compressed, particles bump right up against each other to produce a kind of gas, called a degenerate gas, that behaves more like a solid. Normal gas exerts higher pressure when it is heated and expands, but the pressure in a degenerate gas does not depend on the temperature. The laws of quantum mechanics must be used for gases of ultra-high densities.

The first rule is that only certain energies are permitted in a closely confined space. The particles are arranged in energy levels like rungs of an energy ladder. In ordinary gas, most of the energy levels are unfilled and the particles are free to move about. But in a degenerate gas, all of the lower energy levels are filled. The second rule is that only two particles can share the same energy level in a given volume at one time. For white dwarfs the degenerate particles are the electrons. For neutron stars the degenerate particles are neutrons. The third rule is that how close particles can be spaced depends inversely on their masses. Electrons are spaced further apart in a degenerate electron gas than the neutrons in a degenerate neutron gas because electrons are much less massive than neutrons.

Let’s see how these rules affect the core remnant.

  1. Degenerate gases strongly resist compression. The degenerate particles (electrons or neutrons) are locked into place because all of the lower energy shells are filled up. The only way they can move is to absorb enough energy to get to the upper energy shells. This is hardto do! Compressing a degenerate gas requires a change in the motions of the degenerate particle. But that requires A LOT of energy. Degenerate particles have no “elbow room” and their jostling against each other strongly resists compression. The degenerate gas is like hardened steel!energy levels of degenerate matter
  2. The pressure in a degenerate gas depends only on the speed of the degenerate particles NOT the temperature of the gas.But to change the speed of degenerate particles requires A LOT of energy because they are locked into place against each other. Adding heat only causes the non-degenerate particles to move faster, but the degenerate ones supplying the pressure are unaffected.
  3. Increasing the mass of the stellar core increases the compression of the core. The degenerate particles are forced closer together, but not much closer together because there is no room left. A more massive stellar core remnant will be smaller than a lighter core remnant. This is the opposite behavior of regular materials: usually adding mass to something makes it bigger!

adding mass SHRINKS size

13.3.2 White Dwarfs

White dwarfs form as the outer layers of a low-mass red giant star puff out to make a planetary nebula. Since the lower mass stars make the white dwarfs, this type of remnant is the most common endpoint for stellar evolution. If the remaining mass of the core is less than 1.4 solar masses, the pressure from the degenerate electrons (called electron degeneracy pressure) is enough to prevent further collapse.

what holds degenerate stars up

Because the core has about the mass of the Sun compressed to something the size of the Earth, the density is tremendous: around 106 times denser than water (one sugarcube volume’s worth of white dwarf gas has a mass > 1 car)! A higher mass core is compressed to a smaller radius so the densities are even higher. Despite the huge densities and the “stiff” electrons, the neutrons and protons have room to move around freely—they are not degenerate.

White dwarfs shine simply from the release of the heat left over from when the star was still producing energy from nuclear reactions. There are no more nuclear reactions occurring so the white dwarf cools off from an initial temperature of about 100,000 K. The white dwarf loses heat quickly at first cooling off to 20,000 K in only about 100 million years, but then the cooling rate slows down: it takes about another 800 million years to cool down to 10,000 K and another 4 to 5 billion years to cool down to the Sun’s temperature of 5,800 K.

Their rate of cooling and the distribution of their current temperatures can be used to determine the age of our galaxy or old star clusters that have white dwarfs in them. However, their small size makes them extremely difficult to detect. Because it is above the atmosphere, the Hubble Space Telescope can detect these small dead stars in nearby old star clusters called globular clusters. Analysis of the white dwarfs may provide an independent way of measuring the ages of the globular clusters and provide a verification of their very old ages derived from main sequence fitting. Select the image below to enlarge it (will display in another window).

white dwarfs in a globular cluster
HST image

13.3.3 Novae and Supernovae Type Ia

An isolated white dwarf has a boring future: it simply cools off, dimming to invisibility. White dwarfs in binary systems where the companion is still a main sequence or red giant star can have more interesting futures. If the white dwarf is close enough to its red giant or main sequence companion, gas expelled by the star can fall onto the white dwarf. The hydrogen-rich gas from the star’s outer layers builds up on the white dwarf’s surface and gets compressed and hot by the white dwarf’s gravity.

Eventually the hydrogen gas gets dense and hot enough for nuclear reactions to start. The reactions occur at an explosive rate. The hydrogen gas is blasted outward to form an expanding shell of hot gas. The hot gas shell produces a lot of light suddenly. From the Earth, it looks like a new star has appeared in our sky. Early astronomers called them novae (“new” in Latin). They are now known to be caused by old, dead stars. The spectra of a nova shows blue-shifted absorption lines showing that a hot dense gas is expanding towards us at a few thousands of kilometers per second. The continuum is from the hot dense gas and the absorption lines are from the lower-density surface of the expanding cloud. After a few days the gas has expanded and thinned out enough to just produce blue-shifted emission lines.

After the nova burst, gas from the regular star begins to build up again on the white dwarf’s surface. A binary system can have repeating nova bursts. If enough mass accumulates on the white dwarf to push it over the 1.4 solar mass limit, the degenerate electrons will not be able to stop gravity from collapsing the dead core. The collapse is sudden and heats the carbon and oxygen nuclei left from the dead star’s red giant phase to temperatures great enough for nuclear fusion. The carbon and oxygen quickly fuse to form silicon nuclei. The silicon nuclei fuse to create nickel nuclei. A huge amount of energy is released very quickly with such power that the white dwarf blows itself apart. This explosion is called a Type Ia supernova to distinguish them from the other types of supernova that occurs when a massive star’s core implodes to form a neutron star or black hole.

Type I supernovae happen in close binary systems and do not show strong hydrogen emission lines. Type I (especially Ia) supernova create most of the iron and nickel found in the interstellar medium. Type II supernovae happen in single star systems (or at least far enough away from any companion star to retain their hydrogen outer layers) and have strong hydrogen emission lines. Type II create most of the oxygen found in the interstellar medium. Type Ia supernovae are several times more luminous than Type Ib, Ic, and Type II supernovae, leave no core remnant behind, and result from when a low-mass star’s core remnant (a white dwarf) detonates. They have a strong ionized silicon emission line at 615 nm. Type Ib and Ic supernovae result from the collapse of a massive star’s core whose outer hydrogen layers have been transferred to a companion star or blown off from strong winds which is why they do not show hydrogen emission lines. Type Ib have strong helium emission lines and Type Ic do not.

Since the Type Ia supernova form from the collapse of a stellar core of a particular mass, rather than the range of core masses possible for the other types of supernova, the Type Ia supernova are expected to have the same luminosity. The distances to very luminous objects can be derived using the inverse square law of light brightness if their luminosity is known. Because of their huge luminosities, the Type Ia supernovae could be used to measure distances to very distant galaxies. In practice there is a range of luminosities for the Type Ia, but the luminosity can be derived from the rate at which the supernova brightens and then fades—the more luminous ones take longer to brighten and then fade. Astronomers using Type Ia supernova to measure distances to very distant galaxies have come to some surprising conclusions about the history and future of the universe (see the cosmology chapter for more about that).

13.3.4 Neutron Stars

If the core mass is between 1.4 and 3 solar masses, the compression from the star’s gravity will be so great the protons fuse with the electrons to form neutrons. The core becomes a super-dense ball of neutrons. Only the rare, massive stars will form these remnants in a supernova explosion. Neutrons can be packed much closer together than electrons so even though a neutron star is more massive than a white dwarf, it is only about the size of a city.

what holds degenerate stars up

The neutrons are degenerate and their pressure (called neutron degeneracy pressure) prevents further collapse. Neutron stars are about 30 kilometers across, so their densities are much larger than even the incredible densities of white dwarfs: 2 × 1014 times the density of water (one sugarcube volume’s worth has a mass = mass of humanity)! Recently, the Hubble Space Telescope was able to image one of these very small objects. It is shown in the figure below (the arrow points to it). Even though it is over 660,000 K, the neutron star is close to the limit of HST’s detectors because it is at most 27 kilometers across.

HST sees bare neutron star

13.3.5 Pulsars

In the late 1960’s astronomers discovered radio sources that pulsated very regularly with periods of just fractions of a second to a few seconds. The periods are extremely regular—only the ultra-high precision of atomic clocks can show a very slight lengthening in the period. At first, some thought they were picking up signals from extra-terrestrial intelligent civilizations. The discovery of several more pulsars discounted that idea—they are a natural phenomenon called pulsars (short for “pulsating star”).

Normal variable stars (stars near the end of their life in stages 5 to 7) oscillate brightness by changing their size and temperature. The density of the star determines the pulsation period—denser stars pulsate more quickly than low density variables. However, normal stars and white dwarfs are not dense enough to pulsate at rates of under one second. Neutron stars would pulsate too quickly because of their huge density, so pulsars must pulsate by a different way than normal variable stars. A rapidly rotating object with a bright spot on it could produce the quick flashes if the bright spot was lined up with the Earth. Normal stars and white dwarfs cannot rotate fast enough because they do not have enough gravity to keep themselves together; they would spin themselves apart. Neutron stars are compact enough and strong enough to rotate that fast. The pulsar at the center of the Crab Nebula rotates 30 times every second. In the figure below, it is the left one of the two bright stars at the center of the Hubble Space Telescope image (right frame).

HST view of Crab Nebula pulsar
HST image

Another clue comes from the length of each pulse itself. Each pulse lasts about 1/1000th of a second (the time between pulses is the period mentioned above). An important principle in science is that an object cannot change its brightness faster than it takes light to cross its diameter. Even if the object could magically brighten everywhere simultaneously, it would take light from the far side of the object longer to reach you than the near side. The observed change in brightness would be smeared out over a time interval equal to the time it would take the light from the far side of the object to travel to the near side of the object. If the object did not brighten everywhere simultaneously, then a smaller object could produce a pulse in the same interval. The brightness fluctuation timescale gives the maximum size of an object.

smaller fluctuation timescale means smaller diameter

The 1/1000th of second burst of energy means that the pulsars are at most (300,000 kilometers/second) × (1/1000 second) = 300 kilometers across. This is too small for normal stars or white dwarfs, but fine for neutron stars. When neutron stars form they will be spinning rapidly and have very STRONG magnetic fields (109 to 1012 times the Sun’s). The magnetic field is the relic magnetic field from the star’s previous life stages. The magnetic field is frozen into the star, so when the core collapses, the magnetic field is compressed too. The magnetic field becomes very concentrated and much stronger than before.

must spin fast to keep (size*spin speed) the same

Why would neutron stars be fast rotators? Conservation of angular momentum! Just as a spinning ice skater can spin very fast by pulling in her arms and legs tight about the center of her body, a star will spin faster when it brings its material closer to its center. The angular momentum of an object = its mass × its equatorial spin speed × its radius. The mass remains constant. In order to keep the angular momentum constant the spin speed must increase if the radius decreases. This will keep the product of spin speed × radius the same value. A slowly rotating red giant star will have the same angular momentum when it becomes a tiny, fast rotating neutron star. See the Angular Momentum appendix for other examples.

spinning ice skater increases spin speed

13.3.5.1 Lighthouse Model

The spinning neutron star produces beams of radiation that sweep across your line of sight like a lighthouse beam does for ships at sea. In the lighthouse model the neutron star’s strong magnetic field creates a strong electric field. The electric field makes charged particles (mostly electrons) flow out of the magnetic poles. As the charged particles spiral around the magnetic field lines, they produce electromagnetic radiation (recall from the electromagnetic radiation chapter that any moving charge will create electromagnetic radiation). The energy is called non-thermal radiation because it is not produced by a hot, dense object, but by accelerated charges. The shape of the continuous spectrum is different from a normal thermal spectrum and does not depend on the temperature. A type of particle accelerator in physics laboratories here on Earth called a “synchrotron” produces this kind of radiation too, so it is sometimes called “synchrotron radiation.”

The neutron star’s magnetic field lines converge at the magnetic poles, so the charges get focused and a narrow cone of non-thermal radiation is beamed outward. If the beam sweeps past Earth, you see a flash of light. However, given the wide range of angles the magnetic poles could be aligned in space, it is more likely that the beam will miss the Earth. There are probably many more pulsars out there that cannot be detected because their beams do not happen to cross our line of sight.

why pulsars pulsate

The energy of the non-thermal radiation beam comes from the rotational energy of the pulsar. Since the light energy escapes, the production of the energy beam robs energy from the pulsar so the pulsar’s rotation slows down (angular momentum does slowly decrease). Another equivalent way to view the process is from Newton’s 3rd law of motion. The magnetic field exerts a force on the charged particles, speeding them up. The charged particles exert a reaction force on the magnetic field slowing it and the pulsar down. Eventually, the pulsar dies away when the neutron star is rotating too slowly (periods over several seconds long) to produce the beams of radiation.

Every now and then, a “glitch” is seen in the pulse rate from a pulsar. The pulsar suddenly increases its spin rate. What causes this is the neutron star suddenly shrinks by about 1 millimeter. The spin rate suddenly increases to conserve angular momentum. The spin rate can be greatly increased if the pulsar is in a close binary system and its companion dumps gas onto the pulsar. The pulsar gains angular momentum from the infalling gas and ramps up its spin rate as more gas falls onto it. The pulsars that spin hundreds of times per second are thought to be the result of such a transfer.

13.3.6 Black Holes

If the core remnant has a mass greater than 3 solar masses, then not even the super-compressed degenerate neutrons can hold the core up against its own gravity. Gravity finally wins and compresses everything to a mathematical point at the center. The point mass is a black hole. Only the most massive, very rare stars (greater than 10 solar masses) will form a black hole when they die. As the core implodes it briefly makes a neutron star for just long enough to produce the supernova explosion.

what holds degenerate stars up

13.3.6.1 Ultra-strong gravity

The gravity of the point mass is strong enough close to the center that nothing can escape, not even light! Within a certain distance of the point mass, the escape velocity is greater than the speed of light. Remember from the gravity chapter that the escape velocity is the speed an object needs to avoid being pulled back by the gravity of a massive body. The escape velocity

vescape = Sqrt[(2G × Mass)/(distance to the center)],where G is the gravitational constant.

Since the mass is in the top of the fraction, the escape velocity is greater for larger masses. The escape velocity is smaller for larger distances from the center because the distance is in the bottom of the fraction. The Earth’s escape velocity at its surface is about 11 kilometers/second and the Sun’s surface escape velocity is about 620 kilometers/second. White dwarfs and neutron stars have very large surface escape velocities because they have roughly the mass of the Sun packed into an incredibly small volume. A solar mass white dwarf has a radius of only 8,800 kilometers, so its surface escape velocity is about 5500 kilometers/second. A solar mass neutron star would have a radius of just 17 kilometers, so its surface escape velocity would be an incredible 125,000 kilometers/second! (Real neutron stars have masses above 1.4 solar masses and smaller radii, so their escape velocities are even larger!)

A black hole probably has no surface, so astronomers use the distance at which the escape velocity equals the speed of light for the size of the black hole. This distance is called the event horizon because no messages of events (via electromagnetic radiation or anything else) happening within that distance of the point mass make it to the outside. The region within the event horizon is black. Rearranging the formula above for the escape velocity and putting in the speed of light c for the escape velocity, you find the event horizon is at a distance of

r = (2G × Mass)/(c2)from the point mass. This approximately equals 3 × Mbh kilometers, where the black hole mass Mbh is in units of solar masses (a solar mass black hole would have a radius of 3 kilometers, a 10 solar mass black hole would have a radius of 30 kilometers, etc.).

Black holes have been portrayed as cosmic vacuum cleaners in Hollywood films, sucking up everything around them. Black holes are dangerous only if something gets too close to them. Because all of their mass is compressed to a point, it is possible to get very close to them and still be outside all of the mass. Recall that gravity is an inverse square law force, so at very small distances, the strength of gravity around a point mass becomes very large. But objects far enough away will not sense anything unusual. If the Sun were replaced by a black hole of the same mass, the orbits of the planets would remain unchanged (it would be much colder in the solar system, though!).

13.3.7 General Relativity

For very strong gravitational fields, Newton’s description of gravity becomes inadequate. Einstein’s theory of General Relativity must be used to describe the gravitational effects. Einstein found that gravity is not a force in the usual Newtonian description of force. Gravity is a result of a warping or distortion of spacetime around a massive object. The stronger the gravity is, the more the spacetime is warped or curved. I discuss the developments of the concept of spacetime and the theory of General Relativity in the Einstein’s Relativity chapter. That chapter also gives several observations of curved spacetime. The definite discovery of a black hole would provide more evidence for General Relativity.

Within the event horizon space is so curved that any light emitted is bent back to the point mass. Karl Schwarzschild worked out the equations in General Relativity for a non-rotating black hole and found that the light rays within a certain distance of the point mass would be bent back to the point mass. The derived distance is the same as the event horizon value above. The event horizon is sometimes called the Schwarzschild radius in his honor.

Falling toward a black hole would not be a pleasant experience. If you fell in feet-first, your body would be scrunched sideways and stretched along the length of your body by the tidal forces of the black hole. Your body would look like a spaghetti noodle! The stretching happens because your feet would be pulled much more strongly than your head. The sideways scrunching happens because all points of your body would be pulled directly toward the center of the black hole. Therefore, your shoulders would be squeezed closer and closer together as you fell closer to the center of the black hole. The tidal stretching/squeezing of anything falling into a black hole is an effect conveniently forgotten by Hollywood movie writers and directors.

Your friend watching you from a safe distance far from the black hole as you fell in would see your clock run slower and slower as you approached the event horizon. This is the effect of “time dilation” (see General Relativity predictions section). In fact, your friend would see you take an infinite amount of time to cross the event horizon—time would appear to stand still. However, in your reference frame your clock would run forward normally and you would reach the center very soon. If you beamed back the progress of your journey into a black hole, your friend would have to tune to progressively longer wavelengths (lower frequencies) as you approached the event horizon. This is the effect of “gravitational redshift” (see General Relativity predictions section). Eventually, the photons would be stretched to infinitely long wavelengths.

13.3.8 Detecting Black Holes

Since the black holes themselves (their event horizons) are only several miles across, they are too small be visible from a even short distance away. Looking for black circles silhouetted against a background of stars would be an impossible task. You detect their effect on surrounding material and stars. If the black hole is in a binary system and its visible companion is close enough to the black hole, then the effects will be noticeable. There are two signatures of a black hole in a binary system:

  1. The black hole and visible star will orbit around a center of mass between them. You look at how the black hole moves its visible companion around. Applying Kepler’s 3rd law the system, you can determine the total mass, visible star mass + black hole mass = (separation distance)3/(orbital period)2. After making an educated guess of the mass of the visible companion from the correlation of the luminosity, mass, and temperature for normal stars, the rest of the total mass is the unseen object’s mass. If the mass of the unseen object is too big for a neutron star or a white dwarf, then it is very likely a black hole!black holes found by the radiation from a hot accretion disk
    However, measuring the masses of all of the binary systems in the Galaxy would take much too long a time—there are over a hundred billion binary systems in the Galaxy! Even if it took you just one second to somehow measure a binary’s total mass and subtract out one star’s mass, it would take you over 3000 years to complete your survey. How could you quickly hone on the binary system that might have a black hole? Fortunately, black holes can advertise their presence loud and clear with X-rays.
  2. If the visible star is close enough to the black hole, some of its gas will be attracted to the black hole. The gas material will form an accretion disk around the black hole as it spirals onto the black hole. The gas particles in the disk will rub against each and heat up from the friction. The amount of friction increases inward causing increasing temperature closer to the event horizon. The disk will produce a wide spectrum of radiation. Close to the event horizon, the disk will be hot enough to emit X-rays. X-ray sources in the Galaxy are rare. Stars are bright in the optical band. A very small percentage of them can also put out significant amounts of ultraviolet radiation, but all stars are faint in the X-ray band. If you find an X-ray source, then you know something strange is happening with the object. Therefore, a bright X-ray source is actually the first signature that you look for. Once you have found a bright X-ray source, then you measure its mass (the secondsignature) to rule out a white dwarf or neutron star.If the unseen companion is very small, then the X-ray brightness of the disk will be able to change rapidly.To make rapidly varying X-rays, the unseen companion must be small! The fluctuation timescale gives us the maximum possible diameter of the object. Since the speed of light is finite, it takes a given amount of time for light to travel across the object. The time it takes for any interaction to occur is diameter/speed, where the speed can be up to the speed of light if the object could somehow brighten everywhere simultaneously. The diameter = (time interval) × speed. The maximum diameter possible is for a speed equal to the speed of light. The quicker the fluctuations are, the smallerthe object must be.smaller fluctuation timescale means smaller diameter

Black holes themselves are invisible, but they produce very visible effects on nearby objects. Several stellar mass black hole candidates have been found. Examples include Cygnus X-1 and V404 Cygni in the constellation of Cygnus, LMC X-3 in the constellation Dorado, V616 Mon in the Monocerotis constellation, J1655-40 in Scorpius, and the closest one, V4641 Sgr in Sagittarius, is about 1600 light years away. Recently, astronomers have used the differences in how neutron stars and black holes accrete material from their accretion disks to show that black holes exist. Material falling toward a neutron star will emit x-rays as it spirals inward and also as it impacts onto the neutron star’s surface. But material falling toward a black hole does not impact a surface; it vanishes through the event horizon. Comparing the brightness of compact objects heavier than 3 solar masses with those lighter than 3 solar masses, shows that the heavier masses are dimmer than the lighter masses even if they have the same orbital periods. Since the accretion rate should be the same for two objects with the same orbital period, the faintness of the heavier masses can only be explained if they are swallowing matter and energy like a black hole would do. In the Other Galaxies chapter more strong evidence is given for the existence of black holes in that “supermassive” black holes provide a simple explanation for the extremely energetic nuclei of peculiar galaxies called “active galaxies.”

Sections Review

Vocabulary

  • accretion disk
  • degenerate gas
  • electron degeneracy pressure
  • event horizon
  • General Relativity
  • gravitational lens
  • gravitational redshift
  • lighthouse model
  • neutron degeneracy pressure
  • nova
  • pulsar
  • Schwarzschild radius

Formulae

  1. Escape velocity = Sqrt[2G × Mass)/(distance to the center)], where G is the gravitational constant.
  2. Event horizon (Schwarzschild radius) = 2G × (black hole mass)/c2, where G is the gravitational constant, and c is the speed of light.
  3. Event horizon = [3 × black hole mass] kilometers, where the black hole mass is measured in solar masses.
  4. Maximum size of an object = fluctuation time interval × speed of light.

Review Questions 3

  1. What type of star will become a white dwarf? Describe the characteristics of a white dwarf.
  2. How does electron degeneracy pressure keep the white dwarf from collapsing any further?
  3. What is the upper bound for the mass of a white dwarf? How would the fact that stars up to 5 solar masses become white dwarfs show that stars lose mass to the interstellar medium as they evolve? How is most of this mass lost?
  4. How is a neutron star created? What type of star will become a neutron star? Describe the characteristics of a neutron star.
  5. How does neutron degeneracy pressure keep the neutron star from collapsing to a point at the center?
  6. What is the upper bound for the mass of a neutron star?
  7. What are the ingredients for a pulsar?
  8. Why does a pulsar spin so fast?
  9. Why could a collapsed star spinning many times each second not be a regular star or white dwarf?
  10. What type of star will become a black hole? Does anything keep it from collapsing to a point at the center? Describe the characteristics of a black hole.
  11. What is the sole determining thing that specifies the size of the event horizon?
  12. What are the signatures of a black hole—observations indicating the presence of a super-compact nearly invisible object?
  13. How do the rapid fluctuations of the X-rays from a black hole’s accretion disk show that the object at the center is small? If the fluctuations were slower (taking longer to brighten and then fade), would the implied size be smaller or larger?

Is this page a copy of Strobel’s Astronomy Notes?