After reaching the main sequence, stars spend more than 90% of their lives on the main sequence. After this time, when the stars begin to run out of fuel and die, stars travel an evolutionary path taking them off the main sequence. The ultimate fate of the star depends primarily on the mass of the star, although interactions with other stars can play a role.
No one has ever witnessed (or will witness) the complete lifetime of a star. Stars take millions, billions and even trillions of years to evolve. Almost all low mass stars that have formed still exist. All M class stars (red dwarfs) are still on the main sequence because of how slowly they burn their fuel. Most O and B type stars exhaust their fuel and leave the main sequence after only a few million years. Most high mass stars that have ever existed died long ago. The modern theory of the lives and deaths of stars is the scientific method in action. This is derived from viewing many stars in different stages of their development and deaths.
Astronomers use the term “evolution” differently from how it is used in biology. In astronomy, evolution means change during the lifetime of an individual star. In biology, it means change in the characteristics of a population of plants or animals over many generations. Thus in astronomical terminology, “stellar evolution” refers to the changes that occur during a single stellar lifetime.
On the main sequence, a star slowly fuses hydrogen to helium in its core. This process of nuclear fusion is called core hydrogen burning. The proton-proton fusion chain powers the Sun. This is called the CNO Cycle.
The CNO cycle is another fusion mechanism capable of converting hydrogen into helium, this time starting with carbon-12(12C), proceeding according to the following six steps with nitrogen (N) and oxygen (O) created as intermediate products.
12C + 1H -> 13N + energy
13N -> 13C + positron + neutrino
13C + 1H -> 14N + energy
14N + 1H -> 15O + energy
15O -> 15N + positron + neutrino
15N + 1H -> 12C + 4He
The CNO cycle, aside from the radiation and neutrinos produced, create a sum total of reactions as:
12C + 4(1H) -> 12C + 4He
In other words, the net result is the fusion of four protons into a single helium-4 nucleus, just as in the proton-proton chain. Carbon-12 acts merely as a catalyst (an agent of change that is not itself consumed in the reaction).
The electromagnetic forces of repulsion in the CNO cycle are greater than in the proton-proton chain because the charges on the heavy-element nuclei are larger (6 times more for carbon, 7 times more for nitrogen, and 8 times more for oxygen). As such, higher temperatures are needed to push the heavy nuclei into the realm of the strong nuclear force and ignite fusion. Therefore, the proton-proton chain is the dominate form of fusion at lower temperatures, up to about 16 million K (remember – the core temperature of our Sun is about 15 million K). Above 16 million K, the CNO cycle is the more important fusion process . Both contribute to core hydrogen burning. The CNO cycle contributes to no more than 10% of the observed solar radiation. However, stars more massive than our Sun often have core temperatures much higher than 20 million K, making the CNO cycle the dominant energy production mechanism in them. See the chart below – This graphically shows that proton-proton is dominant at lower temperatures, and CNO at higher temperatures.
This sequence is of great importance for stars of more mass than the Sun. It accomplishes the same basic result as the proton-proton chain, just in a very different way. This is where astronomers use another term in a different way. To astronomers, “burning” refers to nuclear fusion in a star’s core, not the chemical reaction we normally think of in every day speech. Chemical burning does not directly affect atomic nuclei.
A main sequence star is always in a state of hydrostatic equilibrium, where pressure’s outward push is exactly offset by gravity’s inward pull. This is a stable balance where a small change in one is compensated by a change in the other. A small increase in a star’s temperature (pressure) causes the star to expand and cool, thus recovering its equilibrium. Conversely, a small decrease in temperature leads to a slight decrease in pressure, and gravity causes the star to contract and heat up again, and again, equilibrium is restored.
As a main sequence star ages, the core temperature rises, and both luminosity and radius increase. These changes are slow (only a factor of three or four in luminosity over the Sun’s entire 10 billion year main sequence lifetime as an example). As a result, the star stays in virtually the same location on the H-R diagram during this stage (stage 7). As hydrogen in the core is consume, the internal balance of the star starts to shift, and the internal structure and outward appearance change more rapidly – the star leaves the main sequence.
Once a star begins to move away from the main sequence, it is on the final stages of its stellar evolution. The post-main-sequence stages depend critically on the star’s mass. Low mass stars die gently, whereas high mass stars die catastrophically. The dividing line between the masses is about 8 solar masses. High mass stars are those with more than 8 solar masses. Low mass stars are those with less than 8 solar masses.
The stages described next are for a 1 solar mass star (like our Sun). The cumbers continue the stage sequences, going from stage 7 (on the main sequence) to the next stage – Stage 8, where it becomes a subgiant.
Currently, the surface of a main-sequence star like our Sun occasionally has flares and spots, but for the most part, does not exhibit any sudden, large-scale changes in its properties. Average surface temperature remains fairly constant, and luminosity increases very slowly with time. The Sun has roughly the same surface temperature as it had when it formed nearly 5 billion years ago, although it is 30% brighter than it was at that time. The stable state cannot continue indefinitely, though. After approximately 10 billion years of steady core hydrogen burning, a Sun-like star begins to run out of fuel.
The following table shows the stages, starting at stage 7, for the evolution of a Sun-like Star
Stage 8: The Sugbiant Branch – As the nuclear fusion proceeds, a star burns off its hydrogen, and produces helium. The hydrogen is depleted, and replaced by helium. The increase in helium is mostly abundant and happens fastest at the center, where temperatures are highest and burning is fastest. The helium content also increases near the edge of the core, but more slowly because the burning rate is less rapid there. Eventually, about 10 billion years after the star arrived on the main sequence, hydrogen becomes depleted at the center. The nuclear burning there subside, and location of principal burning moves to higher layers in the core. An inner core of nonburning pure helium starts to grow.
Without nuclear burning to maintain it, the outward pushing gas pressure weakens in the helium core. The inward pull of gravity, however, does not. This causes the inner core to begin to contract. When all the hydrogen at the center is gone, the process accelerates. If the hydrogen in the center began burning, fusing into some heavier element, more heat would be generated and the core might regain its equilibrium. However, the helium at the center cannot yet burn. The core is far too cold to fuse helium into anything heavier.
For hydrogen, it takes 107 K to fuse it into helium. Because helium is heavier (2 protons rather than 1), they carry a greater positive charge, and their electromagnetic repulsion is larger. Even higher temperatures are needed to cause them to fuse – at least 108 K. A core composed of helium at 107 K cannot generate energy through fusion.
The shrinkage of the helium core releases gravitational energy, driving up the central temperature and heating the overlying burning layers. The higher temperatures cause hydrogen nuclei to fuse even more rapidly than before. The hydrogen is burning at a furious rate in a shell surrounding the nonburning inner core of helium “ash” (which is in the center). This is known as the hydrogen-shell-burning stage. The hydrogen shell generates energy faster than did the original main-sequence star’s hydrogen-burning core. The shell’s energy production continues to increase as the helium core continues to shrink. The star’s response to the disappearance of the fire at its center is to get brighter.
After a lengthy stay on the main sequence, the star’s temperature and luminosity are again beginning to change. The changes can be traced on the H-R diagram. The star first evolves to the right on the diagram, as surface temperature decreases, while luminosity increases only slightly. By stage 8, the radius has increased to about 3 times the radius of the Sun. At this point, the star is called a supergiant. The roughly horizontal path from main sequence to stage 8 is called the subgiant branch.
Stage 9: The Red-Giant Branch – The star is no longer in stable equilibrium. The helium in the core is unbalanced and shrinking, and the rest of the core is also unbalanced, fusing hydrogen into helium at an ever increasing rate. The pressure from the increased hydrogen burning causes the outer layers to increase in radius. While the core is shrinking and heating up, the nonburning outer layers are expanding and cooling. The transformation from main sequence to elderly red giant takes about 100 million years.
By stage 8, the surface temperature has fallen to the point that the interior is opaque to the radiation from within. Beyond this point, convection carries the energy to the surface. Once consequence of this is that the star’s surface temperature remains nearly constant between stages 8 and 9. The almost vertical path between stages 8 and 9 is the red-giant branch. By stage 9, the luminosity is many hundreds of times the solar value, and the radius is about 100 solar radii.
The red giant is about the size of Mercury’s orbit. The helium core, however, is only about a thousandth the size of the entire star, making it just a few times larger than Earth. About 25% of the star’s entire mass is packed into the planet sized core.
Stage 10: Helium Flash – If the unbalanced state of a red-giant continues, the core would eventually collapse, and the rest of the star drift slowly into space. The forces and pressure within the star would literally tear the red giant apart. For stars less than about ¼ solar mass, that is what will eventually happen in a few hundred billion years.
For a star like the Sun, however, the simultaneous shrinking and expanding does not continue indefinitely. A few hundred million years after leaving the main sequence, helium begins to burn in the core. By the time the central density has risen to about 108 kg/m3 (stage 9), the temperature has reached the 108 K needed for helium to fuse into carbon, and central fires reignite.
The process to turn helium into carbon happens in two steps. Two helium nuclei form beryllium-8 (a highly unstable isotope that would normally break up into 2 helium nuclei in about 10-12 s). The beryllium-8 quickly encounters another helium nucleus before it can break up, fusing to form carbon 12 (12C). This is represented as:
4He + 4He -> 8Be + energy
8Be + 4He -> 12C + energy
Helium-4 is known as the alpha particle. This dates back to the early days of nuclear physics, when the nature of these particles (emitted by many radioactive materials) was unknown. Because the process involves 3 helium-4 particles to create the carbon-12, the reaction is called the triple-alpha process.
Up to now, the laws of classic physics have governed the nuclear fusions in the star. As helium fusion begins, the high densities found in the core causes the gas to enter a new state of matter whose properties are governed by the laws of quantum mechanics (the branch of physics describing the behavior of matter on subatomic scales). To this point, we’ve been concentrating primarily with the nuclei (protons, alpha particles, etc.) that make up the star’s mass. The star also contains a vast sea of electrons that have been stripped from their parent nuclei by the ferocious heat in the stellar interior. Under the conditions found in stage 9, a rule of quantum mechanics known as the Pauli exclusion principle prohibits the electrons in the core from being squeezed too close together. The exclusion principle states that we can picture the electrons as tiny rigid spheres that can be squeezed easily up to the point of contact, but become virtually incompressible beyond that point. This is known as electron degeneracy. The pressure associated with the contact of the tiny electron spheres is called electron degeneracy pressure. The term refers to an idealized condition in which all electrons are in their lowest possible energy state, and as a result, the star cannot be compressed into a more compact configuration. At this point, the red giant’s core pressure resisting the force of gravity is supplied almost entirely by degenerate electrons, and hardly any from the “normal” thermal pressure.
Under nondegenerate circumstances, the core could react to the onset of helium burning, but in the core’s degenerate state, the burning becomes unstable. In a star supported by thermal pressure, the increase in temperature produced by the onset of helium fusion would lead to an increase in pressure. Gas would expand and cool, reducing the burning rate, and reestablishing equilibrium. In the electron-supported core, the pressure is largely independent of the temperature. When burning starts and temperature increases, there is no corresponding rise in pressure, no expansion of the gas, no drop in the temperature and stabilization of the core. Instead, the pressure remains more or less unchanged as the nuclear reaction rates increase, and the temperature rises rapidly in a runaway condition called the helium flash.
After a few hours, the helium burns ferociously. Eventually, the flood of energy released heats the core to the point at which normal thermal pressure once again dominates. The core expands, density drops, and equilibrium is restored. The core, now stable, begins to fuse helium into carbon at temperatures well above 108 K.
Helium flash stops the giant star’s ascent of the red-giant branch on the H-R diagram. Despite the violent ignition of helium in the core, the flash does not increase the star’s luminosity. The star jumps from stage 9 to 10, a stable state with steady helium burning in the core. The star resides in a well-defined region of the H-R diagram called the horizontal branch, where core helium burning stars remain for a time before resuming their journey around the H-R diagram. The star’s position on the horizontal branch is determined not by its original mass, but by the amount of mass remaining after its ascent of the red-giant branch. The two masses differ because during the red-giant stage, strong stellar winds eject large amounts of matter from a star’s surface – as much as 20 to 30% of the original stellar mass. More massive stars have lower surface temperatures at this stage, but all stars have roughly the same luminosity after the helium flash. Therefore, more massive stars tend to be towards the right, and less massive stars towards the left, of the horizontal branch.
Stage 11: Back to the Giant Branch – Whatever helium exists in the core is rapidly consumed. The dying star again ascends the giant branch. The triple-alpha process (like the proton-proton and CNO cycle before it) increases rapidly with temperature. At the extremely high temperatures in the horizontal-branch core, helium doesn’t last long – no more than a few tens of millions of years after the initial flash.
Helium becomes depleted at the center of the star, and eventually fusion ceases there. The nonburning carbon core shrinks in size, even as its mass increases due to helium fusion, and heats pu as gravity pulls it inward causing the hydrogen and helium burning rates in the overlying layers of the core to increase. The core now consists of a contracting carbon core surrounded by a helium burning shell, which is surrounded by a hydrogen burning shell. The nonburning layers surround the core (the envelope of the star) expand. By the time it reaches stage 11, it has become a swollen red giant for the second time.
To distinguish the second ascent of the giant branch from the first, the track during the second phase is often called the asymptotic giant branch. The star’s radius and luminosity increase to values even greater than those reached at the helium flash on the first ascent. The carbon core continues to grow in mass as more carbon is produced in the helium burning shell, but continues to shrink in radius, driving the hydrogen burning and helium burning shells to higher and higher temperatures and luminosities.
Stage 12: A Planetary Nebula – As the star moves from stage 10 to 11, the envelope swells, and inner carbon core (too cool for further nuclear burning) continues to contract. If the central temperature could become high enough for carbon fusion to occur, heavier products could be synthesized and the newly generated energy might restore equilibrium between gravity and heat. However, only in high mass stars can temperatures high enough for this to occur be reached. For 1 solar mass stars, the central temperature never reaches the 600 million K needed for a new round of nuclear reactions to occur. Before the carbon core can attain the high temperatures needed for carbon ignition, its density reaches a point beyond which it cannot be compressed further. At 1010 kg/m3 the electrons in the core again become degenerate, the core contraction ceases, and the core’s temperature stops rising. This stage (stage 12) represents the maximum compression that the star can achieve. The core density is extremely high – a single cubic centimeter of core matter would weigh 1000 kg on Earth, a ton of matter compressed into the volume of about the size of a grape. Despite the extreme compression, the central temperature is only 300 million K. Some oxygen is formed due to carbon and helium reacting at the inner edge of the helium burning shell. This is represented as:
12C + 4He -> 16O + energy
Collisions among nuclei are neither frequent nor violent enough to create any heavier elements. For all practical purposes, the central fires go out once carbon has formed.
The stage 12 star’s inner carbon core no longer generates energy. The outer core shells continue to burn hydrogen and helium, and more and more of the inner core reaches its final high density state. Nuclear burning increases in intensity. The envelope continues to expand and cool, reaching a maximum radius about 300 times that of the Sun – enough to engulf Mars. The burning becomes quite unstable. The helium burning shell is subject to a series of explosive helium-shell flashes, caused by enormous pressure in the helium-burning shell and the extreme sensitivity of the triple-alpha burning rate to small changes in temperature. These flashes produce large fluctuations in the intensity of radiation reaching the outermost layers. This causes those layers to pulsate as the envelope repeatedly is heated, expands, cools, and contracts. The amplitude of the pulsations grows as the temperature of the core continues to increase and nuclear burning intensifies in the surrounding shells. Driven by increasingly intense radiation from within, and accelerated by instabilities in the core and the outer layers, virtually all of the star’s envelope is ejected into space in less than a few million years at a speed of a few tens of kilometers per second.
The star now consists of two distinct parts, both of which constitute stage 12. At the center is a small well defined core of mostly carbon ash. Only the outermost layers of this core still fuse helium into carbon and oxygen. The ejected envelope of the giant forms an expanding cloud of dust and cool gas, spread over a volume roughly the size of our solar system. As the core exhausts the last of its remaining fuel, it contracts and heats up. It eventually becomes so hot that its ultraviolet radiation ionizes the inner parts of the surrounding cloud, producing a display called a planetary nebula. More than 1500 planetary nebulae are known in our galaxy. The name originated in the 18th century, when viewed at poor resolution through small telescopes, these shells of glowing gas looked to some astronomers like the circular disks of planets in our solar system, but in reality, these objects have no association with planets.
These are similar to emission nebula, in that both are caused by ionizing radiation from a hot star embedded In a cool gas cloud. However, where the emission nebula indicates recent stellar birth, the planetary nebula indicates impending stellar death.
For reasons not yet fully understood, the final stages of red-giant mass loss are often nonspherical. Planetary nebula may be a ring, or exhibit jetlike and other irregular structures. Both the details of the gas-ejection process and the star’s environment play important roles in determining the nebula’s shape and appearance.
The central star fades and cool, and the expanding gas cloud becomes more and more diffuse, eventually dispersing into interstellar space. After a fe tens of thousands of years, the glowing planetary nebula disappears from view. During the final stages of the red giant’s life, nuclear reactions between carbon and helium create osygen and in some cases heavier elements. All of these elements are dredged up from the depths of the core into the envelope by convection during the star’s final years. The evolution of low mass stars is the source of virtually all the carbon rich dust observed throughout the plane of our own and other galaxies.
Stage 13: White Dwarf – The carbon core (the remnant at the center of the planetary nebula) continues to evolve. The core becomes visible as the envelope recedes. By the time that the envelope is ejected as a planetary nebula, the core is about the size of the Earth. Its mass is about half the mass of the Sun. It shines by stored heat, not nuclear reactions, and has a white-hot surface. The core’s temperature and size give the star a new name. It is now a white dwarf – a dwarf star with sufficiently high surface temperature that it glows white.
Not all white dwarfs are composed of carbon and oxygen. Very low mass stars (less than ¼ solar mass) will never reach the point of helium fusion. The core of such a star will become supported by electron degeneracy pressure before its central temperature reaches the 100 million K needed to start the triple-alpha process. The star’s envelope will be ejected in a manner similar to that of a more massive star, forming a helium white dwarf. The time needed for this kind of transformation is very long (hundreds of billions of years), so no helium white dwarfs have ever actually formed in this way. However, if a slar-mass star is part of a binary system, it is possible or its envelope to be stripped away during the red-giant stage by the gravitational pull of the companion star, exposing the helium core, and terminating the star’s evolution before helium fusion can begin.
In stars somewhat more massive than the Sun (close to 8 solar mass limit on low mass stars at the time the carbon core forms), temperatures in the core may become high enough to have an additional reaction occur:
16O + 4He -> 20Ne + energy
This ultimately leads to the formation of a rare neon-oxygen white dwarf.
Stage 14: Black Dwarf – Once a star becomes a white dwarf, its evolution is over. The isolated white dwarf continues to cool and dim, and eventually becomes a black dwarf – a cold, dense, burned-out ember in space. This is the graveyard of stars. The dwarf does not shrink much as it fades away. Although heat is leaking away into space, gravity does not compress it further. The resistance of electrons to being squeezed together supports the star, even as its temperature drops almost to absolute zero. As the dwarf cools, it remains about the size of Earth.
In star clusters, there are stars that appear at first slight to be in contrast to the stellar evolution theory. These stars remain on the main sequence while other stars in the cluster of the same size have already moved off into white dwarfs. These stars are called blue stragglers. They are main-sequence stars, but they did not form when the cluster did. They formed more recently through mergers of lower mass stars. These mergers are from stellar evolution in binary systems, as the component stars evolve, grow and come into contact. Some mergers are thought to be the result of actual collisions between stars. The dense central cores of globular clusters are among the few places in the entire universe where stellar collisions are likely to occur.
High mass stars evolve much faster than their low mass counterparts. All evolutionary changes happen much more rapidly for high mass stars because their large mass and stronger gravity generate more heat, speeding up all phases of stellar evolution. In fact, helium fusion proceeds so quickly that the high mass star has a very different evolutionary track. Its envelope swells and cools as the star becomes a supergiant.
Where stars of 1 solar mass move almost vertically away from the main sequence up the red giant branch, stars of higher mass move nearly horizontally across the H-R diagram after leaving the upper main sequence. Their luminosities stay roughly constant as their radii increase and their surface temperature drops. In suns of greater than 2.5 solar masses, there is no helium flash. Helium burning begins smoothly and stably, not explosively. The more massive the star, the lower its core density when the temperature reaches the 108 K needed for helium to ignite, and the smaller the contribution of pressure from degenerate electrons. The unstable core described earlier does not occur. There is no sudden jump to the horizontal branch and no renascent of the giant branch. Instead, the star loops smoothly back and forth near the top of the H-R Diagram.
At 8 solar masses, the dividing line between high and low mass stars, a much more important divergence occurs. Where low mass stars never achieve the 600 million K needed to fuse carbon nuclei (so it ends its life as a carbon-oxygen, or possibly neon-oxygen, white dwarf), a high mass star can fuse only only hydrogen and helium, but also carbon, oxygen, and even heavier elements as its inner core continues to contract and its central temperature continues to rise. The rate of burning accelerates as the core evolves. As each element is burned to depletion at the center, the core contracts and heats up, and fusion starts again. A new inner core forms, contracts, heats again, and so on. The star’s track continues smoothly across the supergiant region of the H-R diagram, seemingly unaffected by each new phase of burning. The star’s radius increases as temperature drops, so the star swells to become a red supergiant. With heavier and heavier elements forming at increasing rates, the high mass star’s evolution and ultimate fate is destined to end in a violent supernova – a catastrophic explosion releasing energy that will literally blow the star to pieces soon after carbon and oxygen begin to fuse in its core. High mass stars evolve so rapidly that they explode and die shortly after leaving the main sequence.
Protostars and stars evolve because gravity always tends to cause a nonburning stellar core to contract and heat up. The contraction continues until either electron degeneracy pressure or the onset of a new round of nuclear fusion halts it. In the latter case, a new core builds up and the process repeats. The more massive the star, the more repetitions occur before the star finally dies. The following table shows the end points of evolution for stars of different masses:
Initial Mass (solar units) -> Final State
Less than 0.08 -> (hydrogen) brown dwarf
0.08 – 0.25 -> helium white dwarf
0.25 – 8 -> carbon-oxygen white dwarf
8 – 12 (approximately) -> neon-oxygen white dwarf
Greater than 12 -> supernova
The dividing line of 8 solar masses refers to the mass at the time the carbon core forms. Since very luminous main sequence stars often have strong stellar winds, stars as massive as 10 to 12 times the mass of the Sun may still manage to avoid going supernova.
Star clusters are excellent test sites for the theory of stellar evolutions. Every star in a cluster formed at the same time from the same cloud with virtually the same composition. The mass of each star varies, allowing us to check the accuracy of the theoretical models in a straightforward way. Starting from the zero-age main sequence, astronomers can predict exactly how a newborn cluster should look at any subsequent time – which stars are on the main sequence, which are becoming giants, and which have already burned themselves out. Although we can’t see the interiors of stars to test the models, we can compare the outward appearances with theoretical predictions.
The study starts after the cluster’s formation, with the upper main sequence already fully formed and stars of lower mass just beginning to arrive on the main sequence. The appearance of clusters at this early stage is dominated by the most massive stars: the bright blue supergiants. The cluster can then be followed forward in time and seen how it evolves by using an H-R diagram. At any point during the cluster’s evolution, the original main sequence is intact up to some stellar mass corresponding to the stars that are just leaving the main sequence. You can imagine the main sequence being “peeled away” from the top down. The high luminosity end of the observed main sequence is the main-sequence turnoff. The mass of a star that is just evolving off the main sequence at any moment is known as the turnoff mass. By studying H-R diagrams of clusters, and comparing them to stellar theory, it has been determined that all the globular clusters in our galaxy formed between about 10 and 12 billion years ago.
The previous look at stellar evolution focused on isolated stars. Most stars in our galaxy are not isolated, but are actually members of binary-star systems. How does the presence of a stellar companion affect a star’s stellar evolution? The answer depends on the distance between the two stars in question.
If the stars are widely separated (greater than about a thousand stellar radii), the stars evolve more or less independently of one another, each following the track appropriate to an isolated star. If the stars are closer, then the gravitational pull of one may influence the envelope of the other. In that case, physical properties of both may deviate greatly from those calculated for isolated single stars.
Each star in a binary system is surrounded by a Roche lobe, a teardrop shaped “zone of influence” inside of which its gravitational pull dominates the effects of both the other star and the overall rotation of the binary. Any matter within that region belongs to the star and cannot easily flow onto the other component or out of the system. Outside the two regions, it is possible for the gas to flow toward either star relatively easily. The Roche lobes of the two stars meet at a point on the line joining them – the inner Lagrangian point. The Lagrangian point is a point in the plane of two massive bodies orbiting one another, where a third body of negligible mass can remain in equilibrium. In other words, this is the point where the gravitational pulls of the two stars exactly balance the rotation of the binary system.
Normally both stars lie well within their respective Roche lobes, and such a binary is said to be detached. As a star leaves the main sequence and moves toward the giant branch, it is possible for its radius to become so large that the star overflows its Roche lobe. Gas begins to flow onto the companion through the Lagrangian point. In this case, the binary is said to be semidetatched. Because matter flows from one star to the other, semidetatched binaries are also known as mass-transfer binaries. If for some reason the other star overflows it’s Roche lobe (either due to stellar evolution or because so much extra material is dumped on it), the surfaces of the two stars merge. This is a contact binary – a binary system that consist of two nuclear-burning stellar cores surrounded by a single continuous common envelope.
Although most stars shine steadily day after day, year after year, some change dramatically in brightness over very short periods of time. One type is called a nova, or novae (plural). This type of star may increase enormously in brightness by a factor of 10,000 or more in a matter of days and then slowly return to its initial luminosity over a period of weeks or months. Nova means new in Latin. Astronomers now know that nova is not a new star, but is instead a white dwarf – a normally very faint star – undergoing an explosion on its surface that results in a rapid temporary increase in the star’s luminosity. On average, two or three novae are observed each year. There are also recurrent novae – stars that have been observed to “go nova” several times over the course of a few decades.
Nova are caused when a white dwarf is part of a binary system. If the distance between the two stars is small enough, the dwarf’s tidal gravitational field can pull matter (primarily hydrogen and helium) away from the surface of its main-sequence or giant companion. The system becomes a mass-transferring binary. The material leaves the star, travels through the Lagrangian point, and flows towards the white dwarf. It does not flow directly on it, however, but rather loos around behind it, and goes into orbit around the dwarf. The material forms a swirling disk of matter called an accretion disk. Due to viscosity (friction) within the gas, the matter in the disk drifts gradually inward, its temperature increasing steadily as it spirals down onto the dwarf’s surface. The inner part of the disk becomes so hot that it radiates strongly in the visible, ultraviolet, and even X-ray portions of the electromagnetic spectrum. In many systems, the disk outshines the dwarf and is the main source of the light emitted between the nova outbursts.
The stolen gas becomes hotter and denser as it builds up on the white dwarf’s surface. Eventually, the temperature exceeds 107 K, and hydrogen ignites, fusing into helium at a furious rate. This surface burning is both brief and violent. The star flares up in luminosity, and then fades away as some of the fuel is exhausted and the remainder is blown off into space.
A low mass star (less than about 8 solar masses) never gets hot enough to burn carbon in its core. It ends its life as either a carbon-oxygen or neon-oxygen white dwarf. A high mass star can fuse carbon, and even oxygen, into heavier elements. As the temperature increases with depth, the ash of each burning stage becomes the fuel for the next stage. At the relatively cool periphery of the core, hydrogen fuses into helium. In the intermediate layers, the shells of helium, carbon and oxygen burn to form heavier nuclei. Deeper down are neon, magnesium, silicon, and other heavy nuclei – all produced by nuclear fusion in the layers overlying the core. The core itself is composed of iron.
As each element is depleted at the center, the core contracts, heats up, and starts to fuse the ash of the previous burning stage. A new inner core forms, contracts again, heats again, etc. The star’s central temperature increases, and nuclear reactions speed up, causing the newly released energy to support the star for shorter periods of time. As an example, a 20 solar mass star burns hydrogen for 10 million years, helium for 1 million years, carbon for a thousand years, oxygen for a year, and silicon for a week. Its iron core grows for less than a day.
Iron is the most stable element there is. Lighter nuclei fuse together to make a new nuclei, such as fusing four protons to make helium-4 nucleus. The new nucleus has less mass than the 4 protons, so energy is released. Heavier elements take a different approach. Rather than using fusion to create energy, heavier elements (such as uranium or lead) use fission – where heavy nuclei are split into lighter ones to create energy. This is because with the heavier nuclei, combining them will increase mass, and not produce energy (in fact, it absorbs energy). Iron lies right on the dividing line between these two processes. Iron nuclei are so compact, energy cannot be extracted either by combining into heavier elements, nor splitting into lighter ones.
In stars, iron acts like a fire extinguisher, damping the inferno in the stellar core. When there are substantial quantities of iron, the central fires cease for the last time, and the star’s internal support begins to dwindle. The star’s equilibrium is gone forever. Although the inner temperature is several billion K, the enormous inward gravitational pull of matter overwhelms the pressure and the star implodes, falling in on itself.
The core temperature rises to nearly 10 billion K. AT that temperature, individual photons have enough energy to split iron into lighter nuclei and then break those lighter nuclei apart until only protons and neutrons remain. This process is known as photodisintegration of the heavy elements in the core. It takes less than a second to undo all the effects of nuclear fusion that occurred during the previous 10 million years. To split iron and lighter nuclei into smaller pieces requires a lot of energy. Photodisintegration absorbs some of the core’s thermal energy. It cools the core and thus reduces the pressure there. As nuclei are destroyed, the core of the star becomes less able to support itself against its own gravity, and the collapse accelerates.
AT this point, the core consists of simple elementary particles – electrons, protons, neutrons, and photons – all at enormously high densities, and still shrinking. The protons and electrons are pushed together, forming neutrons and neutrions:
P + e -> n + neutrino
This process is sometimes referred to as the nuetronization of the core. The central density has reached 1012 kg/m3 (or more). However, because neutrinos hardly interact with matter at all, they pass through the core as if it weren’t there, escaping into space, carrying away energy, and further reducing the core’s pressure support.
The disappearance of the electrons and neutrinos leave nothing to prevent the core from collapsing to the point at which neutrons come into contact with each other. At about 1015 kg/m3 the neutrons in the core give rapidly increasing resistance to further compression, producing pressures that finally slow the core’s gravitational collapse. By the time the collapse actually halts, however, the core has reached densities of 1017 or 1018 kg/m3. Because it has shrunk down so much, it begins reexpanding.
These events do not take long. Only about a second goes by from the start of the collapse to the reexpansion of nuclear densities. At this point, an enormously energetic shock wave sweeps through the star at high speed, blasting the overlying layers (including all the heavy elements just formed outside the inner iron core) into space. The star explodes. The exploding star may rival in brightness the entire galaxy in which it resides for a period of a few days. This spectacular death rattle of a high mass star is known as a core-collapse supernova.
Like a nova, a supernova is a star that suddenly increases dramatically in brightness and then slowly dims again, eventually fading from view. In its unexploded state, a star that will become a nova is known as the supernova’s progenitor. The light curves for a supernova can appear similar to a nova, and a distant supernova can look like a nearby nova. Supernova are much more energetic events, driven by different underlying physical processes. However, astronomers still tend to blur the distinction between the observed event (sudden appearance and brightening of an object in the sky), process responsible (violent explosion in or on a star), and the object itself (the star itself is called a nova or supernova). The two terms can have any of the three meanings, depending on the context.
A supernova is more than a million times brighter than a nova. It produces a burst of light billions of times brighter than the Sun, reaching that level of brightness within a few hours. During the few months it takes the supernova to brighten and fade away, it will create roughly 1043 J of electromagnetic energy. This is almost as much as the Sun will radiate during its entire lifetime. Another difference between nova and supernova is that a star may become a nova many times, but can only be a supernova once.
There are also differences among supernova. Some contain very little hydrogen, where others contain a lot. The light curves for these two types are qualitatively different. Because of this, astronomers divide supernovae into two categories. These are type I and type II supernovae.
The hydrogen poor type have a light curve somewhat similar to that of a typical novae. These are known as type I supernovae. A Type I supernova is where a white dwarf in a binary star system can accrete enough mass that it cannot support its own weight. The star collapses and temperatures become high enough for carbon fusion to occur. Fusion begins throughout the white dwarf almost simultaneously and an explosion results. Since a white dwarf is held together by electron degeneracy instead of thermal pressure, there is a limit to the pressure that the electrons can produce. There is, therefore, a limit to the amount of mass a white dwarf can have. This is about 1.4 solar masses, which is called the Chandraeskhar mass. If the white dwarf exceeds this mass, then the star starts to collapse. Carbon fusion begins everywhere throughout the white dwarf almost simultaneously, and the entire star explodes. This is called a carbon-detonation supernova. This can also be caused by two white dwarfs in a binary star colliding and merging to form a massive, unstable star.
The other type, whose spectra shows lots of hydrogen, have a characteristic plateau in the light curve a few months after the maximum. These are type II supernovae. A core-collapse supernova is also known as a Type II supernova. In short, the highly evolved stellar core rapidly implodes and then explodes, destroying the surrounding star.
Despite the similarities in total amounts of energy involved, the two types of supernovae are unrelated to one another. All high mass stars become type II (core-collapse) supernovae. Only a tiny fraction of low mass stars evolve into white dwarfs that ultimately explode as type I (carbon-detonation) supernovae. However, because there are far more low mass stars than high mass stars, the two types of supernova occur at roughly the same rate.
A supernova remnant is the scattered glowing remains from a supernova that occurred in the past. The Crab Nebula is one of the best studied supernova remnants. The Chinese observed the supernova explosion that caused the Crab Nebula in 1054 AD. The explosion was so brilliant that ancient Chinese and Middle Eastern astronomers claim its brightness greatly exceeded that of Venus, and according to some, rivaled that of the Moon. The exploded star could reportedly be seen in broad day light for nearly a month.
A viewable Milky Way star has not exploded since Galileo first turned his telescope to the heavens almost 4 centuries ago. The last supernovae observed in our galaxy was by Tycho in 1572, and Kepler (and others) in 1604. Stellar evolution theory suggests that an observable supernova should occur in our galaxy every 100 years or so. Even at several kiloparsecs, it would outshine Venus. A truly nearby supernova (within a few hundred parsecs) would be very rare, about one every 100,000 years or so.
We currently know of 115 different elements, ranging from the simplest (hydrogen containing one proton) to the most complex (first reported in 2004 and known for now as ununpentium which as 115 protons and 184 neutrons in its nucleus). In 1999, researchers claimed the discovery of elements 116 and 118. However, the experimental findings have not been replicated, and these are not officially recognized. All elements exist in different isotopes, each having the same number of protons, but different number of neutrons. The “normal” form of an element is the most common or stable isotope. Some elements and many isotopes are radioactively unstable, meaning that they eventually decay into other more stable nuclei.
There are 81 stable elements found on Earth that make up the bulk of matter in the universe. In addition, 10 radioactive elements (including radon and uranium) also occur naturally on our planet. Half lives of the elements refers to the time that it takes for half the nuclei to decay into something else. These 10 elements have very long half lives, but the slow steady decay over 4.5 billion years mean that they are scarce on Earth.
There are also 19 more radioactive elements that have been artificially produced on Earth. Unlike the 10 natural elements, the 19 artificially created ones decay quite quickly (much less than a million years). Two other elements round out the list: Promethium is a stable element that is found on our planet only as a by-product of nuclear lab experiments; technetium is an unstable element that is found in stars, but does not exist on Earth. Any that did exist decayed long ago.
Hydrogen and most of the helium in the universe are primordial – these elements date from the very earliest times. All other elements result from stellar nucleosynthesis. They were formed by nuclear fusion in the hearts of stars. The table below shows the abundances of the elements in the universe:
The most obvious feature is that heavy elements are generally much less abundant than lighter elements.
As we discussed before, at temperatures of at least 10 million K, the proton-proton chain starts a series of nuclear reactions, ultimately forming a nucleus of ordinary helium (4He) from four protons (1H).
4(1H) -> 4He + 2 positrons + 2 neutrinos + energy
Positrons react immediately with nearby free electrons, producing high energy gamma rays through matter-antimatter annihilation. Neutrinos rapidly escape, carrying energy with them. In massive stars, the CNO cycle may greatly accelerate the hydrogen burning process, but the basic four protons to one helium nucleus reaction is unchanged.
As helium builds up in the core, the burning ceases, the core contracts and heats up. At about 100 million K, the triple-alpha reaction occurs:
3(4He) -> 12C + energy
The net result is that three helium-4 nuclei are combined into one carbon-12 nucleus releasing energy in the process.
At about 600 million K (reached only in the cores of stars much more massive than the Sun), carbon nuclei fuse to form magnesium.
12C + 12C -> 24Mg + energy
Fusion reactions between any nuclei larger than carbon require such high temperatures that they are actually quite uncommon in stars. The formation of most heavier elements occurs by way of an easier path. Since the repulsive force between two carbon nuclei is three times greater than the force between carbon and helium, carbon-helium fusion occurs at a lower temperature than carbon-carbon fusion occurs. At about 200 million K, carbon-12 nucleus colliding with a helium-4 nucleus can produce oxygen-16.
12C + 4He -> 16O + energy
At about 1 billion K, w oxygen-16 nuclei form sulfur-32
16O + 16O -> 32S + energy
At a lower temperature than necessary for oxygen-oxygen fusion, oxygen-16 can fuse with helium-4 to form neon-20
16O + 4He -> 20Ne + energy
As stars evolve, heavier elements tend to form through helium capture (the formation of heavy elements by the capture of a helium nucleus) rather than by fusion of like nuclei. As a result, elements with nuclear masses of 4 (helium), 12 (carbon), 16 (oxygen), 20 (neon), 24 (magnesium) and 28 (silicon) stand out more.
Helium capture is not the only type of nuclear reaction occurring in evolved stars. In some, protons and neutrons are freed from their parent nuclei and are absorbed by others, forming new nuclei with masses intermediate between those formed by helium capture. Lab experiences confirm that common nuclei such as fluorine-19, sodium-21, phosphorus-31, and many others are created in this way. Their abundances are not as great as those produced directly by helium capture, simply because the helium capture reactions are much more common in stars.
Around the time silicon-28 appears, a competitive struggle begins between the continued capture of helium to produce even heavier nuclei and the tendency of more complex nuclei to break down into simpler ones. The cause of this breakdown is heat. This happens when the core temperature reaches 3 billion K, and gamma rays have enough energy to break a nucleus apart. Under this intense heat, silicon-28 breaks apart into seven helium-4 nuclei. Other heavier nuclei capture some or all of these helium-4 leading to the formation of heavier elements. In succession, the star forms sulfur-32, argon-36, calcium-40, titanium-44, chromium-48, iron-52 and nickel-56. The chain of reactions building from silicon to nickel is:
28Si + 7(4He) -> 56Ni + energy
This two-step process (photodisintegration followed by the direct capture of some or all of the resulting helium-4) is often called the alpha process.
Nickel-56 is unstable, decaying rapidly first into cobalt-56, and then into a stable iron-56 nucleus. Any unstable nucleus will continue to decay until stability is achieved. Iron-56 is the most stable of all nuclei.
Neutron capture (the formation of heavier nuclei by the absorption of neutrons) is the process that forms heavier elements (such as copper, zinc and gold) than iron. Adding a neutron (no electric charge, so no repulsion) to an element does not change it to another element. It merely makes it a more massive isotope of the same element. Eventually so many neutrons have been added to the nucleus that it becomes unstable and then decays to form a stable nucleus of some other element. For example, an iron-56 nucleus can capture a single neutron to form a stable isotope, iron-57. This reaction may be followed by another neutron capture and another until iron-59 is produced. This is radioactively unstable, and decays to cobalt-59, which is stable.
Each successive capture of aneutron by a nucleus typically takes about a year. This slow neutron-capture is called the s-process (slow process). It is the origin of copper, silver, lead, gold, etc. These reactions are thought to be particularly important during the late (asymptotic-giant branch) stages of low mass stars.
The s-process explains the creation of stable nuclei up to and including bismuth-209 (the heaviest known nonradioactive element). It cannot, however account for heavier elements such as thorium-232, uranium-238, or plutonium-242. Any attempt to form elements heavier than bismuth through s-process fail because they decay back to bismuth as fast as they form. The process to make the heavier elements is known as r-process (rapid process). This happens during the supernova explosion that signals the death of a massive star. The r-process is responsible for the creation of the heaviest-known elements, jamming neutrons into light and middleweight nuclei. The heaviest of the heavy elements are actually created after their parent stars have died. Because the time available for synthesizing these heaviest nuclei is so brief, then never become very abundant. Elements heavier than iron are a billion times less common than hydrogen and helium.
Observational evidence of the creation of the elements in stars is found by three particularly convincing pieces of evidence. First, the rates at which various nuclei are captured and the rates at which they decay are known from lab experiments. Second is the presence of technetium-99. The presence of this material (with a half life of 200,000 years) in the spectra of many red-giant stars is taken as proof that the s-process really does operate in evolved stars. Third is the stufy of typical light curves from Type I supernovae indicates that radioactive nuclei form as a result of the explosion.
Because the heavy elements are produced in the core, and the outer layers largely retain the star’s original composition (only at the end of a star’s life are the elements released and scattered itno space), only the youngest stars show the most heavy elements in their spectra. This is because the interstellar clouds that they formed from contained these elements, because they were placed there by stars that died out and exploded previously. Each new generation of stars increases the concentration of these elements in the interstellar coulds from which the next generation forms.
To briefly summarize the three steps that make up the complete cycle of star formation and evolution in our galaxy:
1. Stars form when part of an interstellar cloud is compressed beyond the point at which it can suppor itself against its own gravity.
2, Within the cluster, stars evolve. The most massive stars evolve faster, creating the heaviest elements in their cores, and sending them out into the interstellar medium in supernovae. Lower mass stars take longer to evolve, but can create heavy elements and contribute to the seeding of interstellar space when they shed their envelopes as planetary nebulae. Low mass stars are responsible for most of the carbon, nitrogen and oxygen; high mass stars produce the iron and silicon, as well as the heavier elements.
3. The creation and explosive dispersal of newly formed elements are accompanied by shock waves, which pass though the interstellar medium and both enrich and compress it into star formation. Each generation of stars increases the concentration of heavy elements in the interstellar clouds from which the next generation forms.
Neutron Stars and Black Holes
For Type I carbon-detonation supernovae, it is unlikely that any central remnant is left after the explosion. For Type II supernova, part of the star may survive. The explosion destroys the star, but may leave a tiny ultracompressed remnant at its center. As the Type II star collapses, electrons smash violently with protons creating neutrons and neutrinos. The neutrinos escape, causing the core to collapse even faster. This causes the particles inside to come into contact, at which point the central portion of the core "bounces" creating a shock wave that rips the star apart, expelling matter violently into space. Since the shock wave does not start at the very center of the core, the inner most part of the core remains intact as the shock wave destroys the rest of the star. This ball of neutrons that is left (the core remnant) is called a neutron star, although it is not a star in any true sense of the word, because all of its nuclear reactions have ceased forever.
Neutron stars are extremely small and very massive. They are composed of neutrons packed tightly together in a ball about 20 km across. A typical neutron star is not much bigger than a small asteroid or a city. Its mass, however, is greater than that of the Sun. The average density can reach 10^17 or even 10^18 kg/m^3, nearly a billion times denser than a white dwarf. A normal atomic nucleus has a density of about 3 X 10^17 kg/m^3. A thimbleful of neutron star material would weigh 100 million tons (the amount of a good-sized mountain). A neutron star is, in a sense, a single enormous nucleus with an atomic mass of around 10^57. At this density, neutrons resist further packing. This neutron degeneracy pressure supports the neutron star much the same way that electron degeneracy pressure supports the white dwarf.
Neutron stars have extreme gravity. A 70-kg (150 pound) person on Earth would weight the equivalent of about 10 trillion kg (10 billion tons) if he were standing on a neutron star. In addition to large mass and small size, neutron stars also have two other very important properties. First, they rotate rapidly with periods measured in fractions of a second. Second, newborn neutron stars have very strong magnetic fields. The original field of the progenitor star is amplified by the collapse of the core because the contracting material squeezes the magnetic field lines closer together, creating a magnetic field trillions of times stronger than Earth's. Theory indicates that over time, the neutron star will spin slower and slower as it radiates its energy into space, and its magnetic field will diminish. For a few million years after its birth, however, these two properties combine to provide the primary means of detecting and studying the neutron stars.
The first observation of a neutron star occurred in 1967. Jocelyn Bell observed an astronomical object emitting radio radiation in the form of rapid pulses. Each pulse was a 0.01 second burst of radiation, after which there was nothing, then 1.34 seconds later another pulse. There are more than 1500 of these pulsating objects known in the Milky Way, called pulsars. Pulsars emit periodic bursts of radiation. Each has its own characteristic pulse period and duration. In some cases, the pulse periods are stable enough to set a clock by them. Some are predicted to change periods by only a few seconds in a million years. Pulsars are described as a compact, spinning neutron star that periodically flashes radiation toward Earth.
Two “hot spots” on the surface of a neutron star, or in the magnetosphere just above the surface, continuously emit radiation in a narrow “searchlight” pattern. These spots are localized regions near the neutron star’s magnetic poles, where charged particles emit radiation along the star’s magnetic axis. The hot spots radiate more or less steadily, and the resulting beams sweep through space like a revolving lighthouse beacon. This pulsar model is often known as the lighthouse model. If the neutron star happesn to be oriented such that the beam sweeps across Earth, we see the star as a pulsar. The beams are observed as a series of rapid pulses. The period of the pulses is the star’s rotation period.
The neutron star’s strong magnetic field and rapid rotation channel high energy particles from near the star’s surface into the surrounding nebula. The result is an energetic pulsar wind that flows outward at almost the speed of light, primarily in the star’s equatorial plane. Most pulsars emit pulses in the form of radio radiation. Some have been observed to pulse in the visible, X-ray and gamma ray parts of the spectrum as well. The periods of most pulsars are quite short, ranging from about 0.03 to 0.3 seconds (3 to 30 times per second). The human eye is insensitive to such rapid flashes, making it impossible to observe the flickering of a pulsar by eye.
Most known pulsars are observed to have high speeds – much greater than the typical speeds of stars in the Galaxy. If the supernova’s enormous energy is channeled even slightly in one direction, the newborn neutron star can recoil in the opposite direction with a speed of many tens or even hundreds of kilometers per second.
All pulsars are neutron stars, but not all neutron stars are pulsars. The two ingredients that make a neutron star pulse (rapid rotation and strong magnetic field) diminish with time. The pulses gradually weaken and become less frequent. Also, even a young, bright neutron star is not necessarily detectable as a pulsar from Earth’s vantage point.
Pulsar observations are consistent with three ideas of star formation, stellar evolution and neutron stars. (1) Every high mass star dies in a supernova explosion. (2) Most supernovae leaves a neutron star behind. (3) All young neutron stars emit beams of radiation. At least some neutron stars have binary pairs. Because of this pairing, the masses of some neutron stars have been determined quite accurately. All the measured masses are close to 1.4 times the mass of the Sun (the Chandrasekhar mass of the stellar core that collapsed to form the neutron star remnant).
An x-ray burster is an x-ray source that radiates thousands of times more energy than our Sun in short bursts lasting only a few seconds. A neutron star in a binary system accretes matter onto its surface until temperatures reach the level needed for hydrogen fusion to occur. The result is a sudden period of rapid nuclear burning and release of energy. Not all infalling gas makes it to the neutron star’s surface. Instead, it is shot completely out of the system at enormously high speeds in the form of two oppositely directed narrow jets moving roughly perpendicular to the disk. The jets move at speeds of almost 80,000 km/s (over 25% the speed of light). Jets of this sort are quite common in systems in which an accretion disk surrounds a compact object. Note that these jets are not the lighthouse beams of radiation from the neutron star itself, nor are they associated with a pulsar wind. As the jets interact with interstellar medium, they emit radio radiation.
A microquasar is a stellar sized source of energetic X and gamma radiation, powered by accretion onto a neutron star or black hole, somewhat like a quasar but on a much smaller scale.
In the mid 90’s, a new category of pulsars was found. Millisecond pulsars are a class of very rapidly rotating objects. More than 200 are currently known in the galaxy. They spin hundreds of times per second. This speed is about as fast as a typical neutron star can spin without flying apart. In some cases, the equator of the star is moving at more than 20% the speed of light.
Some neutron stars are at least 10 billion years old. We know this because they are found in globular clusters. These should have slowed down after tens of millions of years, but they are still going. The most likely explanation for the high rotation rate of pulsars is that the neutron star has been spun up by drawing in matter from a companion star. As matter spirals down onto the star’s surface in an accretion disk, it provides the push needed to make the neutron star spin faster.
Although a pulsar is a direct result of a supernova, millisecond pulsars are the product of a two-stage process. First, the neutron star forms. Second, through recent interactions with a binary companion, the neutron star then achieved rapid spin. This is similar to the way x-ray bursters form. Many x-ray bursters become millisecond pulsars, and many millisecond pulsars are x-ray sources.
Gamma-ray bursts consist of bright, irregular flashes of gamma rays typically lasting only a few seconds, possibly due to the collision and merger of two neutron stars initially in orbit around one another. The bursts never repeat at the same location, show no obvious clustering, and appear unaligned with any known large-scale structure, near or far. They are distributed uniformly across the sky (isotropic) rather than confined to the relatively narrow band of the Milky Way.
Gamma-ray observations do not provide enough information of themselves to tell how far away a burst is. In order to determine the distance, we must associate the burst with some other object in the sky whose distance can be measured. These objects are referred to as burst counterparts. However, gamma rays are far too penetrating to be focused by conventional optics. Also, the “afterglows” of a burst at x-ray or optical wavelengths fade quite rapidly limiting the time available to complete the search.
In all nearly 100 afterglows of gamma-ray bursts have been detected, and about 2 dozen distances are known. All are very large, meaning that the bursts must be extremely energetic. We find that each burst apparently generates much more energy (in some cases hundreds of times more energy) than a typical supernova explosion – all in a matter of seconds. As we have seen, finding the counterpart of a gamma-ray burst requires an accurate measurement of the burst’s location and fast communication.
A hypernova is a failed supernova. A very massive star undergoes core collapse much as described earlier for a Type II supernova. Instead of forming a neutron star, the core collapses to a black hole. AT the same time, the blast wave racing outward through the star stalls. Instead of being blown to pieces, the inner part of the star begins to implode, forming an accretion disk around the black hole and creating a jet. The jet punches its way out of the star, producing a gamma-ray burst as it slams into the surrounding shells of gas expelled romt he star during the final stages of the nuclear burning lifetime.
Hypernova are the explanation for “long” gamma ray bursts (defined as lasting more than about 2 seconds). The model has difficulty explaining the “short” bursts that are also observed. The neutron star merger model naturally produces short bursts.
Properties of stellar remnants
Although we do not have precise figures, most researches concur that the mass of a neutron star cannot exceed about 3 solar masses. That is the neutron star equivalent of the white dwarf’s Chandrasekhar mass limit. Above this limit, not even tightly packed neutrons can overcome the star’s gravitational pull. We know of no force that can counteract gravity once neutron degeneracy pressure is overwhelmed. If enough material is left behind after a supernova to exceed the 3 solar mass limit, gravity beats pressure and the star’s central core collapses forever. This is the fate of any star with a main sequence mass of over 25 times the mass of the Sun. As the core shrinks, the gravitational pull becomes so great that not even light can escape it. The resulting object emits no light, no radiation, no information whatsoever. This bizarre end point of stellar evolution, in which a massive core remnant collapses in on itself and vanishes forever, is a black hole.
Newtonian mechanics break down in a black hole. However, the Newtonian concept of escape speed can be supplemented by two facts from Einstein’s general theory of relativity: (1) Nothing can travel faster than the speed of light, and (2) all things, including light, are attracted by gravity. Since the formula for escape velocity consists of the square root of the object’s mass over radius, as an object gets compressed smaller and smaller (but keeping the same radius), the escape velocity increases. If Earth could be squeezed to a radius of about 1 cm, the escape velocity would be about 300,000 km/s – the speed of light. Any smaller, say less than the size of a grape, and the escape velocity would be greater than the speed of light. Since nothing can travel faster than the speed of light, absolutely nothing – not even light – could escape from the surface of the highly compressed body.
With no photons leaving, the object would be invisible and uncommunicative. No signal of any sort could be sent to the universe. For all practically purposes, such an object could be said to have disappeared from the universe. Only the gravitational field would remain behind.
Only three physical properties of a black hole can be measured: mass, charge and angular momentum. All other information is lost once matter enters the hole.
The Schwarzschild radius is the critical radius at which the escape speed from an object would equal the speed of light, and within which the object could no longer be seen. The radius is the object’s mass (in solar mass units) times 3 km. Thus the Sun’s radius is 3 km. A 2 solar mass object is 6 km. The Earth is 1 cm.
The event horizon is a sphere centered on a collapsing star with a radius equal to the Schwarzschild radius. Although there is no matter to it, this is considered the surface of the black hole. A 1.4 solar mass neutron star has a radius of about 10 km and a Schwarzschild radius of 4.2 km.
The speed of light is independent of its source or observer. No matter what our motion may be relative to the source of the radiation, we always measure precisely the same value for c (speed of light): 299,792,458 km/s. This was proved by the Michelson-Morley Experiment in 1887.
Einstein has two theories of relativity. They are special relativity and general relativity.
Special relativity deals with the preferred status of the speed of light. The essential features of the theory are:
1. The speed of light © is the maximum possible speed in the universe, and all observers measure the same value for c, regardless of their motion. Einstein broadened this statement into the principle of relativity: The basic laws of physics are the same to all unaccelerated observers.
2. There is no absolute frame of reference in the universe; that is, there is no “preferred” observer relative to whom all other velocities can be measured. Put another way, there is no way to tell who is moving and who is not. Instead, only relative velocities between observers matter.
3. Neither space nor time can be considered independently of one another. Rather, they are each components of a single spacetime. There is no absolute, universal time – observers’ clocks tick at different rates, depending on the observers’ motions relative to one another.
The Lorentz contraction is where there is an apparent contraction of an object in the direction in which it is moving. This occurs as an object’s velocity approaches the speed of light. Because of Lorentz contraction, a meterstick moving at 90% the speed of light would shrink to a little less than half a meter (this is not an optical illusion, but an actual shrinkage).
In order to compensate for gravity in Einstein’s theory of special relativity, he created the equivalence principle – there is no way to tell the difference between a gravitational field and an accelerated frame of reference. This was demonstrated with the thought problem of being in an elevator where you cannot see outside and in space. The upward push you would feel (as you are weightless in space) is caused by either gravity from an object pulling you down, or the acceleration of the elevator going up. Without being able to see where you are relative to the rest of space, you cannot know the difference. In adding this in, the math showed that spacetime (as one object) had to be curved. General relativity is the resulting theory of including gravity within the framework of special relativity. The central concept is that all matter tends to warp space in its vicinity. Objects such as planets and stars react by changing their paths. As John Archibald Wheeler stated: “Spacetime tells matter how to move, and matter tells spacetime how to curve.”
Because a black hole will accrete at least a little material from its surroundings, its mass, and therefore also the radius of the event horizon, will increase slowly over time. Tidal forces at work in and near a black hole are the same basic phenomenon responsible for ocean tides on Earth, except that tidal forces near a black hole are far stronger than any other force we know in the solar system. Whatever falls into a black hole is vertically stretched and horizontally squeezed, and accelerated to high speeds in the process.
Gravitational redshift is a prediction of Einstein’s general theory of relativity. Photons lose energy as they escape the gravitational field of a massive object. Because a photon’s energy is proportional to its frequency, a photon that loses energy suffers a decrease in frequency, which corresponds to an increase (or redshift) in wavelength. Time dilation is closely related to the gravitational redshift. To an outside observer, a clock lowered into a strong gravitational field will appear to run slow (but time will appear to run normal for the clock).
A point in which both a star’s density and its gravitational field become infinite is known as a singularity. Singularities are not physical. They always signal the breakdown of the theory producing them. In other words, the present laws of physics are simply inadequate to describe the final moments of a star’s collapse.
A supermassive black hole is a black hole having a mass a million to a billion times greater than the mass of the Sun. Usually these are found in the central nucleus of a galaxy.