Introduction

Ancient astronomers knew that the sky is not static. They observed the regular motions of the planets across the sky, and they noted the dramatic and unexpected appearances of comets in the sky. The most striking events they saw were the stars that would suddenly appear in the sky and then fade away after a month. In Europe these transient stars were given the Latin name “nova,” meaning new. The ancient Chinese astronomers cataloged many novae as part of their duties to keep the emperor informed of occurrences in the sky—if an emperor were truly the intermediary between heaven and Earth, as he proclaimed, he had to show his subjects that we was aware of what the heavens were up to.

Today several different events in astronomy go by the name nova. The classical novae are outbursts by cataclysmic variable stars. These binary stars repeatedly produce outbursts. More striking than the classical nova are the supernovae, which are given this name because of the tremendous amount of energy they produce. The energy generated by a supernova is a significant fraction of the rest-mass energy of a solar mass star. A supernova at its peak outshines its host galaxy. It is so luminous that it can be seen across the universe by the most powerful telescopes. The nova seen by the Danish astronomer Tycho Brahe in 1572 was a supernova.

The search for supernovae is intense, and dozens are found every year through automated searches with ground-based telescopes. Supernovae are very rare events. They are expected to take place in the Milky Way only at a rate of about once every 50 years, and this despite being in an unusually large galaxy with many young, massive stars. To observe large numbers of supernovae in a short time, one must observe many galaxies, which means observing out to the high-redshift limits of the universe. The supernovae that are found are labeled by their year and a letter that indicates their sequence of discover, so the first supernova of 2009 is called SN 2009a.

A supernova is an explosion of a massive supergiant star. It may shine with the brightness of 10 billion suns! The total energy output may be 1044 joules, as much as the total output of the sun during its 10 billion year lifetime. The likely scenario is that fusion proceeds to build up a core of iron. The “iron group” of elements around mass number A=60 are the most tightly bound nuclei, so no more energy can be gotten from nuclear fusion.

The core collapse supernova occurs when a massive star has consumed all of its thermonuclear fuel, so that the core is composed of iron. If the core of the star exceeds the Chandrasekhar mass limit, it collapses under its own gravity. The core shrinks from a radius of tens of thousands of kilometers to a radius of tens of kilometers, where the star is stabilized by the degeneracy exerted by protons and neutrons. The collapse liberates gravitational potential energy that blows away the layers overlying the star's core in an enormous explosion; the energy travels from the core to the outer layers as neutrinos.

Under the most popular theory for the thermonuclear detonation supernova, an explosion occurs when a white dwarf is pushed above the Chandrasekhar limit. This would happen in cataclysmic variable systems, where a white dwarf is pulling mass from a companion star onto itself. As the white dwarf grows in mass, it becomes gravitationally unstable, much as the core of a massive star becomes gravitationally unstable. The difference for the white dwarf is that it was formed from a fusion-powered star of several solar masses before all of the thermonuclear fuel was consumed. Many white dwarfs are composed of carbon and oxygen. When such a white dwarf collapses gravitationally, the pressure and temperature inside the star increase until the explosive thermonuclear fusion of carbon and oxygen commences. This thermonuclear release of energy is sudden, and the amount of energy released far exceeds the star's gravitational potential energy, so the star is blown apart.

Regardless of the energy source, whether gravitational or thermonuclear, one ends up with high-temperature stellar debris flung into space at high velocity. The brightening we see as a new star is the expansion of the photosphere of this debris. Eventually the brightening caused by the expansion is countered by the cooling of the debris, and the supernova fades from view.

The supernova shock we are so familiar with in the pictures of ancient supernova remnants is caused by the stellar debris plowing into the surround interstellar gas, driving a shock wave into the gas.

One of the more interesting features of the core-collapse supernovae is that they create elements heavier than iron. The interior of a fusion-powered star is cool compared to the energy required to convert iron into any other element, so the natural thermodynamic equilibrium is for hydrogen to combine into heavier elements until the matter is in its lowest energy state, which is pure iron. In the stellar debris of a supernova, however, the temperature exceeds the temperature at the core of the hottest star, and this drives the material in this debris to a thermal equilibrium comprised of elements much heavier than iron.

We owe our existence to supernovae, because many of the basic elements that make up our bodies were created in a supernova explosion. Extremely heavy elements like silver and gold are created only in supernovae, so if gold is the root of all evil, then supernovae provide the soil for that root. Supernovae created the radioactive elements like uranium, so when we create energy with a solar panel, we are harnessing the thermonuclear fusion of hydrogen in the Sun, but when we create energy from the nuclear fission of uranium, we are harnessing the power of an ancient supernova. We find mankind linked to the supernova, with our life, our well-being, the object of our greed, and the means to our destructiveness directly provided by an ancient supernova explosion.

Classification

Over the years, observers have developed a classification scheme for supernovae based on their spectra. The first broad distinction is between supernova that have the emission lines for helium—type I supernovae, where I is the Roman numeral 1—and those that have the emission lines for hydrogen—type II supernovae. These two types are further subdivided based on the specific pattern of spectral lines they possess. As with the spectral classification of stars, the supernova spectral subtypes are labeled as letters, starting with the letter a. So there is a type Ia supernova, for instance (this particular supernova type is widely used in cosmological studies to establish distance).

Like observers, theorists also divide supernovae into two classes: the core-collapse supernovae, and the thermonuclear detonation supernovae. These two classes are not aligned with the observers' type I and type II classes. The thermonuclear detonation supernova is associated only with the type Ia supernova, while the core-collapse supernova is associated with the type II and several of the type I supernovae.

Type I and Type II Supernovae

Supernovae are classified as Type I if their light curves exhibit sharp maxima and then die away smoothly and gradually. The maxima may be about 10 billion solar luminosities. The model for the initiation of a Type I supernova is the detonation of a carbon white dwarf when it collapses under the pressure of electron degeneracy. It is assumed that the white dwarf accretes enough mass to exceed the Chandrasekhar limit of 1.4 solar masses for a white dwarf. The fact that the spectra of Type I supernovae are hydrogen poor is consistent with this model, since the white dwarf has almost no hydrogen. The smooth decay of the light is also consistent with this model since most of the energy output would be from the radioactive decay of the unstable heavy elements produced in the explosion.

A type Ia supernova reaches its peak brightness about 20 days after the explosion, with an absolute visual magnitude of about −19.3, or almost 10 billion time the luminosity of the Sun. After peaking, the supernova declines in brightness by 3 magnitudes over a month and then by 1 magnitude every subsequent month until it fades from sight.

The features that mark a supernova as type Ia are the absence of hydrogen lines and the presence of silicon lines in the spectrum. The spectrum also shows the lines of intermediate mass elements such as oxygen, calcium, magnesium, and sulfur. Two weeks after the supernova reaches its peak magnitude, its spectrum shows the lines of iron and other elements of similar mass such as cobalt. The debris emitting this light moves at a very high velocity away from the explosion site. The highest velocities are about 10% of the speed of light.

The type Ia supernovae behave as though a single variable determines all of their characteristics; the shape of the spectrum, the change in luminosity with time, and the velocity of the debris are all set by the total amount of energy released in the explosion. Most supernovae differ from the average peak visual absolute magnitude by less than 0.3 magnitudes. Low-luminosity supernovae are redder and shorter-lived, with debris moving at a lower velocity, than high-luminosity supernovae. A consequence of this behavior is that if one knows the spectrum of a type Ia supernova at the peak apparent magnitude, one can infer the peak absolute magnitude. This property permits astronomers to use the type Ia supernovae as a standard candle for deriving the distances to the farthest galaxies and for studying the expansion of the universe.

Strictly speaking, not all type Ia supernovae behave in the same way. About 85% of these supernovae behave according to the single-variable pattern just described. The remaining nonconforming type Ia supernovae can differ in a variety of ways, including being several magnitudes less luminous than the conforming 85%. They are believed to have a different origin than the conforming 85%. They may be produced by the thermonuclear explosion of white dwarfs under different conditions than the conforming supernovae, or they may be from massive stars undergoing core collapse.

Type II supernovae have less sharp peaks at maxima and peak at about 1 billion solar luminosities. They die away more sharply than the Type I. Type II supernovae are modeled as implosion-explosion events of a massive star. They show a characteristic plateau in their light curves a few months after initiation. This plateau is reproduced by computer models which assume that the energy comes from the expansion and cooling of the star's outer envelope as it is blown away into space. This model is corroborated by the observation of strong hydrogen and helium spectra for the Type II supernovae, in contrast to the Type I. There should be a lot of these gases in the extreme outer regions of the massive star involved.

Type II supernovae are not observed to occur in elliptical galaxies, and are thought to occur in Population I type stars in the spiral arms of galaxies. Type I supernovae occur typically in elliptical galaxies, so they are probably Population II stars. Type Ia supernovae occur in all kinds of galaxies, whereas Type Ib and Type Ic have been seen only in spiral galaxies near sites of recent star formation (H II regions). This suggests that Types Ib and Ic are associated with short-lived massive stars, but Type Ia is significantly different.

With the observation of a number of supernova in other galaxies, a more refined classification of supernovae has been developed based on the observed spectra. They are classified as Type I if they have no hydrogen lines in their spectra. The subclass type Ia refers to those which have a strong silicon line at 615 nm. They are classified as Ib if they have strong helium lines, and Ic if they do not. Type II supernovae have strong hydrogen lines. These spectral features are illustrated below for specific supernovae.

Type II

  • A massive supergiant star (the supergiant must be very young -- as young as 1 million years)
  • gravity (collapse of the iron core)
  • A gaseous supernova remnant, containing elements heavier than iron. In addition, a type II supernova leaves behind a compressed stellar core, which is now a neutron star or black hole.
  • Hydrogen and heavier elements seen in the spectrum
  • Due to the collapse of a degenerate Fe core in a star with an initial mass › 8 or 9 Msun
  • Rate is one every 44 yr in our Galaxy

Examples:

  • SN1054 (“The Crab Nebula”) documented by Chinese astronomers
  • SN1987A (in the LMC)

Subdivided into two classes based on the shape of their light curve

  • Type II-L - Light decline relatively smoothly
  • Type II-P - Light curves exhibit a “plateau” 1 to 3 months after the peak due to the radioactive decay of 56Ni (t1/2 = 6.1 days) produced by the shock front as it passed through the stellar material

decay of other species also seen

  • 57Co (t1/2= 271 days)
  • 22Na (t1/2= 2.6 yr)
  • 44Ti (t1/2= 47 yr)

Type I

  • A white dwarf in a close binary system (the white dwarf might be very old -- up to 10 billion years)
  • nuclear fusion (carbon and oxygen to iron)
  • a gaseous supernova remnant, very rich in iron
  • Supernovae that do NOT show prominent Hydrogen in their spectra (all the hydrogen has been “burnt”)
  • One every 36 years in the Milky Way

Examples:

  • SN1572 (“The Tycho SNR”)
  • SN1604 (“The Kepler SNR”)

Subdivided into three main classes

  • Type Ic have weak He lines in their spectra
  • Type Ib have strong He lines in their spectra
  • Type Ia have strong SiII (615nm) lines

Type Ia

  • Occur in all types of galaxies
  • Thought to be due to the “explosion” of a White Dwarf (WD) in a close binary system with a Carbon-Oxygen (C-O) core
  • Most stars are actually binary systems (two stars orbiting their center of mass) In any binary, system, clearly mattter follows its gravitational destiny. The matter is the outer atmosphere of the normal star is strongly influenced of the gravity from both the normal star itself and that of WD. It will be more attracted to either the “normal star”, or the (in this case) WD star. In one location the gravitational fields will be equal. What determines what happens to the matter (and under what circumstances) at these points is (again) beyond the scope of this course. However under some circumstances matter (ie. mass) can be transferred to the WD

The additional mass desposited in this way will disrupt the equilibrium of the WD

  • When the mass of the WD reaches 1.3 Msun “Carbon burning” starts at the center. The increase in temperature does not produce an expansion of the degnerate core that would slow the reaction rate. The front of vigourous Carbon burning therefore moves towards the surface. [Carbon deflagration for those who have taken the Stellar course]
  • The subsequent expansion produces a cooling that eventually dampens the nuclear burning, leaving a mixture of partially processed intermediate-mass elements surrounding a Nickel-iron core. The energy release completely disrupts the star resulting in a Type Ia SN

The outer layers are expelled at 104 km/s

Types Ib and Ic

  • Appear to occur only in Spirals
  • Occur near regions of recent star formation
  • Thought to be due to the core collapse of short-lived massive stars (similar to Type II SNe)

Standard Candle

Type Ia supernovae have become very important as the most reliable distance measurement at cosmological distances, useful at distances in excess of 1000 Mpc.

One model for how a Type Ia supernova is produced involves the accretion of material to a white dwarf from an evolving star as a binary partner. If the accreted mass causes the white dwarf mass to exceed the Chandrasekhar limit of 1.44 solar masses, it will catastrophically collapse to produce the supernova. Another model envisions a binary system with a white dwarf and another white dwarf or a neutron star, a so-called “doubly degenerate” model. As one of the partners accretes mass, it follows what Perlmutter calls a “slow, relentless approach to a cataclysmic conclusion” at 1.44 solar masses. A white dwarf involves electron degeneracy and a neutron star involves neutron degeneracy.

A critical aspect of these models is that they imply that a Type Ia supernova happens when the mass passes the Chandrasekhar threshold of 1.44 solar masses, and therefore all start at essentially the same mass. One would expect that the energy output of the resulting detonation would always be the same. It is not quite that simple, but they seem to have light curves that are closely related, and can be related to a common template.

At maximum light they reach an average maximum magnitude in the blue and visible wavelength bands of

with a typical spread of less than about 0.3 magnitudes. Their light curves vary in a systematic way: the peak brightness and their subsequent rate of decay are inversely proportional.

The above illustration is a qualitative sketch of the data reported by Perlmutter, Physics Today 56, No.4, 53, 2003. It illustrates the results of careful study of supernova Type Ia light curves which has led to two approaches for standardizing those curves. The above curves illustrate the “stretch method” in which the curves have been stretched or compressed in time, and the standardized peak magnitude determined by the stretch factor. With such a stretch, all the observed curves on the left converge to the template curve on the right with very little scatter.

Another method for standardizing the curves is called the multicolor light curve shapes (MCLS) method. It compares the light curves to a family of parameterized light curves to give the absolute magnitude of the supernova at maximum brightness. The MCLS method allows the reddening and dimming effect of interstellar dust to be detected and removed.

Carroll and Ostlie give as an example of distance determination the Type Ia supernova SN 1963p in the galaxy NGC 1084 which had a measured apparent blue magnitude of B = m = 14.0 at peak brilliance. There was a measured extinction of A = 0.49 magnitude. Using the template maximum of M=19.6 as a standard candle gives a distance to the supernova

Distance uncertainties for Type Ia supernovae are thought to approach 5% or an uncertainty of just 0.1 magnitude in the distance modulus, m-M.

Evidence for an accelerating universe

One of the observational foundations for the big bang model of cosmology was the observed expansion of the universe. Measurement of the expansion rate is a critical part of the study, and it has been found that the expansion rate is very nearly “flat”. That is, the universe is very close to the critical density, above which it would slow down and collapse inward toward a future “big crunch”. One of the great challenges of astronomy and astrophysics is distance measurement over the vast distances of the universe. Since the 1990s it has become apparent that type Ia supernovae offer a unique opportunity for the consistent measurement of distance out to perhaps 1000 Mpc. Measurement at these great distances provided the first data to suggest that the expansion rate of the universe is actually accelerating. That acceleration implies an energy density that acts in opposition to gravity which would cause the expansion to accelerate. This is an energy density which we have not directly detected observationally and it has been given the name “dark energy”.

The type Ia supernova evidence for an accelerated universe has been discussed by Perlmutter and the diagrams below follows his illustration in Physics Today.

The data summarized in the illustration above involve the measurement of the redshifts of the distant supernovae. The observed magnitudes are plotted against the redshift parameter z. Note that there are a number of Type 1a supernovae around z=.6, which with a Hubble constant of 71 km/s/mpc is a distance of about 5 billion light years.

Mechanism

Overview

White dwarfs (degenerate dwarfs) are the biggest thermonuclear bombs in the universe; we see their explosions as the type Ia supernovae. The amount of thermonuclear energy locked within a white dwarf is consistent with the energy released in a type Ia supernova. More important for the association between white dwarfs and supernovae, most type Ia supernovae consistently release about the same amount of energy, which would be expected if the exploding white dwarfs were all about the same mass. Specifically, if a white dwarf were pushed above the 1.4 solar mass Chandrasekhar limit, where it is gravitationally unstable, it would collapse and release its thermonuclear energy in a massive explosion. This is the original theory for type Ia supernovae, but other theories exist for triggering a thermonuclear explosion in a white dwarf.

Basic Bomb Theory

Theorists uniformly believe that the conforming 85% of type Ia supernovae are white-dwarf thermonuclear explosions. Most of the theoretical effort has been directed at the explosion of carbon-oxygen white dwarfs, although some theorists believe that the detonation of oxygen-neon-magnesium white dwarfs may be responsible for some other supernova subclass. The basic theory is that a white dwarf composed of carbon and oxygen releases most of its thermonuclear energy in a sudden burst. Thermonuclear burning in the outer parts of the star convert the carbon and oxygen into intermediate-mass elements, such as sulfur. The burning in the white-dwarf interior converts the carbon and oxygen into nickel, which is the lowest-energy atomic nucleus that can be rapidly created through fusion. This sudden release of energy heats the interior to energies far above the white dwarf's gravitational binding energy, so the star expands outward at a very high velocity, leaving nothing behind. As the stellar debris expands and dissipates, it is heated by the radioactive decay of nickel into cobalt and then iron. The expanding photosphere drifts to deeper, hotter regions within the debris. This combination of increasing surface area and increasing temperature of the photosphere causes the debris to emit more power over time, causing the brightening that we see in a supernova. The lines we see in the spectrum of a type Ia supernova is the progression of thermonuclear products created in the supernova, starting with the intermediate elements created in the outer layers of the expanding debris, and ending with cobalt and iron. When the debris has expanded enough for light to escape from the center of the explosion, it cools, and the supernova fades from sight.

All of these properties fit in nicely with the view that the type Ia supernova is the explosion of a degenerate dwarf star. Computer simulations show that the detonation of a white dwarf fits the rise and fall of the supernova's luminosity very nicely, and the elements generated in the detonation of a white dwarf matches the elements portrayed by the supernova's spectrum. For these reasons, astrophysicists working on this problem accept the theory that a degenerate dwarf creates the supernova. The only real disagreement is over the detonator for the explosion.

Three Detonator Theories

At the end of a star's evolution, when electron degeneracy pressure halts the gravitational shrinking of a star, it also halts the thermonuclear fusion of carbon and oxygen into heavier elements. With a fixed density and a cooling core, a white dwarf is unable to sustain thermonuclear fusion. If the thermonuclear energy in a white dwarf is to be released, something must drive up the temperature and density within the white dwarf. Theorists have come up with three plausible ways of detonating a white dwarf. All three rely on the white dwarf being in a compact binary system.

In the first theory, detonation occurs when the white dwarf's mass grows larger than the Chandrasekhar mass limit; the white dwarf grows by pulling gas from its companion onto itself, and when its mass exceeds the Chandrasekhar mass limit, it becomes gravitationally unstable, shrinking in radius until the temperature and density within the white dwarf ignites thermonuclear fusion. In the second theory, the white dwarf is detonated by the thermonuclear explosion of an outer layer of helium. The helium layer is created when the white dwarf pulls gas from a companion helium star onto itself. If the helium layer remains cool enough to prevent the slow thermonuclear conversion of helium to carbon, helium can accumulate to a point that the layer becomes unstable to a thermonuclear runaway. This runaway is triggered by the high density at the base of the helium layer. The helium layer then acts like a blasting cap, driving a shock wave into the white dwarf that initiates thermonuclear fusion of the carbon and oxygen. In the third theory, two white dwarf stars are in a binary system together. Over time, as the binary system emits gravitational radiation, the distance between the white dwarfs shrinks, until the two stars merge into a single star with a mass above the Chandrasekhar mass limit. As in the first theory, the newly-created white dwarf collapses under its own gravity, igniting a thermonuclear explosion.

Each of these three theories have problems. The first theory, where a degenerate dwarf is pushed over the Chandrasekhar limit, produces an explosion that fits the observations very well, but theorists have a difficult time getting the degenerate star to accumulate sufficient mass from its companion to reach the Chandrasekhar limit. The second theory, where a layer of helium acts as a detonator, produces the correct evolution of the supernova, but it places an outermost layer of helium around the supernova remnant that would be observed, but is not. The theory that two degenerate dwarfs merge and explode has the greatest difficulty, because the simulations find that the merger does not immediately create a giant white dwarf above the Chandrasekhar limit. Instead, one star is disrupted, forming a disk around the other star. As material flows onto the remaining star, thermonuclear fusion converts the star into oxygen, neon, and magnesium. Eventually this star collapses to a neutron star.

While each theory may appear fatally wounded, the shortcomings may have more to do with the difficulty of simulating these theories on current computers than with the physics behind the theory. Think of any picture of a fireball you have seen; the boiling convection seen in those explosions are present in the cores of a burning degenerate dwarf. Making matters more difficult, the thermonuclear fusion within a degenerate dwarf is not uniformly spread throughout the star, as is the case during hydrogen fusion within a main-sequence star; instead, it is confined to a complex surface that separates burned material from unburned material. Long fingers of burned material poke into the unburned material. The inability to accurately simulate with computers this and other complex structures within the degenerate dwarf and the binary system may be the reason that none of these theories produce entirely satisfactory results. For this reason, all three theories persist. Of them, the degenerate dwarf at the Chandrasekhar limit remains the favorite theory of the theoretical community.

Frequency

Although many supernovae have been seen in nearby galaxies, supernova explosions are relatively rare events in our own galaxy, happening once a century or so on average. The last nearby supernova explosion occurred in 1680, It was thought to be just a normal star at the time, but it caused a discrepancy in the observer's star catalogue, which historians finally resolved 300 years later, after the supernova remnant (Cassiopeia A) was discovered and its age estimated. Before 1680, the two most recent supernova explosions were observed by the great astronomers Tycho Brahe and Johannes Kepler in 1572 and 1604 respectively.

In 1987, there was a supernova explosion in the Large Magellanic Cloud, a companion galaxy to the Milky Way. Supernova 1987A, which is shown at the top of the page, is close enough to continuously observe as it changes over time, thus greatly expanding astronomers' understanding of this fascinating phenomenon.

Details

Energetics

Degenerate (white) dwarfs come in three flavors: helium, carbon-oxygen, and oxygen-neon-magnesium. The helium white dwarfs are the evolutionary endpoint of low-mass main-sequence stars that evolve over tens of billions of years and of intermediate-mass main-sequence stars in binary systems that lose their outer envelopes of hydrogen after they have converted their core hydrogen into helium. Helium white dwarfs are rare, since only the second evolutionary scenario has had time to run to completion over the 16 billion year age of the universe. The carbon-oxygen white dwarfs are the most common white dwarfs, because they evolve from solar mass stars, which complete their evolution in only about 10 billion years; the prevalence of carbon-oxygen white dwarfs makes them the natural origin of the type Ia supernovae. The oxygen-neon-magnesium white dwarfs descend from main-sequence stars of several solar masses. Because the lives of these main-sequence stars is much shorter than the age of the universe, most of these stars born over the lifetime of our Galaxy have already evolved to white dwarfs. Because relatively few high-mass stars are born relative to solar-mass stars, the oxygen-neon-magnesium white dwarfs are less common than the carbon-oxygen white dwarfs. The oxygen-neon-magnesium white dwarfs may be associated with other, less common, types of supernovae.

The energetics of an exploding white dwarf is well matched to the characteristics of the type Ia supernovae. The amount of thermonuclear energy available in the conversion of intermediate elements into iron is considerable. The conversion of carbon-12 (12C) to iron-56 (56Fe) releases 0.12% of the rest mass energy of carbon. Other intermediate elements release less energy. The conversion of oxygen-16 (16O) to 56Fe releases 0.084% of the rest mass energy of oxygen, while neon-20 (20Ne) releases 0.078% of its rest mass energy, and magnesium-24 (24Mg) releases 0.054% of its rest mass energy. In comparison, the conversion of hydrogen (1H) into helium (4He) in the sun converts 0.7% of the rest mass of hydrogen into thermal energy.

The amount of thermonuclear energy available from the intermediate elements is just enough to blow a white dwarf apart. The gravitational binding energy of a white dwarf is 3GM2/5R, where G is the gravitational constant, M is the mass of the star, and R is the radius of the star. To blow the star apart, the amount of rest mass energy converted into thermonuclear energy must be greater than the binding energy, so the fraction α of rest mass energy that must be released is given by this inequality:

α › 3GM/5Rc2 = 0.042% (M/Mch) (R/3x108 cm) − 1,

where c is the speed of light and Mch = 1.4 solar masses is the Chandrasekhar limit.

For a white dwarf of pure 12C with a mass of 1.4 solar masses and a radius of 3x108 cm, only 0.35% of the star must be converted to iron to blow the star apart. The requirements become more stringent as we move to higher-mass elements, with a 50% conversion rate required of 16O, a 53% conversion rate required of 20Ne, and a 78% conversion rate required of 24Mg. The precise values, of course, depend on the structure of the star; if the equation of state of the degenerate material in the star permits a larger radius for a given mass, then the amount of material that must burn to blow the star apart is smaller.

All of the thermonuclear energy immediately released in the explosion is converted into thermal energy that is trapped, unable to immediately escape from the white dwarf. It exerts a pressure that exceeds the gravitational pressure of the white dwarf. The white dwarf therefore expands, and all of the thermal energy trapped within the star goes to accelerate this expansion. Virtually all of the thermal energy released in the explosion is therefore converted into kinetic energy.

We can get an upper limit on the velocity of the debris from the explosion by assuming that all of the thermonuclear energy is released and converted into kinetic energy after subtracting out the binding energy of the star. For a star composed of 12C, the maximum average velocity is about 4% of the speed of light, while for a star composed of 16O, the maximum average velocity is about 3% of the speed of light. A pure 20Ne star gives the same maximum average velocity as 16O, and a pure 24Mg star gives a maximum average velocity of about 2% the speed of light. The actual maximum velocity can be a little higher than these values, because when the star expands, most of the kinetic energy goes to the outer regions of the star, while the core of the star moves out more slowly. For this reason, the outer layers have a higher than average velocity. Velocities for the stellar debris are derived from the Doppler shifts measured for the spectral lines. The maximum observed velocities are less than 10% of the speed of light, so the estimated average velocities are consistent with maximum observed velocities.

Because most of the thermonuclear energy released in the explosion goes into expanding the star, relatively little of this energy is emitted as light. But a type Ia supernova is brilliant, with a peak luminosity two weeks after the explosion of nearly 10 billion times the Sun's luminosity. Somehow energy is generated within the stellar debris long after the shell has been accelerated to high velocities. This energy source is radioactive decay.

While iron is the lowest energy state for nuclear matter, transforming carbon and oxygen into iron on a very short timescale is not really possible. The problem is that the stable isotopes of iron have more neutrons than protons, while the most abundant isotopes of carbon, oxygen, neon, and magnesium have equal numbers of neutrons and protons. To get stable iron from these intermediate elements requires converting some protons into neutrons, which happens through very slow beta decays. In the hot environment of a white-dwarf thermonuclear explosion, the dominant intermediate mass elements combine to give heavier elements with equal numbers of neutrons and protons; in fact, they combine to give heavier elements that are multiples of helium atoms—multiples of 2 neutrons and 2 protons—because they themselves are multiples of helium atoms. Fusion of the intermediate atomic nuclei therefore does not produce much iron, but instead it produces massive amounts of the isotope nickel-56 (56Ni), which is the lowest-energy atomic nucleus that is a multiple of a helium nucleus. This isotope is unstable, undergoing beta decay in six days to cobalt-56 (56Co). Cobalt-56 is also unstable, decaying in 77 days to 56Fe, which is stable. What this means is that the energy we see two weeks after the supernova explosion is from the decay of 56Ni, and the energy we see in the following months is from the decay of 56Co. The total amount of energy released in these two decays is about 11% of the total thermonuclear energy available in carbon. This means that the light emitted by a type Ia supernova accounts for no more than 0.013% of the white dwarf's rest mass energy. Theorists find that this energy is sufficient to explain the brightness of type Ia supernovae if about 1 solar mass of 56Ni is created in the thermonuclear explosion. The progression from 56Ni to 56Fe also matches the observed spectra, where iron and cobalt lines are seen 2 weeks after the explosion, and the cobalt lines weaken over the following months.

The fraction of thermonuclear energy tied up in nickel become more severe for the other intermediate elements. The energy released by 56Ni constitutes 15% and 16% of the thermonuclear energy in 16O and 20Ne, and it constitutes 24% of the energy in 24Mg. The fraction of thermonuclear energy from 24Mg that is tied up in 56Ni is so great that the fusion of 24Mg does not immediately release enough energy to overcome the binding energy of the star. The the amount of thermonuclear energy from 16O and 20Ne tied up in 56Ni is half of the amount of kinetic energy carried by the debris from the explosion. A white dwarf without carbon should therefore produce an explosion with a much smaller ratio of kinetic energy to radiated energy than is seen.

The energetics and ubiquity of the carbon-oxygen white dwarfs make them favored among theorists over the oxygen-neon-magnesium white dwarfs as the bomb behind the type Ia supernovae. Whether nature comes to the same conclusion, of course, is another, unresolved issue.

Nuclear Reactions

The energetics of a thermonuclear supernova are easy to understand; carbon and oxygen within a white dwarf are converted into nickel, releasing more than enough energy to blow the star apart. The reactions themselves, however, are not simple, involving many small steps that build up and tear apart atomic nuclei. This complexity is reflected in the richness of the chemical composition of our world.

The principle characteristic of the reactions in a thermonuclear supernova is that they go fast, consuming a white dwarf's carbon (12C) and oxygen (16O) in less than 1 second. This means that beta decays (decays that emit an electron or positron along with a neutrino), which are slow by their nature, play no part in the explosion. This is very different from the reactions in the Sun, where the timescale for converting hydrogen into helium is governed by the emission of a positron and a neutrino in conversion of two hydrogen nuclei into a deuterium nucleus. In the thermonuclear reactions present in an exploding white dwarf, these reactions take too long , and are therefore bypassed as atomic nuclei combine to form heavier nuclei. As a consequence, the number of protons and the number of neutrons in a white dwarf do not change during the explosion.

The conversion of carbon and oxygen into nickel (56Ni) loosely follows the path

12C → 16O → 20Ne → 24Mg → 28Si → 32S → 36Ar → 40Ca → 44Ti → 48Cr → 52Fe → 56Ni.

Each nucleus in this chain has a composition that is a multiple of the helium nucleus, and with each step in the chain, the number of nucleons increases by two protons and two neutrons. The flow of atomic nuclei along this path, however, is very complex, involving reactions that combine pairs of carbon or oxygen nuclei, as well as reactions that combine atomic nuclei with protons, neutrons, and helium-4 nuclei (4He).[1] Unlike in the thermonuclear fusion of a main-sequence star, where the reactions flow only in the direction that generates energy as nuclei combine to create higher mass nuclei with lower mass per nucleon, the reactions in a supernova explosion can absorb energy and break apart nuclei into helium nuclei. This is all a consequence of the high temperature generated as carbon and oxygen undergo their fusion reactions—several billion degrees Kelvin, which is equivalent to about 0.5 MeV. This high temperature means that many atomic nuclei have kinetic energies of several MeV, which enable them to undergo thermonuclear reactions that remove energy from the exploding star, particularly through reactions that create helium nuclei from carbon or oxygen. In effect, some of the reactions that occurred during the star's main-sequence phase are reversed during a supernova explosion.

The first reactions to take place in the explosion are between carbon nuclei. They do not directly follow the most energetic path, forming magnesium-24 (24Mg) in a single reaction that releases 14.0 MeV of energy; instead, they create smaller nuclei that each have a larger mass per nucleon than 24Mg. The preferred reactions are the following:

12C + 12C → 20Ne + 4He + 4.6 MeV (66%)

12C + 12C → 23Na + p + 2.2 MeV (32%)

12C + 12C → 23Mg + n − 2.6 MeV (2%)

The preferred products are therefore neon-20 (20Ne), sodium-23 (23Na), and magnesium-23 (23Mg). In these reactions, p is a proton, and n is a neutron. The amount of energy released (positive sign) or absorbed (negative sign) in the reaction is given in units of MeV. The percentages in parenthesis gives the percentage of times the reaction produces the given products.

The products of these reaction do not survive long. Usually, 23Mg combines with a free neutron to create 23Na and a proton, and 23Na combines with a free proton to create 20Ne and a 4He nucleus. The 20Ne can then combine with 4He to form 24Mg. So carbon does eventually evolve into magnesium, but it involves many small drops in energy rather than one big drop.

Two additional reactions work along with the carbon-carbon creation of neon to liberate a total of three helium nuclei in a cycle that converts carbon to neon, neon to oxygen, and oxygen back to carbon. These two reactions involve the absorption of a gamma-ray (γ), so each is called a photodisintegration.

12C + 12C → 20Ne + 4He

20Ne + γ → 16O + 4He

16O + γ → 12C + 4He

The gamma-rays are part of the thermal radiation within the hot material of the white dwarf, and they carry enough energy to break helium nuclei away from neon and oxygen nuclei. This loop creates much of the helium that enable nuclei to gain mass in four-nucleon increments.

Reactions involving oxygen are similarly weighted to reactions that throw out protons, neutrons, and helium nuclei in preference to directly creating sulfur-32 (32S).

16O + 16O → 31P + p + 7.7 MeV (56%)

16O + 16O → 28Si + 4He + 9.6 MeV (34%)

16O + 16O → 31S + n + 1.5 MeV (5%)

16O + 16O → 30P + 2H - 2.4 MeV (5%)

The principal products when oxygen combines with oxygen are therefore phosphorus-31 (31P), silicon-28 (28Si), sulfur-31 (31S), and phosphorus-30 (30P). In these reactions, 2H is deuterium, a hydrogen isotope. The nuclei created in these reactions tend to combine with the particle thrown out at their creation to form 32S, so 32S is ultimately formed from the oxygen thermonuclear reactions.

The freeing of protons, neutrons, and helium nuclei from carbon and oxygen nuclei is a characteristic that persists in the reactions that build up and tear down heavier nuclei. These reactions form a network that causes an atomic nucleus to change its mass by small amounts as it interacts with protons, neutrons, helium nuclei, and gamma-rays. These reactions populate the white dwarf with nuclei that are not multiples of 4He in composition. An example of how the network does this is the reaction of 24Mg with 4He, which, through the release of a proton, can generate 27Al, the only stable aluminum isotope. A second example is provided by 32S; it can combine with a free neutron to create 33S, which can then combine with a neutron and release a 4He nucleus to create 30Si, the rarest of the stable silicon isotopes found on Earth. In this way, every stable isotope and many unstable isotopes lighter than nickel-56 can be created as a white dwarf turns itself into nickel-56. So, while the white dwarf is predominately composed of nuclei that are multiples of 4He, many other elements and isotopes are also present.

The material in the white dwarf is composed only of 56Ni and 4He if thermonuclear fusion can run to completion throughout the star. In general, however, only part of a white dwarf burns to nickel-56. The energy released in the thermonuclear burning causes the star to expand, which causes the temperature to drop, halting the thermonuclear fusion in the outer parts of the star before burning is complete. This can freeze the composition of the star early in the burning process, so that the star is composed of many elements and isotopes. These elements are dispersed in the interstellar medium, and, along with elements created in core-collapse supernovae and in red giant stars, they constitute the diverse mixture of chemicals found in the universe. The relative abundance of elements such as silicon, sulfur, and calcium, over elements such as phosphorus, potassium, and chlorine is a direct consequence of the common isotopes of silicon, sulfur, and calcium being multiples of 4He, while no isotope of phosphorus, potassium, and chlorine is a multiple of 4He. The complexity of the thermonuclear burning of carbon and oxygen is therefore directly responsible for the diverse chemical composition found here on Earth.

Additional Information

The stellar explosion, given the nickname SN Primo, will help astronomers place better constraints on the nature of dark energy — a mysterious repulsive force that is causing the universe to fly apart ever faster.

SN Primo is the farthest Type Ia supernova whose distance has been confirmed through spectroscopic observations. Spectroscopy is the “gold standard” for measuring supernova distances. A spectrum splits the light from a supernova into its constituent colors. By analyzing those colors, astronomers can confirm its distance by measuring how much the supernova's light has been stretched, or reddened, into near-infrared wavelengths due to the expansion of the universe.

The sighting is the first result from a three-year Hubble program to survey faraway Type Ia supernovae, opening a new distance realm for searching for this special class of stellar explosion. The remote supernovae will help astronomers determine whether the exploding stars remain dependable cosmic yardsticks across vast distances of space in an epoch when the cosmos was only one-third its current age of 13.7 billion years.

Called the CANDELS+CLASH Supernova Project, the census is using the sharpness and versatility of Hubble's Wide Field Camera 3 (WFC3) to help astronomers search for supernovae in near-infrared light and verify their distance with spectroscopy. WFC3 is looking in regions targeted by two large Hubble programs called the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) and the Cluster Lensing and Supernova Survey with Hubble (CLASH).

“In our search for supernovae, we had gone as far as we could go in optical light,” said the project's lead investigator, Adam Riess of the Space Telescope Science Institute and The Johns Hopkins University in Baltimore, Md. “But it's only the beginning of what we can do in infrared light. This discovery demonstrates that we can use the Wide Field Camera 3 to search for supernovae in the distant universe.”

The new results are being presented today at the American Astronomical Society meeting in Austin, Texas. A paper describing the study has been accepted for publication in The Astrophysical Journal.

The supernova team's search technique involved taking multiple near-infrared images over several months, looking for a supernova's faint glow. Once the team spotted the stellar blast in October 2010, they used WFC3's spectrograph to verify SN Primo's distance and to decode its light, finding the unique signature of a Type Ia supernova. The team then re- imaged SN Primo periodically for eight months, measuring the slow dimming of its light.

By taking the census, the astronomers hope to determine the frequency of Type Ia supernovae during the early universe and glean insights into the mechanisms that detonated them.

“If we look into the early universe and measure a drop in the number of supernovae, then it could be that it takes a long time to make a Type Ia supernova,” said Steve Rodney of The Johns Hopkins University, the science paper's first author. “Like corn kernels in a pan waiting for the oil to heat up, the stars haven't had enough time at that epoch to evolve to the point of explosion. However, if supernovae form very quickly, like microwave popcorn, then they will be immediately visible, and we'll find many of them, even when the universe was very young. But each supernova is unique. It's possible that there are multiple ways to make a supernova.”

If astronomers discover that Type Ia supernovae begin to depart from how they expect them to look, they might be able to gauge those changes and make the measurements of dark energy more precise, Riess explained. Riess and two other astronomers shared the 2011 Nobel Prize in Physics for discovering dark energy 13 years ago, using Type Ia supernovae to plot the universe's expansion rate.

After extending the frontier for supernova discoveries with Hubble, a full scrutiny of this new territory will have to wait for the James Webb Space Telescope (JWST). Scheduled to launch later this decade, JWST will probe exploding stars at much farther distances than Hubble can reach.

JWST will be able to see farther into the infrared than Hubble does. This capability will push back the frontier by probing more than 11 billion years back in time, when the universe was only 2 billion years old.