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Two explosions told apart by a missing line

The classification of supernovae is a decision tree on absences — is hydrogen there, is silicon there, is helium there — and it was drawn up decades before anybody knew what any of these events were. It nevertheless separates a detonating white dwarf from a collapsing stellar core almost perfectly, and the reason it does is worth the essay.

Assumes Supernovae, Stellar evolution and Degeneracy.

18 min read 10 figures Light is the only messengerMeasuring the unreachableScales that defeat intuition

The naming scheme is old and it is a little absurd. Supernovae were divided into two classes in 1941, on the presence or absence of hydrogen lines in the spectrum near maximum light — at a time when nobody knew what exploded, why, or whether the two had anything to do with each other. Subdivisions accumulated as more spectra arrived: Ia, Ib, Ic, then II-P and II-L and IIn and IIb, each defined by another line being present or absent.

A classification built that way ought to be a filing system rather than a physical statement. This one turned out to be very nearly a physical statement, and the reason is that the lines being looked for are lines of the star’s outermost layers — so a taxonomy of absences is a measurement of how much of the star was still there when it exploded. That is an accident of what is easy to see rather than a piece of insight, and it is the reason the scheme survived: it happened to be reading the one variable that most strongly distinguishes the possible histories.

Four kinds of explosion, told apart by which line is missing. Spectra of 4 supernova types — Ia, II, Ib, Ic — near maximum light, stacked, over the same wavelength range and drawn with the same photospheric expansion speed of 10,000 kilometres per second. Every feature is a P Cygni profile: a trough blueshifted by the material expanding towards the observer and a peak at rest wavelength from the material moving across the line of sight, and the width of both is the expansion speed. Reading the silicon trough of the type Ia off the drawing puts it at 614.0 nanometres, which recovers 10,131 km/s from a rest wavelength of 635.5. The classification is a decision tree on absences. Hydrogen present makes it a type II; no hydrogen but silicon makes it a Ia; no hydrogen and no silicon but helium makes it a Ib; none of the three makes it a Ic. That tree was written down before anybody knew what these objects were, and it separates a detonating white dwarf from a collapsing massive core almost perfectly — because what the letters are actually reading is how much of the star's outer envelope was still there when it exploded. The type II kept its hydrogen, the Ib had lost it and shows the helium beneath, the Ic had lost that too.
Fig. 1 The four principal types near maximum light, stacked, all drawn at the same photospheric expansion speed of ten thousand kilometres a second. Every feature is a P Cygni profile — a trough blueshifted by the material expanding towards the observer, a peak at rest wavelength from the material moving across the line of sight — and the width of both is the expansion speed. Reading the silicon trough of the type Ia back off the drawing recovers the speed it was drawn at.

The decision tree, and what each branch is asking

Is there hydrogen? If yes, it is a type II. A star that still has its hydrogen envelope at the moment of explosion is a red supergiant, and a red supergiant that explodes is a core collapse.

A red supergiant is what a massive star becomes when its centre contracts and its envelope swells in response, and the envelope is enormous and loosely bound — a thousand solar radii of hydrogen held on by almost nothing.

If not, is there silicon? If yes, it is a type Ia. Silicon at ten thousand kilometres a second means intermediate-mass elements freshly synthesised by explosive burning of carbon and oxygen, which is the signature of a thermonuclear runaway rather than a collapse.

If neither, is there helium? If yes, type Ib; if no, type Ic. Both are core collapses of stars that lost their hydrogen — and, in the Ic case, their helium as well — before exploding.

So the sequence II → IIb → Ib → Ic is a sequence of increasing stripping, and the classification is reading the star’s outer boundary. What did the stripping is a separate question with two answers — a stellar wind, or a binary companion pulling the envelope off — and the mass a star does not keep is large enough by either route that the distinction is hard to settle. The current view leans towards binaries, largely because the stripped-envelope events are commoner than single-star wind models can produce. The type Ia sits outside that sequence entirely, and it is the only one of the four that is not a massive star.

Four kinds of explosion, told apart by which line is missing. Spectra of 4 supernova types — Ia, II, Ib, Ic — near maximum light, stacked, over the same wavelength range and drawn with the same photospheric expansion speed of 15,000 kilometres per second. Every feature is a P Cygni profile: a trough blueshifted by the material expanding towards the observer and a peak at rest wavelength from the material moving across the line of sight, and the width of both is the expansion speed. Reading the silicon trough of the type Ia off the drawing puts it at 603.3 nanometres, which recovers 15,214 km/s from a rest wavelength of 635.5. The classification is a decision tree on absences. Hydrogen present makes it a type II; no hydrogen but silicon makes it a Ia; no hydrogen and no silicon but helium makes it a Ib; none of the three makes it a Ic. That tree was written down before anybody knew what these objects were, and it separates a detonating white dwarf from a collapsing massive core almost perfectly — because what the letters are actually reading is how much of the star's outer envelope was still there when it exploded. The type II kept its hydrogen, the Ib had lost it and shows the helium beneath, the Ic had lost that too.
Fig. 2 The same four at a higher expansion speed. Every trough moves further to the blue and every feature broadens, in proportion — because a P Cygni profile’s blueshift and its width are the same quantity. That is the second thing a supernova spectrum gives up: the velocity of the photosphere, directly, with no distance and no calibration, from the displacement of a line whose rest wavelength is known.

Two mechanisms with nothing in common

The physical divide runs between the type Ia and everything else, and the two mechanisms share neither their fuel nor their energy source nor their remnant.

Core collapse. A star above about eight solar masses builds an iron core by burning through a sequence of shells, each hotter and shorter-lived than the last — hydrogen for millions of years, helium for hundreds of thousands, and silicon for about a day. Iron cannot be burned for energy. Thermonuclear. A white dwarf accreting from a companion approaches the Chandrasekhar mass, its centre ignites carbon under degenerate conditions, and because a degenerate gas does not expand when heated the burning runs away instead of being regulated. The star is unbound entirely; there is no remnant. The energy comes from fusion, and the amount available is fixed by the mass being burned — which is why the events are so nearly identical to one another and why they are useful.

The contrast in energy budgets is worth stating because it is the opposite of what the appearances suggest. A core collapse releases a hundred times more total energy than a thermonuclear explosion, and is not a hundred times brighter, because nearly all of it leaves as neutrinos. A type Ia releases far less and converts a much larger share of it into light. The brightest events in the optical sky are the less energetic of the two.

Four kinds of explosion, told apart by which line is missing. Spectra of 4 supernova types — Ia, II, Ib, Ic — near maximum light, stacked, over the same wavelength range and drawn with the same photospheric expansion speed of 7,000 kilometres per second. Every feature is a P Cygni profile: a trough blueshifted by the material expanding towards the observer and a peak at rest wavelength from the material moving across the line of sight, and the width of both is the expansion speed. Reading the silicon trough of the type Ia off the drawing puts it at 620.5 nanometres, which recovers 7,064 km/s from a rest wavelength of 635.5. The classification is a decision tree on absences. Hydrogen present makes it a type II; no hydrogen but silicon makes it a Ia; no hydrogen and no silicon but helium makes it a Ib; none of the three makes it a Ic. That tree was written down before anybody knew what these objects were, and it separates a detonating white dwarf from a collapsing massive core almost perfectly — because what the letters are actually reading is how much of the star's outer envelope was still there when it exploded. The type II kept its hydrogen, the Ib had lost it and shows the helium beneath, the Ic had lost that too.
Fig. 3 The same four types at seven thousand kilometres a second rather than ten. Every trough moves back towards its rest wavelength and every feature narrows, in proportion — the blueshift of a P Cygni trough is the photospheric velocity, so the whole spectrum is a velocity measurement before it is a classification. The identification of a line therefore depends on already knowing the expansion speed, which is why the classification is done by fitting a template rather than by reading a wavelength off a chart.

The light curves say the same thing differently

A supernova is bright for months, and nothing about the explosion itself lasts months. The light has to come from somewhere else. Core-collapse light curves are shaped by something else: the hydrogen envelope, which recombines as it cools and releases the energy stored in its ionisation. That produces the characteristic plateau of a type II-P, lasting a hundred days at nearly constant brightness, and its length is a measurement of how much envelope there was. A stripped-envelope event — a Ib or Ic — has no plateau at all, and its light curve looks much more like a type Ia’s, because with the envelope gone the only remaining energy source is the same nickel decay.

So the light curve and the spectrum are asking the same question from two directions, and they agree: how much envelope was left decides both which lines appear and what shape the curve takes.

There is a third reading of the same variable, and it is the one that closes the case. The ejecta expand freely after the first few minutes, so a spectrum taken later probes deeper layers: the photosphere recedes inwards through the expanding material, and its velocity, read off the line blueshift, falls with time. Following a supernova for months therefore produces a velocity profile of the star’s interior, from the outermost layers to the innermost, in order. What that sequence shows for a stripped-envelope event is helium above and oxygen beneath — the shell structure of the progenitor, unwrapped.

An absorption spectrum at 22000 K. A blackbody continuum at 22000 K with absorption lines cut out of it, each line's depth computed from how much of the gas is in a state that can absorb it. 3 of the 8 lines are strong enough to see at this temperature, which is the whole reason the spectral sequence is a temperature sequence.
Fig. 4 A hot stellar photosphere, for comparison with the two expanding ones. Its hydrogen lines are narrow — a few tenths of a nanometre — because the gas is moving at thermal speeds of a few kilometres a second. The supernova lines above are hundreds of times wider, because the absorbing material is moving at ten thousand. That contrast is the reason a supernova spectrum can be classified at a glance: nothing in a stellar atmosphere produces a feature that broad, so the width identifies the object before any line is identified.
Three kinds of explosion, told apart by which line is missing. Spectra of 3 supernova types — Ia, Ib, Ic — near maximum light, stacked, over the same wavelength range and drawn with the same photospheric expansion speed of 10,000 kilometres per second. Every feature is a P Cygni profile: a trough blueshifted by the material expanding towards the observer and a peak at rest wavelength from the material moving across the line of sight, and the width of both is the expansion speed. Reading the silicon trough of the type Ia off the drawing puts it at 614.0 nanometres, which recovers 10,131 km/s from a rest wavelength of 635.5. The classification is a decision tree on absences. Hydrogen present makes it a type II; no hydrogen but silicon makes it a Ia; no hydrogen and no silicon but helium makes it a Ib; none of the three makes it a Ic. That tree was written down before anybody knew what these objects were, and it separates a detonating white dwarf from a collapsing massive core almost perfectly — because what the letters are actually reading is how much of the star's outer envelope was still there when it exploded. The type II kept its hydrogen, the Ib had lost it and shows the helium beneath, the Ic had lost that too.
Fig. 5 The three hydrogen-free types alone. Stacked without the type II they are harder to tell apart, not easier: the silicon trough separates the Ia cleanly, and the difference between Ib and Ic is one helium feature whose strength varies with epoch and with how much helium happens to be excited. The decision tree’s last branch is the least secure one, and a meaningful fraction of published Ib/Ic classifications have been revised on better spectra.

Where each one happens, and what that confirms

The two mechanisms have different progenitors, so they should occur in different places, and they do.

Core collapses require stars above eight solar masses, which live under forty million years — the biggest stars die first — so they occur only where stars are being formed now: in spiral arms, in star-forming galaxies, never in ellipticals. Type Ia supernovae occur in all galaxy types including old ellipticals, which is a statement that their progenitors can be old.

Two kinds of explosion, told apart by which line is missing. Spectra of 2 supernova types — II, Ib — near maximum light, stacked, over the same wavelength range and drawn with the same photospheric expansion speed of 10,000 kilometres per second. Every feature is a P Cygni profile: a trough blueshifted by the material expanding towards the observer and a peak at rest wavelength from the material moving across the line of sight, and the width of both is the expansion speed. Reading the silicon trough of the type Ia off the drawing puts it at 614.0 nanometres, which recovers 10,131 km/s from a rest wavelength of 635.5. The classification is a decision tree on absences. Hydrogen present makes it a type II; no hydrogen but silicon makes it a Ia; no hydrogen and no silicon but helium makes it a Ib; none of the three makes it a Ic. That tree was written down before anybody knew what these objects were, and it separates a detonating white dwarf from a collapsing massive core almost perfectly — because what the letters are actually reading is how much of the star's outer envelope was still there when it exploded. The type II kept its hydrogen, the Ib had lost it and shows the helium beneath, the Ic had lost that too.
Fig. 6 The two core-collapse types that bracket the stripping sequence: one that kept its hydrogen envelope and one that lost it. Everything else about the explosion is the same — the same iron core, the same collapse, the same energy — and the spectra look like different objects. The classification is reading the envelope and not the engine, which is the sentence this whole essay turns on, and it is why the type Ia’s separation from all three is a statement of a different kind.

The chemical signature, which settles it independently

The two mechanisms make different elements, in different proportions, on different timescales — and the composition of later generations of stars records the difference.

Core collapses make the alpha elements: oxygen, magnesium, silicon, calcium, in roughly solar proportions relative to each other. Type Ia supernovae make mostly iron-peak elements and very little of the alphas. And because core collapses come from short-lived stars while type Ia events lag by a gigayear or more, the ratio of alpha elements to iron in a population records the timing.

Four kinds of explosion, told apart by which line is missing. Spectra of 4 supernova types — Ia, II, Ib, Ic — near maximum light, stacked, over the same wavelength range and drawn with the same photospheric expansion speed of 20,000 kilometres per second. Every feature is a P Cygni profile: a trough blueshifted by the material expanding towards the observer and a peak at rest wavelength from the material moving across the line of sight, and the width of both is the expansion speed. Reading the silicon trough of the type Ia off the drawing puts it at 594.0 nanometres, which recovers 19,589 km/s from a rest wavelength of 635.5. The classification is a decision tree on absences. Hydrogen present makes it a type II; no hydrogen but silicon makes it a Ia; no hydrogen and no silicon but helium makes it a Ib; none of the three makes it a Ic. That tree was written down before anybody knew what these objects were, and it separates a detonating white dwarf from a collapsing massive core almost perfectly — because what the letters are actually reading is how much of the star's outer envelope was still there when it exploded. The type II kept its hydrogen, the Ib had lost it and shows the helium beneath, the Ic had lost that too.
Fig. 7 And the same classification at the earliest epoch, when the ejecta are fastest. At twenty thousand kilometres a second the features are so broad that neighbouring lines blend into single troughs, and a spectrum taken days after the explosion is harder to type than one taken weeks later — the identification improves as the photosphere recedes into slower material. The width is the clock: it falls through the first months, and where a given line sits in that sequence is a measurement of how deep into the ejecta the observation is seeing.

The same argument runs in the other direction as a check. A galaxy whose star formation was cut off early should show a high alpha-to-iron ratio at every metallicity, because the type Ia contribution never arrived; and the most massive elliptical galaxies, which are believed to have formed their stars quickly and stopped, do show exactly that. A histogram of stellar metallicities that says the box was not closed is the same style of argument applied to a different ratio.

That the knee exists at all is the strongest confirmation the taxonomy is physical. It requires two distinct production sites with two distinct delay times and two distinct yield patterns, which is exactly what the spectroscopic classification asserted on entirely different grounds forty years earlier.

How the rates compare, and what that costs

Both types are rare, and their rates differ by a factor that matters for how they are found.

In a galaxy like this one a core collapse happens perhaps twice a century and a type Ia perhaps once every three or four. Neither is a rate anyone can wait for, so every statistical result about supernovae comes from surveying many galaxies at once — which introduces the same selection problem that afflicts every flux-limited catalogue. A survey finds intrinsically bright events out to a larger volume than faint ones, so the observed mix of types is not the true mix, and recovering the true rates requires knowing the luminosity function of each class, which is what the survey was supposed to measure.

The type Ia case is the one where this has been pushed hardest, because the cosmological use demands it. The correction is done by injecting artificial supernovae into the real images and counting how many are recovered as a function of brightness, epoch and host galaxy — an efficiency measured rather than modelled. It is the same discipline that an occurrence rate demands in the exoplanet census, arrived at independently and about twenty years earlier.

An absorption spectrum at 15000 K. A blackbody continuum at 15000 K with absorption lines cut out of it, each line's depth computed from how much of the gas is in a state that can absorb it. 3 of the 8 lines are strong enough to see at this temperature, which is the whole reason the spectral sequence is a temperature sequence.
Fig. 8 A stellar photosphere at fifteen thousand kelvin, for comparison with the twenty-two thousand above. The same eight lines are drawn and a different subset of them is strong, because what decides a line’s depth is how much of the gas is in the state that can absorb it. Nothing about a supernova spectrum works differently: the features are absorption by ions at some excitation, and the reason a supernova is harder to read is that its photosphere is moving at a twentieth of the speed of light rather than that its physics is new.

The knee that dates a population

The independent check the classification survives is worth setting out in full, because it is a measurement made on stars that were never anywhere near a supernova.

The two mechanisms make different elements. A core collapse builds the alpha elements — oxygen, neon, magnesium, silicon, calcium — in the shells of a massive star and ejects them, along with a modest amount of iron. A thermonuclear explosion burns most of a white dwarf to the iron peak and makes comparatively little of anything lighter.

They also operate on different clocks. Massive stars die within tens of millions of years of forming, so core collapses begin almost immediately after a burst of star formation. A type Ia requires a white dwarf to form and then to be pushed over its limit, which takes at least several hundred million years and typically longer.

So a population’s chemistry has a sequence in it. Early on, only core collapses have contributed, and the ratio of alpha elements to iron sits at a high value fixed by their yields alone. Later, the thermonuclear events begin adding iron without adding much else, and the ratio falls.

Plot that ratio against the overall iron abundance for a population of stars and the result is a plateau followed by a decline — a knee — and the iron abundance at which the knee occurs says how far enrichment had got before the second source switched on. That in turn measures how fast the population was forming stars: a galaxy that formed its stars quickly reaches a high iron abundance before the delay expires and has its knee far to the right, and one that formed them slowly has a knee at low abundance.

Measured knees run across two orders of magnitude in iron abundance — the Milky Way’s disc high, the dwarf spheroidal satellites very low — and reading them is now the standard way of dating a population’s star formation history from the composition of stars alive today.

Two supernova types, distinguished a century ago by whether a hydrogen line was present, leave a signature in the chemistry of stars that formed billions of years later, and the size of the delay between them is legible in it.

An absorption spectrum at 7500 K. A blackbody continuum at 7500 K with absorption lines cut out of it, each line's depth computed from how much of the gas is in a state that can absorb it. 8 of the 8 lines are strong enough to see at this temperature, which is the whole reason the spectral sequence is a temperature sequence.
Fig. 9 And at seven and a half thousand kelvin, near the temperature at which hydrogen’s Balmer lines are strongest. That maximum is not where hydrogen is most abundant — it is where the fraction of hydrogen in the first excited state peaks — and the same caution applies to every line in a supernova spectrum. The absence of a line is evidence of absence only after the excitation has been checked, and for helium in a type Ic that check is the whole of the argument.

What arrives before the light

There is one more discriminant, and it is the only one that does not involve a spectrum at all.

A core collapse releases about ninety-nine per cent of its energy as neutrinos, at the instant the core becomes a neutron star. The light comes much later: the shock has to travel outward through the star’s envelope, which takes hours for a red supergiant, and nothing is visible until it reaches the surface.

So the two signals are separated in time. For the 1987 event in the Large Magellanic Cloud the neutrinos arrived about three hours before the first optical brightening, which is exactly what a shock crossing a supergiant’s envelope predicts.

A thermonuclear explosion produces no such burst. It unbinds the star entirely, there is no collapse and no neutron star, and the energy emerges as light and as the kinetic energy of the ejecta.

That is the sharpest distinction available between the two mechanisms and the least usable, because the neutrinos are detectable only for an event in this galaxy or its nearest neighbours — which is a handful of opportunities per century against the thousands of supernovae a survey now catalogues each year.

It is nevertheless the reason the neutrino detectors of the world are kept running continuously, and the reason a nearby core collapse would be the best-observed astronomical event in history rather than merely a bright one.

The last such opportunity was in 1987 and produced two dozen events; the detectors now in operation would record thousands from the same distance.

The difference between those two numbers is the difference between confirming a picture and measuring the collapse itself.

An absorption spectrum at 4500 K. A blackbody continuum at 4500 K with absorption lines cut out of it, each line's depth computed from how much of the gas is in a state that can absorb it. 8 of the 8 lines are strong enough to see at this temperature, which is the whole reason the spectral sequence is a temperature sequence.
Fig. 10 A cool photosphere at four and a half thousand kelvin, where nearly every line drawn is strong. This is the regime a type II’s spectrum enters weeks after maximum as its photosphere recedes and cools — and it is why the classification is defined at maximum light rather than whenever the object was observed. A spectrum taken late enough looks like a cool star with peculiar velocities, and the branch of the decision tree it lands on is not the branch it started from.

Where the picture stops

Nobody has caught a type Ia progenitor. For core collapses, archival images of the site have identified the star that exploded in a couple of dozen cases, and the identifications match the expected red supergiants. For type Ia there is nothing: no progenitor has ever been imaged, no surviving companion has been convincingly found, and the two leading pictures — accretion from a normal companion, or the merger of two white dwarfs — make predictions that observations have so far failed to separate.

And the Chandrasekhar mass may not be the trigger. Several lines of evidence now suggest a substantial fraction of type Ia events explode below the limit, ignited by a helium detonation on the surface rather than by carbon in the centre. If that is right, the uniformity that makes them standardisable is not the uniformity of a fundamental mass limit, and the empirical relation used to correct them has no principled reason to hold at high redshift — which is the assumption every cosmological result from supernovae rests on.

The classification also frays at the edges. Type IIb events show hydrogen early and lose it within weeks, sitting between II and Ib; type IIn events show narrow lines from circumstellar material and can be either mechanism underneath; and superluminous supernovae are ten to a hundred times brighter than any of the above and are not well accounted for by either. Two consequences of defining the classes at maximum light are worth separating, because one is a nuisance and the other is the reason the scheme survives.

The nuisance is that the class is a statement about one epoch. A type IIb has hydrogen at maximum and has lost it a month later, at which point its spectrum is a type Ib’s; a type Ib observed late enough loses its helium features and is reported as a Ic. So the sequence of increasing stripping that the branches encode is also, for a single object, a sequence in time, and a classification without an epoch attached is ambiguous by roughly one branch. Surveys handle this by requiring a spectrum within a few days of peak and by re-classifying when a better one arrives, which is why the published type of a well-observed supernova sometimes changes.

The reason the scheme survives is that the one class whose spectra are nearly identical from object to object is the one that turned out to be useful. Type Ia spectra at maximum agree closely enough that a template fit returns the epoch to a day or two, and that homogeneity is what makes them standardisable as distance indicators. The exceptions are classified by the same rule and are informative for the same reason: the Iax subclass is spectroscopically a Ia with lower velocities and lower luminosity, and its existence says that whatever makes an ordinary Ia uniform is a condition that can fail rather than a law.

What the classification cost, and what it bought

It is worth being clear about the epistemic shape of what happened, because it is unusual.

A taxonomy assembled from surface features, by people with no theory of the objects, turned out to track the deepest available distinction between them. That is not how classifications usually behave. Most schemes built on appearances — the historical classifications of nebulae, of variable stars, of galaxy morphologies — turn out to be mixtures, and unpicking them takes decades.

This one worked because of a coincidence that can be stated exactly: the variable the spectrum is most sensitive to at maximum light, namely the composition of the outermost layers, is also the variable that most strongly distinguishes the possible progenitor histories. Had supernovae differed mainly in some property the outer layers do not record — the rotation of the core, say — the letters would have been a filing system and nothing more.

The lesson generalises modestly. A classification is worth trusting to the extent that its diagnostic happens to be causally close to the thing being classified, and the way to find out is to check whether an entirely independent measurement — here, the chemical abundances of later stellar generations — draws the same line.

A final observation about the scheme’s shape. The branches are ordered by which element is looked for first, and that order is historical rather than physical: hydrogen was the 1941 division, silicon was added in 1985 when the hydrogen-free class was found to be two things, and helium followed. A classification built from the physics forward would separate thermonuclear from core-collapse at the root and then subdivide, and would put the type Ia alone on one side of the first branch rather than two levels down. That the historical tree nonetheless recovers the physical division exactly is the fact worth keeping — the spectral features happen to encode the distinction that matters, and they do so because the fuel and the envelope are not independent. A star that can build an iron core is a star massive enough to have had a hydrogen envelope to lose, and a white dwarf has neither — so the presence of hydrogen and the presence of silicon are two readings of the same fact about what exploded, arrived at from opposite ends of the periodic table.

Where this ladder goes next

Later rungs on this anchor: the progenitor problem, and what a surviving companion would look like; sub-Chandrasekhar detonations and the double-detonation mechanism; the physics of the type II-P plateau and what its length measures; the nucleosynthetic yields in detail, and the elements neither mechanism accounts for; and the shock breakout, the first minutes of a core collapse, which is now being caught by wide-field surveys and which measures the progenitor’s radius directly.

Where this goes next

A light curve that is a decay chain. Bolometric luminosity against days since explosion, for three Type Ia models synthesising 0.3 M☉, 0.6 M☉, 0.9 M☉ of ⁵⁶Ni, from Arnett's one-zone diffusion model. Nothing in the shape is fitted: the two timescales are the laboratory half-lives of ⁵⁶Ni and ⁵⁶Co, 8.8 and 111.3 days, and the rise is those decays seen through an envelope that takes 11.3, 15.5, 18.6 days to leak. Each peaks at 14, 18, 21 days, and at maximum the luminosity equals the instantaneous deposited power to within 0.6% — Arnett's rule, and the only reason a peak brightness can be read as a mass of nickel. After maximum the curves settle to nearly straight lines on this logarithmic axis, declining at 0.0360 magnitudes a day against ⁵⁶Co's own 0.0098. The difference is gamma-ray escape: the ejecta become transparent to the very photons that are supposed to be heating them, and the tail is therefore steeper than the isotope. The one thing the tail is not is a property of the star — it is a half-life, plus a column density that is falling as t⁻². The candle that has to be standardised A Type Ia's light is the decay of half a solar mass of nickel-56 seen through an expanding envelope. Their peak brightnesses span six-tenths of a magnitude — and it is the width of the light curve, not anything else, that says which. A furnace with the thermostat taken out. Left, the two pressures in a red giant's helium core at 10⁶ g/cm³. The ideal-gas pressure rises with temperature, as the whole regulation of a star depends on it doing; the degenerate electron pressure is a horizontal line, because the exclusion principle does not know the temperature. At the ignition point near 10⁸ K the degenerate term is 5.1 times the gas term, so a temperature rise there raises the total pressure by almost nothing and the core does not expand. Right, what that costs. Both curves start at the same temperature with the same triple-alpha rate, whose logarithmic slope is 41 — the famous T⁴⁰, differentiated here rather than quoted. The regulated core settles; the degenerate one, with nowhere to put the extra energy, goes vertical. The flash reaches 10¹⁰ solar luminosities for a few seconds and not one photon of it is seen: every erg goes into lifting the degeneracy, and the star's visible response is to become fainter and settle on the horizontal branch. The explosion that never reaches the surface When helium ignites in a degenerate core the thermostat every other burning stage runs on is disconnected. The runaway reaches ten billion solar luminosities for a few seconds, and the star's visible response is to get fainter. 7 solar masses of progenitor become 0.56 of white dwarf. Above: the initial–final mass relation. The steep line is what a star would leave if it kept everything; the shallow one is what it actually leaves, M_f = 0.08M_i + 0.489, fitted to white dwarfs in open clusters. Everything between 1 and 8 solar masses ends up between 0.57 and 1.13 — a range of 7 compressed by a factor of 12 — and the fraction thrown away rises from 43% at the bottom to 86% at the top. A star spends most of its mass in the last per cent of its life, at rates no theory predicts from first principles, and this relation is measured by running stellar evolution backwards: a cluster's turn-off gives the age, a white dwarf's temperature gives its cooling time, the difference gives how long its progenitor lived, and a model turns that into the mass it was born with. Below: the white dwarf mass distribution that follows, from a Salpeter initial mass function pushed through the relation above. It peaks at 0.61 solar masses, which is what every survey of white dwarfs measures. Two things make that peak and the flatness of the relation is only one of them: the unsmoothed distribution (the stepped curve) falls monotonically and is largest at its low-mass edge, because the initial mass function is steep. The edge is where it is because no star lighter than about 1.0 solar masses has had time to die yet, and the scatter of the measurement rounds that cliff into a maximum a little above it. A flat relation produces a narrow range; it takes the age of the Galaxy to produce a peak. The mass a star does not keep The initial–final mass relation is nearly flat, so everything from one to eight solar masses ends as a white dwarf between 0.57 and 1.13 — and the observed distribution piles up at 0.6 almost regardless of what went in. The relation is measured by running stellar evolution backwards, because nothing predicts the loss.

What links here

Essays that link to this one from their own argument.

The objects this essay names

Each one links to every other essay that touches it.

Core-collapseMass transferNickel-56Nucleosynthetic yieldP cygni profilePhillips relationPhotospheric velocityProgenitorRadioactive decay chainStripped envelopeSupernova taxonomyA type Ia supernova