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Mercury, November/December 1999 Table of Contents

In the next year, observations of a distant, newly discovered supernova may provide us an opportunity to identify a black hole in the debris of such a stellar explosion. For the first time, we mayh obtain unmistakable evidence that supernova explosions can give birth to black holes.

Shmuel Balberg
University of Illinois at Urbana-Champaign

Monica Colpi
Università degli Studi di Milano

Stuart L. Shapiro
University of Illinois at Urbana-Champaign

Luca Zampieri
University of Illinois at Urbana-Champaign
and Università degli Studi di Padova

Identifying black holes has been one of the greatest challenges in astronomy over the last few decades. Black holes are a theoretical consequence of Albert Einstein's general theory of relativity, where the entire mass of an object has collapsed to a size approaching that of a mathematical point. As a result, the gravitational field very close to such an object is so great that nothing—not even light—can escape; it appears as a "black hole" in space.

In the absence of any direct emission of light, astronomers can only hope to identify black holes indirectly, through the effect of their gravitational pull on gas and stars in their vicinity. Over the past decade significant progress in observational techniques and theoretical modeling has led to the identification of over twenty "black hole candidates." These can be divided into two distinct groups: stellar-mass black holes, with masses several times that of our Sun (commonly denoted M°, where 1 M° = 2 x 10³³ grams); and supermassive black holes, with masses of the order of millions of M°. The latter are associated with the centers of galaxies, including our own Milky Way, and quasars.

The most compelling evidence for a supermassive black hole is a disk of hydrogen observed to be rotating around the center of the galaxy NGC 4258. Applying Kepler's laws to the orbital radius and velocity requires a compact central object with a mass of about 36 million M°. The stellar-mass black hole candidates are detected when they accrete material, supplied by a binary companion star. The first and best known candidate of this type is found in the constellation Cygnus of our galaxy, and is denoted as Cyg X-1. In essence, a fraction of the gravitational potential energy released in the accretion is converted into internal energy as the material spiraling into the black hole compresses and heats. Some of this heat escapes as radiation, providing the observational signature of the accreting object. In the case of the black holes, the temperature of the material is so great that its typical emission is in the x-ray band of the spectrum.

Classifying these objects as black hole "candidates" relies mostly on a mass estimate—since no other object is known to be both massive and compact enough to account for the observations. It also has been suggested that an identification could be made on the basis of the emitted radiation. Gas accreting onto a black hole will produce a different radiative luminosity and spectrum from those of gas accreting onto other compact objects (such as neutron stars) which have hard surfaces.

A closely related challenge has been the gathering of observational evidence to identify astronomical scenarios where black holes are created. Theorists have suggested several such scenarios, spanning from creation of black holes during the birth of the Universe via the Big Bang, to a secular merger of many stars in the centers of galaxies, to a catastrophic collapse of a massive or supermassive star, or even a relativistic cluster of stars. Here we focus on the formation of a stellar-mass black hole in the explosion of an evolved massive star, a supernova. After the explosion, some of the debris will gradually fall back onto the black hole, giving rise to a source of radiant energy. Can we detect this energy source and thereby uncover a black hole formed in the midst of such an explosion? It seems that nature may finally provide us with an opportunity to do so.

When Big Stars Go Boom

Supernovae are one of nature's grandest spectacles: when a massive star explodes, it emits about as much energy in a matter of seconds as it did throughout its entire life of tens of millions of years. For a few weeks, the exploding star out-shines its entire host galaxy (see Figure 1)!

This fantastic display of power allows us to observe supernovae in very distant galaxies; with present day satellites and telescopes astronomers detect several dozens of supernovae a year. The best studied supernova was observed to explode in the Large Magellanic Cloud, a satellite galaxy of the Milky Way Galaxy, in February 1987, giving its name-SN1987A (previous page). The proximity of this supernova, only 160,000 lightyears away, has made it the brightest supernova observed on Earth since Kepler's time (1604), and has provided astronomers with ample opportunity for study over the last twelve years.

Why do stars explode and how might a black hole form? The theory of stellar evolution suggests that stars with masses larger than 8 M° can go through all the stages of thermonuclear burning, or fusion. Close to the end of its life, a massive star is expected to resemble a cosmic onion, composed of an iron core, surrounded by concentric shells of hot, fusing material: silicon and magnesium rich, oxygen and carbon rich, helium rich, and an envelope of unburned hydrogen (see Figure 2). Each inner layer forms when conditions in the star allow the lighter element above it to initiate fusion. Iron is the most tightly bound of all nuclei; it cannot produce energy by thermonuclear fusion. Hence, the iron core cannot generate thermal energy to support itself against the gravitational load of its own mass, and when it is large enough—theoretical estimates give a critical mass somewhat larger than 1 M°—it becomes unstable and collapses.

Within a few seconds the inner part of the collapsing iron core contracts from its original, roughly Earth size, to a radius of a few tens of kilometers. The density reaches about 1014 grams per cubic centimeter—the density of atomic nuclei. The collapsed core becomes a gigantic nucleus: a mixture of neutrons, protons, and electrons, supported against further collapse by nuclear forces. These forces resist the compression of the matter, and are able to halt the collapse of the inner part of the core (about 0.6 M°). A shock wave forms and slows the rest of the core material that continues to rain inward. At least temporarily, the dying star is saved.

The gravitational potential energy made available by the collapse of the core is fantastic—several times 10⁵³ ergs—similar to the power output of the entire observable Universe in the course of one day, and several thousand times the energy required to detach the envelope of the star from the collapsed core. Initially much of this energy is stored in the very dense core as heat. The core can gradually radiate this energy away in the form of neutrinos because only these very weakly interacting particles can escape the extreme densities of the core. Most of the neutrinos escape without any further effect, but a small fraction scatter off particles in the outer part of the collapsing core, heating the material and increasing its pressure, like a hot plate boiling a column of water ascending onto it. Theoretical simulations show that within about one second, the neutrinos deposit about one percent of their total energy in the infalling material and induce a pressure that is large enough to stop the inflow of matter. The inflow motion is then reversed and material is pushed outward, which subsequently leads to the explosion of the star.

Figure 1. An image of the galaxy NGC 1536 before (left) and after the explosion of supernova 1997D. SN1997D was serendipitously discovered on 14 January 1997 by De Mello and Benetti (IAU Circular no. 6537). The parent galaxy NGC 1536 is located about 14 Mpc from our Solar System. Images courtesy of the authors.

Neutrinos' Surprising Role

This amazing hypothesis, that the weakly interacting neutrinos are the drivers of the Universe's grandest explosions, has been the subject of intense investigation. Researchers use computer simulations to study the complex competition of neutrinos and gravity. It is no easy task: one must model the physics of neutrino interactions and nuclear forces, both of which are not well known, and couple them with the turbulent hydrodynamics of matter falling onto the core in a strong gravitational field. Although the different research groups performing such simulations are not without disagreements, the physical underpinnings of the explosion mechanism are commonly accepted. Our confidence in the fundamentals of supernova theory was significantly strengthened when a pulse of neutrinos was detected by terrestrial detectors in coincidence with the initial optical burst from SN1987A, yielding a neutrino number and energy consistent with theory.

And what of the compact core left behind as a remnant of the explosion? In most cases it remains a giant nucleus held together by the force of gravity: a neutron star. To date several hundred neutron stars have been detected, mostly as radio "pulsars"-rotating neutron stars which produce beamed electromagnetic emission, due to an extremely strong surface magnetic field. If the beam is not aligned with the spin axis we see a pulse, like from a lighthouse, every time the beam sweeps Earth. Neutron stars are the only known objects that can provide such rapid, steady pulses, some with periods as low as milliseconds.

Figure 2. Interior cut-away of a massive progenitor star, showing its characteristic "onion" structure close to the end of its life. A Hydrogen plus Helium envelope surrounds internal concentric layers rich in heavier elements (Oxygen and Silicon); at the center, the iron core (Fe). Illustration courtesy of authors.

One crucial feature of neutron stars is that they have a maximum mass beyond which the gravitational load is too great even for the immense power of the strong interactions. The exact value of this mass is unknown, due to the uncertainties in our theory of the nuclear forces. However, theoretical studies suggest that it is about 2 M°, and most likely no more than 3 M°. Should a neutron star accrete enough matter to push its mass beyond this maximum mass, it must collapse into a black hole.

Since there exists such a maximum mass, the nature of the compact remnant of a supernova is uncertain. First, the explosion itself is not guaranteed: The neutrinos must deposit enough energy in the incoming matter to reverse its flow before the collapsed inner core accretes enough mass to crush it into a black hole. If a black hole forms too early, the neutrino stream is cut off, and no more pressure can be built and the entire star will collapse onto the new black hole. Such an event is often referred to as a "failed supernova." The rate at which material falls onto the core is therefore critical to the explosion. This rate tends to depend on the initial mass of the iron core, which in turn is larger when the total mass of the progenitor star is larger. According to current computer simulations, the critical limit lies at a progenitor mass of about 40 M°. The iron cores in stars with larger mass will lead to an infall rate that will defeat the neutrinos, forming a black hole before an explosion can be driven. Stars even more massive, which have reached this evolutionary stage, end up entirely as black holes.

Watching Out for Fallback

Neutrinos are expected to triumph and drive a successful explosion in lower mass stars, but the details depend strongly on the amount of kinetic energy the envelope can obtain. If the rate of infalling material is large, more energy is required to reverse its motion, and less energy remains available to drive the explosion. Insufficient kinetic energy means that some of the material originally close to the core will not be able to fully escape its gravitational pull, but will instead reach some maximum distance and then reverse and accrete onto it. This process is generally referred to as "fallback."

Most of this fallback occurs very early in the course of the explosion, so that even as the supernova progresses, the core may find that it has exceeded the maximum mass it can support and collapses to a black hole. In this case, a successful supernova will leave behind a black hole, not a neutron star.

Larger mass stars tend to experience larger fallback rates as the neutrinos build up the pressure, and so, they usually give rise to weaker explosions. Furthermore, the explosion energy must overcome the gravitational binding energy, which is naturally larger when the star is more massive. This combination implies that more massive stars experience a larger amount of fallback, even when a successful explosion does take place.

Computer simulations indicate that stars with masses between 8 M° and about 20-25 M° will undergo rather little fallback and are likely to produce a neutron star. The exact upper limit depends on the maximum stable mass of neutron stars and the details of neutrino-interaction physics. In fact, several pulsars have been associated with sites of known supernovae, like the Vela and Crab nebulae, confirming that they were indeed born in supernovae.

The rarer stars with masses in the range 25-40 M° are also expected to explode successfully, but the rate of fallback will be sufficient to induce collapse and the formation of a black hole. It is evidence for this particular scenario that we are currently pursuing.

Clues to Black Hole Formation

We do indeed expect that fallback will be a continuous process: at any given instant of time, there is always some material that has just inverted its outward motion and has started to fall back onto the black hole, even as the bulk of the envelope continues to stream outward. This late fallback will continue for many years, at an ever decreasing rate, generating energy in a similar fashion to the x-ray sources we described earlier. However, in the case of a supernova, this process is embedded in a multitude of other phenomena caused by the explosion.

Can we hope that at some stage the presence of the black hole in the aftermath of the supernova explosion will be unveiled? Consider the sources of energy for the radiation a supernova generates. Observers of supernovae often refer to this radiation as the light curve, the curve that describes the total observed luminosity, or power, of the supernova as a function of time.

When the exploding shock wave travels through the envelope of the star, about one half of its energy transforms into kinetic energy that accelerates the material, and the other half transforms into heat, generating a temperature of about one million degrees. At such a temperature the material in the expanding envelope is completely ionized, and hence highly opaque to photons. Distant observers see only the photons emitted at the very surface. While the supernova is brighter than any main sequence star could ever be, only a small fraction of the enormous energy stored in the envelope can leak out at this stage.

As the envelope expands it must cool. Typically after 50-80 days, the temperature in the outer part of it, which consists mostly of ionized hydrogen, decreases to about ten thousand degrees so that the protons and electrons recombine to form hydrogen atoms. Neutral atoms are transparent to photons, and a domino-like effect can then rapidly propagate through the envelope. When a layer in the envelope recombines, it becomes transparent to the photons trapped in the layer just below it; these photons stream out, and this lower layer cools so that its own material recombines, and now the photons trapped beneath it can also escape. A recombination front thus "sweeps" through the envelope, so that practically all the internal energy that was trapped in it is rapidly radiated. As a result, an increase, or peak, in the luminosity is clearly observed. In SN1987A, this peak dominated the light curve from between 50 and 120 days after the explosion.

After the recombination front has swept through the envelope, all the initial energy from the explosion has been radiated, and any further luminosity is possible only if there exists some continuous source of energy to power it. Here is where the black hole can reveal its presence through late-time fallback, which continues as the hole accretes matter at the base of the envelope. The energy generated by fallback at this stage heats the envelope, and can power a late-time "tail" in the light curve. Observation of such a tail will mark the signature of the black hole.

Unfortunately there is a competing and usually more powerful source of energy in the form of radioactive decays, which complicates the detection of the black hole. As the progenitor star explodes, the shock wave is powerful enough to initiate a final flash of thermonuclear reactions (in fact, we believe that nucleosynthesis in supernovae is the source for all the heavier elements that exist in the Universe, including our Earth and us). Some of these reactions produce radioactive nuclei, which then decay, each with its own typical lifetime. Most notably, ⁵⁶Ni, which has a half-life of 5.5 days, decays to ⁵⁶Co, also unstable, with a half-life of 77 days as it decays to the stable ⁵⁶Fe. Also of importance is ⁴⁴Ti, which decays more slowly with a half-life of about 55 years. In their decays, these nuclei release energy mostly in the form of high-energy gamma-ray photons which are then degraded to lower energy through scattering with electrons in the envelope, and are eventually absorbed by the medium. The energy they deposit heats up the supernova ejecta and continues to power the light curve.

Figure 3. Light curve of SN1987A. The luminosity (L) is plotted as a function fo time (t). The black pyramids show the observed total, or bolometric, luminosity of SN1987A. The dashed lines represent the expected contribution from the decay of radioactive elements (0.075 Ms° of ⁵⁶Co, 2 x 10^-3 M° of ⁵⁷Co, and 10^-4 M° of ⁴⁴Ti). Note the immense power of supernovae: the Sun radiates with a luminosity L approximately 4 x 10³³ ergs/sec. The dotted line represents the calculated accretion luminosity, and the arrow marks the estimated time of black hole emergence. Plot courtesy of authors.

In order to determine what is the dominant source of energy in an observed light curve, we must resort to theory. In the case of radioactive decays, theory is fairly simple. We know that the decay rate is exponential in time: L(t) = L_0-rad e^-t, with L_0-rad denoting the luminosity at some arbitrary early time.

A light curve powered by radioactive decays must exhibit an exponential decline in its power. The luminosity produced by fallback of matter from the envelope depends primarily on the rate at which gas is being swallowed by the black hole. In this case, theory is more complex, and requires computer simulations. In such a simulation one must include a hydrodynamic treatment of the flow, radiative transfer of the photons, and the effects of general relativity: the gravitational field is so strong that the gas accretes onto the black hole with a velocity close to the speed of light.

Searching for Profound Subtlety

We have recently performed such simulations, and we find that within a few days after the explosion the temperature in the envelope is low enough so that pressure forces become negligible and the motion of gas in the ejecta can be described simply in terms of ballistic motion in the gravitational field of the hole. The luminosity which arises from the fallback onto the hole then has a power-law decay in time: L(t) = L_0-acc t^-a, with @ approximately 1.4. We note that such a decline is unique to a black hole, due to the existence of its "event horizon," a one-way membrane through which everything passes smoothly but cannot escape (in the case of a neutron star, all the gravitational energy gained in the accretion must be radiated away, due to the impact on a hard matter surface).

The key here is that a power-law decline is decisively different than an exponential one. For example, the power from accretion reduces by a factor of ten for every fivefold increase in time: five years after the explosion it is about one tenth of its value one year after the explosion. The power from ⁵⁶Co decay (which is the dominant source of radioactive energy after recombination) decreases by a factor of ten about every 250 days, which is much more rapid. It is this fundamental difference on which we can hope to discover the signature of a black hole. Just by examining the temporal shape of the tail of a light curve, we can immediately distinguish whether the power source is radioactive decays or accretion onto a black hole.

The competition between the black hole accretion and the radioactive sources depends on the quantities of radioactive nuclei synthesized in the explosion and the rate of fallback onto the black hole. Typical supernovae produce several hundredths of a solar mass of ⁵⁶Ni and about 10^-4 M° of ⁴⁴Ti, which is more than enough to overpower the maximum possible luminosity available from accretion. Note that since power from accretion declines more slowly than the power from radioactive decays, accretion must eventually become the dominant source for the light curve tail. However, in most cases, this is expected to happen at such late times that the absolute luminosity will be too low for detection. For example, even assuming that SN1987A did produce a black hole, it is expected that the abundance of 44Ti will allow accretion to become the dominant power source 900 years from now; by that time the luminosity will be much lower even than that of a common star (see Figure 3).

So Where Should We Look?

To detect the fallback luminosity from the accretion onto a black hole, we require a low-energy explosion of a massive star. A lower explosion energy will lead to a larger fallback rate and a larger accretion power output. It also has a complementing effect of reducing the abundance of radioactive elements in the envelope: the relevant radioactive elements are synthesized rather close to the collapsed core in the supernova, and some are actually captured by the nascent black hole during the early fallback. In a weak explosion the amount of radioactive nuclei that remains available to power the late light curve becomes significantly smaller than the standard quantities cited above. We expect that more massive stars, which are less abundant, are those more likely to fit this description.

Figure 4. Light curve of SN1997D. The black dots show the observed total, or bolometric, luminosity of SN1997D. The dashed lines represent the expected contribution from the d4ecay of radioactive elements (0.002 M° of ⁵⁶Co, 5 x 10^-5 M° of ⁵⁷Co, and s.5 x 10^-6 M° of ⁴⁴Ti). The dotted line represents the calculated accretion luminosity at late times. The coninuous line is the total calculated bolometric light curve, and the arrow marks the extimated time of the black hole emergence. Plot courtesy of authors.

In early 1997 a candidate for such a supernova was detected in the galaxy NGC 1536, at a distance of 14 Mpc from us. Recent observations combined with theoretical modeling of the light curve indicate that it was produced by an explosion of a star of mass 26 M°, with an explosion energy of less than a third of its counterpart that generated SN1987A.

The observed light curve of SN1997D is shown in Figure 4. The supernova was detected by telescopes on Earth about at the time of maximum brightness of the recombination peak, which is believed to correspond to about 50 days after the explosion. The recombination peak then declined rapidly for another month, at which point it transformed into an exponentially declining tail. The rate of exponential decline clearly indicates that the tail is powered by the decay of ⁵⁶Co, but its absolute magnitude implies that the abundance of ⁵⁶Co is exceptionally low—only about two thousandths of a solar mass. This is about forty times lower than the abundance of the same isotope observed in the "prototype" supernova 1987A. Theoretical models of nucleosynthesis in supernovae suggest that the amount of 44Ti will also be significantly lower than its standard value.

The low energy of the explosion has probably induced a rather high fallback rate onto the black hole formed in this supernova, which is likely to have a mass of about 3 M°. This fallback will produce an accretion luminosity significantly higher than what it might be in SN1987A. The accretion luminosity may therefore become dominant over the low-abundant radioactive elements in powering the light curve tail very early. Our theoretical simulation of the light curve for supernova 1997D is shown in Figure 4, and the arrow marks the point of emergence of the black hole accretion luminosity in the light curve. It is only about 1050 days (less than three years) after the explosion. We predict that evidence for the presence of a black hole in the aftermath of SN1997D may be observable within a year!

Due to the large distance to SN1997D its optical and infrared emission at the time of black hole emergence will be very weak, but still within the reach of powerful telescopes such as the Hubble Space Telescope or the Very Large Telescope (VLT). We are now eagerly anticipating the revelation in a few month's time of the unique signature of a black hole in the light curve of SN1997D. If observed, it will mark another milestone in our pursuit and detection of these exotic and elusive objects.

SHMUEL BALBERG is a Research Associate at the University of Illinois at Urbana-Champaign (UIUC), where he performs research in theoretical astrophysics. He can be reached by email at sbalberg@astro.physics.uiuc.edu.

MONICA COLPI is a Research Associate Professor at the University of Milano, where she studies neutron stars and black holes. Her email address is colpi@astmiu.uni.mi.astro.it.

STUART L. SHAPIRO is a Professor of Physics and Astronomy and an NCSA Senior Research Scientist at UIUC. He has done research on many topics in theoretical astrophysics and general relativity and is a coauthor of the textbook Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects (Wiley). His email address is shapiro@astro.physics.uiuc.edu.

LUCA ZAMPIERI is a Research Associate at UIUC and the University of Padova, where his present research involves supernova fallback and emission from gas accretion onto black holes and neutron stars. His email address is zampieri@donald.physics.uiuc.edu.