The Violent Universe
- Extra Reading
A look at the most violent events that occur in our Universe, from supernovae and hypernovae to the cause of gamma ray bursts and what was the biggest explosion of all - the Big Bang origin of the Universe itself.
Gresham Lecture, Wednesday 19 January 2011
The Violent Universe
Professor Ian Morison
In this lecture we are going to examine what are the most powerful explosions in the universe that can be observed today and also study the Big Bang origin of the universe itself - an explosion of a very different and unique type. The story begins with the serendipitous discovery of what are termed “Gamma Ray Bursts or GRBs - a discovery that came out of the cold war.
It’s an interesting point as to what “today” means. We see these events now but, as we will see, they arise in galaxies in the distant reaches of the universe and so we are seeing events that actually happened many billion of years ago.
The discovery of Gamma Ray Bursts
As nuclear test ban treaties were negotiated in the late 1950s, President Eisenhower's science advisors cautioned him that the USSR might try to secretly carry out nuclear tests in space. It was decided to design and launch a series of satellites that could detect the characteristic double burst of gamma rays (very highly energetic photons) that result from a nuclear blast.
The project was code-named Vela (meaning “watchers”) and the first spacecraft was launched in October 1963 orbiting at an altitude of 120,000 km (74,400 miles). It carried six gamma ray detectors along with other instruments. The gamma ray detectors were made cesium iodide which scintillates – giving flashes of visible light - when gamma rays pass through it.
The data had to be analysed by hand and in 1969 scientists, working with data recorded on July 2nd 1967, found a spike in the data, a dip, a second spike, and a long, gradual tail off. As the team leader, Ray Klebasabel said: "One thing that was immediately apparent was that this was not a response to a clandestine nuclear test". His team checked for possible solar flares and supernovae and found none that might have caused the mysterious event. The number of recorded events rose rapidly as more sensitive detectors were carried by later generations of Vela satellites.
Later, as pairs of satellites were launched with improved timing capabilities, it became possible to approximately determine the directions from which the gamma ray pulses originated. The arrival times of the pulses at the satellite pairs Vela 5a and 5b and 6a and 6b could be measured to an accuracy of 1/64 of a second whilst the light travel time between the satellite pairs across their orbital diameters was around 1 second. This enabled the direction of the event relative to the line between each pair of satellites to be determined to about 1/5th of a radian or 10 degrees. Given the two pairs of satellites one could then derive one or two possible directions for the source of the event.
As they suspected, they found was that the bursts came from outside the solar system and also by their random scatter across the sky, the data hinted that the sources lay, not in our galaxy (in which case one would expect the sources to lie along the plane of the milky way) but in the universe beyond.
Klebasabel published the first results in 1973, detailing 16 confirmed bursts in a paper in the journal Nature entitled “Observations of Gamma-Ray Bursts of Cosmic Origin". As a result, a far more sensitive gamma ray satellite observatory was designed and built. Called the Compton Gamma Ray Observatory, it was launched in 1991 and joined a wide array of Earth satellites and deep space probes that carried much smaller detectors. Over a period of 6 years it observed nearly 2000 bursts which showed that they had an isotropic distribution across the sky and so confirmed that they were not associated with our own galaxy.
[Note: On September 22, 1979, the Vela satellites did detect one possible nuclear test that appeared to have taken place over the Atlantic and is sometimes referred to as the South Atlantic Flash. In addition, the Arecibo ionospheric observatory in Puerto Rico detected an anomalous ionospheric wave during that morning - an event which had not been observed previously by the scientists. Unconfirmed reports indicate that it was a nuclear test initiated by South Africa with possible assistance from Israel.]
Gamma ray burst profiles: those on the left are typical of the short bursts (less than 2 seconds) whilst those on the right are typical of long bursts (greater than 2 seconds).
What causes the Gamma Ray bursts?
For many years after the discovery of GRBs, astronomers searched for a counterpart: an astronomical object whose position agreed with that of a recently observed burst. All such searches were unsuccessful, and where, in a few cases, the position of the GRB was particularly well defined, no bright objects of any nature could be seen. This suggested that the origin of these bursts were either very faint stars or extremely distant galaxies. What was really required were exceedingly fast follow up observations at other wavebands so that, should a gamma ray burst be observed, its source could be immediately identified.
The breakthrough came in February 1997 when the satellite BeppoSAX detected a gamma-ray burst (GRB 970228). Its X-ray camera was immediately pointed towards the direction from which the burst had originated and detected rapidly fading X-ray emission. More significantly still, 20 hours after the burst, the UK’s William Herschel Telescope on La Palma was able to identify a fading optical counterpart. Once the GRB had faded, deep imaging was able to identify a faint, distant host galaxy at the location of the GRB.
Because of the very faint luminosity of this galaxy, its exact distance was not measured for several years but well before, a further breakthrough occurred with the BeppoSAX discovery of GRB 970508 later that year. The position of this event was found within four hours of its discovery so allowing research teams to begin making observations much sooner than for any previous burst. The spectrum of the object revealed a redshift of z = 0.835, placing the burst at a distance of roughly 6 billion light years from Earth so providing the first accurate determination of the distance to a GRB. This proved that GRBs occur in extremely distant galaxies.
As time is of the essence in making follow up observations after the detection of a GRB, the locations determined by the current gamma-ray telescopes such as Swift, are instantly transmitted over the Gamma-ray Burst Coordinates Network (GRBCN). These positions can then be used to rapidly slew earth based telescopes onto the source position in time to observe the afterglow emission at longer wavelengths. The Swift spacecraft, which was launched in 2004 and still operational, is equipped with on-board X-ray and optical telescopes which can be rapidly and automatically slewed to observe the afterglow emission following a burst detected by its very sensitive gamma ray detector.
The swift satellite observing a GRB with an artist’s impression of how one might look.
On the ground, numerous optical telescopes have now been built or modified to incorporate robotic control software that responds immediately to signals sent through the GRBCN. This allows the telescopes to rapidly slew towards a GRB within seconds of receiving the positional data and make follow-up observations whilst the gamma-ray emission is still present.
There was an interesting, though not realised, possibility in 2008. The GRB, 080319B, had an extremely luminous optical counterpart that peaked at a visible magnitude of 5.8. Given a very dark and transparent sky this could have been seen with the unaided eye. Should anyone have been looking in the right direction at this time, the photons that fell on their retina would have been travelling for 7.5 billion light years as so he or she would have looked back in time more than halfway towards the origin of the universe!
In 2009, the Swift Gamma-Ray Burst Mission detected GRB 090423 in the constellation Leo. Its afterglow was detected in the infrared and this allowed astronomers to determine its redshift. Having a z of 8.2, this makes GRB 090423 the second most distant object currently known in the universe. At the time of its discovery it was earliest object ever detected and its light was emitted when the universe was only 630 million years old!
[In October 2010, the European Southern Observatory’s Very Large Telescope in Chile observed a galaxy in the infrared that has a redshift of 8.55 giving a distance of 13.12 billion light years. Its light was emitted just 600 million years after the origin of the universe. As the universe has been expanding since its light was emitted, it is now though to be at a distance of 30 billion light years!]
So let us summarise what was known: gamma-ray bursts are flashes of gamma rays associated with extremely energetic explosions in distant galaxies and are the most luminous electromagnetic events known to occur in the universe. Bursts can last from milliseconds to several minutes, although a typical burst lasts a few seconds. The bursts are classified into two types, short – less than 2 seconds in length – and long – greater than 2 seconds. The initial burst is usually followed by a longer-lived "afterglow" emitted at longer wavelengths (X-ray, ultraviolet, optical, infrared and radio).
How much energy is released?
The measurement of the approximate distance to the gamma-ray burst 970508 in 1997 made it possible to calculate the energy emitted during the event. One knows the energy, say E, falling on the detector which has a given area – say 1/10th of a square metre. As the detector is unlikely to be face on to the burst direction its effective area will be less, say 1/20th sq metre. So the energy falling on one square metre would be E x 20. If the energy from the burst was emitted isotropically (equally in all directions) then one simply calculates the area in metres, say A, of the surface of a sphere centred on the galaxy at the distance of the Earth and multiplies this by the energy falling on one square metre giving: E x 20 x A. Though E is very small, A is enormous, and the calculated emitted energy turns out to be roughly equal to the energy that would be released if the total mass of the Sun were instantly converted into electromagnetic energy!
No known process in the Universe can produce this much energy in such a short time and one can thus deduce that the energy must be beamed, almost certainly in a pair of diametrically opposed beams emitted along the rotation axis of the progenitor object. There is no doubt that this must be a black hole. Nuclear fusion can convert just under 1% of the rest mass energy of an object into energy, but as matter falls into a rotating black hole 30% of the rest mass energy could be converted into energy – this being the most efficient conversion of mass to energy that is known.
Observations indicate that the beams have an angular width of a few degrees. As a result, the gamma rays emitted by most bursts are expected to miss the Earth and will never be detected. However, when one of the two beams is pointed towards Earth, the focusing of its energy causes the burst to appear much brighter than it would have been were its energy emitted isotropically. This greatly reduces the energy that must be released in the explosion. Taking this into account, typical gamma-ray bursts appear to convert about 1/2000th of a solar mass into energy. This is theoretically possible and comparable to the energy released in a bright type Ib supernova.
From the statistics that have been built up over the past 20 years, it appears that GRBs are extremely rare with only a few occurring per galaxy in a million years. None have been observed within our Milky Way galaxy which is not surprising given that there would only be an exceedingly low chance of one occurring in the last 40 years.
What causes Gamma Ray Bursts?
It is now believed that the two types of burst, short and long, are the result of two distinct causes. In both cases the burst is emitted as a black hole is formed, but the two scenarios are quite different. Both result from the evolution of giant stars, so we need to summarise what happens in the final stages of the life of stars.
In the case of stars similar in mass to our Sun, when all nuclear fusion ceases in its core there is nothing to oppose gravity and what is left at the centre of the star (mostly carbon and oxygen) will contract under gravity. The fact that contraction finally ceases is due to a quantum-mechanical effect. In 1926, R.H. Fowler realised that, as a result of the Pauli exclusion principle, no more than two electrons (of opposite spin) could occupy a given energy state. As the allowed energy levels fill up, the electrons begin to provide a pressure - the electron degeneracy pressure - which finally halts the contraction.
A further consequence of being supported by electron degeneracy pressure is that there is a limiting mass which cannot be exceeded. This depends on the composition of the star; for a mix of carbon and oxygen, it turns out to be ~1.4 solar masses. This result was published in 1931 by Subramanyan Chandrasekhar when he was only 19! In 1983, Chandrasekhar rightly received the Nobel Prize for this and other work. The remaining object – the ember of a nuclear fusion reactor – is about the size of the Earth and exceedingly hot. They are called “White Dwarfs”. The largest being comparable to the size of our Earth whose radius is 0.009 times that of the Sun. The masses of observed white dwarfs lie in the range 0.17 up to 1.33 solar masses so it is thus obvious that they must have a very high density. As a mass comparable to our Sun is packed into a volume one million times less, its density must be of order one million time greater - about 1 million grams per cubic centimetre. (A ton of white dwarf material could fit into a matchbox!)
The cores at the centre of stars more massive than our Sun reach higher temperatures and pressures and, as a result, can continue to build up heavier elements than carbon and oxygen. In fact, they can gradually build up elements until no further energy can be released by nuclear fusion. This occurs when the elements Iron and Nickel are reached. Once the core reaches its iron state, things progress very rapidly. At the temperatures that exist in the core (of order 8 x 109 K for a 15 solar mass star) the photons have sufficient energy to break up the heavy nuclei, a process known as photodisintegration. An iron nucleus may produce 13 helium nuclei in the reaction:
56Fe + γ → 13 4He + 4n
These helium nuclei then break up to give protons and neutrons:
4He + γ → 2 p+ + 2n
As energy is released when the heavy elements were produced, these inverse processes are highly endothermic (requiring energy to progress) and thus the temperature drops catastrophically. There is then not sufficient pressure to support the core of the star which begins to collapse to form what is called a neutron star.
In the forming neutron star, free electrons combine with the protons produced by the photodisintegration of helium to give neutrons, in the reaction:
p+ + e- → n + ne
The electron neutrinos barely interact with the stellar material, so can immediately leave the star carrying away vast amounts of energy - the neutrino luminosity of a 20 solar mass star exceeds it photon luminosity by 7 orders of magnitude for a brief period of time! The outer parts of the core collapses at speeds up to 70,000 km per sec and, within about a second, the core, whose initial size was similar to the Earth, is compressed to a radius of about 40 km! This is so fast that the outer parts of the star, including the oxygen, carbon, and helium burning shells, are essentially left suspended in space and begin to infall towards the core.
The core collapse continues until the density of the inner core reaches about three times that of an atomic nucleus, ~8 x 1014 grams per cubic centimetre. At this density, the strong nuclear force, which in nuclei is attractive, becomes repulsive - an effect caused by the operation of the Pauli Exclusion Principle to neutrons and termed neutron degeneracy pressure. As a result of this pressure, the core rebounds and a shock wave is propagated outwards into the infalling outer core of the star. As the material above is now so dense, not all the neutrinos escape immediately and give the shock front further energy which then continues to work its way out to the surface of the star - there producing a peak luminosity of roughly 109 times that of our Sun. This is comparable to the total luminosity of the galaxy in which the star resides!
This sequence of events is called a Type II supernova. The peak absolute magnitude of about -18 then drops by around six to eight magnitudes per year so that it gradually fades from view. We believe that such supernovae will occur in our galaxy on average about once every 44 years. Sadly, the dust in the plane of the galaxy only allows us to see about 10 to 20% of these and so they are not often seen.
What remains from this cataclysmic stellar explosion depends on the mass of the collapsing core. When stars, whose total mass is greater than ~ 8 solar masses, but less than ~ 12 solar masses, collapse the result is a Neutron Star - the core being supported by neutron degeneracy pressure as described above. The typical mass of such a neutron star would be ~ 1.4 solar masses so that it is, in effect, a giant nucleus containing ~ 1057 neutrons. It will have a radius between 10 to 15 km - the theoretical models are not all that precise. Assuming a radius of 10 km, the average density would be 6.65 x 1014 grams per cubic centimetre - more than that of an atomic nucleus!
Stars rotate as, for example, our Sun which rotates once every ~ 25 days at its equator. The core of a star will thus have angular momentum. As the core collapses, much of this must be conserved (some is transferred to the surrounding material), so the neutron star that results will be spinning rapidly with rotational periods of perhaps a few milliseconds. The neutron star will also be expected to have a very intense magnetic field. This rotating field has observational consequences that have allowed us to discover neutron stars and investigate their properties.
The Discovery of Pulsars
In July 1967 a young research student at Cambridge, Jocelyn Bell, observed a "little bit of scruff" that on the chart output that she was studying. Looking through the charts, she discovered that a similar signal had been seen earlier from the same location in the sky. She observed that it reappeared again at always a precise number of sidereal days later which implied that the radio source, whatever it was, was amongst the stars rather that within the solar system. Tony Hewish, her supervisor, and Bell then equipped the receiver with a high speed chart recorder to observe the "scruff" in more detail and discovered to their amazement that it was not random, but a series of precisely spaced radio pulses having a period of 1.33724 seconds.
Jocelyn Bell with the Cambridge array which discovered the first pulsar and the discovery record
At that time, no one in the radio astronomy group at Cambridge group could conceive of a natural phenomena that could give rise to such highly precise periodic signals - it seemed that no star, not even a white dwarf could pulsate at such a fast rate - and they wondered if it might be a signal from an extraterrestrial civilisation. Bell, who called the source LGM1 (Little Green Men 1), was somewhat annoyed about this as it was disrupting her real observations. When, later, a second source with similar characteristics but a slight faster period of 1.2 seconds was discovered she was somewhat relieved as "it was highly unlikely that two lots of Little Green Men could choose the same unusual frequency and unlikely technique to send a signal to the same inconspicuous planet Earth!"
Fred Hoyle suggested that they might result from the oscillations of a neutron star, then a theoretical concept, but it seemed unlikely that they could oscillate so rapidly. After the press conference about their discoveries, the science correspondent of the Daily Telegraph coined the name Pulsar for these enigmatic objects and, some three months later, the physicist Thomas Gold gave a satisfying explanation for the pulsed signals. Gold suggested that the radio signals were indeed coming from neutron stars, but that the neutron star was not oscillating, but instead spinning rapidly around its axis. He surmised that the rotation, coupled with the expected intense magnetic field generates two steady beams of radio waves along the axis of the magnetic field lines, one beam above the north magnetic pole and one above the south magnetic pole. If (as in the case of the Earth) the magnetic field axis is not aligned with the neutron star's rotation axis, these two beans would sweep around the sky rather like the beam from a lighthouse. If then, by chance, one of the two beams crossed our location in space, our radio telescopes would detect a sequence of regular pulses - just as Bell had observed - whose period was simply determined by the rotation rate of the neutron star.
Gold, in this paper, pointed out that a neutron star (due to the conservation of angular momentum when it was formed) could easily be spinning at such rates. He expected that most pulsars should be spinning even faster than the first two observed by Jocelyn Bell and suggested a maximum rate of around 100 pulses per second.
Since then, nearly 2000 pulsars have been discovered. The majority have periods between 0.25 and 2 seconds. It is thought that as the pulsar rotation rate slows the emission mechanism breaks down and the slowest pulsar detected has a period of 4.308 seconds. Pulsars slowly radiate energy, which is derived from their angular momentum. This is so high that the rate of slowdown is exceptionally slow and so pulsars make highly accurate clocks and some may even be able to challenge the accuracy of the best atomic clocks
Our understanding of the probable cause of the short gamma ray bursts was given a fillip by the discovery of a dual pulsar system by astronomers at Jodrell Bank Observatory. Called the “Double Pulsar”, it has produced some of the most stringent tests of General Relativity to date. It was discovered in a survey carried out at the Parkes Telescope in Australia using receivers and data acquisition equipment built at the University of Manchester’s Jodrell Bank Observatory. In analysis of the resulting data using a super-computer at Jodrell Bank the double pulsar was discovered in 2003. It comprises two pulsars of masses 1.25 and 1.34 solar masses spinning with rotation rates of 2.8 seconds and 23 milliseconds respectively. They orbit each other every 2.4 hours with an orbital major axis just less than the diameter of the Sun. The neutron stars are moving at speeds of 0.01% that of light and it is thus a system in which the effects of general relativity are more apparent than any other known system.
Artist’s impressions of the “Double Pulsar” and the distortion of “space-time” they cause (left) and the gamma ray burst as they merge to form a black hole (right).
A key prediction of Einstein’s General Theory of Relativity is that a pair of co-orbiting objects will emit gravitational waves – ripples of space-time that propagate out into the universe at the speed of light. As a result, the the system is losing energy. This energy is derived from the angular momentum of the system and it its loss causes the two pulsars to gradually come together. At this moment in time, General Relativity predicts that the two neutron stars should be spiraling in towards each other at a rate of 7mm per day. Observations made across the world since then, including those using the Lovell Telescope at Jodrell Bank, have show this to be exactly as predicted.
Eventually these two pulsars will fuse into one. In the case of the double pulsar this will not happen for about 84 million years, but there will be many such systems in our own and other galaxies where the combined mass of the pair of neutron stars will exceed the mass limit for neutron stars of about 3 solar masses. It is the final merging of a pair of neutron stars to form a black hole that is believed to be the cause of the short period gamma ray bursts. The explosion is powered by the infall of matter into the new black hole from a surrounding accretion disk.
Some other models that have also been proposed to explain short gamma-ray bursts include the merger of a neutron star and a black hole and the collapse of a single neutron star as material falls on it from a surrounding accretion disk until its mass exceeds that which can be supported by neutron degeneracy pressure and so collapses into a black hole. They could even possibly result from the evaporation of primordial black holes (due to Hawking radiation) that might have been formed in the Big Bang. [If this could be proved, then Stephen Hawking would get a Nobel Prize!]
Long Period Bursts
Most observed gamma ray bursts have a duration of greater than two seconds and are classified as long gamma-ray bursts. As these are in the majority and tend to have the brightest afterglows, they have been studied in much greater detail than their short period (less than two seconds) counterparts. Virtually every well-studied long gamma-ray burst has been associated with star-burst galaxies having high rates of star formation and in many cases a very bright supernova as well, thus unambiguously linking long period GRBs with the deaths of massive stars. Thus most observed GRBs are believed to be a narrow beam of intense radiation released during a supernova or hypernova event.
What stars give rise to long period gamma ray bursts?
Because of the immense distances of most gamma-ray burst sources from Earth, identification of the progenitor systems that produce these explosions, is a major challenge. The most widely-accepted mechanism for the origin of long-duration GRBs is the collapsar model, in which the core of an extremely massive, rapidly-rotating star collapses into a black hole in the final stages of its evolution. [The mass of the core is greater that that which can be supported by Neutron Degeneracy Pressure and so the collapse continues until a black hole is formed as described in my lecture on Black Holes.] Matter surrounding the newly formed black hole falls down towards the centre and forms an accretion disk. The infall of this material into the black hole drives a pair of relativistic jets out along the rotational axis, which bore through the outer layers of the star. As they eventually break through the stellar surface the beams of gamma rays radiate into space.
The closest stars to us that are likely to produce long gamma-ray bursts are likely to be of a type called Wolf-Rayet stars. These are extremely hot and massive stars which have shed most or all of their hydrogen due to radiation pressure. The stars Eta Carinae and WR 104 are both considered to be possible gamma-ray burst progenitors
Hubble Space Telescope image of the star Eta Carina and the Wolf-Rayet star WR 124 and their surrounding nebulae. Both stars are candidates for being progenitors of long-duration GRBs.
It should perhaps be pointed out that, as yet, there is still no generally accepted model for how gamma-ray bursts convert energy into radiation. Any successful model of GRB emission must explain the physical process for generating gamma-ray emission that matches the wide range of light-curves, spectra, and other characteristics that are observed. A particular challenge is the need to explain the very efficient energy conversions that are inferred from some explosions. It appears that some gamma-ray bursts may convert as much as half of the explosion energy into gamma-rays. Based on the recent observations (in 2008) of the bright optical counterpart of GRB 080319B, whose light curve was correlated with the gamma-ray light curve it has been suggested that the “Inverse Compton Effect” may be the cause. In this model, low-energy photons are scattered by the relativistic electrons that result from the explosion, so augmenting their energy by a large factor and transforming them into gamma-rays.
The nature of the afterglows seen at longer-wavelengths (from X-ray to radio) that follow gamma-ray bursts is easier to explain. Any energy released by the explosion that is not radiated away in the burst itself accelerates matter to speeds close to the speed of light. As this matter collides with the surrounding interstellar gas, it creates a shock wave that then propagates forward at relativistic speed into interstellar space. As energetic electrons within the shock wave are accelerated by strong magnetic fields they radiate synchrotron emission (so called because it was first observed being emitted by electrons orbiting at relativistic speeds within a circular synchrotron accelerator) across much of the electromagnetic spectrum giving rise to the observed afterglows.
Should we be afraid?
At the present time an average of about one gamma-ray burst is detected per day. As we observe them across most of the observable universe, so encompassing many billions of galaxies, this suggests that, in a single galaxy, gamma-ray bursts must be exceedingly rare events. In our own Milky Way galaxy we might expect the one burst every 100,000 to 1,000,000 years. As the radiation is beamed only a small fraction of these would be beamed towards Earth so we should not be too worried. However, if there were a gamma-ray burst close enough to Earth, and beamed towards us, it could have significant effects on the Earth’s biosphere. The absorption of radiation in the atmosphere would cause the photo-dissociation of nitrogen, to give nitric oxide that would destroy ozone. It is thought that a GRB at a distance of ~3,000 light-years could destroy up to half of Earth's ozone layer. This would allow more ultra-violet light from the Sun to reach the Earth’s surface which, coupled with the direct UV irradiation from the burst could have a major impact on the food chain and potentially trigger a mass extinction. It is estimated that one such event might happen every billion years and, though there is no direct evidence, it is possible that the Ordovician-Silurian extinction event, 440 million years ago, could have been the result of such a burst.
There seems to be some evidence that the giant stars that produce GRB’s at the end of their lives were far more common in the past when stars were formed largely of hydrogen and helium and there were far fewer heavier elements present. Because the Milky Way has now a good proportion of heavier elements this effect may reduce the number of such long duration gamma ray bursts that might occur now or in the future. Good! However, the merging of two neutron stars of a neutron star with a black hole to give a short duration burst could happen at any time and if one were sufficiently close and beamed towards us, life on Earth could still be at long term risk.
The Big Bang Origin of the Universe
This is rightly said to be the biggest explosion of all time but it was very different to any explosions that we observe today:
It did not happen in space - it created space.
It did not happen in time - it created time.
As St Augustine said “The Universe was created with time, not in time.”
It was everywhere – every part of the universe that we see today was, at the instant of creation, at the same point.
In the original Big Bang Theory, the universe arose from a “singularity” of infinite density and zero volume containing all the energy that now exists, much in the form of mass, in our universe.
Singularities occur in theories when they can no longer capable of describing the physics of extreme conditions. Even if there was no singularity, one real worry is how all the mass that we observe in the universe (with even more that we do not observe) could have been contained in an almost infinitesimally small region of empty space. The answer is that it didn’t. As we shall see, a period of what is called inflation gave rise to a vast amount of energy which, in turn, produced the fundamental particles that make up our universe. But still, how can all of this come from essentially nothing? Surprisingly, the answer is that the total energy content of the universe is zero. This sounds stupid. But there are two forms of “energy”: the energy that is related to the matter in the universe given by Einstein’s formula E = mc2 together with its energy of motion (kinetic energy) we might consider to be “positive” energy but there is also a “negative” energy in the form of gravitational potential energy. It turns out that in our universe (as it must) these two forms of energy are equal and opposite giving a zero sum!
Consider a car at the top of a hill it has a potential gravitational energy of mgh where m is the mass of the car, g is the acceleration due to gravity and h is the height above the surrounding land. If the car were pushed off the top and rolled down to the bottom, this energy would be released and the car would reach some speed giving it kinetic energy. Einstein’s special theory of relativity also states that it will gain some mass. So energy has been converted from one form to another. You can easily see that gravity is associated with negative energy: the car has gained energy of motion (kinetic energy) as it rolled down the hill. But this gain is exactly balanced by an increased negative gravitational energy as it comes closer to Earth’s centre, so the sum of the two energies remains zero.
In the sequence of events that made up the Big Bang that will be outlined below, all the matter, antimatter, and photons were produced by the energy which was released following a period that we call Inflation. All of these particles and their kinetic energy consist of positive energy. This energy is, however, exactly balanced by the negative gravitational energy of everything pulling on everything else. The total energy of the universe is zero! This idea of a zero energy universe initiated by inflation suggests that all one needed to start of our universe was just a miniscule volume of energy in which inflation can begin.
The ultimate question is then what produced this pocket of energy and where was it? Some, as we will discuss in the final lecture, think that it might have happened in some pre-existing space and time but, as stated earlier, it could have arisen from nothing and the concepts of space and time were created along with the universe itself.
Heisenberg’s uncertainty principle - a fundamental tenant of quantum theory - provides a natural explanation for how that energy may have come out of nothing. Throughout the universe, quantum fluctuations cause particles and antiparticles to form spontaneously. Provided they annihilate each other within the time frame determined by the uncertainty principle (the greater the combined mass, the shorter the time) this does not violate the law of conservation of energy. The spontaneous birth and death of these "virtual particle" pairs are known as "quantum fluctuations" and are a very well tested part of physics. Indeed quantum fluctuations must be taken into account when calculating the energy levels of atoms. Unless the effects of virtual particle pairs (such as electrons and positrons) are included, the predicted energy levels disagree with the experimentally measured levels.
Perhaps, before the birth of our universe, quantum fluctuations were happening. The vast majority may have quickly disappeared, but one lived for a sufficiently long time and had the right conditions for inflation to have been initiated. So the original tiny volume of space inflated by an enormous factor, and our universe was born. If this hypothesis is true, then the answer to the question as to where it came from is that it came from nothing and its total energy is zero. But, amazingly this has produced a universe of incredible structure and complexity and, not least, beauty.
The idea of inflation is an integral part of our current understanding of the Big Bang scenario. Apart from its role in creating the matter the universe it neatly explains two problems that that haunted the standard big bang theories.
When Penzias and Wilson discovered the radiation called the Cosmic Microwave Background they found that the temperature of the whole of the visible universe was the same. If we look in one direction the radiation (which tells us the temperature of that part of space) has travelled for13.6 thousand million years – the age of the universe. If we look in the opposite direction we see exactly the same temperature – that radiation has also travelled for 13.6 thousand million years. In the standard Big Bang models there has not been sufficient time to allow radiation to travel from one of these regions to the other - they cannot "know" what each other's temperature is, as this information cannot travel faster than the speed of light. So why are they at precisely the same temperature? This is called the “horizon problem”.
Observations had shown that the space in the universe was very close to being Euclidian (having no curvature and often called “flat space”) so that, in the absence of mass, light would travel in straight lines. The Big Bang theory gives no particular reason why this should be so. Any curvature that the Universe has close to its origin tends to get enhanced as the Universe ages - a slightly positively curved space become more and more so and vice versa. The fact that our observations show us that space has no curvature implies incredibly fine tuning, and there is nothing in the standard Big Bang theory to explain why this should be so. This is called the "flatness" problem.
These problems were addressed with the idea of "inflation", first proposed by Alan Guth and refined by others. In this scenario the whole of the visible universe would have initially been contained in a volume of order the size of a proton. Some 10-35 of a second after the origin this volume of space began to expand exponentially and increased in size by a factor of order 1050 - 1060 in a time of ~10-32 seconds - to the size of a sphere of order a metre in size. (Some say a golf ball or a grape fruit.) This massive expansion of space would force the geometry of space to become Euclidian or "flat", just as the surface of a balloon appears to become flatter and flatter as it expands. (Hence inflation naturally gives a "flat" universe.) Inflation would also ensure that the whole of the visible universe would have a uniform temperature so also addressing the horizon problem. This is a result of the fact that prior to the inflationary period the volume of space-time that now forms the visible universe was sufficiently small that radiation could easily travel across it and so bring it to thermal equilibrium.
A Time Line of the Early Universe
0 – 10-43 s - The Planck Epoch:
The pre-inflationary period. A tiny volume of space, perhaps containing a very small amount of matter, at exceedingly high temperatures.
The four forces of the universe - gravitation, strong nuclear force, weak nuclear force and the electromagnetic force - were one combined into one. (We currently have no theory that describes this.)
10-43 – 10-35 s - The Grand Unification Epoch:
As the universe expands and cools from the Planck epoch, gravity begins to separate from the other forces: electromagnetism and the strong and weak nuclear forces. Physics at this scale may be described by a grand unified theory. Eventually, the grand unification is broken as the strong nuclear force separates from the combined weak nuclear force and the electromagnetic (electroweak) force.
10-35 – 10-33 s - The Inflationary Period:
The strong nuclear force separated from the combined weak nuclear force and the electromagnetic forces. This initiated the era of inflation when the size of the universe increased in size by a factor of order 1050 times. The final size of the universe after this time is uncertain, but estimates range from the size of a golf ball, through that of a grapefruit up to a metre in diameter. From this point onwards, the universe expanded at a far slower rate – the Hubble expansion – which was initially slowing down due to the gravitational attraction of the matter within it. Quantum fluctuations in the energy density produce the “seeds” that allowed the later structure of the universe to form.
A “phase transition” ended the inflationary expansion and released a vast amount of energy producing a hot, relativistic plasma of particles and radiation. An almost equal number of particles and antiparticles are initially created but with a very small excess (~1 part in a billion) of matter particles.
10-12 – 10-6 s - The Quark Epoch:
All the fundamental particles are believed to acquire a mass via the Higgs mechanism. The fundamental interactions of gravitation, electromagnetism, the strong interaction and the weak interaction have now taken their present forms, but the temperature of the universe is still too high to allow quarks to bind together to form hadrons (including protons and neutrons). Interestingly, a form of quark-gluon soup has been recreated recently in the Large Hadron Collider at CERN so enabling physicists to study the conditions that were in existence just a billionth of a second after the origin of the universe!
10-6 – 1 s - The Hadron Epoch:
The quark-gluon plasma that composed the universe cooled sufficiently allowing hadrons, including baryons such as protons and neutrons, to form. At approximately 1 second after the Big Bang neutrinos decouple and begin travelling freely through space.
1s – 10 s - The Lepton Epoch:
The majority of particles and anti-particles annihilate each other at the end of the hadron epoch, leaving leptons and anti-leptons (such as photons) dominating the mass of the universe. Approximately 10 seconds after the Big Bang the temperature of the universe falls to the point at which new lepton/anti-lepton pairs are no longer created and most leptons and anti-leptons are eliminated in annihilation reactions, leaving a small residue of leptons.
3 minutes to 17 minutes - The Era of Nucleosynthesis:
The up and down quarks had formed an almost equal number of Protons and Neutrons. Up quarks have a charge of +2/3 and down quarks a charge of -1/3. A proton is made up of two up and one down quark so has a charge of (+2/3) + (+2/3) + (-1/3) = +3/3 = +1 and the neutron is made up of one up quark and two down quarks and so has a charge of (+2/3) + (-1/3) + (-1/3) = 0. However the free neutron is unstable and will decay into a proton, an electron and an anti-neutrino with a half life of just over 10 minutes. So, over the next few minutes, the number of neutrons falls and the number of protons increases. The only neutrons that can survive are those that have been incorporated into helium nuclei (also called alpha particles) by the process of nuclear fusion. At the same time small amounts of Helium 3 (2 protons, 1 neutron), Deuterium (1 proton, 1 neutron) and Lithium (3 protons, 4 neutrons) were produced. The relative amounts of these elements that would have been produced depended on the density of the universe at this time, and so measurements of their current abundances (taking account the nuclear synthesis that has taken place in stars since which has, over time, increased the abundance of helium and reduced that of hydrogen) can tell us about the conditions that must have prevailed in the early universe. For every proton there was one electron, so overall the universe was neutral. After about 17 minutes the temperature had fallen to the point where no further nucleosynthesis could take place.
3 minutes to 380,000 years - The Photon Epoch:
During this time the energy of the photons was gradually reducing due to the expansion of the universe, but many still had energies greater than 13.6 electron volts (ev), the binding energy of the electron in a hydrogen atom. This meant that, should a proton capture an electron to form a hydrogen atom, very quickly a photon would come along with sufficient energy to split the electron from its nucleus. No atoms could form and the universe was composed of photons, electrons, protons and alpha particles (helium nuclei) along with dark matter. The photons scattered off the electrons and, just as light scattering off water droplets forms an opaque fog, so the universe was opaque to light.
70,000 years - Dark Matter begins to Clump:
According to the standard theory of cosmology, at this stage, dark matter dominates. As it is not coupled to the bath of radiation which is keeping the normal matter distribution very smooth, the dark matter can begin to concentrate into denser regions under gravity - amplifying the tiny inhomogeneities left by cosmic inflation - so making dense regions denser and rarefied regions more rarefied. As yet, we have no theory that describes its origins earlier in the big bang.
A fundamental change came around 380,000 years after the origin. As the universe continued expanding, the typical photon energy dropped below 13.6 ev and hydrogen and helium atoms were able to form. There were then no free electrons to scatter light and the universe became transparent. This is thus as far back in time as we can see. The temperature of the universe was then about 3,000 K, and it was filled with yellow-orange light. Since then the universe has expanded around 1,000 times and the temperature has dropped by the same ratio to ~ 3 K (actually 2.73 K). Thus the radiation is now in the long-infrared/short-wavelength radio part of the radio spectrum and forms what we now call the Cosmic Microwave Radiation or “the afterglow of creation”. Maps of this radiation across the sky show the imprint of the quantum fluctuations that were formed during the inflationary phase of the big bang and provide one piece of evidence that inflation was an integral part of the big bang scenario. They essentially show the distribution of dark matter at this time. The concentrations of dark matter acted as gravitational wells that pulled in normal matter to them. Over the next 500 million years or so, these concentrations of dark and normal matter produced sufficiently dense regions of hydrogen and helium that the first stars and galaxies could form.
The map of the cosmic microwave background that shows the clumpy distribution of matter ~380,000 years after the Big Bang.
A note of caution. Though the above scenario appears to fit virtually all of the known facts and is the current “standard model” of the early evolution of the universe, there are still one or two puzzles and it may not necessarily be true. There are other theories that, for example, do not regard the origin of our universe as being the origin of time and, as yet, there is no theory that explains how the dark matter was created. I will address these ideas in my final lecture “To Infinity and Beyond”.
©Professor Ian Morison, Gresham College 2010
This event was on Wed, 19 Jan 2011
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