Month: May 2018

Semiconductors : Junction Diodes and Transistors

Semiconductors : Junction Diodes and Transistors

Reading Time: 8 minutes

Semiconductors are at the heart of modern human civilization. Every word I type using this laptop is an implicit thank you to the incredible versatility and utility of semiconductors, as well as to the wonderful ingenuity of the scientists and engineers who have harnessed the potential of these magical materials to their fullest.

The following is part I of a brief overview of the physics of semiconductors. This is meant to be a starter pack, so to say. For deeper understanding, I suggest that you read a good textbook.

In this article, The Nerd Druid will talk about intrinsic and extrinsic semiconductors, p-n junctions, p-n junction diodes, and bipolar junction transistors and their applications.

Insulators and conductors

Let’s begin with sodium. Sodium is a metal. This means that it is a good conductor of heat and electricity. However, since sodium is very reactive, it isn’t very smart to use it to conduct electricity. Household wires are usually made of copper, which does a fine job of conducting current.

Image of sodium metal
Sodium metal

In comparison, nonmetallic elements and most compounds are poor conductors. Diamond, an allotrope of the nonmetal carbon, is a very good insulator. Ironically, graphite, another carbon allotrope, is a very good conductor. Graphene–atomic monolayers of graphite–is even better at this conduction business. 1 Air is good insulator, and it takes a huge voltage to pass electrons through air. Happens regularly around thunderstorms. Water is a decent conductor, since it has a lot of free protons (H+ cations) that carry the current.

Image of forked lightning. Extremely high potential differences between the Earth and thunderstorm clouds breaks down the insulation of air, forming forked lightning.
Forked lightning. Extremely high potential differences between the Earth and thunderstorm clouds breaks down the insulation of air, forming forked lightning.

Most natural materials found on Earth are either insulators or conductors.

Semiconductors

Intrinsic semiconductors

Some elements and compounds, however, do not identify themselves as either. Elements such as silicon and germanium, and binary compounds such as gallium arsenide and silicon carbide are semiconductors. When heated, semiconductors begin to conduct electricity. This behaviour is quite the opposite of conductors, where resistance increases with increasing temperature. These are intrinsic semiconductors.

Atomic orbitals

Before we proceed, a quick review of atomic orbitals might be helpful. A more detailed overview can be found here.

Electrons are arranged within atoms in orbitals. The energy of the electrons residing in them groups orbitals together in shells. Shells further away from the nucleus have higher energy than those closer to the nucleus. The most commonly encountered orbitals are s, p, and d. Each orbital can have at max 2 electrons.

Consider silicon. A neutral silicon atom has 14 electrons. These are arranged thus : 1s22s22p63s23p23d0. The first shell of silicon has 2 electrons (lowest energy) residing in the filled s-type orbital (1s). The second shell has 8 electrons (higher energy), 2 in the 2s and six in the 2p. The third shell has the remaining 4 electrons (highest energy); 2 in 3s and 2 is 3p. The 3d orbitals are completely vacant.

Image of silicon electronic configuration
Silicon electronic configuration

Extrinsic semiconductors

The behaviour of intrinsic semiconductors can be altered by adding small amounts of another element. For instance, silicon semiconductors can be thus doped using boron or phosphorus. Boron is trivalent, meaning it has three electrons in its outer shell (1s22s22p63s23p1); phosphorus is pentavalent, meaning it has five electrons in its outer shell (1s22s22p63s23p3). Since silicon has only four, phosphorus doped silicon has extra electrons which are free to move about. Similarly, boron doped silicon has fewer electrons, the absent electrons leaving behind holes, which are also free to hop about. The former is a n-type semiconductor, where electrons are the charge carriers 2. The latter is a p-type semiconductor, where the holes are the charge carriers 3 These extrinsic semiconductors are far more conductive than their undoped counterparts.

p-n junction

A single wafer of semiconductor can also be doped in two different ways; the boundary between the p-type and n-type regions form a p-n junction. When electrodes are attached to the two sides, this becomes the basic building block of all semiconducting electronic devices.

Depletion region

When a p-n junction is fabricated, there are more holes on the p-side and more electrons on the n-side. Immediately, holes and electrons begin migrating across the junction 4. This sets up a diffusion current pointing from the p-side to the n-side.

As holes diffuse over to the n-side, they leave behind negative bound ions. Similarly, diffusing electrons leave behind positive bound ions. Once on the n-side, the holes recombine with the electrons there and disappear. The electrons emulate this behaviour on the p-side. Soon enough, a region forms around the junction which has very few charge carriers. This is the depletion region.

Image showing formation of the depletion region in a p-n junction semiconductor
Formation of the depletion region in a p-n junction semiconductor

The cations and anions left behind set up an electric field pointing from the n-side to the p-side, thus opposing the diffusion current. Once a sufficient number of electrons and holes have diffused, this opposing field is strong enough to stop the diffusion current altogether, and set up its own drift current pointing from the n-side to the p-side.

p-n junction diode

Connect the p-n semiconductor to electrodes. This makes it a p-n junction diode. There are two ways this can be done.

Forward bias

In the first scenario, connect the anode (+ve electrode) to the p-side, and the cathode (-ve electrode) to the n-side. This is the forward bias condition.

The anode will inject holes into the p-side, while the cathode will inject electrons into the n-side. This will push and squeeze the depletion region so that it is narrow enough for electrons and holes to jump across. Once this happens, a current flows across the p-n semiconductor.

Illustration of forward bias in a diode. As the forward bias voltage increases, the deplection region gets narrower and finally collapses
As the forward bias voltage increases, the depletion region gets narrower and finally collapses. This allows current to flow through the diode.

Energetically speaking, the depletion region creates an energy barrier. In forward bias, if the voltage is not high enough, electrons and holes will not have sufficient energy to surmount the depletion barrier. Which is why the current-voltage graph of a p-n junction diode shows a knee in forward bias. The voltage above which the diode turns on is called the cut-in or the forward voltage (VF).

Reverse bias

In the second scenario, reverse the polarity 5. Connect the anode to the n-side and the cathode to the p-side. They will inject holes and electrons as before, though this time this will lead to greater recombinations and will serve to further widen the depletion region.

Illustration of reverse bias in a diode. Reverse bias widens the depletion region, making it almost impossible for current to flow through the diode.
Reverse bias widens the depletion region, making it almost impossible for current to flow through the diode.

Energetically, the reverse voltage will raise the height of the depletion region potential barrier. In this reverse bias state, the diode does not let current pass. Well, not unless the voltage is high enough so that the current flows in the opposite direction as before. That is breakdown. But we don’t want that to happen.

Transistors

Diodes are electronic valves; they allow current to pass in one direction. As such, they are very useful in circuits. However, they can be made much more useful if two p-n junction semiconductors are attached end-to-end in series, creating three separate zones. Attach electrodes to these three zones and you have a bipolar junction transistor (BJT).

There are two ways to do this; you either get a p-n-p transistor or an n-p-n transistor. The middle zone is called the base, and the ones on the two ends are called the collector and the emitter. Now, connect electrodes to each of these regions and apply potentials.

Image of an n-p-n transistor, with n-type collector and emitter, and p-type base.
An n-p-n transistor, with n-type collector and emitter, and p-type base.

Of course, BJTs are not the only type of transistor around. Field effect transistors work in a slightly different fashion. I’ll not be discussing FETs here.

Modes of operation : Switch and amplifier

The transistor can operate in four modes. One can control this by tuning the base voltage VB, the emitter voltage VE and the collector voltage VC. In what follows, I shall use an n-p-n transistor to illustrate the mechanism. You can convert this into a p-n-p by merely flipping the “>” signs and reversing the current.

Saturation mode : VB > VC , VB > VE

Recall that the transistor is n-p-n, so that the base is p and the emitter and collector are n. Thus, VBE > 0 and VBC > 0 imply that both the base-emitter (BE) and base-collector (BC) junctions are in forward bias mode. This setup behaves like a closed circuit; current flows freely between the collector and the emitter. For n-p-n, the collector current IC points from the collector to the emitter. Electrons, the majority carriers in n-p-n, are emitted by the emitter and collected by the collector 6.

The transistor is now ON.

Cut-off mode : VB < VC , VB < VE

The signs are reversed; VBE < 0 and VBC < 0. Both the BE and BC junctions are reverse biased. No current flows in the transistor, and it behaves like an open circuit.

The transistor is now OFF.

By reversing the voltages, one can thus use the transistor as a switch.

Forward active mode : VC > VB > VE

Here, VBE > 0 but VBC < 0; the BE junction is forward biased, while the BC junction is reverse biased. In this mode, the transistor acts as an amplifier–a small input base current IB gives rise to a very large output collector current IC.

IC = β IE

where β is large, usually 100.

Image of a transistor in forward active mode, acting as an amplifier. The n-type emitter emits electrons, a majority of which reach the collector due to the large potential difference between C and E.
A transistor in forward active mode, acting as an amplifier. The n-type emitter emits electrons, a majority of which reach the collector due to the large potential difference between C and E.
Reverse active mode : VC < VB < VE

This is basically the same as forward active, except β is much smaller. This mode is seldom used in practice.

Schematic of the four modes of a transistor; saturation (ON), cutoff (OFF), forward active (amplifier), and reverse active.
The four modes of a transistor; saturation (ON), cutoff (OFF), forward active (amplifier), and reverse active.

Applications

Transistors are the basic building blocks of computers and modern electronics, and have wide-ranging applications.

As a switch

Keep the transistor in switch mode and assign labels to the states of the switch; 0 for OFF, 1 for ON. The transistor now functions as a bit, the fundamental unit of classical computing.

You can string a few transistor switches together and form logic gates. These follow Boolean algebra, and allow you to perform OR, AND and NOT operations. More complex combinations of transistors give NOR, NAND, and XOR gates.

Bits and logic gates can be used together to implement a series of instructions. This implementation of an algorithm is a computer program.

Finally, by connecting transistors together in certain ways, it is possible to make it stay either in the saturation or the cut-off states until a new input has been applied. Such flip-flops can either be in 0 or 1 states, and thus can store bits. These are the building blocks of computer memory.

As an amplifier

Hearing aids are wonderful applications of transistor amplifiers. The microphone converts sounds into electrical current. It then feeds this into the base of a transistor which is operating in the active mode. The collector current, greatly amplified, feeds into a loudspeaker. Prof Calculus (in moon rocket mode) would greatly approve.

A panel from the tintin book Destination Moon, showing Professor Calculus and Captain Haddock
Professor Calculus and Captain Haddock, from Destination Moon.

References and Further Reading

  1. All About Circuits
  2. ExplainThatStuff
  3. SparkFun
Exploring the Subatomic World : Electrons and Nuclei

Exploring the Subatomic World : Electrons and Nuclei

Reading Time: 6 minutes

Atoms were once thought to be indivisible and fundamental. Nineteenth century chemistry was based around atoms, culminating in Dmitry Mendeleev’s extraordinary Periodic Table. The discovery of the electron in 1897 led to a subatomic revolution, and the twentieth century has revealed the rich internal structure of the atom, culminating in the Standard Model, the subatomic counterpart of Mendeleev’s Table. In this series of brief articles, The Nerd Druid traces the wonderful history of the subatomic.

Subatomic particles

Protons, neutrons and electrons are the three most well-known subatomic particles. Earth has an abundance of free protons and electrons. All you need for the former is to somehow make electricity happen. An easy way to do that is to rub amber with fur 1. For the latter, water works pretty well, since it has plenty of free protons roaming about. Of course, it helps to keep in mind that protons are simply ionised hydrogen atoms.

The Electron

The ancient Greeks noticed that if you rub amber with fur, the amber tended to attract small light objects. This, along with lightning strikes, was the only connection humans had with electricity until modern times.

Image of Garfield (the cartoon cat character) rubbing his fur against Jon's pants. This creates static electricity. The charged fur repels each other.
Garfield rubbing his fur against Jon’s pants creates static electricity. The charged fur repels each other.

Cathode Rays

In the latter half of the nineteenth century, German and English physicists found that if you pull air out of sealed container and insert a cathode 2 into it, you see a glowing discharge. Pump out more air, lower the air pressure further, and this cathode discharge glows brighter. The pioneers of cathode ray physics were Johann Hittorf (Germany) and Eugen Goldstein (Germany); they did their work in 1869 and 1876 respectively.

William Crookes (England) created the first cathode ray tube in the 1870s by creating a high vacuum. He observed that the glow had now become a sort of a ray, moving from the cathode to the anode 3. Reckon we’d have to thank Crookes for all the televisions and older computer monitors.

Crookes also applied a magnetic field to the cathode rays and made them deflect. This showed that the rays were charged. Arthur Schuster (Germany-England) modified Crookes’ setup. He sandwiched the cathode ray between two parallel plates, one positive and one negative. The electric potential between the plates made the rays bend and strike the positive plate. This proved that the rays were negatively charged.

Discovery of the electron

Schuster didn’t stop there. By varying the current fed into his parallel capacitor, Schuster was able to vary the degree by which the cathode rays were deflected. He measured and tabulated these results, and was thus able to calculate the charge-to-mass (Q/m) ratio of the cathode rays. His results were astonishing–the Q/m ratio of the cathode rays seemed to be more than a thousand times what was expected!

Unfortunately, Schuster’s results were ignored, probably because they didn’t quite conform to what people knew about atoms. The prevalent idea at that time was that cathode rays were some sort of atoms or molecules, and thus they were expected to have a mass at least equal to the hydrogen ion.

Image of J.J. Thomson, English physicist. Experimentally obtained evidence for the existence of electrons. Thus showed that cathode rays are independent particles. Showed that these negatively charged particles are the same as the ones produced by radioactivity, by heated materials, and by illuminated materials. Suggested the plum pudding model for the distribution of positive charges and electrons within the atom. Discovery of the electron threw open the subatomic realm.
J.J. Thomson, English physicist

In 1897, J.J. Thomson (England), working with colleagues John Townsend (Ireland) and H.A. Wilson (England), showed that cathode rays were, indeed, individual charged particles. A few years later, Millikan and Fletcher performed the famous oil-drop experiment and accurately measured the charge of this new particle, the electron 4. Since the charge-to-mass ratio of the electron had already been measured, it was now simple to calculate the mass of the electron. Simply put, the electron has the same magnitude but opposite sign of the charge of a hydrogen ion. However, it had almost two thousandth its mass.

The Atomic Nucleus

Thanks to Thomson and his fellow cathode ray physicists, the atom was no longer a black box. Negatively charged cathode rays were actually particles called electrons, and they lived inside an atom. Sometimes some of these electrons would get knocked off the atom. The charged atom would then be a positive ion, a cation. At all other times, the atom would be strictly neutral. Clearly, the atom within contained an amount of positive charge equal to the negative charge it contained due to the electrons. The question was, where did the positive charge reside, and where were the electrons in relation to this?

Thomson had an answer to this. He envisaged electrons embedded within a uniform diffuse distribution of positive charge within the atom, much like plums in a pudding. The Geiger-Marsden experiment (1909) put paid to this plum pudding model soon enough.

Image of Thomson's plum pudding model (above) and Rutherford's Gold Foil experiment (below, aka the Geiger-Marsden expt.).
Thomson’s plum pudding model (above) and Rutherford’s Gold Foil experiment (below, aka the Geiger-Marsden experiment)

Hans Geiger 5 (England) and Ernest Marsden (England-New Zealand), working under the direction of Ernest Rutherford (New Zealand-England), fired positively charged alpha particles 6 at a metal foil. While most of the alpha particles whizzed through without any change in momentum, a tiny fraction (1-in-20000) deflected by almost 90 degrees. Rutherford concluded (in 1911) that this must be because all the positive charge in the atom is tightly packed inside a tiny volume at its centre. This, of course, is the atomic nucleus.

There were quite a few experiments performed by Geiger and Marsden. The most famous one is also referred to as Rutherford’s Gold foil experiment.

Nationalities

A quick aside about the nationalities of the people involved. A majority seem to be from England and Germany. The only two scientists from the US are Millikan and Fletcher, and they did their work in the 20th century. This seems to suggest that the nerve-centre of cutting edge physics in the nineteenth century was very much a few nations in Europe.

Nuclear density and pressure

The atom is mostly empty space 7 Atomic diameters are usually of ångström order (1 Å = 10-10 m). Nuclear diameters are a hundred thousand times smaller, usually of femtometer order (1 fm = 10-15 m). However, nuclei carry most of the atom’s mass. Due to their small sizes, they are incredibly dense objects.

A quick back-of-the-envelope calculation for carbon (C-12 isotope) shows that its nuclear density is approximately 1.25×1015 gm/cc. To put that into perspective, the density of ordinary water, under normal atmospheric pressure and standard room temperature, is approximately 1 gm/cc. Atomic nuclei are hundreds of trillion times denser than tap water.

Before we proceed, I’m going to presume that you are aware that atomic nuclei contain protons and neutrons. I’ll get to them in the next part of this series.

You’d think that such high densities would mean that the pressure inside the nucleus would be immense. You’d be correct, but there are places in this universe which make nuclear pressures seem like cotton candy. I’m talking about the interior of neutron stars, where pressures reach absurd values of 1034 pascal. In comparison, standard atmospheric pressure is about a hundred thousand pascal, 105. This of course makes neutron star cores very very hot. The story of how they cool down is quite interesting.

Up until a few days ago, this was the highest pressure found in the universe. Recently however, scientists at Jefferson Lab (the USA) have found that proton pressure is ten times that inside neutron stars. That is a mind-boggling million trillion trillion times that of standard Earth sea-level pressure.

Yes. A million trillion trillion times. 10 followed by 30 zeros.

In the next article, we encounter nucleons.


References

List of People : Who Did What

  1. Dmitry Mendeleev : Russian chemist
    • Designed the Periodic Table of Elements
  2. Johann Wilhelm Hittorf : German physicist
    • Discovered that a cathode within an evacuated chamber emitted a glow
    • Found that the intensity of the glow increased as pressure is lowered
  3. Eugen Goldstein : German physicist
    • Showed that the rays from Hittorf’s glow cast a shadow
    • Named the rays cathode rays
  4. Sir William Crookes : English chemist and physicist
    • Invented the extreme low pressure cathode ray tube
    • Showed that cathode rays travel as a straight beam between a cathode and anode
    • Showed that cathode rays deviate in a magnetic field, proving that they are charged
  5. Arthur Schuster : German-British physicist
    • Placed the cathode ray between the plates of a parallel plate capacitor
    • Showed that the beam deviated towards the positive plate
    • Thus showed that cathode rays are negatively charged
  6. J.J. Thomson : English physicist
    • Experimentally obtained evidence for the existence of electrons
    • Thus showed that cathode rays are independent particles
    • Showed that these negatively charged particles are the same as the ones produced by radioactivity, by heated materials, and by illuminated materials
    • Suggested the plum pudding model for the distribution of positive charges and electrons within the atom
    • Discovery of the electron enabled the subatomic world to be probed
  7. George Johnstone Stoney : Irish physicist
    • Introduced the term electron for units of electricity
  8. Robert Millikan : American physicist
    • Performed the famous oil-drop experiment and measured the charge of the electron
  9. Harvey Fletcher : American physicist
    • Performed the famous oil-drop experiment and measured the charge of the electron
  10. Ernest Rutherford : New Zealand-British physicist
    • The father of subatomic and nuclear physics
    • Called the greatest experimentalist since Faraday
    • Supervised the Geiger-Marsden experiment or the Gold foil experiment that disproved the plum-pudding model and discovered the atomic nucleus
    • Discovered the proton
    • Suggested that protons within the nucleus have a neutral partner
    • Named them neutrons
  11. Hans Geiger : German physicist
    • Performed the Geiger-Marsden experiment that disproved the plum-pudding model and discovered the atomic nucleus
    • Invented the Geiger counter, a detector of radioactivity
  12. Ernest Marsden : New Zealand-English physicist
    • Performed the Geiger-Marsden experiment that disproved the plum-pudding model and discovered the atomic nucleus

Original papers

  1. Thomson, J.J. : Cathode Rays, Philosophical Magazine (1897)
  2. Rutherford, Ernest : The scattering of α and β particles by matter and the structure of the atom, Philosophical Magazine (1911)
  3. Millikan, R.A. : On the Elementary Electrical Charge and the Avogadro Constant
Proton Pressure : How do Quarks Tackle Stress?

Proton Pressure : How do Quarks Tackle Stress?

Reading Time: 9 minutes

Proton pressure, theoretically estimated to be higher than even neutron stars, has been notoriously difficult to measure experimentally. Recently, however, particle physicists have used a nice trick to measure proton pressure. The Nerd Druid delves deeper.


Subnucleonic particles

Quarks

Particle physics is the study of extremely small particles. In the nineteenth century, atoms were thought to be indivisible and fundamental. Then, in 1897, J.J. Thompson discovered the electron. Following the Geiger-Marsden experiment in 1909, Ernest Rutherford in 1911 postulated the existence of the proton. The now-familiar subatomic trio was completed when James Chadwick discovered the neutron in 1932.

Image of a comparison of various physical properties of the three most familiar subatomic particles.
Comparison of various physical properties of the three most familiar subatomic particles.

In the three decades following 1932, the use of higher and higher energies in particle accelerators led to the discovery of a veritable particle zoo. In 1964, Murray Gell-Mann and George Zweig attempted to simplify matters. They proposed that protons, neutrons and all the other hadrons were not as fundamental as once thought. Instead, they suggested that smaller particles called quarks are the true fundamental particles that make up hadrons.

Image of Murray Gell-Mann (left) and George Zweig (right) were the first to propose the existence of quarks. 10 years after their proposal, the discovery of the charm quark in 1974 definitively proved Gell-Mann and Zweig to be correct. Gell-Mann received the Nobel Prize in physics in 1969.
Murray Gell-Mann (left) and George Zweig (right) were the first to propose the existence of quarks. 10 years after their proposal, the discovery of the charm quark in 1974 definitively proved Gell-Mann and Zweig to be correct. Gell-Mann received the Nobel Prize in physics in 1969.

The naming of quarks

Quarks are possibly one of the first particles named without reference to a Greek or Latin dictionary. Murray Gell-Mann, the man responsible for the name, had borrowed the word from the novel Finnegan’s Wake by James Joyce. At one point in the novel, a character, presumably drunk, exclaims

Three quarks for Muster Mark!

the words quarks and Muster possibly drunk modifications of quarts and Mister.

The Nerd Druid has once attempted to read Finnegan’s Wake. In his opinion, had Joyce not written Ulysses, Finnegan’s Wake would have been, without doubt, one of the most difficult books to read in the English language.

The discovery of the quarks

According to Gell-Mann and Zweig, there were three types or flavours of quarks. These were the up, down and the strange quarks. In 1970, Glashow, Iliopoulus and Maiani (GIM) proposed that a fourth flavour, the charm quark, should also exist. Three years later, Kobayashi and Maskawa’s proposal of top and bottom quarks increased the number of quark flavours to six.

Despite such stunning theoretical success, particle physicists were initially unwilling to accept the quark model. Richard Feynman proposed an alternative and called them partons. However, increasingly complex and beautiful experiments in the decade since Gell-Mann and Zweig seemed to weigh evidence in favour of quarks. Deep inelastic scattering experiments at the Stanford Linear Accelerator Centre (SLAC) found particles that would later be identified with the up and the down quark. The SLAC experiment also indirectly suggested that strange quarks should exist.

The November Revolution

The final breakthrough came in the November of 1974. Unlike its more illustrious and political Russian cousin, the particle physics November Revolution took place at SLAC and at Brookhaven National Laboratory, both in the USA. The two teams almost simultaneously discovered the charm quark and its antiparticle, bound together to form a meson. Burton Richter, who led the SLAC team, named it the ψ (psi) meson. Samuel Ting, who led the Brookhaven team, preferred to call it the J meson. Due to the joint announcement of their discovery, the J/ψ meson is the only particle with a two letter name.

Images of Samuel Ting (left) and Burton Richter (right), discoverers of the J/psi meson. They received the 1976 Nobel Prize in Physics for their work.
Samuel Ting (left) and Burton Richter (right), discoverers of the J/ψ meson. They received the 1976 Nobel Prize in Physics for their work.

The J/ψ discovery validated the quark model and led to rapid changes in high-energy particle physics. One of the major innovations to come out of this incredible time is what is known as the Standard Model of particle physics. To put it in a nutshell, the Standard Model puts the entire workings of the universe–sans gravity–in a nutshell. Thus, the name November Revolution.

The Standard Model

The standard model did to high-energy particle physics what Dmitry Mendeleev’s periodic table had done for chemistry almost exactly a hundred years earlier. It cut through all the noise and gave a beautiful tabular representation of all the fundamental particles that interact among each other via the four fundamental forces 1.

Image of a schematic depiction of the Standard Model of elementary particles. Shown are the six quark flavours, the three leptons and their corresponding neutrinos, the four force-carrying vector gauge bosons, and the solitary mass-carrying scalar gauge boson, the Higgs.
A schematic depiction of the Standard Model of elementary particles. Shown are the six quark flavours, the three leptons and their corresponding neutrinos, the four force-carrying vector gauge bosons, and the solitary mass-carrying scalar gauge boson, the Higgs. (Image Credit : Wikipedia).

The Fermions

In the image above, the six purple boxes represent the six flavours of quarks, while the six green boxes represents the three leptons and their neutrino counterparts. These twelve particles are fermions : particles that follow Fermi-Dirac statistics and have half-integer spins.

The Bosons

The particles on the right half of the image are bosons. These follow Bose-Einstein statistics and have integer spins. The four red boxes represent vector gauge bosons. These carry and mediate three of the four fundamental forces of nature; the fourth, gravity and its mediating gravitons, are still out of the standard model’s grasp. The yellow box on the very right represents the solitary scalar gauge boson, the Higgs, which carries and mediates mass.

Thus, all in all, 17 particles (and their antiparticles) are involved in almost everything that happens in the universe. The Nerd Druid will, hopefully, expand on the standard model in a later post.

Proton Constituents

Quarks are the building blocks of protons, neutrons, and a host of other particles. Together, these quark-based particles are called hadrons. For instance, the J/ψ meson is a hadron. There are two types of hadrons:

  1. Baryons : Composed of three quarks. These can be any flavour.
  2. Mesons : Composed of a quark and its antiquark.

The J/ψ is a meson because it comprises the charm (c) quark and its antiquark. Protons are composed to two up quarks and a down quark (uud), while neutrons have two down and one up quark.

Image of the quark composition of protons and neutrons. On the left, two up and one down quark make up a proton. On the right, two down and one up quark make up a neutron. The quarks have different "colour charges" that add up to "white", and are joined by gluon flux tubes.
On the left, two up and one down quark make up a proton. On the right, two down and one up quark make up a neutron. The quarks have different “colour charges” that add up to “white”, and are joined by gluon flux tubes. Do note that the flux tubes as shown here are wrong. They do not act along the sides of the triangle making up the quarks, but rather form a Y-shape, much like the flux capacitor in the movie Back to the Future.

Why does a proton not break up?

An up quark has charge +2/3, a down quark has charge -1/3. This makes the interior of nucleons a very interesting place. Take the proton, for instance. It has two positively charged up quarks within it, each of which is attracted towards, and attracts, the third negatively charged down quark. However, since they are both positive, they repel each other. How in the world does the proton not break up?

{Atomic nuclei have a similar problem. Going by common sense, the positive protons should never be confined to such a small region.}

If conditions are energetically favourable, bound protons transmute into neutrons. Free protons, one of the stablest objects in the universe, only do so if bombarded with high energy particles. The quarks within them never fly apart on their own, although, electromagnetically speaking, they should be flying apart. What the proton needs is an attractive force that keeps the various quarks together. One candidate is gravitation. However, that is approximately 1040 times weaker than the EM force. So that’s no help.

The Strong Force

Luckily, there is a force stronger than even the EM force. This is the imaginatively named strong force. While the EM force is mediated by photons, the strong force is mediated via gluons.

Take a quick peek at the standard model diagram. The topmost red box on the right half is the gluon. It is a vector gauge boson, and functions as a force-carrier. The strong force holding the quarks together manifests as constant exchanges of gluons between the quarks. From a quantum field theoretic viewpoint, the three quarks within the proton live in a sea of frothing bubbling gluon field.

{The strong force is, of course, also responsible for holding the nucleus together, and manifests itself via constant exchange of gluons between protons and neutrons.}

Proton Mass

The mass of an atom is approximately the same as the mass of its nucleus, since electrons are 1839 times lighter than neutrons, and 1836 times lighter than protons. Adding the masses (the rest masses) of the nucleons is the mass of the atom minus the binding energy needed to keep the nucleus together. However, this is still a small percentage of the nucleonic rest masses.

Inside a proton, the situation is rather different. The total rest mass of the three quarks (2u+1d) is only about 10% of the total mass of the proton. The rest 90% of the mass is provided by the highly energetic gluon field. Since it has energy, and by Einstein’s Mass-Energy equivalence, E = mc2, the gluon field has relativistic mass.

Image of a schematic of the masses of the six different quark flavours. The larger the balls, the higher the mass. The mass of the proton (grey) and electron (red) are shown in the southwest corner. Note that the total mass of 2u+1d would be quite a bit lesser than that of the proton.
A schematic of the masses of the six different quark flavours. The larger the balls, the higher the mass. The mass of the proton (grey) and electron (red) are shown in the southwest corner. Note that the total mass of 2u+1d would be quite a bit lesser than that of the proton.

Proton Pressure

Probing the inside of a proton is not easy. While it is possible to build up a three-dimensional image of the proton using the EM force, probing the mechanical properties of the proton is another matter entirely.

The Energy-Momentum Tensor

The energy-momentum tensor provides a complete classical dynamical description of a particle. It encodes information such as its mass and its momentum, and the shear stresses and pressures on it. Einstein’s Field Equations, which form the backbone of general relativity, relates this tensor with the curvature of spacetime. In the image, the E-M tensor is represented as a 4-by-4 matrix. The energy density, shown in the red box on the top left corner, is equivalent to the mass. The rest of the diagonal, the green band, represents pressure.

Image of the energy-momentum tensor, represented as a 4-by-4 matrix. The northwest corner (red) is mass. The northern and western walls (yellow-orange) are momentum. The elements along the diagonal (green) are pressure acting along the three space axes.
The energy-momentum tensor, represented as a 4-by-4 matrix. The northwest corner (red) is mass. The northern and western walls (yellow-orange) are momentum. The elements along the diagonal (green) are pressure acting along the three space axes.

Gravitational Form Factors

To obtain information about the mechanical structure of a proton, you’d need to prod it with a gravity probe. However, a gravity probe will not directly measure the matrix elements of the E-M tensor. Instead, what it can do it measure what are called gravitational form factors. In 1966, Heinz Pagels developed the concept of these GFFs and also analytically calculated them. Pagels, however, was not very confident that it would ever be possible to measure the detailed structure of a particle using the GFFs, since there was

…very little hope of learning anything about the detailed mechanical structure of a particle, because of the extreme weakness of the gravitational interaction.

And therein lies the rub. Gravity is just too weak a force at the scale of subnucleonic particles.

Image of Heinz Pagels, who constructed the gravitation form factors for nucleons in 1966, at the age of 27. He was extremely capable of explaining science in a simple way. Pagel's work in chaos theory provided the inspiration for the character of Ian Malcolm in Michael Crichton's Jurassic Park.
Heinz Pagels constructed the gravitation form factors for nucleons in 1966, at the age of 27. He was extremely capable of explaining science in a simple way. Pagel’s work in chaos theory provided the inspiration for the character of Ian Malcolm in Michael Crichton’s Jurassic Park.

Generalised Parton Distributions

If restricted to EM probes, then, using something called generalised parton distributions, researches can build up a 3D model of the proton. The word parton here is not quite used in the sense Feynman envisioned it; the term parton nowadays collectively refer to quarks, antiquarks, and gluons. GPDs were introduced around the year 1994. In the quarter century till then, they have emerged as an extremely valuable tool for probing hadrons.

However, the puzzle was still incomplete. GPDs are electromagnetic objects, while GFFs are gravitational. Proton investigations required a bridge between these two.

Measuring Proton Pressure

Deeply Virtual Compton Scattering

The bridge was finally proposed in 1997, when the Xiandong Ji suggested that a method called deep virtual compton scattering (DVCS) could be used to map GFFs onto GPDs. In this process, a beam of electrons is fired into atomic nuclei. Some of these electrons shoot through protons. In doing so, they transfer some of their energy to one of the quarks inside the proton. This is mediated by a virtual photon. The proton, thus energised, doesn’t hold on to this excess energy for long. It soon emits another photon and drops down to its original state.

Magnitude of Proton Pressure

By analysing these photons, Jefferson Lab scientists Volker Burkert, Latifa Elouadrhiri, and Francois-Xavier Girod (BEG) have built up a mechanical picture of the interior of the proton. In particular, they have calculated proton pressure for the very first time. BEG have found that quarks near the centre of the proton feel pressures of the order of 1035 pascal.

To put that into perspective, standard atmospheric pressure at sea level on Earth is slightly more than a million pascal. That is 106.

The centres of neutron stars used to be the undisputed champions of the universe when it came to ultrahigh pressures. They’ve been dethroned, for proton pressure is about 10 times the pressure found within neutron stars.

Distribution of Proton Pressure

Image of the proton pressure distribution. The y-axis is in units of force (positive outward), while the x-axis shows distance from proton centre (in femtometer, 10^-15 m). The repulsive proton pressure near the centre, directed outwards, is balanced by the confining proton pressure from the outer edges of the proton, directed inwards.
Pressure distribution within a proton. The y-axis is in units of force (positive outward), while the x-axis shows the distance from proton centre (in femtometer, 10^-15 m). The repulsive pressure near the centre, directed outwards, is balanced by the confining pressure from the outer edges of the proton, directed inwards.

According the BEG analysis, the proton pressure at the centre of the proton is highest. It is also repulsive, threatening to push the three quarks apart. However, proton pressure near its edge, though less in magnitude, is compressive in nature. This confines the quarks to within the interior of the proton, within a diameter of about 2 fm (1 fm = 10-15 m).

BEG are not done yet, though. They are waiting for better and precise data that they hope to obtain soon. This will help them polish some of their current results on the distribution of proton pressure. BEG are confident that their method of DVCS-GPD-GFF will reveal more about the interior of the proton, such as internal shear forces and the its mechanical radius.


References

Original Paper

Burkert, V. and Elouadrhiri, L. and Girod, F-X. : The pressure distribution inside the proton, Nature (2018).

Reference papers

  1. Pagels, Heinz : Energy-Momentum Structure Form Factors of Particles, Physical Review (1966)
  2. Maxim V. Polyakov, Maxim V. and Schweitzer, Peter : Forces inside hadrons: pressure, surface tension, mechanical radius, and all that, arXiv (2018)
  3. Ji, Xiangdong : Gauge-Invariant Decomposition of Nucleon Spin, Physical Review Letters (1997)
  4. Ji, Xiangdong : Deeply virtual Compton scattering, Physical Review D (1997)
  5. Rutherford, Ernest : The scattering of α and β particles by matter and the structure of the atom (2011)
  6. Chadwick, James : Possible Existence of a Neutron, Nature (1932)
  7. Belitsky, A.V. and Radyushkin, A.V. : Unraveling hadron structure with generalized parton distributions, Physics Reports (2005)

Other resources

  1. Perdrisat, Charles and Punjabi, Vina : Nucleon Form Factors, Scholarpedia (2010)
  2. Wikipedia
    1. Atoms#Subatomic Particles
    2. Proton#History
    3. Neutron#Discovery

Articles

  1. Press Release : First measurement of subatomic particle’s mechanical property reveals distribution of pressure inside proton
  2. Press Release : Quarks feel the pressure in the proton
    1. EurekaAlert (2018)
    2. Jefferson Lab (2018)
  3. Mandelbaum, Ryan F. : Scientists Calculate the Pressure Inside a Proton and It’s Higher Than in a Neutron Star, Gizmodo.com (2018)
  4. Micu, Alexandru : Pressure in protons’ cores is over ten times greater that that in neutron stars
  5. News Staff : Physicists Measure Pressure Distribution inside Proton, Sci-News.com (2018)
  6. Yirka, Bob : Best of Last Week – Measuring pressure inside a proton, flying wireless robot insects and yogurt may treat inflammation, ScienceX.com (2018)
  7. McRae, Mike : Protons Contain 10 Times More Pressure Than a Neutron Star, According to First-Ever Measurement, Science Alert (2018)
  8. Grossman, David : Pressures Inside a Proton Are More Extreme Than Inside a Neutron Star, Popular Mechanics (2018).
  9. Williams, Matt : The Pressure Inside Every Photon is 10x That Inside Neutron Stars, Universe Today (2018)
Direct Urca : How Thieving Neutrinos Cool Neutron Stars

Direct Urca : How Thieving Neutrinos Cool Neutron Stars

Reading Time: 11 minutes

Neutron stars are one of the most interesting and exotic objects in the universe. Formed as remnants of stellar cores post-supernova, core temperatures of these ultradense stars at formation can be as high as hundreds of billions of kelvin. Neutron stars cool off by shedding neutrinos–either via the superfast direct Urca process, or by the much more sedate modified Urca process. While the latter mechanism has been observationally confirmed, there has been no compelling evidence for the direct Urca process. Until now. The Nerd Druid investigates how neutrinos rob neutron stars of their heat, and how quick are their ghostly pickpockety hands.

Stars

Stars are fascinating objects. The sun is one. It is middle-aged, having burnt through about half of its ten billion year lifespan. The sun is a yellow-white main sequence star of average luminosity and mass. There are other types of stars; some are far more massive and luminous than the sun, some are far less massive and much dimmer. Some stars shine blue-hot, some are cool and very red. Just like living beings, stars have a beginning and an end. Near the end of their lives, stars shed excess mass, either via spectacular explosions called supernovae or in far more docile fashion. Near the end of their lives, stars shed excess mass, either via spectacular explosions called supernovae or in far more docile fashion. In the latter, small superdense stellar core remnants called white dwarfs are formed. In the former, tiny ultradense stellar core remnants called neutron stars may be formed, unless the mass of the remnant is high enough to trigger an unstoppable collapse, resulting in a black hole.

Image of the white dwarf companion to Sirius, the brightest star in the sky.
Image of Sirius A and Sirius B taken by the Hubble Space Telescope. Sirius B, which is a white dwarf, can be seen as a faint point of light to the lower left of the much brighter Sirius A.

The Chandrasekhar limit

Stars are massive objects, and thus generate high gravitational fields. Logic dictates that this gravity field should act in on itself, squeezing it strongly enough for it to collapse. However, since the star is constantly fusing hydrogen to form helium and, in the process, releasing a lot of energy, the thermal pressure outward balances the gravitational pull inward. When stellar fusion fuel runs out, however, the outward thermal pressure is no longer sufficient, and the star collapses.

But not forever. As the star shrinks, density increases, atoms get compressed, and, as one point of time, electrons try to cram into each other’s orbits. This is when Pauli’s exclusion principle comes in; simply put, it states that identical electrons cannot cohabit. This creates an outward electron degeneracy pressure, and this now balances the inward gravitational pull. This is how white dwarfs are formed.

Image of Indian theoretician and astrophysicist Subrahmanyan Chandrasekhar. He calculated the mass limit for stellar core remnants to collapse to neutrons stars.
Indian theoretical physicist and astrophysicist Subrahmanyan Chandrasekhar

In the 1920s, Subrahmanyan Chandrasekhar, the Indian astrophysicist, was trying to figure out what happens near the end of a star’s life. He calculated that, if after shedding excess material, the stellar remnant had a mass equal or less than 1.4 times that of the sun’s mass (1.4 M), then it will form a white dwarf. This is the Chandrasekhar limit. Stars that originally had a mass of about 8 M or less would typically form white dwarfs.

The TOV limit

For stars with remnant masses higher than 1.4 M, even the electron degeneracy pressure isn’t enough to counteract the grav collapse. Atoms get squished together until their nuclei stand shoulder-to-shoulder, and densities and pressures go through the roof. Between remnant masses 1.4 M to 3 M, however, the gravitational contraction isn’t quite strong enough to breach the final barrier : the neutron degeneracy pressure. For, you see, Pauli’s exclusion principle applies not just to electrons, but to all fermions. Fermions obey something called Fermi-Dirac statistics and have half-integer spins. Electrons, protons and neutrons are some of the familiar fermions; all of them are spin-½ particles.

Compact stars of remnant masses between 1.4 M and 3 M are neutron stars. The extreme pressure and temperature within the star causes nucleonic transmutations–neutrons get converted into protons and vice versa. The extreme pressure and temperature within the star causes nucleonic transmutations–neutrons get converted into protons and vice versa, though the latter happens on a far higher scale. The stellar core mass limit of 3 M is called the TOV limit (Tolman-Oppenheimer-Volkoff), and is the counterpart of the Chandrasekhar limit for neutron degeneracy pressure.

Stars whose remnant masses are greater than TOV limit have no further defences. For them, gravitational collapse in unstoppable, eventually leading to black holes and singularities.

The Chandrasekhar limit has been theoretically and observationally confirmed to be 1.4 M. The TOV limit is theoretically anywhere between 1.5M to 3M, though most estimates have put at around 3 M. Recent observational evidence from the LIGO and Virgo gravitational wave detectors, obtained during the merging of two neutron stars, sets a lower bound on the TOV limit at 2.17M.

What are Neutron stars?

Black holes

Black holes are regions where the curvature of spacetime is so high that the escape velocity from within this region is greater than c, the speed of light. Basically, nothing escapes a black hole. Black holes enclose singularities, which are regions of spacetime where pressure and density are infinite. Black holes and singularities are formed as a result of stellar collapse : the singularity is the supernova remnant of the massive star, while the black hole is the spacetime envelope that separates the singularity from the rest of the universe. This separation is necessary since the laws of physics, especially those of general relativity, cease to work at the singularity.

Characteristics of a neutron star

A teaspoonful of neutron star (volume about 5 ml) would have a mass of almost 900 times the Great Pyramid of Giza, and a weight about 15 times the weight of the moon.

Unlike spacetime singularities, pressure, density and gravity within neutron stars aren’t infinite. But they are massively high, higher than most macroscopic regions in this universe. A teaspoonful of neutron star (volume about 5 ml) would have a mass of almost 900 times the Great Pyramid of Giza, and a weight about 15 times the weight of the moon. The gravity of a neutron star is about 200 billion times that of the Earth, resulting in escape velocities that are a third to a half of lightspeed. Magnetic fields of neutron stars can be anywhere from a 100 million to 1 quadrillion (1 million billion, 1015) times as strong as Earth’s.

And all of that is a diameter of about 10 km. That’s about the size of a decent-to-smallish city.

The small size of a neutron star also makes it spin very very fast. Most stars, if not all, spin about their axis. After supernova, the stellar neutron cores retain this angular momentum. However, these are much smaller than the stars themselves. Thus, by conservation of angular momentum, neutron stars spin very fast. Typical rotational periods are of the order of seconds. However, some neutron stars spin much faster. One, in particular, spins at 716 Hz. That is 716 times a second, giving it a surface speed of about 0.24 c.

How hot are neutron stars?

The high pressure, density, and gravity ensure that, at birth or post-supernova, a neutron star is immensely hot. Initial temperatures can be as high as 100 billion to 1 trillion kelvin (1011 – 1012 K). As a comparison, the temperature at the sun’s core is a paltry 15 million kelvin (15*106 K). However, unlike the sun, a neutron star has no nuclear furnace within it to keep generating energy. Thus, by the laws of thermodynamics, neutron stars must cool down.

How do neutron stars cool down?

High school physics has taught us that objects cool via three primary mechanisms:

  • Conduction : Heat is transferred from the hot body to the cooler body via direct contact
  • Convection : Heat is transferred from a hot part of a fluid to a cooler part via actual movement of mass
  • Radiation : Heat is given off by a hot body in waves of electromagnetic radiation
What neutron stars need are phantom particles that are capable of smuggling energy away. Neutrinos fill this role rather nicely.

The first two are not applicable here, obviously. Conduction is irrelevant because there isn’t a cold body that the neutron star can lean up against and give up its heat. Also, convection will simply redistribute heat within the neutron star. So that’s no good either.

Curiously, cooling via typical electromagnetic radiation is also not an option during the earlier turbulent times of a neutron star’s life. Its interior is too opaque for photons of any wavelength to breach–any photons that do attempt to escape quickly encounter something to interact with, and are either reabsorbed or scattered away.

What neutron stars need are phantom particles that are capable of ferrying energy away while passing under the radar of most electromagnetic interference effects that the roiling innards of the neutron star can cough up. Neutrinos fill this role rather nicely.

George Gamow

George Gamow was a Russian-American astrophysicist and cosmologist. Apart from his many contributions towards physics, especially the physics of the big bang, Gamow was also a well-known science educator. His book One Two Three…Infinity, aimed at school-level readers, explains concepts of science and mathematics in fascinatingly simple ways. In his series of books Mr Tompkins…, the protagonist, CGH Tompkins, dreams of various worlds where the values of the physical constants are different from that of this universe. Tompkins’ initials stand for, arguably, the three most important physical constants:
* c : lightspeed; special relativity
* G : Newtonian gravitation constant; classical gravity
* h : Planck’s constant; quantum mechanics.

Image of Russian theoretician and cosmologist George Gamow. In the 1940s, he, along with fellow astrophysicist Mario Schenberg, coined the term "Urca process" (that is, the direct Urca process) and coined the term after the casino they were visiting at the time.
Russian theoretical physicist, cosmologist, and popular science author George Gamow.

Sometime in the 1940s, much before One Two Three…Infinity or Mr Tompkins…, George Gamow was visiting a casino in Rio de Janeiro with friend and fellow astrophysicist Mário Schenberg. They were both working on supernova remnants at that time and, seeing their money disappear on the roulette table, one of them said to the other that

“the energy disappears in the nucleus of the supernova as quickly as the money disappeared at that roulette table”

Now I’m not entirely sure who said this to whom; some sources attribute this to Schenberg, while others claim that it was Gamow who said it. Nevertheless, what is true is that this was said, and it is a wonderful description of how these supernova remnants cool.

Beta decay

Neutron stars are so-called because most of the protons within them have, via a process called beta decay, transformed into neutrons. Clearly, it isn’t possible to this to occur : p → n, since protons are positively charged and neutrons are chargeless. Thankfully, the proton-to-neutron transformation also yields a positron, which is basically an antielectron and has positive charge, balancing out the proton charge. A cascade of these p-to-n processes mean that neutron stars are left with far more neutrons than protons.

Image of the two types of beta decay. In the neutron-to-proton decay, Carbon-14 transmuted to Nitrogen-14, having gained a proton and lost a neutron. In the p-to-n decay, Carbon-10 transmutes to Boron-10, having lost a proton and gained a neutron. In the first, an electron and an antineutrino are also emitted. In the second, a neutrino and a positron are emitted. These reactions are similar to the direct Urca process.
The two types of beta decay. (Top) A neutron decays to form a proton, an electron, and an antineutrino. (Bottom) A proton decays to form a neutron, a positron, and a neutrino.

The quark picture

A quick digression here. Protons and neutrons are not fundamental particles; they can be further subdivided into quarks. There are six types (or flavours, as they are curiously called) of quarks. Of these, the up and down quarks are the most common. A proton consists of two up quarks and a single down quark, while a neutron has one up and two down quarks; p = uud, n = udd. An up quark has a charge of +2/3, while a down quark has a charge of -1/3, where the unit and sign of charge is fixed by that of the electron, which, of course, has charge -1. Clearly, therefore, a proton’s charge is (+2/3 + 2/3 – 1/3 =) +1 and a neutron’s is (+2/3 – 1/3 – 1/3 =) 0, as expected.

Protons and neutrons are baryons, particles that contain a triplet of quarks. These are distinct from electrons and neutrinos, which are leptons. The former are composite particles, while the latter are fundamental particles.

Neutrinos and antineutrinos

Apart from positrons, the decay of a proton also creates a neutrino:

(1) p → n + e+ + νe

Neutrinos are phantom particles that are nearly massless, carry no charge, and almost never interact with normal baryonic matter. Trillions of neutrinos pass through the Earth every second; only a few are either absorbed or scattered. Here the symbol stands for an electron neutrino. There are two other types of neutrinos, though they won’t feature here.

The proton-to-neutron reaction is not the only one going on inside a neutron star. The reverse also happens, when a neutron transmutes into a proton while releasing an electron (to balance the electric charge) and an antineutrino (νe). The reaction is

(2) n → p + e + νe

Neutrinos and antineutrinos are similar in most respects. They differ in two aspects : lepton number and chirality. The first is easy enough to explain, the second not as much.

Consider the reactions (1) and (2). They involve the baryons p and n, and the leptons e and νe. A fundamental principle of particle physics reactions states that the baryon number and the lepton number in a reaction must be conserved. This is a bit like atomic and molecular chemistry, where oxidation numbers need to be conserved. In both the reactions, there is one baryon on either side of the reaction, thus conserving baryon number. As for lepton number, there is one anti electron and one neutrino on the RHS, giving a total lepton number of (-1) + (+1) = 0, which is fine. The same is true in Eq 2, where the electron has lepton number +1 and the antineutrino has lepton number -1.

The p ↔ n transmutation reactions are called beta decay because of the emitted electrons/positrons that form beta rays.

The Urca processes

The direct Urca process

Post-supernova, something similar to beta decay happens within a neutron star. Neutrons are converted into protons and vice versa, while neutrinos and antineutrinos are emitted. The reactions are:

(1) n → p + ee

(2) p + e → n + νe

This is the direct Urca process, and is the simplest and fastest method by which neutron stars can cool down. A neutron star with an initial temperature of 100 billion to even 1 trillion kelvin can, by utilising the direct Urca, cool down to 1 billion kelvin in the order of minutes. That is seriously fast. Almost as fast as coins disappearing down the roulette wheel.

A neutron star with an initial temperature of 100 billion to even 1 trillion kelvin can, by utilising the direct Urca, cool down to 1 billion kelvin in the order of minutes.

However, such fast cooling drastically reduces the number of nucleons that are thermally excited enough to agree to direct Urca. If the proton fraction falls below 1/9, then it is no longer possible to simultaneously conserve energy and momentum via the direct Urca process. If the temperature falls below 1 billion K, then, at standard neutron star densities, calculations indicate that the proton fraction should be 1/25, thus stopping the direct Urca process.

The modified Urca process

At this point, the modified Urca process then takes over:

(1) N +n → N + p + ee

(2) N +p + e → N + n + νe

where N is any nucleon, n or p. Notice that the only difference between the modified and the direct processes is in the number of baryonic reactants : the direct process has a single baryon on the LHS, the modified process has two. At lower proton concentrations and lower temperatures, this modification helps conserve energy and momentum at the same time. However, it is far less efficient than the direct process, with a rate of cooling that is almost a million times slower. After a while, the interior cools sufficiently for it to be transparent to X-ray photons, and, for the next million years or so, neutron stars remain visible in the X-ray EM band.

Evidence for the direct Urca process

There is sufficient evidence for neutron star cooling via modified Urca and X-ray emission. However, it is far more difficult to observe cooling via direct Urca. Also, it is quite possible that the initial proton concentration might be too low, and direct Urca never actually takes place. Until now, this has been a purely theoretical question. Recently, however, scientists have been able to measure the X-ray output of a quiescent neutron star and have concluded that the direct Urca process must have taken place.

MXB 1659-29

The neutron star in question is labelled MXB 1659-29. Given that there are almost 2000 known neutron stars in the Milky Way and the neighbouring Magellanic Clouds, we are perhaps lucky that the label is as simple as that. MXB 1659-29 is actually a binary star, one of whose members is a neutron star. Neutron stars as one member of a binary are actually quite common. The neutron star pulls in matter from its companion star, the accretion showing up as X-ray emissions of intensity far higher than the usual.

Illustration of the accretion disk around a neutron star, created when matter is pulled in from its binary companion star. After accretion, neutron stars need to cool down. Analysis of X-ray emissions from such cooldowns provide insights about the direct Urca process of neutrino cooling.
An artists’ view of accreting neutron star (Credit: Tony Piro)

This accretion is not always a continuous process. In recent times, MXB 1659-29 has accreted matter twice, once in 2001 and then, fifteen years later, in 2016. In between these two accretion events, MXB 1659-29 was in a quiescent phase. It is during this quiet phase that researchers observed and analysed the X-ray emission spectra of MXB 1659-29. And came to the conclusion that MXB 1659-29 has indeed, during its formative years, gone through a phase of enhanced cooling via the direct Urca process.

Proton fraction

The findings also set a lower bound on the proton fraction. If direct Urca has indeed taken place, then the proton fraction must have, during that time, been at least 1/9. Theories that predict a far lower proton fraction than 1/9 would have to be discarded or modified. Thus, theories that predict a far lower proton fraction would have to be discarded, or at least given a stringent dressing-down.

Besides, further analysis of these observational finding should tell scientist more about the inner workings of the ultradense high-temperature regions within neutron stars. Particularly, it should shine further light on the superconductivity and superfluidity of the interiors of neutron stars. However, that is a topic for another day.

The name URCA

The name URCA,, or rather, Urca, is not an acronym. The casino that Gamow and Schenberg visited was the Cassino de Urca. In Gamow’s southern Russian dialect, urca meant robber or gangster. This gels well with astrophysicist and neutron star expert Madappa Prakash’s statement, where he states that

“The neutrino is a thief; it robs energy from the star…”

I prefer calling the neutrinos the magpies of the neutron star Marlinspike Hall. Naturally, Castafiore’s emerald plays the role of heat, to be stolen away by La gazza ladra.

A panel from "The Castafiore Emerald" by Herge, showing Tintin having recovered the eponymous and presumed missing emerald. The emerald was actually stolen by a magpie, in much the same way that neutrinos steal a neutron star's heat away via the direct Urca process.
From “The Castafiore Emerald”, by Herge

Sources

Original papers

  1. Brown, Cumming, Fattoyev, Horowitz, Page, Reddy : Rapid Neutrino Cooling in the Neutron Star MXB 1659-29, Physical Review Letters (2018).
  2. Lattimer, Pethick, Prakash, Haensel : Direct URCA process in neutron stars, Physical Review Letters (1991).

Articles

  1. Lattimer, James M. : A Rapidly Cooling Neutron Star, APS Physics Viewpoint (2018).
  2. Conover, Emily : Neutron stars shed neutrinos to cool down quickly, ScienceNews (2018).

Other resources

  1. Redd, Noah T. : Neutron Stars: Definition & Facts, Space.com (2018).
  2. Miller, M. Coleman : Introduction to Neutron stars
  3. Cartlidge, Edwin : Neutron star has superfluid core, PhysicsWorld (2011).
  4. Conover, Emily : Collision illuminates the mysterious makeup of neutron stars, ScienceNews (2017)
  5. Wikipedia : The Urca Process