Direct Urca : How Thieving Neutrinos Cool Neutron Stars

Direct Urca : How Thieving Neutrinos Cool Neutron Stars

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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

 

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