Category: Astrophysics

E 0102 : A mysterious isolated neutron star

E 0102 : A mysterious isolated neutron star

Reading Time: 11 minutes

Neutron stars are exotic remnants of supernova explosions of massive stars. Most rotating neutron stars have extraordinarily high magnetic fields. These pulsars very often have a binary companion star from which they steal stellar matter. Recently, a neutron star in a neighbouring galaxy was found to have neither a binary companion nor a strong magnetic field. Curiously, the position of the supernova remnant with respect to the gases thrown off at the time of supernova does not quite tally. The Nerd Druid investigates E 0102, the lonely offset neutron star.

Neutron stars

Neutron stars are supernova remnants that are not quite massive enough to form black holes1. They are extremely dense objects and have phenomenally strong gravitational fields. The pressure in the interior of a neutron star one of the highest found naturally in the universe, second only to the pressure inside protons. Temperatures within neutron stars right after formation can be as high as hundreds of billions of degrees, but escaping neutrinos cool the star down.

Schematic of pulsar, showing the rotation axis, the magnetic axis, and the twin beams.
Schematic view of a pulsar. The sphere in the middle represents the neutron star, the curves indicate the magnetic field lines, the protruding cones represent the emission beams and the green line represents the axis on which the star rotates. Image and caption from Wikipedia.

Pulsars

Rotating neutrons stars that also have high magnetic field emit synchrotron radiation2. This radiation forms a beam along the magnetic axis of the neutron star; as the star rotates about its rotational axis–which may or may not coincide with the magnetic axis–these beams are observed at precise regular intervals. These are pulsars, celestial timekeepers that are highly accurate. Thanks to the beams, pulsars are easy to detect.

Optical mosaic image of the Crab nebula, thanks to the Hubble Space Telescope. The bluish glow from the central region is due to synchrotron radiation.
Hubble Space Telescope mosaic optical image of the Crab Nebula. The bluish glow from the central region of the nebula is due to synchrotron radiation.

Pulsars are almost always binary stars; their stellar companions are often main-sequence or giant stars that have not yet reached supernova, or, due to lack of mass, never will. Most pulsars are found in the Milky Way galaxy and its neighbourhood.

So, basically, pulsar neutron stars are social beings that have magnetic personalities, but you’re likely to get burnt if you venture too close. Clearly, they have issues.

Composite optical and X-ray image of the inner Crab nebula. The central part shows the pulsar wind nebula, with the red star in the centre being the Crab pulsar.
Composite optical/X-ray image of the Crab Nebula, showing synchrotron emission in the surrounding pulsar wind nebula, powered by injection of magnetic fields and particles from the central pulsar. Image and caption from Wikipedia.

Central Compact Objects (CCOs)

However, not all neutron stars are pulsars. There are some that have very low magnetic fields compared to their pulsar cousins. Called central compact objects (CCOs), these supernova remnants lack the active wind nebulae3 that are a telltale signature of pulsars. The pulsars PuppisA and CassiopeiaA (CasA), both located within the Milky Way, are excellent examples of CCOs.

Similarly, not all neutron stars have a binary companion. The Magnificent Seven, named after the spaghetti Western, are a group of seven isolated neutron stars. A decade ago, an eighth such star was found, and was promptly named Calvera, after the villain of the movie. Going by that logic, a ninth star might well be named Gabbar4.

It is quite rare to find neutron stars that both CCOs and isolated. Vogt et al have recently found one that is located outside the Milky Way. However, in doing so, they have uncovered a rather puzzling mystery.

E 0102

The object of interest is the supernova remnant 1E 0102.2-7219. E 0102 for short, it is one of the few oxygen-rich young supernova remnants (O-rich SNR) in the Magellanic clouds5, and the only low magnetic field isolated neutron star outside the Milky Way. E 0102 is a little more than 200,000 light years away from Earth, and is only about two thousand years old.

Chandra/ACIS X-ray image of E 0102. The blue and the purple are false-coloured fast-moving highly ionized gases. This forms a lightyears-wide shell around what is thought to be the origin of the supernova. Note the small blue dot south-south-west of the centre, and about midway to the outer ring.
Chandra/ACIS X-ray image of E 0102. The blue and the purple are false-coloured fast-moving highly ionized gases. This forms a lightyears-wide shell around what is thought to be the origin of the supernova. Note the small blue dot south-south-west of the centre, and about midway to the outer ring.

Observing E 0102 with Chandra and Hubble

Unlike pulsars, CCOs such as E 0102 cannot be detected by looking for synchrotron radiation. Instead, one has to rely on blackbody radiation from both the CCO and the supernova debris surrounding the CCO. Images from NASA’s Chandra X-ray Observatory (CXO, named after Indian astrophysicist S. Chandrasekhar) show that E 0102 is dominated by a fast-moving large ring-shaped structure (blue and purple in the X-ray image). This is, quite possibly, the forward envelope of the supernova blast wave. Ejected at supernova at speeds of millions of kilometres per hour, this shell is now, two thousand years later, approximately 12 light years wide. Older optical images from the Hubble Space Telescope show beautiful filaments of superheated highly ionized oxygen filaments (green in the optical image) within the shell.

Hubble Space Telescope (HST) and VLT/MUSE optical image of E 0102. The green filaments (HST) are highly-ionized oxygen-rich filaments of supernova ejecta. The bright red ring (MUSE) is slow-moving low-ionization gas surrounding an optical dark spot.
Hubble Space Telescope (HST) and VLT/MUSE optical image of E 0102. The green filaments (HST) are highly ionized oxygen-rich filaments of supernova ejecta. The bright red ring (MUSE) is slow-moving low-ionization gas surrounding an optical dark spot.

Position of E 0102 supernova remnant

Usually, one would expect, given the data available, that the supernova remnant should be right in the middle of the ring that Chandra observed. Unfortunately, as you can see from the X-ray image above, there is no corresponding X-ray source at the centre of the ring. There is, however, an X-ray point source slightly offset from the centre of this large ring, a bit towards the south-west. Given available data, that cannot be the remnant.

Vogt et al disagree. And they evidence, persuasive evidence. And to do that, they have moved beyond what NASA has had to offer.

ESO, VLT, & MUSE

The European Southern Observatory is an international collaborative effort at observing the southern skies. Established in 1962 with 5 members, ESO now boasts a roster of 15 member states that sponsor the installation, operation and maintenance of state-of-the-art telescopes, all located in Chile. Of them, the imaginatively named Very Large Telescope (VLT) is probably one of the most advanced optical telescopes available for research now.

The Multi Unit Spectroscopic Explorer (MUSE) is an advanced spectrograph attached to the VLT. Unlike older devices, MUSE provides high-end resolution in both spatial and spectral domains. Which basically means that it produces very clear pictures with sharp colours.

Observing E 0102 with MUSE

Instead of relying on old Hubble and Chandra data, Vogt et al pointed the VLT towards E 0102. New optical data from MUSE showed that, in addition to the highly ionized fast-moving large gaseous ring, E 0102 also shows a smaller low-ionization slow-moving gas ring (bright red in the optical image) that is about a sixth of the former’s size. The origin of this new ring cannot be explained from the optical picture alone.

Animation of the optical and X-ray channels of E 0102. Overlaying one on the other strongly indicates that the blue off-centre dot in the X-ray image is indeed the CCO.
Superimposing the Chandra X-ray image on top of the HST+MUSE optical one shows that the blue off-centre X-ray dot does indeed fall within the red optical gas ring, and that it is indeed the CCO.

The fun begins when you put the optical and X-ray images on top of each other. It is immediately obvious that the smaller red optical ring neatly encircles the small blue X-ray dot. This perfect coincidence convinced Vogt et al that the small blue dot was indeed the hitherto undiscovered supernova remnant they had been looking for.

Is that really the supernova remnant?

Apparent and absolute magnitudes

Well, sort of. Stargazing is a funny job. Since the stars are so far away, the night sky looks more or less like an upturned bowl, with the stars stuck to its underside. Take Venus and Sirius, for instance. Venus is the brightest point object in the night sky, while Sirius is the brightest star in the night sky. Naturally, the Sun and the Moon are disq-ualified.6 Now, going by apparent brightness, Venus outshines Sirius by a factor of 23.337. Actually, of course, Venus is a planet, while Sirius is a really bright star. This is evident in their actual luminosities : Sirius is 22.5 times as luminous as the Sun, which in turn is 550 million times brighter than Venus.

Constellations and distances

The same confusion holds for distances. Constellations are groupings of stars that are close together. For instance, Orion (Kalpurush), one of the most distinctive and conspicuous constellations in the night sky, has seven major stars. Of these, the two brightest are Rigel, a blue-white supergiant, and Betelgeuse, a red supergiant. The most distinctive feature of the constellation is the belt; Alnitak, Alnilam and Mintaka are the three stars that make up Orion’s belt. All these stars, being part of the same constellation, seem to lie close to each other on the same plane.

Photograph of Orion's belt. On the northeast (top right) is Mintaka, on the southwest is Alnitak, and at the centre is Alnilam, the brightest of the trio.
Orion’s belt. On the northeast (top right) is Mintaka, on the southwest is Alnitak, and at the centre is Alnilam, the brightest of the trio. Image credit : Davide De Martin (http://www.skyfactory.org); Digitized Sky Survey, ESA/ESO/NASA FITS Liberator.

The operative word is, naturally, seem. Here is how far the stars actually are from Earth (lyr = lightyear) :

  1. Betelgeuse = 640 lyr
  2. Rigel = 863 lyr
  3. Alnitak = 800 lyr
  4. Alnilam = 1340 lyr
  5. Mintaka = 915 lyr

Clearly then, if we move away from Earth, the constellations will not retain their familiar shapes.

So, is it the CCO or not?

The same issue is relevant when it comes to E 0102’s CCO. Wouldn’t it be possible that the blue X-ray point source simply lies in the background of the red low-ionization ring of gas. Is it impossible to imagine that the extraordinary evidence provided by MUSE might simply be chance alignment?

Well, after four paragraphs and 300 words, you would be entitled to a detailed explanation. Sadly, Vogt et al simply say that the area of the structure seen by MUSE is too small. They calculate that there might be at most 8 × 10-5 sources in the background that are as bright or brighter.

Rather compelling, that number, ain’t it.

What’s more, the MUSE data does not provide any evidence for active pulsar wind nebulae, or the presence of a binary companion to the supernova remnant. Vogt et al can very well claim to have found the first truly isolated CCO outside the Milky Way.

Which is when all hell breaks loose.

The E 0102 offset mystery

The problem, of course, is that the E 0102 CCO does not quite lie at the centre of the large gas ring.

A bit of firecrackers

Picture a firecracker going off in the night sky. Imagine one of those expensive ones that, um, look good and are made well. Soon after explosion, the expanding sparkles form a ball, while whatever part did not explode (there’s always some) stays more or less at the centre of this ball. Of course, gravity soon makes all of this come crashing down onto the Earth.

Now imagine you are in charge of firecrackers on a cricket night, and you are a bit short on funds. You buy perhaps one of those fancy firecrackers and scrounge the bottom of the barrel for the rest. Your idea is to impress people with that one good one, the one that looks very symmetric, and then quickly pass the other asymmetric ones under the radar. You succeed, for there are people in the audience that are clearly more interested in the badly made ones, the ones where the explosion remnant doesn’t quite remain in the middle of the ball.

Photograph of fireworks at the Sydney Harbour Bridge, taken on New Year's Day 2017. Image credit : Saeed Khan.
Fireworks at the Sydney Harbour Bridge, taken on New Year’s Day 2017. Image credit : Saeed Khan.

Why does that happen? Well, simply because the explosive mixture in the cracker wasn’t uniform or homogeneous enough. There might have been bumps or hollows, or some parts might have had more or less of one component than necessary for the correct amount of burn. Essentially, the firecracker must have had some asymmetry to begin with.

How a supernova works

A similar specific set of circumstances might have been applicable with E 0102. Here’s how a supernova works : at the end of its life, massive stars8 throw off most their stellar material in a titanic explosion. What remains behind is the superdense core; if massive enough, it forms a black hole; if not, neutron star. The stellar material is thrown off at the rate of thousands of kilometers a second. This translates into a speed of a few lightyears every thousand years. The gaseous material thrown off forms a spherical shell around the supernova remnant, very much like the fast-moving large ring of high-ionization gas in E 0102 as detected by Chandra’s Advanced CCD Imaging Spectrometer (ACIS).

Two scenarios

Had E 0102 behaved like that good high-end expensive firecracker, its supernova remnant should have been right at the centre of this big shell. However, given the large offset, clearly this isn’t the case. This leaves us with two scenarios :

  1. The supernova was indeed centred at the centre of the large X-ray ring, and that, somehow, the supernova remnant has migrated to where it is now.
  2. The supernova was centred at the centre of the smaller optical ring, more or less where the CCO is now, and somehow the larger gas envelope got distorted.

Both scenarios are plausible. Both scenarios are problematic. Which is of course what makes this such a delicious mystery.

Supernova remnant migrated

Optical image (VLT/MUSE) of the centre of large gas shell (white +) and CCO position (white crosshairs) in E 0102. Image taken from Vogt et al, arXiv:1803.01006
Optical image (VLT/MUSE) of the centre of large gas shell (white +) and CCO position (white crosshairs) in E 0102. The black bar in the key equals 3 parsec or 9.78 lightyear. Image taken from Vogt et al, arXiv:1803.01006

For

The greenish blob is optical light from the oxygen-rich gases floating around E 0102. The small white + is where the centre of this expanding mass of gas should lie. The white crosshair marker slightly southwest of the centre marks the position of the CCO. As you can see, that portion does not have any oxygen. The scale below converts between seconds of arc and parsecs (pc); the thick black line is equal to 3 pc or 9.78 lyr. If you take a ruler and measure it, you’ll find that the distance between the centre and the CCO is approximately 1.8 pc or about 6 lyr.

6 lightyear! That is a lot of distance to cover. If our first scenario is correct, and the stellar core was indeed at the white + when the progenitor star went supernova, then it must have given a mighty kick to the CCO for it to have travelled 6 lyr in 2000 yr. However, the radius of the green blob is almost 4.5 pc (= 14.5 lyr). Also, 6 lyr in 2000 yr equates to a speed of about 9000 km/s (about 3% lightspeed), which is about what a supernova is capable of. The idea of a massive kick seems legit.

Against

However, there is a but. Where did the low-ionization slow-moving gas ring come from? The smaller ring is centred on the current position9 of the CCO, which means that somehow, the CCO must have reached the crosshair position, stopped (which is impossible), ejected a whole lot of gas (also impossible), and then waited as that gas very quickly spread to a diameter of a lightyear.

The timeline doesn’t match. Nor do the evidences tally with one another. And the physics is quite impossible. Stellar cores post-supernova do not have any more gas to expend. Yet we have a new gas ring. Optical analysis proves that this gas is slow-moving. Yet the timeline demands that it move ultrafast. Also, how in the world would a stellar core moving at 0.03c brake?

Hmm, trouble. Shall we try the alternate scenario, then?

Large gas ring distorted

Optical image of the inner gas ring (pink) and CCO position (crosshairs) in E 0102. Image taken from Vogt et al, arXiv:1803.01006
Optical image of the inner gas ring (pink) and CCO position (black crosshairs) in E 0102. The black bar in the key equals 3 parsec or 9.78 lightyear. Image taken from Vogt et al, arXiv:1803.01006

For

In the second scenario, the supernova didn’t kick the remnant away, and the CCO has been drifting more or less at its present position, as indicated by the black crosshair. The pink shell of low-ionization gas almost perfectly, but not exactly, encircles the CCO. Vogt et al show that the CCO has drifted only about 0.36 pc (= 1.17 lyr) from the centre of the smaller ring, thereby setting an upper limit for its drift velocity to be 170 kms-1, a far cry from 9000 km-1 in the kick scenario.

The pink inner shell could well have been ejected at supernova. Alternatively, the progenitor star might have been ejected it a few thousand years before supernova. This indicates that E 0102 might have been unstable, a variable star that would shed stellar matter periodically.

Against

Which begs the question : why did the bow shock of the supernova not blow this inner ring away? Also, and this is a bigger problem, the explosion site is now located well away from the centre of the X-ray emissions. In the image below, the white crosshair again marks the position of the CCO, while the bright bands of white, red, blue and some green make up a false-coloured image of the Chandra ACIS X-ray data.

X-ray image (Chandra/ACIS) of the outer gas ring and CCO position (white crosshairs) in E 0102. Image taken from Vogt et al, arXiv:1803.01006
X-ray image (Chandra/ACIS) of the outer gas ring and CCO position (white crosshairs) in E 0102. The black bar in the key equals 3 parsec or 9.78 lightyear. Image taken from Vogt et al, arXiv:1803.01006

According to Vogt et al, this might have been possible due a very specific set of circumstances. For instance, before exploding, stellar wind from the progenitor might have skewed the direction of the shock wave so that it is now off-kilter–a bit like one of those cheap firecrackers. Alternatively, variations in density in interstellar dust and gas might have altered the flow of the ejecta, so that some parts would move faster than the others. Thinking in terms of electricity10, the interstellar medium, though a vacuum, would have enough dust and gas to be inhomogeneous enough to distort the ejecta.

A specific set of circumstances

Which begs the question : how is the outer ring so round and regular?

Vogt et al attribute this to a specific set of circumstances. Essentially, it still is a mystery. However, with increased precision analysis of MUSE data, Vogt et al are confident they will have the answer for us. Until that time, here is a composite image of the Crab Nebula, showing infrared (Spitzer), optical (Hubble), and X-ray (Chandra) bands. You can make out the remnant as a bright blue-white dot near the centre.

Chandra (X-ray), Hubble (optical), and Spitzer (infrared) composite image of the Crab Nebula. Credit : X-ray: NASA/CXC/SAO/F.Seward; Optical: NASA/ESA/ASU/J.Hester & A.Loll; Infrared: NASA/JPL-Caltech/Univ. Minn./R.Gehrz.
Chandra (X-ray), Hubble (optical), and Spitzer (infrared) composite image of the Crab Nebula. Credit : X-ray: NASA/CXC/SAO/F.Seward; Optical: NASA/ESA/ASU/J.Hester & A.Loll; Infrared: NASA/JPL-Caltech/Univ. Minn./R.Gehrz.

 

References

Papers

  1. Vogt et al. : Identification of the Central Compact Object in the young supernova remnant 1E0102.2-7219, arXiv (2018)

Articles

  1. Press Release : Astronomers Spot a Distant and Lonely Neutron Star, Chandra X-ray Observatory (2018)
  2. PTI/Firstpost : NASA discovers rare neutron star outside of Milky Way and releases a stunning image of it (2018)

The Great Telescopes and their instruments

  1. Hubble Space Telescope (NASA)
  2. Chandra X-ray Observatory (NASA)
  3. Very Large Telescope (ESO)
  4.  Spitzer Space Telescope (NASA)

Image sources

  1. Composite, Optical, and X-ray images of E 0102 : Chandra X-ray Observatory
  2. Other images linked directly
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