neutron stars

Physicists observe long-expected helium superfluid phase

Physicists have reported that they have finally observed helium 3 existing in a long-predicted type of superfluid, called the ß phase.

This is an important discovery, if it’s borne out, for reasons that partly have to do with its isotope, helium 4. Helium 4 is a fascinating substance because the helium 4 atom is a boson – a type of particle whose quantum properties and behaviour are explained by rules called Bose-Einstein statistics. Helium 3, on the other hand, is a fermion, and fermions are governed by Fermi-Dirac statistics.

Bosons and fermions have one important difference: bosons are allowed to disobey Pauli’s exclusion principle, and by doing so they can assume exotic states of matter rarely found in nature, with many unusual properties.

For example, when helium 4 is cooled below a certain temperature, it becomes a superfluid: a liquid that flows without experiencing any resistance. If you poured a superfluid into a bowl, it will be able to climb the walls of the bowl and spill out without any help. But helium 3 atoms are fermions, so they are bound to obey Pauli’s exclusion principle and can’t become a superfluid.

At least this is what physicists believed for a long time, until the early 1970s, when two independent groups of physicists found – one in theory and the other in experiments – that helium 3 could indeed enter a superfluid phase, but at a temperature 1,000-times lower than the critical temperature of helium 4. The theory group, led by Anthony Leggett at the University of Sussex, had in fact made a significant discovery.

Today, we know that the flow of superfluid helium 4 is analogous to the flow of electrons in a conventional superconductor, which also move around as if they face no resistance from the surrounding atoms. Leggett and co. found that the theory used to explain these superconductors could also be used to explain helium 3 superfluidity. This theory is called Bardeen-Cooper-Schrieffer (BCS) theory, and the materials whose superconductivity it can explain are called BCS superconductors.

Electrons are fermions and cannot ‘super-flow’. But in a BCS superconductor that has been cooled below its critical temperature, some forces in the material cause the electrons to overcome their mutual repulsion (“like charges repel”) and pair up. These electron pairs, while being made of two individual fermions, actually behave like bosons. Similarly, Leggett and co. found that helium 3 atoms could pair up to form a bosonic composite and super-flow.

Over many years, physicists used what they had learnt through these discoveries to expand our understanding of this substance. They found, among other things, that superfluid helium 3 can exist in many phases. The superfluidity would persist in each phase but with different characteristics.

Superfluid helium 3 was first thought to have two phases, called A and B. The temperature-pressure plot below clearly shows the conditions in which each phase emerges.

Credit: E.V. Thuneberg, *Encyclopedia of Condensed Matter Physics*, 2005

When physicists subjected superfluid helium 3 in its A phase to a strong magnetic field, they found another phase that they called A1, whose atom-pairs had different spin characteristics.

In 2015, a group of researchers led by Vladimir Dmitriev, at the P.L. Kapitza Institute for Physical Problems, Moscow, discovered a fourth phase, which they called the polar, or P, phase. Here, they confined helium 3 in a nematic aerogel and exposed the setup to a low magnetic field. Aerogels are ultra-light materials that are extremely porous; nematic means its molecules were arranged in parallel. The aeorogel in the Dmitriev and co. experiment was 98% porous, and whose pores “were much longer than they were wide” (source). That is, the team had found that the shape of the container in which helium 3 was confined also affected the phase of its superfluidity.

In August 2021 (preprint), the same team reported that it had observed a long-expected-to-exist fifth phase called the ß phase.

They reported that they took the setup they used to force superfluid helium 3 into the P phase, but this time exposed it to a high magnetic field. According to their paper, they found that while the superfluid earlier moved into the P phase through a single transition, as the temperature was brought down, this time it did so in two steps. First, it moved into an intermediate phase and then into the P phase. The intermediate is the ß phase.

(If this sounds simple, it wasn’t: the discoveries were each limited by the availability of specially designed instruments capable of picking up on very small-scale changes unavailable to the naked eye. Second, researchers also have had to know in advance what changes they should expect to happen in each phase, and this requires the corresponding theoretical clarity.)

The temperatures at which the phase transition between the two polar phases differ as the magnetic field strength increases. The gap between the two phases is bridged by the ß phase. Source: https://doi.org/10.1103/PhysRevLett.127.265301

I have considerably simplified helium 3’s transition from the ‘normal’ to the superfluid phase in this post. To describe it accurately, physicists use advanced mathematics and associated concepts in high-energy physics. One such concept is symmetry-breaking. When a helium 3 atom pairs up with another to form a bosonic composite, the pair must have a ‘new’ spin and orbital momentum; and their combined wavefunction will also have a ‘new’ phase. All these steps break different symmetries.

There’s a theory called Grand Unification in particle physics, in which physicists expect that at higher and higher energies, the three fundamental forces that affect subatomic particles – the strong-nuclear, the weak-nuclear and the electromagnetic – will combine into a single unified force. Physicists have found in their mathematical calculations that the symmetries that will break in this super-transition resemble those broken by helium 3 during its transition to superfluidity.

Understanding helium 3 can also be rewarding for insights into the insides of neutron stars. Neutron stars are extreme objects – surpassed in their extremeness only by black holes, which exist at the point where known theories of gravitational physics collapse into meaninglessness. A few lakh years after a neutron star is born, it is expected to have cooled sufficiently for its interiors to be composed of superfluids and superconductors.

We may never be able to directly observe these materials in their natural environment. But by studying helium 3’s various phases of superfluidity, we can get a sense of what a neutron star’s innards could be like, and whether their interactions among themselves and the neutrons on the surface could explain these objects’ still-mysterious characteristics.

Featured image: The liquid helium is in the superfluid phase. A thin invisible film creeps up the inside wall of the cup and down on the outside. A drop forms. It will fall off into the liquid helium below. This will repeat until the cup is empty – provided the liquid remains superfluid. Caption and credit: Alfred Leitner, public domain.

Onto drafting the gravitational history of the universe

It’s finally happening. As the world turns, as our little lives wear on, gravitational wave detectors quietly eavesdrop on secrets whispered by colliding blackholes and neutron stars in distant reaches of the cosmos, no big deal. It’s going to be just another day.

On November 15, the LIGO scientific collaboration confirmed the detection of the fifth set of gravitational waves, made originally on June 8, 2017, but announced only now. These waves were released by two blackholes of 12 and seven solar masses that collided about a billion lightyears away – a.k.a. about a billion years ago. The combined blackhole weighed 18 solar masses, so one solar mass’s worth of energy had been released in the form of gravitational waves.

The announcement was delayed because the LIGO teams had to work on processing two other, more spectacular detections. One of them involved the VIRGO detector in Italy for the first time; the second was the detection of gravitational waves from colliding neutron stars.

Even though the June 8 is run o’ the mill by now, it is unique because it stands for the blackholes of lowest mass eavesdropped on thus far by the twin LIGO detectors.

LIGO’s significance as a scientific experiment lies in the fact that it can detect collisions of blackholes with other blackholes. Because these objects don’t let any kind of radiation escape their prodigious gravitational pulls, their collisions don’t release any electromagnetic energy. As a result, conventional telescopes that work by detecting such radiation are blind to them. LIGO, however, detects gravitational waves emitted by the blackholes as they collide. Whereas electromagnetic radiation moves over the surface of the spacetime continuum and are thus susceptible to being trapped in blackholes, gravitational waves are ripples of the continuum itself and can escape from blackholes.

Processes involving blackholes of a lower mass have been detected by conventional telescopes because these processes typically involve a light blackhole (5-20 solar masses) and a second object that is not a blackhole but instead usually a star. Mass emitted by the star is siphoned into the blackhole, and this movement releases X-rays that can be spotted by space telescopes like NASA Chandra.

So LIGO’s June 8 detection is unique because it signals a collision involving two light blackholes, until now the demesne of conventional astronomy alone. This also means that multi-messenger astronomy can join in on the fun should LIGO detect a collision of a star and a blackhole in the future. Multi-messenger astronomy is astronomy that uses up to four ‘messengers’, or channels of information, to study a single event. These channels are electromagnetic, gravitational, neutrino and cosmic rays.

The masses of stellar remnants are measured in many different ways. This graphic shows the masses for black holes detected through electromagnetic observations (purple); the black holes measured by gravitational-wave observations (blue); neutron stars measured with electromagnetic observations (yellow); and the masses of the neutron stars that merged in an event called GW170817, which were detected in gravitational waves (orange). GW170608 is the lowest mass of the LIGO/Virgo black holes shown in blue. The vertical lines represent the error bars on the measured masses. Credit: LIGO-Virgo/Frank Elavsky/Northwestern

The detection also signals that LIGO is sensitive to such low-mass events. The three other sets of gravitational waves LIGO has observed involved black holes of masses ranging from 20-25 solar masses to 60-65 solar masses. The previous record-holder for lowest mass collision was a detection made in December 2015, of two colliding blackholes weighing 14.2 and 7.5 solar masses.

One of the bigger reasons astronomy is fascinating is its ability to reveal so much about a source of radiation trillions of kilometres away using very little information. The same is true of the June 8 detection. According to the LIGO scientific collaboration’s assessment,

When massive stars reach the end of their lives, they lose large amounts of their mass due to stellar winds – flows of gas driven by the pressure of the star’s own radiation. The more ‘heavy’ elements like carbon and nitrogen that a star contains, the more mass it will lose before collapsing to form a black hole. So, the stars which produced GW170608’s [the official designation of the detection] black holes could have contained relatively large amounts of these elements, compared to the stellar progenitors of more massive black holes such as those observed in the GW150914 merger. … The overall amplitude of the signal allows the distance to the black holes to be estimated as 340 megaparsec, or 1.1 billion light years.

The circumstances of the discovery are also interesting. Quoting at length from a LIGO press release:

A month before this detection, LIGO paused its second observation run to open the vacuum systems at both sites and perform maintenance. While researchers at LIGO Livingston, in Louisiana, completed their maintenance and were ready to observe again after about two weeks, LIGO Hanford, in Washington, encountered additional problems that delayed its return to observing.

On the afternoon of June 7 (PDT), LIGO Hanford was finally able to stay online reliably and staff were making final preparations to once again “listen” for incoming gravitational waves. As part of these preparations, the team at Hanford was making routine adjustments to reduce the level of noise in the gravitational-wave data caused by angular motion of the main mirrors. To disentangle how much this angular motion affected the data, scientists shook the mirrors very slightly at specific frequencies. A few minutes into this procedure, GW170608 passed through Hanford’s interferometer, reaching Louisiana about 7 milliseconds later.

LIGO Livingston quickly reported the possible detection, but since Hanford’s detector was being worked on, its automated detection system was not engaged. While the procedure being performed affected LIGO Hanford’s ability to automatically analyse incoming data, it did not prevent LIGO Hanford from detecting gravitational waves. The procedure only affected a narrow frequency range, so LIGO researchers, having learned of the detection in Louisiana, were still able to look for and find the waves in the data after excluding those frequencies.

But what I’m most excited about is the quiet announcement. All of the gravitational wave detection announcements before this were accompanied by an embargo, lots of hype building up, press releases from various groups associated with the data analysis, and of course reporters scrambling under the radar to get their stories ready. There was none of that this time. This time, the LIGO scientific collaboration published their press release with links to the raw data and the preprint paper (submitted to the Astrophysical Journal Letters) on November 15. I found out about it when I stumbled upon a tweet from Sean Carroll.

And this is how it’s going to be, too. In the near future, the detectors – LIGO, VIRGO, etc. – are going to be gathering data in the background of our lives, like just another telescope doing its job. The detections are going to stop being a big deal: we know LIGO works the way it should. Fortunately for it, some of its more spectacular detections (colliding intermediary-mass blackholes and colliding neutron stars) were also made early in its life. What we can all look forward to now is reports of first-order derivatives from LIGO data.

In other words, we can stop focusing on Einstein’s theories of relativity (long overdue) and move on to what multiple gravitational wave detections can tell us about things we still don’t know. We can mine patterns out of the data, chart their variation across space, time and their sources, and begin the arduous task of drafting the gravitational history of the universe.

Featured image credit: Lovesevenforty/pixabay.

Awk CZTI result from Crab pulsar

An instrument onboard the ISRO Astrosat space-telescope has studied how X-rays being emitted by the Crab pulsar are being polarised, and how such polarisation varies from one pulse to the next. This is very important information for understanding how pulsars create and emit high-energy radiation – information that we haven’t been able to obtain from any other pulsars in the known universe. The underpinning study was published in Nature Astronomy on November 6, 2017.

Quick recap: CZTI stands for the Cadmium Zinc Telluride Imager, a 16-MP X-ray camera and, as The Wire has discussed before, one of the best in its class – in the league of the NASA Fermi and Swift detectors and even better in the 80-250 keV range. Pulsars are rotating neutron stars that emit focused beams of high-energy radiation from two polar locations on their surface. (As it rotates, the beams sweep past Earth like a lighthouse sweeping past ships, giving the impression that it’s blinking, or pulsating). We study them because they’re extreme environments that can help validate theories by pushing them to their limits.

There are two things notable about the current study: how CZTI studied the pulsar and what it found as a result.

1. How – The Crab pulsar, the remnant of a star that went supernova in 1,058 AD, is located 6,500 lightyears away in the direction of the Taurus constellation. Second, pulsars – despite their remarkable radiation output – emit few X-ray photons that can be studied from near Earth. Third, the Crab pulsar has a rotation period of 33 ms (i.e. very fast). For these reasons, CZTI couldn’t just study the pulsar directly and hope to find what it eventually did. Whatever X-ray was collected would’ve had to be precisely calibrated in time. So the CZTI team* partnered up with the Giant Metrewave Radio Telescope in Pune and the Ooty Radio Telescope in Muthorai (Tamil Nadu) for the ephemeris data. In all, there were 21 observations made over (CZTI’s first) 18 months.

2. What – Like a Ferrero Rocher from hell, a pulsar is a rotating neutron star on the inside, wrapped in a very strong magnetic field. Astronomers think charged particles are accelerated by this field and the energy they emit is shot into space, as X-rays + other frequencies of radiation. So studying how these X-rays are polarised could provide more info on how a pulsar produces its famous sweeping pulses. The CZTI data had a surprise: hard X-rays are being emitted by the Crab pulsar in the off-pulse – or the-beam-is-not-pointing-at-us – phase. In other words, the magnetic field isn’t involved in producing these X-rays; the neutron star itself is. Dun dun duuuuuuun!

It’s always nice to get science results that send researchers back to the proverbial drawing board, like the CZTI result has. It’s sweeter still when local researchers are involved – and even sweeter to be reminded that we haven’t been entirely left behind in non-theoretical particle physics research. There’s even more X-ray astronomy in India’s future. After Astrosat, launched in September 2015, ISRO has okayed a proposal from the Raman Research Institute (RRI), Bengaluru, to build an X-ray polarimeter instrument that the org will launch in the future (date not known). Called Polix, it is similar to the NASA GEMS probe that stalled in 2012.

*The CZTI team had scientists from Physical Research Laboratory, Ahmedabad; Tata Institute of Fundamental Research, Mumbai; Inter-University Centre for Astronomy and Astrophysics, Pune; IIT Powai; National Centre for Radio Astronomy, Pune; Vikram Sarabhai Space Centre, Thiruvananthapuram; ISRO, Bengaluru; and RRI.

Featured image: A composite image of the Crab Nebula showing the X-ray (blue), and optical (red) images superimposed. The size of the X-ray image is smaller because the higher energy X-ray emitting electrons radiate away their energy more quickly than the lower energy optically emitting electrons as they move. Caption and credit: NASA/ESA.

The Wire
November 7, 2017

On that 'Last Word on Nothing' post

A post published on the Last Word On Nothing blog yesterday has been creating quite the stir on Twitter. Excerpt:

While I can appreciate that this is an important scientific discovery, I still have a hard time mustering excitement over gravitational waves. I would not have read these articles had I not embarked on this experiment. And I wanted to stop reading some of these articles as I was conducting the experiment. Space is not my thing. I don’t think it ever will be, at least not without a concerted effort on my part to get a basic handle on physics and astronomy. …

Physics writers, this is how you nab the physics haters — human emotion. You can explain gravitational waves using the cleanest, clearest, most eloquent words that exist — and you should! — but I want the story of the scientists in all their messy, human glory.

Cassandra Willyard, the post’s author, was writing about the neutron-star collision announcement from LIGO. Many of those who are dissing the point the post is making are saying that Willyard is vilifying the ‘school’ of science writing that focuses on the science itself over its relationship with the human condition. I think she’s only expressing her personal opinion (as the last line in the excerpt suggests) – so the levels of indignation that has erupted in some pockets of the social media over these opinions suggests Willyard may have touched off some nerves.

I myself belong to the school that prefers to excite science readers over the science itself over its human/humanist/humanitarian aspects. In the words of Tracy, who wrote them as a comment on Willyard’s post,

So many amazing things happen in this universe without a human noticing it, reflecting on it, understanding it, being central to it. So many wondrous mysteries abound despite the ego. The human story is just one of billions.

And I will concede from personal experience that it’s quite difficult as a result to sell such stories to one’s editors as well as readers. I’ve written about this many times before, e.g. here; edited excerpt:

I couldn’t give less of a fuck for longer pieces, especially because they’re all the same: they’re concerned with science that is deemed to be worthy of anyone’s attention because it is affecting us directly. And I posit that they’ve kept us from recognising an important problem with science journalism in the country: it is becoming less and less concerned with the science itself; what has been identified as successful science journalism is simply a discussion – no matter how elaborate and/or nuanced – of how science impacts us. Instead, I’d love to read a piece reported over 5,000 words about molecules, experiments, ideas. It should be okay to want to write only about particle physics because that’s all I’m interested in reading. Okay to want to write only about this even if I don’t have any strength to hope that QCD will save lives, that Feynman diagrams will help repeal AFSPA, that the LHC will accelerate India’s economic growth, that the philosophies of fundamental particles will lead to the legalisation of same-sex marriage. I haven’t been presented with any evidence whatsoever to purchase my faith in the possibility that the obscurities of particle physics will help humans in any way other than to enlighten them, that there is neither reward nor sanction in anxiously bookending every articulation of wonder with the hope that we will find a way to profit from all of our beliefs, discoveries and perceptions.

For many people in this ‘school’, this fight is almost personal because it’s arduous and requires tremendous conviction, will and resilience on one’s part to see coverage of such kind through. In this scenario, to have a science writer come forward and say “I won’t write about this science because I don’t understand this science” can be quite dispiriting. It’s a science writer’s job to disentangle some invention, discovery or whatever and then communicate it to those who are interested in knowing more about it. So when Willyard writes in her post that “The day I write about a neutron star collision is the day hell will freeze over” – it’s a public abdication of an important responsibility, and arguably one of the most complicated responsibilities in journalism in the Information Age thanks to its fiercely non-populist nature.

(Such a thing happened recently with Natalie Wolchover as well. Her words – written against topological physics – were more disappointing to come across because Wolchover writes very good physics pieces for Quanta. And while she apologised for the “flippancy” of her tweet shortly after, saying that she’d been in a hurry at 5.45 am, that’s precisely the sort of sentiment that shouldn’t receive wider coverage without the necessary qualifications. So my thanks to Chad Orzel for the thread he published in response.)

However, it must be acknowledged that the suggestion Willyard makes (in the second paragraph of the excerpt) is quite on point. To have to repeatedly pander to the human condition in one way or another when in fact you think the science in and of itself is incredibly cool can become frustrating over time – but this doesn’t mean that a fundamental disconnect between writers like me and the statistically average science reader out there doesn’t exist. If I’m to get her attention, then I’ve found from experience that one must begin with the humans of science and then flow on to the science itself. As Alice Bell recommends here, you start upstream and go downstream. And once you’ve lured them in, you can begin to discuss the science more freely.

(PS: Some areas of Twitter have gone nuts, claiming Willyard shouldn’t be called a science journalist. I’m making no such judgment call. To be clear, I’m only criticising a peer’s words. I still consider Willyard to be a science journalist – though my fingers cry as I type this because it’s so embarrassing to have to spell it out – and possibly a good one at that going by her willingness to introspect.)

Featured image credit: Pexels/pixabay.

When the hype for the announcement of the previous GW detection was ramping up, I had a feeling LIGO was about to announce the detection of a neutron-star collision. It wasn’t to be – but in my excitement, I’d written a small part of the article. I’m sharing it below. I’d also recommend reading this post: The Secrets of How Planets Form.

Stars die. Sometimes, when that happens, their outer layers explode into space in a supernova. Their inner layers collapse inwards under the gravity of their own weight in a violent rush. If the starstuff can be packed dense enough, the collapse produces a blackhole – a volume of space where the laws of quantum mechanics and relativity break down and the particles of matter are plunged into a monumental identity crisis. However, if the dying star wasn’t heavy enough when it blew up, then the inward rush will create a very, very, very dense object – but not a blackhole: a neutron star.

Neutron stars are the densest objects in the universe that astronomers can observe. The only things we know are denser than them are blackholes.

You’d think observed means ‘saw’, but what is ‘seeing’ but the light – a form of electromagnetic energy – from an event reaching our eyes? We can’t directly ‘see’ blackholes collide because the collision doesn’t release any electromagnetic energy. So astronomers have built a special kind of eyes – called gravitational wave detectors – that can observe ripples of gravitational energy that the collision lets loose.

The Laser Interferometer Gravitational-wave Detector (LIGO) we already know about. Its twin eyes, located in Washington and Louisiana, US, have detected three blackhole-blackhole collisions thus far. Two of the scientists who helped build it are hot favourites to win the Nobel Prize for physics next week. The other set of eyes involved in the last find is Virgo, a detector in Italy.

You’ve been told that blackholes are freaks of nature. Heavy objects bend spacetime around themselves. Blackholes are freaks because they step it up: they fold it. They’re so heavy that when spacetime bends around them, it goes all the way around and becomes a three-dimensional loop. Thus, a blackhole traps one patch of the cosmos around a vanishingly small heart of darkness. Even light, if it comes close enough, becomes trapped in this loop and can never escape. This is why astronomers can’t observe blackholes directly, and use gravitational-wave detectors instead.

But neutron stars they can observe. They’re exactly what their names suggest: a ball of neutrons. And neutrons experience a force of nature called the strong nuclear force, and it can be 100,000 billion billion billion times stronger than gravity. This makes neutron stars extremely dense and altogether incredibly heavy as well. On their surface, a classic can of Coke will weigh 355,000 billion tonnes, a thousand-times heavier than all the humans on Earth combined.

Sometimes, a neutron star is ravaged by a powerful magnetic field. This field focuses charged particles on the neutron star’s surface into a tight beam of radiation shooting off into space. If the orb is also spinning, then this beam of radiation sweeps through space like the light from a lighthouse sweeps over the sea near it. Such neutron stars are called pulsars.

The secrets of how planets form

Astronomers who were measuring the length of one day on an exoplanet for the first time were in for a surprise: it was shorter than any planet’s in the Solar System. Beta Pictoris b, orbiting the star Beta Pictoris, has a sunrise every eight hours. On Jupiter, there’s one once every 10 hours; on Earth, every 24 hours.

This exoplanet is located 63.4 light-years from the Solar System. It is a gas giant, a planet made mostly of gases of light elements like hydrogen and helium, and more than 10 times heavier than Earth. In fact, Beta Pictoris b is about eight times as heavy as Jupiter. It was first discovered by the Very Large Telescope and the European Southern Observatory in 2003. Six years and more observations later, it was confirmed that it was orbiting the star Beta Pictoris instead of the star just happening to be there.

On April 30, a team of scientists from The Netherlands published a paper in Nature saying Beta Pictoris b was rotating at a rate faster than any planet in the Solar System does. At the equator, its equatorial rotation velocity is 25 km/s. Jupiter’s equatorial rotation velocity is almost only half of that, 13.3 km/s.

The scientists used the Doppler effect to measure this value. “When a planet rotates, part of the planet surface is coming towards us, and a part is moving away from us. This means that due to the Doppler effect, part of the spectrum is a little bit blueshifted, and part of it a little redshifted,” said Ignas Snellen, the lead author on the Nature paper and an astronomy professor at the University of Leiden.

So a very high-precision color spectrum of the planet will reveal the blue- and redshifting as a broadening of the spectral lines: instead of seeing thin lines, the scientists will have seen something like a smear. The extent of smearing will correspond to the rate at which the planet is rotating.

Bigger is faster

So much is news. What is more interesting is what the Leiden team’s detailed analysis tells us, or doesn’t, about planet formation. For starters, check out the chart below.

Spin_rate_chart — Image: Macclesfield Astronomical Society

This chart shows us the relationship between a planet’s mass (X-axis) and its spin angular momentum (Y-axis), the momentum with which it spins on an axis. Clearly, the heavier a planet is, the faster it spins. Pluto and Charon, its moon, are the lightest of the lot and their spin rate is therefore the lowest. Jupiter, the heaviest planet in the Solar System, is the heaviest and its spin rate is also the highest. (Why are Mercury and Venus not on the line, and why have Pluto and Earth been clubbed with their moons? I’ll come to that later.)

“Apparently the more massive the planet, the more angular momentum it acquires,” Prof. Snellen said. This would put Beta Pictoris b farther along the line, possibly slightly beyond the boundaries of this chart – as this screenshot from the Leiden team’s pre-print paper shows.

planet_spin_rate1

Unfortunately, science doesn’t yet know why heavier planets spin faster, although there are some possible explanations. A planet forms from grains of dust floating around a star into a large, discernible mass (with many steps in between). This mass is rotating in order to conserve angular momentum. As it accrues more matter over time, it has to conserve the kinetic and potential energy of that matter as well, so its angular momentum increases.

There have been a few exceptions to this definition. Mercury and Venus, the planets closest to the Sun, will have been affected by the star’s gravitational pull and experienced a kind of dragging force on their rotation. This is why their spin-mass correlations don’t sit on the line plotted in the chart above.

However, this hypothesis hasn’t been verified yet. There is no fixed formula which, when plotted, would result in that line. This is why the plots shown above are considered empirical – experimental in nature. As astronomers measure the spin rates of more planets, heavy and light, they will be able to add more points on either side of the line and see how its shape changes.

At the same time, Beta Pictoris b is a young planet – about 20 million years old. Prof. Snellen used this bit of information to explain why it doesn’t sit so precisely on the line:

planet_spin_rate2

Sitting precisely on the line would be an equatorial velocity of around 50 km/s. But because of its youth, Prof. Snellen explained, this exoplanet is still giving off a lot of heat (“this is why we can observe it”) and cooling down. In the next hundreds of millions of years, it will become the size of Jupiter. If it conserves its angular momentum during this process, it will go about its life pirouetting at 50 km/s. This would mean a sunrise every 3 hours.

I think we can stop complaining about our days being too long.

Spin velocity v. Escape velocity

Should the empirical relationship hold true, it will mean that the heaviest planets – or the lightest stars – will be spinning at incredible rates. In fact, the correlation isn’t even linear: even the line in the first chart is straight, the axes are both logarithmic. It is a log-log plot where, like shown in the chart below, even though the lines are straight, equal lengths of the axis demarcate exponentially increasing values.

If the axes were not logarithmic, the line f(x) = x³ (red line) between 0.1 and 1 would look like this:

The equation of a line in a log-log plot is called a monomial, and goes like this: y = ax^k. In other words, y varies non-linearly with x, i.e. a planet’s spin-rate varies non-linearly with its mass. Say, if k = 5 and a (a scaling constant) = 1, then if x increases from 2 to 4, y will increase from 32 to 1,024!

Of course, a common, and often joked-about, assumption among physicists has been made: that the planet is a spherical object. In reality, the planet may not be perfectly spherical (have you known a perfectly spherical ball of gas?), but that’s okay. What’s important is that the monomial equation can be applied to a rotating planet.

Would this mean there might be planets out there rotating at hundreds of kilometres per second? Yes, if all that we’ve discussed until now holds.

… but no, if you discuss some more. Watch this video, then read the two points below it.

The motorcyclists are driving their bikes around an apparent centre. What keeps them from falling down to the bottom of the sphere is the centrifugal force, a rotating force that, the faster they go, pushes them harder against the sphere’s surface. In general, any rotating body experiences this force: something in the body’s inside will be fleeing its centre of rotation and toward the surface. And such a rotating body can be a planet, too.
Any planet – big or small – exerts some gravitational pull. If you jumped on Earth’s surface, you don’t shoot off into orbit. You return to land because Earth’s gravitational pull doesn’t let you go that easy. To escape once and for all, like rockets sometimes do, you need to jump up on the surface at a speed equal to the planet’s escape velocity. On Earth, that speed is 11.2 km/s. Anything moving up from Earth’s surface at this speed is destined for orbit.

Points 1 and 2 together, you realize that if a planet’s equatorial velocity is greater than its escape velocity, it’s going to break apart. This inequality puts a ceiling on how fast a planet can spin. But then, does it also place a ceiling on how big a planet can be? Prof. Snellen to the rescue:

Yes, and this is probably bringing us to the origin of this spin-mass relation. Planets cannot spin much faster than this relation predicts, otherwise they would spin faster than the escape velocity, and that would indeed break the planet apart. Apparently a proto-planet accretes near the maximum amount of gas such that it obtains a near-maximum spin-rate. If it accretes more, the growth in mass becomes very inefficient.

(Emphasis mine.)

Acting forces

The answer will also depend on the forces acting on the planet’s interior. To illustrate, consider the neutron star. These are the collapsed cores of stars that were once massive but are now dead. They are almost completely composed of neutrons (yes, the subatomic particles), are usually 10 km wide, and weigh 1.5-4 times the mass of our Sun. That implies an extremely high density – 1,000 litres of water will weigh 1 million trillion kg, while on Earth it weighs 1,000 kg.

Neutron stars spin extremely fast, more than 600 times per second. If we assume the diameter is 10 km, the circumference would be 10π = ~31 km. To get the equatorial velocity,

V_spin = circumference × frequency = 31 × 600/1 km/s = 18,600 km/s.

Is its escape velocity higher? Let’s find out.

V_e = (2GM/r)^0.5

G = 6.67×10-11 m³ kg^-1 s^-2

M = density × volume = 10¹⁸ × (4/3 × π × 125) = 5.2×10²⁰ kg

r = 5 km

∴ V_e = (2 × 6.67×10^-11 × 5.2×10²⁰/5)^0.5 = ~37,400 km/s

So, if you wanted to launch a rocket from the surface of a neutron star and wanted it to escape the body’s gravitational pull, it has to take off at more than 30 times the speed of sound. However, you wouldn’t get this far. Water’s density should have given it away: any object would be crushed and ground up under the influence of the neutron star’s phenomenal gravity. Moreover, at the surface of a neutron star, the strong nuclear force is also at play, the force that keeps neutrons from disintegrating into smaller particles. This force is 10³² times stronger than gravity, and the equation for escape velocity does not account for it.

However, neutron stars are a unique class of objects – somewhere between a white dwarf and a black hole. Even their formation has nothing in common with a planet’s. On a ‘conventional’ planet, the dominant force will be the gravitational force. As a result, there could be a limit on how big planets can get before we’re talking about some other kinds of bodies.

This is actually the case in the screenshot from the Leiden team’s pre-print paper, which I’ll paste here once again.

planet_spin_rate1

See those circles toward the top-right corner? They represent brown dwarfs, which are gas giants that weigh 13-75 times as much as Jupiter. They are considered too light to sustain the fusion of hydrogen into helium, casting them into a limbo between stars and planets. As Prof. Snellen calls them, they are “failed stars”. In the chart, they occupy a smattering of space beyond Beta Pictoris b. Because of their size, the connection between them and other planets will be interesting, since they may have formed in a different way.

Disruption during formation is actually why Pluto-Charon and Earth-Moon were clubbed in the first chart as well. Some theories of the Moon’s formation suggest that a large body crashed into Earth while it was forming, knocking off chunks of rock that condensed into our satellite. For Pluto and Charon, the Kuiper Belt might’ve been involved. So these influences would have altered the planets’ spin dynamics, but for as long as we don’t know how these moons formed, we can’t be sure how or how much.

The answers to all these questions, then, is to keep extending the line. At the moment, the only planets for which the spin-rate can be measured are very massive gas giants. If this mass-spin relation is really universal, than one would expect them all to have high spin-rates. “That is something to investigate now, to see whether Beta Pictoris b is the first of a general trend or whether it is an outlier.”

Reference:

Fast spin of the young extrasolar planet β Pictoris b. Nature. doi:10.1038/nature13253