An astronomy professor at the University of Leiden, Ignas Snellen,called brown dwarfs ‘failed stars‘ because they were too heavy to be typical planets (13-75 times as heavy as Jupiter) and too light to sustain the fusion of hydrogen into helium. As a result, they exist in a limbo in astronomers’ textbooks, with the precise mechanism of their formation remaining a mystery.
However, failed or no, brown dwarfs are still massive objects and make for interesting features in the universe. One stellar example is the pithily named J1407b. It was discovered in 2012 by astronomers at the Leiden Observatory and University of Rochester, New York, orbiting a star – J1407 – about 420 light-years from Earth. J1407b is young – about 16 million years old. But it’s most striking feature is an extended ring system.
In 2012, the astronomers studying it surmised that the dwarf likely has 37 rings, altogether 120 million km in diameter (as wide as Mercury’s orbit around the Sun). Compare this to Saturn’s ring system, which is at most 300,000 km wide*. There are conspicuous gaps between these rings as well – notably at a distance of about 60 million km from the inside – indicating that there might be moons inhabiting them, formed by sweeping up the missing material.
The research team estimates that the amount of material orbiting as rings might all together weigh as much as hundred-times Earth’s moon, which is not anomalous considering J1407b is still young and likely not fully formed yet.
The way it was discovered is interesting. An exoplanet shows itself when seen through a telescope when it passes in front of its host star and casts a weak but persistent shadow on the telescope lens. When observing the J1407 system using the Super Wide Angle Search for Planets project in 2007, the astronomers found something was taking 56 days to move all the way across the face of its star. It was either an extremely large object or it had rings.
A second observation supported the rings hypothesis: the amount of starlight blocked wasn’t constant, but rose and dipped as if the amount of material passing in front of it was uneven. In fact, at one point, fully 95% of the starlight was blocked.
“The star is much too far away to observe the rings directly, but we could make a detailed model based on the rapid brightness variations in the star light passing through the ring system,” noted Leiden’s Matthew Kenworthy, who analyzed the data. “If we could replace Saturn’s rings with the rings around J1407b, they would be easily visible at night and be many times larger than the full moon.”
Estimating the mass of the ring-system would’ve required Doppler spectroscopy data as well, which wasn’t available until late 2014.
Curiously, the planet J1407b hasn’t been spotted directly yet. The astronomers are assuming it’s there simply because something like it has to hold this ring system together. In fact, its characterization as a brown dwarf is simply what it has to be at the least. The Doppler data indicates it has to weight some 10-40 times as much as Jupiter, i.e. much bigger than a gas giant, much smaller than a main-sequence star.
A paper discussing the team’s results was accepted for publication in the Astrophysical Journal on December 28, 2014. Even as studies of this giant will continue, the astronomers have called on their amateur counterparts from around the world to help them. “J1407’s eclipses will allow us to study the physical and chemical properties of satellite-spawning circumplanetary disks,” Kenworthy said of incentives.
Even after the loss of a critical stabilization system on-board, the NASA Kepler space telescope has made an important discovery. Scientists from the University of California have used the telescope to find a nearby star-system comprising a cool red M-dwarf and three planets slightly larger than Earth orbiting it. The find’s significance stems from various reasons, not the least of which is that this system is only 150 light-years away, close enough for astronomers to make direct observations of the star and the planets’ atmospheres*.
The three planets’ radii are 2.1-, 1.7- and 1.5-times that of Earth. The outermost planet, with the radius 1.5 RE, is in fact on the inner edge of the system’s habitability zone and receives 1.4-times the light that Earth does from our Sun. Moreover, follow-up observations made from the Automated Planet Finder telescope, California, and the Keck Telescope, Hawaii, indicate that the planets’ surfaces are cool and not scorched as exoplanets’ surfaces have often been found to be. The ‘lukewarm’ temperature is a sign that the planets are fully-formed.
For these reasons and others, finding this star-system has been like striking gold for astronomers. Its proximity permits them to closely monitor its evolution than if it had been farther away. The red M-dwarf at its center – designated EPIC 201367065 – is not too bright or its electromagnetic flux would have ‘bleached’ out observations; its moderate emission also means the planets’ surfaces aren’t scorched. The almost Earth-sized planet just about in the habitable zone means they can study if its surface conditions are conducive to life (A recent analysis concluded that one in five Sun-like stars in the Milky Way hosts an Earth-sized planet in the habitable zone, which means there are 40 billion such planets in our galaxy alone). Making matters easier overall is the proximity of the system itself, which also means investigations can be more detailed for the same resources.
One such detail that has not been explored with any great precision among farther exoplanets is composition. With sizes in the 1.5-2.1 RE range, the study’s authors think “they may span the gap between rock-dominated ‘Earths’/’super-Earths’ and low-density ‘sub-Neptunes’ with considerable volatile content”. Compositional analyses are important to understand what kind of planets can form under what conditions and how their orbits could have migrated within the system before attaining equilibrium. Additionally, they could also help astronomers understand why there are no planets heavier than Earth but lighter than Neptune in our Solar System.
Anyway, the next course of action will be to use the Hubble space telescope to compose a spectroscopic map of the outermost planet’s atmosphere. Many exoplanets that possess atmospheres also possess hydrogen-rich atmospheres, with no hints of the oxygen and nitrogen that have been able to support life on Earth. If the outermost planet’s atmosphere is also dominated by hydrogen, then the gas’s presence will show up in Hubble’s measurements. As the study’s lead author Ian Crossfield, from the Lunar & Planetary Laboratory at the University of Arizona, noted, the presence of large quantities of hydrogen doesn’t preclude life but only life as we’ve known it on Earth.
The study’s paper was uploaded to the arXiv pre-print server on January 15 and has been submitted to the Astrophysical Journal.
*Although the ten closest star-systems that have exoplanets are within 20 ly of the Sun.
The ALMA telescope in Chile has, for the first time, observed a star system that might be in the early stages of planet formation. The picture has astronomers drooling over it because the study of the origins of planets has until now been limited to simulated computer models and observations of planets made after they formed.
According to a statement put out by the European Southern Observatory (ESO), the observation was one of the first made with the ALMA, which opened in September 2014 for a ‘Long Baseline Campaign’ (ESO is the institution through which European countries fund the telescope). ALMA uses a technique called very-long baseline interferometry to achieve high resolutions that lets it observe objects hundreds of light-years away in fine detail. It makes these observations in the millimeter/sub-millimeter range of wavelengths; hence its name: Atacama Large Millimeter/sub-millimeter Array.
The image shows a disc of gas, dust and other debris orbiting the star HL Tauri, located about 450 light-years from Earth. A system like this is originally a large cloud of gas and dust. At some point, the cloud collapses under its own gravitation and starts to form a star, further accruing matter from the cloud and growing in size. The remaining matter in the cloud then settles into a disc formation over millions of years around the young star.
In the disc, the gas and dust continue to clump, this time into rocky lumps like planets and asteroids. This is why the disc is called a proto-planetary disc. As a planet forms and its gravitational pull gets stronger, it starts to clear a space in the disc of matter by either sucking it for itself or knocking it out. The gaps that are formed as a result are good indicators of planet formation.
According to the ESO statement, “HL Tauri’s disc appears much more developed than would be expected from the age of the system [less than 100,000 years]. Thus, the ALMA image also suggests that the planet-formation process may be faster than previously thought.”
In the Solar System, similar gaps exist called Kirkwood gaps. They represent matter cleared by Jupiter, whose prodigious gravitational pull has been pushing and pulling the orbits of asteroids around the Sun into certain locations. In fact, Jupiter’s movement within the Solar System – first moving away, then toward, and then away once more from the Sun – has been used to explain why the material composition of some asteroids between Mars and Jupiter is similar to those of Kuiper Belt objects situated beyond the present orbit of Neptune. Jupiter’s migration mixed them up.
Similarly, the gaps forming around HL Tauri, though they may represent planetesimals, may not result in planets in the exact same orbits as they could move around under the influence of subsequent gravitational disruptions. They could acquire unexpectedly eccentric orbits if their star system comes too close to another, as was found in the nearby binary star system HK Tauri in July 2014. Or, the gaps are probably being emptied by the gravitational effects of an object in another gap.
However, astronomers think the presence of multiple gaps is likely evidence of planet formation more than anything else.
Talking to dynamicists, they say that they would expect more spiral structure if these were empty gaps. So maybe they do each host a planet!
Astronomers will use this and other details as they continue their investigation into the HL Tauri system and how planets – at least planets in this system – form. The Long Baseline Campaign, which corresponds to the long-baseline configuration of the ALMA telescope that enabled this observation, will continue into December.
One of the biggest benefits of being a journalist is that you become aware of interesting things from various fields. As a science journalist, the ambit is narrowed but the interestingness, not at all. And one of the most interesting things I’ve come across is a relationship between the rate at which planets rotate – the equatorial rotation velocity – and their mass. It seems the lighter the planet, the lower its equatorial rotation velocity. This holds true for all the planets in the Solar System, as well as large asteroids and Kuiper belt objects such as Pluto. The plot below shows logarithm of planet mass (kg) on the x-axis and logarithm of equatorial rotation velocity (km/h) on the y-axis.
The blue line running through the points is a local regression fit and represents a statistical connection. However, there are four prominent outliers. They represent Mercury, Venus, Earth and Mars, the System’s rocky, inner planets. Their spin-mass correlation deviates from the normal because they are close to the Sun, whose gravitational pull exerts a tidal force on the planets that slows them down. Earth and Mars are also influenced by the gravitational effects of their moons. Anyway, I’ve already written at length about this fascinating connection. What I want to highlight here are more such connections.
And before that, a note: it’s probably obvious that they exist because the connection between mass and equatorial velocity could just as well be a connection between mass and a string of other properties that eventually influence the equatorial velocity. This thought was what led me to explore more connections.
Mass and rotation period
The rotation period of a planet describes the time taken for the planet to rotate once around its axis. If mass and equatorial velocity are related, then mass and rotation period can be related, too, if there is a connect between mass and planetary radius, which in turn implies there is a connect between radius and density, which in turn implies that planets that can get only so big and so dense before they become implausible, presumably – a conclusion borne out by a study released on May 26.
Image: A log-log plot between planetary mass and rotation period.
Density and rotation period
If a planet can only get so big before it becomes puffy, and its mass is related to its rotation period, then its density and rotation period must be connected, too. The chart below shows that that hypothesis is indeed borne out (it’s not my hypothesis, FYI): log(density) increases as log(rotation period) does, so denser planets rotate faster. However, the plot shows significant variation. How do you explain that?
Image: A log-log plot between density and rotation period.
Turn to the Solar System’s early days. The Sun has formed and there is a huge disk of gas, rocks, dust and other debris floating around it. It exerts a gravitational pull that draws heavier things in the disk toward itself. As it becomes more energetic, however, it exerts a radiation pressure that pushes lighter things in the disk away. Thus, the outermost areas of the disk are mostly dust while the inner areas are heavier and denser. It’s possible that this natural stratification could have created different bands of material in the disk of different densities. These different kinds of materials could have formed different kinds of planets, each now falling on a specific part of the log(density) v. log(rotation period) plot.
Mass and density
Of course mass and density are related: the relation is called volume. But what’s interesting is that the volume isn’t arbitrary among the Solar System’s planets. It rises and then dips, which means heavier planets are less dense and, thus, more voluminous. For example, Jupiter is the heaviest planet in the Solar System – it weighs as much as 317 Earths. Its volume is more than 1,300-times Earth’s. However, its density – 1.33 g/cm3 versus Earth’s 5.52 g/cm3 – shouldn’t be surprising because it’s made of mostly hydrogen and helium. Which is just what we deduced based on the mass-period connection.
Image: A log-log plot between mass and density.
One way to find out if there’s any merit in this exercise is to conduct a detailed study. Another way is to perform a regression analysis. I’m not smart enough to do that, but I’ll blog in detail about that when I am.
Billing its mission as a journey to the beginning of the Solar System, the NASA Dawn probe has revealed more information about the asteroid Vesta that has scientists both eager and cautious about what they have learned.
The second largest in the belt of bodies between the orbits of Mars and Jupiter, Vesta is almost as old as the Solar System itself. Of late, its internal structure has spurred more interest because it is similar to that of Earth’s: with a crust, mantle and core.
One team, headed by Harold Clenet, a scientist at the Earth and Planetary Science Laboratory, Ecole Polytechnique Federale de Lausanne, has concluded that the asteroid’s newly discovered features defy conventional beliefs of how they may have formed.
Because Vesta’s formation and internal composition are thought to be similar to Earth’s, Dr. Clenet asserts that based on his team’s findings, we rethink some aspects of how the Solar System was formed, too.
On the other hand, the science team behind Dawn, led by principal investigator Christopher Russell, a professor of space physics at the University of California, Los Angeles, contends the Clenet et al team’s reliance on “simplistic” models to come to broad conclusions without sorting out other possibilities first.
Dr. Clenet and his colleagues from the Universities of Bern, Brittany and Arizona used observations made by Dawn between July 2011 and September 2012 of two large craters near Vesta’s south pole. These craters were formed by meteorite impacts so powerful that the material they dislodged comprises 5% of the meteorites that fall on Earth. And what information we had of Vesta pre-Dawn came from their fragments.
More pertinently, the impacts also dug out enough material to provide scientists with a glimpse of what they thought was Vesta’s mantle.
But they were in for a surprise. They found that a common silicate mineral of the mantle, called olivine, was missing in observations of the southern hemisphere craters. “Olivine is a very common mineral on Earth and represents about 60% of Earth’s upper mantle,” Dr. Clenet said.
In the absence of this signature material in the craters, Dr. Clenet was led to believe Vesta’s mantle has not been exposed at all, and what they were observing might still be the crust. That would mean the crust is some 20 km thick in the northern regions of Vesta, and about 80 km thick in parts of the southern.
“This does not fit with the chondritic models of planet formation,” he added, chondrites being the most primitive material that formed at the beginning of the Solar System, “and thus question the nature of the initial material that formed Vesta.”.
Because of the shared principles of their origins, Dr. Clenet’s findings, published online in Nature on July 16, also cast doubt on what Earth’s early years may have been like, he thinks.
However, Prof. Russell advised more caution because observations of Vesta by Dawn have proved the chondritic model more simplistic than correct.
Not the last word
Planetary bodies that have a hot, inner core also have distinct layers of material: the crust and the mantle. The mantle is formed by cooling magma, and olivine is the first mineral to crystallize when magma cools. In this picture, Prof. Russell said, “One of the predictions is that the differentiation would make a deep magma ocean in which olivine was the major constituent of the mantle, but a pure olivine mantle clearly does not exist.”
“Why? Is there a different chemistry?”
He contends the Clenet et al team’s reliance on the “simplistic” absence of olivine to come to such broad conclusions without sorting out other possibilities. Dr. Clenet argues that olivine may have been superficially removed from Vesta’s upper mantle by “huge impacts”, but the fact that the dislodged mineral can’t be found anywhere else in the asteroid belt lends credence to the hypothesis that the crust is thicker.
Prof. Russell, on the other hand, thinks maybe the body didn’t heat up enough to make an olivine-rich mantle in the first place, or the composition of hot radioactive substances was different, or the overlying material didn’t percolate the way we think it might have.
Similarly, Maria Cristina De Sanctis, Dawn co-investigator at the National Institute of Astrophysics, Rome, is also wary. She said that although Vesta is similar to Earth, “it is much smaller and it is difficult to have such a small object similar to our planet, and mass is an important factor in the evolution of planets.”
While the research community sorts out the possibilities, “the present paper in my opinion contains little new real insight into the problem,” Prof. Russell concluded. “Its publication has puzzled a number of us on the Dawn team.”
The probe is currently on its way to Ceres, the largest asteroid in the belt between Mars and Jupiter, and will get there in March 2015.
Interested in Vesta’s colorful history? Read this. Featured image credit: Once Dawn arrives at Ceres, it will spiral in (from blue to red) toward the asteroid’s surface and map it. Photo: NASA/JPL
By the time the NASA Kepler mission failed in 2013, it had gathered evidence that there were at least 962 exoplanets in 76 stellar systems, not to mention the final word is awaited on 2,900 more. In the four years it had operated it far surpassed its envisioned science goals. The 12 gigabytes of data it had transmitted home contained a wealth of information on different kinds of planets, big and small, hot and cold, orbiting a similar variety of stars.
Sifting through it, scientists have found many insightful patterns, many of which evade a scientific explanation and keep the cosmos as wonderful as it has been. In the most recent instance of this, astronomers from Harvard, Berkeley and Honolulu have unearthed a connection between some exoplanets’ size, density and prevalence.
They have found that most exoplanets with radii 1.5 times more than Earth’s are not rocky. Around or below this cut-off, they were rocky and could hypothetically support human life. Larger exoplanets – analogous to Neptune and heavier – have rocky cores surrounded by thick gaseous envelopes with atmospheric pressures too high for human survival.
“We do not know why rocky planetary cores begin to support thick gaseous layers at about 1.5 Earth radii as opposed to 1.2 or 1.8 Earth radii, and as the community answers this question, we will learn something about planet formation,” said Lauren Weiss, a third year graduate student at UC Berkeley.
She is the second author on the group’s paper published in Proceedings of the National Academy of Sciences on May 26. The first author is Geoff Marcy the “planet hunter”, who holds the Watson and Marilyn Alberts Chair for SETI at UC Berkeley.
Not necessarily the bigger the heavier
The group analyzed the masses and radii of more than 60 exoplanets, 33 of which were discussed in the paper. “Many of the planets our study straddle the transition between rocky planets and planets with gaseous envelopes,” Weiss explained. The analysis was narrowed down to planets with orbital periods of five to 100 days, which correspond to orbital distances of 0.05 to 0.42 astronomical units. One astronomical unit (AU) is the distance between Earth and the Sun.
Fully 26.2% of such planets, which orbit Sun-like stars, have radii 1 to 1.41 times that of Earth, denoted as R⊕, and have an orbital distance of around 0.4 AU. Accounting for planets with radii up to 4R⊕, their prevalence jumps to more than half. In other words, one in every two planets orbiting a Sun-like star was bound to be just as wide to eight times as wide as Earth.
And in this set, the connection between exoplanet density and radius showed itself. The astronomers found that the masses of Earth-sized exoplanets steadily increased until their radii touched 1.5R⊕, and then dropped off after. In fact, this relationship was so consistent with their data that Weiss & co. were able to tease out a relation between density and radius for 0-1.5R⊕ exoplanets – one they found held with Mercury Venus and Earth, too.
Density = 2.32 + 3.19R/R⊕
So, the astronomers were able to calculate an Earth-like planet’s density from its radius, and vice versa, using this equation. Beyond 1.5R⊕, however, the density dropped off as the planet accrued more hydrogen, helium and water vapor. At 1.5R⊕, they found the maximum density to be around 7.6 g/cm3, against Earth’s 5.5 g/cm3.
The question of density plays a role in understanding where life could arise in the universe. While it could form on any planet orbiting any kind of star, we can’t also forget that Earth is the only planet on which life has been found to date. It forms an exemplary case.
There’s nothing inbetween
Figuring out how many Earth-like planets, possibly around Sun-like stars, there could be in the galaxy could therefore help us understand what the chances are like to find life outside the Solar System.
And because Earth leads the way, we think “humans would best be able to explore planets with rocky surfaces.” In the same way, Weiss added, “we would better be able to explore, or colonize, the rocky planets smaller than 1.5 Earth radii.”
This is where the astronomers hit another stumbling block. While data from Kepler showed that most exoplanets were small and in fact topped off at 4R⊕, the Solar System doesn’t have any such planets. That is, there is no planet orbiting the Sun which is heavier than Earth but lighter than Neptune.
“It beats all of us,” Weiss said. “We don’t know why our Solar System didn’t make sub-Neptunes.” The Kepler mission is also responsible for not providing information on this front. “At four years, it lasted less time than a single orbit of Jupiter, 11 years, and so it can’t answer questions about the frequency of Jupiter, Saturn, Uranus, or Neptune analogs,” Weiss explained.
It seems the cosmos has lived up to its millennia-old promise, then, as more discoveries trickle in on the back of yet more questions. We will have to keep looking skyward for answers.
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.
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.
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:
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 = axk. 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.
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,
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.
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.”