How to understand exactly why gravity darkening happens on rotating stars?

How to understand exactly why gravity darkening happens on rotating stars?

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Upon completion, a link will appear to access the found materials.'s TESS delivers new insights into an ultrahot world links to KELT-9 b's Asymmetric TESS Transit Caused by Rapid Stellar Rotation and Spin-Orbit Misalignment (readable in arXiv)

The assymetric dip in the light curve comes from a near-polar transit across a rotating, oblate star where the poles are hotter and therefore brighter due to gravity darkening:

KELT-9's high internal angular momentum ($ u sin(i)$ = 111.4 ± 1.3 km/s) flattens it into an oblate spheroid, making the equatorial radius of the star larger than the polar radius. Additionally, the star's abundant centrifugal force near its equator distorts its hydrostatic equilibrium, causing its effective temperature to vary by nearly a thousand Kelvin over the surface of the star. These two effects of stellar oblateness and varying effective temperature - together commonly referred to as gravity darkening (Barnes 2009) - change the total irradiance on KELT-9 b (Ahlers 2016).

Those links discuss gravity darkening but don't offer a simple explanation.

Wikipedia's Gravity darkening says:

When a star is oblate, it has a larger radius at its equator than it does at its poles. As a result, the poles have a higher surface gravity, and thus higher temperature and brightness.

Question: Why exactly does the increased surface gravity at some places on a given star lead to a higher temperature at those locations? Is it related to the difference in scale heights? The surface brightness relates to the temperature at the photosphere, is the reason simply that a higher pressure therefore higher temperature is needed to support the same density in a higher gravitational field?

Figure 2. (Left) KELT-9 b begins its transit near the star's hot pole and moves toward the star's cooler equator. Our transit analysis directly measures the stellar inclination (i), the planet's projected alignment (λ), and the orbital inclination (i.e., the impact parameter b). We find that KELT-9 varies in effective temperature by ∼ 800 K between its hot poles and cooler equator. (Right) KELT-9 b's phase-folded primary transit from TESS. The transit depth steadily decreases throughout the eclipse, indicating that KELT-9 b begins its transit near one of the host star's hotter poles and moves toward the dimmer stellar equator.

The argument goes something like this.

Hydrostatic equilibrium means that the local pressure gradient is proportional to the local density multiplied by a latitude-dependent local gravity. If the pressure just depends on density and temperature, this means that those quantities will also just depend on latitude and therefore will be constant along an equipotential surface. i.e. pressure, temperature and density are functions of the effective gravitational potential $phi$.

For stars with radiative outer envelopes, the heat flux is proportional to the temperature gradient, multiplied by some stuff (like inverse opacity) that just depends on density and temperature.

But $$ abla T(phi) = frac{dT}{dphi} abla phi = f(phi)g_{ m eff}$$

If we now say that at the surface $sigma T_{ m eff}^4$ equals the radiative flux, then we recover the Von Zeipel gravity darkening law that $T_{ m eff}$ is proportional to $g_{ m eff}^{1/4}$.

The missing step in this argument is to show the $f(phi)$ is constant. Given that the photosphere is defined as where the optical depth is some fixed value (usually 1 or 2/3), and may be assumed to depend only on temperature and density, then this also lies on an equipotential. But $dT/dphi$ also only depends on $phi$ and so must also be constant along an equipotential.

For more detail, although missing the last paragraph above(!), see .

The situation is much more complex for stars with convective envelopes or differential rotation and I think can only be tackled through detailed modelling.

From the same Wikipedia page:

This means that equatorial regions of a star will have a greater centrifugal force when compared to the pole. The centrifugal force pushes mass away from the axis of rotation, and results in less overall pressure on the gas in the equatorial regions of the star. This will cause the gas in this region to become less dense, and cooler.

So it appears that the equatorial bulge is caused centrifugally via rapid rotation (as expected). This outwards-directed force relieves the pressure acting inwards arising from gravitational contraction, and of course temperature is proportional to pressure. Therefore surface temperature will be higher at the poles than the equator.

How a weird theory of gravity could break cause-and-effect

Astronomers have known that galaxies across the universe are behaving badly. Some are spinning too fast, while others are just way too hot and still others glommed into super structures too quickly.

But they don't know why. Perhaps some new hidden particle, like dark matter, could explain the weirdness. Or perhaps gravity is acting on these coalescing clusters of stars in a way scientists hadn't expected.

For decades, astronomers have debated the possibilities. While most astronomers believe that dark matter exists, some still think that we need to modify our theory of gravity. However, new research has found a critical flaw in modified gravity theories: They allow for effects to occur without causes and for information to travel faster than the speed of light. This is bad … for modified gravity.

"It may change this … research area considerably, forcing it in rather new directions," lead researcher and Tufts University astrophysicist Mark Hertzberg told Live Science.

Tasting neutrinos: Flavor changing in the cores of exploding stars

I have long wondered about the Universe's wry sense of humor. After all, how else can it be that one of the most ethereal and ghostly particles in the cosmos is fundamentally responsible for some of the most colossal and violent explosions in it?

New research indicates that not only do neutrinos play an important role in supernova explosions, but we need to account for all their characteristics to truly understand why stars explode.

More Bad Astronomy

Stars generate energy in their cores, fusing lighter elements into heavier ones. This is how a star prevents its own gravity from making it collapse the heat generated inflates the star, creating pressure that holds it up.

The most massive stars take this energy production process to the extreme while lower mass stars like the Sun stop after fusing helium into carbon and oxygen, massive stars continue on, fusing elements all the way up to iron.

However, once a mighty star's core is iron, a series of events takes place that actually removes energy from the core, allowing gravity to dominate. The core collapses, setting up a huge blast of energy that is so immense it blows away the outer layers of the star, creating an explosion we call a supernova.

M 1, the Crab Nebula supernova remnant, observed by Hubble Space Telescope. Credit: NASA, ESA, J. Hester and A. Loll (Arizona State University)

A crucial part of this event is the generation of staggering numbers of neutrinos. These are subatomic particles, that, taken individually, are as insubstantive a thing as the Universe makes. They are so loathe to interact with normal matter that they can pass through vast amounts of material without notice to them, the Earth itself is wholly transparent and they travel through it as if it weren't there at all.

But when the iron core of a massive star collapse, neutrinos of such high energy and in such numbers are created that the infalling material just outside the star's core actually absorbs vast numbers of them it helps too that the material rushing downward is extraordinarily dense and able to capture so many.

The amount of energy this soul-vaporizing wave of neutrinos imparts on the matter is enough to not only stop the collapse but also reverse it, sending octillions of tons of stellar matter exploding outward at an appreciable fraction of the speed of light.

The energy of a supernova just in visible light is so huge it can equal the output of an entire galaxy. Yet this is only 1% of the total energy of the event the vast majority of it is released as energetic neutrinos. That's how powerful a role they play.

Before this was understood, theoretical astronomers had a difficult time getting the core collapse to actually create the explosion. Simple models of the physics showed the star's explosion would stall, and a supernova wouldn't occur. Over the years, as computers got more sophisticated, it was possible to make the equations input into the models more complicated, doing a better job matching reality. Once neutrinos were added to the mix it became clear what a key part they added.

The models do quite well now, but there is always room for improvement. For example, we know that neutrinos come in three different kinds, called flavors: tau, electron, and muon neutrinos. We also know that under certain conditions the flavors oscillate, meaning one kind of neutrino can change into another kind. All three have different characteristics and interact with matter differently. How does this affect supernovae?

A team of scientists looked into this. They created a very sophisticated computer model of the core of a star as it explodes, allowing the neutrinos to not only change flavor, but also to interact with each other. When this happens the flavor changes happen much more rapidly, what they call a fast conversion.

What they found is that including all three flavors and allowing them to interact and convert does potentially change the conditions inside the collapsing star's core. For example, neutrinos may not be emitted isotropically (in all directions) but instead have an angular distribution they can be emitted in some directions preferentially.

This can have a very different affect on the explosion than assuming istropism. We know that some supernovae explosions are not symmetric, occurring off-center in the core or with the energy blasting out in one direction more than another. The amount of energy in the neutrino release is so huge that even a slight asymmetry can give the core a huge kick, sending the collapsed core (now a neutron star or black hole) off like a rocket.

The models the scientists used are a first step in understanding this effect and how big it might be. They've shown it's possible that including all the neutrino characteristics may be important, but what happens in detail is still to be determined.

A stunning image of the supernova remnant Cas A combines visible light images from Hubble with X-ray observations by Chandra. The different colors represent different energies of the light, which tend to come from different elements like oxygen, calcium, and iron. Credit: X-ray: NASA/CXC/RIKEN/T. Sato et al. Optical: NASA/STScI

Still, this is exciting. When I was in grad school taking classes in the physics of stellar interiors the state-of-the-art models were still having trouble getting stars to explode. And now we have models that not only work but are starting to reveal previously unknown aspects of these events. Not only that, but we can turn this around, observe real supernovae in the sky and see what their explosions can tell us about the neutrinos themselves.

It's funny: Supernova explosions create a fair amount of the matter you see around you: The calcium in your bones, the iron in your blood, the elements that make up life and air and rocks and nearly everything. Neutrinos are crucial for this creation, in a few moments giving birth to so much that we need to live. Yet, once made, these particles ignore that matter, passing through it without a care, ghosts ignoring the residents as they move through walls from one place to the next.

Once made, matter is old news to neutrinos.

I anthropomorphize the Universe, thinking it has a sense of humor. But I think sometimes the Universe provides the evidence that I'm right.

The mysterious dark energy that speeds the universe's rate of expansion

How do we think about something we can’t see and don’t experience in our everyday lives, but seems to be pushing our universe apart ever faster? Credit: NASA, ESA, G. Illingworth, D. Magee, and P. Oesch (University of California, Santa Cruz), R. Bouwens (Leiden University), and the HUDF09 Team, CC BY

The nature of dark energy is one of the most important unsolved problems in all of science. But what, exactly, is dark energy, and why do we even believe that it exists?

Step back a minute and consider a more familiar experience: what happens when you toss a ball straight up into the air? It gradually slows down as gravity tugs on it, finally stopping in mid-air and falling back to the ground. Of course, if you threw the ball hard enough (about 25,000 miles per hour) it would actually escape from the Earth entirely and shoot into space, never to return. But even in that case, gravity would continue to pull feebly on the ball, slowing its speed as it escaped the clutches of the Earth.

But now imagine something completely different. Suppose that you tossed a ball into the air, and instead of being attracted back to the ground, the ball was repelled by the Earth and blasted faster and faster into the sky. This would be an astonishing event, but it's exactly what astronomers have observed happening to the entire universe!

Scientists have known for almost a century that the universe is expanding, with all of the galaxies flying apart from each other. And until recently, scientists believed that there were only two possible options for the universe in the future. It could expand forever (like the ball that you tossed upward at 25,000 miles an hour), but with the expansion slowing down as gravity pulled all of the galaxies toward each other. Or gravity might win out in the end and bring the expansion of the universe to a halt, finally collapsing it back down in a "big crunch," just like your ball plunging back to the ground.

What goes up must come down… right? Credit:

So imagine scientists' surprise when two different teams of astronomers discovered, back in 1998, that neither of these behaviors was correct. These astronomers were measuring how fast the universe was expanding when it was much younger than today. But how could they do this without building a time machine?

Luckily, a telescope is a time machine. When you look up at the stars at night, you aren't seeing what they look like today – you're seeing light that left the stars a long time ago – often many hundreds of years. By looking at distant supernovae, which are tremendously bright exploding stars, astronomers can look back hundreds of millions of years. They can then measure the expansion rate back then by comparing the distance to these far-off supernovae with the speed at which they are flying away from us. And by comparing how fast the universe was expanding hundreds of millions of years ago to its rate of expansion today, these astronomers discovered that the expansion is actually speeding up instead of slowing down as everyone had expected.

Instead of pulling the galaxies in the universe together, gravity seems to be driving them apart. But how can gravity be repulsive, when our everyday experience shows that it's attractive? Einstein's theory of gravity in fact predicts that gravity can repel as well as attract, but only under very special circumstances.

Repulsive gravity requires a new form of energy, dubbed "dark energy," with very weird properties. Unlike ordinary matter, dark energy has negative pressure, and it's this negative pressure that makes gravity repulsive. (For ordinary matter, gravity is always attractive). Dark energy appears to be smoothly smeared out through the entire universe, and it interacts with ordinary matter only through the action of gravity, making it nearly impossible to test in the laboratory.

This illustration shows abstracted ‘slices’ of space at different points in time as the universe expands. Credit: Ævar Arnfjörð Bjarmason, CC BY-SA

The simplest form of dark energy goes by two different names: a cosmological constant or vacuum energy. Vacuum energy has another strange property. Imagine a box that expands as the universe expands. The amount of matter in the box stays the same as the box expands, but the volume of the box goes up, so the density of matter in the box goes down. In fact, the density of everything goes down as the universe expands. Except for vacuum energy - its density stays exactly the same. (Yes, that's as bizarre as it sounds. It's like stretching a string of taffy and discovering that it never gets any thinner).

Since dark energy can't be isolated or probed in the laboratory, how can we hope to understand exactly what it's made of? Different theories for dark energy predict small differences in the way that the expansion of the universe changes with time, so our best hope of probing dark energy seems to come from ever more accurate measurements of the acceleration of the universe, building on that first discovery 17 years ago. Different groups of scientists are currently undertaking a wide range of these measurements. For example, the Dark Energy Survey is mapping out the distribution of galaxies in the universe to help resolve this puzzle.

There is one other possibility: maybe scientists have been barking up the wrong tree. Maybe there is no dark energy, and our measurements actually mean that Einstein's theory of gravity is wrong and needs to be fixed. This would be a daunting undertaking, since Einstein's theory works exceptionally well when we test it in the solar system. (Let's face it, Einstein really knew what he was doing). So far, no one has produced a convincing improvement on Einstein's theory that predicts the correct expansion for the universe and yet agrees with Einstein's theory inside the solar system. I'll leave that as a homework problem for the reader.

  • What pushes galaxies like these in the Hubble deep field apart? Credit: NASA and A. Riess (STScI), CC BY
  • Scientists used to think that the expansion of the universe was described by the yellow, green, or blue curves. But surprise, it’s actually the red curve instead.

This story is published courtesy of The Conversation (under Creative Commons-Attribution/No derivatives).

Unique prediction of 'modified gravity' challenges dark matter theory

The best example is represented by the Sunflower galaxy (NGC 5055) with the strongest external fieldamong SPARC galaxies, whose well-measured rotation curve shows a mildly declining behavior at largeradial distance and can be accurately modeled only with an external field effect. Credit: Creative Commons

An international group of scientists, including Case Western Reserve University Astronomy Chair Stacy McGaugh, has published research contending that a rival idea to the popular dark matter hypothesis more accurately predicts a galactic phenomenon that appears to defy the classic rules of gravity.

This is significant, the astrophysicists say, because it further establishes the hypothesis—called modified Newtonian dynamics (MOND), or "modified gravity"—as a viable explanation for a cosmological dilemma: that galaxies appear to buck the long-accepted rules of gravity traced to Sir Isaac Newton in the late 1600's.

The mystery: For decades, we've measured more gravitational pull in space than we think we should have—that there's not enough visible or known matter to account for it all.

So, dark matter proponents theorize that most of the known universe is actually made of material that doesn't interact with light, making it invisible and undetectable— but that this material accounts for much of the gravitational pull among galaxies. It has been the prevailing theory for nearly 50 years.

MOND theory, a counter explanation introduced by physicist Mordehai Milgrom from Weizmann Institute (Israel) in the early 1980s, says this gravitational pull exists because the rules of gravity are slightly altered.

Instead of attributing the excess gravitational pull to an unseen, undetectable dark matter, MOND suggests that gravity at low accelerations is stronger than would be predicted by a pure Newtonian understanding.

In addition, MOND made a bold prediction: the internal motions of an object in the cosmos should not only depend on the mass of the object itself, but also the gravitational pull from all other masses in the universe—called "the external field effect" (EFE).

Milgrom said the findings, if robustly confirmed, would be "the smoking gun proving that galaxies are governed by modified dynamics rather than obeying the laws of Newton and of general relativity."

150 galaxies tested for EFE

McGaugh and his collaborators, led by Kyu-Hyun Chae, from Sejong University in South Korea, say they detected this EFE in more than 150 galaxies studied.

Their findings were published recently in The Astrophysical Journal.

"The external field effect is a unique signature of MOND that does not occur in Newton-Einstein gravity," McGaugh said. "This has no analogy in conventional theory with dark matter. Detection of this effect is a real head-scratcher."

The team of six astrophysicists and astronomers includes lead author Chae and other contributors from the United Kingdom, Italy and the United States.

"I have been working under the hypothesis that dark matter exists, so this result really surprised me," Chae said. "Initially, I was reluctant to interpret our own results in favor of MOND. But now I cannot deny the fact that the results as they stand clearly support MOND rather than the dark matter hypothesis."

Analyzing rotating galaxies

The group analyzed 153 rotation curves of disk galaxies as part of their study. The galaxies were selected from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database, created by another collaborator, Federico Lelli, during his postdoctoral studies at Case Western Reserve, McGaugh and co-author James Schombert, of the University of Oregon.

In addition to Chae, McGaugh, Lelli and Schombert, the authors of the research were Pengfei Li from Case Western Reserve and Harry Desmond from the University of Oxford.

The scientists said they deduced the EFE by observing that galaxies in strong external fields slowed (or exhibited declining rotation curves) more frequently than galaxies in weaker external fields—as predicted by MOND alone.

Lelli said he was skeptical by the results at first "because the external field effect on rotation curves is expected to be very tiny. We spent months checking various systematics. In the end, it became clear we had a real, solid detection."

McGaugh said that skepticism is part of the scientific process and understands the reluctance of many scientists to consider MOND as a possibility.

"I came from the same place as those in dark matter community," he said. "It hurts to think that we could be so wrong. But Milgrom predicted this over 30 years ago with MOND. No other theory anticipated the observed behavior."

Why hunting for fast radio bursts is an 'exploding field' in astronomy

FRB 121102, a repeating burst, was discovered in 2015. This discovery enabled astronomers to figure out what galaxy the FRB came from and in turn locate hundreds more FRBs. Credit: Gemini Observatory / AURA / NSF / NRC

Little more than a decade ago, two astronomers discovered mysterious bursts of radio waves that seem to take place all over the sky, often outshining all the stars in a galaxy. Since then, the study of these fast radio bursts, or FRBs, has taken off, and while we still don't know what exactly they are or what causes them, scientists are now edging closer to some answers.

FRBs were first detected in 2007 by astronomers Duncan Lorimer and David Narkevic. While using the Parkes Observatory in Australia, the duo were stunned to witness an incredibly bright flash of radio waves coming from space. This strange event was called a Lorimer burst.

Since then, about 100 FRB discoveries have been announced. We've been able to pinpoint the location of some to other galaxies—none appear to take place inside the Milky Way—as well as see some happening in real-time and even witness FRBs that repeat. Despite numerous observations and plenty of data, we're still at a loss to explain exactly what they are.

'It's not so often in astrophysics that there's a new phenomenon that we really don't understand and we have the opportunity to learn something genuinely new,' said Dr. Jason Hessels from the University of Amsterdam in the Netherlands.

Dr. Hessels coordinated a project called DRAGNET, which ran from 2014 to 2018 and sought to observe and study more FRBs. It used radio telescopes around the world—including the Low-Frequency Array, or LOFAR telescope, in the Netherlands—to hunt for exotic stars and FRBs. At the time the project was proposed in 2012, however, people weren't certain that FRBs were even real.

Yet, in 2015 the project made a key breakthrough. It discovered that a known FRB in another galaxy—dubbed FRB 121102—was repeating. This discovery allowed astronomers to work out where the FRB was coming from—a faint dwarf galaxy 3 billion light-years from Earth. We've since found a second repeating burst, but until that first one, all FRBs had been single events.

'That's been a huge treasure chest of information,' said Dr. Hessels, referring to FRB 121102. 'We've detected hundreds of bursts from it.'

Each flash lasts just a millisecond or so but can emit more energy than 500 million suns. As such, FRB 121102 is clearly noticeable against the backdrop of a galaxy, especially one as faint as this. Even at such a great distance, and having been produced before multicellular life on Earth began, the flash is intense enough for us to measure today.

When FRBs were first discovered, it was thought that they might be caused by cataclysmic events such as neutron stars—the remnant cores of collapsed giant stars—or black holes merging together. The fact that some FRBs repeat, however, suggests that might not be the case, although there could be multiple types of FRB.

Our best explanation so far is that they are caused by magnetars, neutron stars that have incredibly strong magnetic fields. It's thought that these stars have enough energy to produce the bright flashes associated with FRBs, experiencing 'star quakes' as the magnetic field rips the crust of the star apart, releasing a huge amount of energy (although recent results released on 27 June suggest a possible unknown alternative origin for some FRBs).

'That released energy could be ramming into all the material surrounding the magnetar, and that causes a shock and can accelerate particles that produce radio waves and a radio burst like we observe,' said Dr. Hessels.

To better answer this question, the ongoing MeerTRAP project is trying to find more FRBs, which might get us closer to an answer. The project uses the MeerKAT radio telescope array in South Africa to look for pulses of radio waves in the sky. During the array's standard astronomical observations, the MeerTRAP team piggybacks onboard to obtain the data—about 10 gigabytes a second—to look for FRBs.

'We just take data from where they have chosen to point,' said Dr. Benjamin Stappers from the University of Manchester, UK, and the project coordinator for MeerTRAP. 'It doesn't matter too much where the telescope is pointing, because they should be uniform across the sky.'

The project hasn't started looking for FRBs yet, but plans to start doing so in July 2019. The MeerTRAP team hopes to find between two and five FRBs per week, with the possibility of looking for both FRBs that occur just once and repeating ones, as the telescopes will return to the same part of the sky on regular occasions.

All of this data should help us better work out the origin of FRBs. 'One way to work out what the cause of them is, is to understand where they happen in a galaxy, and what types of galaxies they happen in,' said Dr. Stappers.

Astronomers also want to work out how many types of FRB there are. So far, we know that some of them repeat and some do not, but how many repeat is still unknown. It could be that these two types are formed in different ways, so finding more of them could help us better answer that question.

'There's also the probability that FRBs will also pass through the outer regions of other galaxies that lie along the line of sight,' said Dr. Stappers. 'So you can use them like shining a torch and see what happens to the light as it passes through those other galaxies. You can learn something about the nature of those intervening galaxies.'

The MeerTRAP project will also be looking for rapidly rotating neutron stars, called pulsars, to better test our theories of gravity. If a pulsar was found orbiting another star or even a black hole, the change in its rotation could tell us more about how gravity works at the extreme end of physics.

It's FRBs, however, that are garnering the headlines at the moment. With more and more discoveries on the way, it's hoped we might have an answer soon about some of their mysteries.

'The field is really exploding,' said Dr. Hessels, noting we may know of more than 1,000 by the end of the year. 'Probably in the next few years we will have a pretty good idea of what's causing them.'

No need for dark matter?

Erik Verlinde of University of Amsterdam at the 29th Jerusalem Winter School in Theoretical Physics, 2010, via YouTube.

Theoretical physicist Erik Verlinde has a new theory of gravity, which describes gravity not a force but as an illusion. The theory says gravity is an emergent phenomenon, possible to be derived from the microscopic building blocks that make up our universe’s entire existence. This week, he published the latest installment of his theory showing that – if he’s correct – there’s no need for dark matter to describe the motions of stars in galaxies.

Verlinde, who is at the University of Amsterdam, first released his new theory in 2010. According to a statement released this week (November 8, 2016):

… gravity is not a fundamental force of nature, but an emergent phenomenon. In the same way that temperature arises from the movement of microscopic particles, gravity emerges from the changes of fundamental bits of information, stored in the very structure of spacetime.

Dark matter – the invisible “something” that most modern physicists believe makes up a substantial fraction of our universe – came to be necessary when astronomers found in the mid-20th century they couldn’t explain why stars in galaxies moved as they did. The outer parts of galaxies, including our own Milky Way, rotate much faster around their centers than they should, according to the theories of gravity as explained by Isaac Newton and Albert Einstein. According to these very accepted theories, there must be more mass in galaxies than that we can see, and thus scientists began speaking of invisible matter, which they called dark matter.

They’ve been speaking of it, and trying to understand it, ever since.

Verlinde is now saying we don’t need dark matter to explain what’s happening in galaxies. He says his new theory of gravity accurately predicts star velocities in the Milky Way and other galaxies. In his statement, he said:

We have evidence that this new view of gravity actually agrees with the observations. At large scales, it seems, gravity just doesn’t behave the way Einstein’s theory predicts.

Early in the 20th century, it was the great revelation of Albert Einstein that gravity can be described in terms of curved spacetime. Image via

If true, it’s a revolution in science, since essentially all of modern cosmology – including the Big Bang theory that describes how our universe began – is based on Einstein’s theory of gravity. In recent decades, dark matter and its cousin dark energy have been bugaboos to the accepted theories despite searches, for example, no one has ever actually observed dark matter.

If Verlinde’s theory of gravity is true, it doesn’t mean Einstein’s theory is wrong, just as Einstein’s description of gravity didn’t exactly nullify Isaac Newton’s theory of gravity from two centuries before. Newton’s theory is still taught in physics classes, but Einstein’s theory was a refinement – a major one – in our way of thinking about gravity. Likewise, Verlinde’s theory, if correct, would be a refinement of Einstein’s ideas and a chance to have a deeper understanding of the way our universe works. Verlinde commented in his statement:

Many theoretical physicists like me are working on a revision of the [accepted modern theories of gravity], and some major advancements have been made. We might be standing on the brink of a new scientific revolution that will radically change our views on the very nature of space, time and gravity.

Or learn more about it from Verlinde himself. The video below is from Big Think, in 2011:

Bottom line: The latest installment of Erik Verlinde’s new theory of emergent gravity – released November 8, 2016 – explains the motions of stars around the centers of galaxies without having to call on dark matter.

How to understand exactly why gravity darkening happens on rotating stars? - Astronomy

Why do the planets rotate? What force cause them to rotate?

There is no force that causes the planets to rotate. Most of the rotation comes about from the conservation of angular momentum. Angular momentum is given by L=m*w*r 2 where m is the mass, w is the angular velocity in radians per second, and r is the radius of the circular motion. Due to conservation of angular momentum, if the radius of the orbit decreases, then its angular velocity must increase (as the mass is constant).

All planetary and stellar systems are born from the collapse of dense interstellar clouds. The clouds may originally be very large (even thousands of light years across). Consider a portion of the cloud the collapses from a size of a light year or so to the size of the solar system. That is a huge change in the size of the system. So, the very slight rotation that the cloud has in the beginning is increased dramatically when the collapse takes place. In fact, this is one of the barriers in star formation: there is excess angular momentum and there has to be a way of losing angular momentum before you can form a star.

Anyway, the bottom line is that stars like the Sun spin from the original angular momentum that was there in the solar nebula from which it formed. Not only that, all orbital motion of the planets (including the spin) is due to this orginal angular momentum.

You are saying that original angular momentum of the cloud causes orbital motions and rotations of the planets(mostly). But in the case of orbital motions we have gravitational force that gives us some restrictions of movement(Kepler laws,for example).

What I am saying is that there will be no planets if there was no initial angular momentum in the primordial solar nebula. If a nebula with absolutely no rotation collapses, then there will only be a central non-rotating star and there will not be any planets. Planets form out of a protostellar disk, which itself forms only because of the initial angular momentum of the cloud. The dynamics of a rotating body is of course controlled by forces like gravity. Kepler's laws are a direct consequence of gravity.

Are there some laws also in the case of rotations?

The only thing that has to be kept in mind in rotation is that it results in a centrifugal acceleration that points radially from the center of motion. Hence, there has to be some force that conteracts this acceleration otherwise the body will fly away (in case of orbital motion) or will disintegrate (in case of spinning). In the case of orbital motion, the counteracting force is gravity gravity causes the body to continually fall towards the center, and this exactly conteracts the force resulting from the centripetal acceleration. In the case of a spinning object, it is the self-adhesion of the body itself that keeps it together. This results in a limit for how fast an object can rotate and still keep itself together. If it rotates too fast, the outward acceleration felt by the elements in the body may be more than the force that keeps them bonded together, and if this happens, the body breaks up. Other than this, there is no real law concerning rotations. (Note that rotational motion involves conservation of angular momentum just like linear motion conserves linear momentum).

This page updated on July 18, 2015.

About the Author

Jagadheep D. Pandian

Jagadheep built a new receiver for the Arecibo radio telescope that works between 6 and 8 GHz. He studies 6.7 GHz methanol masers in our Galaxy. These masers occur at sites where massive stars are being born. He got his Ph.D from Cornell in January 2007 and was a postdoctoral fellow at the Max Planck Insitute for Radio Astronomy in Germany. After that, he worked at the Institute for Astronomy at the University of Hawaii as the Submillimeter Postdoctoral Fellow. Jagadheep is currently at the Indian Institute of Space Scence and Technology.

Rotating Gas in a Quasar’s Heart

By: Camille M. Carlisle January 7, 2019 0

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Astronomers have “imaged” gas as it orbits a supermassive black hole some 2 billion light-years away.

This Hubble image shows the ancient and brilliant quasar 3C 273, which resides in a giant elliptical galaxy in the constellation of Virgo. It was the first quasar ever to be identified. The cloudy streak to the left is a jet shot out by the central black hole and extends some 200,000 light-years.
ESA / Hubble & NASA

In the last few months, astronomers working with the Gravity instrument on the Very Large Telescope Interferometer in Chile have released a series of impressive measurements. These results include preliminary data that show a long-sought gravitational effect on a star’s light as it passed the Milky Way’s central black hole. But the result I want to talk about here involves a much larger, more distant black hole, the 300-million-solar-mass leviathan that powers the brightest “nearby” quasar, 3C 273.

(I put nearby in quotation marks because this active galaxy in the constellation Virgo lies so far away that its light has taken some 2 billion years to reach us.)

Quasars essentially look like brilliant dots in the sky. They are galaxy cores that blaze brightly due to the hot gas their supermassive black holes chow down on and burp out as gigantic plasma jets. But thanks to an inventive approach by the Gravity Collaboration, 3C 273’s pinprick is now transformed into a map of gas moving right around the black hole, exploring a region we’ve heretofore only been able to probe indirectly with spectra and flickers of light.

Taking full advantage of the freedom that having a dedicated black holes blog gives me (wahahaha), I’d like to take you on a deep-dive into the Gravity Collaboration’s observations of the gas around 3C 273’s black hole to explain the unique approach this work involved.

Shifting Images

Like other quasars, 3C 273 has a region of hot gas zooming around in the black hole’s vicinity that’s called the broad-line region. The name comes from the shape of the gas’s spectral lines, which are smeared out. In normal circumstances, a spectral line is a narrow thing — a single wavelength. But when the gas moves, the spectral line shifts: to longer, redder wavelengths if the gas is moving away from us, and to bluer, shorter wavelengths if the motion is toward us. This Doppler effect is the same reason that an ambulance siren cascades through the sound spectrum as it races past you.

If you could combine all the notes you hear as the ambulance passes, you would hear a broad, multi-note sound, with the central note being the siren’s actual or “rest” frequency. The same thing happens with moving gas, creating a broadened spectral line.

The amount of smearing tells us how fast the gas is moving. Gas orbiting close to a black hole can move faster around the beast than gas farther out, just as the inner planets of the solar system orbit the Sun at a faster clip than the outer ones do. Based on the smear, astronomers infer that the BLR is one of the closest regions to the black hole that we can detect.

Observers use the BLR as a diagnostic, indicating things like the black hole’s mass. But even though the BLR is central to quasar studies, astronomers don’t actually know what it looks like. Is it the inner part of a disk around the black hole? Is it a halo of whizzing clouds?

Previous studies have tackled this question by inferring the gas’s motion and size from spectral patterns or the travel time of light echoes across the region. Reporting in the November 29th Nature, the Gravity Collaboration has now taken a completely different approach to studying the BLR, using blurry images of the gas itself.

A view of the four 8.2-meter VLT Unit Telescopes at the Paranal Observatory in Chile.

The team paired up the VLT’s four scopes in six different ways. Each pair of telescopes is separated by a unique distance, and their combined data create an image with the same resolution you’d obtain using a telescope as wide as the scopes’ separation. Telescopes closer together see the big, broad-brush picture, while telescopes farther apart home in on finer detail.

But turbulence in the atmosphere wiggles the image a wee bit. Each telescope pair sees a slightly different shift in where the image’s center is, explains Gravity team member Jason Dexter (Max Planck Institute for Extraterrestrial Physics, Germany). The center’s location also changes depending on which wavelength the astronomers observe.

Instead of taking these shifts as confusion that needs to be overcome, the researchers have used the complexity in their favor. The key is that in the case of the BLR’s gas, each wavelength corresponds to a redshift or blueshift caused by the gas’s velocity. By measuring how the image shifts at a series of different wavelengths, the astronomers could see where in the image there was stuff going at the speed and in the direction that corresponds to that Doppler shift. So even though Gravity only sees a blurry image, by tracking how the center of that blur changes position from wavelength to wavelength, the team can reconstruct how the blurred-out gas is moving around the black hole.

Evidence of Rotation

This diagram shows the principle geometry of the broad-line region (BLR) of the quasar 3C 273. The individual clouds are distributed in a thick ring (green shaded area) and rotate around the central black hole. The astronomers on Earth view this system at a slight angle (i).
© GRAVITY Collaboration

This charting reveals that one side of the BLR glow is moving toward us, the other away, just as you’d expect if the gas is rotating. The pattern matches what you might see if the gas inhabits a puffed-up disk, with clouds orbiting at a range of inclinations to our line of sight. Furthermore, the gas is rotating around the axis drawn by the black hole’s powerful jet, which is exactly what should happen if the gas is rotating around the black hole.

No one’s been able to clearly show this toward-and-away motion in the BLR’s spectra before. It’s been one of the great mysteries of this gas, Dexter says: Before, astronomers could only see a “featureless lump,” a big, fat emission line with no clear pattern in the gas’s motion. Gravity’s data prove the gas is indeed rotating.

Now that they can see (if only vaguely) the structure, researchers can estimate how big the BLR is. The size, about 145 light-days, is within the range of previous estimates but on the small side.

Details aside, here’s the takeaway: We’re actually watching gas orbit a gargantuan black hole more than a billion light-years from Earth.

Why does this feat matter? The BLR enables astronomers to study what happens near supermassive black holes. The better we understand the gas’s motion and the size of the region it moves through, the better we’ll understand how these black holes feed and how they power quasars.

Nature in the Balance

Throughout human history the same side of the moon has faced the earth. This is because the moon’s orbital speed and rotational speed are precisely matched so that as the moon orbits, the same side always faces towards the earth. If you know a lot about gravity this makes sense. The earth’s tidal forces make bulges in the moon. The moon’s rotation causes these bulges to be off center, and the earth’s gravity provided enough torque on the bulges to slow the moon’s rotation until it matched the speed of its orbit. To ancient people, who didn’t know a lot about gravity, this balance would have seemed like an unlikely coincidence, and it may have hindered their understanding of astronomy.

Phenomena like the near side of the moon abound in nature. In circular orbits the centrifugal force due to momentum is exactly balanced by the centripetal force of gravity. For elliptical orbits, like the moon, these forces are not matched exactly, but the imbalance cancels out with each orbital rotation, so the moon can continue in its seemingly unending procession. No doubt this cancellation is why it took until the 1680s for Newton to connect gravity with the moon.

Balance is not limited to astronomy. Electric charge plays a vital role in chemistry. The electric charge of a proton is exactly cancelled out by the charge of an electron, and molecules have exactly the same number of protons and electrons, masking the importance of properties to early chemists. Similarly the strong nuclear force was concealed for years, because quarks come in six different “colors,” but quarks never exist alone and these particles always add up to a colorless combination (the charges were named so that their combinations would be analogous to the way that combining red, blue and green light appears as white light).

In hindsight, the balance in some systems seems obvious. It wasn’t until 1628 that William Harvey realized that blood flow in the arteries is balanced with blood flow in the veins, and that blood circulates around our bodies.

So how does this apply to modern science? Today there is no greater mystery than the phenomena that are attributed to dark matter — phenomena that have resisted explanation for over 85 years. During this time many scientists have tried to explain dark matter. Some have tried using an unknown kind of particle, including WIMPs or axions. Some have proposed an unanticipated feature of gravity, like MOND. Others have proposed that we’ve missed larger objects, like primordial black holes or MaCHOs.

All of these theories are united in that they propose that there’s just one thing we’ve missed. “If only we knew about this one thing,” these theories seem to say, “that would explain everything.” If history is a guide, it’s unlikely that we’re wrong about just one thing. It’s much more likely that there is an unseen balance of nature that obscures the truth.

I proposed a theory to explain the dark matter phenomena, the entropy scale factor, that uses balanced changes to the scale of space and time. These balanced changes work to increase the effects of my theory on phenomena like galaxy rotation, while at the same time minimizing many effects used to test general relativity. I’m looking for collaborators to help with the calculations needed to test this theory. If interested, please email me at [email protected]

More work will need to be done before we can tell if the entropy dependent scale factor is a useful theory of nature. But if I had to bet, I’d say that we’re not wrong about one thing with dark matter, we’re wrong about two things, and they’re balanced.