Interstellar

A black hole Pokémon

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The world is currently going mad for Pokémon Go, so it seems like the perfect time to answer the most burning of scientific questions: what would a black hole Pokémon be like?

Black hole Pokémon

Type: Dark/Ghost

Black holes are, well, black. Their gravity is so strong that if you get close enough, nothing, not even light, can escape. I think that’s about as dark as you can get!

After picking Dark as a primary type, I thought Ghost was a good secondary type, since black holes could be thought of as the remains of dead stars. This also fit well with black holes not really being made of anything—they are just warped spacetime—and so are ethereal in nature. Of course, black holes’ properties are grounded in general relativity and not the supernatural.

In the games, having a secondary type has another advantage: Dark types are weak against Fighting types. In reality, punching or kicking a black hole is a Bad Idea™: it will not damage the black hole, but will certainly cause you some difficulties. However, Ghost types are unaffected by Fighting-type moves, so our black hole Pokémon doesn’t have to worry about them.

Height: 0’04″/0.1 m

Real astrophysical black holes are probably a bit too big for Pokémon games.  The smallest Pokémon are currently the electric bug Joltik and fairy Flabébé, so I’ve made our black hole Pokémon the same size as these. It should comfortably fit inside a Pokéball.

Measuring the size of a black hole is actually rather tricky, since they curve spacetime. When talking about the size of a black hole, we normally think in terms of the Schwarzschild radius. Named after Karl Schwarzschild, who first calculated the spacetime of a black hole (although he didn’t realise that at the time), the Schwarzschild radius correspond to the event horizon (the point of no return) of a non-spinning black hole. It’s rather tricky to measure the distance to the centre of a black hole, so really the Schwarzschild radius gives an idea of the circumference (the distance around the edge) of the event horizon: this is 2π times the Schwarschild radius. We’ll take the height to really mean twice the Schwarzschild radius (which would be the Schwarzschild diameter, if that were actually a thing).

Weight: 7.5 × 1025 lbs/3.4 × 1025 kg

Although we made our black hole pocket-sized, it is monstrously heavy. The mass is for a black hole of the size we picked, and it is about 6 times that of the Earth. That’s still quite small for a black hole (it’s 3.6 million times less massive than the black hole that formed from GW150914’s coalescence). With this mass, our Pokémon would have a significant effect on the tides as it would quickly suck in the Earth’s oceans. Still, Pokémon doesn’t need to be too realistic.

Our black hole Pokémon would be by far the heaviest Pokémon, despite being one of the smallest. The heaviest Pokémon currently is the continent Pokémon Primal Groudon. This is 2,204.4 lbs/999.7 kg, so about 34,000,000,000,000,000,000,000 times lighter.

Within the games, having such a large weight would make our black hole Pokémon vulnerable to Grass Knot, a move which trips a Pokémon. The heavier the Pokémon, the more it is hurt by the falling over, so the more damage Grass Knot does. In the case of our Pokémon, when it trips it’s not so much that it hits the ground, but that the Earth hits it, so I think it’s fair that this hurts.

Gender: Unknown

Black holes are beautifully simple, they are described just by their mass, spin and electric charge. There’s no other information you can learn about them, so I don’t think there’s any way to give them a gender. I think this is rather fitting as the sun-like Solrock is also genderless, and it seems right that stars and black holes share this.

Ability: Sticky Hold
Hidden ability: Soundproof

Sticky Hold prevents a Pokémon’s item from being taken. (I’d expect wild black hole Pokémon to be sometimes found holding Stardust, from stars they have consumed). Due to their strong gravity, it is difficult to remove an object that is orbiting a black hole—a common misconception is that it is impossible to escape the pull of a black hole, this is only true if you cross the event horizon (if you replaced the Sun with a black hole of the same mass, the Earth would happily continue on its orbit as if nothing had happened).

Soundproof is an ability that protects Pokémon from sound-based moves. I picked it as a reference to sonic (or acoustic) black holes. These are black hole analogues—systems which mimic some of the properties of black holes. A sonic black hole can be made in a fluid which flows faster than its speed of sound. When this happens, sound can no longer escape this rapidly flowing region (it just gets swept away), just like light can’t escape from the event horizon or a regular black hole.

Sonic black holes are fun, because you can make them in the lab. You can them use them to study the properties of black holes—there is much excitement about possibly observing the equivalent of Hawking radiation. Predicted by Stephen Hawking (as you might guess), Hawking radiation is emitted by black holes, and could cause them to evaporate away (if they didn’t absorb more than they emit). Hawking radiation has never been observed from proper black holes, as it is very weak. However, finding the equivalent for sonic black holes might be enough to get Hawking his Nobel Prize…

Moves:

Start — Gravity
Start — Crunch

The starting two moves are straightforward. Gravity is the force which governs black holes; it is gravity which pulls material in and causes the collapse  of stars. I think Crunch neatly captures the idea of material being squeezed down by intense gravity.

Level 16 — Vacuum Wave

Vacuum Wave sounds like a good description of a gravitational wave: it is a ripple in spacetime. Black holes (at least when in a binary) are great sources of gravitational waves (as GW150914 and GW151226 have shown), so this seems like a sensible move for our Pokémon to learn—although I may be biased. Why at level 16? Because Einstein first predicted gravitational waves from his theory of general relativity in 1916.

Level 18 — Discharge

Black holes can have an electric charge, so our Pokémon should learn an Electric-type move. Charged black holes can have some weird properties. We don’t normally worry about charged black holes for two reasons. First, charged black holes are difficult to make: stuff is usually neutral overall, you don’t get a lot of similarly charged material in one place that can collapse down, and even if you did, it would quickly attract the opposite charge to neutralise itself. Second, if you did manage to make a charged black hole, it would quickly lose its charge: the strong electric and magnetic fields about the black hole would lead to the creation of charged particles that would neutralise the black hole. Discharge seems like a good move to describe this process.

Why level 18? The mathematical description of charged black holes was worked out by Hans Reissner and Gunnar Nordström, the second paper was published in 1918.

Level 19 —Light Screen

In general relativity, gravity bends spacetime. It is this warping that causes objects to move along curved paths (like the Earth orbiting the Sun). Light is affected in the same way and gets deflected by gravity, which is called gravitational lensing. This was the first experimental test of general relativity. In 1919, Arthur Eddington led an expedition to measure the deflection of light around the Sun during a solar eclipse.

Black holes, having strong gravity, can strongly lens light. The graphics from the movie Interstellar illustrate this beautifully. Below you can see how the image of the disc orbiting the black hole is distorted. The back of the disc is visible above and below the black hole! If you look closely, you can also see a bright circle inside the disc, close to the black hole’s event horizon. This is known as the light ring. It is where the path of light gets so bent, that it can orbit around and around the black hole many times. This sounds like a Light Screen to me.

Black hole and light bending

Light-bending around the black hole Gargantua in Interstellar. The graphics use proper simulations of black holes, but they did fudge a couple of details to make it look extra pretty. Credit: Warner Bros./Double Negative.

Level 29 — Dark Void
Level 36 — Hyperspace Hole
Level 62 — Shadow Ball

These are three moves which with the most black hole-like names. Dark Void might be “black hole” after a couple of goes through Google Translate. Hyperspace Hole might be a good name for one of the higher dimensional black holes theoreticians like to play around with. (I mean, they like to play with the equations, not actually the black holes, as you’d need more than a pair of safety mittens for that). Shadow Ball captures the idea that a black hole is a three-dimensional volume of space, not just a plug-hole for the Universe. Non-rotating black holes are spherical (rotating ones bulge out at the middle, as I guess many of us do), so “ball” fits well, but they aren’t actually the shadow of anything, so it falls apart there.

I’ve picked the levels to be the masses of the two black holes which inspiralled together to produce GW150914, measured in units of the Sun’s mass, and the mass of the black hole that resulted from their merger. There’s some uncertainty on these measurements, so it would be OK if the moves were learnt a few levels either way.

Level 63 — Whirlpool
Level 63 — Rapid Spin

When gas falls into a black hole, it often spirals around and forms into an accretion disc. You can see an artistic representation of one in the image from Instellar above. The gas swirls around like water going down the drain, making Whirlpool and apt move. As it orbits, the gas closer to the black hole is moving quicker than that further away. Different layers rub against each other, and, just like when you rub your hands together on a cold morning, they heat up. One of the ways we look for black holes is by spotting the X-rays emitted by these hot discs.

As the material spirals into a black hole, it spins it up. If a black hole swallows enough things that were all orbiting the same way, it can end up rotating extremely quickly. Therefore, I thought our black hole Pokémon should learn Rapid Spin as the same time as Whirlpool.

I picked level 63, as the solution for a rotating black hole was worked out by Roy Kerr in 1963. While Schwarzschild found the solution for a non-spinning black hole soon after Einstein worked out the details of general relativity in 1915, and the solution for a charged black hole came just after these, there’s a long gap before Kerr’s breakthrough. It was some quite cunning maths! (The solution for a rotating charged black hole was quickly worked out after this, in 1965).

Level 77 — Hyper Beam

Another cool thing about discs is that they could power jets. As gas sloshes around towards a black hole, magnetic fields can get tangled up. This leads to some of the material to be blasted outwards along the axis of the field. We’ve some immensely powerful jets of material, like the one below, and it’s difficult to imagine anything other than a black hole that could create such high energies! Important work on this was done by Roger Blandford and Roman Znajek in 1977, which is why I picked the level. Hyper Beam is no exaggeration in describing these jets.

Galaxy-scale radio jets

Jets from Centaurus A are bigger than the galaxy itself! This image is a composite of X-ray (blue), microwave (orange) and visible light. You can see the jets pushing out huge bubbles above and below the galaxy. We think the jets are powered by the galaxy’s central supermassive black hole. Credit: ESO/WFI/MPIfR/APEX/NASA/CXC/CfA/A.Weiss et al./R.Kraft et al.

After using Hyper Beam, a Pokémon must recharge for a turn. It’s an exhausting move. A similar thing may happen with black holes. If they accrete a lot of stuff, the radiation produced by the infalling material blasts away other gas and dust, cutting off the black hole’s supply of food. Black holes in the centres of galaxies may go through cycles of feeding, with discs forming, blowing away the surrounding material, and then a new disc forming once everything has settled down. This link between the black hole and its environment may explain why we see a trend between the size of supermassive black holes and the properties of their host galaxies.

Level 100 — Spacial Rend
Level 100 — Roar of Time

To finish off, since black holes are warped spacetime, a space move and a time move. Relativity say that space and time are two aspects of the same thing, so these need to be learnt together.

It’s rather tricky to imagine space and time being linked. Wibbly-wobbly, timey-wimey, spacey-wacey stuff gets quickly gets befuddling. If you imagine just two space dimension (forwards/backwards and left/right), then you can see how to change one to the other by just rotating. If you turn to face a different way, you can mix what was left to become forwards, or to become a bit of right and a bit of forwards. Black holes sort of do the same thing with space and time. Normally, we’re used to the fact that we a definitely travelling forwards in time, but if you stray beyond the event horizon of a black hole, you’re definitely travelling towards the centre of the black hole in the same inescapable way. Black holes are the masters when it comes to manipulating space and time.

There we have it, we can now sleep easy knowing what a black hole Pokémon would be like. Well almost, we still need to come up with a name. Something resembling a pun would be traditional. Suggestions are welcome. The next games in the series are Pokémon Sun and Pokémon Moon. Perhaps with this space theme Nintendo might consider a black hole Pokémon too?

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12 Astronomy Highlights of Christmas

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I regularly help out with Astronomy in the City here at the University. Our most recent event was a Christmas special, and we gave a talk on 12 festive highlights covering events past, present and future, somewhat biased towards our research interests. Here is our count-down again.

A Newton under an apple tree

Isaac Newton, arguably the greatest physicist of all time, was born on 25 December 1642. I expect he may have got many joint birthday–Christmas presents. Newton is most famous for his theory of gravity, which he allegedly thought up after being hit on the head by a falling apple. Realising that the same force could be responsible for mundane things like falling as for keeping celestial bodies such as the planets in their orbits, was a big leap (or fall?). Netwon’s theory of gravity is highly successful, it’s accurate enough to get us to the Moon (more on that later) and only breaks down for particularly strong gravitational fields. That’s when you need Einstein’s theory of general relativity.

The Dark Side of the Moon

Newton may have been a Pink Floyd fan, we may never know.

Newton also did much work on optics. He nearly blinded himself while prodding his eye to see how that would affect his sight. Even smart people do stupid things. Newton designed the first practical reflecting telescope. Modern astronomical telescopes are reflecting (using a mirror to focus light) rather than refracting (using a lens). The first telescope installed at the University’s Observatory was a Newtonian reflector.

Newton's reflecting telescope

Newton’s reflecting telescope, one of the treasures of the Royal Society. Newton was President of the Royal Society, as well as Master of the Royal Mint, Member of Parliament for University of Cambridge and Lucasian Professor of Mathematics. It’s surprising he had any time for alchemy.

2 clear nights

At Astronomy in the City, we have talks on the night sky and topics in astrophysics, a question and answer session, plus some fun activities after to accompany tea and biscuits. There’s also the chance to visit the Observatory and (if it’s clear) use the Astronomical Society’s telescopes. Since the British weather is so cooperative, we only had two clear observing nights from this year’s events (prior to the December one, which was clear).

If you had made one of the clear nights, you could have viewed the nebulae M78 and M42, or Neptune and its moons. Neptune, being one of the ice giants, is a good wintry subject for a Christmas talk. It’s pretty chilly, with the top of its atmosphere being −218 °C. You don’t have a white Christmas on Neptune though. It’s blue colouring is due to methane, which with ammonia (and good old water) makes up what astronomers call ices (I guess you should be suspicious of cocktails made by astronomers).

One of the most exciting views of the year was supernova 2014J, back in January. This was first spotted by students at University College London (it was cloudy here at the time). It’s located in nearby galaxy M82, and we got some pretty good views of it. You can see it out-shine its entire host galaxy. Supernovae are pretty bright!

BOOM!

Supernova 2014J in M82. Image from the University of Birmingham Observatory.

3 components of a cluster

Galaxy clusters are big. They are the largest gravitationally-bound objects in the Universe. They are one of astrophysical objects that we’re particularly interested in here at Birmingham, so they’ll pop up a few times in this post.

Galaxy clusters have three main components. Like trifles. Obviously there are the galaxies, which we can see because they are composed of stars. Around the galaxies there is lots of hot gas. This is tens of millions of degrees and we can spot it because it emits X-rays. Don’t put this in your trifles at home. The final component is dark matter, the mysterious custard of our trifle. We cannot directly see the dark matter (that’s why it’s dark), but we know its there because of the effects of its gravity. We can map out its location using gravitational lensing: the bending of light by gravity, one of the predictions of general relativity.

Different views of cluster Abell 209

Different views of cluster Abell 209. The bottom right is a familiar optical image. Above that is a smoothed map of infra-red luminosity (from old stars). The top left is a map of the total mass (mostly due to dark matter) as measured with gravitational lensing. The bottom left is a X-ray map of the hot intergalactic gas. Credit: Subaru/UKIRT/Chandra/University of Birmingham/Nordic Optical Telescope/University of Hawaii.

Measuring the dark matter is tricky, but some of the work done in Birmingham this year shows that is closely follows the infra-red emission. You can use the distribution of jelly in your trifle to estimate how much custard there should be. In the picture above of galaxy cluster Abell 209, you can see how similar the top two images are. Using the infra-red could be a handy way of estimating the amount of dark matter when you don’t have access to gravitational-lensing measurements.

4 km long laser arms

A highlight for next year: the first observing run of Advanced LIGO. Advanced LIGO is trying to make the first direct detection of gravitational waves. Gravitational waves are tiny stretches and squeezes in spacetime, to detect them you need to very carefully measure the distance between two points. This is where the 4 km arms come in: the Advanced LIGO detectors bounce lasers up and down their arms to measure the distance between the mirrors at the ends. The arms need to be as long as possible to make measuring the change in length as easy as possible. A typical change in length may be one part in 1021 (that is 1,000,000,000,000,000,000,000 or one sextillion… ). For comparison, that’s the same as measuring the distance between the Earth and the Sun to the diameter of a hydrogen atom or the distance from here to Alpha Centuri to the width of a human hair.

LIGO Livingston, Louisiana

Aerial shot of LIGO Livingston, Louisiana. Two arms come out from the central building, one goes up the middle of the picture, the other goes off to the left out of shot. I think this gives a fair indication of the scale of the detectors. In addition to the instruments in Livingston, there is another LIGO in Hanford, Washington.

Making such an precise instrument is tricky. At least twice as tricky as remembering the names of all seven of the dwarfs. We shouldn’t be Bashful about saying how difficult it is. We need to keep the mirrors extremely still, any little wibbles from earth tremors, nearby traffic, or passing clouds need to be filtered out. Lots of clever Docs have been working on cunning means of keeping the mirrors still and then precisely measuring their position with the lasers. Some of that work was done here in Birmingham, in particular some of the mirror suspension systems. We’ll be rather Grumpy if those don’t work. However, things seem to be going rather well. Getting the mirrors working isn’t as simple as pushing a big red button, so it takes a while. On the 3 December, which is when we gave this talk at Astronomy in the City, the second detector achieved its first full lock: lock is when the mirrors are correctly held stably in position. This made me Happy. Also rather Sleepy, as it was a late night.

Inspection of LIGO optical systems.

Team inspecting the optical systems at LIGO Livingston back at the start of 2014. (It’s a bit harder to detect the systems now, since they’re in a vacuum). You need to wear masks in case you are Sneezy, you’d feel rather Dopey if you ruined the mirrors by sneezing all over them. Credit: Michael Fyffe

5 (or more) planet-forming rings!

ALMA image of the planet-forming disc around HL Tau.

ALMA image of the young star HL Tau and its protoplanetary disc. The gaps in the disc indicate the formation of planets that sweep their orbits clear of dust and gas. Credit: ALMA, C. Brogan & B. Saxton

One of the most exciting discoveries of 2014 is this remarkable image of a planet-forming disc.There may be more than five planets, but it seemed like a shame not to fit this into our countdown here. The image is of the star HL Tauri. This is a young star, only a million years old (our Sun is about 4.6 billion years old). Remarkably, even at this young age, there seems to be indication of the formation of planets. The gaps are where planets have sucked up the dust, gas and loose change of the disc. This is the first time we’ve seen planet-formation in such detail, and matches predictions extremely well.

6 Frontier Fields

The six Frontier Fields are a group of six galaxy clusters that are being studied in unprecedented detail. They are being observing with three of NASA’s great observatories, the Hubble Space Telescope, the Spitzer Space Telescope (which observes in the infra-red) and the Chandra X-ray Observatory. These should allow us to measure all three components of the clusters (even the custard of the trifle). The clusters are all selected because the show strong gravitational lensing. This should give us excellent measurements of the mass of the clusters, and hence the distribution of dark matter.

Gravitational lensing by a galaxy cluster.

Gravitational lensing by a galaxy cluster. The mass of the galaxy cluster bends spacetime. Light travelling through this curved spacetime is bent, just like passing through a lens. The amount of bending depends upon the mass, so we can weigh galaxy clusters by measuring the lensing. Credit: NASA, ESA & L. Calcada.

7 months until New Horizons reaches Pluto

New Horizons is a planetary mission to Pluto (and beyond). Launched in January 2006, New Horizons has been travelling through the Solar System ever since. In 2007 it made a fly-by of Jupiter, taking some amazing pictures. It is now just 7 months from reaching Pluto. This will give us the first ever detailed look at Pluto and its moons. You’ll need to wrap up warm if you wanted to head there yourself. I hope that New Horizons packed some mittens. New Horizons will tell us about Pluto and other icy (yes, that’s astronomers’ definition of ice again) items in the Kuiper belt.

Full trajectory of New Horizons

Full trajectory of New Horizons, it’s come a long way! Credit: John Hopkins

New Horizons has been in hibernation for much of its flight. Who doesn’t like a good nap? New Horizons was woken up ahead of arriving at Pluto on 7 December. It got a special wake-up call from Russell Watson. I don’t think it has access to coffee though.

800 TB of data

This year’s Interstellar featured the most detailed simulations of the appearance of black holes. This involved a truly astounding amount of data. I’ve previously written about some of the science in Interstellar. I think it’s done a good at getting people interested in the topic of gravity. It’s scientific accuracy can be traced to the involvement of Kip Thorne, who has written a book on the film’s science (which might be a good Christmas present). Kip has done many things during his career, including being one of the pioneers of LIGO. After an exciting 2014 with the release of Interstellar, I’m sure he’s looking forward to 2015 and the first observations of Advanced LIGO too.

Black hole and light bending

Light-bending around the black hole Gargantua in Interstellar. This shows the accretion disc about the black hole, the disc seen above and below the hole are actually the top and bottom of the disc behind the black hole. This extreme light-bending is a consequence of the extremely curved spacetime close to the black hole. This light-bending is exactly the same as the gravitational-lensing done by galaxy clusters, except much stronger!

999 Kepler exoplanets

When we gave the talk on 3 December, Kepler had discovered 998 exoplanets. It’s now 999, which I think means we get all the bonus points! Kepler is still doing good science, despite some technical difficulties. Kepler has been hugely successful. We now know that planets (as well as forming in quite short times) are common, that they are pretty much everywhere. Possibly even down the back of the sofa. Some of the work done here in Birmingham has been to estimate just how common planets are. On average, stars similar to the Sun have around 4 planets with periods shorter than 3 years (and radii bigger than 20% of Earth’s). That’s quite a few planets! But, if Christopher Nolan wants to direct another reasonably accurate sci-fi, we need to know how many of those are Earth-like. We don’t have enough data to work out details of atmospheres, but just looking at how many planets have a radius and period about the same as Earth’s, it seems that about 4% of these stars have Earth-like planets.

Kepler-186, a system which has a planet on the edge of the habitable zone.

Kepler-186, the first system discovered with an Earth-sized planet on the edge of the habitable zone (where liquid water could exist), was discovered in 2014.

10 lunar orbits

A Christmas highlight from 1968. On December 21, Apollo 8 launched. This was the first manned mission to ever leave Earth orbit. On Christmas Eve, it entered into orbit about the Moon. It’s three-man crew of Frank Borman, James Lovell and William Anders were the first people ever to orbit a body other than the Earth. To date, only 24 men have ever done so. Of course, even fewer have actually walked on the Moon, perhaps we should go back? Jim Lovell was also on the ill-fated Apollo 13 mission (you may have seen the film), making him the only person to orbit the Moon on two separate occasions and never land. Apollo 8 was successful, it orbited the Moon 10 times, giving us the first ever peek at the dark side of the moon (not the Pink Floyd album). This was also the first viewing of an Earthrise. Their Christmas Eve broadcast was most watched TV broadcast at the time. After orbiting, Apollo 8 returned home, splashing down December 27. I’m guessing they had a good New Year’s celebration!

Earthrise

Earthrise taken by the crew of Apollo 8, Christmas Eve 1968. Credit: NASA

11 (10 ¾) years for Rosetta

This year we landed on a comet. Rosetta has received fair amount of press. It is an amazing feat, Rosetta was in space for almost 11 years before making its comet rendezvous. It’ll be doing lots of science form orbit, such as determining that comets are unlikely to have delivered water to Earth. Most of the excitement surrounded the landing of Philae on the surface of the comet. That didn’t go quite as planned, but still taught us quite a bit. Rosetta has been heralded as one of the science breakthroughs of 2014. We’ll have to see what 2015 brings.

Colour image of a comet

Colour image (yes, it’s grey) of 67P/Churyumov-Gerasimenko from Rosetta. Credit: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA

12 (or more) galaxies in a cluster

To finish up, back to galaxy clusters. Galaxy clusters grow by merging. We throw two trifles together to get a bigger one. As you might imagine, if you throw two triffles together, you don’t get a nice, neat trifle. The layers do tend to mix. For galaxy clusters, you can get layers separating out: dark matter passes freely through everything, so it isn’t affected by a collision. The gas, however, does feel the shock and ends up a turbulent mess. It has been suggested that turbulence caused by mergers could trigger star formation: you squeeze the gas and some of it collapses down into stars. However, recent observational work at Birmingham can’t find any evidence for this. We’ll have to see if this riddle gets unravelled in 2015.

The bullet cluster

The merging bullet cluster. A composite of an optical image (showing galaxies), an X-ray image (in red, showing the hot gas), and a map of the total mass (in blue, from gravitational lensing). Dark matter, making up most of the mass, has past straight through the collision without interacting. Credit: NASA/CXC/CfA/STScI/ESO/U.Arizona/M. Markevitch/D. Clowe

Interstellar—science and fiction

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Interstellar black hole

Planet and accretion disc orbiting Gargantua, the black hole in Interstellar. Visual effects produced by the cunning people of Double Negative.

Interstellar is the latest film from Christopher Nolan. After completing his work with the Dark Knight, it seems he has moved onto even darker material: black holes. I have been looking forward to the film for some time, but not because of Nolan’s involvement (even though I have enjoyed his previous work). The film is based upon the ideas of Kip Thorne, an eminent theoretical physicist. Kip literally wrote the book on general relativity. He was a pioneer of gravitational-wave science, and earlier versions of the script included the detection of gravitational waves (I’m sad that this has been removed). Here, I’ll briefly discuss the film, before going on to look at it’s science (there are some minor spoilers).

General relativity textbooks

My copies of Gravitation by Misner, Thorne & Wheeler, and General Theory of Relativity by Dirac. The difference in length might tell you something about the authors. MTW (as Gravitation is often called) is a useful textbook. It is so heavy that you can actually use it for experiments testing gravity.

Last week, my research group organised a meeting for our LIGO collaborators. We all got together in Birmingham to work on how we analyse gravitational-wave data. It was actually rather productive. We decided to celebrate the end of our meeting with a trip to see Interstellar. The consensus was that it was good. We were rather pleased by the amount of science in the film, undoubtedly due to Kip’s involvement (even if he doesn’t approve of everything)—we also liked how there was a robot called KIPP.

My favourite characters were, by far, the robots. They had more personality than any of the other characters: I was more concerned for their survival than for anyone else. (No-one was wearing red, but I thought it was quite obvious who was expendable). Michael Caine’s character is apparently based upon Kip—they do have similar beards.

The film is beautiful. Its visualisations have been much hyped (we’ll discuss these later). It shows an obvious debt to Kubrick’s 2001: A Space Odyssey. This is both for better and worse: mimicking the wonderful cinematography and the slow pacing. However, the conclusion lacks the mystery of 2001 or even the intelligence of Nolan’s earlier work Memento or Inception (both of which I would highly recommend).

I don’t want to say too much about the plot. I (unsurprisingly) approve of its pro-science perspective. There were some plot points that irked me. In particular, why on Earth (or off Earth) would a mission with the aim of continuing the human race only take one woman? Had no-one heard about putting all your eggs in one basket? Also, using Morse code to transmit complicated scientific data seems like a bad idea™. What if there were a typo? However, I did enjoy the action sequences and the few tense moments.

Why so scientific?

I expect that if you were after a proper film critique you’d be reading something else, so let’s discuss science. There is a lot of science in Interstellar, and I can’t go through it all, so I want to highlight a couple of pieces that I think are really cool.

Time is relative

An interesting story device is the idea that time is relative, and its passing depends upon where you are in gravitational field. This is entirely correct (and although time might flow at different apparent speeds, it never goes backwards). Imagine that you are tied to a length of extremely long and strong string, and lowered towards a black hole. (I wonder if that would make a good movie?) Let’s start off by considering a non-rotating black hole. The passage of time for you, relative to your friend with the other end of the string infinitely far away from the black hole, depends how close to the black hole you are. Times are related by

\displaystyle \Delta T_\mathrm{infinity} = \left(1 - \frac{2 G M}{c^2 r}\right)^{-1/2} \Delta T_\mathrm{string},

where M is the black hole’s mass, G is Newton’s gravitational constant, c is the speed of light, and r measures how far you are from (the centre of) the black hole (more on this in a moment). If you were to flash a light every \Delta T_\mathrm{string}, your friend at infinity would see them separated by time \Delta T_\mathrm{infinity}; it would be as if you were doing things in slow motion.

You might recognise 2GM/c^2 as the location of the event horizon: the point of no return from a black hole. At the event horizon, we would be dividing by zero in the equation above, time would appear to run infinitely slowly for you. This is rather curious, time continues to run fine for you, but watching from infinity you would fade to a complete stand-still.

Actually, you would also fade from view too. The frequency of light gets shifted by gravity. Light is a wave, it’s frequency is set by how fast it completes one cycle. The period of the wave gets stretched using the formula above. As you get closer to a black hole, light from you becomes more red (then infra-red, radio, etc.), and also becomes dimmer (as less energy arrives at your friend at infinity in a given time). You appear to fade to to black as you approach the event horizon. This stretching of light to lower frequencies is known as red-shifting (as red light has the lowest frequencies of the visible spectrum). I didn’t see much sign of it in Interstellar (we’ll see the effect it should have had below), although it has appeared in an episode of Stargate: SG-1 as a plot device.

The event horizon is also the point where the force on the string would become infinite. Your friend at infinity would only be able to pull you back up if they ate an infinite amount of spinach, and sadly there is not enough balsamic dressing to go around.

A technicality that is often brushed over is what the distance r actually measures. I said it tells you how how you are from the centre of the black hole, but it’s not as simple as dropping a tape measure in the see where the singularity is. In fact, we measure the distance differently. We instead measure the distance around the circumference of a circle, and divide this by 2\pi to calculate r. The further away we are, the bigger the circle, and so the larger r. If space were flat, this distance would be exactly the same as the distance to the middle, but when considering a black hole, we do not have flat space!

This time stretching due to gravity is a consequence of Einstein’s theory of general relativity. There is another similar effect in his theory of special relativity. If something travels past you with a speed v, then time is slowed according to

\displaystyle \Delta T_\mathrm{you} = \left(1 - \frac{v^2}{c^2}\right)^{-1/2} \Delta T_\mathrm{whizzing\:thing}.

If it were to travel closer and closer to the speed of light, the passage of time for it would slow to closer and closer to a standstill. This is just like crossing the event horizon.

Imagine that while you were sitting on the end of your string, a planet orbiting the black hole whizzed by. Someone of the planet flashes a torch every second (as they measure time), and when you see this, you flash your torch to your friend at infinity. The passage of time on the planet appears slowed to you because of the planet’s speed (using the special relativity formula above), and the passage of time for you appears slowed because of gravity to your friend at infinity. We can combine the two effects to work out the total difference in the apparent passage of time on the planet and at infinity. We need to know how fast the planet moves, but it’s not too difficult for a circular orbit, and after some algebra

\displaystyle \Delta T_\mathrm{infinity} = \left(1 - \frac{3 G M}{c^2 r}\right)^{-1/2} \Delta T_\mathrm{planet}.

In Interstellar, there is a planet where each hour corresponds the seven years at a distance. That is a difference of about 61000. We can get this with our formula if r \approx 3GM/c^2. Sadly, you can’t have a stable orbit inside r = 6GM/c^2, so there wouldn’t be a planet there. However, the film does say that the black hole is spinning. This does change things (you can orbit closer in), so it should work out. I’ve not done the calculations, but I might give it a go in the future.

Black holes

Interstellar does an excellent job of representing a black hole. Black holes are difficult to visualise, but the film correctly depicts them as three-dimensional: they are not a two-dimensional hole.

As nothing escapes from a black hole (and they don’t have a surface), they are dark, a shadow on the sky. However, we can see their effects. The image at the top shows a disc about the black hole. Material falling into a black hole often has some angular momentum: it doesn’t fall straight in, but goes off to the side and swirls about, exactly as water whirls around the plug-hole before falling in. This material swirling around is known as an accretion disc. In the disc, things closer to the black hole are orbiting faster (just as planets closer to the Sun orbit faster than those further away). Hence different parts of the disc rub against each other. This slows the inner layers (making them lose angular momentum so that they move inwards), and also heats the disc. Try rubbing your hands together for a few seconds, they soon warm up. In an accretion disc about a black hole, things can become so hot (millions of degrees) that they emits X-rays. You wouldn’t want to get close because of this radiation! Looking for these X-rays is one way of spotting black holes.

The video below shows a simulation from NASA of an accretion disc about a black hole. It’s not quite as fancy as the Interstellar one, but it’s pretty cool. You can see the X-rays being red-shifted and blue-shifted (the opposite of red-shifted, when radiation gets squashed to higher frequencies) as a consequence of their orbital motion (the Doppler effect), but I’m not sure if it shows gravitational red-shifting.

Black holes bend spacetime, so light gets bent as it travels close to them. The video above shows this. You can see the light ring towards the centre, from light that has wrapped around the black hole. You can also see this in Interstellar. I especially like how the ring is offset to one side. This is exactly what you should expect for a rotating black hole: you can get closer in when you’re moving with the rotation of the black hole, getting swept around like a plastic duck around a whirlpool. You can also see how the disc appears bent as light from the back of the disc (which has to travel around the black hole) gets curved.

Light-bending and redshifting of an accretion disc around a black hole.

Light-bending around a black hole. This is figure 15 from James, von Tunzelmann, Franklin & Thorne (2015). The top image shows an accretion disc as seen in Interstellar, but without the lens flare. The middle image also includes (Doppler and gravitational) red-shifting that changes the colour of the light. To make the colour changes clear, the brightness has been artificially kept constant. The bottom image also includes the changes in brightness that would come with red-shifting. The left side of the disc is moving towards us, so it is brighter and blue-shifted, the right side is moving away so it is red-shifted. You can see (or rather can’t) how red-shifting causes things to fade from view. This is what the black hole and accretion disc would actually look like, but it was thought too confusing for the actual film.

It’s not only light from the disc that gets distorted, but light from stars (and galaxies) behind the black hole. This is known as gravitational lensing. This is one way of spotting black holes without accretion discs: you watch a field of stars and if a black hole passes in front of one, it’s gravitational lensing will magnify the star. Spotting that change tells you something has passed between you and the star, working our its mass and size can tell you if it’s a black hole.

Looking at the shadow of a black hole (the region from which there is no light, which is surrounded by the innermost light ring) can tell you about the structure of spacetime close to the black hole. This could give you an idea of its mass and spin, or maybe even test if it matches the predictions of general relativity. We are hoping to do this for the massive black hole at the centre of our Galaxy and the massive black hole of the galaxy Messier 87 (M87). This will be done using the Event Horizon Telescope, an exciting project to use several telescopes together to make extremely accurate images.

Simulated Event Horizon Telescope image

False-colour image of what the Event Horizon Telescope could see when look at Sagittarius A* (Dexter et al. 2010). Red-shifting makes some part of the the disc appear brighter and other parts dimmer.

Interstellar is science fiction, it contains many elements of fantasy. However, it does much better than most on getting the details of the physics correct. I hope that it will inspire many to investigate the fact behind the fiction (there’s now a paper out in Classical & Quantum Gravity about the visualisation of the black hole, it comes with some interesting videos). If you’ve not seen the film yet, it’s worth a watch. I wonder if they could put the gravitational waves back in for an extended DVD version?

Score out of 5 solar masses: enough for a neutron star, possibly not enough for a black hole.

Update: The Event Horizon Telescope Team did it! They have an image of M87’s black hole. It compares nicely to predictions. I’m impressed (definitely cake-worthy). Science has taken another bite out of science fiction.

The Event Horizon Telescope's image of M87*

The shadow of a black hole reconstructed from the radio observations of the Event Horizon Telescope. The black hole lies at the center of M87, and is about 6.5 billion solar masses. Credit: Event Horizon Team