Category Archives: Astronomy

The Earth’s Shape and Size? You Can Measure it Yourself — Part 1

This week, I’ll describe how one can easily use the Jan 15th explosive volcanic eruption in Tonga to obtain strong evidence that the Earth’s a sphere and determine its circumference, using nothing more than simple arithmetic.   This illustration of scientific measurement is perfect for any science classroom, because it uses publicly accessible data, is straightforward enough for a 12-year-old to follow, and is meaningful to every human being.  Moreover, students can be set free to find their own data sets online, and yet all will get the same answer in the end.  It is my hope that science teachers worldwide will begin to include this exercise in their classrooms.

In this first post, I’ll explain how to verify that the Earth’s approximately a sphere. It’s not quite a proof yet, because there are loopholes to close; but before the end of the week the evidence will be conclusive.

Background

Fortunately, volcanic eruptions as powerfully explosive as Tambora (1815), or even Krakatoa (1883), are seen only a few times a millennium.  When they do occur, loss of life and destruction of homes and livelihoods can be immense.  The full human cost of the tremendous blast ten days ago, at a mostly underwater volcano in the Kingdom of Tonga, is still not fully known; some islands in the archipelago were completely swamped by large tsunami waves, and the toll in lives and houses is not yet clear. Meanwhile, many aspects of the explosion itself are still puzzling scientists. But these are not the stories for today.

The explosion created a (literally) deafening blast of sound, and a wave of pressure so powerful that it could easily be detected by weather stations around the globe, both those of professionals and those in the homes of ordinary people.  In fact, many stations detected the wave passage multiple times.  Not since the era of thermonuclear weapons tests, prior to the 1963 nuclear test ban treaty, have we (to my knowledge) observed such a crisply defined pressure wave from an explosion of this magnitude. (The explosion, probably a combination of water flashing to steam upon contacting rising magma, along with the release of gas dissolved in that magma, has been estimated as equivalent to at least 10 megatons of TNT, nearly a thousand times larger than the atomic bombs of World War II and comparable to the largest thermonuclear weapons ever tested.)  Back in the ’60s, ordinary people had no easy access to precise data from weather stations, and there were fewer stations around the world, too.  Because of today’s technology, this explosion, more than any prior, offers us a unique educational opportunity, a silver lining to this disaster that science teachers across the world should take advantage of.

The Method of Great Circles

How can you tell if the surface you live on is a sphere?  Easy, if it’s small enough, like the planet of the Little Prince.  You start from your home, and start walking in any direction you choose.  Just keep walking straight ahead; you will eventually come home again.  Let’s say it took you one hour.  Well, now that you’re home, pick another direction, and start walking straight ahead at the same steady pace until you again return home.  This second trip should also take you one hour.  Repeat as desired; every round trip, in every direction, should cover the same distance, and assuming your walking speed is always the same, it will take the same amount of time.

Each of these trips would be on a path called a “great circle”, which is a circle that divides a sphere into two equal halves; these are the longest circles that you can draw on a sphere, and they each have the same length — the circumference of the sphere. Here’s a drawing with three of them. Famous great circles on the Earth are the equator and all lines of longitude (but not lines of non-zero latitude, which don’t divide the world into equal halves.)

Of course, walking around the Earth would be impractical; not only would it take too long, the oceans would get in your way.  You could consider taking an airplane on a series of trips, starting from your home airport and traveling straight ahead until you came back home — but expense, politics and weather would interfere, and the technology for a non-stop round-trip tour isn’t in place.

What’s so useful about a blast wave, for this purpose, is that the wave takes all these great circle trips around the world, in all directions, simultaneously, at no cost to you — not to mention that it’s apolitical.  The wave spreads out in all directions, forming an expanding circle; that this was true for the Tonga explosion can be confirmed from pressure measurements, but can also be seen in the satellite images below, of water vapor around the Earth in the hours following the explosion.

Such a wave will continue to spread until its size is as large as the Earth’s circumference; then it shrinks down until it converges at a point exactly on the opposite side of the Earth from the volcano.   It then passes through itself and retraces its steps, beginning to grow again. Here’s a visualization, showing an entire round-trip, by @StefFun. Note that one round trip has four stages: expanding from the volcano, shrinking down to the opposite point, expanding again from that point, and shrinking down back the volcano’s location.  We can call the first half the “outbound” portion, and the second half the “returning” or “inbound” portion. This pattern repeats over and over until the wave has lost too much energy to be detectable any longer.

It might appear, from these animations, that the wave is going halfway round the Earth and then bouncing back. But in fact, the wave is passing through itself! What’s happening in this round trip is that each little part of the pressure wave is making its own great-circle loop of the Earth. All those great-circle trips happen simultaneously, giving the pattern seen above. And like a sedentary Little Prince, you can use that pattern to see if the Earth’s a sphere.

That’s the Theory. Is it True?

Everything that I’ve just described will be true under two assumptions:

  1. The Earth really is almost spherical.
  2. The shock wave really does travel at an almost constant speed in all directions.

These two assumptions can be tested, and if they are (approximately) true, they can be used to measure (approximately) the size of the Earth.  [Note: We’re actually also assuming the atmosphere is thin compared to the size of the Earth, so that the wave’s energy stays trapped in a relatively thin region above the ground.]

Here’s the logic.  If the Earth’s a sphere and the pressure wave’s a circle moving at constant speed v, then

  • each little section of the pressure wave travels around the Earth in a “great circle”, whose length is the circumference of the sphere C.
  • the “round-trip time”, which we’ll call “T”, is the same for every part of the pressure wave, as illustrated in the tweet above, with T = C / v .

From this behavior of the pressure wave, we obtain a prediction: no matter where you are located on the Earth relative to Tonga, the wave as it passes over you is on a round-the-Earth trip that will take a round-trip time T.  During that trip one bit of wave will pass you once during its outbound portion, and the opposite bit of wave, going the other direction, will pass you during its inbound portion; so you will see the wave twice each round trip.  Because all parts of the wave are moving at the same speed (by assumption) and all are traveling the same distance (by assumption), you should get the same value of T no matter where you live. If you can measure T, and you have fourteen friends in fourteen other countries who can also measure T in an analogous way, the fifteen of you should all get the same answer.

But how can we measure T, the round-trip time, while sitting at home?

Measuring the Round-Trip Time T

The volcano exploded at about 415 UTC on January 15th. (UTC is a 24 hour universal time which is used world-wide to avoid getting confused by time zones, but it corresponds to a time zone used by several nations in far western Europe and in west Africa.) Its pressure wave was strong enough to create sudden spikes and/or drops in the pressure each time the wave passed by (but let me just refer to this Fdisturbance as a “spike” for brevity.) These could be measured by barometers on the ground.  In many places, the wave was strong enough, the atmosphere calm enough, and the barometers precise enough that several spikes were seen.

Here’s an example from the Met Office in the United Kingdom, and one (with average pressure removed to make the spikes easier to see) from Iceland.

The UK’s Met office observed two disturbances in first two days hours following the Tonga Eruption. The timing of these spikes will be our focus.
Spikes obtained from pressure measurements in Iceland, with slow pressure variations removed to make the spikes clearer (credit Halldór Björnsson @halbjo via Prof. Evgenia Ilyinskaya @EIlyinskaya and volcanodiscovery.com)

Let’s imagine you yourself have a barometer which shows as many as four spikes.  Let’s call T1 the time between the volcano’s explosion and the appearance of first spike.  (I used different notation in my last and more detailed post: T1=t1-ts .) We’ll similarly define T2, T3, T4 for the second, third and fourth spike.  Then from these four time measurements, there are three independent methods you can use to measure T, and they should all give the same answer.

The key thing to remember, before interpreting these disturbances, is that the pressure wave passes you twice on each of its round trips, and so you see the pressure spike twice per round trip.  (Remember each round trip involves four stages, two of them the expansion and contraction of the outbound portion, and two of them the expansion and contraction of the inbound portion.  You may want to look at the tweet above if you need a reminder.)  

What that means is that spike 1 is caused by the shockwave when it is outbound on its first round trip, and spike 3 is caused when it is outbound on its second round trip, so they are separated by the round-trip time.  In other words

  • T3 – T1 = T

Similarly, spikes 2 and 4 are caused by the shockwave when it is inbound on its first and second round trips, so they too are separated by the round-trip time.

  • T4 – T2 = T

Now the last way to measure T is slightly more subtle, although the answer’s very simple. It turns that

  • T1 + T2 = T

Why is this true? It is visualized in the Figure below  The key is that the speed v (which we don’t know yet) is constant. The bit of the wave that headed from the volcano towards you took a time T1 to reach you, during which the wave covered a distance D1 = T1 v. (Remember T1 is the time that elapsed from the volcanic explosion until your observations of the first spike.) But the second spike was caused by the bit of wave that started in the opposite direction, heading away from you; it reached you after going the long way around the Earth.  This required a time T2, and during that time the wave covered a distance D2 = T2 v.  But as you can see from the figure, D1 + D2 is the entire circumference C of the Earth! So if T1 is the time it takes to travel a distance D1 , and T2 is the time it takes to travel a distance D2, then their sum must be the time it takes to travel the distance C — and that, by definition, is the round trip time T.

From the volcano at bottom left to the observer at right, there are two paths that one can take on a great circle. The shorter one, of length D1 , can be covered at speed v in time T1 ; the longer, of length D2 can be covered at the same speed in time T2 . As the circumference of the great circle is D1 + D2, the time required to traverse it entirely is T1 + T2 .

So if you see four spikes, you get three ways to measure T that should all agree, as long as the shockwave moves at a constant speed and the line from the volcano to you forms a part of a great circle.  If you see three spikes you get two measurements, but even with just two spikes — no simple repeats — you still get one measurement of T.

But if the Earth’s a sphere and the wave’s speed is constant, then everyone around the world should agree on the measurement of T, even though each of us will measure a different T1, T2, T3, T4 depending on where we live.  If all our measurements of T are the same, then the assumptions we started with — that the eruption caused a circular shock wave of constant speed that moved around a spherical Earth — are consistent with the data. If they are slightly off, then our assumptions are only approximately true, but close enough to give us roughly the right idea.

Let’s grab some data from around the world and see what we get.

Data and Measurement

I obtained data from a variety of places, and did my own estimates of the spike arrival times (which can be done to within an accuracy of 30 to 90 minutes, typically). I then converted those to the time elapsed since the volcanic explosion, being careful to account for time zones and convert to UTC. In some cases I could only determine T1 and T2, but sometimes I could get T3 or even T4 . Then, I computed as many estimates of the round-trip time T that I could obtain with the two, three or four spikes from each location. All this information is given in the table below. You are encouraged to find other sources of data and try this yourself.

LocationT1T2T3T4T1 + T2T3T1T4T2
Iceland131523004915590035hr 15min36hr 00min36hr 00min
Beijing09102635452035hr 45min36hr 10min
Netherlands150021305015561536hr 30min35hr 15min34hr 45min
Hawaii, USA044531153945674536hr 00min35hr 00min36hr 30min
New Jersey, USA1115243535hr 40min
Switzerland1545210036hr 45min
Seattle, USA083027454415634536hr 15min35hr 45min36hr 00min
Southern Chile0845280536hr 50min
Miami10152530451535hr 45min35hr 00min

Remarkably, from these places that lie in wildly different directions and distances from Tonga, all of the values of T that I obtained fall between 34 3/4 hours and 36 3/4 hours, a variation of less than 10%. (I couldn’t find data from Australia, New Zealand or Southern Africa that showed multiple spikes; do you know of any?) My time measurements were often ambiguous at the 5% level, because the pressure wave often consisted of multiple spikes and dips, so just from my measurement uncertainty one would expect to see several percent variation in these values of T.

The close agreement among the values of T then implies that both of our starting assumptions — that the Earth is spherical and that the pressure wave traveled with a constant speed — are consistent with data, to better than 10%.

About the assumptions: Of course I know, from other data, that the Earth is spherical to within 2% — it is slightly squashed, so that a great circle of longitude is 2% shorter than the length of the equator. So I knew beforehand that the first assumption would be okay to 2%. But given that the speed of waves can vary with temperature and perhaps other atmospheric effects, it wasn’t obvious that the second assumption would work out. Since the numbers all agree, apparently it was more or less correct too.

Is The Earth a Sphere? Mmm… We’re Not Quite Done

So there you have it.  Within less than 10%, our assumptions of a roughly spherical Earth and a roughly circular pressure wave of roughly constant speed are consistent with data.

Is this a complete proof of a near-spherical Earth?  Nope. We’re close, but there are still loopholes.  For example, suppose the Earth looked like an ellipsoid, with the volcano placed exactly at one end. We’d all still find equal values of T. Can you see why?

If the Earth were shaped like an ellipsoid, and the Tonga volcano were exactly at one end, the measurement we just performed would also have given a universal value for the round-trip time. (Image produced with Mathematica 11.3).

There’s even a flat-earth hypothesis that we haven’t quite excluded yet! Can you identify which one? (It would easily be ruled out for other reasons, but not from this data alone.)

In the next two posts I’ll show you how to identify the origin of the loophole, and then close it for good. And after that, we’ll measure the circumference of the Earth.

(to be continued)

Geometry From Within: Evidence for a Round Earth

It’s a lot easier to map the Earth than it used to be.  Before satellites, you had to do many careful measurements of distances and directions, at many different locations around the world, and combine them all to build a picture of a world you couldn’t see.  That’s part of why maps and globes made in past centuries had so many inaccuracies and distortions; it was a tough business.  

How that changed in the 1960s!   The first full photograph of the Earth that I’m aware of was made in 1967 by the ATS-3 satellite (were there earlier ones?)  So much simpler… the whole planet laid out in front of you.  You just need a few photographs like this, and the era of measuring from one point on the ground to another is mostly over.

But the challenge of trying to measure things when you’re stuck within them, and can’t step outside them, hasn’t gone away.  Just as we could see in telescopes that the Moon and Mars are ball-shaped, long before we could observe the Earth itself, today we can see other galaxies in great detail, but we still struggle to build a complete picture of our own, the Milky Way. The Gaia satellite is trying hard.

To determine the Earth’s two-dimensional surface is really round took some clever thinking. Aristotle, in ancient Greek times, noted that the Earth’s shadow on the Moon during a lunar eclipse is always curved in the same way — it doesn’t matter what time of day or year the eclipse occurs, or whether the shadow is on the north, east, west or south side of the Moon.  This feature is to be expected if the Earth’s a ball, like the Moon and Sun, and very difficult to explain otherwise.  [Try to figure out what you might see if it were cylinder-shaped!]

But there are other tricks you can use if you have a hunch that the place you live on, or in, is of finite size.

One Dimension: the Possibly Circular Canal

Suppose you live on the banks of a canal, a long thin channel extending off to the horizon, like a river without any flow.  And suppose you suspect that this canal forms a loop, surrounding a large island.  How could you check?   Well, if you had a boat, you could row yourself down the canal; or you could walk along the shore. If the canal is really in the shape of a loop, you’ll eventually come back to your starting point.  But maybe you’re worried such a journey would be too long, difficult, risky, expensive. Do you have other options?  

Here’s one: suppose you could make a big wave moving in the clockwise direction around the canal.  The wave, unlike you, wouldn’t need any food and drink or fuel for the journey — so time and money would not be a problem. The wave would move down the canal at a definite speed [I’m assuming here that it maintains its height], and if the canal were really a loop, then after some time T you’d see the wave return, still moving clockwise, and pass by you.  If you waited the same amount of time T again, you’d see the same wave a second time, again clockwise.  After the same amount of time T, you’d see it a third time. 

If instead the canal were a finite strip, then the wave would reflect off the end, and so the wave would return from the opposite direction. If it were infinite in length, it would never return. And if it had a complicated shape — perhaps a P or an R or a B instead of an O — you would get multiple waves in a complex pattern. But the simple pattern in which the waves return again and again, from the same direction, after a time T, is consistent with the canal being a simple loop.

You could try sending a wave counterclockwise too, and you’d expect the same pattern if the canal’s a loop.

As the wave passes you, you can also estimate its speed v. Having also measured T, you can now determine the length L of the canal. It’s the wave speed times the time T for the wave to go round once:

  • L = v T
Figure 1: You live on the shore of a canal, which you suspect is circular. You could find out how big it is by sending a large wave in either direction, and measuring the time T that it takes to return.

Perhaps making such a wave is too difficult for you, but if you’re lucky, someone or something down the canal may make a giant splash. Then you’ll see the ripples from the splash come by in a similar pattern. Now waves will travel both counterclockwise and clockwise around the canal, and they probably won’t arrive at the same time. That doesn’t matter, though. You’ll see the clockwise waves repeat after a time T, and you’ll see the same for the counterclockwise waves. Seeing both of them repeat after the same time T will give you confidence that the canal’s really a simple loop

To be specific, let’s call t1 the time you measure the first wave, t2 the second wave, t3 the third, t4 the fourth, and so on; if the first wave is counterclockwise, then the second is clockwise (see Figure 2), the third counterclockwise, and so on. (This won’t be true if instead of a loop the canal is in the form of a line segment! A reflection off the end could make the first two waves come from the same direction.) As the clockwise waves will repeat after a time T, and the same for the counterclockwise waves, it will be the case, if the canal’s a loop, that

  • t3 – t1 = t4 – t2 = T
  • L = v T

There’s more; if you know the time ts when the splash happened and you know the wave speed, then you can learn how far away the splash was from you:

  • D = v ( t1 – ts )

But even if you don’t know what time the splash happened, you can figure it out; see Figure 2. The distance traveled by the counterclockwise wave to get to you, plus the distance traveled by the clockwise wave to do the same, equals the full distance round the circle (Figure 2), so the time that the counterclockwise wave required to reach you ( t1 – ts ) plus the corresponding time for the clockwise wave ( t2 – ts ) must be equal to T.

  • T = ( t1 – ts ) + ( t2 – ts ) = t1 + t2 – 2ts , which implies ts = 1/2 (t1 + t2 – T)

If you look closely at these four bold-faced equations, they tell you that you can determine T, L, D and ts , properties of the loop and the splash, if you know t1, t2 and t3 and v, which are all things that you can measure without going anywhere. From this point of view t4 is a bonus, a nice check that things are working as expected.

Even better, if you have a friend down the canal who makes the same measurements, that friend won’t get the same answers for t1, t2, t3 and t4 ; the waves arrive at different times for your friend than for you. But when you obtain T and L and ts from the waves you see, and your friend does the same, you’d better get the same answer — because these are properties of the loop and splash, and don’t care where either you or your friend is located.

Figure 2: A large splash occurs at time ts, and waves travel both counterclockwise (green), in which case they reach you at time t1, and clockwise (red), reaching you at time t2.

By themselves, these equations do not prove the canal is round, though they are consistent with it. They only tell you that it’s a loop of length L, with no kinks which could cause extra reflections. Still, it’s a lot of information for a very low price, without taking a boat around the loop, walking all around it, or sending up a drone to take a photograph. The waves have done all the work for you.

Figure 3: After the counterclockwise wave passes you at time t1, it continues round the canal, and passes you again at time t3 = t1 + T.

Two Dimensions: the Possibly Round Surface of the Earth

What would be different if you lived on a sphere?  (A subtlety of language: by “sphere,” I do not mean “ball”, which is three-dimensional; I mean the surface of the ball, which is two-dimensional.  In this terminology, the Earth is a ball, while its surface is a sphere, approximately.)  Again, of course, you always have the option of traveling round the sphere yourself and exploring it, checking that no matter what direction you go in, if you walk in a perfectly straight line, you will always come back to your starting point after you travel the circumference of the sphere.  But that’s expensive and time-consuming and not very practical.  What other options do you have?

You could wait for a big splash in the atmosphere — a natural one like a volcanic eruption, or an artificial one of similar size (fortunately now forbidden by nuclear testing treaties).   This opportunity, if you want to call it that, came this past week, unfortunately near an inhabited area and at the ocean’s surface within the Kingdom of Tonga, with ensuing loss of life, as well as the destruction of crops and homes; the resulting tsunami even took lives far across the Pacific ocean.  It’s not an experiment we would happily have chosen. But nature has carried it out without asking us; we may as well learn what we can from it.

When water hits hot magma and turns to steam, there’s an immense release of energy, especially if the magma is itself packed with compressed gasses. This is partly why some of the largest explosions in the last two hundred years have occurred when volcanic islands self-destructed; Krakatoa is the most famous.  The latest estimate as of the time of writing is that the one in Tonga last week was overall perhaps only 1/20 times as powerful as Krakatoa, but its plume was enormous, and its shock waves were strong enough to be detected multiple times, in many places, as they traveled round and round the Earth.

The shock wave emanated from the explosion in all directions, moving outward as an ever expanding circle, as you can guess by pure reasoning but also as confirmed by satellite.  After traveling 1/4 of the way around the Earth, the wave front reached a maximum extent — the same size and shape as the equator, though with a different orientation — and then shrank again, converging to a point in Africa exactly halfway around the Earth from the explosion’s location. (A nice visualization of this, and of what I’ll say next, can be found here.) Then the shockwave continued onward, again expanding to the Earth’s full extent, and then shrinking and converging on the very spot where it was created in the first place.   And this process repeated, until the shock wave, gradually losing its energy, faded beyond the point of detectability.

This pattern of outward expansion, convergence to the opposite point, return-ward expansion, and convergence to the original point, means that the waves from the explosion passed every point on Earth multiple times, and did so first moving away from the explosion, then returning, then again moving away, and again returning, until finally they were too small to observe.  That this pattern was seen everywhere, in countries widely spread around the globe, by both professional and civilian weather stations, gives some qualitative evidence that the Earth’s a smooth object with a rounded surface of some type.  For example, here is the pattern of multiple waves crossing, returning, re-crossing and re-returning as measured by weather stations in China; we can see three wave passages clearly (the fourth is too dim to measure well).  And here is a similar pattern in the Netherlands; though it’s only at one location, and only the main shock wave is detected, the shock is seen six times. 

What’s nice is that for a sphere — and only for a sphere [see caveat below] — the equations I wrote earlier for a circular canal still hold, and importantly, they hold everywhere, and have to give the same circumnavigation time T and the same splash time ts. That’s because if you are on a sphere, motion away from the volcano (or indeed any point), in any direction, will take you on a circular path of length equal to the sphere’s circumference. On any other shape, this won’t be true.

[To be fair, I am making a couple of assumptions: for instance, that the volcano was located on a random, not special, point on the Earth. (For example, if the Earth’s surface was oblong instead of circular, then the two points at either end of the oblong are special.) To make a long story short, there are still loopholes to the argument I’m giving here, but they are only relevant if there are very special and unlikely coincidences. Additional volcanoes, would quickly close the loopholes.]

In particular, the equations I introduced earlier should hold in China, about 1/4 around the Earth from Tonga. And they should also hold in the Netherlands, much further from Tonga, in a quite different direction. If the Earth had an uneven shape, then the time to go round the Earth in the direction from Tonga to Beijing would be different from the time to go round it from Tonga to the Netherlands; you wouldn’t get the same T. And if the Earth had edges (as in the absurd flat-earth map), you would see reflection waves; you wouldn’t get the same T or the same ts, and the second big wave across China wouldn’t look like the original one retracing its steps (a fact which already gives qualitative evidence for a round Earth.)

Using publicly available data from anywhere in the world, including what I’ve shown you from China and from the Netherlands, we can check ourselves that the Earth’s a ball and measure its circumference. Let’s do it.

So as not to spoil the fun, I’m going to wait until after the weekend to post the results. You are all encouraged to gather your children together and to try to measure:

  • T, the time it took for the waves to travel around the Earth; do this both with the data from the Netherlands and that from China; do you get similar answers?
  • ts, the time when the eruption occurred; use both the data from the Netherlands and the data from China (make sure you’re using UTC time, so you don’t get confused by time zones). Do you get similar and roughly accurate answers? Is it close to the time reported in this article?
  • v, the speed of the waves, which you can determine by watching how long it takes them to cross a part of China and comparing that time with the distance of that path; caution, make sure you trace a path perpendicular to the wave front.
  • C = T v , the circumference of the Earth, equal to the time it took for the waves to circumnavigate the Earth times their speed. Can you get fairly close?

Caution: You’re not going to get exactly the precise scientifically-known answers, nor will your answers be perfectly consistent, because the data I’ve linked to was neither taken nor presented with scientific levels of precision. But you should be able to get within 10-20%, enough to convince you the Earth’s surface pretty darn close to a sphere. If you want more precision, I’m sure precision data is available (anybody have a good link?) [Also note that there are some extra waves seen in the China map, some of them reverberations from the original explosion, and some due to later, smaller explosions; they travel in the same directions as the original ones, showing they come from the same place. For our purpose here, just keep your focus on the biggest waves.]

The point is that we can learn the Earth is ball-shaped without ever stepping off the Earth, and in fact without even traveling; and we can even learn, from the timing, how big the Earth is.  All it takes is a natural explosion, measurements from a few places, some logic, and simple algebra.   The data is now publicly available, and every science teacher in the world ought to encourage their teenage students to do this exercise!  Not only does it confirm we live on a sphere, it shows that one needs neither a photograph taken from outer space, nor a flight around the world, nor specialized map-making skills, to obtain that proof.

Three Dimensions: The Universe

Now what about the universe as whole?  The Earth and Sun are carrying us along as they travel within a three-dimensional surface.  What is its shape?  How can we know?  [There is also the question of the four-dimensional surface that makes up the space and time of the universe.  I’m not addressing that here, that’s even more complex.]

A circle is a one-dimensional sphere; the surface of the Earth (not its interior) is a two-dimensional sphere. Could the universe be a three-dimensional sphere?   We can’t stand outside it to find out.  In fact it’s far from clear there is meaning to “outside” since, after all, it’s the universe, and might be everything there is. Nevertheless, we can imagine, at least, trying to do a similar experiment.  If there were a huge supernova explosion, or a tremendous flare from a distant black hole as it ripped apart a star, maybe we would see the light arrive from one side of us, and then later see it arrive from the other side, and yet again from the first direction, and so on.

Back before we knew the huge scale of the universe and the tiny speed of light, that might have seemed plausible.  We can’t hope to do anything like this, unfortunately.   But it’s not because the question makes no sense.  The natural Tonga volcano experiment worked thanks to the fact that it’s a small world (after all) and the speed of sound is relatively fast, so it all took less than a day or two.  In the universe, it’s the reverse; it’s a big place and the speed of light is relatively slow.  Our own galaxy, the Milky Way, is itself 100,000 light-years across [i.e. it’s so big that it takes 100,000 years for light, traveling at the fastest speed our universe allows, to cross it], so even if our galaxy were the entire cosmos, as was thought until the 1920s, it would take at least 100,000 years to do this experiment.  And of course we now know the universe is immensely larger than our own galaxy; indeed the most recent map of galaxies extends out, for the brightest galaxies, as far as 10,000,000,000 light years.  Hopeless.

Nevertheless, the possibility that the universe has an interesting shape, and though huge might be small enough that we could see some evidence of its shape, remains a topic of research.  The light from events in the distant past might give us clues.  While a blast wave isn’t something we’d be able to see from multiple perspectives, a long-lasting bright spot on the sky could potentially be seen reaching us from different paths around a complex universe.  The fact that the universe has been expanding over the billions of years since the Hot Big Bang began complicates the thinking, but also provides opportunities.

To give insight into how this could be done is beyond the scope of this blog post, but if you’re curious about it, you might try this long-form article from Quanta Magazine (a highly recommended source for interesting articles.)  

The Lesson for Humankind

The big lesson here: geometry can be learned from the inside.  You don’t need to be outside an object to map it and learn its shape and size. That this is possible explains how mapmakers knew the shapes of continents long before satellites, and how one can determine that the universe is expanding while remaining within it (though the story of how scientists did this, without using the methods described in this post, is for another day.) And if the object is finite, so that no wave can travel forever without eventually returning to you, then it’s possible to infer its shape just by learning how waves travel and bounce around the object. That’s how the depth of the ocean’s deepest point was recently measured, as I described in my last post; and that’s how children (of all ages) should prove for themselves, using publicly available data from last weekend and simple algebra, that the Earth is indeed round.

Mapping the Unknown, Times Three

I took a short break from other projects this weekend. Poking around, I found three particularly lovely science stories, which I thought some readers might enjoy as well. They all involve mapping, but the distances involved are amazingly different.

Starbirth Near to Home

The first one has been widely covered in the media (although a lot of the articles were confused as to what is new news and what is old news.) Our galaxy is full of stars, but also of gas (mainly hydrogen and helium) and dust (tiny grains of material made mainly from heavier elements forged in stars, such as silicon). That gas and dust, referred to as the “interstellar medium”, is by no means uniform; it is particularly thin in certain regions which are roughly in the shape of bubbles. These bubbles were presumably “blown” by the force of large stellar explosions, i.e. supernovas, whose blast waves cleared out the gas and dust nearby.

It’s been known for several decades that the Sun sits near the middle of such a bubble. The bubble and the Sun are moving relative to one another, so the Sun’s probably only been inside the bubble for a few million years; since we’re just passing through, it’s an accident that right now we’re near its center. Called simply the “Local Bubble”, it’s an irregularly shaped region where the density of gas and dust is 1% of its average across the galaxy. If you orient the galaxy in your mind so that its disk, where most of the stars lie, is horizontal, then the bubble stretches several hundred light-years across in the horizontal direction, and is elongated vertically. [For scale: a light-second is 186,000 miles or 300,000 km; the Sun is 8 light-minutes from Earth; the next-nearest star is 4 light-years away; and our Milky Way galaxy is about 100,000 light years across.] It’s been thought for some time that this bubble was created some ten to twenty million years ago by the explosion of one or more stars, probably siblings that were born close by in time and in space, and which at their deaths were hundreds of light-years from the Sun, far enough away to do no harm to Earthly life. [For scale: recall the Sun and Earth are about 5 billion years old.]

Meanwhile, it’s long been suggested that explosion debris from such supernovas can sweep up gas and dust like a snowplow, and that the compression of the gas can lead it to start forming stars. It’s a beautiful story; large stars live fast and hot, and die young, but perhaps as they expire they create the conditions for the next generation. [A star with 40 times the raw material as the Sun has will burn so hot that it will last only a million years, and most such stars die by explosion, unlike Sun-like stars.]

If this is true, then in the region near the Sun, most if not all the gas clouds where stars are currently forming should lie on the current edge of this bubble, and moreover, all relatively young stars, less than 10 million years old, should have formed on the past edge of the bubble. Unfortunately, this has been hard to prove, because measuring the locations, motions and ages of all the stars and clouds isn’t easy. But the extraordinary Gaia satellite has made this possible. Using Gaia’s data as well as other observations, a team of researchers (Catherine Zucker, Alyssa A. Goodman, João Alves, Shmuel Bialy, Michael Foley, Joshua S. Speagle, Josefa Groβschedl, Douglas P. Finkbeiner, Andreas Burkert, Diana Khimey & Cameren Swiggum) has claimed here that indeed the star-forming regions lying within a few hundred light-years of the Sun all lie on the Local Bubble’s surface, and that nearby stars younger than ten million years were born on the then-smaller shell of the expanding bubble. Moreover they claim that the bubble probably formed 14-15 million years ago, at a time when the Sun was about 500 light-years distant.

Continue reading

A Ring of Controversy Around a Black Hole Photo

[Note Added: Thanks to some great comments I’ve received, I’m continuing to add clarifying remarks to this post.  You’ll find them in green.]

It’s been a couple of months since the `photo’ (a false-color image created to show the intensity of radio waves, not visible light) of the black hole at the center of the galaxy M87, taken by the Event Horizon Telescope (EHT) collaboration, was made public. Before it was shown, I wrote an introductory post explaining what the ‘photo’ is and isn’t. There I cautioned readers that I thought it might be difficult to interpret the image, and controversies about it might erupt.EHTDiscoveryM87

So far, the claim that the image shows the vicinity of M87’s black hole (which I’ll call `M87bh’ for short) has not been challenged, and I’m not expecting it to be. But what and where exactly is the material that is emitting the radio waves and thus creating the glow in the image? And what exactly determines the size of the dark region at the center of the image? These have been problematic issues from the beginning, but discussion is starting to heat up. And it’s important: it has implications for the measurement of the black hole’s mass (which EHT claims is that of 6.5 billion Suns, with an uncertainty of about 15%), and for any attempt to estimate its rotation rate. Continue reading

A Non-Expert’s Guide to a Black Hole’s Silhouette

[Note added April 16: some minor improvements have been made to this article as my understanding has increased, specifically concerning the photon-sphere, which is the main region from which the radio waves are seen in the recently released image. See later blog posts for the image and its interpretation.]

[Note added June 14: significant misconceptions concerning the photon-sphere and shadow, as relevant to the black hole ‘photo’, dominated reporting in April, and I myself was also subject to them.  I have explained the origin of and correction to these misconceptions, which affect the interpretation of the image, in my post “A Ring of Controversy”.]

About fifteen years ago, when I was a professor at the University of Washington, the particle physics theorists and the astronomer theorists occasionally would arrange to have lunch together, to facilitate an informal exchange of information about our adjacent fields. Among the many enjoyable discussions, one I was particularly excited about — as much as an amateur as a professional — was that in which I learned of the plan to make some sort of image of a black hole. I was told that this incredible feat would likely be achieved by 2020. The time, it seems, has arrived.

The goal of this post is to provide readers with what I hope will be a helpful guide through the foggy swamp that is likely to partly obscure this major scientific result. Over the last days I’ve been reading what both scientists and science journalists are writing in advance of the press conference Wednesday morning, and I’m finding many examples of jargon masquerading as English, terms poorly defined, and phrasing that seems likely to mislead. As I’m increasingly concerned that many non-experts will be unable to understand what is presented tomorrow, and what the pictures do and do not mean, I’m using this post to answer a few questions that many readers (and many of these writers) have perhaps not thought to ask. Continue reading

“Seeing” Double: Neutrinos and Photons Observed from the Same Cosmic Source

There has long been a question as to what types of events and processes are responsible for the highest-energy neutrinos coming from space and observed by scientists.  Another question, probably related, is what creates the majority of high-energy cosmic rays — the particles, mostly protons, that are constantly raining down upon the Earth.

As scientists’ ability to detect high-energy neutrinos (particles that are hugely abundant, electrically neutral, very light-weight, and very difficult to observe) and high-energy photons (particles of light, though not necessarily of visible light) have become more powerful and precise, there’s been considerable hope of getting an answer to these question.  One of the things we’ve been awaiting (and been disappointed a couple of times) is a violent explosion out in the universe that produces both high-energy photons and neutrinos at the same time, at a high enough rate that both types of particles can be observed at the same time coming from the same direction.

In recent years, there has been some indirect evidence that blazars — narrow jets of particles, pointed in our general direction like the barrel of a gun, and created as material swirls near and almost into giant black holes in the centers of very distant galaxies — may be responsible for the high-energy neutrinos.  Strong direct evidence in favor of this hypothesis has just been presented today.   Last year, one of these blazars flared brightly, and the flare created both high-energy neutrinos and high-energy photons that were observed within the same period, coming from the same place in the sky.

I have written about the IceCube neutrino observatory before; it’s a cubic kilometer of ice under the South Pole, instrumented with light detectors, and it’s ideal for observing neutrinos whose motion-energy far exceeds that of the protons in the Large Hadron Collider, where the Higgs particle was discovered.  These neutrinos mostly pass through Ice Cube undetected, but one in 100,000 hits something, and debris from the collision produces visible light that Ice Cube’s detectors can record.   IceCube has already made important discoveries, detecting a new class of high-energy neutrinos.

On Sept 22 of last year, one of these very high-energy neutrinos was observed at IceCube. More precisely, a muon created underground by the collision of this neutrino with an atomic nucleus was observed in IceCube.  To create the observed muon, the neutrino must have had a motion-energy tens of thousand times larger than than the motion-energy of each proton at the Large Hadron Collider (LHC).  And the direction of the neutrino’s motion is known too; it’s essentially the same as that of the observed muon.  So IceCube’s scientists knew where, on the sky, this neutrino had come from.

(This doesn’t work for typical cosmic rays; protons, for instance, travel in curved paths because they are deflected by cosmic magnetic fields, so even if you measure their travel direction at their arrival to Earth, you don’t then know where they came from. Neutrinos, beng electrically neutral, aren’t affected by magnetic fields and travel in a straight line, just as photons do.)

Very close to that direction is a well-known blazar (TXS-0506), four billion light years away (a good fraction of the distance across the visible universe).

The IceCube scientists immediately reported their neutrino observation to scientists with high-energy photon detectors.  (I’ve also written about some of the detectors used to study the very high-energy photons that we find in the sky: in particular, the Fermi/LAT satellite played a role in this latest discovery.) Fermi/LAT, which continuously monitors the sky, was already detecting high-energy photons coming from the same direction.   Within a few days the Fermi scientists had confirmed that TXS-0506 was indeed flaring at the time — already starting in April 2017 in fact, six times as bright as normal.  With this news from IceCube and Fermi/LAT, many other telescopes (including the MAGIC cosmic ray detector telescopes among others) then followed suit and studied the blazar, learning more about the properties of its flare.

Now, just a single neutrino on its own isn’t entirely convincing; is it possible that this was all just a coincidence?  So the IceCube folks went back to their older data to snoop around.  There they discovered, in their 2014-2015 data, a dramatic flare in neutrinos — more than a dozen neutrinos, seen over 150 days, had come from the same direction in the sky where TXS-0506 is sitting.  (More precisely, nearly 20 from this direction were seen, in a time period where normally there’d just be 6 or 7 by random chance.)  This confirms that this blazar is indeed a source of neutrinos.  And from the energies of the neutrinos in this flare, yet more can be learned about this blazar, and how it makes  high-energy photons and neutrinos at the same time.  Interestingly, so far at least, there’s no strong evidence for this 2014 flare in photons, except perhaps an increase in the number of the highest-energy photons… but not in the total brightness of the source.

The full picture, still emerging, tends to support the idea that the blazar arises from a supermassive black hole, acting as a natural particle accelerator, making a narrow spray of particles, including protons, at extremely high energy.  These protons, millions of times more energetic than those at the Large Hadron Collider, then collide with more ordinary particles that are just wandering around, such as visible-light photons from starlight or infrared photons from the ambient heat of the universe.  The collisions produce particles called pions, made from quarks and anti-quarks and gluons (just as protons are), which in turn decay either to photons or to (among other things) neutrinos.  And its those resulting photons and neutrinos which have now been jointly observed.

Since cosmic rays, the mysterious high energy particles from outer space that are constantly raining down on our planet, are mostly protons, this is evidence that many, perhaps most, of the highest energy cosmic rays are created in the natural particle accelerators associated with blazars. Many scientists have suspected that the most extreme cosmic rays are associated with the most active black holes at the centers of galaxies, and now we have evidence and more details in favor of this idea.  It now appears likely that that this question will be answerable over time, as more blazar flares are observed and studied.

The announcement of this important discovery was made at the National Science Foundation by Francis Halzen, the IceCube principal investigator, Olga Botner, former IceCube spokesperson, Regina Caputo, the Fermi-LAT analysis coordinator, and Razmik Mirzoyan, MAGIC spokesperson.

The fact that both photons and neutrinos have been observed from the same source is an example of what people are now calling “multi-messenger astronomy”; a previous example was the observation in gravitational waves, and in photons of many different energies, of two merging neutron stars.  Of course, something like this already happened in 1987, when a supernova was seen by eye, and also observed in neutrinos.  But in this case, the neutrinos and photons have energies millions and billions of times larger!

 

The Significance of Yesterday’s Gravitational Wave Announcement: an FAQ

Yesterday’s post on the results from the LIGO/VIRGO network of gravitational wave detectors was aimed at getting information out, rather than providing the pedagogical backdrop.  Today I’m following up with a post that attempts to answer some of the questions that my readers and my personal friends asked me.  Some wanted to understand better how to visualize what had happened, while others wanted more clarity on why the discovery was so important.  So I’ve put together a post which  (1) explains what neutron stars and black holes are and what their mergers are like, (2) clarifies why yesterday’s announcement was important — and there were many reasons, which is why it’s hard to reduce it all to a single soundbite.  And (3) there are some miscellaneous questions at the end.

First, a disclaimer: I am *not* an expert in the very complex subject of neutron star mergers and the resulting explosions, called kilonovas.  These are much more complicated than black hole mergers.  I am still learning some of the details.  Hopefully I’ve avoided errors, but you’ll notice a few places where I don’t know the answers … yet.  Perhaps my more expert colleagues will help me fill in the gaps over time.

Please, if you spot any errors, don’t hesitate to comment!!  And feel free to ask additional questions whose answers I can add to the list.

BASIC QUESTIONS ABOUT NEUTRON STARS, BLACK HOLES, AND MERGERS

What are neutron stars and black holes, and how are they related?

Every atom is made from a tiny atomic nucleus, made of neutrons and protons (which are very similar), and loosely surrounded by electrons. Most of an atom is empty space, so it can, under extreme circumstances, be crushed — but only if every electron and proton convert to a neutron (which remains behind) and a neutrino (which heads off into outer space.) When a giant star runs out of fuel, the pressure from its furnace turns off, and it collapses inward under its own weight, creating just those extraordinary conditions in which the matter can be crushed. Thus: a star’s interior, with a mass one to several times the Sun’s mass, is all turned into a several-mile(kilometer)-wide ball of neutrons — the number of neutrons approaching a 1 with 57 zeroes after it.

If the star is big but not too big, the neutron ball stiffens and holds its shape, and the star explodes outward, blowing itself to pieces in a what is called a core-collapse supernova. The ball of neutrons remains behind; this is what we call a neutron star. It’s a ball of the densest material that we know can exist in the universe — a pure atomic nucleus many miles(kilometers) across. It has a very hard surface; if you tried to go inside a neutron star, your experience would be a lot worse than running into a closed door at a hundred miles per hour.

If the star is very big indeed, the neutron ball that forms may immediately (or soon) collapse under its own weight, forming a black hole. A supernova may or may not result in this case; the star might just disappear. A black hole is very, very different from a neutron star. Black holes are what’s left when matter collapses irretrievably upon itself under the pull of gravity, shrinking down endlessly. While a neutron star has a surface that you could smash your head on, a black hole has no surface — it has an edge that is simply a point of no return, called a horizon. In Einstein’s theory, you can just go right through, as if passing through an open door. You won’t even notice the moment you go in. [Note: this is true in Einstein’s theory. But there is a big controversy as to whether the combination of Einstein’s theory with quantum physics changes the horizon into something novel and dangerous to those who enter; this is known as the firewall controversy, and would take us too far afield into speculation.]  But once you pass through that door, you can never return.

Black holes can form in other ways too, but not those that we’re observing with the LIGO/VIRGO detectors.

Why are their mergers the best sources for gravitational waves?

One of the easiest and most obvious ways to make gravitational waves is to have two objects orbiting each other.  If you put your two fists in a pool of water and move them around each other, you’ll get a pattern of water waves spiraling outward; this is in rough (very rough!) analogy to what happens with two orbiting objects, although, since the objects are moving in space, the waves aren’t in a material like water.  They are waves in space itself.

To get powerful gravitational waves, you want objects each with a very big mass that are orbiting around each other at very high speed. To get the fast motion, you need the force of gravity between the two objects to be strong; and to get gravity to be as strong as possible, you need the two objects to be as close as possible (since, as Isaac Newton already knew, gravity between two objects grows stronger when the distance between them shrinks.) But if the objects are large, they can’t get too close; they will bump into each other and merge long before their orbit can become fast enough. So to get a really fast orbit, you need two relatively small objects, each with a relatively big mass — what scientists refer to as compact objects. Neutron stars and black holes are the most compact objects we know about. Fortunately, they do indeed often travel in orbiting pairs, and do sometimes, for a very brief period before they merge, orbit rapidly enough to produce gravitational waves that LIGO and VIRGO can observe.

Why do we find these objects in pairs in the first place?

Stars very often travel in pairs… they are called binary stars. They can start their lives in pairs, forming together in large gas clouds, or even if they begin solitary, they can end up pairing up if they live in large densely packed communities of stars where it is common for multiple stars to pass nearby. Perhaps surprisingly, their pairing can survive the collapse and explosion of either star, leaving two black holes, two neutron stars, or one of each in orbit around one another.

What happens when these objects merge?

Not surprisingly, there are three classes of mergers which can be detected: two black holes merging, two neutron stars merging, and a neutron star merging with a black hole. The first class was observed in 2015 (and announced in 2016), the second was announced yesterday, and it’s a matter of time before the third class is observed. The two objects may orbit each other for billions of years, very slowly radiating gravitational waves (an effect observed in the 70’s, leading to a Nobel Prize) and gradually coming closer and closer together. Only in the last day of their lives do their orbits really start to speed up. And just before these objects merge, they begin to orbit each other once per second, then ten times per second, then a hundred times per second. Visualize that if you can: objects a few dozen miles (kilometers) across, a few miles (kilometers) apart, each with the mass of the Sun or greater, orbiting each other 100 times each second. It’s truly mind-boggling — a spinning dumbbell beyond the imagination of even the greatest minds of the 19th century. I don’t know any scientist who isn’t awed by this vision. It all sounds like science fiction. But it’s not.

How do we know this isn’t science fiction?

We know, if we believe Einstein’s theory of gravity (and I’ll give you a very good reason to believe in it in just a moment.) Einstein’s theory predicts that such a rapidly spinning, large-mass dumbbell formed by two orbiting compact objects will produce a telltale pattern of ripples in space itself — gravitational waves. That pattern is both complicated and precisely predicted. In the case of black holes, the predictions go right up to and past the moment of merger, to the ringing of the larger black hole that forms in the merger. In the case of neutron stars, the instants just before, during and after the merger are more complex and we can’t yet be confident we understand them, but during tens of seconds before the merger Einstein’s theory is very precise about what to expect. The theory further predicts how those ripples will cross the vast distances from where they were created to the location of the Earth, and how they will appear in the LIGO/VIRGO network of three gravitational wave detectors. The prediction of what to expect at LIGO/VIRGO thus involves not just one prediction but many: the theory is used to predict the existence and properties of black holes and of neutron stars, the detailed features of their mergers, the precise patterns of the resulting gravitational waves, and how those gravitational waves cross space. That LIGO/VIRGO have detected the telltale patterns of these gravitational waves. That these wave patterns agree with Einstein’s theory in every detail is the strongest evidence ever obtained that there is nothing wrong with Einstein’s theory when used in these combined contexts.  That then in turn gives us confidence that our interpretation of the LIGO/VIRGO results is correct, confirming that black holes and neutron stars really exist and really merge. (Notice the reasoning is slightly circular… but that’s how scientific knowledge proceeds, as a set of detailed consistency checks that gradually and eventually become so tightly interconnected as to be almost impossible to unwind.  Scientific reasoning is not deductive; it is inductive.  We do it not because it is logically ironclad but because it works so incredibly well — as witnessed by the computer, and its screen, that I’m using to write this, and the wired and wireless internet and computer disk that will be used to transmit and store it.)

THE SIGNIFICANCE(S) OF YESTERDAY’S ANNOUNCEMENT OF A NEUTRON STAR MERGER

What makes it difficult to explain the significance of yesterday’s announcement is that it consists of many important results piled up together, rather than a simple takeaway that can be reduced to a single soundbite. (That was also true of the black hole mergers announcement back in 2016, which is why I wrote a long post about it.)

So here is a list of important things we learned.  No one of them, by itself, is earth-shattering, but each one is profound, and taken together they form a major event in scientific history.

First confirmed observation of a merger of two neutron stars: We’ve known these mergers must occur, but there’s nothing like being sure. And since these things are too far away and too small to see in a telescope, the only way to be sure these mergers occur, and to learn more details about them, is with gravitational waves.  We expect to see many more of these mergers in coming years as gravitational wave astronomy increases in its sensitivity, and we will learn more and more about them.

New information about the properties of neutron stars: Neutron stars were proposed almost a hundred years ago and were confirmed to exist in the 60’s and 70’s.  But their precise details aren’t known; we believe they are like a giant atomic nucleus, but they’re so vastly larger than ordinary atomic nuclei that can’t be sure we understand all of their internal properties, and there are debates in the scientific community that can’t be easily answered… until, perhaps, now.

From the detailed pattern of the gravitational waves of this one neutron star merger, scientists already learn two things. First, we confirm that Einstein’s theory correctly predicts the basic pattern of gravitational waves from orbiting neutron stars, as it does for orbiting and merging black holes. Unlike black holes, however, there are more questions about what happens to neutron stars when they merge. The question of what happened to this pair after they merged is still out — did the form a neutron star, an unstable neutron star that, slowing its spin, eventually collapsed into a black hole, or a black hole straightaway?

But something important was already learned about the internal properties of neutron stars. The stresses of being whipped around at such incredible speeds would tear you and I apart, and would even tear the Earth apart. We know neutron stars are much tougher than ordinary rock, but how much more? If they were too flimsy, they’d have broken apart at some point during LIGO/VIRGO’s observations, and the simple pattern of gravitational waves that was expected would have suddenly become much more complicated. That didn’t happen until perhaps just before the merger.   So scientists can use the simplicity of the pattern of gravitational waves to infer some new things about how stiff and strong neutron stars are.  More mergers will improve our understanding.  Again, there is no other simple way to obtain this information.

First visual observation of an event that produces both immense gravitational waves and bright electromagnetic waves: Black hole mergers aren’t expected to create a brilliant light display, because, as I mentioned above, they’re more like open doors to an invisible playground than they are like rocks, so they merge rather quietly, without a big bright and hot smash-up.  But neutron stars are big balls of stuff, and so the smash-up can indeed create lots of heat and light of all sorts, just as you might naively expect.  By “light” I mean not just visible light but all forms of electromagnetic waves, at all wavelengths (and therefore at all frequencies.)  Scientists divide up the range of electromagnetic waves into categories. These categories are radio waves, microwaves, infrared light, visible light, ultraviolet light, X-rays, and gamma rays, listed from lowest frequency and largest wavelength to highest frequency and smallest wavelength.  (Note that these categories and the dividing lines between them are completely arbitrary, but the divisions are useful for various scientific purposes.  The only fundamental difference between yellow light, a radio wave, and a gamma ray is the wavelength and frequency; otherwise they’re exactly the same type of thing, a wave in the electric and magnetic fields.)

So if and when two neutron stars merge, we expect both gravitational waves and electromagnetic waves, the latter of many different frequencies created by many different effects that can arise when two huge balls of neutrons collide.  But just because we expect them doesn’t mean they’re easy to see.  These mergers are pretty rare — perhaps one every hundred thousand years in each big galaxy like our own — so the ones we find using LIGO/VIRGO will generally be very far away.  If the light show is too dim, none of our telescopes will be able to see it.

But this light show was plenty bright.  Gamma ray detectors out in space detected it instantly, confirming that the gravitational waves from the two neutron stars led to a collision and merger that produced very high frequency light.  Already, that’s a first.  It’s as though one had seen lightning for years but never heard thunder; or as though one had observed the waves from hurricanes for years but never observed one in the sky.  Seeing both allows us a whole new set of perspectives; one plus one is often much more than two.

Over time — hours and days — effects were seen in visible light, ultraviolet light, infrared light, X-rays and radio waves.  Some were seen earlier than others, which itself is a story, but each one contributes to our understanding of what these mergers are actually like.

Confirmation of the best guess concerning the origin of “short” gamma ray bursts:  For many years, bursts of gamma rays have been observed in the sky.  Among them, there seems to be a class of bursts that are shorter than most, typically lasting just a couple of seconds.  They come from all across the sky, indicating that they come from distant intergalactic space, presumably from distant galaxies.  Among other explanations, the most popular hypothesis concerning these short gamma-ray bursts has been that they come from merging neutron stars.  The only way to confirm this hypothesis is with the observation of the gravitational waves from such a merger.  That test has now been passed; it appears that the hypothesis is correct.  That in turn means that we have, for the first time, both a good explanation of these short gamma ray bursts and, because we know how often we observe these bursts, a good estimate as to how often neutron stars merge in the universe.

First distance measurement to a source using both a gravitational wave measure and a redshift in electromagnetic waves, allowing a new calibration of the distance scale of the universe and of its expansion rate:  The pattern over time of the gravitational waves from a merger of two black holes or neutron stars is complex enough to reveal many things about the merging objects, including a rough estimate of their masses and the orientation of the spinning pair relative to the Earth.  The overall strength of the waves, combined with the knowledge of the masses, reveals how far the pair is from the Earth.  That by itself is nice, but the real win comes when the discovery of the object using visible light, or in fact any light with frequency below gamma-rays, can be made.  In this case, the galaxy that contains the neutron stars can be determined.

Once we know the host galaxy, we can do something really important.  We can, by looking at the starlight, determine how rapidly the galaxy is moving away from us.  For distant galaxies, the speed at which the galaxy recedes should be related to its distance because the universe is expanding.

How rapidly the universe is expanding has been recently measured with remarkable precision, but the problem is that there are two different methods for making the measurement, and they disagree.   This disagreement is one of the most important problems for our understanding of the universe.  Maybe one of the measurement methods is flawed, or maybe — and this would be much more interesting — the universe simply doesn’t behave the way we think it does.

What gravitational waves do is give us a third method: the gravitational waves directly provide the distance to the galaxy, and the electromagnetic waves directly provide the speed of recession.  There is no other way to make this type of joint measurement directly for distant galaxies.  The method is not accurate enough to be useful in just one merger, but once dozens of mergers have been observed, the average result will provide important new information about the universe’s expansion.  When combined with the other methods, it may help resolve this all-important puzzle.

Best test so far of Einstein’s prediction that the speed of light and the speed of gravitational waves are identical: Since gamma rays from the merger and the peak of the gravitational waves arrived within two seconds of one another after traveling 130 million years — that is, about 5 thousand million million seconds — we can say that the speed of light and the speed of gravitational waves are both equal to the cosmic speed limit to within one part in 2 thousand million million.  Such a precise test requires the combination of gravitational wave and gamma ray observations.

Efficient production of heavy elements confirmed:  It’s long been said that we are star-stuff, or stardust, and it’s been clear for a long time that it’s true.  But there’s been a puzzle when one looks into the details.  While it’s known that all the chemical elements from hydrogen up to iron are formed inside of stars, and can be blasted into space in supernova explosions to drift around and eventually form planets, moons, and humans, it hasn’t been quite as clear how the other elements with heavier atoms — atoms such as iodine, cesium, gold, lead, bismuth, uranium and so on — predominantly formed.  Yes they can be formed in supernovas, but not so easily; and there seem to be more atoms of heavy elements around the universe than supernovas can explain.  There are many supernovas in the history of the universe, but the efficiency for producing heavy chemical elements is just too low.

It was proposed some time ago that the mergers of neutron stars might be a suitable place to produce these heavy elements.  Even those these mergers are rare, they might be much more efficient, because the nuclei of heavy elements contain lots of neutrons and, not surprisingly, a collision of two neutron stars would produce lots of neutrons in its debris, suitable perhaps for making these nuclei.   A key indication that this is going on would be the following: if a neutron star merger could be identified using gravitational waves, and if its location could be determined using telescopes, then one would observe a pattern of light that would be characteristic of what is now called a “kilonova” explosion.   Warning: I don’t yet know much about kilonovas and I may be leaving out important details. A kilonova is powered by the process of forming heavy elements; most of the nuclei produced are initially radioactive — i.e., unstable — and they break down by emitting high energy particles, including the particles of light (called photons) which are in the gamma ray and X-ray categories.  The resulting characteristic glow would be expected to have a pattern of a certain type: it would be initially bright but would dim rapidly in visible light, with a long afterglow in infrared light.  The reasons for this are complex, so let me set them aside for now.  The important point is that this pattern was observed, confirming that a kilonova of this type occurred, and thus that, in this neutron star merger, enormous amounts of heavy elements were indeed produced.  So we now have a lot of evidence, for the first time, that almost all the heavy chemical elements on and around our planet were formed in neutron star mergers.  Again, we could not know this if we did not know that this was a neutron star merger, and that information comes only from the gravitational wave observation.

MISCELLANEOUS QUESTIONS

Did the merger of these two neutron stars result in a new black hole, a larger neutron star, or an unstable rapidly spinning neutron star that later collapsed into a black hole?

We don’t yet know, and maybe we won’t know.  Some scientists involved appear to be leaning toward the possibility that a black hole was formed, but others seem to say the jury is out.  I’m not sure what additional information can be obtained over time about this.

If the two neutron stars formed a black hole, why was there a kilonova?  Why wasn’t everything sucked into the black hole?

Black holes aren’t vacuum cleaners; they pull things in via gravity just the same way that the Earth and Sun do, and don’t suck things in some unusual way.  The only crucial thing about a black hole is that once you go in you can’t come out.  But just as when trying to avoid hitting the Earth or Sun, you can avoid falling in if you orbit fast enough or if you’re flung outward before you reach the edge.

The point in a neutron star merger is that the forces at the moment of merger are so intense that one or both neutron stars are partially ripped apart.  The material that is thrown outward in all directions, at an immense speed, somehow creates the bright, hot flash of gamma rays and eventually the kilonova glow from the newly formed atomic nuclei.  Those details I don’t yet understand, but I know they have been carefully studied both with approximate equations and in computer simulations such as this one and this one.  However, the accuracy of the simulations can only be confirmed through the detailed studies of a merger, such as the one just announced.  It seems, from the data we’ve seen, that the simulations did a fairly good job.  I’m sure they will be improved once they are compared with the recent data.

 

 

 

A Scientific Breakthrough! Combining Gravitational and Electromagnetic Waves

Gravitational waves are now the most important new tool in the astronomer’s toolbox.  Already they’ve been used to confirm that large black holes — with masses ten or more times that of the Sun — and mergers of these large black holes to form even larger ones, are not uncommon in the universe.   Today it goes a big step further.

It’s long been known that neutron stars, remnants of collapsed stars that have exploded as supernovas, are common in the universe.  And it’s been known almost as long that sometimes neutron stars travel in pairs.  (In fact that’s how gravitational waves were first discovered, indirectly, back in the 1970s.)  Stars often form in pairs, and sometimes both stars explode as supernovas, leaving their neutron star relics in orbit around one another.  Neutron stars are small — just ten or so kilometers (miles) across.  According to Einstein’s theory of gravity, a pair of stars should gradually lose energy by emitting gravitational waves into space, and slowly but surely the two objects should spiral in on one another.   Eventually, after many millions or even billions of years, they collide and merge into a larger neutron star, or into a black hole.  This collision does two things.

  1. It makes some kind of brilliant flash of light — electromagnetic waves — whose details are only guessed at.  Some of those electromagnetic waves will be in the form of visible light, while much of it will be in invisible forms, such as gamma rays.
  2. It makes gravitational waves, whose details are easier to calculate and which are therefore distinctive, but couldn’t have been detected until LIGO and VIRGO started taking data, LIGO over the last couple of years, VIRGO over the last couple of months.

It’s possible that we’ve seen the light from neutron star mergers before, but no one could be sure.  Wouldn’t it be great, then, if we could see gravitational waves AND electromagnetic waves from a neutron star merger?  It would be a little like seeing the flash and hearing the sound from fireworks — seeing and hearing is better than either one separately, with each one clarifying the other.  (Caution: scientists are often speaking as if detecting gravitational waves is like “hearing”.  This is only an analogy, and a vague one!  It’s not at all the same as acoustic waves that we can hear with our ears, for many reasons… so please don’t take it too literally.)  If we could do both, we could learn about neutron stars and their properties in an entirely new way.

Today, we learned that this has happened.  LIGO , with the world’s first two gravitational observatories, detected the waves from two merging neutron stars, 130 million light years from Earth, on August 17th.  (Neutron star mergers last much longer than black hole mergers, so the two are easy to distinguish; and this one was so close, relatively speaking, that it was seen for a long while.)  VIRGO, with the third detector, allows scientists to triangulate and determine roughly where mergers have occurred.  They saw only a very weak signal, but that was extremely important, because it told the scientists that the merger must have occurred in a small region of the sky where VIRGO has a relative blind spot.  That told scientists where to look.

The merger was detected for more than a full minute… to be compared with black holes whose mergers can be detected for less than a second.  It’s not exactly clear yet what happened at the end, however!  Did the merged neutron stars form a black hole or a neutron star?  The jury is out.

At almost exactly the moment at which the gravitational waves reached their peak, a blast of gamma rays — electromagnetic waves of very high frequencies — were detected by a different scientific team, the one from FERMI. FERMI detects gamma rays from the distant universe every day, and a two-second gamma-ray-burst is not unusual.  And INTEGRAL, another gamma ray experiment, also detected it.   The teams communicated within minutes.   The FERMI and INTEGRAL gamma ray detectors can only indicate the rough region of the sky from which their gamma rays originate, and LIGO/VIRGO together also only give a rough region.  But the scientists saw those regions overlapped.  The evidence was clear.  And with that, astronomy entered a new, highly anticipated phase.

Already this was a huge discovery.  Brief gamma-ray bursts have been a mystery for years.  One of the best guesses as to their origin has been neutron star mergers.  Now the mystery is solved; that guess is apparently correct. (Or is it?  Probably, but the gamma ray discovery is surprisingly dim, given how close it is.  So there are still questions to ask.)

Also confirmed by the fact that these signals arrived within a couple of seconds of one another, after traveling for over 100 million years from the same source, is that, indeed, the speed of light and the speed of gravitational waves are exactly the same — both of them equal to the cosmic speed limit, just as Einstein’s theory of gravity predicts.

Next, these teams quickly told their astronomer friends to train their telescopes in the general area of the source. Dozens of telescopes, from every continent and from space, and looking for electromagnetic waves at a huge range of frequencies, pointed in that rough direction and scanned for anything unusual.  (A big challenge: the object was near the Sun in the sky, so it could be viewed in darkness only for an hour each night!) Light was detected!  At all frequencies!  The object was very bright, making it easy to find the galaxy in which the merger took place.  The brilliant glow was seen in gamma rays, ultraviolet light, infrared light, X-rays, and radio.  (Neutrinos, particles that can serve as another way to observe distant explosions, were not detected this time.)

And with so much information, so much can be learned!

Most important, perhaps, is this: from the pattern of the spectrum of light, the conjecture seems to be confirmed that the mergers of neutron stars are important sources, perhaps the dominant one, for many of the heavy chemical elements — iodine, iridium, cesium, gold, platinum, and so on — that are forged in the intense heat of these collisions.  It used to be thought that the same supernovas that form neutron stars in the first place were the most likely source.  But now it seems that this second stage of neutron star life — merger, rather than birth — is just as important.  That’s fascinating, because neutron star mergers are much more rare than the supernovas that form them.  There’s a supernova in our Milky Way galaxy every century or so, but it’s tens of millenia or more between these “kilonovas”, created in neutron star mergers.

If there’s anything disappointing about this news, it’s this: almost everything that was observed by all these different experiments was predicted in advance.  Sometimes it’s more important and useful when some of your predictions fail completely, because then you realize how much you have to learn.  Apparently our understanding of gravity, of neutron stars, and of their mergers, and of all sorts of sources of electromagnetic radiation that are produced in those merges, is even better than we might have thought. But fortunately there are a few new puzzles.  The X-rays were late; the gamma rays were dim… we’ll hear more about this shortly, as NASA is holding a second news conference.

Some highlights from the second news conference:

  • New information about neutron star interiors, which affects how large they are and therefore how exactly they merge, has been obtained
  • The first ever visual-light image of a gravitational wave source, from the Swope telescope, at the outskirts of a distant galaxy; the galaxy’s center is the blob of light, and the arrow points to the explosion.

  • The theoretical calculations for a kilonova explosion suggest that debris from the blast should rather quickly block the visual light, so the explosion dims quickly in visible light — but infrared light lasts much longer.  The observations by the visible and infrared light telescopes confirm this aspect of the theory; and you can see evidence for that in the picture above, where four days later the bright spot is both much dimmer and much redder than when it was discovered.
  • Estimate: the total mass of the gold and platinum produced in this explosion is vastly larger than the mass of the Earth.
  • Estimate: these neutron stars were formed about 10 or so billion years ago.  They’ve been orbiting each other for most of the universe’s history, and ended their lives just 130 million years ago, creating the blast we’ve so recently detected.
  • Big Puzzle: all of the previous gamma-ray bursts seen up to now have always had shone in ultraviolet light and X-rays as well as gamma rays.   But X-rays didn’t show up this time, at least not initially.  This was a big surprise.  It took 9 days for the Chandra telescope to observe X-rays, too faint for any other X-ray telescope.  Does this mean that the two neutron stars created a black hole, which then created a jet of matter that points not quite directly at us but off-axis, and shines by illuminating the matter in interstellar space?  This had been suggested as a possibility twenty years ago, but this is the first time there’s been any evidence for it.
  • One more surprise: it took 16 days for radio waves from the source to be discovered, with the Very Large Array, the most powerful existing radio telescope.  The radio emission has been growing brighter since then!  As with the X-rays, this seems also to support the idea of an off-axis jet.
  • Nothing quite like this gamma-ray burst has been seen — or rather, recognized — before.  When a gamma ray burst doesn’t have an X-ray component showing up right away, it simply looks odd and a bit mysterious.  Its harder to observe than most bursts, because without a jet pointing right at us, its afterglow fades quickly.  Moreover, a jet pointing at us is bright, so it blinds us to the more detailed and subtle features of the kilonova.  But this time, LIGO/VIRGO told scientists that “Yes, this is a neutron star merger”, leading to detailed study from all electromagnetic frequencies, including patient study over many days of the X-rays and radio.  In other cases those observations would have stopped after just a short time, and the whole story couldn’t have been properly interpreted.