The science of Ophiuchus

It's recently hit the news that there is a 13th astrological sign Ophiuchus.  Furthermore, all other signs have been shifted by about a month; so while I would be classified as a Gemini, technically I'm supposed to be a Taurus.

This is literally ancient news.  The usual dates for astrological signs were defined about 3,000 years ago.  Each sign was named for the constellation that would be behind the sun at that time of year.  But the sun is no longer in front of the same constellation as it was 3,000 years ago at the same time of year.  The dates of the signs should have gradually shifted in a process known as the precession of the equinoxes.

But most astrologers don't use shifted dates.  According to Wikipedia, this is because they emphasize the "symbolic or metaphorical meaning of the star signs".  But I daresay that most people who read their horoscope simply don't know about the precession of the equinoxes.  Myself, I think that the signs have no meaning at all, and the perceived accuracy of horoscopes is merely a testament to how similar our experiences are, or to the power of the Forer effect.

The precession of the equinoxes has to do with the "wobble" of the earth.

(Source: NASA)

The earth has an axis of rotation (in red), but this axis slowly moves in a circle (in white above the earth).  This process is distinct from the spin and orbit of the earth.  The earth spins around its axis once a day.  It orbits around the sun once a year.  The axis of rotation precesses in a full circle approximately every 26,000 years.  Therefore, in 3,000 years, the axis of rotation has moved by more than one ninth of a full circle.

While a spinning object will continue to spin due to inertia, a precessing object needs some force to maintain the precession.  Consider a gyroscope that we've set on a table.

(Source: Wikipedia)

The wobbling of the gyroscope is precession.  In the case of the gyroscope, precession is caused by the weight of the gyroscope, as well as the force of the table holding it up.  But the earth is not lying on a table.  Instead, the precession of the earth is caused by the gravitational forces of the sun and moon.  More specifically, it's caused by tidal forces, the same ones that cause the tides.

How does this affect the dates of the astrological symbols?  It has to do with the tricky definition of a year.  North of the equator, the start of each new year occurs some time in winter.  Winter occurs when the Earth's axis of rotation is pointing away from the sun.  But if the axis of rotation moves, that means that winter moves!

(original image; axial tilt exaggerated for clarity)

To make sure that our calendar keeps up with the seasons, we have a tricky definition of a year.  A year is not the time it takes for the earth to orbit.  A year is defined in such a way that it keeps up with the seasons.  If we want to talk about how long it takes the earth to orbit, we call that a sidereal year, which is slightly longer than the year we normally use, the tropical year.

The thing is, winter moves around, but the constellations don't move much at all.  That's why precession shifts the astrological signs.

But wait!  Why do we have a new astrological sign, Ophiuchus?  It turns out that the answer is far less scientific.  Back in ancient times, when the dates of the astrological signs were solidified, astrologers divided the sun's path through the stars into twelve equally-spaced segments.  Each of the twelve segments was assigned to a different constellation.  But the fact of the matter is that these constellations are not equally sized.  In fact, the "size" of a constellation isn't even very well defined, since what is a constellation but a set of stars that's supposed to look like something (but usually doesn't really).

Seriously, that does not look like a crab, even after you've drawn the imaginary lines.

This didn't do for the International Astronomical Union. So in 1930 they defined specific regions of the sky as belonging to different constellations.  These regions are arbitrary, but hopefully less arbitrary than the regions defined by astrologers thousands of years ago.  Using these definitions, the twelve astrological signs are no longer of equal length in the year, and the sun passes in front of a thirteenth constellation, Ophiuchus.  (source)

And so if you were born between November 29 and December 17, your sign according to the IAU is Ophiuchus, the serpent bearer.  The symbol is the Rod of Asclepius, a snake entwined around a staff.  This almost makes up for Pluto!

The science of closed boxes

A friend pointed me to an article in New Scientist, "Why we shouldn't release all we know about the cosmos". The article suggests that data on the Cosmic Microwave Background Radiation (CMBR) should be released slowly, not all at once.

If the whole data set is released at once, as is planned, any new ideas that cosmologists come up with may have to remain untested because they will have no further data to test them with.

It took a moment, but eventually I realized that they were suggesting the method of blind analysis.

We also used blind analysis in LIGO data (LIGO is the Laser Interferometer Gravitational-wave Observatory, a gigantic device designed to detect gravitational waves). Whenever LIGO records a set of data, only 10% of that data is released. That 10% is called the playground. We analyze the heck out of that playground! There's a huge computer program, called the data analysis pipeline, which is used to decide if there are any events in the playground which look like real gravitational waves. A large group of scientists build on the pipeline, finely adjusting parameters, adding new bells and whistles. And the whole time they are doing this, they are not allowed to peek at the other 90% of the data. That box is closed!

This is the sort of box I want you to visualize

Once the scientists are satisfied with the pipeline, they "open the box". That means they get to look at the other 90% of the data. But once the box is open, they're not allowed to change the pipeline in any way. If they want to add more bells and whistles to the pipeline, they have to wait until the next time LIGO takes a set of data, perhaps in a year or more.

What is the meaning of this silly ritual? Is it some sort of Christmas tradition among data analysts?

There are all sorts of ways you can bias your analysis. If you know what the results are every time you try a different method of data analysis, then you can, to some extent, "select" results you like. That's bad! We want the results to be unbiased, so that everyone can agree on them. Therefore, in blind analysis, there are two stages. First, you choose a method of data analysis without looking at the full results. Then you apply that method to the full results without changing it.

I read the paper which is reported in New Scientist, and they have another cool explanation of the same idea. The goal in science is to compare a bunch of different models, and determine which model best explains our observations. But first, we need to come up with those models. The models will be educated guesses based on all the evidence we've collected thus far. So if we want to test the models, it's somewhat redundant to use the present evidence; we should instead collect new observations to test the models.

The problem in cosmology is that at some point, there will be no new observations to make. There is only one universe. There is only one CMBR map, with all its random statistical fluctuations. If you stare long enough at those statistical fluctuations, chances are good that you'll find some false pattern. The pattern will be very difficult to falsify, since there is no more data to collect after that. The solution? Release data piece by piece, so that there will still be new data to test our models.

So you see, even something which sounds as boring as data analysis can have all these counter-intuitive tricks involved. Hiding data in a closed box? It sounds silly, possibly even counter to science's goal of obtaining as much true information about the world as possible. But if it's necessary to filter out human biases, I think we should do it!

Some crazy LIGO

Everyone is asking me, "Hey mr. miller, what crazy things are you doing this summer?" Well, as I've already let slip, I'm working on LIGO, the Laser Interferometer Gravitational Wave Observatory. We're looking for gravitational waves. Specifically, I'm in the group which looks for gravitational waves which come from compact binary coalescences (CBCs). That basically means when two black holes smash together.

Have we found any gravitational waves yet? Well, the other day, I was at Chandler Cafe, and I found one in my noodles. It looked sort of like this:

Graphic made using a Mathematica Demonstration

Unfortunately, I don't really own a camera, and I was hungry. So I slurped it up, and it made a sound like this: voooooooooooooooooooouP (also available as mp3, from "Gravitational Wave Sounds"). I guess we'll just have to find another one now, huh?

A slightly more serious answer: I couldn't tell you even if we had seen anything. It is "privileged" information. Exciting! But let me say this: We have a fairly good idea of the density of binary neutron stars and black holes, and how "loud" they would be when they merge. So we can calculate the expected rate of detection. By one estimate (see arxiv), the expected detection rate of neutron star mergers is once per two hundred years of observation (probably even smaller for black hole mergers). Basically, we don't expect to see anything. The real excitement will occur when "advanced LIGO" starts in 2013, increasing the observation rate to about 20 per year.

Of course, there are other sources of gravitational waves--Gravitational Wave Pulsars, Big Explodey Things, etc.--so maybe we'll see some of those. I think these other sources aren't as well understood, so we don't have such precise estimates on their expected detection rates. So who knows, we may be lucky.

And if it turns out we're lucky, you probably wouldn't notice right away. LIGO data is littered with what we call "non-Gaussian noise", meaning that every so often, there's a data glitch, causing the measurement to jump up by some really high number. These glitches look like gravitational waves; the computer has trouble telling the difference. And there are so many of them. We toss the glitches through every statistical filter we can think of, and we're still overflooded with them.

But we still have some tricks up our sleeves. I'm working on one of those tricks. What I do, is give the computer a bunch of false signals and a bunch of "real" signals (which are inserted artificially). Then the computer uses these to learn the difference between the two. It's basically Skynet, except it's not even remotely like Skynet.

Instead, I would analogize it to a tree. You throw a bunch of apples and oranges at the tree, and then the tree tries to tell a supercomputer what the difference is between a fruit and a black hole. (I am joking! Don't take my analogy too seriously. It's not really like a tree at all; if anything, it's a forest.)

So basically, if you want to know what I'm doing this summer, you can visualize me tossing a bunch of black holes at trees in hopes of finding delicious spaghetti. That's more or less the right idea.

Great spiraling black holes!

Around this time is when you start to hear about everyone else's exciting plans for the summer. Hey, wait, I have one of those too! I got a research job at Caltech working with LIGO, the Laser Interferometer Gravitational Wave Observatory. It's probably not as glamorous as it sounds, but boy does it sound awesome.

Let's begin with the observatories. There is one observatory in Louisiana, and two in Washington state. The gravitational wave detector consists of two lasers which go in perpendicular directions. Each laser is 4 km (2.5 miles) long, and encased in a vacuum pipe. Once the lasers have bounced back and forth in their tubes many times, they recombine and interfere with each other. By looking at the interference pattern of the lasers, we can determine the difference in length of the two laser paths. And by that, I mean we can measure the difference very sensitively, down to 10^-18 meters. This is about a thousand times smaller than an a proton.

One of the Washington detectors. Credit: NASA

Why do we want to measure so sensitively the length of a laser path? It all goes back to Einstein.

Albert Einstein is most famous for his theories of Special Relativity and General Relativity. Special Relativity describes how physics behaves when things move near the speed of light. General Relativity is the theory which incorporates both Special Relativity and gravity. In fact, General Relativity is the theory which replaces the classical theory of gravity. The classical laws are very accurate under most conditions, but are decidedly incorrect nearby very massive objects and when things are moving near the speed of light.

In a way, it's rather surprising that General Relativity and classical gravity could possibly be describing the same thing. Classical gravity describes everything in terms of forces. General Relativity describes gravity as a distortion of the space-time topology. In other words, gravity influences the distances and time-intervals between different events. These small distortions cause a straight line through time appear to be curved, as if it were acted upon by some force.

One of the predictions of General Relativity is the existence of gravitational waves. Gravitational waves are analogous to electromagnetic waves (aka light). Electromagnetic waves are fluctuations in the electric and magnetic fields. Gravitational waves are fluctuations in the space-time topology. Electromagnetic waves are created whenever an electrically charged object accelerates. Gravitational waves are created whenever a massive object accelerates. Both kinds of waves are characterized by a frequency, which tells you how quickly the waves fluctuate. If a gravitational wave passes through the LIGO detector, it will cause the two laser arms to fluctuate in length. If the gravitational wave has a frequency of 40 Hz, then the lengths will fluctuate 40 times per second.

LIGO is only sensitive enough to detect gravitational waves with frequency 40 Hz or higher. At lower frequencies, it becomes too difficult to distinguish between gravitational waves and regular old earthquake activity.

What could possibly cause a gravitational wave of more than 40 Hz? Gravitational waves are caused by accelerating massive objects. For example, the earth is constantly accelerating towards the sun because it is in a circular orbit. But this should only cause gravitational waves with frequencies of about 1 per year. However, we might be able to detect orbiting objects if they are orbiting much faster than the earth. One of the objects we are interested in is the binary black hole* system. Black holes are very massive objects, and also very small. So two black holes could be orbiting very quickly and closely to each other. If a pair of black holes is what it takes, then let's look for black holes!

*It could also be any other type of massive astrophysical compact halo object (MACHO), like a neutron star.

One other thing about gravitational waves, is that they carry energy, just like light does. As two black holes orbit each other, they emit energy in the form of gravitational waves. This causes the black holes to slowly lose energy, falling slowly towards each other. Because they're closer together, the "force" of gravity is stronger, and they orbit faster and faster. The picture we have here is of two black holes, spiraling around each other, getting closer together and moving faster. Eventually, they collide, coalescing into a single black hole. When there is only one black hole left, it no longer emits gravitational waves, and its signal disappears.

This could really use some animation. So I found some animations on the net from the Numerical Relativity Group.

The detection of gravitational waves is not only a way to test Einstein's theory of General Relativity under new conditions, it is also a new way to do astronomy. It's much like how we build telescopes to detect electromagnetic waves from far away sources. We can use gravitational waves to detect objects like binary black holes, as well as exploding stars, and a certain kind of pulsar. Scientists are also trying to detect something analogous to the cosmic microwave background radiation, only it would be cosmic gravitational background radiation. It would be very difficult to detect, but it comes from a very early point in the universe's history, far earlier than even the microwave background radiation.

Axial Tilt: The Milankovitch Cycles

 [Note: This is not an original image, but the website I was crediting now appears defunct]

Last year, I explained how, exactly, axial tilt causes seasons. This year, I will explain how axial tilt changes over time in what we call the Milankovitch Cycles. The Earth's orbit and spin do not stay constant forever, but change over thousands of years. These changes are much too slow to cause seasons, but they can cause much larger climate changes like ice ages. There are three Milankovitch Cycles:

Precession

I've previously discussed the precession of the Earth, but here is the shorter rehash. Although the Earth's axial tilt is always about 23.5 degrees offset from the orbital plane, the direction of the tilt moves around in a circle every 25,700 years. The cause of this change is the gravity of the sun and moon acting upon Earth's equatorial bulge. Got it?

To understand how this affects climate, we're going to have to understand different kinds of years. Isn't there only one kind of year, you ask? No, there are actually many, many different kinds of years with slightly different definitions and lengths. What do we mean by "year" anyway? If we mean the time it takes for the Earth to complete a full orbit, then what we want is the sidereal year. However, that is not the kind of year that our calendar is based on! Our calendar is based on the time it takes for Earth to complete four seasons, the tropical year. Every tropical year, there is exactly one summer solstice, when the Earth's rotation axis is tilted towards the sun. But because precession changes the direction of Earth's tilt, the summer solstice actually occurs at a slightly different location of Earth's orbit every year. The tropical year is shorter than the sidereal year by about 20 minutes.

But when we're talking about long term climate changes, we're also interested in a third type of year. The Earth's orbit is not a perfect circle, and there exists a point in the Earth's orbit when it is closest to the sun. This closest point is called the perihelion, and it occurs around January 3rd. The gravity from other planets causes the perihelion to occur at a slightly different point in Earth's orbit every year. The time it takes to get from perihelion to perihelion is called the anomalistic year. The anomalistic year is longer than the sidereal year by about 5 minutes.

The reason precession affects climate has to do with the relative location of the summer solstice and perihelion. Currently, the summer solstice in the northern hemisphere is six months away from the perihelion. This makes for milder summers, since Earth is actually a little further away from the sun during the summer. Likewise, it makes for milder winters, since the Earth is closest to the sun during the summer. Incidentally, it also makes for longer summers, because the Earth orbits more slowly when it is further from the sun. However, because the anomalistic year is longer than the tropical year, there is a 21,000 year cycle, in which the perihelion moves from winter to summer and then back again. Therefore, seasons will grow stronger, and then milder again every 21,000 years.

Milder seasons favor ice ages because the summer isn't strong enough to completely melt the ice left over from the previous winter. If the ice never melts, it reflects more light from the sun, cooling Earth and starting a feedback loop which ultimately leads to an ice age. Of course, we could just as easily argue that a milder winter is less likely to start the ice cycle. Ultimately, it comes down to a more quantitative analysis along with experimental observation, and the current evidence says says that when the precession cycle favors milder seasons, it favors ice ages.

Of course, in the southern hemisphere, winter is in June, and summer is in December. When the northern hemisphere has milder seasons, the southern hemisphere has stronger seasons, and vice versa. Why would the 21,000 year cycle affect global climate if there's always one hemisphere with stronger seasons? I don't know the details, but basically, the northern hemisphere is more important (sorry South Africa!) because that's where the majority of the land mass is. Therefore, our current place in the precession cycle favors an ice age, but obviously its effect is being outweighed by something else, possibly the other Milankovitch cycles.

Obliquity

Earth's axial tilt is currently 23.5 degrees, but in fact this number changes slightly over time. Roughly every 41,000 years, the tilt cycles between 22.1 degrees and 24.5 degrees. The cause of this so called obliquity variation is, again, the sun, moon, and planets all tugging on Earth's equatorial bulge. Because axial tilt is the reason for the season, greater axial tilt will cause stronger seasons, and smaller axial tilt will cause milder seasons. Right now, we're near the middle of the cycle, and axial tilt is decreasing. Current arguments say that smaller tilt favors ice ages.

Interestingly, it has been shown that if the moon didn't exist, the Earth's axial tilt would change chaotically from 0 to 60 degrees, causing climate changes that would possibly be fatal to life. This is often used to argue that we're pretty damn lucky to have a moon. On the other hand, current theories say that a mars-sized object crashed into early Earth, and the resulting ejecta coalesced into the moon. If that collision had never occurred, the Earth would be spinning much faster now, and its axial tilt would be stable as a result.

Eccentricity

As I mentioned before, the Earth is not exactly circular. Its orbit is actually in the shape of an ellipse, with the sun placed at one focus of the ellipse. The "focus" is basically a mathematical point in an ellipse, slightly offset from the center. The ratio between the focus's distance from the center and the perihelion's distance from the center is called the eccentricity. An eccentricity near zero means a more circular orbit, and an eccentricity near one means a more elliptical orbit. Earth's eccentricity is about 0.017, meaning it is nearly a perfect circle.

For the same reasons that the perihelion changes its location in Earth's orbit over time, so eccentricity too changes over time. Because of complicated interactions with other planets, the eccentricity varies from 0 to 0.06 in not one but two cycles which last 100,000 years and 400,000 years. Our current eccentricity is a little below a maximum of the 100,000 year cycle, and will get lower over the next 30,000 years. A complicated math calculation shows that the maximum eccentricity causes up to 0.2% more sunlight than the minimum eccentricity, but that's a rather small effect. Perhaps more importantly, a higher eccentricity will amplify the effects of the precession cycle.

We would expect eccentricity to have the smallest effect of the Milankovitch cycles, but it's an unexplained observation that it in fact has the largest effect.

As an aside, we have a rather interesting way of measuring Earth's temperature over long periods of time. See, when marine plankton die, they leave their skeletons on the ocean floor. When the ocean is colder, their skeletons tend to preferentially incorporate the 18-oxygen isotope, which is basically a less common, but heavier version of the oxygen atom. Furthermore, in colder climates, 16-oxygen gets preferentially removed from the ocean and incorporated into the polar ice caps. Thus, during colder climates, the ocean floor sedimentary deposits tend to have a higher percentage of 18-oxygen isotopes. By digging into ocean sediments, we can use this to determine the Earth's temperature for the past several million years.

What the ocean sediments show is that before one million years ago, the biggest cycle in global climate had a period of about 41,000 years, suggesting that obliquity had the biggest effect. However, about a million years ago, something fundamentally changed about the Earth's climate system, and its biggest climate cycle now has a period of 100,000 years, with ice ages slightly lagging the times of low eccentricity. What changed? Why does only the 100,000 year cycle have an effect, while the effect of the 400,000 year cycle remains small? Obviously, there is still science to be done. The current best explanation seems to be that there are "complicated" interactions and feedback mechanisms which amplify the 100,000 year cycle, but obviously the devil is in the details.

So... Seasons: pretty important? Let's celebrate!

[This being a very information-heavy post, I should probably cite my main source: The Earth System, 2nd Ed. by Kump, Kasting, and Crane. Anyways, no one should be looking to my blog as a serious research resource.]

Of waves, sounds, and solar wind

I've got a bunch of links here: sounds generated from scientific data from space! I have a long explanation afterwards, but first take a glance at some of these links so you know which direction I'm going.

Selected Sounds of Space
The Lion Roars
The Music of the Spheres
Sounds of the Magnetosphere
Radio Jove

One of the important parts in thinking like a physicist is understanding waves. Waves appear everywhere. The music I'm currently listening to is a wave. The light coming from my computer screen is a wave. And thanks to quantum theory, we can consider the entire universe to be a many-dimensional wave of sorts.

Making a wave is really not all that difficult. If you have a system that is stable, like a pendulum, for instance, that means that a small push and it will just come swing back towards equilibrium. In some systems, it won't just go straight to equilibrium, but will swing back forth for a little while first. We call this an oscillator. If we have a bunch of oscillators linked together, then one oscillator will cause the next oscillator to move, which causes the next one to move, and so forth. Thus we have a traveling wave.

Nearly anything can be an oscillator. Each individual particle is an oscillator. If you knock a bunch of particles forward, they'll hit another bunch of particles, which will hit another bunch of particles, and so forth. These are sound waves. If you drop a pebble into some water, it will cause a small excess of water in that location, and this will push up the water in the surrounding area, which will push up even more water. This is a ripple, a water wave. If you run a bit of electricity through a wire, it creates electric and magnetic fields. Because of the peculiarities of Maxwell's equations, which govern electric and magnetic fields, the fields will spread outwards. This is an electromagnetic wave (aka light, though not necessarily visible light).

A more mundane example is traffic. Let's say we have a freeway full of cars, and one of them slows down to get a better look at an accident. The car behind it has to slow down too, and then the one behind that one, and then the next car. This wave can propagate backwards through the traffic a long way. This just goes to show, even when we look at non-physical laws (ie traffic laws), waves still appear as an emergent pattern.

In my research, I study yet another kind of wave that travels through something called a plasma. A plasma is basically ionized gas. By ionized, we mean that the gas is energetic enough that most of the atoms have been separated from one of their electrons. As a result, most of the particles in a plasma either have a positive charge (the ions) or a negative charge (the electrons). This gives plasma many electromagnetic properties, since electricity is basically the movement of charges. And recall that sound waves are basically made of moving particles. Thus, you might expect a combination of sound waves and electromagnetic waves to travel through plasma. These plasma waves come in all sorts, depending on the pressure of the plasma, the direction of the fields, the frequency of the wave, and so forth.

Pretty much all of interplanetary space is filled with plasma. I'm talking extremely low density, better than the artificial vacuums we can create down here on earth, but the plasma is still there. I often joke that I study invisible fields and fluids that exist within vacuums (and I must say, the invisible and the non-existent do not look alike). Most of this plasma comes from the sun. The sun ejects a constant stream of particles called the solar wind. The solar wind would be quite deadly for life on earth if it hit us, but luckily it is deflected around the Earth by Earth's magnetic field. It's sort of like a river being deflected by a rock. But let's not take the analogy too far--Earth's magnetic field is a bit squishier than a rock; it is shaped by the solar wind. And this wind is not entirely constant. You can see the temperature, speed, density, and magnetic field change in these graphs of live data. These changes interact with the Earth's field, and create all sorts of plasma waves.

Since plasma waves and sound waves are both waves, it is possible to convert between the two. You can't hear plasma waves, but you can use a special device or some simple software. A radio, for instance, converts radio waves (light waves) into sound waves. And your speaker converts electrical signals (also a wave) into sound. You can do the same with plasma waves, usually by converting it to data, and then into an electrical signal that goes through your speakers.

And these sounds aren't meaningless. If the pitch is higher, that means the wave has a higher frequency. If it's lower, the wave has a lower frequency. If the pitch is descending or ascending, that means the frequency is slowing down or speeding up. If we hear a sound that is pitchless, that means that there are waves of all different frequencies happening all at once. All of these indicate different kinds of important events in the magnetic field.

There are also plenty of waves that are so low frequency that the human ear cannot detect them. Luckily, there are ways to artificially speed up the waves. Some of the links at the top use waves that we can hear; others use slow waves that have been artificially sped up. And there's no reason to confine ourselves to plasma waves near Earth. Some of the links have sounds from Jupiter too.

One of the characteristics of this field is that we have a ton of data. Tens of thousands of numbers every day, from each of the many devices and satellites we have out there all over and above the world. But as anyone intuitively knows, having ten thousand numbers is useless because it's just an information overload. We need to find overall patterns so we can better understand the physics behind it, or even make predictions. Computers tend to be very inefficient at finding patterns, whereas the human mind is hardwired to find patterns (often even when there aren't any). In order to take advantage of this pattern-seeking superpower, we just need to reduce the data to something we can wrap our minds around. One way to do this is with a graph or a visual. Another way is by converting the data to sound. So if you listened to any of the space sounds, you may congratulate yourself for exercising one of the few scientific powers that is inborn.

Bouncing electrons (Part 2)

See Part 1

When we last stopped, I had shown that electrons move along magnetic field lines. But if they simply follow the magnetic field lines, they'll eventually hit the Earth. Some do hit the earth, but others actually bounce back in a process called "magnetic mirroring". Why is this?

Ok, so I'm using the same picture. This time, I want you to notice that near the poles, the lines are very close together. The lines spread out much more when they are far away from the earth. When the lines are closer together, this means the magnetic field is stronger. When they are further apart, it means the magnetic field is weaker. It should come as no surprise that Earth's magnetic field is strongest when you are close to Earth.

This is a bit of an oversimplification, but the basic idea is that stronger magnetic fields repel electrons.* Therefore, if an electron is traveling along a magnetic field line, getting closer to Earth's north pole, it will eventually turn around. And then it will follow the magnetic field line all the way to the south pole. But since the magnetic field is stronger near the south pole, the electron will turn around again. As a result, electrons will bounce back and forth from pole to pole. Each bounce happens in a matter of seconds.

One of the results of this bouncing is that some regions of Earth's magnetic field are like traps for electrons (as well as other charged particles). And so we have the Van Allen Radiation belts, where lots of high energy radiation is trapped. Their shape can be described as "toroidal" or "donut-shaped". There are several other important regions above Earth with similar shapes.

Mmmm... radiation donuts.

Ok, so electrons are doing two things at once. They are gyrating and bouncing from pole to pole. But that's not all!

There is a third type of motion caused by Earth's gravity. Electrons, though very light particles, still fall. Only they don't fall. Remember, they're still trapped on magnetic field lines. If they fall down, they will very quickly circle around back up. So perhaps gravity has no effect at all? But it does have an effect! Unlike the magnetic field, gravity actually slows down and speeds up electrons instead of simply changing their direction. And faster electrons make larger circles! One side of the circle (the one closer to Earth) will be larger while the other side will be smaller. The resulting motion will look something like this.
As weird as it sounds, downward gravity causes the electron to "drift" to the side! Specifically, electrons will drift eastward. It takes a few minutes for them to go all the way around the Earth. Positively charged particles will also drift, but in the westward direction. Negative charges drift east, positive charges drift west, and we've got an electric current! This is called the ring current. Scientists measure the ring current to determine how many particles are in space, which tells us something about how the "space weather" is going.

And so, electrons above Earth have three types of motion. They gyrate, making hundreds of circles every second. They bounce from north pole to south pole in a matter of seconds. They drift eastward, going around the earth in a few minutes.

There's one last detail I want to add (and there are always more details), because it is related what I researched. All of the above types of motion conserve energy. The electron doesn't really change its speed much. However, this assumes that Earth's magnetic field is constant. It isn't. A stream of particles called the solar wind is always coming out from the sun. When these particles hit the Earth's magnetic field, they cause the magnetic field lines to vibrate like harp strings. Now, each of the three types of motion occurs at a different frequency. If the harp strings vibrate at a frequency near one of the types of motion, a resonant interaction will occur! For example, if the magnetic field line fluctuates every few minutes, it will resonate with the drift motion. The electrons might move between field lines, or speed up. We think this is the cause of one of the Van Allen Radiation Belts, but we're not sure. To find out, we must take lots of data in various circumstances to see if the evidence all lines up!

*Electrons don't actually slow down when moving into stronger electric fields, they simply transfer some of their forward motion to their circling motion. The technical description of this is that electrons conserve their "magnetic moment" under ordinary conditions.

Bouncing electrons (Part 1)

An electron is simply a very light particle with a negative charge. Usually, they're paired up with atoms, and they give us the full range of chemical reactions. But when electrons are by themselves, they're not really all that complicated, are they? In fact, above Earth's atmosphere, there are plenty of electrons all by themselves. Of course, by "plenty" I mean a near-perfect vacuum, but it's a lot by empty-space standards. There aren't really enough for them to bump into themselves very often. So what could they possibly do besides float leisurely in space?

It turns out that electrons do a lot, because they interact with Earth's magnetic field.

Magnetic fields, if you didn't know, are different from electric fields. Sometimes people get the electric force and magnetic force mixed up because on the surface they're so similar. The electric force, (which manifests in lightning and static electricity) causes like charges to repel and opposite charges to attract. Similarly, the magnetic force (which manifests in magnets and compasses) causes like poles to repel and opposite poles to attract. But magnetic poles do not attract or repel electric charges. They have a much stranger interaction.

The way that magnets work is by creating a magnetic field. The field consists of invisible lines that go from the north pole to the south pole. Technically, Earth's north magnetic pole is actually in the southern hemisphere, so sometimes "north" and "south" are mixed up (to the dismay of geophysicists).

When electrons, or any charged particles, move through the magnetic field, the magnetic field pushes them in a direction that is perpendicular to their motion and perpendicular to the magnetic field. Since the electron is being pushed neither forward nor backwards, it doesn't speed up or slow down. Instead, it simply changes direction, and travels around in circles. This type of motion is called "gyration".

The arrow V shows which direction that the electron (light blue dot) is going. The arrow F shows which way the magnetic field is pushing the electron. Because F is always perpendicular to V, the electron will constantly change directions and travel in the circular green path. The magnetic field in this example is coming out of the screen towards you.

Now, personally, I think it's just amazing that this weird physical force causes electrons to move around in circles of all things (even more amazing when you find that it is a consequence of Relativity). Another weird consequence is that the electron make circles at the same rate, no matter how fast it's going. If it's going really fast, it will simply make larger circles. In Earth's magnetic field, electrons will make hundreds of circles per second, regardless of their speed. This rate is known as the cyclotron frequency.

The electron cannot get too far away from the magnetic field line because it will simply circle back on itself instead. However, it can travel along the magnetic field lines without any resistance at all. The result is that the electrons are free to move along the magnetic field lines (in helix-shaped paths), but cannot jump from one line to another. It turns out that those invisible magnetic field lines aren't just mathematical curiosities, but they actually tell us where the electrons can move.

So where do the electrons end up? If you follow the magnetic field lines, don't they simply hit the earth? Yes, they do! Some of those particles will hit the upper atmosphere, creating colorful displays of light: the aurora. That's why the aurora is most common near the north and south poles--because that's where most of the particles come down and hit the atmosphere.

But not all of the particles hit the earth. Some of them "bounce" back along the magnetic field line! Find out why in Part 2.

2007 TU24 and the magnetosphere

Today, the asteroid called 2007 TU24 narrowly missed us. By "narrow," I mean about 85 earth radii--1.4 times the distance of the moon. Of course, there are some doomsayers who think this will somehow negatively affect us. They're wrong (duh). Bad Astronomy made an awesome debunking video.

The closest approach has already occurred, but the people at tu24.org don't seem to be letting up. They say they never thought it would hit the earth, and instead think it will cause magnetic disturbance. As it happens, the magnetosphere* is my area of study (mind you, undergraduate research only), and I declare bunk.

They claim that the asteroid traverses the magnetosphere. Well, this is difficult to confirm, since the magnetosphere is constantly changing shape. The magnetosphere extends roughly 15-25 earth radii from the earth, but there is also a very long tail that extends away from the sun. The asteroid just might be in the tail region, but I don't see them actually substantiating such a claim with anything other than this diagram they put together.

In any case, if it did traverse the magnetosphere, this would be of no consequence. Contrary to their claims, the asteroid is electrically neutral, like all large objects. If it had an overall negative charge, then all the surrounding positive ions in interplanetary space would very quickly be attracted to it until it no longer had a charge. So I just don't know how this rock could possibly have a noticeable effect on the magnetosphere. Furthermore, if it did have an effect, we already would have seen it. It doesn't take that long for waves to travel across the magnetosphere--maybe twenty minutes at most.

They throw around ideas like "magnetic reconnection", which is a real phenomenon. But guess what? It's a very common phenomenon that happens all the time even when there is no magnetic activity. Speaking of activity, there was a magnetic storm on November 20. This storm was not, and could not have been caused by a rock. Usually, storms are caused by solar flares and coronal mass ejections. These phenomena are far larger than Earth, and they really do have magnetic properties, since they're made of ionized gas. This gas has no overall electric charge; there are an equal number of positive and negative charges. And yet, do you remember anything happening on November 20? I didn't, and I study this stuff! I only know about it because I checked SpaceWeather.

Really, magnetic storms can have negative effects (see Wikipedia), which is why we need to study it. But mostly they just make pretty lights for the people in auroral regions. And these lights are caused by processes that are far less trivial than 2007 TU24.

*pronounced "mag (as in magnet)-KNEE-toe-sphere"

Precession of the Earth

The earth rotates. It has an angular momentum in the direction from the south pole to the north pole. This axis of rotation, as I explained earlier, is tilted slightly, and this is what causes seasons. The axis of rotation, in fact, does not always tilt in the same direction. This direction moves slowly around in a circle every 25,800 years. This circular motion is called precession. First, I'll explain why it precesses, and then the implications of precession.

Why does the Earth precess?

First, see precession explained

There are two components of precession. First, there's some angular momentum, and second, there's some torque. The angular momentum of the earth is obvious: it spins, about once a day. The source of the torque is less obvious.

It comes from the Earth's equatorial bulge. The bulge is caused by the fact that at the equator, the surface of the earth moves much faster. When an object rotates quickly, what we call the centrifugal force pulls outward on the object. The earth doesn't rotate quickly enough to fling people out into space, but it does weaken gravity very slightly (by less than 1%). This causes the ground near the equator to be further from the center of the earth, making the equatorial bulge.

Because of the equatorial bulge, there is more mass on the earth's equator. The sun and moon both pull on this extra mass. They pull the equator towards the ecliptic plane. If the earth weren't rotating but still had a bulge, then it would be pulled until there was no axial tilt. However, since the earth is spinning, it causes precession instead. The axial tilt doesn't disappear, but instead moves around in circles, just like a wobbling gyroscope.

What are the effects of the Earth's precession?

Because the angular momentum changes direction, "north" changes direction. The north star is just some lucky star that happens to be directly north at the moment. However, over thousands of years, the direction north changes such that the north star is no longer north. There are several other stars that are "north stars" at different times in the precession cycle.

If you think of it from the star's point of view, the star used to point north, but then the world moved. But the world will come around again, eventually giving the star another moment. Perhaps this is symbolic of something?

There is another effect: a difference between the "sidereal year" and the "tropical year". A sidereal year is the amount of time it takes for the earth to complete a full orbit. A tropical year is the amount of time it takes to complete four seasons. The precession of the earth causes the axial tilt to rotate around in a circle every 25,800 years. The direction of the tilt relative to the direction to the sun causes seasons. That means that for every 25,800 sidereal years, there will be an extra four seasons. 25800 sidereal years equals about 25801 tropical years.

New Years and Astrology

Our calendar uses tropical years, not sidereal years, because it is more convenient to farmers, among other people. The end result is that when we celebrate the new year, we are not celebrating a complete orbit of the earth, back to the location at the beginning of the year. We're celebrating a rather arbitrary time marker. But that's ok. I can still wish you a Happy New Year!

I should also note that the positions of stars go by sidereal years, not tropical years. Since we've been using tropical years to count the last 2 millennia, the usual dates for astrological signs are actually off by about a month. Also, there's a new astrological sign in the northern hemisphere. Of course, most people never know this, probably because astrology is equally ineffective either way.

Axial Tilt: The Reason for the Season

[Added 2012: this picture does not belong to me, but the source website went defunct at some point]

 

This picture has been going around the blogosphere. Forget discussions about how this fits into the "War on Christmas"--instead, I'm going to use this opportunity to explain the basic science of seasons.

The Earth moves around the Sun in a roughly circular orbit. The plane that includes Earth's orbit is called the ecliptic plane. While the earth is orbiting around the sun, it is also spinning around itself. When it is spinning, exactly two points on the surface, known as the north and south poles, do not move. The imaginary line going through the two poles is called the axis of rotation.

Seasons are caused by the fact that the axis of rotation is not perpendicular to the ecliptic plane. If they were perpendicular, the Earth's spin and orbit would go in the exact same directions. Instead, they are off by 23.5 degrees. The axis of rotation is tilted towards the sun during summer and away from the sun during winter. Why is the Earth apparently tilted in different directions at different times of year? It is in fact tilted in the same direction all year, it's just that the direction towards the sun changes throughout the year.

[Image from Timezone.com]

The day when the axis of rotation is tilted furthest away from the sun is called the winter solstice. This year, the winter solstice is December 22. The day when the axis is tilted closest towards the sun is called the summer solstice, which is somewhere around June 21 or 22.

[Image from Penn State University - I'm not sure what's up with the smiley faces.]

The reason axial tilt causes seasons is twofold.

First, the power from the sun is not evenly distributed on the Earth's surface. If you look at the above picture, there is about an equal amount of power between each of the yellow lines. However, towards the top and bottom of the Earth, that same amount of power is spread over a larger area of Earth. Therefore, the power per unit area is smaller closer to the poles, and larger at the equator. The power peaks at the Tropic of Capricorn during the winter solstice and at the Tropic of Cancer during the summer solstice.

Second, the length of the day grows shorter in winter, and longer in summer. In the above picture, you might notice that most of the tropic of cancer is in the dark. This indicates a shorter day. Also note that the entire arctic circle is completely in the dark. This indicates that it is perpetually nighttime. During the summer solstice, the arctic circle is in perpetual daylight. If you stand at the north pole, there is exactly one night and one day every year.

Both the length of the day and amount of power from the sun affect the temperature and climate. Around December, the northern hemisphere has shorter days and less power from the sun. However, the southern hemisphere has longer days, and more power from the sun. The southern hemisphere has summer at the same time that we in the northern hemisphere have winter. And vice versa. The southern hemisphere, I imagine, doesn't get many white Christmases.

Now, some people mistakenly think that the reason for the season is the distance from the sun. The Earth's orbit is not exactly circular, meaning that there are times of year when the Earth is closer to the sun, and times when it is further from the sun. This does have a very small effect on the climate, but it is not nearly as large as the effect of axial tilt. In fact, the day when the Earth is furthest from the sun (called the aphelion) is around July 7--in the middle of the northern hemisphere's summer. The Earth is closest to the sun (this point is called the perihelion) around January 3.

So there you have it--third grade science, as explained by me. Next time, I'll talk about more advanced stuff like precession or something.