Circumstellar Masers

The image above is called the Hertzsprung-Russell (H-R) Diagram. In a very simple synopsis, it relates the temperature (and thus, the color) of stars with the amount of light they put out. As you can see, the higher the temperature (and the bluer the color), the greater their total luminosity (energy output per unit time). The long, slightly bent line in the center is called the "main sequence" and is where we find stars in the middle of their life.

If you look at the top corner, though, you'll see two clusters: one a straight line labeled "supergiant" and the other a hockey-stick-shaped line labeled "giants." Both of these branches of the H-R diagram have to do with the death of stars. Everyone is generally familiar with super nova star deaths, where a star explodes in a violent output of energy and is no more. However, most are unfamiliar with the less extravagant, more common method of star death.

Small stars (all stars with a total mass less than about 8 times the mass of our sun) are too small to explode. Instead they swell up. At the end of their life, all of the hydrogen they were so used to fusing into helium is depleted. With no radiation pressure to keep it at the size it was, the star contracts due to its immense gravity, which crushes the helium at the center. Suddenly, the density becomes so great that the helium core starts to fuse the helium into carbon. An enormous amount of energy is released, pushing the edge of the star to an unprecedented radius. In fact, when our sun starts to swell into a red giant, its radius will extend until its surface is at about where the earth is now (about 93 million miles)! The so-called giant branch on the H-R diagram shows us that as stars leave the main sequence in this manner, their luminosity increases by several orders of magnitude (as a result of the brightly burning helium). The star gets so big that its outer layers star to peel off and expand into space, leaving a very hot chuck of carbon ash in the middle (called a white dwarf star) and forming what we call a planetary nebula (an example of which you can see here).

Some stars, however, don't quite make it to that stage without a fight. They get so big that the helium fusion at the center shuts down. As before, with no outward radiation pressure, the star contracts and crushes the helium core until it starts fusing again. This cycle repeats and repeats in a process known simply as "variability." The star increases in luminosity and decreases again in a matter of days or years (depending on the star) but with such regularity that we can spot them a mile away (ok, more).

Even then, a few layers of gas on the very outer edge of the star manage to escape and expand in a sphere around the star. As you would expect, heavier molecules expand slower and lighter ones move faster; we soon see a separation of individual gases. The fascinating thing about these expanding envelopes is that they quite naturally form lasers.

All of the lasers on earth are man-made. A study of the Einstein coefficients and some fancy math told us that they were possible and we gave it a shot. Eventually we created the right conditions to make a concentrated beam of stimulated emission. Looking into space, however, we can see gigantic (some can be almost 5 billion miles wide!) stellar lasers (which we call masers because the photons coming from them are microwaves) which are continually fueled by the variable star in the center.

These huge masers emit in all directions, which means that when we look at variable stars, we commonly see maser emissions (if we're looking for the right wavelength with our telescope). In other words, all over space there are absolutely enormous laser pointers shining directly at the earth. Just another proof that the universe is way cooler and more complicated than you thought before.

The Foucault Pendulum

Have you ever seen one of those pendulums that swings back and forth but over the course of a day or so makes a complete circle? It's called a Foucault Pendulum (and please, people, it's pronounced /Foo-coh/ not /Fow-cult/). I'm going to tell you how it works.

Get some thread and tie a relatively heavy object (a ring, for example) to one end to make a pendulum. Suspend it from your car's rear-view mirror on the windshield. Before you make a 90° turn, start the pendulum swinging so that it swings directly toward and away from the windshield. Execute 90° turn. The pendulum is now swinging side to side towards the passenger- and driver-side windows. BAM. Foucault pendulum.

No, seriously. This is exactly the same idea, but the thing that's turning is the earth. If you get a really heavy pendulum and have it swing with no friction, it's rotational inertial is very high (i.e. it is very hard to get it to start travelling in a circle). So when the earth rotates, it tends to swing in the same absolute plane as when it started. In the car example, if the windshield-rear-window plane is North-South, then when your car turns, the pendulum is still swinging N-S but the plane of oscillation relative to the car has rotated 90°. The car has, in effect, turned around, above, and underneath the pendulum which is still swinging in its original plane.

Interestingly enough, the time it takes for a Foucault pendulum to complete a full revolution in the relative frame (i.e. when it looks like it's swinging the way it started out to observers on earth), varies depending on latitude because of the Coriolis "force" (just a side note here. Please never ever refer to the Coriolis "force" as the thing that makes toilets flush in the opposite direction south of the equator. Hearing that drives me crazy). Simply stated, if you stand on the north (or south) pole, you turn in a full circle once a day (just like everywhere else), but your linear velocity is zero (you just spin around in a circle because you're standing on the axis of rotation). Standing on the equator, you still make one full revolution per day, but now you're 6000 km away from the axis of rotation (thus, your linear velocity is huge. Think of how the middle of a spinning record and the edge of a spinning record both go around at the same frequency. For this to happen, the outside point must be moving much faster than the inside point. Same idea as a marching gate turn (for parades); the inside guy just rotates in place, but the outside guy tears a hole in his pants taking long strides to keep the line straight).

In other words, there is a velocity gradient between the poles and the equator, meaning that as you get closer to the poles, your linear velocity decreases. We don't notice it because frictional forces (our feet on the ground) keep us in the same relative position. A free-swinging pendulum, however, swings above an earth with faster linear velocity at (minutely) lower latitudes and into slower linear velocity at higher latitudes. The earth is travelling faster under the pendulum when it is further to the north. So, think of how a tank turns. If both treads move at the same speed, it goes straight, but if one tread moves faster than the other, it turns. So with the pendulum, when the earth under the pendulum at its northern-most swinging point moves slower than the earth under the pendulum's southern-most point, it appears to turn in place (but we know it's really the earth doing the turning). Now on the equator, the pendulum feels a Coriolis "force" when it swings north, but then the exact opposite "force" when it swings south, so it stays in the same plane. At my latitude (40° N), the pendulum takes a little more than 37 hours to make a full revolution relative to an observer. At the north pole, it takes exactly 24 hours.

So how do they make a pendulum swing without friction? Well, they don't. However, they can counteract the force of friction using a (patented Newton's first law) equal and opposite force (Ok, I know that using the words equal and opposite sounds like the third law, but the law that's really in effect here is that if the net force on something is zero, it doesn't accelerate—first law). At the top of our Foucault pendulum at BYU there is a metal disc (Radius ≅ 3 in) that swings into an electromagnet once per oscillation. At the peak of the swing, the magnet turns on momentarily, turning the disc and undoing the frictional force from the swing. So, we can't really make a frictionless pendulum, but we can make it act like one. In any case, the electromagnet doesn't cause any acceleration, it prevents (or counteracts, rather) negative acceleration.

You may be wondering why I keep putting quotes around the word force when it's next to the word Coriolis. I'll tell you. It is not a force. It just looks like one. Imagine if you sat in a room with a flat floor with no windows. The room is actually on a turntable and spins around in circles (but so slowly that you can't feel it). To you it seems like a normal room, but if you set a ball on the perfectly flat floor, it would start to roll towards whichever wall it was closest to. In your Newtonian-trained mind, you would think "Hey, the ball accelerated. There must be a force on it." But you would be wrong because you are now in a non-inertial (accelerating) reference frame where Newtonian physics doesn't apply. The thing that's feeling the force is the frame of reference itself. The ball rolls because the floor is turning (accelerating by changing direction, not speed) underneath it. Hey! That sounds like a Foucault pendulum. Yep. The "rotating room" we are in is the planet earth. It's so big that we don't notice it spinning (except for the sun, moon, and stars) but sometimes we find things that seem to violate physics. They don't. Trust me.