A star wiggles thrice

If you are even moderately interested in astronomy you’ve heard about the latest discovery of a near-Earth-sized planet. Our buddy The Bad Astronomer lays it out very nicely for us.

The image at right shows the gravitational effect of each of the 3 planets on the star of this system. The y-axis shows the star alternately coming towards us and away from us as it orbits the barycenter of the system. (Our Sun does this too, mainly from the tug of Jupiter.) Note the units are in meters per second (m/s), this is 1/1000th of the unit astronomers generally use (km/s).

This is accomplished by measuring emission and absorption lines in the spectrum of the star. Each of these three sine waves is superimposed on the measurements. The error in these measurements is reported at about 1 m/s, so astronomers are looking for very small movements of the lines.

Thus, the trick is to first get ridiculously high-resolution observations, then measure the spectra with exquisite precision and finally untangle the influence of all of the orbiting bodies on the data. The end result of all of that work is a plot like that at right: proof that something is orbiting that star. Using other physics we can determine the masses and the size of the orbits. Even more recent technology is allowing us to probe the atmospheres of these planets spectroscopically.

I suspect there will be a lot more amazing discoveries along these lines.

Polytropes and Recording Studios

I’ve been an amateur astronomer for a long time but I had never heard the word “polytrope” before. It turns out it is an important concept in stellar astrophysics. It also, in a round about way, brings me back to my first job at a recording studio.

In 1988 I graduated from Berklee College of Music and got a job in Lake Geneva, Wisconsin at a recording studio called Royal Recorders. Unbeknownst to me at the time, Yerkes Observatory is also located on Lake Geneva, just a few miles from where I worked. One of the great theoretical astronomers of the 20th century, Subramanyan Chandrasekhar, aka “Chandra”, worked at Yerkes for almost 30 years.

There was a time in astronomy when we didn’t know for sure that nucleosynthesis was powering the luminosity of stars. We hadn’t figured out how to get the temperature high enough for thermonuclear reactions. Chandra, standing on the shoulders of many giants, helped figure it out and formalized a theory for stars based on an idealized fluid model — a polytropic process. Polytropic means it is a reversible process where the pressure is proportional to a power of the density.

By combining hydrostatic equilibrium with a polytropic model of stars, we could finally solve the equations to predict the temperature and density of stars. When we plugged in the numbers, using the “standard model” of stars developed by Eddington, we found central temperatures in the tens of millions of degrees — plenty hot for nucleosythnesis.

So in terms of astronomy, a polytrope is a mathematical model of a star. You plug in a few assumptions and you get out many of the physical parameters that describe a star — the temperature, density, mass, radius and pressure. We can describe much of the structure of the HR diagram, from first principles, using this model.

Chandra left Yerkes around 1965, the year I was born. I visited Yerkes for the first time just this year. I’m also learning about Chandra’s work for the first time in the astrophysics class I’m taking. It is fun to think that I walked the same streets and drove the same roads as Chandra, in a little corner of Wisconsin, a long time ago.

Cafe Scientifique on “Planetary Systems and Extraterrestrial Life”

This three half-hour collector’s set of MP3s allows you to vicariously live out your dream of being present at a Cafe Scientifique. Ralph Pudritz and Doug Welch of the Department of Physics and Astronomy at McMaster University in Hamilton, Ontario, Canada were the presenters. This informal, discussed-oriented event took place at the King Paisley Pub – an excellent place for astronomy outreach, in my humble opinion.

Listen to the audio by downloading parts 1, 2, and 3.

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SG Interview: Doug Welch on MACHO

Slackerpedia Galactica Interview: Doug Welch and the MACHO project. (MP3 audio file, 13:28, 6.2M)

MACHO, and its sequel, SuperMACHO, are projects that have directly detected dark matter. Dark matter is dark, yet we can observe it through a variety of clever techniques. One such technique involves measuring the brightness of stars and looking for the effects of gravitational microlenses — stars which get brighter for a brief time, once and only once, as the dark matter passes in front of it.

Dark matter is a funny term because it encompasses all the matter we can’t see. Dark matter is not one thing, it is all the things we can’t see but can detect due to their gravity. The dark matter detected by MACHO is likely things like planets, brown dwarfs, white dwarfs or low-mass black holes, if such things exist.

Dr. Doug Welch is one of the researchers involved with the MACHO project. In this podcast interview with Michael Koppelman, Doug talks about all things MACHO.

If you haven’t already subscribe to the podcast or just listen now.

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Stars and Pressure

In my last post I talked about the balance of forces that make stars, like the Sun, stable. I said we could learn things about stars by understanding this balance. Here is an example.

We ended up with this equation:

This is not as complex as it looks. The big G is just a number based on the units we are using. The M is the mass of the star. The funny looking p is the greek letter roh and it is the density of the star. r is the radius and the big P is the pressure. We can make this more simple if we assume the pressure is zero at the surface of the star. We’ll also change the density back to mass divided by volume so we can combine some terms.

The pressure P at the center of the star is proportional to the square of the mass and inversely proportional to the 4th power of the radius.

So if two stars are the same size and one is twice as massive as the other (and obviously much more dense as a result), the pressure in the center increases by a factor of 4. If two stars are the same mass but one is half as big as the other, the pressure at the center will be 16 times more.

If you Google the mass and radius of the sun and the value of the constant G you can calculate the pressure of the sun with the equation above. Try it!

Why Stars are Stable

Hey slackers!

So I am taking a class about the structure and evolution of stars. I have been taking classes for 6 years (albeit one class at at a time) just so I would have the math and physics background to take this class. As someone that got into the quantitative side of astronomy via variable stars, I want to understand stars. Lucky you, I’m going to take you along on some of the concepts as they are introduced in this class. Today I am going to talk about hydrostatic equilibrium. It’s a fancy term that explains why stars are stable most of their lives. It goes like this…

We all know that gravity is an attractive force. So if I have a little blob of material in a star, gravity is going to try to pull that blob towards the center of the star. But we just said that stars are generally stable, meaning that the material can’t be free-falling into the star — something is resisting the force of gravity. In physics if things aren’t moving we call them “static”. So if this blob of material in a star or the sun is static, there must be some force opposing gravity. Mathematically we can write this as an equality:

Here the “g” stands for gravity and the “b” stands for buoyancy. We don’t know the buoyancy force is yet, but we know something is pushing that material outward.

We know how to write the force of gravity:

Newton gave us this equation. The G is the gravitational constant, the big M is the mass of the sun or star and the small m is the mass of the little blob of material.

Pressure is force per unit area. So if I push my hand on your back, the pressure you feel is the amount of force I am exerting divided by the area of my hand. If I used the same amount of force but with a much smaller area, say the point of a knife, the pressure is much greater and I stab you in the back. Much more force can be applied on your back, say by your seat on an airplane as it takes off, provided the area is greater.

We know that gas has pressure, just like the atmospheric pressure here on the surface of the earth. There is a pretty simple formula for gas pressure:

Ignore the n and and the R for now — the P stands for pressure and the T stands for temperature. So the pressure is proportional to the temperature. The force from pressure is a little different in this case, though, because in order for gas pressure to exert a force it has to be unbalanced. In a star (and on Earth) the pressure is greater the closer you get to the center. So even for a small blob of material, the pressure at the bottom is greater than the pressure at the top. Physicists call this a gradient. So the force from gas pressure in this case is related to the difference in pressure between the top and the bottom of the blob. We are calling the “buoyancy” force above by its true name now, the gas pressure.

If you are not familiar with calculus, the small “d” in front of the P (for pressure) and A (for area) means a vanishing small change. So the equation above is stating that the gas pressure is equal to a small change in pressure times the tiny little area of our blob of gas.

With me so far? Now the point: we set the two forces to equal each other, since the material is static and not moving.

One last little bit of algebra, replacing the small “m” on the left with the density and the volume (because density is mass divided by volume so mass is density times volume) lets us cancel some terms and rearranging others we get:

So the gravitational force is equal to the ratio of the change in pressure (dP) to the change in radius (dr). The forces balance and the star is stable for millions of years. Were these two forces to become unbalanced it would cause sizable changes to the star in a matter of hours!

This is all a little deep, perhaps, but congrats for wading through it. This is an extremely important concept in stellar structure. Next time I’ll talk about some cool calculations you can do with this to learn things about the Sun and stars.

More info and illustrations of hydrostatic equilibrium are here: http://jersey.uoregon.edu/~imamura/208/jan27/mech.html

Meteors Striking the Moon