You’ve maybe heard of cataclysmic variable stars. They are binary systems where one of the stars is stealing material from the other star due to their close proximity. This material forms a pancake around the star called an accretion disk. We’ve never imaged one of these systems but we have a very, very good theoretical model of how they work.

Every once in a while that accretion disk gets unstable and essentially blows up in what we call an outburst. Sometimes these outbursts are extra bright and carry a signature in their light curve called “superhumps”. These are large oscillations in the light curve at a period very near, but not exactly equal to, the orbital period of the system.

On 6/30/08 one of these systems, VY Aqr, went into a superoutburst. This is a fairly infrequent event for this star. The outbursts themselves happen every few years and the superoutbursts less often than that.

I was heading out to my observatory when the word came in so I slewed my fancy 0.212m telescope (doesn’t that sound more impressive than 8.3″?) and got some data. So did a few other people and I downloaded all of their data from the AAVSO. If you click the image above a light curve will open in a new window. Let me explain it to you.

This is a phase plot using the superhump period of this star (P_sh = 92.7 minutes). So anything that happens 92.7 minutes after something else is plotted at the same phase. So the X axis is the phase of the superhump period and the Y axis is the brightness of the star. Because the star is getting dimmer, each day’s data is lower on the graph than the previous day. So each night is folded upon itself but each subsequent night is below the previous night.

You can see there are some interesting things going on! The superhump amplitude and phase change over time as the systems fades.

The latest papers on this object included Doppler tomography, new parallax measurements and spectroscopy from the Hubble Space Telescope. There is a lot of interesting physics in these systems and they are the subject of on-going study by astronomers. Including me!

The AAVSO has posted their Variable Star of the Season and this time around it’s FG Sagittae, a star that has given us an opportunity to watch it evolve over human timescales, something very rare in stellar evolution.

…many papers have detailed the remarkable evolution of FG Sge from a faint, hot, blue post-asymptotic giant branch star and planetary nebula in the making to a much cooler and brighter yellow supergiant. Even more exciting for variable star observers, following FG Sge’s four-magnitude brightening and several decades of relative constancy, the star now appears to exhibit the dramatic and seemingly random fluctuations and fadings of the R Coronae Borealis class of variable stars. FG Sge is clearly a star undergoing extreme changes, and we’re fortunate to be treated to its amazing show.

If you have access to a telescope you can go take a look for yourself!

Regulus is the 22nd brightest star in the sky to the naked-eye. Since it lies along the path followed by the Sun, Moon and planets (called the “ecliptic”), bright planets frequently pass close to the line of sight to this majestic star. In fact, it is so close to the ecliptic that the Sun passes within a half degree of it every August. (Don’t go looking for this event visually! If you want to see how close, check out the movie from the SOHO satellite here. The brightest object - besides the Sun! - is Saturn. Regulus pops out from behind the occulting disk right at the end of the MPEG.)

I first became more closely acquainted with Regulus during my postdoctoral fellowship at the Dominion Astrophysical Observatory in Victoria, British Columbia (Canada). I would frequently use the 1.2m telescope with its fantastic high-resolution spectrograph. One of the shortcomings of filament bulbs is that there is precious little light emitted at the blue end of the spectrum - if you want to calibrate the pixel-to-pixel sensitivity of your detector, you can’t get enough blue signal without saturating the red end. What to do, what to do … One fine solution is to observe a bright blue star which is rotating so quickly that all of its spectral lines are smeared out over many, many pixels. Enter Regulus! The few spectral lines in its spectrum were already broad hydrogen lines and the rotation rate of over 300 km/sec smeared them out even more. A great star for calibration.

And a very poor one for measuring the line-of-sight (”radial”) velocity using the Doppler shift! In fact, astronomers last studied it for binarity in 1912-1913 - almost a century ago! Many hot stars are far enough away that lines from interstellar gas can be used as reference points for radial velocities. Not so Regulus - it is only 24 parsecs away and there just isn’t enough gas along the line-of-sight to this neighbor of the Sun.

Regulus came back into favor when its shape and the brightness distribution could be measured by a very cool kind of optical instrument called an interferometer. Work by McAlister and collaborators using the CHARA long-baseline optical inteferometer they created on Mount Wilson found that Regulus is rotationally-flattened and it spinning at 86% of the speed at which the surface gas would cease to be bound to the star. They were able to show that it was darker along the equator of the star, too. This high rotation rate was an anomaly for a star that was as old as Regulus (apparently 150 million years - pretty old for a star of this mass) since similar stars seemed to be fast rotators only early in their lifetimes.

So Doug Gies and his collaborators embarked on a new study using modern instrumentation to see if there was any evidence of it orbiting the center-of-mass of a binary system containing it and a hitherto-unknown companion. As a bright star, there was plenty of light available to be dispersed by high-resolution spectrographs. They used several in their study including two “unusual ones” - the Kitt Peak National Observatory Coude Feed Telescope and the Multiple-Telescope Telescope!

Let me briefly describe these two instruments. A Coude room is very high-resolution spectrograph capable of tearing the light from a telescope into very fine shreds of color. It was designed to be “fed” by the 2.1m telescope at Kitt Peak. However, observatories tend to do deep imaging around the time of New Moon (i.e. when the sky is dark) and the 2.1m served a variety of such needs. It was realized that the a smaller telescope could “feed” the spectrograph during these periods and that brighter stars could be observed with that smaller telescope plus Coude spectrograph while the big telescope was busy imaging!

The Multiple-Telescope Telescope at Hard Labor Creek in Georgia is another ingenious system for bright star spectroscopy. It has nine relatively inexpensive 0.33m mirrors which focus onto nine optical fibers which then feed a stable, bench spectrograph. Since it only studies bright stars, the mirror pointings can each be individually-tweaked to center up on the bright star. It uses a cheap alt-azimuth mount and collects as much useful light as a 1.0 telescope for a tiny fraction of the cost of such a large telescope.

So - you are asking - what did Doug Gies and his collaborators find? They found that Regulus was indeed a spectroscopic binary. Once every 40.11 days, the system completes one orbit. Regulus itself has a mass of about 3.4 times that of the Sun. The companion of Regulus is much less massive - only about 0.30 solar masses. Such a small mass object is either a low-mass star or a white dwarf. The latter possibility provides an explanation for Regulus’ rapid rotation! The idea is that the companion was once the more massive member of the pair and when it finished hydrogen burning in its core, it expanded dramatically and started losing mass to Regulus in a manner which “spun it up”. A mass of 0.30 solar masses is very low for a white dwarf - such objects are found only in systems where it is clear that much mass has been transferred.

A final piece of the puzzle fell into place when spectra taken using the far-ultraviolet Spanish satellite MINISAT-01 were re-examined. When the expected contribution from Regulus was removed, light remained in the ultraviolet region of interest - consistent with a white dwarf but not a cool low-mass star. So Regulus joins the list of bright stars in the sky (which includes Sirius and Procyon) having white dwarf companions and proves once again that “three out of every two stars is a binary”!

Their paper has been accepted for publication in the prestigious Astrophysical Journal Letters.

A Spectroscopic Orbit for Regulus
Doug Gies (GSU) et al

Interview: Juan Collar and Detecting Dark Matter (MP3, 28.3MB, 41:10, Show Notes)

Our own Doug Welch wrote a very nice article in the latest issue of Sky and Telescope called “How to Hunt for Supernova Fossils in the Milky Way“. I can’t find a link to the article itself but S&T has a post about the article.

It’s really cool stuff — an accidental discovery of supernova light echos in the LMC has led to a new way to look for and study supernovae here in our own galaxy.

Doug discusses in detail how you can help hunt for these elusive light echoes. It would be a great multi-year project for a small college astronomy program or for accomplished astrophotographers with a bunch of really nice equipment.

Doug also describes in the article what happens if you find a light echo:

What happens if you find a candidate light echo? You become my new best friend!

How can you pass that up?!?

Check this sh!t out:

Credit: Brant Robertson, Spitzer Fellow, KICP/UChicago

This interview is quite long so we’ve uploaded low and high rez versions. The low rez version is the one in the RSS feeds.

If you subscribe to the feed, the audio is probably already on your box. Or you can check out the show notes or download the MP3 file directly:

Slacker Astronomy podcast interview with Brant Robertson (low rez) (MP3, 24.7MB, 1:11:20)

Slacker Astronomy podcast interview with Brant Robertson (high rez) (MP3, 65.6MB, 1:11:20)

In this case it looks like they got lucky and were able to catch RS Oph, a recurrent nova, in outburst. The surprise was — the dust:

The nuller saw no dust in the bright zone, presumably because the nova’s blast wave vaporized dust particles. But farther from the white dwarf, at distances starting around 20 times the Earth-sun distance, the nuller recorded the spectral chemical signature of silicate dust. The blast wave had not yet reached this zone, so the dust must have pre-dated the explosion.

“This flies in the face of what we expected. Astronomers had previously thought that nova explosions actually create dust,” said Richard Barry of Goddard, lead author of the paper on the observations that will appear in the Astrophysical Journal.

The team thinks the dust is created as the white dwarf plows through the red giant’s wind, creating a pinwheel pattern of higher-density regions that is reminiscent of galaxy spiral arms.

Novae have been studied for a long time and we thought we had them pretty much figured out. If confirmed, this result could trigger a lot of activity in the variable star community.

In 1998 observations of Type Ia supernovae suggested that the expansion of the universe is speeding up. In the past few years, these observations have been corroborated by several independent sources: the cosmic microwave background, gravitational lensing, age of the universe and large scale structure, as well as improved measurements of the supernovae.

When Einstein developed general relativity, as is well known, he added a factor to his equation because it was necessary to reproduce the universe he thought we lived in — a static universe with no expansion or contraction. When we observed that the universe was not only expanding but accelerating in its expansion, that extra term in the equation was already there to express it.

That term is capital lambda (Λ). It’s a pressure term, in one way of thinking. Just like a gas or a fluid has pressure, it appears the universe has some sort of pressure. In another way of thinking, Λ is an energy because pressure and energy density are related in a linear way. So there is an apparently uncompensated energy that results in a universe that is out of balance — it’s being very slowly blown apart.

So, like dark matter, dark energy is “real”, in this case “real” meaning that it’s a name for something that we really do observe. Some people are uncomfortable with this. They think, in the example of dark energy, that we don’t need an extra term in the equation, the rest of the equation is somehow wrong. That is, of course, another perfectly valid option. Either physics is wrong or dark matter/energy exist or both!

But don’t be fooled — the phenomena are real. We really do find an unaccounted for gravitational influence (dark matter) and we really do see something acting like a pressure in our cosmology (dark energy). This is not philosophy, it’s science and it’s very good science at that. The fact that there are still things we don’t know is the fun part!

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.

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.

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

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.

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!

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