Astro Seminar: Finding exoplanets

18Feb07

This week’s seminar topic is HOW TO FIND THINGS, namely brown dwarfs and exoplanets. It covers a nice mix of interesting physics and practical real-world considerations.

Plus, in a stunning display of totally awesome, WordPress added support! Which means I can now present seminar synopses WITH EXTRA EQUATIONS.

Here goes.

When I was a little kid I used to think that if I squinted really hard at a star, I might be able to see planets around it. I never really succeeded. Armed as I am with physics wisdom, I now appreciate that this is completely obvious, and that my seeing any difference at all had mostly to do with my needing glasses. BUT! The usual conception of astronomy does rather assume that, you know, what you do is LOOK at things and take pictures. And then you look even harder with the help of a computer, and you FIGURE STUFF OUT. And sometimes that is the case. Malcolm, the guy I observe for, does pretty much exactly that: he looks at pictures of a supernova and plots its brightness as a function of time. But with exoplanets, the LOOKING method is all kinds of difficult, for two main reasons:

1. CONTRAST. Unlike stars, which are inherently luminous, planets “shine” by reflecting the light of their sun. How much they reflect depends on
   1. The luminosity of the star;
   2. The effective surface area of the planet;
   3. The distance of the planet from the star, ; and
   4. How reflective the planet’s surface is, which is termed its albedo, .

   The ratio of the flux from the planet, , to the flux from the star, , is
   
   For a planet of the size and distance of Jupiter, . Which means the planet, on your pretty photograph, is TWO BILLION times fainter than the star. Which means good luck seeing it.

3. RESOLUTION. The other problem is that in terms of interstellar distances, the distance from a planet to its sun is pretty tiny. If you were looking at the Earth-Sun system from a distance of 10 parsecs (32.6 light years), the Earth-Sun radius would be about 0.1 arcseconds. For comparison, the telescope I usually observe on has a 1.2-meter mirror, and on a good day can resolve objects about 2.0 arcseconds apart. The 6.5-meter Magellan telescopes in Chile (the only other scopes I’ve observed with) can get down to 0.3 arcseconds or so. So even with some fancy scope work, the star and planet tend to blur into one blob of light.

Happily for exoplanets, astronomers are inured to such hardships, and have devised alternative methods of detection. There are three big ones:

1. Astrometry!

which means measuring the position of objects on the sky.

2. Spectrometry!

or tracking the amount of specific colors of light emitted by objects.

3. Photometry!

i.e. measuring the brightness of objects.

Both spectroscopy and astrometry rely on the dynamical truth that PLANETS DO NOT JUST ORBIT THEIR SUN. Heresy! you cry. No, no. In any system of orbiting whatnot, both bodies orbit around the system’s center of mass. Like this:
Which means that the star, too, moves.

The astrometric method is the more straightforward: just watch for a star with an otherwise-inexplicable wobble, take some pictures of it, and figure out its orbit. Then backsolve to find what kind of object is perturbing it. Here, again, you need very fine resolution; you also need the patience to sit around and wait out a good fraction of an orbit. The more massive and farther out the planet is, the larger the star’s wobble — but the longer its orbit.

Josh says that astrometry alone has never succeeded in finding an exoplanet, though it has been used to confirm the exoplanitude of objects otherwise discovered.

Spectrometry is a bit more complex. It combines the star’s orbital motion with the characteristic pattern of different colors of light the star emits: its spectrum. A stellar spectrum generally contains a combination of continuous, rainbow-looking regions and places where a few colors are just missing. Maybe there’s no turquoise-green-but-not-too-green, or none of two kinds of yellow: these absences are called absorption lines, and they’re the result of that color being absorbed by some other atoms in the star. Anyway, these spectroscopic features are useful landmarks within a given star’s spectrum.

When a luminous object moves away from an observer, the observer sees the light as redder than what was originally emitted. Conversely, if a star moves towards the observer, the light is shifted towards the blue (this shifting business is called the Doppler effect, and it’s the same kind of thing that makes the siren on the ambulance passing you go from a high-pitched EEeeEEee to a lower pitched OOooOOoo). So. If we’re looking at a star-planet system edge-on (or at any angle other than face-on) the star moves towards us part of the time, and away from us part of the time. But the pattern of light actually given off by the star hasn’t changed — and that means we can track just how much things are shifted by watching the movement of spectral features over time.

The star’s velocity as a function of time is given by
,
where is the distance from the star to the center of mass, and is the distance from the star to the planet.

The velocity along the observer’s line of sight (that’s the eyeball in the picture) is

where is the inclination angle, i.e. how much the orbital plane is tilted with respect to us.

What you look for, when you’re selecting candidates to check for spectroscopic Doppler effect, are stars with lots of narrow absorption lines. The more lines there are, and the better defined they are, the more accurately you can pin down their movement. You also want “quiet” stars — ones without surface explosions or pulsations or starspots that might mess things up. But the most significant limitation of the spectroscopic method is the ” sin i” term in the equations. The planetary mass you derive from all this work is actually the minimum mass — which means that it could be a planet in that system, or it could be something much larger. Like, I don’t know, a brown dwarf. Or another star. Or a giant alien spacecraft. Furthermore, you have no way of knowing the planet’s radius.

Even so, spectroscopy has been by far the most successful method of exoplanet discovery: of the 212 known planets, something like 185 were found spectroscopically.

Hokay. The final major method is the one Josh is currently working on: photometric detection of exoplanets via transits. A transit, here, is basically an eclipse: a planet passes in front of its star, blocking some of the star’s light. It’s not a lot of the star’s light — it’s on the order of 1% — but it’s enough to be visible. The problem with most planets is that their orbits are just too long and the transits just too short. If we’re talking Sun-Jupiter, the transit happens for 14 hours ever 12 years. And if you don’t know when or where a transit might happen, you have to look EVERYWHERE, ALL THE TIME, and then maybe someday you’ll see something. The happy resolution to this problem is a type of planet called a “hot Jupiter”, which has a period of about three days. Fourteen hours out of three days is not nearly so unmaneageable, and, in fact, such planets have been found. The data for a transit looks like this:

The little dip in the middle? That’s a transit.

The transiting-planet technique is plagued by false positives. A potential planetary transit could be an eclipsing binary star system, or a blending of light from multiple stars, or a complicated artifact of the star field, or who knows what. BUT! If you do find a nice transiting planet, you can learn all manner of things: its mass, its radius, its orbital period, its orbital inclination…all the things that make planet-hunters happy.

Here are the planet-finding-related readings assigned for today’s seminar. I’ve linked to the astro-ph versions.

A new transiting extrasolar giant planet There’s a nicely-explained process of eliminating false positives here.

Evidence for a co-moving sub-stellar companion of GQ Lup. A possible planet — and, contrary to all my objections above, a direct image of it!

Discovery of a cool planet of 5.5 Earth masses through gravitational microlensing. Another method for planet-discovery.

Also, you can read The Transit Light-Curve Project III. Tres transits of TrES-1 which was co-authored by my lab partner, Anna. Which is pretty cool. The paper has some nice plots of transit data fit to a model.

I guess I should get with this publishing-papers business myself, or I will never get into grad school…

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