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Planet Hunting Toolkit IV: Transits March 18, 2009

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Radial velocity and astrometric searches can tell us what stars have planets, how far these planets are from their stars, and how massive each planet is. Unfortunately, that’s about it. If we want to really start to understand these other worlds, and possibly look for clues hinting at the presence of life, we need more. This is where the Transit Method can help.

Transits are astronomer-speak for the event of an object passing between you and a star. You may know them by another name: eclipses.  The most common type of transit that people are most likely familiar with has to do with our Moon.  When the Moon passes between us and the Sun, we find ourselves momentarily in the lunar shadow.  The Moon blocks the light of the Sun, the stars become visible in the middle of the day, and we have ourselves a solar eclipse.  This is the most dramatic example of a transit.

There are two other types of Sun-based transits Earth-bound observers can witness: those of Mercury and Venus.  Whenever either of these two planets pass between us and the Sun, we can watch their shadow trek across the face of the Sun using solar-filtered telescopes.  You can find a list of future transits of Mercury and Venus here.

Transit of Venus

Montage of 2004 transit of Venus (Image Credit: NASA)

Under the right conditions, we can also observe extrasolar planets transit their host stars!  This won’t be possible for all, or even a large fraction of, other planetary systems.  The only time we can see this occur is when we are looking at a distant solar system “edge-on”.  If the planet’s orbit is too steeply inclined relative to the Earth, the planet will never appear between us and its star.  The chance of finding a planet that passes between us and its star is dependant on the size of the star and the size of the planet’s orbit.  The smaller the star or the larger the orbit, the less likely are we to find a transit candidate.  Typical numbers are around 1 percent.  While the chances for finding a transiting planet may seem unlikely, if one studies hundreds of thousands of stars one can potentially find thousands of planets!

When a planet does transit its host star, we can detect the event by a dip in the star’s brightness.  The dip occurs because as the planet passes between us and its star, it blocks some of the light.  For a time, we are in the shadow of a distant world.  How much the light dims depends on the size of the planet, but 1 % is a pretty typical value.

Illustration of a transiting planet and the corresponding dip in the star's brightness.

Illustration of a transiting planet and the corresponding dip in the star's brightness.

The power of exoplanetary transits is in what these events can tell us about these distant worlds.  First, by carefully measuring how long it takes for the transit to reach it’s minimum brightness as well as how long the entire transit event takes, one can directly measure the size of the planet!  When one combines this with the mass as determined by radial velocity measurements, the planet’s density can be calculated.  This is an important first step in determining the bulk composition of the planet and is crucial in distinguishing gas giants like Jupiter from rocky worlds like our own.

Secondly, when the planet transits its star, some of the starlight passes through the planet’s atmosphere while en route to Earth.  In my article on spectra, we learned that measurements of a star’s spectrum can tell us what the star is made of.  Well, the same is true for any starlight passing through the atmosphere of an orbiting planet.  By comparing the spectrum of a star before, during, and after a planetary transit and looking for what changes, astronomers can measure the chemical makeup of exoplanetary atmospheres! Our first indication of life in the Universe will probably not come from a radio signal blaring across the galaxy, but from the subtle chemical effects of biological activity on a distant planet’s skies.

The big disadvantage to relying on transits is that they are very rare.  Not only will most exoplanets never transit their stars, but the ones that do only do so briefly.  If a planet takes years to orbit its star, the transit event itself may only last for hours or days.  That means, in order to be successful, astronomers must stare at the same stars for years at a time if they want to increase their chance of success.  The Kepler space mission will, in fact, do just that.  It will stare at one patch of space, monitoring the brightness of roughly 100,000 stars for four years.  The payoff could be huge: it is currently the only instrument sensitive enough to detect the presence of an Earth-sized planet in an Earth-like orbit!

Transit searches can also be easily tricked by binary stars and normal stellar variability.  Because of this, transit detections require follow-up, typically using radial velocity measurements to confirm the presence of a planet.

Despite the disadvantages, transiting planets are poised to take the exoplanetary community by storm.  The COROT and recently launched Kepler space missions are using transit detections to look for potentially thousands of planets.  By combining the findings of these missions with ground-based follow-up radial velocity measurements, we are standing on the brink of a revolution in understanding the innumerable worlds that orbit other suns!

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Planet Hunting Toolkit III: Radial Velocities March 12, 2009

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In the previous article in this series, I discussed a possible way of getting around the fact that imaging extrasolar planets is incredibly difficult: the wobble imparted on a star by its planets.  However, the current generation of telescopes and instruments can only really make use of the astrometric method in a handful of cases and while future telescopes will be able to leverage astrometric wobble to find Earth-like planets, astronomers can be a bit impatient.  We want to know if there’s anyway to take advantage of what we have now to begin to characterize other planetary systems.  Turns out, there is.

In fact, the method that astronomers use to find the overwhelming majority of exoplanets has a lot in common with how police can catch you for speeding with a radar gun!

Both rely on the concept of doppler shift.  The basic idea is that the speed of a source of a wave (such as an ambulance if we are worried about sound waves, or a flashlight if we’re concerned with light) affects the wavelengths of the waves.  Let me explain with a common example:  Have you ever noticed how the pitch of a train horn changes as a train passes by you?  It starts higher and then dramatically becomes lower once it goes by.  Here’s what’s happening: sound can only travel at a fixed speed through the air (about 700 m.p.h.) – independent of the speed of whatever is making the sound.  When you shout, the sound waves produced by your vocal cords fly off at 700 m.p.h. in all directions.  When a train is moving along at, say, 100 m.p.h. and it blows its horn, the sound doesn’t get to move faster because the train is moving faster.  It’s stuck at 700 m.p.h.  This makes the sound waves “bunch up” in front of the train and get “spread out” behind the train.

Illustration of doppler shift.  When the train is moving, the sound waves in front bunch up; those in back spread out.

Illustration of doppler shift. When the train is moving, the sound waves in front bunch up; those in back spread out.

To take an extreme example, if a jet is moving at the speed of sound (Mach 1), the sound waves can’t get ahead of it because both the jet and the sound waves are traveling at the same speed.  This creates a wall of sound – called a bow shock – in front of the object.  This is what’s responsible for the sonic boom you hear when a plane roars by at Mach 1 or faster.  As the above picture shows, the bunched up sound waves have shorter wavelengths and the stretched out waves have longer ones.  Our ears and brains translate shorter wavelengths into higher pitches and longer wavelengths into lower pitches.  That’s why a train horn sounds higher when it approaches you and then sounds lower once it goes by.

The same thing happens to light waves!  If a star (for example) is moving towards you, all of its light waves get bunched up in front of it thereby making the wavelengths of light shorter.  The opposite happens when a star moves away from you.  Police radar guns take advantage of this by bouncing radar off your car.  By measuring how much shorter the reflected wavelengths are than those that were emitted, the police officer can determine precisely how fast you are driving.

In the Spectra article, I introduced you to the concept of absorption lines (if you haven’t read that article already, you might want to go do that right now!)  If all the wavelengths of light get shorter, that means the absorption lines of a star will appear at shorter wavelengths than we would find them in the lab.  If a star is moving away, the absorption lines show up at longer wavelengths.  Astronomers refer to these two phenomena as blueshift and redshift (because blue is a short wavelength color and red is a long wavelength color).  If we look at a star’s spectrum and find the entire pattern of hydrogen absorption lines (as an example) shifted over to slightly longer wavelengths – that is, if the hydrogen lines are redshifted – we know the star is moving away from us.  In fact, the difference in the observed wavelengths of the absorption lines and those measured in the lab tells you precisely how fast the star is moving away!  If all of the lines are blueshifted, we know the star is moving towards us and how quickly.

The effect of red and blue shifts on absorption lines.

The effect of red and blue shifts on absorption lines.

But what if we find a star where, over time, the lines alternately blueshift and then redshift over and over with a fixed period?  That implies the star is moving towards us and then moving away and then towards….over and over over.  It tells us: the star is wobbling back and forth in space!!!!

This could only happen if there was something we couldn’t see near the star pulling it around.  This, dear reader, is how to find a planet!

This technique of finding planets via the doppler shift (usually called the “radial velocity method”) is responsible for finding the overwhelming majority of planets we know of.  The Extrasolar Planet Encyclopedia (as of the time of this posting) lists 316 of the currently 342 known worlds found this way.  This technique favors larger worlds on short period orbits because these planets produce the largest doppler shifts.  But astronomers have greatly improved on the technology over the past decade which has allowed us to start finding planets several times the mass of the Earth and worlds on multi-year long orbits.  While the vast majority of planets we’ve found thus far are Jupiter-sized worlds orbiting very close to their stars, this is predominately a limitation on the techniques we use and isn’t necessarily an accurate picture of the exoplanetary zoo.

What’s more, the radial velocity technique allows to measure some basic properties of the planet.  By measuring the period of the star’s wobble, we can use Kepler’s Third Law to figure out how far away the planet is from it’s star.  Furthermore, if we know the mass of the star through some other means, than that combined with the star’s velocity and a sprinkling of high school physics can tell us the mass of the planet!  (Actually, it’s a little more complicated than that.  We can really only determine a lower limit for the planet’s mass without knowing something about the tilt of the planet’s orbit relative to the Earth, a topic I may explore further in a later post).

While other techniques can provide astronomers with more information about specific worlds, the radial velocity method is the workhorse method and it is responsible for revealing the wonderous diversity of the exoplanetary zoo.

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Fundamentals I: Spectra March 10, 2009

Posted by CosmicThespian in Fundamentals.
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This article is the first in another series which will appear interspersed with other articles: the Fundamentals Series.  The goal of this series is to introduce you to some basic concepts in astronomy.  These concepts may not be directly related to extrasolar planets but they are core ideas which are needed if you want to really understand what astronomers are doing.  These articles are meant to support the main articles on exoplanets and hopefully will provide you with a greater insight into how astronomers go about the dirty work of exploring the Universe.

This article describes a concept which has direct bearing on how we find the majority of planets around other stars: the spectrum of a star.  Let’s start simple: what happens when you pass sunlight through a prism?  You get a rainbow!  Sunlight is composed of many different colors – including colors our eyes can’t detect like infrared and ultraviolet – and prisms allow us to spread out those colors so we can see them.

A prism casting a rainbow onto a wall.

A prism casting a rainbow onto a wall.

But the Sun doesn’t put out its energy in all colors equally.  If you were to take that rainbow and precisely measure the intensity of each color, you’d find that the Sun actually funnels most of its energy into the color green.  The intensity in each color drops off as you move away from green (towards red and violet).  Different stars have their peak energy in different colors: some around red, some around blue, and some actually peak in those colors we can’t see.  Where the peak happens is determined by a star’s temperature: the hotter stars peak around blue and ultraviolet; the coolest stars peak around red or infrared.

The distribution of color intensities for three objects at different temperatures.  The numbers are temperatures in degrees Kelvin.

The distribution of color intensities for three objects at different temperatures. The numbers are temperatures in degrees Kelvin. 5500 K is roughly how hot our Sun is.

What’s important to remember is that each color is actually a measure of the wavelength of light.  Light can be thought of as a wave – much like the waves on the ocean.  If you were to stand on a pier and watch the waves move by, you might notice that there’s a few fundamental things about them you could measure.  One would be the frequency of the wave: how many waves pass by you in a second.  Another closely related property is the wavelength: the distance from the peak of one wave to the peak of another.  As the name suggests, it’s quite literally a measure of how long a wave is.  Ocean waves generally have wavelengths of several meters.  The wavelengths of visible light are much smaller: billionths of meters (also called a nanometer).  Green light has a wavelength of roughly 550 nanometers (nm).  Red light is somewhere around 700 nm and violet is closer to 400 nm.  Since each color is defined by a single wavelength, when you look at a rainbow, you’re actually looking at how much of the Sun’s energy goes into each wavelength.  That is what I mean by a star’s spectrum.

As an aside, here’s a rather amazing bit of trivia.  If you take any star’s temperature and multiply it by the wavelength at which that star puts out most of its energy, you always get the same number, regardless of what star you pick!  This is true for not just every star, but any object which radiates energy – including you!  Any object will get you this number.  This law is referred to as Wien’s Law.  Pretty remarkable!

The spectra (plural for spectrum) of stars are probably the most useful tool astronomers have for understanding the Universe.  By measuring the spectra of stars and galaxies, astronomers have the ability to measure things like chemical composition, gas pressures, temperatures, surface gravity, and – this is important for us – how fast objects are moving.

If we took a lightbulb and a prism and then let the light from the prism fall on a sheet of paper, we’d see a lovely rainbow.  Now, let’s take a large, clear container filled with, say, hydrogen gas, and place it between the bulb and the prism.  How would this change the rainbow?  You’d see that a series of narrow, dark lines would appear superimposed on the rainbow as if light from very specific colors had suddenly gone missing!  And that’s exactly what would be happening.  Without going into the quantum mechanics of it all, the hydrogen has the effect of absorbing very specific colors – or very specific wavelengths – of light.  Since the hydrogen atoms are stealing those wavelengths, they show up as missing on the rainbow.  Astronomers refer to those dark wavelengths as absorption lines.

The absorption lines are amazing for a number of reasons.  The most important of these is that they tell us exactly what stars and galaxies are made of!  You see, each atom has a unique set of wavelengths it can absorb which means that every element produces a unique set of absorption lines in a spectrum.  Think of it as an element’s “spectral fingerprint”.  By matching the absorption line patterns to those of elements measured in labs here on Earth, astronomers can identify every element in any star, galaxy, planet, or cloud of gas in the Universe – we can precisely measure what the Universe is made of!

The spectrum of our Sun.  The black absorption lines result from the different chemical species in the Suns atmosphere

The spectrum of our Sun. The black absorption lines result from the different chemical species in the Sun's atmosphere

It’s amazing what we can do!

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Planet Hunting Toolkit II: Astrometry March 5, 2009

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In my previous post, Why It’s Hard, I discussed the difficulties inherent in finding planets around other stars by directly imaging them.  Basically, the stars are much brighter than their planets and the planets appear very close to their host stars.  If we want to have any hope of finding other worlds, we’re going to need to do something different than just taking pretty pictures and hoping we see a planet.

Fortunately, nature has provided a way!

While we generally can’t directly see these other planets, we can detect how the presence of an orbiting planet affects the motion of its host star!

The trick to understanding this lies in knowing something about the mechanics of orbiting bodies.  Most people, if asked, would say that the Earth orbits the Sun or that the Moon orbits the Earth.  But, here’s a secret: they’re wrong!

Now, before you run off to some other blog to find someone who is a little more qualified, let me explain.  The notion that the Earth orbits the Sun is only approximately true, but it’s not the whole story.  In truth, the Sun and the Earth orbit around a common center, called the barycenter of the system.  Where this barycenter is located depends predominately on the relative masses of the two bodies.

Let’s take a simpler example:  a see-saw.  Imagine two twin brothers want to balance themselves on a see-saw.  Where should they sit?  It probably doesn’t come as a great surprise that the brothers should sit at equal distances from the center.  Any other arrangement, and the see-saw will tip one way or the other.  When the brothers have got the see-saw balanced, we can say that their center of mass is over the pivot of the see-saw.

Now lets take a 200 lb uncle and his 50 lb niece.  How should they sit?  Without boring you with the math, the uncle, being four times heavier, needs to sit four times closer to the center than his niece in order to achieve balance.  To use some real numbers, if the niece is 6 feet away from the center, the uncle needs to sit a foot and a half away on the other side.  Another way of looking at this is to say that the center of mass of the uncle and niece is four times closer to the uncle than his niece.

What about two objects where one is 1000 times heavier than the other?  That’s right, the center of mass would be 1000 times closer to the heavier object than the lighter one.  Hopefully, you see a trend here.  However many times a heavier object is than another, that’s how many times closer the center of mass is to that object (or, to think in see-saw terms, that’s how many times closer that object needs to be to the center to make the whole thing balance).

By now you’re probably wondering what this has to do with planets.  Well, this barycenter I mentioned is located at the center of mass of the two objects!

If you have two stars in orbit around one another, both with equal mass, they will be orbiting around a point exactly halfway between them.  If one star is four times more massive than the other, they will orbit around a point that is four times closer to the more massive star.  If one is 1000 times heavier…..well, you get the point.

However, when it comes to planets and stars, the difference in masses is enormous!  The Sun is over 330,000 times more massive than the Earth!  Which puts the center of mass of the Earth-Sun system 330,000 times closer to the center of the Sun.  Given the 93 million miles between the two, that means the barycenter of the Earth-Sun orbit is only about 280 miles from the center of the Sun.  But, wait!  The Sun has a radius of nearly 700,000 miles! That means the point around which the Sun and Earth orbit is deep in the interior of the Sun – only 4 hundredths of a percent of the distance from the center of the Sun to its surface!

So you can see that saying the Earth orbits the Sun is a really good approximation.  But, as we’ll see, that slight difference will make all the difference for helping us out.

Let’s make things simple and ignore the other planets for now; we’ll pretend that the Earth is the only planet orbiting the Sun.  In that situation, what we just calculated indicates that the Sun is orbiting around a point in its own interior, wobbling 280 miles to either side (for 560 miles of total wobble).  If a planet can subtly pull on a star, perhaps we can detect this motion rather than look for the planet itself.

The science of measuring the positions of stars on the celestial sphere is called astrometry.  In principle, you could use astrometry to look for changes in those positions that indicate they are wobbling in the sky.  In practice, this is pretty difficult.  The reason is that the wobbles are generally really small.  If an astronomer on a hypothetical planet orbiting the closest star to our Sun, about 4 light years away, were to attempt to measure the wobble of our Sun resulting from the movement of the Earth, she would be trying to measure a wobble that subtended only 4 millionths of an arcsecond!  Yikes!  That would be like trying to measure the thickness of a dime located a quarter of a million miles away – roughly the distance to the Moon 175,000 miles away – roughly 3/4 the distance to the Moon!!

And, remember, this is from a vantage point of only 4 light years distant, basically next door.  Most of the stars we’d want to measure are hundreds or even thousands of light years from Earth.

Unfortunately, no current telescope can come close to doing that.  It gets easier if instead of trying to find Earth-like planets, you instead try to look for more massive Jupiter-like worlds with larger orbits.  Astrometry favors finding massive planets on wide orbits around stars which are relatively close to Earth.  But it’s still very difficult with the current generation of telescopes.; future space missions will improve on that.

At this point, things may seem hopeless.  Planets don’t lend themselves to imaging, and the wobbles they impart on their host stars are just too small to measure.  The next article in this series will show how we can make use of this wobble without worrying about measuring the minute changes in position…

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Planet Hunting Toolkit I: Why it’s Hard March 2, 2009

Posted by CosmicThespian in Toolkit.
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This article is the first in a series called The Planet Hunting Toolkit.  Each entry in the series will introduce the methods that astronomers use to find planets.  Generally, planets must be found using indirect means.  That is, with some exceptions, we can not directly image these other worlds (although this is beginning to change as was made clear in a recent announcement).  The reason that planets are notoriously difficult to see is a result of the combined effects of contrast and angular separation.

By contrast, I am referring to the difference in the amount of light coming off the planet and the star around which it orbits.  A star is self-luminous, a planet is not. The planet’s light is reflected light from the star.   Because the planet only intercepts a tiny fraction of the star’s total light, there isn’t much to reflect.  What’s more, a planet doesn’t reflect all of the light it receives; it actually absorbs some of it.  The fraction of received light a planet reflects is known as the planet’s albedo.  Planets with lots of high cloud cover, like Venus, have high albedo.  Planets covered in predominately charcoal-colored rock, like Mercury, have low albedo.

All of this is to say that the amount of light a planet reflects into space is much, much less than how much light its host star emits.  If we restrict ourselves to visible light – that is, light that our eyes can detect – a star is roughly one billion times brighter than any planets orbiting it!  That’s a one followed by nine zeros: 1,000,000,000!  To help wrap your brain around that, one billion pennies would take the same volume as five school buses or, if stacked, would tower five times higher than the orbit of the space shuttle.

So, that’s one problem.

But the problem is compounded by considering how far apart the star and the planet appear to us.  Consider the Earth and the Sun.  The Earth is, on average, 93 million miles from the Sun – a pretty respectable distance!  If you were to travel just over 2.5 billion miles away (there’s that billion again!) – roughly to the orbit of Neptune – the apparent distance between the Earth and the Sun could be covered by your thumb (about 2 degrees).  Go one light year away (a distance of about 6 trillion miles) and the Earth and Sun would be separated by only about 3 arc seconds (arc seconds are a measure of angles.  There are 60 arc minutes to a degree and 60 arc seconds to an arc minute which gets you 3600 arc seconds in one degree).  Three arc seconds is roughly equivalent to the thickness of a dime seen from about one American football field away (300 feet).  As seen from the nearest star to our Sun, Proxima Centauri – a distance of 4.2 light years – the Earth-Sun distance now subtends less than an arc second.  In other words, take that same dime and place it just over 1000 feet away.

Perhaps now you can start to see our problem.  We’ve got two objects, one a billion times brighter than the other and separated by very small angles.  Trying to see a planet around a star 10 light years from Earth is like trying to see a candle 20 feet from a searchlight in Washington, D.C. while standing in Los Angeles.

That’s really hard!

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