Fun With Kepler!

What is Kepler?

The easiest way to imagine what Kepler is doing is to think of it as staring at the sky, taking measurements at how much light is being received from different spots of the sky at different times. Kepler is focused on one part of the sky, observing continuously, measuring for changes in the flux of light reaching the telescope.

What is Kepler looking for?

Kepler’s primary goal is to find planets. Specifically, Kepler’s aim is to identify planets and planet candidates that will help scientists understand the types of and distribution of planets in the universe. In order to find these planets, Kepler uses the transit method, with measures dips in light as a planet crosses a distant star.

What do these fluctuations in light mean?

Kepler is looking for stars that have a dip in luminosities, because this could indicate a planet transit. For a planet to ‘transit’ a star means that the planet is crossing in between us (the observers) and the star. One example of a transit closer to home is Venus. When Venus transited the sun several years ago, you might remember pictures of the transit showed a dark circle on the sun. That was the planet blocked part of the sun’s light from reaching earth.

When a planet transits a distant star, it decreases the amount of light reaching observers here. So, when Kepler measures a temporary decrease in light from a star, it could mean that a planet is transiting across the star.

Problems with the transit method

Although the transit method is conceptually simple, there are many problems that accompany it. For example, not every dim in light indicates a planet. Other possible causes for the dimming include a transiting binary star, three-star system, or two stars blending their light together. So, if Kepler detects a dip in light from a source, it COULD be, but is not necessarily, a planet. This is why the “planets” Kepler identifies are called “planet candidates.” Scientists have estimates the “false positive” rate – that is, how many sources that are not actually planets are accidentally identified as such by the Kepler mission[i]. This rate, although small, is not insignificant, thus the differentiation between confirmed planets and planet candidates.

In an ideal world...

As the name “direct imaging” implies, the best way to identify an exoplanet is to actually see it. There are two main reasons that this is hard to do, however:

High contrast ratio between luminous sun and planet (which reflects only a very small amount of light)

The atmospheric distortion blends light from distinct sources into what appears to be one source

Adaptive Optics can really help!

This is where adaptive optics comes in! Adaptive optics counteracts the atmospheric distortion. As a result, photons are received in a pattern closer to that by which they were emitted. If there were a dark spot on the star (say… caused by a transiting planet!) then ideally, that spot would also be received by the mirror. Without adaptive optics, it is very difficult if not impossible to see this spot.

Adaptive optics also allow the resolving of very bright stars and the planets next to them. Adaptive optics can measure sources within one arcsecond of each other, even if one of the soruces (a planet!) is 10 million times less luminous than the other (a star!)[ii].

Adaptive optics is really the most reliable way to confirm a planet candidate is actually a planet (or to show that it is NOT a planet).

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[i] http://iopscience.iop.org/0004-637X/644/2/1237/pdf/64043.web.pdf

[ii] http://spie.org/documents/Newsroom/Imported/003471/003471_10.pdf

First Ay 21 class

Since I am waiting for code to run anyway, I thought I would look up some topics from the first Ay 21 lecture that were mentioned but that I wasn’t extremely familiar with/ didn’t know what they were, and briefly summarize what I glean from a quick, superficial review.

String theory

I’ve always thought of string theory as being some crazy theory, but never actually looked up what it was. String theory posits that the universe is made up of one-dimensional vibrating strings, which serve as the most basic particle. The theory also requires extra dimensions – I am very interested in how a theory could require extra dimensions, and how these dimensions are defined. String theory is an attempt to reconcile general relativity and quantum mechanics, which is why it was mentioned with respect to the Age of Quantum Gravity (that bit of time at the beginging of the universe when GR and QM were both important, and you couldn’t describe the physics of a discrete event with only one of the two theories.

M-theory

M-theory is an extension of string theory. There are different ‘types’ of string theory, and M-theory is a unifying theory meant to connect them all.

Curvature of the Universe

It is hard to imagine space itself being curved. Best I can understand it, the exact curvature of the universe is as of yet an unsolved problem. The concepts of curvature, density, and expansion of the universe are all realted: there is a critical density at which expansion would stop, and similarly the density also deteremines whether the universe is curved like a sphere, like a hyperbola, or not at all. In a curved universe, light would bend as it travels.

Carrol and Ostlie has a section on curved spacetime (it beings on page 1185). This sections says that the curvature must be constant throughout the universe for a given point in time, although the curvature may vary as the time elapsed since the big bang changes. Curvature is a time-dependant function.

Dark Energy

In class, dark energy was mentioned as being (possibly) one of the “extra” components of mass in the universe, holding 73% of the mass. Dark energy is something that Einstein predicted when he developed his cosmological costant. Dark energy, different than dark matter, exists throughout the universe, although we are unsure what form it may take. It could be a constant energy density (the cosmological constant) or it could exist in fields or some other form. Dark energy also contributes to the expansion of the universe.

Weak/Strong Forces

There are four fundamental kinds of forces in the universe: weak, strong, gravity, and electromagnetic. Unlike gravity and EM forces, the effects of which dwindle but do not disappear as distance increases, weak and strong forces only act on a atomically small scale.

The strong force is what holds a nucleas together, even as the positively charged protons attempt to repell each other. I can’t believe I never heard about this before! When the protons and neutrons are considered to be composed of quarks, the strong force can be attributed to the “color force” between the quarks. The weak force allows one “flavor” of quark to change to another, allowing nuclear fusion to take place, and is thus necessary for every star that burns.

Quarks

This is another subject I have read about briefly but never really considered until now. I had thought that quarks were as “imaginary” as string theory; however, this is not true. Quarks are the elementary particles of the universe in that the 6 flaovrs of quarks make up the protons, neutrons, mesons, and all other particles which then, successively, make up matter itself. Mesons are particles composed of two quarks, and baryons are particles composed of three quarks. Protons and neutrons are thus mesons (constructed from up and down quarks). Quarks exist in the flavors up, down, strange, charm, bottom, and top.

My code is still running… the more I learn about physics, the more I realize I don’t know! I am super-excited about quarks – I need to go check out a book on elementary particle physics from the library because they seem SUPER COOL and I want to learn more about them!

Sources:

Wikipedia, Carrol & Ostlie

Why is AO imaging important?

In the last post, I included a cool picture showing the difference in imaging resolution due to AO. AO is very useful in direct imaging, because the higher resolution allows better differentiation between different sources. One complication that has always been as issue in detecting exoplanets accurately is that even if observers measure a light curve indicating that there may be a planet, the light dip might actually be due to something else, such as a transiting binary. This is of particular importance when wide-sky surveys are used, because each individual source has probably not been studied at length; therefore, the superficial appearance of their being a planet might be accepted when it should be rejected. Even when studied at length, the false positives may appear so similar to real planets that they continue to fool observers. This paper shows one specific instance where a source appeared to have a planet (indeed, it passed many of the ‘tests’ of planethood) but was actually a false positive. The fact that there is a false positive rate in all planet-finding surveys is a problem: this leads to the difference between a planet candidate and a confirmed planet.

One good thing about the Kepler false-positive rate (the rate at which things that are not planets are being called planets) is that it is not random. There are very specific reasons as to why a light curve might be altered to appear that there was a planet where one did not exist. Some of these reasons might be an eclipsing binary, “blend” (this is when a less bright star, not cataloged in Kepler, ‘mimics’ a planet) or the existence of a “hierarchal triple” (a multiple – three in this case, as its name implies – star system) (On the Low False Positive Probabilities of Kepler Planet Candidates, Morton and Johnson). Knowing the possible reasons that there might be a false positive in the Kepler data allows a statistical correction for this. Using approximations and creating probability distributions, Morton and Johnson developed a possible model for the false positive rate. Although this will not tell which individuals stars have planets, it makes the Kepler distribution as a whole more helpful, as observers have a way to estimate how many planet candidates, on the whole, are likely planets.

The process for determining, after a planet candidate has been found, whether or not it is a real planet can be lengthy. It also shows the importance of adaptive optics in confirming planets, as AO images can be used in either preliminary or follow-up observations. Many false positives are due to light being misattributed to an incorrect source, and adaptive optics reduces the degree to which this happens.