I miss my running buddies!!

Without Clara and Stephanie (off at Berkeley and in Florida, respectively) I've been running on my own a lot recently... and when I say "recently" I mean "in the last three days." The loneliness is getting to me already!!

Fun run today, I thought it would be 6 miles, but apparently it was not. It was pretty safe, didn't run through too many sketchy areas (I think Orange Grove is a pretty road).

See the route I ran! East Orange Grove on MapMyRun.

I also started my SURF this week, with a (luckily) very direct application of the methods I learned last semester in Ay 117! So far, I have been writing code that generates a mock noisy spectra of a B-Star (which is basically a very big star!), then playing with this spectra and attempting to extract from it the shift I put it. This part I've done.

Now, the hard part - I need to write code to extract a doppler shift. This is tricky because a doppler shift or a given magnitude has different effects on different parts of the spectrum. If you don't know what a doppler shift is, imagine a firetruck, sirens blazing, passing you as you stand on the sidewalk. As the truck moves toward you, you will hear a shrill siren, which then becomes deeper after the truck passes you. The reason that this modulation occurs is that the sound waves are experiencing a doppler shift. When the truck is moving towards you, each successive sound wave is being emitted at a decreasing distance from you, meaning that this later wave has a "head start" on the earlier one. The frequency of sound waves reaching your ear is thus higher than the frequency at which they are emitted. The opposite is true if the truck is moving away from you - each successive wave has to travel even farther than the one before it.

The same thing happens with light. If a source emitting photons is moving away from us, then the distance between each photon is greater as time goes on. The effect of a doppler shift on the observed wavelength is given in this relationship:


Which is dependent on the wavelength, represented by lambda. At higher wavelengths, there will be more space between successive wave fronts. This is why we cannot say that with a doppler shift, a 10 nm wave becomes a 12 nm wave and a 16 nm wave becomes a 18 nm wave. the 16 nm wave will actually be larger than 18 nm, since as the wave itself is longer, the shift must also be bigger.

To get this working, I need to tackle interpolating functions. AH! Wish me luck!

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).

---

[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.

Adaptive Optics

Why do we need adaptive optics?

There are two places for optical telescopes: on the surface of the earth and in space. The effort to put a telescope in space and maintain it is much greater than that required for a ground-based telescope, so why would this avenue of observation have ever been pursued? The answer to this question is, simply, the atmosphere. Earth has an atmosphere, which affects light traveling through it.

The variances in the atmosphere consist mainly of differences in temperature from one region to another. The pockets of differing temperatures mean that a path straight from a distant source to a telescope located on the surface of the earth would include regions of higher and lower temperatures? Why does this matter for light?

Photons propagate as waves. The speed of a propagating wave is dependent upon the medium through which it is propagating. For photons from distant stars, the majority of the medium they propagate through is the interstellar medium, which can be approximated as a vacuum (this is what I have been taught, but the fact that Caltech has a whole class on the interstellar medium –Ay 101, which I will take next year – makes me wonder if this is merely a simplistic approximation... anyway, for now I consider space to be roughly a vacuum). Once the photon reaches the atmosphere, however, it is propagating through much denser air. Even this air is not uniformly dense, however: regions of hotter and colder air change the index of refraction for different air pockets, creating what are essentially different mediums.

If you consider the wavefront of light emitted from a distant star, you can see why this would be a problem. When the wavefront reaches the atmosphere, each individual part of the wave front has propagated at the same speed (since the entire wave front has been propagating through the same medium). However, this is no longer true once the photons pass through the atmosphere. Photons that pass through hotter packets of air will propagate at a greater speed than those traveling through cooler air.

You can imagine what happens to the poor wavefront when each photon travels through different temperature air pockets – the poor thing is in disarray by the time it reaches an earth-based telescope! Some areas of the wavefront have travelled faster while other bits have travelled more slowly – what used to be a smooth wavefront is altered by the atmosphere into a much more “squiggly” form.

This is a problem! One solution to this problem is to place your telescope in space, where the wavefronts don’t have to make the perilous journey through the atmosphere. However, in recent years a much more amazing method of avoiding atmospheric distortion has come into being… and this method is adaptive optics!

What does adaptive optics (AO) do?

Adaptive optics corrects for distortions due to the atmosphere in the wavefront. The way that is does is REALLY COOL – I hardly believed it was real the first time I heard about it!

AO uses a deformable mirror. The mirror itself is deformed!!! Now, this mirror is not the mirror that first receives the image. You aren’t deforming the 5 meter mirror at Palomar, for example. Adaptive optics are not a part of the main mirror, but instead an instrument that you can add onto a telescope. The photons are first received by the ‘big mirror,’ as you might expect, but then refracted to the smaller, deformable mirror, which can correct the image.

Basically, AO corrects the image for atmospheric distortion. The goal is that the image received from a ground based telescope using AO would be as good as an image from a space-based telescope.

How do you calibrate AO (find out how air pockets affect the wavefronts)?

The distortions by the atmosphere on the wavefronts are not random. They are very directly caused by the varying temperatures in the atmosphere. So, theoretically, if you could map the air pockets of different temperatures, you could write program to subtract the “noise” caused by said air pockets.

To measure how much correction is needed, AO systems use mainly two methods: a guide star or a laser. Guide stars are those used as references. We already know what we SHOULD get by observing these stars, so if the observed image differs from the expected image, the difference is the interference due to the atmosphere, and can be corrected in subsequent observations.

Lasers are even cooler! The laser used with AO is a sodium laser, which works by emitting a wavelength of light that will excite sodium atoms, which then emit light back to the telescope. This is sort of a fake guide star – it is used in the same way that a real guide star is, but it is much more versatile!

The laser/guide star calibration method is used simultaneously with the observation of whatever source the telescope is studying. That way, corrections are as accurate as possible. As the air pockets change and the wavefront’s “squiggles” change, the corrections to the entire image can be altered (based on whatever the light from the guide star says the change should be) so the image is as accurate as possible.

How does a deformable mirror correct the image?

Firstly – how is a mirror deformed? The method of deformation is pretty cool! I looked at documentation about the PALM-3000, which is an AO system for Palomar, as a case study of how the method works.

Mirrors are deformed by needle-looking things called actuators. The actuators actually push the surface of the mirror into a pattern that counteracts the effects of the atmosphere. If you don’t think about it too much, the idea that you can just physically counteract the distortions in the wavefront makes sense. Where the wave travelled too slow, push the mirror up so it receives the lagging photons sooner. Where the wave travelled too fast, leave the actuator unpushed so the photons must travel farther and thus all photons arrive at the mirror at the same time. If you start thinking more deeply about this, you will realize how complicated writing the code for this algorithm would be! (Image to the left from 4)

Another remarkable fact is the rate of correction – that is, how often AO reads in data from its guide star and adjusts the actuators to counteract the distortions due to the atmosphere. The whole process sounds computationally arduous – can you believe that AO is corrected 2000 times a second (5)?!? This frequency seems CRAZY to me! Imagine the engineering that went into allowing the fast and precise movements of all those actuators – which, on the PALM 3000, is 4356 actuators (4)!

Why is AO useful?

As they say, a picture is worth one thousand words. This Palomar image shows the difference between an observation with adaptive optics (right) and an observation without (left) (image from 2).

Useful links:
1. http://www.mtwilson.edu/ao/ - tells about the AO system used at Mt. Wilson; good explanation about AO more generally as well
2. http://www.astro.caltech.edu/palomar/AO/ - cool images – AO is important at Palomar!
3. http://amazing-space.stsci.edu/resources/explorations/groundup/lesson/basics/g18a/ - good image on what the air pockets do
4. http://spie.org/x39226.xml?ArticleID=x39226 – specifically about the PALM-3000, good explanation on how the actuators work and some cool images!
5. http://www.oir.caltech.edu/twiki_oir/bin/view/Palomar/Palm3000/WebHome - more on PALM-3000

Fixing my mistakes… [lab 3]

When I said “by Wednesday”… I guess I didn’t specifically say WHICH Wednesday I would fix it by…
New information:
• the “ marks in the image are arcseconds, not degrees - I should have converted units to account for this!
• Keep values in radians
• Recheck what K-band really means!

SO! Now, I have 0.009 arcseconds as the value for the separation of the binaries, which I can covert to degrees:

Proceeding with this value, I know that the distance to the first airy ring should be 0.1 arcseconds, not 0.1 degrees. With this knowledge, I can convert again to degrees and then radians (for radians, see summary table way below).

Now, I also need to check the values for the wavelengths of K-band. According to Wikipeida: http://en.wikipedia.org/wiki/Photometric_system
The values of K-band in this system of measurement have a center of around 2190 nm. Using these new values, I can use the same methodology as last time, except my value for theta will be different. Theta in the equation below refers to not the distance from the center to the airy ring, but the entire distance across the diameter of the airy ring. So,



Using small angle approximation, and the fact that 2190 nm = 2.19*10^-6 meters,



This suggests that the aperture is 2.76 meters – not the 10ish meters I previously found.
NOW – which telescope could this be? …. I notice that depending on the measurement for the width of the airy ring, I get different results. This is frustrating because depending on from where I measure (the innermost and smallest distance, or from the center of the outer pixel) I get different values for the minimum angular resolution. I can get what look like equally valid measurements varying from 0.09 to 0.23 arcseconds. These correspond to apertures between roughly 2.5 and 6.5 meters. See graph below, which graphs D as a function of the diameter of the smallest airy ring, measured in arcseconds.

Choosing what telescope this image is from is difficult because of the uncertainty in my original measurement of the diameter of an airy ring. However, based on considerations of where in the sky this source would be visible (see the uncorrected post) I can say that it would be visible from Hawaii, California, or equivalent areas. Combined with my knowledge that this image came from a Caltech-affiliated source, who likely has most easy access to Palomar and Keck, I can hypothesize that the image was taken using the Hale telescope at Palomar, which has an approximately 5 meter aperture, within my error bounds.
Trying to confirm or disprove my hypothesis, I combed through the publications of the two observers listed in the FITS header and found this abstract:
http://adsabs.harvard.edu/abs/2010DPS....42.3930L
So, K-band observing was going on at Palomar April 25-26…. Looks promising! Unfortunately I can’t seem to find a copy of the entire paper – maybe because I am not on the Caltech network?
Also, I found:
http://www.palomar.caltech.edu:8000/calendar.tcl?cal_date=2010%2d04%2d25+00%3a00%3a00%2b00
Which shows that April 27 was used by a different astronomer… but the nights of the 25th and 26th were used by a consistent observer to the file. I would say that the day had just changed and this observation was from the night of the 27th, but the observation time says 11:28. This does not mean that my hypothesis was wrong; I’m not sure which time zones /sidereal time/PST time were used to mark the file; so although the observation was marked 11:29, April 27th it could possibly have been from the 26th.
Also – Knowing that Justin Crepp was the observer, (I feel like such a stalker…) how likely is it that he would, having observed all night on April 26th, then proceed to fly somewhere else and observe AGAIN the next night? I don’t think that would be very likely, and it is always possible that the nights got switched or something else unreported on the observation time website happened. Therefore I will not reject the hypothesis that this image was taken at Palomar on the Hale 200-inch telescope.


Fixing my errors: a summary

Airy ring distance from center: I used to think this was 0.09 degrees.
Now I know it's 0.000025 degrees, or 4.36332 × 10^-7 radians
K-band wavelengths: I used to think it was 7.5*10^-1 to 1.5 cm,
Now I know that it's centered at 2190 nm
Aperture: my first value was 10.48 meters,
My new value was 2.9 meters but I also realized that this number comes with some sizeable error bounds!
Telescope: I used to think it was the Keck2, NIRC2
Now I think the Hale 200 inch at Palomar was used

Becoming a professional astronomer, the final post

So, before I explain how my opinion has changed since the start of this project (affected by the interviews my group and I did – see Iryna and Tommy's blogs for our other posts – as well as the various conversations I have had with post-docs throughout the term), I wanted to post some interesting posts I found while perusing resources online, along with just a couple thoughts I had on each one. Most of the most interesting things online are blog posts. I have never read so many blogs before this class, but they are fun and useful!

http://science-professor.blogspot.com/2011/09/dealing-with-it.html - Just what is the relationship between an advisor and a grad student? If you’ve ever seen the PhD comics, then it appears that grad students are like slaves to uncaring, busy advisors. From my SURF, I thought that grad students and professors were more like friends (both of whom too busy for an undergrad like me!). This article implies that the relationship doesn’t have to be chummy, but merely professional.

http://www.astrobetter.com/valuing-all-kinds-of-astronomy-smarts/ - This is interesting because it discusses the idea of the gap between school skills and practical skills. The people who can do problem sets really well might not be the best scientists…

http://astrobites.com/2011/11/16/for-your-perusing-pleasure-some-preliminary-results-from-the-social-perceptions-of-astronomy-survey/ - on a side note, I tried out Professor Johnson’s idea that telling people on a plane you were an astronomer, as opposed to an astrophysicist, is more conducive to conversation. I had a two-hour conversation with a telephone tech about astronomy on the way home for Thanksgiving… maybe I’ll write one last blog post on this! It was actually pretty cool.

http://astrobites.com/2011/10/02/applying-for-the-nsf-our-own-experiences/ - Oh gosh! I don’t even want to think about this. One of my cross country teammates, a senior, just applied for NSF, and it sounds nerve-wracking.

Now – my own thoughts. I have realized over the course of the semester, after talking to various grad students, that for astronomy there are many different directions you can go. You can be more instrumentation, or theory, but each discipline is different. Also, I have gotten over my hesitation to say the word “astronomy”. I was always worried that “astronomy” was not a real career path. This is what my parents and high school teachers led me to believe; there was always the joke about the student going off to college to pursue something useless like philosophy or astronomy. For that reason, I always answered “astrophysics” when people asked my major.

This term, I have realized that many of the actually parts of astronomy are exciting. Actually observing data is exciting, because of the years of work that lie behind every single observation. It’s not as easy as just looking at the sky; adaptive optics and other modern aspects of telescopes show the field is not static and involves far more than simply looking at stars.

One other contrast that this term has brought to my mind is the difference between astronomy and other fields of science. The research process of biology or chemistry has always seemed a little scary to me; you could spend years working on a project only to see it fail or another group scoop you before you publish. In astronomy, there seem to be far more data than astronomers. I like that idea that even someone like me could comb through public data and find something publishable that simply hasn’t been studied by anyone yet.

The process for becoming a professional astronomer seems less daunting. I have also realized, because of what Jackie said last week, that there is nothing wrong with verbalizing my goal of being a professor, even if I think it might be presumptuous of me to suppose that I “deserve” to have this as a goal. There is no reason to pretend to pursue a career in industry when I know my dream job is to be a professor.

Pursuing this goal, I have learned from this project and the rest of term, will involve facing rejection many times. Not only do I have to apply to grad school and perhaps fellowships, but I will eventually apply to postdocs and eventually faculty positions. I have also realized how important other people are. I would never have learned any of the things I learned this term if I had been in a regular class, because I would have spent my time doing problem sets instead of meeting interesting people and going interesting places (Palomar, the Solar laboratory here, seeing the adaptive optics in the basement). There is nothing wrong with asking questions and there is nothing wrong with having fun.

From the interview with Annelia Sargent, I learned that it is possible to have a family and pursue a career in astronomy simultaneously. She also spoke to us about all the different committees and projects she has been on. It was cool when I read an article of Science a few days later and saw her mention in concert with yet another project that she works on, but the fact that she considers all the extra things she does as “community service” made me realize that it is very difficult to put limits on what a professor does, as every position is different and a lot of what they do is what they choose to do.

Reading posts online, I am struck by the sheer volume of posts by older people in the field giving advice to younger ones seeking to attain their positions. Grad students advise undergrads with seeking guidance from postdocs, and professors offer advice to all. Everyone in the field seems to realize that it is a tough path, and they want to make it easier for those attempting the arduous journey. Astronomy seems, at least as seen through the eyes of the blogosphere, as a cooperative and friendly field. This certainly corroborates my experience this term here at Caltech.

There is also a lot of discussion online about the problems with the current system. Many people lament that the ‘problem set/test/grade’ status quo is alienating to some minds that would be great in astronomy, and theorists have an easier time than people who could be great coders or instrumentationists. I would agree with this – although here at Caltech, we have theory pounded into our brains until it is all we can think, qualities that make a great astronomer cannot necessarily be measured by checking someone’s ability to do a physics problem.

This semester has given me a lot to think about, and changed my habits forever. I really do enjoy talking to others in the field, and now I know how to approach them. One of the goals Professor Johnson gave at the beginning of term was to be able to talk to an astronomer, be it a professor or someone else. He wanted us to see someone that we think is way “above” us, and just be able to talk to them. The me of a year ago could not have done this, and the me of this summer didn’t know to try, but ever since the day I met up with Dr. Kirby on Professor Johnson’s suggestion, I have realized that approaching other people isn’t so scary as it seems. I look forward to continuing the habits of this class, and pursuing the career path of being a professional astronomer.