Sunday, December 4, 2011

A digression from a few Mondays ago

Preface: I was under pressure to do several sets when this was written and now feel much better. :) and am publishing this as it's another post and for attendant points ;)

There's a lot of things I don't know, and that is never more obvious than when someone explains something by physics. It's a little discouraging, at first, to think that you have never noticed -- never cared -- about the simplest things that surround you.

It's interesting. I don't want this, my first post in a while, to be so vague and insecure and uncongealed. But right now I don't want to explain the coolest bit of physics that I've learned in a while. I will, of course. In a while.

I can't let go of this right now. I sat down to finish a few blog posts (that will not happen, due to a variety of reasons, social foremost among them) and got quite off the main road. That's kinda what has happened just recently. I guess this midterm season went not as well as I'd have liked. It didn't go badly, per se, but not well - and that's discouraging, to always be mediocre. Mediocrity at Caltech is not bad, but not exactly desirable either. I should work harder or care less - this middle ground is unfortunate.

I learned this term that I would willingly give up Astrophysics, not because I dislike it or have too much work -- that's not true at all -- I absolutely could do more work-- but because it doesn't come easy to me. Is that a cop-out?

I think it is.

Ignoring this very self-centered vein -- sorry -- I try pretty hard to widen my perspective, to work hard and play a lot, to wake up every morning knowing that my time was well spent the day before and that if I had died, disappeared in the night, even the time I wasted I enjoyed. So much time lost to my memory and lost even from there. But there are few regrets (one, actually, is not learning to play the cello; another, that I hadn't spent more time forgiving the faults of my grandparents).

It's not -- this whole widening perspective thing -- a constant in my thoughts, more a thoughtful constant that I believe (or wish I did) to the fullest of my ability and my reason. (Take the almost-Objectivism here with a grain of salt -- last year I downed all Rand's books only to discover I hated them. I hate her metaphors. I mean this - don't read them if you don't have to). There's not enough meaning in the world to gift it only to one life and one POV - your own -- that is the most limited, restrictive overview of life that I can imagine. Singularity? Uniqueness? Do these apply when there is so much to discover?

Yet there's a problem with knowing that not only is your life so stolidly average this conception of average and uniformity is beyond you. You -- ah, perhaps, only me -- but you see the dilemma there? It's not only me; so let me begin again. You in that giant, heaving mass of humanity -- you have to deal with the consequences of facing it. It, you ask? Facing the fact that you are nothing - that there is always someone more smart, more fun, more interesting and more charismatic and better in all things, even those you cannot imagine. And you feel overwhelmed. And you just...


Alternate career paths

I'm impressed by the brevity of this article. It concisely lists a few articles of reasonable alternatives to unfortunate situations, or times when you may ask "What's the point?"

The article is prefaced with an apology to those who have their lives and futures in astro planned out, noting that grad students are often "plagued by a series of 'what ifs'." The writer, a Maria Drout, asks a question I fear will happen and might one day stop everything in its tracks: "What if, horror of horrors, I get four years into a PhD and realize that research just isn't for me?" Yep. 

Here's a summary of alternate career paths (alternate referencing all those not ending in grad school and tenured professorship at a university):
  1. Research. Instead of working with a university, you can work at federally funded agency, or with a large collaboration research group.
  2. Observatory Staff Scientist! This sounds like fun. You maintain instruments, while doing your own research and helping others with their research! And spending your life at an observatory. I have a few links regarding this. For instance, Keck is hiring technicians right now. :) although those are more relevant to engineers and people with lots of experience with instruments.
  3. Small liberal arts teaching :) or high school
  4. Science writer - for editors for Fermilab, freelance book and magazine article writing, developing physics courses, etc. This is apparently very flexible.
  5. CfA press officer :) or NASA or any science institute
  6. or outreach and education positions (available at most labs and universities) which might include observatory support and running planetariums and museums and teaching.
  7. Industry: R&D positions pay well and give you a lot of autonomy. This particularly interested me. You expect stress and bosses and loss of autonomy, but apparently, after finally finding a job, he works in a cubicle in 'relative obscurity' - but that's a minor obstacle. He had developed  a long-range research plan for jets that he could initiate, develop and control only industry.
    He writes, "There is no adviser poking his head in for frequent updates; there is no grant committee that needs a written progress update. in fact there is no grant committee at all. If I want to do something, I do it. Succeed or fail, I own it. And failure isn't necessarily bad: if half of your projects don't end in complete failure, you're probably not pushing the boundaries enough."
    He goes on to say that there's a lot of waste expected in buying equipment, and no one will pester you about it. :( Spending money is encouraged. Impressively, "Time is worth more than money. If we need something, we buy it. In industry, you will never want for the tools you need to do your job."
    There's a difference in the way hierarchy is approached. You have bosses, sure, but they let you do your work with little supervision - treat you "like an adult...[it's] oddly liberating" because you are the expert on your subject matter, and in that regard you are in charge.
    There's no tenure - everyone is competent and hardworking. His coworkers are, "quite smart but slow to show it off; nobody cares how smart you are if you can't play well with others, and a brilliant person who nobody can stand to work with will soon be out of a job."
    And you get sleep. :) You smile, but never have job security.
    However, he says, "With a physics PhD and a good resume, in Silicon Valley, your starting salary as a minimum should begin with a "1". (knock off 20% for astronomy - sorry!) Wall Street will pay several times that, even now. Close to half a million is not unheard of. What ever you do, do NOT settle for something like $70k, because I guarantee you that jobs that pay that level won't challenge you and won't offer upward mobility. This is not academia."
    But this seems less astronomy/astrophysics based and more applicable to engineering. So it is a little tempting to me, but at the same time I've always idealized academia...
  8. Business manager - managing program development for telescopes or intelligent, law enforcement, and energy.
  9. A comment on the bottom of the page mentioned jobs in the federal government in fields related to science policy. Civil societies (Red Cross, Habitat for humanity, World Bank, IMP), for profits, and the Bureau of Human rights in the state department. "I met two people there that had PhDs in astronomy and three in physics. You may not do astronomy, but with your training in scientific thinking, yuo can really find that your expertise is desperately needed. many scientists got their positions via fellowships, especially the AAAS fellows and APS/AAS fellows. you can find work at State in nuclear weapons control, cyber security, international relations involving large scientific collaborations....There are jobs in the White House too." This was from nicolas Suntzeff, the Mitchell Prof. of Astro at Texas A&M.
Yep. There is it. This pretty much told me that there are jobs outside of academia after grad school, actually! :) This is good. As appealing academia is, there simply are not enough jobs for professorships for all the physics and astro grads, and (on a more personal note) I don't think I'd cut it as a professor anyways :) 

This is good. There are lots of alternative career arcts in industry, national labs, observatories (<3) and engineering and government and teaching. A lot seem to be more managerial positions, in which research is not referenced. That's not too alright with me right now.

P.S. part two of the last part of our project: Daniel, Eric, and Nathan are in this group!

Quitting astronomy

There's a recent article I read about quitting. It's an interesting topic, especially given the taboo associated with it in our high-achieving, success-driven school. There's a certain line  - it's a podcast - that really, really stood out to me. Steven D. Levitt is a professor of economics at the University of Chicago (woah) and Stephan J. Dubner is a journalist writer for the NYTimes, Time, The New Yorker, and elsewhere.

LEVITT: I try to talk my grad students into quitting all the time.
DUBNER: Quitting grad school?
LEVITT: Quitting grad school, yeah. A lot of people — you make choices without a lot of information and then you get new information. And quitting is often the right thing to do. I try to talk my kids into quitting soccer, baseball if they’re not good at it. I mean, I’ve never had any shame in quitting. I’ve quit economic theory, I quit macroeconomics. I’ve pretty much quit everything that I’m bad at.

Per this.

I guess I'm evaluating this in terms of myself - knowing that there are a lot of people who are better at this, at astronomy and physics and that I'm bad at this. Not terribly bad, just not sparkling good.

This is quite relevent to our discussion, I guess, about our future careers in astronomy. These guys, who, in my mind and from what I know of their work in Freakonomics, seem quite well informed from an economic standpoint in decision making and the validity of choices. 

It’s something that Stella Adler, the great acting coach, used to say: Your choice is your talent. So choosing the right path, the right project, the right job or passion or religion — that’s where the treasure lies; that’s where the value lies. So if you realize that you’ve made a wrong choice — even if already you’ve sunk way too much cost into it — well, I’ve got one word to say to you, my friend. Quit.
Same source.

So. To quit or not to quit? That seems to be the question.

Melodie's friend from college quit physics. And she does seem very happy.

Ah. A question with an answer only quitters know. I wouldn't know if it was the right decision until far into the future, and even then I'd not be sure.

For now, I am perfectly content with staying with something I know I am bad at, just because it's too early to tell if I'll get better at it. Chances are that your talent may be hidden in the beginning.

P.S. This is kinda number 3 part 1 for our project, which I did with Nathan and Daniel and Eric.

political space

In late September, China blasted off the Tiangong-1 (the "heavenly palace", literally) into space. It's supposed to be a space-lab module, which can support the docking of manned and unmanned spacecraft, and a testbed for China's future modular space station Tiangong-3 (I'm oddly reminded of origami here...) which will be launched in 2020-22.

Now, the reason why this is so important is that China was rebuffed, again, from the ISS, which incidentally is actually finished now. China decided on an independent path to space, with construction of a space station scheduled and followed by missions to the moon. Ha.

So this space station, Tiangong-3, will be 100 tons, five times lighter than the ISS. They expect to be the only power that can reach the moon within a few years of launching it. Former NASA administrator Michael Friffin states, "In my opion, China understands what it takes to be a great power. We have written the script for them....They are a near-peer competitor of ours and I would worry very much about the future of this nation if we were not -- and if we were not seen by all -- to be a world leader...When the Chinese can reach the moon and we cannot, I don't see why any other nation would regard us as a world leader."

That is a demoralizing thought. And he has an interesting take on what it means to be a world leader or power. But nevertheless, I think it is true that a lot of people would feel emasculated if the US could not do something China can easily do in the sciences and in advancing human discovery.

This is, even more interestingly, most probably our own fault. Read the second reference article, written in May this year. "A clause included in the US spending bill approaved by Congress to avert a govt shutdown....has prohibited NASA from coordinating any joint scientific activity with China. The cluase also extends to the White House Office of Science and Technology Policy."

Wow. That just seems amazingly shortsighted and xenophobic.

Contrary to what our politicians believe, I don't think that there is anything wrong with international cooperation. Actually, note the very specific ban with China, but not the other EU, Russia countries included in the ISS endeavor. I am confounded by this apparent attempt to slow China down - not to mention such a brazen, bold, and very weak and ineffective attempt.

The superficial reasons is the cyberattack/espionage theories that are almost certainly true and almost certainly overplayed.

Hopefully this doesn't lead to too much distrust between the nations. Or terrible wars in space.


Wednesday, November 16, 2011

Diffraction in lasers

I met an amazingly smart 2nd year grad student on my geology trip. A bit of background - two dozen geologists (actually, two astro kids and a Mech E were included in the jovial bunch) traipsed their way down to Baja California -- not in such a lackadaisical manner, with more intent -- but we made our way down to explore a bunch of rock formations, paleomag, a bit of cretaceous-dinosaur-fauna things, etc.

A few of us had wandered down to the beach at the Salton Sea the first night. When lasers came out, there was a period of comparing the power output of the lights and the distance this corresponded too.

But when you put a slight obstruction in the beam of the light -- we were using green lasers, best for seeing in the dark and for pointing out stars -- you get a diffraction pattern in the output light. There is a very obvious pattern of dark and light. Now, apparently, these are the Fourier transform of a single slit diffraction pattern! The light is blocked for exactly a top-hat function, and the resultant pattern has an intensity (not energy) that we see. The transform of the energy is the sinc function, but the intensity of the light is the sinc function squared.

Now, imagine two obstructions -- two hairs. On the ground, then, you see the pattern repeated, the standard diffraction of light and dark that progressively gets dimmer farther from the center. This is the first and the second fourier transform.

Yay :) You can do this for any number of obstructions!

Reflecting the laser off your teeth, your are confronted with a large number of organic shapes that have an apparent depth to the layers. They form moving shapes that crawl in green shadows across the ground, changing and disappearing. These are the fourier transform of...saliva. Ha ;)

Impressions of astronomy

Why hello!

The sense I currently have about astronomy, astronomers, and the goals involved is perhaps quite normal. To be a professional astronomer seems to take a significant amount of time in studies, years spent toiling in grad school and beyond as a postdoc and researcher. Then perhaps a career in academia, hard-won and deserved.

It takes a good work ethic and a certain level of intelligence, as well as patience and creativity and pride. An astronomer must be able to stand in awe of the universe and simultaneously label it, unfold it, render it in one dimension so that the world is much less mysterious than it was a moment ago. (Or for some, the opposite -- thinking too hard about something in the field often reveals untold complexities...)

And he needs to enjoy it.

What's the ultimate goal? It's certainly not wealth and fame -- those are attendent much more commonly upon other professions -- but, I think, a chance to resolve your fundamental questions on -- dare I say it? -- life, the universe, and everything.

It's a nigh impossible ambition.

And yet it's a conviction and creed that so many hold onto. The aim of an astonomer is to work hard, perhaps, in order to ascribe some meaning to the vastness we inhabit one miniscule fraction of.

I'm not currently sure this is what I want to do. In a dream world (not the best or first, but very close; in the timeline that includes astronomy), I guess, my goal is to graduate with a doctorate, work in deserted observatories for a while, and move on to a job in industry. How? Well, I've been in love with our sun (yes, it's proprietary) for years. Perhaps there is some more practical application of knowing how the sun works, how it reacts, how the earth reacts to it. There might be some correlated study in the much-hyped "green tech", which is a huge fancy of mine.

I guess I see the world as a multifaceted template, which needs to be slightly better understood. What better way to approach this than through the most far-away, esoteric examples of creation?

Friday, October 28, 2011

Wednesday, October 26, 2011


A few more things of interest:

Vis Viva: orbital energy conservation equation; for any Kepler orbit (elliptic, parabolic, hyperbolic, or radial), the vis viva equation is v^2 = G(M\!+\!m) \left({{ 2 \over{r}} - {1 \over{a}}}\right), where is the relative speed of the two bodies, r is the distance between them, and a is the semimajor axis (a>0 for ellipses, a= for parabolas, and a<0 for hyperbolas).

Redshift1+z = \frac{\lambda_{\mathrm{obsv}}}{\lambda_{\mathrm{emit}}}

Surface Gravity: the luminosity of a star L* goes as logg*.

Hill sphere: the region around a body where it dominates the attraction of satellites
r \approx a (1-e) \sqrt[3]{\frac{m}{3 M}}
Lies between L1 and L2, although the true region of stable satellite orbit is inside 1/2 or 1/3 of this and dependent on other forces (radiation pressure, Yarkovsky effect). Note that retrograde orbits at a wider orbit are more stable than prograde orbits. Also, in any very loworbit, a spherical body must be extremely dense in order to fit inside its own Hill sphere and be capable of supporting an orbit.

Yarkovsky effect: for small bodies (d<10km) a force caused by anisotopic thermal emmision (photons with momentum)

Roche limit: the radius at which an (only) gravitationally-bound satellite disintegrates by tidal forces.

If held together by their tensile strength (Jupiter's Metis and Saturn's Pan) satellites can orbit within their Roche limits. Almost all planetary rings are located within their Roche limit, with Saturn's E Ring and Phoebe ring being notable exceptions.

Roche lobe: the region around a star which orbiting material is gravitationally bound to the star.
If the star expands past its Roche lobe, material can escape. In a binary system escaped material will fall in through the inner Lagrangian point (mass transfer).

Just some things we should understand. :P

Sunday, October 23, 2011

Thursday, October 20, 2011

Electron degeneracy pressure

Sirius A (center) and Sirius B,  a white dwarf .
Sirius B is the point in the bottom left.
Sounds cool, eh?

You're right.
It is cool.

Imagine a star. Imagine a dying star, one with an incomprehensibly large number of atoms, of electrons.

Given the right star (a main-sequence star with a mass of 0.07 to 10 solar masses, over 97% of the stars in our galaxy) which expands to a red giant, loses its ability to fuse carbon, and sheds its outer layers, you are left with a dense core mostly of carbon and oxygen, supported against gravitational collapse only by its electron degeneracy pressure.

When electrons are compressed in tiny volumes, they gain a large momentum and kinetic energy, a repulsive force that prevents further compression.

The Pauli Exclusion Principle disallows two half integer spin particles from occupying the same quantum state at a given time, so there is a resultant repulsive force manifested as a pressure against compression of matter into smaller volumes of space. To add another electron to a given volume requires raising an electron's energy level to make room; there is a requirement for energy to compress the material which appears as pressure.

Solid matter is...solid because of this degeneracy, instead of electrostatic repulsion. For stars which are sufficiently large, electron degeneracy pressure is not enough to prevent them from collapsing under their own weight once nuclear fusion has ceased, and then neutron degeneracy pressure prevents the star from collapsing further. In a nonrelativistic material, this is computed as:

This pressure is in addition to the normal gas pressure P = nkT / V,  and neglected unless the density (proportional to n/V) is high enough and the temperature is low enough.

Another way of looking at it is through the uncertainty principle. The Heisenberg uncertainty principle \Delta x \Delta p   \ge \frac{\hbar}{2}   lets us see that as matter is condensed (uncertainty in position decreases) the momenta uncertainty increases and the electrons must be traveling at a certain speed. When the pressure due to this speed exceed that of the pressure from the thermal motions of the electrons, the electrons are degenerate.

Electron degeneracy pressure will halt the gravitational collapse of a star if its mass is below the Chandrasekhar Limit (1.38 solar masses). This pressure prevents a white dwarf from collapsing. After the limit, the star will collapse to either a neutron star or black hole (by gravity).

See also

  • White dwarf, the wikipedia article
  • Simulating a white dwarf supernova; popular article
  • Apparently, Betelgeuse is predicted to cataclysmically explode! See the Fox article

Friday, October 14, 2011

Satellite tracking and ROSAT

Satellites in the sky :)

A schedule:

The big news is the deorbit of a massive x-ray satellite. The ROSAT X-ray observatory, launched in 1990 by NASA and managed for years by the German Aerospace Center (DLR), will return to Earth within the next two weeks. Current best estimates place the re-entry between Oct. 22nd and 24th over an unknown part of Earth. ROSAT will produce a spectacular fireball when it re-enters, but not all of the satellite will disintegrate. According to the DLR, heat-resistant fragments as massive as 1.7 tons could reach Earth's surface. :) As ROSAT slowly descends it is growing brighter. During favorable passes, the satellite can now be seen shining as brightly as a first magnitude star in the night sky.

It is deorbiting due to increased solar activity! The atmosphere has expanded, increasing the friction of the satellite's orbit. That is outstanding. This is reason why the sun is still the most relevant subject in astrophysics!

Thursday, October 13, 2011

Geothermal Activity

This has nothing to do with astro, but with my Ge136 class, which involves a field trip to the Salton Sea and Mexico. By Jesse Rogers.

Wednesday, October 12, 2011

Tuesday, October 11, 2011

Dawn and 4 Vesta

In the newest e&s issue (Engineering & Science, published by Caltech) I discovered that on July 15, around 10 pm, JPL's Dawn spacecraft got into orbit around the brightest asteroid 4 Vesta.

Vesta has a mean diameter of about 530 km, and only smaller in the asteroid belt than the dwarf planet Ceres. It's about 9% (estimated, as these estimates were recently downgraded a lot) of the mass of asteroid belt.

The northern hemisphere from 5,200km
Dawn has a two-part mission. It will orbit Vesta for a year, and then is scheduled to reach Ceres in 2015. This has never been done before as there has never before been the right kind of propulsion system to let this happen. All former multi-target missions using conventional drives, such as the Voyager program, were restricted to flybys of the bodies that they wanted to study. Conventional drives rely on chemical fuels.

The ion drive used for this mission is innovative. It accelerates xenon ions to generate thrusts from three thrusters, and everything is powered by a 10 kW (at 1AU) triple-junction pv array.

It has already tried to tightly constrain and calculate the asteroids mass as well by its gravitational pull, which will reveal whether Vesta, like Earth, has a nickel-iron core and an olivine mantle. Earth and, perhaps, Vesta, has this differentiated interior because of a formerly molten interior.

Craters in various states of degradation.
Taken in August.
Detailed mapping of the entire surface of the asteroid will continue to study the apparently dry/rocky protoplanet, to help our understanding of rocky planet formation. Vesta is achondritic (basaltic instead of filled with molten droplets found in space and accreted to asteroids), so it seems that it has experienced significant heating and differentiation, with a Mars-like density and lunar-like basaltic flows. However, it probably differentiated quickly (from analyzing radionuclide dating of pieces thought to come from Vesta). All these theories will be tested.

Again, the plasma drive enables it to be the first spacecraft to orbit two extraterrestrial bodies (and the sun). Dawn used 275 kg of zenon to get to Vesta. With the propellant it carries, it can perform a velocity change of over 10 km/s!

Monday, October 10, 2011

Rossiter-McLaughlin effect

Heya peeps.

Has it ever struck you that a greeting is quite a revealing reflection? Or perhaps not. Maybe it's just me, maybe just some slight inability to suppress introspection and self-evaluation; although it's a gnawing suspicion in my head that almost every Techer is highly suspect to this trait. But I can recall exactly why I say 'sup to some peoples, name the two unrelated, separated-by-thousands-of-miles persons who called Howdy on a regular basis, and explain my tendency to salute some others.

We should find some sort of formalism for this. Does that even make any sense? Eh.

Radial velocity measurements (in km/s) of the transit
 of CoRoT-2 b, around an active G star. The
spin-orbit misalignment angle is +7.2 ± 4.5 degrees.
Anyways, the point. We've all heard of this Rossiter-McLaughlin effect and its usefulness, but I didn't really get it until I realized it allows for some cool sciencey stuff to be done. These are a kind of unique signature, a kind of hello or greeting unique and individualized to the extrasolar planet in question, which grants observers a lot more inferred information than could be hoped for. For instance, the asymmetry in the revealed stellar spectrum due to the spin of the star lets us extract the projected angle between the planetary orbit axis and the stellar spin axis, as well as the stellar spin velocity (which is useful for calculating the predicted precision of an observing run -- the faster the star spins, the more line broadening occurs, and the less precise measurements will be).


In a sentance, the Rossiter-McLaughlin effect is the change in the observed radial velocity/mean redshift of a star due to an eclipsing binary's secondary star or an extrasolar planet during transit.

A star's rotation means that at any time, one quadrant of its photosphere will be seen coming towards the viewer, and one quadrant moving away. These motions produce blueshifts and redshifts, respectively, which we observe only as spectral line broadening. However, during transit, the orbiting object blocks part of the disk, preventing some of the shifted light from reaching the observer and changing the observed mean redshift, resulting in a positive-to-negative anomaly if the orbit is prograde, and vice versa if the orbit is retrograde.
The view is situated at the bottom. The light is blueshifted on the approaching side and redshifted on the receding side. As the planet passes in front of the star it causes the star's apparent radial velocity to change.

This effect has been used to show that as many as 25% of hot Jupiters are orbiting in a retrograde direction with respect to their parents stars, strongly suggesting that dynamical interactions, rather than planetary migration, produce these objects. For cool stuff on misaligned orbits of hot Jupiters, see this.

Actually, I'll overview the link a bit. ESO claimed that "Most hot Jupiters are misaligned...the histogram of projected obliquities matches closely the theoretical distributions of using Kozai cycles and tidal friction...most hot Jupiters are formed by this very mechanism without the need to use type I or II migration." Greg Laughlin, a professor at UCSC, discusses this and comes to the conclusion that Kozai-migration, well understood for HD80606 (and explained very nicely in the post), "plays a larger role is sculpting the planet distribution than previously believed."

These transits are quite amazing bits of work. With the knowledge of the effect and the subsequent radial velocity measurements, we can better understand the fundamental formation scenarios and dynamical processes that bring the companion, including the hot jupiter, into the observed orbital state (semi-major axis/orbit, the inclination, eccentricity).

See also

  • Paper on the math behind the Rossiter-McLaughlin effect
  • Paradigm upended, an importnat reference for this post

Sunday, October 9, 2011

Lab 1: Radius of the Earth at the beach

The instructions for the lab, for which we traveled to Santa Monica Beach!
lab1 wksht

The writeup, calculating for the radius and mass of the earth:
Lab 1
The major conclusions was an estimate of the radius of the earth that was three times too large (within an order of magnitude) and a mass estimate that was ~5000 times too large.

Kozai mechanism

The Kozai mech is the periodic exchange between inclination and eccentricity; see this.

It is a secular interaction between a wide-binary companion and a planet, in a triple system. When the relative inclination angle between the two orbital planes is greater than 39.2 degrees (the Kozai angle) a cyclic and long-term exchange of angular momentum occurs between the planet and more distant companion.

For an orbiting body with eccentricity and inclination i,   \sqrt{(1-e^2)} \cos i is conserved. A perturbation may lead to a resonance between the two. Typcally, this results in the precession of the argument of pericenter, which then librates (oscillates) around either 90° or 270°. Increasing eccentricity while keeping the semimajor axis constant reduces the periapsis distance (the distance at closest approach), and the periapse occurs when the body is at highest inclination. The maximum eccentricity reached is independent of orbital parameters like mass and period: .

Oribital parameters, mass and semimajor axes only affect the period of the Kozai cycles. This is estimated as , where the indices are 0) central star, 1) planet, and 2) binary companion. If the Kozai period is large, it is highly unlikely the planet is highly eccentric at a given point in time. The binary companions are probably either a brown dwarf (larger orbital range, mass can approach Jupiter masses) and main-sequence dwarfs, about the mass of the sun. The Kozai period is inversely proportional to the mass of the binary companion, so oscillation periods of brown-dwarf companion systems are hundreds of times longer than that of a main-sequence dwarf star.

lasers in the sky

Listen to some Blink-182 to get the sense I had of this concert! Or Daylight :)

I was at a concert at Hollywood Bowl just a few hours ago. A group of us headed out to hear Matt and Kim, My Chemical Romance, and Blink-182. The concert should have been great, but as it was sort of a last minute thing for me, and the people around us weren't too much into dancing, and Matt and Kim were terrible, it was slightly boring (yep...but still fun at times!)

The best part was this amazing laser show for the headliners. These were legit. There were three, which could cycle through all the colors. The white light would separate into green and red and other colors, as would magenta and green, when they hit the trees ringing the top of the compound.

At some point, staring at the mountains behind the stage, another kid and I attempted to calculate the height of the mountains. Using as an arm length of 2.5 ft pointing towards the bottom of the mountains around 1-2 miles away, and a height from that arm to the top of the mountains of about 8 inches, we estimated that it was 0.8 miles straight up, and more. Our plan is to come a couple hours early for the next concert here and climb up!

I looked up into the sky before the show started, around 7pm, and noticed some stars in a y-shape - there aren't too many visible stars in LA, and these were to the northeast, so I think it was Andromeda!  The greatest thing was approx. every hour, I looked up and saw a significant angular displacement and a slight turning to the configuration of stars as they advanced along the elliptic, like explicated in our readings/problems.

Yep, that was the main point of this. :)

However, I discovered a really cool website: which explicates notable constellations, stars, galaxies, objects, meteor showers, and planets visible in the sky! WOW.

Observing, Oct 7-8

Look up We the Kings' She takes me high <3

One of the greatest things about Caltech is scientific opportunities for our undergrads, viz. myself. :)

This was really enforced yesterday (the general case, not only the specific :D).  Melodie, who has joined our ay20 problem solving sessions, generously invited me to observe using Keck's HIRES off-link thing at Caltech! We had a couple of lab write ups we wanted to do, and a Friday night seemed the best time to attempt them.

Around eight to midnight, we were on-and-off working on the second worksheet, the results which were posted. But a lot of the time was just spent chatting about school and astronomy, as well as significant periods where Melodie was amazing and taught me about Fourier transforms - their purpose, and why we love them.

For instance, imagine a double slit (like that in the famed experiment). The slits are of width w and are D apart. As w->0 we have two delta functions, at +/-D/2 from the center, at least in normal space. This must needs be convolved with a top hat function to achieve a graphical representation of the intensity of light received through a receptor (telescope opening) of width D. Unfortunately there is not a simple way to do this. So in Fourier space, the two delta functions are actually a cosine, with a wavelength of λ=1/w. Note that the wider they are, the smaller their frequency and the lower the angular resolution of the instrument in question. In Fourier space, the convolution turns into a multiplication, and so you multiply the cosine with the representation of a top hat in Fourier space, which is a  sinc, a function with a symmetric peak at the center.

Here are the relevant graphs in normal and fourier space:
Delta function; in Fourier space it is a cosine function

the top hat function, in normal (left) and fourier space

This means we can multiply the sinc and the cosine function and get, from the square of the convolution, the intensity and energy of the observed lines!

One of the most important things to take into account are the full-width-half-max (FWHM) of each line. The line is broader with more scatter, and a wider w. This is generally bad. By thinking about it, I think we came to the conclusion that angular resolution was better as w increased and the wavelength of observed light decreased. 

But as a wider line gives us a different angular resolution, this can be helpful sometimes. That's why the Very Large Array (VLA) has such great radio accuracy - it couples dishes into different angular resolutions so large and small scale structures in the received waves can be resolved out of the data. (See Juliette's post for a great overview on this!) Moreover, if most of our photons come from a single section, it may distort the actual depths of the emission/absorption lines, because in the data it looks relatively much deeper or shallower. All this is important to any informed observer.

Our setup, which included a
video link to people in Hawaii at
9000ft elevation and at the
actual telescope. Later we linked
with the  Princeton team.
Conditions at the telescope were terrible. There was a lot of cloud cover, which is obviously terrible. The target S/N ratio was (maybe) around 200 for brighter stars, with an absolute time limit spent on each star of about 500s (these numbers and any following may be kind of off, as its all coming from a mal-adjusted memory). This was far from achievable, esp. during the early part of observation. Under perfect conditions, seeing - a measure related to how nice the spectrum taken will look, i.e. 0 is no attenuation - you have about a 0.3-0.5 seeing from atmospheric affects. We were at 1.5-2.0 the whole night, with the horizon obscured almost constantly and the clouds luckily breaking up into patches by the end of our 6-ish hour shift, ending around 3:00-3:30 am.

At one point, another of the first -year grad students, a theorist from Oxford, wandered in. He was really excited and cool, and asked a very interesting question. Professor Johnson would love him - Avinash? maybe :) - kept apologizing for having so many "dumb" questions to our lead observer, Sebastian, that actually were amazingly insightful. For instance, apparently clouds do not matter much regarding the actual spectra we read (at least for HIRES, as the water absorption lines are in the (near-)infrared and not so relevant when we are taking observations in the visible light spectrum.

Yep. They're observing now, in Cahill, so props to Melodie and Sebastian!

Apologies for any mistakes in the above: no notes were taken during lectures in the wee hours of the morning.

Saturday, October 8, 2011

The Celestial Sphere and Observational Planning

Wksht 2 was very, very long, and we were able to write up problems one and two. We got quite far on Problem seven, but Jackie informed us that it was unnecessary, so if we have time we might attempt it ater. (Maybe not - but we got through the theory of it very well and now could do it quite easily!) Here's the problem set: Ws Celestial Sphere And here are our solutions: wksht2

Two drawings are also necessary, which will be uploaded soon. But here is my graph of tau Ceti's time of meridian crossing (see problem 2):

Sunday, October 2, 2011

El Mayor-Cucapah rupture

Pull up Joshua Bell's rendition of the first movement of Vivaldi's Winter, while you scan this 
It's absolutely perfect. Then wander into Chopin's E-flat nocturne, played by Mr. Rubinstein.

There's a lot of geological work that constantly astounds me. I am an astrophysicist because I believe, fundamentally, that my life is useless and cannot begin to be meaningful until I get a sense of perspective. But astro is not the only thing I love. The histories of the earth are no less great than the beauty of the stars; it's a story and an exposition on possibility instead of a cold, lonely universe where a galaxy is nothing; and yet geology still works in inconceivable timescales; it gives me a beginning to that unreachable perspective I crave.

There was a recent article and paper on this El Mayor-Cucapah rupture. From the abstract,
The geometry of faults is usually thought to be more complicated at the surface than at depth...The fault system that runs from southern California into Mexico is a simple strike-slip boundary: the west side of California and Mexico moves northwards with respect to the east. However, the Mw 7.2 2010 El Mayor–Cucapah earthquake on this fault system produced a pattern of seismic waves that indicates a far more complex source than slip on a planar strike-slip fault...
The earthquake was on a system of faults that forms  part of the late boundary between the Pacific Plate and the North American Plate. In the standard model, transform plate boundary structures are vertically orientated. But this 120 km rupture involved angled faults that were initiated on a connecting extension fault between the two segments. The surface trace is nearly linear, but the seismic rupture traveled through a complicated set of preexisting faults that dipped in various directions.

Interferogram of Kilauea
This anomaly was modeled from interferometric synthetic aperture radar (InSAR), optical imaging, and seismological data. The remote sensing techniques provide measurements of surface displacement when combined with GPS data, aiding the analysis of the rupture.

This young fault broke in an impossible-to-predict scenario. The geologic structures involved in the new fault system are not clear enough (one previously unmapped fault had been buried by river sediments).

There's so much discovery right under our feet, enfolded in the earth.

Saturday, October 1, 2011

Melodie, a grad student

Hot Jupiter
On Thursday, Melodie Kao and I had lunch together. We met and chatted about her undergrad at MIT and her research, here at LIGO and in Chile.

Melodie is a new first year grad student in Professor Johnson's lab! She's newly from MIT, that 'other school' as Techers see it. She's writing a proposal for an NSF grant for work on the Cold Friends of Hot Jupiters project, which I was lucky enough to work a little on earlier this summer. 

At age nine, she had already decided that she was going to be an architect. (This is so cool.) She got into many schools with amazing architecture programs, but luckily chose MIT over Cornell or CMU. Luckily, as she discovered that she missed the math and the science involved, so she changed to aerospace engineering. Engineering was not her favorite; she mentioned that she hated coming up with an answer, testing it, implementing it, discovering that it didn't work, fixing it, and then redoing it all over again, over and over. As an astronomer, she didn't have to deal with that, not with the people who work at telescopes and understand them so much. 

Side note: this is so true! When I sat in on the observing nights, the lady and other people in charge knew every in and out of every problem and could resolve it. I had the most utterly unshakable faith in their abilities. (end of digression)

I love architecture. [1] [2] [3] [4]
Amazingly, she switched into Physics with a concentration in architecture, and was able to finish her requirements early. She did prior research (including at LIGO, trying to reduce the noise involved in the measurements by decreasing the thermoelastic deformation of the mirrors), but did something amazing her senior year. For the southern hemisphere's summer, she worked in Chile somewhere for 5-6 months, resolving a large problem in determining the mass of galaxy clusters. (This part is beyond cool.) Because the normal method to determine the mass of a cluster of galaxies is highly dependent on the  assumption that the system in is dynamic equilibrium (enough time has passed since any galaxies/objects disturbed the cluster) it didn't work for anything but old clusters. At first, she had to find which galaxies were part of the cluster, instead of simply being in front of or passing by her cluster (which I forgot the name of, unfortunately).  

My personal favorite, M13, a globular cluster in
Hercules. It was one of the first things I saw through
a telescope, in the middle of  Joshua Tree. 
(This part is possibly uncool, i.e., wrong.) It might have something to do with the virial equation and timescales to equilibrium, which this post implies is going to be taught! :D Cool. 

But by mapping the parameter space of individual galaxy velocity relative to the cluster and the displacement between the galaxy and the center of mass? a spacial center of the cluster? (a radius, I think) she could get a very good estimate of the shape of the cluster's age, and better calculate the mass.

When I say the shape, she was able to take account of differences in age of the galaxies and each massed according to a formula-function of time, and thus mass the the entire cluster much better!

I'm happy she'll be working with Professor Knutson!

See also