Aurora borealis

I LOVE THESE

so much

 Wow.

THAT IS SO INEFFABLY

GORGEOUS

<3

Notes

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 , where v 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).

Redshift: 

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

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

Dark Skies

http://www.visualastronomy.com/2009/01/find-dark-sky-site-near-you.html

I wanted to see the Orionids, but there were no cars willing to go in Lloyd. Next year! ;D

Electron degeneracy pressure

Sirius A (center) and Sirius B,  a white dwarf .
Sirius B is the point in the bottom left.
Hubble.

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   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

Satellite tracking and ROSAT

Satellites in the sky :)

A schedule: http://spaceweather.com/flybys/flybys.php?zip=91126

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! http://www.newscientist.com/blogs/onepercent/2011/10/space-telescopes-re-entry-brou.html

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.

Geothermal Energy At The Salton Sea

View more documents from rogers160

By Jesse Rogers.

Reading

The entirety of Surely You're Joking, Mr. Feynman online! Here's the part where science books are discussed: http://webpages.charter.net/leutzdave/Feynman/part-5.html#49

Links

http://www.khanacademy.org/
Go to the Cosmology and Astronomy section!

Outstanding. One weekend I will sit through and just watch a bunch of these.

Links

http://www.spacedaily.com/Exo_Worlds.html
News about extra solar planets :)

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!

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).

Yeah.

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

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 e and inclination 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: http://hubblesite.org/explore_astronomy/tonights_sky/ 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.

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):

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 M_w 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.

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 in...science, 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

• her abstract for ligo: Numerical Thermal Noise Modeling
• her presentation at the 2010 Summer Student Symposium on the Star Formation History of the Dwarf Galaxy Holmberg IX
• My blog for this summer: Searching for Cold Friends of Hot Jupiters