Keeping the Beat

I haven't been posting here recently, since I've been busy with research, but the stuff I'm doing at the moment is a bit slow-moving, so I thought I'd stop in and give an update.  In February, I mentioned work I was doing on approximations to a piece of solar system dynamics code for LIGO.  I'm still working on it, and I wanted to talk about an interesting issue I just resolved.

The coordinates we use to specify a direction in the sky are called equatorial coordinates, given in right ascension and declination.  These correspond to taking the longitude and latitude at the spring equinox, and projecting them into space.  Since the coordinates are referenced to a specific position of the Earth, as the Earth moves the stars stay fixed in the coordinates, e.g. Procyon is always at 114.8° RA, 5.2° dec.  However, since this system assumes a fixed Earth, the planets and even the Sun will move around.  That means that as data is being collected from a source, the sun could cross the path and introduce the time delays I mentioned in the previous post.

Over a short time scale, say a week, the dominant frequency will be daily, due to Earth's rotation, but what kind of day?  The ones we're used to are called solar days, which correspond to the time it takes for the sun to return to the same position in the sky.  However, since the Earth is also moving around the sun, this is a bit longer than the time for the stars to return to their previous positions.  That period is called a sidereal day, and is about 4 minutes shorter than a solar day.

I tried fitting the parameters I need using these two frequencies, but comparing the fitted values to the data still showed some structure:

That plot of errors covers 1 week, so there's clearly something with a period of about a day, but not quite a solar or sidereal day.  That plot just shows a single point in the sky, but I also tried making a plot of the error over the whole sky, animated in time (a bit hypnotic, so don't stare too long):

I couldn't figure out what this other frequency could be, until my colleague Vladimir pointed out that it could be a beat frequency.

When two sinusoidal waves with slightly different frequencies are added, they result in a wave with a frequency related to the sum and the difference of the two original frequencies:

The blue curve is the sum of the red and green dashed curves.  Even though the red curve has a period much longer than the green, the resulting curve is only a little off from the original green.  Vladimir's suggestion was to add in the period of the moon, 27.3 days.  That resulted in this error curve:

It's significantly smaller, and there are no more sinusoidal wiggles!  These barycenter approximations I'm doing will likely be a chapter of my thesis, so I'm pleased to be making good progress.

Demo Day 2017

Yesterday, I participated in a demo day for elementary school-aged girls, hosted by FEMMES.  I always have tons of fun showing off the department's cool physics demos, and I thought I'd talk a bit about the one I was showing this time: A levitating superconductor.

Most materials fall into two categories: conductors, which allow electric current to flow through them; and insulators, which don't.  Even though conductors allow current flow, there's always some resistance – The electrons lose energy as they move.  Superconductors, however, allow charge to move with zero resistance, which leads to some interesting effects.

For the purposes of the demo, we used a "high-temperature" ceramic superconductor:

The temperature where it transitions to a superconducting state is only high compared to other superconductors – It needs to be cooled to 77 Kelvin, or about -321°F.  Luckily, that's the temperature of liquid nitrogen, which is a common tool in science labs.

This is a type-II superconductor, which means that when it is cooled to the proper temperature, it can "pin" the magnetic flux passing through it.  In simpler terms, it remembers the magnetic field it was in when it was cooled.  That means if we set up a magnetic track like this,

we can make the superconductor levitate!  On the left is a styrofoam cup holding the superconductor in liquid nitrogen.  Underneath the cup are magnets arranged in a pattern that matches the one on the track to the right.  When the superconductor is set on the track, it settles into the exact field it was in when pinned, resulting in levitation:

Big thanks to the Demo Lab for providing the equipment, and FEMMES for organizing the event!

LVC Meeting 2017

This week I'm at the LIGO-Virgo Collaboration Meeting!  Every March, we get together in Pasadena, CA to talk about what we've been working on, and trade insights.  Similar to the APS Meeting earlier this year, I'll be updating this page with my experiences as the conference unfolds.

Sunday
I arrived late in the evening, zigzagging my local time through +1 hour for daylight savings followed by -3 hours for Pacific time.  While waiting for my shuttle to the hotel, I listened to an announcement repeatedly detailing the use of the various lanes, not unlike this scene from Airplane!.

Monday
The first two days of the meeting are devoted to parallel sessions for the various search groups.  The one I belong to, Continuous Waves, has about 30 members.

One speaker, Lilli Sun, presented work on a search for waves from the Scorpius X-1 binary system.  The system consists of a neutron star that sucks up mass from a neighboring sun.

An artist's impression of the Scorpius X-1 LMXB system. (Courtesy of Ralf Schoofs)

In a binary system, the two bodies revolve around a common point between them, usually quite rapidly.  This causes a Doppler shift in the gravitational waves that oscillates between two frequencies:

At one of my first meetings with the LIGO group at Michigan, this shape was compared to the Tower of Sauron, from Lord of the Rings.  In that moment, I knew I was with my people.

An interesting bit of vocabulary I can give you from the Scorpius talk is "torque balance limit".  As you may know, torque is the rotational equivalent of force – Applying a torque makes things rotate faster or slower.  We can observe systems like Scorpius X-1 slowing down their rotation, which implies that there is a torque acting on them.  The torque balance limit says, "If all the slowdown we see is due to gravitational wave emission, how strong would those waves have to be?"  That lets us set a threshold for how good our detectors need to be to pick up waves from these sources.

Another group of talks (including mine!) was on noise sources in the detectors, and our efforts to eliminate them.  One big source of noise turned out to be an extra network cable in one of the end stations, where the laser is reflected back.  Any wire is essentially an antenna that can send out signals that interfere with other electronics.  The precision of our measurements require total electromagnetic silence.

I'll leave you with this image from the poster gallery:

Tuesday
Today opened with an interesting talk on pulsar glitches.  Normally, pulsars emit continuous electromagnetic waves (and theoretically gravitational waves) with a frequency that gradually drops over time.  However, two known pulsars, Crab and Vela, have been observed to suddenly increase in frequency, before continuing the downward trend.  Any change in EM frequency would also appear in gravitational waves, so the presenter, Greg Ashton, was discussing ways to account for glitches in gravitational wave searches.  This sparked a discussion among the Michigan LIGO members over lunch about whether our searches could account for glitches – The whole point of meetings like this!

Most of the other presentations today were practice runs of plenary talks to be given to the whole collaboration tomorrow.  I probably won't see the real ones, since I'll be at the LAAC (LIGO Academic Affairs Council) Tutorials that introduce parts of LIGO research I don't get to see in my continuous wave bubble.

Wednesday
As I mentioned yesterday, I spent most of today at the LAAC talks.  It started with a panel on finding academic career opportunities.  The main takeaway seemed to be "Send out LOTS of applications, and don't get discouraged!"  The usual path after graduate school is 2-4 years of postdoctoral positions before applying to faculty positions.  The panelists emphasized the importance of showing you're able to communicate the purpose and requirements of your work, since even if you're not looking for a teaching position, you need to explain why you should be funded.  They suggested finding opportunities to give talks, and participate in public outreach.

During lunch, I went to a presentation on the Pegasus tool, which acts as a wrapper for the program we use to run jobs on our computing clusters.  It had some nice display features for giving info on the status of jobs, but I decided it would probably be too much trouble to switch over the infrastructure I have now.

I took the evening off to spend time with my Aunt Kaylyn, who was kind enough to drive out for a visit!

Thursday
Final day of the meeting!  Lots of plenary talks today, summarizing the work each group has been doing.  One, by Vuk Mandic and Florent Robinet, addressed the topic of cosmic strings, which I hadn't heard too much about before.  Reading the summary from Wikipedia makes them sound a bit like the "crack in time" that Doctor Who revolved around a few seasons ago, but sadly for sci-fi fans, the talk was about how our observations had mostly ruled them out.

During lunch, there was a diversity open-mic, where people were invited to discuss issues they had seen within the LVC.  The main subject was gender pronouns, and our ombudsperson, Beverly Berger, made a great point about why people shouldn't complain about new ones: Around the turn of century, we started using Ms. as a way to leave the marital status of a woman unspecified.

The afternoon included talks about the improvements that have been made to the detectors.  At the Hanford, WA detector, they could sometimes get 20 mph winds that would move the building enough to knock the equipment out of its delicate alignment.  Some precision engineering led to the detector staying "locked" in January, and collecting some important data I'm not at liberty to discuss!

I always enjoy these meetings, since it gives me a chance to see the scope of the collaboration I'm part of.  I hope to have a long career in this field!

It's a Trap(pist)!

I didn't get around to posting last week, since I was busy moving in with my amazing fiancee, but there was some big news from the astronomical community!  In case you missed it, a number of groups confirmed the existence of seven Earth-size planets in the habitable zone of the star Trappist-1.  I thought I'd talk a little bit about how these planets get detected.

Isolated stars are generally too small and too distant for us to see them as more than single points of light, even with powerful telescopes, so you might wonder how we can find the significantly smaller planets that orbit them.  The key is when the planet passes between the star and our line of sight, it casts a shadow on the star:

We can figure out the total light blocked from the two bodies' apparent size:

where d is the diameter of the body, and D is the distance from Earth to the body.  Since the 39 light-years to Trappist-1 is a lot bigger than any orbit the planets would have, we can assume D is the same for the planets and the star.

Closer to home, the apparent size of the sun and the moon from Earth are approximately equal, which is how we can get a total solar eclipse, even though their diameters differ by a factor of 400.

In the case of Trappist-1 though, the amount of light blocked is approximately the ratio of the cross-sections:

where Rp is the radius of the planet, and Rs is the radius of the star.  That leads to data that look like this:

From Nature paper

That plot shows the drop in intensity as each of the seven planets passes in front of the star.  The height of the drop tells us how big the planet is, but we can also use the duration of the drop to find the orbit.

Assuming a circular orbit, we can find the angular velocity of the planet from Newton's gravitational equation:

where G is Newton's constant, M is the mass of the star, and R is the orbital radius of the planet.  To figure out how long the planet takes to cross in front of the star, a picture helps:

The angular distance over which the planet is crossing the star is

Combing this with the previous equation, the transit time is

We measured the transit time from the dimming of the star, and we can figure out the radius and mass of the star from stellar dynamics, so this gives the orbital radius of the planet!

If you want to know more about the discovery, I highly recommend my friend Josh Sokol's piece at New Scientist.

"A Temper That Never Tires"

Last week, I talked about how Marika was looking out for our health with fitness-tracking watches.  This week, I moved us in the opposite direction by making Valentine's Day truffles.

Like most chocolate candies, the recipe involves tempering the chocolate.  If you've ever melted chocolate, then let it resolidify, you may have noticed it doesn't go back to the crunchy texture you usually expect.  This is because only one of cocoa butter's six crystal forms has the properties we want.

Crystals are repeating patterns of atomic links.  Depending on the angles between these links, the crystals have different properties.  Here's a pair of examples:

On the left is a square grid, while the right is triangular.  In addition to different angles, the atoms also have different numbers of neighbors, which can also affect the bonds.

Tempering chocolate involves heating it enough to break the bonds, then cooling rapidly to form the beta crystals that have the desired texture.  The method I use suggests adding some unmelted chocolate during the cooling process, which partly cools the mixture further, but it may also provide a starting point for the crystals.  Existing structures play a big part in how a crystal grows.

In the video below, the presenter drops a salt crystal into a supersaturated solution.  The presence of the crystal causes salt in the solution to precipitate out and join the structure:

My brother went to Vassar College, and every year at parents' weekend the Chemistry Department would put on a "Chemistry Magic Show" – This was always one of the features.

Through a Glass Magnetically

About a month ago, my wonderful fiancee bought us each an Apple watch, so we can keep track of our fitness goals.  To make the watch water-proof, the designers avoided any external ports for charging, which means the watch uses a type of wireless power transfer, which I've mentioned before.

The charging pad consists of a coil of wire with current running in a spiral.  The power is transferred thanks to the Maxwell-Faraday law:

The "∇ ×" is called the curl operator, and quantifies how much the current is going in a circle. The equation says that anytime you have an electric field going in a circle, you get a changing magnetic field in the middle.  This magnetic field can carry energy into another coil of wire in the watch, but there's a problem: The law applies to any material the field moves through.

Metal is a conductor, which means it has electrons that are free to move.  If the field passes by them, they'll start moving in a circle too, and absorb some of the energy. The amount the field is absorbed is quantified by the skin depth:

where ρ measures how easily the electrons move in the conductor, ω is the frequency of the electromagnetic wave, and μ tells how magnetic fields behave in the material.  Wireless power is usually transferred with a frequency on the order of 5 kHz, which for aluminum gives a depth of about 1 mm.  That may seem like a reasonable amount, but the effect is exponential – For every 1 mm, the efficiency drops by about 37%.

To avoid wasting power, Apple used a disk of glass on the back of the watch, allowing the waves to pass freely:

Initially, I had assumed the glass was purely for the heart rate sensor, but after reading the rumors that the next iPhone may have wireless charging, and therefore a glass case, I realized the true purpose.

Shapiro's Potholes

This week, I thought I'd talk about some of the research I've been doing.  Lately I've been working on a suite of tools called LALBarycenter.  LAL is the LIGO Analysis Library, and Barycenter refers to the solar system's center of mass, the point around which the sun and all the planets revolve.  Contrary to popular belief, the sun is not quite the center of our solar system:

From Wikipedia

Calculating the positions of everything in the solar system and their effect on the incoming signal can be time-consuming, so we were interested in finding a faster, approximate method.

One of the important functions of this set of tools is to determine the time at which a signal was emitted from a source given its position relative to the Earth at the time it was detected.  This seems like it would be as simple as dividing the distance by the speed of light, but it's more complicated than that, thanks to something called the Shapiro delay.

As I described in my RELATE video, massive objects bend space and time around them.  That means that if a signal passes near the sun, it can end up traveling a longer distance:

Because our measurements are so precise, we have to keep track of every deviation.  My hope is push the calculation to the edge of the required accuracy, while cutting down on the processing requirements.

APS Meeting 2017

This weekend I'm in DC for the "April" meeting of the American Physical Society.  I thought I'd try a sort of slow-motion live blog of the various talks I attend.  I'll be updating this page with my experiences.

Tuesday
Final day of the meeting!  The opening session was on black holes, and I learned some interesting things about black hole entropy (which I've mentioned before).  One of the presenters, Raphael Bousso, emphasized that "This is how we do physics in the US – We have collaborators all over the world," and showed this slide of his colleagues:

 

 (The cat was a stand-in for someone he couldn't get a photo of).  Bousso had a few other quotes I enjoyed:

Physics is the process of describing more and more phenomena with fewer and fewer laws.

Put tea in the fridge, it cools down, while the fridge releases heat and increases entropy.  Same thing happens when you throw the tea in a black hole

I went by the "Contact Congress" booth and sent a copy of the APS letter to my congresspeople – I'm not sure how much effect it will have, since they're all Democrats, but at least they know we're behind them.

I gave my talk in the final session of the day, and it went great!  I got some nice suggestions for future directions from the crowd.  In the same session, someone spoke on using machine learning to identify "chirp" signals in LIGO.  He opened by saying, "Machine learning is not just a plot by Amazon and Google to take over the world.  It's also a data analysis technique."

I had a great time out here, and learned a lot, but I'll be glad to head back to Michigan tomorrow and get back to work on my PhD!

Something Fishy

The other day, I happened to glance through the peephole of Marika's apartment into the building's lot:

It got me thinking about the wide, but distorted image you get from them, and I thought I'd talk a bit about the optics behind it.

Lenses use refraction to bend light in specific ways.  When a beam passes from one material to another, it changes direction according to the properties of the two substances.  The angle of the change is determined by Snell's law (diagram from Wikipedia):

I've mentioned refraction before, in the context of the Principle of Least Time.  The general rule for refraction is that when a beam passes from a material with lower index to higher index (like air-to-glass) the beam bends toward the perpendicular, and when it passes from higher to lower index, it bends away.

Peepholes use a type of fisheye lens to gather lots of light from the outside, and focus it into a smaller area that can enter your eye:

At the same time, if you try to look from the other side of the door,  all the light from a small spot gets spread out:

That makes the lens essentially one-way, allowing you to see outside, without others seeing inside.  It seems strange to me that we call something designed for privacy and security a "peephole" when the other uses of "peep" I can think of (outside of Easter) are so salacious: "peepshow" and "peeping Tom".  I suppose that's why I'm sticking to physics!

A Sorrowful Shooting Star

I'm currently reading a book suggested by my brother called House of Suns.  It's about an interstellar civilization divided into familial factions with an uneasy peace.  A recently-read portion concerned the funeral rites of a character from one of the families.  The deceased is raised into the air by a platform,

Not long after, [redacted] reached space and the platform tilted to release [them] for [their] long fall back to Neume's atmosphere.  We watched as [they] scratched a line of glorious fire across the sky...

 This passage gave me pause, because I thought I recalled that Felix Baumgartner's record-setting 2012 skydive was technically from space.  It turns out his dive was from 39 km above the surface, while space is defined to begin at the Kármán line, 100 km up.

Aerodynamic heating is caused by the friction between an object and the air it passes though, and is proportional to the object's kinetic energy, given by

where m is the object's mass, and v its velocity.  We can consider how much extra energy something would have after falling from 100 km to 39 km from the gravitational potential energy

where g is the acceleration due to gravity, and h is the distance fallen.  Using the average human mass of 62 kg, the extra energy picked up is 37 megajoules.  In the absence of atmosphere, that would produce a speed of about 2,400 mph, exceeding Mach 3 (once there was enough air for the speed of sound to be meaningful).

The density of the atmosphere drops off quite rapidly, so this may not be such a bad approximation:

It certainly seems that those extra 61 km make all the difference.  I suppose I was taken in by the marketing of Baumgartner's "space jump" that, while impressive, was nothing of the sort.