Vanishing Trick

Back in March, I was at the LIGO/Virgo/KAGRA meeting, and during breakfast one morning, a fellow researcher posed an interesting question: Suppose a cluster of stars are all moving in the same direction. What can we learn from their vanishing point?

The concept of a vanishing point is often used in art: When parallel lines recede into the distance, they appear to converge at a point on the horizon. It seems logical then that our parallel stars will also converge to a point in the sky, which could tell us about how they're arranged in space. First though, we need to be able to generate a set of parallel lines in 3 dimensions. In 2D, this is fairly simple: Any lines with the same slope but different intercepts will be parallel. I found a page giving a simple way to express 3D parallel lines using a "double-equals" form:

The intercepts for each line are different, but the slopes associated with each dimension must be proportional between the lines.

This format is a bit difficult to imagine plotting, but we can fix that by setting the three terms equal to a parameter t, and then solving:

Once we have the paths in x, y, z, we can transform them into the right ascension and declination angles used by astronomers:

We have all the machinery in place now, so let's try it on a trio of lines. First, we can look at them in 3D, to check that we got parallel lines as expected:

Looks good! Now we'll run it through the projection...

Uh oh, the three lines don't share the same vanishing point! For a while I was sure I had made a mistake somewhere, but I think this can be explained by the fact that we're projecting onto a sphere, not a plane, as is usually done. I made a feeble effort at proving this to myself, but we're still running ourselves ragged getting things set up in our new home in Florida (hence the long silence here)!

Not a Sunscreen

This week, I was at the 25th General Congress of la Société Française de Physique, or SFP 25. One of my coworkers from LAPP was chairing a session there, and asked me to present my work on localizing gravitational wave events. A lot of the talks were in French, but not nearly as many as I expected. In fact, several of the plenary talks were in English, and each time there was one audience member who seemed to be lodging a complaint about such a choice at the Society of French Physicists, though I can't be sure exactly what he said, since it was in French. I thought I'd tell you about some of the talks I attended.

The conference covered all areas of physics, but I tried to choose sessions closely related to my work. The first one I went to was about an object called Sagittarius A*, named for being inside the constellation. It emits strong radio waves, and is near the center of the Milky Way, leading astronomers to believe it's the supermassive black hole that our galaxy rotates around. All spiral and elliptical galaxies are believed to have black holes at their center. Sagittarius A* produces light as matter falls into it, but the optical range is blocked by dust clouds between Earth and the galactic core. The radio waves make it through though, allowing astronomers to study the black hole.

My session came on the second day, and was focused on multi-messenger astronomy. This refers to combining observations from traditional electromagnetic telescopes, and gravitational wave detectors. I was talking about how we localize gravitational wave signals on the sky, so that astronomers can point their telescopes in time to catch other parts of the signal. The main example I used was GW170817, our first binary neutron star detection. We were able to narrow the source region on the sky using information about the three detectors:

LIGO/Virgo/NASA/Leo Singer

With only a small region to search, astronomers were able to find a burst of gamma rays, a type of high-energy photon that was predicted to result from neutron star mergers. The talk was well-received, and I was approached at lunch the next day by someone who had followup questions.

My favorite session was about a physics perspective on the origins of life. One of the topics discussed in that session was the Miller-Urey experiment, which sought to demonstrate how some of the prerequisite amino acids could have been created in the environment of the early Earth. The reason I enjoyed it so much? Similarities to the work of the esteemed V. Frankenstein, of course!

Wikipedia

The researchers combined water vapor, methane, ammonia, and hydrogen, all believed to be present in Earth's atmosphere around 4 billion years ago. Then they ran a current through the mixture, simulating (though probably not using) lightning, and collected the results. Analysis showed the presence of a significant number of the amino acids present in lifeforms.

The sessions entirely in French were a bit of an ordeal for me, but overall I'm glad to have had the opportunity to go. Along with the conference, Marika found many wonderful museums and historical sites in Nantes. We're both still exhausted, but we have a lot of great memories!