Introit (Introduction):
For those who don't know me well, I'm about four years out of grad school. It was rough going, and I actually left with a masters degree with a full year of NSF fellowship money to go. I suppose I could've stayed another year and no one would've bothered me too much, as I had my own money. But it was hell, mostly self-inflicted. It's tricky though to still be uncertain about whether it was the right choice.
During that time, I worked on something called non-redundant aperture masking interferometry. It's a lot of words, and it deserves them. I'll do my best to explain it without much jargon.
Assuming little or no science background
Because light behaves as a wave, it can form interference patterns. I used a specially designed device that "created" the interference pattern by forcing a star's light to pass through a small metal disk in a detector. The metal disk had a number of holes drilled into it (9 or 18), spaced apart just so that it would generate a snowflake pattern that was both pretty and scientifically useful. Very Important Fact - the spacings were such that no two holes were the same distance apart, and were arranged at a variety of angles along the disk. By analyzing the pattern using some sophisticated software, it was possible to identify binary stars that were otherwise too close together. The software could also be modified to do things like detect asymmetry - as in a planetary nebula. Second Very Important Fact: this only works at telescopes that have adaptive optics, which can help correct for atmospheric turbulence.
I was part of observations at Palomar Observatory, a couple hours outside of San Diego. (Fun aside: one of the observatory staff told me stories of a former Cornell professor who shall remain nameless who, back in the day, would take his students to TJ when they were rained out. Once in TJ, they would get completely drunk. Needless to say, I'm guessing he had an all-male research group, and that he's a particular outlier as far as professionalism/personal adventurousness. I believe he's still a professor, and quite successful.)
Analogy for high school/early college physics students (non-majors):
Remember Young's double-slit experiment? Well, instead of two slits, I had pinholes arranged such that each set of pinholes was essentially a double-slit, each in a different direction. This is the non-redundant part.
More complicated, for engineers and scientists
The non-redundant mask generated an interference pattern that was spread across the near-IR detector (InGaAs, if I recall). The baselines ranged from about half the pupil length to nearly the full pupil, and sampled pretty comprehensively different orientations on the sky. The hole diameter was made to be smaller than the scale of an atmospheric turbulence cell, given by the Kolmogorov 5/3 law.
To wit, you use a (inverse) Fourier transform on the interferogram to reconstruct the original image. The key is to use closure phase, which basically says that for a flat incoming wave, the difference in phase across each leg of a triangle array should be zero. Any nonzero results are due to asymmetry in the wavefront, which is corrected using the telescope's adaptive optics system and a nearby calibration star.
Don't ask me for any more mathematical details. It'll just remind me of the stony silence I got at my committee meetings when I struggled with the presentations.
Note: I realize this is fairly elementary to radio astronomers. The key excitement factor is getting the technique to work in optical and near-IR wavelengths. It deserves to be kind of a big deal.
Astronomer's note: the targets were nearby low-mass stars (class M), identified as such by spectroscopy and their high proper motions.
Kyrie (frustration):
One of the frustrating things is that it often didn't work well. I was using someone else's software, and to be honest, I had trouble following the math. I had the background, but it was still a challenge, and my Fourier Transforms class at Mudd was right after lunch. (This means I fell asleep a few times, even though it was a class of only about 25 people.) Also, I'm guessing atmospheric turbulence made it challenging. Additionally, the targets we were looking at were relatively dim. More dim means less light, which means the snowflake pattern gets pretty weak. All of this conspired to make it such that, when it came time to present my work, I had no results from the dozen or so stars I looked at that actually used the technique. (I did identify a half-dozen or so previously undiscovered companions using standard adaptive optics.)
Rex tremendae (Research insight):
So here comes the dream. I'm in a Harvey Mudd classroom, specifically the electronics/modern physics lab in the physics department with people from high school. Then it hits me - the problem is throughput. Therefore, move the targets to brighter stars (sun-like stars). We did that for the calibration stars. But wait! This could be used to analyze the host of transiting systems detected by ground observations and the Kepler mission. (These are systems where a planet passes in front of the star, which is detectable from Earth as a small decrease in the star's brightness.)
Non-redundant aperture masking could actually improve the resolution such that it would be possible to determine the precise orientation of the planet and star along the sky. Coupled with radial velocity data, it might lead to improved resolution on the planetary masses.
Lacrymosa (Problems with this insight):
As I wake up more fully, I'm realizing a couple problems with this.
First, the point of this research was to get resolved data on a binary system. By taking snapshots at regular intervals, it would be possible to determine the orbit in 3-D space, allowing for a precise mass determination of both components in a binary. (It could be generalized to more complicated star systems, but the analysis gets - you guessed it - more complicated.)
Sampling from just across the planetary disk won't provide enough information on the orbit to actually provide a full 3-D picture of the orbit. Or, more accurately, it provides little that can't be determined just from regular techniques.
Another problem: Transiting systems are ideal for analysis precisely because they are edge-on systems. What this means is that the line of observation (Earth to the transiting system) is necessarily perpendicular to the angular momentum vector of the system. This means the radial velocity data provides not a lower mass limit, but the actual mass.
The potential improvement in determining this angle is minor, at best.
The only possibility for actually useful results would be if this technique still provided enough information about asymmetry that it could, with standard photometry, get a more accurate sense of the size of these planets. This could provide information about its density and potential composition, which could prove important for formation models.
But again, as I wake up a bit more, I'm less confident about this.
Agnus Dei (Conclusion):
It was interesting - I told a classmate in the dream that I was going to blog this.
Unfortunately, the wakeful, somewhat thoughtful part of me is now questioning the value of this "insight" gained in the dream. This is unfortunate, not because I felt like making a contribution to observational astronomy and extrasolar planet research, but because it was going to be the first problem I had solved in a dream. (During my first semester in college, I occasionally had dreams about programming and math, but I never actually solved anything this way. Also, in dreams where I'm being chased by bad guys, my gun never works. I wonder if my subconscious is trying to suggest I'm sterile or impotent. In that case, fuck you subconscious!)
Poo. This wasn't worth waking up and breaking Facebook fast.
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