I spent the day at Chicago talking about engineering matters. It was great.
Schiminovich and I spent the day hiding out in an undisclosed location. We looked at the data he took (in the optical) of our (UV-discovered) transiting white-dwarf binaries. Unfortunately, our systems look like they have main-sequence rather than planet companions, but we aren't done yet! We are trying to get ready for his next MDM run.
Fadely came up for the day to work on his project with Willman and me to model the spectral energy distributions of stars and galaxies in deep, multi-epoch surveys. The idea is to go fully hierarchical, which has not been done before (to our knowledge), and to use the results to perform both engineering tasks (like star–galaxy separation and target selection) and science tasks (like provide statistics on stellar populations, substructure, and so on). We discussed nuts and bolts in the morning, and Fadely wrote code in the afternoon. Foreman-Mackey joined in in the afternoon, and we pair-coded and discussed a robust calibration model for the SDSS Stripe 82 data, where we are definitely reinventing a whole bunch of wheels.
Schiminovich and I spent the morning discussing our GALEX projects to find eclipsing binaries. Agol's recent paper points out that we might be the first people to find a habitable-zone planet! Schiminovich, on spring break with astronomy students, followed up two of our candidates and got confirmed eclipses and therefore periods. We need to publish something! He also pointed out that WISE might be relevant for finding hot stars with colder companions.
Lang and I worked on the title, abstract, and figures for the Holmes paper. The figures involved permissions from an enormous number of people; Lang has been heroically collecting these. This is definitely a problem with citizen science!
Hou and I spoke about his attempts to model jitter or velocity variability in giant stars with a Gaussian-process model of damped, randomly forced oscillations. He can't confirm reported oscillations; is this because our model is deficient, the code is broken, or because those oscillations aren't there? I hope it is the latter!
After a great blackboard talk at lunch-time by Itay Yavin (NYU) about the radius of the proton (there is an anomaly brewing), I read and commented on Dmitry Malyshev's draft of our paper on very faint sources in the Fermi data. Malyshev has reinvented the classic techniques for looking at sources too faint to detect directly, invented in the early days of radio astronomy and reinvented in the early days of x-ray astronomy. The results are nice, if not revolutionary. We put a fairly strong constraint on the sources of the unresolved Fermi background.
Lang and I added parameters to our Comet Holmes model that capture the statistics of where an astrophotographer locates her or his subject within the frame. These seemed to improve our model likelihood, confirming intuitions from Iain Murray. Oddly we are learning a lot more in this project about astrophotographers than we are about comets! We also figured out by detective work that this image (below), which was torquing some of our fits, is not an image of Comet Holmes, but rather a faint galaxy!
Today was almost all administration, but I did have a great email conversation with Iain Murray about the Comet Holmes project. I was saying that Lang and I are getting biased answers, and his response was: If your model is good, the posterior PDF pretty-much has to include the right answer. That is, you can be biased, but Bayes never confidently rules out the truth. I have many things to say about that, but the blogosphere doesn't have room for it all! He said: Go hierarchical. I said: Argh! (because he is right).
Lang and I worked on the Comet Holmes project more today. We encountered an interesting issue when we tried to marginalize out the time at which an image was taken: If you think an image was taken of a comet (and we do), and you don't know either the orbit of the comet or the time at which the image was taken (and we don't, by construction), then you are inclined to infer a slowly-moving comet! This comes from the fact that the only sensible likelihood (probability of the image given the comet parameters) involves a marginalization over times, and more time gets into each image the slower the comet goes. A slow comet is a distant comet, and that is a less observable (and less likely to be observed) comet, so we are doing something wrong, but it is not trivial to find a principled solution to this one. Bayesians out there? This is a general issue for all parametric curve fitting is it not?
In our clandestine activities of the weekend, we wrote down a generative model for how amateur astrophotographers point their telescopes. Here (above) are some parameters of that model, superimposed on a sky picture of the footprints of their images.
Lang and I spent every waking minute of the weekend working on our quasi-secret paper about Comet Holmes that has an end-of-month deadline. Of course I say quasi-secret because absolutely everything we do is exposed on the web at all times in our SVN repository, and I have probably posted about it ten times previously! We got Foreman-Mackey's version of Goodman and Weare's affine-invariant ensemble sampler working (the same sampler Hou is using, but a new implementation), we figured out a new kind of likelihood function for image pointings (a generative model of astrophotographers if you will), we experimented with multiprocessor stuff, and we made figures. My kind of weekend!
Adrian Price-Whelan and I met with some prospective undergraduate researchers, Abi Polin and Layla Quinones, to look at computational photography things; they are both amateur photographers. We discussed the baby steps towards doing some calibration of commercial digital cameras.
In the afternoon, Scott Hughes (MIT) brought us up to date on the two-body problem in general relativity, where there has been enormous progress in the six years or so since his last visit. He showed that the leading-order Newtonian approximation of GR contains a gravitometric term, which (in my opinion) should have been discovered way before GR: It permits the speed of gravity to be finite but objects to continue in Keplerian orbits! Hughes's talk was not particularly about this, but I have been thinking about it ever since I read Sciama's excellent (out of print) book.
Today was a nearly zero-research day, with me occupied with all the administrative stuff that I have been ignoring. In a surprise I ran into Nitya Kallivayalil (Yale) at Think where she showed me a new, incredibly high signal-to-noise measurement of the proper motion of the LMC. With the precision she showed, she ought to be able to measure the transverse rotation too.
I gave my dark-matter talk at Drexel today, and had great conversations with various Drexelians. Also a nice dinner with Gordon Richards (Drexel) and Willman and Fadely (the latter two took the train from Haverford for the occasion). Willman pointed out over dinner that our hierarchical model that will do star–galaxy separation for LSST at faint levels, using a hierarchical bayesian approach on all information available, will actually answer all possible astrophysics questions of any kind, ever. That's the kind of project I like to be working on. What she says is true because the project involves building a rich and justified model of the data.
I spent most of the day reading and commenting on student work, plus a bit of work with Lang and Price-Whelan on detecting faint sources in multi-epoch imaging (my recent distraction). This was interrupted by a very nice blackboard talk by Roman Scoccimarro (NYU) about galaxy bias—the relationship between the galaxy density field and the mass density field. He showed that even if bias starts out
local (that is, if galaxy density depends only on the local value of the density), it evolves with time into a configuration that is non-local. The effect is unavoidable given gravity. This point is obvious, but I had never noticed it before. He showed that it has a big effect on cosmological measurements, especially the three-point function, where the non-locality term enters at leading order.
In a low-research day, Peter Goldreich (IAS) spoke in our seminar about Tektites, the glassy remnants from massive impacts. He spoke about the physics of the size and shape distribution of these melted-and-cooled remnants. For me the most interesting thing is that the most recent large impact (780,000 years ago) is well located in Asia but nonetheless has no discovered crater.
Lang showed today that there is no sensible co-addition of imaging data that permits the detection of sources as well as estimating significance jointly in the not co-added images. The best formulation of this is to create not a co-add, but a significance map that maps out on the sky the likelihood of a source as a function of position. The combination of these significance maps is non trivial—it is not simple signal-to-noise-squared weighting of signal-to-noise maps—but it is tractable and no harder than most current co-adding schemes. Now we will sell this technology to any survey team in exchange for the fraction of observing time or operating cash we save them!