finding very long signals in very short data streams

So many things. I love Wednesdays. Here's one: I spent a lot of the day working with Adrian Price-Whelan (Flatiron) on our issues with The Joker. We found some simple test cases, we made a toy version that has good properties, we compared to the code. Maybe we found a sign error!? But all this is in service of a conceptual data-analysis project I want to think about much more: What can you say about signals with periodicity (or structure) on time scales far, far longer than the baseline of your observations? Think long-period companions in RV surveys or Gaia data. Or the periods of planets that transit only once in your data set. Or month-long asteroseismic modes in a giant star observed for only a week. I think it would be worth getting some results here (and I am thinking information theory) because I think there will be some interesting scalings (like lots of things might have precisions that scale better (faster I mean) than the square-root of time baseline).

In Stars & Exoplanets meeting at Flatiron, many cool things happened! But a highlight for me was a discovery (reported by Saurabh Jha of Rutgers) that the bluest type Ia supernovae are more standardizeable (is that a word?) candles than the redder ones. He asked us how to combine the information from all supernovae with maximum efficiency. I know how to do that! We opened a thread on that. I hope it pays off.

Planck maps

Today Kristina Hayhurst (NYU) came to my office and, with a little documentation-hacking, we figured out how to read and plot ESA Planck data or maps released in the Planck archive! I am excited, because there is so much to look at in these data. Hayhurst's project is to look at the “Van Gogh” plot of the polarization: Can we do this better?

connections between the dark and standard sectors

In the CCPP Brown-Bag seminar today, Neal Weiner (NYU) spoke about the possible connections between the dark sector (where dark matter lives) and our sector (where the standard model lives). He discussed the WIMP miracle, and then where we might look in phenomenology space for the particle interactions that put the WIMPs or related particles in equilibrium with the standard-model particles in the early Universe.

In the afternoon, I worked with Abby Shaum (NYU) and Kate Storey-Fisher (NYU) to get our AAS abstracts ready for submission for the AAS Winter Meeting in Honolulu.

got it!

Adrian Price-Whelan (Flatiron) and I spent time this past week trying to factorize products of Gaussians into new products of different Gaussians. The context is Bayesian inference, where you can factor the joint probability of the data and your parameters into a likelihood times a prior or else into an evidence (what we here call the FML) times a posterior. The factorization was causing us pain this week, but I finally got it this weekend, in the woods. The trick I used (since I didn't want to expand out enormous quadratics) was to use a determinant theorem to get part of the way, and some particularly informative terms in the quadratic expansion to get the rest of the way. Paper (or note or something) forthcoming...

mitigating p-modes in EPRV

Megan Bedell (Flatiron) and I continued our work from earlier this week on making a mechanical model of stellar asteroseismic p-modes as damped harmonic oscillators driven by white noise. Because the model is so close to closed-form (it is closed form between kicks, and the kicks are regular and of random amplitude), the code is extremely fast. In a couple minutes we can simulate a realistic, multi-year, dense, space-based observing campaign with a full forest of asteroseismic modes.

The first thing we did with our model is check the results of the recent paper on p-mode mitigation by Chaplin et al, which suggest that you can obtain mitigation of p-mode noise in precision radial-velocity observation campaigns by good choice of exposure time. We expected, at the outset, that the results of this paper are too optimistic: We expected that a fixed exposure time would not do a good job all the time, given the stochastic nature of the driving of the modes, and that there are many modes in a frequency window around the strongest modes. But we were wrong and the Chaplin et al paper is correct! Which is good.

However, we believe that we can do better than exposure-time-tuning for p-mode mitigation. We believe that we can fit the p-modes with the (possibly non-stationary) integral of a stationary Gaussian process, tuned to the spectrum. That's our next job.

rotating stars, a mechanical model for an asterosesmic mode

Our weekly Stars and Exoplanets Meeting at Flatiron was all about stellar rotation somehow this week (no we don't plan this!). Adrian Price-Whelan (Flatiron) showed that stellar rotations can get so large in young clusters that stars move off the main sequence and the main sequence can even look double. We learned (or I learned) that a significant fraction of young stars are born spinning very close to break-up. This I immediately thought was obviously wrong and then very quickly decided was obvious: It is likely if the last stages of stellar growth are from accretion. Funny how an astronomer can turn on a dime.

And in that same meeting, Jason Curtis (Columbia) brought us up to date on his work on on stellar rotation and its use as a stellar clock. He showed that the usefulness is great (by comparing clusters of different ages); it looks incredible for at least the first Gyr or so of a stars lifetime. But the usefulness decreases at low masses (cool temperatures). Or maybe not, but the physics looks very different.

In the morning, before the meeting, Megan Bedell (Flatiron) and I built a mechanical model of an asteroseismic mode by literally making a code that produces a damped, driven harmonic oscillator, driven by random delta-function kicks. That was fun! And it seems to work.

testing and modifying GR

The highlight of a low-research day was a great NYU Astro Seminar by Maria Okounkova (Flatiron) about testing or constraining extensions to general relativity using the LIGO detections of black hole binary inspirals. She is interested in terms in a general expansion that adds to Einstein's equations higher powers of curvature tensors and curvature scalars. One example is the Chern–Simons modification, which adds some anisotropy or parity-violation. She discussed many things, but the crowd got interested in the point that the Event Horizon Telescope image of the photon sphere (in principle) constrains the Chern–Simons terms! Because the modification distorts the photon sphere. Okounkova emphasized that the constraints on GR (from both gravitational radiation and imaging) get better as the black holes in question get smaller and closer. So keep going, LIGO!

calibrating spectrographs; volcanic exo-moons

I had a conversation with Ana Bonaca (Harvard) early today about the sky emission lines in sky fibers in Hectochelle. We are trying to understand if the sky is at a consistent velocity across the device. This is part of calibrating or really self-calibrating the spectrograph. It's confusing though, because the sky illuminates a fiber differently than the way that a star illuminates a fiber. So this test only tests some part of the system.

At the Brown-bag talk, Bob Johnson (Virginia) spoke about exo-moons and in particular exo-Ios. Yes, analogs of Jupiter's moon Io. The reason this is interesting is that Io interacts magnetically and volcanically with Jupiter, producing an extended distribution of volcanically produced ions in Jupiter's magnetic field. It is possible that transmission spectroscopy of hot Jupiters is being polluted by volcanic emissions of very hot moons! That would be so cool! Or hot?

scooped!

My loyal reader knows that earlier this week I got interested in (read: annoyed with) the standard description of the optimal extraction method of obtaining one-dimensional spectra from two-dimensional spectrograph images, and started writing about it on a trip. On return to New York, Lily Zhao (Yale) listened patiently to my ranting and then pointed out this paper by Zechmeister et al on flat-relative extraction, which (in a much nicer way) makes all my points!

This is a classic example of getting scooped! But my feeling—on learning that I have been scooped—was of happiness, not sadness: I hadn't spent all that much time on it; the time I spent did help me understand things; and I am glad that the community has a better method. Also, it means I can concentrate on extracting, not on writing about extracting! So I found myself happy about learning that I was scooped. (One problem with not reading the literature very carefully is that I need to have people around who do read the literature!)

the statistics of box least squares

I had a quick pair-coding session with Anu Raghunathan (NYU) today to discuss the box least squares algorithm that is used so much in finding exoplanets. We are looking at the statistics of this algorithm, with the hope of understanding it in simple cases. It is such a simple algorithm, many of the things we want to know about uncertainty and false-positive rate can be determined in closed form, given a noise model for the data. But I'm interested in things like: How much more sensitive is a search when you know (in advance) the period of the planet? Or that you have a resonant chain of planets? These questions might also have closed-form answers, but I'm not confident of them, so we are making toy data.

optimal extraction; adversarial attacks

On the plane home, I wrote words about optimal extraction, the method for spectral analysis used in most extreme precision radial-velocity pipelines. My point is so simple and dumb, it barely needs to be written. But if people got it, it would simplify pipelines. The point is about flat-field and PSF: The way things are done now is very sensitive to these two things, which are not well known for rarely or barely illuminated pixels (think: far from the spectral traces).

Once home, I met up with a crew of data-science students at the Center for Data Science to discuss making adversarial attacks against machine-learning methods in astronomy. We talked about different kinds of machine-learning structures and how they might be sensitive to attack. And how methods might be made robust against attack, and what that would cost in training and predictive accuracy. This is a nice ball of subjects to think about! I have a funny fake-data example that I want to promote, but (to their credit) the students want to work with real data.

goals: achieved

I achieved my goals for Terra Hunting Experiment this week! After my work on the plane and the discussion we had yesterday, we (as a group) were able to draft a set of potentially sensible and valuable high-level goals for the survey. These are, roughly, maximizing the number of stars around which we have sensitivity to Earth-like planets, delivering statistically sound occurrence rate estimates, and delivering scientifically valuable products to the community. In that order! More about this soon. But I'm very pleased.

Another theme of the last two days is that most or maybe all EPRV experiments do many things slightly wrong. Like how they do their optimal extraction. Or how they propagate their simultaneous reference to the science data. Or how they correct the tellurics. None of these is a big mistake; they are all small mistakes. But precision requirements are high! Do these small mistakes add up to anything wrong or problematic at the end of the day? Unfortunately, it is expensive to find out.

Related: I discovered today that the fundamental paper on optimal extraction contains some conceptual mistakes. Stretch goal: Write a publishable correction on the plane home!

categorizing noise sources; setting goals

Today at the Terra Hunting Experiment Science Team meeting (in the beautiful offices of the Royal Astronomical Society in London) we discussed science-driven aspects of the project. There was way too much to report here, but I learned a huge amount in presentations by Annelies Mortier (Cambridge) and by Samantha Thompson (Cambridge) about the sources of astrophysical variability in stars that is (effectively) noise in the RV signals. In particular, they have developed aspects of a taxonomy of noise sources that could be used to organize our thinking about what's important to work on and what approaches to take. I got excited about working on mitigating these, which my loyal reader knows is the subject of my most recent NASA proposal.

Late in the day, I made my presentation about possible high-level goals for the survey and how we might flow decisions down from those goals. There was a very lively discussion of these. What surprised me (given the diversity of possible goals, from “find an Earth twin” to “determine the occurrence rate for rocky planets at one-year periods”) was that there was a kind of consensus: One part of the consensus was along the lines of maximizing our sensitivity where no other survey has ever been sensitive. Another part of the consensus was along the lines of being able to perform statistical analyses of our output.

setting high-level goals

I flew today to London for a meeting of the Terra Hunting Experiment science team. On the plane, I worked on a presentation that looks at the high-level goals of the survey and what survey-level and operational decisions will flow down from those goals. Like most projects, the project was designed to have a certain observing capacity (number of observing hours over a certain—long—period of time). But in my view, how you allocate that time should be based on (possibly reverse-engineered) high-level goals. I worked through a few possible goals and what they might mean for us. I'm hoping we will make some progress on this point this week.

Gotham fest, day 3

Today was the third day of Gotham Fest, three Fridays in September in which all of astronomy in NYC meets all of astronomy in NYC. Today's installment was at NYU, and I learned a lot! But many four-minute talks just leave me wanting much, much more.

Before that, I met up with Adrian Price-Whelan (Flatiron) and Kathryn Johnston (Columbia) to discuss projects in the Milky Way disk with Gaia and chemical abundances (from APOGEE or other sources). We discussed the reality or usefulness of the idea that the vertical dynamics in the disk is separable from the radial and azimuthal dynamics, and how this might impact our projects. We'd like to do some one-dimensional problems, because they are tractable and easy to visualize. But not if they are ill-posed or totally wrong. We came up with some tests of the separability assumption and left it to Price-Whelan to execute.

At lunch, I discussed machine learning with Gabi Contardo (Flatiron). She has some nice results on finding outliers in data. We discussed how to make her project such that it could find outliers that no-one else could find by any other method.