coherent oscillator injection and recovery

Coherent oscillators—astronomical sources that pulse or oscillate in a phase-stable way over long timescales—have been useful astrophysical tools. For two examples: Stably pulsing pulsars were used to discover gravitational radiation (and are being used to find the stochastic background). Delta-scuti star asteroseismic modes were used to find orbital companions. This led undergrad Nana Miller (NYU) and me and others to look for all the coherent modes we can find among all the stars in the NASA Kepler Mission data. We have have technology to find modes, and we have technology to test for coherence. Now we have to do injection–recovery tests to estimate our detection limits. Today I delivered a simple plan for doing injections.

Our plan is to produce a catalog, not of stars but of modes, every one of which has a coherence time that is longer than the lifetime (4 years) of the Kepler Mission. Then: What do we use them for?

possible Trojan planet?

In group meeting last week, Stefan Rankovic (NYU undergrad) presented results on a very low-amplitude possible transit in the lightcurve of a candidate long-period eclipsing binary system found in the NASA Kepler data. The weird thing is that (even though the period is very long) the transit of the possible planet looks just like the transit of the secondary star in the eclipsing binary. Like just like it, only lower in amplitude (smaller in radius).

If the transit looks identical, only lower in amplitude, it suggests that it is taking an extremely similar chord across the primary star, at the same speed, with no difference in inclination. How could that be? Well if they are moving at the same speed on the same path, maybe we have a 1:1 resonance, like a Trojan? If so, there are so many cool things about this system. It was an exciting group meeting, to be sure.

an alternative to the L–S periodogram

Following some experiments and rants over the last few days with Nora Eisner (Flatiron), I wrote down today an algorithm for a hacky replacement of the Lomb–Scargle periodogram. This periodogram method has various bad pathologies, the worst of which is that it presumes that there is exactly one frequency that fully generates the data. If there are two, the assumptions are broken and the good properties are lost.

Not that my alternative has any good properties! It is like the radio interferometry method called CLEAN: It involves iteratively identifying frequencies and fitting them out. It's terrible. But it might be better than some of the wacky hacks that people do right now in the asteroseismology community.

a likelihood for our Phi-M radio

There are AM radios and FM radios and (if you are a nerd) PCM radios. But Abby Shaum (CUNY) and I have built a Phi-M radio, which demodulates phase variations in a carrier signal. We (with Keaton Bell, CUNY) are using it to find binary companions and planets around stars that show coherent pulsation modes in their photometry. Today I wrote down a noise model for the output of our demodulator. It isn't completely trivial. But it's good, because we can make a likelihood function for fitting our companions. Our model will end up being a limit of the more general model called Maelstrom by Dan Hey (Hawai'i).

Are there young, alpha-rich stars?

I asked this question in Data Group meeting: With Emily Jo Griffith (Colorado) and I have a data-driven nucleosynthetic story for essentially every red-giant-branch star in the SDSS-IV APOGEE survey. Since the parameters of this model relate to the build-up of elements over time, they might be used to indicate age. We matched to the NASA Kepler asteroseismic sample and indeed, our nucleosynthetic parameters do a very good job of predicting ages.

On the RGB, age is mass, and the asteroseismology gives you masses, not ages. There are some funny outliers: Stars with large masses, which means young ages, but with abundances that strongly indicate old ages. Are they young or old? I am betting that they are old, but they’ve undergone mass transfer, accretion, or mergers. If I’m right, what should we look for? The Data Group (plus visitors) suggest looking for binarity, for vertical action (indicating age), for ultraviolet excess (indicating white dwarf companion), for abundance anomalies, and Gaia RUWE. Will do! My money is that all these stars are actually old.

phase and frequency variations

If a star has a (relatively) coherent oscillation mode, and you can monitor it over a long period of time, then orbital motion of the star can be seen as either phase or frequency variations of that mode. I've been working on this in different collaborations, with Dan Hey, with Simon J Murphy, with Abby Shaum (CUNY), and recently with Nora Eisner (Flatiron). Right now, Shaum, Eisner, and I are looking at signal-processing approaches that look like demodulators. What I'm interested in—at least in terms of me learning about signal processing—is how can we make a demodulator that demodulates both phase and frequency simultaneously. There must be hybrid and combined approaches. I'm also interested in what we can measure from incoherent oscillators.

simulating data for phase and frequency modulation

Abby Shaum (CUNY) and I have been working on phase demodulation for binary detection and characterization, using coherent oscillation modes in stellar light curves. We are taking a pure signal-processing approach, which is lightweight and fast, such that we could automatically apply it to everything in Kepler or TESS. We also want to do frequency modulation for incoherent modes (which somehow our people think won't work; won't it?).

Today we discussed how to build fake data to fully test our systems. In the coherent case, this is easy! In the incoherent case this is harder. We discussed simulating it by drawing from a Gaussian Process. And we discussed simulating it by forward modeling a stochastically forced, damped harmonic oscillator.

time dependences in ultra-short-period planets

I had a great conversation with Noah Sodickson (high schooler) about ultra-short planets in the NASA Kepler data. He has been filtering the light curves, running astronomers'-favorite “box least squares” and plotting the folded light curves. When he does this in quarters (meaning, cutting the data into 90-day chunks), he can see small variations in the transit shapes. These have been attributed to various things. My goal is to figure out a way to model these variations without averaging the data. Binning is sinning, after all. Sodickson can see that everything we see is a strong function of how we filter the light curves, so we have to think pretty hard about that.

radio reboot

[Somehow this blog keeps failing. I will try to get back into it, but no promises! I apologize to my loyal reader.]

Today I met with Abby Shaum (IPAC) who worked with me a few years ago making a phase demodulator to find stellar companions. The idea is that if a star is broadcasting a coherent (or even incoherent) asteroseismic or pulsation mode, and if the star is orbiting a companion, the kinematics of the orbit will be imprinted on phase and frequency modulations of the carrier frequency. Like a radio! Indeed we built a signal-processing method that looks just like a radio demodulator. Today we discussed how to reboot this project and write a paper for the refereed literature.

re-parameterizing Kepler orbits

As many exoplaneteers know, parameterizing eccentric gravitational two-body orbits (ellipses or Kepler orbits) for inferences (MCMC sampling or, alternatively, likelihood optimizations) is not trivial. One non-triviality is that there are combinations of parameters that are very-nearly degenerate for certain kinds of observations. Another is that when the eccentricity gets near zero (as it does for many real systems), some of the orientation parameters become unconstrained (or unidentifiable or really non-existent). Today Adrian Price-Whelan (Flatiron) was hacking on this with the thought that the time or phase of maximum radial velocity (with respect to the observer) and the time or phase of minimum radial velocity could be used as a pair of parameters that give stable, well-defined combinations of phase, eccentricity, and ellipse orientation (when that exists). We spent an inordinate amount of time in the company of trig identities.

predicting the future of a periodic variable star

Gaby Contardo (Flatiron) showed me an amazingly periodic star from the NASA Kepler data a few days ago, and today she showed me the results of trying to predict points in the light curve from prior points in the light curve (like in a recurrent method). When the star is very close to periodic, and when the region of the star used to predict a new data point is comparable in length to the period or longer, then even linear regression does a great job! This all relates to auto-regressive processes.

stellar flares

Gaby Contardo (Flatiron) and I have been trying to construct a project around light curves, time domain, prediction, feature extraction, and the arrow of time, for months now. Today we decided to look closely at a catalog of stellar flares (which are definitely time-asymmetric) prepared by Jim Davenport (UW). Can we make a compact or sparse representation? Do they cluster? Do those properties have relationships with stellar rotation phase or other context?

constructing a bilinear dictionary method for light curves

After having many conversations with Gaby Contardo (Flatiron) and Christina Hedges (Ames) about finding events of various kinds in stellar light curves (from NASA Kepler and TESS), I was reminded of dictionary methods, or sparse-coding methods. So I spent some time writing down a possible sparse-coding approach for Kepler light curves, and even a bit of time writing some code. But I think we probably want something more general than the kind of bilinear problem I find it easy to write down: I am imagining a set of words, and a set of occurrences (and amplitudes) of those words in the time domain. But real events will have other parameters (shape and duration parameters), which suggests using more nonlinear methods.

forwards/backwards project evolution

Gaby Contardo (Flatiron) and I have been working on time asymmetry in NASA Kepler light curves. Our first attempts on this have been about prediction: Is it easier to predict a point in a light curve using its past or its future? It turns out that, for very deep mathematical reasons, there is a lot of symmetry here, even when the light curve is obviously time asymmetric in seemingly relevant ways. So deep, I think we might have some kind of definition of “stationary”. So we are re-tooling around just observable asymmetries. We discussed many things, including dictionary methods. It also occurred to us that in addition to time-reversal questions, there are also flux-reversal questions (like if you flip a light-curve event upside down).

CPM rises from the ashes

I had a great call today with So Hattori (NYUAD) and Dan Foreman-Mackey (Flatiron), about Hattori's reboot of the causal pixel model by Dun Wang (that we used in NASA Kepler data) for new use on NASA TESS data. Importantly, Hattori has generalized the model so it can be used in way more science cases than we have looked at previously, including supernovae and tidal disruption events. And his paper is super-pedagogical, so it will invite and support (we hope) new users. Very excited to help finish this up!

our forwards-backwards results are fading

Gaby Contardo (Flatiron) and I have been working on predicting light-curve data points from their pasts and their futures, to see if there is a time asymmetry. And we have been finding one! But today we discussed results in which Contardo was much more aggressive in removing data at or near spacecraft issues (this is NASA Kepler data). And most of our results go away! So we have to decide where we go from here. Obviously we should publish our results even if they are negative! But how to spin it all...?

forwards vs backwards modeling of light curves

My day started with a conversation with Gaby Contardo (Flatiron) about modeling light curves of stars. We have projects in which we try to predict forwards and backwards in time, and compare the results. We're trying to make a good scope for a paper, which could involve classification, regression, or causal inference. Or all three. As usual, we decided to write an abstract to help us picture the full scope of the first paper.

group meeting awesome; color light curves from CoRoT

Today at the Astronomical Data Group meeting (led by Dan Foreman-Mackey) we did our quasi-monthly thing of getting a quick update from everyone who shows up. And 18 people showed up! Everyone gave an update; it was great to see the breadth of activity in the group. One contribution that got me excited was Christina Hedges (Ames, but still part of the Group!), who is looking at ESA CoRoT data. The mission was designed to have some tiny bit of color sensitivity, which makes it possible to look at colored light-curve variations and distinguish causal effects. This builds on work by Hedges to look at tiny point-spread-function changes in NASA Kepler and TESS data to get a tiny bit of color information in those white-light missions. Colored light curves are the future.

forward and backward modeling of stellar light curves

I got some weekend research time in, which was fun: When I work on the weekends, I try to make it things that I want to do, rather than things I have to do. I wrote code to predict a point in a NASA Kepler light curve from the preceding points and then from the following points. And it appears that the two predictions disagree, as expected, at gaps in the light curve (where there is a stretch of missing data) and at discontinuities in the light curve (like those created by small stellar flares). So it is interesting! And just linear regression of course (that's my brand). Now: Can we do science with it?

This was originally inspired by a comment by Bernhard Schölkopf (MPI-IS), years ago, about whether we can predict the past from the future better than we can predict the future from the past, which might have relationships to causal inference. I'm enjoying thinking about the philosophical aspects.

Dr Sandford!

An absolutely great PhD defense today by Emily Sandford (Columbia), who has worked on planet transits and what can be learned therefrom. And so wide-ranging: She worked on what you learn about a star from a single transit, what you learn about an orbit from a single transit, what you learn about the shape of the transiter, and even what you learn about the population of planetary systems from the statistics of the transits. The discussion was excellent and enlightening. One thing I loved was a little discussion about what it would mean to think of zero-planet systems as planetary systems. And lots about the representation of multi-planet systems (where Sandford has a grammar or natural-language-like approach).

I loved the defense so much, in part because Sandford crushed it and in part because I generally love PhD defenses: They remind me of all the reasons that I love my job. I was reflecting afterwards that the PhD is a kind of model of education: It is student-centered, it is customized and personalized for every student, it is self-directed, it is constructive, and it is success-oriented. And it produces some amazing scientists, including the brand-new Dr Sandford.