EPRV capabilities

I had a conversation with Jacob Bean (Chicago) and Ben Montet (UNSW) about various radial-velocity projects we have going. We spent some time talking about what projects are better for telescopes of different apertures, and whether there is any chance the EPRV community could be induced to work together. I suggested that the creation of a big software effort in EPRV could bring people together, and help all projects. We also talked about data-analysis challenges for different kinds of spectrographs. One project we are going to do is get a gas cell component added in to the wobble model. I volunteered Matt Daunt (NYU) in his absence.

asteroseismic p-mode noise mitigation

I had a call with part of the HARPS3 team today, the sub-part working on observations of the Sun. Yes, Sun. That got us arguing about asteroseismic modes and me claiming that there are better approaches for ameliorating p-mode noise in extreme precision radial-velocity measurements than setting your exposure times carefully to null the modes. The crew asked me to get specific, so I had a call with Bedell (Flatiron) later in the day to work out what we need to assemble. The issues are about correlated noise: Asteroseismic noise is correlated; those correlations can be exploited for good, or ignored for bad. That's the argument I have to clearly make.

re-scoping a paper on spectrograph calibration

In a long conversation, Lily Zhao (Yale), Megan Bedell (Flatiron), and I looked at a possible re-scope of our new paper on spectrograph calibration. Zhao is finishing one paper that builds a hierarchical, non-parametric wavelength solution. It does better than fitting polynomials independently for different exposure groups, even in the full end-to-end test of measuring and fitting stellar radial-velocities. But the paper we were discussing today is about the fact that the same distortions to the spectrograph that affect the wavelength solution also (to the same order) affect the positions of the spectroscopic traces on the device. That is, the relationship between (say) x position on the detector and wavelength can be inferred (given good training data) from the y position on the detector of the spectral traces. We have been struggling with how to implemnent and use this but then we realized that we could instead write a paper showing that it is true, and defer implementations to the pipeline teams. Implementation isn't trivial! But the result is nice. And kind-of obvious in retrospect.

Gaia and EPRV

Megan Bedell (Flatiron) and I discussed some possible projects that connect ESA Gaia astrometric exoplanet information with ground-based spectroscopic radial-velocity information to discover sub-threshold planets that aren't detectable in either data set individually. We are planning possible undergraduate research projects for summer students. And we are thinking about the conditions under which a planet can be said to be discovered or confirmed.

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.

precise spectroscopy

I spent my research time today writing notes on paper and then LaTeX in a document, making more specific plans for the projects we discussed yesterday with Zhao (Yale) and Bedell (Flatiron). Zhao also showed me issues with EXPRES wavelength calibration (at the small-fraction-of-a-pixel level). I opined that it might have to do with pixel-size issues. If this is true, then it should appear in the flat-field. We discussed how we might see it in the data.

looking at stars in the joint domain of time and wavelength

Today I had a great conversation with Lily Zhao (Yale) and Megan Bedell (Flatiron) about Zhao's projects for the semester at Flatiron that she is starting this moth. We have projects together in spectrograph calibration, radial-velocity measurement, and time-variability of stellar spectra. On that last part, we have various ideas about how to see the various kinds of variability we expect in the joint domain of wavelength and time. And since we have a data-driven model (wobble) for stellar spectra under the assumption that there is no time variability, we can look for the things we seek in the residuals (in the data space) away from that time-independent model. We talked about what might be the lowest hanging fruit and settled on p-mode oscillations, which induce radial-velocity variations but also brightness and temperature variations. I hope this works!

information theory and noise

In my small amount of true research time today, I wrote an abstract for the information-theory (or is it data-analysis?) paper that Bedell and I are writing about extreme-precision radial-velocity spectroscopy. The question is: What is the best precision you can achieve, and what data-analysis methods saturate the bound? The answer depends, of course, on the kinds of noise you have in your data! Oh, and what counts as noise.

imaging asteroseismic modes on the stellar surface

Many threads of conversation over the past weeks came together today in a set of coincidences. Conversations with Bedell (Flatiron), Pope (NYU), Luger (Flatiron), and Farr (Flatiron) ranging around stochastic processes and inferring stellar surface features from doppler imaging all overlap at stellar asteroseismic p modes: In principle, with high-resolution, high-signal-to-noise stellar spectral time series (and we have these, in hand!) we should be able not only to see p modes but also see their footprint on the stellar surface. That is, directly read ell and em off the spectral data. In addition, we ought to be able to see the associated temperature variations. This is all possible because the stars are slowly rotating, and each mode projects onto the rotating surface differently. Even cooler than all this: Because the modes are coherent for days in the stars we care about, we can build very precise matched filters to combine the data coherently from many exposures. There are many things to do here.

avoiding active stars

Today Megan Bedell (Flatiron) and I had a telecon with the Terra Hunting Experiment team to discuss target selection. The idea is to use existing good data to choose a small set of (40-ish) stars to study for ten years. That's ambitious, which is (of course) why I love it! But how to select these stars? Our big argument today was about magnetic activity, which has some interesting properties. One is that it generally declines with age, so maybe we could just choose the stars to be not-young? Another is that there are activity cycles, so determination of low activity now might not guarantee low activity over the next decade.

One thing this caused me to ask (inside my head, that is) was: If you know that activity varies over time with some stochastic time scales, and if you need to be observing only low-activity stars, what does this imply for an adaptive observing program? That's a very nice question in experimental design. I smell the multi-armed bandit coming around the corner.

#tellurics, day 4

Today was the last day and wrap-up from the Telluric Line Hack Week at Flatiron. What an impressive meeting it was; I learned a huge amount. Here are a few highlights from the wrap-up, but I warn you that these highlights are very subjective and non-representative of the whole meeting! If you want to see more, the wrap-up slides are here.

The most surprising thing to me—though maybe I shouldn't be surprised—was the optimism expressed at the wrap-up. The theoretical modelers of atmospheric absorption were optimistic that data-driven techniques could fill in the issues in their models, and the data-driven modelers were optimistic that the theory is good enough to do most of the heavy lifting. That is, there was nearly a consensus that telluric absorption can be understood to the level necessary to achieve 10-cm/s-level radial-velocity measurements.

Okay maybe just as surprising to me was the demos that various people showed of the Planetary Spectrum Generator that can take your location, a time, and an airmass, and make a physical prediction for the tellurics you will see, even broken down by molecular species. It is outright incredible, and remarkably accurate. It is obvious to me that our data-driven techniques would be much better applied to residuals away from this PSG model. That's an example of the kind of hybrid methods many participants at the meeting were interested in exploring.

One of the main things I learned at the meeting (and I am embarrassed to say this, since in retrospect it is so damned obvious) came from Sharon X Wang (DTM): Even if you have a perfect tellurics model, dividing it out even from your extremely high signal-to-noise spectrum is not exactly correct! The reason is duh: The spectrum is generated by a star times tellurics, convolved with the LSF. That's not the same as the LSF-convolved star times the LSF-convolved tellurics. That is a bit subtle, but seriously, Duh! Foreman-Mackey, Bedell, and I spoke a tiny bit about the point that this subtlety could be incorporated into wobble without too much trouble, and we might need to do that for infrared regions of the spectrum, where the tellurics are very strong. We have gotten away with the wobble approximation because HARPS is high resolution, and in the visible.

And finally (but importantly for me), many of the participants tried out the wobble model or understood it or applied it to their data. We have new users and the good ideas in that code (the very simple, but good, ideas) will propagate into the community. That's very good for us; it justifies our work; and it makes me even more excited to be part of the EPRV community.

measuring the Galaxy with HARPS? de-noising

Megan Bedell (Flatiron) was at Yale yesterday; they pointed out that some of the time-variable telluric lines we see in our wobble model of the HARPS data are not telluric at all; they are in fact interstellar medium lines. That got her thinking: Could we measure our velocity with respect to the local ISM using HARPS? The answer is obviously yes, and this could have strong implications for the Milky Way rotation curve! The signal should be a dipolar pattern of RV shifts in interstellar lines as you look around the Sun in celestial coordinates. In the barycentric reference frame, of course.

I also got great news first thing this morning: The idea that Soledad Villar (NYU) and I discussed yesterday about using a generative adversarial network trained on noisy data to de-noise noisy data was a success: It works! Of course, being a mathematician, her reaction was “I think I can prove something!” Mine was: Let's start using it! Probably the mathematical reaction is the better one. If we move on this it will be my first ever real foray into deep learning.

investigating residuals

The day started with a conversation with Bedell (Flatiron) about projects that arose during or after the Terra Hunting Experiment collaboration meeting last week. We decided to prioritize projects we can do right now, with residuals away from our wobble code fits to HARPS data. The nice thing is that because wobble produces a very accurate generative model of the data, the residuals contain lots of subtle science. For example, covariances between residuals in flux space and local spectral slope expectations (from the model) will point to individual pixel or stitching-block offsets on the focal plane. Or for another, regressions of flux-space residuals against radial-velocity residuals will reveal spectroscopic indicators of spots and plages. There are lots of things to do that are individually publishable but which will also support the THE project.

Simpson's Paradox, Li, self-calibration

On the plane home from the UK, I worked on three things. The first was a very nice paper by Ivan Minchev (AIP) and Gal Matijevic (AIP) about Simpson's Paradox in Milky Way stellar statistics, like chemodynamics. Simpson's paradox is the point that a trend can have a different sign in a subset of a population than it does in the whole population. The classic example is of two baseball players over two season: In the first season, player A has a higher batting average than player B. And in the second season, player A again has a higher batting average than player B. And yet, overall, player B has a higher average! How is that possible? It works if player A bats far more in one season, and player B bats far more in the other, and they both bat higher in that other season. Anyway, the situation is generic in statistics about stars!

The second thing I worked on was a new paper by Andy Casey (Monash) and company about how red-giant stars get Lithium abundance anomalies. He shows that Li anomalies happen all over the RGB, and even on stars descending the branch (as per asteroseismology) and thus he can show that the Li anomalies are not caused by any particular stellar evolutionary phase. That argues for either planet engulfment or binary-induced convection changes. The former is also disfavored because of the stars descending the RGB. The real triumph is the huge sample of Li-enhanced stars he has found, working with The Cannon and Anna Y. Q. Ho (Caltech). It's a really beautiful use of The Cannon as a spectral synthesis tool.

The third thing I worked on was a plan to self-calibrate HARPS (and equivalent spectrograph) pixel offsets (that is, calibration errors at the pixel level) using the science data from the instrument. That is, you don't need arcs or Fabry–Perot to find these offsets; since they matter to data interpretation, they can be seen in the data directly! I have a plan, and I think it is easy to implement.

THE Meeting, day 2

Today at the Terra Hunting Experiment meeting, we got deeply into software and calibration issues. The HARPS family of instruments are designed to be extremely stable in all respects, but also monitored by a Fabry–Perot signal imprinted on the detector during the science exposures. The calibration data are taken such that the data obtain absolute calibration information (accuracy) from arc exposures and relative calibration (precision) from F—P data. There was discussion of various replacements for the arcs, including Uranium–Neon lamps, for which the atlas of lines is not yet good enough, and laser-frequency combs, which are not yet reliable.

Another big point of discussion today was the target selection. We (the Experiment) plan to observe a small number (40-ish) stars for a long time (1000-ish individual exposures for each star). The question of how to choose these targets was interesting and contentious. We want the targets to be good for finding planets! But this connects to brightness, right ascension, stellar activity, asteroseismic mode amplitudes, and many other things, none of which we know in advance. How much work do we need to do in early observing to cut down a parent sample to a solid, small sample? And how much can we figure out from public data already available? By the end of the day there was some consensus that we would probably spend the first month or so of the project doing sample-selection observations.

At the end of the day we discussed data-analysis techniques and tellurics and stellar activity. There are a lot of scientific projects we could be doing that would help with extreme-precision radial-velocity measurements. For instance, Suzanne Aigrain (Oxford) showed a toy model of stellar activity which, if correct at zeroth order, would leave an imprint on a regression of stellar spectrum against measured radial velocity. That's worth looking for. The signal will be very weak, but in a typical spectrum we have tens of thousands of pixels, each of which has signal-to-noise of more than 100. And if a linear regression works, it will deliver a linear subspace-projector that just straight-up improves radial-velocity measurements!

THE meeting, day 1

Today was the first day of the Terra Hunting Experiment collaboration meeting. This project is to use HARPS3 for a decade to find Earth-like planets around Sun-like stars. The conversation today was almost entirely about engineering and hardware, which I loved, of course! Many things happened, too many to describe here. One of the themes of the conversation, both in session and out, is that these ultra-precise experiments are truly integrated hardware–software systems. That is, there are deep interactions between hardware and software, and you can't optimally design the hardware without knowing what the software is capable of, and vice versa.

One presentation at the meeting that impressed me deeply was by Richard Hall (Cambridge), who has an experiment to illuminate CCD detectors with a fringe pattern from an interferometer. By sweeping the fringe pattern across the CCD and looking at residuals, he can extremely precisely measure the effective centroid in device coordinates of every pixel center. That is impressive, and it is now known to be one of the leading systematics in extreme precision radial velocity. That is, we can't just assume that the pixels are on a perfect, regular, rectangular grid. I also worked out (roughly) a way that he could do this mapping with the science data, on sky! That is, we could self-calibrate the sub-pixel shifts. This is highly related to things Dustin Lang (Perimeter) and I did for our white paper about post-wheel Kepler.

expected future-discounted discovery rate

My tiny bit of research today was on observation scheduling: I read a new paper by Bellm et al about scheduling wide-field imaging observations for ZTF and LSST. It does a good job of talking about the issues but it doesn't meet my (particular, constrained) needs, in part because Bellm et al are (sensibly) scheduling full nights of observations (that is, not going just-in-time with the scheduling), and they have separate optimizations for volume searched and slew overheads. However, it is highly relevant to what I have been doing. It also had lots of great references that I didn't know about! They also make a strong case for optimizing full nights rather than going just-in-time. I agree that this is better, provided that your conditions aren't changing under you. If they are changing under you, you can't really plan ahead. Interesting set of issues, and something that differentiates imaging-survey scheduling from spectroscopic follow-up scheduling.

I also did some work comparing expected information gain to expected discovery rate. One issue with information gain is that if it isn't information gain in this exposure (and it isn't, because we have to look ahead), then it is hard to write down the information gain, because it depends strongly on future decisions (for example, if we decide to stop observing the source entirely!). So I am leaning towards making my first contribution on this subject be about discovery rate.

Expected future-discounted discovery rate, that is.

the limits of wobble

The day was pretty-much lost to non-research in the form of project management tasks and refereeing and hiring and related. But I did get in a good conversation with Bedell (Flatiron) with Luger (Flatiron) and Foreman-Mackey (Flatiron) about the hyper-parameter optimization in our new wobble code. It requires some hand-holding, and if Bedell is going to “run on everything” as she intends to this month, it needs to be very robust and hands-free. We discussed for a bit and decided that she should just set the hyper-parameters to values we know are pretty reasonable right now and just run on everything, and we should only reconsider this question after we have a bunch of cases in hand to look at and understand. All this relates to the point that although we know that wobble works incredibly well on the data we have run it on, we don't currently know its limits in terms of signal-to-noise, number of epochs, phase coverage in the barycentric year, and stellar temperature.

scientific priorities

I spent a piece of the morning exhaustively going through short-term priorities with Bedell (Flatiron). We discussed strategy given her stage. She has enough projects to last a decade! I guess we all do, but it is still amazing when we list them. We decided to focus on things that make direct use of the technologies we have built and not particularly build new technology for a bit. We also decided to submit the wobble paper right after the break.

After this, we segued into a conversation about the (badly named) Rossiter-McLaughlin effect with Luger (Flatiron) and Beale (Flatiron). The effect is the effective change in a star's radial velocity as a planet transits its surface, since it is rotating and has a spatial gradient in surface RV. We discussed what is involved in modeling this more accurately than is currently done. There were some philosophical issues coming up around flux conservation, limb darkening, and continuum normalization. All hard issues!

At the end of the day I got in a short quality conversation (over wine) with Alex Barnett (Flatiron) so I could pre-flash him the correlation-function and power-spectrum problems that Storey-Fisher (NYU) and I will bring him in January. He agreed that we are going to effectively unify fourier-space and real-space approaches when we make them all more efficient and more accurate. So excited about a winter of clustering!

almost nothing

My only research today was a short conversation with Bedell (Flatiron) about finishing up our paper on wobble.