Great Astro Seminar today by Carles Badenes (Pitt), who has been studying binary stars, in the regime that you only have a few radial-velocity measurements. In this regime, you can tell that something is a binary, but you can't tell what its period or velocity amplitude is with any precision (and often almost no precision). He showed results relevant to progenitors of supernovae and other stellar explosions, and also exoplanet populations. Afterwards, Andy Casey (Monash) and I continued the discussion over drinks.
Much excellent science today. I am creating a Monday-morning check-in and parallel working time session for the undergraduates I work with. We spoke about box-least-squares for exoplanet transit finding, about FM-radio demodulators and what they have to do with timing approaches to timing-based planet finding, scientific visualization and its value in communication, and software development for science.
At lunch, the Brown-Bag talk (my favorite hour of the week) was by two CCPP PhD students. Cedric Yu (NYU) spoke about the topological form of general relativity. As my loyal reader could possibly know, I love the reformulation of GR in which you take the square-root of the metric (the tetrad, in the business). Yu showed that if you augment this with some spin fields, you can reformulate GR entirely in terms of topological invariants! That's amazing and beautiful. It relates to some cool things relating geometry and topology in old-school math. Oliver Janssen (NYU) spoke about the wave function of the Universe, and what it might mean for the initial conditions. There is a sign ambiguity, apparently, in the argument of an exponential in the action! That's a big deal. But the ideas are interesting because they force thinking about how quantum mechanics relates to the entire Universe (and hence gravity).
In addition to all this, today was the first-ever meeting of the NYU Time Domain Astrophysics group meeting, which brings together a set of people at NYU working in the time domain. It is super diverse, because we have people working on exoplanets, asteroseismology, stellar explosions, stellar mergers, black-hole binaries, tidal disruption events, and more. We are hoping to use our collective wisdom and power to help each other and also influence the time-domain observing projects in which many of us are involved.
As my loyal reader knows, I like to call the phase spiral in the vertical structure of the disk (what's sometimes called the Antoja spiral) by the name The Snail. Today I discussed with Suroor Gandhi (NYU) how we might use the Snail to measure the disk midplane, the local standard of rest (vertically), the mass density of the disk, and the run of this density with Galactocentric radius. We have a 9-parameter model to fit, in each angular-momentum slice. More as this develops!
It's a bad week, research-wise. But I did chat with Bonaca (Harvard) this morning, and she showed that it is at least possible (not confirmed yet, but possible) that the dark substructure we infer from the GD-1 stream has kinematics consistent with it having fallen into the Milky Way along with the Sagittarius dwarf galaxy. This, if true, could lead to all sorts of new inferences and measurements.
Reminder: The idea is that there is a gap and spur in the stream, which we think was caused by a gravitational interaction with an unseen, compact mass. We took radial-velocity data which pin down the kinematics of that mass, and put joint constraints on mass, velocity, and timing. Although these constraints span a large space, it would still be very remarkable, statistically, if the constraints overlap the Sagittarius galaxy stream.
Philosophically, this connects to interesting ideas in inference: We can assume that the dark mass has nothing to do with Sag. This is conservative, and we get conservative constraints on its properties. Or we can assume that it is associated with Sag. This is not conservative, but if we make the assumption, it will improve enormously what we can measure or predict. It really gets at the conditionality or subjectivity of inference.
The day started with the Event Horizon Telescope press release conference, which I watched at Flatiron (but could have watched at NYU or Columbia; a huge fraction of the community was watching!). It really is a beautiful result, and the data analysis looks (on cursory inspection of the papers) to be excellent and conservative. It is just incredible that we can observe a photon sphere, if that really is what it is! It seemed like such a thing of legend and story.
Interesting to think about language: Is this the first observation of a black hole? Or image of one? I'd say not, because any image of a quasar is just as much an image of the radiation around a black hole as this is. I think maybe it is the first image of the parts where strong gravity is acting (photons are orbiting!). But these are not objections in any way to the importance of the result! Just musing on the language. In what sense is this the first time we have taken an image of a black hole? And is it that? And etc.
In the afternoon, Kate Storey-Fisher and I went to the board and got confused about 6-dimensional integrals. We need them to understand correlation-function estimators. The “RR” term in the correlation function estimators is a 6-d integral over an outer product of space with space!
My only research time today was a nice astro seminar by Chris Sheehy (BNL), who convinced us that detecting primordial gravitational radiation in the b-mode polarization of the CMB at large scales will be hard but possible. It depends on some inflation physics, of course! He also showed some novel uses of what you might call “compressive sensing” to CMB foreground analyses, scooping some of my thoughts on the subject!
Most of my research time over the weekend and today was taken up reading proposals for a funding review. That doesn't count as research, by my Rules. I don't love that part of my job. But I did get in some time with students, reading thesis chapters by Malz (NYU), planning two papers with Storey-Fisher (NYU), and discussing graduate school options with Birky (UCSB). I love these parts of my job!
In the conversation with Storey-Fisher, we set the minimal (though still very large) scope for a paper that competes or tests large-scale structure correlation-function estimators in realistic and toy data. Our issues are: We have identified biases in the standard estimators, and we (additionally) don't love the tests or arguments that say that Landy–Szalay is optimal. So we want to test them again, and also add some new estimators, from the math literature on point processes.
In Astronomical Data Group Meeting at Flatiron today, Rodrigo Luger (Flatiron) spoke about what he calls the “null space” for reconstruction of stellar surface features (or exoplanet surface features) from light curves. If you just have a rotating ball, glowing but with a surface pattern of emissivity, and you just get to see an integrated light curve, you can only reconstruct certain parts of any representation of its surface. For example, all the odd-ell modes (after ell of 1) contribute exactly zero signal! And there are other degeneracies, depending on orientation. These degeneracies are exact!
What Luger showed today is that some of these degeneracies are broken just by limb darkening! And others are broken if you have transiting planets. And if you are reconstructing a planet, others are broken by the terminator of any reflected light. All of these results and considerations will feed into an information theory of stellar and exoplanet light curves.
Last semester, I started a project with Anu Raghunathan (NYU) on the question of how much more sensitive we could be to planets in resonances than we are in more blind searches. My loyal reader knows that I'm interested in this. I think it has a simple answer, but even if it does, some playing in this statistical sandbox is fun. Today Raghunathan and I realized that we can generate a whole set of great results around box least squares, which is the dumb (but very effective, and very easy-to-analyze; I'm a fan) method that is used to generate candidate exoplanets in many transit surveys and searches. My vague idea is to use this as a place to understand multiple hypothesis testing (the physicists' “look-elsewhere effect”) and derive analytic false-positive rates for simple noise distributions, with searches of different kinds in data of different kinds.
I spent my science time today commenting on the first draft of a nice paper on phase-space volume by Matt Buckley (Rutgers). He shows that it is possible, in some cases, to measure the phase-space volume (six-volume) of structures in the ESA Gaia data. He wants to use Liouville's Theorem (that 6-volume is conserved) to measure the former bound masses of structures in the Milky Way halo that are now disrupted.
At Stars & Exoplanets Meeting at Flatiron, we discussed the Luger et al and Burns et al April-Fools papers. They both represent very impressive results, and are also a bit silly. On the Burns paper, we learned how to continue a spherical spectral representation down to zero radius without introducing a singularity. Reminded me of undergraduate quantum mechanics!
In addition, Bedell (Flatiron) spoke a bit about cool things that happened at #TessNinja2 last week in Chicago. Among other things, she showed a system that Foreman-Mackey (Flatiron) and collaborators set up to automatically fit the light curves of every announced TESS Object of Interest. It's hilarious: It produces a complete executable (and modifiable) Jupyter notebook for every TOI.
I went down to Princeton to give a seminar to the particle physicists about dark matter, and in particular what we know or could know from dynamical and kinematic measurements of stars. Before my talk, I had a great conversation with Oren Slone (Princeton) and Matt Moschella (Princeton) about gravitational redshifts. They have been thinking about where gravitational redshifts might be both measurable and physically interesting. Ideas include: Surfaces of stars, stars as a function of location in our Galaxy, and different parts of external galaxies. The magnitudes are tiny! So although the gravitational redshift is an incredibly direct tool of some gravitational dynamics, it is very hard to measure.
After my talk at Princeton, I got in a short but fun conversation with Jim Peebles (Princeton) on point processes and estimators of two-point functions. Peebles, after all, wrote down the first estimators of the clustering of large-scale structure. He admitted that the history is unprincipled: They more-or-less made things up! I presented the things that I have been discussing with Kate Storey-Fisher (NYU) and Alex Barnett (Flatiron) and he was interested. And intrigued. Can we make better estimators?
The day began with a call with Ana Bonaca (Harvard), in which she showed me that she can take her models of the GD-1 stream perturbation and predict the present-day location of the substructure (or dark mass) that created the perturbation. Because the model space is broad, the “error box” is large, but the fact that we have such a prediction is fun, and interesting. All this progress flows from the fact that we now have some radial-velocity data on the stream and the spur (which is the feature we think was raised by a dark-matter interaction).
On the arXiv today were the annual set of April Fools papers. My loyal reader knows that I love papers in this category when they are silly or funny but in fact contain an interesting or important calculation or inference. There were two in this category today with Flatiron origins. One was Luger et al, inferring the mean cloud cover on Earth from systematic effects in the NASA TESS imaging! Another was Burns et al, showing that instead of “cubing the sphere” (what climate modelers do to avoid spherical coordinate singularities in discretization) you can “sphere the cube” (embed a cubical simulation volume in a natively spherical-representation simulation). This latter project was ridiculous, but it showed very dramatically that they have a representation for simulating spherical domains with no singularity anywhere (and especially not at the center of the sphere, and at no angular position on the surface).
Today was the last day and wrap-up for the 2019 SB Gaia Sprint. It was quite a week! A few highlights from the wrap-up (for me, very subjective, not fair or complete) were: Schwab Abrahams (Berkeley) showed that stars which are flagged in certain ways in the Gaia data are reliably variable stars, by looking at TESS light curves. Coronado (MPIA) showed that stars with small orbital-action differences tend to also have small element-abundance differences. Brown (Leiden) and others worked on making “Gold” samples in Gaia data that make it easy for people to look at or follow up spectroscopically. Mateu (UdelaR) improved her catalog of, and meta-data on, stellar streams in the halo. El Badry (Berkeley) convincingly showed us that there is an excess of very precisely equal-mass binary stars even at very large separations. Widrow (Queen's) showed first attempts at trying to perform a regression that can be used to infer the Galactic bar density from velocity fields. Hunt (Toronto) showed velocity and density maps of a simulated disk that look very much like the features that Eilers (MPIA) and I see in the data! And Laporte (UVic) showed a great movie of the data in the phase spiral (The Snail!) that shows its beautiful and informative dependence on azimuthal action (or really vertical frequency I think!). It was a great week with great people doing great things in a great location. I'm exhausted! The wrap-up slides are available here.
Each day at the Sprint, we have a check-in, in which daily results are discussed. Today Cecilia Mateu (UdelaR) showed improvements she has made to the database or list she maintains of known or reported stellar streams in the Milky Way halo. With the encouragement of Ana Bonaca (Harvard) and the help of Adrian Price-Whelan (Princeton), she made an astropy-compatible data file that delivers coordinate transformations into the stellar stream reference frames (great-circle coordinates). This will make it much, much easier for people to perform analyses on streams and compare new detections to known objects.
At lunch, a subset of the group that discussed the ESA Gaia selection function yesterday met again to discuss the possibility of putting together a large funding proposal to create what's needed. Many interesting things came up in this discussion. One is that many more projects are enabled by the selection function. So a small investment here greatly increases the impact of Gaia. Another is that we need to have a set of clearly defined example problems that illustrate the relevant issues. Another is that many of these possible example projects need not just an observational selection function but also a 3-d dust map in the Milky Way. Is that the same project or a different one? Another is that there aren't a lot of possible funding avenues that would be appropriate in both scale and international scope. It was a valuable discussion, but I don't know where we are at the end.
The highlight of the day was a long discussion of the kinematics of the Milky Way bar with Larry Widrow (Queen's) and Ortwin Gerhard (MPE) and Christina Eilers (MPIA) and Sarah Pearson (Flatiron). We almost became convinced that we are seeing the bar at the center of the Galaxy kinematically. It appears as a quadrupole in the velocity field. But if we are seeing it, we are seeing it at the wrong angle! So there is work to do. And many of the simple ideas about what we see depend on some kind of steady-state assumption, when in practice the bar evolves on a time-scale comparable to it's rotation period. More soon!
At the Gaia Sprint, there is no formal program. It is just work, work, and more work! But we do let the participants self-organize some break-out sessions that are more like sessions in a (highly interactive) workshop. Today, we ran a session on a possible ESA Gaia DR2 selection function. There is no selection function, and this seriously limits the science we can do with the mission and its data. I opened the session with some generalities about what a selection function should or could be and how we would use it, working from notes that Rix (MPIA) and I have been working on. I learned that we are describing it all wrong, and that we need much better and more worked-out example problems. It is very interesting to classify projects into those that do and those that don't need a selection function. Rix and I put it on our to-do list to re-work our paper outline on this.
In the sprinting part of the day, Eilers (MPIA) and I stepped back and realized that we should make all nine obvious kinematic plots of the Milky Way disk: Mean velocity (three plots), mean squared velocity (three plots) and mean velocity-velocity cross-correlation components (three plots). We started on that, and the bar looks like it just pops right out in the plot of the mean-square vertical velocity component! We are starting to realize that the things we want to plot that relate to the bar are very different from the things we want to plot that relate to the spiral arms.