substellar objects (brown dwarfs)

I spent the day at the NSBP / NSHP meeting in San José. My favorite session of the day was the morning astro session, which was entirely about brown dwarfs. I learned a lot in a very short time. Caprice Phillips (UCSC) introduced the session with an introduction to the scientific and technical questions in play. She put a lot of emphasis on using binaries and clusters to put detailed abundance ratios onto substellar objects. This was what I expected: I thought (walking in to this session) that all known abundance ratios for brown dwarfs were from such kinds of studies. I learned different (keep reading).

Gabriel Munoz Zarazua (SFSU) followed by showing spectra from M-dwarfs, brown dwarfs, and Jupiter. It definitely looks like a sequence. He does spectral fitting (what they call, in this business, retrievals). It looks like he is getting very good, somewhat precise, abundance ratios for the photospheres of substellar objects! I asked more about this in the question period, and apparently I am way behind the times (Emily Rauscher, Michigan, helpfully pointed this out to me): Now brown-dwarf photosphere models are so good, they can be used to measure abundances, and pretty well.

I also learned in this session (maybe from Jorge Sanchez, ASU, or maybe from Efrain Alvarado, SFSU) that there is a very strong mass–abundance relation in the Solar System. That is, we don't expect, if brown dwarfs form the way planets do, that the detailed abundances of the brown dwarfs will match exactly the detailed abundances of the primary stars. But now we are really in a position to test that. Sanchez showed that we can get, from even photometry, abundances for substellar objects in the Milky Way halo. Again, totally new to me! And he finds metallicities at or below −3. Alvarado showed data on an amazing system J1416, which is an L–T binary with no stellar companion. Apparently it is the only known completely substellar binary.

how did the Solar System form?

I saw a very nice talk today by Philippine Griveaud (MPIA) about how the Solar System formed. The idea is that the giant planets formed in an accretion disk. Their formation opened gaps and caused migration (first Type I and then Type II, if you must know :). That migration pulled them into a resonant chain. That is, if the giant planets formed the way we think they formed, they must have been in a resonant chain. But they aren't in such a chain now; what gives?

The idea is that when the gas is expended (or blown out by winds), the remaining planetestimals (think: asteroids, comets, Kuiper Belt objects) interact with the planets such that they get moved from orbit to orbit and eventually ejected. These dynamical interactions break the resonant chain, migrate the giant planets to their current locations, and scatter rocks and ice balls into the interstellar regions.

It was a great talk, but also led to a lot of interesting questions, such as: How does this all fit in with the formation of the rocky planets? And how does this square with our observations (growing rapidly, apparently) of interstellar asteroids? Oh and: How does all this connect to observations of debris disks, which I now (officially) love.

what is measured with stellar kinematics?

In work on Galaxy dynamics, from stellar kinematics, we measure relative velocities and relative positions, of nearby stars relative to the Sun (or really the Solar System barycenter). These relative positions and velocities are coordinate free, in the sense that they don't imply a rest frame for anything (and indeed, the SS barycenter is not anywhere near the rest-frame position or rest-frame velocity of the Milky Way or Local Group or anything else).

In addition to this, any measurements we make are insensitive to any overall or external acceleration: If the Milky way is in free-fall, accelerating towards some external “great attractor” or anything else, none of these observables are affected in any way by that acceleration. So what is it that stellar kinematics can really be used to measure? I think somehow the answer has to be Galilean covariant (covariant to boosts and translations), but even better it should be generally covariant (in the Newtonian sense, which is well defined, apparently).

I did some research on this subject, and the literature is all about Newton–Cartan theory, but this theory is a Newtonian limit of general relativity. That isn't quite what we care about in stellar kinematics, since in stellar kinematics, we don't get to see any orbits as a function of time (we don't observe geodesics or geodesic deviation). What, exactly do we observe? I think what we observe is something about gradients of accelerations, but I don't know yet. Great project for this summer.

black holes as the dark matter

Today Cameron Norton (NYU) gave a great brown-bag talk on the possibility that the dark matter might be asteroid-mass-scale black holes. This is allowed by all constraints at present: If the masses are much smaller, the black holes evaporate or emit observably. If the black holes are much smaller, they would create observable microlensing or dynamical signatures.

She and Kleban (NYU) are working on methods for creating such black holes primordially, by modifying hte potential at inflation, creating opportunities for bubble nucleations in inflation that would subsequently collapse into small black holes after the Universe exits inflation. It's speculative obviously, but not ruled out at present!

An argument broke out during and after the talk whether you would be injured if you were intersected by a 10²⁰ g black hole! My position is that you would be totally fine! Everyone else in the room disagreed with me, for many different reasons. Time to get calculating.

Another great idea: Could we find stars that have captured low-mass black holes by looking for the radial-velocity signal? I got really interested in this one at the end.

philosophy

I've been working on two philosophical projects this month. The first has been an interaction with Jim Peebles (Princeton) around a paper he has been writing, setting down his philosophy of physics. I am pretty aligned with his position, which I expect to hit the arXiv soon. I'm not a co-author of that. But one of the interesting things about science is how much of our work in in anonymous (or quasi-anonymous) support of others.

The second philosophical project is a paper about machine learning and science: I am trying to set down my thoughts about how ML can and can't help the sciences. This is fundamentally a philosophy-of-science question, not a science question.

conjectures about pre-training

On Monday of this week, Shirley Ho (Flatiron) gave a talk at NYU in which she mentioned the unreasonable effectiveness of pre-training a neural network: If, before you train your network on your real (expensive, small) training data, you train it on a lot of (cheap, approximate) pre-training data, you get better overall performance. Why? Ho discussed this in the context of PDE emulation: She pre-trains with cheap PDEs and then trains on expensive PDEs and she gets way better performance than she does if she just trains on the expsensive stuff.

Why does this work? One interesting observation is that even pre-training on cat videos helps with the final training! Ho's belief is that the pre-training gets the network understanding time continuity and other smoothness kinds of things. My conjecture is that the pre-training teaches the network about (approximate) diffeomorphism invariance (coordinate freedom). The cool thing is that these conjectures could be tested with interventions!

unitary evolution of the Universe

I spent the day with Juna Kollmeier (CITA) talking about epistemology, physical cosmology, and project management (especially academic management). I found myself saying to her the following argument (which I have not seen written down anywhere): Imagine that our Universe is hamiltonian (or lagrangian; it doesn't matter for these purposes). And imagine that our Universe is a simulation being run inside some bigger universe, which is also hamiltonian.

If our Universe is being observed in any sense by any system in that bigger universe, then there ought to be a loss of unitarity in our Universe. That is, there should be a violation of Liouville's theorem, or a violation of key conservation laws, or an information sink. And there is! At black hole horizons, there is an information paradox: Information that goes in never comes back (an evaporating black hole evaporates thermally, or so we think). Thoughts?

symmetry day: crossing, permutation

Today's brown-bag talk, by Grant Remmen (NYU), was about (in part) crossing symmetry. This is the symmetry that any Feynman diagram can be rotated through 90 degrees (converting time into space and vice versa) and the interaction will have the same scattering amplitude. This symmetry relates electron–positron annihilation to electron–electron scattering. The symmetry has an important role in string theory, because it is a constraint on any possible fundamental theory. This symmetry has always seemed incredible to me, but it is rarely discussed outside very theoretical circles.

After the talk, and in the Blanton–Hogg group meeting, I brought up things about invariant functions that I learned from Soledad Villar (JHU) that are really confusing me: It is possible (in principle, maybe not in practice) to write any permutation-invariant function of N objects as a function of a sum of universal functions of the N objects (that's proven). How does that relate to k-point functions? Most physicists believe that any k-point function estimate will require a sum over all N-choose-k k-tuples. That's a huge sum, way bigger than a sum over N. What gives? I puzzled some of the mathematical physicists with this and I remain confused.

is the world lagrangian?

My day started with a long and very fun conversation with Monica Pate (NYU) about conservation laws in classical physics. As we all know, conservation laws are related to symmetries; each symmetry of the laws of physics creates a conservation law. Or does it? Well, it's a theorem! But it's a theorem when the laws of physics are lagrangian (or hamiltonian). That is, every symmetry of a hamiltonian system is associated with a conservation law in that system. So I asked: How do we know if or whether the world is lagrangian or hamiltonian? How could we know that? My best guess is that we know it because of these very conservation laws! The situation is complex.

planets forming in a disk

At the end of last week I had a great conversation with Valentina Tardugno (NYU) and Phil Armitage (Flatiron) about how planets form. I spent the whole weekend thinking about it: If a few planets are forming in a proto-planetary disk, there are all sorts of interactions between the planets and the disk, and the planets and each other, and the disk with itself. You can think of this (at least) two different ways:

You can think of planets which are interacting not just directly with one another, but also with a disk, and with each other as mediated by that disk. This is the planet-centric view. In this view, the planets are what you are tracking, and the disk is a latent object that makes the planets interact and evolve.

Alternatively, you can think of the disk, with planets in it. In this disk-centric view, the planets are latent objects that modify the disk, creating gaps and spiral waves.

Both views are legitimate, and both have interesting science questions. We will explore and see where to work. I am partial to the planet-centric view: I want to know where planetary systems come from!

four kinds of emulators

I wrote in a draft grant proposal related to machine-learning emulators today. I wrote about five different kinds of emulators. Yes I think there are five qualitatively distinct kinds. Here they are:

Full replacement

The most extreme—and most standard—kind of emulator is one that simply replaces the full input–output relationship of the entire simulation. Thus if the simulation starts with initial conditions and boundary conditions, and ends with a final state (after an integration), the full-replacement emulator would be trained to learn the full relationship between the initial and boundary conditions and the final state. A full-replacement emulator is a complete, plug-in replacement for the simulator.

Integrator

Simulation run times generally scale linearly with the number of time steps required to execute the integration. A set of emulators can be trained on a set of snapshots of the simulation internal state at a set of times that is much smaller than the full set of integration time steps. Each emulator is trained to learn the relationship between the internal state of the simulation at one time tA and the internal state of the simulation at a later time tB, such that the emulator can be used to replace the integrator during the time interval from tA to tB. A set of such emulators can be used to replace part or all of the integration performed by the simulator.

Resolution translator

Simulation run times generally scale with the number of grid points or basis functions in the representations of the state. Thus the simulator gets faster as resolution is reduced. An emulator can be trained to learn the relationship between a low-resolution simulation and a matched high-resolution simulation. Then a high-resolution simulation can be emulated by running a fast low-resolution simulation and applying the learned translation.

Physics in-painter

In most physical systems, there are coupled physics domains with different levels of computational complexity. For example, in cosmology, the pure gravitational part of the simulation is relatively low in computational cost, but the baryonic part—the atoms, photons, ram pressures, magnetic fields—is very high in computational cost. The simulator gets faster as physics domains, or equations, or interaction terms, are dropped. An emulator can be trained to learn the relationship between a simulation with some physics dropped and a matched full simulation. Then a full-physics simulation can be emulated by running a partial-physics simulation and applying the learned in-painting of the missing physics.

Statistics generator

In many contexts, the goal of the simulation is not to produce the full state of the physical system, but only certain critical statistics, such as the two-point correlation function (in the case of some cosmology problems). In this case, there is no need to emulate the entire simulation state. Instead, it makes sense to train the emulator to learn only the relationship between the initial and boundary conditions of the simulation and the final statistics of particular interest.

building trust in emulators

I started writing in a possible grant proposal (that would be in collaboration with others) about the trustworthiness of machine-learning emulators. Emulators are systems that learn the input–output relationship of a computationally expensive simulation and produce (or speed the computation of) new simulation outputs, reducing total computational requirements for a given number of simulations. These are so important now that the ESA Euclid and Simons Observatory data-analysis plans crucially involve emulation.

The issue is: How do we trust that the emulators are giving good outputs? There is no obvious way to test them, except by comparing to held-out training data. But in large-scale structure contexts, no amount of held-out data can test the enormous input data space. I don't know how we will ever trust such systems (and damn do we need to!), but I have some ideas about how to improve the situation. One involves enforcing physics symmetries on the emulators. Another involves running adversarial attacks on them.

convection, granulation, stellar spectra

I had a great and long conversation today with Maria Bergemann (MPIA) about building a model of a full stellar spectrum out of the models they build of small patches of stellar surface, with full 3D convection and full radiative transfer. Their models are sophisticated, and give a full spectrum in every direction from the surface patch. Thus we can integrate a set of patches into a surrogate combined spectrum for one rotating star covered in convecting patches. We discussed how we might do that, technically, and what projects we might then do with the output. What I want to do (yes, you guessed it) is build data-driven models of stellar granulation to improve radial-velocity surveys.

a well-posed problem in gastrophysics

Magda Siwek (Harvard) gave an execellent NYU Astrophysics Seminar today, about evolution of binary systems when the binary is accreting from a circumbinary disk. She sets a few (just a few) disk parameters, and then sets the mass ratio and eccentricity of the binary, and seeks steady-state (low disk-mass or low accretion-rate) solutions. By ignoring electromagnetic fields and various bits of microphysics, she can create a setup that is completely scale-free, so it applies (approximately) from all scales from exoplanets to super-massive black holes. That's brilliant. She finds that the eccentricities are in general driven to non-zero steady-state values, which depend (strongly) on mass ratio and (maybe weakly) on disk parameters. That's a nice problem, and observationally relevant to projects we are doing right now.

water forces on bacteria

Today we had a really great colloquium by Ned Wingreen (Princeton), about water forces on bacteria and how communities of bacteria can be seen as an active material. He showed theory and data for simple experiments in which they can change the osmotic pressure on a wet surface where bacteria are moving. They can tune the water-driven forces on the bacteria and change their behaviors.

After that, at wine and cheese, David Grier (NYU) showed me (and lots of students) a home-built device that levitates (or really traps) tiny objects using acoustic waves. It was awesome.

doing cosmology differently

Today Chirag Modi (Flatiron) gave a really great lunchtime talk about new technologies in cosmology and inference or measurement of cosmological parameters. He beautifully summarized how cosmology is done now (or traditionally): Make summary statistics of the observables, make a theory of the summary statistics, make up a surrogate likelihood function for use in inference, measure covariance matrices to use in the latter, and go. He's trying to obviate all of these things by using the simulations directly to make the measurements. He has nice results in forward modeling of the galaxy field, and in simulation-based inferences. Many interesting things came up in his talk, including the idea that I have discussed over the years with Kate Storey-Fisher (NYU) of enumerating all possible cosmological statistics! So much interesting stuff in the future of large-scale structure.

dimensionless and coordinate-free?

A lot of talk about Buckingham pi in my world. This is a theorem that says that any dimensional equation in physics with k dimensional inputs can be re-written as a dimensionless equation with fewer than k dimensionless inputs. But this is useless when we think about geometric equations—and many equations in physics are geometric.

Consider, for example, the coordinate-free equation F=ma. This equation has two dimensional vector terms. If we apply Buckingham pi, we get three coupled equations with non-scalar, non-coordinate-free dimensionless ratios. That's terrible, and useless! Can we replace Buckingham pi with something that makes equations that are both dimensionless and coordinate-free?

the stability of the vacuum

The research highlight of my day today was our weekly lunchtime blackboard talk, as it often is on Mondays. TOday it was Isabel Garcia Garcia (NYU), talking about the stability of the vacuum. She was specifically talking about the stability of a false vacuum, and specifically when there are large extra dimensions. The weird thing is, in all string-like models for the fundamental particle physics model there are both large extra dimensions and an exceedingly low probability that we live in the true vacuum state. That means a decay to a different state is possible (inevitable?). Why has this vacuum lived so long?

geometric convolutional networks

Today I had a great meeting with Wilson Gregory (JHU), Drummond Fielding (Flatiron), and Soledad Villar (JHU) about a project to learn partial differential equations from simulation data. This is a toy problem from our perspective, but it is a baby step towards big, real computational problems in physics. Fielding produces training data, Gregory produces geometric convolution networks, Villar proves things, and I cheer from the sidelines.

Our approach is to replace convolutional neural networks with geometric operators that are generalizations of convolutions that know more about geometric forms like vectors, tensors, pseudovectors, and so on. By building methods that use geometric objects responsibly, we automatically enforce coordinate freedom and other deep symmetries.

halo mass assembly

On Fridays, Kate Storey-Fisher (NYU) organizes a small meeting to discuss her projects on dark-matter halos using equivariant scalar objects constructed from n-body simulation outputs. Today we included Yongseok Jo (Flatiron), who has worked on building tools to paint galaxies onto dark-matter-only n-body simulations. We discussed joint projects, and conceptual issues about mass-assembly histories. In particular, I am interested in how we can predict formation histories of dark-matter halos from the galaxy contents alone, or infer the dark matter distribution in phase space from the stellar distribution in phase space. I love these projects, because they combine growth of structure, gravitational dynamics, galaxy formation, and machine learning.