is it surprising that there are high-redshift supermassive black holes?

A nice talk at MPIA by Hanna Ũbler (MPE) about very high-redshift (redshifts 8 to 14 even) galaxies and their black-hole contents started some nice discussions in the audience and afterwards about the formation of black holes. Because of the Eddington limit (which is a limit on luminosity), black-hole growth is probably limited. The limit is on luminosity, not mass accretion rate, and the relationship between these is the radiative efficiency. As the efficiency goes down, the mass accretion rate of an Eddington accretor goes up. So the question: When can you first form a super-massive (10 million solar masses, say) black hole is a question simultaneously about seed black holes and about radiative efficiency. Anyway, this is all unfortunate, because if the efficiency couldn't get very low, then the black holes we find with NASA JWST would already be putting very strong pressure on fundamental physics in the early Universe.

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.

Dr Kate Storey-Fisher

Kate Storey-Fisher (NYU) defended her PhD here at NYU today. She killed it! She talked about emulating cosmological simulations (at the level of statistics, not maps), making invariant scalars that encode the shapes and dynamics of dark-matter halos, and her awesome 1.2 million all-sky quasar catalog from ESA Gaia and NASA WISE. It was all things my loyal reader knows lots about but I loved it. It has been an honor and a privilege to work with KSF these years, and I will miss her very very much.

distances between point clouds

I spent the last two days working at Apple Paris, which was fun! I worked with the open-source ott-jax package, which can do some amazing things. I worked with Soledad Villar (Apple & JHU) to generalize the k-means algorithm to point clouds! It can cluster point clouds morphologically, even if the different point clouds have different numbers of points, and even if the different point clouds live in spaces of different dimensions! Everything obeys permutation and rotation symmetries.

abundance moments are the new actions

I had fun today talking to Neige Frankel (CITA) about all things Snail-y. We discussed how to verify the stellar parameters we are using for our Snail studies. One issue is that we want to check that things are (fairly) well mixed along orbits, but we need a theory of the orbits to check this. I recommended that, instead of computed actions (integrals of motion), we use statistics of the abundance distribution. After all, if the stars are well mixed, moments of the abundance distribution ought to be constant on orbits. If you just need the actions to label the orbits, abundance moments serve as replacements. Actions are theoretical and unobservable. Abundance moments are observable and measurable (noisily maybe!).

thermodynamics of cosmic gas

The day ended today at Flatiron with a great Colloquium by Eichiro Komatsu (MPA) about the temperature of cosmic gas. Gravitational collapse heats the gas, and that takes it up to something like 2 million degrees. This was computed ages ago by Peebles and others, but is now measured. There was a lot of discussion during and after about other heating mechanisms, and what things constitute gravitational heating. I'm interested in whether this result meaningfully constrains scattering interactions between the dark matter and baryons; if they scatter, and the dm is heavier, the baryons will (eventually) get exceedingly hot.

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.

Dagstuhl, day 1

Today was day 1 of Machine Learning for Science: Bridging Data-driven and Mechanistic Modeling at Schloss Dagstuhl. The first day was mainly about applications of machine learning, in Earth science, livestock management, astrophysics (dark matter), cells, and mechanical engineering. I had many thoughts and realizations. Here are a few random ones:

The problems that appear in Earth science, and the data types, are very similar to those that appear in astrophysics! But in Earth science, biology is a big driver of global processes, and there is no good mechanistic model for (say) how plants grow and take up carbon. The world is filled with mobile phones, with good cameras, and the methods we could could be employing to be doing science in a distributed way are way, way under-used. Cells are incredibly complicated. The mechanistic model involves literally thousands of individual processes. Like our model for the cell is as complicated as our model for the entire Earth system (which, by the way, depends on cells!), or even more complicated.

In the areas of the cell and the Earth, a theme was that the investigators want to preserve the causal structure we believe, and just use the machine learning to replace one tiny piece, with a data-driven model. Related: You can think of the machine learning as an effective theory for something (a sub-part of the problem) that doesn't work well from first principles. That's a good idea!

regularities of dark-matter halos

There is a regular dynamics meeting (maybe Galactic dynamics meeting?) at Flatiron. I went today and I learned a lot, from Ivana Escala (Princeton) and Danny Horta-Darrington (Flatiron). I briefly presented Kate Storey-Fisher's project of describing dark-matter halos with coordinate-free nonlinear geometric scalars, which isn't really a dynamics project but it could be, because these scalars could be part of a canonical transformation of the dark sector. Anyway, the crowd had interesting things to say. In particular, the idea came up that the subspace in which the dark-matter halos live (subspace of the space of these scalars) is likely to be very compact (or low-dimensional, or both) and that the susbspace probably depends on the dark-matter model. That's a great idea, and suggests that maybe we can construct new tests of gravity.

Dr Tomer Yavetz

Today Tomer Yavetz (Columbia) defended his PhD, which was in part about the dynamics of stellar streams, and in part about macroscopically quantum-mechanical dark matter. The dissertation was great. The stellar-stream part was about stream morphologies induced by dynamical separatrices in phase space: If the stars on a stream are on orbits that span a separatrix, all heck breaks loose. The part of the thesis on this was very pedagogical and insightful about theoretical dynamics. The dark-matter part was about fast computation of steady-states using orbitals and the WKB approximation. Beautiful physics and math! But my favorite part of the thesis was the introduction, in which Yavetz discusses the point that dynamics—even though we can't see stellar orbits—does have directly observable consequences, like the aforementioned streams and their morphologies (and also Saturn's rings and the gaps in the asteroid belt and the velocity substructure in the Milky Way disk). After the defense we talked about re-framing dynamics around this idea of observability. Congratulations, and it has been a pleasure!

extragalactic stellar stream

Sarah Pearson (NYU) is working on modeling a stellar stream (disrupted satellite galaxy) around an external galaxy. The goal is to figure out what observables are most critical, and what properties of the host galaxy are most strongly constrained by a good model. That is, information theory. Pearson showed beautiful results today to Adrian Price-Whelan (Flatiron) and me: She can show that the mass of the galaxy's dark-matter halo is covariant with velocity gradients along the stream. Those would be hard to measure but not impossible. One high-level objective is to understand what would be the scientific merit of a big program with new imaging data and follow-up spectroscopy.

six-quark state?

Today was a great blackboard talk at CCPP by Glennys Farrar (NYU) about a possible six-quark state in QCD. She has been thinking about this for a decade or so, because it might have implications for dark matter and issues in QCD. Today she focused on the latter: There are terms in the g−2 calculation for the muon that can be estimated either with lattice QCD or by integrating some observed branching ratios from experiment. These two methods disagree, and the observational method disagrees (more strongly) with the g−2 measurement. But Farrar shows that if there is a long-lived 6-quark state, it can potentially affect the QCD calculation (implicitly) but would be evaded by the branching-ratio measurements (because it would evade all event triggers). Her model requires some good luck with QCD parameters and bound states, but if that luck holds, she can pull dark matter into the standard model and solve some precision-measurement issues! After her talk we discussed a bit about just how hard lattice QCD is. It's absurd!

me reading?

As my collaborators and friends know, if there is one thing I hate to do, it is spend all day reading the literature. I love and respect the literature! But don't make me actually read it. But today I sucked it up and read some 20-ish papers about characterizing dark-matter halo shapes, to find out if the coordinate-free shape measurements that Kate Storey-Fisher (NYU) and I are measuring are new. I think they are! In almost every paper I read, the word “shape” translated to eigenvalues of the positional variance tensor, or maybe ratios of those. Am I wrong?

shapes of dark-matter halos

I had a very very long meeting today with Kate Storey-Fisher (NYU) in which we talked through every aspect of our current project, at every level of abstraction. It was great! And at the end of it, I had a way simpler description of our project than I think I could have articulated even yesterday: We are asking whether high-order, coordinate-free measurements of dark-matter halo shapes can predict galaxy contents.

how can linear regression be hard?

Maybe I'm known in astronomy for being both a machine-learning developer and a machine-learning skeptic. I hope so! Anyway, I love linear regression, because it has a lot of the power of bigger ML models, but it's easy to implement and to understand. And yet!

Today Kate Storey-Fisher (NYU) and I looked at her code to predict galaxy properties given dark-matter-halo properties in a set of n-body simulations. We are doing very simple regressions but the condition numbers of the matrices are blowing up and some of our answers don't look great. And this is generic: Many linear-regression models are messed up by condition numbers and numerical linear algebra, and it is hard to diagnose, and it is hard to treat. And if linear regression is hard—and hard for us—why do I believe anything that inovolves 42 layers of fully-connected RELU network?

is an eigenvector a vector?

I spent time today talking to Kate Storey-Fisher about features to use in her cosmological regression projects. The point is that we are only considering features that have well-defined, coordinate-free meanings, because we are trying to do regressions that are invariant to coordinate transformations. These features include scalars, vectors, and tensors, which we contract into scalars. But what can you do with a tensor? At order 2, a tensor has a trace (its self-contraction); it can be contracted with two vectors; it has eigenvalues and eigenvectors. The eigenvalues are classical scalars; good! But are the eigenvectors classical vectors? No, they aren't, because they don't have signs. What can you do with them? I have some theories...

feature engineering for dark-matter halos

Kate Storey-Fisher and I spoke about adding eigenvalues (scalars) and eigenvectors (vectors) to our geometric features of dark-matter halos. For regression! But the problem with this is that the eigenvectors have ambiguous sign; is that an issue? Yes! They are descriptions of an order-2 tensor, not order-1 vectors. Hmmm. We also spoke about whether the feature engineering should be deterministic, or chosen by hand.

fitting, or fitting residuals?

Today Storey-Fisher (NYU) and I decided to modify her regression model for understanding galaxies in dark-matter halos from a regression in which we try to predict the properties of the galaxies directly, to a regression in which we try to predict the residuals away from a standard-practice smooth fit based on halo mass. The issues are complex here! But we want to look at simple models, and simple models can't capture the zeroth-order effects. My expectation (to be tested) is that the residuals are better fit by simple models than the zeroth-order trend. Why do I expect this? In my mind it has something to do with linearization.

weak-lensing inconsistency

Tocay Alexie Leauthaud (UCSC) gave the NYU Astro Seminar, about various things related to cosmological tests with weak lensing. She showed an impressive result, which is that essentially all galaxy–galaxy lensing projects find a weak-lensing signal that is too low by tens of percent relative to what we expect from the Planck cosmological parameters and simple galaxy–halo occupation models. I am interested in looking into this more with Storey-Fisher and her (new, exploratory) models of galaxy occuption in hydro simulations. I have an intuition that the predictions might be overly naive if halo occupation is slightly more complex than expected. I am particularly interested in this issue because I think the galaxy–galaxy weak-lensing signal has been a very fundamental test of our picture of the dark sector.