Publications

The initial conditions of cosmological simulations are commonly drawn from a Gaussian ensemble. The limited number of modes inside a simulation volume gives rise to statistical fluctuations known as \textit{sample variance}, limiting the accuracy of simulation predictions. Fixed fields offer an alternative initialization strategy; they have the same power spectrum as standard Gaussian fields but without intrinsic amplitude scatter at linear order. Paired fixed fields consists of two fixed fields with opposite phases that cancel phase correlations which otherwise induce second-order scatter in the non-linear power spectrum. We study the statistical properties of those fields for 19 different quantities at different redshifts through a large set of 600 N-body and 506 state-of-the-art magneto-hydrodynamic simulations covering a wide range of scales, mass and spatial resolutions. We find that paired fixed simulations do not introduce a bias on any of the examined quantities. We quantify the statistical improvement brought by these simulations, over standard ones, on different power spectra such as matter, halos, CDM, gas, stars, black-holes and magnetic fields, finding that they can reduce their variance by factors as large as 106. We quantify the improvement achieved by fixing and by pairing, showing that sample variance in some quantities can be highly suppressed by pairing after fixing. Paired fixed simulations do not change the scatter in quantities such as the probability distribution function of matter density, or the halo, void or stellar mass functions. We argue that procedures aiming at reducing the sample variance of those quantities are unlikely to work. Our results show that paired fixed simulations do not affect either mean relations or scatter of galaxy properties, and suggest that the information embedded in 1-pt statistics is highly complementary to that in clustering.

In cryo-electron microscopy, the three-dimensional (3D) electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy two-dimensional images. The volume maps representing these potentials typically exhibit a great deal of structural variability, which is described by their 3D covariance matrix. Typically, this covariance matrix is approximately low rank and can be used to cluster the volumes or estimate the intrinsic geometry of the conformation space. We formulate the estimation of this covariance matrix as a linear inverse problem, yielding a consistent least-squares estimator. For $n$ images of size N-by-N pixels, we propose an algorithm for calculating this covariance estimator with computational complexity O(n * N^4+√κ * N^6 * log(N)), where the condition number κ is empirically in the range 10-200. Its efficiency relies on the observation that the normal equations are equivalent to a deconvolution problem in six dimensions. This is then solved by the conjugate gradient method with an appropriate circulant preconditioner. The result is the first computationally efficient algorithm for consistent estimation of the 3D covariance from noisy projections. It also compares favorably in runtime with respect to previously proposed nonconsistent estimators. Motivated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrix estimation, we incorporate a shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We evaluate our methods on simulated datasets and achieve classification results comparable to state-of-the-art methods in shorter running time. We also present results on clustering volumes in an experimental dataset, illustrating the power of the proposed algorithm for practical determination of structural variability.

We present the first kinematical detection of embedded protoplanets within a protoplanetary disk. Using archival ALMA observations of HD 163296, we demonstrate a new technique to measure the rotation curves of CO isotopologue emission to sub-percent precision relative to the Keplerian rotation. These rotation curves betray substantial deviations caused by local perturbations in the radial pressure gradient, likely driven by gaps carved in the gas surface density by Jupiter-mass planets. Comparison with hydrodynamic simulations shows excellent agreement with the gas rotation profile when the disk surface density is perturbed by two Jupiter mass planets at 83 au and 137 au. As the rotation of the gas is dependent on the pressure of the total gas component, this method provides a unique probe of the gas surface density profile without incurring significant uncertainties due to gas-to-dust ratios or local chemical abundances which plague other methods. Future analyses combining both methods promise to provide the most accurate and robust measures of embedded planetary mass. Furthermore, this method provides a unique opportunity to explore wide-separation planets beyond the mm continuum edge and to trace the gas pressure profile essential in modelling grain evolution in disks.

Ultra-long gamma-ray bursts (ULGRBs) are a distinct class of GRBs characterized by durations of several thousands of seconds, about two orders of magnitude longer than those of standard long GRBs (LGRBs). The driving engine of these events has not yet been uncovered, and ideas range from magnetars, to tidal disruption events, to extended massive stars, such as blue super giants (BSG). BSGs, a possible endpoint of stellar evolution, are attractive for the relatively long freefall times of their envelopes, allowing accretion to power a long-lasting central engine. At the same time, their large radial extension poses a challenge to the emergence of a jet. Here, we perform an end-to-end simulation aimed at assessing the viability of BSGs as ULGRB progenitors. The evolution to the core-collapse of a BSG star model is calculated with the MESA code. We then compute the accretion rate for the fraction of envelope material with enough angular momentum to circularize and form an accretion disk, and input the corresponding power into a jet, which we evolve through the star envelope with the FLASH code. Our simulation shows that the jet can emerge, and the resulting light curves resemble those observed in ULGRBs, with durations T90 ranging from ≈4000 s to ≈104 s, depending on the viewing angle.

We develop and apply a model to quantify the global efficiency of radial orbit migration among stars in the Milky Way disk. This model parameterizes the possible star formation and enrichment histories, radial birth profiles, and combines them with a migration model that relates present-day orbital radii to birth radii through a Gaussian probability, broadening with age τ as σRM8 τ/8 Gyr‾‾‾‾‾‾‾√. Guided by observations, we assume that stars are born with an initially tight age--metallicity relation at given radius, which becomes subsequently scrambled by radial orbit migration, thereby providing a direct observational constraint on radial orbit migration strength σRM8. We fit this model with MCMC to the observed age--metallicity distribution of low-α red clump stars with Galactocentric radii between 5 and 14 kpc from APOGEE DR12, sidestepping the complex spatial selection function and accounting for the considerable age uncertainties. This simple model reproduces well the observed data, and we find a global (in radius and time) radial orbit migration efficiency in the Milky Way of σRM8=3.6±0.1 kpc when marginalizing over all other model aspects. This shows that radial orbit migration in the Milky Way's main disk is indeed rather strong, in line with theoretical expectations: stars migrate by about a half-mass radius over the age of the disk. The model finds the Sun's birth radius at ∼5.2 kpc. If such strong radial orbit migration is typical, this mechanism plays indeed an important role in setting the structural regularity of disk galaxies.

We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach involves a minor modification of a classical formulation. In the electrostatic or acoustic setting, we introduce a new vector partial differential equation, from which the desired solution is easily obtained. It is the vector equation for which we derive a well-conditioned integral equation. In addition to providing a unified framework for these solvers, we illustrate their performance using iterative solution methods coupled with the FFT-based technique of [1] to discretize and apply the relevant integral operators.

Upcoming cosmic microwave background (CMB) surveys will soon make the first detection of the polarized Sunyaev-Zel’dovich effect, the linear polarization generated by the scattering of CMB photons on the free electrons present in collapsed objects. Measurement of this polarization along with knowledge of the electron density of the objects allows a determination of the quadrupolar temperature anisotropy of the CMB as viewed from the space-time location of the objects. Maps of these remote temperature quadrupoles have several cosmological applications. Here we propose a new application: the reconstruction of the cosmological reionization history. We show that with quadrupole measurements out to redshift 3, constraints on the mean optical depth can be improved by an order of magnitude beyond the CMB cosmic variance limit.