arXiv subjects

David C. Collins

Publications and source records attributed to David C. Collins.

At least 19 recordsLinked to original sources

arXiv2026

From 2D to 3D: Recovering Turbulent Density Dispersions from Noisy Data

Turbulence plays a central role in shaping the structure and dynamics of the interstellar medium (ISM), governing the star formation rate (SFR) and the initial mass function (IMF). A key consequence of turbulence is the generation of density fluctuations, which regulate the amount of dense gas available for star formation. Accurate measurements of the three-dimensional (3D) turbulent density dispersion are therefore essential for understanding molecular-cloud structure and star formation. However, observations typically provide only two-dimensional (2D) column densities and are often affected by measurement/detector noise. The Brunt method estimates the 3D density dispersion from 2D column-density maps, but it does not account for finite signal-to-noise ratio (SNR). Here, we extend the method to recover the 3D turbulent density dispersion from noise-contaminated observations. Using numerical simulations spanning a range of density perturbation amplitudes and noise types, we identify a characteristic noise wavenumber, k_noise, corresponding to the intersection of the signal and noise spectra. Restricting the Brunt reconstruction to wavenumbers below k_noise yields a denoised density-dispersion estimate that closely reproduces the noise-free result. We provide a practical prescription to determine k_noise directly from the measurement SNR and image resolution. Alternatively, if the noise spectrum is known, it can be subtracted directly from the observed spectrum, eliminating the need to estimate k_noise. The proposed correction recovers the noise-free density dispersion with errors of <~5% for SNR>=3 and <~15% for SNR>=1, enabling substantially more reliable estimates of turbulent density fluctuations from noisy column-density data.

astro-ph.GA↗

arXiv2026

ML in Astrophysical Turbulence I: Predicting Prestellar Cores in Magnetized Molecular Clouds using eXtreme Gradient Boosting

Giant Molecular Clouds (GMCs) are dominated by supersonic turbulence, creating a complex network of shocks and filaments that regulate star formation. While the global inefficiency of star formation is well-observed, predicting exactly which gas parcels within a turbulent cloud will collapse to form stars remains a challenge. In this work, we present a supervised machine learning framework to forecast the Lagrangian history of prestellar cores in magnetohydrodynamic (MHD) turbulence. We utilize Extreme Gradient Boosting (XGBoost) to train a regression model on the trajectories of $\sim 2.1$ million tracer particles evolved within a self-gravitating, turbulent MHD simulation. By mapping the instantaneous phase-space state (position, velocity, and density) of gas parcels to their future coordinates, our model successfully predicts the 3D evolution of star-forming cores over a horizon of $\sim 0.45$ Myr ($0.25~t_{\rm ff}$). We achieve a global coefficient of determination of $R^2 > 0.99$ and demonstrate that the model captures the non-linear convergent flows characteristic of gravitational collapse. Crucially, we show that local phase-space information alone is sufficient to distinguish between transient density fluctuations and bound collapsing cores. This data-driven approach offers a computationally efficient alternative to traditional sink-particle algorithms and provides a pathway for developing high-fidelity subgrid models for galaxy-scale simulations.

astro-ph.GA↗

arXiv2025

The Energy Cascade Rate in Supersonic Magnetohydrodynamic Turbulence

Three-dimensional direct numerical simulations (DNS) are implemented to investigate the energy cascade rate in compressible isothermal magnetohydrodynamic (MHD) turbulence. Utilizing an exact law derived from the K\'arm\'an-Howarth equation, we examine the contributions of flux and non-flux terms to the cascade rate across a broad range of sonic and Alfv\'enic Mach numbers, from subsonic to supersonic regimes and varying mean magnetic fields. Cascade rates are computed using on-grid 3-D decomposition and two plasma increment approaches: signed and absolute values. Anisotropy induced by strong magnetic fields is analyzed through angular-dependent scaling of the cascade terms. Moreover, the increment calculation method significantly influences the relative contributions of flux and non-flux terms, with absolute methods tending to overestimate the latter. These findings extend current studies of compressible turbulence and offer critical insights into energy transfer mechanisms relevant to many astrophysical phenomena.

physics.plasm-ph↗

arXiv2024

Planck dust polarization power spectra are consistent with strongly supersonic turbulence

The polarization of the Cosmic Microwave Background (CMB) is rich in information but obscured by foreground emission from the Milky Way's interstellar medium (ISM). To uncover relationships between the underlying turbulent ISM and the foreground power spectra, we simulated a suite of driven, magnetized, turbulent models of the ISM, varying the fluid properties via the sonic Mach number, $\mathcal{M_S}$ and magnetic (Alfv\'en) Mach number,$\mathcal{M_A}$. We measure the power spectra of density ($\rho$), velocity ($v$), magnetic field ($H$), total projected intensity ($T$), parity-even polarization ($E$), and parity-odd polarization ($B$). We find that the slopes of all six quantities increase with $\mathcal{M_S}$ Most increase with $\mathcal{M_A}$, while the magnetic field spectrum steepens with $M_A$. By comparing spectral slopes of $E$ and $B$ to those measured by Planck, we infer typical values of $\mathcal{M_S}$ and $\mathcal{M_A}$ for the ISM. As the fluid velocity increases, $\mathcal{M_S}> 4$, the ratio of BB power to EE power increases to approach a constant value near the Planck-observed value of $\sim 0.5$, regardless of the magnetic field strength. We also examine correlation-coefficients between projected quantities, and find that $r^{\rm{TE}}\approx 0.3$, in agreement with Planck, for appropriate combinations of $\mathcal{M_S}$ and $\mathcal{M_A}$. Finally, we consider parity-violating correlations $r^{\rm{TB}}$ and $r^{\rm{EB}}.$

astro-ph.GA↗

arXiv2023

Statistics of Energy in Isothermal Supersonic Turbulence

Turbulence is a key process in many astrophysical systems. In this work we explore the statistics of thermal and kinetic energy of isothermal, supersonic, turbulent gas. We develop analytic formulas for the PDF of thermal and kinetic energies and their joint PDF. We compare these analytical models with a suite of simulations with a fixed resolution of $1024^3$ cells across 4 different Mach numbers (1, 2, 4, 8) and three different driving patterns (compressive, mixed, solenoidal). We discover an interesting jump discontinuity in the thermal energy PDF, which carries onto the joint PDF.

astro-ph.GA↗

arXiv2023

Density and Velocity Correlations in Isothermal Supersonic Turbulence

In star-forming clouds, high velocity flow gives rise to large fluctuations of density. In this work we explore the correlation between velocity magnitude (speed) and density. We develop an analytic formula for the joint probability distribution (PDF) of density and speed, and discuss its properties. In order to develop an accurate model for the joint PDF, we first develop improved models of the marginalized distributions of density and speed. We confront our results with a suite of 12 supersonic isothermal simulations with resolution of $1024^3$ cells in which the turbulence is driven by 3 different forcing modes (solenoidal, mixed and compressive) and 4 r.m.s. Mach numbers (1, 2, 4, 8). We show, that for transsonic turbulence, density and speed are correlated to a considerable degree and the simple assumption of independence fails to accurately describe their statistics. In the supersonic regime, the correlations tend to weaken with growing Mach number. Our new model of the joint and marginalized PDFs are a factor of 3 better than uncorrelated, and provides insight into this important process.

astro-ph.GA↗

arXiv2023

Collapsing molecular clouds with tracer particles: Part II, Collapse Histories

In order to develop a complete theory of star formation, one essentially needs to know two things: what collapses, and how long it takes. This is the second paper in a series, where we query how long a parcel of gas takes to collapse and the process it undergoes. We embed pseudo-Lagrangian tracer particles in simulations of collapsing molecular clouds, identify the particles that end in dense knots, and then examine the collapse history of the gas. We find a nearly universal behavior of cruise-then-collapse, wherein a core stays at intermediate densities for a significant fraction of its life before finally collapsing. We identify time immediately before each core collapses, $t_{\rm{sing}}$, and examine how it transitions to high density. We find that the time to collapse is uniformly distributed between $0.25 t_{\rm{ff}}$ and the end of the simulation at $\sim 1 t_{\rm{ff}}$, and that the duration of collapse is universally short, $\Delta t \sim 0.1 t_{\rm{ff}}$, where $t_{\rm{ff}}$ is the free-fall time at the mean density. We describe the collapse in three stages; collection, hardening, and singularity. Collection sweeps low density gas into moderate density. Hardening brings kinetic and gravitational energies into quasi-equipartition. Singularity is the free-fall collapse, forming an envelope in rough energy balance and central over density in $\sim 0.1 t_{\rm{ff}}$.

astro-ph.GA↗

arXiv2022

Finite shock model of density in supersonic turbulence

The probability distribution of density in isothermal, supersonic, turbulent gas is approximately lognormal. This behaviour can be traced back to the shock waves travelling through the medium, which randomly adjust the density by a random factor of the local sonic Mach number squared. Provided a certain parcel of gas experiences a large number of shocks, due to the central limit theorem, the resulting distribution for density is lognormal. We explore a model in which parcels of gas undergo finite number of shocks before relaxing to the ambient density, causing the distribution for density to deviate from a lognormal. We confront this model with numerical simulations with various r.m.s. Mach numbers ranging from subsonic as low as 0.1 to supersonic at 25. We find that the fits to the finite formula are an order of magnitude better than a lognormal. The model naturally extends even to subsonic flows, where no shocks exist.

astro-ph.GA↗

arXiv2022

Collapsing Molecular Clouds with Tracer Particles: Part I, What Collapses?

To understand the formation of stars from clouds of molecular gas, one essentially needs to know two things: What gas collapses, and how long it takes to do so. We address these questions by embedding pseudo-Lagrangian tracer particles in three simulations of self-gravitating turbulence. We identify prestellar cores at the end of the collapse, and use the tracer particles to rewind the simulations to identify the preimage gas for each core at the beginning of each simulation. This is the first of a series of papers, wherein we present the technique and examine the first question: What gas collapses? For the preimage gas at the t=0, we examine a number of quantities; the probability distribution function (PDF) for several quantities, the structure function for velocity, several length scales, the volume filling fraction, the overlap between different preimages, and fractal dimension of the preimage gas. Analytic descriptions are found for the PDFs of density and velocity for the preimage gas. We find that the preimage of a core is large and sparse, and we show that gas for one core comes from many turbulent density fluctuations and a few velocity fluctuations. We find that binary systems have preimages that overlap in a fractal manner. Finally, we use the density distribution to derive a novel prediction of the star formation rate.

astro-ph.GA↗

arXiv2022

Turbulence Generation by Shock Interaction with a Highly Non-Uniform Medium

An initially planar shock wave propagating into a medium of non-uniform density will be perturbed, leading to the generation of post-shock velocity perturbations. Using numerical simulations we study this phenomenon in the case of highly-non-uniform density (order-unity normalized variance, $σ_ρ/\overlineρ \sim 1$) and strong shocks (shock Mach numbers $\overline{M}_s \gtrsim 10$). This leads to a highly disrupted shock and a turbulent post-shock flow. We simulate this interaction for a range of shock drives and initial density configurations meant to mimic those which might be presently achieved in experiments. Theoretical considerations lead to scaling relations, which are found to reasonably predict the post-shock turbulence properties. The turbulent velocity dispersion and turbulent Mach number are found to depend on the pre-shock density dispersion and shock speed in a manner consistent with the linear Richtymer-Meshkov instability prediction. We also show a dependence of the turbulence generation on the scale of density perturbations. The post-shock pressure and density, which can be substantially reduced relative to the unperturbed case, are found to be reasonably predicted by a simplified analysis that treats the extended shock transition region as a single normal shock.

physics.plasm-ph↗

arXiv2022

The driving mode of shock-driven turbulence

Turbulence in the interstellar medium (ISM) is crucial in the process of star formation. Shocks produced by supernova explosions, jets, radiation from massive stars, or galactic spiral-arm dynamics are amongst the most common drivers of turbulence in the ISM. However, it is not fully understood how shocks drive turbulence, in particular whether shock driving is a more solenoidal(rotational, divergence-free) or a more compressive (potential, curl-free) mode of driving turbulence. The mode of turbulence driving has profound consequences for star formation, with compressive driving producing three times larger density dispersion, and an order of magnitude higher star formation rate than solenoidal driving. Here, we use hydrodynamical simulations of a shock inducing turbulent motions in a structured, multi-phase medium. This is done in the context of a laser-induced shock, propagating into a foam material, in preparation for an experiment to be performed at the National Ignition Facility (NIF). Specifically, we analyse the density and velocity distributions in the shocked turbulent medium, and measure the turbulence driving parameter $b=(σ^{2 Γ}_{ρ/\langle ρ\rangle}-1)^{1/2} (1-σ_{ρ\langle ρ\rangle}^{-2})^{-1/2}\mathcal{M}^{-1}Γ^{-1/2}$ with the density dispersion $σ_{ρ/ \langle ρ\rangle}$, the turbulent Mach number $\mathcal{M}$, and the polytropic exponent $Γ$. Purely solenoidal and purely compressive driving correspond to $b \sim 1/3$ and $b \sim 1$, respectively. Using simulations in which a shock is driven into a multi-phase medium with structures of different sizes and $Γ< 1$, we find $b \sim 1$ for all cases, showing that shock-driven turbulence is consistent with strongly compressive driving.

astro-ph.GA↗

arXiv2021

Physics of Thermonuclear Explosions: Magnetic Field Effects on Deflagration Fronts and Observable Consequences

We present a study of the influence of magnetic field strength and morphology in Type Ia Supernovae and their late-time light curves and spectra. In order to both capture self-consistent magnetic field topologies as well evolve our models to late times, a two stage approach is taken. We study the early deflagration phase (1s) using a variety of magnetic field strengths, and find that the topology of the field is set by the burning, independent of the initial strength. We study late time (~1000 days) light curves and spectra with a variety of magnetic field topologies, and infer magnetic field strengths from observed supernovae. Lower limits are found to be 106G. This is determined by the escape, or lack thereof, of positrons that are tied to the magnetic field. The first stage employs 3d MHD and a local burning approximation, and uses the code Enzo. The second stage employs a hybrid approach, with 3D radiation and positron transport, and spherical hydrodynamics. The second stage uses the code HYDRA. In our models, magnetic field amplification remains small during the early deflagration phase. Late-time spectra bear the imprint of both magnetic field strength and morphology. Implications for alternative explosion scenarios are discussed.

astro-ph.SR↗

arXiv2019

The Power Spectra of Polarized, Dusty Filaments

We develop an analytic model for the power spectra of polarized filamentary structures as a way to study the Galactic polarization foreground to the Cosmic Microwave Background. Our approach is akin to the cosmological halo-model framework, and reproduces the main features of the Planck 353 GHz power spectra. We model the foreground as randomly-oriented, three-dimensional, spheroidal filaments, accounting for their projection onto the sky. The main tunable parameters are the distribution of filament sizes, the filament physical aspect ratio, and the dispersion of the filament axis around the local magnetic field direction. The abundance and properties of filaments as a function of size determine the slopes of the foreground power spectra, as we show via scaling arguments. The filament aspect ratio determines the ratio of $B$-mode power to $E$-mode power, and specifically reproduces the Planck-observed dust ratio of one-half when the short axis is roughly one-fourth the length of the long axis. Filament misalignment to the local magnetic field determines the $TE$ cross-correlation, and to reproduce Planck measurements, we need a (three-dimensional) misalignment angle with a root mean squared dispersion of about 50 degrees. These parameters are not sensitive to the particular filament density profile. By artificially skewing the distribution of the misalignment angle, this model can reproduce the Planck-observed (and parity-violating) $TB$ correlation. The skewing of the misalignment angle necessary to explain $TB$ will cause a yet-unobserved, positive $EB$ dust correlation, a possible target for future experiments.

astro-ph.CO↗

arXiv2018

The Impact of Enhanced Halo Resolution on the Simulated Circumgalactic Medium

Traditional cosmological hydrodynamics simulations fail to spatially resolve the circumgalatic medium (CGM), the reservoir of tenuous gas surrounding a galaxy and extending to its virial radius. We introduce the technique of Enhanced Halo Resolution (EHR), enabling more realistic physical modeling of the simulated CGM by consistently forcing gas refinement to smaller scales throughout the virial halo of a simulated galaxy. We investigate the effects of EHR in the Tempest simulations, a suite of Enzo-based cosmological zoom simulations following the evolution of an L* galaxy, resolving spatial scales of 500 comoving pc out to 100 comoving kpc in galactocentric radius. Among its many effects, EHR (1) changes the thermal balance of the CGM, increasing its cool gas content and decreasing its warm/hot gas content; (2) preserves cool gas structures for longer periods; and (3) enables these cool clouds to exist at progressively smaller size scales. Observationally, this results in a boost in "low ions" like H I and a drop in "high ions" like O VI throughout the CGM. These effects of EHR do not converge in the Tempest simulations, but extrapolating these trends suggests that the CGM in reality is a mist consisting of ubiquitous, small, long-lived, cool clouds suspended in a hot medium at the virial temperature of the halo. Additionally, we explore the physical mechanisms to explain why EHR produces the above effects, proposing that it works both by (1) better sampling the distribution of CGM phases enabling runaway cooling in the denser, cooler tail of the phase distribution; and (2) preventing cool gas clouds from artificially mixing with the ambient hot halo and evaporating. Evidence is found for both EHR mechanisms occurring in the Tempest simulations.

astro-ph.GA↗

arXiv2018

Magneto-Hydrodynamical Effects on Nuclear Deflagration Fronts in Type Ia Supernovae

This article presents the study of the effects of magnetic fields on non-distributed nuclear burning fronts as a possible solution to a fundamental problem for the thermonuclear explosion of a Chandrasekhar mass ($M_{Ch}$) white dwarf (WD), the currently favored scenario for the majority of Type Ia SNe (SNe~Ia). All existing 3D hydrodynamical simulations predict strong global mixing of the burning products due to Rayleigh-Taylor (RT) instabilities, which is in contradiction with observations. As a first step and to study the flame physics we present a set of computational magneto-hydrodynamic (MHD) models in rectangular flux tubes, resembling a small inner region of a WD. We consider initial magnetic fields up to $10^{12}\,\,\mathrm{G}$ of various orientations. We find an increasing suppression of RT instabilities starting at about $10^9\,\,\mathrm{G}$. The front speed tends to decrease with increasing magnitude up to about $10^{11}\,\,\mathrm{G}$. For even higher fields new small scale finger-like structures develop, which increase the burning speed by a factor of 3 to 4 above the field-free RT-dominated regime. We suggest that the new instability may provide sufficiently accelerated energy production during the distributed burning regime to go over the Chapman-Jougey limit and trigger a detonation. Finally we discuss the possible origins of high magnetic fields during the final stage of the progenitor evolution or the explosion.

astro-ph.SR↗

arXiv2017

The Anatomy of the Column Density Probability Distribution Function (N-PDF)

The column density probability distribution function (N-PDF) of GMCs has been used as a diagnostic of star formation. Simulations and analytic predictions have suggested the N-PDF is composed of a low density lognormal component and a high density power-law component, tracing turbulence and gravitational collapse, respectively. In this paper, we study how various properties of the true 2D column density distribution create the shape, or "anatomy" of the PDF. We test our ideas and analytic approaches using both a real, observed, PDF based on Herschel observations of dust emission as well as a simulation that uses the ENZO code. Using a dendrogram analysis, we examine the three main components of the N-PDF: the lognormal component, the power-law component, and the transition point between these two components. We find that the power-law component of an N-PDF is the summation of N-PDFs of power-law substructures identified by the dendrogram algorithm. We also find that the analytic solution to the transition point between lognormal and power-law components proposed by Burkhart, Stalpes & Collins (2017) is applicable when tested on observations and simulations, within the uncertainties. We reconfirm and extend the results of Lombardi, Alves & Lada (2015), which stated that the lognormal component of the N-PDF is difficult to constrain due to the artificial choice of the map area. Based on the resulting anatomy of the N-PDF, we suggest avoiding analyzing the column density structures of a star forming region based solely on fits to the lognormal component of an N-PDF. We also suggest applying the N-PDF analysis in combination with the dendrogram algorithm, to obtain a more complete picture of the global and local environments and their effects on the density structures.

astro-ph.GA↗

arXiv2015

Self-generated turbulence in magnetic reconnection

Classical Sweet-Parker models of reconnection predict that reconnection rates depend inversely on the resistivity, usually parameterized using the dimensionless Lundquist number ($\Lund$). We describe magnetohydrodynamic (MHD) simulations using a static, nested grid that show the development of a three-dimensional instability in the plane of a current sheet between reversing field lines without a guide field. The instability leads to rapid reconnection of magnetic field lines at a rate independent of $\Lund$ over at least the range $3.2\times 10^3 \lesssim \Lund \lesssim 3.2 \times 10^5$ resolved by the simulations. We find that this instability occurs even for cases with $\Lund \lesssim 10^4$ that in our models appear stable to the recently described, two-dimensional, plasmoid instability. Our results suggest that three-dimensional, MHD processes alone produce fast (resistivity independent) reconnection without recourse to kinetic effects or external turbulence. The unstable reconnection layers provide a self-consistent environment in which the extensively studied turbulent reconnection process can occur.

astro-ph.SR↗

arXiv2015

Observational Diagnostics of Self-Gravitating MHD Turbulence in Giant Molecular Clouds

We study the observable signatures of self-gravitating MHD turbulence by applying the probability density functions (PDFs) and the spatial density power spectrum to synthetic column density maps. We find that there exists three characterizable stages of the evolution of the collapsing cloud which we term "early," "intermediate," and "advanced." At early times, i.e. $t<0.15t_{ff}$, the column density has a power spectral slope similar to nongravitating supersonic turbulence and a lognormal distribution. At an intermediate stage, i.e. $0.15t_{ff}< t \leq 0.35t_{ff}$, there exists signatures of the prestellar cores in the shallower PDF and power spectrum power law slopes. The column density PDF power law tails at these times have line of sight averaged slopes ranging from -2.5 to -1.5 with shallower values belonging to simulations with lower magnetic field strength. The density power spectrum slope becomes shallow and can be characterized by $P(k)=A_1k^{β_2}e^{-k/k_c}$, where $A_1$ describes the amplitude, $k^{β_2}$ describes the classical power law behavior and the scale $k_c$ characterizes the turn over from turbulence dominated to self-gravity dominated. At advanced stages of collapse, i.e. $\approx t>0.35t_{ff}$, the power spectral slope is positive valued, and a dramatic increase is observed in the PDF moments and the Tsallis incremental PDF parameters, which gives rise to deviations between PDF-sonic Mach number relations. Finally, we show that the imprint of gravity on the density power spectrum can be replicated in non-gravitating turbulence by introducing a delta-function with amplitude equivalent to the maximum valued point in a given self-gravitating map. We find that the turbulence power spectrum restored through spatial filtering of the high density material.

astro-ph.SR↗