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Abstract Supersonic isothermal turbulence is a common process in astrophysical systems. In this work, we explore the energy in such systems. We show that the conserved energy is the sum of the kinetic energy (K) and Helmholtz free energy (F). We develop analytic predictions for the probability distributions,P(F) andP(K), as well as their nontrivial joint distribution,P(F,K). We verify these predictions with a suite of driven turbulence simulations, finding excellent agreement. The turbulence simulations were performed at Mach numbers ranging from 1 to 8, and three modes of driving: purely solenoidal, purely compressive, and mixed. We find thatP(F) is discontinuous atF= 0, with the discontinuity increasing with Mach number and compressive driving.P(K) resembles a lognormal with a negative skew. The joint distribution,P(F,K), shows a bimodal distribution, with gas either existing at highFand highKor at lowFand lowK. 

The polarization of the cosmic microwave background 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 and magnetic (Alfvén) Mach number, . We measure the power spectra of density (ρ), 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 sonic Mach number. Most increase with Alfven Mach number, while the magnetic field spectrum steepens with Alfven Mach number. By comparing spectral slopes of E and B to those measured by Planck, we infer typical values of sonic and Alfven Mach numbers for the ISM. As the fluid velocity increases and the sonic Mach number exceed 4, the ratio of BB power to EE power increases to approach a constant value near the Planck-observed value of ~0.5, regardless of the magnetic field strength. We also examine correlation coefficients between projected quantities, and find that the TE cross-correlation is ~0.3, in agreement with Planck, for appropriate combinations of Mach numbers. Finally, we consider parity-violating correlations.. 

ABSTRACT 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 function (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 rms 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. 

ABSTRACT 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 rms 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. 

ABSTRACT 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 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. Analytical 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. 

Abstract 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 and evolve our models to late times, a two-stage approach is taken. We study the early deflagration phase (∼1 s) 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 10 6 G. 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.