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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. 

Abstract 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, ${\mathcal{M}}_{\mathcal{S}}$, and magnetic (Alfvén) Mach number, ${\mathcal{M}}_{\mathrm{A}}$. 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 ${\mathcal{M}}_{\mathcal{S}}$. Most increase with ${\mathcal{M}}_{\mathrm{A}}$, while the magnetic field spectrum steepens with ${\mathcal{M}}_{\mathrm{A}}$. By comparing spectral slopes ofEandBto those measured by Planck, we infer typical values of ${\mathcal{M}}_{\mathcal{S}}$and ${\mathcal{M}}_{\mathrm{A}}$for the ISM. As the fluid velocity increases, ${\mathcal{M}}_{\mathcal{S}}>4$, 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 thatr^TE≈ 0.3, in agreement with Planck, for appropriate combinations of ${\mathcal{M}}_{\mathcal{S}}$and ${\mathcal{M}}_{\mathrm{A}}$. Finally, we consider parity-violating correlationsr^TBandr^EB. 

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 Contamination by polarized foregrounds is one of the biggest challenges for future polarized cosmic microwave background (CMB) surveys and the potential detection of primordialB-modes. Future experiments, such as Simons Observatory (SO) and CMB-S4, will aim at very deep observations in relatively small (f_sky∼ 0.1) areas of the sky. In this work, we investigate the forecasted performance, as a function of the survey field location on the sky, for regions over the full sky, balancing between polarized foreground avoidance and foreground component separation modeling needs. To do this, we simulate observations by an SO-like experiment and measure the error bar on the detection of the tensor-to-scalar ratio,σ(r), with a pipeline that includes a parametric component separation method, the Correlated Component Analysis, and the use of the Fisher information matrix. We forecast the performance over 192 survey areas covering the full sky and also for optimized low-foreground regions. We find that modeling the spectral energy distribution of foregrounds is the most important factor, and any mismatch will result in residuals and bias in the primordialB-modes. At these noise levels,σ(r) is not especially sensitive to the level of foreground contamination, provided the survey targets the least-contaminated regions of the sky close to the Galactic poles. 

Abstract We present theDustFilamentscode, a full-sky model for the millimeter Galactic emission of thermal dust. Our model, composed of millions of filaments that are imperfectly aligned with the magnetic field, is able to reproduce the main features of the dust angular power spectra at 353 GHz as measured by the Planck mission. Our model is made up of a population of filaments with sizes following a Pareto distribution $\propto L_a^{-2.445}$, with an axis ratio between short and long semiaxesϵ∼ 0.16 and an angle of magnetic field misalignment with a dispersion rms(θ_LH) = 10°. On large scales, our model follows a Planck-based template. On small scales, our model produces spectra that behave like power laws up toℓ∼ 4000 or smaller scales by considering even smaller filaments, limited only by computing power. We can produce any number of Monte Carlo realizations of small-scale Galactic dust. Our model will allow tests of how the small-scale non-Gaussianity affects CMB weak lensing and the consequences for the measurement of primordial gravitational waves or relativistic light relic species. Our model also can generate frequency decorrelation on the modified blackbody spectrum of dust and is freely adjustable to different levels of decorrelation. This can be used to test the performance of component separation methods and the impact of frequency spectrum residuals on primordialB-mode surveys. The filament density we paint in the sky is also able to reproduce the general level of non-Gaussianities measured by Minkowski functionals in the Planck 353 GHz channel map.