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, , 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 . Most increase with , while the magnetic field spectrum steepens with . By comparing spectral slopes ofEandBto those measured by Planck, we infer typical values of and for the ISM. As the fluid velocity increases, , 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 thatrTE≈ 0.3, in agreement with Planck, for appropriate combinations of and . Finally, we consider parity-violating correlationsrTBandrEB.
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On the generalization of the Kruskal–Szekeres coordinates: a global conformal charting of the Reissner–Nordström spacetime
Abstract The Kruskal–Szekeres coordinate construction for the Schwarzschild spacetime could be interpreted simply as a squeezing of thet-line into a single point, at the event horizon . Starting from this perspective, we extend the Kruskal charting to spacetimes with two horizons, in particular the Reissner–Nordström manifold, . We develop a new method to construct Kruskal-like coordinates through casting the metric in new null coordinates, and find two algebraically distinct ways to chart , referred to as classes: type-I and type-II within this work. We pedagogically illustrate our method by crafting two compact, conformal, and global coordinate systems labeled and as an example for each class respectively, and plot the corresponding Penrose diagrams. In both coordinates, the metric differentiability can be promoted to in a straightforward way. Finally, the conformal metric factor can be written explicitly in terms of thetandrfunctions for both types of charts. We also argued that the chart recently reported in Soltani (2023 arXiv:2307.11026) could be viewed as another example for the type-II classification, similar to .
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- Award ID(s):
- 2310363
- PAR ID:
- 10529685
- Publisher / Repository:
- IOP
- Date Published:
- Journal Name:
- Classical and Quantum Gravity
- Volume:
- 41
- Issue:
- 13
- ISSN:
- 0264-9381
- Page Range / eLocation ID:
- 135005
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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