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Abstract Synchrotron emissivities, absorptivities, and Faraday rotation and conversion coefficients are needed in modeling a variety of astrophysical sources, including Event Horizon Telescope (EHT) sources. We develop a method for estimating transfer coefficients that exploits their linear dependence on the electron distribution function, decomposing the distribution function into a sum of parts each of whose emissivity can be calculated easily. We refer to this procedure as stochastic averaging and apply it in two contexts. First, we use it to estimate the emissivity of an isotropicκdistribution function with a high-energy cutoff. The resulting coefficients can be evaluated efficiently enough to be used directly in ray-tracing calculations, and we provide an example calculation. Second, we use stochastic averaging to assess the effect of subgrid turbulence on the volume-averaged emissivity and along the way provide a prescription for a turbulent emissivity. We find that for parameters appropriate to EHT sources turbulence reduces the emissivity slightly. In the infrared, turbulence can dramatically increase the emissivity.
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Parameter estimation in the stochastic superparameterization of two-layer quasigeostrophic flows
Geophysical turbulence has a wide range of spatiotemporal scales that requires a multiscale prediction model for efficient and fast simulations. Stochastic parameterization is a class of multiscale methods that approximates the large-scale behaviors of the turbulent system without relying on scale separation. In the stochastic parameterization of unresolved subgrid-scale dynamics, there are several modeling parameters to be determined by tuning or fitting to data. We propose a strategy to estimate the modeling parameters in the stochastic parameterization of geostrophic turbulent systems. The main idea of the proposed approach is to generate data in a spatiotemporally local domain and use physical/statistical information to estimate the modeling parameters. In particular, we focus on the estimation of modeling parameters in the stochastic superparameterization, a variant of the stochastic parameterization framework, for an idealized model of synoptic-scale turbulence in the atmosphere and oceans. The test regimes considered in this study include strong and moderate turbulence with complicated patterns of waves, jets, and vortices.
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- Award ID(s):
- 1912999
- PAR ID:
- 10175404
- Date Published:
- Journal Name:
- Research in the mathematical sciences
- Volume:
- 7
- Issue:
- 14
- ISSN:
- 2197-9847
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/doi.org/10.1007/s40687-020-00213-8
