Influence of inhomogeneous stochasticity on the falsifiability of mean-field theories and examples from accretion disc modelling
[1];
[2]
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden, Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA, Laboratory for Laser Energetics, University of Rochester, Rochester NY 14623, USA
- Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA, Laboratory for Laser Energetics, University of Rochester, Rochester NY 14623, USA
ABSTRACT Despite spatial and temporal fluctuations in turbulent astrophysical systems, mean-field theories can be used to describe their secular evolution. However, observations taken over time scales much shorter than dynamical time scales capture a system in a single state of its turbulence ensemble. Comparing with mean-field theory can falsify the latter only if the theory is additionally supplied with a quantified precision. The central limit theorem provides appropriate estimates to the precision only when fluctuations contribute linearly to an observable and with constant coherent scales. Here, we introduce an error propagation formula that relaxes both limitations, allowing for non-linear functional forms of observables and inhomogeneous coherent scales and amplitudes of fluctuations. The method is exemplified in the context of accretion disc theories, where inhomogeneous fluctuations in the surface temperature are propagated to the disc emission spectrum – the latter being a non-linear and non-local function of the former. The derived precision depends non-monotonically on emission frequency. Using the same method, we investigate how binned spectral fluctuations in telescope data change with the spectral resolving power. We discuss the broader implications for falsifiability of a mean-field theory.
- Research Organization:
- Princeton University, NJ (United States); University of Rochester, NY (United States)
- Sponsoring Organization:
- Horton Fellowship; National Science Foundation (NSF); USDOE; USDOE Office of Science (SC)
- Grant/Contract Number:
- SC0020103; SC0020432; SC0020434
- OSTI ID:
- 1818175
- Journal Information:
- Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Journal Issue: 2 Vol. 507; ISSN 0035-8711
- Publisher:
- Oxford University PressCopyright Statement
- Country of Publication:
- United Kingdom
- Language:
- English
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