http://arxiv.org/abs/2012.06807
Axisymmetric, time-independent accretion disc models are necessarily mean-field theories when applied to turbulent discs since axisymmetry and stationarity apply only upon averaging. Observations with short exposure times represent members in the turbulence ensemble, and comparing with theoretical mean values can falsify the latter only if the theory is additionally supplied with a quantified precision. We previously identified “intrinsic” and “filtering” errors as two contributions to the precision of mean-field theories. Here we generalize to cases where the turbulent scales vary in space. In the geometrically thin, optically thick accretion disc models, disc emission at a given frequency has non-local contributions from the entire disc, and we develop a framework to propagate local fluctuations to the integrated spectrum. In addition, the nonlinear relation between the disc temperature and overall spectrum contributes a systematic “mismatch error” that has not been previously identified. The total error in the calculated disc spectrum is also sensitive to the choice of binning used to compare with data from a telescope of given temporal and spectral resolving powers. For the thin disc example, we show that precision errors are generally small, but vary with emission frequency. In general this means that accurately assessing falsifiability would require a frequency-dependent likelihood function. The thin disc exemplifies our more important purpose: to highlight the need and provide a framework for calculating the imprecision of a mean-field theory.
H. Zhou and E. Blackman
Tue, 15 Dec 20
131/136
Comments: 11 pages, 3 figures. Submitted to MNRAS
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