Optimum 1D average of 3D model
Background
Microturbulence is a construct used in 1D atmospheric modelling to account for spectral line broadening (from velocities) that is not spatially resolved. To study how one goes from a 3D model atmosphere complete with velocities to a 1D model with microturbulence, we need to consider how to horizontally average a 3D into a 1D model atmosphere, a so-called \(\langle3\mathrm{D}\rangle\) model.
The choice of average method is not trivial. The synthetic spectra from the \(\langle3\mathrm{D}\rangle\) should be as close as possible to the spatially-averaged spectra of the 3D model. A good averaging method should go beyond a simple geometric average and take into account the non-linear contribution of each column in the 3D model into the path of light. Magic et al. (2013) performed a comprehensive analysis on how to create \(\langle3\mathrm{D}\rangle\) from a grid of model atmospheres, including averaging over column mass, optical depth, flux-weighed average temperature, and enforced-hydrostatic equilibrium. They found that column mass averaging is the most accurate method, but their analysis was restricted to photospheric lines. It is unclear if column mass averaging will still be the better method for chromospheric lines, which are formed in regions with stronger spatial gradients. (See also Uitenbroek & Criscuoli 2011.) For a general overview of the Solar chromosphere, see Carlsson et al. 2019. For a description of the Bifrost model used in the project, see Carlsson et al. 2016.
Goal
The goal of the project is identify what is the best method of averaging a 3D model into a 1D model for chromospheric lines of singly-ionised calcium.
Method
The RH 1.5D code is used to solve the equations of statistical equilibrium for a given model atom and model atmosphere.
Procedure
Average one or more snapshots from a 3D Bifrost simulation into \(\langle3\mathrm{D}\rangle\) using different methods, including at least averaging over:
- geometric height
- column mass
- optical depth at 500 nm
Use RH to synthesize Ca II profiles from the 3D model and the different \(\langle3\mathrm{D}\rangle\) averages. To restrict this analysis to the temperature/density stratification, velocities and microturbulences should be set to zero in both cases.
Analyse the resulting spectra and find out which averaging method minimises the differences between \(\langle3\mathrm{D}\rangle\) and spatially-averaged 3D Ca II spectra.
One 3D Bifrost simulation snapshot is in /mn/stornext/u3/matsc/rh/Atmos/en024048hion385.ncdf The simulation is described in Carlsson et al 2016. The simulation, and especially snapshot 385, has been extensively used to study line formation. For references, see [Carlsson et al 2019](