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TEP005_formal_integral.rst

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TEP005: Formal Integral Method for noise-free spectra

Status

Discussion

Responsible

@unoebauer

Branches and Pull requests

N/A

Description

The main drawback of Monte Carlo methods is the inevitable introduction of stochastic fluctuations, i.e. noise. In the case of Tardis, this is particular relevant for the synthetic spectrum, the main product of Tardis calculations: to perform a detailed spectral analysis, the line features must be distinguishable from the noise. Thus, devising and implementing algorithms to improve the signal-to-noise ratio is a crucial part of the Tardis development process.

Currently, the so-called virtual packet scheme (see Long & Knigge 2002, Sim et al. 2010, Kerzendorf & Sim 2014) is used in Tardis to improve the fidelity of the calculated synthetic spectra. Spectra calculated with this scheme are still subject to noise, but its main advantage lies in its applicability to cases with complex line-interaction treatments (e.g. the Macro Atom scheme).

In cases in which only the resonance-scattering or the downbranching line interaction treatments are used, a compelling alternative to the virtual packet scheme exists. This approach, relying on a formal integration of the source function has been developed by Lucy 1999 and produces noise-free spectra.

This formal-integral approach should be implemented into Tardis and made an alternative to the virtual packet scheme, whenever the scatter or downbranch line interaction modes are used.

Implementation

  • The main procedure, namely determining the line emissivities an performing the integral should be performed in the C-part of Tardis
  • It should be activated through the configuration file
  • Some safety checks should be in place, e.g. not allowing the parallel use of the formal integral and the virtual packet scheme or prohibiting the use of the formal integral approach in conjunction with the macroatom line interaction treatment

Backward compatibility

Should not affect backwards compatibility. The virtual packet scheme will not be affected by this.

Alternatives

Concerning the aim of the formal integral approach (improving the signal-to-noise in the synthetic spectrum), an alternative is already in place, namely the virtual packet scheme. However, for Tardis calculations using the downbranching scheme, the formal integral approach should be superior.