[TEP005][DOC] Documentation #745
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This PR included the first draft for the documentation by Tomas Bylund and serves as a starting point for the upcomming documentation.
| The current implementation only works with the downbranch line interaction scheme. | ||
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| :cite:`Lucy1999a` describes an alternative method for the generation of spectram for the supernova ejecta. Instead of using the frequency and energy of virtual montecarlo packets to create a spectrum through binning, one can use estimators collected during the montecarlo simulation to formally integrate the radiation field. Spectra generated using this method do not contain montecarlo noise directly. Here the monte carlo nature of the simulation only affects the strengths of lines and thus the spectra appear to be of better quality. |
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better: "...generation of synthetic supernova spectra."
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Important: The description should reflect that the method formally integrates over the line source functions and that these are determined during the simulation using volume-based estimators.
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| \dot E_{lu} = \frac{1}{\Delta t V} \left( 1- e^{-\tau_{lu}}\right) \sum \epsilon | ||
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| where the sum is over all the packages in a given shell that come into resonance with the transition :math:`u \rightarrow l` during the monte carlo run, :math:`\epsilon` is the energy of one such packet, and :math:`\tau_{lu}` the optical depth of the line. |
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| \dot E_u = \sum_{i < u} \dot E_{iu} | ||
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| that is, by summing all the line absorption estimators below the currently selected level. |
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the summation includes all levels which lie below the target level
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| where :math:`\lambda_{ul}` is the wavelength of each line :math:`u \rightarrow l`, and :math:`q_{ul}` is the corresponding branching ratio. The attenuating factor is kept on the left hand side because it is the product of the two that will appear in later formulae. | ||
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| Having thus produced attenuated source functions from our Monte Carlo run, we move on to using these to calculate the emerging intensity and finally the luminosity per wavelength. The final integral is given as |
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The formal integration is based on the so-called "elementary supernova" model, which is described in detail in Jeffery & Branch 1990.
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| We seek to integrate all emissions at a certain wavelength :math:`\nu` along a | ||
| ray with impact parameter :math:`p`. Because the supernova ejecta is expanding | ||
| homologously, along any ray parallel to the line of sight, the Doppler effect |
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the co-moving frame frequency is continuously shifted to longer wavelength due to the relativistic Doppler effect as the packet/photon propagates.
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Sorry to be picky, but we should at least use a uniform spelling of "Monte Carlo". Please change this @yeganer and then I'd say we can merge this. Later on, when the formal integral is fully implemented we will have to expand this documentation in any case. Then we can polish it up more.
This is a first version of the documentation regarding the formal integral.
There are two parts to this documentation:
Quick overview of the algorithm and the physics that are involved
An example of how this new module can be used.
For details about the implementation, please refer to the comments in the code.