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andreatramacere / jetset

JetSeT a framework for self-consistent modeling and fitting of astrophysical relativistic jets
BSD 3-Clause "New" or "Revised" License
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What‘s the meaning of "beaming factor" #86

Closed bluecandyrain closed 1 month ago

bluecandyrain commented 1 month ago

I'm sorry to ask you about the simple question, but I do feel confusing. I know beaming effect and Doppler factor, but I heard about "beaming factor" little. In your document it's said that "beaming factor" is calculated by the bulk Lorenz factor and viewing angle, I know the two, but I can't find the calculating formula. I checked in a dictionary and find no "beaming factor". I have read some papers that define the "beaming factor" as a parameter that relate to jet open angle only. So I guess that "beaming factor" is a more customized noun.

andreatramacere commented 1 month ago

Hi @bluecandyrain, you can find a pedagogical derivation here: https://arxiv.org/pdf/1202.5949 in Chapter 3, the formula is given in Eq. 3.15. The beaming factor is the result of special relativity and doppler effect. This definition holds for spherical sources, such as a blob. For more complex cases, such as expanding shell in GRBs, with a significant variation of the bulk factor within a short timescale, there is further effect given by the relation between the jet opening angle and the bulk Lorentz factor, which impacts on the fraction of the visible jet, and this is typically mentioned as beaming fraction. In the code I use only the former definition, but if when I will implement the GRB plugin, I will take into account also the latter.

bluecandyrain commented 1 month ago

@andreatramacere I see it. Thank you!