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Identification of photon sources, stochastically embedded in an interstellar cloud

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  • Photon transport is considered in an interstellar cloud containing one or several photon sources (stars), defined by $q_i\delta( x- x_{\i})\,i=1,2,\ldots,$ where the locations $x_i$'s are given in a stochastic way. First, the case is examined of a single source of intensity $q_1$ and located at $x_1$ with a probability density $p_1 = \p(x_1)$, such that $\p(x_1)\geq 0$ and $\int_V \p(x_1)\dx_1 = 1$, where $V \subset \R^3$ is the region occupied by the cloud. Then, a Boltzmann-like equation for the average photon distribution function < n >$(x,u;x_1)$ is derived and it is shown that $\p(x_1)$ can be evaluated starting from a far-field measurement of < n >. Finally, the case of two or more photon sources is discussed: the corresponding results are reasonably simple if $\p(x_1,x_2) = \p_1(x_1)\p_2(x_2)$, i.e. if the locations of the two photon source are "independent".
    Mathematics Subject Classification: 85A25, 35R30.


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