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September  2009, 2(3): 425-432. doi: 10.3934/krm.2009.2.425

Identification of photon sources, stochastically embedded in an interstellar cloud

S. Aiello 1, , Luigi Barletti 2, and  Aldo Belleni-Morante 3,

1. 

Dipartimento di Astronomia e Scienza dello Spazio, Università di Firenze, Largo Fermi 2, 50125 Firenze, Italy
2. 

Dipartimento di Matematica, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
3. 

Dipartimento di Ingegneria Civile, Università di Firenze, Via S. Marta 3, 50139 Firenze, Italy

Received  November 2008 Revised  November 2008 Published  July 2009

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".
Keywords: inverse problems., radiation transport, interstellar clouds.
Mathematics Subject Classification: 85A25, 35R3.
Citation: S. Aiello, Luigi Barletti, Aldo Belleni-Morante. Identification of photon sources, stochastically embedded in an interstellar cloud. Kinetic and Related Models, 2009, 2 (3) : 425-432. doi: 10.3934/krm.2009.2.425
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