By J. Trujillo-Bueno, F. Moreno-Insertis, F. Sanchez

This booklet comprises the lectures introduced on the XII Canary Islands iciness tuition of Astrophysics on Astrophysical Spectropolarimetry. It highlights how fresh advancements in theoretical astrophysics and astronomical instrumentation are prime an ever-growing variety of astrophysicists to understand the large diagnostic power provided via spectropolarimetry.

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We consider first the case of an atomic transition between two atomic levels, the lower level having angular momentum Jt = 0 and the upper level having angular momentum Ju = 1. We also suppose the atom to be irradiated by a unidirectional, unpolarized radiation beam characterized by a given intensity IQ a t the transition frequency vo. Assuming for simplicity the quantization axis to be directed along the direction of the beam, it follows, due to the transversality character of the electric field, that the only transitions that can be induced by the incident radiation are those satisfying the selection rule AM = ±1.

Finally, the same phenomenon was discovered by Michael Faraday in the light travelling through a medium subjected to a strong magnetic field (aligned with the direction of propagation), and, since then, it is also known as the Faraday effect, or as Faraday rotation. The matrix appearing in the transfer equation satisfies an important symmetry property. 4), and 1 is the 4 x 4 identity matrix. 5) A 5 . = _ST / K T X + XK) 5 = -2mV V ds ds This equation assures that, during the transfer, a physical Stokes vector (for which V > 0) always remains a physical vector.

This implies that, to a good approximation, the fractional polarization of the radiation emitted in direction n is independent of frequency and is given by Qw{n) sin26> Iu (n) 1 + cos2 0 This equation implies that the radiation is totally linearly polarized when emitted in the plane perpendicular to the velocity of the colliding beam, the direction of polarization being contained in the same plane. Vice versa, the radiation emitted along the direction of the colliding beam is not polarized. Concerning the radiation diagram, we have a ^-dependency of the form (1 + cos2 6) showing that the radiation emitted towards the "poles" is twice as much the radiation emitted in the "equatorial plane".

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