Polarized Light Scattering in Magnetic Fields: Astrophysical application
The linearly polarized spectrum of the Sun, known as the ''second solar spectrum'', contains a wealth of information about the physics of light scattering on atoms and molecules. The solution of the polarized line radiative transfer equation is used to interpret the shapes of observed Stokes line profiles. The solar atmosphere with its magnetically active regions harbors a whole range of field strengths (milligauss to kilogauss fields). To model the distribution of such fields, we require light scattering theories that are valid in a whole range of field strengths. Weak field theories were formulated in the past 3 decades. We have recently formulated a scattering theory applicable for arbitrary field strengths, based on the early work by Stenflo (1994, Solar magnetic fields, Kluwer Acad. Publ.).
Polarized light scattering in spectral lines is governed by a (4 X 4) matrix that describes how the Stokes vector is scattered and redistributed in frequency and direction. We have developed a classical theory to calculate this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction (Sampoorna, M., Nagendra, K. N., and Stenflo, J. O.: Astrophysical Journal, 663, 625, 2007a). This general case of scattering in the presence of magnetic fields is called the Hanle-Zeeman regime, as it covers both the partially overlapping (weak), and the well separated (strong-field) Zeeman components, in which the Hanle and Zeeman effects respectively dominate the scattering polarization.
The Hanle-Zeeman redistribution matrix accounts for the intricate coupling in frequency, angle, and polarization of the incoming and outgoing radiation, and embodies the physics of the scattering process. For a J = 0 --> 1 --> 0 scattering transition, we have established the equivalence between the Hanle-Zeeman redistribution matrix that is derived through quantum electrodynamics, and the one derived from classical time-dependent oscillator theory (Sampoorna, M., Nagendra, K. N., and Stenflo, J. O.: Astrophysical Journal, 670, 1485, 2007b). This equivalence holds for all strengths and directions of the magnetic field. In view of the rich symmetries and complex mathematical behavior of the general redistribution matrix, the proof of this equivalence is a remarkable result and has a deeper physical meaning.
Recently we (Sampoorna, M., Nagendra, K. N., and Stenflo, J. O.: Astrophysical Journal, 679, 889, 2008) have incorporated this Hanle-Zeeman redistribution matrix into the polarized line transfer equation, and solved it by a two stage perturbation method (where polarization is treated as a perturbation to the intensity). Our numerical calculations show that only Hanle-Zeeman theory allows a smooth transition from the scattering dominated weak field Hanle regime, to the strong magnetic field Zeeman regime (see Figure).
Emergent Stokes (polarized) line profiles formed in an optically very thin planar slab medium. Notice a gradual transition from a weak field Hanle regime to a strong field Zeeman regime as the field strength increases. Different line types refer to different value of the field strength.
In conclusion, for arbitrary strength magnetic fields encountered in the Solar atmosphere, it is necessary to apply the Hanle-Zeeman line transfer theory developed by us.
(M. Sampoorna, K. N. Nagendra, J. O. Stenflo)
