F -state interference significantly modifies the polarization produced by scattering processes in the solar atmosphere. Its signature in the emergent Stokes spectrum in the absence of magnetic fields is depolarization in the line core. In the present paper, we derive the partial frequency redistribution (PRD) matrix that includes interference between the upper hyperfine structure states of a two-level atom in the presence of magnetic fields of arbitrary strengths. The theory is applied to the Na i D 2 line that is produced by the transition between the lower J = 1/2 and upper J = 3/2 states which split into F states because of the coupling with the nuclear spin I s = 3/2. The properties of the PRD matrix for the single-scattering case is explored, in particular, the effects of the magnetic field in the Paschen-Back regime and their usefulness as a tool for the diagnostics of solar magnetic fields.

Obtaining measurements of chromospheric and photometric activity of stars with near-solar fundamental parameters and rotation periods is important for a better understanding of solar–stellar connection. We select a sample of 2603 stars with near-solar fundamental parameters from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST)-Kepler field and use LAMOST spectra to measure their chromospheric activity and Kepler light curves to measure their photospheric activity (i.e., the amplitude of the photometric variability). While the rotation periods of 1556 of these stars could not be measured due to the low amplitude of the photometric variability and highly irregular temporal profile of light curves, 254 stars were further identified as having near-solar rotation periods. We show that stars with near-solar rotation periods have chromospheric activities that are systematically higher than stars with undetected rotation periods. Furthermore, while the solar level of photospheric and chromospheric activity appears to be typical for stars with undetected rotation periods, the Sun appears to be less active than most stars with near-solar rotation periods (both in terms of photospheric and chromospheric activity).

The emission in the near-ultraviolet Ca ii H and K lines is modulated by stellar magnetic activity. Although this emission, quantified via the S-index, has been serving as a prime proxy of stellar magnetic activity for several decades, many aspects of the complex relation between stellar magnetism and Ca ii H and K emission are still unclear. The amount of measured Ca ii H and K emission is suspected to be affected not only by the stellar intrinsic properties but also by the inclination angle of the stellar rotation axis. Until now, such an inclination effect on the S-index has remained largely unexplored. To fill this gap, we develop a physics-based model to calculate S-index, focusing on the Sun. Using the distributions of solar magnetic features derived from observations together with Ca ii H and K spectra synthesized in non-local thermodynamic equilibrium, we validate our model by successfully reconstructing the observed variations of the solar S-index over four activity cycles. Further, using the distribution of magnetic features over the visible solar disk obtained from surface flux transport simulations, we obtain S-index time series dating back to 1700 and investigate the effect of inclination on S-index variability on both the magnetic activity cycle and the rotational timescales. We find that when going from an equatorial to a pole-on view, the amplitude of S-index variations decreases weakly on the activity cycle timescale and strongly on the rotational timescale (by about 22% and 81%, respectively, for a cycle of intermediate strength). The absolute value of the S-index depends only weakly on the inclination. We provide analytical expressions that model such dependencies.

Quantum interference effects together with partial frequency redistribution (PFR) in line scattering produce subtle signatures in the so called Second Solar Spectrum (the linearly polarized spectrum of the Sun). These signatures are modified in the presence of arbitrary strength magnetic fields via the Hanle, Zeeman, and Paschen-Back effects. In the present paper we solve the problem of polarized line formation in a magnetized atmosphere taking into account scattering in a two-level atom with hyperfine structure splitting together with PFR. To this end we incorporate the collisionless PFR matrix derived in Sowmya et al. (2014) in the polarized transfer equation. We apply the scattering expansion method to solve this transfer equation. We study the combined effects of PFR and Paschen-Back effect on polarized line profiles formed in an isothermal one-dimensional planar atmosphere. For this purpose, we consider the cases of D 2 lines of Li i and Na i.

The quantum interference between the fine structure states of an atom modifies the shapes of the emergent Stokes profiles in the Second Solar Spectrum. This phenomenon has been studied in great detail both in the presence and absence of magnetic fields. By assuming a flat-spectrum for the incident radiation, the signatures of this effect have been explored for arbitrary field strengths. Even though the theory which takes into account the frequency dependence of the incident radiation is well developed, it is restricted to the regime in which the magnetic splitting is much smaller than the fine structure splitting. In the present paper, we carry out a generalization of our scattering matrix formalism including the effects of partial frequency redistribution (PRD) for arbitrary magnetic fields. We test the formalism using available benchmarks for special cases. In particular we apply it to the Li i 6708Å D 1 and D 2 line system, for which observable effects from the Paschen-Back regime are expected in the Sun's spectrum.