Theoretical formulation of Doppler redistribution in scattering polarization within the framework of the velocity-space density matrix formalism

Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications by adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the Non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a two-level atom with infinitely sharp upper and lower levels, and we derive the corresponding statistical equilibrium equations neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as R_I) is derived starting from the statistical equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches.Comment: Accepted for publication in Astronomy & Astrophysic

Isotropic inelastic and superelastic collisional rates in a multiterm atom

The spectral line polarization of the radiation emerging from a magnetized astrophysical plasma depends on the state of the atoms within the medium, whose determination requires considering the interactions between the atoms and the magnetic field, between the atoms and photons (radiative transitions), and between the atoms and other material particles (collisional transitions). In applications within the framework of the multiterm model atom (which accounts for quantum interference between magnetic sublevels pertaining either to the same J-level or to different J-levels within the same term) collisional processes are generally neglected when solving the master equation for the atomic density matrix. This is partly due to the lack of experimental data and/or of approximate theoretical expressions for calculating the collisional transfer and relaxation rates (in particular the rates for interference between sublevels pertaining to different J-levels, and the depolarizing rates due to elastic collisions). In this paper we formally define and investigate the transfer and relaxation rates due to isotropic inelastic and superelastic collisions that enter the statistical equilibrium equations of a multiterm atom. Under the hypothesis that the atom-collider interaction can be described by a dipolar operator, we provide expressions that relate the collisional rates for interference between different J-levels to the usual collisional rates for J-level populations. Finally, we apply the general equations to the case of a two-term atom with unpolarized lower term, illustrating the impact of inelastic and superelastic collisions on scattering polarization through radiative transfer calculations in a slab of stellar atmospheric plasma anisotropically illuminated by the photospheric radiation field.Comment: Accepted for publication in Astronomy & Astrophysic

Observational indications of magneto-optical effects in the scattering polarization wings of the Ca I 4227 \AA\ line

Several strong resonance lines, such as H I Ly-$\alpha$, Mg II k, Ca II K, Ca I 4227 \AA\, which are characterized by deep and broad absorption profiles in the solar intensity spectrum, show conspicuous linear scattering polarization signals when observed in quiet regions close to the solar limb. Such signals show a characteristic triplet-peak structure, with a sharp peak in the line core and extended wing lobes. The line core peak is sensitive to the presence of magnetic fields through the Hanle effect, which however is known not to operate in the line wings. Recent theoretical studies indicate that, contrary to what was previously believed, the wing linear polarization signals are also sensitive to the magnetic field through magneto-optical effects (MO). We search for observational indications of this recently discovered physical mechanism in the scattering polarization wings of the Ca I 4227 \AA\ line. We performed a series of spectropolarimetric observations of this line using the Zurich IMaging POLarimeter (ZIMPOL) camera at the Gregory-Coud\'e telescope of IRSOL (Switzerland) and at the GREGOR telescope in Tenerife (Spain). Spatial variations of the total linear polarization degree and of the linear polarization angle are clearly appreciable in the wings of the observed line. We provide a detailed discussion of our observational results, showing that the detected variations always take place in regions where longitudinal magnetic fields are present, thus supporting the theoretical prediction that they are produced by MO effects.Comment: Accepted by A&

Spatial variations of the Sr i 4607 {\AA} scattering polarization peak

Context. The scattering polarization signal observed in the photospheric Sr i 4607 {\AA} line is expected to vary at granular spatial scales. This variation can be due to changes in the magnetic field intensity and orientation (Hanle effect), but also to spatial and temporal variations in the plasma properties. Measuring the spatial variation of such polarization signal would allow us to study the properties of the magnetic fields at subgranular scales, but observations are challenging since both high spatial resolution and high spectropolarimetric sensitivity are required. Aims. We aim to provide observational evidence of the polarization peak spatial variations, and to analyze the correlation they might have with granulation. Methods. Observations conjugating high spatial resolution and high spectropolarimetric precision were performed with the Zurich IMaging POLarimeter, ZIMPOL, at the GREGOR solar telescope, taking advantage of the adaptive optics system and the newly installed image derotator. Results. Spatial variations of the scattering polarization in the Sr i 4607 {\AA} line are clearly observed. The spatial scale of these variations is comparable with the granular size. Small correlations between the polarization signal amplitude and the continuum intensity indicate that the polarization is higher at the center of granules than in the intergranular lanes.Comment: 5 pages, 4 figure

Infrapatellar Fat Pad Stem Cells Responsiveness to Microenvironment in Osteoarthritis: From Morphology to Function

Recently, infrapatellar fat pad (IFP) has been considered as a source of stem cells for cartilage regeneration in osteoarthritis (OA) due to their ability for differentiation into chondrocytes. However, stressful conditions, like that related to OA, may induce a pathogenic reprograming. The aim of this study was to characterize the structural and functional properties of a new population of stem cells isolated from osteoarthritic infrapatellar fat pad (OA-IFP). Nine OA patients undergoing total knee arthroplasty (TKA) were enrolled in this study [median age = 74 years, interquartile range (IQR) = 78.25-67.7; median body mass index = 29.4 Kg/m2, IQR = 31.7-27.4]. OA-IFP stem cells were isolated and characterized for morphology, stemness, metabolic profile and multi-differentiative potential by transmission electron microscopy, flow cytometric analysis, gene expression study and cytochemistry. OA-IFP stem cells displayed a spindle-like morphology, self-renewal potential and responsiveness (CD44, CD105, VEGFR2, FGFR2, IL1R, and IL6R) to microenvironmental stimuli. Characterized by high grade of stemness (STAT3, NOTCH1, c-Myc, OCT-4, KLF4, and NANOG), the cells showed peculiar immunophenotypic properties (CD73+/CD39+/CD90+/CD105+/CD44\u2013/+/CD45\u2013). The expression of HLA-DR, CD34, Fas and FasL was indicative of a possible phenotypic reprograming induced by inflammation. Moreover, the response to mechanical stimuli together with high expression level of COL1A1 gene, suggested their possible protective response against in vivo mechanical overloading. Conversely, the low expression of CD38/NADase was indicative of their inability to counteract NAD+-mediated OA inflammation. Based on the ultrastructural, immunophenotypic and functional characterization, OA-IFP stem cells were hypothesized to be primed by the pathological environment and to exert incomplete protective activity from OA inflammation

Evidence for the Operation of the Hanle and Magneto-Optical Effects in the Scattering Polarization Signals Observed by CLASP2 Across the Mg II h and k Lines

Radiative transfer investigations of the solar Mg II h and k resonance lines around 280~nm showed that, while their circular polarization (Stokes V) signals arise from the Zeeman effect, the linear polarization profiles (Stokes Q and U) are dominated by the scattering of anisotropic radiation and the Hanle and magneto-optical (MO) effects. Using the unprecedented observations of the Mg II and Mn I resonance lines obtained by the Chromospheric LAyer Spectro-Polarimeter (CLASP2), here we investigate how the linear polarization signals at different wavelengths (i.e., at the center, and at the near and far wings of the k line) vary with the longitudinal component of the magnetic field ($B_{L}$) at their approximate height of formation. The $B_{L}$ is estimated from the V signals in the aforementioned spectral lines. Particular attention is given to the following quantities that are expected to be influenced by the presence of magnetic fields through the Hanle and MO effects: the sign of the U signals, the total linear polarization amplitude ($LP$) and its direction ($\chi$) with respect to a reference direction. We find that at the center and near wings of the $k$ line, the behavior of these quantities is significantly different in the observed quiet and plage regions, and that both $LP$ and $\chi$ seem to depend on $B_{L}$. These observational results are indicative of the operation of the Hanle effectComment: 26 pages, 18 figures, accepted for publication in the Astrophysical Journa