D. M. Fluri

POLARIZED REFLECTED LIGHT FROM THE EXOPLANET HD189733b: FIRST MULTICOLOR OBSERVATIONS AND CONFIRMATION OF DETECTION

We report the first multicolor polarimetric measurements (UBV bands) for the hot Jupiter HD189733b and confirm our previously reported detection of polarization in the B band. The wavelength dependence of polarization indicates the dominance of Rayleigh scattering with a peak in the blue B and U bands of ~10–4 ± 10–5 and at least a factor of two lower signal in the V band. The Rayleigh-like wavelength dependence, also detected in the transmitted light during transits, implies a rapid decrease of the polarization signal toward longer wavelengths. Therefore, the nondetection by Wiktorowicz, based on a measurement integrated within a broad passband covering the V band and partly covering the B and R bands, is inconclusive and consistent with our detection in B. We discuss possible sources of the polarization and demonstrate that effects of incomplete cancellation of stellar limb polarization due to starspots or tidal perturbations are negligible as compared with scattering polarization in the planetary atmosphere. We compare the observations with a Rayleigh-Lambert model and determine effective radii and geometrical albedos for different wavelengths. We find a close similarity of the wavelength-dependent geometrical albedo with that of the Neptune atmosphere, which is known to be strongly influenced by Rayleigh and Raman scattering. Our result establishes polarimetry as a reliable means for directly studying exoplanetary atmospheres.

First Detection of Polarized Scattered Light from an Exoplanetary Atmosphere

We report the first direct detection of an exoplanet in the visible polarized light. The transiting planet HD 189733b is one of the very hot Jupiters with shortest periods and, thus, smallest orbits, which makes them ideal candidates for polarimetric detections. We obtained polarimetric measurements of HD 189733 in the B band well distributed over the orbital period and detected two polarization maxima near planetary elongations with a peak amplitude of ∼2 # 10 . Assuming Rayleigh scattering, we estimated the effective size of the scattering atmo4 sphere (Lambert sphere) to be 1.5 0.2 , which is 30% larger than the radius of the opaque body previously RJ inferred from transits. If the scattering matter fills the planetary Roche lobe, the lower limit of the geometrical albedo can be estimated as 0.14. The phase dependence of polarization indicates that the planetary orbit is oriented almost in a north-south direction with a longitude of ascending node Q p (16 or 196) 8. We obtain independent estimates of the orbit inclination i p 98 8 and eccentricity e p 0.0 (with an uncertainty of 0.05), which are in excellent agreement with values determined previously from transits and radial velocities. Our findings clearly demonstrate the power of polarimetry and open a new dimension in exploring exoplanetary atmospheres even for systems without transits. Subject headings: planetary systems — stars: individual (HD 189733)techniques: polarimetric Online material: color figures

Comparison between KPVT/SPM and SoHO/MDI magnetograms with an application to solar irradiance reconstructions

To be able to use both space- and ground-based solar magnetograms and construct long time series of derived parameters it is important to cross-calibrate them so that we can estimate their reliability and combine them. Using two different techniques, we compare magnetograms as well as continuum images recorded by the Spectropolarimeter (SPM) on Kitt Peak and the Michelson Doppler Interferometer (MDI) on board SoHO. We find that the result obtained depends on the method used. The method we favour gives almost identical umbral and penumbral areas and very similar total magnetic fluxes in faculae. The magnetic fluxes in umbrae and penumbrae returned by the two instruments, however, differ considerably. We also demonstrate that SPM data can be employed to reconstruct total solar irradiance variations with almost the same accuracy as recently shown for MDI data.

Evidence for the Hanle effect in molecular lines

In many wavelength regions molecular lines dominate the second solar spectrum that results from coherent scattering. Scattering polarization is modified by magnetic fields via the Hanle effect. This allows us to explore the magnetic field regime with weak field strengths and mixed polarities, which is not seen with the Zeeman effect and thus contains complementary information. Molecular lines are particularly well suited to diagnose such turbulent fields because they exhibit a broad range of magnetic sensitivities within narrow spectral regions. Thus, it is possible to employ the technique of the differential Hanle effect, i.e. to obtain field strengths by observing polarization ratios in various lines. We have identified one R- and one P-triplet of C2 at 5140 A and 5141 A, respectively, that satisfy all conditions to be used in the differential Hanle effect. Based on these lines we have developed a model that can diagnose turbulent magnetic fields using the Hanle effect. The tool is sensitive over a broad range of magnetic field strengths from a few Gauss up to several hundred Gauss. This tool has allowed us to find a significant Hanle depolarization of C2 lines in quiet Sun observations, which corresponds to a magnetic field strength of 15 ± 3G.

Scattering polarization in strong chromospheric lines. I. Explanation of the triplet peak structure

Although the triplet polarization structure of the Na  D2 and Ca  4227 A lines in the second solar spectrum has been known for more than two decades, a clear and consistent explanation has been lacking. Here we show that the qualitative profile shape may be explained in terms of the anisotropy of the radiation field and partial frequency redistribution (PRD) effects. The complicated frequency and depth dependence of the anisotropy can be understood in terms of simple arguments that involve the source function gradient and boundary effects. We show in particular that the triplet peak structure of the polarization profile of Na  D2 has basically the same origin as for the Ca  4227 A line. Hyperfine structure and lower-level atomic polarization only modify the core polarization without altering the overall qualitative features. For our calculations we adopt a numerical method that combines the advantages of both the classical formalism with integral source function and the density-matrix formalism. In a first step, a multi-level, PRD-capable MALI code, which solves the statistical equilibrium and the radiative transfer equation self-consistently, computes intensity, opacities and collision rates. Keeping these quantities fixed, we obtain the scattering polarization in a second step by solving the radiative transfer equation for the transitions of interest with the classical formalism, which assumes a two-level atomic model with unpolarized lower level. Quantum interferences and lower-level atomic polarization are included in terms of a wavelength dependent polarizability W2, which is independently obtained with the density-matrix formalism.

NLTE modeling of Stokes vector center-to-limb variations in the CN violet system

Context. The solar surface magnetic field is connected with and even controls most of the solar activity phenomena. Zeeman e ect diagnostics allow for measuring only a small fraction of the fractal-like structured magnetic field. The remaining hidden magnetic fields can only be accessed with the Hanle e ect. Aims. Molecular lines are very convenient for applying the Hanle e ect diagnostics thanks to the broad range of magnetic sensitivities in a narrow spectral region. With the UV version of the Zurich Imaging Polarimeter ZIMPOL II installed at the 45 cm telescope of the Istituto Ricerche Solari Locarno (IRSOL), we simultaneously observed intensity and linear polarization center-to-limb variations in two spectral regions containing the (0,0) and (1,1) bandheads of the CN B 2 X 2 system. Here we present an analysis of these observations. Methods. We have implemented coherent scattering in molecular lines into a NLTE radiative transfer code. A two-step approach was used. First, we separately solved the statistical equilibrium equations and compute opacities and intensity while neglecting polarization. Then we used these quantities as input for calculating scattering polarization and the Hanle e ect. Results. We have found that it is impossible to fit the intensity and polarization simultaneously at di erent limb angles in the framework of standard 1D modeling. The atmosphere models that provide correct intensity center-to-limb variations fail to fit linear polarization center-to-limb variations due to lacking radiation field anisotropy. We had to increase the anisotropy by means of a specially introduced free parameter. This allows us to successfully interpret our observations. We discuss possible reasons for underestimating the anisotropy in the 1D modeling.

A New Mechanism for Polarizing Light from Obscured Stars

Recent spectropolarimetric observations of Herbig Ae/Be stellar systems show linear polarization variability with wavelength and epoch near their obscured Ha emission. Surprisingly, this polarization is not coincident with the Ha emission peak but is variable near the absorptive part of the line profile. With a new and novel model, we show here that this is evidence of optical pumping—anisotropy of the incident radiation that leads to a linear polarization-dependent optical depth within the intervening hydrogen wind or disk cloud. This effect can yield a larger polarization signal than scattering polarization in these systems.

Ca II K polarization as a diagnostic of temperature bifurcation

Aims. We compute the linearly polarized spectrum of Ca ii K caused by coherent scattering and exploit the line for chromospheric diagnosis, with particular attention to temperature bifurcation, by comparing the theory with solar observations. Methods. We numerically solve the statistical equilibrium equations and the radiative transfer equation taking into account polarized coherent scattering with partial frequency redistribution. All calculations are performed in 1D within a plane-parallel atmosphere. Results. We find strong evidence of a chromospheric temperature bifurcation. This suggests that the linearly polarized spectrum of Ca ii K might become a valuable tool to study cool components and the dynamics of the chromosphere independently of observations of molecular CO lines and millimeter and sub-millimeter continua.

The FeH F4 Δ-X4 Δ system. Creating a valuable diagnostic tool to explore solar and stellar magnetic fields

Context. Lines of diatomic molecules are ideal tools for studying cool stellar atmospheres and the internal structure of sunspots and starspots, given their temperature and pressure sensitivities, which are typically higher than in atomic lines. The Wing-Ford FeH F 4 Δ-X 4 Δ system represents such a diatomic molecule that is, in addition, highly sensitive to magnetic fields. The current theoretical description of those transitions that include the involved molecular constants, however, are only based on intensity measurements because polarimetric observations have not been available until now, which limits their diagnostic value. Furthermore, the theory has so far been optimized to reproduce energy levels and line strengths without taking magnetic sensitivities into account. Aims. The FeH F 4 Δ-X 4 Δ system is produced by transitions between two electronic states with the coupling of the angular momenta that is intermediate between limiting Hunds cases (a) and (b). Our goal is to investigate the diagnostic capabilities of the current theoretical description of the molecule FeH. Methods. Using the most precise available Hamiltonian, we carried out the perturbation calculation of the molecular Zeeman effect for this transition and computed the Lande factors of the energy levels and of transitions. We extracted Lande factors from a comparison of observed and calculated Stokes I and V profiles. Certain spectral lines, most frequently with high magnetic sensitivity, exhibited discrepancies between the theory and observations. We extended the theoretical model with a semi-empirical approach to obtain a diagnostic tool that is able to reproduce many of the interesting spectral lines. Results. We find that the current theory successfully reproduces the magnetic properties of a large number of lines in the FeH F 4 Δ-X 4 Δ system and that the modified Hamiltonian allows us to synthesize and successfully reproduce the most sensitive lines. Thus, our observations have provided valuable constraints for determining empirical molecular constants and Lande factors. Conclusions. The FeH F 4 Δ-X 4 Δ system is found to be a very sensitive magnetic diagnostic tool. Polarimetric data of these lines, in contrast to intensity measurements, provide us with more direct and detailed information to study the coolest parts of sunspot and starspot umbrae, as well as cool active dwarfs.

Orbital parameters of extrasolar planets derived from polarimetry

Polarimetry of extrasolar planets becomes a new tool for their investigation, which requires the development of diagnostic techniques and parameter case studies. Our goal is to develop a theoretical model which can be applied to interpret polarimetric observations of extrasolar planets. Here we present a theoretical parameter study that shows the influence of the various involved parameters on the polarization curves. Furthermore, we investigate the robustness of the fitting procedure. We employ the physics of Rayleigh scattering to obtain polarization curves of an unresolved extrasolar planet. Calculations are made for two cases: (i) assuming an angular distribution for the intensity of the scattered light as from a Lambert sphere and for polarization as from a Rayleigh-type scatterer, and (ii) assuming that both the intensity and polarization of the scattered light are distributed according to the Rayleigh law. We show that the difference between these two cases is negligible for the shapes of the polarization curves. In addition, we take the size of the host star into account, which is relevant for hot Jupiters orbiting giant stars.