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    The Polarimetric and Helioseismic Imager on Solar Orbiter
    (Les Ulis : EDP Sciences , 2020) Solanki, S.K.; del Toro Iniesta, J.C.; Woch, J.; Gandorfer, A.; Hirzberger, J.; Alvarez-Herrero, A.; Appourchaux, T.; Martínez Pillet, V.; Pérez-Grande, I.; Sanchis Kilders, E.; Schmidt, W.; Garranzo-García, D.; Laguna, H.; Martín, J.A.; Navarro, R.; Villanueva, J.; Núñez Peral, A.; Royo, M.; Sánchez, A.; Silva-López, M.; Fourmond, J.-J.; Berkefeld, Th.; Ruiz de Galarreta, C.; Bouzit, M.; Hervier, V.; Le Clec'h, J.C.; Szwec, N.; Chaigneau, M.; Buttice, V.; Volkmer, R.; Dominguez-Tagle, C.; Philippon, A.; Baumgartner, J.; Boumier, P.; Le Cocguen, R.; Baranjuk, G.; Bell, A.; Heidecke, F.; Maue, T.; Blanco Rodríguez, J.; Nakai, E.; Scheiffelen, T.; Sigwarth, M.; Soltau, D.; Domingo, V.; Fiethe, B.; Ferreres Sabater, A.; Gasent Blesa, J.L.; Rodríguez Martínez, P.; Osorno Caudel, D.; Bosch, J.; Casas, A.; Carmona, M.; Gómez Cama, J.M.; Herms, A.; Roma, D.; Guan, Y.; Alonso, G.; Gómez-Sanjuan, A.; Piqueras, J.; Torralbo, I.; Lange, T.; Michel, H.; Michalik, H.; Bonet, J.A.; Fahmy, S.; Müller, D.; Zouganelis, I.; Deutsch, W.; Busse, D.; Fernandez-Rico, G.; Grauf, B.; Gizon, L.; Heerlein, K.; Kolleck, M.; Lagg, A.; Meller, R.; Müller, R.; Schühle, U.; Staub, J.; Enge, R.; Albert, K.; Alvarez Copano, M.; Beckmann, U.; Bischoff, J.; Frahm, S.; Germerott, D.; Guerrero, L.; Löptien, B.; Meierdierks, T.; Oberdorfer, D.; Papagiannaki, I.; Ramanath, S.; Bellot Rubio, L.R.; Schou, J.; Werner, S.; Yang, D.; Zerr, A.; Bergmann, M.; Bochmann, J.; Heinrichs, J.; Meyer, S.; Monecke, M.; Müller, M.-F.; Cobos Carracosa, J.P.; Sperling, M.; Álvarez García, D.; Aparicio, B.; Balaguer Jiménez, M.; Girela, F.; Hernández Expósito, D.; Herranz, M.; Labrousse, P.; López Jiménez, A.; Orozco Suárez, D.; Ramos, J.L.; Barandiarán, J.; Vera, I.; Bastide, L.; Campuzano, C.; Cebollero, M.; Dávila, B.; Fernández-Medina, A.; García Parejo, P.
    This paper describes the Polarimetric and Helioseismic Imager on the Solar Orbiter mission (SO/PHI), the first magnetograph and helioseismology instrument to observe the Sun from outside the Sun-Earth line. It is the key instrument meant to address the top-level science question: How does the solar dynamo work and drive connections between the Sun and the heliosphere? SO/PHI will also play an important role in answering the other top-level science questions of Solar Orbiter, as well as hosting the potential of a rich return in further science. SO/PHI measures the Zeeman effect and the Doppler shift in the FeI 617.3nm spectral line. To this end, the instrument carries out narrow-band imaging spectro-polarimetry using a tunable LiNbO_3 Fabry-Perot etalon, while the polarisation modulation is done with liquid crystal variable retarders (LCVRs). The line and the nearby continuum are sampled at six wavelength points and the data are recorded by a 2kx2k CMOS detector. To save valuable telemetry, the raw data are reduced on board, including being inverted under the assumption of a Milne-Eddington atmosphere, although simpler reduction methods are also available on board. SO/PHI is composed of two telescopes; one, the Full Disc Telescope (FDT), covers the full solar disc at all phases of the orbit, while the other, the High Resolution Telescope (HRT), can resolve structures as small as 200km on the Sun at closest perihelion. The high heat load generated through proximity to the Sun is greatly reduced by the multilayer-coated entrance windows to the two telescopes that allow less than 4% of the total sunlight to enter the instrument, most of it in a narrow wavelength band around the chosen spectral line.
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    Cycle dependence of a quasi-biennial variability in the solar interior
    (Oxford : Oxford Univ. Press, 2022) Mehta, T.; Jain, K.; Tripathy, S.C.; Kiefer, R.; Kolotkov, D.; Broomhall, A.-M.
    We investigated the solar cycle dependence on the presence and periodicity of the Quasi-Biennial Oscillation (QBO). Using helioseismic techniques, we used solar oscillation frequencies from the Global Oscillations Network Group (GONG), Michelson Doppler Imager (MDI), and Helioseismic and Magnetic Imager (HMI) in the intermediate-degree range to investigate the frequency shifts over Cycles 23 and 24. We also examined two solar activity proxies, the F10.7 index and the Mg ii index, for the last four solar cycles to study the associated QBO. The analyses were performed using Empirical Mode Decomposition (EMD) and the Fast Fourier Transform (FFT). We found that the EMD analysis method is susceptible to detecting statistically significant Intrinsic Mode Functions (IMFs) with periodicities that are overtones of the length of the data set under examination. Statistically significant periodicities, which were not due to overtones, were detected in the QBO range. We see a reduced presence of the QBO in Cycle 24 compared to Cycle 23. The presence of the QBO was not sensitive to the depth to which the p-mode travelled, nor the average frequency of the p-mode. The analysis further suggested that the magnetic field responsible for producing the QBO in frequency shifts of p-modes is anchored above approximately 0.95 R⊙.
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    The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element
    (London : Institute of Physics Publ., 2017) Kiefer, René; Schad, Ariane; Roth, Markus
    Where is the solar dynamo located and what is its modus operandi? These are still open questions in solar physics. Helio- and asteroseismology can help answer them by enabling us to study solar and stellar internal structures through global oscillations. The properties of solar and stellar acoustic modes are changing with the level of magnetic activity. However, until now, the inference on subsurface magnetic fields with seismic measures has been very limited. The aim of this paper is to develop a formalism to calculate the effect of large-scale toroidal magnetic fields on solar and stellar global oscillation eigenfunctions and eigenfrequencies. If the Lorentz force is added to the equilibrium equation of motion, stellar eigenmodes can couple. In quasi-degenerate perturbation theory, this coupling, also known as the direct effect, can be quantified by the general matrix element. We present the analytical expression of the matrix element for a superposition of subsurface zonal toroidal magnetic field configurations. The matrix element is important for forward calculations of perturbed solar and stellar eigenfunctions and frequency perturbations. The results presented here will help to ascertain solar and stellar large-scale subsurface magnetic fields, and their geometric configuration, strength, and change over the course of activity cycles.
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    The Effect of Toroidal Magnetic Fields on Solar Oscillation Frequencies
    (London : Institute of Physics Publ., 2018) Kiefer, René; Roth, Markus
    Solar oscillation frequencies change with the level of magnetic activity. Localizing subsurface magnetic field concentrations in the Sun with helioseismology will help us to understand the solar dynamo. Because the magnetic fields are not considered in standard solar models, adding them to the basic equations of stellar structure changes the eigenfunctions and eigenfrequencies. We use quasi-degenerate perturbation theory to calculate the effect of toroidal magnetic fields on solar oscillation mean multiplet frequencies for six field configurations. In our calculations, we consider both the direct effect of the magnetic field, which describes the coupling of modes, and the indirect effect, which accounts for changes in stellar structure due to the magnetic field. We limit our calculations to self-coupling of modes. We find that the magnetic field affects the multiplet frequencies in a way that depends on the location and the geometry of the field inside the Sun. Comparing our theoretical results with observed shifts, we find that strong tachocline fields cannot be responsible for the observed frequency shifts of p modes over the solar cycle. We also find that part of the surface effect in helioseismic oscillation frequencies might be attributed to magnetic fields in the outer layers of the Sun. The theory presented here is also applicable to models of solar-like stars and their oscillation frequencies.