Point spread functions for the Solar Optical Telescope onboard Hinode

The combined PSF of the BFI and the SOT onboard the Hinode spacecraft is investigated. Observations of the Mercury transit from November 2006 and the solar eclipse(s) from 2007 are used to determine the PSFs of SOT for the blue, green, and red continuum channels of the BFI. For each channel large grids of theoretical point spread functions are calculated by convolution of the ideal diffraction-limited PSF and Voigt profiles. These PSFs are applied to artificial images of an eclipse and a Mercury transit. The comparison of the resulting artificial intensity profiles across the terminator and the corresponding observed profiles yields a quality measure for each case. The optimum PSF for each observed image is indicated by the best fit. The observed images of the Mercury transit and the eclipses exhibit a clear proportional relation between the residual intensity and the overall light level in the telescope. In addition there is a anisotropic stray-light contribution. ... BFI/SOT operate close to the diffraction limit and have only a rather small stray-light contribution. The FWHM of the PSF is broadened by only ~1% with respect to the diffraction-limited case, while the overall Strehl ratio is ~ 0.8. In view of the large variations -- best seen in the residual intensities of eclipse images -- and the dependence on the overall light level and position in the FOV, a range of PSFs should be considered instead of a single PSF per wavelength. The individual PSFs of that range allow then the determination of error margins for the quantity under investigation. Nevertheless the stray-light contributions are here found to be best matched with Voigt functions with the parameters sigma = 0."008 and gamma = 0."004, 0."005, and 0."006 for the blue, green, and red continuum channels, respectively.Comment: 14 pages, 9 figures, accepted by A&

Small-scale structure and dynamics of the lower solar atmosphere

The chromosphere of the quiet Sun is a highly intermittent and dynamic phenomenon. Three-dimensional radiation (magneto-)hydrodynamic simulations exhibit a mesh-like pattern of hot shock fronts and cool expanding post-shock regions in the sub-canopy part of the inter-network. This domain might be called "fluctosphere". The pattern is produced by propagating shock waves, which are excited at the top of the convection zone and in the photospheric overshoot layer. New high-resolution observations reveal a ubiquitous small-scale pattern of bright structures and dark regions in-between. Although it qualitatively resembles the picture seen in models, more observations - e.g. with the future ALMA - are needed for thorough comparisons with present and future models. Quantitative comparisons demand for synthetic intensity maps and spectra for the three-dimensional (magneto-)hydrodynamic simulations. The necessary radiative transfer calculations, which have to take into account deviations from local thermodynamic equilibrium, are computationally very involved so that no reliable results have been produced so far. Until this task becomes feasible, we have to rely on careful qualitative comparisons of simulations and observations. Here we discuss what effects have to be considered for such a comparison. Nevertheless we are now on the verge of assembling a comprehensive picture of the solar chromosphere in inter-network regions as dynamic interplay of shock waves and structuring and guiding magnetic fields.Comment: 8 pages, 2 figures, to appear in the proceedings of the IAU Symposium No. 247, Waves & Oscillations in the Solar Atmosphere: Heating and Magneto-Seismology (Venezuela 2007

Dynamic Models of the Sun from the Convection Zone to the Chromosphere

The chromosphere in internetwork regions of the quiet Sun was regarded as a static and homogeneous layer for a long time. Thanks to advances in observations and numerical modelling, the wave nature of these atmospheric regions received increasing attention during the last decade. Recent three-dimensional radiation magnetohydrodynamic simulations with CO5BOLD feature the chromosphere of internetwork regions as a dynamic and intermittent phenomenon. It is a direct product of interacting waves that form a mesh-like pattern of hot shock fronts and cool post-shock regions. The waves are excited self-consistently at the top of the convection zone. In the middle chromosphere above an average height of 1000 km, plasma beta gets larger than one and magnetic fields become more important. The model chromosphere exhibits a magnetic field that is much more homogeneous than in the layers below and evolves much faster. That includes fast propagating (MHD) waves. Further improvements of the simulations like time-dependent hydrogen ionisation are currently in progress. This class of models is capable of explaining apparently contradicting diagnostics such as carbon monoxide and UV emission at the same time.Comment: 6 pages, 2 figures, to appear in proceedings of IAU symposium 239, August 21 - 25, 2006, Pragu

Three-dimensional magnetohydrodynamic simulations of M-dwarf chromospheres

We present first results from three-dimensional radiation magnetohydrodynamic simulations of M-type dwarf stars with CO5BOLD. The local models include the top of the convection zone, the photosphere, and the chromosphere. The results are illustrated for models with an effective temperature of 3240 K and a gravitational acceleration of log g = 4.5, which represent analogues of AD Leo. The models have different initial magnetic field strengths and field topologies. This first generation of models demonstrates that the atmospheres of M-dwarfs are highly dynamic and intermittent. Magnetic fields and propagating shock waves produce a complicated fine-structure, which is clearly visible in synthetic intensity maps in the core of the Ca II K spectral line and also at millimeter wavelengths. The dynamic small-scale pattern cannot be described by means of one-dimensional models, which has important implications for the construction of semi-empirical model atmospheres and thus for the interpretation of observations in general. Detailed three-dimensional numerical simulations are valuable in this respect. Furthermore, such models facilitate the analysis of small-scale processes, which cannot be observed on stars but nevertheless might be essential for understanding M-dwarf atmospheres and their activity. An example are so-called "magnetic tornadoes", which have recently been found on the Sun and are presented here in M-dwarf models for the first time.Comment: 4 pages, 4 figures; proceedings article, CoolStars 17 (June 2012); accepted version, Astron. Nachr. 334, issue 1-2, 133-136 (2013); published online 2013 Feb

Vortices, shocks, and heating in the solar photosphere: effect of a magnetic field

Aims: We study the differences between non-magnetic and magnetic regions in the flow and thermal structure of the upper solar photosphere. Methods: Radiative MHD simulations representing a quiet region and a plage region, respectively, which extend into the layers around the temperature minimum, are analyzed. Results: The flow structure in the upper photospheric layers of the two simulations is considerably different: the non-magnetic simulation is dominated by a pattern of moving shock fronts while the magnetic simulation shows vertically extended vortices associated with magnetic flux concentrations. Both kinds of structures induce substantial local heating. The resulting average temperature profiles are characterized by a steep rise above the temperature minimum due to shock heating in the non-magnetic case and by a flat photospheric temperature gradient mainly caused by Ohmic dissipation in the magnetic run. Conclusions: Shocks in the quiet Sun and vortices in the strongly magnetized regions represent the dominant flow structures in the layers around the temperature minimum. They are closely connected with dissipation processes providing localized heating.Comment: Accepted for publicaton in A&

Non-equilibrium calcium ionisation in the solar atmosphere

Our aim is to determine the dominant processes and timescales for the ionisation equilibrium of calcium under solar chromospheric conditions. The study is based on numerical simulations with the RADYN code, which includes hydrodynamics, radiative transfer, and a detailed non-equilibrium treatment of hydrogen, calcium, and helium. The simulations are characterised by upwards propagating shock waves, which cause strong temperature fluctuations and variations of the ionisation degree of calcium. The passage of a hot shock front leads to a strong net ionisation of Ca II, rapidly followed by net recombination. The relaxation timescale of the Ca ionisation state is found to be of the order of a few seconds at the top of the photosphere and 10 to 30 s in the upper chromosphere. Generally, the timescales are significantly reduced in the wakes of hot shock fronts. The timescales can be reliably determined from a simple analysis of the eigenvalues of the transition rate matrix. The timescales are dominated by the radiative recombination from Ca III into the metastable Ca II energy levels of the 4d 2D term. These transitions depend strongly on the density of free electrons and therefore on the (non-equilibrium) ionisation degree of hydrogen, which is the main electron donor. The ionisation/recombination timescales derived here are too long for the assumption of an instantaneous ionisation equilibrium to be valid and, on the other hand, are not long enough to warrant an assumption of a constant ionisation fraction. Fortunately, the ionisation degree of Ca II remains small in the height range, where the cores of the H, K, and the infrared triplet lines are formed. We conclude that the difference due to a detailed treatment of Ca ionisation has only negligible impact on the modelling of spectral lines of Ca II and the plasma properties under the conditions in the quiet solar chromosphere.Comment: 9 pages, 8 figures; recommended for publicatio

Carbon monoxide in the solar atmosphere II. Radiative cooling by CO lines

The role of carbon monoxide as a cooling agent for the thermal structure of the mid-photospheric to low-chromospheric layers of the solar atmosphere in internetwork regions is investigated. The treatment of radiative cooling via spectral lines of carbon monoxide (CO) has been added to the radiation chemo-hydrodynamics code CO5BOLD. [...] The CO opacity indeed causes additional cooling at the fronts of propagating shock waves in the chromosphere. There, the time-dependent approach results in a higher CO number density compared to the equilibrium case and hence in a larger net radiative cooling rate. The average gas temperature stratification of the model atmosphere, however, is only reduced by roughly 100 K. Also the temperature fluctuations and the CO number density are only affected to small extent. A numerical experiment without dynamics shows that the CO cooling process works in principle and drives the atmosphere to a cool radiative equilibrium state. At chromospheric heights, the radiative relaxation of the atmosphere to a cool state takes several 1000 s. The CO cooling process thus would seem to be too slow compared to atmospheric dynamics to be responsible for the very cool temperature regions observed in the solar atmosphere. The hydrodynamical timescales in our solar atmosphere model are much too short to allow for the radiative relaxation to a cool state, thus suppressing the potential thermal instability due to carbon monoxide as a cooling agent. Apparently, the thermal structure and dynamics of the outer model atmosphere are instead determined primarily by shock waves.Comment: 5 pages, 4 figures. A&A, accepted 06/12/200