Solar Magnetic Flux Tube Simulations with Time-Dependent Ionization

In the present work we expand the study of time-dependent ionization previously identified to be of pivotal importance for acoustic waves in solar magnetic flux tube simulations. We focus on longitudinal tube waves (LTW) known to be an important heating agent of solar magnetic regions. Our models also consider new results of wave energy generation as well as an updated determination of the mixing length of convection now identified as 1.8 scale heights in the upper solar convective layers. We present 1-D wave simulations for the solar chromosphere by studying tubes of different spreading as function of height aimed at representing tubes in environments of different magnetic filling factors. Multi-level radiative transfer has been applied to correctly represent the total chromospheric emission function. The effects of time-dependent ionization are significant in all models studied. They are most pronounced behind strong shocks and in low density regions, i.e., the middle and high chromosphere. Concerning our models of different tube spreading, we attained pronounced differences between the various types of models, which were largely initiated by different degrees of dilution of the wave energy flux as well as the density structure partially shaped by strong shocks, if existing. Models showing a quasi-steady rise of temperature with height are obtained via monochromatic waves akin to previous acoustic simulations. However, longitudinal flux tube waves are identified as insufficient to heat the solar transition region and corona in agreement with previous studies.Comment: 13 pages, 9 figures, 4 tables; Mon. Not. R. Astron. Soc.; in pres

Time-dependent hydrogen ionisation in the solar chromosphere. I: Methods and first results

An approximate method for solving the rate equations for the hydrogen populations was extended and implemented in the three-dimensional radiation (magneto-)hydrodynamics code CO5BOLD. The method is based on a model atom with six energy levels and fixed radiative rates. It has been tested extensively in one-dimensional simulations. The extended method has been used to create a three-dimensional model that extends from the upper convection zone to the chromosphere. The ionisation degree of hydrogen in our time-dependent simulation is comparable to the corresponding equilibrium value up to 500 km above optical depth unity. Above this height, the non-equilibrium ionisation degree is fairly constant over time and space, and tends to be at a value set by hot propagating shock waves. The hydrogen level populations and electron density are much more constant than the corresponding values for statistical equilibrium, too. In contrast, the equilibrium ionisation degree varies by more than 20 orders of magnitude between hot, shocked regions and cool, non-shocked regions. The simulation shows for the first time in 3D that the chromospheric hydrogen ionisation degree and electron density cannot be calculated in equilibrium. Our simulation can provide realistic values of those quantities for detailed radiative transfer computations.Comment: 8 pages, 7 figure

Interplay between microstructural evolution and tribo-chemistry during dry sliding of metals

Understanding the microstructural and tribo-chemical processes during tribological loading is of utmost importance to further improve the tribological behavior of metals. In this study, the friction, wear and tribo-chemical behavior of Ni with different initial microstructures (nanocrystalline, bi-modal, coarse-grained) is investigated under dry sliding conditions. In particular, the interplay be-tween frictional response, microstructural evolution and tribo-oxidation is considered. Friction tests are carried out using ball-on-disk experiments with alumina balls as counter-bodies, varying the load between 1 and 5 N. The microstructural evolution as well as the chemical reactions beneath the samples’ surface is investigated by means of cross-sections. The samples with finer microstructures show a faster run-in and lower maximum values of the coefficient of friction (COF) which can be attributed to higher oxidation kinetics and a higher hardness. It is observed that with increasing sliding cycles, a stable oxide layer is formed. Furthermore, initially coarse-grained samples show grain refinement, whereas initially finer microstructures undergo grain coarsening converging towards the same superficial grain size after 2,000 sliding cycles. Consequently, the experimental evidence supports that, irrespective of the initial microstructure, after a certain deformation almost identical steady-state COF values for all samples are achieved

The energy of waves in the photosphere and lower chromosphere: IV. Inversion results of Ca II H spectra

Most static 1D atmosphere models in the quiet Sun predict a rise of the gas temperature at chromospheric layers, but numerical simulations only yield an increase in the brightness temperature. We investigate the thermal structure in the solar chromosphere as derived from an LTE inversion of Ca II H spectra in QS and active regions. We investigate the temperature stratifications on differences between magnetic and field-free regions in the QS, and between QS and ARs. We determine the energy content of individual calcium bright grains (BGs). The rms temperature fluctuations are below 100 K in the photosphere and 200-300 K in the chromosphere. The average temperature stratification in the QS does not exhibit a clear chromospheric temperature rise, opposite to the AR case. We find an energy content of about 7*10E18 J for BGs that repeat with a cadence of about 160 secs. The precursors of BGs have a vertical extent of about 200 km and a horizontal extent of about 1 Mm. The comparison of observed with synthetic NLTE profiles confirms that the solar chromosphere in the QS oscillates between an atmosphere in radiative equilibrium and one with a moderate chromospheric temperature rise. Two-dimensional x-z temperature maps exhibit nearly horizontal canopy-like structures with a few Mm extent around photospheric magnetic field concentrations at a height of about 600 km. The large difference between QS regions and ARs, and the better match of AR and non-LTE reference spectra suggest that magnetic heating processes are more important than commonly assumed. The temperature fluctuations in QS derived by the LTE inversion do not suffice on average to maintain a stationary chromospheric temperature rise. The spatially and vertically resolved information on the temperature structure allows one to investigate in detail the topology and evolution of the thermal structure in the lower solar atmosphere.Comment: 16 pages, 16 figures + 1 page Appendix, accepted by A&

The energy of waves in the photosphere and lower chromosphere: III. Inversion setup for Ca II H spectra in local thermal equilibrium

The Ca II H line is one of the strongest lines in the solar spectrum and provides continuous information on the solar atmosphere from the photosphere to the lower chromosphere. We describe an inversion approach that reproduces observed Ca II H spectra assuming LTE. We developed an inversion strategy based on the SIR code. The approach uses a two-step procedure with an archive of pre-calculated spectra to fit the line core and a subsequent iterative modification to improve the fit in the line wing. Simultaneous spectra in the 630nm range can optionally be used to fix the continuum temperature. The method retrieves 1D temperature stratifications neglecting lateral radiative transport. LOS velocities are included by an empirical approach. An archive of about 300.000 pre-calculated spectra is more than sufficient to reproduce the line core of observed Ca II H spectra both in quiet Sun and in active regions. The final thermodynamical stratifications match observed and best-fit spectra to a level of about 0.5 (1) % of Ic in the line wing (core). Inversion schemes based on pre-calculated spectra allow one a reliable and relatively fast retrieval of solar properties from observed chromospheric spectra. The approach can be easily extended to an 1D NLTE case by a simple exchange of the pre-calculated archive spectra.Comment: 15 pages, 15 figures, accepted for publication in A&A. The animation will only be provided in the A&A online sectio

Approximations for radiative cooling and heating in the solar chromosphere

Context. The radiative energy balance in the solar chromosphere is dominated by strong spectral lines that are formed out of LTE. It is computationally prohibitive to solve the full equations of radiative transfer and statistical equilibrium in 3D time dependent MHD simulations. Aims. To find simple recipes to compute the radiative energy balance in the dominant lines under solar chromospheric conditions. Methods. We use detailed calculations in time-dependent and 2D MHD snapshots to derive empirical formulae for the radiative cooling and heating. Results. The radiative cooling in neutral hydrogen lines and the Lyman continuum, the H and K and intrared triplet lines of singly ionized calcium and the h and k lines of singly ionized magnesium can be written as a product of an optically thin emission (dependent on temperature), an escape probability (dependent on column mass) and an ionization fraction (dependent on temperature). In the cool pockets of the chromosphere the same transitions contribute to the heating of the gas and similar formulae can be derived for these processes. We finally derive a simple recipe for the radiative heating of the chromosphere from incoming coronal radiation. We compare our recipes with the detailed results and comment on the accuracy and applicability of the recipes.Comment: accepted for publication in Astronomy & Astrophysic

Basal Chromospheric Flux and Maunder Minimum-type Stars: The quiet-Sun Chromosphere as a Universal Phenomenon

Aims: We demonstrate the universal character of the quiet-Sun chromosphere among inactive stars (solar-type and giants). By assessing the main physical processes, we shed new light on some common observational phenomena. Methods: We discuss measurements of the solar Mt. Wilson S-index, obtained by the Hamburg Robotic Telescope around the extreme minimum year 2009, and compare the established chromospheric basal Ca II K line flux to the Mt. Wilson S-index data of inactive ("flat activity") stars, including giants. Results: During the unusually deep and extended activity minimum of 2009, the Sun reached S-index values considerably lower than in any of its previously observed minima. In several brief periods, the Sun coincided exactly with the S-indices of inactive ("flat", presumed Maunder Minimum-type) solar analogues of the Mt. Wilson sample; at the same time, the solar visible surface was also free of any plages or remaining weak activity regions. The corresponding minimum Ca II K flux of the quiet Sun and of the presumed Maunder Minimum-type stars in the Mt. Wilson sample are found to be identical to the corresponding Ca II K chromospheric basal flux limit. Conclusions: We conclude that the quiet-Sun chromosphere is a universal phenomenon among inactive stars. Its mixed-polarity magnetic field, generated by a local, "fast" turbulent dynamo finally provides a natural explanation for the minimal soft X-ray emission observed for inactive stars. Given such a local dynamo also works for giant chromospheres, albeit on larger length scales, i.e., l ~ R/g, with R and g as stellar radius and surface gravity, respectively, the existence of giant spicular phenomena and the guidance of mechanical energy toward the acceleration zone of cool stellar winds along flux-tubes have now become traceable.Comment: 6 pages, 4 figures; Astronomy & Astrophysics (Research Note), in pres

Reversal-free CaIIH profiles: a challenge for solar chromosphere modeling in quiet inter-network

We study chromospheric emission to understand the temperature stratification in the solar chromosphere. We observed the intensity profile of the CaIIH line in a quiet Sun region close to the disk center at the German Vacuum Tower Telescope. We analyze over 10^5 line profiles from inter-network regions. For comparison with the observed profiles, we synthesize spectra for a variety of model atmospheres with a non local thermodynamic equilibrium (NLTE) radiative transfer code. A fraction of about 25% of the observed CaIIH line profiles do not show a measurable emission peak in H_{2v} and H_{2r} wavelength bands (reversal-free). All of the chosen model atmospheres with a temperature rise fail to reproduce such profiles. On the other hand, the synthetic calcium profile of a model atmosphere that has a monotonic decline of the temperature with height shows a reversal-free profile that has much lower intensities than any observed line profile. The observed reversal-free profiles indicate the existence of cool patches in the interior of chromospheric network cells, at least for short time intervals. Our finding is not only in conflict with a full-time hot chromosphere, but also with a very cool chromosphere as found in some dynamic simulations.Comment: 8 pages, accepted in A&