Search

Applications often require a fast, single-threaded search algorithm over sorted data, typical in table-lookup operations. We explore various search algorithms for a large number of search candidates over a relatively small array of logarithmically-distributed sorted data. These include an innovative hash-based search that takes advantage of floating point representation to bin data by the exponent. Algorithms that can be optimized to take advantage of SIMD vector instructions are of particular interest. We then conduct a case study applying our results and analyzing algorithmic performance with the EOSPAC package. EOSPAC is a table look-up library for manipulation and interpolation of SESAME equation-of-state data. Our investigation results in a couple of algorithms with better performance with a best case 8x speedup over the original EOSPAC Hunt-and-Locate implementation. Our techniques are generalizable to other instances of search algorithms seeking to get a performance boost from vectorization.

Under the assumption that the photospheric quiet-Sun magnetic field is turbulent, the cancellation function has previously been used to estimate the true, resolution-independent mean, unsigned vertical flux $<|B_z|>_{\mathrm{true}}$. We show that the presence of network elements, noise, and seeing complicate the measurement of accurate cancellation functions and their power-law exponents $\kappa$. Failure to exclude network elements previously led to too low estimates of both the cancellation exponent $\kappa$ and of $<|B_z|>_{\mathrm{true}}$. However, both $\kappa$ and $<|B_z|>_{\mathrm{true}}$ are over-estimated due to noise in magnetograms. While no conclusive value can be derived with data from current instruments, our {\it Hinode}/SP results of $\kappa\lessapprox0.38$ and $<|B_z|>_{\mathrm{true}}\lessapprox 270 $gauss can be taken as upper bounds., Comment: Accepted for publication in Solar Physics

The migration of magnetic bright point-like features (MBP) in the lower solar atmosphere reflects the dispersal of magnetic flux as well as the horizontal flows of the atmospheric layer they are embedded in. We analyse trajectories of the proper motion of intrinsically magnetic, isolated internetwork Ca II H MBPs (mean lifetime 461 +- 9 s) to obtain their diffusivity behaviour. We use seeing-free high spatial and temporal resolution image sequences of quiet-Sun, disc-centre observations obtained in the Ca II H 3968 {\AA} passband of the Sunrise Filter Imager (SuFI) onboard the Sunrise balloon-borne solar observatory. Small MBPs in the internetwork are automatically tracked. The trajectory of each MBP is then calculated and described by a diffusion index ({\gamma}) and a diffusion coefficient (D). We further explore the distribution of the diffusion indices with the help of a Monte Carlo simulation. We find {\gamma} = 1.69 +- 0.08 and D = 257 +- 32 km^2/s averaged over all MBPs. Trajectories of most MBPs are classified as super-diffusive, i.e., {\gamma} > 1, with the determined {\gamma} being to our knowledge the largest obtained so far. A direct correlation between D and time-scale ({\tau}) determined from trajectories of all MBPs is also obtained. We discuss a simple scenario to explain the diffusivity of the observed, relatively short-lived MBPs while they migrate within a small area in a supergranule (i.e., an internetwork area). We show that the scatter in the {\gamma} values obtained for individual MBPs is due to their limited lifetimes. The super-diffusive MBPs can be well-described as random walkers (due to granular evolution and intergranular turbu- lence) superposed on a large systematic (background) velocity, caused by granular, mesogranular and supergranular flows., Comment: 10 pages, 7 figures, 3 tables

We aim to improve our picture of the low chromosphere in the quiet-Sun internetwork by investigating the intensity, horizontal velocity, size and lifetime variations of small bright points (BPs; diameter smaller than 0.3 arcsec) observed in the Ca II H 3968 {\AA} passband along with their magnetic field parameters, derived from photospheric magnetograms. Several high-quality time series of disc-centre, quiet-Sun observations from the Sunrise balloon-borne solar telescope, with spatial resolution of around 100 km on the solar surface, have been analysed to study the dynamics of BPs observed in the Ca II H passband and their dependence on the photospheric vector magnetogram signal. Parameters such as horizontal velocity, diameter, intensity and lifetime histograms of the isolated internetwork and magnetic Ca II H BPs were determined. Mean values were found to be 2.2 km/s, 0.2 arcsec (150 km), 1.48 average Ca II H quiet-Sun and 673 sec, respectively. Interestingly, the brightness and the horizontal velocity of BPs are anti-correlated. Large excursions (pulses) in horizontal velocity, up to 15 km/s, are present in the trajectories of most BPs. These could excite kink waves travelling into the chromosphere and possibly the corona, which we estimate to carry an energy flux of 310 W/m^2, sufficient to heat the upper layers, although only marginally. The stable observing conditions of Sunrise and our technique for identifying and tracking BPs have allowed us to determine reliable parameters of these features in the internetwork. Thus we find, e.g., that they are considerably longer lived than previously thought. The large velocities are also reliable, and may excite kink waves. Although these wave are (marginally) energetic enough to heat the quiet corona, we expect a large additional contribution from larger magnetic elements populating the network and partly also the internetwork., Comment: 19 pages, 13 figures, 4 tables; Accepted for publication in A&A

The characterization of solar surface differential rotation (SDR) from disk-integrated chromospheric measurements has important implications for the study of differential rotation and dynamo processes in other stars. Some chromospheric lines, such as Ca II K, are very sensitive to the presence of activity on the disk and are an ideal choice for investigating SDR in Sun-as-a star observations. Past studies indicate that when the activity is low, the determination of Sun's differential rotation from integrated-sunlight measurements becomes uncertain. However, our study shows that using the proper technique, SDR can be detected from these type of measurements even during periods of extended solar minima. This paper describes results from the analysis of the temporal variations of Ca II K line profiles observed by the Integrated Sunlight Spectrometer (ISS) during the declining phase of Cycle 23 and the rising phase of Cycle 24, and discusses the signature of SDR in the power spectra computed from time series of parameters derived from these profiles. The described methodology is quite general, and could be applied to photometric time series of other Main-Sequence stars for detecting differential rotation., Comment: Accepted for publication in The Astrophysical Journal. 38 pages, 10 figures

We compare photospheric line-of-sight magnetograms from the Synoptic Long-term Investigations of the Sun (SOLIS) vector spectromagnetograph (VSM) instrument with observations from the 150-foot Solar Tower at Mt. Wilson (MWO), Helioseismic and Magnetic Imager (HMI) on Solar Dynamics Observatory (SDO), and Michelson Doppler Imager (MDI) on Solar and Heliospheric Observatory (SOHO). We find very good agreement between VSM and the other data sources for both disk-averaged flux densities and pixel-by-pixel measurements. We show that the VSM mean flux density time series is of consistently high signal-to-noise with no significant zero-offsets. We discuss in detail some of the factors -spatial resolution, flux dependence and position on the solar disk- affecting the determination of scaling between VSM and SOHO/MDI or SDO/HMI magnetograms. The VSM flux densities agree well with spatially smoothed data from MDI and HMI, although the scaling factors show clear dependence on flux density. The factor to convert VSM to HMI increases with increasing flux density (from $\approx$1 to $\approx$1.5). The nonlinearity is smaller for the VSM vs. ~SOHO/MDI scaling factor (from $\approx$1 to $\approx$1.2)., Comment: Accepted for publication in Solar Physics

We present a methodology to determine the best turbulence closure for an eddy-permitting ocean model through measurement of the error-landscape of the closure's subgrid spectral transfers and flux. We apply this method to 6 different closures for forced-dissipative simulations of the barotropic vorticity equation on a f-plane (2D Navier-Stokes equation). Using a high-resolution benchmark, we compare each closure's model of energy and enstrophy transfer to the actual transfer observed in the benchmark run. The error-landscape norms enable us to both make objective comparisons between the closures and to optimize each closure's free parameter for a fair comparison. The hyper-viscous closure most closely reproduces the enstrophy cascade, especially at larger scales due to the concentration of its dissipative effects to the very smallest scales. The viscous and Leith closures perform nearly as well, especially at smaller scales where all three models were dissipative. The Smagorinsky closure dissipates enstrophy at the wrong scales. The anticipated potential vorticity closure was the only model to reproduce the upscale transfer of kinetic energy from the unresolved scales, but would require high-order Laplacian corrections in order to concentrate dissipation at the smallest scales. The Lagrangian-averaged alpha-model closure did not perform successfully for forced 2D isotropic Navier-Stokes: small-scale filamentation is only slightly reduced by the model while small-scale roll-up is prevented. Together, this reduces the effects of diffusion., Comment: 44 pages, 21 figures, 1 Appendix, submitted to Ocean Modeling

We use SDO/HMI and SOLIS/VSM photospheric magnetic field measurements to model the force-free coronal field above a solar active region, assuming magnetic forces to dominate. We take measurement uncertainties caused by, e.g., noise and the particular inversion technique into account. After searching for the optimum modeling parameters for the particular data sets, we compare the resulting nonlinear force-free model fields. We show the degree of agreement of the coronal field reconstructions from the different data sources by comparing the relative free energy content, the vertical distribution of the magnetic pressure and the vertically integrated current density. Though the longitudinal and transverse magnetic flux measured by the VSM and HMI is clearly different, we find considerable similarities in the modeled fields. This indicates the robustness of the algorithm we use to calculate the nonlinear force-free fields against differences and deficiencies of the photospheric vector maps used as an input. We also depict how much the absolute values of the total force-free, virial and the free magnetic energy differ and how the orientation of the longitudinal and transverse components of the HMI- and VSM-based model volumes compares to each other., Comment: 9 pages, 5 figures

The magnetic field plays a pivotal role in many fields of Astrophysics. This is especially true for the physics of the solar atmosphere. Measuring the magnetic field in the upper solar atmosphere is crucial to understand the nature of the underlying physical processes that drive the violent dynamics of the solar corona -- that can also affect life on Earth. SolmeX, a fully equipped solar space observatory for remote-sensing observations, will provide the first comprehensive measurements of the strength and direction of the magnetic field in the upper solar atmosphere. The mission consists of two spacecraft, one carrying the instruments, and another one in formation flight at a distance of about 200m carrying the occulter to provide an artificial total solar eclipse. This will ensure high-quality coronagraphic observations above the solar limb. Solmex integrates two spectro-polarimetric coronagraphs for off-limb observations, one in the EUV and one in the IR, and three instruments for observations on the disk. The latter comprises one imaging polarimeter in the EUV for coronal studies, a spectro-polarimeter in the EUV to investigate the low corona, and an imaging spectro-polarimeter in the UV for chromospheric studies. SOHO and other existing missions have investigated the emission of the upper atmosphere in detail (not considering polarization), and as this will be the case also for missions planned for the near future. Therefore it is timely that SolmeX provides the final piece of the observational quest by measuring the magnetic field in the upper atmosphere through polarimetric observations., Comment: Submitted to Experimental Astronomy. 30 pages, 19 figures

Understanding the in situ amplification of large scale magnetic fields in turbulent astrophysical rotators has been a core subject of dynamo theory. When turbulent velocities are helical, large scale dynamos that substantially amplify fields on scales that exceed the turbulent forcing scale arise, but the minimum sufficient fractional kinetic helicity f_h,C has not been previously well quantified. Using direct numerical simulations for a simple helical dynamo, we show that f_h,C decreases as the ratio of forcing to large scale wave numbers k_F/k_min increases. From the condition that a large scale helical dynamo must overcome the backreaction from any non-helical field on the large scales, we develop a theory that can explain the simulations. For k_F/k_min>8 we find f_h,C< 3%, implying that very small helicity fractions strongly influence magnetic spectra for even moderate scale separation., Comment: 5 pages, 4 figures

We present high spatial and temporal resolution Ca II 8542 observations of a kink wave in an on-disk chromospheric active region fibril. The properties of the wave are similar to those observed in off-limb spicules. From the observed phase and period of the wave we determine a lower limit for the field strength in the chromospheric active region fibril located at the edge of a sunspot to be a few hundred Gauss. We find indications that the event was triggered by a small-scale reconnection event higher up in the atmosphere., Comment: 16 pages, 6 figures. Accepted for publication in ApJ

The bisector of the strong chromospheric Ca II 854.2 nm line has an inverse-C shape the cause of which is not yet fully understood. We show that the amplitude of the bisector in Sun-as-a-star observations exhibits a solar cycle variation with smaller amplitudes during highest activity. The line core intensity is lower during solar minima while the part of the bisector most sensitive to the line core shows no systematic change with activity. Our results support the use of Ca II 854.2 nm bisectors in studying the relationship between convection and magnetic fields, not only in the Sun but in other stars as well., Comment: Accepted to ApJ

We study the velocity structure of penumbral filaments in the deep photosphere to obtain direct evidence for the convective nature of sunspot penumbrae. A sunspot was observed at high spatial resolution with the 1-m Swedish Solar Telescope in the deep photospheric C I 5380 {\AA} absorption line. The Multi-Object Multi-Frame Blind Deconvolution (MOMFBD) method is used for image restoration and straylight is filtered out. We report here the discovery of clear redshifts in the C I 5380 {\AA} line at multiple locations in sunspot penumbral filaments. For example, bright head of filaments show larger concentrated blueshift and are surrounded by darker, redshifted regions, suggestive of overturning convection. Elongated downflow lanes are also located beside bright penumbral fibrils. Our results provide the strongest evidence yet for the presence of overturning convection in penumbral filaments and highlight the need to observe the deepest layers of the penumbra in order to uncover the energy transport processes taking place there., Comment: accepted for ApJL

We quantify possible differences between turbulent dynamo action in the Sun and the dynamo action studied in idealized simulations. For this purpose we compare Fourier-space shell-to-shell energy transfer rates of three incrementally more complex dynamo simulations: an incompressible, periodic simulation driven by random flow, a simulation of Boussinesq convection, and a simulation of fully compressible convection that includes physics relevant to the near-surface layers of the Sun. For each of the simulations studied, we find that the dynamo mechanism is universal in the kinematic regime because energy is transferred from the turbulent flow to the magnetic field from wavenumbers in the inertial range of the energy spectrum. The addition of physical effects relevant to the solar near-surface layers, including stratification, compressibility, partial ionization, and radiative energy transport, does not appear to affect the nature of the dynamo mechanism. The role of inertial-range shear stresses in magnetic field amplification is independent from outer-scale circumstances, including forcing and stratification. Although the shell-to-shell energy transfer functions have similar properties to those seen in mean-flow driven dynamos in each simulation studied, the saturated states of these simulations are not universal because the flow at the driving wavenumbers is a significant source of energy for the magnetic field., Comment: 16 pages, 9 figures, accepted for publication in ApJ

With the help of a model of magnetohydrodynamic (MHD) turbulence tested previously, we explore high Reynolds number regimes up to equivalent resolutions of 6000^3 grid points in the absence of forcing and with no imposed uniform magnetic field. For the given initial condition chosen here, with equal kinetic and magnetic energy, the flow ends up being dominated by the magnetic field, and the dynamics leads to an isotropic Iroshnikov-Kraichnan energy spectrum. However, the locally anisotropic magnetic field fluctuations perpendicular to the local mean field follow a Kolmogorov law. We find that the ratio of the eddy turnover time to the Alfven time increases with wavenumber, contrary to the so-called critical balance hypothesis. Residual energy and helicity spectra are also considered; the role played by the conservation of magnetic helicity is studied, and scaling laws are found for the magnetic helicity and residual helicity spectra. We put these results in the context of the dynamics of a globally isotropic MHD flow which is locally anisotropic because of the influence of the strong large-scale magnetic field, leading to a partial equilibration between kinetic and magnetic modes for the energy and the helicity., Comment: 11 pages, 7 figures, submitted to Phys. Rev. E

Recent observations have revealed that 8% of linear polarization patches in the internetwork quiet Sun are fully embedded in downflows. These are not easily explained with the typical scenarios for the source of internetwork fields which rely on flux emergence from below. We explore using radiative MHD simulations a scenario where magnetic flux is transported from the magnetic canopy overlying the internetwork into the photosphere by means of downward plumes associated with convective overshoot. We find that if a canopy-like magnetic field is present in the simulation, the transport of flux from the canopy is an important process for seeding the photospheric layers of the internetwork with magnetic field. We propose that this mechanism is relevant for the Sun as well, and it could naturally explain the observed internetwork linear polarization patches entirely embedded in downflows., Comment: Accepted to ApJ

We present the first observations of the transverse component of photospheric magnetic field acquired by the imaging magnetograph Sunrise/IMaX. Using an automated detection method, we obtain statistical properties of 4536 features with significant linear polarization signal. Their rate of occurrence is 1-2 orders of magnitude larger than values reported by previous studies. We show that these features have no characteristic size or lifetime. They appear preferentially at granule boundaries with most of them being caught in downflow lanes at some point in their evolution. Only a small percentage are entirely and constantly embedded in upflows (16%) or downflows (8%)., Comment: Accepted for the Sunrise Special Issue of ApJL

Context: The expansion of network magnetic fields with height is a fundamental property of flux tube models. A rapid expansion is required to form a magnetic canopy. Aims: We characterize the observed expansion properties of magnetic network elements and compare them with the thin flux tube and sheet approximations, as well as with magnetoconvection simulations. Methods: We used data from the Hinode SOT NFI NaD1 channel and spectropolarimeter to study the appearance of magnetic flux concentrations seen in circular polarization as a function of position on the solar disk. We compared the observations with synthetic observables from models based on the thin flux tube approximation and magnetoconvection simulations with two different upper boundary conditions for the magnetic field (potential and vertical). Results: The observed circular polarization signal of magnetic flux concentrations changes from unipolar at disk center to bipolar near the limb, which implies an expanding magnetic field. The observed expansion agrees with expansion properties derived from the thin flux sheet and tube approximations. Magnetoconvection simulations with a potential field as the upper boundary condition for the magnetic field also produce bipolar features near the limb while a simulation with a vertical field boundary condition does not. Conclusions: The near-limb apparent bipolar magnetic features seen in high-resolution Hinode observations can be interpreted using a simple flux sheet or tube model. This lends further support to the idea that magnetic features with vastly varying sizes have similar relative expansion rates. The numerical simulations presented here are less useful in interpreting the expansion since the diagnostics we are interested in are strongly influenced by the choice of the upper boundary condition for the magnetic field in the purely photospheric simulations., Comment: accepted for publication in A&A

Context: Using unique quadrature observations with the two STEREO spacecraft, we investigate coronal dimmings at the onset of small-scale eruptions. In CMEs they are believed to indicate the opening up of the coronal magnetic fields at the start of the eruption. Aims: It is to determine whether coronal dimming seen in small-scale eruptions starts before or after chromospheric plasma ejection. Methods: One STEREO spacecraft obtained high cadence, 75 s, images in the He II 304A channel, and the other simultaneous images in the Fe IX/FeX 171A channel. We concentrate on two well-positioned chromospheric eruptions that occurred at disk center in the 171A images, and on the limb in 304A. One was in the quiet Sun and the other was in an equatorial coronal hole. We compare the timing of chromospheric eruption seen in the 304A limb images with the brightenings and dimmings seen on disk in the 171A images. Further we use off-limb images of the low frequency 171A power to infer the coronal structure near the eruptions. Results: In both the quiet Sun and the coronal hole eruption, on disk 171A dimming was seen before the chromospheric eruption, and in both cases it extends beyond the site of the chromospheric eruption. The quiet Sun eruption occurred on the outer edge of the enclosing magnetic field of a prominence and may be related to a small disruption of the prominence just before the 171A dimming. Conclusions: These small-scale chromospheric eruptions started with a dimming in coronal emission just like their larger counterparts. We therefore suggest that a fundamental step in triggering them was the removal of overlying coronal field., Comment: 4 pages, 8 figures. To appear A&A Letters. Movies accompanying this Letter are at http://www.mps.mpg.de/data/outgoing/innes/dims/

One goal of helioseismology is to determine the subsurface structure of sunspots. In order to do so, it is important to understand first the near-surface effects of sunspots on solar waves, which are dominant. Here we construct simplified, cylindrically-symmetric sunspot models, which are designed to capture the magnetic and thermodynamics effects coming from about 500 km below the quiet-Sun $\tau_{5000}=1$ level to the lower chromosphere. We use a combination of existing semi-empirical models of sunspot thermodynamic structure (density, temperature, pressure): the umbral model of Maltby et al. (1986) and the penumbral model of Ding and Fang (1989). The OPAL equation of state tables are used to derive the sound speed profile. We smoothly merge the near-surface properties to the quiet-Sun values about 1mm below the surface. The umbral and penumbral radii are free parameters. The magnetic field is added to the thermodynamic structure, without requiring magnetostatic equilibrium. The vertical component of the magnetic field is assumed to have a Gaussian horizontal profile, with a maximum surface field strength fixed by surface observations. The full magnetic field vector is solenoidal and determined by the on-axis vertical field, which, at the surface, is chosen such that the field inclination is 45$^\circ$ at the umbral-penumbral boundary. We construct a particular sunspot model based on SOHO/MDI observations of the sunspot in active region NOAA 9787. The helioseismic signature of the model sunspot is studied using numerical simulations of the propagation of f, p$_1$, and p$_2$ wave packets. These simulations are compared against cross-covariances of the observed wave field. We find that the sunspot model gives a helioseismic signature that is similar to the observations., Comment: 18 pages, 9 Figures submitted to Solar Physics

The existence of a turbulent small-scale solar surface dynamo is likely, considering existing numerical and laboratory experiments, as well as comparisons of a small-scale dynamo in MURaM simulations with Hinode observations. We find the observed peaked probability distribution function (PDF) from Stokes-V magnetograms is consistent with a monotonic PDF of the actual vertical field strength. The cancellation function of the vertical flux density from a Hinode SP observation is found to follow a self-similar power law over two decades in length scales down to the ~200 km resolution limit. This provides observational evidence that the scales of magnetic structuring in the photosphere extend at least down to 20 km. From the power law, we determine a lower bound for the true quiet-Sun mean vertical unsigned flux density of ~43 G, consistent with our numerically-based estimates that 80% or more of the vertical unsigned flux should be invisible to Stokes-V observations at a resolution of 200 km owing to cancellation. Our estimates significantly reduce the order-of-magnitude discrepancy between Zeeman- and Hanle-based estimates., Comment: Proceedings of the Second Hinode Science Meeting, ASP Series 2009. 8 pages, 4 figures

The subfilter-scale (SFS) physics of regularization models are investigated to understand the regularizations' performance as SFS models. The strong suppression of spectrally local SFS interactions and the conservation of small-scale circulation in the Lagrangian-averaged Navier-Stokes alpha-model (LANS-alpha) is found to lead to the formation of rigid bodies. These contaminate the superfilter-scale energy spectrum with a scaling that approaches k^1 as the SFS spectra is resolved. The Clark-alpha and Leray-alpha models, truncations of LANS-alpha, do not conserve small-scale circulation and do not develop rigid bodies. LANS-alpha, however, is closest to Navier-Stokes in intermittency properties. All three models are found to be stable at high Reynolds number. Differences between L^2 and H^1 norm models are clarified. For magnetohydrodynamics (MHD), the presence of the Lorentz force as a source (or sink) for circulation and as a facilitator of both spectrally nonlocal large to small scale interactions as well as local SFS interactions prevents the formation of rigid bodies in Lagrangian-averaged MHD (LAMHD-alpha). We find LAMHD-alpha performs well as a predictor of superfilter-scale energy spectra and of intermittent current sheets at high Reynolds numbers. We expect it may prove to be a generally applicable MHD-LES., Comment: Proceedings of the Quality and Reliability of Large-Eddy Simulations II 2009 Workshop, Springer ERCOFTAC volume 16 (2011); submitted to Journal of Scientific Computing; 22 pages, 8 figures

We demonstrate that a magneto-convection simulation incorporating essential physical processes governing solar surface convection exhibits turbulent small-scale dynamo action. By presenting a derivation of the energy balance equation and transfer functions for compressible magnetohydrodynamics (MHD), we quantify the source of magnetic energy on a scale-by-scale basis. We rule out the two alternative mechanisms for the generation of small-scale magnetic field in the simulations: the tangling of magnetic field lines associated with the turbulent cascade and Alfvenization of small-scale velocity fluctuations ("turbulent induction"). Instead, we find the dominant source of small-scale magnetic energy is stretching by inertial-range fluid motions of small-scale magnetic field lines against the magnetic tension force to produce (against Ohmic dissipation) more small-scale magnetic field. The scales involved become smaller with increasing Reynolds number, which identifies the dynamo as a small-scale turbulent dynamo., Comment: accepted by ApJ

Context: Except for the Ca II resonance lines, fibrils are ubiquitously present in most high-resolution observations of chromospheric lines. Aims: We show that fibrils are also a prevailing feature in Ca II K, provided the spatial-resolution is sufficiently high. Methods: We present high spatial resolution observations of an active region in the Ca I} K line from the Swedish Solar Telescope. Through a comparison between photospheric intensity and magnetic field data, we study the connection between bright chromospheric fibrils and photospheric structures. Additionally, using Fourier analysis we study how the fibrils are linked to the observed dynamics. Results: We find that very narrow, bright fibrils are a prevailing feature over large portions of the observed field. We also find a clear connection between the fibril footpoints and photospheric magnetic features. We show that the fibrils play two distinct roles in the observed dynamics: depending on their location they can act as a canopy suppressing oscillations or they can channel low-frequency oscillations into the chromosphere. Conclusions: The Ca II K fibrils share many characteristics with fibrils observed in other chromospheric lines, but some features, such as the very small widths, are unique to these observations., Comment: To be published in A&A. High resolution version can be downloaded from: http://www.mps.mpg.de/homes/pietarila/fibrils.pdf

We present two models for turbulent flows with periodic boundary conditions and with either rotation, or a magnetic field in the magnetohydrodynamics (MHD) limit. One model, based on Lagrangian averaging, can be viewed as an invariant-preserving filter, whereas the other model, based on spectral closures, generalizes the concepts of eddy viscosity and eddy noise. These models, when used separately or in conjunction, may lead to substantial savings for modeling high Reynolds number flows when checked against high resolution direct numerical simulations (DNS), the examples given here being run on grids of up to 1536^3 points., Comment: 8 pages, 4 figures

Using turbulent MHD simulations (magnetic Reynolds numbers up to 8000) and Hinode observations, we study effects of turbulence on measuring the solar magnetic field outside active regions. Firstly, from synthetic Stokes V profiles for the FeI lines at 630.1 and 630.2 nm, we show that a peaked probability distribution function (PDF) for observationally-derived field estimates is consistent with a monotonic PDF for actual vertical field strengths. Hence, the prevalence of weak fields is greater than would be naively inferred from observations. Secondly, we employ the fractal self-similar geometry of the turbulent solar magnetic field to derive two estimates (numerical and observational) of the true mean vertical unsigned flux density. We also find observational evidence that the scales of magnetic structuring in the photosphere extend at least down to an order of magnitude smaller than 200 km: the self-similar power-law scaling in the signed measure from a Hinode magnetogram ranges (over two decades in length scales and including the granulation scale) down to the 200 km resolution limit. From the self-similar scaling, we determine a lower bound for the true quiet-Sun mean vertical unsigned flux density of ~50 G. This is consistent with our numerically-based estimates that 80% or more of the vertical unsigned flux should be invisible to Stokes-V observations at a resolution of 200 km owing to the cancellation of signal from opposite magnetic polarities. Our estimates significantly reduce the order-of-magnitude discrepancy between Zeeman- and Hanle-based estimates., Comment: 26 pages, 9 figures

We demonstrate that, for the case of quasi-equipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics alpha-model (LAMHD) reproduces well both the large-scale and small-scale properties of turbulent flows; in particular, it displays no increased (super-filter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the sub-filter-scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes alpha-model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of super-filter-scale spectral properties. No such regions are found in LAMHD, making this method capable of large reductions in required numerical degrees of freedom; specifically, we find a reduction factor of 200 when compared to a direct numerical simulation on a large grid of 1536^3 points at the same Reynolds number., Comment: 22 pages, 9 figures; accepted Phys.Rev.E

We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier-Stokes. The consequences on the applicability of the regularizations as SGS models are also shown by examining their effects on superfilter-scale properties. Numerical solutions of the Clark-alpha model are compared to two previously employed regularizations, LANS-alpha and Leray-alpha (at Re ~ 3300, Taylor Re ~ 790) and to a DNS. We derive the Karman-Howarth equation for both the Clark-alpha and Leray-alpha models. We confirm one of two possible scalings resulting from this equation for Clark as well as its associated k^(-1) energy spectrum. At sub-filter scales, Clark-alpha possesses similar total dissipation and characteristic time to reach a statistical turbulent steady-state as Navier-Stokes, but exhibits greater intermittency. As a SGS model, Clark reproduces the energy spectrum and intermittency properties of the DNS. For the Leray model, increasing the filter width decreases the nonlinearity and the effective Re is substantially decreased. Even for the smallest value of alpha studied, Leray-alpha was inadequate as a SGS model. The LANS energy spectrum k^1, consistent with its so-called "rigid bodies," precludes a reproduction of the large-scale energy spectrum of the DNS at high Re while achieving a large reduction in resolution. However, that this same feature reduces its intermittency compared to Clark-alpha (which shares a similar Karman-Howarth equation). Clark is found to be the best approximation for reproducing the total dissipation rate and the energy spectrum at scales larger than alpha, whereas high-order intermittency properties for larger values of alpha are best reproduced by LANS-alpha., Comment: 21 pages, 8 figures

We study non-LTE inversions of the Ca II infrared triplet lines as a tool for inferring physical properties of the quiet Sun. The inversion code is successful in recovering the temperature, velocity and longitudinal magnetic flux density in the photosphere and chromosphere, but the height range where the inversions are sensitive is limited, especially in the chromosphere. We present results of inverting spectropolarimetric observations of the lines in a quiet Sun region. We find three distinct ranges in chromospheric temperature: low temperatures in the internetwork, high temperatures in the enhanced magnetic network and intermediate temperatures associated with low magnetic flux regions in the network. The differences between these regions become more pronounced with height as the plasma-$\beta$ decreases. These inversions support the picture of the chromosphere, especially close to the magnetic network, being highly inhomogeneous both in the vertical and horizontal directions., Comment: 31 pages, 13 figures, accepted to ApJ

We compute solutions of the Lagrangian-Averaged Navier-Stokes alpha-model (LANS) for significantly higher Reynolds numbers (up to Re 8300) than have previously been accomplished. This allows sufficient separation of scales to observe a Navier-Stokes (NS) inertial range followed by a 2nd LANS inertial range. The analysis of the third-order structure function scaling supports the predicted l^3 scaling; it corresponds to a k^(-1) scaling of the energy spectrum. The energy spectrum itself shows a different scaling which goes as k^1. This latter spectrum is consistent with the absence of stretching in the sub-filter scales due to the Taylor frozen-in hypothesis employed as a closure in the derivation of LANS. These two scalings are conjectured to coexist in different spatial portions of the flow. The l^3 (E(k) k^(-1)) scaling is subdominant to k^1 in the energy spectrum, but the l^3 scaling is responsible for the direct energy cascade, as no cascade can result from motions with no internal degrees of freedom. We verify the prediction for the size of the LANS attractor resulting from this scaling. From this, we give a methodology either for arriving at grid-independent solutions for LANS, or for obtaining a formulation of a LES optimal in the context of the alpha models. The fully converged grid-independent LANS may not be the best approximation to a direct numerical simulation of the NS equations since the minimum error is a balance between truncation errors and the approximation error due to using LANS instead of the primitive equations. Furthermore, the small-scale behavior of LANS contributes to a reduction of flux at constant energy, leading to a shallower energy spectrum for large alpha. These small-scale features, do not preclude LANS to reproduce correctly the intermittency properties of high Re flow., Comment: 37 pages, 17 figures

We present a study of two spectral lines, Fe I 6173 Angstroms and Ni I 6768 Angstroms, that were candidates to be used in the Helioseismic and Magnetic Imager (HMI) for observing Doppler velocity and the vector magnetic field. The line profiles were studied using the Mt. Wilson Observatory, the Advanced Stokes Polarimeter and the Kitt Peak McMath telescope and one meter Fourier transform spectrometer atlas. Both Fe I and Ni I profiles have clean continua and no blends that threaten instrument performance. The Fe I line is 2% deeper, 15% narrower and has a 6% smaller equivalent width than the Ni I line. The potential of each spectral line to recover pre-assigned solar conditions is tested using a least-squares minimization technique to fit Milne-Eddington models to tens of thousands of line profiles that have been sampled at five spectral positions across the line. Overall, the Fe I line has a better performance than the Ni I line for vector magnetic field retrieval. We selected the Fe I spectral line for use in HMI due to its better performance for magnetic diagnostics while not sacrificing velocity information.

The Ca II infrared triplet around 8540 A is a good candidate for observing chromospheric magnetism. We show results from combining a radiation hydrodynamic simulation with a Stokes synthesis code. The simulation shows interesting time-varying behavior of the Stokes V profiles as waves propagate through the lines' formation regions. Disappearing and reappearing lobes in the Stokes V profiles as well as profile asymmetries are closely related to the atmospheric velocity gradients., Comment: Submitted to ApJ

SPINOR is a new spectro-polarimeter that will serve as a facility instrument for the Dunn Solar Telescope at the National Solar Observatory. This instrument is capable of achromatic polarimetry over a very broad range of wavelengths, from 430 up to 1600 nm, allowing for the simultaneous observation of several visible and infrared spectral regions with full Stokes polarimetry. Another key feature of the design is its flexibility to observe virtually any combination of spectral lines, limited only by practical considerations (e.g., the number of detectors available, space on the optical bench, etc)., Comment: To appear in Solar Physics. Note: Figures are low resolution versions due to file size limitations

Ellerman bombs are bright emission features observed in the wings of H$\alpha$, usually in the vicinity of magnetic concentrations. Here we show that they can also be detected in the Ca II infrared triplet lines, which are easier to interpret and therefore allow for more detailed diagnostics. We present full Stokes observations of the 849.8 and 854.2 nm lines acquired with the new spectro-polarimeter SPINOR. The data shows no significant linear polarization at the level of 3x10$^{-4}$. The circular polarization profiles exhibit measureable signals with a very intricate pattern of peaks. A non-LTE analysis of the spectral profiles emerging from these features reveal the presence of strong downflows (~10 km/s) in a hot layer between the upper photosphere and the lower chromosphere., Comment: Submitted to Solar Physics

We present an extension of the Karman-Howarth theorem to the Lagrangian averaged magnetohydrodynamic (LAMHD-alpha) equations. The scaling laws resulting as a corollary of this theorem are studied in numerical simulations, as well as the scaling of the longitudinal structure function exponents indicative of intermittency. Numerical simulations for a magnetic Prandtl number equal to unity are presented both for freely decaying and for forced two dimensional MHD turbulence, solving directly the MHD equations, and employing the LAMHD-alpha equations at 1/2 and 1/4 resolution. Linear scaling of the third-order structure function with length is observed. The LAMHD-alpha equations also capture the anomalous scaling of the longitudinal structure function exponents up to order 8., Comment: 34 pages, 7 figures author institution addresses added magnetic Prandtl number stated clearly

We present direct numerical simulations and Lagrangian averaged (also known as alpha-model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha-model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations. The alpha-model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed., Comment: Finite size box effects have been taken into account in the definition of the partition function. This has resulted in a more clear scaling in all figures. Several points are clarified in the text