Observations with the Hinode space observatory led to the discovery of predominantly horizontal magnetic fields in the photosphere of the quiet internetwork region. Here we investigate realistic numerical simulations of the surface layers of the Sun with respect to horizontal magnetic fields and compute the corresponding polarimetric response in the Fe I 630 nm line pair. We find a local maximum in the mean strength of the horizontal field component at a height of around 500 km in the photosphere, where it surpasses the vertical component by a factor of 2.0 or 5.6, depending on the initial and boundary conditions. From the synthesized Stokes profiles we derive a mean horizontal field component that is, respectively, 1.6 and 4.3 times stronger than the vertical component. This is a consequence of both the intrinsically stronger flux density of, and the larger area occupied by the horizontal fields. We find that convective overshooting expels horizontal fields to the upper photosphere, making the Poynting flux positive in the photosphere, while this quantity is negative in the convectively unstable layer below it.

Aims. We investigate the relationship between the photospheric magnetic field and the emission of the mid chromosphere of the Sun. Methods. We simultaneously observed the Stokes parameters of the photospheric iron line pair at 630.2 nm and the intensity profile of the chromospheric Ca  H line at 396.8 nm in a quiet Sun region at a heliocentric angle of 53• . Various line parameters have been deduced from the Ca  H line profile. The photospheric magnetic field vector has been reconstructed from an inversion of the measured Stokes profiles. After alignment of the Ca and Fe maps, a common mask has been created to define network and inter-network regions. We perform a statistical analysis of network and inter-network properties. The H-index is the integrated emission in a 0.1 nm band around the Ca core. We separate a non-magnetically, H non , and a magnetically, H mag , heated component from a non-heated component, H co in the H-index. Results. The average network and inter-network H-indices are equal to 12 and 10 pm, respectively. The emission in the network is correlated with the magnetic flux density, approaching a value of H ≈ 10 pm for vanishing flux. The inter-network magnetic field is dominated by weak field strengths with values down to 200 G and has a mean absolute flux density of about 11 Mx cm −2 . Conclusions. We find that a dominant fraction of the calcium emission caused by the heated atmosphere in the magnetic network has non-magnetic origin (H mag ≈ 2 pm, H non ≈ 3 pm). Considering the effect of straylight, the contribution from an atmosphere with no temperature rise to the H-index (H co ≈ 6 pm) is about half of the observed H-index in the inter-network. The H-index in the inter-network is not correlated to any property of the photospheric magnetic field, suggesting that magnetic flux concentrations have a negligible role in the chromospheric heating in this region. The height range of the thermal coupling between the photosphere and low/mid chromosphere increases in presence of magnetic field. In addition, we demonstrate that a poor signal-to-noise level in the Stokes profiles leads to a significant over-estimation of the magnetic field strength.

We have investigated a time series of continuum intensity maps and corresponding Dopplergrams of granulation in a very quiet solar region at the disk center, recorded with the Imaging Magnetograph eXperiment (IMaX) on board the balloon-borne solar observatory SUNRISE. We find that granules frequently show substructure in the form of lanes composed of a leading bright rim and a trailing dark edge, which move together from the boundary of a granule into the granule itself. We find strikingly similar events in synthesized intensity maps from an ab initio numerical simulation of solar surface convection. From cross sections through the computational domain of the simulation, we conclude that these 'granular lanes' are the visible signature of (horizontally oriented) vortex tubes. The characteristic optical appearance of vortex tubes at the solar surface is explained. We propose that the observed vortex tubes may represent only the large-scale end of a hierarchy of vortex tubes existing near the solar surface.

Context. Sunspots are the longest-known manifestation of solar activity, and their magnetic nature has been known for more than a century. Despite this, the boundary between umbrae and penumbrae, the two fundamental sunspot regions, has hitherto been solely defined by an intensity threshold. Aims. Here, we aim at studying the magnetic nature of umbra-penumbra boundaries in sunspots of different sizes, morphologies, evolutionary stages, and phases of the solar cycle. Methods. We used a sample of 88 scans of the Hinode/SOT spectropolarimeter to infer the magnetic field properties in at the umbral boundaries. We defined these umbra-penumbra boundaries by an intensity threshold and performed a statistical analysis of the magnetic field properties on these boundaries. Results. We statistically prove that the umbra-penumbra boundary in stable sunspots is characterised by an invariant value of the vertical magnetic field component: the vertical component of the magnetic field strength does not depend on the umbra size, its morphology, and phase of the solar cycle. With the statistical Bayesian inference, we find that the strength of the vertical magnetic field component is, with a likelihood of 99%, in the range of 1849-1885 G with the most probable value of 1867 G. In contrast, the magnetic field strength and inclination averaged along individual boundaries are found to be dependent on the umbral size: the larger the umbra, the stronger and more horizontal the magnetic field at its boundary. Conclusions. The umbra and penumbra of sunspots are separated by a boundary that has hitherto been defined by an intensity threshold. We now unveil the empirical law of the magnetic nature of the umbra-penumbra boundary in stable sunspots: it is an invariant vertical component of the magnetic field.

Context. The formation of a penumbra is crucial for our understanding of solar magnetism, but it has not been observed in detail. Aims. We aim to enhance our knowledge of how a sunspot penumbra forms and how sunspots grow in size.Methods. We present a data set of the active region NOAA 11024 acquired at the German VTT with speckle-reconstructed images in the G-band and Ca ii K. The data set includes spectropolarimetric profiles from GFPI in Fe i 617.3 nm and TIP in Fe i 1089.6 nm.Results. On 2009 July 4, at 08:30 UT, a leading spot without penumbra and pores of opposite polarity were present in the active region. For the next 4:40 h, we observed the formation of a penumbra in the leading spot at a cadence of 5 images per second. We produced speckle reconstructed images of 0. 3 spatial resolution or better, interrupted by one large gap of 35 min and a few more small gaps of about 10 min. The leading spot initially has a size of 230 arcsec 2 with only a few penumbral filaments and then grows to a size of 360 arcsec 2 . The penumbra forms in segments, and it takes about 4 h until it encircles half of the umbra, on the side opposite the following polarity. On the side towards the following polarity, elongated granules mark a region of magnetic flux emergence. Conclusions. This ongoing emergence appears to prevent a steady penumbra from forming on this side. While the penumbra forms, the umbral area is constant; i.e., the increase in the total spot area is caused exclusively by the growth of the penumbra. From this we conclude that the umbra has reached an upper size limit and that any new magnetic flux that joins the spot is linked to the process of penumbral formation.

Context. The heating process that balances the solar chromospheric energy losses has not yet been determined. Conflicting views exist on the source of the energy and the influence of photospheric magnetic fields on chromospheric heating.Aims. We analyze a 1-h time series of cospatial Ca ii H intensity spectra and photospheric polarimetric spectra around 630 nm to derive the signature of the chromospheric heating process in the spectra and to investigate its relation to photospheric magnetic fields. The data were taken in a quiet Sun area on disc center without strong magnetic activity.Methods. We have derived several characteristic quantities of Ca ii H to define the chromospheric atmosphere properties. We study the power of the Fourier transform at different wavelengths and the phase relations between them. We perform local thermodynamic equilibrium (LTE) inversions of the spectropolarimetric data to obtain the photospheric magnetic field, once including the Ca intensity spectra.Results. We find that the emission in the Ca ii H line core at locations without detectable photospheric polarization signal is due to waves that propagate in around 100 s from low forming continuum layers in the line wing up to the line core. The phase differences of intensity oscillations at different wavelengths indicate standing waves for ν < 2 mHz and propagating waves for higher frequencies. The waves steepen into shocks in the chromosphere. On average, shocks are both preceded and followed by intensity reductions. In field-free regions, the profiles show emission about half of the time. The correlation between wavelengths and the decorrelation time is significantly higher in the presence of magnetic fields than for field-free areas. The average Ca ii H profile in the presence of magnetic fields contains emission features symmetric to the line core and an asymmetric contribution, where mainly the blue H 2V emission peak is increased (shock signature).Conclusions. We find that acoustic waves steepening into shocks are responsible for the emission in the Ca ii H line core for locations without photospheric magnetic fields. We suggest using wavelengths in the line wing of Ca ii H, where LTE still applies, to compare theoretical heating models with observations.

Solar observations with the Atacama Large Millimeter/submillimeter Array (ALMA) provide us with direct measurements of the brightness temperature in the solar chromosphere. We study the temperature distributions obtained with ALMA Band 6 (in four subbands at 1.21, 1.22, 1.29, and 1.3 mm) for various areas at, and in the vicinity of, a sunspot, comprising quasi-quiet and active regions with different amounts of underlying magnetic fields. We compare these temperatures with those obtained at near-and far-ultraviolet (UV) wavelengths (and with the line-core intensities of the optically-thin far-UV spectra), co-observed with the Interface Region Imaging Spectrograph (IRIS) explorer. These include the emission peaks and cores of the Mg ii k 279.6 nm and Mg ii h 280.4 nm lines as well as the line cores of C ii 133.4 nm, O i 135.6 nm, and Si iv 139.4 nm, sampling the mid-to-high chromosphere and the low transition region. Splitting the ALMA sub-bands resulted in an slight increase of spatial resolution in individual temperature maps, thus, resolving smaller-scale structures compared to those produced with the standard averaging routines. We find that the radiation temperatures have different, though somewhat overlapping, distributions in different wavelengths and in the various magnetic regions. Comparison of the ALMA temperatures with those of the UV diagnostics should, however, be interpreted with great caution, the former is formed under the local thermodynamic equilibrium (LTE) conditions, the latter under non-LTE. The mean radiation temperature of the ALMA Band 6 is similar to that extracted from the IRIS C ii line in all areas with exception of the sunspot and pores where the C ii poses higher radiation temperatures. In all magnetic regions, the Mg ii lines associate with the lowest mean radiation temperatures in our sample. These will provide constraints for future numerical models.

Aims. We study the magnetic flux emergence and formation of a sunspot penumbra in the active region NOAA 11024. Methods. We simultaneously observed the Stokes parameters of the photospheric iron lines at 1089.6 nm with the TIP and 617.3 nm with the GFPI spectropolarimeters along with broad-band images using G-band and Ca ii K filters at the German VTT. The photospheric magnetic field vector was reconstructed from an inversion of the measured Stokes profiles. Using the AZAM code, we converted the inclination from line-of-sight (LOS) to the local reference frame (LRF). Results. Individual filaments are resolved in maps of magnetic parameters. The formation of the penumbra is intimately related to the inclined magnetic field. No penumbra forms in areas with strong magnetic field strength and small inclination. corresponds to the merging of one SFP per minute. We also find that, during the formation of the spot penumbra, a) the maximum magnetic field strength of the umbra does not change; b) the magnetic neutral line keeps the same position relative to the umbra; c) the new flux arrives on the emergence side of the spot while the penumbra forms on the opposite side; d) the average LRF inclination of the light bridges decreases from 50• to 37• ; and e) as the penumbra develops, the mean magnetic field strength at the spot border decreases from 1.0 to 0.8 kG.Conclusions. The SFPs associated with elongated granules are the building blocks of structure formation in active regions. During the sunspot formation, their contribution is comparable to the coalescence of pores. Besides a set of critical parameters for the magnetic field, a quiet environment in the surroundings is important for penumbral formation. As remnants of trapped granulation between merging pores, the light bridges are found to play a crucial role in the formation process. They seem to channel the magnetic flux through the spot during its formation. Light bridges are also the locations where the first penumbral filaments form.