Vigorous convection in a sunspot granular light bridge

Light bridges are the most prominent manifestation of convection in sunspots. The brightest representatives are granular light bridges composed of features that appear to be similar to granules. An in-depth study of the convective motions, temperature stratification, and magnetic field vector in and around light bridge granules is presented with the aim of identifying similarities and differences to typical quiet-Sun granules. Spectropolarimetric data from the Hinode Solar Optical Telescope were analyzed using a spatially coupled inversion technique to retrieve the stratified atmospheric parameters of light bridge and quiet-Sun granules. Central hot upflows surrounded by cooler fast downflows reaching 10 km/s clearly establish the convective nature of the light bridge granules. The inner part of these granules in the near surface layers is field free and is covered by a cusp-like magnetic field configuration. We observe hints of field reversals at the location of the fast downflows. The quiet-Sun granules in the vicinity of the sunspot are covered by a low-lying canopy field extending radially outward from the spot. The similarities between quiet-Sun and light bridge granules point to the deep anchoring of granular light bridges in the underlying convection zone. The fast, supersonic downflows are most likely a result of a combination of invigorated convection in the light bridge granule due to radiative cooling into the neighboring umbra and the fact that we sample deeper layers, since the downflows are immediately adjacent to the slanted walls of the Wilson depression.Comment: 10 pages, 11 figure

Measuring the Wilson depression of sunspots using the divergence-free condition of the magnetic field vector

Context: The Wilson depression is the difference in geometric height of unit continuum optical depth between the sunspot umbra and the quiet Sun. Measuring the Wilson depression is important for understanding the geometry of sunspots. Current methods suffer from systematic effects or need to make assumptions on the geometry of the magnetic field. This leads to large systematic uncertainties of the derived Wilson depressions. Aims: We aim at developing a robust method for deriving the Wilson depression that only requires the information about the magnetic field that is accessible from spectropolarimetry, and that does not rely on assumptions on the geometry of sunspots or on their magnetic field. Methods: Our method is based on minimizing the divergence of the magnetic field vector derived from spectropolarimetric observations. We focus on large spatial scales only in order to reduce the number of free parameters. Results: We test the performance of our method using synthetic Hinode data derived from two sunspot simulations. We find that the maximum and the umbral averaged Wilson depression for both spots determined with our method typically lies within 100 km of the true value obtained from the simulations. In addition, we apply the method to Hinode observations of a sunspot. The derived Wilson depression (about 600 km) is consistent with results typically obtained from the Wilson effect. We also find that the Wilson depression obtained from using horizontal force balance gives 110 - 180 km smaller Wilson depressions than both, what we find and what we deduce directly from the simulations. This suggests that the magnetic pressure and the magnetic curvature force contribute to the Wilson depression by a similar amount.Comment: 12 pages, 8 figures. Accepted for publication in Astronomy & Astrophysic

Vertical flows and mass flux balance of sunspot umbral dots

A new Stokes inversion technique that greatly reduces the effect of the spatial point spread function of the telescope is used to constrain the physical properties of umbral dots (UDs). The depth-dependent inversion of the Stokes parameters from a sunspot umbra recorded with Hinode SOT/SP revealed significant temperature enhancements and magnetic field weakenings in the core of the UDs in deep photospheric layers. Additionally, we found upflows of around 960 m/s in peripheral UDs (i.e., UDs close to the penumbra) and $\approx$ 600 m/s in central UDs. For the first time, we also detected systematic downflows for distances larger than 200 km from the UD center that balance the upflowing mass flux. In the upper photosphere, we found almost no difference between the UDs and their diffuse umbral background.Comment: Accepted for publication in Astronomy and Astrophysic

Structure of sunspot penumbral filaments: a remarkable uniformity of properties

The sunspot penumbra comprises numerous thin, radially elongated filaments that are central for heat transport within the penumbra, but whose structure is still not clear. To investigate the fine-scale structure of these filaments, we perform a depth-dependent inversion of spectropolarimetric data of a sunspot very close to solar disk center obtained by Hinode (SOT/SP). We have used a recently developed spatially coupled 2D inversion scheme which allows us to analyze the fine structure of individual penumbral filaments up to the diffraction limit of the telescope. Filaments of different sizes in all parts of penumbra display very similar magnetic field strengths, inclinations and velocity patterns. The similarities allowed us to average all these filaments and to extract the physical properties common to all of them. This average filament shows upflows associated with an upward pointing field at its inner, umbral end and along its axis, downflows along the lateral edge and strong downflows in the outer end associated with a nearly vertical, strong and downward pointing field. The upflowing plasma is significantly hotter than the downflowing plasma. The hot, tear-shaped head of the averaged filament can be associated with a penumbral grain. The central part of the filament shows nearly horizontal fields with strengths of ~1kG. The field above the filament converges, whereas a diverging trend is seen in the deepest layers near the head of the filament. We put forward a unified observational picture of a sunspot penumbral filament. It is consistent with such a filament being a magneto-convective cell, in line with recent MHD simulations. The uniformity of its properties over the penumbra sets constraints on penumbral models and simulations. The complex and inhomogeneous structure of the filament provides a natural explanation for a number of long-running controversies in the literature.Comment: 19 pages; 12 figures; accepted for publication in A&

Inclinations of small quiet-Sun magnetic features based on a new geometric approach

High levels of horizontal magnetic flux have been reported in the quiet-Sun internetwork, often based on Stokes profile inversions. Here we introduce a new method for deducing the inclination of magnetic elements and use it to test magnetic field inclinations from inversions. We determine accurate positions of a set of small, bright magnetic elements in high spatial resolution images sampling different photospheric heights obtained by the Sunrise balloon-borne solar observatory. Together with estimates of the formation heights of the employed spectral bands, these provide us with the inclinations of the magnetic features. We also compute the magnetic inclination angle of the same magnetic features from the inversion of simultaneously recorded Stokes parameters. Our new, geometric method returns nearly vertical fields (average inclination of around 14 deg with a relatively narrow distribution having a standard deviation of 6 deg). In strong contrast to this, the traditionally used inversions give almost horizontal fields (average inclination of 75+-8 deg) for the same small magnetic features, whose linearly polarised Stokes profiles are adversely affected by noise. The almost vertical field of bright magnetic features from our geometric method is clearly incompatible with the nearly horizontal magnetic fields obtained from the inversions. This indicates that the amount of magnetic flux in horizontal fields deduced from inversions is overestimated in the presence of weak Stokes signals, in particular if Stokes Q and U are close to or under the noise level. By combining the proposed method with inversions we are not just improving the inclination, but also the field strength. This technique allows us to analyse features that are not reliably treated by inversions, thus greatly extending our capability to study the complete magnetic field of the quiet Sun.Comment: 12 pages, 9 figures, 1 table; Accepted for publication in Astronomy & Astrophysic

No universal connection between the vertical magnetic field and the umbra-penumbra boundary in sunspots

Context. It has been reported that the boundary between the umbra and the penumbra of sunspots occurs at a canonical value of the strength of the vertical magnetic field, independently of the size of the spot. This critical field strength is interpreted as to be the threshold for the onset of magnetoconvection. Aims. Here we investigate the reasons why this criterion, also called the Jur\v{c}\'ak criterion in the literature, does not always identify the boundary between umbra and penumbra. Methods. We perform a statistical analysis of 23 sunspots observed with Hinode/SOT. We compare the properties of the continuum intensity and the vertical magnetic field between filaments and spines and how they vary between spots of different sizes. Results. We find that the inner boundary of the penumbra is not related to a universal value of the vertical magnetic field. The properties of spines and filaments vary between spots of different sizes. Both components are darker in larger spots and the spines exhibit stronger vertical magnetic field. These variations of the properties of filaments and spines with spot size are also the reason for the reported invariance of the averaged vertical magnetic field at 50% of the mean continuum intensity. Conclusions. The formation of filaments and the onset of magnetoconvection are not related to a canonical value of the strength of the vertical magnetic field. Such a seemingly unique magnetic field strength is rather an effect of the filling factor of spines and penumbral filaments.Comment: 15 pages, 11 figures. Accepted for publication in Astronomy and Astrophysic

Like or dislike? Adolescents’ responses to personalized social network site advertising

Increasingly, personal data posted by users of social network sites (SNSs) can be used to personalize advertising. The present study investigates how adolescents respond to personalized ads in terms of attitude toward the ad, brand engagement and intention to forward, and whether privacy concerns moderate their responses. According to pretest results, a medium level of personalization was expected to be optimal in terms of advertising effectiveness. A within-subjects experiment involving 40 participants aged 14–18 years was performed. Three conditions of personalized advertising were designed with, respectively, low, medium, and high levels of personalization. The study found that the highest personalization condition generated the most positive response and that privacy concerns did not moderate the effects of personalization. The privacy paradox is discussed as an alternative explanation, along with other implications of the results

Influence of NLTE effects in Fe I lines on inverted atmosphere II. 6301 A and 6302 A lines formed in 3DNLTE

This paper forms the second part of our study on how the neglect of NLTE conditions in the formation of Fe I 6301.5 A and the 6302.5 A lines influences the atmosphere obtained by inverting their profiles in LTE. The main cause of NLTE effects is the line opacity deficit due to the excess ionization of the Fe I atoms by the UV photons in the Sun. In the first paper, the above photospheric lines were assumed to have formed in 1DNLTE and the effects of horizontal radiation transfer (RT) were neglected. In the present paper, the iron lines are computed in 3DNLTE. We investigate the influence of horizontal RT on the inverted atmosphere and how it can enhance or reduce the errors due to the neglect of 1DNLTE effects. The iron lines are computed in LTE, 1DNLTE and 3DNLTE. They all are inverted using an LTE inversion code. The atmosphere from the inversion of LTE profiles is taken as the reference model. The test atmospheres from the inversion of 1DNLTE and 3DNLTE profiles are compared with it. The differences between models are analysed and correspondingly attributed to NLTE and 3D effects. The effects of horizontal RT are evident in regions surrounded by strong horizontal gradients in temperature. In some regions, the 3D effects enhance the 1DNLTE effects while in some, they weaken. The errors due to neglecting the 3D effects are less than 5% in temperature while the errors are mostly less than 20% in both velocity and magnetic field strength. These errors are found to survive spatial and spectral degradation. The neglect of horizontal RT is found to introduce errors in the derived atmosphere. How large the errors are depends on how strong the local horizontal gradients are in temperature. Compared to the 1DNLTE effect, the 3D effects are more localised to specific regions in the atmosphere and overall less dominant.Comment: Accepted for publication in A&A. Abstract abridged for arxiv submissio

Detection of the strongest magnetic field in a sunspot light bridge

Traditionally, the strongest magnetic fields on the Sun have been measured in sunspot umbrae. More recently, however, much stronger fields have been measured at the ends of penumbral filaments carrying the Evershed and counter-Evershed flows. Superstrong fields have also been reported within a light bridge separating two umbrae of opposite polarities. We aim to accurately determine the strengths of the strongest fields in a light bridge using an advanced inversion technique and to investigate their detailed structure. We analyze observations from the spectropolarimeter on board the Hinode spacecraft of the active region AR 11967. The thermodynamic and magnetic configurations are obtained by inverting the Stokes profiles using an inversion scheme that allows multiple height nodes. Both the traditional 1D inversion technique and the so-called 2D coupled inversions, which take into account the point spread function of the Hinode telescope, are used. We find a compact structure with an area of 32.7 arcsec$^2$ within a bipolar light bridge with field strengths exceeding 5 kG, confirming the strong fields in this light bridge reported in the literature. Two regions associated with downflows of $\sim$5 km s$^{-1}$ harbor field strengths larger than 6.5 kG, covering a total area of 2.97 arcsec$^2$. The maximum field strength found is 8.2 kG, which is the largest ever observed field in a bipolar light bridge up to now.Comment: ApJ 2020, 895:12