Context: In sunspots, the geometric height of continuum optical depth unity is depressed compared to the quiet Sun. This so-called Wilson depression is caused by the Lorentz force of the strong magnetic field inside the spots. However, it is not understood in detail yet, how the Wilson depression is related to the strength and geometry of the magnetic field or to other properties of the sunspot.
Aims: We aim to study the dependence of the Wilson depression on the properties of the magnetic field of the sunspots and how exactly the magnetic field contributes to balancing the Wilson depression with respect to the gas pressure of the surroundings of the spots.
Methods: Our study is based on 24 spectropolarimetric scans of 12 individual sunspots performed with Hinode. We derived the Wilson depression for each spot using both, a recently developed method that is based on minimizing the divergence of the magnetic field, and an approach developed earlier that enforces an equilibrium between the gas pressure and the magnetic pressure inside the spot and the gas pressure in the quiet Sun, thus neglecting the influence of the curvature force. We then performed a statistical analysis by comparing the Wilson depression resulting from the two techniques with each other and by relating them to various parameters of the sunspots, such as their size or the strength of the magnetic field.
Results: We find that the Wilson depression becomes larger for spots with a stronger magnetic field, but not as much as one would expect from the increased magnetic pressure. This suggests that the curvature integral provides an important contribution to the Wilson depression, particularly for spots with a weak magnetic field. Our results indicate that the geometry of the magnetic field in the penumbra is different between spots with different strengths of the average umbral magnetic field.
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 spectropo…
The distributions of sunspot longitude at first appearance and at disappearance display an east-west asymmetry that results from a reduction in visibility as one moves from disk centre to the limb. To first order, this is explicable in terms of simple geometrical foreshortening. However, the centre-to-limb visibility variation is much larger than that predicted by foreshortening. Sunspot visibility is also known to be affected by the Wilson effect: the apparent dish shape of the sunspot photosphere caused by the temperature-dependent variation of the geometrical position of the tau=1 layer. In…
In order to assess the ability of helioseismology to probe the subsurface structure and magnetic field of sunspots, we need to determine how helioseismic travel times depend on perturbations to sunspot models. Here we numerically simulate the propagation of f, p1, and p2 wave packets through magnetic sunspot models. Among the models we considered, a ~50 km change in the height of the Wilson depression and a change in the subsurface magnetic field geometry can both be detected above the observational noise level. We also find that the travel-time shifts due to changes in a sunspot model must be…
Improving methods for determining the subsurface structure of sunspots from their seismic signature requires a better understanding of the interaction of waves with magnetic field concentrations. We aim to quantify the impact of changes in the internal structure of sunspots on local helioseismic signals. We have numerically simulated the propagation of a stochastic wave field through sunspot models with different properties, accounting for changes in the Wilson depression between 250 and 550 km and in the photospheric umbral magnetic field between 1500 and 3500 G. The results show that travel-…
Wave propagation through sunspots involves conversion between waves of acoustic and magnetic character. In addition, the thermal structure of sunspots is very different than that of the quiet Sun. As a consequence, the interpretation of local helioseismic measurements of sunspots has long been a challenge. With the aim of understanding these measurements, we carry out numerical simulations of wave propagation through sunspots. Helioseismic holography measurements made from the resulting simulated wavefields show qualitative agreement with observations of real sunspots. We use additional numeri…
A crucial feature not widely accounted for in local helioseismology is that surface magnetic regions actually open a window from the interior into the solar atmosphere, and that the seismic waves leak through this window, reflect high in the atmosphere, and then re-enter the interior to rejoin the seismic wave field normally confined there. In a series of recent numerical studies using translation invariant atmospheres, we utilised a "directional time-distance helioseismology" measurement scheme to study the implications of the returning fast and Alfvén waves higher up in the solar atmosphere …
We report on the discovery of mostly horizontal field channels just outside sunspot penumbrae (in the so-called `moat' region) that are seen to sustain supersonic flows (line-of-sight component of 6 km s{-1}). The spectral signature of these supersonic flows corresponds to circular polarization profiles with an additional, satellite, third lobe of the same sign as the parent sunspot' Stokes V blue lobe, for both downflows and upflows. This is consistent with an outward directed flow that we interpret as the continuation of the magnetized Evershed flow outside sunspots at supersonic speeds. In …
Many previous studies have shown that magnetic fields as well as sunspot structures present rapid and irreversible changes associated with solar flares. In this paper we first use five X-class flares observed by SDO/HMI to show that not only the magnetic fields and sunspot structures do show rapid, irreversible changes but also these changes are closely related, both spatially and temporally. The magnitudes of the correlation coefficients between the temporal variations of horizontal magnetic field and sunspot intensity are all larger than 0.90, with a maximum value of 0.99 and an average valu…
In this study, we investigate magnetic properties of umbra of magneto-conjugate leading and following sunspots, i.e. connected through magnetic field lines. We established dependences between individual sunspot umbra field characteristics, and between these characteristics on the umbra area ($S$) separately for sunspot pairs, for which the minimal angle between the umbra magnetic field line of the leading ($L$) sunspot and the positive normal line to the Sun surface is smaller, than that in the following ($F$) sunspot ($α_{min-L}<α_{min-F}$; such sunspot pairs are the bulk) and, on the contrar…
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 param…
$δ$-sunspots, with highly complex magnetic structures, are very productive in energetic eruptive events, such as X-class flares and homologous eruptions. We here study the formation of such complex magnetic structures by numerical simulations of magnetic flux emergence from the convection zone into the corona in an active-region-scale domain. In our simulation, two pairs of bipolar sunspots form on the surface, originating from two buoyant segments of a single subsurface twisted flux rope, following the approach of Toriumi et al. (2014). Expansion and rotation of the emerging fields in the two…
Characteristics of the depression contribution functions are studied for the Stokes line profiles formed in a magnetic field. The form of the depression functions depends mainly on the strength of splitting and the Zeeman component intensity, and is of a complicated character with a distinctly pronounces asymmetry. The depths of formation of magnetically sensitive lines are found by means of these contribution functions. The calculations reveal that the steep section of the line profile is formed higher than the profile center when a strong longitudinal magnetic field is present. The Stokes pr…
Sunspot light bridges are known to exhibit a variety of dynamic and persistent phenomena such as surges, small-scale jets etc. in the chromosphere and transition region. While it has generally been proposed that magnetic reconnection is responsible for this small-scale dynamism, persistent flaring activity lasting several hours from the same spatial location on a sunspot light bridge, has rarely been reported. We combine observations from the Atmospheric Imaging Assembly and the Helioseismic Magnetic Imager on board the Solar Dynamics Observatory to investigate homologous flaring activity over…
We address a possibility of the flare process initiation and further maintenance of its energy release due to a transformation of sunspot longitudinal waves into transverse magnetic loop oscillations with initiation of reconnection. This leads to heating maintaining after the energy release peak and formation of a flat stage on the X-ray profile. We applied the time-distance plots and pixel wavelet filtration (PWF) methods to obtain spatio-temporal distribution of wave power variations in SDO/AIA data. To find magnetic waveguides, we used magnetic field extrapolation of SDO/HMI magnetograms. T…
Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale. However, without establishing a geometrical height scale their three-dimensional geometrical structure can not be derived. This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness. The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the d…
A theory of the mean tilt of sunspot bipolar regions (the angle between a line connecting the leading and following sunspots and the solar equator) is developed. A mechanism of formation of the mean tilt is related to the effect of Coriolis force on meso-scale motions of super-granular convection and large-scale meridional circulation. The balance between the Coriolis force and the Lorentz force (the magnetic tension) determines an additional contribution caused by the large-scale magnetic field to the mean tilt of the sunspot bipolar regions at low latitudes. The latitudinal dependence of the…
The maximum phase of the solar cycle is characterized by several interesting features in the solar activity, heliospheric characteristics and the galactic cosmic ray (GCR) intensity. Recently the maximum phase of the current solar cycle (SC) 24, in many relations anomalous when compared with solar cycles of the second half of the 20-th century, came to the end. The corresponding phase in the GCR intensity cycle is also in progress. In this paper we study different aspects of the sunspot, heliospheric and GCR behavior around this phase. Our main conclusions are as follows: 1) The maximum phase …
Polar Filaments Capture High Latitude Solar Poloidal Field Interactions and can Foretell the Future Sunspot Cycle Amplitude before Polar Field Precursors
Although sunspots have been systematically observed on the Sun's surface over the last four centuries, their magnetic properties have been revealed and documented only since the early 1900s. Sunspots typically appear in pairs of opposite magnetic polarities which have a systematic orientation. This polarity orientation is opposite across the equator -- a trend that has persisted over the last century over which magnetic field observations exist. Taken together with the configuration of the global poloidal field of the Sun -- that governs the heliospheric open flux and cosmic ray flux at Earth …
In this study we report detailed observations of magnetic environment at four footpoints of two warm coronal loops observed on 5 May 2016 in NOAA AR 12542 (Loop I) and 17 Dec 2015 in NOAA AR 12470 (Loop II). These loops were connecting a plage region with sunspot periphery (Loop I) and a sunspot umbra (Loop II). We used Solar Dynamics Observatory (SDO) and Goode Solar Telescope (GST) data to describe the phenomenon and understand its causes. The study indicates loop brightening episodes were associated with magnetic flux emergence and cancellation processes observed in SDO's Helioseismic and M…
The inverse Evershed flow (IEF) is a mass motion towards sunspots at chromospheric heights. We combined high-resolution observations of NOAA 12418 from the Dunn Solar Telescope and vector magnetic field measurements from the Helioseismic and Magnetic Imager (HMI) to determine the driver of the IEF. We derived chromospheric line-of-sight (LOS) velocities from spectra of H$α$ and Ca II IR. The HMI data were used in a non-force-free magnetic field extrapolation to track closed field lines near the sunspot in the active region. We determined their length and height, located their inner and outer f…
To better understand a preferred magnetic field configuration and its evolution during Coronal Mass Ejection events, we investigated the spatial and temporal evolution of photospheric magnetic fields in the active region NOAA 9236 that produced eight flare-associated CMEs during the time period of 2000 November 23-26. The time variations of the total magnetic helicity injection rate and the total unsigned magnetic flux are determined and examined not only in the entire active region but also in some local regions such as the main sunspots and the CME-associated flaring regions using SOHO/MDI m…
Inversion techniques applied to the radiative transfer equation for polarized light are capable of inferring the physical parameters in the solar atmosphere (temperature $T$, magnetic field ${\bf B}$, and line-of-sight velocity $v_{\rm los}$) from observations of the Stokes vector (i.e., spectropolarimetric observations) in spectral lines. Inferences are usually performed in the $(x,y,τ_c)$ domain, where $τ_c$ refers to the optical-depth scale. Generally, their determination in the $(x,y,z)$ volume is not possible due to the lack of a reliable estimation of the gas pressure, particularly in re…
Sunspots are the most spectacular manifestation of solar magnetism, yet, 99% of the solar surface remains 'quiet' at any time of the solar cycle. The quiet sun is not void of magnetic fields, though; they are organized at smaller spatial scales and evolve relatively fast, which makes them difficult to detect. Thus, although extensive quiet Sun magnetism would be a natural driver to a uniform, steady heating of the outer solar atmosphere, it is not clear what the physical processes involved would be due to lack of observational evidence. We report the topology and dynamics of the magnetic field…
Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D): II. A Physics-Informed Machine Learning Method for 3D Solar Photosphere Reconstruction
Sunspots, which harbor both magnetic polarities within one penumbra, are called delta-spots. They are often associated with flares. Nevertheless, there are only very few detailed observations of the spatially resolved magnetic field configuration. We present an investigation performed with the Tenerife Infrared Polarimeter at the Vacuum Tower Telescope in Tenerife. We observed a sunspot with a main umbra and several additional umbral cores, one of them with opposite magnetic polarity (the delta-umbra). The delta-spot is divided into two parts by a line along which central emissions of the spec…
We use images of high spatial and temporal resolution, obtained using both ground- and space-based instrumentation, to investigate the role magnetic field inclination angles play in the propagation characteristics of running penumbral waves in the solar chromosphere. Analysis of a near-circular sunspot, close to the center of the solar disk, reveals a smooth rise in oscillatory period as a function of distance from the umbral barycenter. However, in one directional quadrant, corresponding to the north direction, a pronounced kink in the period-distance diagram is found. Utilizing a combination…
We study the physical properties and behavior of the solar atmosphere during the GOES X1.6 solar flare on 2014 September 10. The steady plasma flows and the fast sausage MHD waves were analysed with the wavelet separation method. The magnetically coupled atmosphere and the forced magnetic field reconnection were studied with the help of the Vertical-Current Approximation Non-linear Force-Free Field code. We studied a mechanism of MHD wave transfer from the photosphere without dissipation or reflection before reaching the corona and a mechanism of the wave energy distribution over the solar cor…
