arXiv subjects

Markus Schmassmann

Publications and source records attributed to Markus Schmassmann.

5 recordsLinked to original sources

arXiv2026

Sunspot simulations with MURaM -- I. Parameter study using potential field initial conditions

Context. Existing sunspot simulations fail to reproduce the observed magnetic field distribution due to an artificially increased $B_{hor}$ at the upper boundary. Aims. We explore alternative ways to better reproduce the magnetic and dynamic properties of observed sunspots. Methods. We used the radiative MHD code MURaM. As initial conditions, we placed a potential magnetic field into small-scale dynamo simulations and used potential-field extrapolation at the top. Results. We find that: (1) Simulations with increasing initial magnetic field strengths (20, 40, 80, and 160 kG) show larger spots, umbrae, and penumbrae. (2) Penumbral-to-spot sizes are smaller than those measured in observed sunspots. (3) In none of the runs are pure Evershed (radially outward) flows. Instead, bi-directional flows with inflows in the inner penumbra and outflows in the outer penumbra were measured, consistent with to early observations of penumbra formation for runs with $\ge80$ kG at 96/32 km resolution, whereas runs with $\le40$ kG or less showed pure inflows. (4) Simulations with 160 kG at 32/16 km resolution contain filaments with bi-directional and Evershed flows. (5) Simulations with fluxes $>10^{22}$ Mx show unrealistically strong fields in the umbra. (6) The best runs with 160 kG and $10^{22}$ Mx give realistic radial profiles of $B_z$ and $B_r$, although stronger fields than observed. (7) Increasing the width of the box and reducing the overall flux by subtracting a uniform opposing vertical field have little influence on internal spot dynamics and fields, but change the mean vertical field beyond the spot. Conclusions. Simulations of small ($10^{22}$) sunspots with an initial potential field and intensified bottom magnetic field strength best reproduce observations of the initial stages of sunspot formation. Numerical resolution may be critical for achieving fully developed penumbrae.

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arXiv2025

The magnetic origin of the outer boundaries of sunspots

Context. Sunspot boundaries are commonly outlined by contours of the continuum intensity. However, their magnetic nature has not yet been fully characterised. Aims. We investigate the properties of the outer boundary of a long-lived sunspot to identify the magnetic property that defines it. Methods. We analysed the magnetic properties of AR NOAA11591 spot during its two passages across the solar disc, using SDO/HMI continuum intensity and magnetic field, and determined their contours to outline the outer boundary. Results. During the 1st disc passage, in which the sunspot is in its stable phase, the intensity contours at 0.9 of the mean quiet Sun intensity and isocontours of the magnetic field strength of 625G provide an almost perfect match between the two contours. With these thresholds, the time-averaged area of mismatch is minimised, yielding an average distance between the contours of 0.58 pixel, corresponding to less than 0.26 arcsec. During the 2nd disc passage, the spot shows clear signs of decay, and we find that the 0.9 intensity and 625G magnetic isocontours detach from each other, coupled to the disappearance of penumbra. In this super-equipartition area, granulation still operates. Conclusions. Based on a comparison with simulation data from our previous work, and in agreement with findings of other authors, we conclude that the outer boundary of stable sunspots is defined by an invariant magnetic field: the equipartition field. From the discrepancy between intensity and magnetic contours during the decaying phase of the sunspot, we surmise that alongside the well-established (magneto-)convective regimes of the photosphere - granular, penumbral, and umbral - a super-equipartition granular regime can be identified. In this regime, bright, but smaller granules occur where the magnetic field exceeds equipartition but remains sub-critical for convection suppression.

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arXiv2025

Apparent motion of penumbral grains in a sunspot simulation

Context. The bright heads of penumbral filaments, penumbral grains (PGs), are manifestations of hot plasma flows rising to the surface. They are observed to move horizontally toward the sunspot umbra or away from it. Recent analyses of observations indicate that the direction of this motion is related to the inclination of the surrounding magnetic field. Aims. The penumbra of a sunspot simulated by the radiative magnetohydrodynamic code MURaM is analysed to get typical physical conditions in PGs, compare them to those in the surroundings, describe their spatial distribution, and study their evolution. Methods. We use time series of images that map intensity, temperature, magnetic field vector, and velocity vector in horizontal slices at the visible surface, in subsurface layers, and in vertical cuts through the simulation box to track PGs and compare, statistically and in individual cases, the physical quantities inside them with those in the surroundings. Results. The statistical analysis of simulation results provides average values of temperature, magnetic field strength and inclination, vertical velocity, and their changes with radial distance from the spot centre. We find a subtle difference between simulated PGs with opposite directions of motions when comparing the magnetic field inclinations inside and outside the PGs. The case studies, documented by movies, show that the differences of inclinations and the direction of motions may change during the lifetime of some PGs and that the turbulence in the surface layers introduces some randomness in the apparent motions of PGs.

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arXiv2020

A distinct magnetic property of the inner penumbral boundary III. Analysis of simulated sunspots

The analyses of sunspot observations revealed a fundamental magnetic property of the umbral boundary, the invariance of the vertical component of the magnetic field. We aim to analyse the magnetic properties of the umbra-penumbra boundary in simulated sunspots and thus assess their similarity to observed sunspots. Also, we aim to investigate the role of plasma $β$ and the ratio of kinetic to magnetic energy in simulated sunspots on the convective motions. We use a set of non-grey simulation runs of sunspots with the MURaM code. These data are used to synthesise the Stokes profiles that are then degraded to the Hinode spectropolarimeter-like observations. Then, the data are treated like real Hinode observations of a sunspot and magnetic properties at the umbral boundaries are determined. Simulations with potential field extrapolation produce a realistic magnetic field configuration on their umbral boundaries. Two simulations with potential field upper boundary, but different subsurface magnetic field structures, differ significantly in the extent of their penumbrae. Increasing the penumbra width by forcing more horizontal magnetic fields at the upper boundary results in magnetic properties that are not consistent with observations. This implies that the size of the penumbra is given by the subsurface structure of the magnetic field. None of the sunspot simulations is consistent with observed properties of the magnetic field and direction of the Evershed flow at the same time. Strong outward directed Evershed flows are only found in setups with artificially enhanced horizontal component of the magnetic field at the top boundary that are not consistent with the observed magnetic field properties at the UP boundary. We want to stress out that the `photospheric' boundary of simulated sunspots is defined by a magnetic field strength of equipartition field value.

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arXiv2018

Magnetic properties of a long-lived sunspot - Vertical magnetic field at the umbral boundary

Context. In a recent statistical study of sunspots in 79 active regions, the vertical magnetic field component $B_\text{ver}$ averaged along the umbral boundary is found to be independent of sunspot size. The authors of that study conclude that the absolute value of $B_\text{ver}$ at the umbral boundary is the same for all spots. Aims. We investigate the temporal evolution of $B_\text{ver}$ averaged along the umbral boundary of one long-lived sunspot during its stable phase. Methods. We analysed data from the HMI instrument on-board SDO. Contours of continuum intensity at $I_\text{c}=0.5I_\text{qs}$, whereby $I_\text{qs}$ refers to the average over the quiet sun areas, are used to extract the magnetic field along the umbral boundary. Projection effects due to different formation heights of the Fe I 617.3 nm line and continuum are taken into account. To avoid limb artefacts, the spot is only analysed for heliocentric angles smaller than $60^{\circ}$. Results. During the first disc passage, NOAA AR 11591, $B_\text{ver}$ remains constant at 1693 G with a root-mean-square deviation of 15 G, whereas the magnetic field strength varies substantially (mean 2171 G, rms of 48 G) and shows a long term variation. Compensating for formation height has little influence on the mean value along each contour, but reduces the variations along the contour when away from disc centre, yielding a better match between the contours of $B_\text{ver}=1693$ G and $I_\text{c}=0.5I_\text{qs}$. Conclusions. During the disc passage of a stable sunspot, its umbral boundary can equivalently be defined by using the continuum intensity $I_\text{c}$ or the vertical magnetic field component $B_\text{ver}$. Contours of fixed magnetic field strength fail to outline the umbral boundary.

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