Small-scale dynamos on the solar surface: dependence on magnetic Prandtl number

The question of possible small-scale dynamo action in the surface layers of the Sun is revisited with realistic 3D MHD simulations. As in other MHD problems, dynamo action is found to be a sensitive function of the magnetic Prandtl number ${\rm P_{\rm m} }=\nu/\eta$; it disappears below a critical value ${\rm P_{\rm c}}$ which is a function of the numerical resolution. At a grid spacing of 3.5 km, ${\rm P_{\rm c}}$ based on the hyperdiffusivities implemented in the code (STAGGER) is $\approx 1$, increasing with increasing grid spacing. As in other settings, it remains uncertain whether small scale dynamo action is present in the astrophysical limit where ${\rm P_{\rm m} }<<1$ and magnetic Reynolds number ${\rm R_m}\gg 1$. The question is discussed in the context of the strong effect that external stray fields are observed to have in generating and maintaining dynamo action in other numerical and laboratory systems, and in connection with the type-II hypertransient behavior of dynamo action observed in the absence of such external fields

Brightness of the Sun's small scale magnetic field: proximity effects

The net effect of the small scale magnetic field on the Sun's (bolometric) brightness is studied with realistic 3D MHD simulations. The direct effect of brightening within the magnetic field itself is consistent with measurements in high-resolution observations. The high 'photometric accuracy' of the simulations, however, reveal compensating brightness effects that are hard to detect observationally. The influence of magnetic concentrations on the surrounding nonmagnetic convective flows (a 'proximity effect') reduces the brightness by an amount exceeding the brightening by the magnetic concentrations themselves. The net photospheric effect of the small scale field (~ -0.34% at a mean flux density of 50 G) is thus negative. We conclude that the main contribution to the observed positive correlation between the magnetic field and total solar irradiance must be magnetic dissipation in layers around the temperature minimum and above (not included in the simulations). This agrees with existing inferences from observations

Spiral-shaped wavefronts in a sunspot umbra

Solar active regions show a wide variety of oscillatory phenomena. The presence of the magnetic field leads to the appearance of several wave modes, whose behavior is determined by the sunspot thermal and magnetic structure. We aim to study the relation between the umbral and penumbral waves observed at the high photosphere and the magnetic field topology of the sunspot. Observations of the sunspot in active region NOAA 12662 obtained with the GREGOR telescope (Observatorio del Teide, Spain) were acquired on 2017 June 17. The data set includes a temporal series in the Fe I 5435 \AA\ line obtained with the imaging spectrograph GREGOR Fabry-P\'erot Interferometer (GFPI) and a spectropolarimetric raster map acquired with the GREGOR Infrared Spectrograph (GRIS) in the 10830 \AA\ spectral region. The Doppler velocity deduced from the restored Fe I 5435 \AA\ line has been determined, and the magnetic field vector of the sunspot has been inferred from spectropolarimetric inversions of the Ca I 10839 \AA\ and the Si I 10827 \AA\ lines. A two-armed spiral wavefront has been identified in the evolution of the two-dimensional velocity maps from the Fe I 5435 \AA\ line. The wavefronts initially move counterclockwise in the interior of the umbra, and develop into radially outward propagating running penumbral waves when they reach the umbra-penumbra boundary. The horizontal propagation of the wavefronts approximately follows the direction of the magnetic field, which shows changes in the magnetic twist with height and horizontal position. The spiral wavefronts are interpreted as the visual pattern of slow magnetoacoustic waves which propagate upward along magnetic field lines. Their apparent horizontal propagation is due to their sequential arrival to different horizontal positions at the formation height of the Fe I 5435 \AA\ line, as given by the inclination and orientation of the magnetic field.Comment: Accepted for publication in A&

Collective Quartics and Dangerous Singlets in Little Higgs

Any extension of the standard model that aims to describe TeV-scale physics without fine-tuning must have a radiatively-stable Higgs potential. In little Higgs theories, radiative stability is achieved through so-called collective symmetry breaking. In this letter, we focus on the necessary conditions for a little Higgs to have a collective Higgs quartic coupling. In one-Higgs doublet models, a collective quartic requires an electroweak triplet scalar. In two-Higgs doublet models, a collective quartic requires a triplet or singlet scalar. As a corollary of this study, we show that some little Higgs theories have dangerous singlets, a pathology where collective symmetry breaking does not suppress quadratically-divergent corrections to the Higgs mass.Comment: 4 pages; v2: clarified the existing literature; v3: version to appear in JHE

Algebraic methods for dynamic systems

Algebraic methods for application to dynamic control system

Natural flood management: Opportunities to implement nature‐based solutions on privately owned land

The implementation of Natural Flood Management (NFM), as an example of a nature‐based solution (NbS), is promoted as a risk reduction strategy to support sustainable flood risk management and climate change adaptation more widely. Additionally, as an NbS, NFM aims to provide further multiple benefits, such as increased biodiversity and improved water quality as well as improved mental health. The implementation of NbS often needs private‐owned or managed land, yet can create conflicts between the different stakeholders which can undermine the social consensus required for successful implementation. Consequently, a main question is how the multiple benefits and requirements of NFM can be delivered to meet the different goals of the wide variety of stakeholders who must be involved. This article discusses the challenges and potential of implementing NFM as an alternative to the traditional technical mitigation measures in flood risk management. We outline four opportunities in the implementation of NFM: physical conditions of the catchment, social interaction, financial resources, and institutional setting. Their importance is then demonstrated and compared to different examples across the globe. Nevertheless, the core drivers reflect the social interaction and institutional setting and the role of stakeholders in the successful implementation of NFM