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The butterfly diagram of the solar cycle exhibits a poleward migration of the diffuse magnetic field resulting from the decay of trailing sunspots. It is one component of what is sometimes referred to as the "rush to the poles". We investigate under which conditions the rush to the poles can be reproduced in flux-transport Babcock-Leighton dynamo models. We identify three main ways to reproduce it: a flux emergence probability that decreases rapidly with latitude; a threshold in subsurface toroidal field strength between slow and fast emergence; and an emergence rate based on magnetic buoyancy. We find that all three mechanisms lead to solar-like butterfly diagrams, but which present notable differences between them. The shape of the butterfly diagram is very sensitive to model parameters for the threshold prescription, while most models incorporating magnetic buoyancy converge to very similar butterfly diagrams, with butterfly wings widths of $\lesssim\pm 30^\circ$, in very good agreement with observations. With turbulent diffusivities above $35~\text{km}^2/\text{s}$ but below about $40~\text{km}^2/\text{s}$, buoyancy models are strikingly solar-like. The threshold and magnetic buoyancy prescriptions make the models non-linear and as such can saturate the dynamo through latitudinal quenching. The period of the models involving buoyancy is independent of the source term amplitude, but emergence loss increases it by $\simeq 60\%$. For the rush to the poles to be visible, a mechanism suppressing (enhancing) emergences at high (low) latitudes must operate. It is not sufficient that the toroidal field be stored at low latitudes for emergences to be limited to low latitudes. From these models we infer that the Sun is not in the advection-dominated regime, but also not in the diffusion-dominated regime. The cycle period is set through a balance between advection, diffusion and flux emergence., Comment: 12 pages, 17 figures, accepted for publication in A&A

Besides a dense coverage of their high latitudes by starspots, rapidly rotating cool stars also display low-latitude spots in Doppler images, although generally with a lower coverage. In contrast, flux emergence models of fast-rotating stars predict strong poleward deflection of radially rising magnetic flux as the Coriolis effect dominates over buoyancy, leaving a spot-free band around the equator. To resolve this discrepancy, we consider a flux tube near the base of the convection zone in a solar-type star rotating eight times faster than the Sun, considering field intensification by weak-tube explosions. For the intensification to continue into to the buoyancy-dominated regime, the upper convection zone must have a significantly steeper temperature gradient than in the Sun, by a factor that is comparable with that found in 3D simulations of rotating convection. Within the hypothesis that stellar active regions stem from the base of the convection zone, flux emergence between 1-20 degree latitudes requires highly supercritical field strengths of up to 500 kG in rapidly rotating stars. These field strengths require explosions of 100-kG tubes within the convection zone, compatible with reasonable values of the superadiabatic temperature gradient associated with the more rapid rotation., Comment: 12 pages, 9 figures, accepted for publication in ApJ

The Sun's global inertial modes are very sensitive to the solar differential rotation and to properties of the deep solar convection zone which are currently poorly constrained. These properties include the superadiabatic temperature gradient, the latitudinal entropy gradient, and the turbulent viscosity. The inertial modes also play a key role in controlling the Sun's large-scale structure and dynamics, in particular the solar differential rotation. This paper summarizes recent observations and advances in the (linear and nonlinear) modeling of the solar inertial modes., Comment: Submitted on 05-Mar-2024 for publication in procs. IAU Symp 365, Eds. A. Getling and L. Kitchatinov

Emerging active regions are associated with convective flows on the spatial scale and lifetimes of supergranules. To understand how these flows are involved in the formation of active regions, we aim to identify where active regions emerge in the supergranulation flow pattern. We computed supergranulation scale flow maps at the surface for all active regions in the Solar Dynamics Observatory Helioseismic Emerging Active Region Survey. We classified each of the active regions into four bins, based on the amplitude of their average surface flow divergence at emergence. We then averaged the flow divergence over the active regions in each bin as a function of time. We also considered a corresponding set of control regions. We found that, on average, the flow divergence increases during the day prior to emergence at a rate independent of the amount of flux that emerges. By subtracting the averaged flow divergence of the control regions, we found that active region emergence is associated with a remaining converging flow at 0.5-1 days prior to emergence. This remnant flow, $\Delta \, \mathrm{div} \, \mathbf{v_h} = (-4.9 \pm 1.7) \times 10^{-6}$ 1/s, corresponds to a flow speed of 10-20 m/s (an order of magnitude less than supergranulation flows) out to a radius of about 10 Mm. We show that these observational results are qualitatively supported by simulations of a small bipole emerging through the near-surface convective layers of the Sun. The question remains whether these flows are driving the emergence, or are caused by the emergence., Comment: 22 pages, 27 figures, accepted to be published in MNRAS

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

The difference between individual solar cycles in the magnetic butterfly diagram can mostly be ascribed to the stochasticity of the emergence process. We aim to obtain the expectation value of the butterfly diagram from observations of four cycles. This allows us to further determine the generation rate of the surface radial magnetic field. We use data from Wilcox Solar Observatory to generate time-latitude diagrams spanning cycles 21 to 24 of the surface radial and toroidal magnetic fields, symmetrize them across the equator and cycle-average them. From the mean butterfly diagram and surface toroidal field we then infer the mean poloidal field generation rate at the surface of the Sun. The averaging procedure removes realization noise from individual cycles. The amount of emerging flux required to account for the evolution of the surface radial field is found to match that provided by the observed surface toroidal field and Joy's law. Cycle-averaging butterfly diagrams removes realization noise and artefacts due to imperfect scale separation, and corresponds to an ensemble average that can be interpreted in the mean-field framework. The result can then be directly compared to $\alpha\Omega$-type dynamo models. The Babcock-Leighton $\alpha$-effect is consistent with observations, a result that can be appreciated only if the observational data is averaged in some way., Comment: 5 pages, 6 figures, accepted for publication in A&A

Rapidly rotating fluids have a rotation profile which depends only on the distance from the rotation axis, in accordance with the Taylor-Proudman theorem. Although the Sun was expected to be such a body, helioseismology showed that the rotation rate in the convection zone is closer to constant on radii. It has been postulated that this deviation is due to the poles being warmer than the equator by a few degrees. Using numerical simulations, we show that the pole-to-equator temperature difference cannot exceed 7 Kelvin as a result of the back-reaction of the high-latitude baroclinically unstable inertial modes. The observed amplitudes of the modes further indicate that this maximum temperature difference is reached in the Sun. We conclude that the Sun's latitudinal differential rotation reaches its maximum allowed value., Comment: 52 pages, 21 figures, 2 tables. Published in Science Advances on 27 Mar 2024. The authors' version

Stars appear darker at their limbs than at their disk centers because at the limb we are viewing the higher and cooler layers of stellar photospheres. Limb darkening derived from state-of-the-art stellar atmosphere models systematically fails to reproduce recent transiting exoplanet light curves from the Kepler, TESS, and JWST telescopes -- stellar brightness obtained from measurements drops less steeply towards the limb than predicted by models. All previous models assumed atmosphere devoid of magnetic fields. Here we use our new stellar atmosphere models computed with the 3D radiative magneto-hydrodynamic code MURaM to show that small-scale concentration of magnetic fields on the stellar surface affect limb darkening at a level that allows us to explain the observations. Our findings provide a way forward to improve the determination of exoplanet radii and especially the transmission spectroscopy analysis for transiting planets, which relies on a very accurate description of stellar limb darkening from the visible through the infrared. Furthermore, our findings imply that limb darkening allows measuring the small-scale magnetic field on stars with transiting planets., Comment: 19 pages, 6 figures This is the submission version of manuscript to Nature Astronomy

For Sun-like stars, the generation of toroidal magnetic field from poloidal magnetic field is an essential piece of the dynamo mechanism powering their magnetism. Previous authors have estimated the net toroidal flux generated in each hemisphere of the Sun by exploiting its conservative nature. This only requires observations of the surface magnetic field and differential rotation. We explore this approach using a 3D magnetohydrodynamic dynamo simulation of a cool star, for which the magnetic field generation is known throughout the entire star. Changes to the net toroidal flux in each hemisphere were evaluated using a closed line integral bounding the cross-sectional area of each hemisphere, following the application of Stokes-theorem to the induction equation; the individual line segments corresponded to the stellar surface, base, equator, and rotation axis. The influence of the large-scale flows, the fluctuating flows, and magnetic diffusion to each of the line segments was evaluated, along with their depth-dependence. In the simulation, changes to the net toroidal flux via the surface line segment typically dominate the total line integral surrounding each hemisphere, with smaller contributions from the equator and rotation axis. The bulk of the toroidal flux is generated deep inside the convection zone, with the surface observables capturing this due to the conservative nature of the net flux. Surface magnetism and rotation can therefore be used to estimate the net toroidal flux generated in each hemisphere, allowing us to constrain the reservoir of magnetic flux for the next magnetic cycle. However, this methodology cannot identify the physical origin, nor the location, of the toroidal flux generation. In addition, not all dynamo mechanisms depend on the net toroidal field produced in each hemisphere, meaning this method may not be able to characterise every magnetic cycle., Comment: Accepted to A&A. 8 Pages + Appendix. 6 Figures + 2 Appendix Figures

Some of the quiet solar magnetic flux could be attributed to a small-scale dynamo (SSD) operating in the convection zone. An SSD operating in cool main-sequence stars is expected to affect the atmospheric structure, in particular the convection, and should have observational signatures. We aim to investigate the distribution of these fields as well as their effect on intensity characteristics, velocities and spatial distribution of kinetic (KE) and magnetic energy (ME) in the lower photosphere of spectral types F3V, G2V, K0V and M0V using 3D radiative-MHD simulations. PDFs of field strength at the $\tau=1$ surface are quite similar for all cases. The M0V star displays the strongest fields, but relative to the gas pressure, the fields on the F3V star reach the largest values. All stars display an excess of horizontal field relative to vertical field in the middle photosphere, with this excess becoming increasingly prominent towards later spectral types. These fields result in a decrease in upflow velocities, slightly smaller granules as well as the formation of bright points in intergranular lanes. The spatial distribution of KE and ME is also similar for all cases, implying a simple pressure scale height proportionality of important scales. SSD fields have rather similar effects on the photospheres of cool main-sequence stars, namely, a significant reduction in convective velocities as well as a slight reduction in granule size, and concentration of field to kG levels in intergranular lanes associated with the formation of bright points. The distribution of field strengths and energies is also rather similar., Comment: 11 pages, 14 figures, accepted for publication in A&A

It has long been understood that dilute samples of chiral molecules such as rarefied gases should exhibit Rayleigh optical activity. We extend the existing theory by accounting for molecular dynamics and correlations, thus obtaining a more general theory of Rayleigh-Brillouin optical activity applicable to dense samples such as neat liquids.

Three-dimensional (3D) radiative magnetohydrodynamics (MHD) simulations are the only way to model stellar atmospheres without any ad hoc parameterisations. Several 3D radiative MHD codes have achieved good quantitative agreement with observables for our Sun. We aim to validate the most up-to-date version of the MURaM code against well established quiet Sun measurements, in particular spatially averaged measurements that are relevant for stellar studies. This validation extends the number of solar observables that MURaM can reproduce with high precision. It is also an essential condition for using MURaM to accurately calculate spectra of other cool stars. We simulate the solar upper convection zone and photosphere harbouring a small-scale-dynamo. Using time series of 3D snapshots we calculate the spectral irradiance, limb darkening and selected spectral lines, which we compare to observations. The computed observables agree well with the observations, in particular the limb darkening of the quiet Sun is reproduced remarkably well., Comment: 9 Page, 7 figures, accepted in A&A

Magnetic features on the surface of stars, such as spots and faculae, cause stellar spectral variability on time-scales of days and longer. For stars other than the Sun, the spectral signatures of faculae are poorly understood, limiting our ability to account for stellar pollution in exoplanet transit observations. Here we present the first facular contrasts derived from magnetoconvection simulations for K0, M0 and M2 main-sequence stars and compare them to previous calculations for G2 main-sequence stars. We simulate photospheres and immediate subsurface layers of main-sequence spectral types between K0 and M2, with different injected vertical magnetic fields (0 G, 100 G, 300 G and 500 G) using MURaM, a 3D radiation-magnetohydrodynamics code. We show synthetic spectra and contrasts from the UV (300 nm) to the IR (10000 nm) calculated using the ATLAS9 radiative transfer code. The calculations are performed for nine viewing angles to characterise the facular radiation across the disc. The brightness contrasts of magnetic regions are found to change significantly across spectral type, wavelength and magnetic field strength, leading to the conclusion that accurate contrasts cannot be found by scaling solar values. This is due to features of different size, apparent structure and spectral brightness emerging in the presence of a given magnetic field for different spectral types., Comment: 17 pages, 12 figures, to be published in MNRAS

Theoretical models for the solar dynamo range from simple low-dimensional ``toy models'' to complex 3D-MHD simulations. Here we mainly discuss appproaches that are motivated and guided by solar (and stellar) observations. We give a brief overview of the evolution of solar dynamo models since 1950s, focussing upon the development of the Babcock-Leighton approach between its introduction in the 1960s and its revival in the 1990s after being long overshadowed by mean-field turbulent dynamo theory. We summarize observations and simple theoretical deliberations that demonstrate the crucial role of the surface fields in the dynamo process and and give quantitative analyses of the generation and loss of toroidal flux in the convection zone as well as of the production of poloidal field resulting from flux emergence at the surface. Furthermore, we discuss possible nonlinearities in the dynamo process suggested by observational results and present models for the long-term variability of solar activity motivated by observations of magnetically active stars and the inherent randomness of the dynamo process., Comment: submitted to Space Science Reviews

Drawing inspiration from a remarkable chiral force found in nature, we show that a static electric field combined with an optical lin$\perp$lin polarization standing wave can exert a chiral optical force on a small chiral molecule that is several orders of magnitude stronger than other chiral optical forces proposed to date, being based on leading electric-dipole interactions rather than relying on weak magnetic-dipole and electric-quadrupole interactions. Our chiral optical force applies to most small chiral molecules, including isotopically chiral molecules, and does not require a specific energy-level structure. Potential applications range from chiral molecular matter-wave interferometry for precision metrology and tests of fundamental physics to the resolution of enantiomers for use in chemistry and biology.

Despite investments in multiple space and ground-based solar observatories by the global community, the Sun's polar regions remain unchartered territory - the last great frontier for solar observations. Breaching this frontier is fundamental to understanding the solar cycle - the ultimate driver of short-to-long term solar activity that encompasses space weather and space climate. Magnetohydrodynamic dynamo models and empirically observed relationships have established that the polar field is the primary determinant of the future solar cycle amplitude. Models of solar surface evolution of tilted active regions indicate that the mid to high latitude surges of magnetic flux govern dynamics leading to the reversal and build-up of polar fields. Our theoretical understanding and numerical models of this high latitude magnetic field dynamics and plasma flows - that are a critical component of the sunspot cycle - lack precise observational constraints. This limitation compromises our ability to observe the enigmatic kilo Gauss polar flux patches and constrain the polar field distribution at high latitudes. The lack of these observations handicap our understanding of how high latitude magnetic fields power polar jets, plumes, and the fast solar wind that extend to the boundaries of the heliosphere and modulate solar open flux and cosmic ray flux within the solar system. Accurate observation of the Sun's polar regions, therefore, is the single most outstanding challenge that confronts Heliophysics. This paper argues the scientific case for novel out of ecliptic observations of the Sun's polar regions, in conjunction with existing, or future multi-vantage point heliospheric observatories. Such a mission concept can revolutionize the field of Heliophysics like no other mission concept has - with relevance that transcends spatial regimes from the solar interior to the heliosphere., Comment: This White Paper was submitted in 2022 to the United States National Academies Solar and Space Physics (Heliophysics) Decadal Survey

The reliable characterization of planetary atmospheres with transmission spectroscopy requires realistic modeling of stellar magnetic features, since features that are attributable to an exoplanet atmosphere could instead stem from the host star's magnetic activity. Current retrieval algorithms for analysing transmission spectra rely on intensity contrasts of magnetic features from 1D radiative-convective models. However, magnetic features, especially faculae, are not fully captured by such simplified models. Here we investigate how well such 1D models can reproduce 3D facular contrasts, taking a G2V star as an example. We employ the well established radiative magnetohydrodynamic code MURaM to obtain three-dimensional simulations of the magneto-convection and photosphere harboring a local small-scale-dynamo. Simulations without additional vertical magnetic fields are taken to describe the quiet solar regions, while simulations with initially 100 G, 200 G and 300 G vertical magnetic fields are used to represent different magnetic activity levels. Subsequently, the spectra emergent from the MURaM cubes are calculated with the MPS-ATLAS radiative transfer code. We find that the wavelength dependence of facular contrast from 1D radiative-convective models cannot reproduce facular contrasts obtained from 3D modeling. This has far reaching consequences for exoplanet characterization using transmission spectroscopy, where accurate knowledge of the host star is essential for unbiased inferences of the planetary atmospheric properties., Comment: 7 pages, 2 figures, submitted to APJL

A striking feature of the solar cycle is that at the beginning, sunspots appear around mid-latitudes, and over time the latitudes of emergences migrate towards the equator.The maximum level of activity (e.g., sunspot number) varies from cycle to cycle.For strong cycles, the activity begins early and at higher latitudes with wider sunspot distributions than for weak cycles. The activity and the width of sunspot belts increase rapidly and begin to decline when the belts are still at high latitudes. Surprisingly, it has been reported that in the late stages of the cycle the level of activity (sunspot number) as well as the widths and centers of the butterfly wings all have the same statistical properties independent of how strong the cycle was during its rise and maximum phases.We have modeled these features using a Babcock--Leighton type dynamo model and show that the flux loss through magnetic buoyancy is an essential nonlinearity in the solar dynamo.Our study shows that the nonlinearity is effective if the flux emergence becomes efficient at the mean-field strength of the order of $10^4$~G in the lower part of the convection zone., Comment: Accepted in Phys.Rev.Lett. (PRL)

The Babcock-Leighton (BL) flux-transport model is a widely-accepted dynamo model of the Sun. This dynamo model has been extensively studied in a two-dimensional (2D) mean-field framework in both kinematic and non-kinematic regimes. Recent three-dimensional (3D) models have been restricted to the kinematic regime. In these models, the surface poloidal flux is produced by the emergence of bipolar magnetic regions (BMRs) that are tilted according to Joy's law. We investigate the prescription for emergence of a BMR in 3D non-kinematic simulations. We also report initial results of cyclic BL dynamo simulation. We extend a conventional 2D mean-field model of the BL flux-transport dynamo into 3D non-kinematic regime. The large-scale mean flows are driven by the parameterized $\Lambda$-effect in this model. For the induction equation, we use a BL source term by which the surface BMRs are produced in response to the dynamo-generated toroidal field inside the convection zone. We find that, in the 3D non-kinematic regime, the tilt angle of a newly-emerged BMR is very sensitive to the prescription for the subsurface structure of the BMR. Anti-Joy tilt angles are found unless the BMR is deeply embedded in the convection zone. We also find that the leading spot tends to become stronger than the following spot. The anti-Joy's law trend and the morphological asymmetry of the BMRs can be explained by the Coriolis force acting on the Lorentz-force-driven flows. Furthermore, we demonstrate that the solar-like magnetic cycles can be successfully obtained if the Joy's law is explicitly given in the BL $\alpha$-effect. In these cyclic dynamo simulation, a strong Lorentz force feedback leads to cycle modulations in the differential rotation and meridional circulation. The non-axisymmetric components of the flows are found to exist as inertial modes such as the equatorial Rossby modes., Comment: 18 pages, 19 figures, accepted for publication in A&A

Several types of inertial modes have been detected on the Sun. Properties of these inertial modes have been studied in the linear regime but have not been studied in nonlinear simulations of solar rotating convection. Comparing the nonlinear simulations, the linear theory, and the solar observations is important to better understand the differences between the models and the real Sun. We wish to detect and characterize the modes present in a nonlinear numerical simulation of solar convection, in particular to understand the amplitudes and lifetimes of the modes. We developed a code with a Yin-Yang grid to carry out fully-nonlinear numerical simulations of rotating convection in a spherical shell. The stratification is solar-like up to 0.96R. The simulations cover a duration of about 15 solar years. Various large-scale modes at low frequencies are extracted from the simulation. Their characteristics are compared to those from the linear model and to the observations. Among other modes, both the equatorial Rossby modes and the columnar convective modes are seen in the simulation. The columnar convective modes contain most of the large-scale velocity power outside the tangential cylinder and substantially contribute to the heat and angular momentum transport. Equatorial Rossby modes with no radial node (n=0) are also found: They have the same spatial structures as the linear eigenfunctions. They are stochastically excited by convection and have the amplitudes of a few m/s and mode linewidths of about 20-30 nHz, which are comparable to those observed on the Sun. We also confirm the existence of the mixed modes between the equatorial Rossby modes and the columnar convective modes in our nonlinear simulation, as predicted by the linear eigenmode analysis. We also see the high-latitude mode with m=1 in our nonlinear simulation but its amplitude is much weaker than that observed on the Sun., Comment: 18 pages, 21 figures, 1 table. Astronomy & Astrophysics

Some of the small-scale solar magnetic flux can be attributed to a small-scale dynamo (SSD) operating in the near-surface convection. The SSD fields have consequences for solar granular convection, basal flux, as well as chromospheric heating. A similar SSD mechanism is expected to be active in the near-surface convection of other cool main-sequence stars, but this has never been investigated. We aim to investigate changes in stratification and convection due to inclusion of SSD fields for F3V, G2V, K0V and M0V spectral types in the near-surface convection. 3D magnetohydrodynamic (MHD) models of the four stellar boxes, covering the subsurface convection zone up to the lower photosphere in a small cartesian box, are studied using the \textit{MURaM} radiative-MHD simulation code. The SSD runs are compared against reference hydrodynamic runs. An SSD is found to efficiently produce magnetic field with energies ranging between 5\% to 80\% of the plasma kinetic energy at different depths. This ratio tends to be larger for larger $T_{\mathrm{eff}}$. The relative change in density and gas pressure stratification for the deeper convective layers due to SSD magnetic fields is negligible, except for the F-star. For the F-star, there is a substantial reduction in convective velocities due to Lorentz force feedback from magnetic fields, which, in turn, reduces the turbulent pressure. SSD in near-surface convection for cool main-sequence stars introduces small but significant changes in thermodynamic stratification (especially for the F-star) due to reduction in convective velocities., Comment: Update (20.07.2023): an errata (appendix D) has been included to correct a small error in the derivation of turbulent pressure in appendix B. In addition, the text has been updated with the published version. 10 pages, 7 figures, accepted for publication in A&A

On the one hand, several types of global-scale inertial modes of oscillation have been observed on the Sun. They include the equatorial Rossby modes, critical-latitude modes, and high-latitude modes. On the other hand, the columnar convective modes (predicted by simulations; also known as banana cells or thermal Rossby waves) remain elusive. We aim to investigate the influence of turbulent diffusivities, non-adiabatic stratification, differential rotation, and a latitudinal entropy gradient on the linear global modes of the rotating solar convection zone. We solve numerically for the eigenmodes of a rotating compressible fluid inside a spherical shell. We identify modes in the inertial frequency range including the columnar convective modes, as well as modes of mixed character. The corresponding mode dispersion relations and eigenfunctions are computed for azimuthal orders $m \leq 16$. The three main results are as follows. Firstly, we find that, for $m \gtrsim 5$, the radial dependence of the equatorial Rossby modes with no radial node ($n=0$) is radically changed from the traditional expectation ($r^m$) for turbulent diffusivities $\gtrsim 10^{12}$ cm$^2$ s$^{-1}$. Secondly, we find mixed modes, i.e. modes that share properties of the equatorial Rossby modes with one radial node ($n=1$) and the columnar convective modes. Thirdly, we show that the $m=1$ high-latitude mode in the model is consistent with the solar observations when the latitudinal entropy gradient corresponding to a thermal wind balance is included (baroclinally unstable mode). To our knowledge, this work is the first realistic eigenvalue calculation of the global modes of the rotating solar convection zone. This calculation reveals a rich spectrum of modes in the inertial frequency range, which can be directly compared to the observations. In turn, the observed modes can inform us about the solar convection zone., Comment: 24 pages, 29 figures, submitted to Astronomy & Astrophysics on 20 Jan 2022

In this paper, we present a re-analysis of SuperCDMS data using a profile likelihood approach to search for sub-GeV dark matter particles (DM) through two inelastic scattering channels: bremsstrahlung radiation and the Migdal effect. By considering possible inelastic scattering channels, experimental sensitivity can be extended to DM masses that would otherwise be undetectable through the DM-nucleon elastic scattering channel, given the energy threshold of current experiments. We exclude DM masses down to $220~\textrm{MeV}/c^2$ at $2.7 \times 10^{-30}~\textrm{cm}^2$ via the bremsstrahlung channel. The Migdal channel search excludes DM masses down to $30~\textrm{MeV}/c^2$ at $5.0 \times 10^{-30}~\textrm{cm}^2$., Comment: This paper is being withdrawn due to an error in data selection during the analysis. Although incorrect, the limits are roughly representative of the sensitivity. The new corrected version of the result will be uploaded once ready

Active regions (ARs) play an important role in the magnetic dynamics of the Sun. Solar surface flux transport models (SFTMs) are used to describe the evolution of the radial magnetic field at the solar surface. There is however uncertainty about using these models in the early stage of AR evolution. We aim to test the applicability of SFTMs in the first days after the emergence of ARs by comparing them with observations. The models we employ range from passive evolution to models where the inflows around ARs are included. We simulate the evolution of the surface magnetic field of 17 emerging active regions using a local surface flux transport simulation. We selected regions that do not form fully-fledged sunspots that exhibit moat flows. The simulation includes diffusion and advection. We use observed flows from local correlation tracking of solar granulation, as well as parametrizations of the inflows around ARs. To evaluate our simulations, we measure the cross correlation between the observed and the simulated magnetic field, as well as the total unsigned flux of the ARs, over time. We also test the validity of our simulations by varying the starting time relative to the emergence of flux. We find that the simulations using observed surface flows can reproduce the evolution of the observed magnetic flux. The effect of buffeting of the field by supergranulation can be described as a diffusion process. The SFTM is applicable after 90% of the peak total unsigned flux of the AR has emerged. Diffusivities in the range between $D=250$ to $720$ km$^2$/s are consistent with the evolution of the AR flux in the first five days after this time. We find that the converging flows around emerging ARs are not important for the evolution of the total flux of the AR in these first five days; their effect of increasing flux cancellation is balanced by the decrease of flux transport away from the AR., Comment: Accepted for publication in Astronomy & Astrophysics. 13 pages, 11 figures

The oscillations of a slowly rotating star have long been classified into spheroidal and toroidal modes. The spheroidal modes include the well-known 5-min acoustic modes used in helioseismology. Here we report observations of the Sun's toroidal modes, for which the restoring force is the Coriolis force and whose periods are on the order of the solar rotation period. By comparing the observations with the normal modes of a differentially rotating spherical shell, we are able to identify many of the observed modes. These are the high-latitude inertial modes, the critical-latitude inertial modes, and the equatorial Rossby modes. In the model, the high-latitude and critical-latitude modes have maximum kinetic energy density at the base of the convection zone, and the high-latitude modes are baroclinically unstable due to the latitudinal entropy gradient. As a first application of inertial-mode helioseismology, we constrain the superadiabaticity and the turbulent viscosity in the deep convection zone., Comment: Forthcoming article, Astronomy and Astrophysics

We study the properties of slow magneto-acoustic waves that are naturally excited due to turbulent convection and investigate their role in the energy balance of a plage region using three dimensional (3D) radiation-MHD simulations. We calculate the horizontally averaged (over the whole domain) frequency power spectra for both longitudinal and vertical (i.e. the component perpendicular to the surface) components of velocity. To compare our results with the observations we degrade the simulation data with Gaussian kernels having FWHM of 100 km and 200 km, and calculate horizontally averaged power spectra for the vertical component of velocity. The power spectra of the longitudinal component of velocity, averaged over field lines in the core of a kG magnetic flux concentration, reveal that the dominant period of oscillations shifts from around 6.5 minutes in the photosphere to around 4 minutes in the chromosphere. At the same time, the velocity power spectra, averaged horizontally over the whole domain, show that low frequency waves (approximately 6.5 minute period) may reach well into the chromosphere. Importantly, waves with frequencies above 5 mHz propagating along different field lines are found to be out of phase with each other even within a single magnetic concentration. The horizontally averaged power spectra of the vertical component of velocity at various effective resolutions show that the observed acoustic wave energy fluxes are underestimated, by a factor of three even if determined from observations carried out at a high spatial resolution of 200 km. Our results show that longitudinal waves carry (just) sufficient energy to heat the chromosphere in solar plage. We conjecture that current observations (with spatial resolution around 200 km) underestimate the energy flux by roughly a factor of three, or more if the observations have lower spatial resolution., Comment: Accepted for publication in A & A

A mission to view the solar poles from high helio-latitudes (above 60$^\circ$) will build on the experience of Solar Orbiter as well as a long heritage of successful solar missions and instrumentation (e.g. SOHO \cite{SOHO}, STEREO \cite{stereo}, Hinode \cite{Hinode}, SDO \cite{SDO}), but will focus for the first time on the solar poles, enabling scientific investigations that cannot be done by any other mission. One of the major mysteries of the Sun is the solar cycle. The activity cycle of the Sun drives the structure and behaviour of the heliosphere and is, of course, the driver of space weather. In addition, solar activity and variability provides fluctuating input into the Earth climate models, and these same physical processes are applicable to stellar systems hosting exoplanets. One of the main obstructions to understanding the solar cycle, and hence all solar activity, is our current lack of understanding of the polar regions. In this White Paper, submitted to the European Space Agency in response to the Voyage 2050 call, we describe a mission concept that aims to address this fundamental issue. In parallel, we recognise that viewing the Sun from above the polar regions enables further scientific advantages, beyond those related to the solar cycle, such as unique and powerful studies of coronal mass ejection processes, from a global perspective, and studies of coronal structure and activity in polar regions. Not only will these provide important scientific advances for fundamental stellar physics research, they will feed into our understanding of impacts on the Earth and other planets' space environment., Comment: 29 pages, 9 figures, White paper for ESA Voyage 2050

Size distribution of sunspots provides key information about the generation and emergence processes of the solar magnetic field. Previous studies on the size distribution have primarily focused on either the whole group or individual spot areas. In this paper, we investigate the organization of spot areas within sunspot groups. In particular, we analyze the ratio, $\rm{R}$, of the area of the biggest spot ($\rm{A_{big\_spot}}$) inside a group, to the total area of that group ($\rm{A_{group}}$). We use sunspot observations from Kislovodsk, Pulkovo and Debrecen observatories, together covering solar cycles 17 to 24. We find that at the time when the group area reaches its maximum, the single biggest spot in a group typically occupies about 60% of the group area. For half of all groups, $\rm R$ lies in the range between roughly 50% and 70%. We also find R to change with the group area, $\rm{A_{group}}$, such that $\rm{R}$ reaches a maximum of about 0.65 for groups with $\rm{A_{group}}\approx 200\mu$Hem and then remains at about 0.6 for lager groups. Our findings imply a scale invariant emergence pattern, providing an observational constraint on the emergence process. Furthermore, extrapolation of our results to larger sunspot groups may have a bearing on the giant unresolved starspot features found in Doppler images of highly active sun-like stars. Our results suggest that such giant features are composed of multiple spots, with the largest spot occupying roughly 55--75% of the total group area (i.e. of the area of the giant starspots seen in Doppler images)., Comment: Accepted for publication in Astronomy and Astrophysics

The fluting instability has been suggested as the driver of the subsurface structure of sunspot flux tubes. We conducted a series of numerical experiments where we used flux tubes with different initial curvatures to study the effect of the fluting instability on the subsurface structure of spots. We used the MURaM code, which has previously been used to simulate complete sunspots, to first compute four sunspots in the slab geometry and then two complete circular spots of opposite polarities. We find that the curvature of a flux tube indeed determines the degree of fluting the flux tube will undergo - the more curved a flux tube is, the more fluted it becomes. In addition, sunspots with strong curvature have strong horizontal fields at the surface and therefore readily form penumbral filaments. The fluted sunspots eventually break up from below, with lightbridges appearing at the surface several hours after fluting commences., Comment: 8 pages, 5 figures, Accepted to ApJ

Vortex-flows exist across a broad range of spatial and temporal scales in the solar atmosphere. Small-scale vortices have been proposed to play an important role in energy transport in the solar atmosphere. However, their physical properties remain poorly understood due to the limited spatial resolution of the observations. We aim to explore and analyze the physical properties of small-scale vortices inside magnetic flux tubes using numerical simulations, and to investigate whether they contribute to heating the chromosphere in a plage region. Using the three-dimensional (3D) radiative magnetohydrodynamic (MHD) simulation code 'MURaM', we perform numerical simulations of a unipolar solar plage region. To detect and isolate vortices, we use the Swirling Strength criterion and select the locations where the fluid is rotating with an angular velocity greater than a certain threshold. We concentrate on small-scale as they are the strongest and carry most of the energy. We explore the spatial profiles of physical quantities viz. density, horizontal velocity, etc. inside these vortices. Moreover, to apprehend their general characteristics, a statistical investigation is performed. Magnetic flux tubes have a complex filamentary substructure harbouring an abundance of small-scale vortices. At the interfaces between vortices strong current sheets are formed that may dissipate and heat the solar chromosphere. Statistically, vortices have higher densities and higher temperatures than the average values at the same geometrical height in the chromosphere. We conclude that small-scale vortices are ubiquitous in solar plage regions, and they are denser and hotter structures that contribute to chromospheric heating, possibly by dissipation of the current sheets formed at their interfaces., Comment: accepted for publication in A&A

The tilt of solar active regions described by Joy's law is essential for converting a toroidal field to a poloidal field in Babcock-Leighton dynamo models. In thin flux tube models the Coriolis force causes Joy's law, acting on east-west flows as they rise towards the surface. Our goal is to measure the evolution of the average tilt angle of hundreds of active regions as they emerge, so that we can constrain the origins of Joy's law. We measured the tilt angle of the primary bipoles in 153 emerging active regions in the Solar Dynamics Observatory Helioseismic Emerging Active Region survey. We used line-of-sight magnetic field measurements averaged over 6 hours to define the polarities and measure the tilt angle up to four days after emergence. We find that at the time of emergence the polarities are on average aligned east-west, and that neither the separation nor the tilt depends on latitude. We do find, however, that ARs at higher latitudes have a faster north-south separation speed than those closer to the equator at the emergence time. After emergence, the tilt angle increases and Joy's law is evident about two days later. The scatter in the tilt angle is independent of flux until about one day after emergence, when higher-flux regions have a smaller scatter in tilt angle than lower-flux regions. Our finding that active regions emerge with an east-west alignment is surprising since thin flux tube models predict that tilt angles of rising flux tubes are generated below the surface. Previously reported tilt angle relaxation of deeply anchored flux tubes can be largely explained by the change in east-west separation. We conclude that Joy's law is caused by an inherent north-south separation speed present when the flux first reaches the surface, and that the scatter in the tilt angle is consistent with buffeting of the polarities by supergranulation., Comment: accepted in Astronomy and Astrophysics

Magnetic activity of the Sun and other stars causes their brightness to vary. We investigate how typical the Sun's variability is compared to other solar-like stars, i.e. those with near-solar effective temperatures and rotation periods. By combining four years of photometric observations from the Kepler space telescope with astrometric data from the Gaia spacecraft, we measure photometric variabilities of 369 solar-like stars. Most of the solar-like stars with well-determined rotation periods show higher variability than the Sun and are therefore considerably more active. These stars appear nearly identical to the Sun, except for their higher variability. Their existence raises the question of whether the Sun can also experience epochs of such high variability., Comment: Accepted for publication in Science. 3 (main) + 10 (supplementary) figures

There are no direct spatially resolved observations of spots on stars other than the Sun and starspot properties are inferred indirectly through lightcurves and spectropolarimetric data. We present the first self-consistent 3D radiative MHD computations of starspots on G2V, K0V and M0V stars, which will help to better understand observations of activity, variability and magnetic fields in late-type main-sequence stars. We used the MURaM code, which has been extensively used to compute "realistic" sunspots, for our simulations. We aim to study how fundamental starspot properties such as intensity contrast, temperature and magnetic field strength vary with spectral type. We first simulated in 2D, multiple spots of each spectral type to find out appropriate initial conditions for our 3D runs. We find that with increasing stellar effective temperature, there is an increase in the temperature difference between the umbra of the spot and its surrounding photosphere, from 350K on the M0V star to 1400K on the G2V star. This trend in our simulated starspots is consistent with observations. The magnetic field strengths of all the starspot umbrae are in the 3-4.5 kG range. The G2V and K0V umbrae have comparable magnetic field strengths around 3.5 kG, while the M0V umbra has a relatively higher field strength around 4 kG. We discuss the physical reasons behind both these trends. All of the three starspots develop penumbral filament-like structures with Evershed flows. The average Evershed flow speed drops from 1.32 km s$^{-1}$ in the G2V penumbra to 0.6 km s$^{-1}$ in the M0V penumbra., Comment: Accepted to ApJ

The 1-D mean-field equation describing the evolution of the subsurface toroidal field can be used together with the observed surface radial field to model the subsurface toroidal flux density. We aim to test this model and determine the relationship between the observationally inferred surface toroidal field (as a proxy for flux emergence), and the modelled subsurface toroidal flux density. We use a combination of sunspot area observations, the surface toroidal field inferred from WSO line-of-sight magnetic field observations, and compare with the results of a 1-D mean-field evolution equation for the subsurface toroidal field, driven by the observed radial field from the National Solar Observatory/Kitt Peak and SOLIS observations. We derive calibration curves relating the subsurface toroidal flux density to the observed surface toroidal field strengths and sunspot areas. The calibration curves are for two regimes, one corresponding to ephemeral region emergence outside of the butterfly wings, the other to active region emergence in the butterfly wings. We discuss this in terms of the size and vertical velocity associated with the two types of flux emergence., Comment: A&A, accepted

Our goal is to constrain models of active region formation by tracking the average motion of active region polarity pairs as they emerge onto the surface. We measured the motion of the two main opposite polarities in 153 emerging active regions (EARs) using line-of-sight magnetic field observations from the Solar Dynamics Observatory Helioseismic Emerging Active Region (SDO/HEAR) survey (Schunker et al. 2016). We first measured the position of each of the polarities eight hours after emergence and tracked their location forwards and backwards in time. We find that, on average, the polarities emerge with an east-west orientation and the separation speed between the polarities increases. At about 0.1 days after emergence, the average separation speed reaches a peak value of 229 +/- 11 m/s, and then starts to decrease, and about 2.5 days after emergence the polarities stop separating. We also find that the separation and the separation speed in the east-west direction are systematically larger for active regions with higher flux. Our results reveal two phases of the emergence process defined by the rate of change of the separation speed as the polarities move apart. Phase 1 begins when the opposite polarity pairs first appear at the surface, with an east-west alignment and an increasing separation speed. We define Phase 2 to begin when the separation speed starts to decrease, and ends when the polarities have stopped separating. This is consistent with the picture of Chen, Rempel, & Fan (2017): the peak of a flux tube breaks through the surface during Phase 1. During Phase 2 the magnetic field lines are straightened by magnetic tension, so that the polarities continue to move apart, until they eventually lie directly above their anchored subsurface footpoints., Comment: accepted A&A

Power spectra of solar activity based on historical records of sunspot numbers and on cosmogenic isotopes show peaks with enhanced power apart from the dominant 11-year solar cycle, such as the 90-year Gleissberg cycle or the 210-year de Vries cycle. In a previous paper we have shown that the overall shape of the power spectrum is well represented by the results of the generic normal form model for a noisy and weakly nonlinear limit cycle, with parameters all determined by observations. Using this model as a null case, we show here that all local peaks with enhanced power, apart from the 11-year band, are consistent with realisation noise. Even a $3\sigma$ peak is expected to occur with a probability of about 0.25 at least once among the 216 period bins resolved by the cosmogenic isotope data. This casts doubt upon interpretations of such peaks in terms of intrinsic periodicities of the solar dynamo process., Comment: A&A accepted

We point out that data collected by the Event Horizon Telescope or a similar project might yield new information about the photon rest mass $m_\gamma$, in the form of evidence that $m_\gamma\ne 0$ together with a lower bound on $m_\gamma$ or a new upper bound on $m_\gamma$. Using Sgr A*, there is scope to improve on the best upper bound obtained via laboratory tests of Coulomb's law by up to nineteen orders of magnitude.

We give an explicit and general description of the energy, linear momentum, angular momentum and boost momentum of a molecule to order $1/c^2$, where it necessary to take account of kinetic contributions made by the electrons and nuclei as well as electromagnetic contributions made by the intramolecular field. A wealth of interesting subtleties are encountered that are not seen at order $1/c^0$, including relativistic Hall shifts, anomalous velocities and hidden momenta. Some of these have well known analogues in solid state physics.