arXiv subjects

Robert H. Cameron

Publications and source records attributed to Robert H. Cameron.

At least 19 recordsLinked to original sources

arXiv2026

Self-consistent numerical simulations for the formation and dynamics of solar prominences

Solar prominences are cool and dense plasma structures floating in the hot solar corona. They are ubiquitous features in the solar atmosphere, but their formation mechanism is still unclear. Here we perform comprehensive fully three-dimensional numerical simulations of prominence formation including the physics necessary to describe all atmospheric layers of the sun. With appropriate initial conditions for the magnetic field, solar prominences form self-consistently in the simulations. The formation starts by the random ejection of a dense plasma seed from the chromosphere into the corona. Subsequently, the prominence is built up by a combination of plasma injections from the chromosphere and condensation of inflowing coronal plasma. The prominence properties qualitatively match those of observed prominences. Our findings demonstrate the importance of the dynamics at and below the solar surface in the formation and evolution of solar prominences. This suggests that subsurface dynamics should also be considered in the study of prominence eruptions, which can be associated with coronal mass ejections.

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arXiv2026

Simulations of facular magnetic fields on cool stars I: Main sequence stars with solar metallicity

Stellar convection in the presence of magnetic field affects the emergent intensity, as well as the structure and evolution of cool main-sequence dwarfs. We aim to understand the effect of faculae-like field strengths on near-surface stellar convection using 3D radiative MHD simulations of near-surface magneto-convection. We compare simulations of F, G, K and M main-sequence stars with a small-scale dynamo (SSD) to faculae-like spatially averaged field strengths (from 100 to 500 G). We focus on the effect of imposed magnetic field on the thermodynamic stratification and velocities, along with the bolometric intensity and surface field strength. Imposed magnetic fields result in reduced average density and gas pressure near the surface compared to the SSD simulations. The temperature stratification also shows a dip at and just below the stellar surface. The changes in average bolometric intensity are within a percent, with different trends with field strength for different stellar types. In addition, the convective velocities are reduced. The magnitude of changes in thermodynamic quantities are related to field strength as well as the stellar $T_{\rm eff}$. Faculae-strength magnetic fields modify the near surface convection by reducing gas pressure and density as well as suppressing convection in regions with strong field concentrations. The strength of these effects depends on the stellar type.

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arXiv2025

Coriolis force acting on near-surface horizontal flows during simulations of flux emergence produces a tilt angle consistent with Joy's law on the Sun

Joy's law describes the tilt of bipolar active regions on the Sun away from an east-west orientation, where the flux of the polarity concentrated at the prograde side tends to be closer to the equator than the polarity on the retrograde side. Joy's law is attributed to the Coriolis force because of the observed increase in tilt angle at higher latitudes. This tilt plays a crucial role in some solar dynamo models. Our goal is to model the effects of the Coriolis force on a flux tube as it rises through the near-surface convection zone. We use a three-dimensional Cartesian magnetohydrodynamic simulation of an untwisted flux tube ascending from a depth of 11 Mm. We model the Coriolis effect using the f-plane approximation, that only considers and acts on horizontal flows. On the Sun, Joy's law is weak and is only evident as an average over many active regions. To achieve a measurable effect in a single simulation, we consider a rotation rate 110 times faster than the Sun. The simulation shows that the flux tube emerges at the surface with a tilt angle consistent with Joy's law when scaled to the Sun's slower rotation, and the tilt angle does not substantially change after emergence. This shows that the Coriolis force acting on flows horizontal to the surface within the near-surface convection zone is consistent with Joy's law.

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arXiv2025

Enhanced magnetic activity in rapidly rotating binary stars

Stellar activity is fundamental to stellar evolution and the formation and habitability of exoplanets. The interaction between convective motions and rotation in cool stars results in a dynamo process that drives magnetic surface activity. In single stars, activity increases with rotation rate until it saturates for stars with rotation periods Prot < 3 - 10 d. However, the mechanism responsible for saturation remains unclear. Observations indicate that red giants in binary systems that are in spin-orbit resonance exhibit stronger chromospheric activity than single stars with similar rotation rates, suggesting that tidal flows can influence surface activity. Here, we investigate the chromospheric activity of main-sequence binary stars to understand the impact of tidal forces on saturation phenomena. For binaries with 0.5 < Prot/d < 1, mainly contact binaries that share a common thermal envelope, we find enhanced activity rather than saturation. This result supports theoretical predictions that a large-scale $α$ - $ω$ dynamo during common-envelope evolution can generate strong magnetic fields. We also observe supersaturation in chromospheric activity, a phenomenon tentatively noted previously in coronal activity, where activity levels fall below saturation and decrease with shorter rotation periods. Our findings emphasise the importance of studying stellar activity in stars with extreme properties compared to the Sun's.

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arXiv2024

Low-latitude magnetic flux emergence on rapidly rotating solar-type stars

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, assuming 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.

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arXiv2024

Combined Surface Flux Transport and Helioseismic Far-side Active Region Model (FARM)

Maps of the magnetic field at the Sun's surface are commonly used as boundary conditions in space-weather modeling. However, continuous observations are only available from the Sun's Earth-facing side. One commonly used approach to mitigate the lack of far-side information is to apply a surface flux transport (SFT) model to model the evolution of the magnetic field as the Sun rotates. Helioseismology can image active regions on the far side using acoustic oscillations, and hence has the potential to improve the modeled surface magnetic field. In this study, we propose a novel approach for estimating magnetic fields of active regions on the Sun's far side based on seismic measurements, and then include them into a SFT model. To calibrate seismic signal to magnetic field, we apply our SFT model to line-of-sight magnetograms from SDO/HMI to obtain reference maps of global magnetic fields. The resulting maps are compared with seismic maps on the Sun's far side computed using helioseismic holography. The spatial structure of the magnetic field within an active region is reflected in the spatial structure of seismic phase shifts. We assign polarities to the unipolar magnetic-field concentrations based on Hale's law and require approximate flux balance between the two polarities. From 2010 to 2024, we modeled 859 active regions, with an average total unsigned flux of $7.84\cdot 10^{21}$ Mx and an average area of $4.48\cdot 10^{10}$ km$^{2}$. Approximately $4.2\%$ of the active regions were found to have an anti-Hale configuration, which we manually corrected. Comparisons between modeled open-field areas and EUV observations reveal a substantial improvement in agreement when far-side active regions are included. This proof of concept study demonstrates the potential of the ``combined surface flux transport and helioseismic Far-side Active Region Model'' (FARM) to improve space-weather modeling.

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arXiv2024

The rush to the poles and the role of magnetic buoyancy in the solar dynamo

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.

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arXiv2024

The mean solar butterfly diagram and poloidal field generation rate at the surface of the Sun

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 $αΩ$-type dynamo models. The Babcock-Leighton $α$-effect is consistent with observations, a result that can be appreciated only if the observational data is averaged in some way.

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arXiv2024

Solar Inertial Modes

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.

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arXiv2024

A flux-independent increase in outflows prior to the emergence of active regions on the Sun

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, $Δ\, \mathrm{div} \, \mathbf{v_h} = (-4.9 \pm 1.7) \times 10^{-6}$ 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.

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arXiv2024

The Sun's differential rotation is controlled by high-latitude baroclinically unstable inertial modes

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.

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arXiv2024

Stellar Surface Magnetic Fields Impact Limb Darkening

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.

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arXiv2023

Small-scale Dynamo in Cool Stars III. Changes in the photospheres of F3V to M0V stars

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 $τ=1$ 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.

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arXiv2023

Small-scale Dynamo in Cool Stars: I. Changes in stratification and near-surface convection for main-sequence spectral types

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.

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arXiv2022

Exploring the Solar Poles: The Last Great Frontier of the Sun

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.

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arXiv2022

Three-dimensional non-kinematic simulation of post-emergence evolution of bipolar magnetic regions and Babcock-Leighton dynamo of the Sun

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 $Λ$-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 $α$-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.

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arXiv2022

Theory of solar oscillations in the inertial frequency range: Amplitudes of equatorial modes from a nonlinear rotating convection simulation

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.

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arXiv2022

Theory of solar oscillations in the inertial frequency range: Linear modes of the convection zone

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.

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