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M. Rempel

Publications and source records attributed to M. Rempel.

At least 37 records · Page 2Linked to original sources
arXiv2020

Acoustic-gravity wave propagation characteristics in 3D radiation hydrodynamic simulations of the solar atmosphere

There has been tremendous progress in the degree of realism of three-dimensional radiation magneto-hydrodynamic simulations of the solar atmosphere in the past decades. Four of the most frequently used numerical codes are Bifrost, CO5BOLD, MANCHA3D, and MURaM. Here we test and compare the wave propagation characteristics in model runs from these four codes by measuring the dispersion relation of acoustic-gravity waves at various heights. We find considerable differences between the various models. The height dependence of wave power, in particular of high-frequency waves, varies by up to two orders of magnitude between the models, and the phase difference spectra of several models show unexpected features, including $\pm180^\circ$ phase jumps.

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arXiv2020

On the contribution of quiet Sun magnetism to solar irradiance variations: Constraints on quiet Sun variability and grand minimum scenarios

While the quiet Sun magnetic field shows only little variation with the solar cycle, long-term variations cannot be completely ruled out from first principles. We investigate the potential effect of quiet Sun magnetism on spectral solar irradiance through a series of small-scale dynamo simulations with zero vertical flux imbalance ($\langle B_z\rangle=0$) and varying levels of small-scale magnetic field strength, and one weak network case with an additional flux imbalance corresponding to a flux density of $\langle B_z\rangle=100$ G. From these setups we compute the dependence of the outgoing radiative energy flux on the mean vertical magnetic field strength in the photosphere at continuum optical depth $τ=1$ ($\langle \vert B_z\vert\rangle_{τ=1}$). We find that a quiet Sun setup with a mean vertical field strength of $\langle \vert B_z\vert\rangle_{τ=1}=69$ G is about $0.6~\%$ brighter than a non-magnetic reference case. We find a linear dependence of the outgoing radiative energy flux on the mean field strength $\langle \vert B_z\vert\rangle_{τ=1}$ with a relative slope of $1.4\cdot 10^{-4}$ G$^{-1}$. With this sensitivity, only a moderate change of the quiet Sun field strength by $10\%$ would lead to a total solar irradiance variation comparable to the observed solar cycle variation. While this does provide strong indirect constraints on possible quiet Sun variations during a regular solar cycle, it also emphasizes that potential variability over longer time scales could make a significant contribution to longer-term solar irradiance variations.

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arXiv2019

Combining magneto-hydrostatic constraints with Stokes profiles inversions

Inversion codes for the polarized radiative transfer equation can be used to infer the temperature $T$, line-of-sight velocity $v_{\rm los}$, and magnetic field $\rm{\bf B}$ as a function of the continuum optical-depth $τ_{\rm c}$. However, they do not directly provide the gas pressure $P_{\rm g}$ or density $ρ$. In order to obtain these latter parameters, inversion codes rely instead on the assumption of hydrostatic equilibrium (HE) in addition to the equation of state (EOS). Unfortunately, the assumption of HE is rather unrealistic across magnetic field lines. This is because the role of the Lorentz force, among other factors, is neglected. This translates into an inaccurate conversion from optical depth $τ_{\rm c}$ to geometrical height $z$. We aim at improving this conversion via the application of magneto-hydrostatic (MHS) equilibrium instead of HE. We develop a method to solve the momentum equation under MHS equilibrium (i.e., taking the Lorentz force into account) in three dimensions. The method is based on the solution of a Poisson-like equation. Considering the gas pressure $P_{\rm g}$ and density $ρ$ from three-dimensional magneto-hydrodynamic (MHD) simulations of sunspots as a benchmark, we compare the results from the application of HE and MHS equilibrium. We find that HE retrieves the gas pressure and density within an order of magnitude of the MHD values in only about 47 \% of the domain. This translates into an error of about $160-200$ km in the determination of the $z-τ_{\rm c}$ conversion. On the other hand, the application of MHS equilibrium allows determination of $P_{\rm g}$ and $ρ$ within an order of magnitude in 84 \% of the domain. In this latter case, the $z-τ_{\rm c}$ conversion is obtained with an accuracy of $30-70$ km.

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arXiv2019

Superstrong photospheric magnetic fields in sunspot penumbrae

Recently, there have been some reports of unusually strong photospheric magnetic fields (which can reach values of over 7 kG) inferred from Hinode SOT/SP sunspot observations within penumbral regions. These superstrong penumbral fields are even larger than the strongest umbral fields on record and appear to be associated with supersonic downflows. The finding of such fields has been controversial since they seem to show up only when spatially coupled inversions are performed. Here, we investigate and discuss the reliability of those findings by studying in detail observed spectra associated with particularly strong magnetic fields at the inner edge of the penumbra of active region 10930. We apply classical diagnostic methods and various inversions with different model atmospheres to the observed Stokes profiles in two selected pixels with superstrong magnetic fields, and compare the results with a magnetohydrodynamic simulation of a sunspot whose penumbra contains localized regions with strong fields (nearly 5 kG at $τ=1$) associated with supersonic downflows...

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arXiv2017

Evershed and counter-Evershed flows in sunspot MHD simulations

There have been a few reports in the literature of counter-Evershed flows observed in well developed sunspot penumbrae, i.e. flows directed towards the umbra along penumbral filaments. Here we investigate the driving forces of such counter-Evershed flows in a radiative magnetohydrodynamic simulation of a sunspot and compare them with the forces acting on the normal Evershed flow. The simulation covers a timespan of 100 solar hours and generates an Evershed outflow exceeding 8 km s$^{-1}$ in the penumbra along radially aligned filaments where the magnetic field is almost horizontal. Additionally, the simulation produces a fast counter-Evershed flow (i.e., an inflow near $τ= 1$) in some regions within the penumbra, reaching peak flow speeds of $\sim$12 km s$^{-1}$. The counter-Evershed flows are transient and typically last a few hours before they turn into outflows again. By using the kinetic energy equation and evaluating its various terms in the simulation box, we found that the Evershed flow occurs due to overturning convection in a strongly inclined magnetic field while the counter-Evershed flows can be well described as siphon flows.

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arXiv2017

Nature of grand minima and maxima from fully non-linear Flux-Transport Dynamos

We aim to investigate the nature and occurrence characteristics of grand solar minimum and maximum periods, which are observed in the solar proxy records such as 10Be and 14C, using a fully non-linear Babcock-Leighton type flux-transport dynamo including momentum and entropy equations. The differential rotation and meridional circulation are generated from the effect of turbulent Reynolds stress and are subjected to back-reaction from the magnetic field. To generate grand minimum and maximum-like periods in our simulations, we used random fluctuations in the angular momentum transport process, namely the Lambda-mechanism, and in the Babcock-Leighton mechanism. To characterise the nature and occurrences of the identified grand minima and maxima in our simulations, we used the waiting time distribution analyses, which reflects whether the underlying distribution arises from a random or a memory-bearing process. The results show that, in majority of the cases, the distributions of grand minima and maxima reveal that the nature of these events originates from memoryless processes. We also found that in our simulations the meridional circulation speed tends to be smaller during grand maximum, while it is faster during grand minimum periods. The radial differential rotation tend to be larger during grand maxima, while it is smaller during grand minima. The latitudinal differential rotation on the other hand is found to be larger during grand minima.

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arXiv2016

Observed and Simulated Power Spectra of Kinetic and Magnetic Energy retrieved with 2D inversions

We try to retrieve the power spectra with certainty to the highest spatial frequencies allowed by current instrumentation. For this, we use 2D inversion code that were able to recover information up to the instrumental diffraction limit. The retrieved power spectra have shallow slopes extending further down to much smaller scales than found before. They seem not to show any power law. The observed slopes at subgranular scales agree with those obtained from recent local dynamo simulations. Small differences are found for vertical component of kinetic energy that suggest that observations suffer from an instrumental effect that is not taken into account.

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arXiv2016

Internetwork magnetic field as revealed by 2D inversions

Properties of magnetic field in the internetwork regions are still fairly unknown due to rather weak spectropolarimetric signals. We address the matter by using the 2D inversion code that is able to retrieve the information on smallest spatial scales, up to the diffraction limit, while being less susceptible to noise than most of the previous methods used. Performance of the code and the impact of the various effects on the retrieved field distribution is tested first on the realistic MHD simulations. The best inversion scenario is then applied to the real Hinode/SP data. Tests on simulations show: (1) the best choice of node position ensures a decent retrieval of all parameters, (2) code performs well for different configurations of magnetic field, (3) slightly different noise level or slightly different defocus included in the spatial PSF produces no significant effect on the results and (4) temporal integration shifts the field distribution to the stronger, more horizontally inclined field. Although the contribution of the weak field is slightly overestimated due to noise, the 2D inversions are able to recover well the overall distribution of the magnetic field strength. Application of the 2D inversion code on the Hinode/SP internetwork observations reveals a monotonic field strength distribution. The mean field strength at optical depth unity is $\sim 130$~G. At the higher layers, field strength drops as the field becomes more horizontal. Regarding the distribution of the field inclination, tests show that we cannot directly retrieve it with the observations/tools at hand, however the obtained distributions are consistent with those expected from simulations with a quasi-isotropic field inclination after accounting for observational effects.

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arXiv2015

Numerical simulations of sunspot decay: On the penumbra -- Evershed flow -- moat flow connection

We present a series of high-resolution sunspot simulations that cover a time span of up to 100 hours. The simulation domain extends about 18 Mm in depth beneath the photosphere and 98 Mm horizontally. We use open boundary conditions that do not maintain the initial field structure against decay driven by convective motions. We consider two setups: A sunspot simulation with penumbra, and a "naked-spot" simulation in which we removed the penumbra after 20 hours through a change in the magnetic top boundary condition. While the sunspot has an Evershed outflow of 3-4 km/s, the naked spot is surrounded by an inflow of 1-2 km/s in close proximity. However, both spots are surrounded by an outflow on larger scales with a few 100 m/s flow speed in the photosphere. While the sunspot has almost constant magnetic flux content for the simulated time span of 3-4 days, the naked spot decays steadily at a rate of $10^{21}$ Mx/day. A region with reduced downflow filling factor, which is more extended for the sunspot, surrounds both spots. The absence of downflows perturbs the upflow/downflow massflux balance and leads to a large-scale radially overturning flow system, the photospheric component of this flow is to the observable moat flow. The reduction of the downflow filling factor also inhibits submergence of magnetic field in the proximity of the spots, which stabilizes them against decay. While this effect is present for both spots, it is more pronounced for the sunspot and explains the almost stationary magnetic flux content.

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arXiv2015

Efficient small-scale dynamo in solar convection zone

We investigate small-scale dynamo action in the solar convection zone through a series of high resolution MHD simulations in a local Cartesian domain with 1$R_\odot$ (solar radius) of horizontal extent and a radial extent from 0.715 to 0.96$R_\odot$. The dependence of the solution on resolution and diffusivity is studied. For a grid spacing of less than 350 km, the root mean square magnetic field strength near the base of the convection zone reaches 95% of the equipartition field strength (i.e. magnetic and kinetic energy are comparable). For these solutions the Lorentz force feedback on the convection velocity is found to be significant. The velocity near the base of the convection zone is reduced to 50% of the hydrodynamic one. In spite of a significant decrease of the convection velocity, the reduction in the enthalpy flux is relatively small, since the magnetic field also suppresses the horizontal mixing of the entropy between up- and downflow regions. This effect increases the amplitude of the entropy perturbation and makes convective energy transport more efficient. We discuss potential implications of these results for solar global convection and dynamo simulations.

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arXiv2014

High-resolution calculation of the solar global convection with the reduced speed of sound technique: II. Near surface shear layer with the rotation

We present a high-resolution, highly stratified numerical simulation of rotating thermal convection in a spherical shell. Our aim is to study in detail the processes that can maintain a near surface shear layer (NSSL) as inferred from helioseismology. Using the reduced speed of sound technique we can extend our global convection simulation to $0.99\,R_{\odot}$ and include near the top of our domain small-scale convection with short time scales that is only weakly influenced by rotation. We find the formation of a NSSL preferentially in high latitudes in the depth range $r=0.95-0.975R_\odot$. The maintenance mechanisms are summarized as follows. Convection under weak influence of rotation leads to Reynolds stresses that transport angular momentum radially inward in all latitudes. This leads to the formation of a strong poleward directed meridional flow and a NSSL, which is balanced in the meridional plane by forces resulting from the $\langle v'_r v'_θ\rangle$ correlation of turbulent velocities. The origin of the required correlations depends to some degree on latitude. In high latitudes a positive correlation $\langle v'_rv'_θ\rangle$ is induced in the NSSL by the poleward meridional flow whose amplitude increases with the radius, while a negative correlation is generated by the Coriolis force in bulk of the convection zone. In low latitudes a positive correlation $\langle v'_rv'_θ\rangle$ results from rotationally aligned convection cells ("banana cells"). The force caused by these Reynolds stresses is in balance with the Coriolis force in the NSSL.

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arXiv2014

Comparison of inversion codes for polarized line formation in MHD simulations. I. Milne-Eddington codes

Milne-Eddington (M-E) inversion codes for the radiative transfer equation are the most widely used tools to infer the magnetic field from observations of the polarization signals in photospheric and chromospheric spectral lines. Unfortunately, a comprehensive comparison between the different M-E codes available to the solar physics community is still missing, and so is a physical interpretation of their inferences. In this contribution we offer a comparison between three of those codes (VFISV, ASP/HAO, and HeLIx$^+$). These codes are used to invert synthetic Stokes profiles that were previously obtained from realistic non-grey three-dimensional magnetohydrodynamical (3D MHD) simulations. The results of the inversion are compared with each other and with those from the MHD simulations. In the first case, the M-E codes retrieve values for the magnetic field strength, inclination and line-of-sight velocity that agree with each other within $σ_B \leq 35$ (Gauss), $σ_γ\leq 1.2°$, and $σ_{\rm v} \leq 10$ ms$^{-1}$, respectively. Additionally, M-E inversion codes agree with the numerical simulations, when compared at a fixed optical depth, within $σ_B \leq 130$ (Gauss), $σ_γ\leq 5°$, and $σ_{\rm v} \leq 320$ ms$^{-1}$. Finally, we show that employing generalized response functions to determine the height at which M-E codes measure physical parameters is more meaningful than comparing at a fixed geometrical height or optical depth. In this case the differences between M-E inferences and the 3D MHD simulations decrease to $σ_B \leq 90$ (Gauss), $σ_γ\leq 3°$, and $σ_{\rm v} \leq 90$ ms$^{-1}$.

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arXiv2014

Time-Distance Helioseismology of Two Realistic Sunspot Simulations

Linear time-distance helioseismic inversions are carried out using several filtering schemes to determine vector flow velocities within two $\sim100^2\,{\rm Mm^2}\times 20\,{\rm Mm}$ realistic magnetohydrodynamic sunspot simulations of 25~hr. One simulation domain contains a model of a full sunspot (i.e. one with both an umbra and penumbra), while the other contains a pore (i.e. a spot without a penumbra). The goal is to test current helioseismic methods using these state-of-the-art simulations of magnetic structures. We find that horizontal flow correlations between inversion and simulation flow maps are reasonably high ($\sim0.5$--0.8) in the upper 3~Mm at distances exceeding 25--30~Mm from spot center, but are substantially lower at smaller distances and larger depths. Inversions of forward-modeled travel times consistently outperform those of our measured travel times in terms of horizontal flow correlations, suggesting that our inability to recover flow structure near these active regions is largely due to the fact that we are unable to accurately measure travel times near strong magnetic features. In many cases the velocity amplitudes from the inversions underestimate those of the simulations by up to 50\%, possibly indicating nonlinearity of the forward problem. In every case, we find that our inversions are unable to recover the vertical flow structure of the simulations at any depth.

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arXiv2014

The Role of Subsurface Flows in Solar Surface Convection: Modeling the Spectrum of Supergranular and Larger Scale Flows

We model the solar horizontal velocity power spectrum at scales larger than granulation using a two-component approximation to the mass continuity equation. The model takes four times the density scale height as the integral (driving) scale of the vertical motions at each depth. Scales larger than this decay with height from the deeper layers. Those smaller are assumed to follow a Kolomogorov turbulent cascade, with the total power in the vertical convective motions matching that required to transport the solar luminosity in a mixing length formulation. These model components are validated using large scale radiative hydrodynamic simulations. We reach two primary conclusions: 1. The model predicts significantly more power at low wavenumbers than is observed in the solar photospheric horizontal velocity spectrum. 2. Ionization plays a minor role in shaping the observed solar velocity spectrum by reducing convective amplitudes in the regions of partial helium ionization. The excess low wavenumber power is also seen in the fully nonlinear three-dimensional radiative hydrodynamic simulations employing a realistic equation of state. This adds to other recent evidence suggesting that the amplitudes of large scale convective motions in the Sun are significantly lower than expected. Employing the same feature tracking algorithm used with observational data on the simulation output, we show that the observed low wavenumber power can be reproduced in hydrodynamic models if the amplitudes of large scale modes in the deep layers are artificially reduced. Since the large scale modes have reduced amplitudes, modes on the scale of supergranulation and smaller remain important to convective heat flux even in the deep layers, suggesting that small scale convective correlations are maintained through the bulk of the solar convection zone.

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arXiv2014

Numerical simulations of quiet Sun magnetism: On the contribution from a small-scale dynamo

We present a series of radiative MHD simulations addressing the origin and distribution of mixed polarity magnetic field in the solar photosphere. To this end we consider numerical simulations that cover the uppermost 2-6 Mm of the solar convection zone and we explore scales ranging from 2 km to 25 Mm. We study how the strength and distribution of magnetic field in the photosphere and subsurface layers depend on resolution, domain size and boundary conditions. We find that 50% of the magnetic energy at the τ=1 level comes from field with the less than 500 G strength and that 50% of the energy resides on scales smaller than about 100 km. While probability distribution functions are essentially independent of resolution, properly describing the spectral energy distribution requires grid spacings of 8 km or smaller. The formation of flux concentrations in the photosphere exceeding 1 kG requires a mean vertical field strength greater than 30-40 G at τ=1. The filling factor of kG flux concentrations increases with overall domain size as magnetic field becomes organized by larger, longer lived flow structures. A solution with a mean vertical field strength of around 85 G at τ=1 requires a subsurface RMS field strength increasing with depth at the same rate as the equipartition field strength. We consider this an upper limit for the quiet Sun field strength, which implies that most of the convection zone is magnetized close to equipartition. We discuss these findings in view of recent high-resolution spectropolarimetric observations of quiet Sun magnetism.

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arXiv2014

Validating Time-Distance Helioseismology With Realistic Quiet Sun Simulations

Linear time-distance helioseismic inversions are carried out for vector flow velocities using travel times measured from two $\sim 100^2\,{\rm Mm^2}\times 20\,{\rm Mm}$ realistic magnetohydrodynamic quiet-Sun simulations of about 20 hr. The goal is to test current seismic methods on these state-of-the-art simulations. Using recent three-dimensional inversion schemes, we find that inverted horizontal flow maps correlate well with the simulations in the upper $\sim 3$ Mm of the domains for several filtering schemes, including phase-speed, ridge, and combined phase-speed and ridge measurements. In several cases, however, the velocity amplitudes from the inversions severely underestimate those of the simulations, possibly indicating nonlinearity of the forward problem. We also find that, while near-surface inversions of the vertical velocites are best using phase-speed filters, in almost all other example cases these flows are irretrievable due to noise, suggesting a need for statistical averaging to obtain better inferences.

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arXiv2014

High-resolution calculations of the solar global convection with the reduced speed of sound technique: I. The structure of the convection and the magnetic field without the rotation

We carry out non-rotating high-resolution calculations of the solar global convection, which resolve convective scales of less than 10 Mm. To cope with the low Mach number conditions in the lower convection zone, we use the reduced speed of sound technique (RSST), which is simple to implement and requires only local communication in the parallel computation. In addition, the RSST allows us to expand the computational domain upward to about $0.99 R_{\odot}$ as it can also handle compressible flows. Using this approach, we study the solar convection zone on the global scale, including small-scale near-surface convection. In particular, we investigate the influence of the top boundary condition on the convective structure throughout the convection zone as well as on small-scale dynamo action. Our main conclusions are: 1. The small-scale downflows generated in the near-surface layer penetrate into deeper layers to some extent and excite small-scale turbulence in the region $>0.9R_\odot$, where $R_\odot$ is the solar radius. 2. In the deeper convection zone ($<0.9R_\odot$), the convection is not influenced by the location of the upper boundary. 3. Using an LES approach, we can achieve small-scale dynamo action and maintain a field of about $0.15-0.25 B_\mathrm{eq}$ throughout the convection zone, where $B_\mathrm{eq}$ is the equipartition magnetic field to the kinetic energy. 4. The overall dynamo efficiency varies significantly in the convection zone as a consequence of the downward directed Poynting flux and the depth variation of the intrinsic convective scales.

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