Surface Magnetograms Research Articles

Estimation of Spectral Solar Irradiance in the Ecliptic Plane Using Synthetic Solar Surface Magnetograms

AbstractThe primary external energy input to planetary atmospheres comes from solar radiation. Accurate estimates of solar irradiance are needed in order to understand atmospheric conditions at other planets. Many studies have interpolated Earth‐based irradiance measurements at other planets, disregarding the evolution of solar features, which are responsible for the irradiance variability. We present an approach for assessing solar irradiance at other planets by using synthetic full surface magnetograms of the Sun, generated by the Surface Flux Transport Model, and then converted into sunspots and faculae areas. Following the Spectral And Total Irradiance REconstruction approach, we compute the irradiance as the sum of contributions from sunspots, faculae, and the quiet Sun. We calculate the S‐index, which is a proxy for near‐ultraviolet irradiance, and the total solar irradiance (TSI), which is the wavelength‐integrated value. We demonstrate that a simple phase shift of the Earth‐observed TSI does not produce reliable estimates in the ecliptic. By comparing and correlating our results with the interpolated measurements, we find that the two models agree in the S‐index variability, because faculae have a long lifetime, so the effect of the solar rotation becomes less important. Conversely, the methods disagree strongly in the TSI, since sunspots have a short lifetime, and the interpolation does not take into account their emergence and evolution on the far‐side of the Sun, as it only uses the information of the disc visible for an Earth‐bound observer.

Effects of mesh topology on MHD solution features in coronal simulations

Magnetohydrodynamic (MHD) simulations of the solar corona have become more popular with the increased availability of computational power. Modern computational plasma codes, relying upon computational fluid dynamics (CFD) methods, allow the coronal features to be resolved using solar surface magnetograms as inputs. These computations are carried out in a full three-dimensional domain and, thus, selection of the correct mesh configuration is essential to save computational resources and enable/speed up convergence. In addition, it has been observed that for MHD simulations close to the hydrostatic equilibrium, spurious numerical artefacts might appear in the solution following the mesh structure, which makes the selection of the grid also a concern for accuracy. The purpose of this paper is to discuss and trade off two main mesh topologies when applied to global solar corona simulations using the unstructured ideal MHD solver from the COOLFluiD platform. The first topology is based on the geodesic polyhedron and the second on$UV$mapping. Focus is placed on aspects such as mesh adaptability, resolution distribution, resulting spurious numerical fluxes and convergence performance. For this purpose, first a rotating dipole case is investigated, followed by two simulations using real magnetograms from the solar minima (1995) and solar maxima (1999). It is concluded that the most appropriate mesh topology for the simulation depends on several factors, such as the accuracy requirements, the presence of features near the polar regions and/or strong features in the flow field in general. If convergence is of concern and the simulation contains strong dynamics, then grids which are based on the geodesic polyhedron are recommended compared with more conventionally used$UV$-mapped meshes.

Deciphering the Deep Origin of Active Regions via Analysis of Magnetograms

Abstract In this work, we derive magnetic toroids from surface magnetograms by employing a novel optimization method, based on the trust region reflective algorithm. The toroids obtained in this way are combinations of Fourier modes (amplitudes and phases) with low longitudinal wavenumbers. The optimization also estimates the latitudinal width of the toroids. We validate the method using synthetic data, generated as random numbers along a specified toroid. We compute the shapes and latitudinal widths of the toroids via magnetograms, generally requiring several m's to minimize residuals. A threshold field strength is chosen to include all active regions in the magnetograms for toroid derivation, while avoiding non-contributing weaker fields. Higher thresholds yield narrower toroids, with an m = 1 dominant pattern. We determine the spatiotemporal evolution of toroids by optimally weighting the amplitudes and phases of each Fourier mode for a sequence of five Carrington Rotations (CRs) to achieve the best amplitude and phases for the middle CR in the sequence. Taking more than five causes “smearing” or degradation of the toroid structure. While this method applies no matter the depth at which the toroids actually reside inside the Sun, by comparing their global shape and width with analogous patterns derived from magnetohydrodynamic (MHD) tachocline shallow water model simulations, we infer that their origin is at/near the convection zone base. By analyzing the “Halloween” storms as an example, we describe features of toroids that may have caused the series of space weather events in 2003 October–November. Calculations of toroids for several sunspot cycles will enable us to find similarities/differences in toroids for different major space weather events.

Radio Occultation Observations of the Solar Corona Over 1.60–1.86 R⊙: Faraday Rotation and Frequency Shift Analysis

AbstractThe study of coronal energy transport, central to the solar wind acceleration problem, relies upon accurate representation of magnetic fields and plasma electron densities. This information is difficult to obtain in middle‐to‐lower coronal regions that may contain complex magnetic structures. Faraday rotation (FR) solar radio occultation observations, which reveal line‐of‐sight (LOS) integrated product of the coronal magnetic field and electron density, can help characterize the coronal environment and constrain magnetic field strengths. Global magnetohydrodynamic (MHD) models use specified synoptic solar surface magnetograms and may be used to facilitate FR interpretation by estimating detailed magnetic field properties along the radio LOS. We present a hybrid FR analysis incorporating magnetic field solutions from an MHD coronal model, and an electron density radial profile conforming to radio frequency shift observations. The FR modeled by the hybrid method is compared to MErcury Surface, Space ENvironment, GEochemistry and Ranging spacecraft radio FR observations through a coronal region of low heliolatitudes and radial distance 1.60–1.86 R⊙ from the heliocenter, collected during a state of relative solar quiescence. The hybrid model reasonably reproduces the form, polarity, and magnitude of the observed FR. For this specific coronal region, the calculated radial profile of electron concentrations and varied magnetic field strengths indicate Alfvén wave speeds below 50 km/s close to the point of closest approach but near 400 km/s in adjacent regions along the sounding LOS. The new approach of combining MHD models with radio sounding observations supports study of MHD wave processes in the challenging middle‐coronal magneto‐ionic environment.

Reconstructing nonlinear force-free fields by a constrained optimization

It seems that the potential and linear force-free magnetic fields are inadequate to represent the observed magnetic events occurring in different regions of the solar corona. To reconstruct the nonlinear force-free fields from the solar surface magnetograms, various analytical and numerical methods have already been examined by different authors. Here, using the Lagrange multiplier technique, a constrained optimization approach for reconstructing force-free magnetic fields is proposed. In the optimization procedure the solenoidal property is considered as a constraint on the initial non-force-free field. In the Wheatland et al. (2000) method as an unconstrained optimization, both solenoidal and force-free conditions are fulfilled approximately. In contrast, the constrained optimization method, up to numerical precision, leads us to a nearly force-free magnetic field with exactly zero divergence. The solutions are obtained and tested by the Low and Lou (1990) semi-analytic solution.

The Effect of Magnetic Variability on Stellar Angular Momentum Loss. I. The Solar Wind Torque during Sunspot Cycles 23 and 24

Abstract The rotational evolution of cool stars is governed by magnetized stellar winds that slow the stellar rotation during their main sequence lifetimes. Magnetic variability is commonly observed in Sun-like stars, and the changing strength and topology of the global field is expected to affect the torque exerted by the stellar wind. We present three different methods for computing the angular momentum loss in the solar wind. Two are based on MHD simulations from Finley & Matt (2018), with one using the open flux measured in the solar wind, and the other using remotely observed surface magnetograms. Both methods agree in the variation of the solar torque seen through the solar cycle and show a 30%–40% decrease from cycles 23 to 24. The two methods calculate different average values, 2.9 × 1030 erg (open flux) and 0.35 × 1030 erg (surface field). This discrepancy results from the already well-known difficulty of reconciling the magnetograms with the observed open flux, which is currently not understood, leading to an inability to discriminate between these two calculated torques. The third method is based on the observed spin rates of Sun-like stars, which decrease with age, directly probing the average angular momentum loss. This method gives 6.2 × 1030 erg for the solar torque, larger than the other methods. This may be indicative of further variability in the solar torque on timescales much longer than the magnetic cycle. We discuss the implications for applying the formula to other Sun-like stars, where only surface field measurements are available, and where the magnetic variations are ill-constrained.

Global Solar Magnetic Field Organization in the Outer Corona: Influence on the Solar Wind Speed and Mass Flux Over the Cycle

Abstract The dynamics of the solar wind depends intrinsically on the structure of the global solar magnetic field, which undergoes fundamental changes over the 11-year solar cycle. For instance, the wind terminal velocity is thought to be anti-correlated with the expansion factor, a measure of how the magnetic field varies with height in the solar corona, usually computed at a fixed height ( , the source surface radius that approximates the distance at which all magnetic field lines become open). However, the magnetic field expansion affects the solar wind in a more detailed way, its influence on the solar wind properties remaining significant well beyond the source surface. We demonstrate this using 3D global magnetohydrodynamic (MHD) simulations of the solar corona, constrained by surface magnetograms over half a solar cycle (1989–2001). A self-consistent expansion beyond the solar wind critical point (even up to ) makes our model comply with observed characteristics of the solar wind, namely, that the radial magnetic field intensity becomes latitude independent at some distance from the Sun, and that the mass flux is mostly independent of the terminal wind speed. We also show that near activity minimum, the expansion in the higher corona has more influence on the wind speed than the expansion below .

THE DEPENDENCE OF STELLAR MASS AND ANGULAR MOMENTUM LOSSES ON LATITUDE AND THE INTERACTION OF ACTIVE REGION AND DIPOLAR MAGNETIC FIELDS

Rotation evolution of late-type stars is dominated by magnetic braking and the underlying factors that control this angular momentum loss are important for the study of stellar spin-down. In this work, we study angular momentum loss as a function of two different aspects of magnetic activity using a calibrated Alfv\'en wave-driven magnetohydrodynamic wind model: the strengths of magnetic spots and their distribution in latitude. By driving the model using solar and modified solar surface magnetograms, we show that the topology of the field arising from the net interaction of both small-scale and large-scale field is important for spin-down rates and that angular momentum loss is not a simple function of large scale magnetic field strength. We find that changing the latitude of magnetic spots can modify mass and angular momentum loss rates by a factor of two. The general effect that causes these differences is the closing down of large-scale open field at mid- and high-latitudes by the addition of the small-scale field. These effects might give rise to modulation of mass and angular momentum loss through stellar cycles, and present a problem for ab initio attempts to predict stellar spin-down based on wind models. For all the magnetogram cases considered here, from dipoles to various spotted distributions, we find that angular momentum loss is dominated by the mass loss at mid-latitudes. The spin-down torque applied by magnetized winds therefore acts at specific latitudes and is not evenly distributed over the stellar surface, though this aspect is unlikely to be important for understanding spin-down and surface flows on stars.

Coronal magnetic field modeling using stereoscopy constraints

Aims. Nonlinear force-free field (NLFFF) extrapolation has been used extensively in the past to extrapolate solar surface magnetograms to stationary coronal field models. In theoretical tests with known boundary conditions, the nonlinear boundary value problem can be solved reliably. However, if the magnetogram is measured with errors, the extrapolation often yields field lines that disagree with the shapes of simultaneously observed and stereoscopically reconstructed coronal loops. We here propose an extension to an NLFFF extrapolation scheme that remedies this deficiency in that it incorporates the loop information in the extrapolation procedure.Methods. We extended the variational formulation of the NLFFF optimization code by an additional term that monitors and minimizes the difference of the local magnetic field direction and the orientation of 3D plasma loops. We tested the performance of the new code with a previously reported semi-analytical force-free solution.Results. We demonstrate that there is a range of force-free and divergence-free solutions that comply with the boundary measurements within some error bound. With our new approach we can obtain the solution out of this set the coronal fields which is well aligned with given loops.Conclusions. We conclude that the shape of coronal loops reconstructed by stereoscopy may lead to an important stabilization of coronal NLFFF field solutions when, as is typically the case, magnetic surface measurements with limited precision do not allow determining the solution solely from photospheric field measurements.

Modelling the hidden magnetic field of low-mass stars

Zeeman-Doppler imaging is a spectropolarimetric technique that is used to map the large-scale surface magnetic fields of stars. These maps in turn are used to study the structure of the stars' coronae and winds. This method, however, misses any small-scale magnetic flux whose polarisation signatures cancel out. Measurements of Zeeman broadening show that a large percentage of the surface magnetic flux may be neglected in this way. In this paper we assess the impact of this 'missing flux' on the predicted coronal structure and the possible rates of spin down due to the stellar wind. To do this we create a model for the small-scale field and add this to the Zeeman-Doppler maps of the magnetic fields of a sample of 12 M dwarfs. We extrapolate this combined field and determine the structure of a hydrostatic, isothermal corona. The addition of small-scale surface field produces a carpet of low-lying magnetic loops that covers most of the surface, including the stellar equivalent of solar 'coronal holes' where the large-scale field is opened up by the stellar wind and hence would be X-ray dark. We show that the trend of the X-ray emission measure with rotation rate (the so-called 'activity-rotation relation') is unaffected by the addition of small-scale field, when scaled with respect to the large-scale field of each star. The addition of small-scale field increases the surface flux; however, the large-scale open flux that governs the loss of mass and angular momentum in the wind remains unaffected. We conclude that spin-down times and mass loss rates calculated from surface magnetograms are unlikely to be significantly influenced by the neglect of small-scale field.

Influence of surface stressing on stellar coronae and winds

The large-scale field of the Sun is well represented by its lowest energy (or potential) state. Recent observations, by comparison, reveal that many solar-type stars show large-scale surface magnetic fields that are highly non-potential - that is, they have been stressed above their lowest-energy state. This non-potential component of the surface field is neglected by current stellar wind models. The aim of this paper is to determine its effect on the coronal structure and wind. We use Zeeman-Doppler surface magnetograms of two stars - one with an almost potential, one with a non-potential surface field - to extrapolate a static model of the coronal structure for each star. We find that the stresses are carried almost exclusively in a band of uni-directional azimuthal field that is confined to mid-latitudes. Using this static solution as an initial state for an MHD wind model, we then find that the final state is determined primarily by the potential component of the surface magnetic field. The band of azimuthal field must be confined close to the stellar surface as it is not compatible with a steady-state wind. By artificially increasing the stellar rotation rate we demonstrate that the observed azimuthal fields can not be produced by the action of the wind but must be due to processes at or below the stellar surface. We conclude that the background winds of solar-like stars are largely unaffected by these highly-stressed surface fields. Nonetheless, the increased flare activity and associated coronal mass ejections that may be expected to accompany such highly-stressed fields may have a significant impact on any surrounding planets.

On the Reconstruction of the Convection Pattern Below an Active Region of Solar Corona

In order to better understand magneto-convective patterns and flux emergence, we use the Nudging Back and Forth, a data assimilation method with an anelastic convection model to reconstruct the convection zone below a solar active region from observed solar surface magnetograms. To mimic photosphere, vector magnetograms are computed using force free hypothesis. We find that the observed arcade system of AR9077-20000714 ("the slinky") of magnetic lines is actually formed by Ω and U loops generated in the convection zone. We generate temperature maps at top of the convective zone and find that high magnetic fields on either sides of the neutral line produce a local cooling by impeding the overturning motions.

Modelling stellar coronae from surface magnetograms: the role of missing magnetic flux

Recent advances in spectropolarimetry have allowed the reconstruction of stellar coronal magnetic fields. This uses Zeeman-Doppler magnetograms of the surface magnetic field as a lower boundary condition. The ZDI maps, however, suffer from the absence of information about the magnetic field over regions of the surface due to the presence of dark starspots and portions of the surface out of view due to a tilt in the rotation axis. They also suffer from finite resolution which leads to small scale field structures being neglected. This paper explores the effects of this loss of information on the extrapolated coronal fields. For this we use simulated stellar surface magnetic maps for two hypothetical stars. Using the potential field approximation, the coronal fields and emission measures are calculated. This is repeated for the cases of missing information due to, (i) starspots, (ii) a large area of the stellar surface out of view, (iii) a finite resolution. The largest effect on the magnetic field structure arises when a significant portion of the stellar surface remains out of view. This changes the nature of the field lines that connect to this obscured hemisphere. Nonetheless, the field structure in the visible hemisphere is reliably reproduced. Thus the calculation of the locations and surface filling factors of accretion funnels is reasonably well reproduced for the observed hemisphere. The decrease with height of the magnetic pressure, which is important in calculating disc truncation radii for accreting stars, is also largely unaffected in the equatorial plane. The fraction of surface flux that is open and therefore able to supply angular momentum loss in a wind, however, is often overestimated in the presence of missing flux.

The non-dipolar magnetic fields of accreting T Tauri stars

Models of magnetospheric accretion on to classical T Tauri stars often assume that stellar magnetic fields are simple dipoles. Recently published surface magnetograms of BP Tau and V2129 Oph have shown, however, that their fields are more complex. The magnetic field of V2129 Oph was found to be predominantly octupolar. For BP Tau the magnetic energy was shared mainly between the dipole and octupole field components, with the dipole component being almost four times as strong as that of V2129 Oph. From the published surface maps of the photospheric magnetic fields we extrapolate the coronal fields of both stars, and compare the resulting field structures with that of a dipole. We consider different models where the disc is truncated at, or well-within, the Keplerian corotation radius. We find that although the structure of the surface magnetic field is particularly complex for both stars, the geometry of the larger scale field, along which accretion is occurring, is somewhat simpler. However, the larger scale field is distorted close to the star by the stronger field regions, with the net effect being that the fractional open flux through the stellar surface is less than would be expected with a dipole magnetic field model. Finally, we estimate the disc truncation radius, assuming that this occurs where the magnetic torque from the stellar magnetosphere is comparable to the viscous torque in the disc.

Why are accreting T Tauri stars observed to be less luminous in X-rays than non-accretors?

Abstract Accreting T Tauri stars are observed to be less luminous in X-rays than non-accretors, an effect that has been detected in various star-forming regions. To explain this we have combined, for the first time, a radiative transfer code with an accretion model that considers magnetic fields extrapolated from surface magnetograms obtained from Zeeman–Doppler imaging. Such fields consist of compact magnetic regions close to the stellar surface, with extended field lines interacting with the disc. We study the propagation of coronal X-rays through the magnetosphere and demonstrate that they are strongly absorbed by the dense gas in accretion columns. The reduction in the observed X-ray emission depends on the field geometry, which may explain why accreting T Tauri stars show a larger scatter in their observed X-ray luminosity compared with non-accreting stars.

Why are accreting T Tauri stars less luminous in X-rays than non-accretors?

AbstractAccreting T Tauri stars are observed to be less luminous in X-rays than non-accretors, an effect that has been detected in various star forming regions. To explain this we have combined, for the first time, a radiative transfer code with an accretion model that considers magnetic fields extrapolated from surface magnetograms obtained from Zeeman-Doppler imaging. Such fields consist of compact magnetic regions close to the stellar surface, with extended field lines interacting with the disk. We study the propagation of coronal X-rays through the magnetosphere and demonstrate that they are strongly absorbed by the dense gas in accretion columns.

Rotationally modulated X-ray emission from T Tauri stars

We have modelled the rotational modulation of X-ray emission from T Tauri stars assuming that they have isothermal, magnetically confined coronae. By extrapolating surface magnetograms, we find that T Tauri coronae are compact and clumpy, such that rotational modulation arises from X-ray emitting regions being eclipsed as the star rotates. Emitting regions are close to the stellar surface and inhomogeneously distributed about the star. However, some regions of the stellar surface, which contain wind bearing open field lines, are dark in X-rays. From simulated X-ray light curves, obtained using stellar parameters from the Chandra Orion Ultradeep Project, we calculate X-ray periods and make comparisons with optically determined rotation periods. We find that X-ray periods are typically equal to, or are half of, the optical periods. Further, we find that X-ray periods are dependent upon the stellar inclination, but that the ratio of X-ray to optical period is independent of stellar mass and radius.

X-ray emission from T Tauri stars

We have modelled the X-ray emission of T Tauri stars assuming that they have isothermal, magnetically-confined coronae. These coronae extend outwards until either the pressure of the hot coronal gas overcomes the magnetic field, or, if the corona interacts with a disk before this happens, by the action of the disk itself. This work is motivated by the results of the Chandra Orion Ultradeep Project (COUP) that show an increase in the X-ray emission measure with increasing stellar mass. We find that this variation (and its large scatter) result naturally from the variation in the sizes of the stellar coronae. The reduction in the magnitude of the X-ray emission due to the presence of a disk stripping the outer parts of the stellar corona is most pronounced for the lower mass stars. The higher mass stars with their greater surface gravities have coronae than typically do not extend out as far as the inner edge of the disk and so are less affected by it. For these stars, accretion takes place along open field lines that connect to the disk. By extrapolating surface magnetograms of young main sequence stars we have examined the effect on the X-ray emission of a realistic degree of field complexity. We find densities consistent with estimates from modelling of individual flares. A simple dipole field in contrast gives densities typically an order of magnitude less. We suggest that T Tauri stars have coronal fields that are slightly more extended than their main sequence counterparts, but not as extended as a purely dipolar fields.

Coronal stripping in supersaturated stars

A recent unambiguous detection of X-ray rotational modulation of the supersaturated star VXR45 (P = 0.223 days) has shown that its corona has discrete dark and bright X-ray regions. We suggest that due to the rapid rotation, the X-ray emitting corona has been centrifugally stripped away, creating open field regions that are dark in X-rays. This leads naturally both to a significant rotational modulation in X-rays but also to the lower X-ray luminosity of supersaturated stars compared to those rotating more slowly. To demonstrate the effect, we take as an example a more slowly rotating star for which surface magnetograms are available. We extrapolate the potential coronal magnetic field based on these magnetograms and determine for a hydrostatic, isothermal atmosphere the structure of the density and of the optically-thin X-ray emission. We show that if the rotation rate of this star were increased, the magnitude of the X-ray luminosity would decrease while its rotational modulation would increase in a way that is consistent with the recent observations of VXR45.

Magnetic Loop Models: from Sun to Stars

I review recent progress in determining the nature of the loop structures that form the coronae of solar-like stars. This progress has been driven by observational advances, in particular the new results from X-ray satellites (Chandra and XMM-Newton) and the availability of surface magnetograms from Zeeman-Doppler imaging. It is now clear that stars that are similar to the Sun in mass, but which rotate more rapidly, have a very different magnetic field structure. Their surfaces are more heavily spotted, with spots appearing at all latitudes, extending all the way up to the rotation pole. Their coronae are correspondingly much brighter in X-rays, containing plasma that is hotter and denser than on the Sun. In addition, stellar coronae can support massive co-rotating prominences out to many stellar radii. Recent efforts in modelling these magnetic structures are now bringing together both the surface magnetograms and also the coronal X-ray emission. The resulting coronal loop models show complex loop structures on all scales, with much of the X-ray emission coming from high latitudes where is does not suffer rotational self-eclipse. The observed high densities and X-ray emission measures are a natural consequence of the high magnetic flux density at the surface. The stripping of the corona due to centrifugal effects at high rotation rates can also explain the saturation and supersaturation of X-ray emission with increasing rotation rates, and the recent observation of a high rotational modulation in a supersaturated star.