Search

We report on a study of the Multiview Observatory for Solar Terrestrial Science (MOST) mission that will provide comprehensive imagery and time series data needed to understand the magnetic connection between the solar interior and the solar atmosphere/inner heliosphere. MOST will build upon the successes of SOHO and STEREO missions with new views of the Sun and enhanced instrument capabilities. This article is based on a study conducted at NASA Goddard Space Flight Center that determined the required instrument refinement, spacecraft accommodation, launch configuration, and flight dynamics for mission success. MOST is envisioned as the next generation great observatory positioned to obtain three-dimensional information of large-scale heliospheric structures such as coronal mass ejections, stream interaction regions, and the solar wind itself. The MOST mission consists of 2 pairs of spacecraft located in the vicinity of Sun-Earth Lagrange points L4 (MOST1, MOST3) and L5 (MOST2 and MOST4). The spacecraft stationed at L4 (MOST1) and L5 (MOST2) will each carry seven remote-sensing and three in-situ instrument suites, including a novel radio package known as the Faraday Effect Tracker of Coronal and Heliospheric structures (FETCH). MOST3 and MOST4 will carry only the FETCH instruments and are positioned at variable locations along the Earth orbit up to 20{\deg} ahead of L4 and 20{\deg} behind L5, respectively. FETCH will have polarized radio transmitters and receivers on all four spacecraft to measure the magnetic content of solar wind structures propagating from the Sun to Earth using the Faraday rotation technique. The MOST mission will be able to sample the magnetized plasma throughout the Sun-Earth connected space during the mission lifetime over a solar cycle., Comment: 42 pages, 19 figures, 8 tables, to appear in J. Atmospheric and Solar Terrestrial Physics

A physical magnetic field has a divergence of zero. Numerical error in constructing a model field and computing the divergence, however, introduces a finite divergence into these calculations. A popular metric for measuring divergence is the average fractional flux $\langle |f_{i}| \rangle$. We show that $\langle |f_{i}| \rangle$ scales with the size of the computational mesh, and may be a poor measure of divergence because it becomes arbitrarily small for increasing mesh resolution, without the divergence actually decreasing. We define a modified version of this metric that does not scale with mesh size. We apply the new metric to the results of DeRosa et al. (2015), who measured $\langle |f_{i}| \rangle$ for a series of Nonlinear Force-Free Field (NLFFF) models of the coronal magnetic field based on solar boundary data binned at different spatial resolutions. We compute a number of divergence metrics for the DeRosa et al. (2015) data and analyze the effect of spatial resolution on these metrics using a non-parametric method. We find that some of the trends reported by DeRosa et al. (2015) are due to the intrinsic scaling of $\langle |f_{i}| \rangle$. We also find that different metrics give different results for the same data set and therefore there is value in measuring divergence via several metrics., Comment: Accepted for publication in ApJ

The heliospheric magnetic field is of pivotal importance in solar and space physics. The field is rooted in the Sun's photosphere, where it has been observed for many years. Global maps of the solar magnetic field based on full disk magnetograms are commonly used as boundary conditions for coronal and solar wind models. Two primary observational constraints on the models are (1) the open field regions in the model should approximately correspond to coronal holes observed in emission, and (2) the magnitude of the open magnetic flux in the model should match that inferred from in situ spacecraft measurements. In this study, we calculate both MHD and PFSS solutions using fourteen different magnetic maps produced from five different types of observatory magnetograms, for the time period surrounding July, 2010. We have found that for all of the model/map combinations, models that have coronal hole areas close to observations underestimate the interplanetary magnetic flux, or, conversely, for models to match the interplanetary flux, the modeled open field regions are larger than coronal holes observed in EUV emission. In an alternative approach, we estimate the open magnetic flux entirely from solar observations by combining automatically detected coronal holes for Carrington rotation 2098 with observatory synoptic magnetic maps. This approach also underestimates the interplanetary magnetic flux. Our results imply that either typical observatory maps underestimate the Sun's magnetic flux, or a significant portion of the open magnetic flux is not rooted in regions that are obviously dark in EUV and X-ray emission.

With the global view and high-cadence observations from SDO/AIA and STEREO, many spatially separated solar eruptive events appear to be coupled. However, the mechanisms for "sympathetic" events are still largely unknown. In this study, we investigate the impact of an erupting flux rope on surrounding solar structures through large-scale magnetic coupling. We build a realistic environment of the solar corona on 2011 February 15 using a global magnetohydrodynamics (MHD) model and initiate coronal mass ejections (CMEs) in active region (AR) 11158 by inserting Gibson-Low analytical flux ropes. We show that a CME's impact on the surrounding structures depends not only on the magnetic strength of these structures and their distance to the source region, but also on the interaction between the CME with the large-scale magnetic field. Within the CME expansion domain where the flux rope field directly interacts with the solar structures, expansion-induced reconnection often modifies the overlying field, thereby increasing the decay index. This effect may provide a primary coupling mechanism underlying the sympathetic eruptions. The magnitude of the impact is found to depend on the orientation of the erupting flux rope, with the largest impacts occurring when the flux rope is favorably oriented for reconnecting with the surrounding regions. Outside the CME expansion domain, the influence of the CME is mainly through field line compression or post-eruption relaxation. Based on our numerical experiments, we discuss a way to quantify the eruption impact, which could be useful for forecasting purposes., Comment: 38 pages, 13 figures

The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/SOT-SP scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-consistent results. The free energies of the resulting solutions generally trend higher with increasing resolution, while relative magnetic helicity values vary significantly between resolutions for all methods. All methods require changing the horizontal components, and for some methods also the vertical components, of the vector magnetogram boundary field in excess of nominal uncertainties in the data. The solutions produced by the various methods are significantly different at each resolution level. We continue to recommend verifying agreement between the modeled field lines and corresponding coronal loop images before any NLFFF model is used in a scientific setting., Comment: Accepted to ApJ; comments/corrections to this article are welcome via e-mail, even after publication

Seeking to establish whether active region upflow material contributes to the slow solar wind, we examine in detail the plasma upflows from Active Region (AR)10978, which crossed the Sun's disc in the interval 8 to 16 December, 2007 during Carrington rotation (CR)2064. In previous work, using data from the Hinode/EUV Imaging Spectrometer, upflow velocity evolution was extensively studied as the region crossed the disc while a linear force-free magnetic extrapolation was used to confirm aspects of the velocity evolution and to establish the presence of quasi-separatrix layers at the upflow source areas. The plasma properties, temperature, density and first ionisation potential bias (FIP-bias) were measured with the spectrometer during the disc passage of the active region. Global potential field source surface (PFSS) models showed that AR 10978 was completely covered by the closed field of a helmet streamer that is part of the streamer belt. Thus it is not clear how any of the upflowing AR-associated plasma could reach the source surface at 2.5 R(Sun)and contribute to the slow solar wind. However a detailed examination of solar-wind in-situ data obtained by the Advanced Composition Explorer (ACE) spacecraft at the L1 point shows that the increase in O^7+/O^6+, C^6+/C^5+ and Fe/O - a FIP-bias proxy - are present before the heliospheric current sheet crossing. These increases, along with an accompanying reduction in proton velocity and an increase in density are characteristic of both AR and slow-wind plasma. Finally we describe a two-step reconnection process by which some of the upflowing plasma from the AR could reach the heliosphere.

The shapes of solar coronal loops are sensitive to the presence of electrical currents that are the carriers of the nonpotential energy available for impulsive activity. We use this information in a new method for modeling the coronal magnetic field of AR 11158 as a nonlinear force-free field (NLFFF). The observations used are coronal images around time of major flare activity on 2011/02/15, together with the surface line-of-sight magnetic field measurements. The data are from the Helioseismic and Magnetic Imager and Atmospheric Imaging Assembly (HMI and AIA, respectively) onboard the Solar Dynamics Observatory (SDO). The model fields are constrained to approximate the coronal loop configurations as closely as possible, while also subject to the force-free constraints. The method does not use transverse photospheric magnetic field components as input, and is thereby distinct from methods for modeling NLFFFs based on photospheric vector magnetograms. We validate the method using observations of AR 11158 at a time well before major flaring, and subsequently review the field evolution just prior to and following an X2.2 flare and associated eruption. The models indicate that the energy released during the instability is about $1\times10^{32}$ erg, consistent with what is needed to power such a large eruptive flare. Immediately prior to the eruption the model field contains a compact sigmoid bundle of twisted flux that is not present in the post-eruption models, which is consistent with the observations. The core of that model structure is twisted by $\approx0.9$ full turns about its axis., Comment: ApJ, in press

The high-cadence, comprehensive view of the solar corona by SDO/AIA shows many events that are widely separated in space while occurring close together in time. In some cases, sets of coronal events are evidently causally related, while in many other instances indirect evidence can be found. We present case studies to highlight a variety of coupling processes involved in coronal events. We find that physical linkages between events do occur, but concur with earlier studies that these couplings appear to be crucial to understanding the initiation of major eruptive or explosive phenomena relatively infrequently. We note that the post-eruption reconfiguration time scale of the large-scale corona, estimated from the EUV afterglow, is on average longer than the mean time between CMEs, so that many CMEs originate from a corona that is still adjusting from a previous event. We argue that the coronal field is intrinsically global: current systems build up over days to months, the relaxation after eruptions continues over many hours, and evolving connections easily span much of a hemisphere. This needs to be reflected in our modeling of the connections from the solar surface into the heliosphere to properly model the solar wind, its perturbations, and the generation and propagation of solar energetic particles. However, the large-scale field cannot be constructed reliably by currently available observational resources. We assess the potential of high-quality observations from beyond Earth's perspective and advanced global modeling to understand the couplings between coronal events in the context of CMEs and solar energetic particle events., Comment: ApJSS, in press

We test a nonlinear force-free field (NLFFF) optimization code in spherical geometry using an analytical solution from Low and Lou. Several tests are run, ranging from idealized cases where exact vector field data are provided on all boundaries, to cases where noisy vector data are provided on only the lower boundary (approximating the solar problem). Analytical tests also show that the NLFFF code in the spherical geometry performs better than that in the Cartesian one when the field of view of the bottom boundary is large, say, $20^\circ \times 20^\circ$. Additionally, We apply the NLFFF model to an active region observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) both before and after an M8.7 flare. For each observation time, we initialize the models using potential field source surface (PFSS) extrapolations based on either a synoptic chart or a flux-dispersal model, and compare the resulting NLFFF models. The results show that NLFFF extrapolations using the flux-dispersal model as the boundary condition have slightly lower, therefore better, force-free and divergence-free metrics, and contain larger free magnetic energy. By comparing the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly (AIA) on board SDO, we find that the NLFFF performs better than the PFSS not only for the core field of the flare productive region, but also for large EUV loops higher than 50 Mm., Comment: 34 pages, 8 figures, accepted for publication in ApJ

The variable magnetic field of the solar photosphere exhibits periodic reversals as a result of dynamo activity occurring within the solar interior. We decompose the surface field as observed by both the Wilcox Solar Observatory and the Michelson Doppler Imager into its harmonic constituents, and present the time evolution of the mode coefficients for the past three sunspot cycles. The interplay between the various modes is then interpreted from the perspective of general dynamo theory, where the coupling between the primary and secondary families of modes is found to correlate with large-scale polarity reversals for many examples of cyclic dynamos. Mean-field dynamos based on the solar parameter regime are then used to explore how such couplings may result in the various long-term trends in the surface magnetic field observed to occur in the solar case., Comment: Accepted to ApJ; comments/corrections to this article are welcome via e-mail, even after publication

Ground level events (GLEs) occupy the high-energy end of gradual solar energetic particle (SEP) events. They are associated with coronal mass ejections (CMEs) and solar flares, but we still do not clearly understand the special conditions that produce these rare events. During Solar Cycle 23, a total of 16 GLEs were registered, using ground-based neutron monitor data. We first ask if these GLEs are clearly distinguishable from other SEP events observed from space. Setting aside possible difficulties in identifying all GLEs consistently, we then try to find observables which may unmistakably isolate these GLEs by studying the basic properties of the associated eruptions and the active regions (ARs) that produced them. It is found that neither the magnitudes of the CMEs and flares nor the complexities of the ARs give sufficient conditions for GLEs. It is possible to find CMEs, flares or ARs that are not associated with GLEs but that have more extreme properties than those associated with GLEs. We also try to evaluate the importance of magnetic field connection of the AR with Earth on the detection of GLEs and their onset times. Using the potential field source surface (PFSS) model, a half of the GLEs are found to be well-connected. However, the GLE onset time with respect to the onset of the associated flare and CME does not strongly depend on how well-connected the AR is. The GLE onset behavior may be largely determined by when and where the CME-driven shock develops. We could not relate the shocks responsible for the onsets of past GLEs with features in solar images, but the combined data from the Solar TErrestrial RElations Observatory (STEREO) and the Solar Dynamics Observatory (SDO) have the potential to change this for GLEs that may occur in the rising phase of Solar Cycle 24., Comment: 25 pages, 9 figures, accepted by Space Science Reviews

Presently, many models of the coronal magnetic field rely on photospheric vector magnetograms but these data have been shown to be problematic as the sole boundary information for nonlinear force-free field (NLFFF) extrapolations. Magnetic fields in the corona manifest themselves in high-energy images (X-rays and EUV) in the shapes of coronal loops, providing an additional constraint that at present is not used due to the mathematical complications of incorporating such input into numerical models. Projection effects and the limited number of usable loops further complicate the use of coronal information. We develop and test an algorithm to use images showing coronal loops in the modeling of the solar coronal magnetic field. We first fit projected field lines with field lines of constant-\als force-free fields to approximate the three-dimensional distribution of currents in the corona along a sparse set of trajectories. We then apply a Grad-Rubin-like iterative technique to obtain a volume-filling nonlinear force-free model of the magnetic field, modifying method presented in \citet{Wheatland2007}. We thoroughly test the technique on known analytical and solar-like model magnetic fields previously used for comparing different extrapolation techniques \citep{Schrijver2006, Schrijver2008} and compare the results with those obtained by presently available methods that rely only on the photospheric data. We conclude that we have developed a functioning method of modeling the coronal magnetic field by combining the line-of-sight component of photospheric magnetic field with information from coronal images. Vector magnetograms over the full or partial photospheric boundary of the numerical domain could optionally be used., Comment: Submitted to ApJ

We constrain the velocity spectral distribution of global-scale solar convective cells at depth using techniques of local helioseismology. We calibrate the sensitivity of helioseismic waves to large-scale convective cells in the interior by analyzing simulations of waves propagating through a velocity snapshot of global solar convection via methods of time-distance helioseismology. Applying identical analysis techniques to observations of the Sun, we are able to bound from above the magnitudes of solar convective cells as a function of spatial convective scale. We find that convection at a depth of $r/R_\odot = 0.95$ with spatial extent $\ell <20$, where $\ell$ is the spherical harmonic degree, comprise weak flow systems, on the order of 15 m/s or less. Convective features deeper than $r/R_\odot = 0.95$ are more difficult to image due to the rapidly decreasing sensitivity of helioseismic waves., Comment: accepted, ApJ Letters, 5 figures, 10 pages (in this version)

The magnetic field of the solar corona has a large-scale dipole character, which maps into the bipolar field in the solar wind. Using standard representations of the coronal field, we show that high-energy ions can be trapped stably in these large-scale closed fields. The drift shells that describe the conservation of the third adiabatic invariant may have complicated geometries. Particles trapped in these zones would resemble the Van Allen Belts and could have detectable consequences. We discuss potential sources of trapped particles.

The solar magnetic field is key to understanding the physical processes in the solar atmosphere. Nonlinear force-free codes have been shown to be useful in extrapolating the coronal field from underlying vector boundary data [see Schrijver et al. 2006 for an overview]. However, we can only measure the magnetic field vector routinely with high accuracy in the photosphere with, e.g., Hinode/SOT, and unfortunately these data do not fulfill the force-free consistency condition as defined by Aly (1989). We must therefore apply some transformations to these data before nonlinear force-free extrapolation codes can be legitimately applied. To this end, we have developed a minimization procedure that uses the measured photospheric field vectors as input to approximate a more chromospheric like field The method was dubbed preprocessing. See Wiegelmann et al. 2006 for details]. The procedure includes force-free consistency integrals and spatial smoothing. The method has been intensively tested with model active regions [see Metcalf et al. 2008] and been applied to several ground based vector magnetogram data before. Here we apply the preprocessing program to photospheric magnetic field measurements with the Hinode/SOT instrument., Comment: 2 pages, 1 figure, ASP Conference Series, Hinode Science Meeting, Dublin, 20-24th August 2007

The solar magnetic field is key to understanding the physical processes in the solar atmosphere. Nonlinear force-free codes have been shown to be useful in extrapolating the coronal field upward from underlying vector boundary data. However, we can only measure the magnetic field vector routinely with high accuracy in the photosphere, and unfortunately these data do not fulfill the force-free condition. We must therefore apply some transformations to these data before nonlinear force-free extrapolation codes can be self-consistently applied. To this end, we have developed a minimization procedure that yields a more chromosphere-like field, using the measured photospheric field vectors as input. The procedure includes force-free consistency integrals, spatial smoothing, and -- newly included in the version presented here -- an improved match to the field direction as inferred from fibrils as can be observed in, e.g., chromospheric H$\alpha$ images. We test the procedure using a model active-region field that included buoyancy forces at the photospheric level. The proposed preprocessing method allows us to approximate the chromospheric vector field to within a few degrees and the free energy in the coronal field to within one percent., Comment: 22 pages, 6 Figure

Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and powered by the partial dissipation of electrical currents in the solar atmosphere. A critical unanswered question is whether the currents involved are induced by the motion of pre-existing atmospheric magnetic flux subject to surface plasma flows, or whether these currents are associated with the emergence of flux from within the solar convective zone. We address this problem by applying state-of-the-art nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA Active Region 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with 4 different codes and a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We discuss the relative merits of these models in a general critique of present abilities to model the coronal magnetic field based on surface vector field measurements. For our application in particular, we find a fair agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the ~10^32 erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection.

The differential rotation of the sun, as deduced from helioseismology, exhibits a prominent radial shear layer near the top of the convection zone wherein negative radial gradients of angular velocity are evident in the low- and mid-latitude regions spanning the outer 5% of the solar radius. Supergranulation and related scales of turbulent convection are likely to play a significant role in the maintenance of such radial gradients, and may influence dynamics on a global scale in ways that are not yet understood. To investigate such dynamics, we have constructed a series of three-dimensional numerical simulations of turbulent compressible convection within spherical shells, dealing with shallow domains to make such modeling computationally tractable. These simulations are the first models of solar convection in a spherical geometry that can explicitly resolve both the largest dynamical scales of the system (of order the solar radius) as well as smaller-scale convective overturning motions comparable in size to solar supergranulation (20--40 Mm). We find that convection within these simulations spans a large range of horizontal scales, and that the radial angular velocity gradient in these models is typically negative, especially in low- and mid-latitude regions. Analyses of the angular momentum transport indicates that such gradients are maintained by Reynolds stresses associated with the convection, transporting angular momentum inward to balance the outward transport achieved by viscous diffusion and large-scale flows in the meridional plane. We suggest that similar mechanisms associated with smaller-scale convection in the sun may contribute to the maintenance of the observed radial shear layer located immediately below the solar photosphere., Comment: 45 pages, 17 figures, ApJ in press. A preprint of paper with hi-res figures can be found at http://www-lcd.colorado.edu/~derosa/modelling/modelling.html