Current Sheet Source Surface Model Research Articles

An elliptic expansion of the potential field source surface model

Context. The potential field source surface model is frequently used as a basis for further scientific investigations where a comprehensive coronal magnetic field is of importance. Its parameters, especially the position and shape of the source surface, are crucial for the interpretation of the state of the interplanetary medium. Improvements have been suggested that introduce one or more additional free parameters to the model, for example, the current sheet source surface model. Aims. Relaxing the spherical constraint of the source surface and allowing it to be elliptical gives modelers the option of deforming it to more accurately match the physical environment of the specific period or location to be analyzed. Methods. A numerical solver is presented that solves Laplace’s equation on a three-dimensional grid using finite differences. The solver is capable of working on structured spherical grids that can be deformed to create elliptical source surfaces. Results. The configurations of the coronal magnetic field are presented using this new solver. Three-dimensional renderings are complemented by Carrington-like synoptic maps of the magnetic configuration at different heights in the solar corona. Differences in the magnetic configuration computed by the spherical and elliptical models are illustrated.

Revisiting the coronal current sheet model: Parameter range analysis and comparison with the potential field model

Aims. We study the properties of the coronal magnetic field according to the current sheet source surface (CSSS) model in 1976–2017 for all physically reasonable values of the three model parameters (cusp surface radius Rcs, source surface radius Rss, and current parameter a), and compare the CSSS field with the potential field source surface (PFSS) model field. Methods. We used the synoptic maps of the photospheric magnetic field from the Wilcox Solar Observatory (WSO), National Solar Observatory/Kitt Peak (NSO/KP), and the NSO Synoptic Optical Long-term Investigations of the Sun Vector Spectromagnetograph (SOLIS/VSM) in order to calculate the coronal magnetic field according to the CSSS and PFSS models. We calculated the coronal field strength, its latitudinal variation and neutral line location, as well as its polarity match with the heliospheric magnetic field. Results. The CSSS model can correct the erroneous latitudinal variation of the PFSS model if the source surface is sufficiently far out with respect to the cusp surface (Rss ≥ 3 ⋅ Rcs). The topology of the neutral line only slightly depends on source surface radius or current parameter, but excludes very low values of the cusp surface (Rcs ≤ 1.5). A comparison of the polarities gives an optimum cusp surface radius that varies in time between 2 and 5; a stronger current yields a larger optimum Rcs. Interestingly, the optimum polarity match percentages and optimum radii vary very similarly in the two models over the four solar cycles we studied. Conclusions. The CSSS model can produce a stronger total coronal flux than the PFSS model and correct its latitudinal variation. However, the topology of the CSSS model is rather independent of horizontal currents and remains very similar to that of the PFSS model. Therefore, the CSSS model cannot improve the match of field polarities between corona and heliosphere.

A Daily Determination of BZ Using the Russell‐McPherron Effect to Forecast Geomagnetic Activity

AbstractSince the middle of the last decade, UCSD has incorporated magnetic field data in its Institute for Space‐Earth Environmental Research interplanetary scintillation tomographic analysis. These data are extrapolated upward from the solar surface using the Current Sheet Source Surface model (Zhao & Hoeksema, 1995, https://doi.org/10.1029/94JA02266) to provide predictions of the interplanetary field in RTN coordinates. Over the years this technique has become ever more sophisticated, and allows different types of magnetogram data (SOLIS, Global Oscillation Network Group, etc.,) to be incorporated in the field extrapolations. At Earth, these fields can be displayed in a variety of ways, including Geocentric Solar Magnetospheric (GSM) Bx, By, and Bz coordinates. Displayed daily, the Current Sheet Source Surface model‐derived GSM Bz shows a significant positive correlation with the low‐resolution (few day variation) in situ measurements of the Bz field. The nano‐Tesla variations of Bz maximize in spring and fall as Russell and McPherron (1973, https://doi.org/10.1029/JA078i001p00092) have shown. More significantly, we find that the daily variations are correlated with geomagnetic Kp and Dst index variations, and that a decrease from positive to negative Bz has a high correlation with minor‐to‐moderate geomagnetic storm activity, as defined by NOAA Space Weather Prediction Center planetary Kp values. Here we provide an 11‐year study of the predicted Bz field, from the extrapolation of the Global Oscillation Network Group‐magnetograms. We provide a skill‐score analysis of the technique's geomagnetic storm prediction capability, which allows forecasts of moderate enhanced geomagnetic storm activity. UCSD and the Korean Space Weather Center currently operate a website that predicts this low‐resolution GSM Bz field component variation several days in advance.

Exploration of solar photospheric magnetic field data sets using the UCSD tomography

AbstractThis article investigates the use of two different types of National Solar Observatory magnetograms and two different coronal field modeling techniques over 10 years. Both the “open‐field” Current Sheet Source Surface (CSSS) and a “closed‐field” technique using CSSS modeling are compared. The University of California, San Diego, tomographic modeling, using interplanetary scintillation data from Japan, provides the global velocities to extrapolate these fields outward, which are then compared with fields measured in situ near Earth. Although the open‐field technique generally gives a better result for radial and tangential fields, we find that a portion of the closed extrapolated fields measured in situ near Earth comes from the direct outward mapping of these fields in the low solar corona. All three closed‐field components are nonzero at 1 AU and are compared with the appropriate magnetometer values. A significant positive correlation exists between these closed‐field components and the in situ measurements over the last 10 years. We determine that a small fraction of the static low‐coronal component flux, which includes the Bn (north‐south) component, regularly escapes from closed‐field regions. The closed‐field flux fraction varies by about a factor of 3 from a mean value during this period, relative to the magnitude of the field components measured in situ near Earth, and maximizes in 2014. This implies that a relatively more efficient process for closed‐flux escape occurs near solar maximum. We also compare and find that the popular Potential Field Source Surface and CSSS model closed fields are nearly identical in sign and strength.

CONTROLLING INFLUENCE OF MAGNETIC FIELD ON SOLAR WIND OUTFLOW: AN INVESTIGATION USING CURRENT SHEET SOURCE SURFACE MODEL

ABSTRACT This Letter presents the results of an investigation into the controlling influence of large-scale magnetic field of the Sun in determining the solar wind outflow using two magnetostatic coronal models: current sheet source surface (CSSS) and potential field source surface. For this, we made use of the Wang and Sheeley inverse correlation between magnetic flux expansion rate (FTE) and observed solar wind speed (SWS) at 1 au. During the period of study, extended over solar cycle 23 and beginning of solar cycle 24, we found that the coefficients of the fitted quadratic equation representing the FTE–SWS inverse relation exhibited significant temporal variation, implying the changing pattern of the influence of FTE on SWS over time. A particularly noteworthy feature is an anomaly in the behavior of the fitted coefficients during the extended minimum, 2008–2010 (CRs 2073–2092), which is considered due to the particularly complex nature of the solar magnetic field during this period. However, this variation was significant only for the CSSS model, though not a systematic dependence on the phase of the solar cycle. Further, we noticed that the CSSS model demonstrated better solar wind prediction during the period of study, which we attribute to the treatment of volume and sheet currents throughout the corona and the more accurate tracing of footpoint locations resulting from the geometry of the model.

A DETERMINATION OF THE NORTH–SOUTH HELIOSPHERIC MAGNETIC FIELD COMPONENT FROM INNER CORONA CLOSED-LOOP PROPAGATION

A component of the magnetic field measured in situ near the Earth in the solar wind is present from north–south fields from the low solar corona. Using the Current-sheet Source Surface model, these fields can be extrapolated upward from near the solar surface to 1 AU. Global velocities inferred from a combination of interplanetary scintillation observations matched to in situ velocities and densities provide the extrapolation to 1 AU assuming mass and mass flux conservation. The north–south field component is compared with the same ACE in situ magnetic field component—the Normal (Radial Tangential Normal) Bn coordinate—for three years throughout the solar minimum of the current solar cycle. We find a significant positive correlation throughout this period between this method of determining the Bn field compared with in situ measurements. Given this result from a study during the latest solar minimum, this indicates that a small fraction of the low-coronal Bn component flux regularly escapes from closed field regions. The prospects for Space Weather, where the knowledge of a Bz field at Earth is important for its geomagnetic field effects, is also now enhanced. This is because the Bn field provides the major portion of the Geocentric Solar Magnetospheric Bz field coordinate that couples most closely to the Earth's geomagnetic field.

VALIDATING SOLAR WIND PREDICTION USING THE CURRENT SHEET SOURCE SURFACE MODEL

We have carried out a comparative study of the predicted solar wind based on the flux tube expansion factor computed using the current sheet source surface (CSSS) model and the potential field source surface (PFSS) model, with the aim of determining whether the CSSS model represents the solar wind sources better than the PFSS model. For this, we obtained the root mean square errors (RMSEs) and the correlation coefficients between the observed solar wind speed and that predicted by the models, the ratio of RMSEs between the two models, and a skill score. On average, the CSSS predictions are more accurate than the PFSS predictions by a factor of 1.6, taking RMSE as the metric of accuracy. The RMSEs increased as the solar cycle progressed toward maximum, indicating the difficulty in modeling the corona as the global field becomes more complex. We also compared the WSA/ENLIL predictions for a few Carrington rotations; the Wang-Sheeley-Arge (WSA) model makes use of the PFSS extrapolations to model the wind source. We found that the average value of RMSE ratio between the CSSS and the WSA/ENLIL predictions was about 1.9, implying that the CSSS predictions are nearly twice better than the WSA/ENLIL predictions, despite the simplicity of the CSSS model compared to ENLIL. We conclude, based on the present analysis, that the CSSS model is a valid proxy for solar wind measurements and that it improves upon existing commonly used methods of wind prediction or proxy analysis.

Probe of the Solar Magnetic Field Using the “Cosmic-Ray Shadow” of the Sun

We report on a clear solar-cycle variation of the Sun’s shadow in the 10 TeV cosmic-ray flux observed by the Tibet air shower array during a full solar cycle from 1996 to 2009. In order to clarify the physical implications of the observed solar cycle variation, we develop numerical simulations of the Sun’s shadow, using the potential field source surface model and the current sheet source surface (CSSS) model for the coronal magnetic field. We find that the intensity deficit in the simulated Sun’s shadow is very sensitive to the coronal magnetic field structure, and the observed variation of the Sun’s shadow is better reproduced by the CSSS model. This is the first successful attempt to evaluate the coronal magnetic field models by using the Sun’s shadow observed in the TeV cosmic-ray flux.

Modeling the Sun's open magnetic flux

Context. The heliospheric magnetic field can be extrapolated from the photospheric field distribution using models based upon various approximations. Such models are required for the reconstruction of the open solar magnetic flux prior to the time of direct measurements on the basis of surface flux transport simulations. Aims. We evaluate the consistency of extrapolation models with direct measurements of the heliospheric magnetic field. Furthermore, we study whether extrapolations on the basis of a surface flux transport model for the photospheric magnetic field reproduce the temporal evolution of the measured near-Earth magnetic field. Methods. We use the potential field source surface (PFSS) model and the current sheet source surface (CSSS) model to extrapolate the heliospheric field on the basis of the Wilcox Solar Observatory (WSO) synoptic maps of the solar surface field from 1976-2005. The results are compared with the near-Earth measurements of the radial heliospheric field and its independence of latitude found with Ulysses. Furthermore, we determine extrapolations on the basis of photospheric flux distributions computed with a surface flux transport code, using as input sunspot group areas from the SOON database. Results. The CSSS model based upon WSO data, with a source surface located at >10 R ⊙ and cusp surface at 1.7 R ⊙ . yields the best agreement with the measurements. The flux transport simulations reproduce the observed surface flux together with the open flux if the tilt angle of emerging bipolar magnetic regions is smaller than commonly assumed, but consistent with sunspot observations. Conclusions. The CSSS model with a source surface in the vicinity of the Alfvenic point of the solar wind leads to a good extrapolation of the heliospheric field from solar surface data. A surface flux transport model based upon sunspot data with consistently calibrated tilt angles reproduces the observed evolution of the solar total open flux.

Predicting the heliospheric magnetic field using the current sheet-source surface model

We have developed a current sheet-source surface (CSSS) model for quantitatively predicting the coronal and interplanetary magnetic field (IMF) from measurements of the photospheric magnetic field /1/. In-ecliptic OMNI data from Solar Cycle 21 were used to infer a set of model parameters that reproduce the observed IMF radial component ( B x ) better than earlier models. Here we extend the model calculation to Cycle 22 and compare the results with both ecliptic and high latitude observations. Comparison with the in-ecliptic data shows that the same set of model parameters can be used in Solar Cycle 22. Furthermore, the predicted maximum latitude of the heliospheric current sheet (HCS) is consistent with Ulysses' observation of the disappearance of the IMF sector pattern near 30°S between April and June, 1993. The computed B x along Ulysses' trajectory shows a similar trend to the observed total field amplitude at lower latitude. A more detailed comparison between the model prediction and Ulysses observations should allow a determination of an optimal model parameter set. The computed heliomagnetic latitude variation of B x suggests a dipole-like configuration of the large-scale coronal and heliospheric magnetic field. This may be used to understand the the 3-D structure of the solar wind speed in the declining phase of the solar cycle.