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Register a new userA new method to quantify and reduce projection error in whole-solar-active-region parameters measured from vector magnetograms
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Projection error limits the use of vector magnetograms of active regions (ARs) far from disk center. In this Letter, for ARs observed up to 60o from disk center, we demonstrate a method of measuring and reducing the projection error in the magnitude of any whole-AR parameter derived from a vector magnetogram that has been deprojected to disk center. The method assumes that the center-to-limb curve of the average of the parameters absolute values measured from the disk passage of a large number of ARs and normalized to each ARs absolute value of the parameter at central meridian, gives the average fractional projection error at each radial distance from disk center. To demonstrate the method, we use a large set of large-flux ARs and apply the method to a whole-AR parameter that is among the simplest to measure: whole-AR magnetic flux. We measure 30,845 SDO/HMI vector magnetograms covering the disk passage of 272 large-flux ARs, each having whole-AR flux >1022 Mx. We obtain the center-to-limb radial-distance run of the average projection error in measured whole-AR flux from a Chebyshev fit to the radial-distance plot of the 30,845 normalized measured values. The average projection error in the measured whole-AR flux of an AR at a given radial distance is removed by multiplying the measured flux by the correction factor given by the fit. The correction is important for both the study of evolution of ARs and for improving the accuracy of forecasting an ARs major flare/CME productivity.
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This paper investigates a quiescent (non-flaring) active region observed on July 13, 2010 in EUV, SXR, and HXRs to search for a hot component that is speculated to be a key signature of coronal heating. We use a combination of RHESSI imaging and long-duration time integration (up to 40 min) to detect the active regions in the 3-8 keV range during apparently non-flaring times. The RHESSI imaging reveals a hot component that originates from the entire active region, as speculated for a nanoflare scenario where the entire active region is filled with a large number of unresolved small energy releases. An isothermal fit to the RHESSI data gives temperatures around ~7 MK with emission measure of several times 10^46 cm^-3. Adding EUV and SXR observations taken by AIA and XRT, respectively, we derive a differential emission measure (DEM) that shows a peak between 2 and 3 MK with a steeply decreasing high-temperature tail, similar to what has been previously reported. The derived DEM reveals that a wide range of temperatures contributes to the RHESSI flux (e.g. 40 % of the 4 keV emission being produced by plasma below 5 MK, while emission at 7 keV is almost exclusively from plasmas above 5 MK) indicating that the RHESSI spectrum should not be fitted with an isothermal. The hot component has a rather small emission measure (~0.1 % of the total EM is above 5 MK), and the derived thermal energy content is of the order of 10 % for a filling factor of unity, or potentially below 1 % for smaller filling factors.
The presence of elongations in active region (AR) polarities, called magnetic tongues, are mostly visible during their emergence phase. AR tilts have been measured thoroughly using long-term white-light (WL) databases, sometimes combined with magnetic field information. Since the influence of magnetic tongues on WL tilt measurements has not been taken into account before, we aim to investigate their role in tilt-angle values and to compare them with those derived from LOS magnetograms. We apply four methods to compute the tilt angle of generally bipolar ARs: one applies the k-means algorithm to WL data, a second one includes the magnetic field sign of the polarities to WL data, and a third one uses the magnetic flux-weighted center of each polarity. The tilt values computed in any of these ways are affected by the presence of magnetic tongues. Therefore, we apply the newly developed Core Field Fit Estimator (CoFFE) method to separate the magnetic flux in the tongues from that in the AR core. We compare the four computed tilt-angle values, as well as these with the ones reported in long-term WL databases. For ARs with low magnetic flux tongues the different methods report consistent tilt-angle values. But for ARs with high flux tongues there are noticeable discrepancies between all methods indicating that magnetic tongues affect differently WL and magnetic data. However, in general, CoFFE achieves a better estimation of the main bipole tilt because it removes both the effect of tongues as well as the emergence of secondary bipoles when it occurs in between the main bipole magnetic polarities.
The minimum-energy configuration for the magnetic field above the solar photosphere is curl-free (hence, by Amperes law, also current-free), so can be represented as the gradient of a scalar potential. Since magnetic fields are divergence free, this scalar potential obeys Laplaces equation, given an appropriate boundary condition (BC). With measurements of the full magnetic vector at the photosphere, it is possible to employ either Neumann or Dirichlet BCs there. Historically, the Neumann BC was used with available line-of-sight magnetic field measurements, which approximate the radial field needed for the Neumann BC. Since each BC fully determines the 3D vector magnetic field, either choice will, in general, be inconsistent with some aspect of the observed field on the boundary, due to the presence of both currents and noise in the observed field. We present a method to combine solutions from both Dirichlet and Neumann BCs to determine a hybrid, least-squares potential field, which minimizes the integrated square of the residual between the potential and actual fields. This has advantages in both not overfitting the radial field used for the Neumann BC, and maximizing consistency with the observations. We demonstrate our methods with SDO/HMI vector magnetic field observations of AR 11158, and find that residual discrepancies between the observed and potential fields are significant, and are consistent with nonzero horizontal photospheric currents. We also analyze potential fields for two other active regions observed with two different vector magnetographs, and find that hybrid potential fields have significantly less energy than the Neumann fields in every case --- by more than 10^(32) erg in some cases. This has major implications for estimates of free magnetic energy in coronal field models, e.g., non-linear force-free field extrapolations.
Stellar winds govern the angular momentum evolution of solar-like stars throughout their main-sequence lifetime. The efficiency of this process depends on the geometry of the stars magnetic field. There has been a rapid increase recently in the number of stars for which this geometry can be determined through spectropolarimetry. We present a computationally efficient method to determine the 3D geometry of the stellar wind and to estimate the mass loss rate and angular momentum loss rate based on these observations. Using solar magnetograms as examples, we quantify the extent to which the values obtained are affected by the limited spatial resolution of stellar observations. We find that for a typical stellar surface resolution of 20$^{rm o}$-30$^{rm o}$, predicted wind speeds are within 5$%$ of the value at full resolution. Mass loss rates and angular momentum loss rates are within 5-20$%$. In contrast, the predicted X-ray emission measures can be under-estimated by 1-2 orders of magnitude, and their rotational modulations by 10-20$%$.
Both coronal holes and active regions are source regions of the solar wind. The distribution of these coronal structures across both space and time is well known, but it is unclear how much each source contributes to the solar wind. In this study we use photospheric magnetic field maps observed over the past four solar cycles to estimate what fraction of magnetic open solar flux is rooted in active regions, a proxy for the fraction of all solar wind originating in active regions. We find that the fractional contribution of active regions to the solar wind varies between 30% to 80% at any one time during solar maximum and is negligible at solar minimum, showing a strong correlation with sunspot number. While active regions are typically confined to latitudes $pm$30$^{circ}$ in the corona, the solar wind they produce can reach latitudes up to $pm$60$^{circ}$. Their fractional contribution to the solar wind also correlates with coronal mass ejection rate, and is highly variable, changing by $pm$20% on monthly timescales within individual solar maxima. We speculate that these variations could be driven by coronal mass ejections causing reconfigurations of the coronal magnetic field on sub-monthly timescales.
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