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Register a new userOn estimating the force-freeness based on observed magnetograms
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It is a common practice in the solar physics community to test whether or not measured photospheric or chromospheric vector magnetograms are force-free, using the Maxwell stress as a measure. Some previous studies have suggested that magnetic fields of active regions in the solar chromosphere are close to be force-free whereas there is no consistency among previous studies on whether magnetic fields of active regions in the solar photosphere are force-free or not. Here we use three kinds of representative magnetic fields (analytical force-free solutions, modeled solar-like force-free fields and observed non-force-free fields) to discuss on how the measurement issues such as limited field of view, instrument sensitivity and measurement error could affect the estimation of force-freeness based on observed magnetograms. Unlike previous studies that focus on discussing the effect of limited field of view or instrument sensitivity, our calculation shows that just measurement error alone can significantly influence the results of force-freeness estimate, due to the fact that measurement errors in horizontal magnetic fields are usually ten times larger than that of the vertical fields. This property of measurement errors, interacting with the particular form of force-freeness estimate formula, would result in wrong judgments of the force-freeness: a truly force-free field may be mistakenly estimated as being non-force-free and a true non-force-free field may be estimated as being force-free. Our analysis calls for caution when interpreting the force-freeness estimates based on measured magnetograms, and also suggests that the true photospheric magnetic field may be further away from being force-free than they currently appear to be.
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Low-mass stars are known to have magnetic fields that are believed to be of dynamo origin. Two complementary techniques are principally used to characterise them. Zeeman-Doppler imaging (ZDI) can determine the geometry of the large-scale magnetic field while Zeeman broadening can assess the total unsigned flux including that associated with small-scale structures such as spots. In this work, we study a sample of stars that have been previously mapped with ZDI. We show that the average unsigned magnetic flux follows an activity-rotation relation separating into saturated and unsaturated regimes. We also compare the average photospheric magnetic flux recovered by ZDI, $langle B_Vrangle$, with that recovered by Zeeman broadening studies, $langle B_Irangle$. In line with previous studies, $langle B_Vrangle$ ranges from a few % to $sim$20% of $langle B_Irangle$. We show that a power law relationship between $langle B_Vrangle$ and $langle B_Irangle$ exists and that ZDI recovers a larger fraction of the magnetic flux in more active stars. Using this relation, we improve on previous attempts to estimate filling factors, i.e. the fraction of the stellar surface covered with magnetic field, for stars mapped only with ZDI. Our estimated filling factors follow the well-known activity-rotation relation which is in agreement with filling factors obtained directly from Zeeman broadening studies. We discuss the possible implications of these results for flux tube expansion above the stellar surface and stellar wind models.
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$%$.
We compare photospheric line-of-sight magnetograms from the Synoptic Long-term Investigations of the Sun (SOLIS) vector spectromagnetograph (VSM) instrument with observations from the 150-foot Solar Tower at Mt. Wilson (MWO), Helioseismic and Magnetic Imager (HMI) on Solar Dynamics Observatory (SDO), and Michelson Doppler Imager (MDI) on Solar and Heliospheric Observatory (SOHO). We find very good agreement between VSM and the other data sources for both disk-averaged flux densities and pixel-by-pixel measurements. We show that the VSM mean flux density time series is of consistently high signal-to-noise with no significant zero-offsets. We discuss in detail some of the factors -spatial resolution, flux dependence and position on the solar disk- affecting the determination of scaling between VSM and SOHO/MDI or SDO/HMI magnetograms. The VSM flux densities agree well with spatially smoothed data from MDI and HMI, although the scaling factors show clear dependence on flux density. The factor to convert VSM to HMI increases with increasing flux density (from $approx$1 to $approx$1.5). The nonlinearity is smaller for the VSM vs. ~SOHO/MDI scaling factor (from $approx$1 to $approx$1.2).
Context: Knowledge about the coronal magnetic field is important to the understanding the structure of the solar corona. We compute the field in the higher layers of the solar atmosphere from the measured photospheric field under the assumption that the corona is force-free. Aims: Here we develop a method for nonlinear force-free coronal magnetic field medelling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure. Methods: We describe a newly developed code for the extrapolation of nonlinear force-free coronal magnetic fields in spherical coordinates over a restricted area of the Sun. The program uses measured vector magnetograms on the solar photosphere as input and solves the force-free equations in the solar corona. We develop a preprocessing procedure in spherical geometry to drive the observed non-force-free data towards suitable boundary conditions for a force-free extrapolation. Results: We test the code with the help of a semi-analytic solution and assess the quality of our reconstruction qualitatively by magnetic field line plots and quantitatively with a number of comparison metrics for different boundary conditions. The reconstructed fields from the lower boundary data with the weighting function are in good agreement with the original reference fields. We added artificial noise to the boundary conditions and tested the code with and without preprocessing. The preprocessing recovered all main structures of the magnetogram and removed small-scale noise. The main test was to extrapolate from the noisy photospheric vector magnetogram with and without preprocessing. The preprocessing was found to significantly improve the agreement between the extrapolated and the exact field.
The SDO/HMI instruments provide photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semi-analytic and numeric equilibria and been applied before to vector magnetograms from Hinode and ground based observations. Recently we implemented a new version which takes measurement errors in photospheric vector magnetograms into account. Photospheric field measurements are often due to measurement errors and finite nonmagnetic forces inconsistent as a boundary for a force-free field in the corona. In order to deal with these uncertainties, we developed two improvements: 1.) Preprocessing of the surface measurements in order to make them compatible with a force-free field 2.) The new code keeps a balance between the force-free constraint and deviation from the photospheric field measurements. Both methods contain free parameters, which have to be optimized for use with data from SDO/HMI. Within this work we describe the corresponding analysis method and evaluate the force-free equilibria by means of how well force-freeness and solenoidal conditions are fulfilled, the angle between magnetic field and electric current and by comparing projections of magnetic field lines with coronal images from SDO/AIA. We also compute the available free magnetic energy and discuss the potential influence of control parameters.
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