Direct Measurements of Magnetic Twist in the Solar Corona

In the present work we study evolution of magnetic helicity in the solar corona. We compare the rate of change of a quantity related to the magnetic helicity in the corona to the flux of magnetic helicity through the photosphere and find that the two rates are similar. This gives observational evidence that helicity flux across the photosphere is indeed what drives helicity changes in solar corona during emergence. For the purposes of estimating coronal helicity we neither assume a strictly linear force-free field, nor attempt to construct a non-linear force-free field. For each coronal loop evident in Extreme Ultraviolet (EUV) we find a best-matching line of a linear force-free field and allow the twist parameter alpha to be different for each line. This method was introduced and its applicability was discussed in Malanushenko et. al. (2009). The object of the study is emerging and rapidly rotating AR 9004 over about 80 hours. As a proxy for coronal helicity we use the quantity averaged over many reconstructed lines of magnetic field. We argue that it is approximately proportional to "flux-normalized" helicity H/Phi^2, where H is helicity and Phi is total enclosed magnetic flux of the active region. The time rate of change of such quantity in the corona is found to be about 0.021 rad/hr, which is compatible with the estimates for the same region obtained using other methods Longcope et. al. (2007), who estimated the flux of normalized helicity of about 0.016 rad/hr

Using Coronal Loops to Reconstruct the Magnetic Field of an Active Region Before and After a Major Flare

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 pres

A Survey of z ~ 6 Quasars in the Sloan Digital Sky Survey Deep Stripe. II. Discovery of Six Quasars at z AB>21

We present the discovery of six new quasars at z ~ 6 selected from the Sloan Digital Sky Survey (SDSS) southern survey, a deep imaging survey obtained by repeatedly scanning a stripe along the celestial equator. The six quasars are about 2 mag fainter than the luminous z ~ 6 quasars found in the SDSS main survey and 1 mag fainter than the quasars reported in Paper I. Four of them comprise a complete flux-limited sample at 21 < z_(AB) < 21.8 over an effective area of 195 deg^2. The other two quasars are fainter than z_(AB) = 22 and are not part of the complete sample. The quasar luminosity function at z ~ 6 is well described as a single power law Φ(L_(1450))α L^β_(1450) over the luminosity range –28 < M_(1450) < –25. The best-fitting slope β varies from –2.6 to –3.1, depending on the quasar samples used, with a statistical error of 0.3-0.4. About 40% of the quasars discovered in the SDSS southern survey have very narrow Lyα emission lines, which may indicate small black hole masses and high Eddington luminosity ratios, and therefore short black hole growth timescales for these faint quasars at early epochs

Deep SDSS optical spectroscopy of distant halo stars II. Iron, calcium, and magnesium abundances

We analyze a sample of 3,944 low-resolution (R ~ 2000) optical spectra from the Sloan Digital Sky Survey (SDSS), focusing on stars with effective temperatures 5800 < Teff < 6300 K, and distances from the Milky Way plane in excess of 5 kpc, and determine their abundances of Fe, Ca, and Mg. We followed the same methodology as in the previous paper in this series, deriving atmospheric parameters by chi2 minimization, but this time we obtained the abundances of individual elements by fitting their associated spectral lines. Distances were calculated from absolute magnitudes obtained by a statistical comparison of our stellar parameters with stellar-evolution models. The observations reveal a decrease in the abundances of iron, calcium, and magnesium at large distances from the Galactic center. The median abundances for the halo stars analyzed are fairly constant up to a Galactocentric distance r ~ 20 kpc, rapidly decrease between r ~ 20 and r ~ 40 kpc, and flatten out to significantly lower values at larger distances, consistent with previous studies. In addition, we examine the [Ca/Fe] and [Mg/Fe] as a function of Fe/H and Galactocentric distance. Our results show that the most distant parts of the halo show a steeper variation of the [Ca/Fe] and [Mg/Fe] with iron. We found that at the range -1.6 < [Fe/H] < -0.4 [Ca/Fe] decreases with distance, in agreement with earlier results based on local stars. However, the opposite trend is apparent for [Mg/Fe]. Our conclusion that the outer regions of the halo are more metal-poor than the inner regions, based on in situ observations of distant stars, agrees with recent results based on inferences from the kinematics of more local stars, and with predictions of recent galaxy formation simulations for galaxies similar to the Milky Way

Thermal Diagnostics with the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory: A Validated Method for Differential Emission Measure Inversions

We present a new method for performing differential emission measure (DEM) inversions on narrow-band EUV images from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). The method yields positive definite DEM solutions by solving a linear program. This method has been validated against a diverse set of thermal models of varying complexity and realism. These include (1) idealized gaussian DEM distributions, (2) 3D models of NOAA Active Region 11158 comprising quasi-steady loop atmospheres in a non-linear force-free field, and (3) thermodynamic models from a fully-compressible, 3D MHD simulation of AR corona formation following magnetic flux emergence. We then present results from the application of the method to AIA observations of Active Region 11158, comparing the region's thermal structure on two successive solar rotations. Additionally, we show how the DEM inversion method can be adapted to simultaneously invert AIA and XRT data, and how supplementing AIA data with the latter improves the inversion result. The speed of the method allows for routine production of DEM maps, thus facilitating science studies that require tracking of the thermal structure of the solar corona in time and space.Comment: 21 pages, 18 figures, accepted for publication in Ap

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. II. Numeric Code and Tests

Based on a second-order approximation of nonlinear force-free magnetic field solutions in terms of uniformly twisted field lines derived in Paper I, we develop here a numeric code that is capable to forward-fit such analytical solutions to arbitrary magnetogram (or vector magnetograph) data combined with (stereoscopically triangulated) coronal loop 3D coordinates. We test the code here by forward-fitting to six potential field and six nonpotential field cases simulated with our analytical model, as well as by forward-fitting to an exactly force-free solution of the Low and Lou (1990) model. The forward-fitting tests demonstrate: (i) a satisfactory convergence behavior (with typical misalignment angles of $\mu \approx 1^\circ-10^\circ$), (ii) relatively fast computation times (from seconds to a few minutes), and (iii) the high fidelity of retrieved force-free $\alpha$-parameters ($\alpha_{\rm fit}/\alpha_{\rm model} \approx 0.9-1.0$ for simulations and $\alpha_{\rm fit}/\alpha_{\rm model} \approx 0.7\pm0.3$ for the Low and Lou model). The salient feature of this numeric code is the relatively fast computation of a quasi-forcefree magnetic field, which closely matches the geometry of coronal loops in active regions, and complements the existing {\sl nonlinear force-free field (NLFFF)} codes based on photospheric magnetograms without coronal constraints.Comment: Solar PHysics, (in press), 25 pages, 11 figure

Reconstructing the Local Twist of Coronal Magnetic Fields and the Three-Dimensional Shape of the Field Lines from Coronal Loops in EUV and X-Ray Images

Non-linear force-free fields are the most general case of force-free fields, but the hardest to model as well. There are numerous methods of computing such fields by extrapolating vector magnetograms from the photosphere, but very few attempts have so far made quantitative use of coronal morphology. We present a method to make such quantitative use of X-Ray and EUV images of coronal loops. Each individual loop is fit to a field line of a linear force-free field, allowing the estimation of the field line's twist, three-dimensional geometry and the field strength along it. We assess the validity of such a reconstruction since the actual corona is probably not a linear force-free field and that the superposition of linear force-free fields is generally not itself a force-free field. To do so, we perform a series of tests on non-linear force-free fields, described in Low & Lou (1990). For model loops we project field lines onto the photosphere. We compare several results of the method with the original field, in particular the three-dimensional loop shapes, local twist (coronal alpha), distribution of twist in the model photosphere and strength of the magnetic field. We find that, (i) for these trial fields, the method reconstructs twist with mean absolute deviation of at most 15% of the range of photospheric twist, (ii) that heights of the loops are reconstructed with mean absolute deviation of at most 5% of the range of trial heights and (iii) that the magnitude of non-potential contribution to photospheric field is reconstructed with mean absolute deviation of at most 10% of the maximal value.Comment: submitted to Ap