Evidence for Wave Heating of the Quiet Sun Corona

We have measured the energy and dissipation of Alfvenic waves in the quiet Sun. A magnetic field was used to infer the location and orientation of the magnetic field lines along which the waves are expected to travel. The waves were measured using spectral lines to infer the wave amplitude. The waves cause a non-thermal broadening of the spectral lines, which can be expressed as a non-thermal velocity v_nt. By combining the spectroscopic measurements with this magnetic field model we were able to trace the variation of v_nt along the magnetic field. At the footpoints of the quiet Sun loops we find that waves inject an energy flux in the range of 1.2-5.2 x 10^5 erg cm^-2 s^-1. At the minimum of this range, this amounts to more than 80% of the energy needed to heat the quiet Sun. We also find that these waves are dissipated over a region centered on the top of the loops. The position along the loop where the damping begins is strongly correlated with the length of the loop, implying that the damping mechanism depends on the global loop properties rather than on local collisional dissipation.Comment: Submitted to the Astrophysical Journa

Observational Quantification of the Energy Dissipated by Alfv\'en Waves in a Polar Coronal Hole: Evidence that Waves Drive the Fast Solar Wind

We present a measurement of the energy carried and dissipated by Alfv\'en waves in a polar coronal hole. Alfv\'en waves have been proposed as the energy source that heats the corona and drives the solar wind. Previous work has shown that line widths decrease with height in coronal holes, which is a signature of wave damping, but have been unable to quantify the energy lost by the waves. This is because line widths depend on both the non-thermal velocity v_nt and the ion temperature T_i. We have implemented a means to separate the T_i and v_nt contributions using the observation that at low heights the waves are undamped and the ion temperatures do not change with height. This enables us to determine the amount of energy carried by the waves at low heights, which is proportional to v_nt. We find the initial energy flux density present was 6.7 +/- 0.7 x 10^5 erg cm^-2 s^-1, which is sufficient to heat the coronal hole and acccelerate the solar wind during the 2007 - 2009 solar minimum. Additionally, we find that about 85% of this energy is dissipated below 1.5 R_sun, sufficiently low that thermal conduction can transport the energy throughout the coronal hole, heating it and driving the fast solar wind. The remaining energy is roughly consistent with what models show is needed to provide the extended heating above the sonic point for the fast solar wind. We have also studied T_i, which we found to be in the range of 1 - 2 MK, depending on the ion species.Comment: Accepted for the Astrophysical Journa

Inferring the Coronal Density Irregularity from EUV Spectra

Understanding the density structure of the solar corona is important for modeling both coronal heating and the solar wind. Direct measurements are difficult because of line-of-sight integration and possible unresolved structures. We present a new method for quantifying such structure using density-sensitive EUV line intensities to derive a density irregularity parameter, a relative measure of the amount of structure along the line of sight. We also present a simple model to relate the inferred irregularities to physical quantities, such as the filling factor and density contrast. For quiet Sun regions and interplume regions of coronal holes, we find a density contrast of at least a factor of three to ten and corresponding filling factors of about 10-20%. Our results are in rough agreement with other estimates of the density structures in these regions. The irregularity diagnostic provides a useful relative measure of unresolved structure in various regions of the corona.Comment: Submitted to the Astrophysical Journa

Functoriality and the Inverse Galois Problem

We prove that there are infinitely many finite simple groups of symplectic Lie type, of any specified characteristic and rank, which appear as Galois groups over the field of rational numbers. This generalizes a result of Wiese, which inspired this paper.Comment: This is a major revision in which several errors are corrected at the cost of a somewhat weakened main theorem. 32 page

Relative Abundance Measurements in Plumes and Interplumes

We present measurements of relative elemental abundances in plumes and interplumes. Plumes are bright, narrow structures in coronal holes that extend along open magnetic field lines far out into the corona. Previous work has found that in some coronal structures the abundances of elements with a low first ionization potential (FIP) < 10 eV are enhanced relative to their photospheric abundances. This coronal-to-photospheric abundance ratio, commonly called the FIP bias, is typically 1 for element with a high-FIP (> 10 eV). We have used EIS spectroscopic observations made on 2007 March 13 and 14 over an ~24 hour period to characterize abundance variations in plumes and interplumes. To assess their elemental composition, we have used a differential emission measure (DEM) analysis, which accounts for the thermal structure of the observed plasma. We have used lines from ions of iron, silicon, and sulfur. From these we have estimated the ratio of the iron and silicon FIP bias relative to that for sulfur. From the results, we have created FIP-bias-ratio maps. We find that the FIP-bias ratio is sometimes higher in plumes than in interplumes and that this enhancement can be time dependent. These results may help to identify whether plumes or interplumes contribute to the fast solar wind observed in situ and may also provides constraints on the formation and heating mechanisms of plumes.Comment: 21 pages; 3 tables; 12 figure

Evidence of Wave Damping at Low Heights in a Polar Coronal Hole

We have measured the widths of spectral lines from a polar coronal hole using the Extreme Ultraviolet Imaging Spectrometer onboard Hinode. Polar coronal holes are regions of open magnetic field and the source of the fast solar wind. We find that the line widths decrease at relatively low heights. Previous observations have attributed such decreases to systematic effects, but we find that such effects are too small to explain our results. We conclude that the line narrowing is real. The non-thermal line widths are believed to be proportional to the amplitude of Alfven waves propagating along these open field lines. Our results suggest that Alfven waves are damped at unexpectedly low heights in a polar coronal hole. We derive an estimate on the upper limit for the energy dissipated between 1.1 and 1.3 solar radii and find that it is enough to account for up to 70% of that required to heat the polar coronal hole and accelerate the solar wind.Comment: Accepted for publication in the Astrophysical Journal, April 201

Spectroscopic measurements of the ion velocity distribution at the base of the fast solar wind

In situ measurements of the fast solar wind reveal non-thermal distributions of electrons, protons, and minor ions extending from 0.3 au to the heliopause. The physical mechanisms responsible for these non-thermal properties and the location where these properties originate remain open questions. Here, we present spectroscopic evidence, from extreme ultraviolet spectroscopy, that the velocity distribution functions (VDFs) of minor ions are already non-Gaussian at the base of the fast solar wind in a coronal hole, at altitudes of &lt;1.1 R ⊙. Analysis of Fe, Si, and Mg spectral lines reveals a peaked line-shape core and broad wings that can be characterized by a kappa VDF. A kappa distribution fit gives very small kappa indices off-limb of κ ≈ 1.9–2.5, indicating either (a) ion populations far from thermal equilibrium, (b) fluid motions such as non-Gaussian turbulent fluctuations or non-uniform wave motions, or (c) some combination of both. These observations provide important empirical constraints for the source region of the fast solar wind and for the theoretical models of the different acceleration, heating, and energy deposition processes therein. To the best of our knowledge, this is the first time that the ion VDF in the fast solar wind has been probed so close to its source region. The findings are also a timely precursor to the upcoming 2018 launch of the Parker Solar Probe, which will provide the closest in situ measurements of the solar wind at approximately 0.04 au (8.5 solar radii)