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NASA NTRS2023

A Technique to Measure Coronal Electron Density, Temperature, and Velocity Above 2.5 R from Sun Center Using Polarized Brightness Spectrum

The current model for the polarized brightness (pB) spectrum has a decades-long history of progressively incorporating its dependence on electron density N(e), temperature T(e), and flow velocity in the radial direction V(e). The pBNe spectrum follows the exact shape of the photosphere spectrum, which is not smooth, which is expected from the thermal Doppler broadening of the photosphere spectrum due to the high coronal T(e). The pBN(e) spectrum is smooth, but the free coronal electrons remain static and unaffected by solar wind, and the pBN(e)T(e)V(e) spectrum is red-shifted by electrons seeing a red-shifted photosphere spectrum as they flow away from the Sun as solar wind, which takes a radial direction above 2.5 R from Sun center. In this article, we review the progress of the above three model pB spectra in describing the observations and highlight the differences, first by comparing the three model pB spectra against wavelength using a model for Ne and constant values for T(e) and V (e), and second by generating three model 2D pB maps by integrating over a selected wavelength region in the three model pB spectra along lines of sight passing through the 14 July 2000 (“Bastille Day”) coronal mass ejection (CME) model, which contains 3D information on N(e), T(e), and V e. In this regard, the COronal Diagnostic EXperiment (CODEX) on the International Space Station (ISS) in 2024 will measure N(e), T(e), and V(e) by matching the measured pB with modeled pBN(e)T(e)V(e) in selected wavelength regions using multiple filters.

Electron density↗
NASA NTRS2023

A Technique to Measure Coronal Electron Density, Temperature, and Velocity Above 2.5 R⨀ from Sun Center using Polarized Brightness Spectrum

The current model for the polarized brightness (pB) spectrum has a decades-long history of progressively incorporating its dependence on electron density Ne, temperature Te, and flow velocity in the radial direction V e . The pB N e spectrum follows the exact shape of the photosphere spectrum, which is not smooth, which is expected from the thermal Doppler broadening of the photosphere spectrum due to the high coronal T e ; the pB N e T e spectrum is smooth, but the free coronal electrons remain static and unaffected by solar wind, and the pB N e T e V e spectrum is red-shifted by electrons seeing a red-shifted photosphere spectrum as they flow away from the Sun as solar wind, which takes a radial direction above 2.5 R ⨀ from Sun center. In this article, we review the progress of the above three model pB spectra in describing the observations and highlight the differences, first by comparing the three model pB spectra against wavelength using a model for Ne and constant values for T e and V e , and second by generating three model 2D pB maps by integrating over a selected wavelengthregion in the three model pB spectra along lines of sight passing through the 14 July 2000 (“Bastille Day”) coronal mass ejection (CME) model, which contains 3D information on N e , T e , and V e . In this regard, the COronal Diagnostic EXperiment (CODEX) on the International Space Station (ISS) in 2024 will measure N e , T e , and V e by matching the measured pB with modeled pB N e T e V e in selected wavelength regions using multiple filters.

Electron density↗
NASA NTRS1994

Coronal temperature, density, and magnetic field maps of a solar acitve region using the Owens Valley Solar Array

We present the first results of solar active region observations with the recently completed five-element Owens Valley Solar Array. On 1991 October 24, maps of Active Region AR 6891 were obtained at 22 frequencies from 1.2-7.0 GHz to provide brightness temperature spectra at each point. This is the first time that both high spatial and frequency-resolution brightness temperature spectra have been available over such a broad radio-frequency range. We find that over most of the region the spectra fall into one of the two well-defined categories: thermal free-free or thermal gyroresonance. In these cases, we use the spectra to deduce the spatial variation of physical parameters-electron temperature, column emission measure (intergral n(sup 2)(sub e) dl), and the coronal magnetic field strength-in and around the active region. Over a limited area of the region, the spectra resemble neither of the simple types, and alternative interpretations are required. The possibilties include the presence of fine structure that is unresolved at low frequencies; the presence of a small number of nonthermal electrons; or the presence of overlying, cooler 10(exp 6) K material which at low frequencies absorbs the hot (3 x 10(exp 6) K) thermal emission generated below.

Gary, Dale E.↗
NASA NTRS1995

Heating of coronal holes by the resonant absorption and dissipation of Alfven waves and its relation to solar wind acceleration

Coronal hole regions are well known sources of high-speed solar wind, however to account for the observed properties of the solar wind a source of momentum and heat must be included. Alfven waves were suggested as the possible source of heating that accelerates the solar wind. We investigate the propagation of the Alfven waves in coronal holes via numerical solution of the linearized 2-D resistive MHD equations in slab geometry. The Alfven waves are driven at the lower boundary of the coronal hole and propagate into the corona. The waves are reflected at the coronal hole boundary and part of the wave energy leaks out of the coronal hole. We compare the calculated wavelengths and the attenuation rate of the fast mode Alfven waves in the leaky waveguide formed by the coronal hole with the analytical ideal MHD solutions. The formation of resonance heating layers is found to occur when shear Alfven waves propagate in an inhomogeneous coronal hole. The heating is enhanced when fast mode waves couple to the shear Alfven waves. The narrow heating layers are formed near the location of the ideal resonance, which might occur near the coronal hole boundary for a nearly constant density coronal hole, surrounded by a higher density plasma. We investigate the dependence of the heating on the driver frequency, the Lundquist number, and on the heliocentric distance. and find that the low frequency Alfven waves can be an efficient source of heating at large distances from the Sun. We discuss the relation of our results to the observed properties of high-speed solar wind and coronal holes.

Ofman, L.↗
NASA NTRS1996

An Estimate of Solar Wind Density and Velocity Profiles in a Coronal Hole and a Coronal Streamer

Using the total electron content data obtained by the Ulysses Solar Corona Experiment (SCE) during the first solar conjunction in summer 1991, two data sets were selected, one associated with a coronal hole and the other associated with coronal streamer crossings. In order to determine coronal streamer density profiles, the electron content of the tracking passes embedded in a coronal streamer were corrected for the contributions from coronal hole densities.

coronal density coronal velocity velocity profiles↗
NASA NTRS1989

Line-of-sight effects on spectroscopic measurements in the inner solar wind region

The effect of the integration along the line of sight on the spectral line profiles of the resonantly scattered Lyman alpha radiation emitted by low-density coronal holes at heights above 1.5 Rs from sun center is investigated. It is shown how the spectral lines from this region are influenced by the Lyman alpha emission from surrounding regions with higher densities. The coronal hole and the surrounding areas are described by a two-fluid solar wind model. It is shown that the line-of-sight effects can be important for the interpretation of the Lyman alpha spectral line measurements in the outer corona and inner solar wind.

Esser, Ruth↗
NASA NTRS2011

Coronal Plumes in the Fast Solar Wind

The expansion of a coronal hole filled with a discrete number of higher density coronal plumes is simulated using a time-dependent two-dimensional code. A solar wind model including an exponential coronal heating function and a flux of Alfven waves propagating both inside and outside the structures is taken as a basic state. Different plasma plume profiles are obtained by using different scale heights for the heating rates. Remote sensing and solar wind in situ observations are used to constrain the parameter range of the study. Time dependence due to plume ignition and disappearance is also discussed. Velocity differences of the order of approximately 50 km/s, such as those found in microstreams in the high-speed solar wind, may be easily explained by slightly different heat deposition profiles in different plumes. Statistical pressure balance in the fast wind data may be masked by the large variety of body and surface waves which the higher density filaments may carry, so the absence of pressure balance in the microstreams should not rule out their interpretation as the extension of coronal plumes into interplanetary space. Mixing of plume-interplume material via the Kelvin-Helmholtz instability seems to be possible within the parameter ranges of the models defined here, only at large di stances from the Sun, beyond 0.2-0.3 AU. Plasma and composition measurements in the inner heliosphere, such as those which will become available with Solar Orbiter and Solar Probe Plus, should therefore definitely be able to identify plume remnants in the solar wind.

Velli, Marco↗
NASA NTRS1987

Rapid temporal evolution of radiation from non-thermal electrons in solar flares

Solutions of the time dependent Fokker-Planck equation was found for accelerated electrons undergoing Coulomb collisions in a magnetized, fully ionized plasma. An exact solution was found for arbitrary pitch angle and energy distribution in a uniform background plasma. Then, for an inhomogeneous plasma, a solution was found for particles with small pitch angles. These solutions were used to calculate the temporal evolution of bremsstrahlung x-rays from short bursts of nonthermal electron beams, and these spectra were compared with observed high time resolution spectra of short timescale solar hard x-ray bursts. It is shown that the observed softening in time of the spectra rules out a homogeneous background and therefore the possibility of electrons being confined to the corona either because of converging magnetic field or high densities. The inhomogeneous solution was also applied to a model with constant coronal density and exponentially rising chromospheric density. The spectra are shown to be consistent with that produced by a collimated beam of electrons accelerated in the corona with certain given conditions. These conditions could be violated if large pitch angle electrons are present.

Lu, Edward T.↗
NASA NTRS1988

Rapid temporal evolution of radiation from nonthermal electrons in solar flares

Solutions of the time dependent Fokker-Planck equation was found for accelerated electrons undergoing Coulomb collisions in a magnetized, fully ionized plasma. An exact solution was found for arbitrary pitch angle and energy distribution in a uniform background plasma. Then, for an inhomogeneous plasma, a solution was found for particles with small pitch angles. These solutions were used to calculate the temporal evolution of bremsstrahlung X-rays from short bursts of nonthermal electron beams, and these spectra were compared with observed high time resolution spectra of short timescale solar hard X-ray bursts. It is shown that the observed softening in time of the spectra rules out a homogeneous background and therefore the possibility of electrons being confined to the corona either because of converging magnetic field or high densities. The inhomogeneous solution was also applied to a model with constant coronal density and exponentially rising chromospheric density. The spectra are shown to be consistent with that produced by a collimated beam of electrons accelerated in the corona with certain given conditions. These conditions could be violated if large pitch angle electrons are present.

Lu, Edward T.↗
NASA NTRS2014

Validation of Spherically Symmetric Inversion by Use of a Tomographically Reconstructed Three-Dimensional Electron Density of the Solar Corona

Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.

corona↗
NASA NTRS1986

Interpretation of coronal synoptic observations

Three-dimensional reconstruction techniques used to determine coronal density distributions from synoptic data are complicated and time consuming to employ. Current techniques also assume time invariant structures and thus mix both temporal and spatial variations present in the coronal data. The observed distribution of polarized brightness, pB, and brightness, B, of coronal features observed either at eclipses or with coronagraphs depends upon both the three-dimensional distribution of electron density within the structure and the location of the feature with respect to the plane-of-the-sky. By theoretically studying the signature of various coronal structures as they would appear during a limb transit, it is possible to recognize these patterns in real synoptic data as well as estimate temporal evolutionary effects.

Munro, R. H.↗
NASA NTRS1991

Model dependence of velocities derived from coronal resonance lines

Intensity measurements of coronal resonance lines can be used to determine the outflow velocities of the scattering particles, provided the distribution of the densities, temperatures and velocities along the line of sight is known. A parameter study is designed and carried out to investigate the effect of surrounding denser regions with different temperatures and velocities on the velocity deduced from intensity measurements of the H I Lyman-alpha line in low density coronal holes.

Esser, Ruth↗
NASA NTRS1983

Solar cycle evolution of the solar wind in three dimensions

Measurements of the solar wind speed both in and out of the ecliptic are presented for 1971-82. The speed estimates, which were made with the interplanetary scintillation system at UC San Diego, have been compared to in situ for large, slowly evolving structures, and thus such structures can be studied up to 60 degrees north and south heliographic latitude. Annual average wind speeds are presented versus latitude for an entire solar cycle. Fast wind streams from the poles persisted through declining and low solar activity, but were closed off during four years of high activity. This evolution follows that of the polar coronal holes, as displayed by comparing averaged speed and coronal density over latitude and longitude. The most recent data (1982) show the reestablishment of large tilted polar holes and associated fast streams. Coronal magnetic field data show that the neutral sheet is confined to low latitudes at solar minimum and extends to high latitudes at solar maximum; thus the slow solar wind comes from the same latitude range as that of the neutral sheet.

Rickett, B. J.↗
NASA NTRSDate not supplied

Modeling EUV Intensity at the Top of the Transition Region Using SPICE Data on Board Solar Orbiter

The Spectral Imaging of Coronal Environment (SPICE; SPICE Consortium et al. 2020) provides an extraordinary opportunity to study the chromosphere and transition region using EUV wavelengths, e.g., Ne VIII 770 Å, CIII 977 Å, OVI 1032 Å, and Lyman-𝛽 025 Å. We present results modeling Ne VIII 770 Å intensity using images from SPICE and the COronal DEnsity and Temperature (CODET) model. This model is based on relationships between the magnetic field, density, and temperature. It uses a flux transport model, the Potential Field Extrapolation model (PFSS), an emission model based on Chianti atomic database 10.0.2, and an optimization algorithm. In addition, we assume that the emission from the top of the transition region (Ne VIII 770 Å) can be described using the magnetic field in the coronal base at 1.014𝑅⨀ (from PFSS). We found the mean full disc electron density in the transition region obtained from the CODET model for Ne VIII 770 Å (𝑙𝑜𝑔10𝑇[𝐾] = 5.8) corresponds to ∼ 𝑙𝑜𝑔10𝑁 𝑐𝑚−3 >9, and temperature value is 𝑙𝑜𝑔10𝑇[𝐾]~6. This value agrees with the Ne VIII 770 Å temperature formation 𝑙𝑜𝑔10𝑇[𝐾]~5.8. The density above sunspots (𝐵 > 50 𝐺) corresponds to 𝑙𝑜𝑔10𝑁 𝑐𝑚−3 > 9, while in quiet Sun regions (𝐵 < 50 𝐺) the mean density is 𝑙𝑜𝑔10𝑁[𝑐𝑚−3 ] = 8 .

Jenny M Rodriguez Gomez↗
NASA NTRS2006

Ultra-fine-scale filamentary structures in the Outer Corona and the Solar Magnetic Field

Filamentary structures following magnetic field lines pervade the Sun's atmosphere and offer us insight into the solar magnetic field. Radio propagation measurements have shown that the smallest filamentary structures in the solar corona are more than 2 orders of magnitude finer than those seen in solar imaging. Here we use radio Doppler measurements to characterize their transverse density gradient and determine their finest scale in the outer corona at 20-30 R(circled dot operator), where open magnetic fields prevail. Filamentary structures overly active regions have the steepest gradient and finest scale, while those overlying coronal holes have the shallowest gradient and least finest scale. Their organization by the underlying corona implies that these subresolution structures extend radially from the entire Sun, confirming that they trace the coronal magnetic field responsible for the radial expansion of the solar wind. That they are rooted all over the Sun elucidates the association between the magnetic field of the photosphere and that of the corona, as revealed by the similarity between the power spectra of the photospheric field and the coronal density fluctuations. This association along with the persistence of filamentary structures far from the Sun demonstrate that subresolution magnetic fields must play an important role not only in magnetic coupling of the photosphere and corona, but also in coronal heating and solar wind acceleration through the process of small-scale magnetic reconnection. They also explain why current widely used theoretical models that extrapolate photospheric magnetic fields into the corona do not predict the correct source of the solar wind.

Sun : Corona↗
NASA NTRS2011

What Dominates the Coronal Emission Spectrum During the Cycle of Impulsive Heating and Cooling?

The smoking gun of small-scale, impulsive events heating the solar corona is expected to be the presence of a hot ( > 5 MK) plasma component. Evidence for this has been scarce, but has gradually begun to accumulate due to recent studies designed to constrain the high temperature part of the emission measure distribution. However, the detected hot component is often weaker than models predict and this is due in part to the common modeling assumption that the ionization balance remains in equilibrium. The launch of the latest generation of space-based observing instrumentation aboard Hinode and the Solar Dynamics Observatory (SDO) has brought the matter of the ionization state of the plasma firmly to the forefront. It is timely to consider exactly what emission current instruments would detect when observing a corona heated impulsively on small-scales by nanoflares. Only after we understand the full effects of nonequilibrium ionization can we draw meaningful conclusions about the plasma that is (or is not) present. We have therefore performed a series of hydrodynamic simulations for a variety of different nanoflare properties and initial conditions. Our study has led to several key conclusions. 1. Deviations from equilibrium are greatest for short-duration nanoflares at low initial coronal densities. 2. Hot emission lines are the most affected and are suppressed sometimes to the point of being invisible. 3. The emission detected in all of the SDO-AIA channels is generally dominated by warm, over-dense, cooling plasma. 4. It is difficult not to create coronal loops that emit strongly at 1.5 MK and in the range 2 to 5 MK, which are the most commonly observed kind, for a broad range of nanoflare scenarios. 5. The Fe XV (284.16 ) emission in most of our models is about 10 times brighter than the Ca XVII (192.82 ) emission, consistent with observations. Our overarching conclusion is that small-scale, impulsive heating inducing a nonequilibrium ionization state leads to predictions for observable quantities that are entirely consistent with what is actually observed.

Bradshaw, Stephen J.↗
NASA NTRS1988

Constraints on the neutral hydrogen corona at Uranus from its interaction with magnetospheric plasma

Models of collisional reactions between the hot (several keV) protons and neutral atomic hydrogen corona observed at Uranus by Voyager 2 are compared with observations in order to deduce constraints on the coronal density. An upper limit is found for n sub H (5R sub U) of several tens of H/cu cm on the sunward side of Uranus and several H/cu cm on the dark side. The possibility that the hot plasma population might arise from photoionization and electron impact ionization of coronal and interstellar medium hydrogen in the magnetotail, followed by pickup and energization while convecting toward Uranus, is examined and rejected.

Herbert, Floyd↗