arXiv subjects

David R. Williams

Publications and source records attributed to David R. Williams.

At least 19 recordsLinked to original sources

arXiv2024

How does the critical torus instability height vary with the solar cycle?

The ideal magnetohydrodynamic torus instability can drive the eruption of coronal mass ejections. The critical threshold of magnetic field strength decay for the onset of the torus instability occurs at different heights in different solar active regions, and understanding this variation could therefore improve space weather prediction. In this work, we aim to find out how the critical torus instability height evolves throughout the solar activity cycle. We study a significant subset of HMI and MDI Space-Weather HMI Active Region Patches (SHARPs and SMARPs) from 1996-2023, totalling 21584 magnetograms from 4436 unique active region patches. For each magnetogram, we compute the critical height averaged across the main polarity inversion line, the total unsigned magnetic flux and the separation between the positive and negative magnetic polarities. We find the critical height in active regions varies with the solar cycle, with higher (lower) average critical heights observed around solar maximum (minimum). We conclude this is because the critical height is proportional to the separation between opposite magnetic polarities, which in turn is proportional to the total magnetic flux in a region, and more magnetic regions with larger fluxes and larger sizes are observed at solar maximum. This result is noteworthy because, despite the higher critical heights, more CMEs are observed around solar maximum than at solar minimum.

astro-ph.SR↗

arXiv2023

Slow Solar Wind Connection Science during Solar Orbiter's First Close Perihelion Passage

The Slow Solar Wind Connection Solar Orbiter Observing Plan (Slow Wind SOOP) was developed to utilise the extensive suite of remote sensing and in situ instruments on board the ESA/NASA Solar Orbiter mission to answer significant outstanding questions regarding the origin and formation of the slow solar wind. The Slow Wind SOOP was designed to link remote sensing and in situ measurements of slow wind originating at open-closed field boundaries. The SOOP ran just prior to Solar Orbiter's first close perihelion passage during two remote sensing windows (RSW1 and RSW2) between 2022 March 3-6 and 2022 March 17-22, while Solar Orbiter was at a heliocentric distance of 0.55-0.51 and 0.38-0.34 au from the Sun, respectively. Coordinated observation campaigns were also conducted by Hinode and IRIS. The magnetic connectivity tool was used, along with low latency in situ data, and full-disk remote sensing observations, to guide the target pointing of Solar Orbiter. Solar Orbiter targeted an active region complex during RSW1, the boundary of a coronal hole, and the periphery of a decayed active region during RSW2. Post-observation analysis using the magnetic connectivity tool along with in situ measurements from MAG and SWA/PAS, show that slow solar wind, with velocities between 210 and 600 km/s, arrived at the spacecraft originating from two out of the three of the target regions. The Slow Wind SOOP, despite presenting many challenges, was very successful, providing a blueprint for planning future observation campaigns that rely on the magnetic connectivity of Solar Orbiter.

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arXiv2022

Plasma composition measurements in an active region from Solar Orbiter/SPICE and Hinode/EIS

A key goal of the Solar Orbiter mission is to connect elemental abundance measurements of the solar wind enveloping the spacecraft with EUV spectroscopic observations of their solar sources, but this is not an easy exercise. Observations from previous missions have revealed a highly complex picture of spatial and temporal variations of elemental abundances in the solar corona. We have used coordinated observations from Hinode and Solar Orbiter to attempt new abundance measurements with the SPICE (Spectral Imaging of the Coronal Environment) instrument, and benchmark them against standard analyses from EIS (EUV Imaging Spectrometer). We use observations of several solar features in AR 12781 taken from an Earth-facing view by EIS on 2020 November 10, and SPICE data obtained one week later on 2020 November 17; when the AR had rotated into the Solar Orbiter field-of-view. We identify a range of spectral lines that are useful for determining the transition region and low coronal temperature structure with SPICE, and demonstrate that SPICE measurements are able to differentiate between photospheric and coronal Mg/Ne abundances. The combination of SPICE and EIS is able to establish the atmospheric composition structure of a fan loop/outflow area at the active region edge. We also discuss the problem of resolving the degree of elemental fractionation with SPICE, which is more challenging without further constraints on the temperature structure, and comment on what that can tell us about the sources of the solar wind and solar energetic particles.

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arXiv2022

Evolution of the critical torus instability height and CME likelihood in solar active regions

Aims. Working towards improved space weather predictions, we aim to quantify how the critical height at which the torus instability drives coronal mass ejections (CMEs) varies over time in a sample of solar active regions. Methods. We model the coronal magnetic fields of 42 active regions and quantify the critical height at their central polarity inversion lines throughout their observed lifetimes. We then compare these heights to the changing magnetic flux at the photospheric boundary and identify CMEs in these regions. Results. In our sample, the rates of CMEs per unit time are twice as high during phases when magnetic flux is increasing than when it is decreasing, and during those phases of increasing flux, the rate of CMEs is 63% higher when the critical height is rising than when it is falling. Furthermore, we support and extend the results of previous studies by demonstrating that the critical height in active regions is generally proportional to the separation of their magnetic polarities through time. When the separation of magnetic polarities in an active region increases, for example during the continuous emergence and expansion of a magnetic bipole, the critical height also tends to increase. Conversely, when the polarity separation decreases, for example due to the emergence of a new, compact bipole at the central inversion line of an existing active region or into a quiet Sun environment, the critical height tends to decrease.

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arXiv2022

Experimental quantification of unsteady leading-edge flow separation

We propose here a method to experimentally quantify unsteady leading-edge flow separation on aerofoils with finite thickness. The methodology relies on the computation of a leading-edge suction parameter based on measured values of the partial circulation around the leading-edge and the stagnation point location. We validate the computation of the leading-edge suction parameter for both numerical and experimental data under steady and unsteady flow conditions. The leading-order approximation of the definition of the leading-edge suction parameter is proven to be sufficiently accurate for the application to thin aerofoils such as the NACA0009 without a-priori knowledge of the stagnation point location. The higher-order terms including the stagnation point location are required to reliably compute the leading-edge suction parameter on thicker aerofoils such as the NACA0015. The computation of the leading-edge suction parameter from inviscid flow theory does not assume the Kutta condition to be valid at the trailing edge which allows us to compute its value for separated flows. The relation between the leading-edge suction parameter and the evolution of the shear layer height is studied in two different unsteady flow conditions, a fixed aerofoil in a fluctuating free-stream velocity and a pitching aerofoil in a steady free-stream. We demonstrate here that the instantaneous value of the leading-edge suction parameter based on the partial circulation around the leading edge is unambiguously defined for a given flow field and can serve as a directly quantitative measure of the degree of unsteady flow separation at the leading edge.

physics.flu-dyn↗

arXiv2020

Lift Coefficient Estimation for a Rapidly Pitching Airfoil

We develop a method for estimating the instantaneous lift coefficient on a rapidly pitching airfoil that uses a small number of pressure sensors and a measurement of the angle of attack. The approach assimilates four surface pressure measurements with a modified nonlinear state space model (Goman-Khrabrov model) through a Kalman filter. The error of lift coefficient estimates based only on a weighted-sum of the measured pressures are found to be noisy and biased, which leads to inaccurate estimates. The estimate is improved by including the predictive model in an conventional Kalman filter. The Goman-Khrabrov model is shown to be a linear parameter-varying system and can therefore be used in the Kalman filter without the need for linearization. Additional improvement is realized by modifying the algorithm to provide more accurate estimate of the lift coefficient. The improved Kalman filtering approach results in a bias-free lift coefficient estimate that is more precise than either the pressure-based estimate or the Goman-Khrabrov model on their own. The new method will enable performance enhancements in aerodynamic systems whose performance relies on lift.

physics.flu-dyn↗

arXiv2019

A Hybrid Model for Lift Response to Dynamic Actuation On A Stalled Airfoil

The current research focuses on modeling the lift response due to dynamic (time-varying) 'burst-type' actuation on a stalled airfoil. Dynamic `burst-type' actuation exhibits two different characteristic dynamic behaviors within the system, namely the high-frequency and low-frequency components. These characteristics introduce modeling challenges. In this paper, we propose a hybrid model composed of two individual sub-models, one for each of the two frequencies. The lift response due to high-frequency single burst actuation is captured using a convolution model. The low-frequency component due to nonlinear burst-burst interactions are captured using a Wiener model, consisting of linear time-invariant dynamics and a static output nonlinearity. The hybrid model is validated using data from wind tunnel experiments.

physics.flu-dyn↗

arXiv2019

Response of the Separated Flow over an Airfoil to Actuator Bursts

The separated flow response to single and multiple burst mode actuation over a 2-D airfoil at $12^o$ angle of attack was studied experimentally. For the single-burst actuation case, surface pressure signals were correlated with the flowfield observations of the roll-up and convection of a large-scale vortex structure that follows the actuator burst input. A spatially localized region of high pressure occurs below and slightly upstream of a "kink" that forms in the shear layer, which is responsible for the lift reversal that occurs within $2.0t^+$ after the burst signal was triggered. Proper orthogonal decomposition of the single-burst flow field shows that the time-varying coefficients of the first two modes correlate with the negative of the lift coefficient and pitching moment coefficient. The dynamic mode decomposition (DMD) of the single-burst flow field data identified the modes related to the kinetic energy growth of the disturbance. The mode with the largest growth rate had a Strouhal number close to that associated with the separation bubble dynamics. However, when multiple bursts are used to control the separation, the interactions between the bursts were observed which depend on the time intervals between the bursts. The convolution integral and DMD were performed on the multi-burst flow field datasets. The results indicate that the nonlinear burst-burst interaction only affects the reverse flow strength within the separation bubble, which is related to the main trend of the lift. On the other hand, the linear burst-burst interaction contributes to the high-frequency lift variation associated with the bursts.

physics.flu-dyn↗

arXiv2019

Understanding the plasma and magnetic field evolution of a filament using observations and Nonlinear force-free field modelling

We present observations and magnetic field models of an intermediate filament present on the Sun in August 2012, associated with a polarity inversion line that extends from AR 11541 in the east into the quiet sun at its western end. A combination of SDO/AIA, SDO/HMI, and GONG H alpha data allow us to analyse the structure and evolution of the filament from 2012 August 4 23:00 UT to 2012 August 6 08:00 UT when the filament was in equilibrium. By applying the flux rope insertion method, nonlinear force-free field models of the filament are constructed using SDO/HMI line-of-sight magnetograms as the boundary condition at the two times given above. Guided by observed filament barbs, both modelled flux ropes are split into three sections each with a different value of axial flux to represent the non-uniform photospheric field distribution. The flux in the eastern section of the rope increases by 4$\times$10$^{20}$ Mx between the two models, which is in good agreement with the amount of flux cancelled along the internal PIL of AR 11541, calculated to be 3.2$\times$10$^{20}$ Mx. This suggests that flux cancellation builds flux into the filament's magnetic structure. Additionally, the number of field line dips increases between the two models in the locations where flux cancellation, the formation of new filament threads and growth of the filament is observed. This suggests that flux cancellation associated with magnetic reconnection forms concave-up magnetic field that lifts plasma into the filament. During this time, the free magnetic energy in the models increases by 0.2$\times$10$^{31}$ ergs.

astro-ph.SR↗

arXiv2018

Coronal Elemental Abundances in Solar Emerging Flux Regions

The chemical composition of solar and stellar atmospheres differs from that of their photospheres. Abundances of elements with low first ionization potential (FIP) are enhanced in the corona relative to high FIP elements with respect to the photosphere. This is known as the FIP effect and it is important for understanding the flow of mass and energy through solar and stellar atmospheres. We used spectroscopic observations from the Extreme-ultraviolet Imaging Spectrometer (EIS) onboard the Hinode observatory to investigate the spatial distribution and temporal evolution of coronal plasma composition within solar emerging flux regions inside a coronal hole. Plasma evolved to values exceeding those of the quiet Sun corona during the emergence/early decay phase at a similar rate for two orders of magnitude in magnetic flux, a rate comparable to that observed in large active regions containing an order of magnitude more flux. During the late decay phase, the rate of change was significantly faster than what is observed in large, decaying active regions. Our results suggest that the rate of increase during the emergence/early decay phase is linked to the fractionation mechanism leading to the FIP effect, whereas the rate of decrease during the later decay phase depends on the rate of reconnection with the surrounding magnetic field and its plasma composition.

astro-ph.SR↗

arXiv2017

Non-Equilibrium Processes in the Solar Corona, Transition Region, Flares, and Solar Wind \textit{(Invited Review)}

We review the presence and signatures of the non-equilibrium processes, both non-Maxwellian distributions and non-equilibrium ionization, in the solar transition region, corona, solar wind, and flares. Basic properties of the non-Maxwellian distributions are described together with their influence on the heat flux as well as on the rates of individual collisional processes and the resulting optically thin synthetic spectra. Constraints on the presence of high-energy electrons from observations are reviewed, including positive detection of non-Maxwellian distributions in the solar corona, transition region, flares, and wind. Occurrence of non-equilibrium ionization is reviewed as well, especially in connection to hydrodynamic and generalized collisional-radiative modelling. Predicted spectroscopic signatures of non-equilibrium ionization depending on the assumed plasma conditions are summarized. Finally, we discuss the future remote-sensing instrumentation that can be used for detection of these non-equilibrium phenomena in various spectral ranges.

astro-ph.SR↗

arXiv2015

Constraining Hot Plasma in a Non-flaring Solar Active Region with FOXSI Hard X-ray Observations

We present new constraints on the high-temperature emission measure of a non-flaring solar active region using observations from the recently flown Focusing Optics X-ray Solar Imager sounding rocket payload. FOXSI has performed the first focused hard X-ray (HXR) observation of the Sun in its first successful flight on 2012 November 2. Focusing optics, combined with small strip detectors, enable high-sensitivity observations with respect to previous indirect imagers. This capability, along with the sensitivity of the HXR regime to high-temperature emission, offers the potential to better characterize high-temperature plasma in the corona as predicted by nanoflare heating models. We present a joint analysis of the differential emission measure (DEM) of active region 11602 using coordinated observations by FOXSI, Hinode/XRT and Hinode/EIS. The Hinode-derived DEM predicts significant emission measure between 1 MK and 3 MK, with a peak in the DEM predicted at 2.0-2.5 MK. The combined XRT and EIS DEM also shows emission from a smaller population of plasma above 8 MK. This is contradicted by FOXSI observations that significantly constrain emission above 8 MK. This suggests that the Hinode DEM analysis has larger uncertainties at higher temperatures and that >8 MK plasma above an emission measure of 3x10^44 cm^-3 is excluded in this active region.

astro-ph.SR↗

arXiv2015

Imaging and Spectroscopic Observations of a Transient Coronal Loop: Evidence for the Non-Maxwellian $κ$-Distributions

We report on the SDO/AIA and Hinode/EIS observations of a transient coronal loop. The loop brightens up in the same location after the disappearance of an arcade formed during a B8.9-class microflare three hours earlier. EIS captures this loop during its brightening phase as observed in most of the AIA filters. We use the AIA data to study the evolution of the loop, as well as to perform the DEM diagnostics as a function of $κ$. Fe XI--XIII lines observed by EIS are used to perform the diagnostics of electron density and subsequently the diagnostics of $κ$. Using ratios involving the Fe XI 257.772Åselfblend, we diagnose $κ$ $\lesssim$ 2, i.e., an extremely non-Maxwellian distribution. Using the predicted Fe line intensities derived from the DEMs as a function of $κ$, we show that, with decreasing $κ$, all combinations of ratios of line intensities converge to the observed values, confirming the diagnosed $κ$ $\lesssim$ 2. These results represent the first positive diagnostics of $κ$-distributions in the solar corona despite the limitations imposed by calibration uncertainties.

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arXiv2014

The energetics of a global shock wave in the low solar corona

As the most energetic eruptions in the solar system, coronal mass ejections (CMEs) can produce shock waves at both their front and flanks as they erupt from the Sun into the heliosphere. However, the amount of energy produced in these eruptions, and the proportion of their energy required to produce the waves, is not well characterised. Here we use observations of a solar eruption from 2014 February 25 to estimate the energy budget of an erupting CME and the globally-propagating "EIT wave" produced by the rapid expansion of the CME flanks in the low solar corona. The "EIT wave" is shown using a combination of radio spectra and extreme ultraviolet images to be a shock front with a Mach number greater than one. Its initial energy is then calculated using the Sedov-Taylor blast-wave approximation, which provides an approximation for a shock front propagating through a region of variable density. This approach provides an initial energy estimate of $\approx$2.8$\times$10$^{31}$ ergs to produce the "EIT wave", which is approximately 10% the kinetic energy of the associated CME (shown to be $\approx$2.5$\times$10$^{32}$ ergs). These results indicate that the energy of the "EIT wave" may be significant and must be considered when estimating the total energy budget of solar eruptions.

astro-ph.SR↗

arXiv2014

Investigating the Dynamics and Density Evolution of Returning Plasma Blobs from the 2011 June 7 Eruption

This work examines infalling matter following an enormous Coronal Mass Ejection (CME) on 2011 June 7. The material formed discrete concentrations, or blobs, in the corona and fell back to the surface, appearing as dark clouds against the bright corona. In this work we examined the density and dynamic evolution of these blobs in order to formally assess the intriguing morphology displayed throughout their descent. The blobs were studied in five wavelengths (94, 131, 171, 193 and 211 Å) using the Solar Dynamics Observatory Atmospheric Imaging Assembly (SDO/AIA), comparing background emission to attenuated emission as a function of wavelength to calculate column densities across the descent of four separate blobs. We found the material to have a column density of hydrogen of approximately 2 $\times$ 10$^{19}$ cm$^{-2}$, which is comparable with typical pre-eruption filament column densities. Repeated splitting of the returning material is seen in a manner consistent with the Rayleigh-Taylor instability. Furthermore, the observed distribution of density and its evolution are also a signature of this instability. By approximating the three-dimensional geometry (with data from STEREO-A), volumetric densities were found to be approximately 2 $\times$ 10$^{-14}$ g cm$^{-3}$, and this, along with observed dominant length-scales of the instability, was used to infer a magnetic field of the order 1 G associated with the descending blobs.

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arXiv2013

Measuring the Magnetic Field Strength of the Quiet Solar Corona Using "EIT Waves"

Variations in the propagation of globally-propagating disturbances (commonly called "EIT waves") through the low solar corona offer a unique opportunity to probe the plasma parameters of the solar atmosphere. Here, high-cadence observations of two "EIT wave" events taken using the Atmospheric Imaging Assembly (AIA) instrument onboard the Solar Dynamics Observatory (SDO) are combined with spectroscopic measurements from the Extreme ultraviolet Imaging Spectrometer (EIS) onboard the Hinode spacecraft and used to examine the variability of the quiet coronal magnetic-field strength. The combination of pulse kinematics from SDO/AIA and plasma density from Hinode/EIS is used to show that the magnetic-field strength is in the range ~2-6 G in the quiet corona. The magnetic-field estimates are then used to determine the height of the pulse, allowing a direct comparison with theoretical values obtained from magnetic-field measurements from the Helioseismic and Magnetic Imager (HMI) onboard SDO using PFSS and local-domain extrapolations. While local-scale extrapolations predict heights inconsistent with prior measurements, the agreement between observations and the PFSS model indicates that "EIT waves" are a global phenomenon influenced by global-scale magnetic field.

astro-ph.SR↗

arXiv2009

Hinode/Extreme-Ultraviolet Imaging Spectrometer Observations of the Temperature Structure of the Quiet Corona

We present a Differential Emission Measure (DEM) analysis of the quiet solar corona on disk using data obtained by the Extreme-ultraviolet Imaging Spectrometer (EIS) on {\it Hinode}. We show that the expected quiet Sun DEM distribution can be recovered from judiciously selected lines, and that their average intensities can be reproduced to within 30%. We present a subset of these selected lines spanning the temperature range $\log$ T = 5.6 to 6.4 K that can be used to derive the DEM distribution reliably. The subset can be used without the need for extensive measurements and the observed intensities can be reproduced to within the estimated uncertainty in the pre-launch calibration of EIS. Furthermore, using this subset, we also demonstrate that the quiet coronal DEM distribution can be recovered on size scales down to the spatial resolution of the instrument (1$"$ pixels). The subset will therefore be useful for studies of small-scale spatial inhomogeneities in the coronal temperature structure, for example, in addition to studies requiring multiple DEM derivations in space or time. We apply the subset to 45 quiet Sun datasets taken in the period 2007 January to April, and show that although the absolute magnitude of the coronal DEM may scale with the amount of released energy, the shape of the distribution is very similar up to at least $\log$ T $\sim$ 6.2 K in all cases. This result is consistent with the view that the {\it shape} of the quiet Sun DEM is mainly a function of the radiating and conducting properties of the plasma and is fairly insensitive to the location and rate of energy deposition. This {\it universal} DEM may be sensitive to other factors such as loop geometry, flows, and the heating mechanism, but if so they cannot vary significantly from quiet Sun region to region.

astro-ph.SR↗

arXiv2008

Observations of Active Region Loops with the EUV Imaging Spectrometer on Hinode

Previous solar observations have shown that coronal loops near 1 MK are difficult to reconcile with simple heating models. These loops have lifetimes that are long relative to a radiative cooling time, suggesting quasi-steady heating. The electron densities in these loops, however, are too high to be consistent with thermodynamic equilibrium. Models proposed to explain these properties generally rely on the existence of smaller scale filaments within the loop that are in various stages of heating and cooling. Such a framework implies that there should be a distribution of temperatures within a coronal loop. In this paper we analyze new observations from the EUV Imaging Spectrometer (EIS) on \textit{Hinode}. EIS is capable of observing active regions over a wide range of temperatures (\ion{Fe}{8}--\ion{Fe}{17}) at relatively high spatial resolution (1\arcsec). We find that most isolated coronal loops that are bright in \ion{Fe}{12} generally have very narrow temperature distributions ($σ_T \lesssim 3\times10^5$ K), but are not isothermal. We also derive volumetric filling factors in these loops of approximately 10%. Both results lend support to the filament models.

astro-ph↗