arXiv subjects

Stephen J. Bradshaw

Publications and source records attributed to Stephen J. Bradshaw.

At least 19 recordsLinked to original sources

arXiv2025

Direct calculation of steady-state hydrodynamic solar wind solutions with newtonian viscosity

Steady-state solutions to the Navier-Stokes equations are known to admit solutions that are singular at the sonic point. Consequently, inviscid solar wind models require special treatment of the solution near the sonic points, and this has proven to be a significant impediment to efficient modeling of the solar wind. In this paper we revisit the governing hydrodynamic equations for the expanding solar wind, with the inclusion of the classical (Newtonian) viscous stress , and we show how this inclusion eliminates the singularities that emerge from the inviscid equations. This result has been previously reported and used to generate solar wind profiles from initial conditions in the asymptotic limit; however, those studies did not include realistic treatments of the inner corona, and generally rejected the prospect of extrapolating solutions outward from the Sun into the heliosphere. Here, we expand this method to include external heating and optically thin radiative losses and show that solutions can be computed from initial conditions near the solar surface, thereby capturing the entire range of scales from below the transition region to the outer heliosphere in a single solution. Our approach is to cast the steady-state Navier-Stokes equations as a system of five coupled, ordinary differential equations (ODEs), which we solve using conventional methods, without any special treatment of the governing equations in the vicinity of the sonic point. The representative solutions that we present here demonstrate the utility and efficiency of this extrapolation method, which is considerably more realistic than commonly used analytical or empirical models. This method provides a direct approach to generating accurate solar wind profiles subject to observationally motivated initial conditions near the solar surface, at a fraction of the computational cost of comparable relaxation-based models.

astro-ph.SR↗

arXiv2024

Simulation of Thermal Nonequilibrium Cycles in the Solar Wind

Thermal nonequilibrium (TNE) is a condition of the plasma in the solar corona in which the local rate of energy loss due to radiation increases to the point that it cannot be sustained by the various heating terms acting on the plasma, precluding the existence of a steady state. The limit cycles of precipitation and evaporation that result from TNE have been simulated in 1D models of coronal loops, as well as 2D and 3D models of the solar chromosphere and lower corona. However, a careful study of TNE in the solar wind has not been performed until now. Here we demonstrate that for suitable combinations of local and global heating rates it is possible for the plasma to exhibit a TNE condition, even in the context of a transonic solar wind with appreciable mass and energy fluxes. This implies limits on the amount of foot-point heating that can be withstood under steady-state conditions in the solar wind, and may help to explain the variability of solar wind streams that emanate from regions of highly concentrated magnetic flux on the solar surface. The implications of this finding pertain to various sources of high-density solar wind, including plumes that form above regions of mixed magnetic polarity in polar coronal holes and the slow solar wind (SSW) that emanates from coronal hole boundaries.

astro-ph.SR↗

arXiv2024

Exploring Standing and Reflected Slow-mode Waves in Flaring Coronal Loops: A Parametric Study Using 2.5D MHD Modeling

Recent observations of reflected propagating and standing slow-mode waves in hot flaring coronal loops have spurred our investigation into their underlying excitation and damping mechanisms. To understand these processes, we conduct 2.5D magnetohydrodynamic (MHD) simulations using an arcade active region model that includes a hot and dense loop. Our simulations allow for in-depth parametric investigations complementing and expanding our previous 3D MHD modeling results. We excite these waves in two distinct models as motivated by observations from the SDO/AIA. Model 1 incorporates classical compressive viscosity coefficient, while Model 2 adopts a 10-times enhanced viscosity coefficient. We find that: (1) Our 2.5D MHD simulations reinforce previous conclusions derived from 1D and 3D MHD models that significantly enhanced viscosity is crucial for the rapid excitation of standing slow waves with damping times consistent with observations by Wang et al. (2015). (2) We uncover that nonlinearity in Model 1 delays the conversion of a reflected propagating wave into a standing wave. In contrast, Model 2 exhibits a much weak influence of nonlinearity. (3) Our results reveal that the transverse temperature structure holds more influence on wave behavior than the density structure. In Model 1, increased loop temperature contrast significantly enhances wave trapping within the structure, mitigating the impact of temperature-dependent viscous damping. Conversely, in Model 2, the impact of temperature structure on wave behavior weakens in comparison to the effect of viscosity. (4) Model 1 displays evident nonlinear coupling to the fast and kink magnetoacoustic waves and pronounced wave leakage into the corona. However, analyzing three observed wave events by SDO/AIA aligns with Model 2 predictions, providing further support for the substantial viscosity increase.

astro-ph.SR↗

arXiv2022

Temperature and Differential Emission Measure Profiles in Turbulent Solar Active Region Loops

We examine the temperature structure of static coronal active region loops in regimes where thermal conductive transport is driven by Coulomb collisions, by turbulent scattering, or by a combination of the two. (In the last case collisional scattering dominates the heat transport at lower levels in the loop where temperatures are low and densities are high, while turbulent scattering dominates the heat transport at higher temperatures/lower densities.) Temperature profiles and their corresponding differential emission measure distributions are calculated and compared to observations, and earlier scaling laws relating the loop apex temperature and volumetric heating rate to the loop length and pressure are revisited. Results reveal very substantial changes, compared to the wholly collision-dominated case, to both the loop scaling laws and the temperature/density profiles along the loop. They also show that the well-known excess of differential emission measure at relatively low temperatures in the loop may be a consequence of for by the flatter temperature gradients (and so increased amount of material within a specified temperature range) that results from the predominance of turbulent scattering in the upper regions of the loop.

astro-ph.SR↗

arXiv2022

The Dynamic Evolution of Solar Wind Streams Following Interchange Reconnection

Interchange reconnection is thought to play an important role in determining the dynamics and material composition of the slow solar wind that originates from near coronal hole boundaries. To explore the implications of this process we simulate the dynamic evolution of a solar wind stream along a newly-opened magnetic flux tube. The initial condition is composed of a piecewise continuous dynamic equilibrium in which the regions above and below the reconnection site are extracted from steady-state solutions along open and closed field lines. The initial discontinuity at the reconnection site is highly unstable and evolves as a Riemann problem, decomposing into an outward-propagating shock and inward-propagating rarefaction that eventually develop into a classic N-wave configuration. This configuration ultimately propagates into the heliosphere as a coherent structure and the entire system eventually settles to a quasi-steady wind solution. In addition to simulating the fluid evolution we also calculate the time-dependent non-equilibrium ionization of oxygen in real time in order to construct in situ diagnostics of the conditions near the reconnection site. This idealized description of the plasma dynamics along a newly-opened magnetic field line provides a baseline for predicting and interpreting the implications of interchange reconnection for the slow solar wind. Notably, the density and velocity within the expanding N-wave are generally enhanced over the ambient wind, as is the O7+/O6+ ionization ratio, which exhibits a discontinuity across the reconnection site that is transported by the flow and arrives later than the propagating N-wave.

astro-ph.SR↗

arXiv2020

Expansion of Ultracold Neutral Plasmas with Exponentially Decaying Density Distributions

We present a study of the expansion of an ultracold neutral plasma (UCNP) with an initial density distribution that decays exponentially in space, created by photoionizing atoms shortly after their release from a quadrupole (or biconic cusp) magnetic trap. A characteristic ion acoustic timescale is evident in the evolution of the plasma size and velocity, indicating the dynamics are reasonably well described by a model of hydrodynamic expansion of a quasi-neutral plasma. However, for low plasma density and high initial electron temperature, excess ion kinetic energy in the vicinity of the central density peak suggests significant local non-neutrality at early times. Observations are compared to the well-understood self-similar expansion of an UCNP with an initial Gaussian density distribution, and a similar scaling law describes the evolution of plasma size for both cases.

physics.plasm-ph↗

arXiv2020

Scaling Laws for Dynamic Solar Loops

The scaling laws which relate the peak temperature $T_M$ and volumetric heating rate $E_H$ to the pressure $P$ and length $L$ for static coronal loops were established over 40 years ago; they have proved to be of immense value in a wide range of studies. Here we extend these scaling laws to {\it dynamic} loops, where enthalpy flux becomes important to the energy balance, and study impulsive heating/filling characterized by upward enthalpy flows. We show that for collision-dominated thermal conduction, the functional dependencies of the scaling laws are the same as for the static case, when the radiative losses scale as $T^{-1/2}$, but with a different constant of proportionality that depends on the Mach number $M$ of the flow. The dependence on the Mach number is such that the scaling laws for low to moderate Mach number flows are almost indistinguishable from the static case. When thermal conduction is limited by turbulent processes, however, the much weaker dependence of the scattering mean free path (and hence thermal conduction coefficient) on temperature leads to a limiting Mach number for return enthalpy fluxes driven by thermal conduction between the corona and chromosphere.

astro-ph.SR↗

arXiv2020

Critical Science Plan for the Daniel K. Inouye Solar Telescope (DKIST)

The Daniel K. Inouye Solar Telescope (DKIST) will revolutionize our ability to measure, understand and model the basic physical processes that control the structure and dynamics of the Sun and its atmosphere. The first-light DKIST images, released publicly on 29 January 2020, only hint at the extraordinary capabilities which will accompany full commissioning of the five facility instruments. With this Critical Science Plan (CSP) we attempt to anticipate some of what those capabilities will enable, providing a snapshot of some of the scientific pursuits that the Daniel K. Inouye Solar Telescope hopes to engage as start-of-operations nears. The work builds on the combined contributions of the DKIST Science Working Group (SWG) and CSP Community members, who generously shared their experiences, plans, knowledge and dreams. Discussion is primarily focused on those issues to which DKIST will uniquely contribute.

astro-ph.SR↗

arXiv2020

Electron Beams Cannot Directly Produce Coronal Rain

Coronal rain is ubiquitous in flare loops, forming shortly after the onset of the solar flare. Rain is thought to be caused by a thermal instability, a localized runaway cooling of material in the corona. The models that demonstrate this require extremely long duration heating on the order of the radiative cooling time, localized near the footpoints of the loops. In flares, electron beams are thought to be the primary energy transport mechanism, driving strong footpoint heating during the impulsive phase that causes evaporation, filling and heating flare loops. Electron beams, however, do not act for a long period of time, and even supposing that they did, their heating would not remain localized at the footpoints. With a series of numerical experiments, we show directly that these two issues mean that electron beams are incapable of causing the formation of rain in flare loops. This result suggests that either there is another mechanism acting in flare loops responsible for rain, or that the modeling of the cooling of flare loops is somehow deficient. To adequately describe flares, the standard model must address this issue to account for the presence of coronal rain.

astro-ph.SR↗

arXiv2019

Solar Active Region Heating Diagnostics from High Temperature Emission using the Marshall Grazing Incidence X-ray Spectrometer (MaGIXS)

The relative amount of high temperature plasma has been found to be a useful diagnostic to determine the frequency of coronal heating on sub-resolution structures. When the loops are infrequently heated, a broad emission measure (EM) over a wider range of temperatures is expected. A narrower EM is expected for high frequency heating where the loops are closer to equilibrium. The soft X-ray spectrum contains many spectral lines that provide high temperature diagnostics, including lines from Fe XVII-XIX. This region of the solar spectrum will be observed by the Marshall Grazing Incidence Spectrometer (MaGIXS) in 2020. In this paper, we derive the expected spectral lines intensity in MaGIXS to varying amounts of high temperature plasma to demonstrate that a simple line ratio of these provides a powerful diagnostic to determine the heating frequency. Similarly, we examine ratios of AIA channel intensities, filter ratios from a XRT, and energy bands from the FOXSI sounding rocket to determine their sensitivity to this parameter. We find that both FOXSI and MaGIXS provide good diagnostic capability for high-temperature plasma. We then compare the predicted line ratios to the output of a numerical model and confirm the MaGIXS ratios provide an excellent diagnostic for heating frequency.

astro-ph.SR↗

arXiv2019

Coronal Loop Scaling Laws for Various Forms of Parallel Heat Conduction

The solar atmosphere is dominated by loops of magnetic flux which connect the multi-million-degree corona to the much cooler chromosphere. The temperature and density structure of quasi-static loops is determined by the continuous flow of energy from the hot corona to the lower solar atmosphere. Loop scaling laws provide relationships between global properties of the loop (such as peak temperature, pressure, and length); they follow from the physical variable dependencies of various terms in the energy equation, and hence the form of the loop scaling law provides insight into the key physics that controls the loop structure. Traditionally, scaling laws have been derived under the assumption of collision-dominated thermal conduction. Here we examine the impact of different regimes of thermal conduction -- collision-dominated, turbulence-dominated, and free-streaming -- on the form of the scaling laws relating the loop temperature and heating rate to its pressure and half-length. We show that the scaling laws for turbulence-dominated conduction are fundamentally different than those for collision-dominated and free-streaming conduction, inasmuch as the form of the scaling laws now depend primarily on conditions at the low-temperature, rather than high-temperature, part of the loop. We also establish regimes in temperature and density space in which each of the applicable scaling laws prevail.

astro-ph.SR↗

arXiv2019

Quantifying the Influence of Key Physical Processes on the Formation of Emission Lines Observed by IRIS: I. Non-Equilibrium Ionization and Density-Dependent Rates

In the work described here we investigate atomic processes leading to the formation of emission lines within the IRIS wavelength range at temperatures near $10^5$~K. We focus on (1) non-equilibrium and (2) density-dependent effects influencing the formation and radiative properties of S IV and O IV. These two effects have significant impacts on spectroscopic diagnostic measurements of quantities associated with the plasma that emission lines from S IV and O IV provide. We demonstrate this by examining nanoflare-based coronal heating to determine what the detectable signatures are in transition region emission. A detailed comparison between predictions from numerical experiments and several sets of observational data is presented to show how one can ascertain when non-equilibrium ionization and/or density-dependent atomic processes are important for diagnosing nanoflare properties, the magnitude of their contribution, and what information can be reliably extracted from the spectral data. Our key findings are the following. (1) The S/O intensity ratio is a powerful diagnostic of non-equilibrium ionization. (2) Non-equilibrium ionization has a strong effect on the observed line intensities even in the case of relatively weak nanoflare heating. (3) The density-dependence of atomic rate coefficients is only important when the ion population is out of equilibrium. (4) In the sample of active regions we examined, weak nanoflares coupled with non-equilibrium ionization and density-dependent atomic rates were required to explain the observed properties (e.g. the S/O intensity ratios). (5) Enhanced S/O intensity ratios cannot be due solely to the heating strength and must depend on other processes (e.g. heating frequency, non-Maxwellian distributions).

astro-ph.SR↗

arXiv2018

Efficient Calculation of Non-Local Thermodynamic Equilibrium Effects in Multithreaded Hydrodynamic Simulations of Solar Flares

Understanding the dynamics of the solar chromosphere is crucial to understanding energy transport across the solar atmosphere. The chromosphere is optically thick at many wavelengths and described by non-local thermodynamic equilibrium (NLTE), making it difficult to interpret observations. Furthermore, there is considerable evidence that the atmosphere is filamented, and that current instruments do not sufficiently resolve small scale features. In flares, it is likely that multithreaded models are required to describe the heating. The combination of NLTE effects and multithreaded modeling requires computationally demanding calculations, which has motivated the development of a model that can efficiently treat both. We describe the implementation of a solver in a hydrodynamic code for the hydrogen level populations that approximates the NLTE solutions. We derive an accurate electron density across the atmosphere, that includes the effects of non-equilibrium ionization for helium and metals. We show the effects on hydrodynamic simulations, which are used to synthesize light curves using a post-processing radiative transfer code. We demonstrate the utility of this model on IRIS observations of a small flare. We show that the Doppler shifts in Mg II, C II, and O I can be explained with a multithreaded model of loops subjected to electron beam heating, so long as NLTE effects are treated. The intensities, however, do not match observed values very well, which is due to assumptions about the initial atmosphere. We briefly show how altering the initial atmosphere can drastically alter line profiles, and therefore derived quantities, and suggest that it should be tuned to pre-flare observations.

astro-ph.SR↗

arXiv2018

Hard X-Ray Constraints on Small-Scale Coronal Heating Events

Much evidence suggests that the solar corona is heated impulsively, meaning that nanoflares may be ubiquitous in quiet and active regions (ARs). Hard X-ray (HXR) observations with unprecedented sensitivity $>$3~keV are now enabled by focusing instruments. We analyzed data from the \textit{Focusing Optics X-ray Solar Imager (FOXSI)} rocket and the \textit{Nuclear Spectroscopic Telescope Array (NuSTAR)} spacecraft to constrain properties of AR nanoflares simulated by the EBTEL field-line-averaged hydrodynamics code. We generated model X-ray spectra by computing differential emission measures for homogeneous nanoflare sequences with heating amplitudes $H_0$, durations $τ$, delay times between events $t_N$, and filling factors $f$. The single quiescent AR observed by \textit{FOXSI-2} on 2014 December 11 is well fit by nanoflare sequences with heating amplitudes 0.02 erg cm$^{-3}$ s$^{-1}$ $<$ $H_0$ $<$ 13 erg cm$^{-3}$ s$^{-1}$ and a wide range of delay times and durations. We exclude delays between events shorter than $\sim$900 s at the 90\% confidence level for this region. Three of five regions observed by {\nustar} on 2014 November 1 are well fit by homogeneous nanoflare models, while two regions with higher fluxes are not. Generally, the {\nustar} count spectra are well fit by nanoflare sequences with smaller heating amplitudes, shorter delays, and shorter durations than the allowed \textit{FOXSI-2} models. These apparent discrepancies are likely due to differences in spectral coverage between the two instruments and intrinsic differences among the regions. Steady heating ($t_N$ = $τ$) was ruled out with $>$99\% confidence for all regions observed by either instrument.

astro-ph.SR↗

arXiv2016

Chromospheric Nanoflares as a Source of Coronal Plasma: II. Repeating Nanoflares

The million degree plasma of the solar corona must be supplied by the underlying layers of the atmosphere. The mechanism and location of energy release, and the precise source of coronal plasma, remain unresolved. In earlier work we pursued the idea that warm plasma is supplied to the corona via direct heating of the chromosphere by nanoflares, contrary to the prevailing belief that the corona is heated in-situ and the chromosphere is subsequently energized and ablated by thermal conduction. We found that single (low-frequency) chromospheric nanoflares could not explain the observed intensities, Doppler-shifts, and red/blue asymmetries in Fe XII and XIV emission lines. In the present work we follow up on another suggestion that the corona could be powered by chromospheric nanoflares that repeat on a timescale substantially shorter than the cooling/draining timescale. That is, a single magnetic strand is re-supplied with coronal plasma before the existing plasma has time to cool and drain. We perform a series of hydrodynamic experiments and predict the Fe XII and XIV line intensities, Doppler-shifts, and red/blue asymmetries. We find that our predicted quantities disagree dramatically with observations and fully developed loop structures cannot be created by intermediate- or high-frequency chromospheric nanoflares. We conclude that the mechanism ultimately responsible for producing coronal plasma operates above the chromosphere, but this does not preclude the possibility of a similar mechanism powering the chromosphere; extreme examples of which may be responsible for heating chromospheric plasma to transition region temperatures (e.g. type II spicules).

astro-ph.SR↗

arXiv2016

Patterns of Activity in a Global Model of a Solar Active Region

In this work we investigate the global activity patterns predicted from a model active region heated by distributions of nanoflares that have a range of frequencies. What differs is the average frequency of the distributions. The activity patterns are manifested in time lag maps of narrow-band instrument channel pairs. We combine hydrodynamic and forward modeling codes with a magnetic field extrapolation to create a model active region and apply the time lag method to synthetic observations. Our aim is not to reproduce a particular set of observations in detail, but to recover some typical properties and patterns observed in active regions. Our key findings are the following. 1. cooling dominates the time lag signature and the time lags between the channel pairs are generally consistent with observed values. 2. shorter coronal loops in the core cool more quickly than longer loops at the periphery. 3. all channel pairs show zero time lag when the line-of-sight passes through coronal loop foot-points. 4. there is strong evidence that plasma must be re-energized on a time scale comparable to the cooling timescale to reproduce the observed coronal activity, but it is likely that a relatively broad spectrum of heating frequencies are operating across active regions. 5. due to their highly dynamic nature, we find nanoflare trains produce zero time lags along entire flux tubes in our model active region that are seen between the same channel pairs in observed active regions.

astro-ph.SR↗

arXiv2015

X-ray Source Heights in a Solar Flare: Thick-target versus Thermal Conduction Front Heating

Observations of solar flares with RHESSI have shown X-ray sources traveling along flaring loops, from the corona down to the chromosphere and back up. The 28 November 2002 C1.1 flare, first observed with RHESSI by Sui et al. 2006 and quantitatively analyzed by O'Flannagain et al. 2013, very clearly shows this behavior. By employing numerical experiments, we use these observations of X-ray source height motions as a constraint to distinguish between heating due to a non-thermal electron beam and in situ energy deposition in the corona. We find that both heating scenarios can reproduce the observed light curves, but our results favor non-thermal heating. In situ heating is inconsistent with the observed X-ray source morphology and always gives a height dispersion with photon energy opposite to what is observed.

astro-ph.SR↗

arXiv2014

On Sunspot and Starspot Lifetimes

We consider the lifetimes of spots on the Sun and other stars from the standpoint of magnetic diffusion. While normal magnetic diffusivity predicts lifetimes of sunspots that are too large by at least two orders of magnitude, turbulent magnetic diffusivity accounts for both the functional form of the solar empirical spot-lifetime relation and for the observed sunspot lifetimes, provided that the relevant diffusion length is the supergranule size. Applying this relation to other stars, the value of turbulent diffusivity depends almost entirely on supergranule size, with very weak dependence on other variables such as magnetic field strength and density. Overall, the best observational data for other stars is consistent with the extension of the solar relation provided that stellar supergranule sizes for some stars are significantly larger than they are on the Sun.

astro-ph.SR↗