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The Cooling of Coronal Plasmas. iv: Catastrophic Cooling of Loops  

Stephen Bradshaw   Submitted: 2013-05-24 10:30

We examine the radiative cooling of coronal loops and demonstrate that the recently identified catastrophic cooling (Reale and Landi, 2012) is due to the inability of a loop to sustain radiative / enthalpy cooling below a critical temperature, which can be > 1 MK in flares, 0.5 - 1 MK in active regions and 0.1 MK in long tenuous loops. Catastrophic cooling is characterised by a rapid fall in coronal temperature while the coronal density changes by a small amount. Analytic expressions for the critical temperature are derived and show good agreement with numerical results. This effect limits very considerably the lifetime of coronal plasmas below the critical temperature.

Authors: Cargill, P. J. and Bradshaw, S. J.
Projects: None

Publication Status: ApJ (in press)
Last Modified: 2013-05-28 00:48
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The influence of numerical resolution on coronal density in hydrodynamic models of impulsive heating  

Stephen Bradshaw   Submitted: 2013-05-09 15:13

The effect of the numerical spatial resolution in models of the solar corona and corona / chromosphere interface is examined for impulsive heating over a range of magnitudes using one dimensional hydrodynamic simulations. It is demonstrated that the principle effect of inadequate resolution is on the coronal density. An underresolved loop typically has a peak density of at least a factor of two lower than a resolved loop subject to the same heating, with larger discrepencies in the decay phase. The temperature for under-resolved loops is also lower indicating that lack of resolution does not ''bottle up'' the heat flux in the corona. Energy is conserved in the models to under 1% in all cases, indicating that this is not responsible for the low density. Instead, we argue that in under-resolved loops the heat flux ''jumps across'' the transition region to the dense chromosphere from which it is radiated rather than heating and ablating transition region plasma. This emphasises the point that the interaction between corona and chromosphere occurs only through the medium of the transition region. Implications for three dimensional magnetohydrodynamic coronal models are discussed.

Authors: Bradshaw, S. J., and Cargill, P. J.
Projects: None

Publication Status: ApJ (in press)
Last Modified: 2013-05-10 12:01
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Collisional and Radiative Processes in Optically Thin Plasmas  

Stephen Bradshaw   Submitted: 2013-03-18 20:07

Most of our knowledge of the physical processes in distant plasmas is obtained through measurement of the radiation they produce. Here we provide an overview of the main collisional and radiative processes and examples of diagnostics relevant to the microphysical processes in the plasma. Many analyses assume a time-steady plasma with ion populations in equilibrium with the local temperature and Maxwellian distributions of particle velocities, but these assumptions are easily violated in many cases. We consider these departures from equilibrium and possible diagnostics in detail.

Authors: Stephen J. Bradshaw, John C. Raymond
Projects: None

Publication Status: Published
Last Modified: 2013-03-19 09:40
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Diagnosing the time-dependence of active region core heating from the emission measure: II. Nanoflare trains  

Stephen Bradshaw   Submitted: 2013-03-18 20:05

The time-dependence of heating in solar active regions can be studied by analyzing the slope of the emission measure distribution cool-ward of the peak. In a previous study we showed that low-frequency heating can account for 0% to 77% of active region core emission measures. We now turn our attention to heating by a finite succession of impulsive events for which the timescale between events on a single magnetic strand is shorter than the cooling timescale. We refer to this scenario as a ``nanoflare train'' and explore a parameter space of heating and coronal loop properties with a hydrodynamic model. Our conclusions are: (1) nanoflare trains are consistent with 86% to 100% of observed active region cores when uncertainties in the atomic data are properly accounted for; (2) steeper slopes are found for larger values of the ratio of the train duration Delta_H to the post-train cooling and draining timescale Delta_C, where Delta_H depends on the number of heating events, the event duration and the time interval between successive events ( au_C); (3) au_C may be diagnosed from the width of the hot component of the emission measure provided that the temperature bins are much smaller than 0.1~dex; (4) the slope of the emission measure alone is not sufficient to provide information about any timescale associated with heating - the length and density of the heated structure must be measured for Delta_H to be uniquely extracted from the ratio Delta_H/Delta_C.

Authors: Jeffrey W. Reep, Stephen J. Bradshaw, James A. Klimchuk
Projects: Hinode/EIS

Publication Status: Published
Last Modified: 2013-03-19 09:40
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Diagnosing the time-dependence of active region core heating from the emission measure: I. Low-frequency nanoflares  

Stephen Bradshaw   Submitted: 2012-09-04 19:41

Observational measurements of active region emission measures contain clues to the time-dependence of the underlying heating mechanism. A strongly non-linear scaling of the emission measure with temperature indicates a large amount of hot plasma relative to warm plasma. A weakly non-linear (or linear) scaling of the emission measure indicates a relatively large amount of warm plasma, suggesting that the hot active region plasma is allowed to cool and so the heating is impulsive with a long repeat time. This case is called {it low-frequency} nanoflare heating and we investigate its feasibility as an active region heating scenario here. We explore a parameter space of heating and coronal loop properties with a hydrodynamic model. For each model run, we calculate the slope α of the emission measure distribution EM(T) propto T α . Our conclusions are: (1) low-frequency nanoflare heating is consistent with about 36% of observed active region cores when uncertainties in the atomic data are not accounted for; (2) proper consideration of uncertainties yields a range in which as many as 77% of observed active regions are consistent with low-frequency nanoflare heating and as few as zero; (3) low-frequency nanoflare heating cannot explain observed slopes greater than 3; (4) the upper limit to the volumetric energy release is in the region of 50~erg~cm-3 to avoid unphysical magnetic field strengths; (5) the heating timescale may be short for loops of total length less than 40~Mm to be consistent with the observed range of slopes; (6) predicted slopes are consistently steeper for longer loops.

Authors: Stephen J. Bradshaw, James A. Klimchuk, Jeffrey W. Reep
Projects: None

Publication Status: ApJ (in press)
Last Modified: 2012-09-05 13:41
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Enthalpy-based Thermal Evolution of Loops: II. Improvements to the Model  

Stephen Bradshaw   Submitted: 2012-04-27 12:21

This paper develops the zero-dimensional (0D) hydrodynamic coronal loop model ?Enthalpy-based Thermal Evolution of Loops? (EBTEL) proposed by Klimchuk et al (2008), which studies the plasma response to evolving coronal heating, especially impulsive heating events. The basis of EBTEL is the modelling of mass exchange between the corona and transition region and chromosphere in response to heating variations, with the key parameter being the ratio of transition region to coronal radiation. We develop new models for this parameter that now include gravitational stratification and a physically motivated approach to radiative cooling. A number of examples are presented, including nanoflares in short and long loops, and a small flare. The new features in EBTEL are important for accurate tracking of, in particular, the density. The 0D results are compared to a 1D hydro code (Hydrad) with generally good agreement. EBTEL is suitable for general use as a tool for (a) quick-look results of loop evolution in response to a given heating function, (b) extensive parameter surveys and (c) situations where the modelling of hundreds or thousands of elemental loops is needed. A single run takes a few seconds on a contemporary laptop.

Authors: Peter J. Cargill, Stephen J. Bradshaw, James A. Klimchuk
Projects: None

Publication Status: ApJ (in press)
Last Modified: 2012-04-28 10:35
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What Dominates the Coronal Emission Spectrum During the Cycle of Impulsive Heating and Cooling?  

Stephen Bradshaw   Submitted: 2011-09-06 09:18

The 'smoking gun' of small-scale, impulsive events heating the solar corona is expected to be the presence of hot (>5 MK) plasma. 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 on board 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) For the many scenarios we have considered, the emission detected in several of the SDO-AIA channels (131, 193, and 211 Å) would be dominated by warm, overdense, cooling plasma. (4) It is difficult not to create coronal loops that emit strongly at 1.5 MK and in the range 2-6 MK, which are the most commonly observed kind, for a broad range of nanoflare scenarios. (5) The Fe XV (284.16 Å) emission in most of our models is about 10 times brighter than the Ca XVII (192.82 Å) 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.

Authors: Bradshaw, S.J., Klimchuk, J.A.
Projects: Hinode/EIS,SDO-AIA

Publication Status: Published
Last Modified: 2011-09-06 11:15
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A reconnection-driven rarefaction wave model for coronal outflows  

Stephen Bradshaw   Submitted: 2011-09-06 09:11

This abstract was corrupted following database problems and is being recovered. It will be restored as quickly as possible. Any questions, please send them to Alisdair. Sorry for any incovenience.


Authors: Bradshaw, S.J., Aulanier, G., Del Zanna, G.
Projects:

Publication Status: In press
Last Modified: 2011-09-06 14:43
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Abstracts by Author
The Cooling of Coronal Plasmas. iv: Catastrophic Cooling of Loops
The influence of numerical resolution on coronal density in hydrodynamic models of impulsive heating
Collisional and Radiative Processes in Optically Thin Plasmas
Diagnosing the time-dependence of active region core heating from the emission measure: II. Nanoflare trains
Diagnosing the time-dependence of active region core heating from the emission measure: I. Low-frequency nanoflares
Enthalpy-based Thermal Evolution of Loops: II. Improvements to the Model
What Dominates the Coronal Emission Spectrum During the Cycle of Impulsive Heating and Cooling?
A reconnection-driven rarefaction wave model for coronal outflows

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