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.

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 principal 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 discrepancies in the decay phase. The temperature for underresolved 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 underresolved 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 emphasizes 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.

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 e ffects 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 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 -3consistent with what is actually observed.

Context. This paper addresses the impulsive heating of very diffuse coronal loops, such as can occur in a nanoflare-heated corona with low filling factor. Aims. We study the physics associated with nanoflare heating in this scenario and aim to determine whether there exist any observable signatures. Methods. We derive an analytical model in order to gain some simple physical insights into the system and use a one dimensional hydrodynamic model that treats the electrons and ions as a coupled fluid to simulate nanoflare heating with time-scales of 30 s. Our analytical model also provide a means of verifying our numerical results. Results. We find that diffuse loops containing plasma at T > 20 MK can be rapidly created and subsequently filled by the violent evaporation of chromospheric plasma driven by near-saturated thermal conduction. Most importantly, we find order-of-magnitude departures from equilibrium of the ionisation balance for iron and use this result to identify a potential signature of this heating mechanism. Conclusions. We conclude that nanoflare heating can account for the presence of extremely high temperature plasma in a corona with low filling factor. We find that near-saturated thermal conduction may play a key role at the onset of chromospheric evaporation and a non-equilibrium ionisation balance is absolutely inevitable. The high temperatures could never be directly measured in the corona due to the small emission measure and the most promising signature of such heating is blue-shifted plasma from the loop footpoints. We find reason for cautious optimism that this signature can be detected by future space-based spectroscopic instrumentation (e.g. SolarB-EIS).

Abstract. We perform a hydrodynamic simulation of a cooling coronal loop and calculate the time-dependent ion populations of the most abundant elements of the solar atmosphere at each time-step. We couple the time-dependent ion balance equations to the hydrodynamic equations in order to treat the energy loss through radiation in a self-consistent way by allowing for the emission from a potentially nonequilibrium ion population. We present results for the response to the changing conditions in the loop of the population of C VII ions and find significant deviations from equilibrium in the coronal and footpoint regions of the loop. The former is due to the tenuous nature of the coronal plasma causing recombinations to be rare and the latter is due to the strong downflows that develop as the loop cools, which carry persistent C VII ions into the lower regions of the loop. We also present a comparison between total plasma emissivity curves calculated during this simulation and an almost identical simulation that assumed an equilibrium ion population for the calculation of the radiation term. As a result of the nonequilibrium ion populations we find significant differences between the emissivity curves of each simulation and the loop cooling times. We suggest that a consideration of nonequilibrium ionisation and radiation might help to (a) explain the thermal broadening observed in some emission lines during explosive events, and (b) reconcile differences between theory and observations relating to the longevity of some loops observed in the TRACE filters.