S. J. Bradshaw

Footpoint excitation of standing acoustic waves in coronal loops

A new theoretical model for the study of slow standing sausage mode oscillations in hot (T > 6 MK) active region coronal loops is presented. These oscillations are observed by the SUMER spectrometer on board the SoHO satellite. The model contains the transition region and the upper chromosphere which enables us to study the entire process of hot loop oscillations -from the impulsive footpoint excitation phase to the rapid damping phase. It is shown that standing acoustic waves can be excited by an impulsive heat deposition at the chromospheric footpoint of a loop if the duration of the pulse matches the fundamental mode period. The pulse is immediately followed by a standing wave consistent with the SUMER observations in hot loops. The amount of released energy determines the oscillation amplitude. The combined effects of thermal conduction and radiation on the behaviour of the standing acoustic waves in hot gravitationally stratified loops are investigated. In addition to damping, these effects lead to downflows which are superimposed on the oscillations. The implications of the results in coronal seismology are discussed.

DIAGNOSING THE TIME-DEPENDENCE OF ACTIVE REGION CORE HEATING FROM THE EMISSION MEASURE. I. LOW-FREQUENCY NANOFLARES

Observational measurements of active region emission measures contain clues to the time dependence of the underlying heating mechanism. A strongly nonlinear scaling of the emission measure with temperature indicates a large amount of hot plasma relative to warm plasma. A weakly nonlinear (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 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)∝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.

Forward Modeling of Hot Loop Oscillations Observed by SUMER and SXT

An example of hot active region loop oscillations observed by SUMER and SXT is presented. The hypothesis that a fundamental mode standing slow sausage (acoustic) wave is initiated by a footpoint microflare is tested and confirmed using a forward modeling approach. The oscillation is set up immediately after the heating pulse. The duration, temporal behavior, and total heat input of the microflare are estimated using the oscillation parameters. The rapid energy release is followed by cooling. The time-distance profile of the heating rate along the loop is recovered using the intensity and Doppler-shift time series. Hot loop oscillations are mainly observed in the Doppler shift. The absence of intensity oscillations in this and similar cases is explained. It is also found that the intensity oscillation, unlike the Doppler shift oscillation, undergoes half a period phase variation when the background intensity passes through its maximum, thus making it more difficult to detect.

ENTHALPY-BASED THERMAL EVOLUTION OF LOOPS. III. COMPARISON OF ZERO-DIMENSIONAL MODELS

Zero-dimensional (0D) hydrodynamic models provide a simple and quick way to study the thermal evolution of coronal loops subjected to time-dependent heating. This paper presents a comparison of a number of 0D models that have been published in the past and is intended to provide a guide for those interested in either using the old models or developing new ones. The principal difference between the models is the way the exchange of mass and energy between corona, transition region, and chromosphere is treated, as plasma cycles into and out of a loop during a heating-cooling cycle. It is shown that models based on the principles of mass and energy conservation can give satisfactory results at some or, in the case of the Enthalpy-based Thermal Evolution of Loops model, all stages of the loop evolution. Empirical models can have significant difficulties in obtaining accurate behavior due to invocation of assumptions incompatible with the correct exchange of mass and energy between corona, transition region, and chromosphere.

Are chromospheric nanoflares a primary source of coronal plasma

It has been suggested that the hot plasma of the solar corona comes primarily from impulsive heating events, or nanoflares, that occur in the lower atmosphere, either in the upper part of the ordinary chromosphere or at the tips of type II spicules. We test this idea with a series of hydrodynamic simulations. We find that synthetic Fe XII (195) and Fe XIV (274) line profiles generated from the simulations disagree dramatically with actual observations. The integrated line intensities are much too faint; the blueshifts are much too fast; the blue-red asymmetries are much too large; and the emission is confined to low altitudes. We conclude that chromospheric nanoflares are not a primary source of hot coronal plasma. Such events may play an important role in producing the chromosphere and powering its intense radiation, but they do not, in general, raise the temperature of the plasma to coronal values. Those cases where coronal temperatures are reached must be relatively uncommon. The observed profiles of Fe XII and Fe XIV come primarily from plasma that is heated in the corona itself, either by coronal nanoflares or a quasi-steady coronal heating process. Chromospheric nanoflares might play a role in generating waves that provide this coronal heating.

On the consequences of a non-equilibrium ionisation balance for compact flare emission and dynamics

We carry out a hydrodynamic simulation of a compact flare and find significant non-equilibrium distributions for the ionisation balance during the impulsive and gradual phases, which can strongly alter the radiative emission. This has major implications for attempts to derive the theoretical intensities of emission lines used for spectroscopic diagnostic analyses of the plasma properties. During the impulsive phase we find that the emissivities of He I, He II and C IV in the transition region can be strongly enhanced above their expected equilibrium values, followed by a significant reduction which increases the amount of chromo- spheric plasma ablated into the corona. Furthermore, during the flare heating the overall charge state of the coronal ions can be significantly lower than is suggested by an equilibrium ionisation balance and, therefore, line ratio measurements will yield plasma temperatures that are much greater than the formation temperature of the emitting ion. During the gradual phase the emissivity at transition region temperatures remains suppressed, compared with its equilibrium value, with correspondingly reduced downflow velocities and increased radiative cooling time-scales. Finally, we synthesise the emission as it would be detected by TRACE in its 171 A and 195 A wavelength bands, and find that the filter ratio technique can give reasonably good estimates of the plasma temperature in quiescence, though when the populations of Fe VIII, Fe IX, Fe X and Fe XII exhibit departures from equilibrium the temperatures derived from filter ratio measurements become unreliable.

A New Enthalpy-Based Approach to the Transition Region in an Impulsively Heated Corona

Observations of the solar corona reveal persistent and ubiquitous redshifts, which correspond to bulk downflows. For an impulsively heated corona (e.g., by nanoflares), this indicates that a majority of the component loop structures are in the radiatively cooling phase of their lifecycle, and these motions should not be used to verify the predictions of any proposed theory of heating. However, the nature of the bulk downflows raises the possibility that enthalpy may play a key role in the energy balance of the loops and in particular that it powers the transition region radiation. In this Letter, we use one-dimensional hydrodynamic simulations of loop cooling to show that enthalpy losses from the corona are easily sufficient to power the transition region radiation. This contrasts with the long-held view that downward thermal conduction powers the transition region. The traditional distinction between the transition region and the corona in terms of temperature alone is then a grossly unphysical simplification, and a proper definition of the interface between these atmospheric layers requires a detailed knowledge of their energy balance. To this end, we propose a robust new definition of the transition region.

Coronal loop oscillations and diagnostics with Hinode/EIS

Context.Standing slow (acoustic) waves commonly observed in hot coronal loops offer a unique opportunity to understand the properties of the coronal plasma. The lack of evidence for similar oscillations in cooler loops is still a puzzle. Aims.The high cadence EIS instrument on board recently launched Hinode has the capability to detect wave motion in EUV lines both in the imaging and spectroscopy modes. The paper aims to establish the distinct characteristics of standing and propagating acoustic waves and to predict their footprints in EIS data. Methods.A 1D hydrodynamic loop model is used and the consequences of various types of heating pulses are examined. In each case, the resulting hydrodynamic evolution of the loop is converted into observables using a selection of available EIS spectral lines and windows. Results.Propagating/standing acoustic waves are a natural response of the loop plasma to impulsive heating. Synthetic EIS observations of such waves are presented both in the imaging and spectroscopy modes. The waves are best seen and identified in spectroscopy mode observations. It is shown that the intensity oscillations, unlike the Doppler shift oscillations, continuously suffer phase shifts due to heating and cooling of the plasma. It is therefore important to beware of this effect when interpreting the nature of the observed waves.

Study of a transient siphon flow in a cold loop

Context. The nature of loops is still a matter of debate with several explanations having been put forward. Simultaneous spectral and imaging data have the capacity to provide a new insight into mass motions, dynamics and energetics of loops. Aims. We report on spectral data taken with the Solar Ultraviolet Measurements of Emitted Radiation spectrograph (SUMER) and imaging data from the Transition Region and Coronal Explorer (TRACE) of a transient event which occurred in a cold loop, lasting a few minutes. Methods. A sequence of TRACE images in the 1550 ¯ and 171 ¯ lters show a disturbance which originated at one foot-point and propagates along the loop. The SUMER slit was placed at the other foot-point of the loop. In order to interpret the results, numerical simulations were performed with the results then converted into observable quantities and compared with the data. Results. During the event a radiance increase and a relative red shift of 20 km s 1 was detected in the Nv 1238.82 ¯ line. 1D numerical simulations are performed and observable quantities derived from the results of the simulations. The observed dynamic behaviour of the Nv 1238.82 ¯ line proles was recovered. Conclusions. The results suggest that the observations could be interpreted in terms of a short-lived siphon o w reaching a speed of 120 km s 1 and driven by a nonlinear heating pulse. The energies required to drive the observed red-shifts are estimated to be about 10 25 erg. The absence of a signicant blue-shift caused by the return o w is explained.

Modelling nanoflares in active regions and implications for coronal heating mechanisms.

Recent observations from the Hinode and Solar Dynamics Observatory spacecraft have provided major advances in understanding the heating of solar active regions (ARs). For ARs comprising many magnetic strands or sub-loops heated by small, impulsive events (nanoflares), it is suggested that (i) the time between individual nanoflares in a magnetic strand is 500–2000 s, (ii) a weak ‘hot’ component (more than 106.6 K) is present, and (iii) nanoflare energies may be as low as a few 1023 ergs. These imply small heating events in a stressed coronal magnetic field, where the time between individual nanoflares on a strand is of order the cooling time. Modelling suggests that the observed properties are incompatible with nanoflare models that require long energy build-up (over 10 s of thousands of seconds) and with steady heating.