Parameterizations of Chromospheric Condensations in dG and dMe Model Flare Atmospheres

The origin of the near-ultraviolet and optical continuum radiation in flares is critical for understanding particle acceleration and impulsive heating in stellar atmospheres. Radiative-hydrodynamic simulations in 1D have shown that high energy deposition rates from electron beams produce two flaring layers at T~10^4 K that develop in the chromosphere: a cooling condensation (downflowing compression) and heated non-moving (stationary) flare layers just below the condensation. These atmospheres reproduce several observed phenomena in flare spectra, such as the red wing asymmetry of the emission lines in solar flares and a small Balmer jump ratio in M dwarf flares. The high beam flux simulations are computationally expensive in 1D, and the (human) timescales for completing NLTE models with adaptive grids in 3D will likely be unwieldy for a time to come. We have developed a prescription for predicting the approximate evolved states, continuum optical depth, and the emergent continuum flux spectra of radiative-hydrodynamic model flare atmospheres. These approximate prescriptions are based on an important atmospheric parameter: the column mass (m_ref) at which hydrogen becomes nearly completely ionized at the depths that are approximately in steady state with the electron beam heating. Using this new modeling approach, we find that high energy flux density (>F11) electron beams are needed to reproduce the brightest observed continuum intensity in IRIS data of the 2014-Mar-29 X1 solar flare and that variation in m_ref from 0.001 to 0.02 g/cm2 reproduces most of the observed range of the optical continuum flux ratios at the peaks of M dwarf flares.Comment: 29 pages, 9 figures, accepted for publication in the Astrophysical Journa

Using Models for How Energetic Electrons Heat the Atmosphere During Flares

Using models for how energetic electrons heat the atmosphere during flares, we simulate the radiative-hydrodynamic response of the lower solar atmosphere to flare heating. The simulations account for much of the non-LTE, optically thick radiative transfer that occurs in the chromosphere. Our models predict an increase in white light continuum during the flare on the order of 20%, but this is highly sensitive to the electron beam flux used in the simulation. We find that a majority of the white light continuum originates in the chromosphere as a result of Balmer and Paschen recombinations, but a significant portion also forms in the photosphere which has been heated by radiative backwarming

Models of the Solar Atmospheric Response to Flare Heating

I will present models of the solar atmospheric response to flare heating. The models solve the equations of non-LTE radiation hydrodynamics with an electron beam added as a flare energy source term. Radiative transfer is solved in detail for many important optically thick hydrogen and helium transitions and numerous optically thin EUV lines making the models ideally suited to study the emission that is produced during flares. I will pay special attention to understanding key EUV lines as well the mechanism for white light production. I will also present preliminary results of how the model solar atmosphere responds to Fletcher & Hudson type flare heating. I will compare this with the results from flare simulations using the standard thick target model

A Unified Computational Model for Solar and Stellar Flares

We present a unified computational framework which can be used to describe impulsive flares on the Sun and on dMe stars. The models assume that the flare impulsive phase is caused by a beam of charged particles that is accelerated in the corona and propagates downward depositing energy and momentum along the way. This rapidly heats the lower stellar atmosphere causing it to explosively expand and dramatically brighten. Our models consist of flux tubes that extend from the sub-photosphere into the corona. We simulate how flare-accelerated charged particles propagate down one-dimensional flux tubes and heat the stellar atmosphere using the Fokker-Planck kinetic theory. Detailed radiative transfer is included so that model predictions can be directly compared with observations. The flux of flare-accelerated particles drives return currents which additionally heat the stellar atmosphere. These effects are also included in our models. We examine the impact of the flare-accelerated particle beams on model solar and dMe stellar atmospheres and perform parameter studies varying the injected particle energy spectra. We find the atmospheric response is strongly dependent on the accelerated particle cutoff energy and spectral index.Comment: Accepted for publication by the Astrophysical Journa

Complementing Büchi automata with a subset-tuple construction

Complementation of Büchi automata is well known for being difficult. In the worst case, a state-space growth of (0:76n)n is unavoidable. Recent studies suggest that “simpler” algorithms perform better than more involved ones on practical cases. In this paper, we present a simple “direct” algorithm for complementing Büchi automata. It involves a structured subset construction (using tuples of subsets of states) that produces a deterministic automaton. This construction leads to a complementation procedure that resembles the straightforward complementation algorithm for deterministic Büchi automata, the latter algorithm actually being a special case of our construction

Data-driven Radiative Hydrodynamic Modeling of the 2014 March 29 X1.0 Solar Flare

Spectroscopic observations of solar flares provide critical diagnostics of the physical conditions in the flaring atmosphere. Some key features in observed spectra have not yet been accounted for in existing flare models. Here we report a data-driven simulation of the well-observed X1.0 flare on 2014 March 29 that can reconcile some well-known spectral discrepancies. We analyzed spectra of the flaring region from the Interface Region Imaging Spectrograph (IRIS) in MgII h&k, the Interferometric BIdimensional Spectropolarimeter at the Dunn Solar Telescope (DST/IBIS) in H$\alpha$ 6563 \AA\ and CaII 8542 \AA, and the Reuven Ramaty High Energy Solar Spectroscope Imager (RHESSI) in hard X-rays. We constructed a multi-threaded flare loop model and used the electron flux inferred from RHESSI data as the input to the radiative hydrodynamic code RADYN to simulate the atmospheric response. We then synthesized various chromospheric emission lines and compared them with the IRIS and IBIS observations. In general, the synthetic intensities agree with the observed ones, especially near the northern footpoint of the flare. The simulated MgII line profile has narrower wings than the observed one. This discrepancy can be reduced by using a higher microturbulent velocity (27 km/s) in a narrow chromospheric layer. In addition, we found that an increase of electron density in the upper chromosphere within a narrow height range of $\approx$800 km below the transition region can turn the simulated MgII line core into emission and thus reproduce the single peaked profile, which is a common feature in all IRIS flares.Comment: 14 pages, 18 figures, accepted in Ap

Modeling Mg II h, k and Triplet Lines at Solar Flare Ribbons

Observations from the \textit{Interface Region Imaging Spectrograph} (\textsl{IRIS}) often reveal significantly broadened and non-reversed profiles of the Mg II h, k and triplet lines at flare ribbons. To understand the formation of these optically thick Mg II lines, we perform plane parallel radiative hydrodynamics modeling with the RADYN code, and then recalculate the Mg II line profiles from RADYN atmosphere snapshots using the radiative transfer code RH. We find that the current RH code significantly underestimates the Mg II h \& k Stark widths. By implementing semi-classical perturbation approximation results of quadratic Stark broadening from the STARK-B database in the RH code, the Stark broadenings are found to be one order of magnitude larger than those calculated from the current RH code. However, the improved Stark widths are still too small, and another factor of 30 has to be multiplied to reproduce the significantly broadened lines and adjacent continuum seen in observations. Non-thermal electrons, magnetic fields, three-dimensional effects or electron density effect may account for this factor. Without modifying the RADYN atmosphere, we have also reproduced non-reversed Mg II h \& k profiles, which appear when the electron beam energy flux is decreasing. These profiles are formed at an electron density of $\sim 8\times10^{14}\ \mathrm{cm}^{-3}$ and a temperature of $\sim1.4\times10^4$ K, where the source function slightly deviates from the Planck function. Our investigation also demonstrates that at flare ribbons the triplet lines are formed in the upper chromosphere, close to the formation heights of the h \& k lines

Radiative hydrodynamic modelling and observations of the X-class solar flare on 2011 March 9

We investigated the response of the solar atmosphere to non-thermal electron beam heating using the radiative transfer and hydrodynamics modelling code RADYN. The temporal evolution of the parameters that describe the non-thermal electron energy distribution were derived from hard X-ray observations of a particular flare, and we compared the modelled and observed parameters. The evolution of the non-thermal electron beam parameters during the X1.5 solar flare on 2011 March 9 were obtained from analysis of RHESSI X-ray spectra. The RADYN flare model was allowed to evolve for 110 seconds, after which the electron beam heating was ended, and was then allowed to continue evolving for a further 300s. The modelled flare parameters were compared to the observed parameters determined from extreme-ultraviolet spectroscopy. The model produced a hotter and denser flare loop than that observed and also cooled more rapidly, suggesting that additional energy input in the decay phase of the flare is required. In the explosive evaporation phase a region of high-density cool material propagated upward through the corona. This material underwent a rapid increase in temperature as it was unable to radiate away all of the energy deposited across it by the non-thermal electron beam and via thermal conduction. A narrow and high-density ($n_{e} \le 10^{15}$ cm$^{-3}$) region at the base of the flare transition region was the source of optical line emission in the model atmosphere. The collision-stopping depth of electrons was calculated throughout the evolution of the flare, and it was found that the compression of the lower atmosphere may permit electrons to penetrate farther into a flaring atmosphere compared to a quiet Sun atmosphere.Comment: 12 pages, 12 figure