The document summarizes a student's summer project modeling solar flares using tapered coronal loops. The student developed a heating function to distribute energy over the length and time of the flare loop based on Gaussian and triangle functions. This heating function was used as input for models developed by the student's advisors to simulate the evolution of temperature, density, and x-ray light curves of the flare. The goals of the project were to better understand the relationship between energy release and x-ray emissions and determine the conditions needed to reproduce observed flare properties.
1. Modeling Solar Flares Using Tapered Coronal Loops Natalie Larson Dr. Kathy Reeves, Dr. Trae Winter Harvard Smithsonian Center for Astrophysics Solar Physics REU 2010
->Made up of an arcade of loops Temperature greatest near loop top Density greatest at footpoints Red: ultraviolet; cool, dense gas Blue: 171Å pass band; 1 million degrees K Green: over 1.5 million degrees up to approximately 10 million degrees K Red-coolest Blue-hotter Green-hottest
Magnetic field lines in sunspot pair poking out of chromosphere Shearing from different parts of sun rotating at different rates Hot gas trapped beneath field lines puts pressure on them and causes them to twist Current sheet forms when field lines pointing in opposite directions are near each other Sometimes pressure is too great and preferred configuration is a new one: magnetic field lines snap and release energy, then reconnect Thermal particles: Thermal particles can be modeled as a fluid because they move collectively and are in thermal equilibrium with each other. As they move, they emit photons and are detected as soft X-rays Non-thermal particles: produce hard X-rays Start at loop top, move down, hit chromosphere, thermalize or mirror The model we use does include a CME, but we are focusing on modeling the “flare” aspect of the event, not the CME aspect, i.e. we care about the hard and soft X-ray emissions
Loops are not of constant cross-section: tapered at ends 1. Better matches real flare loops 2. Because the volume along the loop changes (unlike a model in which the loop ends are not tapered), the temperature and density are no longer the same at all places along the loop; therefore, we use a non-uniform grid in order to measure these changes: with closer grid spacings near the footpoints to represent more rapid changes in temperature and density. 3. Given tapered loop-ends, we know that non-thermal particles will mirror; we can model mirroring by using tapered loop ends: mirroring is important because it causes particles to be ‘recycled’; they keep releasing energy and X-rays instead of thermalizing: important to accurately modeling solar flares A particle will mirror when the angle between the velocity direction of the particle and the magnetic field it is circling is 90 degrees. The pitch angle of a particle moving into stronger magnetic field will increase. Field lines in loops converge on both sides which causes field strength to increase: the non-thermal particles are recycled ->We compared the GOES and XRT light curves for the old and new models to see: are they different, how and why? ->We compared the temperatures and densities in the loops for each of the models: are they different, how and why?
1. Generate solar flare using Kathy’s model: get loop geometry (lower and upper bounds of loops) and total energy in loop at each time step 2. Energy given by Kathy’s model distributed over time and space using my heating function, which works in conjunction with Trae’s model to describe the evolution of the temperatures and densities in loops; multiplied to get an arcade of loops. 3. Temperature and density output used by my code to calculate flare intensity that would be measured by GOES and XRT
1. No way to directly measure amount of energy input into a flare 2. Neupert Effect is a temporal correlation of the hard X-ray flux with the time derivative of the soft X-ray flux (NT particles produce thermal particles) 3. Reeves and Moats found previously that F α E^(1.54-2.54) , not F α E, as previously thought ->Most previous research assumes that appearance of the Neupert Effect means that peak soft X-ray flux (F) α total thermal energy input (E). Kathy and Moats found previously that F α E^(1.54-2.54) for all flares By measuring hard X-ray light curves we can find where Neupert effect is exhibited, and then observe whether F is proportional to E in these cases
Loss-of-equilibrium model: flux rope begins in equilibrium with magnetic tension, compression, and gravity balancing each other. Flare footpoints moved together, simulating phosopheric motions, until no longer a possible equilibrium state for flux rope, and eruption (CME) occurs. Current sheet forms under flux rope, flare loops formed by reconnecting magnetic fields. Input: Original magnetic configuration, input energy Output: Poynting flux (total electomagnetic energy, essentially: E x B) integrated over the current sheet, which is used as a proxy for the thermal energy released by the eruption. Loop length and thickness Total energy input into the loop (magnetic energy + thermal energy released) p – distance from bottom tip of the current sheet q – distance from top tip of the current sheet h - height of the flux rope Velocity of the flux rope
Output agrees well with observed flares; is a good method for calculating the total energy in a flare loop and the shape of the loop ->STERO differencing image Kathy’s previous model does not model non-thermal particles uses loops of constant cross-section calculates the average energy in a flare loop Kathy’s new model accounts for tapered ends Trae’s model: can accurately model the effects of having loops with tapered ends includes NT particles, so can model magnetic mirroring calculates evolution of temperature and volume in the loop based on grid system; can account for differences in temperature and volume caused by differences in volume along the loop
HyLoop: The code controller. “Combines a hydrodynamic equation solver with a nonthermal particle tracking code to simulate the thermal and nonthermal dynamics and emission of solar flares.” SHReC: uses MHD equations in 1D (length) to calculate evolution of temperature and density of thermal plasma. Used to determine initial conditions of loop as well as evolution of T and density during the flare. Thermal particle modeling code used to simulate the initial plasma in the coronal loops, before the flare starts: input particle energy and density into magnetic loop and wait for the particles to spread through loop and let loop come to temporary equilibrium, so that its parameters are no longer changing Thermal particles emit soft X-rays. Code also used to model thermal particles generated during the flare as well as non-thermal particles that have been thermalized (different ratios for different flare sizes) PATC: uses kinematics and a Monte Carlo approximation method to track the evolution of nonthermal particle beams Produce hard X-rays Injected at loop top and move down to footpoints. Most thermalize: emit hard X-rays, when they hit the much denser chromosphere, and having lost energy turn into thermal particles. Some do not thermalize and instead are mirrored at intervals back up the legs of the loop Use Monte Carlo method to model: In general: uses repeated random sampling to make approximations Used to simulate speeds and trajectories of non-thermal particles, which cannot be modeled like thermal plasma (MHD) because travelling too fast to have group motion; they do not have time to exchange heat with each other. Particles’ paths through space must be tracked individually: but this takes too much time. Instead, simulate the trajectories of a small representative portion of the particles, then perform simulation again and again, and average all of the runs. Gives a good approximation for the locations and speeds of the particles over time. Particles input in direction of loop footpoints Red: Soft X-Rays Blue: Hard X-Rays
Heating function: takes total energy input into a loop and length of the loop from Kathy’s model and combines with Trae’s volume grid (which uses Kathy’s geometry) and a constant background heating to get energy per volume per second: ergs per cm^3*s. Energy is input for 40 seconds using my heating function, after which the function only inputs the background heating. Uses an equation for heating developed earlier by Kathy: Total Energy in Loop = Integral over time * Integral over length * Eflare (scaling factor) * Area Uses Gaussian to distribute energy over loop length b/c want smooth transition from loop footpoints to loop top and b/c energy is input at the loop-top, Uses Triangle function to distribute energy over time b/c want most energy in the loop at 20 seconds: 20 seconds of build-up energy, reconnection causing more and more energy input, then 20 seconds of less and less energy model a total of 9,000 seconds, but only input energy for 40 GOES flux simulation: takes temperature and emission measure (number of electrons squared * volume chunk) at each second in each loop, puts this information into function that gives GOES flux (Watts/m^2), sums all flux in the flare at each second
->Measures the intensity of soft X-rays ->Overestimate GOES flux without spacial information b/c curve is lower for tapered loops ->Soft X-ray flux is a way of classifying flares ->Method for calculating GOES flux from emission measure and temperature is highly dependent on the electron density, since emission measure is number of electrons squared * volume chunk, and the temperature term is not raised to a power
-> Loop 12 is representative of all loops -> Density is MUCH higher in previous, non-tapered version of the program * ->1.Smaller area at footpoints for chromospheric evaporation to flow up into the loop causes fewer particles to be swept into the loop and therefore less density in the loop (->2.HyLoop maintains a constant number of particles in the loop, while the number of particles in Ebtel change: ex.-when non-thermal particles hit chromosphere and chromospheric evaporation occurs) (->3.Ebtel and HyLoop use the same equation for [electron density] but Ebtel makes approximations, while HyLoop does not) -> Temperature is higher in HyLoop ->1.Smaller volume, same amount of energy input -> Main two ways of dispersing energy are hampered: ->2.Conduction: happens less because area in contact with the transition region (cool dense plasma) is smaller: less area available to cool off the loop ->3.Radiative losses (heat lost as light/electromagnetic radiation): lower because radiative losses are maximized at a temperature near that of the transition region: less of the loop has this temperature
Maybe add a movie like this made with this loop’s information somewhere earlier in the presentation
![What is a solar flare? ,[object Object],TRACE XRT](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)