Year: 2019
Type: article
Abstract: The solar atmosphere is dominated by loops of magnetic fluxes that connect the multi-million degree corona to the much cooler chromosphere. The temperature and density structure of quasi-static loops are determined by the continuous flow of energy from the hot corona to the lower solar atmosphere. Loop scaling laws provide relationships between global properties of the loop (such as the peak temperature, pressure, and length); they follow from the physical variable dependencies of various terms in the energy equation, and, hence, the form of the loop scaling law provides insight into the key physics that control the loop structure. Traditionally, scaling laws have been derived under the assumption of collision-dominated thermal conduction. Here, we examine the impact of different regimes of thermal conduction—collision-dominated, turbulence-dominated, and free-streaming—on the form of the scaling laws relating the loop temperature and heating rate to its pressure and half-length. We show that the scaling laws for turbulence-dominated conduction are fundamentally different than those for collision-dominated and free-streaming conduction, inasmuch as the form of the scaling laws now depend primarily on conditions at the low-temperature, rather than high-temperature, part of the loop. We also establish regimes in the temperature and density space in which each of the applicable scaling laws prevail.
Source: The Astrophysical Journal
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
Awards: CAREER: Exploring New Regimes of Physics to Constrain the Properties of Heating in the Solar Corona, G6671297155, MOST FLARE MODELS ASSUME THAT ELECTRONS ARE ACCELERATED IN A CORONAL POINT SOURCE. HOWEVER THE APPEARANCE OF EXTENDED CORONAL SOURCES SHOWS THAT THE ACCELERATED ELECTRONS CAN BE FULLY STOPPED IN THE CORONA AND RHESSI DATA ON THE VARIATION OF HXR SOURCE SIZE WITH ENERGY POINT TO A MODEL IN WHICH TRANSPORT INVOLVES BOTH COLLISIONS AND DIFFUSIVE SCATTERING (AN ESSENTIAL INGREDIENT IN MHD RECONNECTION) OCCURRING COSPATIALLY. THIS REQUIRES THAT WE PUSH MODELS BEYOND A POINT-SOURCE INJECTION SCENARIO TOWARD A MORE PHYSICALLY REALISTIC SCENARIO INVOLVING AN EXTENDED REGION IN WHICH ACCELERATION AND TRANSPORT OPERATE UNDER A UNIFIED PHYSICAL MODEL. THE INVESTIGATION WILL ADDRESS ELECTRON ENERGIES FROM A FEW KT UPWARDS A RANGE THAT IS RESPONSIBLE NOT ONLY FOR MOST OF THE ACCELERATED ELECTRON ENERGY CONTENT BUT ALSO FOR DETERMINING THE COEFFICIENTS OF THERMAL AND ELECTRICAL CONDUCTIVITY. OUR APPROACH WILL USE THE CONCEPT OF EFFECTIVE MEAN FREE PATH. FOR COLLISIONS THE ANGULAR DIFFUSION COEFFICIENT D~1/V^3 AND THUS?~V/D~V^4. FOR DIFFUSIVE SCATTERING THE CHARACTERISTIC MEAN FREE PATH?_T WILL HAVE A VELOCITY DEPENDENCE DETERMINED BY THE SCATTERING MECHANISM PARAMETRIZED AS?_T =?_0 V^A. THUS IN THE PRESENCE OF BOTH COLLISIONS AND TURBULENT ACCELERATION THE ELECTRON TRANSPORT IS CHARACTERIZED BY A MEAN FREE PATH?(V) =?_CE (V/V_E )^4/( R (V/V_E )^(4-A) + 1); R =?_CE/?_0 . IN THE PRESENCE OF BOTH A TEMPERATURE GRADIENT DT/DX AND AN ELECTRIC FIELD E THE ELECTRON DISTRIBUTION FUNCTION CAN BE WRITTEN AS A CHAPMAN-ENSKOG EXPANSION ABOUT A MAXWELLIAN FORM F0 WITH A FIRST-ORDER ANISOTROPIC TERM F1(V ) = -?(V)[((V/V_E)^2-5/2) D LN T/DX + EE/KT]F0 . (1) SUBSTITUTING THIS IN THE RESPECTIVE EXPRESSIONS FOR THE HEAT FLUX AND CURRENT DENSITY Q =? M_EDV V^5D F1(V ); J = -2?EDV V^3D F1(V ) (2) GIVES THE THERMOELECTRIC RELATIONS Q = - K DT/DX E ; J =?E +? DT/DX WHERE K ? ? AND ARE DETERMINED FROM EQUATIONS (1) AND (2). PRELIMINARY RESULTS SHOW THAT THESE COEFFICIENTS GENERALLY DECREASE WITH R AND CAN ALSO EXHIBIT SOME INTERESTING SIGN CHANGES AS A RESULT OF THE MORE COMPLICATED VELOCITY DEPENDENCE OF?. WE PROPOSE TO EVALUATE K ? ? AND FOR DIFFERENT TURBULENCE MODELS AND USE THE RESULTS TO PREDICT OBSERVATIONALLY TESTABLE QUANTITIES SUCH AS THE COOLING TIME PROFILE FOR CORONAL PLASMA. MODEL PREDICTIONS WILL BE COMPARED WITH RHESSI/AIA IMAGING SPECTROSCOPY DATA IN ORDER TO INFER THE VALUE OF?_T AND HENCE CONSTRAIN THE TURBULENT SCATTERING MECHANISM AND TO GENERATE REVISED ELECTRON ENERGY TRANSPORT MODELS FOR USE IN CALCULATING THE ATMOSPHERIC HEATING PROFILE. THE PROPOSED RESEARCH ADDRESSES DECADAL SURVEY GOALS 1 (DETERMINE THE ORIGINS OF THE SUN S ACTIVITY) AND 4 (DISCOVER AND CHARACTERIZE FUNDAMENTAL PROCESSES THAT OCCUR BOTH WITHIN THE HELIOSPHERE AND THROUGHOUT THE UNIVERSE). THE RESULTS WILL HAVE IMPACT IN SEVERAL AREAS. FOR EXAMPLE CORONAL PLASMA IS OBSERVED TO BE SUSTAINED AT HIGH TEMPERATURES WELL BEYOND THE CONDUCTIVE COOLING TIME LEADING TO THE GENERAL SUPPOSITION THAT ADDITIONAL ENERGY IS INJECTED INTO THE CORONA AFTER THE IMPULSIVE PHASE HAS CEASED. HOWEVER SUCH LONG COOLING TIMES COULD ALSO BE A CONSEQUENCE OF A DECREASE IN THE THERMAL CONDUCTIVITY COEFFICIENT K. LOWERING K WOULD ALSO LEAD TO A HIGHER STEADY-STATE CORONAL TEMPERATURE POSSIBLY ACCOUNTING FOR LOOPTOP CORONAL HARD X-RAY SOURCES. A REDUCTION IN THE ELECTRICAL CONDUCTIVITY? ENHANCES OHMIC LOSSES ASSOCIATED WITH THE BEAM-NEUTRALIZING RETURN CURRENT AFFECTING NOT ONLY ELECTRON TRANSPORT DYNAMICS BUT ALSO THE ASSOCIATED HEATING PROFILE AND HENCE THE HYDRODYNAMIC RESPONSE OF THE SOLAR ATMOSPHERE. AND BECAUSE THE HARD X-RAY PRODUCTION OF A POPULATION OF ACCELERATED ELECTRONS DEPENDS INVERSELY ON THE ENERGY LOSS RATE THE RESULTS WILL IMPACT THE TOTAL ENERGY CONTENT IN ACCELERATED ELECTRONS, G943238223
OpenAlex ID: W2948703172