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The spectral indices of X-ray and radio producing electrons in solar flares
Institution:1. University of Houston, 4800 Calhoun Rd, Houston, TX 77204, USA;2. KBR, 601 Jefferson Street, Houston, TX 77002, USA;3. NASA Johnson Space Center, 2101 E NASA Pkwy, Houston, TX 77058, USA;4. NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA;5. Department of Astronomy, University of Maryland, 4296 Stadium Dr., College Park, MD 20742, USA;6. Leidos, Inc., 555 Forge River Rd, Ste 150A, Webster, TX 77598, USA;7. NASA Ames Research Center, Mail Stop 204-14 Moffett Field, CA 94035, USA;8. Georgia State University, 25 Park Place NE, Atlanta, GA 30303, USA;9. CIRES, University of Colorado Boulder, 216 UCB, Boulder, CO 80309, USA;10. NOAA Space Weather Prediction Center, 325 Broadway, Boulder, CO 80305, USA;11. Royal Belgian Institute for Space Aeronomy, Ringlaan 3, B-1180 Brussels, Belgium;12. Space Sciences Laboratory, University of California at Berkeley, 7 Gauss Way, Berkeley, CA 94720, USA;13. University of Malaga, Av. de Cervantes, 2, 29016 Malaga, Spain;14. Air Force Research Laboratory, Space Vehicles Directorate, 3550 Aberdeen Avenue, Kirtland AFB, NM 87117, USA;15. Atmospheric Environmental Research, 3550 Aberdeen Ave. SE, Albuquerque, NM 87110, USA;p. SSSRC, 100 Tennyson Avenue, Nashua, NH 03062, USA;q. University of Michigan, 500 S. State Street, Ann Arbor, MI 48109, USA;r. Utah State University, 0500 Old Main Hill, Logan, UT 84322-0500, USA;s. Met Office, FitzRoy Road, Exeter, DevonEX1 3PB, UK;t. University of Central Lancashire, Fylde Rd, Preston, Lancashire PR1 2HE, UK;u. University of New Hampshire, 105 Main St, Durham, NH 03824, USA;v. Institute of Astronomy and National Astronomical Observatory, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee Blvd., 1784 Sofia, Bulgaria;w. Cray Inc., 2131 Lindau Ln 1000, Bloomington, MN 55425, USA;x. INAF, Institute for Space Astrophysics and Planetology, via del Fosso del Cavaliere 100, 00133 Roma, Italy;y. National Solar Observatory, 3665 Discovery Dr 3rd, Boulder, CO 80303, USA;z. Universitá di Roma Tor Vergata, Via Cracovia, 50, 00133 Roma, Italy;11. National Observatory of Athens, Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, Vas. Pavlou & I. Metaxa, GR-15 236 Penteli, Athens, Greece;12. Space Applications & Research Consultancy (SPARC), Aiolou St. 73, 10551 Athens, Greece;13. RCAAM of the Academy of Athens, 4 Soranou Efesiou Street, 115 27 Athens, Greece;14. University of Alabama at Huntsville, 301 Sparkman Drive, Huntsville, AL 35899, USA;15. National and Kapodistrian University of Athens, Athens 157 72, Greece;17. NASA Marshall Space Flight Center, Martin Rd SW, Huntsville, AL 35812, USA;18. Stanford University, 450 Serra Mall, Stanford, CA 94305, USA;19. Princeton University, P.O. Box 430, Princeton, NJ 08544, USA;110. Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78238, USA;111. Southwest Research Institute Boulder, 1050 Walnut St 300, Boulder, CO 80302, USA;112. University of Texas at San Antonio, 1 UTSA Circle, San Antonio, TX 78249, USA;113. Catholic University of America, 620 Michigan Ave NE, Washington, DC 20064, USA;114. University of California at Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90095, USA;115. Department of Mathematics/Centre for Mathematical Plasma Astrophysics, KU Leuven, Celestijnenlaan 200 B 3001 Leuven, Leuven, Belgium;1p. Departament de Física Quántica i Astrofísica, Institut de Ciècies del Cosmos (ICCUB), Universitat de Barcelona, UB-IEEC, Martí i Franquès, 1 Barcelona, Spain;1q. Institute of Physics, University of Maria Curie-Skłodowska, ul.Radziszewskiego 10, 20-031 Lublin, Poland;1r. IRAP, 9 Av.du Colonel Roche, 31400 Toulouse, France;1s. Department of Physics and Astronomy, FI-20014 University of Turku, Finland;1t. Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation (IZMIRAN), Russian Academy of Sciences, 108840 Moscow Troitsk, Russia;1u. IEAP, Christian-Albrechts-Universitaet, Leibnizstraße 11-19, 24118 Kiel, Germany;1v. New Jersey Institute of Technology, 323 Dr Martin Luther King Jr Blvd, Newark, NJ 07102, USA;1w. Department of Mechanics and Mathematics, Moscow State University, Ulitsa Kolmogorova, 1, Moscow 119991, Russia;1x. Moscow Center of Fundamental and Applied Mathematics, Moscow 119234, Russia;1y. George Mason University, 4400 University Dr, Fairfax, VA 22030, USA;1z. The Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Rd, Laurel, MD 20723, USA;21. European Space Research and Technology Centre (ESTEC), Space Environment and Effects Section Keperlaan 1, 2200AG Noordwijk, the Netherlands;22. Lockheed Martin Solar & Astrophysics Laboratory, 3176 Porter Dr, Palo Alto, CA 94304, USA;23. Predictive Science Inc., , 9990 Mesa Rim Rd, Ste 170, San Diego, CA 92121, USA;24. Space Applications Systems, 1932 Zaventem, Belgium;25. Centre for Space Research, North-West University, Building G5, Potchefstroom Campus, North-West University, Potchefstroom, South Africa;26. South African National Space Agency, Hospital St, Hermanus 7200, South Africa;27. ASTRON, The Netherlands Institute for Radio Astronomy, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, the Netherlands;28. NextGen Federal Systems, 1399 Stewartstown Road, Suite 350, Morgantown, WV 26505, USA;29. Florida Institute of Technology, 150 W University Blvd, Melbourne, FL 32901, USA;1. Institute of Physics, University of Graz, 8010 Graz, Austria;2. Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, NH 03824, USA;3. Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA;4. Department of Astronomy, University of Maryland, College Park, MD 20742, USA;5. Max-Planck-Institut für Sonnensystemforschung, 37077 Göttingen, Germany;6. Department of Physics, University of Helsinki, FI-00014 Helsinki, Finland;7. Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, USA;8. Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA;9. RAL Space, United Kingdom Research and Innovation – Science & Technology Facilities Council, Harwell Campus, Oxfordshire, OX11 0QX, UK;10. Austrian Space Weather Office, GeoSphere Austria, 8020 Graz, Austria;11. Department of Meteorology, University of Reading, Reading RG6 6BB, UK;12. Institute of Atmospheric Physics, 14100 Prague 4, Czech Republic;13. Leibniz-Institut for Astrophysics Potsdam (AIP), 14482 Potsdam, Germany;14. Institute for Space-Earth Environmental Research, Nagoya University, Nagoya 464-8601, Japan;15. Center for Astrophysics and Space Sciences, University of California San Diego, La Jolla, CA 92093, USA;p. Predictive Science Inc., San Diego, CA 92121, USA;q. Radio Astronomy Centre, National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, Tamil Nadu 643001, India;r. Arecibo Observatory, University of Central Florida, Arecibo, PR 00612, USA;s. Indian Institute of Astrophysics, Bengaluru 560034, India;t. Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France;u. IRAP, Université Toulouse III — Paul Sabatier, CNRS, CNES, 31028 Toulouse, France;v. Centre for mathematical Plasma Astrophysics (CmPA), KU Leuven, 3001 Leuven, Belgium;w. Solar–Terrestrial Centre of Excellence—SIDC, Royal Observatory of Belgium, 1180 Brussels, Belgium;x. Center for Space Plasma and Aeronomic Research, The University of Alabama in Huntsville, AL 35805, USA;y. CIRES, University of Colorado at Boulder, Boulder, CO 80309, USA;z. Narula Institute of Technology, Kolkata, West Bengal 700109, India;1. Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138-1516, USA;2. Department of Physics, Harvard University, 17 Oxford Street Cambridge, MA 02138, USA;3. John A. Paulson School of Engineering and Applied Sciences, Harvard University, 150 Western Ave, Allston, MA 02134, USA;4. Faculty of Arts and Sciences Research Computing, Harvard University, 52 Oxford Street, Cambridge, MA 02138, USA;5. The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, USA;1. Department of Physics, St. Xavier''s College, Tribhuvan University, Kathmandu, Nepal;2. Department of Physics and Astronomy, Clemson University, Clemson, SC, USA;3. School of Land Surveying, Geodesy and Mapping Engineering, Technical University of Madrid, Madrid, Spain;4. Department of Physics, Patan Multiple College, Tribhuvan University, Nepal;5. School of Remote Sensing and Geomatics Engineering, Nanjing University Information Science Technology, China;6. Department of Space Sciences, Institute of Space Technology, Islamabad, Pakistan;7. Department of Space Science, The University of Alabama in Huntsville, Huntsville, AL, USA;8. Space and Astroparticle Group, University of Alcalá, Madrid, Spain;9. Center of Pulsed Laser (CLPU), Edif. M5, Parque Científico, C/ Adaja 8, E-37185, Salamanca, Spain;1. Department of Physics, Tripura University, Suryamaninagar, Agartala, Tripura, India;2. Department of Physics, Iswarchandra Vidyasagar College, Belonia, Tripura, India
Abstract:In the homogeneous model of solar radio burst model, the spectral index of the optically thick part of the spectrum is almost independent of the spectral index of the electron energy, while from the optically thin part, the derived electron index δR is far smaller than that derived from the X-ray emission, δX. An inhomogeneous model is proposed, in which, by adjusting two parameters within reasonable limits, we can make δR, derived from both the optically thick and thin parts, to equal δX. The model is exemplified by the 1981 April 27 0800 UT burst.
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