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Understanding the the Central Engine of of GRBGRBDenitsa Staicova, Plamen Fiziev,Sofia University23-th of July 2009, Dubna BLTP seminar


More about GRB●Collimated jets of ultrarelativisticparticles● Extremely powerful: E tot~ 10 51 -10 56erg●Maximal redshift z=8.2 = 13.01billions of light years distance●F~t -α ν -β , α-temporal index, β-spectral index●●●●●Duration – from seconds to daysTwo types of bursts – short andlongTwo phases – prompt emission andafterglowHighly variable in timeObserved by SWIFT, FERMI, AGILEand ground-based observatories


GRB Light Curves profilesNASA compilation of differentprofilesSwift bursts showing various behaviourpatterns: a steep-to-shallow transition (GRB050315); a large flare (GRB 050502B), and agradually declining afterglow (GRB 050826).


Theories of GRB origin; Fireball modelCollapsar model:(long GRBs)-galaxies withactive starformation-softer emission-GRB/SN connectionMerger of doublesystem-NS-NS, NS-BHor the magnetarscenario: (shortGRBs)-older galaxies-harder emission


arxiv:astro-ph/0806.3607


Problems in the theory?●●●●●Flares – evidence of latetime activity of thecentral engineTwo distinct types of GRB– or not?Dark bursts, missing SNWhere are thegravitational waves?!Mechanisms of accelerationthe jets to such energiesUltimately what is thephysical nature of theCentral Engine!


Our modelRotating massive object – a black hole – describedby the Kerr metricPerturbation to the metric described by theTeukolsky Master Equation (s=spin!)


=e tmi S Rrseparates the Tukolsky Master Equation into angularand radial part with ω and A – complex parameters ofseparation


Confluent Heun FunctionSome transformations:Highly non-trivial profile:


The Angular Equation:●u=cos(θ), Ω=aω, s=-1, m=0,±1,±2,... and can besolved in terms of HeunC functions...●The polynomial requirements:imposed on HeunC allows usto obtain:A s=−1, m=− 2 −2 m±2 2 m¿


Radial Equation:Here, the horizons:andare regular singularities, while infinity is irregularsingularity.● This equation can be also solved in terms of HeunC


The solutions:


Boundary conditions:●ω = ω R+ iω Iand ω I>0 is the stability conditions● For the radial equation we impose black hole boundaryconditions:1.On the BH horizon, we have only incoming waves:choice of R 1or R 22.On spatial infinity, the solution is a linearcombination of incoming and outgoing waves.● In order to have only outgoing waves, we need:


Studied by:● Zel'dovich● Starobinsky&Churilov● Teukoslky&PressSuperradianceWe find critical frequency that is COMPLEX:The appearance of imaginary part of the critical frequencyof superradiance could mean the end of the idea ofgravitational bomb!Fiziev P P, D.S., 2009 arxiv: astro-ph:HE/0902.2408, BAJ 10, 2009Fiziev P P, D.S., 2009 arxiv: astro-ph:HE/0902.2411, BAJ 10, 2009


m=0, s=-1, M=1/2More complete results:


The case m=1


Casesm=0 and m=1together


●●●●●●Our model so far...Collimated jets fromthe angular equationCritical frequencyappearanceComplex part of thecritical frequencyTransition tonegative roots forthe criticalfrequency for nakedsingularity case form=0Number of modes forthe case m=0Highly non-trivialrelation ω(a)


Thank you for your attention!For more information:http://tcpa.uni-sofia.bg/research


Bibliography●Burrows, D. N., et al. 2006, ApJ, 653, 468●M. Nysewander, A.S. Fruchter & A. Pe’er, A Comparison of the Afterglows of Short- and Long-Duration Gamma-RayBursts, astro-ph:HE/0806.3607v2●Ferrari V., Gualtieri L., 2008 Class. Quant. Grav. 40 945-970●ABBOTT at al., IMPLICATIONS FOR THE ORIGIN OF GRB 070201 FROM LIGO OBSERVATIONS,arXiv:0711.1163v2[astro-ph]●Teukolsly S A, 1972 PRL 16, 1114 ; Teukolsly S A, 1973 ApJ 185, 635; Press W H, Teukolsly S A, 1973 ApJ 185, 649;Teukolsly S A, Press W H, 1974 ApJ 193, 443●Kokkotas K, 1999 Quasi-Normal Modes of Stars and Black Holes, Living Review 22●Decarreau A, Dumont-Lepage M C, Maroni P, Robert A, Ronveaux A, 1978, “Formes Canoniques de Equationsconfluentes de l’equation de Heun, Annales de la Societe Scientifique de Bruxelles 92, I-II, 53”; Decarreau A, Maroni P andRobert A, 1978 Ann. Soc. Buxelles 92 151.●Ronveaux A (ed.), 1995 Heun’s Differential Equations, Oxford Univ. Press, New York●Fiziev P P, 2006 Class. Qunt. Grav., 23, 2447; Fiziev P P, 2006 Exact Solutions of Regge-Wheeler Equation in theSchwarzschild Black Hole Interior, gr-qc/0603003; Fiziev P P, 2007 Jour, Phys.: Conf. Ser. 66, 012016;●Fiziev P P, Staicova D R, 2009 A new model of the Central Engine of GRB and the Cosmic Jets astro-ph:HE/0902.2408 ;Fiziev P P, Staicova D R, 2009 Toward a New Model of the Central Engine of GRB astro-ph:HE/0902.2411 ;●Fiziev P P, 2009 Classes of Exact Solutions to Regge-Wheeler and Teukolsky Equations, gr-qc/0902.1277\


Picture credits:●●●●●●●●●●http://www.star.le.ac.uk/~julo/research.htmlhttp://www.swift.ac.uk/xrt_curves/http://heasarc.gsfc.nasa.gov/docs/objects/grbs/grbs.htmlhttp://tcpa.uni-sofia.bg/conf/GAS/files/Plamen Fiziev.pdfhttp://tcpa.uni-sofia.bg/conf/GAS/files/GRB Central Engine.pdfhttp://tcpa.uni-sofia.bg/research/DStaicova Lesvos.pdfhttp://tcpa.uni-sofia.bg/researchhttp://imagine.gsfc.nasa.gov/docs/science/know_l1/grbs.htmlhttp://cerncourier.com/cws/article/cern/38294http://en.wikipedia.org/wiki/Gamma-ray_burst


For more information, checkFiziev P P, 2009 Classes of Exact Solutions toRegge-Wheeler and Teukolsky Equations, grqc/0902.1277\

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