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Development of coefficients k_phi and w in accretion flow

Development of coefficients k_phi and w in accretion flow

Development of coefficients k_phi and w in accretion flow

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Abstract:In this paper we consider the magnetohydrodynamicof the hot advectionaccretion disk. We investigate distributioncoefficients k φ(r, z) and ω(r, z) andconnection with behavior of otherparameters in disk. We will show what ishappening in cases of binary system andAGN. Discussion over result.


Introduction• In this paper we investigate the problem for and generation ofcorona in hot magnetic advection accretion disk. We consider theconnection MRI with aid to originate of corona. We chose twowell-known objects:• Cyg X-1 – invisible component of binary system (BS) inconstellation Cygnet – candidate of low massive black hole (BH).• SgrA*– probable representative of super-massive BH. Nucleus ofour galaxy is not selected accidentally. This is most near to usobject до of that type.• Choice of this BS is not accidentally, too. Cyg X-1 and more AGNhave many mutual ait. In theirs spectra we find low and highlystate in X-ray range, reflection from inner regions of disk, Кα ofiron, and γ-ray, too.


Model and resultsIn [4] are constructed non-stationary, non-axisymmetric,one-temperature MHD model of Keplerian accretion diskwith advection in the normal dipole magnetic field of thecentral object. Used equations are: the mass continuity,magnetic flux conservation, equation of motion, andmagnetic induction, without the heating in disc, because thebasic system splits and local average warming for ring is notnecessary and comfortable to use here.The model is elaborate in [2,3,4] and results for theoreticaldisk are presents in [5,6]. Here we check for workability intwo concrete cases, objects representative of low massiveand super-massive BH – Cyg X-1 and Sgr A*.


We accept that:B z3r for equatorial plane and is independence of φ and tGM v ( vr, k , v )2 zr(r rg) mv sH ; mconst ;because disk is KeplerianGMmiT Tvir because disk is advective.kr


The disk is not axis-symmetric, but we willsee that can to use for parameters of disk :FiFi0i(xrr0,Zz/r0)exp[k(x,Z) ω(x,Z)t]Fi0fi(x,Z)There we obtain solution for theperimeters of disk and here will usesome of our results:


The figure show distribution coefficientω(r, z)The development of coefficientω(r,z) shows max in (1,0). This we canexpect, because for φ=0 we have thepoint of inflow on disk. We see thatω(r,z) decrease toward center and toequator plane.


00.20.40.60.81x00.020.040.060.08y-10-5051000.2 0.4 0.6 0.8 1x00.020.040.060.08y00.511.5200.20.40.60.81x00.020.040.060.08y00.20.40.60.81x00.020.040.060.08y051015202530


The figure show distribution coefficientk φ(r, z)The coefficient k φ (r, z) increase fasterthan ω(r,z) decrease, but distributionhas a strong hyperbolical character andescape the equatorial plane.


The figure show distribution coefficientk φ(r, z) by Cyg X-10 00.20.000210000800060004000200000.00020.00040.00060.00080.001y10.80.6 x0.40.2010.80.4x0.60.0004y0.00060.00080.001


The figure show distribution coefficientω(r, z) by Sgr A *0 010000800060004000200000.020.04 y0.060.0810.80.6 x0.40.2010.80.4x0.60.20.020.04 y0.060.08


The figure show distribution coefficientk φ(r, z) by Sgr A *0 00-20-40-60-80-10000.020.04 y0.060.0810.80.6 x0.40.2010.80.4x0.60.20.020.04 y0.060.08


The behavior of coefficient k φ (r, z) indicatethat in depth of disk the instabilitiesreduces.The behavior of coefficient ω(r, z) indicate that inthe inner radiuses of disk the instabilities stayless in time, but we know that region is muchunstable (look like contradiction). Let to seelocal condition v s > v a for Cyg X-1 and Sgr A*.


Figure up is showing profiles over x forz=(0;0.00005) of v s (r, z ) and v a (r, z ) for Cyg X-1(left) and z=(0.0008;0.0009) for Sgr A* (right).Figure down is showing profiles over z forx=(0.05;0.06) of v s (r, z ) and v a (r, z ) forCyg X-1 (left) and x=(0.04;0.05) for Sgr A*(right).


3000025000200001500010000500000 0.02 0.04x0.06 0.08 0.110864200 0.02 0.04x0.06 0.08 0.11000001080000860000640000420000200 2e-05 4e-05 6e-05 8e-05 0.0001y00 0.002 0.004 0.006 0.008 0.01y


To exist magneto-rotation instabilities (MRI) is requirelocal in the flow |v a | < |v s |. But if strongly is to infringethe condition and |v a | >|v s |, that automatic forbiddenMRI.• For Cyg X-1 the condition is infringe by the20-25Rg. Estimate from observation, numericalresults and simulations, for outer radius of thedisk’s corona vary from 15–250Rg [7] forspherical corona to 320–640Rg [8].• For Sgr A* the condition is infringe by the 4-5Rg.• For Cyg X-1 the condition is infringe by the level0.02-0.03Rg over equatorial plane.• For Sgr A* the condition is infringe by the level0.3Rg over equatorial plane.


• Therefore the instabilities in inner regionare existing on the smaller highs, where v sis enough large. But this is not correspondto the behaviors of the coefficients k φ (x,z)and ω(x,z).• It is possible the MRI will not concentratearound equatorial plane. They will be raisewith magnetic line on surface or above disk.


Figure is showing a vector field (v r ,v z ) in disk in(x,z)plane for Cyg X-1 (left) andSgr A* (right).0.0060.080.0050.0040.060.003y0.04 y0.0020.0010.0200.2 0.4 0.6 0.8 1x00.2 0.4 0.6 0.8 1xPlasma is rising with magnetic lines, but with increasing ofheight material piecemeal gliding conversely in disk [1].


Conclusion• The developments of coefficients k φand ω arecoordinate with the behavior of local condition in disc.• If we investigate in detail the local condition along x wecan obtain valuation to outer radius of the disk’scorona [4] and [5].• The profile of the local condition along z show theexistence of channels (layers) with high or loweraccretion values toward the neighborhood.• The appearance of vector fields in the two cases showthat in disks there are no vertical convection.


• Discrepancy of developments of coefficients k φand ωwith the idea that MRI sink in disk and missingconvection suggestive that MRI avoid from disk bydifferent way. This happen most probably by Parkerinstability, because the ВН there are notmagnetosphere, there are no what to hold field come tothe surface and radiating pressure is enough to deflect(saturated) magnetic lines. Therefore MRI contributefor generate of corona and assure her energetic.• Accretion channels reduce the radius of destroying(fume) of disk in corona.


Reference:• Fromang S., Terquem C., arXiv: astro-ph/0402373v1, 16Feb, 2004.• Iankova Kr. D., Filipov L. G., ”Influence of the magnetic field of the compactobject on the accretion disk", July 4th - 11th, 2003, Belogradchik, BULGARIA, inpress.• Iankova Kr. D., Filipov L. G., ”Influence of the magnetic field of the compactobject on the accretion disk – results’’ BAM 2004, 14-18 June, Rogen, Bulgaria,2004, 148. http://www.space.bas.bg/astro/Rogen2004/StPh-2.pdf• Iankova Kr. D.,’’ Ocenka na predimstvata I nedostatacite v metoda za poluchavanena analitichno reshenie na izbrania model’’, collection of scientific reports 2005:”120 years of Unity”, 90-92, 2005,(Bulgarian).• Iankova Kr. D.,’’ Generate of corona on magnetized disk’’, SES'2005, Book I: 31,2005. http://www.space.bas.bg/astro/SES2005/a4.pdf• Iankova Kr. D.,’’ Development of accretion flow with MRI for the select case’’,Third Advanced Research Workshop:"GRAVITY, ASTROPHYSICS ANDSTRINGS AT THE BLACK SEA", June 13-20, 2005, BULGARIA, in press.• Novak M.A., Wilms J., Vanghan B., Dove J., Begelmeni M., AJ 515:726-737, 1999.• Pottschidt K., Konig M., Wilms J., Stanbert R., A&A, 1998.


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