# 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 magnetohydrodynamic**of** the hot advection**accretion** disk. We **in**vestigate distribution**coefficients** k φ(r, z) **and** ω(r, z) **and**connection with behavior **of** otherparameters **in** disk. We will show what ishappen**in**g **in** cases **of** b**in**ary system **and**AGN. Discussion over result.

Introduction• In this paper we **in**vestigate the problem for **and** generation **of**corona **in** hot magnetic advection **accretion** disk. We consider theconnection MRI with aid to orig**in**ate **of** corona. We chose twowell-known objects:• Cyg X-1 – **in**visible component **of** b**in**ary system (BS) **in**constellation Cygnet – c**and**idate **of** low massive black hole (BH).• SgrA*– probable representative **of** super-massive BH. Nucleus **of**our 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 f**in**d low **and** highlystate **in** X-ray range, reflection from **in**ner regions **of** disk, Кα **of**iron, **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 cont**in**uity,magnetic flux conservation, equation **of** motion, **and**magnetic **in**duction, without the heat**in**g **in** disc, because thebasic system splits **and** local average warm**in**g for r**in**g 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 **in**two concrete cases, objects representative **of** low massive**and** super-massive BH – Cyg X-1 **and** Sgr A*.

We accept that:B z3r for equatorial plane **and** is **in**dependence **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 obta**in** 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 thepo**in**t **of** **in****flow** 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) **in**crease fasterthan ω(r,z) decrease, but distributionhas a strong hyperbolical character **and**escape 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) **in**dicatethat **in** depth **of** disk the **in**stabilitiesreduces.The behavior **of** coefficient ω(r, z) **in**dicate that **in**the **in**ner radiuses **of** disk the **in**stabilities 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 show**in**g pr**of**iles 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 show**in**g pr**of**iles 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 **in**stabilities (MRI) is requirelocal **in** the **flow** |v a | < |v s |. But if strongly is to **in**fr**in**gethe condition **and** |v a | >|v s |, that automatic forbiddenMRI.• For Cyg X-1 the condition is **in**fr**in**ge 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 **in**fr**in**ge by the 4-5Rg.• For Cyg X-1 the condition is **in**fr**in**ge by the level0.02-0.03Rg over equatorial plane.• For Sgr A* the condition is **in**fr**in**ge by the level0.3Rg over equatorial plane.

• Therefore the **in**stabilities **in** **in**ner regionare exist**in**g 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 l**in**e on surface or above disk.

Figure is show**in**g a vector field (v r ,v z ) **in** disk **in**(x,z)plane for Cyg X-1 (left) **and**Sgr 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 ris**in**g with magnetic l**in**es, but with **in**creas**in**g **of**height material piecemeal glid**in**g conversely **in** disk [1].

Conclusion• The developments **of** **coefficients** k φ**and** ω arecoord**in**ate with the behavior **of** local condition **in** disc.• If we **in**vestigate **in** detail the local condition along x wecan obta**in** valuation to outer radius **of** the disk’scorona [4] **and** [5].• The pr**of**ile **of** the local condition along z show theexistence **of** channels (layers) with high or lower**accretion** 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 φ**and** ωwith the idea that MRI s**in**k **in** disk **and** miss**in**gconvection suggestive that MRI avoid from disk bydifferent way. This happen most probably by Parker**in**stability, because the ВН there are notmagnetosphere, there are no what to hold field come tothe surface **and** radiat**in**g pressure is enough to deflect(saturated) magnetic l**in**es. Therefore MRI contributefor generate **of** corona **and** assure her energetic.• Accretion channels reduce the radius **of** destroy**in**g(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, **in**press.• 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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