قرص مزود: الفرق بين النسختين
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سطر 18:
ونشاهدها في أجرام منضغطة مثل [[نجم نيوتروني|نجوم نيوترونية]] وحول [[ثقب أسود]] حيث يكفي اكتسابها [[طاقة وضع |لطاقة وضع ]] عالية ناتجة عن [[جاذبية]] الجسم المركزي إلى تألق القرص . بهذه الطريقة وبحسب شدة الاحتكاك بين الجسيمات فيمكن أن تصدر [[موجة كهرومغناطيسية|موجات كهرومغناطسية ]] عالية الطاقة مثلما تنتج من [[تفاعل نووي|تفاعلات نووية]] . وهذا ما يفسر شدة [[ضياء|الضياء ]] العالية التي نشاهدها في [[نجم زائف|النجوم الزائفة]] والتي تراها على الرغم من بعدها الشاسع عنا .
== نموذج قرص ألفا==
افترض كل من نيقولاي شاكورا و راشد سونايف عام 1973
<ref name="SS1973"/>
أن دوامات تحدث للغاز في القرص تكون مصدرا لزيادة [[لزوجة|اللزوجة]]. وبافتراض أن الدوامات تحدث عند سرعات تحت سرعة الصوت واعتبار أن سمك القرص هو أقصي حد لحجم الدوامات فيمكن حساب اللزوجة من المعادلة الآتية:
<math> \nu=\alpha c_{\rm s}H</math>
حيث:
<math>c_{\rm s}</math> [[سرعة الصوت]],
<math>H</math> ارتفاع القرص
<math>\alpha</math> معامل يساوي صفر (في حالة عدم وجود تزويد) أو 1 .
Note that in turbulent motion <math> \nu\approx v_{\rm turb} l_{\rm turb} </math>, where <math> v_{\rm turb} </math> is the velocity of turbulent cells relative to the mean gas motion, and <math> l_{\rm turb} </math> is the size of the largest turbulent cells, which is estimated as <math>l_{\rm turb} \approx H = c_{\rm s}/\Omega</math> and <math> v_{\rm turb} \approx c_{\rm s} </math>, where <math>\Omega = (G M)^{1/2} r^{-3/2}</math> is the Keplerian orbital angular velocity, <math>r</math> is the radial distance from the central object of mass <math>M</math>.<ref>{{Citation | last=Landau and Lishitz | year=1959 | title=Fluid Mechanics | edition=31}}</ref>
By using the equation of [[hydrostatic equilibrium]], combined with conservation of [[angular momentum]] and assuming that the disc is thin, the equations of disk structure may be solved in terms of the <math>\alpha</math> parameter. Many of the observables depend only weakly on <math>\alpha</math>, so this theory is predictive even though it has a free parameter.
Using Kramers' law for the opacity it is found that
:<math>H=1.7\times 10^8\alpha^{-1/10}\dot{M}^{3/20}_{16} m_1^{-3/8} R^{9/8}_{10}f^{3/5} {\rm cm}</math>
<br>
:<math>T_c=1.4\times 10^4 \alpha^{-1/5}\dot{M}^{3/10}_{16} m_1^{1/4} R^{-3/4}_{10}f^{6/5}{\rm K}</math>
<br>
:<math>\rho=3.1\times 10^{-8}\alpha^{-7/10}\dot{M}^{11/20}_{16} m_1^{5/8} R^{-15/8}_{10}f^{11/5}{\rm g\ cm}^{-3}</math>
where <math>T_c</math> and <math>\rho</math> are the mid-plane temperature and density respectively.
<math>\dot{M}_{16}</math> is the accretion rate, in units of <math>10^{16}{\rm g\ s}^{-1}</math>,
<math>m_1</math> is the mass of the central accreting object in units of a solar mass, <math> M_\bigodot</math>, <math>R_{10}</math> is the radius of a point in the disc, in units of <math>10^{10}{\rm cm}</math>, and
<math>f=\left[1-\left(\frac{R_\star}{R}\right)^{1/2} \right]^{1/4}</math>, where <math>R_\star</math> is the radius where angular momentum stops being transported inwards.
The Shakura-Sunyaev <math>\alpha</math>-Disc model is both thermally and viscously unstable.
An alternative model, known as the <math>\beta</math>-disk, which is stable in both sense assumes that the viscosity is proportional to the gas pressure <math>\nu \propto \alpha p_{\mathrm{gas}}</math>.
<ref>{{Citation | last=Lightman and Eardley | year=1974 | title=Black Holes in Binary Systems: Instability of Disk Accretion | periodical=The Astrophysical Journal, | first2=Douglas M. | volume=187 | issue= | last2=Eardley| pages=1 | bibcode=1974ApJ...187L...1L | doi=10.1086/181377 | first1=Alan P. }}</ref>
<ref>{{Citation | last=Piran | year=1978 | title=The role of viscosity and cooling mechanisms in the stability of accretion disks | periodical=The Astrophysical Journal, | volume=221 | issue= | pages=652 | bibcode=1978ApJ...221..652P | doi=10.1086/156069 | first1=T. }}</ref>
Note that in the standard Shakura-Sunyaev model, viscosity is proportional to the total pressure <math> p_{\mathrm{tot}} = p_{\mathrm{rad}} + p_{\mathrm{gas}} = \rho c_{\rm s}^2</math> since
<math>\nu = \alpha c_{\rm s} H = \alpha c_s^2/\Omega = \alpha p_{\mathrm{tot}}/(\rho \Omega)</math> .
The Shakura-Sunyaev model assumes that the disk is in local thermal equilibrium, and can radiate its heat efficiently. In this case, the disk radiates away the viscous heat, cools, and becomes geometrically thin. However, this assumption may break down. In the radiatively inefficient case, the disk may "puff up" into a [[torus]] or some other three dimensional solution like an Advection Dominated Accretion Flow ([[ADAF]]). The ADAF solutions usually require that the accretion rate is smaller than a few percent of the [[Eddington limit]]. Another model is the case of [[Rings of Saturn|Saturn's rings]], where the disk is so gas poor that its angular momentum transport is dominated by solid body collisions and disk-moon gravitational interactions. The model is in agreement with recent astrophysical measurements using [[gravitational lensing]]
<ref>{{Citation | last=Poindexter et al. | year=2008 | title=The Spatial Structure of An Accretion Disk | first3=Christopher S. | last3=Kochanek | periodical=The Astrophysical Journal, | first2=Nicholas | volume=673 | issue= 1| last2=Morgan| pages=34 | arxiv=0707.0003 | doi=10.1086/524190 | first1=Shawn }}</ref>
<ref>{{Citation | last=Eigenbrod et al. | year=2008 | title=Microlensing variability in the gravitationally lensed quasar QSO 2237+0305 = the Einstein Cross. II. Energy profile of the accretion disk | periodical= Astronomy & Astrophysics, | volume=490 | issue= | pages=933 | arxiv=0810.0011 }}</ref>
<ref>{{Citation | last=Mosquera et al. | year=2009 | title=Detection of chromatic microlensing in Q 2237+0305 A | first3=E. | last3=Mediavilla | periodical=The Astrophysical Journal, | first2=J. A. | volume=691 | issue= 2| last2=Muñoz| pages=1292 | arxiv=0810.1626 | doi=10.1088/0004-637X/691/2/1292 | first1=A. M. }}</ref>
.<ref>{{Citation | last1=Floyd et al. | year=2009 | title=The accretion disc in the quasar SDSS J0924+0219 | periodical= ArXiv:0905.2651v1 [astro-ph.HE] | arxiv=0905.2651}}</ref>
==اقرأ أيضا==
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