# Download MHD Flows in Compact Astrophysical Objects: Accretion, Winds by Vasily S. Beskin PDF

By Vasily S. Beskin

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Extra resources for MHD Flows in Compact Astrophysical Objects: Accretion, Winds and Jets

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2 sin θ Pm (cos θ ), Qm = (2m)! 124) and the eigenvalues qm = −m(m + 1). 125) Here Pm (x) are the Legendre polynomials and the dash indicates their derivatives. Thus, neglecting their dimension, the eigenfunctions of the full operator Lˆ have the form 1. m = 1 • Φ1(1) = r 2 sin2 θ —a homogeneous flow (Fig. 4a), Fig. 4 Eigenfunctions of the operator Lˆ for m = 1 and m = 2. (a) Homogeneous flow. (b) Dipole flow. (c) Flow in the vicinity of the zero point. (d) Quadrupole flow 36 1 Hydrodynamical Limit—Classical Problems of Accretion and Ejection Fig.

Therefore, in the case of accretion the standard singular point must be located at a shorter distance from a compact object. As a result, as shown in Fig. 7, the separatrix characteristics coming out from the nonstandard singular point and moving practically along the sonic surface are again tangent to it at the standard singular point and only later start a spiral motion to the gravitational center. 157) √ 10 − 6Γ −1 Γ +1 ε1 , D12 = 4(2 − b1 )2 − (Γ + 1)(6 − 6b1 + b12 + 2b3 ). 159) 1 under study we have a > −1/8, so that Therefore, for the subsonic motion ε1 at the nonstandard singular point there is no bifurcation of the characteristics.

43) In other words, the transonic flows are two-parameter ones. As shown in Fig. 1, the sonic surface is the X -point on the (distance r )–(velocity v) plane. Fig. 1 Spherically symmetric accretion structure for the given values n ∞ and c∞ and the different values Φ. 56). 5 For the case of the spherically symmetric transonic accretion (the so-called Bondi accretion), when an accreting matter has a zero velocity for r → ∞, the Bernoulli integral E n can be expressed in terms of the velocity of sound at infinity: E n = w∞ = 2 c∞ .