[3] GS Znajek [4] 1982 Thorne 3+1 [5, 6] [7, 8] 3+1 GS GS 2005 Menon Dermer [9] Blandford Znajek [3] GS Pan Yu [10] Komissarov 2004 [11] 2005 M
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1 33 3 Vol. 33, No PROGRESS IN ASTRONOMY Aug., 2015 doi: /j.issn ( ) BZ Grad-Shafranov ( GS ) GS P145.8 A 1 : Blandford-Znajek 1969 Penrose [1], 1977 Blandford Znajek [2] [3] BZ BZ ( ) B (XDB ) zyxu88@ynao.ac.cn
2 [3] GS Znajek [4] 1982 Thorne 3+1 [5, 6] [7, 8] 3+1 GS GS 2005 Menon Dermer [9] Blandford Znajek [3] GS Pan Yu [10] Komissarov 2004 [11] 2005 Menon Dermer [9] 1977 Brennan [12] Lupsasca Kerr/CFT [13, 14] 2001 [11, 15, 16] 2004 Komissarov BZ Uzdensky [17] 2005 Light Surfaces Contopoulos [18] 2013 Light Surfaces 2014 Nathanail [19] Blandford-
3 3 349 Znajek GS Menon Dermer Blandford Znajek 1982 Thorne Mackond 3+1 [5, 6] 3+1 [20] Boyer-Lindquist 2004 Komissarov [11] [11], Boyer-Lindquist t, r, θ, ϕ ds 2 = g tt dt 2 + 2g tϕ dϕdt + g ϕϕ dϕ 2 + g rr dr 2 + g θθ dθ 2. (1) [1] 3+1 ds 2 = (β 2 α 2 ) dt 2 + 2β i dx i dt + γ ij dx i dx j, (2) β 2 α 2 = 1 + 2Mr ρ 2, β ϕ = 2Mra sin2 θ ρ 2, γ rr = ρ2, γ θθ = ρ 2, γ ϕϕ = Σ2 sin 2 θ ρ 2,
4 ρ 2 = r 2 + a 2 cos 2 θ, = r 2 2Mr + a 2, Σ 2 = (r 2 + a 2 ) 2 a 2 sin 2 θ, α 2 = ρ2 Σ 2, β 2 = β2 ϕ γ ϕϕ, g = α γ = ρ 2 sin θ. (3) i = r, θ, ϕ α β M a γ ij β F αβ = 0, (4) β F αβ = I α, (5) F αβ F αβ I α 3+1 B = 0, (6) t B + E = 0, (7) D = ρ, (8) t D + H = J. (9)
5 Komissarov [11] E = αd + β B, (10) H = αb β D. (11) α β α = 1, β = 0 B = H, E = D. (12) t e + S = (E J), (13) t l + L = (ρe + J B) m. (14) e = 1 (E D+B H) l = (D B) m S = E H 2 L = (E m)d (H m)b + 1 (E D + B H)m ϕ 2 [21] F αβ J α = 0. (15) E J = 0, (16) ρe + J B = 0. (17)
6 (10) (11) E T = 0, (18) E P B P = 0. (19) (18) (19) ω = Ω ϕ Ω E = ω B, (20) B Ω = 0, B H ϕ = 0. (21) Ω H ϕ 3 GS Ω r θ 3 [22] B P = Λ γ ( Ω,θ r + Ω,r θ ), (22) Λ r θ Λ,r Ω,θ = Λ,θ Ω,r. (23) Blandford Znajek [3] 1977 ΛdΩ da ϕ E P = Λd (Ω 2 /2) = d ΛΩdΩ, (24) D = D P = Λ α (Ω + βϕ ) dω. (25)
7 3 353 H P = (α 2 β 2 β ϕ Ω) B P α. (26) D P H P [ Λ γρ = r α γ (γ ϕϕω + β ϕ ) γ θθ Ω,r [ Λ θ α γ (γ ϕϕω + β ϕ )γ rr Ω,θ ] + ], (27) [ ] Λ γj ϕ = H θ,r H r,θ = r α γ (α2 β 2 β ϕ Ω) γ θθ Ω,r + [ ] Λ θ α γ (α2 β 2 β ϕ Ω) γ rr Ω,θ. (28) GS 1 dhϕ 2 2Λ dω = α (ρωγ ϕϕ J ϕ ). (29) GS 1 dhϕ 2 2Λ dω = αγ [ ( ϕϕ Ω r γ ( Λ r Λ α γ (γ ϕϕω + β ϕ )γ θθ Ω,r α γ (β2 α 2 + β ϕ Ω)γ θθ Ω,r ) + Ω θ ( Λ ) α γ (γ ϕϕω + β ϕ )γ rr Ω,θ + ) ] γ rr Ω,θ ). (30) ) + θ ( Λ α γ (β2 α 2 + β ϕ Ω Ω Λ H ϕ Ω H ϕ = H ϕ (Ω) 3 Ω Λ H ϕ Znajek [4] H φ = sin2 θ (2r + Ω a)b r = (2r +Ω a) sin θ α + r+ 2 + a 2 cos 2 θ A φ,θ. (31)
8 BZ 1977 Blandford Znajek [3] [23] 4 4 [3] BZ 5 K Blandford Znajek [3] 3+1
9 [24] d 2 E dadt = Sr γ rr = H ϕ ΩB r γ rr, (32) d 2 L dadt = Lr γ rr = H ϕ B r γ rr. (33) GS Blandford-Znajek [3, 16] Blandford-Znajek BZ [25] MHD BZ [26 28] MHD [26, 27, 29, 30] [31] [32 35] BZ MHDBZ [36] 2.4 BZ
10 [3, 5, 6, 37] [38 42] AGN Blandford Znajek [3] BZ BZ [43] [44, 45] 2014 Zamaninasab [46] AGN BZ AGN [47] 3 BZ
11 GS [6, 48, 49] [50 52] [3, 53 55] [56, 57] Ghosh 2000 [58] Thorne Mackond GS 1977 Blandford Znajek [3] Pan Yu [10] Komissarov Menon Dermer H ϕ Λ Ω GS [9] Ω Ω (θ) Λ Λ (θ) f = ΛΩ,θ r 2 1 dhϕ 2 2f(θ) dθ = Ω sin θ d (fω sin θ) + dθ sin θ r 2 [ a 2 Ω sin 2 θ d dθ (fω sin θ) + d dθ ( )] f sin θ. (34) [9] f, Ω f Ω = a 2Mr + + ρ 2 +, (35) f = C 1 sin θ (aω sin 2 θ) 2 1. (36)
12 (a) (b) (c) (d) m = 2 (e) (f) [58] B r = 1 γ B 0 sin θ 2ρ + aωh Ω +, E θ = γω + B r, αb ϕ = H ϕ = γω + B r sin θ, (37) Ω H = a/2mr +
13 (a) (b) [3] r r + d 2 E dadt aω H r 2 ( B0 2 ) 2 sin 2 θ ρ 2 + dl dt = 2π 3 B2 0Ω H + 1 de Ω H dt, (38). (39) 3.4 [24] [59] [12] [13, 14] Brennan [12] Li [60] 2014 Lupsasca Kerr/CFT [13, 14] Menon Dermer Komissarov GS
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16 New Advances in Mangetospheres Analytical Study of Black Hole XU Zhao-yi, WANG Jian-cheng (China Key Laboratory for the Structure and Evolution of Celestial Objects, Yunnan Observatories, Chinese Academy of Sciences, Kunming, China) Abstract: Black hole steady state force-free magnetosphere theories play an important role in the high energy astrophysics study, such as the emission mechanism of relativistic jets in active galactic nuclei, Gamma-ray bursts and ultra-luminous X-ray binaries etc. In order to know the steady state force-free magnetospheres property, One needs to find the solution to the Grad-Shafranov equation(gs). Therefore, finding the analytic solutions of black hole steady state force-free magnetospheres is important for understanding these astrophysical phenomena. In this paper, we give a detailed review on this topic including the histories, recent progresses and future prospects. We first present the black hole electrodynamics and black hole force-free magnetosphere. We introduce the electromagnetic extraction of energy from Kerr black hole: Blandford- Znajek mechanism. We also introduce the black hole force-free magnetosphere in the aspect of application to active galactic nuclei relativistic jets and accretion disk. Next, we outline progress in solving the black hole steady state force-free magnetosphere equations in the past decades, including the solutions of Schwarzschild black hole, the perturbation solutions of low speed rotating black hole, and the asymptotic solutions, with an emphasis on the asymptotic solutions. These solutions are important to study the black hole magnetosphere. We discuss the inspiration of these work on searching analytic solution. The main problem and challenges in solving the GS equation are also introduced. Finally we discuss the future of solving the GS equation. Key words: Kerr black hole; force-free magnetosphere; GS equation; analytical solution
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太阳物理研究与发展* 文/颜毅华 谭宝林 中国科学院国家天文台 中国科学院太阳活动重点实验室 北京 100012 摘 要 太阳是离地球最近的一颗恒星 也是人类可以进行具有一定空间分辨率 地详细观测和研究的唯一恒星 在现代物理学和天文学的发展中扮演着重要的角 色 同时 太阳为人类家园带来了温暖和光明 太阳的剧烈活动也对人类产生重大 影响 探索太阳对现代社会的可持续发展具有极其重要的意义 本文简要介绍了
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科 研 信 息 化 技 术 与 应 用,2015, 6 (1) of identity and the framework of identity management, this paper analyses the development trend of Identity Management
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