Appendices Appendix A

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Mathematical Notation Used in this Book

This appendix gives a brief description of the mathematical notation used in this book, especially in Chapters 5 to 9. In all cases scalar quantities are presented in simple math mode. Examples are mass m or M; fundamental constants c, G, etc.; and Greek letters γ, δ, φ, etc.. This does not include components of vectors and tensors, which are discussed below.

A.1 Vector and Tensor Notation for Two- and Three-Dimensional Spaces

Two and three-dimensional space notation is the same, as neither contains a time coordinate.

A.1.1 Two- and Three-Dimensional Vector and 1-Form Notation

Vectors in two and three dimensions are written as bold capital letters in math mode. Examples are momentum and velocity P and V ; electric and magnetic ﬁeld E and B; etc. Components of vectors are written in the same font as the geometrical quantity, but not in boldface and with a upper index indicating which component it represents. Examples: P x, V r, Ey, and Bz. Roman subscripts are sometimes added to vectors or their components to distinguish which object or type of physics problem is being discussed. Examples are the φ velocity of object #2 V2 or orbital velocity in Schwarzschild geometry Vorb,SH. 1-Forms for the above quantities are written in bold lower-case letters, also in math mode. Examples are the momentum and velocity 1-forms p and v; electric and magnetic 1-forms e and b; etc. Components are of these written in the same

D.L. Meier, Black Hole Astrophysics: The Engine Paradigm, Springer Praxis Books, 833 DOI 10.1007/978-3-642-01936 - 4 , © Springer-V erlag Berlin Heidelberg 2012 834 A Mathematical Notation Used in this Book font as the 1-form geometrical quantity, but not in boldface and with a lower index. Examples: pz, vx, er, and by. In ﬂat two- and three-dimensional space, even when the coordinates are curvilinear, there usually is no distinction between vector and 1-form components. This is because they usually are written in a local orthonormal frame rather than a coordinate frame and because the metric in the that frame is simply the identity matrix. For example, in polar coordinates, the velocity V θ is actually the linear velocity V θˆ = rdθ/dt, not the speed of the angular coordinate θ (V θ = dθ/dt). Therefore, θˆ vθˆ = V , so there is no distinction between vectors and 1-forms.

A.1.2 Tensor Notation

Contravariant tensors in two and three dimensions are written as bold, sans serif capital letters. An example is the three-dimensional stress tensor T. Components are written in non-bold sans serif capital letters, with upper indices: Txx. Covariant tensors in two and three dimensions also are bold, sans serif letters, but lower-case is used. The covariant version of the stress tensor is t, and its components are written txx, txy, etc. The metric tensor g follows this form, but its contravariant version does not, because it is the inverse of the metric G = g−1. In order to limit confusion, mixed tensors are avoided in this book.

A.2 Vector and Tensor Notation for Four-Dimensional Spacetime

In order to emphasize the fundamental difference between three-vectors and four- vectors (and between three- and four-dimensional tensors), we use a different notation for spacetime quantities.

A.2.1 Vector and 1-Form Notation in Four-Dimensional Spacetime

As above, four-vector geometric quantities are written as bold capital letters. How- ever, the font is a roman one, not math mode. Examples are four-momentum and four-velocity P and U; four-current J and four-potential A. Components also are non-bold characters of the same font and again with upper indices: Px, Ur, Jy, and Az. Similarly, 1-form quantities in four dimensions are written as bold lower-case roman letters, with their components in non-bold roman font and having lower indices: pz, ux, jr, and ay. A.3 Miscellaneous Notation 835 A.2.2 Tensor Notation in Four-Dimensional Spacetime

Contravariant tensors in four dimensions are written as bold, calligraphic capital letters. Examples are the stress-energy tensor T and the Faraday and Maxwell tensors F and M. The components are written as upper indices: T ww, F xy, Mwz. Because calligraphic letters are available only in upper-case, for covariant four- dimensional tensors we re-use the regular math mode letters. (There should be no ambiguity, as this notation is rarely used for three-dimensional 1-forms in this book. See above.) Examples are the metric g with components gxx, etc or the Faraday 2- form f . As in three-space, the covariant forms are written with the same letter, but in lower-case. The exception again is the metric, because its contravariant form is also its inverse g −1. In the rare case when we need to express a tensor with more than two indices (e.g., the Riemann tensor), we use the Fraktur font: R or Rαβγδ.

A.3 Miscellaneous Notation

Dipole and quadrupole moments often use similar letters to other physical quantities, so here we distinguish them by writing them in a Fraktur font. The same is true of other rare quantities used herein, including three-force per unit volume F in a Fraktur font (as opposed to a simple force F ) and four-force per unit volume F in a script font. Occasionally a vector or tensor of the same spatial dimensions and rank will be needed to indicate the time and spatially-independent coefﬁcients of a sinusoidal wave function. In that case we use the same letter (lower or upper-case) with a slightly different, but related, font. Examples are the Euler font A for the coefﬁcient of the three-vector potential A or the blackboard font A for the four-vector potential A. Appendix B

Derivatives of Vectors and Tensors: Differential Geometry

Physics, and therefore astrophysics, is described by equations that involve the spatial and time derivatives of vectors and tensors. In order to properly describe physics in a curved spacetime (and even in ﬂat spacetime that is spanned by curvilinear coordinates) we will need to understand how gradients and divergences of these quantities are calculated when the coordinates are not Euclidean or Minkowskian. This requires the mathematics of differential geometry, which is a broad subject. Here we provide only a very brief introduction. Gradients and divergences will depend, of course, on how the metric changes with those coordinates. The derivatives of g are best embodied by a single function, called the “Christoffel symbol” or “connection coefﬁcient”, and it takes into account all possible derivatives1 1 ∂g ∂g ∂g Γ ≡ λμ + λν − μν (B.1) λμν 2 ∂xν ∂xμ ∂xλ

The indices λ, μ, and ν range over the dimension of the space (e.g., 0–3 for spacetime). While the connection coefﬁcients appear rather ugly, and the reader may be in- clined to ignore them, they are of enormous importance in physics and even our daily lives. They give rise to • Formulae for the gradient, divergence, and curl in curvilinear coordinates that are routinely used in ﬂuid dynamics, plasma physics, mechanics, etc. • Pseudo-forces like centrifugal and Coriolis forces, which arise because our frame of reference is accelerated. • The force of gravity, which in Einstein’s view is also a pseudo-force, arising because of the curvature of space and time.

1 There are a few places in this book where matrix notation is not adequate, so we shall revert to component notation. This is the case here, and in a few other places, where we must deal with quantities with more than two indices.

D.L. Meier, Black Hole Astrophysics: The Engine Paradigm, Springer Praxis Books, 837 DOI 10.1007/978-3-642-01936 - 4 , © Springer-V erlag Berlin Heidelberg 2012 838 B Vector and Tensor Differentiation B.1 Covariant Gradients in Curved Spacetime

The gradient of a geometric quantity (scalar, vector, tensor) increases the number of indices on that quantity by 1: a scalar becomes a vector; a vector becomes a 2-tensor, etc. Using connection coefﬁcients, the gradient can be written as follows: ∂Φ (∇Φ) = γ ∂xγ ∂Vβ ∇Vβ = + gβλ Γ Vμ γ ∂xγ λμγ λ, μ T αβ " # αβ ∂ αλ μβ λβ αμ ∇T = + g Γλμγ T + g Γλμγ T (B.2) γ ∂xγ λ, μ

The sums in the above formulae are performed over the number of dimensions in the space or spacetime. Similar formulae also exist for 1-forms, 2-forms, etc. ∂v (∇v ) = β − Γ vμ β γ ∂xγ βμγ μ ∂t " # (∇t ) = αβ − gμλ Γ t + gμλ Γ t (B.3) αβ γ ∂xγ αμγ λβ βμγ αλ λ, μ

These are called “covariant” gradients, because they can be used in physical laws that are invariant under any coordinate transformation. Furthermore, the formulae are true for any metric and so are quite amazing, if rather messy. We can simplify the look of them, using the matrix notation we used in Chapters 6 and 7 if we deﬁne a simple derivative ∂γ to be the operator ∂ ∂ ≡ γ ∂xγ

∂γ is similar to ∇γ , but it takes the derivative of only the components of the geometric quantities, not of their unit vectors as well. We then can write equations (B.2) as

∇Φ = ∂Φ " # ∇V = ∂V + g −1 · Γ · V " # " # ∇T = ∂T + g −1 · Γ · T + T · g −1 · Γ (B.4)

While these are much more intuitive than equations (B.3), they have much less computational power, because it is not clear over which indices the dot products occur. B.2 Divergences in Curved Spacetime 839 B.2 Divergences in Curved Spacetime

The divergence of a geometrical quantity is simply the “contraction” of the gradient. This means that we set one upper index equal to the lower differentiating one and sum. Because it requires an upper index, the divergence applies only to vectors and tensors, not forms. Setting γ = β in equations (B.2) and summing over β we have ⎧ ⎫ ⎨ ⎬ ∂Vβ ∇ · V = + gβλ Γ Vμ ⎩ ∂xβ λμβ ⎭ β ⎧ λ, μ ⎫ ⎨ ⎬ ∂T αβ " # (∇ · T )α = + gαλ Γ T μβ + gλβ Γ T αμ (B.5) ⎩ ∂xβ λμβ λμβ ⎭ β λ, μ

However, these can be simpliﬁed considerably by introducing the determinant of the metric

g ≡g (B.6)

Again, we can write these in our matrix notation as 1 ( ∇ · V = ( ∂ · |g| V |g| 1 ( " # ∇ · T = ( ∂ · |g| T + g −1 · Γ : T (B.8) |g|

In three-dimensional curvilinear coordinates, the metric is often diagonal, with 2 elements gii = hi . The vector divergence in equations (B.7) then gives us the familiar form for the divergence in curvilinear coordinates 1 3 ∂ h h h V i ∇·V = 1 2 3 h h h ∂xi 1 2 3 i=1 This equation is useful only for diagonal three-metrics; however, equations (B.7) work for any metric and so are much more powerful. 840 B Vector and Tensor Differentiation B.3 The Metric Has No Gradient or Divergence

If we plug the metric tensor g −1 into the tensor form of equations (B.2), (B.3), and (B.5), and use the deﬁnition of Γ (equation (B.1)), we ﬁnd that

∇ g −1 =0 ∇ g =0 and, therefore, ∇ · g =0. The metric, therefore, has no covariant derivative or divergence, even though its components do change, in general, as we move through spacetime. The covariant derivative ∇, therefore, picks up only those changes in a vector or tensor that are independent of the coordinates, not those that are generated by motion or curvature. This is why ∇ is used to cast the equations of physics in a coordinate-invariant (covariant) form. In fact, we can now return to equation (B.1) and see how it was derived in the ﬁrst place. We begin by simply imposing the requirement that the metric have no gradient or divergence. The formula for Γλμν , therefore, must involve a linear combination of all possible derivatives of the symmetric metric tensor g ∂g ∂g ∂g Γ ≡ a λμ + b λν + c μν (B.9) λμν ∂xν ∂xμ ∂xλ

If we now express ∇g in the general form (B.3), require it to be zero, require Γλμν to be symmetric in μ and ν, and solve for the coefﬁcients a, b, and c, we recover the formula for Γ in equation (B.1). Appendix C

Derivation of the Adiabatic Relativistic Stellar Structure Equations

This appendix derives the equations for the structure and evolution of a relativistic star in spherical symmetry. Because of this assumption, there will be no time- dependent quadrupole moment of the star’s mass and, therefore, no gravitational radiation emitted. This derivation, while fairly basic in relativistic physics is a little beyond the scope of the main part of the book. Nevertheless, it is an important demonstration of the use of the Einstein field equations (7.21) in solving for the time evolution of a relativistic gravitational field and an excellent example of black hole formation. The equations presented here were first derived by Charles Mis- ner (University of Maryland) and David Sharp (Princeton University) [638], and independently by Michael May and Richard White of the Lawrence Radiation Lab- oratory (now known as Lawrence Livermore National Laboratory or LLNL) [639]. We will follow May and White’s work most closely.

C.1 The Spherical Metric in Mass Coordinates

We begin with the spherically symmetric metric written in a manner similar to the Schwarzschild metric

ds2 = −a¯ 2 c2 dt¯2 + ¯b 2 dr2 + r2 dΩ2 (C.1) where dΩ2 = dθ2 +sin2 θdφ2. Indeed, outside the star we do have Schwarzschild −1 1/2 ¯ geometry, with a = b =(1− rS/r) . However, inside the star a¯ and b will be functions of time as well as of the radius r. For many reasons, detailed in Section 5.2.2, it is more convenient to use a coordinate system in which the independent radial coordinate is the integral of rest mass from the center of the star to some ﬁxed speciﬁc value m ≡ ρdV (C.2) V

D.L. Meier, Black Hole Astrophysics: The Engine Paradigm, Springer Praxis Books, 841 DOI 10.1007/978-3-642-01936 - 4 , © Springer-V erlag Berlin Heidelberg 2012 842 C Relativistic Stellar Structure Equations where dV is the proper volume (including the curvature of space) and ρ is the rest mass density only (no internal or kinetic energy included). The amount of rest mass m inside this point will remain ﬁxed during the evolution, but the radius of that shell r(m, t) will change with time. It is helpful in this gauge to think of the star as composed of concentric shells, each with a mass dm = ρdV, which can (1) collapse under their own gravitational weight if there are no other forces, (2) press against one another to keep the star in equilibrium if there are restoring pressure forces, or (3) even explode outward if the pressure can overcome gravity. A given value of m sits at the outer edge of a given mass shell and follows that shell’s motion as the star evolves. Switching from r to the mass coordinate m, then, gives us a new metric

ds2 = −a2 c2 dt2 + b2 dm2 + r2 dΩ2 (C.3) where a, b, and r are functions of m and the new time variable t only (the spherically symmetric assumption). In particular, r will be the outer radius of the spherical mass shell at position m and radial mass width dm. (To be precise, r will be equal to 1/2π times the circumference of the mth spherical shell.) Now, the proper three-dimensional volume element of each spherical shell in this metric is

dV = bdmrdθr sin θdφ

So equation (C.2) becomes 2π π m m = dφ sin θdθ ρr2 bdm 0 0 0 m = 4πr2 ρbdm (C.4) 0 Because the differential of both sides of equation (C.4) must be equal (i.e., dm = 4πr2 ρbdm) we immediately can write down the metric coefﬁcient of dm 1 b = (C.5) 4πr2 ρ

As with Newtonian stellar structure, the choice of mass coordinates automatically enforces the conservation of mass.

C.2 The Field Equations and Conservation Laws

The remainder of the metric coefficients (a and r) and the state variables (ρ and internal energy ε) are determined by two Einstein field equations and two conservation laws. We will use the stress-energy-momentum tensor written in the rest frame C.2 The Field Equations and Conservation Laws 843 of each mass shell (i.e., in the moving [m, t] coordinate system) (equation (6.69)). The Gtt =8πGT tt/c4 Einstein field equation is, then $ & '% c2 ∂ 1 ∂r 2 1 ∂r 2 ε ∂r r 1+ − =4πG ρ + r2 2 ∂m a2 c2 ∂t b2 ∂m c2 ∂m (C.6) and the Gtm component has no source

∂2r 1 ∂a ∂r 1 ∂b ∂r − − (C.7) ∂m∂t a ∂m ∂t b ∂t ∂m Finally, the t and m components of ∇ · T =0are ∂ ε 1 ∂b 2 ∂r ρ + = −ξρ + (C.8) ∂t c2 b ∂t r ∂t ξρc2 ∂a ∂p = − (C.9) a ∂m ∂m where we have deﬁned the inertia per unit rest mass to be

(ε + p) ξ ≡ 1+ (C.10) ρc2

It is helpful, both mathematically and physically, to deﬁne the gravitational mass m ε ∂r M ≡ 2 4πr ρ + 2 dm (C.11) 0 c ∂m which does include both the internal energy and the kinetic energy, as well as rest mass, inside the shell at coordinate m. It also is useful to to deﬁne two quantities 1 ∂r u ≡ (C.12) a ∂t 1 ∂r W ≡ (C.13) b ∂m These will turn out to be the m-component of the four-velocity of the mass shell and a geometric factor W telling us how dm and 4πr2 ρdrare related. The coordinate derivatives of the gravitational mass M have simple expressions ∂M ε ∂r ε =4πr2 ρ + = 1+ W (C.14) ∂m c2 ∂m ρc2 ∂M p ∂r ap =4πr2 u = −4πr2 u (C.15) ∂t c2 ∂t c2 844 C Relativistic Stellar Structure Equations

The ﬁrst of these follows directly from the mass derivative of equation (C.11). The second can be derived by taking the time derivative of that equation, folding in equations (C.7) to (C.10), and integrating over dm. (It also can be derived by computing the [redundant] Grr =8πGT rr/c4 Einstein ﬁeld equation, which is an equivalent amount of work.)

C.3 The Adiabatic, Relativistic Stellar Evolution Equations

We now are in a position to solve for some of the variables and put the equations in simple, familiar forms.

C.3.1 The Mass Shell Geometric Factor

Using equation (C.14) we can replace the right-hand side of equation (C.6) with G∂M/∂m and integrate over dm. Applying deﬁnition (C.13), this gives

u2 2 G M W 2 =1 + − (C.16) c2 c2 r If there were no gravity (G =0), the geometric factor W would be simply the Lorentz factor. On the other hand, if we had gravity but no motion (u =0), then W 1/2 would have the Schwarzschild form 1 − 2 G M/(c2 r) .

C.3.2 The Density Equation

Equations (C.5) and (C.12) can be differentiated with respect to t and m, respectively, and plugged into equation (C.7) to yield an equation analogous to the New- tonian density equation (5.58)

1 1 ∂(ρr2) ∂u/∂m = − (C.17) ρr2 a ∂t ∂r/∂m

This looks exactly like the Newtonian version if we identify 1 ∂ ∂ = (C.18) a ∂t ∂τ as the time derivative in the rest frame of each mass shell (cf., equation (C.12)). C.3 Adiabatic, Relativistic Stellar Evolution Equations 845 C.3.3 Conservation of Energy Equation

If we substitute the mass metric coefﬁcient (equation (C.5)) and its time derivative into the conservation of energy equation (equation (C.8)), we obtain

∂ε (ε + p) ∂ρ = (C.19) ∂t ρ ∂t which is the first law of thermodynamics (equation (5.50)) with no heating or cooling (adiabatic flow). The lack of any heat flow terms (T tm) in the stress-energy tensor is where the adiabatic assumption was made. This ensures that the gas re- mains isentropic.

C.3.4 Equation of Motion in Mass Coordinates

Because the mass shell coordinate system is a moving (Lagrangian) one, it should come as no surprise that the conservation of momentum equation comes mainly from the Einstein ﬁeld equation (the rr one) with only some help from equation (C.9), rather than the other way around. To derive it, we differentiate the equation for the geometric factor W with respect to time ∂W u ∂u G ∂M G M ∂r W = − + (C.20) ∂t c2 ∂t c2 r ∂t c2 r2 ∂t We then substitute into the above equation an expression for ∂W/∂t derived from equations (C.5), (C.7), (C.9), and (C.13)

∂W 4πr2 ∂p ∂r = − (C.21) ∂t ξc2 ∂m ∂t plus the expressions for ∂M/∂t, and ∂r/∂t. The result, after multiplying by c2/u, is 1 ∂u W ∂p G M +4πr3 p/c2 = −4πr2 − (C.22) a ∂t ξ ∂m r2

This is the relativistic version of the Newtonian conservation of momentum in mass coordinates (equation (5.61)). In the non-relativistic Newtonian limit, the mass contributed by pressure and internal energy in equation (C.22) will be negligible (ξ → 1 and 4πr3 p/M c2 → 0), Also, because of equation (C.9), the lapse function a will become be unity throughout the star, so ∂τ = ∂t, and we will have W → 1 as well. So the equation of motion does indeed reduce to the Newtonian one derived in Chapter 5. 846 C Relativistic Stellar Structure Equations C.3.5 Equation of Motion in Schwarzschild–Hilbert-like Coordinates

We also can write the relativistic equation of motion in terms the radial pressure gradient. It still will be in the Lagrangian frame of reference, but will appear more familiar. Because r is a monotonic function of m at any time t, we can write ∂p ∂p ∂r ∂p W ∂p = = Wb = (C.23) ∂m ∂r ∂m ∂r 4πr2 ρ ∂r

So we now can convert equation (C.22) into one involving derivatives in proper time τ and the shell radius r ∂u u2 r ∂p 4πr3 p G M ρ = − 1+ − S − 1+ ξ (C.24) ∂τ c2 r ∂r M c2 r2

The relativistic corrections in equation (C.23) have the following interpretations: acceleration term (inertia due to internal energy and pressure must be included); pressure term (one factor of W comes from the ∂/∂r gradient and one comes from a Lorentz-like boost of the pressure itself); gravitational force (as pressure increases, its gravitational mass must be included, both in the enthalpy inertia and in the inertia of the mechanical force itself). Appendix D

Derivation of the General Relativistic MHD Equations from Kinetic Theory

The equations of general relativistic magnetohydrodynamics, which play a central role in this book, can be derived from the general relativistic Boltzmann equation in a two-step process. First, we take velocity moments of that equation to generate the multi-ﬂuid GRMHD equations. Then we perform weighted sums of those equations, over mass and over charge, to produce conservation laws for mass, charge, four- momentum, and four-current. The derivation presented here follows an article by D. Meier [346] on the generalized Ohm’s law (conservation of current).

D.1 The Multi-Fluid Equations of General Relativistic Magnetohydrodynamics

D.1.1 The Zeroth Moment: Conservation of Particle Number

We begin by re-writing the general relativistic Boltzmann equation (9.2) as ˙ Ui · ∇ℵi + Fi · ∇Pℵi = ℵi, coll (D.1)

1 where Ui = P/mi is a function (like Fi), not a coordinate. It can be shown [346] that the momentum integral of the second term on the left and of the collision term on the right vanish. And, because X and P are independent phase space coordinates, ∇ · Ui ∝ ∇ · P =0, so the zeroth velocity moment of the Boltzmann equation becomes simply 4 ∇ · Ui ℵi d P =0 (D.2)

1 As in Chapter 9, we use the blackboard font to indicate quantities pertaining to a given volume in eight-dimensional phase space (X, P, U, F) and the script font in six-dimensional phase space (X, P, V, F), while regular bold characters are used for average quantities in four- or three-dimensional physical space. See Appendix A.

D.L. Meier, Black Hole Astrophysics: The Engine Paradigm, Springer Praxis Books, 847 DOI 10.1007/978-3-642-01936 - 4 , © Springer-V erlag Berlin Heidelberg 2012 848 D GRMHD Equations

This can be written in a more familiar form if we decompose Ui into an average center-of-mass velocity . m U ℵ d4P U ≡ .i i i i (D.3) ℵ 4 i mi i d P and the drift velocity Vi, which is always orthogonal to U, giving us

Ui = γi (U + Vi) (D.4) where the Lorentz factor for each volume of phase space is deﬁned as

1 − γ ≡− (U · U )=(1− V · V ) 1/2 (D.5) i c2 i i i

The second half of equation (D.5) is true if we measure the components of Vi in the rest frame of the ﬂuid. Note that, while Vi is formally a four-vector, because U · Vi =0, Vi has only three non-zero (spatial) components in the rest frame of the ﬂuid. The w (time) component of Vi is zero and can be ignored. Equation (D.2) now can be written as the conservation of particle species i

∇ · ni (U + Vi)=0 (D.6) where the particle density of species i is 4 3 ni = γi ℵi d P = fi d P (D.7) and the average drift velocity for that species is 1 4 1 3 Vi = γi Vi ℵi d P = Vi fi d P (D.8) ni ni

(Here we have used the relation between ℵi and fi (equation (9.4)) and have performed the integral over the mass shell, as discussed in Section 9.1.) With these deﬁnitions we see that equation (D.3) implies that the mass weighted drift velocity vanishes. ni mi Vi =0 (D.9) i

D.1.2 The First Moment: Conservation of Particle Four-Momentum

The ﬁrst velocity moment of the general relativistic Boltzmann equation can be obtained by ﬁrst multiplying equation (D.1) by Ui. This produces a vector Boltzmann D.1 Multi-Fluid GRMHD Equations 849 equation qi ˙ ∇ · (ℵi Ui Ui)+Ui (Ui · Fi) · ∇P ℵi = Ui ℵi, coll mi c

With Fi given by equation (9.3), the integral of this equation over momentum four- space yields the conservation of four-momentum for particles of species i

∇ · n U U n UV n V U Π [ i i i + i i + i i + i] 1 (D.10) = Ji ·F − ν ni (U + Vi) mi c where we now see two new averaged quantities: the relativistic particle density n ≡ 2 ℵ 4P 3P i γi i d = γi fi d and the beamed drift velocity 1 1 V ≡ 2 V ℵ 4P V 3P i γi i i d = γi i fi d ni ni We also now have a deﬁnition of the partial electric current contributed by each particle species

Ji ≡ qi ni (U + Vi) and the partial pressure tensor Π ≡ 2 V V ℵ 4P V V 3P i γi ( i i i) d = γi ( i i fi) d

Equations (D.6) and (D.10) are the general relativistic multi-ﬂuid MHD equations for each particle species density ni and velocity (U + Vi). These equations do not close (i.e., have the same number of equations as unknowns), because Πi involves the second velocity moment, which we have not computed yet. There are only two ways to continue with the calculation and compute Πi: (1) compute the second velocity moment of equation (D.1) (which will only perpetuate the problem by producing an equation that needs the third velocity moment) or (2) assume a known equilibrium form for fi(P), which allows us to explicitly calculate Πi (and n P also i). We choose the second method and further assume that fi( ) is isotropic over the solid angle in momentum three-space dn f d3P = f 4 π P2 dP ≡ i dP i i dP The partial pressure tensor then becomes diagonal 850 D GRMHD Equations ⎛ ⎞ 0000 ⎜ ⎟ ⎜ 0 pi 00⎟ Πi = ⎝ ⎠ 00pi 0 00 0pi where the partial pressure is given by 1 dn p = PV i dP (D.11) i 3 i dP since P = γi mi Vi.

D.2 The One-Fluid Equations of General Relativistic Magnetohydrodynamics

The most popular form of the MHD equations eliminates all reference to individual particle species i and considers the system to be composed of a single neutral ﬂuid in which currents are generated by the collective drift of charge.

D.2.1 Conservation of Rest Mass and Four-Momentum

If we multiply equations (D.6) and (D.10) by the particle mass mi and then sum over all species i, we reduce these equations to the familiar forms

∇ · (ρ U)=0 (D.12)

1 ∇ · T = J · F (D.13) GAS c

The gas stress-energy tensor obtained from this sum is given by ε 1 T = ρ + UU + [QU + UQ]+p P (D.14) GAS c2 c2 where the projection tensor is given by 1 P = UU + g c2 the rest mass density is given by D.2 One-Fluid GRMHD Equations 851 ρ ≡ ni mi i the total internal energy and total pressure are given by the sum over all particle species ε = εi p = pi i i and the heat ﬂux four-vector is given by Q n 2 V n 2 V − V = i mi c i = i mi c ( i i) i i (The second equality is valid because of equation (D.9).) In addition to the partial pressure pi, we now have an integral expression for the internal (kinetic) energy of a relativistic gas n − n 2 2 − 3P εi =( i i) mi c = mi c (γi 1) fi d or dn ε = ε i dP (D.15) i iK dP

2 where εiK ≡ (γi − 1) mi c is deﬁned as the particle kinetic energy. Since the right- hand side of equation (D.13) can be written as the divergence of a tensor 1 J · F = −∇ · T c EM where T EM is given by equation (6.119). Equation (D.13) then becomes, simply,

∇ · T =0 where T = T GAS + T EM. This exercise, therefore, shows us specifically how to calculate the stress-energy tensor for a conducting fluid in an electromagnetic field. It is this T that must be inserted into Einstein’s field equations (7.21) in order to generate the evolution equations for the gravitational field.

D.2.2 Conservation of Charge and Four-Current

Another summation over all particle species can be done if we instead multiply equations (D.6) and (D.10) by the particle charge qi before summing. We then obtain the conservation of charge and of four-current 852 D GRMHD Equations

∇ · J =0 (D.16)

ω2 1 ∇ · C = p (U + hJ) · F − η (ρ U + J) (D.17) 4π c q q where the spatial current four-vector is given by

J ≡ J − ρq U and is orthogonal to the four-velocity

U · J =0

The total four-current density and charge density are deﬁned as J ≡ Ji i ρq ≡ qi ni i The charge-current tensor looks similar to the stress-energy tensor ε C = ρ + q UU + U J + J U + p P (D.18) q c2 q and the beamed spatial current is deﬁned as J ≡ n V qi i i i

In addition to ρq, some other new charge-weighted thermodynamic quantities appear, like the charge-weighted internal energy 2 3 εq ≡ qi c (γi − 1) fi d P i dn = q c (γ − 1) i dP i 2 i dP i q = i ε m i i i and the charge-weighted pressure D.2 One-Fluid GRMHD Equations 853 q dn p ≡ i PV i dP q 3 m dP i i q = i p m i i i Finally, we see new plasma state variables, like the plasma frequency

& '1/2 q2 n ω = 4 π i i p m i i the electrical resistivity

≡ ν ηq 4 π 2 ωp and the coefﬁcient of the Hall-effect term 4 π q h ≡ i |J| ω2 |J| m p i i which is related to the classical Hall coefﬁcient RH as h RH = |B| ηq c

(|B| being the strength of the magnetic ﬁeld). Equation (D.17) is often referred to as the generalized Ohm’s law. When the −1 left-hand side is small compared to the terms on the right (i.e., when ωp is much smaller than other time scales in the system), we obtain the classical Ohm’s law, with the Hall term 1 (U + h J) · F = η J c q (which eventually reduces to the well-known V = IR Ohm’s law taught in fresh- man physics and electrical engineering classes). If the time-dependent terms on the left-hand side (in the four-divergence of C) are not negligible, the generalized Ohm’s law shows how the current evolves toward its equilibrium value given above. Appendix E

Derivation of the General Relativistic Grad–Schluter–Shafranov¨ Equation

The Grad–Schluter–Shafranov¨ equation is a general statement of force-free degenerate electrodynamics (FFDE) under the assumptions of a steady state and axisymmetry. The non-relativistic version is used to study the structure of Tokamak and other terrestrial and solar system fields, while the relativistic version is used to study the electrodynamics of pulsars and black holes. Here I re-derive the GSS equation in the Kerr metric using the general relativistic notation employed in this book, with the electrodynamic definitions of B, D, E, and H given in Section 9.5.1 (adopted from Komissarov [322]), to arrive at the version published by Uzdensky [486] (but with c = G =1 ; see also [640] for the Schwarzschild case). Equation (E.11) below is useful for analyzing the magnetospheres of black holes in Kerr spacetime, as well as those of pulsars in a flat metric.

E.1 The Magnetic Induction Equation

In the Kerr metric in Boyer–Lindquist coordinates, under the assumption of axisymmetry (∂/∂φ =0) Maxwell’s solenoidal condition (∇·B =0) gives the following poloidal magnetic induction 1 B = ∇Ψ × e (E.1) p R φˆ where Bp = Bp(Brˆ,Bθˆ, 0) and the cylindrical radius is given by Σ sin θ R ≡ ρ and Σ and ρ are the usual Kerr area and radius parameters. The magnetic ﬂux is a function of the poloidal coordinates

D.L. Meier, Black Hole Astrophysics: The Engine Paradigm, Springer Praxis Books, 855 DOI 10.1007/978-3-642-01936 - 4 , © Springer-V erlag Berlin Heidelberg 2012 856 E General Relativistic GSS Equation 1 Ψ(r, θ)= B · dS = RA (E.2) 2π φˆ integrated over a disk surface with radius R that is centered on, and normal to, the rotation axis. Aφˆ is the azimuthal component of the three-vector potential A. The goal of this derivation is to ﬁnd a single partial differential equation for the magnetic ﬂux function Ψ. Then, using secondary equations we will be able to derive all other electromagnetic quantities (B, H, D, and E) from Ψ. The azimuthal component of the magnetic induction comes from Ampere’s` law (with ∂/∂t =0), integrated over the same surface dS

H ˆ I B = φ = − (E.3) φˆ α αRc where Hφˆ is the φ component of the magnetic ﬁeld, α is the Kerr lapse function, and the current distribution function is 1 I = − J · dS (E.4) 2 Because I and Ψ are integrals over the same surface, I is a function of Ψ,or

I = I(Ψ)

Together, equations (E.1) and (E.3) give the complete magnetic induction three- vector for steady-state, axisymmetric FFDE

1 I B = ∇Ψ × e − e (E.5) R φˆ αRc φˆ

E.2 The Electric and Magnetic Field Equations

The degeneracy condition of FFDE (B · D =0; see Section 9.5.2) implies that the electric displacement three-vector must be (equation (9.126)) 1 D = − (V − αβc) × B αc f where β is the Kerr drift vector. (This is also the ideal form of Ohm’s law.) Further- more, in order for B and D to be perpendicular, the field velocity Vf must be in the φ direction only. So we now can define a field angular velocity to be

|V | Ω ≡ f f R Plugging in B from equation (E.5) we obtain D in terms of Ψ E.3 The Charge and Current Densities 857

(Ω − ω) D = − f ∇Ψ (E.6) αc where ω is the angular velocity in the Kerr metric. We also get E in terms of Ψ

Ω E = − f ∇Ψ (E.7) c

Note that, as implied by equations (7.67) D and E are the electric field measured in the rotating and fixed frames, respectively. As they both depend on ∇Ψ only, they are both poloidal functions only. Finally, now that we know D, we can calculate the magnetic field from the right- hand part of equation (9.124) as α R2 I H = 1+ ω (Ω − ω) ∇Ψ × e − e (E.8) R α2 c2 f φˆ Rc φˆ

E.3 The Charge and Current Densities

From Gauss’s law, we can immediately determine the charge density 1 (Ω − ω) ρ = − ∇· f ∇Ψ (E.9) q 4πc α

Calculation of the current density is a little more tricky: it is best done by computing the poloidal (Jp) and toroidal (Jφˆ eφˆ) components separately and then combining the results. Because I = I(Ψ), and therefore

dI ∇I = ∇Ψ dΨ then the poloidal current Jp must be parallel to the poloidal magnetic ﬁeld Bp. From equations (E.2) and (E.4), this proportionality must be 1 dI J = − B p 4π dΨ p which gives us the poloidal component of the current density.

The toroidal component is found by dotting eφˆ into a version of equation (9.122), also with ∂/∂t =0, to obtain c 1 J = ρ (E × B) + (B · J) B φˆ B2 q φˆ B2 φˆ 858 E General Relativistic GSS Equation

The total current density, then, is the vector sum of both components

1 dI J = ρ Ω R e − B (E.10) q f φˆ 4π dΨ

That is, the current is the sum of that flowing along the twisted magnetic field (second term) plus those charges that are dragged around as the magnetic field rotates (first term).

E.4 The GSS Equation

The only independent equation that we have not yet incorporated into this discussion is the φ component of Ampere’s` law (right-hand equation (9.123)). (The r and θ components of Ampere’s` law are redundant with the deﬁnition of the current I.) Because the spatial part of the Kerr metric in Boyer–Lindquist coordinates is diagonal, equation (E.8) gives c (∇×H) = −R ∇· ∇Ψ φˆ R

Inserting this and 4πJφˆ/c into the φ component of Ampere’s` law, and noting that D has no φ component and ∂/∂t =0, and combining some terms, gives us the general relativistic version of the GSS equation / 0 α R2 ∇· 1 − (Ω − ω)2 ∇Ψ + R2 α2 c2 f (E.11) (Ω − ω) dΩ 1 dI2 f f (∇Ψ)2 + =0 αc2 dΨ 2 αR2 c2 dΨ where we have used the relation dΩ ∇Ω (Ψ)= f ∇Ψ f dΨ The GSS equation, plus appropriate boundary conditions, gives us an equation for the scalar potential Ψ, under the assumptions of time independence and axisymmetry, in the stationary and axisymmetric Kerr metric. Appendix F

Derivation of the Equations for Stationary, Axisymmetric Ideal SRMHD in Newtonian Gravity

Ideal, stationary, axisymmetric magnetohydrodynamics is the main method for treating the acceleration and collimation of jets in black hole systems. This appendix begins with the standard ideal MHD vector equations, given in Section 9.5.1, and shows how the assumptions of stationarity and axisymmetry simplify these to the ones used in Section 9.5.6. The discussion generally will follow that in Mestel’s 1961 paper on the subject [641], but we will do the derivations using the relativistic equations. While we will retain the possibility of ﬂow near the speed of light, we will assume a Newtonian gravitational ﬁeld only (i.e., GM/(Rc2) 1), with no appreciable frame dragging (Kerr drift vector β =0). The actual use of the resulting equations to study jet acceleration and collimation is in Section 15.1. The MHD derivations here are the counterpart to the force-free electrodynamic ones given in Appendix E, except there we retained the possibility of a Kerr black hole metric.

F.1 The Axisymmetric, Stationary Equation(s) Parallel to the Magnetic Field

Under the assumptions of stationarity and axisymmetry magnetohydrodynamics generates two main differential equations, one perpendicular to the magnetic field (as in force-free electrodynamics) and a new one parallel to the field. The new equation describes the flow of plasma along the magnetic field lines, and was not needed in FFDE (where we ignored the matter entirely). We will derive the pieces of this equation below from Maxwell’s laws of electromagnetism and from conservation laws for fluid flow. Then we will discuss the cross-field equation in the MHD case.

D.L. Meier, Black Hole Astrophysics: The Engine Paradigm, Springer Praxis Books, 859 DOI 10.1007/978-3-642-01936 - 4 , © Springer-V erlag Berlin Heidelberg 2012 860 F Stationary Axisymmetric MHD F.1.1 Faraday’s and Ohm’s Laws and Conservation of Mass: The Frozen-in Magnetic Field

The time-independent form of Faraday’s law (9.103) states that

∇×E =0 or E = ∇Φ + E0, where Φ is the scalar electric potential and E0 is a vector uniform in space and constant in time. With the ideal Ohm’s law (9.105), Faraday’s law becomes

∇×(V × B)=0 (F.1)

Now, let us decompose V and B into poloidal and toroidal components

V = Vp + Vt B = Bp + Bt where, for example, in cylindrical coordinates in ﬂat space we have

Vp = VRˆ eRˆ + VZˆ eZˆ Vt = Vφˆ eφˆ Equation (F.1) then can be written as two equations, one in the poloidal plane and one in the toroidal direction ∇× × ∇× × − ∇× 0=[ (V B)]p = (Vp Bp)= c (Eφˆ eφˆ) (F.2) ∇× × ∇× × × 0=[ (V B)]t = [(Vp Bt)+(Vt Bp)] (F.3) × × Note that equation (F.2) has only one term because Vt Bt = Vφˆ Bφˆ (eφˆ eφˆ)=0.

F.1.1.1 The Poloidal Velocity – Magnetic Field Relation

First, we will examine the poloidal equation (F.2). It has the solution 1 ∂Φ E =[∇Φ] = φˆ φˆ R ∂φ

But the axisymmetric assumption means that ∂/∂φ =0for any function, so Eφˆ = 0. That is, Vp is parallel to Bp

Vp = K Bp (F.4) where K is a scalar function of (R, Z). F.1 Equations Parallel to the Magnetic Field 861

F.1.1.2 The Toroidal Velocity – Magnetic Field Relation and the Field Angular Velocity

Next, we will examine the toroidal component (F.3). In cylindrical coordinates this can be written as ! ! ∂ ∂ B (V − K B ) + B (V − K B ) (F.5) ∂R Rˆ φˆ φˆ ∂Z Zˆ φˆ φˆ We now can combine this equation with the axisymmetric version of the solenoidal condition 1 ∂(RBˆ) ∂(RBˆ) ∇·B = R + Z =0 (F.6) p R ∂R ∂Z to produce simply V ˆ − K B ˆ V ˆ − K B ˆ B ·∇ φ φ = B ·∇ φ φ =0 p R R

This means that the gradient of the quantity above in the parentheses is zero along a given magnetic ﬁeld line. That is, the following is constant along each ﬁeld line

V ˆ − K B ˆ φ φ = constant ≡ Ω (F.7) R f which we identify as the angular velocity of the magnetic field line Ωf . Why is Vφˆ not equal to RΩf ? The reason is that, if the magnetic field has a toroidal component (Bφˆ), then no matter what the field rotation rate plasma can flow K freely in the eφˆ direction at the velocity Bφˆ, i.e., with the same proportionality as in the poloidal direction. So the total toroidal velocity of the plasma is, therefore, K Vt = Vφˆ eφˆ =( Bφˆ + RΩf ) eφˆ (F.8)

If there were no field rotation (Ωf =0), then plasma would flow along the field line with the same proportionality in all dimensions. On the other hand, if there were no K matter (as in FFDE), then =0and Vφˆ simply would be equal to RΩf . Combining equations (F.4) and (F.8), we find that the total three-velocity and total magnetic field are related as K V = B + RΩf eφˆ

F.1.1.3 Determining the Proportionality Constant

We now can determine the value of K by considering the conservation of mass equation (9.100) 862 F Stationary Axisymmetric MHD 1 ∂(RΩ ) 0=∇·(γρV )=∇·(γρK B)+ f R ∂φ

If we again apply both the axisymmetry and solenoidal conditions, the conservation of mass reduces to the conservation of another scalar along a field line B ·∇(γ K ρ)=0. For mathematical purposes we define this scalar to be another constant k divided by 4π k γ K ρ = constant ≡ (F.9) 4π Note that k is not unitless; it is the ratio of the constant local poloidal mass flux (4πγρV · dSp) to the constant local poloidal magnetic flux (B · dSp), where dSp is a small poloidal area vector. The final combination of the laws of Faraday, Ohm, and mass conservation yields the axisymmetric, stationary frozen-in condition

k V = B + RΩ e (F.10) 4πγρ f φˆ

F.1.2 Conservation of Speciﬁc Angular Momentum

We now will use the toroidal component of the momentum equation (9.101), which also makes use of Gauss’s (9.117) and Ampere’s` (9.116) laws, to derive a third scalar constant along a magnetic ﬁeld line – the angular momentum per unit mass or speciﬁc angular momentum. The full axisymmetric, stationary vector equation of motion in a Newtonian gravitational potential ψ is E ∇·T = − γρ+ ∇ψ (F.11) c2

The component of this along eφˆ has no gravitational force !

1 ∂ R(R TφˆRˆ) ∂(R T ˆ ˆ) + φZ =0 (F.12) R ∂R ∂Z where the two components of the stress tensor are determined from equation (9.113) k h RBˆ R T = γ 1+ RV − φ B φˆˆi 4π c2 φˆ k i h ≡ h/ρ is the enthalpy per unit mass, and i =(Z, R). (Recall that Eφˆ =0because of axisymmetry.) The momentum equation can be combined with the solenoidal condition again to obtain the conservation of another scalar quantity along a magnetic ﬁeld line F.1 Equations Parallel to the Magnetic Field 863 h RBˆ γ 1+ RV − φ = constant ≡ (F.13) c2 φˆ k which we identify as the angular momentum per unit mass of the plasma .

F.1.3 Conservation of Speciﬁc Entropy

The assumption of an adiabatic equation of state in equation (9.112) leads to a fourth quantity that is conserved along a ﬁeld line: the entropy per unit mass

S p ∝ = K = constant (F.14) ρ ρΓ Γ

While entropy must remain constant along a given ﬁeld line, different ﬁeld lines can have different values for KΓ .

F.1.4 Conservation of Speciﬁc Energy

The ﬁnal equation along each magnetic ﬁeld line is the conservation of energy per unit mass. The master energy equation (9.102) in Newtonian gravity is " # ∇· c2 (P − γρV ) = −P ·∇ψ (F.15) with the axisymmetric, poloidal momentum given by k h RBˆ P = γ 1+ − φ Ω B 4π c2 kc2 f p

Dropping one term in equation (F.15) that is proportional to ψ2/c4 and using the solenoidal condition, we obtain a fourth conserved quantity: the Bernoulli constant (speciﬁc total energy)

( − 1) c2 + ψ = constant ≡ Be (F.16) where c2 is the total speciﬁc internal energy of the plasma, including rest mass h RBˆ = γ 1+ − φ Ω (F.17) c2 kc2 f

When (F.16) is combined with (F.10), (F.13), and (F.14), we can eliminate ρ,

Vφˆ, Bφˆ, and p, producing a single equation that relates poloidal velocity to poloidal 864 F Stationary Axisymmetric MHD magnetic field. This energy equation is essentially the equation of motion along each magnetic field line and is governed by the five free parameters of the problem:

• Ωf : field line angular velocity; • k: plasma mass loading of the field line; • , KΓ , Be: specific angular momentum, entropy, and total energy of the plasma.

F.2 The Axisymmetric, Stationary Equation(s) Normal to the Magnetic Field

We have only two remaining equations in the set (9.100) to (9.117) to consider: the R and Z components of the equation of motion (F.11). The projection of these vector components parallel to the poloidal magnetic field is essentially the equation along the field described above. The projection normal to the field is the cross-field equation that is analogous to the GSS equation derived in Appendix E for force-free electrodynamics. Formally, the component normal to B and in the poloidal plane is E (e × b) · ∇·T + γρ+ ∇ψ =0 φˆ c2 where b ≡ Bp/|Bp|. In cylindrical coordinates this equation becomes

b ∂(R T ) b ∂(R T ) ∂T ∂T Zˆ RˆRˆ − Rˆ RˆZˆ + b RˆZˆ − b ZˆZˆ R ∂R R ∂R Zˆ ∂Z Rˆ ∂Z (F.18) T ˆˆ E ∂ψ ∂ψ − b φφ + γρ+ b − b =0 Zˆ R c2 Zˆ ∂R Rˆ ∂Z where 1 h 1 T = p + (B2 + E2) + γ2 ρ + V 2 − (B2 + E2 ) RˆRˆ 8π c2 Rˆ 4π Rˆ Rˆ h 1 T = γ2 ρ + V V − (B B + E E ) RˆZˆ c2 Rˆ Zˆ 4π Rˆ Zˆ Rˆ Zˆ 1 h 1 T = p + (B2 + E2) + γ2 ρ + V 2 − (B2 + E2 ) ZˆZˆ 8π c2 Zˆ 4π Zˆ Zˆ 1 h 1 T = p + (B2 + E2) + γ2 ρ + V 2 − B2 φˆφˆ 8π c2 φˆ 4π φˆ

The cross-field equation (F.18) becomes quite complex as we substitute in the expressions for Tij, so we will not do that here. Specific cases of the cross-field equation, and their implications for jet production in black hole engines, are discussed in Chapter 15. Appendix G

Physical and Astrophysical Constants Used in this Book

Table G.1: Physical constants used in this book

Name Symbol Value in cgs/Gaussian unitsa Value in SI unitsa 23 −1 23 −1 Avogadro’s number NA 6.02214 × 10 mol 6.02214 × 10 mol Boltzmann constant k 1.38065 × 10−16 erg K−1 1.38065 × 10−23 J K−1 Charge on electron e 4.80321 × 10−10 esu b 1.60218 × 10−19 C Electronvolt e 1.60218 × 10−12 erg 1.60218 × 10−19 J Gas constant R 8.31446 × 107 erg mol−1 K−1 8.31446 J mol−1 K−1 Gravitation constant G 6.6738 × 10−8 erg cm g−2 6.6738 × 10−11 Jmkg−2 −28 −31 Mass of electron me 9.1094 × 10 g 9.1094 × 10 kg −24 −27 Mass of proton mp 1.6726 × 10 g 1.6726 × 10 kg Planck’s constant h 6.62607 × 10−27 erg s 6.62607 × 10−34 Js Planck’s constant (/2π) 1.05457 × 10−27 erg s 1.05457 × 10−34 Js Radiation constant a 7.5658 × 10−15 erg cm−3 K−4 7.5658 × 10−16 Jm−3 K−4 Speed of light c 2.997925 × 1010 cm s−1 2.997925 × 108 ms−1 Stefan–Boltzmann constant σ 5.6704 × 10−5 erg s−1 cm−2 K−4 5.6704 × 10−8 Wm−2 K−4 −25 2 −29 2 Thomson cross-section σT 6.65246 × 10 cm 6.65246 × 10 m a Source: National Institute of√ Standards and Technology (http://physics.nist.gov/cuu/Constants/). b Note: 1 esu = 2997924580 4πε0 C.

Table G.2: Astrophysical constants used in this book Name Symbol Value in cgs/Gaussian unitsa Value in SI unitsa Astronomical unit AU 1.496 × 1013 cm 1.496 × 1011 m Light year ly 9.461 × 1017 cm 9.461 × 1015 m Parsec pc 3.086 × 1018 cm 3.086 × 1016 m Solar mass M 1.989 × 1033 g 1.989 × 1030 kg − Solar luminosity L 3.839 × 1033 erg s 1 3.839 × 1026 W Solar radius (average) R 6.955 × 1010 cm 6.955 × 108 m jansky (unit of radiative ﬂux) Jy 10−19 erg s−1 Hz−1 10−26 WHz−1

a Source: International Astronomical Union (http://www.iau.org/science/publications/proceedings rules/units/).

D.L. Meier, Black Hole Astrophysics: The Engine Paradigm, Springer Praxis Books, 865 DOI 10.1007/978-3-642-01936 - 4 , © Springer-V erlag Berlin Heidelberg 2012 References

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Appendix F 641. Mestel, L., Mon. Not. R. Astron. Soc., 122, 473–478, (1961). Glossary

3C Third Cambridge catalog (of radio sources) 21 3CR Third Cambridge catalog (Revised) 20 3CRR Third Cambridge catalog (Revised a second time) 21

AAAS American Association for the Advancement of Sci- 106 ence AAS American Astronomical Society 9 ADAF Advection-Dominated Accretion Flow 520 ADIOS Advection-Dominated Inflow–Outflow Solutions 567 (for accretion disk winds) ADM formalism Arnowitt–Deser–Misner formalism for expressing 246 Einstein’s equations AGN Active Galactic Nucleus 13 AIGRMHD Adiabatic Ideal General Relativistic MagnetoHy- 335 droDynamics AP Alfven´ Point (on the MHD Alfven´ surface) 657 APS American Physical Society 273 AS Alfven´ Surface 368 ASCA Advanced Satellite for Cosmology and Astrophysics 41 ASIAA Astronomica Sinica Institute of Astronomy and As- 819 trophysics (Taiwan) ASJ Astronomical Society of Japan 651 ASP Astronomical Society of the Pacific 48 ATNF Australia Telescope National Facility 94 AU Astronomical Unit 8 AUI Associated Universities, Inc. 19 AXP Anomalous X-ray Pulsar 70

BAL Broad Absorption Line (QSO) 49

D.L. Meier, Black Hole Astrophysics: The Engine Paradigm, Springer Praxis Books, 883 DOI 10.1007/978-3-642-01936 - 4 , © Springer-V erlag Berlin Heidelberg 2012 884 Glossary

BATSE Burst And Transient Source Experiment, on the 101 Compton Gamma-Ray Observatory BEL Broad Emission Line (QSO) 566 BH Black Hole 109 BL Boyer–Lindquist (coordinate system) 235 blazar Generic name for highly variable AGN (BL Lacer- 32 tae objects, OVV quasars, etc.) BLR Broad-Line Region (of AGN) 16 BLRG Broad-Line Radio Galaxy 22 blue blazar see HBL 32 BP Blandford and Payne 1982 paper on non-relativistic 645 MHD winds from accretion disk [507] BSO Blue Stellar Object (early name for QSO) 43 BSSN method Baumgarte–Shapiro–Shibata–Nakamura 272 method for solving Einstein’s equations BZ Blandford and Znajek 1977 paper on model for 616 black hole magnetospheres [484]

CD Current-Driven 717 CDI Current-Driven Instability 717 CfA Center for Astrophysics (Harvard University) 820 CGRO Compton Gamma-Ray Observatory 101 CGS Centimeter–Gram–Second (system of units) 513 Chandra Chandra X-ray mission 120 CITA Canadian Institute for Theoretical Astrophysics 49 CND Circum-Nuclear Disk 54 CNO Carbon–Nitrogen–Oxygen (nuclear burning cycle) 384 CO Carbon Monoxide 456 Compton depth (y) measure of photon optical depth and energy transfer 333, 513 by Compton electron scattering CR Co-Rotation (disk radius) 605 CS Cusp Surface 367 CSIRO Commonwealth Scientiﬁc and Industrial Research 67 Organisation, Australia CUP Cambridge University Press 729 CV Cataclysmic Variable (binary star) 405

DD Doubly-Degenerate (binary star) 402

EBBH Equal-mass Binary Black Hole 268 ED ElectroDynamics 656 Eddington ratio ratio of a source’s total radiative luminosity to the 60 Eddington luminosity for its mass EGRET Energetic Gamma-Ray Experiment Telescope, on 89 the Compton Gamma-Ray Observatory Glossary 885

EM ElectroMagnetic 192 EMRIBH Extreme Mass-Ratio Inspiral Black Hole 268 ESAC European Space Astronomy Centre 741 ESO European Southern Observatory 117 EUV Extreme UltraViolet (radiation) 806

FB Flaring Branch (of neutron star Z sources) 74 FBG diagram Fender–Belloni–Gallo diagram; see HID 95 FFDE Force-Free Degenerate Electrodynamics 335 FIDO FIDucial Observer (coordinate system) 225 FIX FIXed (FIDO) coordinate system 224 FMS Fast Magnetosonic Surface; classical fast surface 368 FMSS Fast Magnetosonic Separatrix Surface 682 FR Fanaroff & Riley radio source morphological 21 classiﬁcation, 1974 paper [38] FSRQ Flat Spectrum Radio Quasar 25

GHz Giga-Hertz (billion cycles per second) 36 GJ Goldreich–Julian (pulsar magnetosphere model) 594 GLAST Gamma-ray Large Area Space Telescope; a.k.a. 89 Fermi gamma-ray telescope GRB Gamma-Ray Burst 65 GRHD General Relativistic HydroDynamics 335 GRMHD General Relativistic MagnetoHydroDynamics 297 GRO Gamma-Ray Observatory; see CGRO 94 GRS GRanat Source 92 GSFC Goddard Space Flight Center 99 GSS Grad–Schluter–Shafranov¨ (general relativistic 345 magnetosphere equation) GW Gravitational Wave 256 Gyr Giga-year (billion years) 36

H I atomic Hydrogen 456 H II ionized Hydrogen 53 HartRAO Hartebeesthoek Radio Astronomy Observatory 36 HB Horizontal Branch (of neutron star Z sources) 74 HBL High-frequency BL Lacertae object 32 HD HydroDynamics 359 HF QPO High Frequency Quasi-Periodic Oscillation 80 HiBAL High-ionization Broad Absorption Line QSOs 49 HID Hardness–Intensity Diagram 788 HLX Hyper-Luminous X-ray source 117 HMXB High-Mass X-ray Binary 75 886 Glossary horizon, (magneto)sonic locus of points in space beyond which component 681 of ﬂow characteristics along streamlines all have the same sign horizon, black hole Surface surrounding the collapsed star interior to 3, 224, which events cannot affect the outside universe 236 HP Horizon-Penetrating (coordinate system) 234 HR diagram Hertzsprung–Russell (color–magnitude) diagram 96 HST Hubble Space Telescope 19 HyLIRG Hyper-Luminous InfraRed Galaxy 45 HYMOR HYbrid MORphology (FR I/II) radio source 22

ICC Interstellar Cloud Core 321 IDV Intra-Day Variable blazar 34 IGM InterGalactic Medium 22 IKI Institut Kosmicheskix Issledovanii (Space Research 334 Institute, Moscow) IMBH Intermediate Mass Black Hole 13 IMF Initial Mass Function (for newborn stars) 99 INTEGRAL INTErnational Gamma-Ray Astrophysics Labora- 127 tory IR InfraRed (radiation) xx IRAS Infrared Astronomy Satellite 44 IRS InfraRed Source 125 IS Island State (of neutron star atoll sources) 74 ISCO Innermost Stable Circular Orbit (of a black hole) 231 ISM InterStellar Medium 21 IXO Intermediate X-ray luminosity Object; ULX 117

JCMT James Clerk Maxwell Telescope 45 JPL Jet Propulsion Laboratory xxi JWST James Webb Space Telescope 111

KACST King Abdulaziz City for Science and Technology 36 KER KERr (metric) 235 KER–NEW KERr–NEWman (metric) 244 KFD Kinetic- (energy) Flux-Dominated 663 KH Kelvin–Helmholtz 717 KHI Kelvin–Helmholtz Instability 717 KITP Kavli Institute for Theoretical Physics 598

LB Lower Banana state (of neutron star atoll sources) 74 LBL Low-frequency BL Lacertae object 32 LBV Luminous Blue Variable (star) 474 LCB Li, Chiueh, and Begelman 1992 paper on cold, rela- 673 tivistic MHD winds [537] Glossary 887

LF QPO Low Frequency Quasi-Periodic Oscillation 81 LGRB Long-duration Gamma-Ray Burst 102 LIGO Laser Interferometer Gravitational wave Observa- 255 tory LINER Low-Ionization Nuclear Emission-line Region 53 LIRG Luminous InfraRed Galaxy 44 LISA Laser Interferometer Space Antenna 255 LLAGN Low-Luminosity AGN 52 LLNL Lawrence Livermore National Laboratory (formerly 391 Lawrence Radiation Laboratory) LMC Large Magellanic Cloud 87 LMXB Low-Mass X-ray Binary 75 LNRF Local Non-rotating Reference Frame (FIDO coordi- 237 nate system) LoBAL Low-ionization Broad Absorption Line QSOs 49 LSU Louisiana State University 708

MACHO MAssive Compact Halo Object 87 MBH Massive Black Hole 790 MCG Morphological Galaxy Catalog 41 MDAF Magneticallly-Dominated Accretion Flow 531 MERLIN Multi-Element Radio Linked Interferometry Net- 29 work MFP Modified Fast Point (on the MHD modified fast sur- 657 face) MFS Modified Fast Surface; FMSS 661 MHD MagnetoHydroDynamics xx MHz Mega-Hertz (million cycles per second) 21 microquasar Binary black hole system, usually with a jet; μQSR 13 MIT Massachusetts Institute of Technology 93 MK Mega-Kelvin; million kelvins 78 MOV MOVing-body (coordinate system) 224 MPG Max-Planck-institute for Gravitational physics 258 MRI Magneto-Rotational shearing Instability 374 MSFC Manned Space Flight Center 117 MSP Modified Slow Point (on the MHD modified slow 684 surface) MSS Modified Slow Surface; SMSS 684 MSSSO Mount Stromlo & Siding Springs Observatories 87 Myr Mega-year (million years) 54

N-galaxy Galaxy (generally elliptical) with a bright Nucleus; 23 NLRG, BLRG NAOJ National Astronomical Observatory of Japan 246 NB Normal Branch (of neutron star Z sources) 74 888 Glossary neutrinosphere the surface of last neutrino absorption in a source 387 NGC New General Catalog (of Nebulae and Clusters of 14 Stars) NLR Narrow-Line Region (of AGN) 16 NLRG Narrow-Line Radio Galaxy 22 NLSy1 Narrow-Line Seyfert (Type 1) galaxy 42 NOAO National Optical Astronomy Observatory 60 NRAF Non-Radiative Accretion Flow (computational ap- 549 proximation to RIAF/ADAF) NRAO National Radio Astronomy Observatory 22 NRHD Non-Relativistic HydroDynamics 355 NRMHD Non-Relativistic MagnetoHydroDynamics 335 NS Neutron Star 109 NSF National Science Foundation, USA 19 NuSTAR Nuclear Spectroscopic Telescope ARray 46

OGLE Optical Gravitational Lensing Experiment 87 OIS Observer-at-Inﬁnity/Synchronous (coordinate sys- 238 tem) ONeMg Oxygen–Neon–Magnesium (stellar core) 386 peribarathron minimum distance of star orbiting a BH 447 PFD Poynting- (energy) Flux-Dominated 663 photosphere the surface of last photon absorption in a source 484, 569 PNS Proto-Neutron Star 108 PP Papaloizou–Pringle (instability) 670 PWN pulsar wind nebula 69

QPO Quasi-Periodic Oscillation 80, 90 QSO Quasi-Stellar Object; optically-identiﬁed quasar 43 (usually RQQ) QSR Quasi-Stellar Radio source; quasar 13 quasar QUAsi-StellAr Radio source 13 red blazar see LBL 33 RIAF Radiatively-Inefﬁcient Accretion Flow; ADAF 55 RIKEN RIKEN science institute (Japan) 680 RLQ Radio Loud Quasar; classical quasar 13 RMS Root Mean Square 325 ROSAT ROentgen SATellite 72 RQQ Radio Quiet Quasar 47 RRAT Rotating RAdio Transient 71 RSG Red SuperGiant star 395 RXTE Rossi X-ray Timing Explorer 93 Glossary 889

SAS-1 First Small Astronomy Satellite (Uhuru) 73 SAS-2 Second Small Astronomy Satellite 72 SASI Standing Accretion Shock Instability 391 SBH Stellar-mass Black Hole 88 scattersphere the surface of last photon scattering in a source 567 SCH SCHwarzschild (metric) 222 SCUBA Submillimeter Common-User Bolometer Array 45 SDSS Sloan Digital Sky Survey 48 SEW Super-Eddington Wind 582 Seyfert Galaxy (generally spiral) with a bright nucleus, orig- 16 inally discovered by Carl Seyfert; AGN SGR Soft Gamma-ray Repeater 70 SGRB Short-duration Gamma-Ray Burst 102 SH Schwarzschild–Hilbert (coordinate system) 222 SHB Short Hard Burst; SGRB 102 SIM Space Interferometer Mission 435 SIS Singular Isothermal Sphere (distribution of stars) 417 SISSA Scuola Internazionale Superiore di Studi Avanzati 508 SLE Shapiro–Lightman–Eardley (accretion disk solu- 512 tion) SMBH SuperMassive Black Hole 3 SMC Small Magellanic Cloud 91 SMG SubMillimeter Galaxy 45 SMS Slow Magnetosonic Surface 368 SMSS Slow Magnetosonic Separatrix Surface 682 SN SuperNova 65 SNR SuperNova Remnant 118 SPH Smooth Particle Hydrodynamics 155 SPL Steep Power-Law (X-ray binary accretion state) 777 SRMHD Special Relativistic MagnetoHydroDynamics 335 SS Shakura–Sunyaev (accretion disk solutions) 496 STScI Space Telescope Science Institute 117 surface, critical locus of points in space where ﬂow characteristics 362, 681 appear or disappear surface, separatrix locus of points in space where component of ﬂow 368, 681 characteristics along a streamline changes sign surface, singular locus of points in space where denominator of a 488, 682 mathematical accretion/wind equation vanishes SXT Soft X-ray Transient source 77

TOV equation Tolman–Oppenheimer–Volkoff relativistic stellar 287 structure equation traceless-Lorenz gauge see TT gauge 256 TT gauge Transverse–Traceless gauge for the Einstein equa- 256 tions 890 Glossary

UB Upper Banana state (of neutron star atoll sources) 74 UC University of California 287 UCLA University of California Los Angeles 46 UCSB University of California Santa Barbara 552 UCSC University of California Santa Cruz xix UFO Ultra-Fast Outﬂow (from AGN central engines) 794 ULIRG Ultra-Luminous InfraRed Galaxy 45 ULX Ultra-Luminous X-ray source 117 UNAM Universidad Nacional Autonoma´ de Mexico´ 91 UT University of Texas 122 UV UltraViolet (radiation) xx UVOIR UltraViolet–Optical–InfraRed (radiation) 24

VH Very High (X-ray binary accretion state) 777 VHS Very High State (for X-ray binaries) 90 VK Vlahakis and Konigl¨ 2003 paper on warm, relativis- 692 tic MHD winds [368] VLA Very Large Array 19 VLBA Very Long Baseline Array 819 VLBI Very Long Baseline Interferometry 17 VMS Very Massive Star 118, 410 VTST Vlahakis, Tsinganos, Sauty, and Trussoni 2000 pa- 685 per on warm, non-relativistic MHD winds [549]

WC Wolf–Rayet star with strong Carbon emission lines 395 WD White Dwarf 402 WLRG Weak-Lined Radio Galaxy 53 WN Wolf–Rayet star with strong Nitrogen emission lines 395 WNE see WN 396 WO Wolf–Rayet star with strong Oxygen emission lines 395 WPVS Wamsteker, Prieto, Vitores, Schuster et al. Hα 796 galaxy survey

XDIN X-ray Dim Isolated Neutron star 71 XMM X-ray Multi-mirror Mission; a.k.a., XMM Newton 120 XRB X-ray binary 7 XTE X-ray Timing Explorer; see RXTE 95

ZAMO Zero-Angular-Momentum Observer (FIDO coordi- 237 nate system) ZAMS Zero-Age Main Sequence (main locus of stars in HR 785 diagram) Index of Names

Abel, Tom, 414 Blandford, Roger D., 17, 26, 39, 479, Abramowicz, Marek, 95, 515 582, 610, 614, 624, 636, 642, Akiyama, Shizuka, 730 655, 656, 660, 664, 666, 672, Alfven,´ Hannes O. G., 364 685, 701, 714, 721, 759, 761 Aloy, Miguel Angel,´ 708 Bogovalov, Sergey V., 656, 680, 687 Andrew, Bryan H., 30 Bolton, John G., 64 Anninos, Peter, 336 Bondi, Sir Herman, 439, 442, 487 Antonucci, Robert, 38, 39, 671 Boroson, Todd A., 60, 792 Argelander, Friedrich W. A., 30 Boyer, Robert H., 235 Arnowitt, Richard L., 246 Bromm, Volker, 414 Browne, Ian W. A., 29 Baade, W. H. Walter, 68, 84 Burns, Jack, 713 Backer, Donald, 83 Burrows, Adam, 391 Bahcall, John N., 48 Baker, John, 272, 276 Camenzind, Max, 672 Balbus, Steven A., 374, 547, 551 Camm, G. Leslie, 448 Bash, Frank N., 123 Campanelli, Manuela, 272, 274 Baumgardt, Holger, 123 Campbell, W. Wallace, 14 Baumgarte, Thomas W., 272 Castro-Tirado, Alberto J., 92, 105 Becklin, Eric E., 124, 125 Celotti, Annalisa, 32 Begelman, Mitchell C., 119, 391, 492, Centrella, Joan M., 272 515, 555, 582, 656, 673, 674, Chadwick, Sir James, 68 684, 782 Chandrasekhar, Subrahmanyan, 63, 161 Bell, S. Jocelyn, 64 Chen, Xingming, 525 Belloni, Tomaso, 93, 95, 776 Cheung, C. C., 820 Berger, Edo, 110 Chiang, James, 49, 564 Bicknell, Geoffrey, 22, 710, 822 Chiu, Hong-Yee, 24 Biermann, Peter L., 589 Chiueh, Tzihong, 673, 674, 684 Blaes, Omer M., 552 Clarke, David, 706, 710, 713 Cohen, Marshall H., 27

D.L. Meier, Black Hole Astrophysics: The Engine Paradigm, Springer Praxis Books, 891 DOI 10.1007/978-3-642-01936 - 4 , © Springer-V erlag Berlin Heidelberg 2012 892 Index of Names

Cohn, Haldan, 448 Fender, Robert, 74, 95, 741, 747, 751, Colgate, Stirling, 650 755, 766, 773 Comastri, Andrea, 32 Fendt, Christian, 597 Combes, Franc¸oise, 453 FitzGerald, George F., 179 Contopoulos, Ioannis (John), 597, 628, Flammang, Richard A., 489 656, 665, 673, 675, 678, 680, Fossati, Giovanni, 32, 34 692 Fowler, William A., 63 Conway, John, 29 Fragile, P. Christopher, 336, 558, 650 Coroniti, Ferdinand V., 620, 636 Frank, Juhan, 448 Couette, Maurice M. A., 371 Freitag, Marc D., 422 Cowling, Thomas G., 551 Friedrichs, Kurt O., 364 Curtis, Heber D., 14, 19 Fryer, Chris L., 393, 730 Czerny, Bozena,˙ 515, 525 Gallo, Elena, 95, 766 Danby, J. M. Anthony, 448 Gammie, Charles F., 336, 339 De Villiers, Jean-Pierre, 336, 556, 625, Garofalo, David, 632, 672, 817, 820, 653 830 Deser, Stanley, 246 Gebhardt, Karl, 121 Di Matteo, Tiziana, 751 Gehrels, Neil, 110 Doppler, Christian A., 189 Genzel, Reinhard, 54, 125 Dreyer, John L. E., 14 Gerssen, Joris, 122 Duncan, G. Comer, 705, 708, 721 Ghez, Andrea, 8, 125 Duncan, Robert C., 70 Ghisellini, Gabriele, 32 Dunlop, James S., 59 Giacconi, Riccardo, 63, 64 Gillessen, Stefan, 54, 55 Eardley, Douglas M., 507, 512, 514, Godon, Patrick, 648 519 Goldreich, Peter, 594, 597, 599 Ebisuzaki, Toshikazu, 431, 464, 808 Grad, H., 344 Eddington, Sir Arthur, 5, 10 Green, George, 145 Edgington, Samantha, 648 Greiner, Jochen, 93 Eggleton, Peter P., 472 Grifﬁths, Richard E., 118 Einstein, Albert, 165, 177, 209, 210, Groot, Paul J., 407 217, 273 Gunn, James E., 68 Eisenhardt, Peter M. E., 45 Gursky, Herbert, 63 Elitzur, Moshe, 792 Elvis, Martin, 816 Haehnelt, Martin G., 429 Emden, J. Robert, 157 Halpern, Jules P., 42, 72 Esin, Ann A., 527 Hameury, Jean-Marie, 77 Euclid of Alexandria, 166, 176 Hansen, Brad M. S., 125 Euler, Leonhard, 155 Hardee, Philip, 706, 719 Harding, Alice K., 603 Faber, Sandra M., 429, 443 Harmon, B. Alan, 94 Falcke, Heino, 587, 589, 759 Harris, Daniel E., 820 Fanaroff, Bernard L., 21 Harrison, Fiona A., 46 Fath, Edward A., 14 Hawley, John F., 336, 374, 547, 551, 625 Index of Names 893

Hazard, Cyril, 23 Komissarov, Serguei S., xx, 246, 335, Heckman, Timothy M., 53 336, 339, 614, 617, 619, 628, Heger, Alexander, 393, 397, 481, 730, 639, 641, 700, 716 744 Konigl,¨ Arieh, 26, 39, 656, 685, 692, Heinz, Sebastian, 751 694, 699 Hewish, Antony, 64 Kormendy, John, 801 Hirose, Shigenobu, 552, 625, 653 Krasnopolsky, Ruben, 664 Hirotani, Kouichi, 634, 639 Krolik, Julian H., 552, 625 Hjellming, Robert M., 94 Kudoh, Takahiro, 246, 629, 639, 650 Ho, Luis C., 57, 123, 792 Kulsrud, Russell M., 448 Hoffmeister, Cuno, 30 Hoﬂich,¨ Peter, 406 Lacy, Mark, 59 Holt, Stephen S., 72 Lagrange, Joseph-Louis, 148 Honma, Fumio, 508 Lane, Jonathan H., 157 Hoyle, Sir Fred, 439, 442 Larson, Richard B., 432 Hubble, Edwin P., 14 Lasota, Jean-Pierre, 77, 91, 515 Hughes, Philip A., 705, 708–710, 721 LeBlanc, James M., 391, 704 Hughes, Scott A., 479 Li, Hui, 650 Hulse, Russell A., 84 Li, Zhi-Yun, 664, 673, 674, 684 Hutchings, John B., 25, 48 Lightman, Alan P., 448, 507, 512, 514, 519 Ichimaru, Setsuo, 519 Lind, Kevin, 648, 710, 714 Lindquist, Richard W., 235 Jackson, John D., 165 Liu, Bifang, 525 Jackson, Robert E., 429, 443 Livio, Mario, 498, 642, 653 Janiuk, Agnieszka, 525 Long, Knox S., 117 Jeans, Sir James H., 412 Longair, Malcolm S., 701 Jogee, Shardha, 454, 456 Lorentz, Hendrik A., 185, 194 Julian, William H., 594, 597, 599 Lorenz, Ludwig V., 194 Lousto, Carlos O., 272 Kafka, Peter, 35 Lovelace, Richard V. E., 605, 655, Kato, Shoji, 508 656, 665, 673, 690 Kauffmann, Guinevere A. M.-I., 429 Lynden-Bell, Donald, 419, 646, 650 Kaufman, Michele, 45 Lyttleton, Raymond A., 439 Kazanas, Demosthenes, 597 Kerr, Roy P., 234 Maccarone, Thomas J., 120, 128 Khachikian, Edward Ye., 16 Macdonald, Douglas A., 246 Khokhlov, Alexei, 406 MacFadyen, Andrew I., 108, 646 King, Andrew, 77, 119, 430, 805, 812 MacLeod, John M., 30 King, Ivan, 417 Mahadevan, Rohan, 520 van der Klis, Michiel, 74, 737, 739, Maillard, Jean-Pierre, 126 742, 826 Malin, David, 15 Kluzniak,´ Włodek, 95 Maraschi, Laura, 32 Koide, Shinji, xx, 238, 240, 246, 250, van der Marel, Roeland P., 57 336, 620, 629, 639, 641, 651 Margon, Bruce H., 81 Koldoba, Aleksander V., 605 Markarian, Benik E., 16 894 Index of Names

Markoff, Sera, 587, 695, 696, 757, Nakamura, Masanori, 356, 650, 710, 759, 818, 821 712, 717, 718, 820, 822 Marscher, Alan, 821 Nakamura, Takashi, 272 Matsumoto, Ryoji, 508, 650 Narayan, Ramesh, 520, 583, 638 May, Michael M., 841 Natarajan, Priyamvada, 479 Mazurek, Ted J., 406 Nelemans, Gijs, 400, 407 McClintock, Jeffrey E., 762, 775, 777, Neugebauer, Gerald, 124, 125 801 Newman, Ezra T., 244 McKinney, Jonathan C., 336, 339, 558, Newton, Sir Isaac, 133, 166 617, 619, 628, 638, 698, 700, Nishikawa, Ken-Ichi, 708, 719 721 Nordstrom,¨ Gunnar, 210 McLure, Ross J., 59 Norman, Michael L., 704, 710, 713 McMillan, Stephen L. W., 118, 422, Noyola, Eva, 122 784 Meier, David L., 22, 309, 391, 480, O’Leary, Ryan M., 421 515, 558, 568, 648, 650, 670, Ogilvie, Gordon, 498, 642, 653 695, 710, 714, 717, 782, 847 Oppenheimer, J. Robert, 287 Meissner, F. Walther, 619 Osmer, Patrick S., 43 Merloni, Andrea, 751 Osterbrock, Donald, xix, 42 Merritt, David, 432, 448 Ostriker, Jeremiah P., 68 Messier, Charles, 14, 64 Owen, Frazer N., 22 Mesz´ aros,´ Peter, 103 Paczynski,´ Bohdan, 103, 510 Metzger, Mark R., 101 Padovani, Paolo, 60 Meyer, Friedrich, 525 Paolini, Frank, 63 Meyer-Hofmeister, Emmi, 525 van Paradijs, Johannes (Jan), 101 Michel, F. Curtis, 614 Parker, Eugene N., 486, 487 Migliari, Simone, 741, 747, 751, 773 Payne, David G., 642, 648, 656, 660, Miller, John C., 508 666, 672, 685, 714, 759 Miller, Joseph S., 38, 39 Pearson, Timothy J., 27 Miller, Mark A., 405, 708, 721 Perley, Richard A., 29 Milosavljevic,´ Milos,ˇ 125, 432 Phinney, E. Sterl, 636 Minkowski, Hermann, 68, 178 Pineda, Jorge L., 452 Minkowski, Rudolph L. B., 68 Piran, Tsvi, 106 Mirabel, I. Felix, 91, 93, 94 Pogge, Richard, 42 Misner, Charles W., 165, 246, 841 Poisson, Simeon-Denis,´ 145 Mizuno, Yosuke, 719 Polko, Peter, 695, 697, 759 Moore, Joseph H., 14 Portegies Zwart, Simon F., 118, 126, Morgan, Edward H., 93, 776 422, 784 Muno, Michael P., 776 Postnov, Konstantin A., 399, 401 Murdin, Paul G., 88 Pretorius, Frans, 272 Murphy, David W., 29 Price, Richard M., 246, 512 Murray, Norman, 49, 564 Pringle, James, 479, 498, 514 Nakamura, Fumitaka, 414 Proga, Daniel, 49 Ptak, Andrew, 118 Punsly, Brian, 620, 636 Index of Names 895

Pythagoras of Samos, 166 Shibata, Kazunari, 246, 629, 639, 644, 645, 648, 650 Quataert, Eliot, 520 Shibata, Masaru, 272 Shields, Gregory A., 447, 478 Readhead, Anthony C. S., 17, 18, 29 Shklovskii, Iosif S., 73 Rees, Sir Martin J., 17, 27, 103, 448, Slipher, Vesto M., 14 576, 701 Smarr, Larry, 704 Remillard, Ronald A., 93, 762, 775– Smith, Harding E., 383 777, 801 Smith, Malcolm G., 43 Rhoads, James E., 105 Smith, Michael D., 704 Ricci-Curbastro, Gregorio, 218 Soleri, Paolo, 766 Rich, R. Michael, 122 Spitkovsky, Anatoly, 599, 733 Riemann, G. F. Bernhard, 213 Stanek, Krzysztof Z., 114 Riley, Julia M., 21 Stawarz, Łukasz, 820 ´ Roche, Edouard A., 446 Stern, Daniel, 45 Rodriguez, Luis F., 91, 93 Sunyaev, Rashid A., 334, 494, 496, Romanova, Marina M., 605, 606, 608, 507, 551, 795 650, 690, 737 Sutherland, Peter G., 601 Rosen, Alexander, 705 Szuszkiewicz, Ewa, 508, 515 Rossi, Bruno B., 63 Ro´za˙ nska,´ Agata, 525 Taam, Ron, 776 Ruderman, Malvin A., 601 Takahashi, Masaaki, 620, 626, 628, Rupen, Michael P., 94 631, 635 Russell, David, 766 Tan, Loke K., 122 Ryle, Sir Martin J., 17, 64, 701 Tanaka, Yasuo, 41 Tassis, Konstantinos, 452, 454 Sadun, Alberto, 710 Taylor, Joseph H., 84 Salmonson, Jay D., 336 Teukolsky, Saul A., 286 Salpeter, Edwin E., 99, 803 Thompson, Christopher, 70 Sathyaprakash, B. S., 258, 267 Thorne, Kip S., 165, 242, 246, 269, Sauty, Christophe, 680, 685 489, 512 Scalo, John M., 411 Thorsett, Stephen E., 113 Scheuer, Peter A. G., 701 Tingay, Steven, 94 Schluter,¨ A., 344 Titarchuk, Lev G., 334, 795 Schmidt, Maarten, 23, 36, 52, 818 Tolman, Richard C., 287 Schmitt, John L., 30 Tomimatsu, Akira, 626, 628, 631, 635 Schwarzschild, Karl, 222 Toth,´ Gabor,´ 336 Schwarzschild, Martin, 222 Tout, Christopher A., 400 Seyfert, Carl K., 16 Tremaine, Scott, 816 Shafranov, Vitalii D., 344 Trussoni, Edoardo, 680, 685 Shakura, Nikolay I., 494, 496, 507, Tsinganos, Kanaris, 680, 685 551 Turner, Neal J., 552 Shapiro, Stuart L., 272, 286, 448, 512, Turnshek, David, 50, 51 514 Sharp, David H., 841 Uchida, Yutaka, 644, 645, 648 Ulvestad, James S., 122 896 Index of Names

Umemura, Masayuki, 414 Urry, C. Megan, 60 Ustyugova, Galina V., 605, 608, 645, 650, 656, 690 Uzdensky, Dmitri A., 598, 628, 630, 633, 646, 855

Van Riper, Kenneth, 286 Velusamy, Thangasamy, 452 Vlahakis, Nektarios, 656, 685, 692, 694, 699 Volkoff, George M., 287

Wald, Robert M., 618 Walker, R. Craig, 15 Wang, Lifan, 86, 729 Weaver, Thomas A., 397, 744 Webster, B. Louise, 88 Weedman, Daniel W., 16 Werner, Michael J., 43 Wheeler, J. Craig, 391, 406, 447, 478, 480, 729 Wheeler, John A., 24, 48, 165 White, Richard H., 841 Wiita, Paul J., 510 Wilson, James R., 391, 480, 704 Winkler, Karl-Heinz A., 704 Wood, Roger, 419 Woosley, Stanford E., 108, 383, 393, 397, 730, 744 Wright, Edward L., 45

Yi, Insu, 520, 583 Young, Peter J., 447, 478 Yu, Qingjuan, 816

Zepf, Stephen E., 120 Zhang, S. Nan, 94 Znajek, Roman, 610, 614, 636, 761 Zwicky, Fritz, 68, 84 Zytkow,˙ Anna N., 489 Subject Index

Accretion of angular momentum, 437, tidal disruption accretion rate, 475–481, 537–541, 558 448–451 in binary systems, 476–477 tidal disruption of stars by BHs, in black hole mergers, 268–277, 446–448 479–480 tidal orbit, 447 spin–orbit coupling, 274 tidal radius/Roche limit, 446, in collapsing supernova cores, 480– 461–463, 465, 466, 468, 483 481 Accretion of matter, efﬁciency onto central BHs in AGN/globular compared with nuclear burning, clusters, 477–480 438 onto central BHs in galaxy merg- onto black holes, 231, 239, 438 ers, 478–480, 817–818, 830 onto Jupiter, 438 accretion disk/hole alignment, onto neutron stars, 439 479, 480, 830 onto the earth, 438 BH spinup and spindown, 476, onto the Sun, 438 478–480, 616, 635, 818 onto white dwarfs, 438 galaxy core spinup, 478 Accretion of matter, general, 437–475 spin–orbit coupling, 277, 479 critical surfaces, 698, 699 Accretion of matter, carburetion of in binary systems, 470–475 fuel in collapsing supernova cores, 475 in binary systems onto BHs in the ISM, 439–442 Roche/tidal stripping of com- onto central BHs in AGN/globular panion star, 471–474 clusters, 442–470 stars in galactic centers, 444–448 onto central BHs in galaxy merg- BH mass limit for tidal dis- ers, 790, 802–806, 812–813 ruption, 447 stagnation surface, 698, 699 loss cone, angle, 448 wind, ingoing, 698, 699 loss cone, depletion, 434, 448 wind, outgoing, 699 loss cone, reﬁlling, 434, 448

D.L. Meier, Black Hole Astrophysics: The Engine Paradigm, Springer Praxis Books, 897 DOI 10.1007/978-3-642-01936 - 4 , © Springer-V erlag Berlin Heidelberg 2012 898 Subject Index

Accretion of matter, magnetically-dom- Accretion of matter, sources of fuel inated disk theory, 529–547 gas in early-type galaxy mergers magnetically-advective (transitional) cluster inspiral does not fuel accretion, 532–536, 768 SMBHs, 469–470, 811–812 physical structure, 532–533 interstellar gas from mergers, stability, 535 812–813 thermal structure, 533 gas in late-type galaxy centers, magnetically-dominated accretion 451–470 ﬂow (MDAF), 535–547, 768, bar accretion process, 452–455 825 cloud collisions vs. tidal dis- ADAF vs. MDAF, 546–547 ruption, 458–459 example MDAF disk, 542–544 cluster tidal stripping, 465–468 MDAF “end-game” accretion, dynamical friction of H I clumps, 544–546 460–464 physical structure (magneto- dynamical friction process, 455– centrifugal accretion), 535– 460 542 dynamical friction time, 460, singular (Alfven)´ surface, 538 461, 465 singular and non-singular so- nuclear star-formation ring/shock, lutions, 537–541 454, 461–465 thermal structure, 542 star cluster inspiral, 462, 464– observational appearance, 766– 470 771 gas in the ISM, 439–442 simulations, 558–560 accretion by a moving star, 440– Accretion of matter, numerical simu- 442 lations accretion by a stationary star, general MRI simulations, 547– 440–441 560 generic Bondi–Hoyle–Lyttleton limitations, 548–549 accretion, 442 power and promise, 547–548 mass transfer in binary systems, global MRI simulations, 555–560 470–475 non-radiative, with jets, 555– Roche lobe overﬂow, 472–474 558 dynamical, 473 radiative, 558–560 secular, 474 local MRI simulations, 549–553 thermal, 474 Cowling anti-dynamo theorem, wind from companion, 474– 549, 551 475 Maxwell stress, 549–551 stars in galactic centers, 442–451 Reynolds stress, 549–551 mean free path for star–star shearing box approximation, encounters, 446 549 two-body relaxation, 445–446 semi-local MRI simulations, 551– Accretion of matter, spherical wind/ 555 accretion theory radiation-pressure-dominated, thermal, sub-Eddington (Bondi) 552–555 accretion, 485–492 Subject Index 899

accretion equation, polytropic, thermal structure, geometrically non-relativistic, 486–489 thick accretion equation, polytropic, “slim” (super-Eddington) disks, relativistic, 489–490 515–519, 780, 781, 783, 825 general solutions, 486 ADAF (very sub-Eddington) isothermal, 488 disks, 519–525, 765, 768, regular solutions, 486–488 825 singular/critical (sonic) surface, SLE disks (unstable), 511–515 486–488 thermal structure, geometrically thermal, super-Eddington (Begel- thin man) accretion, 490–492 SS disks, “inner” region, 503– advection of photons, 490–491 504, 776, 780, 781, 783, 825 Bondi vs. Begelman accretion, SS disks, “middle” region, 502– 491–492 503, 505, 765, 768, 774, 776, photon mean free path, 492 780, 781, 783, 825 trapping radius, 490–491 SS disks, “outer” region, 499– Accretion of matter, turbulent disk the- 502, 505, 765, 768, 774, 776, ory, 492–529 825 instabilities, 504–508 Active galactic nuclei, xix, 13–55, see secular (viscous), “inner” re- also Black holes, massive; gion, 507, 509 Black holes, supermassive thermal, “inner” region, 507– BALs, 48–50, 61, 450, 451, 566, 509 567, 671, 755, 796–798, 806, thermal, SLE model, 515 812, 826, 829 numerical models, 508–511, 519, HiBALs vs. LoBALs, 49, 51 521, 525–529 blazars, 30–37, 60, 679 observational appearance, 494– BL Lacertae objects, 30, 32, 496, 764–766, 771–784 37, 679, 821–822 physical structure, 493–498 blue blazars/HBLs, 32–34, 37 alpha-model, 496–498 IDVs, 33–35 effective temperature, 495 radio selected, 32 frictional heating, optically thick red blazars/LBLs, 32–34, 37 spectrum, 494–496 X-ray selected, 32 one-zone approximation, 494 BSOs, 42–43 stability, 507 components vertical disk magnetic ﬁeld, 498 BLR, 16, 22, 24, 791–796, 798, simulations, 549–558 806, 828 theoretical models, 492–529, 536, central engine, xix, 7, 16, 24, 546, 765, 768, 774, 776, 780, 25, 38, 53–55, 106, 478, 790– 781, 783 801, 805, 807–809, 811, 812, thermal structure, general, 498– 819 529 dusty torus, 38–42, 46, 49, 53, parameters, 500–501 60, 478, 791 Σ–m˙ plane, 506, 526 light cusp, 9, 57, 121, 445, stability, 507–508 449, 821, 822 900 Subject Index

NLR, 16, 22, 24, 39, 46, 791 RLQs/QSRs, 13, 23–37, 42, UFO, 776, 794–795, 797, 829 45, 47–51, 59–61, 63, 425, warm absorber, 41–42 766, 774, 791, 796, 810, 815– evolution, 35–37, 52 823, 826, 829, 830 H II nuclei, 46, 52–53 RQQs/QSOs, 41–52, 58–61, host galaxies, 14, 17, 32, 47–48, 425, 754, 766, 774, 776, 790– 59, 60, 276, 449, 789, 790, 801, 804, 816, 828 796, 807 radio galaxies, xix, 6, 13, 17–23, “inactive” galactic nuclei, 55–58, 40, 52, 53, 60, 74, 425, 447, 122, 425, 443, 807 529, 701, 710, 818, see also LINERs, 46, 52–53, 800 Black holes, supermassive LLAGN, 52–55, 93, 127, 425, BLRGs, 22, 24–25 449, 450, 775, 789, 790, 800, FR I radio sources, 21, 22, 24, 807 36–37, 51, 679, 695, 708– radio cores, 53 725, 775, 818–823, 830 models, see also Black holes, mas- FR I–II break, 22, 29, 816, sive (MBHs): accretion mod- 823 els FR I–II dichotomy, 819, 830 central ionizing source, 791, FR II radio sources, 21, 22, 792, 795, 828 24, 29, 36–37, 50, 51, 59, broad line clouds, 791–794 60, 679, 695, 701–712, 723, narrow line clouds, 38–40, 791 725, 796, 797, 818, 822– ultra-fast outﬂows, 794–795, 823, 830 797, 829 HYMORs, 22 radio properties of AGN, 790, N-galaxies, 22–24, 47, 53, 790 796–801, 805–806, 810, 815– NLRGs, 22 823 WLRGs, 53 QSOs, see Active galactic nu- Seyfert galaxies, 6, 13–17, 22, clei: quasars: RQQs 38–44, 47, 49, 52, 53, 59– QSRs, see Active galactic nu- 61, 85, 94, 113, 425, 443, clei: quasars: RLQs 449–451, 454, 511, 529, 564, quasars, xix, 4–6, 10, 13, 23– 689, 760, 789–801, 804, 806, 37, 52, 55, 64, 65, 74, 91– 808, 828, 829, see also Black 94, 97, 101, 108, 115, 117, holes, massive 121, 180, 264, 425, 429– dwarf Seyfert galaxies, 52–53 430, 443, 447, 449–451, 469, NLSy1s, 42, 61, 450, 795–796, 470, 483, 496, 523, 529, 561, 798, 800, 801, 806, 826, 829 564–567, 747, 760, 789–801, Type 1, see Active galactic nu- 803, 810–812, see also Black clei: Type 1: Seyferts holes, supermassive Type 2, see Active galactic nu- FR I quasars, 24 clei: Type 2: Seyferts FR II quasars, 21, 24, 29, 37, transition-type, 52–53 50, 59, 796, 797 Type 1 FSRQs, 25–27, 29, 32–34, 36, QSOs, 42–43, 47–52, 790–801, 37, 119, 679 828 Subject Index 901

radio galaxies, see Active galac- gravitational waves from inspi- tic nuclei: radio galaxies: BLRGs raling binaries, 263–270 Seyferts, 14, 16, 22, 38–44, chirp mass, 266 51, 790–801, 828 chirp signal, 265, 266 Type 2 coalescence time, 265–266, 268 HyLIRGs, 45, 46, 53, 425, 434, EBBHs, 267, 268 785, 798, 811, 812 EMRIBHs, 267, 268 LIRGs, 44–46, 53, 458, 459 LIGO/LISA predictions, 266– QSOs, 43–46, 49, 804 268 radio galaxies, see Active galac- gravitational waves from merg- tic nuclei: radio galaxies: NL- ing binaries, 268–277 RGs numerical relativity, 268–277 Seyferts, 16, 22, 38–42, 44, orbital hangup, 273–275, 404 53, 791, 804 perturbation methods, 269 SMGs, 45 post-Newtonian methods, 269 ULIRGs, 45, 46, 111, 425, 434, mass function, 7, 142 458, 459, 785, 798, 811, 812, neutron star, see Neutron stars(NSs): 824 binary Type 3 orbits AGN/QSOs, 46–47 circular, 140–142 uniﬁcation of AGN, 23–35, 37– general, 135–137, 142–143 40, 42–43, 48–50, 58–61, Keplerian frequency, 142 789–823, 828–830 Lagrangian points, 472 orbital phase angle, 140, 141 Binary black holes (BBHs), see dif- Trojan points, 472 ferent mass classes, e.g. Black X-ray (XRBs), xx, 4, 13, 42, 142, holes, stellar-mass (SBHs): 334, 397, 472, 476, 580, 670, binary 696 Binary stars jets, 827 black hole, see different mass classes, masses, 7 e.g. Black holes, stellar-mass theoretical models, 746–760 (SBHs): binary X-ray novae/SXTs, 77–78, 91– close, types 92, 519 contact, 472 Black body detached, 472 multi-colored, 496, 747, 789 semi-detached, 472 Planckian distribution, 315, 318, doubly-degenerate, 402, 407–408 329, 496 effective binary potential, 471, radiation, 6, 45, 78, 495 643, 644 radius, 6 evolution, see Stellar evolution: Black hole astrophysics summary binary stars accretion power, see also Accre- gravitational waves from BH ring- tion of matter, ... down, 269, 270 low m˙ , 746–747, 750–752 kick velocities, 275–277 intermediate/hard-state m˙ , 746– 747, 750–753 902 Subject Index

intermediate-to-high m˙ , 747, viscous transport, 291, 493– 752–753 498, 585 high sub-Eddington m˙ , 747– exhaust systems, energy 748, 754 loss down the hole, 291, 522, moderate super-Eddington m˙ , 640, 777 “slim” disk accretion, 748– photon loss, 291, 498–529 750, 754–755 thermal- and radiation-driven high super-Eddington m˙ , super- wind loss, 291, 562–589 Eddington wind, 748–750, fueling and carburetion, 291, 435– 754–755 481 jet launching Black holes by rotating accretion disks, 755– Galactic population, 99–100, 760, 757 see also Sources in the Milky by rotating BHs, 755–757 Way: black holes jet acceleration and collimation horizon MHD jet models, 758–760 definition, 3 thermal jet models, 757–758 formation, 270–289, 405 jet power magnetic field, 609–641 observed radio luminosity es- Schwarzschild, 223–224, 229– timates, 751 233 total jet luminosity, 751 Kerr, 236, 699, 756 jet suppression Kerr–Newman, 245 by super-Eddington accretion, of SBHs, 743 671, 754 of IMBHs, 784 in the ADAF-to-MDAF tran- of MBHs, 790 sition, 753 of SMBHs, 810 in the geometrically thick-to- magnetospheres, accreting, 621– thin disk transition, 753 641 Black hole binaries (BHBs), see dif- black hole spindown, 615–616, ferent mass classes, e.g. Black 818 holes, stellar-mass (SBHs): BZ process/effect, 638, 640, binary 742, 755–757 Black hole engine closed vs. open field solutions, combustion chamber, 291, 481– 630–634 562 field line types, 624–625 energy generation by gravita- GJ space charge density, role tional accretion, 127, 437– of, 625–630 439, 490–492, 522, 546, 571, magnetic Penrose process, 635, 736, 746–750, 816 639–640 engine block, 381–435 negative energy at infinity, 639– exhaust systems, angular momen- 640 tum sources of black hole magnetic electromagnetic winds and jets, field, 622–625 291, 589–725 very weak intrinsic magnetic gravitational waves, 254–277 fields, 622–623 Subject Index 903

when disk does not reach hori- in SBHs, 766–771, 827 zon, 625–635 in IMBHs, 786–787, 828 when disk reaches into ergo- in MBHs, 806 sphere, 635–640 in SMBHs, 806 wind, ingoing, 634–635, 698, soft state, 771–775 699 SS disk “middle” region model, wind, outgoing, 634–635, 699 773–775 magnetospheres, isolated, 609– fluctuation spectrum, 772–773 621 photon spectrum, 772–773 BZ process/effect, 615–616, 619– suppression of MHD disk jet 620, 634 in the soft state, 773–775 force free model, 614–616 in SBHs, 771–775, 827 frame dragging, 611, 621 in IMBHs, 787–788, 828 GJ space charge density, role not in MBHs or SMBHs, 789 of, 619–620 unstable state, 775–777 GSS equation and singular sur- SS disk “inner” region model, faces, 611–614, 627, 853– 775–777 858, 864 “middle” region-like (soft) sub- numerical models, 616–621 state, 775–776 prograde vs. retrograde BHs, ADAF-like (hard) substate, 775– 612–613 776 weak intrinsic magnetic fields, limit cycle behavior, 775–776 610–611 unsteady jet ejection, 775–777 wind, ingoing, 620–621 in SBHs, 775–777, 827 wind, outgoing, 621 in IMBHs, 788, 828 Black holes, accretion states in MBHs, 790–795, 806–809, hard state (with jet), 762–771 828–829 ADAF model, 764–766 in SMBHs, 807–809 fluctuation spectrum, 763, 766 SPL state, 777–781 photon spectrum, 763–766 “slim” disk model, 777–781 ADAF steady jet radio power, fluctuation spectrum, 777–780 766 photon spectrum, 777, 778 in SBHs, 764–766, 827 suppression of MHD disk jet in IMBHs, 786–789, 828 in the SPL state, 779, 780 in MBHs, 807 in SBHs, 777–781, 826, 827 in SMBHs, 807 in IMBHs, 788, 828 intermediate hard/outlier state, 766– in MBHs, 795–798, 805–809, 771 829 MDAF model, 766–771 in SMBHs, 812–813 band-limited source fluctuation super-soft state, 781–784 spectrum, 770–771 super-Eddington wind model, band-limited source photon spec- 781–784 trum, 769–770 in SBHs, 781–784, 826, 827 MDAF steady jet radio power, in IMBHs, 788–789, 828 767–769 in MBHs, 803–805, 807–809 904 Subject Index

in SMBHs, 812–813 predicted hard state sources in Black holes, formation ISM, 786, 828 SBHs, see Black holes, stellar- jet production, see Black hole mass (SBHs): formation astrophysics summary: jet... IMBHs, see Black holes, inter- Black holes, massive (MBHs), 13– mediate mass (IMBHs): for- 16, 39–42, 52–55, 789–809, mation 828–829, see also Active galac- MBHs, see Black holes, massive tic nuclei: Type 1, 2; Seyfert (MBHs): formation galaxies; LINERs; LLAGN SMBHs, see Black holes, super- definition, 13, 790 massive (SMBHs): forma- accretion models, 802–809, 824, tion see also Active galactic nu- Black holes, intermediate mass (IMBHs), clei: models 13, 57, 115–129, 163, 411, LLAGN as the hard state, 807, 427, 430–435, 464, 784–789, 824 823, 828 outliers(?) as intermediate states, definition, 115–116, 784 806, 824 accretion models, see Black hole Type 1/2 AGN as the unstable astrophysics summary: ac- state, 806, 824 cretion power NLSy1s and BAL AGN as the binary, 786–789 SPL state, 805–806, 824 predicted hard state sources, hidden and unveiled AGN as 786–787 the super-Eddington wind state, ULXs as soft-state super-micro- 803–805, 824 quasars, 787–788 binary, 432–435 predicted unstable state sources, formation, growth, and fueling, 788 801–809 predicted SPL state sources, in galaxy mergers (hidden and 788 unveiled AGN), 802–806 predicted super-Eddington wind with cluster inspiral, 807–809 sources, 788–789 with interstellar gas, 451–470 formation, 408–423, 784–786, 828 with stars, 442–451, 807 from many SBHs in star clus- without galaxy mergers, 806– ters, 421–422 809 in globular cluster core col- horizon, 790 lapse?, 418–420 jet production, see Black holes, in Pop III VMSs and super- supermassive (SMBHs): jet massive stars, 409–414, 785– production 786 Black holes, stellar-mass (SBHs), 87– in young Pop I/II star clusters 114, 117, 127, 129, 588, 743– and VMSs, 118, 414–423, 784, 791, 799, 805, 807, 815, 784–785, 828 819, 821, 826–829 horizon, 784 definition, 63, 743 isolated Subject Index 905

accretion models, see Black hole formation, growth, and fueling, astrophysics summary: ac- 423–435, see also Black holes, cretion power massive (MBHs): formation, binary, 88–100, 397–408, 471, growth, and fueling 761–784, 827 horizon, 810 HMXBs, 90–92, 98–100, 402, jet production, 815–823 745, 762 FR I vs. FR II dichotomy, 20– LMXBs, 90–100, 402, 745, 762 22, 29, 700–725, 816, 822– microquasars, 98–100, 119, 121, 823 562, 761–784, 827–828 recollimation features in radio- X-ray novae, 91–92, 95, 100 loud AGN, 694–700, 818– formation, 743–746, see also γ- 823 ray bursts (GRB) rotating SMBH power, 615– direct collapse of stellar core, 616, 633–634, 815–817 393, 410, 729, 743 why are gE galaxies so radio- failed core-collapse supernovae, loud?, 817–818 108, 393, 394, 397, 410, 729, Blazars, see Active galactic nuclei: 743 blazars in binary star systems, 109– 110, 399, 401–405 Catalogs and surveys in LGRBs, 108–109, 399 optical sources in massive stars, 106, 108–109, Hubble deep ﬁeld, 48 394–399, 403, 408, 409, 729, Markarian catalog, 16 743, 744 Messier catalog, 14, 64 in Pop I/II VMSs, 396 NGC catalog, 14 in SGRBs, 109–110, 405 SDSS, 48 in single stars, 394–397, 409 radio sources horizon, 743 3CR survey, 20, 23, 27 isolated, 87–88, 471, 609–621, Causality, EM 827 light cone, 181–182 detection, 760–761 singular surfaces, 611–614 OGLE/MACHO 1999, 11, 88 causality limit surfaces, 612– jet production, see Black hole 614 astrophysics summary: jet... light surfaces, 612 Black holes, supermassive (SMBHs), Causality, HD, 360–363 16–37, 42–53, 55–58, 809– characteristics, 362–363 823, 829–830, see also Ac- critical (sonic) surface, 362–363 tive galactic nuclei: BALs; Mach cone, 361–362 blazars; RLQs, RQQs, WL- sonic future, 361–362 RGs, etc. Causality, MHD, 360, 366–368, 679– deﬁnition, 13, 810 685 accretion models, see Black holes, characteristics, 366–369, 681 massive (MBHs): accretion critical surfaces, 681 models cusp surface (CS), 366, 367, binary, 432–435 369, 681 906 Subject Index

fast magnetosonic surface (FMS), spatial current four-vector, 307, 368, 369, 681 308, 852 slow magnetosonic surface (SMS), Conservation laws 368, 369, 681 from the Boltzmann equation, 297– separatrix surfaces, 681–682 298, 308, 846–853 Alfven´ surface (AS), 368, 369, generated by gauge symmetries, 681, 682 see Gauge ﬁeld theory: Bianchi fast magnetosonic separatrix identities/symmetries: con- surface (FMSS), 681, 682 servation laws from slow magnetosonic separatrix Newtonian surface (SMSS), 681, 682 conservation of mass, 147–149, singular surfaces, 682 155, 352 Causality, RaHD, 573–578 conservation of energy and mo- critical surface, 574, 576–578 mentum, 149–153, 155, 352 Chandrasekhar mass/limit conservation of charge, 192 deﬁnition, 161 conservation of current (Ohm’s in core-collapse SN, 63, 86, 162, law), 310 386, 389, 407 relativistic in Type Ia SN, 385, 406, 407, conservation of rest mass, 299, 731 850 Charge dynamics, non-relativistic conservation of energy-momentum, generalized Ohm’s law, 310 299–306, 850, 851 Charge dynamics, relativistic conservation of rest charge, 306– conservation of beamed current, 307, 851 see generalized Ohm’s law conservation of beamed cur- beamed spatial current, 307–310, rent (Ohm’s law), 307–312, 852 851 charge-current tensor, 307, 852 Core charge-weighted thermodynamic galaxy, 9, 57, 430, 443, 449, 478– quantities, 308, 852–853 480 conservation of charge, 306–307, cusp, 9, 57, 121, 445, 449, 821 852 mass, 58, 123 current beaming factor, 308 radius, 9, 57, 58, 123, 417, current four-vector, 307, 851 418, 421, 443, 445, 469 equations of state, see Equations spinup, 478 of state: charge dynamic molecular cloud, 456 general relativistic Boltzmann equa- star cluster, 121–123, 163, 416, tion, 296, 847 423–428 generalized Ohm’s law, 307–312, core collapse, 163, 415, 418– 852 423, 428, 431, 789 Hall effect and Hall MHD, 310 stellar Lorentz effect and ideal MHD, C/O, 385–386, 395, 405–408, 309 410 resistive losses and resistive MHD, 310–311 Subject Index 907

core collapse, 85, 388–397, 408, Eddington ratio, 60, 439, 449, 411, 475, 480–481, 728, 826, 450, 564, 791–792 827 in disk accretion, 517, 561, 670, iron/pre-supernova, 85, 389, 475, 744, 748, 754, 775 480–481, 728, 743 in spherical accretion, 492 in winds, 563–582, 782, 805 Doppler in NSs, 740 boosting, see Relativistic motion/beaming in SBHs, 521, 781–784, 827 effect/shift, 23, 41, 189, 190 in IMBHs, 787–789, 828 factor, 28, 189, 190 in MBHs, 791–792, 803–806, 808, Dynamics 829 charge dynamics, see Charge dy- in SMBHs, 430, 791–792, 803– namics 806, 811, 829 electrodynamics (ED), see Elec- Electrodynamics trodynamics Minkowskian 3+1, 191–200 fluid dynamics, see Hydrodynam- conservation laws and gauge ics and MHD freedom, 193–194 galaxy dynamics, see Globular conservation of charge, 191– cluster and galaxy structure 192 & dynamics conservation of current (Ohm’s globular cluster dynamics, see Glob- law), 309–312 ular cluster and galaxy struc- Lorentz force and Joule heat- ture & dynamics ing, 193 hydrodynamics (HD), see Hydro- Maxwell’s field equations, po- dynamics and MHD tential form, 193–194 magnetohydrodynamics (MHD), Maxwell’s field equations, vec- see Hydrodynamics and MHD tor form, 191 radiation hydrodynamics (RaHD), Minkowskian covariant see Hydrodynamics and MHD: conservation laws and gauge RaHD freedom, 204 stellar dynamics, see Stellar struc- conservation of rest charge, 202 ture & dynamics conservation of beamed cur- thermodynamics, see Thermody- rent (Ohm’s law), 307–310 namics Lorentz force and Joule heating, 203 Eddington accretion rate Maxwell’s field equations, po- definition, 439, 501 tential form, 204 in disk accretion, 515–519, 562, Maxwell’s field equations, ten- 567, 580–582, 669–671, 738, sor form, 202 740, 747–750, 754–755, 775, Maxwell’s field equations, vec- 779, 782 tor form, 205 in spherical accretion, 490–492 ADM 3+1 (stationary metrics) Eddington luminosity/limit Lorentz force and Joule heat- as a lower limit on BH mass, 5– ing, 193, 341 6, 116–117 definition, 5 908 Subject Index

Maxwell’s field equations, vec- average molecular weight per tor form, 248–250 electron, 161, 316 equations of state, see Equations average molecular weight per of state: electrodynamic gas particle, 315–316 force-free/FFDE, see Hydrody- chemical potential, 150, 313– namics and MHD: FFDE 314 Engine, black hole, see Black hole Fermi temperature, 319 engine specific heats, 151–152, 315, Equations of state 317, 322 charge dynamic viscosity charge-weighted internal en- bulk, 301–302 ergy and pressure, 308, 852– importance of, 324 853 particle, 323–324 Hall coefficient, 309, 853 shear, 301–303 plasma frequency, 309, 853 turbulent, 324–325, 496–498 resistivity/conductivity, 309, 853 electrodynamic Fluid mechanics, see Hydrodynamics electric permittivity, 191, 250 and MHD magnetic permeability, 191, 250 Frames of reference/coordinate sys- in conservation laws, 312 tems radiative opacity and heat trans- binary star port, see also Radiative pro- center-of-mass, 135–137, 140, cesses (short wavelength) 141, 143, 264, 471, 472 bound–bound, 328, 564–565 inertial, 136, 137, 143, 471 bound–free, 326–328 star-centered (non-inertial), 136 electron scattering opacity, 326 Cartesian, 139, 141, 146–148, 167– free–free, 326–328 170, 172, 174, 175, 187, 212, thermal conductivity, 322–323 223, 342, 353 importance of, 323 circumferential, 213, 222 thermodynamic, internal energy/ curvilinear, 187, 212, 214, 217, pressure 226, 251, 342, 626, 834, 837, adiabatic index, 152, 153, 159, 839 161, 287, 315, 318, 583, 588, cylindrical, 176, 351, 371, 493, 705, 706, 714 505, 520, 532, 536, 658, 663, degenerate electrons, 319 689, 860, 861, 864 degenerate neutrons, 320 Galactic, 68 nonthermal gases, 320–322 mass coordinates (“MOV”), 153– perfect fluid/gas, 315 154, 282, 283, 841–842, 845 photons, 318 non-relativistic polytropic, 152–153, 156, 157, Eulerian (“FIX”), 147, 154– 161, 278, 287, 300, 315, 317, 156 see also Polytropes Lagrangian (“MOV”), 146–154, thermal gases, 314, 315, 317 844–846 thermodynamic, other phase space, 295–297, 415, 847, 848 Subject Index 909

polar, 168–170, 172, 175, 176, AGN hosts, see Active galactic 216, 834 nuclei: host galaxies relativistic ellipticals and spheroidals, 9, 15, Boyer–Lindquist (BL), 209, 234– 22, 25, 48, 53, 56, 57, 59, 242, 244–246, 248, 250, 305, 60, 63, 85, 109, 110, 116, 338, 339, 618, 639, 672, 693, 120–121, 123, 416, 424–425, 855, 858 428, 432, 443–444, 451, 452, drifting/shifting, 233, 234, 242– 454, 458, 480, 786, 790, 801, 243, 245, 247, 251, 841 807, 809–823, 830 harmonic, 272 irregulars, 15, 85, 109, 114, 811 horizon-penetrating (HP), 234, radio, see Active galactic nuclei: 242–243, 245, 339, 639 radio galaxies locally-Lorentz ﬁxed/FIDO/ZAMO Seyfert, see Active galactic nu- (FIX), 224, 225, 237, 238, clei: Seyfert galaxies 305 spirals, 15, 23, 25, 48, 56, 59, moving-body (MOV), 224, 225, 66, 85, 109, 114, 116, 117, 238, 305 122, 123, 451–470, 478, 789– observer-at-inﬁnity/synchronous 809 (OIS), 237–239, 305 Galaxy components Schwarzschild–Hilbert (SH), 222, globular clusters, 7, 115, 120– 224–226, 228, 229, 231, 232, 123, 128, 162–163, 276, 403, 235, 271, 280, 283, 626, 845 416–420, 422, 442, 464, 477, spherical-polar, 146, 148, 176, 785 212, 222, 223, 233, 234, 248, H I clumps, 412–413, 454–455, 658, 684, 692 460–466, 470, 808 Free fall ISM, 22, 34, 39, 382–394, 410– collapse parameter, 138, 282, 283, 414, 439–442, 451–471, 701, 285 702, 705, 710, 728, 731– free-fall time, 456, 570, 650, 653, 732, 760–761, 773, 786, 803– 748 806, 808, 811–813, 829 free-fall/escape speed, 229, 277, molecular clouds, 54, 68, 111, 392, 422, 538, 543, 558, 649, 114, 413, 414, 451–460, 463– 650, 673, 677, 814 466, 477–478, 728, 756, 807, in Newtonian gravity, see Grav- 814 ity: Newton’s law/theory of: star clusters, 118, 128–129, 414– free fall 423, 430–435, 443–444, 450, in stationary Schwarzschild met- 464–470, 784–785, 787, 807, ric, see Geometry/metrics: 808, 813, 828 Schwarzschild: free fall stars, 415–423, 442–451 in evolving Schwarzschild met- γ-ray bursts (GRBs), 100–114 ric, 281–286 beaming break, 103, 105 in Kerr metric, see Geometry/metrics: long-duration γ-ray bursts (LGRBs), Kerr: free fall 102–109 mechanisms Galaxies collapsar, 106, 108–109 910 Subject Index

neutron star merger, 109–110, contravariant tensors, 173, 201, 404–405 219, 254–256, 834, 835 relativistic fireball, 102–104 coordinate transformations short-duration γ-ray bursts (SGRBs), boosts, 185, 201, 238 102, 109–110 coordinate change, 168, 170– stages, 105–107 171, 174–175, 225, 233, 242 supernova connection, 107–108 general, 171–173, 184–185, 201 Gauge field theory global absolute, 167, 174, 175 Bianchi identities/symmetries global differential, 168, 170– algebraic symmetries, 214–215 171, 174, 175, 233, 242 conservation laws from, 191– local differential, 174–175, 185, 192, 202, 205, 218, 261 201, 225, 238, 259 differential symmetries, 202, rotation, 167, 168, 259 205, 210, 215–219, 261 translation, 167, 168 need for gauge constraints, 191– covariant tensors, 173, 256, 834, 192, 202, 218 835 constrained transport, 192, 202 curvature, 209–221, 247, 621, 837, gauge conditions, 191, 194–196, 840, 842 199, 205, 206, 255, 257, 271, tensors and 2-forms, 172–173, 272 187–188, 200–204 gauge freedom, 193–200, 204, vectors, 171 207, 220 Geometry/metrics, non-stationary gauge invariance, 194, 202 perturbed Minkowskian, 219, 254– gauge transformation, 194, 195, 268 220 metric/line element, 254 general description evolving Schwarzschild, 277–289, conservation laws, 192, 203– 840–846 206, 218, 298 gravitational collapse, 277–289 equations of state, 312 metric/line element, 841 field equations, 191, 192, 203– ADM 3+1 spacetime split, 247– 206, 217, 220, 221 250, 268–277 gauge constraints, 191, 192, drift vector, 247, 251 203–206, 220 lapse function, 247, 251 transverse (Lorenz) gauges, 194– line element, 247 196, 199, 205, 206, 256, 257 metric, 247 Geometry/metrics, general shift vector, 247 1-forms/covariant vectors, 170– three-metric, 247–249 172, 176, 183–187, 201, 203– Geometry/metrics, stationary 206, 225, 833, 834, 838 Pythagorean, 166–175, see also 2-forms, 173, 201, 203, 204, 249, Vector and tensor physics: 305, 835, 838 two-vectors 2-tensors, 173, 210, 217–219, 838 coordinate transformations, 167– 4-tensors, 165, 212–218, 835 175 basis 1-forms, 171 coordinates, Cartesian, 167– basis vectors, 171 170, 172, 174, 175 Subject Index 911

coordinates, polar, 168–170, 172, time dilation, 179–180 175 vectors and 1-forms, 183–187, distance, 166–168, 172 201, 203–206, 225 metric/line element in Carte- Schwarzschild, 221–234 sian coordinates, 166, 169 coordinates, horizon-penetrating metric/line element in polar co- (HP), 234 ordinates, 169, 170 coordinates, locally-Lorentz fixed plane geometry, 166–167 (FIX), 224, 225 tensors and 2-forms, 172–173 coordinates, locally-Lorentz mov- vectors and 1-forms, 170–172 ing (MOV), 224, 225 Euclidean, 175–176, see also Vec- coordinates, mass, 282, 283, tor and tensor physics: three- 841–842, 845 vectors coordinates, Schwarzschild–Hilbert coordinate transformations, 176 (SH), 222, 224–226, 228, coordinates, Cartesian, 175 229, 231, 232, 235, 271, 280, coordinates, cylindrical, 176 283, 626, 845 coordinates, spherical-polar, 176 free fall, 229 distance, 175 laws of motion, 226–228 metric/line element in Carte- metric/line element in ingo- sian coordinates, 175 ing HP coordinates, 233 metric/line element in cylin- metric/line element in SH co- drical coordinates, 176 ordinates, 222 metric/line element in spherical- orbits, ISCO, 231 polar coordinates, 176 orbits, marginally bound, 232 tensors and 2-forms, 176 orbits, particle, 230–232 vectors and 1-forms, 176 orbits, photon, 229–230 Minkowskian, 176–183, see also Schwarzschild radius, 222–224 Vector and tensor physics: time warp, 227–228 four-vectors Kerr, 234–243 coordinates, Cartesian, 187 dimensionless angular momen- events, 178, 182–183 tum parameter j, 235 FitzGerald contraction, 179– angular velocity of space, 235, 180 237 geodesics, 182–183 coordinates, Boyer–Lindquist light cone, 181–184 (BL), 209, 234, 242, 246, Lorentz transformations (gen- 248, 250, 305, 338, 339, 618, eral), 184–185 639, 672, 693, 855, 858 metric/line element, 178, 183– coordinates, horizon-penetrating 184 (HP), 242–243, 339, 639 null surface, 178, 181, 182 coordinates, locally-Lorentz fixed/ proper distance, 178–183 FIDO/ZAMO (FIX), 237, 238, proper time, 182–183 305 rest mass, 185, 188 coordinates, observer-at-infinity/ tensors and 2-forms, 187–188, synchronous (OIS), 237, 239, 200–204 305 912 Subject Index

equatorial ergosphere radius, 220, 229, 269, 282, 287, 294, 236, 242, 243 349, 351–353, 471–472, 486, equatorial ISCO radius, 241– 570, 642–643, 859, 863 243 circular orbits, 139–142 free fall, 240 free fall, 137–139 gravitational radius, 235 general potential theory, 144– horizon radius, 236, 242, 243 146 in 3+1 notation, 248, 250–251 gravitational collapse, 138, 162 laws of motion, 239 Green’s function solution, 145 metric/line element in BL co- Poisson’s equation, 145–146, ordinates, 234 155, 211 metric/line element in ingo- Roche potential, 471, 643, 644 ing HP coordinates, 243 pseudo-Newtonian, 510, 862 negative-energy trajectories, 239 Einstein’s theory of, see also Ge- orbits, equatorial marginally bound, ometry/metrics 241–243 connection to Newton’s the- orbits, equatorial particle, 240– ory, 209–212, 219–220 241 Einstein tensor, 217–221 orbits, equatorial photon, 241– ﬁeld equations, 210–212, 217– 243 221, 254–256, 270, 272, 276, Penrose process, 240 278, 335, 404, 841–845, 851 retrograde/prograde BH spin, general relativity, 84, 207–289, 235, 241–243 336–340, 346–348, 405, 846– Kerr–Newman, 243–245 858 dimensionless charge param- Schwarzschild, see Geometry/metrics, eter q, 244 stationary: Schwarzschild coordinates, Boyer–Lindquist evolving Schwarzschild, see Ge- (BL), 244, 245 ometry/metrics, non-stationary: coordinates, horizon-penetrating evolving Schwarzschild (HP), 245 Kerr, see Geometry/metrics, sta- metric/line element in BL co- tionary: Kerr ordinates, 244 Kerr–Newman, see Geometry/metrics, metric/line element in ingo- stationary: Kerr–Newman ing HP coordinates, 245 ADM 3+1 spacetime split, see ADM 3+1 spacetime split Geometry/metrics, non-stationary: electrodynamics, 248–250 ADM 3+1 spacetime split orthonormal vectors in three- Green’s functions, 145, 197, 260 space, 250–251 Globular cluster structure & dynam- Horizon ics, see Star cluster and sphe- event roidal galaxy structure & dy- Schwarzschild, 223–224, 229– namics 233 Gravity Kerr, 236, 699, 756 Newton’s law/theory of, 7, 118, Kerr–Newman, 245 133, 135–146, 209–212, 219– general, 270–289, 405 Subject Index 913

magnetosonic (FMSS), 539, 679– metric shear, 338, 339, 654 692, 694, 696–700, 724, 758– multi-fluid, 293, 847–850 760, 821 one-fluid, 293, 850–853 Hydrodynamics and MHD resistive MHD, 310–311 Electrodynamics, 305–306 Lagrangian frame, 146–154, 844– Eulerian frame, 154–156 846 FFDE, 340–346 NRHD, 143–163 alternate form, 346–347 accretion disk structure, 355, cross-field equation, 345, 858 493 current equation, 342, 858 Couette flow, 370–372 drift current, 342 stellar structure & dynamics, force-free condition, 341, 346, 153, 156, 355 599 vortex flow, 372 GSS equation, 344–346 NRMHD, 335, 351–355 pulsar equation, 346 accretion flow structure, 536 standard form, 341–342 MRI analysis, 372 stationary and axisymmetric, RaHD, 303–305, 569–570, 574– 344–346, 853–858 578 general general radiation stress-energy- conserved variables, 337–340, momentum tensor, 305 349 radiation heat flux and viscos- evolution equations, conserva- ity, 304–305 tive form, 155, 337, 339, radiation pressure and inter- 348 nal energy, 303, 304, 318 gas particle heat flux and vis- SRMHD, general, 348–349 cosity, 300–303 SRMHD, stationary and axisym- gas pressure and internal en- metric, 349–351, 858–864 ergy, 300, 303, 314, 317 cross-field equation, 351, 864 primitive variables, 297, 337, field-parallel equation, 349–351, 340 859–864 pseudo-forces, centrifugal, 187, frozen-in condition, 350, 859– 211, 227, 230, 240, 339, 471, 862 557, 837 mass-loading parameter k, 350, pseudo-forces, Coriolis, 187, 864 211, 339, 372, 837 relation to stationary and ax- pseudo-forces, frame dragging, isymmetric FFDE, 349, 859, 339 861 pseudo-forces, gravity, 209, 211, 212, 220, 227 Inactive galactic nuclei, see Active stress-energy-momentum ten- galactic nuclei: “inactive” galac- sor, 303 tic nuclei GRHD, 335, 347–348 Initial mass function (IMF), 99, 411, GRMHD, 846–853 745 Hall MHD, 310 Instabilities ideal MHD, 311–312 accretion disk 914 Subject Index

secular/Lightman–Eardley/viscous, relativistic vs. non-relativistic, 506–509, 514, 526 705–706 thermal, of SLE hot disk model, working surface/Mach disk, 704, 506, 514–515, 526 705 thermal, of SS “inner” region, three-D, supersonic jets, 705–709 507–509 KH instability, 706–708 HD relativistic vs. non-relativistic, Kelvin–Helmholtz (KH), 705– 708–709 708, 717, 721, 723 birth of the jet concept, 701–702 Rayleigh criterion, 371–372, models for FR II jet formation, 376 725, 823 rotational shearing, 370–372 magnetic field dissipation, 725, in black hole feeding 823 cluster inspiral instability, 808– recollimation shock, 724–725, 809 821–823, 830 in supernovae Jet propagation, MHD jets and FR I pair instability, 409–411, 785 sources, 711–723, 818–823 photodisintegration instability, one-D simulations, super-slow- 411 magnetosonic jets, 712–713 standing accretion shock in- contact discontinuity, 712, 713 stability (SASI), 391 forward fast-mode (bow) shock, MHD, helical-kink/current-driven 712, 713 (CD), 717–721, 723, 725, forward slow-mode shock, 712, 823 713 MHD, magneto-rotational shear- reverse slow-mode shock, 712, ing/MRI, 372–377 713 strong-field, 375–377 two-D simulations, super-fast-mag- suppression, 375–377, 535 netosonic jets, 713–717 weak-field, 373–375 magnetic chamber, 715, 716 MHD, Parker, 497, 542 nose cone, 714–716 Irreducible mass, 235–237, 476 relativistic vs. non-relativistic, accretion of, see Accretion of mat- 716–717 ter, ... reverse fast-mode shock, 715, 716 Jet propagation, HD jets and FR II three-D simulations, super-slow- sources, 701–711, 823 magnetosonic jets, 717–722 one-D, supersonic jets, 702–704 CD instability/helical kink, 717– contact discontinuity, 703 721 forward shock, 703 KH instability, 721–722 reverse shock, 703 relativistic vs. non-relativistic, two-D, supersonic jets, 704–706 721 ambient medium, 704, 705 models for FR I jet formation, bow shock, 704, 705 708–711, 724–725, 822–823 cocoon, 704, 705 HD (disrupted FR II flows), 708–711, 822–823 Subject Index 915

MHD (failed FR II formation), magnetosphere condition, 342– 724–725, 818–823 344, 621 Jets pulsar, see Pulsars: magnetospheres... acceleration and collimation, see stationary electrodynamics, see Wind and jet acceleration Hydrodynamics and MHD: theory FFDE: stationary and ax- current-carrying, see Jet propa- isymmetric gation, MHD jets Mass function kinetic-flux-dominated (KFD), see binary, see Binary stars: mass func- Jet propagation, HD jets tion launching, see Wind and jet launch- stellar initial, see Initial mass func- ing... tion Poynting-flux-dominated (PFD), Microquasars, 13, 61–114, 762 see Jet propagation, MHD black hole, see Black holes, stellar- jets mass (SBHs): binary: mi- propagation, see Jet propagation... croquasars classical, 92–98 King star cluster model, see Star clus- formation, 403 ter and spheroidal galaxy struc- galactic orbits, 760 ture & dynamics: King model neutron star, see Neutron stars core, see also Core: galaxy (NSs): binary: microquasars Miniquasars, 115–129, see also Black Lane–Emden equation, 157–163 holes, intermediate mass Lensing, gravitational MACHO project, 11, 87 Neutron stars (NSs), 65–87, 727–743, microlensing, 10–11, 87, 760 826 OGLE project, 11, 87 binary, 72–84, 397–408, 566, 735– Lorenz (transverse) gauge/condition, 743, 826, see also Binary 194–196, 199, 205, 206, 255, stars: X-ray (XRBs) 257 atoll sources, 73–75, 79, 738– 743, 826 Macroquasars, see Active galactic nu- HMXBs, 74–76, 402, 735 clei... LMXBs, 74–76, 402, 735–739 Magnetars, 70–71, see also Neutron microquasars, 73–75, 81, 737– stars (NSs): isolated: AXPs 743, 826 or SGRs recycled (millisecond) binary Magnetospheres pulsars, 83, 403 black hole, see Black holes: mag- X-ray novae, 77–78, 100 netospheres... X-ray pulsars, 75, 78, 603– general 609, 736–737 current sheet, 309, 342, 595, Z sources, 73–75, 79, 736–743, 600, 615, 617, 618, 627, 629 824, 826 field angular velocity, 593, 611, formation, 84–87, 727–731, see 614, 619, 620, 648, 662, 666, also Supernovae 674, 694, 860–861, 864 916 Subject Index

in binary star systems, 399, 1974, radio astronomy imaging 401–405, 731 techniques and discovery of in core-collapse supernovae, 386– pulsars, 17, 64 394 1983, theoretical work on stars in intermediate-mass stars, 386– and nucleosynthesis, 63 388 1993, discovery of the binary pul- in massive stars, 84–87, 388– sar and applications to grav- 394, 398, 403, 409, 729, 744, itation, 84 826 2002, discovery of cosmic neu- in Pop III stars, 409, 410 trinos and X-ray sources, 64 in single stars, 386–394, 396, 409 Orbits neutron star window, 396–397, in Newtonian gravity 744 binary, see Binary stars: orbits Galactic population, 68, 72, 99, circular, see Gravity: Newton’s 100, see also Sources in the law/theory of: circular or- Milky Way: neutron stars bits isolated, 65–72, 731–735, 826, in Schwarzschild metric, see Ge- see also Pulsars: radio ometry/metrics: Schwarzschild: AXPs, 67, 70 orbits detection, 732, 734 in Kerr metric, see Geometry/metrics: radio pulsars, see Pulsars: ra- Kerr: orbits dio RRATs, 67, 71–72 Particle distribution functions SGRs, 67, 70, 734 gases, nonthermal, 320–322 XDINs, 71–72 gases, thermal, 313–320 jets in binary systems general, 313–315 MHD disk wind-driven jets, Fermi–Dirac, general, 318–320 739–742 Fermi–Dirac, non-relativistic, pulsar propeller-driven jets, 735, 319 739–742, 826 Fermi–Dirac, relativistic, 319 radio power at low accretion Maxwellian, general, 316–317 rate, 742–743 Maxwellian, non-relativistic, 314– suppression of MHD disk jets, 316 739–742 Maxwellian, relativistic, 317 jets in isolated systems, see Pul- Planckian, 317–318 sars: radio Poisson’s equation, 145–146, 155, 211 magnetospheres, see Pulsars: mag- Polytropes netospheres... analytic solution (n =1), 159– Nobel Prize, 273 160, 287 1935, discovery of the neutron, general, 152–153, 157–159 68 isentropic perfect gas (n =3/2), 1970, magnetohydrodynamics and 152, 159–161, 287, 315 plasma physics, 364 relativistic gas (n =3), 152, 159–162, 287, 304 Subject Index 917

singular isothermal sphere (SIS; rotating magnetic dipole radi- n = ∞), 54, 159, 162–163, ation, 66–67, 592–594, 601, 413, 415–418, 430, 443–444, 734 449, 459, 464–466, 468, 469 X-ray, see Neutron stars (NSs): Pulsars binary: X-ray pulsars magnetospheres, accreting, 603– X-ray, anomalous, see Neutron 609 stars (NSs): isolated: AXPs accretion regime, 605–607 co-rotation radius, 605, 608 Quasars magnetic radius, 604, 608, 741 compact, see Active galactic nu- propeller spindown time, 609 clei: quasars: FSRQs propeller/wind turbine regime, extended, see Active galactic nu- 605, 607–609, 735, 739–742, clei: quasars: RLQs 826 hidden, see Active galactic nu- unstable magnetic ﬁeld at high clei: Type 2, 3 m˙ , 606–607 QSOs, see Active galactic nu- magnetospheres, isolated, 592– clei: quasars: RQQs/QSOs 603 QSRs, see Active galactic nu- aligned rotator FFDE models, clei: quasars: RLQs/QSRs 596–598 curvature radiation, 602 Radiation hydrodynamics (RaHD), see force-free model, 594–603 Hydrodynamics and MHD: Goldreich–Julian charge den- RaHD sity, 594 Radiative processes (long wavelength), see Waves and radiation (long light cylinder radius RL, 346, 593, 596, 674, 696, 732 wavelength) oblique rotator FFDE simula- Radiative processes (short wavelength) tions, 598–600 bound–bound particle creation, 601–602 bound–bound absorption, 328, pulsar emission mechanism, 600– 564–565, 794 603 force multiplier, 564–566, 574, pulsar equation and singular 575, 744 surface, 346, 597 iron Kα, 39–41 pulsar spindown time, 66 line emission, 14, 16, 22, 23, vacuum breakdown and spark 43, 44, 52, 82 gaps, 601–603 P Cygni lines, 49 wind, outgoing, 595–596 bound–free radio, 65–70 bound–free absorption, 326– binary, 84 328, 331, 499, 504, 521 dead, 68, 72, 603, 731–732, recombination emission, 327 734, 742, 826 electron scattering interstellar dispersion, 66 Compton cooling, 33, 326, 332– proper motion/kicks, 68–70, 394, 334, 513, 671, 755 730, 733 Compton heating, 79, 326, 566– PWN, 69, 732 567 918 Subject Index

Compton parameter y, 333, 334, 3C 48, 23 513, 795 3C 120, 94, 510, 511, 562, 791, Compton reﬂection, 39–41, 588, 794, 799, 817 817 3C 273, 23, 25–27, 31, 33, 794 Compton thick media, 334, 789, 3C 279, 33 792, 804 3C 345, 25 Compton thin media, 334, 514 3C 371, 22 Klein–Nishina cross-section, 326 3C 390.3, 21, 22, 817 opacity, 5, 326, 501, 564 Andromeda (M31), 121, 787 Thomson cross-section, 326, BL Lac, 30, 37, 821–822 865 Centaurus A (NGC 5128), 17, free–free 25, 787, 810 Bremsstrahlung emission, 329– Cygnus A, 17–19, 21, 25, 701, 330, 332, 333, 504, 765 704, 705 free–free absorption, 326–328, Hercules A, 17 331, 499, 504, 521 M51, 478 synchrotron M81, 52, 588 nonthermal, 19, 588 M84 (3C 272.1, NGC 4374), 21, thermal, 330–332, 521, 559, 52 755 M87/Virgo A, 4, 9, 14, 15, 17, Reducible mass, 235–237, 476, 639 19–21, 30, 53, 57, 445, 751, accretion of, see Accretion of an- 810, 818–823 gular momentum M104, 52 Relativistic motion/beaming, 11, 26– MCG 6-30-15, 41, 817 36, 47, 105, 112–114, 119, Milky Way (Galaxy/Sgr A*), see 188–190, 227, 308 Sources in the Milky Way: Relativity black holes: Sgr A* general, 207–251 Mkn 421, 33 numerical, 268–277 Mkn 501, 33 3+1 ADM method, 271–272 NGC 1068, 14, 16, 38, 39 BSSN modiﬁcations, 272, 273 NGC 2787, 809 gauge conditions (slicing), 271, NGC 4051, 799–801 272 NGC 4151, 14, 16 harmonic coordinates, 272 NGC 4258, 52, 478 history, 271–273 NGC 4261, 39, 40, 478 initial data, 272, 275 NGC 4472, 120, 783 singularity excision/punctures, NGC 5728, 39, 40 271, 273 NGC 6251, 17, 18, 20, 31 special, 163–207 Q1413+113, 50 Sources in globular clusters and dwarf Sources in active galactic nuclei ellipticals 1823+568, 29, 31 G1 (Mayall II), 121–123 1H 0707-495, 817 M15, 122, 123 3C 9, 23 Omega Centauri (NGC 5139), 122, 3C 47, 21, 24, 29 123 Subject Index 919

RZ 2109 in NGC 4472, 120, 783 rapid burster, 77, 111 Sources in other galaxies Scorpius X-1, 64, 65, 73, 75 M82 ULX-1, 117, 118 Vela Pulsar, 69, 730, 733 N1 in M81, 781 other, see also Supernovae: rem- P098 in M101, 569, 781–784, nants 789, 794, 826 IRS 16, 124–126 Sources in the Milky Way, 63–115, SS433, 81–83, 99, 400, 671, 121–128, 268, 746, 760, 786, 755, 781, 798, 826, 827 828 Spheroidal galaxy structure & dynam- black holes ics, see Star cluster and sphe- 1E 1740.7-2942, 91–93 roidal galaxy structure & dy- A0620-00, 92 namics Cygnus X-1 (HDE 226868), Star cluster and spheroidal galaxy struc- 64, 88, 89, 91, 92, 99, 394, ture & dynamics, see also 399, 475, 512, 515, 521, 530, Core: galaxy 747, 769, 781, 782, 794 analytic, singular isothermal sphere/ GRO J1655-40, 94–95, 670, n = ∞ polytrope model, 751, 756, 763, 764, 768, 770 54, 415–418, 430, 443–444, GRS 1915+105, 92–95, 97, 121, 449, 459, 464–466, 468, 469 394, 510–512, 553, 560, 562, core density, 417, 443, 444, 756, 762–764, 768–770, 776, 449 777, 787, 788, 801, 829 core galaxy, 57, 58, 417–418, GS 1124-684, 92 443, 444, 449, 450 GS 2000+251, 92 core mass, 58, 417, 444 GX 339-4, 91, 95, 553, 740, cusp/power-law galaxy, 57, 416– 756, 764 417, 444, 445, 450 IRS 13E, 125–129 mass deﬁcit, 418, 444 J0422+32, 92 core collapse, equal-mass stars, LMC X-1, 91 418–420 LMC X-3, 91 core collapse, mass-segregated, Sgr A*, 4, 8, 52–55, 530, 588, 420–421 695, 790, 825 Fokker–Planck formalism, 415, XTE J1550-564, 95, 756, 764, 418 801 King model, 416–419, 444 XTE J1859+226, 95 core (King) radius, 417, 418, neutron stars 421, 443, 445, 469 Aquila X-1, 77, 740 tidal radius, 162, 417 Centaurus X-3, 73, 76, 88, 399 loss cone Circinus X-1, 77, 566, 567 depletion , 434, 448 Crab Pulsar, 65–70, 73, 84, reﬁlling, 434, 448 108, 594, 730, 733 spheroidal cluster as a single star Geminga, 72, 731 binary burning, 419–420 Hercules X-1, 73, 75, 736 binary hardening, 421, 427, 432– LSI +61 303, 77 434 millisecond pulsar, 83 920 Subject Index

ensemble of stars as a gas, 415– red giants, 112, 114, 384, 386, 423 395, 398, 400, 419, 420, 447, gravo-thermal catastrophe, 418– 449, 451, 729, 790, 807 420 red supergiants, 54, 85, 386, 395, heat conduction, 419–420 397, 398, 400, 403, 447, 449– isothermal velocity distribution, 451, 729, 783, 790, 810, 812, 417 828 temperature/velocity dispersion, structure, see Stellar structure & 415 dynamics Stars variable, 30 binary, see Binary stars white dwarfs black holes, see Black holes... C/O, 385–386, 407, 408, 731 evolution, see Stellar evolution... doubly-degenerate binaries, 407– interiors, see Stellar structure & 408 dynamics ONeMg, 407, 408, 731 lifetimes, 384 Stellar evolution, binary stars luminosities, 384 γ-ray bursts mechanisms mass classes neutron star merger, 109–110, brown dwarfs, 87, 383, 790 404–405 low-mass, 75, 77, 383–384, 396 close binaries, 397–408 solar-type, 24, 384–385, 396, cataclysmic variable stars, 402, 402, 403, 406, 447–450, 729, 405–407, 731 807, 810 common envelope stage/phase, moderate-mass, 385–386, 396, 399–403, 408 406 formation of HMXBs, 398– intermediate-mass, 386–390, 403, 402 406, 408 formation of LMXBs, 401, 403 massive, 68, 76, 84–87, 106– mass transfer Cases A–D, 398, 109, 388–398, 403, 406, 408, 403–404 409, 420, 422–423, 434, 474, merger rates of compact ob- 481, 729, 743, 744, 803, 826, ject binaries, 402, 403 828 spinup of millisecond pulsars, very massive (VMSs), 118, 409– 83, 403, 477 414, 422–423, 784 super-Eddington wind phase(Cyg supermassive, 6, 411, 414, 785, X-1 on steroids), 399, 403, 789 783 neutron, see Neutron stars (NSs) supernova explosion mechanisms Population I, 118, 412, 414–423, carbon deﬂagration/detonation, 784–785, 828 405–407, 731 Population II, 118, 412, 414–423, Stellar evolution, single stars, 381– 784–786, 803, 828 394 Population III, 116, 408–414, 423, γ-ray bursts mechanisms 425–428, 785–786 collapsar, 106, 108–109 core-collapse supernova stage, 386– 388 Subject Index 921

dissociation of iron, 387 stellar wind mass loss, 395– electron capture, 387 396 neutrino emission and neutri- Wolf–Rayet phase, 395–396 nosphere, 387–388 supernova explosion mechanisms PNS (proto-neutron star) phase, core-collapse, magnetic/MHD 387 bipolar outﬂow, 391–393 formation, 462–464 core-collapse, neutrino heat- initial mass function, 411–414 ing, 388 initial metallicity, 396, 409, 410, pair production, 414 412, 414 synthesis of heavy elements/metals, Jeans mass, 412–414 381–394 Pop I stars, 411–413 Stellar structure & dynamics Pop III stars, 411–414 non-relativistic stars, see also Hy- main sequence stages, 383–386 drodynamics and MHD: NRHD: hydrogen-burning, proton–proton stellar structure & dynam- chain, 384 ics hydrogen-burning, CNO cycle, Chandrasekhar mass limit, 63, 384, 386, 389 86, 161, 162, 385, 386, 389, helium-burning, 384, 389, 395 406, 407, 731 lifetimes, 384 collapse parameter, 138 luminosities, 384 free-fall time, 138, 570 red giant stages, 384 Lane–Emden equation, 157– He core, 384, 389 163 hydrogen shell burning, 384, mass coordinates, 153–154 386, 389 polytropes, 156–163 C/O core, 385, 389 relativistic stars helium shell burning, 385–386, black hole/horizon formation, 389 277–289 carbon-burning, degenerate, 385 collapse of relativistic pressure- planetary nebula formation, 385 less dust cloud, 281–286 carbon shell burning, 386 collapse of relativistic star with red supergiant stages, 386, 389 pressure, 286, 288 carbon-burning, non-degenerate, collapse parameter, 282, 283, 386, 389 285 ONeMg core, 386, 389 free-fall time, 282 carbon shell burning, 389 mass coordinates, 282, 283, 841– neon-burning, 389 842, 845 OMgSi core, 389 static structure, 286–288 neon shell burning, 389 thermodynamic equation of state, oxygen-burning, 389 286–287 SiS core, 389 Supernovae oxygen shell burning, 389 core-collapse, 84–87, 99, 107, 386– silicon-burning, 389 388, 727–731, 743 FeNi core, 389 explosion types silicon shell burning, 389 922 Subject Index

Type Ia, 84, 99, 391, 402, 405– VLBI, 17, 18, 25–27, 29, 30, 408, 731 53, 630, 679, 705, 815, 818, Type Ib, 84–86, 107, 112, 390, 819 396, 405, 406, 408 space Type Ic, 84–86, 107, 112, 390, Aerobee sounding rocket, 63 395, 396, 405, 406, 408 ASCA, 41, 118, 119 Type Ic-BL (“Id”, “hypernovae”), Beppo-Sax, 101 86, 87, 107, 111 CGRO, 89, 94, 101, 102 Type II, 85–86, 390, 395, 396, Chandra, 42, 69, 118, 120, 127 406 Einstein X-ray observatory, 42, Type “IIa”, 85 91, 117 Type IIb, 85, 86, 395 Fermi/GLAST, 33, 89 mechanisms, binary stars, see Stel- GRANAT, 92 lar evolution, binary stars: HST, 9, 15, 19, 26, 39, 40, 44, supernova explosion mech- 48, 55, 122, 478 anisms INTEGRAL, 127 mechanisms, single stars, see Stel- IRAS, 44 lar evolution, single stars: JWST, 111, 435, 824 supernova explosion mech- LISA, 255, 267, 268, 273, 402, anisms 435 observed explosions NuSTAR, 46, 127, 731, 760, Crab supernova, 85, 388 786, 803, 804, 826 rates, 87, 113 ROSAT, 72, 109, 118 core-collapse, 72, 99, 108, 397, RXTE, 93, 94 744 SIM, 435 Type Ia, 407–408 Spitzer Space Telescope, 43– remnants 46, 803 Crab Nebula (M1), 64, 68, 69 Swift γ-ray burst mission, 109, Vela Nebula, 69 110 W50, 81, 82 Uhuru (SAS-1), 73, 88, 92 Vela nuclear monitoring satel- Telescopes and techniques lites, 65 ground XMM, 120 Einstein (gravitational wave) Thermodynamics Telescope, 267 adiabatic index, see Equations of JCMT, 45 state: thermodynamic, inter- LIGO, 109, 110, 255, 267, 268, nal energy/pressure: adiabatic 273, 402, 405 index MERLIN, 26, 29 equations of state, see Equations Ryle 5-km telescope, 18 of state: thermodynamic SCUBA, 45 first law (conservation of energy), VLA, 19, 29, 31, 47, 82, 93, 150–152, 845 679, 760, 818 specific heat coefficients, see Equa- VLBA, 15, 819–821 tions of state: thermodynamic, other: specific heats Subject Index 923

Time warps, 227–228 electromagnetic field, 204–205, 210 Vector and tensor physics, see also magnetic potential, 203–206, Geometry/metrics ... 254–256, 834, 835 notation spatial current density, 307– two-dimensional and three-di- 310, 852 mensional, 833–834 beamed spatial current density, four-dimensional, 834–835 307–310, 852 two-vectors tensors inner/scalar/dot product, 169, identity, 156, 169, 198, 203, 171–172 347, 834 three-vectors projection, 301, 310, 850 inner/scalar/dot product, 155, shear, 302, 353, 495 176 stress-energy-momentum, 188, outer/dyadic product, 155, 337 203, 217, 221, 256, 261, 299– unit, 135, 139, 141, 366 301, 303, 305, 835, 850 velocity, 134, 833 charge-current, 307, 852 momentum, 134–136, 295–297, Faraday 2-form/tensor, 201, 203, 337–338, 347, 348, 833, 863 249, 305, 835 force, 133–135, 143–146, 149, Maxwell 2-form/tensor, 201, 156, 192–193, 296 204, 835 current density, 191–193, 249, metric, 169–170, 175, 222, 234, 338, 858 244, 247, 254, 841 electric field, 191–193, 249, Riemann 4-tensor, 212–218, 835 337, 857 Riemann symmetries/Bianchi electric displacement, 191–193, identities, 202, 205, 210, 215– 249, 338, 857 219 magnetic induction, 191–193, Ricci 2-tensor, 217–219 249, 337, 856 Ricci scalar, 217, 218 magnetic field, 191–193, 249, Einstein 2-tensor, 217–221 338, 857 inner/scalar/double-dot prod- magnetic vector/three-potential, uct, 203, 218, 256, 260 193–200, 856 vector and tensor derivatives four-vectors simple gradient, 251, 838 outer/dyadic product, 255 Christoffel symbols/connection unit, 187, 838 coefficients, 214, 219, 226, velocity, 183–184, 188, 202, 254, 837 224–227, 238, 257, 296, 300– covariant gradient, 837–838 305, 307, 834, 847–849 curl, 251 momentum, 185–187, 202, 226, divergence, 251, 838–839 294, 296–297, 834, 847–849 metric has no gradient or di- force, 187, 202–203, 221, 226– vergence, 839–840 228, 294, 296, 849 current density, 202, 204–205, Waves and radiation (long wavelength) 210, 249, 307, 309, 834, 851 electromagnetic 924 Subject Index

dipole, electric, 197–200 wave generation, general, 260– dipole, magnetic, 66–67 277 equations, Maxwell’s in covari- wave generation, star mergers, ant form, 202, 205 268–277 equations, Maxwell’s in sta- HD/sound, non-relativistic tionary 3+1 metrics, 191, characteristics and sonic causal- 193, 249 ity, 362–363 equations, wave, 194, 205 epicyclic modes, 371 gauge, Lorenz transverse, 194, in subsonic (elliptic) flow, 361– 205 362 in a vacuum, 194–197, 205– in supersonic (hyperbolic) flow, 206 361–363 in media, 191, 250 Mach cone, 361–362 polarization, 196, 206 velocity of, adiabatic, 359 Poynting energy flux/power, 199– velocity of, isothermal, 361 200 HD/sound, relativistic velocity of, 195, 206 velocity of, adiabatic, 369, 693 wave generation, 197–200 MHD, non-relativistic general Alfven´ mode, 363–364 dispersion relations, 357–358 magneto-acoustic modes (fast/slow), Friedrich’s polar diagrams, group, 364–366 359, 360, 364, 366 velocity, Alfven,´ 364 Friedrich’s polar diagrams, phase, velocity, cusp, 366 359, 360, 364, 365 velocity, fast magneto-acoustic, velocity, group, 357, 358 365 velocity, phase, 357, 358 velocity, magnetosound, 365 wave number, 356, 357 velocity, slow magneto-acoustic, gravitational, 254–277, see also 365 Binary stars: gravitational waves MHD, relativistic equations, Einstein’s in covari- velocity, Alfven,´ 368, 692 ant form, 220 velocity, cusp, 369 equations, wave, 256 velocity, fast magneto-acoustic, gauge is the coordinate sys- 368, 370 tem, 257–258 velocity, magnetosound, 369, gauge, transverse traceless (Lorenz), 693 257 velocity, slow magneto-acoustic, in a vacuum, 256–260 368, 370 polarization, 258–260 Waves and radiation (short wavelength), Poynting energy flux/power, 260– see Radiative processes (short 263 wavelength) quadrupole, 260–263 Wind and jet acceleration theory, 655– stress-energy-momentum of, 256 700 wave generation, close bina- general prescription ries, 263–268 critical surfaces, 680–682 Subject Index 925

energy equations, 486, 536, 570, Mach number, relativistic Alfven´ 574, 659, 674 MR, 673 momentum equations, 486, 536, Mach number, relativistic mag- 570, 661 netosonic tR, 674 separatrix surfaces, 680–682 magnetization parameter σM, singular surfaces, 680–682 675, 694, 696, 697 stagnation surface, 609, 621, models with large initial toroidal 630, 636, 637, 680, 698, 699 ﬁeld, 677–678 resulting wind/accretion equa- relativistic Alfven´ radius xAlf , tions, 486, 490, 537, 565, 674, 675, 694, 696 574, 661, 673, 685 singular points/surfaces, 674– wind, ingoing, 609, 620–621, 675 630, 634–637, 680, 698, 699 terminal Lorentz factor, 676 wind, outgoing, 595–596, 609, LCB MHD wind equation, 673– 621, 630, 634–637, 680, 699 675 magnetically-driven, cold, non- solutions, 675–677 relativistic (BP) bipolar winds/jets, wind loss rates (energy, mass, 656–672 angular momentum), 676– r-self-similar models, 663–664 677 Alfven´ radius, 662 magnetically-driven, warm, non- black hole spin-dependence, 671– relativistic (VTST) bipolar 672 winds/jets, 678–692 Bernoulli energy equation, 659, observational insight into jet 660 acceleration, 678–679 Mach number, Alfven´ MNR, theoretical insight and causal- 660, 663 ity, 679–685 Mach number, magnetosonic plasma parameter βp, 685 tNR, 661 VTST MHD wind equation, BP momentum (cross-ﬁeld) equa- 685–686 tion, 661 solutions, 686–690 singular points/surfaces, 661– simulations, 690–692 663 magnetically-driven, warm, rel- terminal velocity, 666 ativistic (VK) bipolar winds/jets, BP MHD wind equation, 659– 692–700 661 proper Alfven´ speed, 692 solutions, 663–665 proper gas sound speed, 693 simulations, 664–665 proper magnetosound speed, wind loss rates (energy, mass, 693 angular momentum), 665– singular points/surfaces (SMSS, 672 AS, FMSS), 694 magnetically-driven, cold, rela- warmth parameter Q, 694, 696, tivistic (LCB) bipolar winds/jets, 697 672–678 VK MHD wind equation, 692– r-self-similar models, 675–676 694 solutions, 694–696 926 Subject Index

simulations, 696–700 wind equation, non-relativistic, radiation continuum-driven, super- 486–489 Eddington winds, 567–582, wind equation, relativistic, 489– 780, 781 490 “slim” disk connection, 580– thermally-driven bipolar winds/jets, 582 586–589 adiabatic radius, 575 broad-band jet spectrum, 587, injection radius, 568–569, 573, 589 580 bulk acceleration equation, 587– photosphere radius, 569, 579, 588 580 Compton reflection, 587, 588 scattersphere radius, 569, 573, particle acceleration, 588 578, 580 strong shock in jet, 587, 588 singular/critical radius, 568– synchrotron, 587, 589 569, 578, 580 Wind and jet launching, from accre- structure, physical, 568–578 tion disks, 641–654, 750– structure, thermal, 578–580 757 terminal velocity, 580 gas pressure launching (slow mode), trapping radius, 574–575 645–646 wind equation, adiabatic, 574 magnetocentrifugal (BP) launch- wind equation, radiative, 574 ing (Alfven´ mode) [fling], wind equations, general, 569– 642–644 570 black hole spin-dependence, 632, radiation line-driven, sub-Eddington 671–672 winds, 564–567 Roche potential, 643, 644 force multiplier, 564–566, 574, magnetic pressure launching (fast 575, 744 mode) [spring], 643–654 hitchhiking gas, 49, 566–567, closed field lines (magnetic tower), 793 646–654 line opacity, 564, 565 external pressure role, 646–648 terminal velocity, 566 magnetic switch, 649, 651–653 wind equation, isothermal, 565 open field lines, 643–646, 649 thermally-driven (ADIOS) out- Wind and jet launching, from rotating flow, 582–586 black holes, 609–641, 755– equations, 583–585 757 models, 585–586 binary, 621–641, see also Black terminal velocity, 586 holes: magnetospheres, ac- thermally-driven (Parker) winds, creting 485–492 black hole spin-dependence, 633– adiabatic, 488 634, 815–817 general solutions, 486–487 isolated, 609–621, see also Black isothermal, 488 holes: magnetospheres, iso- regular solutions, 486–488 lated singular/critical (sonic) point/ surface, 486–488 Subject Index 927

Wind and jet launching, from rotating neutron stars, 592–609, 732–733, 739–743 binary, 603–609, 739–743, see also Pulsars: magnetospheres, accreting isolated, 592–603, 732–733, see also Pulsars: magnetospheres, isolated

X-ray binaries, see also Binary stars: X-ray black hole, see also Black holes, stellar-mass (SBHs): binary high mass (HMXB), 74–76, 399, 400, 402 Roche-lobe-overﬂow mass transfer, 76, 399, 472–474, 762, 782 wind mass transfer, 76, 399, 474–475, 735 low mass (LMXB), 74–77, 740 Roche-lobe-overﬂow mass transfer, 75, 77, 472–474, 735 neutron star, see also Neutron stars(NSs): binary persistent, 76–78 sources, see Sources in the Milky Way; Sources in other galaxies transient, 76–78