<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><div class="t m0 x0 h1 y0 ff1 fs0 fc0 sc0 ls2 ws0">Con<span class="_0 blank"></span>ten<span class="_0 blank"></span>ts</div><div class="t m0 x0 h2 y1 ff2 fs1 fc0 sc0 ls2 ws1">Preface <span class="ff3 fs2">xiii</span></div><div class="t m0 x0 h2 y2 ff2 fs1 fc0 sc0 ls2 ws2">1<span class="_1 blank"> </span>In<span class="_0 blank"></span>tro duction<span class="_2 blank"> </span><span class="ff3 fs2">1</span></div><div class="t m0 x1 h3 y3 ff4 fs2 fc0 sc0 ls2 ws3">1.1<span class="_3 blank"> </span>An ov<span class="_0 blank"></span>erview of the observ<span class="_0 blank"></span>ations<span class="_4 blank"> </span><span class="ff3">5</span></div><div class="t m0 x2 h4 y4 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws4">Stars 5<span class="_5 blank"> </span></span>\u2022<span class="ff6 ls2 ws5">The Galaxy 11<span class="_5 blank"> </span></span><span class="ls1">\u2022<span class="ff6 ls2 ws6">Other galaxies<span class="_6 blank"> </span>19<span class="_7 blank"> </span></span></span><span class="ff7">\ue02e<span class="ff6 ls2">Elliptical</span></span></div><div class="t m0 x2 h4 y5 ff6 fs3 fc0 sc0 ls2 ws7">galaxies 20<span class="_5 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws8">Spiral galaxies 25<span class="_5 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws9">Lenticular galaxies 28</span></span></div><div class="t m0 x2 h4 y6 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wsa">Irregular galaxies 28<span class="_3 blank"> </span></span><span class="ff5">\u2022<span class="ff6 ls2 wsb">Op en<span class="_6 blank"> </span>and<span class="_8 blank"> </span>globular<span class="_6 blank"> </span>clusters<span class="_6 blank"> </span>29<span class="_9 blank"> </span></span>\u2022<span class="ff6 ls2">Groups</span></span></div><div class="t m0 x2 h4 y7 ff6 fs3 fc0 sc0 ls2 wsc">and clusters of<span class="_6 blank"> </span>galaxies<span class="_6 blank"> </span>30<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span><span class="wsd">Black holes 32</span></div><div class="t m0 x1 h3 y8 ff4 fs2 fc0 sc0 ls2 wse">1.2<span class="_3 blank"> </span>Collisionless systems<span class="_8 blank"> </span>and<span class="_6 blank"> </span>the<span class="_8 blank"> </span>relaxation<span class="_6 blank"> </span>time<span class="_a blank"> </span><span class="ff3">33</span></div><div class="t m0 x2 h4 y9 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsf">The relaxation time 34</span></div><div class="t m0 x1 h3 ya ff4 fs2 fc0 sc0 ls2 ws10">1.3<span class="_3 blank"> </span>The<span class="_6 blank"> </span>cosmological con<span class="_0 blank"></span>text<span class="_b blank"> </span><span class="ff3">37</span></div><div class="t m0 x2 h4 yb ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws11">Kinematics 38<span class="_5 blank"> </span></span>\u2022<span class="ff6 ls2 ws12">Geometry 39<span class="_5 blank"> </span></span>\u2022<span class="ff6 ls2 ws9">Dynamics 40<span class="_c blank"> </span></span>\u2022<span class="ff6 ls2 ws13">The Big</span></div><div class="t m0 x2 h4 yc ff6 fs3 fc0 sc0 ls2 ws14">Bang and in\ufb02ation 45<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws15">The cosmic<span class="_6 blank"> </span>microw<span class="_0 blank"></span>ave background 48</span></div><div class="t m0 x1 h3 yd ff4 fs2 fc0 sc0 ls2 ws16">Problems <span class="ff3">52</span></div><div class="t m0 x0 h2 ye ff2 fs1 fc0 sc0 ls2 ws17">2<span class="_1 blank"> </span>P<span class="_0 blank"></span>otential Theory<span class="_d blank"> </span><span class="ff3 fs2">55</span></div><div class="t m0 x1 h3 yf ff4 fs2 fc0 sc0 ls2 ws18">2.1<span class="_3 blank"> </span>General results<span class="_e blank"> </span><span class="ff3">56</span></div><div class="t m0 x2 h4 y10 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws19">The<span class="_6 blank"> </span>potential-energy<span class="_8 blank"> </span>tensor<span class="_6 blank"> </span>59</span></div><div class="t m0 x1 h3 y11 ff4 fs2 fc0 sc0 ls2 ws1a">2.2<span class="_3 blank"> </span>Spherical systems<span class="_f blank"> </span><span class="ff3">60</span></div><div class="t m0 x2 h4 y12 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws14">Newton\u2019s theorems 60<span class="_c blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws1b">Poten<span class="_0 blank"></span>tial energy of spherical<span class="_6 blank"> </span>sys-</span></span></div><div class="t m0 x2 h4 y13 ff6 fs3 fc0 sc0 ls2 ws1c">tems 63<span class="_10 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws1d">Poten<span class="_0 blank"></span>tials of some simple systems 63<span class="_11 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws1e">Poin<span class="_0 blank"></span>t</span></span></div><div class="t m0 x2 h4 y14 ff6 fs3 fc0 sc0 ls2 ws1f">mass 63<span class="_12 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws20">Homogeneous sphere 63<span class="_12 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws21">Plummer<span class="_6 blank"> </span>model<span class="_6 blank"> </span>65</span></span></div><div class="t m0 x2 h4 y15 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws22">Isochrone<span class="_6 blank"> </span>potential<span class="_8 blank"> </span>65<span class="_13 blank"> </span></span>\ue02e<span class="ff6 ls2 ws23">Modi\ufb01ed<span class="_6 blank"> </span>Hubble<span class="_8 blank"> </span>mo del<span class="_6 blank"> </span>66</span></div><div class="t m0 x2 h4 y16 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws21">Po<span class="_0 blank"></span>wer-la<span class="_0 blank"></span>w<span class="_6 blank"> </span>density<span class="_8 blank"> </span>mo del<span class="_6 blank"> </span>68<span class="_14 blank"> </span><span class="ff7 ls0">\ue02e</span>Two-pow<span class="_0 blank"></span>er<span class="_6 blank"> </span>density<span class="_8 blank"> </span>models<span class="_6 blank"> </span>70</span></div><div class="t m0 x1 h3 y17 ff4 fs2 fc0 sc0 ls2 ws24">2.3<span class="_3 blank"> </span>P<span class="_0 blank"></span>otential-densit<span class="_0 blank"></span>y pairs for<span class="_6 blank"> </span>\ufb02attened systems<span class="_15 blank"> </span><span class="ff3">72</span></div><div class="t m0 x2 h4 y18 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws21">Kuzmin<span class="_8 blank"> </span>mo dels<span class="_6 blank"> </span>and<span class="_6 blank"> </span>generalizations<span class="_6 blank"> </span>72<span class="_5 blank"> </span></span>\u2022<span class="ff6 ls2 ws19">Logarithmic<span class="_6 blank"> </span>poten-</span></div><div class="t m0 x2 h4 y19 ff6 fs3 fc0 sc0 ls2 ws1d">tials 74<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws25">Poisson\u2019s equation<span class="_6 blank"> </span>in very \ufb02attened systems 77</span></div><div class="t m0 x1 h3 y1a ff4 fs2 fc0 sc0 ls2 ws26">2.4<span class="_3 blank"> </span>Multip ole<span class="_8 blank"> </span>expansion<span class="_16 blank"> </span><span class="ff3">78</span></div><div class="t m0 x1 h3 y1b ff4 fs2 fc0 sc0 ls2 ws27">2.5<span class="_3 blank"> </span>The<span class="_6 blank"> </span>potentials<span class="_8 blank"> </span>of<span class="_8 blank"> </span>spheroidal<span class="_6 blank"> </span>and<span class="_8 blank"> </span>ellipsoidal<span class="_8 blank"> </span>systems<span class="_17 blank"> </span><span class="ff3">83</span></div><div class="t m0 x2 h4 y1c ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws1b">Poten<span class="_0 blank"></span>tials of spheroidal<span class="_6 blank"> </span>shells 84<span class="_18 blank"> </span><span class="ff5 ls0">\u2022</span>Poten<span class="_0 blank"></span>tials of spheroidal</span></div><div class="t m0 x2 h4 y1d ff6 fs3 fc0 sc0 ls2 ws28">systems 87<span class="_18 blank"> </span><span class="ff5 ls0">\u2022</span>Potentials of ellipsoidal systems 94<span class="_5 blank"> </span><span class="ff7 ls1">\ue02e</span><span class="ws1e">F<span class="_0 blank"></span>errers</span></div><div class="t m0 x2 h4 y1e ff6 fs3 fc0 sc0 ls2 ws19">potentials<span class="_6 blank"> </span>95<span class="_14 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws28">P<span class="_0 blank"></span>otential-energy tensors of ellipsoidal<span class="_6 blank"> </span>systems 95</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><div class="t m0 x0 h3 y1f ff3 fs2 fc0 sc0 ls2 ws2a">vi <span class="ff8 ws2b">Conten<span class="_0 blank"></span>ts</span></div><div class="t m0 x1 h3 y20 ff4 fs2 fc0 sc0 ls2 ws27">2.6<span class="_3 blank"> </span>The<span class="_6 blank"> </span>potentials<span class="_8 blank"> </span>of<span class="_8 blank"> </span>disks<span class="_19 blank"> </span><span class="ff3">96</span></div><div class="t m0 x2 h4 y21 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws1d">Disk potentials from<span class="_8 blank"> </span>homo<span class="_1a blank"> </span>eoids 96<span class="_9 blank"> </span><span class="ff7 ls1">\ue02e</span><span class="ws13">The Mestel disk 99<span class="_9 blank"> </span></span></span><span class="ff7">\ue02e<span class="ff6 ls2">The</span></span></div><div class="t m0 x2 h4 y22 ff6 fs3 fc0 sc0 ls2 ws2c">exponential<span class="_8 blank"> </span>disk<span class="_6 blank"> </span>100<span class="_1 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws2d">Thick disks 102<span class="_12 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws19">Disk<span class="_8 blank"> </span>p otentials<span class="_6 blank"> </span>from</span></span></div><div class="t m0 x2 h4 y23 ff6 fs3 fc0 sc0 ls2 ws12">Bessel functions 103<span class="_1 blank"> </span><span class="ff7 ls1">\ue02e</span><span class="ws2e">Application<span class="_6 blank"> </span>to axisymmetric disks<span class="_6 blank"> </span>106</span></div><div class="t m0 x2 h4 y24 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws19">Disk<span class="_8 blank"> </span>p otentials<span class="_6 blank"> </span>from<span class="_8 blank"> </span>logarithmic<span class="_6 blank"> </span>spirals<span class="_6 blank"> </span>107<span class="_12 blank"> </span></span>\u2022<span class="ff6 ls2 ws19">Disk<span class="_6 blank"> </span>potentials</span></div><div class="t m0 x2 h4 y25 ff6 fs3 fc0 sc0 ls2 ws2f">from<span class="_6 blank"> </span>oblate<span class="_8 blank"> </span>spheroidal<span class="_6 blank"> </span>coordinates<span class="_6 blank"> </span>109</div><div class="t m0 x1 h3 y26 ff4 fs2 fc0 sc0 ls2 ws27">2.7<span class="_3 blank"> </span>The<span class="_6 blank"> </span>potential<span class="_8 blank"> </span>of<span class="_8 blank"> </span>our<span class="_6 blank"> </span>Galaxy<span class="_1b blank"> </span><span class="ff3">110</span></div><div class="t m0 x2 h4 y27 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws13">The bulge 111<span class="_1 blank"> </span></span>\ue02e<span class="ff6 ls2 ws30">The dark halo<span class="_6 blank"> </span>112<span class="_1 blank"> </span></span>\ue02e<span class="ff6 ls2 ws31">The stellar<span class="_6 blank"> </span>disk 112</span></div><div class="t m0 x2 h4 y28 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws32">The interstellar medium 112<span class="_14 blank"> </span></span>\ue02e<span class="ff6 ls2 ws33">The bulge as a bar 117</span></div><div class="t m0 x1 h3 y29 ff4 fs2 fc0 sc0 ls2 ws34">2.8<span class="_3 blank"> </span>P<span class="_0 blank"></span>otentials from functional expansions<span class="_1c blank"> </span><span class="ff3">118</span></div><div class="t m0 x2 h4 y2a ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws12">Bi-orthonormal basis functions 120<span class="_11 blank"> </span></span>\ue02e<span class="ff6 ls2 ws35">Designer basis func-</span></div><div class="t m0 x2 h4 y2b ff6 fs3 fc0 sc0 ls2 ws1f">tions 120</div><div class="t m0 x1 h3 y2c ff4 fs2 fc0 sc0 ls2 ws36">2.9<span class="_3 blank"> </span>P<span class="_0 blank"></span>oisson<span class="_6 blank"> </span>solv<span class="_0 blank"></span>ers<span class="_8 blank"> </span>for<span class="_6 blank"> </span>N-b o dy<span class="_8 blank"> </span>co des<span class="_1d blank"> </span><span class="ff3">122</span></div><div class="t m0 x2 h4 y2d ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws37">Direct summation 123<span class="_7 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws38">Softening 123<span class="_c blank"> </span></span></span>\u2022<span class="ff6 ls2 ws2f">T<span class="_0 blank"></span>ree<span class="_6 blank"> </span>codes<span class="_6 blank"> </span>125</span></div><div class="t m0 x2 h4 y2e ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws39">Cartesian<span class="_6 blank"> </span>m<span class="_0 blank"></span>ultip ole<span class="_6 blank"> </span>expansion<span class="_6 blank"> </span>127<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws2f">Particle-mesh<span class="_6 blank"> </span>codes<span class="_6 blank"> </span>129</span></span></div><div class="t m0 x2 h4 y2f ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws19">Periodic<span class="_6 blank"> </span>boundary<span class="_6 blank"> </span>conditions<span class="_8 blank"> </span>131<span class="_12 blank"> </span></span>\ue02e<span class="ff6 ls2 ws19">V<span class="_0 blank"></span>acuum<span class="_8 blank"> </span>boundary<span class="_6 blank"> </span>con-</span></div><div class="t m0 x2 h5 y30 ff6 fs3 fc0 sc0 ls2 ws38">ditions 132<span class="_11 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws3a">Mesh<span class="_6 blank"> </span>re\ufb01nement 135<span class="_11 blank"> </span><span class="ff7 ls1">\ue02e</span><span class="ls3">P<span class="ff9 fs4 ls4 v1">3</span></span><span class="ws2f">M<span class="_6 blank"> </span>codes<span class="_6 blank"> </span>135</span></span></div><div class="t m0 x2 h4 y31 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws2f">Spherical-harmonic<span class="_6 blank"> </span>codes<span class="_6 blank"> </span>136<span class="_18 blank"> </span></span>\u2022<span class="ff6 ls2 ws3b">Simulations of planar sys-</span></div><div class="t m0 x2 h4 y32 ff6 fs3 fc0 sc0 ls2 ws1c">tems 137</div><div class="t m0 x1 h3 y33 ff4 fs2 fc0 sc0 ls2 ws3c">Problems <span class="ff3">137</span></div><div class="t m0 x0 h2 y34 ff2 fs1 fc0 sc0 ls2 ws3d">3<span class="_1 blank"> </span>The Orbits of<span class="_6 blank"> </span>Stars<span class="_1e blank"> </span><span class="ff3 fs2">142</span></div><div class="t m0 x1 h3 y35 ff4 fs2 fc0 sc0 ls2 ws27">3.1<span class="_3 blank"> </span>Orbits<span class="_8 blank"> </span>in<span class="_6 blank"> </span>static<span class="_8 blank"> </span>spherical<span class="_6 blank"> </span>potentials<span class="_1f blank"> </span><span class="ff3">143</span></div><div class="t m0 x2 h4 y36 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws3e">Spherical harmonic oscillator 147<span class="_5 blank"> </span></span>\ue02e<span class="ff6 ls2 ws19">Kepler<span class="_8 blank"> </span>p otential<span class="_6 blank"> </span>147</span></div><div class="t m0 x2 h4 y37 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws22">Isochrone<span class="_6 blank"> </span>potential<span class="_8 blank"> </span>149<span class="_18 blank"> </span></span>\ue02e<span class="ff6 ls2 ws3f">Hyperbolic<span class="_6 blank"> </span>encounters<span class="_8 blank"> </span>153</span></div><div class="t m0 x2 h4 y38 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws40">Constants and integrals of the motion<span class="_6 blank"> </span>155</span></div><div class="t m0 x1 h3 y39 ff4 fs2 fc0 sc0 ls2 ws27">3.2<span class="_3 blank"> </span>Orbits<span class="_8 blank"> </span>in<span class="_6 blank"> </span>axisymmetric<span class="_8 blank"> </span>p otentials<span class="_20 blank"> </span><span class="ff3">159</span></div><div class="t m0 x2 h4 y3a ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws40">Motion in the meridional<span class="_6 blank"> </span>plane 159<span class="_7 blank"> </span></span><span class="ls1">\u2022<span class="ff6 ls2 ws41">Surfaces of section 162</span></span></div><div class="t m0 x2 h4 y3b ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws42">Nearly<span class="_8 blank"> </span>circular<span class="_6 blank"> </span>orbits:<span class="_21 blank"> </span>epicycles<span class="_6 blank"> </span>and<span class="_8 blank"> </span>the<span class="_6 blank"> </span>v<span class="_0 blank"></span>elo city<span class="_8 blank"> </span>ellipsoid<span class="_6 blank"> </span>164</span></div><div class="t m0 x1 h3 y3c ff4 fs2 fc0 sc0 ls2 ws27">3.3<span class="_3 blank"> </span>Orbits<span class="_8 blank"> </span>in<span class="_6 blank"> </span>planar<span class="_8 blank"> </span>non-axisymmetric<span class="_6 blank"> </span>potentials<span class="_22 blank"> </span><span class="ff3">171</span></div><div class="t m0 x2 h4 y3d ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws19">Two-dimensional<span class="_8 blank"> </span>non-rotating<span class="_6 blank"> </span>potential<span class="_6 blank"> </span>171<span class="_23 blank"> </span></span>\u2022<span class="ff6 ls2 ws1e">Two-</span></div><div class="t m0 x2 h4 y3e ff6 fs3 fc0 sc0 ls2 ws19">dimensional<span class="_6 blank"> </span>rotating<span class="_8 blank"> </span>p otential<span class="_6 blank"> </span>178<span class="_24 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws43">W<span class="_0 blank"></span>eak bars 188</span></div><div class="t m0 x2 h4 y3f ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws44">Lindblad resonances 188<span class="_25 blank"> </span></span>\ue02e<span class="ff6 ls2 ws45">Orbits<span class="_8 blank"> </span>trapp ed<span class="_6 blank"> </span>at<span class="_8 blank"> </span>resonance<span class="_6 blank"> </span>193</span></div><div class="t m0 x1 h3 y40 ff4 fs2 fc0 sc0 ls2 ws46">3.4<span class="_3 blank"> </span>Numerical orbit in<span class="_0 blank"></span>tegration<span class="_26 blank"> </span><span class="ff3">196</span></div><div class="t m0 x2 h4 y41 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws47">Symplectic integrators 197<span class="_7 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws23">Modi\ufb01ed<span class="_6 blank"> </span>Euler<span class="_8 blank"> </span>integrator<span class="_6 blank"> </span>197</span></span></div><div class="t m0 x2 h4 y42 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws48">Leapfrog integrator 200<span class="_11 blank"> </span></span><span class="ff5">\u2022<span class="ff6 ls2 ws49">Runge\u2013Kutta<span class="_8 blank"> </span>and<span class="_6 blank"> </span>Bulirsc<span class="_0 blank"></span>h\u2013Sto er</span></span></div><div class="t m0 x2 h4 y43 ff6 fs3 fc0 sc0 ls2 ws4a">integrators 201<span class="_27 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws4b">Multistep predictor-corrector integrators 202</span></div><div class="t m0 x2 h4 y44 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws4c">Multiv<span class="_0 blank"></span>alue integrators 203<span class="_10 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws4d">Adaptiv<span class="_0 blank"></span>e timesteps<span class="_6 blank"> </span>205</span></span></div><div class="t m0 x2 h4 y45 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws4e">Individual timesteps 206<span class="_18 blank"> </span></span>\u2022<span class="ff6 ls2 ws4f">Regularization 208<span class="_12 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2">Burdet\u2013</span></span></div><div class="t m0 x2 h4 y46 ff6 fs3 fc0 sc0 ls2 ws50">Heggie regularization 208<span class="_27 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws15">Kustaanheimo\u2013Stiefel<span class="_6 blank"> </span>(KS) regular-</span></div><div class="t m0 x2 h4 y47 ff6 fs3 fc0 sc0 ls2 ws51">ization 210</div><div class="t m0 x1 h3 y48 ff4 fs2 fc0 sc0 ls2 ws52">3.5<span class="_3 blank"> </span>Angle-action v<span class="_0 blank"></span>ariables<span class="_28 blank"> </span><span class="ff3">211</span></div><div class="t m0 x2 h4 y49 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws53">Orbital tori 212<span class="_c blank"> </span><span class="ff7 ls1">\ue02e</span><span class="ws54">Time av<span class="_0 blank"></span>erages<span class="_6 blank"> </span>theorem 215<span class="_c blank"> </span><span class="ff7 ls0">\ue02e</span>Action</span></span></div><div class="t m0 x2 h4 y4a ff6 fs3 fc0 sc0 ls2 ws55">space 216<span class="_5 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws56">Hamilton\u2013Jacobi equation 217<span class="_13 blank"> </span><span class="ff5 ls0">\u2022</span>Angle-action</span></div><div class="t m0 x2 h4 y4b ff6 fs3 fc0 sc0 ls2 ws19">v<span class="_0 blank"></span>ariables<span class="_6 blank"> </span>for<span class="_6 blank"> </span>spherical<span class="_8 blank"> </span>p otentials<span class="_6 blank"> </span>220<span class="_27 blank"> </span><span class="ff5 ls1">\u2022</span><span class="ws3e">Angle-action v<span class="_0 blank"></span>ariables for</span></div><div class="t m0 x2 h4 y4c ff6 fs3 fc0 sc0 ls2 ws19">\ufb02attened<span class="_8 blank"> </span>axisymmetric<span class="_6 blank"> </span>potentials<span class="_6 blank"> </span>226<span class="_25 blank"> </span><span class="ff7 ls0">\ue02e</span>St¨<span class="_29 blank"></span>ack<span class="_0 blank"></span>el<span class="_6 blank"> </span>potentials<span class="_8 blank"> </span>226</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><div class="t m0 x0 h3 y1f ff8 fs2 fc0 sc0 ls2 ws57">Conten<span class="_0 blank"></span>ts <span class="ff3">vii</span></div><div class="t m0 x2 h4 y20 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws58">Epicycle approximation 231<span class="_1 blank"> </span><span class="ff5 ls1">\u2022</span><span class="ws3e">Angle-action variables for a non-</span></span></div><div class="t m0 x2 h4 y4d ff6 fs3 fc0 sc0 ls2 ws33">rotating bar 234<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws59">Summary 236</span></div><div class="t m0 x1 h3 y4e ff4 fs2 fc0 sc0 ls2 ws27">3.6<span class="_3 blank"> </span>Slo<span class="_0 blank"></span>wly<span class="_6 blank"> </span>v<span class="_0 blank"></span>arying<span class="_8 blank"> </span>p otentials<span class="_2a blank"> </span><span class="ff3">237</span></div><div class="t m0 x2 h4 y4f ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws5a">Adiabatic inv<span class="_0 blank"></span>ariance of actions 237<span class="_13 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws5b">Applications 238</span></span></div><div class="t m0 x2 h4 y50 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws5a">Harmonic oscillator 238<span class="_5 blank"> </span></span>\ue02e<span class="ff6 ls2 ws31">Eccentric orbits in<span class="_6 blank"> </span>a disk 240</span></div><div class="t m0 x2 h4 y51 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws19">T<span class="_0 blank"></span>ransien<span class="_0 blank"></span>t<span class="_6 blank"> </span>perturbations<span class="_6 blank"> </span>240<span class="_7 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws5c">Slow gro<span class="_0 blank"></span>wth of a central black</span></span></div><div class="t m0 x2 h4 y52 ff6 fs3 fc0 sc0 ls2 ws4c">hole 241</div><div class="t m0 x1 h3 y53 ff4 fs2 fc0 sc0 ls2 ws5d">3.7<span class="_3 blank"> </span>P<span class="_0 blank"></span>erturbations and chaos<span class="_2b blank"> </span><span class="ff3">243</span></div><div class="t m0 x2 h4 y54 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws19">Hamiltonian<span class="_6 blank"> </span>perturbation<span class="_6 blank"> </span>theory<span class="_8 blank"> </span>243<span class="_13 blank"> </span></span>\u2022<span class="ff6 ls2 ws2d">T<span class="_0 blank"></span>rapping by reso-</span></div><div class="t m0 x2 h4 y55 ff6 fs3 fc0 sc0 ls2 ws5e">nances 246<span class="_12 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws5f">Levitation 250<span class="_13 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws56">F<span class="_0 blank"></span>rom order to c<span class="_0 blank"></span>haos 253</span></span></div><div class="t m0 x2 h4 y56 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wsa">Irregular orbits 256<span class="_12 blank"> </span></span>\ue02e<span class="ff6 ls2 ws60">F<span class="_0 blank"></span>requency analysis<span class="_6 blank"> </span>258<span class="_12 blank"> </span><span class="ff7 ls1">\ue02e</span><span class="ws1e">Liapuno<span class="_0 blank"></span>v</span></span></div><div class="t m0 x2 h4 y57 ff6 fs3 fc0 sc0 ls2 ws2c">exponents<span class="_8 blank"> </span>260</div><div class="t m0 x1 h3 y58 ff4 fs2 fc0 sc0 ls2 ws61">3.8<span class="_3 blank"> </span>Orbits in elliptical galaxies<span class="_2c blank"> </span><span class="ff3">262</span></div><div class="t m0 x2 h4 y59 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws19">The<span class="_6 blank"> </span>perfect<span class="_6 blank"> </span>ellipsoid<span class="_8 blank"> </span>263<span class="_5 blank"> </span></span>\u2022<span class="ff6 ls2 ws62">Dynamical e\ufb00ects of<span class="_6 blank"> </span>cusps 263</span></div><div class="t m0 x2 h4 y5a ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws62">Dynamical e\ufb00ects of black holes 266</span></div><div class="t m0 x1 h3 y5b ff4 fs2 fc0 sc0 ls2 ws3c">Problems <span class="ff3">268</span></div><div class="t m0 x0 h2 y5c ff2 fs1 fc0 sc0 ls2 ws63">4<span class="_1 blank"> </span>Equilibria of<span class="_6 blank"> </span>Collisionless Systems<span class="_2d blank"> </span><span class="ff3 fs2">274</span></div><div class="t m0 x1 h3 y5d ff4 fs2 fc0 sc0 ls2 ws64">4.1<span class="_3 blank"> </span>The<span class="_6 blank"> </span>collisionless Boltzmann<span class="_8 blank"> </span>equation<span class="_2e blank"> </span><span class="ff3">275</span></div><div class="t m0 x2 h4 y5e ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws56">Limitations of the collisionless<span class="_6 blank"> </span>Boltzmann equation 278<span class="_2f blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2">Finite</span></span></div><div class="t m0 x2 h4 y5f ff6 fs3 fc0 sc0 ls2 ws65">stellar lifetimes 278<span class="_14 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws19">Correlations<span class="_6 blank"> </span>b etween<span class="_8 blank"> </span>stars<span class="_6 blank"> </span>279<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span>Relation</span></div><div class="t m0 x2 h4 y60 ff6 fs3 fc0 sc0 ls2 ws19">between<span class="_8 blank"> </span>the<span class="_6 blank"> </span><span class="ffa ws66">df </span><span class="wsc">and observ<span class="_0 blank"></span>ables 280<span class="_14 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws67">An example 282</span></span></div><div class="t m0 x1 h3 y61 ff4 fs2 fc0 sc0 ls2 ws68">4.2<span class="_3 blank"> </span>Jeans theorems<span class="_30 blank"> </span><span class="ff3">283</span></div><div class="t m0 x2 h4 y62 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws1b">Choice of <span class="ff7 ls5">f</span><span class="ws19">and<span class="_6 blank"> </span>relations<span class="_6 blank"> </span>betw<span class="_0 blank"></span>een<span class="_6 blank"> </span>momen<span class="_0 blank"></span>ts<span class="_6 blank"> </span>285<span class="_c blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws69">DF de-</span></span></span></div><div class="t m0 x2 h4 y63 ff6 fs3 fc0 sc0 ls2 ws19">pending<span class="_6 blank"> </span>only<span class="_8 blank"> </span>on<span class="_6 blank"> </span><span class="ff7 ls6">H</span><span class="ws6a">285 <span class="ff7 ls0">\ue02e</span><span class="ws6b">DF<span class="_8 blank"> </span>dep ending<span class="_6 blank"> </span>on<span class="_8 blank"> </span><span class="ff7 ls6">H</span><span class="wsc">and <span class="ff7 ls7">L</span>286</span></span></span></div><div class="t m0 x2 h4 y64 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws69">DF depending on<span class="_6 blank"> </span></span><span class="ls6">H<span class="ff6 ls2 ws6c">and </span><span class="ls8">L<span class="ffb fs4 ls9 v2">z</span><span class="ff6 ls2">286</span></span></span></div><div class="t m0 x1 h3 y65 ff4 fs2 fc0 sc0 ls2 ws6d">4.3<span class="_3 blank"> </span>DFs for spherical systems<span class="_31 blank"> </span><span class="ff3">287</span></div><div class="t m0 x2 h4 y66 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws45">Ergodic<span class="_6 blank"> </span>DFs<span class="_6 blank"> </span>for<span class="_8 blank"> </span>systems<span class="_6 blank"> </span>288<span class="_32 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws45">Ergodic<span class="_6 blank"> </span>Hernquist,<span class="_6 blank"> </span>Ja\ufb00e<span class="_8 blank"> </span>and</span></span></div><div class="t m0 x2 h4 y67 ff6 fs3 fc0 sc0 ls2 ws21">isochrone<span class="_6 blank"> </span>models<span class="_6 blank"> </span>290<span class="_32 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws4c">Di\ufb00erential energy distribution 292</span></div><div class="t m0 x2 h4 y68 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws43">DFs for anisotropic<span class="_6 blank"> </span>spherical<span class="_6 blank"> </span>systems 293<span class="_33 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws23">Models<span class="_6 blank"> </span>with</span></span></div><div class="t m0 x2 h4 y69 ff6 fs3 fc0 sc0 ls2 ws3a">constant anisotrop<span class="_0 blank"></span>y<span class="_6 blank"> </span>294<span class="_33 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws21">Osipko<span class="_0 blank"></span>v\u2013Merritt<span class="_6 blank"> </span>models<span class="_6 blank"> </span>297</span></div><div class="t m0 x2 h4 y6a ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws21">Other<span class="_8 blank"> </span>anisotropic<span class="_6 blank"> </span>mo dels<span class="_6 blank"> </span>298<span class="_32 blank"> </span></span>\ue02e<span class="ff6 ls2 ws53">Di\ufb00erential-energy distribu-</span></div><div class="t m0 x2 h4 y6b ff6 fs3 fc0 sc0 ls2 ws28">tion for anisotropic systems 299<span class="_13 blank"> </span><span class="ff5 ls0">\u2022</span>Spherical systems de\ufb01ned</div><div class="t m0 x2 h4 y6c ff6 fs3 fc0 sc0 ls2 ws6e">by the DF 299<span class="_5 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws6f">Polytropes<span class="_6 blank"> </span>and<span class="_6 blank"> </span>the<span class="_8 blank"> </span>Plummer<span class="_6 blank"> </span>model<span class="_6 blank"> </span>300</span></div><div class="t m0 x2 h4 y6d ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws20">The isothermal<span class="_6 blank"> </span>sphere 302<span class="_25 blank"> </span></span>\ue02e<span class="ff6 ls2 ws21">Lowered<span class="_8 blank"> </span>isothermal<span class="_6 blank"> </span>mo dels<span class="_6 blank"> </span>307</span></div><div class="t m0 x2 h4 y6e ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws70">Double-power<span class="_8 blank"> </span>models<span class="_6 blank"> </span>311<span class="_14 blank"> </span></span>\ue02e<span class="ff6 ls2 ws21">Michie<span class="_6 blank"> </span>models<span class="_6 blank"> </span>312</span></div><div class="t m0 x1 h3 y6f ff4 fs2 fc0 sc0 ls2 ws71">4.4<span class="_3 blank"> </span>DFs for axisymmetric density distributions<span class="_15 blank"> </span><span class="ff3">312</span></div><div class="t m0 x2 h4 y70 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws72">DF for a<span class="_6 blank"> </span>given axisymmetric system 312<span class="_12 blank"> </span></span>\u2022<span class="ff6 ls2 ws73">Axisymmetric sys-</span></div><div class="t m0 x2 h4 y71 ff6 fs3 fc0 sc0 ls2 ws74">tems<span class="_6 blank"> </span>speci\ufb01ed<span class="_8 blank"> </span>by<span class="_8 blank"> </span><span class="ff7 lsa">f</span><span class="ws1e">(<span class="ff7 ws75">H ,<span class="_34 blank"> </span>L<span class="ffb fs4 lsb v2">z</span></span><span class="ws3a">) 314<span class="_35 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws21">F<span class="_0 blank"></span>ully<span class="_8 blank"> </span>analytic<span class="_6 blank"> </span>models<span class="_6 blank"> </span>314</span></span></span></div><div class="t m0 x2 h4 y72 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws21">Rowley<span class="_8 blank"> </span>mo dels<span class="_6 blank"> </span>318<span class="_9 blank"> </span></span>\ue02e<span class="ff6 ls2 ws76">Rotation and<span class="_6 blank"> </span>\ufb02attening in spheroids 320</span></div><div class="t m0 x2 h4 y73 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws69">The Sch<span class="_0 blank"></span>warzschild DF 321</span></div><div class="t m0 x1 h3 y74 ff4 fs2 fc0 sc0 ls2 ws6d">4.5<span class="_3 blank"> </span>DFs for razor-thin<span class="_6 blank"> </span>disks<span class="_36 blank"> </span><span class="ff3">329</span></div><div class="t m0 x2 h4 y75 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws31">Mestel disk 329<span class="_27 blank"> </span></span>\u2022<span class="ff6 ls2 ws77">Kalna js<span class="_6 blank"> </span>disks<span class="_6 blank"> </span>330</span></div><div class="t m0 x1 h3 y76 ff4 fs2 fc0 sc0 ls2 ws3">4.6<span class="_3 blank"> </span>Using actions as arguments of the DF<span class="_1c blank"> </span><span class="ff3">333</span></div><div class="t m0 x2 h4 y77 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws5a">Adiabatic compression 335<span class="_27 blank"> </span><span class="ff7 ls1">\ue02e</span><span class="ws2d">Cusp around a black hole 336</span></span></div><div class="t m0 x2 h4 y78 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws5">Adiabatic deformation of dark matter 337</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><div class="t m0 x0 h3 y1f ff3 fs2 fc0 sc0 ls2 ws78">viii <span class="ff8 ws2b">Conten<span class="_0 blank"></span>ts</span></div><div class="t m0 x1 h3 y20 ff4 fs2 fc0 sc0 ls2 ws79">4.7<span class="_3 blank"> </span>P<span class="_0 blank"></span>article-based<span class="_6 blank"> </span>and<span class="_6 blank"> </span>orbit-based<span class="_8 blank"> </span>mo dels<span class="_37 blank"> </span><span class="ff3">338</span></div><div class="t m0 x2 h4 y79 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws21">N-bo dy<span class="_6 blank"> </span>modeling<span class="_6 blank"> </span>339<span class="_c blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws38">Softening 341<span class="_11 blank"> </span></span>\ue02e<span class="ff6 ls2 wsd">Instabilit<span class="_0 blank"></span>y and</span></span></div><div class="t m0 x2 h4 y7a ff6 fs3 fc0 sc0 ls2 ws7a">chaos 341<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws21">Sch<span class="_0 blank"></span>warzsc<span class="_0 blank"></span>hild<span class="_6 blank"> </span>models<span class="_6 blank"> </span>344</span></div><div class="t m0 x1 h3 y7b ff4 fs2 fc0 sc0 ls2 ws7b">4.8<span class="_3 blank"> </span>The Jeans and<span class="_6 blank"> </span>virial equations<span class="_38 blank"> </span><span class="ff3">347</span></div><div class="t m0 x2 h4 y7c ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws28">Jeans equations for spherical systems 349<span class="_27 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws5c">E\ufb00ect of a central</span></span></div><div class="t m0 x2 h4 y7d ff6 fs3 fc0 sc0 ls2 ws7c">black<span class="_8 blank"> </span>hole on the observed<span class="_8 blank"> </span>velocity dispersion 350<span class="_32 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws7d">Jeans equa-</span></div><div class="t m0 x2 h4 y7e ff6 fs3 fc0 sc0 ls2 ws28">tions for axisymmetric systems 353<span class="_32 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws7e">Asymmetric drift 354</span></div><div class="t m0 x2 h4 y7f ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws42">Spheroidal<span class="_6 blank"> </span>components<span class="_8 blank"> </span>with<span class="_6 blank"> </span>isotropic<span class="_6 blank"> </span>v<span class="_0 blank"></span>elo city<span class="_8 blank"> </span>disp ersion<span class="_6 blank"> </span>356</span></div><div class="t m0 x2 h4 y80 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws5f">Virial equations 358<span class="_39 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws54">Scalar virial theorem 360</span></span></div><div class="t m0 x2 h4 y81 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws28">Spherical systems 361<span class="_5 blank"> </span></span>\ue02e<span class="ff6 ls2 ws28">The tensor virial theorem and ob-</span></div><div class="t m0 x2 h4 y82 ff6 fs3 fc0 sc0 ls2 ws7f">serv<span class="_0 blank"></span>ational data 362</div><div class="t m0 x1 h3 y83 ff4 fs2 fc0 sc0 ls2 ws80">4.9<span class="_3 blank"> </span>Stellar kinematics as a mass detector<span class="_3a blank"> </span><span class="ff3">365</span></div><div class="t m0 x2 h4 y84 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws2d">Detecting black holes 366<span class="_33 blank"> </span></span>\u2022<span class="ff6 ls2 ws76">Extended mass distributions of</span></div><div class="t m0 x2 h4 y85 ff6 fs3 fc0 sc0 ls2 ws81">elliptical galaxies 370<span class="_27 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws82">Dynamics<span class="_8 blank"> </span>of<span class="_6 blank"> </span>the<span class="_6 blank"> </span>solar<span class="_8 blank"> </span>neighborho o d<span class="_6 blank"> </span>372</span></div><div class="t m0 x1 h3 y86 ff4 fs2 fc0 sc0 ls2 ws83">4.10 The<span class="_6 blank"> </span>c<span class="_0 blank"></span>hoice<span class="_8 blank"> </span>of<span class="_6 blank"> </span>equilibrium<span class="_3b blank"> </span><span class="ff3">376</span></div><div class="t m0 x2 h4 y87 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws6e">The principle<span class="_6 blank"> </span>of maximum entropy 377<span class="_24 blank"> </span></span>\u2022<span class="ff6 ls2 ws4">Phase mix-</span></div><div class="t m0 x2 h4 y88 ff6 fs3 fc0 sc0 ls2 wsc">ing and violent relaxation 379<span class="_39 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws4">Phase mixing 379</span></div><div class="t m0 x2 h4 y89 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wsf">Violent relaxation 380<span class="_1 blank"> </span></span><span class="ff5">\u2022<span class="ff6 ls2 ws40">Numerical simulation of<span class="_6 blank"> </span>the relaxation</span></span></div><div class="t m0 x2 h4 y8a ff6 fs3 fc0 sc0 ls2 ws84">process<span class="_6 blank"> </span>382</div><div class="t m0 x1 h3 y8b ff4 fs2 fc0 sc0 ls2 ws3c">Problems <span class="ff3">387</span></div><div class="t m0 x0 h2 y8c ff2 fs1 fc0 sc0 ls2 ws85">5<span class="_1 blank"> </span>Stabilit<span class="_0 blank"></span>y of<span class="_6 blank"> </span>Collisionless Systems<span class="_3c blank"> </span><span class="ff3 fs2">394</span></div><div class="t m0 x1 h3 y8d ff4 fs2 fc0 sc0 ls2 ws86">5.1<span class="_3 blank"> </span>In<span class="_0 blank"></span>tro duction<span class="_3d blank"> </span><span class="ff3">394</span></div><div class="t m0 x2 h4 y8e ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws84">Linear<span class="_6 blank"> </span>response<span class="_6 blank"> </span>theory<span class="_8 blank"> </span>396<span class="_c blank"> </span></span>\u2022<span class="ff6 ls2 ws5f">Linearized equations for stellar</span></div><div class="t m0 x2 h4 y8f ff6 fs3 fc0 sc0 ls2 wsc">and \ufb02uid systems 398</div><div class="t m0 x1 h3 y90 ff4 fs2 fc0 sc0 ls2 ws87">5.2<span class="_3 blank"> </span>The<span class="_6 blank"> </span>response<span class="_8 blank"> </span>of<span class="_6 blank"> </span>homogeneous<span class="_8 blank"> </span>systems<span class="_37 blank"> </span><span class="ff3">401</span></div><div class="t m0 x2 h4 y91 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws88">Physical basis of the Jeans instabilit<span class="_0 blank"></span>y<span class="_6 blank"> </span>401<span class="_13 blank"> </span><span class="ff5 ls0">\u2022</span>Homogeneous</span></div><div class="t m0 x2 h4 y92 ff6 fs3 fc0 sc0 ls2 wsc">systems and the Jeans<span class="_6 blank"> </span>swindle 401<span class="_3e blank"> </span><span class="ff5 ls1">\u2022</span><span class="ws84">The<span class="_6 blank"> </span>response<span class="_6 blank"> </span>of<span class="_8 blank"> </span>a<span class="_6 blank"> </span>ho-</span></div><div class="t m0 x2 h4 y93 ff6 fs3 fc0 sc0 ls2 wsc">mogeneous \ufb02uid system 403<span class="_3f blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws84">The<span class="_6 blank"> </span>response<span class="_6 blank"> </span>of<span class="_8 blank"> </span>a<span class="_6 blank"> </span>homo-</span></div><div class="t m0 x2 h4 y94 ff6 fs3 fc0 sc0 ls2 ws7f">geneous stellar system 406<span class="_3e blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws89">Unstable solutions<span class="_6 blank"> </span>410</span></div><div class="t m0 x2 h4 y95 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws8a">Neutrally stable solutions<span class="_6 blank"> </span>411<span class="_c blank"> </span></span>\ue02e<span class="ff6 ls2 ws8b">Damped<span class="_6 blank"> </span>solutions<span class="_6 blank"> </span>412</span></div><div class="t m0 x2 h4 y96 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws8c">Discussion 416</span></div><div class="t m0 x1 h3 y97 ff4 fs2 fc0 sc0 ls2 ws87">5.3<span class="_3 blank"> </span>General<span class="_8 blank"> </span>theory<span class="_6 blank"> </span>of<span class="_6 blank"> </span>the<span class="_8 blank"> </span>resp onse<span class="_8 blank"> </span>of<span class="_6 blank"> </span>stellar<span class="_8 blank"> </span>systems<span class="_40 blank"> </span><span class="ff3">417</span></div><div class="t m0 x2 h4 y98 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws19">The<span class="_6 blank"> </span>polarization<span class="_6 blank"> </span>function<span class="_8 blank"> </span>in<span class="_6 blank"> </span>angle-action<span class="_6 blank"> </span>v<span class="_0 blank"></span>ariables<span class="_6 blank"> </span>418<span class="_35 blank"> </span><span class="ff5 ls0">\u2022</span>The</span></div><div class="t m0 x2 h4 y99 ff6 fs3 fc0 sc0 ls2 ws8d">Kalna js<span class="_6 blank"> </span>matrix<span class="_6 blank"> </span>method<span class="_6 blank"> </span>419<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws84">The<span class="_6 blank"> </span>response<span class="_6 blank"> </span>matrix<span class="_8 blank"> </span>421</span></div><div class="t m0 x1 h3 y9a ff4 fs2 fc0 sc0 ls2 ws71">5.4<span class="_3 blank"> </span>The energy principle and secular<span class="_6 blank"> </span>stabilit<span class="_0 blank"></span>y<span class="_41 blank"> </span><span class="ff3">423</span></div><div class="t m0 x2 h4 y9b ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsc">The energy principle for<span class="_6 blank"> </span>\ufb02uid systems 423<span class="_7 blank"> </span></span>\u2022<span class="ff6 ls2 ws40">The energy princi-</span></div><div class="t m0 x2 h4 y9c ff6 fs3 fc0 sc0 ls2 ws8e">ple for stellar<span class="_6 blank"> </span>systems 427<span class="_27 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws19">The<span class="_6 blank"> </span>relation<span class="_6 blank"> </span>betw<span class="_0 blank"></span>een<span class="_6 blank"> </span>the<span class="_8 blank"> </span>stability<span class="_6 blank"> </span>of</span></div><div class="t m0 x2 h4 y9d ff6 fs3 fc0 sc0 ls2 wsc">\ufb02uid and stellar systems<span class="_6 blank"> </span>431</div><div class="t m0 x1 h3 y9e ff4 fs2 fc0 sc0 ls2 ws87">5.5<span class="_3 blank"> </span>The<span class="_6 blank"> </span>response<span class="_8 blank"> </span>of<span class="_6 blank"> </span>spherical<span class="_8 blank"> </span>systems<span class="_20 blank"> </span><span class="ff3">432</span></div><div class="t m0 x2 h4 y9f ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws8f">The<span class="_6 blank"> </span>stabilit<span class="_0 blank"></span>y<span class="_6 blank"> </span>of<span class="_8 blank"> </span>spherical<span class="_6 blank"> </span>systems<span class="_6 blank"> </span>with<span class="_8 blank"> </span>ergo dic<span class="_6 blank"> </span>DFs<span class="_6 blank"> </span>432<span class="_7 blank"> </span><span class="ff5 ls0">\u2022</span>The</span></div><div class="t m0 x2 h4 ya0 ff6 fs3 fc0 sc0 ls2 ws28">stability of anisotropic spherical systems 433<span class="_1 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws90">Physical basis of</span></div><div class="t m0 x2 h4 ya1 ff6 fs3 fc0 sc0 ls2 ws40">the radial-orbit instability 434<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span><span class="wsc">Landau damping<span class="_6 blank"> </span>and resonances</span></div><div class="t m0 x2 h4 ya2 ff6 fs3 fc0 sc0 ls2 ws91">in spherical systems<span class="_6 blank"> </span>437</div><div class="t m0 x1 h3 ya3 ff4 fs2 fc0 sc0 ls2 ws3">5.6<span class="_3 blank"> </span>The stability of uniformly rotating systems<span class="_42 blank"> </span><span class="ff3">439</span></div><div class="t m0 x2 h4 ya4 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws6c">The uniformly rotating sheet 439<span class="_3e blank"> </span></span>\u2022<span class="ff6 ls2 ws77">Kalna js<span class="_6 blank"> </span>disks<span class="_8 blank"> </span>444</span></div><div class="t m0 x2 h4 ya5 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsc">Maclaurin spheroids<span class="_6 blank"> </span>and disks 449</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><div class="t m0 x0 h3 y1f ff8 fs2 fc0 sc0 ls2 ws92">Conten<span class="_0 blank"></span>ts <span class="ff3">ix</span></div><div class="t m0 x1 h3 y20 ff4 fs2 fc0 sc0 ls2 ws3c">Problems <span class="ff3">450</span></div><div class="t m0 x0 h2 ya6 ff2 fs1 fc0 sc0 ls2 ws93">6<span class="_1 blank"> </span>Disk Dynamics and Spiral Structure<span class="_43 blank"> </span><span class="ff3 fs2">456</span></div><div class="t m0 x1 h3 ya7 ff4 fs2 fc0 sc0 ls2 ws94">6.1<span class="_3 blank"> </span>F<span class="_44 blank"></span>undamen<span class="_0 blank"></span>tals of<span class="_6 blank"> </span>spiral structure<span class="_45 blank"> </span><span class="ff3">458</span></div><div class="t m0 x2 h4 ya8 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws95">Images of spiral galaxies<span class="_6 blank"> </span>460<span class="_13 blank"> </span></span>\u2022<span class="ff6 ls2 ws8">Spiral arms at other wa<span class="_0 blank"></span>ve-</span></div><div class="t m0 x2 h4 ya9 ff6 fs3 fc0 sc0 ls2 ws3b">lengths 462<span class="_13 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws96">Dust 464<span class="_18 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws97">Relativistic electrons 465</span></span></div><div class="t m0 x2 h4 yaa ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws98">Molecular gas 465<span class="_33 blank"> </span></span>\ue02e<span class="ff6 ls2 ws99">Neutral atomic gas 465<span class="_18 blank"> </span></span>\ue02e<span class="ff6 ls2 ws9a">HII<span class="_6 blank"> </span>re-</span></div><div class="t m0 x2 h4 yab ff6 fs3 fc0 sc0 ls2 ws9b">gions 467<span class="_23 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws13">The geometry of spiral arms 468<span class="_10 blank"> </span><span class="ff7 ls0">\ue02e</span>The</span></div><div class="t m0 x2 h4 yac ff6 fs3 fc0 sc0 ls2 ws19">strength<span class="_8 blank"> </span>and<span class="_6 blank"> </span>num<span class="_0 blank"></span>b er<span class="_8 blank"> </span>of<span class="_6 blank"> </span>arms<span class="_6 blank"> </span>468<span class="_13 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsc">Leading and trailing</span></div><div class="t m0 x2 h4 yad ff6 fs3 fc0 sc0 ls2 ws1f">arms 469<span class="_5 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws3a">The pitch angle and the winding problem<span class="_6 blank"> </span>471</span></div><div class="t m0 x2 h4 yae ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws74">The<span class="_6 blank"> </span>pattern<span class="_8 blank"> </span>speed<span class="_6 blank"> </span>474<span class="_3e blank"> </span></span><span class="ff5">\u2022<span class="ff6 ls2 ws54">The anti-spiral theorem 477</span></span></div><div class="t m0 x2 h4 yaf ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws9c">Angular-momentum<span class="_8 blank"> </span>transport<span class="_6 blank"> </span>by<span class="_8 blank"> </span>spiral-arm<span class="_6 blank"> </span>torques<span class="_8 blank"> </span>478</span></div><div class="t m0 x1 h3 yb0 ff4 fs2 fc0 sc0 ls2 ws9d">6.2<span class="_3 blank"> </span>W<span class="_44 blank"></span>a<span class="_0 blank"></span>ve mechanics of di\ufb00erentially rotating disks<span class="_46 blank"> </span><span class="ff3">481</span></div><div class="t m0 x2 h4 yb1 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws9e">Preliminaries 481<span class="_10 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws2d">Kinematic density w<span class="_0 blank"></span>av<span class="_0 blank"></span>es<span class="_6 blank"> </span>481</span></span></div><div class="t m0 x2 h4 yb2 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws9f">Resonances 484<span class="_11 blank"> </span></span><span class="ff5">\u2022<span class="ff6 ls2 ws84">The<span class="_6 blank"> </span>dispersion<span class="_6 blank"> </span>relation<span class="_6 blank"> </span>for<span class="_8 blank"> </span>tightly<span class="_6 blank"> </span>w<span class="_0 blank"></span>ound</span></span></div><div class="t m0 x2 h4 yb3 ff6 fs3 fc0 sc0 ls2 ws58">spiral arms 485<span class="_11 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsa0">The tight-winding approximation 485</span></div><div class="t m0 x2 h4 yb4 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wsa1">Poten<span class="_0 blank"></span>tial of<span class="_6 blank"> </span>a tightly wound spiral pattern 486<span class="_9 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws84">The<span class="_6 blank"> </span>dispersion</span></span></div><div class="t m0 x2 h4 yb5 ff6 fs3 fc0 sc0 ls2 wsc">relation for<span class="_6 blank"> </span>\ufb02uid disks 488<span class="_32 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws84">The<span class="_6 blank"> </span>dispersion<span class="_6 blank"> </span>relation<span class="_6 blank"> </span>for<span class="_8 blank"> </span>stellar</span></div><div class="t m0 x2 h4 yb6 ff6 fs3 fc0 sc0 ls2 wsa2">disks 492<span class="_12 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws9a">Local<span class="_6 blank"> </span>stability<span class="_8 blank"> </span>of<span class="_6 blank"> </span>di\ufb00erentially<span class="_8 blank"> </span>rotating<span class="_6 blank"> </span>disks<span class="_6 blank"> </span>494</span></div><div class="t m0 x2 h4 yb7 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsc">Long and short wav<span class="_0 blank"></span>es 497<span class="_23 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws42">Group<span class="_6 blank"> </span>v<span class="_0 blank"></span>elo city<span class="_8 blank"> </span>499</span></span></div><div class="t m0 x2 h4 yb8 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws91">Energy and angular momentum in spiral<span class="_6 blank"> </span>wa<span class="_0 blank"></span>ves 503</span></div><div class="t m0 x1 h3 yb9 ff4 fs2 fc0 sc0 ls2 ws9d">6.3<span class="_3 blank"> </span>Global stability of di\ufb00erentially rotating disks<span class="_47 blank"> </span><span class="ff3">505</span></div><div class="t m0 x2 h4 yba ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws31">Numerical work on disk stability 505<span class="_3f blank"> </span></span>\u2022<span class="ff6 ls2 wsa3">Swing ampli-</span></div><div class="t m0 x2 h4 ybb ff6 fs3 fc0 sc0 ls2 wsa4">\ufb01er<span class="_8 blank"> </span>and<span class="_6 blank"> </span>feedback<span class="_8 blank"> </span>loops<span class="_6 blank"> </span>508<span class="_18 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws13">The swing<span class="_6 blank"> </span>ampli\ufb01er 508</span></div><div class="t m0 x2 h4 ybc ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wsa4">F<span class="_44 blank"></span>eedback<span class="_8 blank"> </span>lo ops<span class="_6 blank"> </span>512<span class="_18 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws56">Physical interpretation of the bar</span></span></div><div class="t m0 x2 h4 ybd ff6 fs3 fc0 sc0 ls2 wsd">instability 513<span class="_48 blank"> </span><span class="ff5 ls1">\u2022</span><span class="wsa5">The<span class="_6 blank"> </span>maxim<span class="_0 blank"></span>um-disk<span class="_8 blank"> </span>hypothesis<span class="_6 blank"> </span>515</span></div><div class="t m0 x2 h4 ybe ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws59">Summary 517</span></div><div class="t m0 x1 h3 ybf ff4 fs2 fc0 sc0 ls2 wsa6">6.4<span class="_3 blank"> </span>Damping and excitation of spiral structure<span class="_49 blank"> </span><span class="ff3">518</span></div><div class="t m0 x2 h4 yc0 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsa7">Response<span class="_6 blank"> </span>of<span class="_6 blank"> </span>the<span class="_8 blank"> </span>interstellar<span class="_6 blank"> </span>gas<span class="_8 blank"> </span>to<span class="_6 blank"> </span>a<span class="_8 blank"> </span>density<span class="_8 blank"> </span>wav<span class="_0 blank"></span>e<span class="_6 blank"> </span>518</span></div><div class="t m0 x2 h4 yc1 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsa7">Response<span class="_6 blank"> </span>of<span class="_6 blank"> </span>a<span class="_8 blank"> </span>density<span class="_8 blank"> </span>wa<span class="_0 blank"></span>ve<span class="_6 blank"> </span>to<span class="_8 blank"> </span>the<span class="_6 blank"> </span>in<span class="_0 blank"></span>terstellar<span class="_6 blank"> </span>gas<span class="_6 blank"> </span>522</span></div><div class="t m0 x2 h4 yc2 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsa8">Excitation of spiral structure 524<span class="_7 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws2d">Excitation by companion</span></span></div><div class="t m0 x2 h4 yc3 ff6 fs3 fc0 sc0 ls2 ws7">galaxies 524<span class="_25 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws2d">Excitation<span class="_6 blank"> </span>by bars 525<span class="_25 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws5">Stationary spiral struc-</span></span></div><div class="t m0 x2 h4 yc4 ff6 fs3 fc0 sc0 ls2 wsa9">ture 525<span class="_14 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsaa">Excitation of<span class="_6 blank"> </span>intermediate-scale structure 526</span></div><div class="t m0 x1 h3 yc5 ff4 fs2 fc0 sc0 ls2 wsab">6.5 Bars<span class="_4a blank"> </span><span class="ff3">528</span></div><div class="t m0 x2 h4 yc6 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws43">Observ<span class="_0 blank"></span>ations 528<span class="_35 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws74">The<span class="_6 blank"> </span>pattern<span class="_8 blank"> </span>sp eed<span class="_6 blank"> </span>531<span class="_11 blank"> </span><span class="ff5 ls0">\u2022</span><span class="wsaa">Dynamics of</span></span></span></div><div class="t m0 x2 h4 yc7 ff6 fs3 fc0 sc0 ls2 wsac">bars 533<span class="_7 blank"> </span><span class="ff7 ls0">\ue02e</span>W<span class="_44 blank"></span>eak bars 534<span class="_7 blank"> </span><span class="ff7 ls0">\ue02e</span>Strong bars 535<span class="_7 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws13">The vertical</span></div><div class="t m0 x2 h4 yc8 ff6 fs3 fc0 sc0 ls2 wsaa">structure of bars<span class="_6 blank"> </span>536<span class="_14 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsad">Gas \ufb02ow in bars 536<span class="_14 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsae">Slow evolution of</span></span></div><div class="t m0 x2 h4 yc9 ff6 fs3 fc0 sc0 ls2 wsac">bars 539</div><div class="t m0 x1 h3 yca ff4 fs2 fc0 sc0 ls2 wsaf">6.6<span class="_3 blank"> </span>W<span class="_44 blank"></span>arping and buckling of disks<span class="_4b blank"> </span><span class="ff3">539</span></div><div class="t m0 x2 h4 ycb ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsa1">W<span class="_44 blank"></span>arps 539<span class="_39 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws1b">Kinematics<span class="_6 blank"> </span>of warps 540<span class="_10 blank"> </span><span class="ff7 ls1">\ue02e</span>Bending</span></span></div><div class="t m0 x2 h4 ycc ff6 fs3 fc0 sc0 ls2 wsd">wa<span class="_0 blank"></span>ves with self-gra<span class="_0 blank"></span>vity 542<span class="_18 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws9">The origin of warps 544</span></div><div class="t m0 x2 h4 ycd ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws14">Buckling instabilit<span class="_0 blank"></span>y 548</span></div><div class="t m0 x1 h3 yce ff4 fs2 fc0 sc0 ls2 ws3c">Problems <span class="ff3">552</span></div><div class="t m0 x0 h2 ycf ff2 fs1 fc0 sc0 ls2 wsb0">7<span class="_1 blank"> </span>Kinetic Theory<span class="_4c blank"> </span><span class="ff3 fs2">554</span></div><div class="t m0 x1 h3 ya4 ff4 fs2 fc0 sc0 ls2 wsb1">7.1<span class="_3 blank"> </span>Relaxation<span class="_8 blank"> </span>pro cesses<span class="_4d blank"> </span><span class="ff3">555</span></div><div class="t m0 x2 h4 ya5 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wsb2">Relaxation 555<span class="_25 blank"> </span></span>\ue02e<span class="ff6 ls2 ws14">Equipartition 556<span class="_25 blank"> </span></span>\ue02e<span class="ff6 ls2 wsa5">Escap e<span class="_6 blank"> </span>556<span class="_25 blank"> </span></span>\ue02e<span class="ff6 ls2">Inelastic</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><div class="t m0 x0 h3 y1f ff3 fs2 fc0 sc0 lsc">x<span class="ff8 ls2 ws2b">Conten<span class="_0 blank"></span>ts</span></div><div class="t m0 x2 h4 y20 ff6 fs3 fc0 sc0 ls2 wsc">encounters 557<span class="_7 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws2d">Binary formation<span class="_6 blank"> </span>by triple encounters 557</span></div><div class="t m0 x2 h4 y21 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wsb3">Interactions with primordial binaries 558</span></div><div class="t m0 x1 h3 yd0 ff4 fs2 fc0 sc0 ls2 ws18">7.2<span class="_3 blank"> </span>General results<span class="_4e blank"> </span><span class="ff3">559</span></div><div class="t m0 x2 h4 yd1 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws54">Virial theorem 559<span class="_18 blank"> </span></span>\u2022<span class="ff6 ls2 ws54">Liouville\u2019s<span class="_6 blank"> </span>theorem 561<span class="_18 blank"> </span></span>\u2022<span class="ff6 ls2">Reduced</span></div><div class="t m0 x2 h4 yd2 ff6 fs3 fc0 sc0 ls2 wsb4">distribution functions 563<span class="_c blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws56">Relation of Liouville\u2019s<span class="_6 blank"> </span>equation to</span></div><div class="t m0 x2 h4 yd3 ff6 fs3 fc0 sc0 ls2 ws40">the collisionless<span class="_6 blank"> </span>Boltzmann equation<span class="_6 blank"> </span>565</div><div class="t m0 x1 h3 yd4 ff4 fs2 fc0 sc0 ls2 wsb5">7.3<span class="_3 blank"> </span>The<span class="_6 blank"> </span>thermodynamics<span class="_8 blank"> </span>of<span class="_6 blank"> </span>self-gra<span class="_0 blank"></span>vitating<span class="_6 blank"> </span>systems<span class="_4f blank"> </span><span class="ff3">567</span></div><div class="t m0 x2 h4 yd5 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsb6">Negative heat capacit<span class="_0 blank"></span>y<span class="_6 blank"> </span>567<span class="_2f blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws13">The gra<span class="_0 blank"></span>vothermal catastrophe 568</span></span></div><div class="t m0 x1 h3 yd6 ff4 fs2 fc0 sc0 ls2 wsb7">7.4<span class="_3 blank"> </span>The F<span class="_44 blank"></span>okk<span class="_0 blank"></span>er\u2013Planck appro<span class="_0 blank"></span>ximation<span class="_50 blank"> </span><span class="ff3">573</span></div><div class="t m0 x2 h4 yd7 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws56">The master equation 573<span class="_18 blank"> </span></span>\u2022<span class="ff6 ls2 ws2d">F<span class="_44 blank"></span>okker\u2013Planck equation 574</span></div><div class="t m0 x2 h4 yd8 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws43">W<span class="_44 blank"></span>eak encounters 574<span class="_33 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws9a">Lo cal<span class="_6 blank"> </span>encounters<span class="_8 blank"> </span>576<span class="_33 blank"> </span><span class="ff7 ls0">\ue02e</span>Orbit-</span></span></div><div class="t m0 x2 h4 yd9 ff6 fs3 fc0 sc0 ls2 wsb8">av<span class="_0 blank"></span>eraging 577<span class="_51 blank"> </span><span class="ff5 ls0">\u2022</span><span class="wsb9">Fluctuation-dissipation theorems 578</span></div><div class="t m0 x2 h4 yda ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws2f">Di\ufb00usion<span class="_6 blank"> </span>coe\ufb03cients<span class="_8 blank"> </span>580<span class="_5 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws31">Heating of<span class="_6 blank"> </span>the Galactic<span class="_6 blank"> </span>disk by</span></span></div><div class="t m0 x2 h4 ydb ff6 fs3 fc0 sc0 ls2 ws8a">MACHOs 583<span class="_13 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws8c">Relaxation<span class="_6 blank"> </span>time 586<span class="_3e blank"> </span><span class="ff5 ls0">\u2022</span><span class="wsba">Numerical meth-</span></span></div><div class="t m0 x2 h4 ydc ff6 fs3 fc0 sc0 ls2 wsbb">ods<span class="_6 blank"> </span>588<span class="_12 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws21">Fluid<span class="_6 blank"> </span>models<span class="_6 blank"> </span>588<span class="_35 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws8d">Monte<span class="_8 blank"> </span>Carlo<span class="_6 blank"> </span>metho ds<span class="_6 blank"> </span>592</span></span></div><div class="t m0 x2 h4 ydd ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws2d">Numerical solution<span class="_6 blank"> </span>of the F<span class="_0 blank"></span>okker\u2013Planc<span class="_0 blank"></span>k equation<span class="_6 blank"> </span>593</span></div><div class="t m0 x2 h4 yde ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wsbb">N-bo dy<span class="_6 blank"> </span>in<span class="_0 blank"></span>tegrations<span class="_6 blank"> </span>594<span class="_14 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsc">Checks and comparisons 595</span></span></div><div class="t m0 x1 h3 ydf ff4 fs2 fc0 sc0 ls2 wsbc">7.5<span class="_3 blank"> </span>The evolution of spherical stellar<span class="_6 blank"> </span>systems<span class="_52 blank"> </span><span class="ff3">596</span></div><div class="t m0 x2 h4 ye0 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws33">Mass loss from stellar<span class="_6 blank"> </span>evolution 600<span class="_5 blank"> </span></span>\u2022<span class="ff6 ls2 wsbd">Evaporation<span class="_6 blank"> </span>and<span class="_8 blank"> </span>ejec-</span></div><div class="t m0 x2 h4 ye1 ff6 fs3 fc0 sc0 ls2 ws1c">tion 602<span class="_2f blank"> </span><span class="ff7 ls1">\ue02e</span><span class="wsb4">The maxim<span class="_0 blank"></span>um<span class="_6 blank"> </span>lifetime of<span class="_6 blank"> </span>a stellar<span class="_6 blank"> </span>system 605<span class="_25 blank"> </span><span class="ff5 ls0">\u2022</span>Core</span></div><div class="t m0 x2 h4 ye2 ff6 fs3 fc0 sc0 ls2 wsbe">collapse 606<span class="_5 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws4c">After core collapse 609<span class="_5 blank"> </span><span class="ff5 ls1">\u2022</span><span class="ws14">Equipartition 612</span></span></div><div class="t m0 x2 h4 ye3 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws84">Tidal<span class="_6 blank"> </span>shocks<span class="_8 blank"> </span>and<span class="_6 blank"> </span>the<span class="_8 blank"> </span>surviv<span class="_0 blank"></span>al<span class="_6 blank"> </span>of<span class="_6 blank"> </span>globular<span class="_8 blank"> </span>clusters<span class="_6 blank"> </span>615</span></div><div class="t m0 x2 h4 ye4 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsbf">Binary stars 616<span class="_7 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 wsc0">Soft binaries 618<span class="_7 blank"> </span></span>\ue02e<span class="ff6 ls2 wsc1">Hard binaries<span class="_6 blank"> </span>620</span></span></div><div class="t m0 x2 h4 ye5 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws37">Reaction rates 621<span class="_12 blank"> </span><span class="ff5 ls1">\u2022</span><span class="wsc2">Inelastic encounters 625<span class="_12 blank"> </span></span></span><span class="ff5">\u2022<span class="ff6 ls2 ws9">Stellar sys-</span></span></div><div class="t m0 x2 h4 ye6 ff6 fs3 fc0 sc0 ls2 ws2d">tems with a<span class="_6 blank"> </span>central blac<span class="_0 blank"></span>k hole<span class="_6 blank"> </span>629<span class="_35 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsc3">Consumption of stars by</span></div><div class="t m0 x2 h4 ye7 ff6 fs3 fc0 sc0 ls2 ws40">the black hole 629<span class="_12 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws2d">The e\ufb00ect of<span class="_6 blank"> </span>a central black hole on the</span></div><div class="t m0 x2 h4 ye8 ff6 fs3 fc0 sc0 ls2 wsc4">surrounding stellar system<span class="_6 blank"> </span>631</div><div class="t m0 x1 h3 ye9 ff4 fs2 fc0 sc0 ls2 wsab">7.6 Summary<span class="_53 blank"> </span><span class="ff3">633</span></div><div class="t m0 x1 h3 yea ff4 fs2 fc0 sc0 ls2 ws3c">Problems <span class="ff3">634</span></div><div class="t m0 x0 h2 yeb ff2 fs1 fc0 sc0 ls2 wsc5">8<span class="_1 blank"> </span>Collisions and Encounters of Stellar Systems<span class="_54 blank"> </span><span class="ff3 fs2">639</span></div><div class="t m0 x1 h3 yec ff4 fs2 fc0 sc0 ls2 wsc6">8.1<span class="_3 blank"> </span>Dynamical friction<span class="_55 blank"> </span><span class="ff3">643</span></div><div class="t m0 x2 h4 yed ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws2d">The v<span class="_0 blank"></span>alidity of Chandrasekhar\u2019s<span class="_6 blank"> </span>formula 646<span class="_11 blank"> </span><span class="ff5 ls0">\u2022</span>Applications</span></div><div class="t m0 x2 h4 yee ff6 fs3 fc0 sc0 ls2 wsc7">of dynamical friction 647<span class="_5 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws2d">Decay of black-hole orbits 647</span></div><div class="t m0 x2 h4 yef ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wsc8">Galactic cannibalism 649<span class="_12 blank"> </span></span>\ue02e<span class="ff6 ls2 ws2d">Orbital decay of the Magellanic</span></div><div class="t m0 x2 h4 yf0 ff6 fs3 fc0 sc0 ls2 wsc9">Clouds 650<span class="_1 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws62">Dynamical friction<span class="_6 blank"> </span>on bars 651<span class="_1 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsca">F<span class="_0 blank"></span>ormation and</span></span></div><div class="t m0 x2 h4 yf1 ff6 fs3 fc0 sc0 ls2 wscb">evolution of binary black holes 652<span class="_14 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wscc">Globular clusters 654</span></div><div class="t m0 x1 h3 yf2 ff4 fs2 fc0 sc0 ls2 wscd">8.2<span class="_3 blank"> </span>High-sp eed<span class="_8 blank"> </span>encoun<span class="_0 blank"></span>ters<span class="_56 blank"> </span><span class="ff3">655</span></div><div class="t m0 x2 h4 yf3 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wsce">Mass loss 657<span class="_11 blank"> </span></span>\ue02e<span class="ff6 ls2 wscf">Return to equilibrium<span class="_6 blank"> </span>657<span class="_c blank"> </span></span>\ue02e<span class="ff6 ls2">Adiabatic</span></div><div class="t m0 x2 h4 yf4 ff6 fs3 fc0 sc0 ls2 wsd0">inv<span class="_44 blank"></span>ariance 658<span class="_48 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws58">The distant-tide appro<span class="_0 blank"></span>ximation 658</span></div><div class="t m0 x2 h4 yf5 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsd1">Disruption<span class="_8 blank"> </span>of<span class="_6 blank"> </span>stellar<span class="_6 blank"> </span>systems<span class="_6 blank"> </span>b<span class="_0 blank"></span>y<span class="_6 blank"> </span>high-speed<span class="_8 blank"> </span>encounters<span class="_6 blank"> </span>661</span></div><div class="t m0 x2 h4 yf6 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws13">The catastrophic regime 662<span class="_5 blank"> </span></span>\ue02e<span class="ff6 ls2 ws4d">The di\ufb00usive regime 663</span></div><div class="t m0 x2 h4 yf7 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wsbd">Disruption<span class="_8 blank"> </span>of<span class="_6 blank"> </span>op en<span class="_6 blank"> </span>clusters<span class="_8 blank"> </span>664<span class="_3e blank"> </span></span>\ue02e<span class="ff6 ls2 ws1c">Disruption of binary</span></div><div class="t m0 x2 h4 yf8 ff6 fs3 fc0 sc0 ls2 wsbf">stars 665<span class="_3e blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws8a">Dynamical constraints on MACHOs 668</span></div><div class="t m0 x2 h4 yf9 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws84">Disk<span class="_8 blank"> </span>and<span class="_6 blank"> </span>bulge<span class="_8 blank"> </span>sho cks<span class="_6 blank"> </span>669<span class="_7 blank"> </span></span>\ue02e<span class="ff6 ls2 wsd2">High-speed<span class="_6 blank"> </span>interactions<span class="_8 blank"> </span>in<span class="_6 blank"> </span>clus-</span></div><div class="t m0 x2 h4 y1e ff6 fs3 fc0 sc0 ls2 ws6c">ters of galaxies 672</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><div class="t m0 x0 h3 y1f ff8 fs2 fc0 sc0 ls2 ws92">Conten<span class="_0 blank"></span>ts <span class="ff3">xi</span></div><div class="t m0 x1 h3 y20 ff4 fs2 fc0 sc0 ls2 wsab">8.3 Tides<span class="_57 blank"> </span><span class="ff3">674</span></div><div class="t m0 x2 h4 y21 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsbb">The<span class="_6 blank"> </span>restricted<span class="_8 blank"> </span>three-b o dy<span class="_6 blank"> </span>problem<span class="_8 blank"> </span>675<span class="_11 blank"> </span></span>\u2022<span class="ff6 ls2 ws13">The sheared-sheet</span></div><div class="t m0 x2 h4 y22 ff6 fs3 fc0 sc0 ls2 ws33">or Hill\u2019s approximation 678<span class="_7 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsd3">The epicycle approximation and</span></div><div class="t m0 x2 h4 y23 ff6 fs3 fc0 sc0 ls2 ws58">Hill\u2019s approximation 679<span class="_2f blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws91">The Jacobi radius<span class="_6 blank"> </span>in Hill\u2019s approxima-</span></div><div class="t m0 x2 h4 y24 ff6 fs3 fc0 sc0 ls2 ws1c">tion 680<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws6c">Tidal tails<span class="_6 blank"> </span>and streamers 681</span></div><div class="t m0 x1 h3 yfa ff4 fs2 fc0 sc0 ls2 wsd4">8.4<span class="_3 blank"> </span>Encoun<span class="_0 blank"></span>ters<span class="_6 blank"> </span>in stellar disks<span class="_58 blank"> </span><span class="ff3">685</span></div><div class="t m0 x2 h4 yfb ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws2d">Scattering of disk<span class="_6 blank"> </span>stars by molecular clouds 687<span class="_7 blank"> </span></span>\u2022<span class="ff6 ls2 wsd5">Scattering of</span></div><div class="t m0 x2 h4 yfc ff6 fs3 fc0 sc0 ls2 ws6e">disk stars<span class="_6 blank"> </span>by spiral arms<span class="_6 blank"> </span>691<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws59">Summary 695</span></div><div class="t m0 x1 h3 yfd ff4 fs2 fc0 sc0 ls2 wsab">8.5 Mergers<span class="_59 blank"> </span><span class="ff3">695</span></div><div class="t m0 x2 h4 yfe ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws7">Peculiar galaxies 696<span class="_3f blank"> </span></span>\u2022<span class="ff6 ls2 ws41">Grand-design spirals 698</span></div><div class="t m0 x2 h4 yff ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsd6">Ring galaxies<span class="_6 blank"> </span>699<span class="_18 blank"> </span></span>\u2022<span class="ff6 ls2 ws76">Shells<span class="_6 blank"> </span>and other \ufb01ne structure 701</span></div><div class="t m0 x2 h4 y100 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsd7">Starbursts 705<span class="_1 blank"> </span></span>\u2022<span class="ff6 ls2 ws1c">The merger<span class="_6 blank"> </span>rate 708</span></div><div class="t m0 x1 h3 y101 ff4 fs2 fc0 sc0 ls2 ws3c">Problems <span class="ff3">710</span></div><div class="t m0 x0 h2 y102 ff2 fs1 fc0 sc0 ls2 wsd8">9<span class="_1 blank"> </span>Galaxy F<span class="_44 blank"></span>ormation<span class="_5a blank"> </span><span class="ff3 fs2">716</span></div><div class="t m0 x1 h3 y103 ff4 fs2 fc0 sc0 ls2 wsd9">9.1<span class="_3 blank"> </span>Linear structure formation<span class="_5b blank"> </span><span class="ff3">717</span></div><div class="t m0 x2 h4 y104 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsb6">Gaussian random<span class="_6 blank"> </span>\ufb01elds 719<span class="_27 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 wsda">Filtering 720<span class="_1 blank"> </span></span>\ue02e<span class="ff6 ls2 ws13">The Harrison\u2013</span></span></div><div class="t m0 x2 h4 y105 ff6 fs3 fc0 sc0 ls2 ws74">Zeldovic<span class="_0 blank"></span>h<span class="_6 blank"> </span>pow<span class="_0 blank"></span>er<span class="_6 blank"> </span>spectrum<span class="_6 blank"> </span>721<span class="_32 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws91">Gravitational<span class="_6 blank"> </span>instability in the</span></div><div class="t m0 x2 h4 y106 ff6 fs3 fc0 sc0 ls2 wsdb">expanding universe 722<span class="_5c blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsc">Non-relativistic \ufb02uid 722<span class="_2f blank"> </span><span class="ff7 ls0">\ue02e</span>Relativistic</span></div><div class="t m0 x2 h4 y107 ff6 fs3 fc0 sc0 ls2 wsc">\ufb02uid 726</div><div class="t m0 x1 h3 y108 ff4 fs2 fc0 sc0 ls2 wsdc">9.2<span class="_3 blank"> </span>Nonlinear structure<span class="_6 blank"> </span>formation<span class="_5d blank"> </span><span class="ff3">733</span></div><div class="t m0 x2 h4 y109 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsdd">Spherical collapse 733<span class="_9 blank"> </span></span><span class="ls1">\u2022<span class="ff6 ls2 ws14">The cosmic web 735<span class="_9 blank"> </span></span></span>\u2022<span class="ff6 ls2 ws1e">Press\u2013Schec<span class="_0 blank"></span>hter</span></div><div class="t m0 x2 h4 y10a ff6 fs3 fc0 sc0 ls2 wscb">theory 739<span class="_1 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws41">The mass<span class="_6 blank"> </span>function 744<span class="_27 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws1c">The merger rate 746</span></span></div><div class="t m0 x2 h4 y10b ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws72">Collapse and<span class="_6 blank"> </span>virialization<span class="_6 blank"> </span>in the cosmic<span class="_6 blank"> </span>web 748</span></div><div class="t m0 x1 h3 y10c ff4 fs2 fc0 sc0 ls2 ws36">9.3<span class="_3 blank"> </span>N-b o dy<span class="_8 blank"> </span>simulations<span class="_8 blank"> </span>of<span class="_8 blank"> </span>clustering<span class="_45 blank"> </span><span class="ff3">751</span></div><div class="t m0 x2 h4 y10d ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws41">The mass function of halos 752<span class="_7 blank"> </span></span><span class="ls1">\u2022<span class="ff6 ls2 ws2d">Radial density pro\ufb01les 753</span></span></div><div class="t m0 x2 h4 y10e ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsde">Internal dynamics of halos 756<span class="_35 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 wsdf">The<span class="_6 blank"> </span>shapes<span class="_6 blank"> </span>of<span class="_5e blank"> </span>halos<span class="_5e blank"> </span>756</span></span></div><div class="t m0 x2 h4 y10f ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wse0">Rotation of halos 757<span class="_14 blank"> </span></span>\ue02e<span class="ff6 ls2 wse1">Dynamics<span class="_6 blank"> </span>of halo<span class="_6 blank"> </span>substructure 759</span></div><div class="t m0 x1 h3 y110 ff4 fs2 fc0 sc0 ls2 wse2">9.4<span class="_3 blank"> </span>Star formation and feedbac<span class="_0 blank"></span>k<span class="_5f blank"> </span><span class="ff3">760</span></div><div class="t m0 x2 h4 y111 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 wse3">Reionization 760<span class="_7 blank"> </span></span>\ue02e<span class="ff6 ls2 ws2d">F<span class="_44 blank"></span>eedback 761<span class="_7 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsc0">Mergers, starbursts and</span></span></div><div class="t m0 x2 h4 y112 ff6 fs3 fc0 sc0 ls2 ws3a">quiescent accretion 762<span class="_7 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsc2">The role of central blac<span class="_0 blank"></span>k holes 764</span></div><div class="t m0 x2 h4 y113 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws41">Origin of the galaxy luminosity function 765</span></div><div class="t m0 x1 h3 y114 ff4 fs2 fc0 sc0 ls2 wsab">9.5 Conclusions<span class="_60 blank"> </span><span class="ff3">765</span></div><div class="t m0 x1 h3 y115 ff4 fs2 fc0 sc0 ls2 ws3c">Problems <span class="ff3">766</span></div><div class="t m0 x0 h2 y116 ff2 fs1 fc0 sc0 ls2 wse4">App endices</div><div class="t m0 x1 h3 y117 ff4 fs2 fc0 sc0 ls2 ws27">A<span class="_18 blank"> </span>Useful<span class="_5e blank"> </span>num<span class="_0 blank"></span>b ers<span class="_61 blank"> </span><span class="ff3">770</span></div><div class="t m0 x1 h3 y118 ff4 fs2 fc0 sc0 ls2 wse5">B<span class="_13 blank"> </span>Mathematical background<span class="_62 blank"> </span><span class="ff3">771</span></div><div class="t m0 x2 h4 y119 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsde">V<span class="_44 blank"></span>ectors 771<span class="_3f blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws2f">Curvilinear<span class="_5e blank"> </span>co ordinate<span class="_5e blank"> </span>systems<span class="_6 blank"> </span>773</span></span></div><div class="t m0 x2 h4 y11a ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wse6">V<span class="_44 blank"></span>ector calculus<span class="_6 blank"> </span>775<span class="_18 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws8">F<span class="_44 blank"></span>ourier series<span class="_6 blank"> </span>and transforms 778</span></span></div><div class="t m0 x2 h4 y11b ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wse7">Abel<span class="_5e blank"> </span>integral<span class="_5e blank"> </span>equation<span class="_5e blank"> </span>780<span class="_3e blank"> </span></span>\u2022<span class="ff6 ls2 ws2d">Sch<span class="_0 blank"></span>warz\u2019s inequality 780</span></div><div class="t m0 x2 h4 y76 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws1b">Calculus of v<span class="_0 blank"></span>ariations<span class="_6 blank"> </span>781<span class="_10 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws13">Poisson distribution 781</span></span></div><div class="t m0 x2 h4 y77 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsc">Conditional probability and Bay<span class="_0 blank"></span>es\u2019s<span class="_6 blank"> </span>theorem 782<span class="_18 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws1e">Central</span></span></div><div class="t m0 x2 h4 y78 ff6 fs3 fc0 sc0 ls2 ws54">limit theorem 783</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><div class="t m0 x0 h3 y1f ff3 fs2 fc0 sc0 ls2 wse8">xii <span class="ff8 ws2b">Conten<span class="_0 blank"></span>ts</span></div><div class="t m0 x1 h3 y20 ff4 fs2 fc0 sc0 ls2 wse9">C<span class="_13 blank"> </span>Sp ecial<span class="_5e blank"> </span>functions<span class="_63 blank"> </span><span class="ff3">785</span></div><div class="t m0 x2 h4 y4d ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws41">Delta function and step function 785<span class="_11 blank"> </span></span>\u2022<span class="ff6 ls2 ws33">F<span class="_0 blank"></span>actorial or gamma</span></div><div class="t m0 x2 h4 y11c ff6 fs3 fc0 sc0 ls2 ws96">function 786<span class="_33 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws6c">Error function, Dawson\u2019s in<span class="_0 blank"></span>tegral,<span class="_6 blank"> </span>and plasma</span></div><div class="t m0 x2 h4 y11d ff6 fs3 fc0 sc0 ls2 ws84">dispersion<span class="_6 blank"> </span>function<span class="_5e blank"> </span>786<span class="_18 blank"> </span><span class="ff5 ls0">\u2022</span><span class="wsea">Elliptic in<span class="_64 blank"></span>tegrals 787<span class="_33 blank"> </span><span class="ff5 ls0">\u2022</span>Legendre</span></div><div class="t m0 x2 h4 y11e ff6 fs3 fc0 sc0 ls2 ws12">functions 788<span class="_1 blank"> </span><span class="ff5 ls0">\u2022</span><span class="wsdd">Spherical harmonics 789<span class="_27 blank"> </span><span class="ff5 ls1">\u2022</span></span>Bessel functions 790</div><div class="t m0 x1 h3 y11f ff4 fs2 fc0 sc0 ls2 wseb">D Mec<span class="_0 blank"></span>hanics<span class="_65 blank"> </span><span class="ff3">792</span></div><div class="t m0 x2 h4 y120 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsa3">Single particles 792<span class="_35 blank"> </span></span>\u2022<span class="ff6 ls2 ws8e">Systems of<span class="_5e blank"> </span>particles<span class="_6 blank"> </span>794<span class="_35 blank"> </span></span>\u2022<span class="ff6 ls2">Lagrangian</span></div><div class="t m0 x2 h4 y121 ff6 fs3 fc0 sc0 ls2 wsec">dynamics 797<span class="_32 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws56">Hamiltonian dynamics 797<span class="_1 blank"> </span><span class="ff7 ls1">\ue02e</span><span class="wsed">Hamilton\u2019s equa-</span></span></div><div class="t m0 x2 h4 y122 ff6 fs3 fc0 sc0 ls2 ws1f">tions 797<span class="_7 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsee">Poincar<span class="_0 blank"></span>´<span class="_29 blank"></span>e inv<span class="_0 blank"></span>ariants 799<span class="_27 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws2e">Poisson<span class="_6 blank"> </span>brack<span class="_0 blank"></span>ets 800</span></span></div><div class="t m0 x2 h4 y123 ff7 fs3 fc0 sc0 ls0">\ue02e<span class="ff6 ls2 ws2f">Canonical<span class="_5e blank"> </span>co ordinates<span class="_6 blank"> </span>and<span class="_5e blank"> </span>transformations<span class="_6 blank"> </span>800<span class="_12 blank"> </span></span><span class="ls1">\ue02e<span class="ff6 ls2">Extended</span></span></div><div class="t m0 x2 h4 y124 ff6 fs3 fc0 sc0 ls2 ws67">phase space 803<span class="_14 blank"> </span><span class="ff7 ls1">\ue02e</span><span class="wsef">Generating functions 803</span></div><div class="t m0 x1 h3 y125 ff4 fs2 fc0 sc0 ls2 wsf0">E<span class="_3e blank"> </span>Delaunay v<span class="_0 blank"></span>ariables for Kepler orbits<span class="_66 blank"> </span><span class="ff3">805</span></div><div class="t m0 x1 h3 y126 ff4 fs2 fc0 sc0 ls2 wsf1">F<span class="_10 blank"> </span>Fluid mec<span class="_0 blank"></span>hanics<span class="_67 blank"> </span><span class="ff3">807</span></div><div class="t m0 x2 h4 y127 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws5f">Basic equations 807<span class="_14 blank"> </span></span><span class="ff7">\ue02e<span class="ff6 ls2 ws2d">Contin<span class="_0 blank"></span>uity equation 807<span class="_14 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsf2">Euler\u2019s equa-</span></span></span></div><div class="t m0 x2 h4 y128 ff6 fs3 fc0 sc0 ls2 ws1c">tion 808<span class="_12 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws91">Energy equation 810<span class="_12 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="ws99">Equation of state 811</span></span></div><div class="t m0 x2 h4 y129 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws13">The ideal gas 812<span class="_35 blank"> </span></span>\u2022<span class="ff6 ls2 wsf3">Sound wa<span class="_0 blank"></span>ves 813<span class="_1 blank"> </span><span class="ff7 ls0">\ue02e</span><span class="wsc">Energy<span class="_5e blank"> </span>and momen-</span></span></div><div class="t m0 x2 h4 y12a ff6 fs3 fc0 sc0 ls2 wsf4">tum in sound w<span class="_0 blank"></span>av<span class="_0 blank"></span>es 814<span class="_27 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws42">Group<span class="_5e blank"> </span>velocity<span class="_5e blank"> </span>817</span></div><div class="t m0 x1 h3 y12b ff4 fs2 fc0 sc0 ls2 wsf5">G<span class="_33 blank"> </span>Discrete F<span class="_44 blank"></span>ourier<span class="_6 blank"> </span>transforms<span class="_68 blank"> </span><span class="ff3">818</span></div><div class="t m0 x1 h3 y12c ff4 fs2 fc0 sc0 ls2 wsf6">H<span class="_33 blank"> </span>The<span class="_6 blank"> </span>An<span class="_0 blank"></span>tonov\u2013Lebovitz<span class="_8 blank"> </span>theorem<span class="_69 blank"> </span><span class="ff3">822</span></div><div class="t m0 x1 h3 y12d ff4 fs2 fc0 sc0 ls2 wsf7">I<span class="_23 blank"> </span>The Doremus\u2013F<span class="_44 blank"></span>eix\u2013Baumann theorem<span class="_6a blank"> </span><span class="ff3">823</span></div><div class="t m0 x1 h3 y12e ff4 fs2 fc0 sc0 ls2 wsf8">J<span class="_48 blank"> </span>Angular-momentum<span class="_8 blank"> </span>transport<span class="_6 blank"> </span>in<span class="_8 blank"> </span>disks<span class="_6b blank"> </span><span class="ff3">825</span></div><div class="t m0 x2 h4 y12f ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 wsc">T<span class="_44 blank"></span>ransp<span class="_1a blank"> </span>ort in<span class="_6 blank"> </span>\ufb02uid and stellar systems<span class="_6 blank"> </span>825<span class="_2f blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws45">T<span class="_0 blank"></span>ransport<span class="_6 blank"> </span>in<span class="_5e blank"> </span>a<span class="_5e blank"> </span>disk</span></span></div><div class="t m0 x2 h4 y130 ff6 fs3 fc0 sc0 ls2 wsaa">with stationary spiral<span class="_6 blank"> </span>structure 826<span class="_5c blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws45">T<span class="_0 blank"></span>ransp ort<span class="_5e blank"> </span>in<span class="_5e blank"> </span>p erturb ed<span class="_5e blank"> </span>axi-</span></div><div class="t m0 x2 h4 y131 ff6 fs3 fc0 sc0 ls2 wsa2">symmetric disks 828<span class="_27 blank"> </span><span class="ff5 ls0">\u2022</span><span class="ws45">T<span class="_44 blank"></span>ransp ort<span class="_6 blank"> </span>in<span class="_5e blank"> </span>the<span class="_5e blank"> </span>WKB<span class="_5e blank"> </span>approximation<span class="_5e blank"> </span>829</span></div><div class="t m0 x1 h3 y132 ff4 fs2 fc0 sc0 ls2 wsf9">K<span class="_33 blank"> </span>Deriv<span class="_0 blank"></span>ation of<span class="_6 blank"> </span>the reduction factor<span class="_6c blank"> </span><span class="ff3">830</span></div><div class="t m0 x1 h3 y133 ff4 fs2 fc0 sc0 ls2 wsfa">L<span class="_39 blank"> </span>The<span class="_5e blank"> </span>di\ufb00usion<span class="_8 blank"> </span>co e\ufb03cien<span class="_64 blank"></span>ts<span class="_6d blank"> </span><span class="ff3">833</span></div><div class="t m0 x1 h3 y134 ff4 fs2 fc0 sc0 ls2 wsfb">M<span class="_35 blank"> </span>The<span class="_5e blank"> </span>distribution of<span class="_5e blank"> </span>binary<span class="_6 blank"> </span>energies<span class="_6e blank"> </span><span class="ff3">838</span></div><div class="t m0 x2 h4 y135 ff5 fs3 fc0 sc0 ls0">\u2022<span class="ff6 ls2 ws13">The evolution of the<span class="_8 blank"> </span>energy distribution of binaries 838<span class="_32 blank"> </span></span>\u2022<span class="ff6 ls2">The</span></div><div class="t m0 x2 h4 y136 ff6 fs3 fc0 sc0 ls2 wsfc">tw<span class="_0 blank"></span>o-b o dy<span class="_5e blank"> </span>distribution<span class="_5e blank"> </span>function<span class="_5e blank"> </span>in<span class="_5e blank"> </span>thermal<span class="_5e blank"> </span>equilibrium<span class="_6 blank"> </span>839<span class="_7 blank"> </span><span class="ff5 ls0">\u2022</span>The</div><div class="t m0 x2 h4 y137 ff6 fs3 fc0 sc0 ls2 wsb4">distribution of binary energies<span class="_6 blank"> </span>in thermal<span class="_6 blank"> </span>equilibrium 839<span class="_32 blank"> </span><span class="ff5 ls0">\u2022</span>The</div><div class="t m0 x2 h4 y138 ff6 fs3 fc0 sc0 ls2 wsfd">principle of detailed balance 841</div><div class="t m0 x0 h2 y139 ff2 fs1 fc0 sc0 ls2 wsfe">References <span class="ff3 fs2">842</span></div><div class="t m0 x0 h2 y13a ff2 fs1 fc0 sc0 ls2 wsff">Index <span class="ff3 fs2">857</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><div class="t m0 x0 h1 y13b ff1 fs0 fc0 sc0 ls2">Preface</div><div class="t m0 x0 h3 y13c ff3 fs2 fc0 sc0 ls2 ws100">Alwa<span class="_0 blank"></span>ys<span class="_8 blank"> </span>ma jestic,<span class="_8 blank"> </span>often<span class="_8 blank"> </span>sp ectacularly<span class="_8 blank"> </span>b eautiful,<span class="_8 blank"> </span>galaxies<span class="_8 blank"> </span>are<span class="_8 blank"> </span>the<span class="_8 blank"> </span>fundamen<span class="_0 blank"></span>tal</div><div class="t m0 x0 h3 y13d ff3 fs2 fc0 sc0 ls2 ws101">building<span class="_6f blank"> </span>blocks<span class="_6f blank"> </span>of<span class="_6f blank"> </span>the<span class="_6f blank"> </span>Universe.<span class="_5c blank"> </span>The<span class="_6f blank"> </span>inquiring<span class="_6f blank"> </span>mind<span class="_6f blank"> </span>cannot<span class="_6f blank"> </span>help<span class="_6f blank"> </span>asking</div><div class="t m0 x0 h3 yab ff3 fs2 fc0 sc0 ls2 ws102">how they formed, ho<span class="_0 blank"></span>w they function,<span class="_70 blank"> </span>and what will b<span class="_1a blank"> </span>ecome of them in<span class="_70 blank"> </span>the</div><div class="t m0 x0 h3 y13e ff3 fs2 fc0 sc0 ls2 ws103">distant<span class="_71 blank"> </span>future.<span class="_70 blank"> </span>The<span class="_8 blank"> </span>principal<span class="_71 blank"> </span>to ol<span class="_8 blank"> </span>used<span class="_71 blank"> </span>in<span class="_8 blank"> </span>answ<span class="_0 blank"></span>ering<span class="_71 blank"> </span>these<span class="_8 blank"> </span>questions<span class="_71 blank"> </span>is<span class="_8 blank"> </span>stellar</div><div class="t m0 x0 h3 y13f ff3 fs2 fc0 sc0 ls2 ws104">dynamics, the study of the motion of a large num<span class="_0 blank"></span>b<span class="_1a blank"> </span>er of point masses orbiting</div><div class="t m0 x0 h3 y140 ff3 fs2 fc0 sc0 ls2 ws105">under the in\ufb02uence of their m<span class="_0 blank"></span>utual self-gravit<span class="_0 blank"></span>y<span class="_0 blank"></span>.<span class="_70 blank"> </span>The main aim of this book is</div><div class="t m0 x0 h3 y141 ff3 fs2 fc0 sc0 ls2 ws106">to provide the reader with<span class="_6 blank"> </span>an understanding of<span class="_5e blank"> </span>stellar<span class="_5e blank"> </span>dynamics at the<span class="_5e blank"> </span>level</div><div class="t m0 x0 h3 y142 ff3 fs2 fc0 sc0 ls2 ws107">required to carry out research<span class="_71 blank"> </span>into the formation and dynamics of galaxies.</div><div class="t m0 x3 h3 y143 ff3 fs2 fc0 sc0 ls2 ws108">Galaxies<span class="_70 blank"> </span>are<span class="_6f blank"> </span>not<span class="_70 blank"> </span>only<span class="_6f blank"> </span>important<span class="_70 blank"> </span>in<span class="_6f blank"> </span>their<span class="_70 blank"> </span>own<span class="_72 blank"> </span>right,<span class="_72 blank"> </span>but<span class="_72 blank"> </span>also<span class="_72 blank"> </span>provide</div><div class="t m0 x0 h3 y144 ff3 fs2 fc0 sc0 ls2 ws100">powerful<span class="_8 blank"> </span>to ols<span class="_5e blank"> </span>for<span class="_5e blank"> </span>investigating<span class="_8 blank"> </span>some<span class="_5e blank"> </span>of<span class="_6 blank"> </span>the<span class="_5e blank"> </span>most<span class="_5e blank"> </span>imp ortant<span class="_5e blank"> </span>and<span class="_5e blank"> </span>fundamen-</div><div class="t m0 x0 h3 y145 ff3 fs2 fc0 sc0 ls2 ws109">tal problems in physics:<span class="_6f blank"> </span>our current expectation that<span class="_6 blank"> </span>the<span class="_70 blank"> </span>great ma<span class="_1a blank"> </span>jority of</div><div class="t m0 x0 h3 y146 ff3 fs2 fc0 sc0 ls2 ws10a">the matter in the universe<span class="_71 blank"> </span>is made up of w<span class="_0 blank"></span>eakly interacting<span class="_71 blank"> </span>elemen<span class="_0 blank"></span>tary parti-</div><div class="t m0 x0 h3 y147 ff3 fs2 fc0 sc0 ls2 ws10b">cles of unknown<span class="_34 blank"> </span>nature arose from studies of the outer reaches<span class="_34 blank"> </span>of galaxies;<span class="_71 blank"> </span>the</div><div class="t m0 x0 h3 y148 ff3 fs2 fc0 sc0 ls2 ws10c">standard theory of<span class="_8 blank"> </span>the<span class="_5e blank"> </span>origin of<span class="_5e blank"> </span>structure in<span class="_8 blank"> </span>the<span class="_5e blank"> </span>universe, whic<span class="_64 blank"></span>h rests<span class="_8 blank"> </span>on<span class="_5e blank"> </span>ex-</div><div class="t m0 x0 h3 y149 ff3 fs2 fc0 sc0 ls2 ws10d">otic hypotheses such as in\ufb02ation and v<span class="_44 blank"></span>acuum energy<span class="_0 blank"></span>, is tested and challenged</div><div class="t m0 x0 h3 y14a ff3 fs2 fc0 sc0 ls2 ws10e">by observ<span class="_0 blank"></span>ations of the<span class="_8 blank"> </span>structure<span class="_8 blank"> </span>of<span class="_8 blank"> </span>galaxies;<span class="_8 blank"> </span>and galaxies are<span class="_8 blank"> </span>frequently used</div><div class="t m0 x0 h3 y14b ff3 fs2 fc0 sc0 ls2 ws101">as<span class="_8 blank"> </span>enormous<span class="_8 blank"> </span>laboratories<span class="_8 blank"> </span>to<span class="_8 blank"> </span>study<span class="_8 blank"> </span>the<span class="_8 blank"> </span>laws<span class="_71 blank"> </span>of<span class="_8 blank"> </span>physics<span class="_8 blank"> </span>in<span class="_8 blank"> </span>extreme<span class="_8 blank"> </span>conditions.</div><div class="t m0 x3 h3 y14c ff3 fs2 fc0 sc0 ls2 ws10f">The study<span class="_70 blank"> </span>of<span class="_70 blank"> </span>galactic dynamics<span class="_70 blank"> </span>carries the<span class="_70 blank"> </span>student to<span class="_70 blank"> </span>the<span class="_72 blank"> </span>frontiers of</div><div class="t m0 x0 h3 y14d ff3 fs2 fc0 sc0 ls2 ws110">knowledge faster than almost<span class="_6f blank"> </span>any other branch of theoretical<span class="_6f blank"> </span>physics,<span class="_6f blank"> </span>in</div><div class="t m0 x0 h3 y14e ff3 fs2 fc0 sc0 ls2 ws111">part because the fundamen<span class="_0 blank"></span>tal issues in the sub<span class="_1a blank"> </span>ject are easy<span class="_5e blank"> </span>to understand</div><div class="t m0 x0 h3 y14f ff3 fs2 fc0 sc0 ls2 ws112">for an<span class="_0 blank"></span>yone with an undergraduate<span class="_5e blank"> </span>training in ph<span class="_64 blank"></span>ysics, and in part because</div><div class="t m0 x0 h3 y150 ff3 fs2 fc0 sc0 ls2 ws113">theorists<span class="_8 blank"> </span>are<span class="_5e blank"> </span>scrambling<span class="_8 blank"> </span>to<span class="_5e blank"> </span>keep<span class="_8 blank"> </span>pace<span class="_8 blank"> </span>with<span class="_6 blank"> </span>a<span class="_8 blank"> </span>\ufb02o o d<span class="_6 blank"> </span>of<span class="_5e blank"> </span>new<span class="_5e blank"> </span>observ<span class="_0 blank"></span>ations.</div><div class="t m0 x3 h3 y151 ff3 fs2 fc0 sc0 ls2 ws103">The<span class="_70 blank"> </span>tools<span class="_70 blank"> </span>required<span class="_70 blank"> </span>to<span class="_70 blank"> </span>reach<span class="_6 blank"> </span>the<span class="_70 blank"> </span>research<span class="_6 blank"> </span>frontier<span class="_70 blank"> </span>in<span class="_70 blank"> </span>galactic<span class="_6 blank"> </span>dynamics</div><div class="t m0 x0 h3 y152 ff3 fs2 fc0 sc0 ls2 ws114">are<span class="_5e blank"> </span>for<span class="_5e blank"> </span>the<span class="_6 blank"> </span>most<span class="_5e blank"> </span>part<span class="_6 blank"> </span>ones<span class="_5e blank"> </span>developed<span class="_5e blank"> </span>in<span class="_6 blank"> </span>other<span class="_5e blank"> </span>\ufb01elds:<span class="_6f blank"> </span>classical,<span class="_5e blank"> </span>celestial,<span class="_5e blank"> </span>and</div><div class="t m0 x0 h3 y153 ff3 fs2 fc0 sc0 ls2 ws115">Hamiltonian mec<span class="_0 blank"></span>hanics, \ufb02uid mechanics, statistical<span class="_6 blank"> </span>mechanics, and<span class="_6 blank"> </span>plasma</div><div class="t m0 x0 h3 y154 ff3 fs2 fc0 sc0 ls2 ws116">physics<span class="_8 blank"> </span>provide the most relev<span class="_44 blank"></span>ant bac<span class="_0 blank"></span>kgrounds, and, although there is little</div><div class="t m0 x0 h3 y155 ff3 fs2 fc0 sc0 ls2 ws114">need<span class="_6 blank"> </span>for<span class="_5e blank"> </span>quantum<span class="_5e blank"> </span>mechanics,<span class="_6 blank"> </span>the<span class="_6 blank"> </span>mathematical<span class="_5e blank"> </span>techniques<span class="_6 blank"> </span>dev<span class="_64 blank"></span>eloped<span class="_6 blank"> </span>in<span class="_6 blank"> </span>an</div><div class="t m0 x0 h3 y156 ff3 fs2 fc0 sc0 ls2 ws117">introductory<span class="_73 blank"> </span>quantum<span class="_73 blank"> </span>mechanics<span class="_34 blank"> </span>course<span class="_73 blank"> </span>are<span class="_71 blank"> </span>in<span class="_73 blank"> </span>constant<span class="_73 blank"> </span>use.<span class="_70 blank"> </span>Brief<span class="_73 blank"> </span>summaries</div><div class="t m0 x0 h3 y157 ff3 fs2 fc0 sc0 ls2 ws118">of the<span class="_6 blank"> </span>required background material are giv<span class="_0 blank"></span>en<span class="_5e blank"> </span>in<span class="_5e blank"> </span>App<span class="_1a blank"> </span>endices<span class="_5e blank"> </span>B<span class="_6 blank"> </span>(mathemat-</div><div class="t m0 x0 h3 y158 ff3 fs2 fc0 sc0 ls2 ws101">ics),<span class="_5e blank"> </span>C<span class="_5e blank"> </span>(special<span class="_6 blank"> </span>functions),<span class="_5e blank"> </span>D<span class="_5e blank"> </span>(mechanics),<span class="_5e blank"> </span>and<span class="_8 blank"> </span>F<span class="_6 blank"> </span>(\ufb02uid<span class="_5e blank"> </span>mechanics).</div><div class="t m0 x3 h3 y159 ff3 fs2 fc0 sc0 ls2 ws100">This<span class="_6 blank"> </span>b o ok<span class="_70 blank"> </span>has<span class="_6 blank"> </span>b een<span class="_70 blank"> </span>designed<span class="_6 blank"> </span>for<span class="_70 blank"> </span>readers<span class="_6 blank"> </span>with<span class="_70 blank"> </span>a<span class="_6 blank"> </span>standard<span class="_6 blank"> </span>undergradu-</div><div class="t m0 x0 h3 y15a ff3 fs2 fc0 sc0 ls2 ws119">ate preparation in<span class="_5e blank"> </span>physics.<span class="_70 blank"> </span>By<span class="_5e blank"> </span>contrast, we hav<span class="_0 blank"></span>e assumed<span class="_5e blank"> </span>no<span class="_5e blank"> </span>background in</div><div class="t m0 x0 h3 y15b ff3 fs2 fc0 sc0 ls2 ws100">astronomy<span class="_44 blank"></span>,<span class="_6 blank"> </span>although<span class="_6 blank"> </span>the<span class="_70 blank"> </span>con<span class="_0 blank"></span>text<span class="_70 blank"> </span>of<span class="_6 blank"> </span>many<span class="_6 blank"> </span>discussions<span class="_6 blank"> </span>will<span class="_70 blank"> </span>be<span class="_70 blank"> </span>clearer<span class="_5e blank"> </span>to<span class="_70 blank"> </span>the</div><div class="t m0 x0 h3 y15c ff3 fs2 fc0 sc0 ls2 ws11a">reader who has<span class="_70 blank"> </span>a<span class="_70 blank"> </span>broad grasp of<span class="_70 blank"> </span>basic astronomy and astrophysics, at<span class="_70 blank"> </span>the</div><div class="t m0 x0 h3 y15d ff3 fs2 fc0 sc0 ls2 ws11b">level of Sh<span class="_0 blank"></span>u (1982).<span class="_9 blank"> </span>A brief summary of the relev<span class="_0 blank"></span>ant observ<span class="_44 blank"></span>ations is pro-</div><div class="t m0 x0 h3 y15e ff3 fs2 fc0 sc0 ls2 ws112">vided in <span class="ffc ws11c">§</span><span class="ws11d">1.1.<span class="_74 blank"> </span>Introductions<span class="_6 blank"> </span>to<span class="_70 blank"> </span>galactic<span class="_6 blank"> </span>astronomy<span class="_6 blank"> </span>are<span class="_6 blank"> </span>given<span class="_6 blank"> </span>in<span class="_70 blank"> </span>Marochnik</span></div><div class="t m0 x0 h3 y15f ff3 fs2 fc0 sc0 ls2 ws11e">& Suchk<span class="_0 blank"></span>ov (1996), Elmegreen<span class="_6 blank"> </span>(1998) and Spark<span class="_0 blank"></span>e & Gallagher (2000).<span class="_74 blank"> </span>F<span class="_44 blank"></span>or</div><div class="t m0 x0 h3 y160 ff3 fs2 fc0 sc0 ls2 ws11f">a<span class="_70 blank"> </span>comprehensive<span class="_6 blank"> </span>description<span class="_70 blank"> </span>of<span class="_70 blank"> </span>the<span class="_70 blank"> </span>prop erties<span class="_70 blank"> </span>of<span class="_70 blank"> </span>galaxies<span class="_70 blank"> </span>and<span class="_70 blank"> </span>other<span class="_70 blank"> </span>stellar</div><div class="t m0 x0 h3 y161 ff3 fs2 fc0 sc0 ls2 ws120">systems,<span class="_21 blank"> </span>see <span class="ffd ws121">Galactic<span class="_21 blank"> </span>Astr<span class="_0 blank"></span>onomy <span class="ff3 ws122">(Binney &<span class="_6f blank"> </span>Merri\ufb01eld 1998),<span class="_21 blank"> </span>which is a</span></span></div><div class="t m0 x0 h3 y162 ff3 fs2 fc0 sc0 ls2 ws100">companion<span class="_8 blank"> </span>to<span class="_5e blank"> </span>the<span class="_5e blank"> </span>present<span class="_8 blank"> </span>b o ok<span class="_5e blank"> </span>and<span class="_6 blank"> </span>will<span class="_5e blank"> </span>b e<span class="_5e blank"> </span>referred<span class="_8 blank"> </span>to<span class="_5e blank"> </span>simply<span class="_5e blank"> </span>as<span class="_5e blank"> </span>BM.</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pfa" class="pf w0 h0" data-page-no="a"><div class="pc pca w0 h0"><div class="t m0 x0 h3 y1f ff3 fs2 fc0 sc0 ls2 ws123">xiv <span class="ff8">Preface</span></div><div class="t m0 x3 h3 y20 ff3 fs2 fc0 sc0 ls2 ws124">A one-semester graduate course<span class="_8 blank"> </span>on galaxies might be based on the fol-</div><div class="t m0 x0 h3 y163 ff3 fs2 fc0 sc0 ls2 ws125">lowing sections<span class="_8 blank"> </span>from the tw<span class="_0 blank"></span>o b<span class="_1a blank"> </span>o<span class="_1a blank"> </span>oks:</div><div class="t m0 x3 h3 y164 ffd fs2 fc0 sc0 ls2 ws126">Galactic Astr<span class="_0 blank"></span>onomy:<span class="_75 blank"> </span><span class="ff3 ws127">1.1, 1.2, 2.1, 2.2, 2.3, 3.6, 3.7, 4.1, 4.2, 4.3,</span></div><div class="t m0 x4 h3 y165 ff3 fs2 fc0 sc0 ls2 ws128">4.6, 9.1, 10.3, 11.1</div><div class="t m0 x3 h3 ya8 ffd fs2 fc0 sc0 ls2 ws129">Galactic Dynamics:<span class="_74 blank"> </span><span class="ff3 ws12a">1.1, 1.2, 2.1, 2.2, 2.3, 2.9, 3.1, 3.2, 3.3, 3.4,</span></div><div class="t m0 x4 h3 y166 ff3 fs2 fc0 sc0 ls2 ws12b">4.1, 4.3, 4.7, 4.8, 4.9, 5.1, 5.2, 6.1, 7.1, 7.2, 7.3, 8.1, 8.3,<span class="_8 blank"> </span>8.5</div><div class="t m0 x0 h3 y167 ff3 fs2 fc0 sc0 ls2 ws100">This<span class="_70 blank"> </span>selection<span class="_72 blank"> </span>assumes<span class="_70 blank"> </span>that<span class="_72 blank"> </span>the<span class="_72 blank"> </span>students<span class="_70 blank"> </span>will<span class="_72 blank"> </span>be<span class="_72 blank"> </span>exp osed<span class="_72 blank"> </span>in<span class="_70 blank"> </span>other<span class="_72 blank"> </span>courses</div><div class="t m0 x0 h3 y168 ff3 fs2 fc0 sc0 ls2 ws12c">to<span class="_5e blank"> </span>the<span class="_5e blank"> </span>material<span class="_5e blank"> </span>on<span class="_5e blank"> </span>cosmology (GD<span class="_6 blank"> </span><span class="ffc ws11c">§§</span><span class="ws12d">1.3 and<span class="_5e blank"> </span>9.1\u20139.3), stellar<span class="_5e blank"> </span>structure<span class="_5e blank"> </span>(GA</span></div><div class="t m0 x0 h3 y169 ffc fs2 fc0 sc0 ls2 ws11c">§§<span class="ff3 ws12e">3.1\u20133.5 and 5.1\u20135.4), and<span class="_70 blank"> </span>the interstellar medium<span class="_6 blank"> </span>(GA</span>§<span class="_1a blank"> </span>§<span class="ff3 ws12f">8.1\u20138.4 and<span class="_6 blank"> </span>9.2\u2013</span></div><div class="t m0 x0 h3 y16a ff3 fs2 fc0 sc0 ls2">9.6).</div><div class="t m0 x3 h3 y16b ff3 fs2 fc0 sc0 ls2 ws130">The<span class="_6 blank"> </span>\ufb01rst<span class="_6 blank"> </span>edition<span class="_70 blank"> </span>of<span class="_5e blank"> </span>this<span class="_70 blank"> </span>bo ok<span class="_6 blank"> </span>app eared<span class="_6 blank"> </span>in<span class="_70 blank"> </span>1987,<span class="_5e blank"> </span>and<span class="_6 blank"> </span>after<span class="_70 blank"> </span>t<span class="_0 blank"></span>wo<span class="_6 blank"> </span>decades</div><div class="t m0 x0 h3 y16c ff3 fs2 fc0 sc0 ls2 ws131">ma<span class="_1a blank"> </span>jor revisions were<span class="_73 blank"> </span>in order, b<span class="_1a blank"> </span>oth to accommo<span class="_1a blank"> </span>date the man<span class="_0 blank"></span>y imp<span class="_1a blank"> </span>ortant ad-</div><div class="t m0 x0 h3 y16d ff3 fs2 fc0 sc0 ls2 ws132">v<span class="_0 blank"></span>ances in the \ufb01eld and<span class="_8 blank"> </span>to re\ufb02ect c<span class="_0 blank"></span>hanges in the persp<span class="_1a blank"> </span>ectives<span class="_8 blank"> </span>of the authors.</div><div class="t m0 x0 h3 y16e ff3 fs2 fc0 sc0 ls2 ws133">The present edition<span class="_5e blank"> </span>makes more<span class="_5e blank"> </span>extensive use of<span class="_5e blank"> </span>Lagrangian and<span class="_5e blank"> </span>Hamilton-</div><div class="t m0 x0 h3 y16f ff3 fs2 fc0 sc0 ls2 ws134">ian mechanics,<span class="_6f blank"> </span>and includes<span class="_6f blank"> </span>new theoretical topics<span class="_6f blank"> </span>such as basis-function</div><div class="t m0 x0 h3 y170 ff3 fs2 fc0 sc0 ls2 ws100">expansions<span class="_72 blank"> </span>for<span class="_6f blank"> </span>p otential<span class="_6f blank"> </span>theory<span class="_44 blank"></span>,<span class="_21 blank"> </span>angle-action<span class="_6f blank"> </span>v<span class="_0 blank"></span>ariables,<span class="_21 blank"> </span>orbit-based<span class="_72 blank"> </span>meth-</div><div class="t m0 x0 h3 y171 ff3 fs2 fc0 sc0 ls2 ws135">ods<span class="_5e blank"> </span>of<span class="_5e blank"> </span>constructing<span class="_5e blank"> </span>stellar<span class="_8 blank"> </span>systems,<span class="_5e blank"> </span>linear<span class="_5e blank"> </span>response<span class="_5e blank"> </span>theory<span class="_0 blank"></span>,<span class="_8 blank"> </span>stability<span class="_8 blank"> </span>analysis</div><div class="t m0 x0 h3 y172 ff3 fs2 fc0 sc0 ls2 ws136">using the Kalna<span class="_76 blank"> </span>js matrix method and energy principles, energy and angular-</div><div class="t m0 x0 h3 y173 ff3 fs2 fc0 sc0 ls2 ws137">momentum<span class="_5e blank"> </span>transp ort<span class="_5e blank"> </span>in<span class="_6 blank"> </span>disks,<span class="_6 blank"> </span>the<span class="_6 blank"> </span>\ufb02uctuation-dissipation<span class="_6 blank"> </span>theorem,<span class="_6 blank"> </span>and<span class="_6 blank"> </span>the</div><div class="t m0 x0 h3 y174 ff3 fs2 fc0 sc0 ls2 ws138">sheared<span class="_71 blank"> </span>sheet.<span class="_72 blank"> </span>N-bo dy<span class="_8 blank"> </span>simulations<span class="_73 blank"> </span>of<span class="_8 blank"> </span>stellar<span class="_71 blank"> </span>systems<span class="_8 blank"> </span>hav<span class="_0 blank"></span>e<span class="_71 blank"> </span>grown<span class="_71 blank"> </span>enormously</div><div class="t m0 x0 h3 y175 ff3 fs2 fc0 sc0 ls2 ws139">in imp<span class="_1a blank"> </span>ortance and sophistication, and we ha<span class="_0 blank"></span>ve added extensiv<span class="_0 blank"></span>e descriptions</div><div class="t m0 x0 h3 y176 ff3 fs2 fc0 sc0 ls2 ws101">of<span class="_6 blank"> </span>modern<span class="_6 blank"> </span>numerical<span class="_5e blank"> </span>metho ds<span class="_6 blank"> </span>for<span class="_5e blank"> </span>ev<span class="_0 blank"></span>aluating<span class="_6 blank"> </span>the<span class="_6 blank"> </span>gravitational<span class="_8 blank"> </span>\ufb01eld<span class="_6 blank"> </span>and<span class="_6 blank"> </span>fol-</div><div class="t m0 x0 h3 y177 ff3 fs2 fc0 sc0 ls2 ws125">lowing orbits.</div><div class="t m0 x3 h3 y178 ff3 fs2 fc0 sc0 ls2 ws100">The<span class="_70 blank"> </span>last<span class="_70 blank"> </span>tw<span class="_0 blank"></span>o<span class="_70 blank"> </span>chapters<span class="_6 blank"> </span>of<span class="_70 blank"> </span>the<span class="_70 blank"> </span>\ufb01rst<span class="_70 blank"> </span>edition<span class="_70 blank"> </span>hav<span class="_0 blank"></span>e<span class="_70 blank"> </span>been<span class="_72 blank"> </span>eliminated;<span class="_72 blank"> </span>muc<span class="_0 blank"></span>h</div><div class="t m0 x0 h3 y179 ff3 fs2 fc0 sc0 ls2 ws132">of the material of the old Chapter 9 is no<span class="_0 blank"></span>w covered<span class="_8 blank"> </span>in <span class="ffd ws13a">Galactic Astr<span class="_0 blank"></span>onomy<span class="ff3">,</span></span></div><div class="t m0 x0 h3 y17a ff3 fs2 fc0 sc0 ls2 ws111">while the topics from the old Chapter 10<span class="_6 blank"> </span>hav<span class="_0 blank"></span>e been integrated in<span class="_0 blank"></span>to earlier</div><div class="t m0 x0 h3 y17b ff3 fs2 fc0 sc0 ls2 ws13b">chapters.</div><div class="t m0 x3 h3 y17c ff3 fs2 fc0 sc0 ls2 ws13c">The most dramatic c<span class="_0 blank"></span>hange in this sub<span class="_76 blank"> </span>ject since the publication of the</div><div class="t m0 x0 h3 y17d ff3 fs2 fc0 sc0 ls2 ws13d">\ufb01rst edition has been the<span class="_6f blank"> </span>developmen<span class="_0 blank"></span>t of a theory of structure formation</div><div class="t m0 x0 h3 y17e ff3 fs2 fc0 sc0 ls2 ws100">in<span class="_6 blank"> </span>the<span class="_6 blank"> </span>universe<span class="_5e blank"> </span>of<span class="_6 blank"> </span>remark<span class="_0 blank"></span>able<span class="_5e blank"> </span>elegance<span class="_6 blank"> </span>and<span class="_6 blank"> </span>predictive<span class="_5e blank"> </span>p ow<span class="_64 blank"></span>er,<span class="_5e blank"> </span>based<span class="_6 blank"> </span>on<span class="_6 blank"> </span>con-</div><div class="t m0 x0 h3 y17f ff3 fs2 fc0 sc0 ls2 ws13e">cepts such as in\ufb02ation, cold dark matter, and v<span class="_0 blank"></span>acuum energy<span class="_0 blank"></span>.<span class="_77 blank"> </span>The study</div><div class="t m0 x0 h3 y180 ff3 fs2 fc0 sc0 ls2 ws13f">of galactic structure and the study of cosmology are no<span class="_0 blank"></span>w inseparable, and</div><div class="t m0 x0 h3 y181 ff3 fs2 fc0 sc0 ls2 ws140">one<span class="_8 blank"> </span>of<span class="_8 blank"> </span>our<span class="_8 blank"> </span>struggles<span class="_8 blank"> </span>w<span class="_0 blank"></span>as<span class="_8 blank"> </span>to<span class="_8 blank"> </span>incorp orate<span class="_8 blank"> </span>the<span class="_8 blank"> </span>rich<span class="_8 blank"> </span>new<span class="_8 blank"> </span>insights<span class="_71 blank"> </span>that<span class="_8 blank"> </span>cosmology</div><div class="t m0 x0 h3 y182 ff3 fs2 fc0 sc0 ls2 ws141">has<span class="_8 blank"> </span>brought<span class="_71 blank"> </span>to<span class="_8 blank"> </span>galactic<span class="_8 blank"> </span>dynamics<span class="_8 blank"> </span>without<span class="_8 blank"> </span>writing<span class="_8 blank"> </span>a<span class="_8 blank"> </span>sup er\ufb02uous<span class="_8 blank"> </span>textb o ok<span class="_8 blank"> </span>on</div><div class="t m0 x0 h3 y183 ff3 fs2 fc0 sc0 ls2 ws142">cosmology<span class="_44 blank"></span>.<span class="_75 blank"> </span>W<span class="_44 blank"></span>e have c<span class="_0 blank"></span>hosen to<span class="_70 blank"> </span>dev<span class="_0 blank"></span>ote the<span class="_70 blank"> </span>\ufb01nal chapter to a short but<span class="_70 blank"> </span>self-</div><div class="t m0 x0 h3 y184 ff3 fs2 fc0 sc0 ls2 ws143">contained<span class="_70 blank"> </span>outline<span class="_72 blank"> </span>of<span class="_72 blank"> </span>the<span class="_72 blank"> </span>contemporary<span class="_70 blank"> </span>theory<span class="_72 blank"> </span>of<span class="_72 blank"> </span>large-scale<span class="_70 blank"> </span>structure<span class="_72 blank"> </span>and</div><div class="t m0 x0 h3 y185 ff3 fs2 fc0 sc0 ls2 ws144">galaxy formation.<span class="_21 blank"> </span>W<span class="_44 blank"></span>e introduce the theory of<span class="_5e blank"> </span>random \ufb01elds and the linear</div><div class="t m0 x0 h3 y186 ff3 fs2 fc0 sc0 ls2 ws145">theory of the gro<span class="_0 blank"></span>wth of \ufb02uctuations in the univ<span class="_0 blank"></span>erse, and give a<span class="_71 blank"> </span>simple treat-</div><div class="t m0 x0 h3 y187 ff3 fs2 fc0 sc0 ls2 ws146">ment<span class="_8 blank"> </span>of<span class="_6 blank"> </span>nonlinear<span class="_5e blank"> </span>structure<span class="_6 blank"> </span>formation<span class="_5e blank"> </span>through<span class="_6 blank"> </span>the<span class="_5e blank"> </span>spherical-collapse<span class="_5e blank"> </span>mo del</div><div class="t m0 x0 h3 y188 ff3 fs2 fc0 sc0 ls2 ws147">and<span class="_70 blank"> </span>extended<span class="_72 blank"> </span>Press\u2013Schec<span class="_0 blank"></span>hter<span class="_70 blank"> </span>theory<span class="_44 blank"></span>.<span class="_9 blank"> </span>The<span class="_70 blank"> </span>\ufb01nal,<span class="_72 blank"> </span>sp eculative<span class="_70 blank"> </span>section<span class="_72 blank"> </span>sum-</div><div class="t m0 x0 h3 y189 ff3 fs2 fc0 sc0 ls2 ws148">marizes our still incomplete<span class="_72 blank"> </span>understanding of<span class="_72 blank"> </span>how the complex physics of</div><div class="t m0 x0 h3 y18a ff3 fs2 fc0 sc0 ls2 ws113">baryons<span class="_8 blank"> </span>giv<span class="_0 blank"></span>es<span class="_5e blank"> </span>rise<span class="_5e blank"> </span>to<span class="_8 blank"> </span>the<span class="_6 blank"> </span>galaxies<span class="_8 blank"> </span>we<span class="_8 blank"> </span>see<span class="_5e blank"> </span>ab out<span class="_5e blank"> </span>us.</div><div class="t m0 x3 h3 y18b ff3 fs2 fc0 sc0 ls2 ws149">There are problems at<span class="_70 blank"> </span>the end<span class="_70 blank"> </span>of each chapter, many of which are in-</div><div class="t m0 x0 h3 y4c ff3 fs2 fc0 sc0 ls2 ws14a">tended<span class="_8 blank"> </span>to<span class="_5e blank"> </span>elucidate<span class="_8 blank"> </span>topics<span class="_8 blank"> </span>that<span class="_5e blank"> </span>are not<span class="_5e blank"> </span>fully<span class="_5e blank"> </span>cov<span class="_0 blank"></span>ered in<span class="_5e blank"> </span>the<span class="_8 blank"> </span>main<span class="_5e blank"> </span>text.<span class="_72 blank"> </span>Their</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
Compartilhar