Dark Matter in the Universe : The Jerusalem Winter School for Theoretical Physics

by Bahcall, John N.; Piran, Tsvi; Weinberg, Steven

• ISBN13: 9789812388407
• ISBN10: 9812388400
• Edition: 2nd
• Format: Hardcover
• Copyright: 2004-09-30
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

If standard gravitational theory is correct, then most of the matter in the universe is in an unidentified form which does not emit enough light to have been detected by current instrumentation. This review volume is the extended editon of the lectures given in the 4th Jerusalem Winter School of Theoretical Physics, with new materials added in. It devoted to the discussion of the so-called "missing matter" problem in the universe - dark matter and dark energy. The goal of this volume is to make current research work on unseen matter accessible to students of faculties without prior experience in this area. Due to the pedagogical nature of the notes and the intense discussions between students and the lecturers, the written lectures included in this volume often contain techniques and explanations not found in more formal journal publications.

Table of Contents

Foreword to the First Edition	v
Chapter 1. Introduction	1	(6)
John N. Bahcall
Chapter 2. Distribution of Dark Matter in the Spiral Galaxy NGC 3198	7	(18)
T.S. van Albada, K. Begeman, R. Sanscisi and J.N. Bahcall
1 Introduction	7	(4)
2 Distribution of Light	11	(1)
3 Rotation Curve	12	(2)
4 Mass Models	14	(5)
4.1 Choice of Components	14	(1)
4.2 Fits with Exponential Disk and Halo	14	(4)
4.3 An Upper Limit for the Mass of the Spheroidal Component	18	(1)
5 Discussion	19	(2)
Appendix: Dark Matter and the Tully-Fisher Relation	21	(1)
References	22	(3)
Chapter 3. Some Possible Regularities in Missing Mass	25	(10)
John N. Bahcall and Stefano Casertano
1 Introduction	25	(1)
2 The Simplicity	25	(2)
3 The Numerical Characteristics	27	(3)
4 The Local Missing Mass	30	(1)
5 Implications	30	(2)
References	32	(3)
Chapter 4. Evolution of Globular Clusters and the Globular Cluster System - I	35	(22)
J.P. Ostriker and C. Thompson
1 Globular Clusters	35	(1)
2 Basic Properties of Globular Clusters	36	(1)
3 Equilibrium Structure of Globular Clusters	37	(5)
4 Methods of Computing the Evolution of a Globular Cluster	42	(1)
5 Early Evolution of an Isolated Globular Cluster	42	(2)
6 Effects of Finite Stellar Size: Heating and Core Bounce	44	(5)
7 External Effects on the Evolution of a Globular Cluster	49	(2)
8 Evolution of the Globular Cluster System: Destruction of Clusters	51	(1)
9 Outstanding Issues	52	(1)
10 Nature of the Dark Halo of Our Galaxy	53	(2)
References	55	(2)
Chapter 5. Positive Energy Perturbations in Cosmology - II	57	(14)
J.P. Ostriker and C. Thompson
1 Hydrodynamics in a Cosmological Setting	57	(3)
2 Various Self-Similar Solutions for Blast Waves	60	(4)
3 Shell Structure	64	(1)
4 Equation of Motion of a Thin Shell	65	(3)
5 Gravitational Instabilily in a Shell	68	(1)
6 Interactions between Cosmological Blasts	69	(1)
References	70	(1)
Chapter 6. Dark Matter in Galaxies and Galaxy Systems	71	(32)
Scott Tremaine and Hyung Mok Lee
1 Introduction	71	(8)
1.1 Virial Theorem	72	(1)
1.2 History of Dark Matter	73	(2)
1.3 A Quick Review of Cosmology	75	(3)
1.4 Mass-to-light Ratio in the Solar Neighbourhood	78	(1)
1.5 Classification Scheme of Dark Matter	78	(1)
2 Theory of Stellar Dynamics	79	(7)
2.1 Collisionless Boltzmann Equation	79	(3)
2.2 The Jeans Theorem	82	(1)
2.3 Examples of Distribution Functions	83	(1)
2.3.1 Plummer model	83	(1)
2.3.2 Isothermal sphere	84	(1)
2.4 Moments of the Collisionless Boltzmann Equation	85	(1)
3 Elliptical Cores and Dwarf Spheroidal Galaxies	86	(4)
4 The Extent of the Galactic Halo	90	(5)
4.1 Local Escape Speed	90	(1)
4.2 Magellanic Stream	91	(1)
4.3 Local Group Timing	91	(1)
4.4 Kinematics of Satellite Galaxies	92	(3)
4.5 Summary	95	(1)
5 Binary Galaxies	95	(2)
6 Masses of Groups and Clusters of Galaxies	97	(3)
6.1 Groups of Galaxies	97	(1)
6.2 Rich Clusters: Coma Cluster	98	(2)
7 Summary	100	(1)
References	101	(2)
Chapter 7. Gravitational Lenses	103	(56)
Roger D. Blandford and Christopher S. Kochanek
1 Introduction	103	(5)
1.1 History	103	(1)
1.2 Simple Estimates	104	(3)
1.3 Uses	107	(1)
1.4 Organization of Lectures	107	(1)
References	108	(1)
2 The Optics of Gravitational Lenses	108	(9)
2.1 Vector Formalism	109	(1)
2.1.1 The lens equation	109	(1)
2.1.2 Image amplification and parity	110	(1)
2.1.3 Distance measures	111	(1)
2.2 Scalar Formalism: Fermat's Principle	112	(3)
2.3 Propagation Formalism: The Optical Scalar Equations	115	(1)
References	116	(1)
3 Gravitational Potential Wells	117	(7)
3.1 Uniform Sheet	117	(1)
3.2 Point Mass (Black Hole)	117	(1)
3.3 Singular Isothermal Sphere	118	(1)
3.4 Isothermal Sphere with Finite Core	118	(3)
3.5 Elliptical Potentials	121	(1)
3.6 Irregular Potentials	122	(1)
3.7 Cosmic Strings	122	(2)
References	124	(1)
4 Generic Features of Images	124	(9)
4.1 Arrival Time Surfaces	124	(3)
4.2 Caustics and Catastrophes	127	(1)
4.2.1 Structural stability of images	127	(1)
4.2.2 Isolated image	128	(1)
4.2.3 Fold catastrophe	129	(1)
4.2.4 Cusp catastrophe	130	(1)
4.2.5 Higher order catastrophes	131	(1)
4.3 Caustics as Conjugate Points of Ray Congruences	132	(1)
References	133	(1)
5 Microlensing	133	(5)
5.1 Order of Magnitude Estimates	133	(2)
5.2 The Character of Microimages: Low Optical Depth	135	(1)
5.3 The Character of Microimages: Moderate Optical Depth	135	(2)
5.4 The Character of Microimages: Large Optical Depth	137	(1)
References	137	(1)
6 Compound Lenses	138	(3)
References	140	(1)
7 The Observational Position	141	(11)
7.1 A Reprise of Existing Candidates	141	(1)
7.1.1 The double QSO: 0957 + 561	141	(1)
7.1.2 PG 1115 + 080	141	(1)
7.1.3 2016 + 112	142	(1)
7.1.4 2237 + 0305	142	(1)
7.1.5 3C324	143	(1)
7.1.6 1042 + 178	143	(1)
7.1.7 The dark matter lenses: 2345 + 007, 1635 + 267, and 0023 + 171	143	(1)
7.1.8 1146 + 111	144	(1)
7.2 Space Density of Sources - Quasars, Galaxies, and Radio Sources	145	(1)
7.3 Space Density of Lenses - Galaxies and Clusters	145	(1)
7.4 Amplification Bias	146	(1)
7.5 Surveys and Future Prospects	146	(1)
References	147	(5)
8 Lenses as Probes of the Universe	152	(5)
8.1 The Hubble Constant	152	(1)
8.2 Galactic Masses	153	(2)
8.3 Lensing by Dark Matter	155	(1)
References	156	(1)
9 Concluding Remarks	157	(2)
Chapter 8. An Introduction to Inflation	159	(10)
William H. Press and David N. Spergel
1 Review of Big Bang Cosmology	159	(3)
2 Inflation	162	(3)
3 Additional Topics Not Covered Here	165	(2)
References	167	(2)
Chapter 9. Wimps in the Sun and in the Lab	169	(14)
William H. Press and David N. Spergel
1 WIMPS and the Solar Neutrino Problem	169	(7)
2 Detecting WIMPS in the Lab	176	(3)
References	179	(4)
Chapter 10. An Introduction to Cosmic Strings	183	(14)
William H. Press and David N. Spergel
1 Birth of Cosmic Strings	183	(3)
2 The Motion of a Cosmic String Loop	186	(3)
3 Cosmic Strings and the Formation of Galaxies	189	(5)
3.1 Spherical Accretion Model	190	(2)
3.2 Competition between Loops	192	(1)
3.3 Galaxy Morphology	193	(1)
4 Observing Cosmic Strings	194	(1)
References	194	(3)
Chapter 11. A Departure from Newtonian Dynamics at Low Accelerations as an Explanation of the Mass-Discrepancy in Galactic Systems	197	(20)
Mordehai Milgrom
1 Introduction	198	(2)
2 Dynamics at Low Accelerations	200	(3)
3 A Nonrelativistic Formulation	203	(2)
4 Effects of an Ambient Field	205	(2)
5 Observational Consequences	207	(8)
5.1 Disc Galaxies	208	(3)
5.2 Elliptical Galaxies	211	(2)
5.3 The General Expression for the "Dark Matter" Density	213	(1)
5.4 The Sign of the Phantom Density-Negative "Dark Matter"	214	(1)
5.5 Phantom Matter in Galactic Discs	214	(1)
References	215	(2)
Chapter 12. Dark Matter in Cosmology	217
Anthony Aguirre
1Introduction	217	(1)
2 Dark Matter and Structure Formation	218	(5)
2.1 Initial Conditions and the Standard Cosmological Model	218	(1)
2.2 Evolution of Perturbations	219	(4)
3 Tests and Constraints from the Microwave Background	223	(2)
4 Tests and Constraints from the Ly-α Forest and Distribution of Galaxies	225	(1)
5 Dark Matter and Galaxy Formation	226	(6)
5.1 Halo Formation	226	(1)
5.2 The Halo Mass Function	227	(1)
5.3 Halo Profiles	228	(1)
5.4 Angular Momentum	228	(1)
5.5 From a Dark Halo to a Galaxy	229	(1)
5.6 Current Status of Galaxy Formation Theory	229	(1)
5.7 Outstanding Problems. and Alternatives to (Cold) Dark Matter	230	(2)
Conclusions	232	(1)
References	232