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Q. Topics in Astrophysics

Most of your Part II Astrophysics courses follow a strictly disciplinary approach: teaching specific physics to tackle specific astrophysical problems.  Yet, much research is inherently interdisciplinary, motivated primarily by outstanding questions about the Universe and then adopting whatever mix of methods, observational and theoretical, are required to address these questions.  In Topics the aim is to develop your familiarity with this more research-oriented, question-first, approach to astrophysics, by exploring interdisciplinary astrophysics via two different, but complementary approaches: applying specific physical concepts to diverse astrophysical phenomena; and, applying diverse physical concepts to specific research themes, focusing on the physics of supernovae and the evolutionary pathway from interstellar gas to the formation of planets.

In the first 3 lectures we present some of the tools that are required in order to get an approximate grasp on problems where all the information is not necessarily available. This is largely an exercise in sorting out the important from the unimportant and requires a good understanding of timescales and distributions. During the remainder of the first half of the course we investigate how a specific physical concept (that of tides) can be applied to understanding a wide diversity of astrophysical phenomena from quasars and supermassive black holes, to stellar clusters, asteroids and moons.  This exemplifies how mastery of specific physical concepts can open up a diverse range of astrophysical processes to investigation. 

In the second half of the course, we focus on two specific research themes: the physics of supernovae and the formation and evolution of protoplanetary discs. In the former we look at issues such as what are the processes determining the properties and evolutionary timescales for emission from supernovae, as well as considering the types of stars that end up as supernovae. In the latter, we look at the evolution of the dust and gas originating in dense cores in the interstellar medium and chart the processes that can ultimately lead to the creation of planets of the types observed in the solar system and amongst the thousands of recently discovered extrasolar planets. Throughout you will be learning how to break problems down into elements that can be tackled by simple calculations using the physics that you already know or will have learned elsewhere in Part II Astrophysics.

To further your understanding of astrophysics as a research discipline, the core lectures from the course are interspersed with `Guest Lectures’, in which a number of staff in astronomy departments across Cambridge will provide a perspective on their cutting-edge research. 

Section 1: Introduction to problem solving techniques [3]

Section 2: The physics of tides and its astronomical applications on all scales [3]

Section 3: The physics of supernovae [6]

Section 4: From molecular cloud cores to discs to the brink of planet formation [6]

Guest lectures will be interspersed among the above lectures, tbd [6]

Recommended Reading

There are no textbooks to support the course. However, for students who are interested in learning more about some of the topics covered, the following books (in addition to those supporting other Part II Astro. courses) are recommended: 

  • P. Armitage, The Astrophysics of Planet Formation, Cambridge University Press, 2010. 
  • Frank, J., King, A., Raine, D., Accretion Power in Astrophysics, Cambridge   University Press, 2002
  • F. Mellia High Energy Astrophysics, Princeton University Press, 2009
  • D. Ward-Thompson & A. Whitworth, An Introduction to Star Formation, Cambridge   University Press, 2011

Q. Astrophysical Fluid Dynamics (shared with Physics)

Fluids are ubiquitous in the Universe on all scales. As well as obvious fluids, (e.g. the gas that is in stars or clouds in the interstellar medium) a variety of other systems are amenable to a fluid dynamical description - including the dust that makes up the rings of Saturn and even the orbits of stars in the galactic potential. Although some of the techniques of conventional (terrestrial) fluid dynamics are relevant to astrophysical fluids, there are some important differences: astronomical objects are often self-gravitating or else may be accelerated by powerful gravitational fields to highly supersonic velocities. In the latter case, the flows are highly compressible and strong shock fronts are often observed (for example, the spiral shocks that are so prominent in the gas of galaxies like the Milky Way). 

In this course, we consider a wide range of topical issues in astronomy, such as the propagation of supernova shock waves through the interstellar medium, the internal structure of stars and the variety of instabilities that affect interstellar/intergalactic gas. These include, perhaps most importantly, the Jeans instability whose action is responsible for the formation of every star and galaxy in the Universe. We also deal with exotic astronomical environments, such as the orbiting discs of gas which feed black holes. 

  1. Introduction: The concept of a fluid. Collisional and collisionless fluids. Kinematics. Conservation of mass. Pressure. (Inviscid) momentum equation for a fluid under gravity. Stress tensor and the concept of ram pressure. [2] 
  2. Basic Concepts of Gravity: Poisson's equation. Gravitational potential. The Virial Theorem. [1] 
  3. Equation of State: Barotropic relation between pressure and density. Energy equation. Hydrostatic equilibrium. Examples: hydrostatic atmosphere under uniform gravity; self-gravitating isothermal slab; self-gravitating polytropes as simple models of stars, mass-radius relation. [4] 
  4. Sound Waves: Sound speed: adiabatic and isothermal case. Sound waves in a stratified atmosphere. [1] 
  5. Supersonic Flows: Rankine-Hugoniot conditions for adiabatic and isothermal shocks. Application to blast waves and supernova remnants. [3] 
  6. Bernoulli's Equation and its Applicability: De Laval nozzle and its relevance to astrophysical jets. Bondi accretion, stellar winds and mass loss. [2] 
  7. Fluid Instabilities: Convective instability, Schwarzschild criterion. Jeans instability. Rayleigh-Taylor and Kelvin-Helmholtz instability. Thermal instability, Field criterion. [3] 
  8. Viscous Flows: Linear shear flow. Navier-Stokes equation. Vorticity and energy dissipation in viscous flows. Accretion discs. Steady thin discs. [3] 
  9. Magnetohydrodynamics: The ideal MHD equations. Alfven waves. [3] 
  10. Computational Astrophysical Fluid Dynamics [2] 

Recommended Reading 

  • Clarke, C.J. & Carswell, R.F. Principles of Astrophysical Fluid Dynamics, Cambridge University Press (2014)  Landau & Lifshitz, Fluid Mechanics, Pergamon Press (1987) 

Further Suggestions 

  • Acheson, D. Elementary Fluid Dynamics Oxford University Press (1990) 
  • Batchelor, G.K. An Introduction to Fluid Dynamics, Cambridge University Press (1967, reprinted 2000) Lamb, H. Hydrodynamics, Cambridge University Press (6th ed 1932, reprinted 1993 

Q. Introduction to Cosmology

  1. Is Cosmology Science?: Causal structure of space-time: our past light cone. Technology horizon, particle horizon and the `size' of the Universe. Importance of symmetry principles in cosmology. Big problems in cosmology. [1] 
  2. The Background Cosmology: Symmetric spaces. The Friedmann-Robertson-Walker metric. Energy Momentum Tensor for Perfect Fluid. Friedman equations and geometry of the Universe. Cosmological redshift. Newtonian cosmology. Cosmological constant. de-Sitter space and time-slicing. Horizons. Distances and age of the Universe.[6] 
  3. Thermal History: The cosmic microwave background (CMB) radiation. Thermal equilibrium: bosons and fermions. Particle content at early times. Neutrinos and neutrino decoupling. Big-bang nucleosynthesis. Relic particles. Dark matter. Baryon asymmetry. Recombination. [5] 
  4. Fluctuations: Newtonian perturbation theory. Fluctuations in the CMB – Silk Damping. Inflation and the origin of fluctuations. Gravitational waves and tests of inflation. What can we learn from the CMB? The LCDM model. The multiverse. Unanswered questions. [5] 
  5. Observational Probes: Standard candles – Type 1a supernovae. Standard ruler – Baryon Acoustic Oscillations. Inverse distance ladder and H0. Forward distance ladder and H0. Gravitational lensing. Redshift space distortions. Is LCDM consistent with observations? [4] 
  6. Non-Linear Evolution of Structure: Spherical collapse model. The mass function. Galaxy formation. [4] 

Recommended Reading

  • Modern Cosmology, Dodelson D., Schmidt F., 2020, Academic Press
  • Principles of Physical Cosmology, Peebles P.J.E., 1993, Princeton University Press
  • General Relativity: An Introduction for Physicists, Hobson M.P., Efstathiou G.  and Lasenby A.N., 2006, Cambridge University Press

Q. Statistical Physics (shared with DAMTP)

Further information about this course is available on the Department of Mathematics course pages.

Examples papers are available on the DAMTP Examples page. 

  1. Fundamentals of Statistical Mechanics: Microcanonical ensemble. Entropy, temperature and pressure. Laws of thermodynamics. Example of paramagnetism. Boltzmann distribution and canonical ensemble. Partition function. Free energy. Specific heats. Chemical potential. Grand Canonical Ensemble. [5] 
  2. Classical Gases: Density of states and the classical limit. Ideal gas. Maxwell distribution. Equipartition of energy. Diatomic gas. Interacting gases. Virial expansion. Van der Waals equation of state. Basic kinetic theory. [3] 
  3. Quantum Gases: Density of states. Planck distribution and black body radiation. Debye model of phonons in solids. Bose-Einstein distribution. Ideal Bose gas and Bose-Einstein condensation. Fermi-Dirac distribution. Ideal Fermi gas. Pauli paramagnetism. [8] 
  4. Thermodynamics: Thermodynamic temperature scale. Heat and work. Carnot cycle. Applications of laws of thermodynamics. Thermodynamic potentials. Maxwell relations. [4] 
  5. Phase Transitions: Liquid-gas transitions. Critical point and critical exponents. Ising model. Mean field theory. First and second order phase transitions. Symmetries and order parameters. [4] 

Recommended Reading 

  • F. Mandl Statistical Physics. Wiley 1988 
  • R.K. Pathria Statistical Mechanics, 2nd ed. Butterworth-Heinemann 1996 
  • L.D. Landau and E.M. Lifshitz Statistical Physics, Part 1 (Course of Theoretical Physics volume 5). 
  • M. Kardar Statistical Physics of Particles. CUP 2007
  • F. Reif Fundamentals of Thermal and Statistical Physics. McGraw-Hill 1965 
  • A.B. Pippard Elements of Classical Thermodynamics. Cambridge University Press, 1957 
  • K. Huang Introduction to Statistical Physics. Taylor and Francis 2001