Astrophysical Sciences

Academic Year 2022 – 2023

General Information

Peyton Hall

Program Offerings:

  • Ph.D.

Director of Graduate Studies:

Graduate Program Administrator:


The Department of Astrophysical Sciences offers advanced training in astrophysics. The faculty and staff in the department conduct world-leading research in theoretical and computational astrophysics, observational astronomy, astronomical surveys, and instrumentation (both hardware and software). The fascinating discoveries of modern astronomy challenge the human understanding of the broadest possible range of physical phenomena. The graduate program in Astrophysical Sciences prepares students for scientific careers in astrophysics through a combination of classes and early and active participation in research projects, culminating in original thesis research. 

The program length is five years. The first two years of the program are dedicated to taking core astrophysics courses and working on up to four semester-long research projects with different faculty members. After the general exam at the end of the second year, students are admitted to candidacy, select a thesis advisor, and work on their thesis research for the remaining three years. 

Under the department’s aegis, an extensive graduate research program in fundamental plasma physics is also conducted at the renowned Princeton Plasma Physics Laboratory (PPPL), located on Princeton’s Forrestal Campus. Please see the Program in Plasma Physics page for information about applying for this program. Students interested in fundamental plasma physics and its laboratory and technology applications should apply to the Program in Plasma Physics. Students interested in astrophysical applications of plasma physics (including high-energy astrophysics) should apply to the graduate program in Astrophysical Sciences. 


Application deadline
December 15, 11:59 p.m. Eastern Standard Time (This deadline is for applications for enrollment beginning in fall 2023)
Program length
5 years
General Test optional/not required; Physics Subject Test optional/not required

Program Offerings


Before standing for the general examination, students must complete four core astrophysics courses (Stellar Structure, Stellar Dynamics, Interstellar Medium, and Cosmology & Extragalactic Astronomy).  Students have the option to complete additional courses in astrophysics (such as High-Energy Astrophysics, Computational Methods, or Plasma Astrophysics), physics, mathematics, statistics, machine learning, and computation. Students may select additional courses with assistance and approval from the faculty.

Additional pre-generals requirements

Seminar Requirement
Graduate students must attend the graduate student seminar every semester, except for their last semester at Princeton. Generally, students take turns giving presentations on various aspects of a field selected by the faculty instructor. The dual purposes are to learn about a topic not covered in the required courses (such as an emerging research field) and gain experience giving presentations. Occasionally, the seminar has a different format, such as a workshop or half-semester modules on various topics.

General exam

At the end of the second year, students take the oral general examination. For the examination, the student chooses four topics out of the following six: dynamics of stellar and planetary systems, cosmology and extragalactic astronomy, stellar structure, high-energy astrophysics, interstellar medium, and plasma astrophysics. These topics are covered by classes offered in the department. A committee of four faculty members tests the student for approximately two hours, primarily about the four chosen subjects and other topics in astrophysics.

Qualifying for the M.A.

The Master of Arts (M.A.) degree is normally an incidental degree on the way to full Ph.D. candidacy. It is earned after a student successfully completes two of the three following requirements: (1) successful completion of the four core courses and any additional courses mapped out by the DGS and/or the adviser; (2) successful completion of the general examination; and (3) production of at least one paper suitable for submission to a journal as part of a departmental research project. The research supervisor must approve the paper. The M.A. may also be awarded to students who, for various reasons, leave the Ph.D. program, provided that these requirements have been met.


Students are required to serve as assistants in instruction for one semester sometime during their graduate career.  The DGS may lift this requirement for students who secure certain competitive fellowships that do not allow teaching.

Dissertation and FPO

The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted, and the final public oral examination sustained.


  • Chair

    • Michael A. Strauss
  • Associate Chair

    • Eve C. Ostriker
  • Director of Graduate Studies

    • Joshua N. Winn
  • Director of Undergraduate Studies

    • Neta A. Bahcall
  • Professor

    • Neta A. Bahcall
    • Gáspár Áron Bakos
    • Amitava Bhattacharjee
    • Adam S. Burrows
    • Christopher F. Chyba
    • Steven C. Cowley
    • Bruce T. Draine
    • Jo Dunkley
    • Nathaniel J. Fisch
    • Robert J. Goldston
    • John J. Goodman
    • Jenny E. Greene
    • Hantao Ji
    • David J. McComas
    • Eve C. Ostriker
    • Felix I. Parra Diaz
    • Eliot Quataert
    • Anatoly Spitkovsky
    • Michael A. Strauss
    • Romain Teyssier
    • Joshua N. Winn
  • Associate Professor

    • Matthew W. Kunz
  • Assistant Professor

    • Peter M. Melchior
  • Associated Faculty

    • Mariangela Lisanti, Physics
    • Lyman A. Page, Physics
    • Frans Pretorius, Physics
    • Suzanne T. Staggs, Physics
    • Paul J. Steinhardt, Physics
    • Robert J. Vanderbei, Oper Res and Financial Eng
  • Lecturer with Rank of Professor

    • Samuel A. Cohen
    • Ilya Y. Dodin
    • Gregory W. Hammett
    • Richard P. Majeski
    • Hong Qin
    • Allan H. Reiman
    • William M. Tang
  • Lecturer

    • Philip C. Efthimion
    • William R. Fox
    • Jong-Kyu Park
    • Yevgeny Raitses
  • Visiting Lecturer with Rank of Professor

    • Matias Zaldarriaga
  • Visiting Lecturer

    • Michael D. Lemonick

For a full list of faculty members and fellows please visit the department or program website.

Permanent Courses

Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.

APC 503 - Analytical Techniques in Differential Equations (also AST 557)

Local analysis of solutions to linear and nonlinear differential and difference equations. Asymptotic methods, asymptotic analysis of integrals, perturbation theory, summation methods, boundary layer theory, WKB theory, and multiple scale theory. Prerequisite: MAE 306 or equivalent.

APC 523 - Numerical Algorithms for Scientific Computing (also AST 523/MAE 507)

A broad introduction to scientific computation using examples drawn from astrophysics. From computer science, practical topics including processor architecture, parallel systems, structured programming, and scientific visualization will be presented in tutorial style. Basic principles of numerical analysis, including sources of error, stability, and convergence of algorithms. The theory and implementation of techniques for linear and nonlinear systems of equations, ordinary and partial differential equations will be demonstrated with problems in stellar structure and evolution, stellar and galactic dynamics, and cosmology.

APC 524 - Software Engineering for Scientific Computing (also AST 506/MAE 506)

The goal of this course is to teach basic tools and principles of writing good code, in the context of scientific computing. Specific topics include an overview of relevant compiled and interpreted languages, build tools and source managers, design patterns, design of interfaces, debugging and testing, profiling and improving performance, portability, and an introduction to parallel computing in both shared memory and distributed memory environments. The focus is on writing code that is easy to maintain and share with others. Students will develop these skills through a series of programming assignments and a group project.

AST 513 - Dynamics of Stellar and Planetary Systems

Discussion of observations of stars in the solar neighborhood, the overall structure of our galaxy, and external galaxies; stellar populations and the evolution of the stellar content of galaxies; dynamical theory of the equilibrium and stability of stellar systems; and relaxation, dynamical friction, and the introduction to the Fokker-Planck equation; evolution of N-body systems.

AST 514 - Structure of the Stars

Theoretical and numerical analysis of the structure of stars and their evolution. Topics include a survey of the physical process important for stellar interiors (equation of state, nuclear reactions, transport phenomena); macroscopic properties of stars and their stability; evolution of single and binary stars; mass loss and accretion of matter; and accretion disks. Emphasis is given to numerical modeling of various types of stars.

AST 517 - Diffuse Matter in Space

Subject of course is the astrophysics of the interstellar medium: theory and observations of the gas, dust, plasma, energetic particles, magnetic field, and electromagnetic radiation in interstellar space. Emphasis will be on theory, including elements of: fluid dynamics; excitation of atoms, molecules and ions; radiative processes; radiative transfer; simple interstellar chemistry; and physical properties of dust grains.The theory will be applied to phenomena including: interstellar clouds (both diffuse atomic clouds and dense molecular clouds); HII regions; shock waves; supernova remnants; cosmic rays; interstellar dust; and star formation.

AST 520 - High Energy Astrophysics

Astrophysical applications of electrodynamics, nuclear, and particle physics. Topics may include synchrotron emission and absorption, comptonization, pair plasmas, jets, extragalactic radio sources, compact objects, cosmic rays, and neutrino astrophysics.

AST 521 - Introduction to Plasma Astrophysics

Introductory course to plasma physics, as it applies to space and astrophysical systems. Fundamental concepts are developed with mathematical rigor, and application to the physics of a wide variety of astrophysical systems are made. Topics include magnetohydrodynamics, kinetic theory, waves, instabilities, and turbulence. Applications to the physics of the solar wind and corona, the intracluster medium of galaxy clusters, the interstellar medium of galaxies, and a wide variety of accretion flows are given.

AST 522 - Extragalactic Astronomy

A survey course covering the principal current areas of research on extragalactic objects, their physical properties, origin, evolution, and distribution in space. Topics covered include quasar physics, formation, evolution, and clustering of galaxies and the general problem of large-scale structure and motion in the universe.

AST 541 - Seminar in Theoretical Astrophysics

Designed to stimulate students in the pursuit of research. Participants in this seminar discuss critically papers given by seminar members. Ordinarily, several staff members also participate. Often topics are drawn from published data that present unsolved puzzles of interpretation.

AST 542 - Seminar in Observational Astrophysics

Students will prepare and deliver presentations and lead discussion about topics of current interest in observational astrophysics and techniques.

AST 551 - General Plasma Physics I (also MAE 525)

This is an introductory course to plasma physics, with sample applications in fusion, space and astrophysics, semiconductor etching, microwave generation: characterization of the plasma state, Debye shielding, plasma and cyclotron frequencies, collision rates and mean-free paths, atomic processes, adiabatic invariance, orbit theory, magnetic confinement of single-charged particles, two-fluid description, magnetohydrodynamic waves and instabilities, heat flow, diffusion, kinetic description, and Landau damping. The course may be taken by undergraduates with permission of the instructor.

AST 552 - General Plasma Physics II

Ideal magnetohydrodynamic (MDH) equilibrium, MHD energy principle, ideal and resistive MHD stability, drift-kinetic equation, collisions, classical and neoclassical transport, drift waves and low-frequency instabilities, high-frequency microinstabilities, and quasilinear theory.

AST 553 - Plasma Waves and Instabilities

Hydrodynamic and kinetic models of nonmagnetized and magnetized plasma dispersion; basic plasma waves and their applications; basic instabilities; mechanisms of collisionless dissipation; geometrics-optics approximation, including ray tracing, field-theoretical description of continuous waves, and ponderomotive effects; conservation laws and transport equations for the wave action, energy, and momentum; mode conversion; quasilinear theory.

AST 554 - Irreversible Processes in Plasmas

Introduction to theory of fluctuations and transport in plasma. Origins of irreversibility, Random walks, Brownian motion and diffusion, Langevin and Fokker-Planck theory. Fluctuation-dissipation theorem; test-particle superposition principle. Statistical closure problem. Derivation of kinetic equations from BBGKY hierarchy and Klimontovich formalism; properties of plasma collision operators. Classicaal transport coefficients in magnetized plasmas; Onsager symmetry. Introduction to plasma turbulence, including quasilinear theory. Applications to current problems in plasma research.

AST 555 - Fusion Plasmas & Plasma Diagnostics

This course gives an introduction to experimental plasma physics, with an emphasis on high-termperature plasmas for fusion. Requirements for fusion plasmas: confinement, beta, power and particle exhaust. Tokamak fusion reactors. Status of experimental understanding: what we know and how we know it. Key plasma diagnostic techniques: magnetic measurements, Langmuir probes, microwave techniques, spectroscopic techniques, electron cyclotron emission, Thomson scattering.

AST 558 - Seminar in Plasma Physics

Advances in experimental and theoretical studies or laboratory and naturally-occurring high-termperature plasmas, including stability and transport, nonlinear dynamics and turbulence, magnetic reconnection, selfheating of "burning" plasmas, and innovative concepts for advanced fusion systems. Advances in plasma applications, including laser-plasma interactions, nonneutral plasmas, high-intensity accelerators, plasma propulsion, plasma processing, and coherent electromagnetic wave generation.

AST 559 - Turbulence and Nonlinear Processes in Fluids and Plasmas (also APC 539)

A comprehensive introduction to the theory of nonlinear phenomena in fluids and plasmas, with an emphasis on turbulence and transport. Experimental phenomenology; fundamental equations, including Navier-Stokes, Vlasov, and gyrokinetic; numerical simulation techniques, including pseudo-spectral and particle-in-cell methods; coherent structures; transition to turbulence; statistical closures, including the wave kinetic equation and direct-interaction approximation; PDF methods and intermittency; variational techiques. Applications from neutral fluids, fusion plasmas, and astrophysics.

AST 560 - Computational Methods in Plasma Physics

Analysis of methods for the numerical solution of the partial differential equations of plasma physics, including those of elliptic, parabolic, hyperbolic, and eigenvalue type. Topics include finite difference, finite element, spectral, particle-in-cell, Monte Carlo, moving grid, and multiple-time-scale techniques, applied to the problems of plasma equilibrium, transport, and stability.

AST 562 - Laboratory in Plasma Physics

The course helps students develop the skills, knowledge, and understanding of basic and advanced laboratory techniques used to measure the properties of behavior of plasmas. Representative experimentss include: low-pressure arc and cold-cathode plasma formation; ambipolar diffusion in afterglow plasmas; Langmuir probe measurements of electron temperture and plasma density; Fabry-Perot spectroscopy for ion energy measurements; optical spectroscopy for species identification; microwave interferometry and cavity resonances for plasma density determination; and momentum generated by a plasma thruster.

AST 568 - Introduction to Classical and Neoclassical Transport and Confinement

The first half of this course intends to provide students with a systematic development of the fundamentals of gyrokinetic (GK) theory, and the second half provides students with an introduction to transport and confinement in magnetically confined plasmas.

MAE 522 - Applications of Quantum Mechanics to Spectroscopy and Lasers (also AST 564)

An intermediate-level course in applications of quantum mechanics to modern spectroscopy. The course begins with an introduction to quantum mechanics as a "tool" for atomic and molecular spectroscopy, followed by a study of atomic and molecular spectra, radiative, and collisional transitions, with the final chapters dedicated to plasma and flame spectroscopic and laser diagnostics. Prerequisite: one semester of quantum mechanics.

MAE 528 - Physics of Plasma Propulsion (also AST 566)

Focus of this course is on fundamental processes in plasma thrusters for spacecraft propulsion with emphasis on recent research findings. Start with a review of the fundamentals of mass, momentum & energy transport in collisional plasmas, wall effects, & collective (wave) effects, & derive a generalized Ohm's law useful for discussing various plasma thruster concepts. Move to detailed discussions of the acceleration & dissipation mechanisms in Hall thrusters, magnetoplasmadynamic thrusters, pulsed plasma thrusters, & inductive plasma thrusters, & derive expressions for the propulsive efficiencies of each of these concepts.

SML 505 - Modern Statistics (also AST 505)

The course provides an introduction to modern statistics and data analysis. It addresses the question, "What should I do if these are my data and this is what I want to know"? The course adopts a model based, largely Bayesian, approach. It introduces the computational means and software packages to explore data and infer underlying parameters from them. An emphasis will be put on streamlining model specification and evaluation by leveraging probabilistic programming frameworks. The topics are exemplified by real-world applications drawn from across the sciences.