Columbia University 
Astronomy and Astrophysics



Admission and Degree Requirements | Courses of Instruction and Research

CHAIR: Professor Jacqueline van Gorkom, 1314 Pupin Hall

DIRECTOR OF GRADUATE STUDIES: Professor James H. Applegate, 1322 Pupin Hall


James H. Applegate
Norman H. Baker
David J. Helfand
Steven Kahn (Physics)
Joseph Patterson
Kevin H. Prendergast
Edward A. Spiegel
Jacqueline van Gorkom


Elena Aprile (Physics)
Arlin P. S. Crotts
Jules P. Halpern


Laura Kay (Barnard)


Michael Allison

Admission and Degree Requirements

The requirements listed below are special to this department and must be read in conjunction with the general requirements of the Graduate School.

For Admission

An undergraduate major in physics, astronomy, or a closely related field is required in addition to a solid background in physics, calculus, and ordinary differential equations.

Participation in Instructional Activities

All graduate students are normally required to participate in the educational activities of the department. Fulfillment of this requirement usually involves the supervision of laboratory or discussion sections.

For the M.A. Degree

Required courses: Astronomy G4001-G4002 and G4686-G4687 (unless waived by the department), 12 points of courses in the series in Astronomy G6000-G6005; a total of 30 points of astronomy or physics courses numbered 4000 or above. Up to 6 points toward the total of 30 may be awarded for a written report on a research project carried out under the direction of a faculty member. This project must be approved by the department. Students may work toward the M.A. degree either on a full-time or part-time basis. Full-time students may receive the M.A. degree as early as the end of the first year of study. Part-time students must complete the degree within four years.

Languages: none.

Qualifying examination: none.

For the M.Phil. Degree

Required courses: same as for the M.A. degree.

Languages: none.

Research projects: By the end of the second year in residence, a student must have completed two, and preferably three, short research projects under the supervision of at least two different faculty members as well as written reports thereof. Committees of the faculty will meet with each student in September of the 2nd and 3rd years to hear a presentation of these projects and discuss the results.

Qualifying examination: to be taken in June at the end of the student's first year. Students failing the qualifying examination in June may take the examination again the following January. The examination covers both physics and astronomy.

For the Ph.D. Degree

After completion of all requirements for the M.Phil. degree, the student must prepare and successfully defend a dissertation.


Research in astronomy and astrophysics is conducted in both the Department of Astronomy and the Department of Physics. Students in the Astronomy Department routinely work with the faculty of both Departments; who are located in the same building. A number of students also work on Ph.D. theses at the neighboring Goddard Institute for Space Studies (GISS), where research in planetary sciences is vigorously pursued. The faculty excel in theory, observations, and the development of new instrumentation, covering particle physics, cosmology and astrophysics, as well as extragalactic, galactic, and stellar astronomy.

Columbia's Astrophysics Laboratory, a joint endeavor involving the Astronomy and Physics departments, has extensive experience in the design and construction of new astronomical instruments for rocket, satellite and Space Shuttle missions. Facilities include laboratories and equipment for testing and assembling experiments, X-ray beam facilities, an electronics shop and a well-equipped and highly skilled instrument machine shop.

The Physics and Astronomy library contains over 35,000 volumes, including essentially all journals relevant to astronomy. The Astronomy department also has its own supplemental collections of reference books.

We maintain an extensive preprint library and hold weekly Journal Club meetings at which the most important recent papers are discussed. Every week, both Physics and Astronomy colloquia are given by invited speakers.

The Astrophysics Laboratory and Astronomy Department have a number of computers, including 30 SUN workstations ranging from SPARC 2's to UltraSparcs, 200 Gigabytes of disk storage, high density tape drives, monochrome and color laser printers, PC's and graphics terminals. All offices have connections to these machines through an Ethernet network. Full versions of AIPS, FIGARO, and IRAF are supported. Columbia University is a member of the Cornell National Supercomputer Facility (CNSF); Columbia researchers have access to this over a fast network.

The Astronomy Department operates a 24-inch reflector at the Harriman Observatory, one hour north of New York City.

Further information may be found in the Graduate Study and Research brochure, obtainable from the Astronomy Department Office (212) 854-3278.

Financial Aid

A comprehensive program of financial aid, including fellowships and appointments in research and in teaching, is available to students in the department.

Courses of Instruction and Research

Not all courses are given every year. To ascertain which of the following courses are given in each of the next two years and their times, consult the separate Registrar's Directory of Classes or ColumbiaNet.

Astronomy G4001. Astrophysics, I. 4.5 pts. N. H. Baker. This is the first semester of a full year introduction to astrophysics. Topics include the physics of stellar structure, stellar spectra, the HR diagram, the determination of distances, stellar evolution, nucleosynthesis, supernovae, white dwarfs, neutron stars, interacting binaries, stellar pulsations.

Astronomy G4002. Astrophysics, II. 4.5 pts. J. van Gorkom. Continuation of Astronomy G4001. Topics include galactic structure, star clusters, the interstellar medium, external galaxies, clusters and superclusters of galaxies, active galactic nuclei, cosmology.

Astronomy G4003. Observational techniques. 3 pts. To be announced. Prerequisites: basic astronomy such as C1103/C1104 or F1001/F1401 and basic Physics courses including optics, electronics and laboratory work on these two topics: General Physics III: Optics & Thermodynamics C1011 or C1111. Detailed introduction to the instrumentation used in astronomy and the methods used to obtain and analyze astronomical data. Six main topics are included: the effects of the Earth's atmosphere on radiation; astronomical optics and telescopes; detectors; observational methods; data reduction and statistical methods. All the main observational methods (imaging, photometry, polarimetry, and spectroscopy) are treated.

Astronomy G4301. Astrophysical and geophysical fluid dynamics. 3 pts. N. H. Baker. Prerequisite: some knowledge of ordinary and partial differential equations. Equations of motion for oceans, atmospheres, planetary interiors, and stars. Dynamics of rotating and stratified flows. Gravity, inertial, acoustic, and rossby waves. Convective, baroclinic, and shear instabilities turbulence. Spin-up and dynamo theory.

Astronomy G4686. Physics of astrophysics, I. 4.5 pts. N. H. Baker. Prerequisite: 3000-level electromagnetic theory and quantum mechanics. Physical processes in gases, with emphasis on those topics important in an astrophysical setting (stars, diffuse nebulae, galaxies). Statistical mechanics; non-equilibrium statistical and continuum physics; classical and semi-classical radiation theory.

Astronomy G4687. Physics of astrophysics, II. 4.5 pts. N. H. Baker. Prerequisite: Astronomy G4686 or permission of the instructor. An introduction to hydrodynamics, magnetohydrodynamics, and plasma physics with applications to problems of astrophysical interest. The Euler and Navier-Stokes equations, linear and non-linear waves rotating fluids, stability theory, supersonic flow and shock waves, similarity solutions, and heuristic theories of turbulent transport. Ideal magnetohydrodynamics, flux conservation, Alfven waves. Motion of changed particles in magnetic fields, adiabatic invariants, Vlasov equation, dispersion relations, and collisional dissipation.

Astronomy G6001. Advanced stellar structure and evolution. 3 pts. N. H. Baker. Topics include solar and stellar seismology, rotating stars, magnetic stars, pulsating stars, stellar mass loss, compact objects, interacting binary stars, pulsars, supernovae, nucleosynthesis.

Astronomy G6002. Radiative transfer and stellar atmospheres. 3 pts. K. H. Prendergast. Topics include the transfer equation, emission, absorption, scattering, line formation, curve of growth, moving atmospheres, non-LTE effects, non-thermal radiation mechanisms, comptonization, synchrotron self-absorption, masers.

Astronomy G6003. Galactic structure and the interstellar medium. 3 pts. K. H. Prendergast. Topics include gaseous nebulae, ionization zones, molecular clouds, star formation, interstellar chemistry, supernova remnants, stellar populations, stellar kinematics, galactic rotation, theory of spiral structure, dark matter in the galaxy, star clusters, chemical evolution of the galaxy.

Astronomy G6004. Internal properties of ordinary and active galaxies. 3 pts. Instructor to be announced. Topics include the stellar and gaseous contents of ordinary galaxies, their luminosities, masses, structures and internal dynamics. Active galaxies including quasars, BL-Lac objects, seyfert galaxies, radio galaxies, emission line galaxies, extragalactic HII regions, and starburst and infrared luminous galaxies. Galaxy formation and evolution will be treated from the perspective of stellar populations, the initial mass function, thermal instabilities, violent relaxation and chemical evolution. Observational and practical methods will receive equal emphasis with theoretical descriptions.

Astronomy G6005. Physical cosmology. 3 pts. Instructor to be announced. Topics include the extragalactic distance scale, Friedmann models, the microwave background, primordial nucleosynthesis, the formation of bound structures, clusters and superclusters of galaxies, measures of the mean density of the university, dark matter, baryosynthesis, inflation, galaxy formation, the particle physics connection.

Astronomy G8001. Planetary fluid dynamics. 3 pts. M. Allison. This course will be devoted to the study of the macroscopic motion of the fluid envelopes of planets (and stars) in response to the effects of rotation, pressure-density gradients, and diabatic forcing. After a brief review of the relevant thermodynamic and radiative processes, the equations of rotational fluid motion will be applied to the comparative analysis of terrestrial meteorology, oceanic flow, and the observed dynamics of planetary atmospheres, with occasional reference to related astrophysical phenomena. Special topics will include potential vorticity, geostrophic and cyclostropic balance, Ekman boundary layers, Rossby waves, and baroclinic instability.

Astronomy G9001-G9002. Special topics in astrophysics. 2 to 4 pts. Members of the staff.

Astronomy G9003-G9004. Research, I and II. 3 pts. Members of the staff.

Astronomy G9201-G9202. Seminar in stellar astrophysics. 2 to 4 pts. Members of the staff.

Astronomy G9203-G9204. Seminar in radio astronomy and galactic astrophysics. 2 to 4 pts. Members of the staff; J. van Gorkom.

Astronomy G9206. Seminar in infrared and radio astronomy. 2 to 6 pts. Members of the staff. Astronomical discoveries driven by instrumental developments. Review of the Fourier transform and its applications, the interferometer in practice, imaging sensitivity, deconvolution, self calibration, spectral line imaging, VLBI, optical interferometry. Discussion of papers on astronomical results obtained with state of the art instrumentation and/or algorithms.

Astronomy-Physics G6011. High-energy astrophysics. 3 pts. J. Halpern. Prerequisite: Physics G4021-G4022 or the equivalent. A survey of galactic and extragalactic X-ray and gamma-ray astronomy. X-ray binaries, bursters, pulsars, supernova remnants, active galactic nuclei, quasars, clusters of galaxies. Cosmic rays, astrophysical plasmas, radiative processes. Diffuse background radiation. Techniques of high-energy astrophysics including detectors, spectrometers, and telescopes.

Astronomy-Physics G6012. High-energy astrophysics. 3 pts. J. Halpern. Prerequisite: Physics G4021-G4022 . A survey of galactic and extragalactic X-ray and gamma-ray astronomy. X-ray binaries, bursters, pulsars, supernova remnants, active galactic nuclei, quasars, clusters of galaxies. Cosmic rays, astrophysical plasmas, radiative processes. Diffuse background radiation. Techniques of high-energy astrophysics including detectors, spectrometers, and telescopes.

Astronomy-Physics G6121. Classical continuum physics. 4.5 pts. E. A. Spiegel. Various aspects of fluid dynamics illustrated by an exposition of nonlinear waves in fluids and plasmas, solitary waves and solutions.

1997 August 28