Graduate Degree Requirements
The Departments of Astronomy and Physics each offer programs of research in astronomy and astrophysics leading to the Ph.D. degree. The degrees of Master of Arts and Master of Philosophy in Astronomy may also be obtained after one or more years of course work, but students are not normally admitted to pursue these degrees only. Advanced standing can be granted for students admitted with post-bachelor’s degrees, based on individual evaluation.
The PhD is awarded for independent, original research. As such, it is qualitatively different from all other degrees and, for most students, from anything they have encountered in their first sixteen years of education, where the knowledge base was already established, the choice of topics was the teacher’s, and success was defined by achievement on papers and exams.
With this in mind, the Columbia Astronomy program emphasizes original research, commencing the very first week new students arrive in Morningside.
First and Second Year Projects
Each year begins with ASTROFEST, a day where each faculty, post-doc, and current graduate student presents a talk or poster explaining their research (accompanied by a generous allocation of comestibles and libations). The following week, first-year students participate in a series of one-hour meetings as a group with each faculty member designed to showcase the range of research projects available; all students then choose a first-year project by the end of September. To ensure all students have adequate time to devote to this project, they are exempted from most teaching responsibilities during the first year. This project, along with two, or at most three courses per semester, constitute the work of the first year.
Over the course of the first two years and the two summers following them, students are expected to complete at least two research projects, each with a different faculty member in a different area of astronomy. Both a written report (either an article for publication or something written in the same style) and an oral presentation on the project results are due each September.
Many students submit results from their research for publication in professional journals. Instead of a traditional qualifying exam, research exams are held at the completion of the first and second year. Our course requirements are designed to impart the knowledge necessary for research in astronomy.
Often, one of these projects then evolves into the dissertation project, a written proposal presented in the first semester of the third year. A three-member faculty committee is assigned to each student to monitor his or her progress throughout the student’s time here at Columbia.
Coursework includes five required graduate courses plus three additional electives in Astronomy, Physics, or some other department in the Graduate School. The required courses are
- Astro 6001 Radiative Processes - Prerequisites: 3000-level electromagnetic theory and quantum mechanics. Radiation mechanisms and interaction of radiation with matter. Applications of classical and semiclassical radiation theory and atomic physics to astrophysical settings. Radiative transfer, polarization, scattering, line radiation, special relativity, bremsstrahlung, synchrotron radiation, inverse compton scattering, ionization losses, shocks and particle acceleration, plasma processes, atomic structure and spectroscopic terms, radiative transitions and oscillator strengths, curve of growth, molecular spectra.
- Astro 6002 The Interstellar and Intergalactic Media -A survey of diffuse matter in the universe with emphasis on astrophysical processes and their observational consequences. Topics include radiative transfer, dust, ionization, thermal balance, magnetic fields, hydrodynamics, shocks and star formaion in the context of gaseous nebulae and the multi-phase ISM, ICM and IGM.
- Astro 6003 Stellar and Galactic Dynamics - An introduction to the study of galaxies, from both observational and theoretical perspectives The course will review our current understanding of the formation and evolution of galaxies through descriptions of: their structure and dynamics; the gas and stellar populations they contain; and what we know about the distribution of dark matter within them.
- Astro 6004 Stellar Structure and Evolution - Topics include the physics of stellar structure, stellar atmospheres, radiation transport, nucleosynthesis, stellar evolution, star formation, pulsation, interacting binary stars, white dwarfs, and neutron stars.
- Astro 6005 Physical Cosmology - 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.
By the end of the second year, it is expected that students will have completed the Master’s course requirements which includes the 30 points of graduate credit and the two years of residence as a full-time student in the program. Students entering with a Master’s degree may be granted advanced standing depending on their performance; this action waives the point and residence units requirements, although most such students still take courses from the curriculum.
The Graduate Student Handbook provides more details on the program and the department.
In order to facilitate their rapid transition to our research-intensive program, first-year students are not expected to teach a Lab section. However, in order to learn to perform this activity effectively in subsequent years, first years often observe and assist more senior students in labs and may also run help sessions for introductory courses in the department.
All second-year students are normally expected to teach one section per semester of Laboratory C1903/1904 (comprising a small class of 10-12 undergraduates). They are responsible in this capacity for designing a syllabus for the lab (based on a library of previously created labs), conducting the lab sessions, and providing evaluations of student work, as well as a recommended final grade for each student. They are also expected to attend TA meetings and to participate in the collective activity of developing new laboratory exercises.
There is no single qualifying examination for advancement to PhD candidacy; the final exams of the five required courses and evaluations from the research examinations fulfill this role instead. Students admitted to candidacy are expected to complete a written dissertation proposal in their third year, present it to their faculty committee, and begin the project. At the end of the third year of residence, the Master of Philosophy Degree is awarded.
Obtaining the PhD in Astronomy at Columbia typically takes students 5 to 7 years.