We have several department-sponsored postdoctoral positions; availability of funds allows us to support one or two people in these positions at any given time. They are:
The Henry Norris Russell Postdoctoral Fellowship, named for the Chair of the Department for much of the first half of the 20th Century, is awarded to highly promising observational researchers.
The Lyman Spitzer Jr. Postdoctoral Fellowship, named for the chair of the department from 1947 to 1979, is given to top theoretical postdoctoral astronomers.
The Carnegie-Princeton Joint Postdoctoral Fellowship, in which the researcher spends roughly half the time at the Carnegie Institution of Washington in Pasadena, California, and half the time at Princeton. They are given access to all observational facilities at both institutions for the full term of the joint position.
These postdocs are typically for three years, although this can be extended for those coming with external sources of funds (such as Hubble, Einstein, NASA/Spitzer, Chandra, or NSF Fellowships).
Many individual professors and research groups sponsor postdoctoral researchers, and a number of postdocs come on various external fellowships.