What's the "Spectral Correlation Function"

& What's it Used For?

...Click here to skip straight to a practical,non-astronomical, application...

Introduction: In Radio Astronomy, we are now blessed with what some people might call "too much data." The Spectral Correlation Function (SCF) Project should give us a better understanding of what these data mean. In a nutshell, the SCF compares observations of the distribution of velocities of gas particles in space, and it can be used to compare the observed distributions with theoretically prediced ones. We use it to understand the physcis of the material between the stars known as the Interstellar Medium (ISM). One of the most interesting physical processes the SCF allows us to study is the formation of new stars like the Sun in the ISM.

More About Spectral-Line Radio Astronomy: Several radio telescopes around the world can now make a measurement that produces a spectrum (which measures the intensity of emission from a particular atom or molecule at thousands of discrete velocities simultaneously) at nearly one hundred neighboring locations at the same time.

The blue figure at right (click to enlarge) shows how the product of the number of velocities we can measure (N_channels), the number of positions observed (N_pixels), and signal-to-noise has increased by a factor of nearly 1 billion since the beginning of Radio Astronomy in the 1950's.

The Problem: So, what do we do with all these data? We cannot, as people have in the past, sit down and look at tens of thousands of spectra by eye. Many researchers choose to compress the information in these large maps by displaying and analyzing the data in ways that eliminate one dimension. For example, one can integrate each spectrum (count all the photons at all velocities and add them up) and just display the integral in a contour diagram, as is shown in the black-and-white diagram at right (click to enlarge): But, as one can see from the sample spectra in the figure, each point actually contains much more information than the "integrated" emission contour map shows. (The contour map shows the integral, or area, under each of the spectral x-y plots shown in the insets.)

The SCF Solution: One of the most important properties of spectral-line maps is how the spectra change from position-to-position. (Notice the big differences in the shapes of the spectra shown next to the contour map.) The Spectral Correlation Function (SCF) simply measures the similarity of a spectrum to its neighbors. The number characterizing this similarity, known as S_0, can then be plotted as a function of position in another contour map, and analyzed statistically. Thus, even though the inherently four-dimensional (position-position-intensity-velocity) set of observations has now been reduced to three dimensions, the new third dimension, S_0, includes information about both of the dimensions (intensity and velocity) it replaces, so all dimensions are essentially preserved.

What's Been Done with the SCF? The SCF has been used very successfully to discriminate amongst various theoretically calculated numerical simulations of the Interstellar Medium. (See Rosolowsky et al. 1999). Currently, the SCF is being refined to take better account of variations in the signal-to-noise and spatial and spectral resolution in the data sets (see Padoan, Goodman & Rosolowsky 1999.) When these refinements are complete, the SCF will be applied to a large range of observed and simulated data sets, with the aim of improving the simulations until they statistically "match" observations. When the simulations match, we can then safely assume that the physical inputs used in the simulations (e.g. gas temperature, density, composition, magnetic field structure, etc.) form a good description of the parts of the "real" ISM being simulated.

What Other Useful Jobs Might the SCF Do? One feature the SCF is very good at finding is an abrupt change in spectral properties over a very small distance. In turbulence theory, which can be used to characterize a good deal of ISM physics, such abrupt changes are often caused by what is known as "shear." Most people who have flown are familiar with "wind shear," and its dangerous effects on aircraft. In conjuntion with velocity-resolved Doppler Radar, the SCF could presumably be used to find wind shear, and the conditions leading to wind shear, in real time.

The People: The original SCF algorithm was sketched out by Dr. Alyssa Goodman (Harvard University), and fully implemented in IDL by Erik Rosolowsky (currently a graduate student at UC Berkeley). Rosolowsky began the project during a Summer Internship at the Harvard-Smithsonian Center for Astrophysics, in collaboration with Dr. Jonathan Williams (U. Florida as of Fall 1999), Dr. David Wilner (Smithsonian Astrophysical Observatory), and Dr. Goodman. In 1998, graduate student Javier Ballesteros (UNAM, Mexico) and Dr. Enrique Vazquez-Semadeni (UNAM, Mexico) joined Goodman in a collaborative project using the SCF to study simulations on a Galactic scale. In April of 1999, Dr. Paolo Padoan (Harvard University), an expert on simulations of the ISM, joined the project in Cambridge.

Our Sponsor: The SCF project is currently funded by a grant to Dr. Goodman from the National Science Foundation's Galactic Astronomy Program.

For more technical information, including code, please visit:

Last Update: August 12, 1999 by Alyssa A. Goodman.