John Shoemaker's pictureJohn Shoemaker

Hope College

Dr. Gonthier

Supported by NSF-REU


I spent ten weeks of the summer at Goddard Space Flight Center (GSFC) in Greenbelt, Maryland, working with Dr. Peter Gonthier and Martin Knecht (an undergraduate at the University of Illinois Urbana-Champaign). Professor Gonthier has been collaborating with Alice Harding and Matthew Baring, two NASA scientists working in the Laboratory for High Energy Astrophysics (LHEA) at Goddard. They have been working on a theoretical model for the mechanisms that produce high-energy photons (particularly gamma rays) in the dipolar magnetic field (magnetosphere) of pulsars. They have also introduced some new ideas to the standard model of pulsars. They have found that photon splitting occurs in higher energy photons in sufficiently high magnetic fields, that inverse Compton scattering could play an important role in the pulsar emission, and that there is some radial dependence of radio polarization. Also, they have been exploring the effect that polarization has on whether or not photons are produced, and what their energies are. Quantitatively analyzing Most of their efforts are directly tied to data taken on pulsars by orbiting satellites such as the Compton Gamma Ray Observatory (CGRO).

Before I continue, let us get some idea of the physical nature of a pulsar. Astronomers believe that a pulsar is a remnant of a supernova. What remains after a supernova event is extremely dense, rapidly rotating (think conservation of angular momentum), and, quite possibly, very magnetic -- this is called a neutron star. A pulsar is a rotating neutron star with an extremely strong corotating magnetic field. An average pulsar has a radius of probably about ten kilometers with a rotational period of between one millisecond to several seconds. A pulsar can have magnetic fields of 107 to 1014 Gauss! The star itself is something like a giant nucleus. The average pulsar also has a total stellar mass 1.4 times the mass of our sun, so the stellar material can have densities ranging from 104 g/cm3 near the surface to 1014 g/cm3 at the core! Surrounding the dense star is a plasma of electrons and photons. As the magnetic field "lines" arc out into the plasma surrounding the pulsar, there comes a limit at which the magnetic field lines would need to travel at speeds greater than the speed of light to "keep up" with the rapidly rotating pulsar. Instead of violating the "speed limit of the universe," the field lines that cross the cylinder that defines this boundary (called the "light cylinder") do not close! At the magnetic poles, there are "polar cap" regions. These polar cap emitting region is somewhat conal in shape with an inclination angle defined by the angle between the tangent to the last closed field line at the surface of the pulsar and the magnetic pole axis.

The most accepted theory of a pulsar's radio polarization is the rotating vector model (RVM). According to this RVM, photon emission occurs at the magnetic polar regions of the pulsar. As the pulsar's pole moves across the earth's line of sight, we observe a "pulse" of light. The light we see results from several processes -- but only the radio polarization data was relevant to my study. In the past, it has been assumed that radiation of photons occurs at a given distance from the star. While the pulsar is reasonably well understood, there are many questions about how and where the pulsar actually produces its light. It is likely that photons have their sources at varying radii; therefore, the polarization of the light we see (which is deeply affected by the position angle of the observer/photon vector relative to the magnetic pole) as a function of time might be better interpreted in terms of some "time-delay" process.

I learned to search the library (Goddard's library is top-rate for professional literature) to find journal articles and other timely resources. These helped us know what had been done before, guiding us down new avenues to take to explore the possibilities. We used the journal articles to find supplemental data on polarization. These articles also helped us understand the RVM model a bit more. We noted that some scientists had questioned the relationship between a photon's polarization and the place along the magnetic field where it was created. This had potentially important results -- then could this affect our polarization observations? This was a question we needed to answer.

We designed a program that would take in to consideration variable emission radii. We assumed that photon emission was directed parallel to the direction of the magnetic field at a radius, r, from the pulsar's center. We also assumed the conventions and parameters specified in Pulsars, by Manchester and Taylor. (These parameters describe the angle between the spin axis and the magnetic pole and the angular velocity of the pulsar.) After satisfying ourselves that the equations given by Manchester and Taylor were correct, we used a model of the dipolar magnetic field to find a relation of a magnetic field line's radial distance to phi, a time dependent measure of the phase of the pulsar's rotation, through theta-gamma, the angle between the magnetic pole and the tangent to the magnetic field line at a given r. We also assumed that the position angle, psi, was independent of r. With these assumptions, I could write a program.

The program first receives the parameters from the user. It then loops through a specified interval of the pulsar's rotation phase, calculating r, theta-gamma, and psi for each phase value. It compares each r to R, which is an arbitrary radial distance -- a technique that allows us to compare the assumption that all radiation is emitted at a fixed radius to our own. From the extra distance the photon presumably travels on its way to this surface described by R, the program calculates a time delay, delta-t. From this delta-t, we calculate a new, "apparent," phi value for the emitted photon. The program then outputs prints out all the related values into a data file. The data can be analyzed via a spreadsheet program.

Both the effects studied, r-dependence and relativistic aberration, do not seem to make a large change in any observables. In fact, these effects are well within the error of observations.

I learned many practical skills this summer: computer programming in ANSI C, becoming familiar with various spreadsheet programs and network tools, using mathematics programs, and library research. Besides that, working at Goddard was a challenge for me. I was forced to become more organized and self-directed in completing some tasks. These are both abilities that I need to develop fully. In addition, there were periodic seminars given by a wide range of scientists on topics ranging from the chemical composition of comets to the physics of cataclysmic variable systems. And these were always fascinating little windows into an area of science I knew little about -- foreign places where I could learn a little of the language. Having only finished a year of undergraduate study, most of the physics I encountered was totally new and interesting. Every day, I was challenged by a phenomenon I had never known before -- of course, I couldn't learn all of it, but I learned a little bit about many areas of physics. In some way, this summer's experience placed my future education in a realistic context. Each class and each experiment will have a real importance because I have a better understanding of how they can all fit together. All in all, I benefitted from learning both practical skills and a better understanding of physics and its context for my future.


shoemakerj@hope.edu