Rachel Costello's pictureRachel Costello

College of Wooster

Dr. Gonthier, Dr. Harding

Supported by the NSF-REU

This summer I participated in the Hope College NSF-REU program. I spent the first three weeks working at Hope. I then traveled with my adviser Dr. Gonthier and another student researcher, Michelle Ouellette, to College Park Maryland just outside DC. For the remaining seven weeks, we worked at the Goddard Space Flight Center, a NASA research facility, so that we could work with two of Dr. Gonthier's colleagues, Alice Harding and Mathew Baring.

Neutron stars are formed from the collapse of super giant stars. A 1.4 solar-mass neutron star would consist of about 1057 neutrons, and be in fact a huge nucleus. Neutron stars are very hot, with surface temperatures of about 105 to 106 Kelvin. This high surface temperature causes them to emit electromagnetic radiation including x-rays. Rapidly rotating neutron stars that emit electromagnetic radiation from their poles in the form of gamma rays, x-rays, visual light, infrared and radio waves are called pulsars.

Recent observations have provided evidence of a class of neutron stars and pulsars called magnetars. These stars have surface magnetic fields exceeding the quantum critical field of 4.4 X 1013 Gauss. Inside magnetic fields of this strength many physical processes behave differently than at lower magnetic field strengths. The overall goal of the project is to develop a Monte Carlo cascade model that simulates the emission of X-rays and gamma rays from the magnetosphere of neutron stars and pulsars. To do this, we must study relativistic Compton scattering as it operates with other QED processes, to develop approximate expressions of the exact cross section. Non-relativistic Compton scattering occurs when a photon collides with an electron causing them to scatter. The electron is excited to a higher energy state as a result of the collision. Inverse Compton scattering occurs in these ultra-strong magnetic fields. The magnetic field accelerates the electron to relativistic velocities. As in classical Compton scattering, the electron is excited to a higher energy state. However, the electron looses kinetic energy, which is transferred to the photon. X-rays emitted from the star's surface can be excited to gamma rays through this process. In our model, we assume the electron to be at rest initially and at an unexcited energy state.

This summer, I have worked towards developing a better understanding of the differential cross section, the probability that the photon will scatter at a given angle from the electron. We used an approximation of the exact QED differential cross section in the rest frame of the electron. I found expressions that help us to better understand the behavior of the differential cross section with respect to the scattered angle, finale energy state of the electron, the magnetic field, and the energy of the incident photon.

Previous studies have ignored strong magnetic field effects and assumed that Compton scattering can be described by the non-relativistic Compton scattering cross section (Thomson limit) below and at the resonance and by the Klein-Nishina cross section for non-resonant (relativistic) scattering. We are testing the exact QED rate expression for the cross section to see if it will agree with the Thomson limit bellow the resonance and with the Klein-Nishina cross section above the resonance. We have found that the exact rate and our approximation of it agree with these expressions for the most part. However, when the electron is accelerated to very high energy states, the exact rate and our approximation both fall short of the Klein-Nishina cross section.