Shawn O'Brien's pictureShawn O'Brien

University of Notre Dame

Research Professor - Dr. Peter Gonthier

Supported by the NSF-REU

Understanding Monte Carlo Simulations of Galactic Pulsar Distributions and Properties

Theories hold that pulsars are highly magnetized, rapidly rotating neutron stars that are generally the end product of supernova explosions. These stars, which are thought to possess characteristics unattainable in a laboratory, generally emit in the radio, visible, x-ray and gamma spectra. Theorists have been attempting to produce highly sensitive computer models to reproduce and predict these extraordinary characteristics and how these features effect the behavior of the pulsar. This summer, I have worked on a computer simulation that was started by Michelle Ouellette ( academic/physics/reu99/ouellette.html) last summer, which attempts to model the distributions and properties of known pulsars. The program uses a Monte Carlo method to randomly select birth positions and velocities of pulsars. Other properties of the pulsar are calculated, such as the period, period derivative, and the magnetic field. These pulsars are then evolved with constant magnetic field to the present day. Next, surveys are run to determine if there is a detection of the pulsar. The entire process is repeated until the selected number of pulsars has been detected. I worked on several sections of the program, including the dispersion and scattering measures, as well as the death valley. The research time for this project was split between Hope College in Holland, MI, and NASA/Goddard Space Flight Center in Beltsville, MD.

The pulses of radiation emitted by pulsars are effected by the Interstellar Medium (ISM) as they propagate towards Earth. The free electron density along the line of sight is mostly responsible for these effects, the scattering and dispersion of the signal. As the pulses travel through regions of different electron density, they are scattered differently, and thus a sharp pulse emitted by the star will appear weaker and smeared. Also affecting the received signal is the amount of dispersion, or lag, caused by the differing indices of refraction in the areas of changing electron density. These two phenomena affect the pulse width of the pulsar, and therefore are major factors in detection.

Taylor and Cordes (1993 ApJ 441,674-684) produced a model that described the distribution of free electrons in the vicinity of Earth. They were able to model important features, such as the galactic spiral arms and the Gum nebula, all of which are major contributors to the electron density. Once incorporated into our model, we were able to more efficiently and effectively determine the amount of pulse broadening due to the ISM. Thus, given this broadening and the parameters of the modeled surveys, the simulation was able to more accurately model the simulated detection of pulsars.

A death line is a theoretical prediction for when the characteristics of a pulsar do not support the pair production necessary for radio emission. There can be no detection if there is no emission, therefore beyond these parameters, no pulsars should be detected. However, there are a few different parameters that can influence the death line. One such topic is the magnetic field configuration. There are two plausible configurations, the dipole and multipole. A dipole pulsar has field lines that resemble a dipole magnet, whereas multipole pulsars have much more complex field lines. The differing geometrical representations of the field configurations result in different quantum electrodynamic situations. The QED effects are also different, and therefore dipole and multipole configurations yield different death lines (Figure 1.). It is common to use the multipole line because there are many observed pulsars that fall past the dipole death line. However, in the simulation, we were having the problem of observing too many pulsars along the multipole death line.

To solve this problem, we attempted to implement a death valley, or a region of pulsars that passed a random selection process to actually be detected. To do this, we used an exponentially decaying distribution to reduce the number of pulsars between the two death lines along lines of constant B-field. The basis for this exponential decay is that the pair production between the two death lines also appears to fall off exponentially. There has been work done on the subject, but a theoretical decay relationship between pair density and radio emission has yet to be determined. Upon implementing the death valley into our code, we seemed to solve the basic problem of detecting too many pulsars near the death line. However, other, more subtle things seem to need some attention.

This program, when completed, will be able to support research in many other areas. Future research on the beam geometry of the radio and gamma ray emissions of pulsars should be able to use our work as a stepping stone. Also, our model leads down the path of taking a more detailed look into radio quite pulsars, such as Geminga, and figuring out if they are regular or extraordinary phenomena. With this research, hopefully an all-encompassing simulation could predict, effectively, the results of the Gamma-ray Large Area Space Telescope, or GLAST.

                        Figure 1. A plot showing the relationship between the different death
                        lines (2000 ApJ, 531, 135), as well as lines of constant B-field (1995,
                        Australian J. Phys., 48, 571).

Click to see a slide show of Shawn O'Briens's work.