Supported by the NSF-REU and Michigan Space Grant Consortium
A pulsar is a rapidly rotating neutron star that emits electromagnetic radiation from its poles in various forms, such as gamma rays, x-rays, visible light, infrared, or radio waves. The typical neutron star has a mass of 1.4 solar masses, a radius on the order of 10 km, a density of about 6.65x1014 g/cm3, and an average gravity of 1.86x1014 cm/s2. Its period can be between 1 ms and 5 s, and is very accurate: accuracy challenging even the best atomic clocks.
As the pulsar rotates, the velocities of the particles traveling along the co-rotating magnetic field lines are limited to the speed of light (c = v = rw). Therefore, there is a cutoff radius created where particles reach this speed, and thus forms the "light cylinder." In the polar cap model, the emission from the pulsar comes from its polar caps, which are regions near the magnetic poles where magnetic field lines do not reconnect to the pulsar. As the pulsar spins on its rotational axis, these "light cones" sweep across the Earth in the same manner as does light from a lighthouse. This model is therefore known as the "Lighthouse Model," and it is this sweeping of light across our line of sight that allows us to detect pulses from the pulsar.
While there have been more than 700 radio pulsars detected, only 8 gamma ray pulsars are known. This is mainly because while radio waves pass easily through the Earths atmosphere, many gamma rays are absorbed, and thus are harder to detect with ground-based equipment. Whereas radio pulsars are detected with ground-based equipment with low flux thresholds, gamma-ray pulsars are detected from Earths orbit with satellites having higher flux thresholds. The comparison between radio and gamma-ray pulsars is important because all but one of the gamma-ray pulsars are also detectable as radio pulsars. If the period of the gamma-ray pulsar is known from its radio emission, then it is much easier to search for the period in the gamma ray region.
My project for the summer was to use Monte Carlo techniques to create pulsars using a more accurate model for pulsar luminosity. We evolved these simulated pulsars to the present time, and then used gamma ray and radio selection effects to predict the observability of these pulsars. This information will be used with EGRET (Energetic Gamma ray Experimental Telescope) and GLAST (Gamma ray Large Area Space Telescope) to predict their ability to observe gamma-ray pulsars.
Information was taken from a paper by Sturner and Dermer [ApJ, 461:872 883, 1996 April 20]. This paper gives the population and distribution probabilities of radio pulsars within the galaxy (assuming radio pulsars also emit in the gamma ray). These probabilities are based on previously published information about the distribution of stars in the galaxy. Using these probabilities and Monte Carlo techniques, we computed initial positions for pulsars with corresponding coordinates r, z, and f with respect to the center of the galaxy. Using the gravitational potential, we could find the circular rotational velocity at the birth location. This gravitational potential is associated with the galactic bulge, the galactic disk, and the halo surrounding the entire galaxy. From another probability function, we calculated a random velocity given to the pulsar by the supernova explosion. With these velocities and a random age less than one million years, the position of the pulsar at the present time could be computed.
From other expressions by Sturner and Dermer, we could calculate the period, period derivative, and the magnetic field of the pulsar. With these, we could then determine the luminosity and the flux by two methods: using one set of expressions by Sturner & Dermer, and another set by Alice Harding (with whom we worked at NASA). We used both sets of expressions in order to compare them.
Comparing these fluxes with flux thresholds for EGRET and GLAST (10-7 photons/cm2/s and 10-9 photons/cm2/s, respectively) with both sets of expressions we got reasonable luminosities and fluxes (as compared to known gamma ray pulsars), but the percentage of observable pulsars differed for each set. This curiosity is one I hope to solve during this coming fall semester.
In addition to this problem, future consideration will also be given to incorporating radio emission and luminosity selection effects for these pulsars. We will also see if this is the best model for predicting these luminosities and fluxes, or if there is a better model.
This summer has been quite rewarding in the fact that I learned much more than I ever would have in the classroom. I got the opportunity to work at NASA as well as enhance both my physics and astronomy knowledge in addition to developing some valuable programming skills. I would like to thank Hope College, REU/NSF, and The Michigan Space Grant Consortium for giving me this wonderful opportunity, as well as NASA and Professor Gonthier for their help and for thinking up a great project for me to work on.