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Timing An X-ray Pulsar
by James Humphreys
Contents
Introduction, Requirements, Lesson
Plan, References
Certain X-ray objects in the sky emit X-rays in a very rapid regular
periodic pattern. These objects are X-ray pulsars. The pulsar
contained in the Crab nebula is the most well known of these objects.
A pulsar is a neutron star with a very strong magnetic field. Neutron
stars are the remnants of massive stars which have reached the
end of their lives. These stars have an initial mass greater than 10
times the mass of the sun. Throughout the star's life, hydrogen burns into
helium through nuclear fusion. Once enough helium has formed and the
pressure is high enough in the star's center, the helium fuses into carbon
and oxygen. This process of lighter elements fusing into heavier elements
continues until an iron core is formed. Iron has the largest binding
energy
of all the elements, and hence it cannot fuse into any heavier element.
Thus iron simply accumulates under the weight of shells of successively
lighter
elements which continue to burn.
When the iron core can no longer support its own weight and the weight
of the rest of the star, it
collapses. Within milliseconds, gravity overwhelms the pressure
of the remaining material and a full collapse ensues. In this
collapse, protons and electrons combine to make neutrons. The energy
released is emitted outward and explosively blows away the remaining
material of the star. This material glows and is visible as a
supernova remnant. The core of the star is left as a neutron star.
The initial magnetic field of the star intensifies during the collapse.
Hence, neutron stars can have very strong magnetic fields. Neutron
stars can "pulse" because of electrons accelerated near the magnetic
poles. These electrons travel outward from the neutron star. They
emit x-rays and gamma rays when they must travel faster than the
speed of light to continue rotating with the magnetic field. An
external observers sees a pulse of radiation whenever the magnetic
pole is visible. The pulses come at the same rate as the
rotation of the neutron star (30 times a second for the Crab pulsar),
and are very regular.
In this segment the student is introduced to the use of X-ray data to
identify an object as a rotating neutron star, and determine its period of
rotation.
Using XTE observations of the Crab Pulsar, the
student will be able to:
Interpret this period as the period of rotation of the object.
Identify this object as a neutron star.
Alternatively, the teacher may instruct the students how to get these
files.
This lesson depends heavily on the student's understanding of
periodicity, and the Principle of Superposition. A brief explanation of
the principle of the Fourier transform is required.
Choose a familiar, common periodic phenomenon. Describe some measurable
parameter that would show this periodicity, including measurements that
could be taken, and devices that could be used to take them. Since you
are already familiar with this phenomenon, calculate the period and
frequency of the variation in the suggested parameter, and express these
in appropriate units.
Distribute the graph with the following directions/questions:
The graph
you have is of a computer generated Fast Fourier Transform over a
light curve
obtained from the Crab Pulsar during 100 seconds. In general, the lowest
frequency spike corresponds with the fundamental frequency of the wave
form being analyzed.
What explanation might you offer for the presence of the
other prominent spikes? (Hint: How do the frequencies compare to
that of the fundamental?)
The usual, and generally accepted explanation of this rapid
variation in intensity is that the neutron star itself is spinning, and
that the "bright spot" is alternately pointed toward and then away
from us. No other theoretical process is able to adequately explain
the brightness changing so rapidly and over so many wavelengths
with such regularity.
To see how this effect is produced, have one lab group member stand,
holding the flashlight, in the center of a small circle formed by the rest
of the lab group. The center person then points the flashlight with an
arbitrary orientation. Then, keeping the flashlight still with respect to
her/himself, this student spins at some comfortable rate. The others
observe the changing intensity of the
light they can observe from the source.
Use a clock or watch to time the "flashes" of light and calculate the
period of the student's rotation. Finally, have the student in the middle
spin as fast as s/he can, measure that period and compare it to the period
of the Crab Pulsar.
Neutron stars have masses up to about 3 solar masses, and radii of the
order of 10 km. Assume such a mass and radius for this object, and use
the period you calculated earlier to answer the following questions:
Express this as a percentage of the speed of light.
What is the centripetal force necessary to keep the material
of the surface near the equator in place (in orbit around the center) ?
What is the gravitational force at the surface of this object
? How does this answer compare to your answer to number
3 above ?
Arny, Thomas. Explorations: an Introduction to
Astronomy. Mosby, St. Louis (1994) pp.395-401
Graham-Smith, Sir Francis. "Pulsars Today." Sky and
Telescope 80 (September 1990): 240
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Introduction
Concept
Theme
Objectives
Determine the period of the light intensity.
Requirements
Lesson Plan
Warm-up
Activity
Using this information, what is the frequency of the variation
in X-ray intensity coming from this object? the period?
Assignment
What is the linear speed of a point on the equator of the
star ?
References
Zeilik, Michael. Astronomy: The Evolving Universe.
John Wiley & Sons, Inc., New York (1991, 6th ed.)
pp.378-382
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This file was last modified on Monday, 16-Dec-2002 13:12:08 EST