14
1 Introduction to the Pulsars
X-ray and gamma-ray pulsars, among which X-rays and gamma rays are high-energy
photons, and most of radiating energy from pulsars is concentrated on these highenergy bands. The X-rays and gamma rays can be easily detected only by using the
miniaturized equipment, but the equipment must be mounted on the vehicles in outer
space to carry out the detections as the X-rays and gamma rays can not cross through
the dense atmosphere of the Earth. Therefore, spacecrafts can navigate autonomously
by using soft X-ray signals (with an energy band of 1–15 keV) from pulsars as natural
beacons. Generally, it should be noted that hard X-rays (15–200 keV) and gamma
rays (more than 200 keV) from pulsars can not be used to autonomously navigate
spacecrafts as their photon fluxes are too low.
Certainly, the same pulsar may radiate the signals simultaneously in several
frequency bands. For example, the signals radiated from the Crab pulsar (PSR
B0531+21) have been observed in the radio, infrared, visible, ultraviolet, X-ray and
gamma-ray bands. Moreover, the infrared and X-ray radiations from PSR B1509–
58 have been also detected. According to different sources of the pulsars’ radiant
energy, the pulsars can be classified into three categories: Rotation Powered pulsar
(RP), Accretion Powered pulsar (AP) and Anomalous X-ray pulsar (AX).
The RP pulsar is a type of neutron stars’ outward radiating energy at the expense of
their own rotational kinetic energies, and many X-ray pulsars belong to the type. It is
shown from the theoretical analysis that the pulse periods are the spinning periods of
neutron stars. Moreover, on the basis of the observational facts that the pulse periods
of radio pulsars are increasing uniformly, it is shown clearly that the rotations of
neutron stars are slowing down and their rotational kinetic energy also decreasing
gradually. For a spherical neutron star with a rotational angular velocity of ω, its
rotational kinetic energy E k can be expressed as
E k =
1
2
J ω
2
,
(1.3)
where J is the moment of inertia of neutron star.
For a sphere with uniform mass distribution, there is
J =
2
5
m R
2
,
(1.4)
where m and R are respectively the mass and radius of the neutron star.
And then, by finding the time derivative on the right and left sides of formula
(1.3), the loss rate of the rotational kinetic energy can be expressed as
˙
E k = J ω ˙
ω = −
4π
2 J ˙
P
P 2 ,
(1.5)
where P is the spinning period of neutron star, and ω =
2π
P
.
1 Introduction to the Pulsars
X-ray and gamma-ray pulsars, among which X-rays and gamma rays are high-energy
photons, and most of radiating energy from pulsars is concentrated on these highenergy bands. The X-rays and gamma rays can be easily detected only by using the
miniaturized equipment, but the equipment must be mounted on the vehicles in outer
space to carry out the detections as the X-rays and gamma rays can not cross through
the dense atmosphere of the Earth. Therefore, spacecrafts can navigate autonomously
by using soft X-ray signals (with an energy band of 1–15 keV) from pulsars as natural
beacons. Generally, it should be noted that hard X-rays (15–200 keV) and gamma
rays (more than 200 keV) from pulsars can not be used to autonomously navigate
spacecrafts as their photon fluxes are too low.
Certainly, the same pulsar may radiate the signals simultaneously in several
frequency bands. For example, the signals radiated from the Crab pulsar (PSR
B0531+21) have been observed in the radio, infrared, visible, ultraviolet, X-ray and
gamma-ray bands. Moreover, the infrared and X-ray radiations from PSR B1509–
58 have been also detected. According to different sources of the pulsars’ radiant
energy, the pulsars can be classified into three categories: Rotation Powered pulsar
(RP), Accretion Powered pulsar (AP) and Anomalous X-ray pulsar (AX).
The RP pulsar is a type of neutron stars’ outward radiating energy at the expense of
their own rotational kinetic energies, and many X-ray pulsars belong to the type. It is
shown from the theoretical analysis that the pulse periods are the spinning periods of
neutron stars. Moreover, on the basis of the observational facts that the pulse periods
of radio pulsars are increasing uniformly, it is shown clearly that the rotations of
neutron stars are slowing down and their rotational kinetic energy also decreasing
gradually. For a spherical neutron star with a rotational angular velocity of ω, its
rotational kinetic energy E k can be expressed as
E k =
1
2
J ω
2
,
(1.3)
where J is the moment of inertia of neutron star.
For a sphere with uniform mass distribution, there is
J =
2
5
m R
2
,
(1.4)
where m and R are respectively the mass and radius of the neutron star.
And then, by finding the time derivative on the right and left sides of formula
(1.3), the loss rate of the rotational kinetic energy can be expressed as
˙
E k = J ω ˙
ω = −
4π
2 J ˙
P
P 2 ,
(1.5)
where P is the spinning period of neutron star, and ω =
2π
P
.