Astrophysik   Astrophysics

Pulsars

A pulsar was discovered first in 1967 by Jocelyn Bell and Anthony Hewish as a stellar source of radio waves characterized by the regularity (pulses with a precise repetition period of 1.337 seconds). By the end of 1968, about 20 pulsars were known. By this time, the most plausible explanation for the phenomenon put forward was that pulsars are rapidly rotating, highly magnetised neutron stars radiating energy out of their magnetic poles. In this "lighthouse'' model, the observed pulses are produced as the magnetic axis crosses our line of sight once per rotation.

In 1934, only two years after the discovery of the neutron by James Chadwick, the existence of neutron stars was proposed by astrophysicists, Baade and Zwicky. They suggested that neutron stars would be about 10 km in diameter and would be formed in a supernova.

The density increases and the electrons are captured by the protons and the core becomes a neutron star.

The discovery of a short period (33 ms) pulsar in the Crab Nebula in 1968, which is the remains of a nearby supernova explosion witnessed by Chinese astronomers in 1054 AD (visible in broad daylight for 23 days), confirmed this prediction: In the 1980s the millisecond pulsars were discovered, having periods of a few milliseconds, instead of order one second for "normal" pulsars.

The shortest possible period T of a pulsar can be estimated be the assumption that the speed v at the pulsar's surface cannot exceed the speed of light:

v = c = 2 π r / T

T = 2 π r / c

For a pulsar of period T = 0.001 s the radius is r = cT/2π = 47 km.

For a star not to lose mass as a result of spinning we have to consider the gravitational acceleration G·M/r2 and the centripetal acceleration v2/r,

G M / r2 = v2 / r = 4π2 r / T2

T2 = 4π2 r3 / GM

Combining the equations for T and T2, we get

r = G M / c2

For M=MSUN=2·1030 kg the pulsar radius is

r = 1.5 km

Taking r=20 km, which is 1/35,000 of the Sun's radius, and 1/4.3·1013 of the Sun's volume, the density of a pulsar must be 4.3·1013 higher than the Sun's, about the density of atomic nuclei.

Reducing the radius of a star by 1/35,000 increases the rotation period (conservation of angular momentum) by 35,0002 = 1.2·109. The Sun (T=25 days) would become a millisecond pulsar (T = 1,8 ms).

The collapse from R=700,000 km to r=20 km at constant mean acceleration of g=GM/rR= 9.5·106 m/s2, will take the time

t = root(2R/g) = 12 s

and cannot be shorter than

t = R/c =2 s

The collapse will release gravitational energy of order

W = G·M2 / (2·R) = 3·1051 J

The total energy output may be 1044 J

About 99% of the collapse energy is carried away by electronic neutrinos