32
1 Introduction to the Pulsars
change rates of ordinary pulsars are 10
–13
−10
–15 s/s, while the millisecond pulsars
have very stable periodicities and their rates can usually get to 10
–19
−10
–21 s/s.
Therefore, the millisecond pulsars are generally credited as the most stable clocks
in nature. The pulsar timing and navigation are studied by utilizing the very stable
periodicity of the pulsars.
Seven millisecond-pulsars, including PSR B1937+21, PSR J1713+0747, PSR
J0621+1002, PSR J0751+1807, PSR B1855+09, PSR J2033+1734 and PSR
J2322+2057, have been observed and investigated in the Arecibo Observatory since
1982, and their periodic change rates are respectively 1.051193 × 10
−19 s/s, 8.5314
× 10
−21 s/s, 4.732 × 10
−20 s/s, 7.7848 × 10
−21 s/s, 1.78354 × 10
−20 s/s, 1.1112
× 10
−20 s/s and 9.650 × 10
−21 s/s [20]. Obviously, the long-term stabilities of the
millisecond pulsars are higher than those of the current hydrogen atomic clocks in
laboratories.
Generally, the upper limits of pulsars’ ages are defined as the ratios of the pulse
periods to the periodic change rates, and also referred to as characteristic ages of
pulsars. For example, the pulse period and its rate of the Crab Pulsar are respectively
0.03372069749 s and 4.2277 × 10
−13 s/s on May 1, 2016, and thus it is easily
calculated that its characteristic age is 2529 years. In fact, the supernova explosion
of the Crab nebula was first observed and recorded by astronomers of the Song
Dynasty in China in 1054, and thereby calculating until 2016, its age should be
962 years. Apparently, there is a large discrepancy between the two ages. According
to the magnetic dipole model of pulsars, a modified formula of the characteristic age
is derived as follows.
τ =
P
(n − 1) ˙
P
,
(1.7)
where τ is the characteristic age of pulsars, P and ˙
P are respectively the pulse period
and its change rate, and n is a modified coefficient and usually is valued as 3.
Consequently, it is calculated by using formula (1.7) that the characteristic age
of the Crab Pulsar is 1264 years and close to the above result of 962 years. In
general, the periodic change rates of the ordinary pulsars with short periods are great
and correspondingly their characteristic ages small. It is also shown clearly that the
short period pulsars are younger. The pulse periods gradually increase with time, the
periodic change rates slow down, and the characteristic ages of the ordinary pulsars
will be older and older.
However, no all pulsars have stable rotation periods. The periods of some pulsars
are suddenly faster under the background of steady growth for a long time, and
then rapidly slow down until recovering the previous period-increasing-rate. The
phenomena, which the periods of pulsars suddenly jump, are usually called glitch.
For the younger pulsars, the glitches happen easily and the relative change rates of
periods are usually 10
–6
− 10
–10 . For example, the glitch of the Vela Pulsar happened
from February 24 to March 3, 1969; the relative change rate of the period got to 2
× 10
–7 and recovered to normal level after the following several weeks. Thereafter,
1 Introduction to the Pulsars
change rates of ordinary pulsars are 10
–13
−10
–15 s/s, while the millisecond pulsars
have very stable periodicities and their rates can usually get to 10
–19
−10
–21 s/s.
Therefore, the millisecond pulsars are generally credited as the most stable clocks
in nature. The pulsar timing and navigation are studied by utilizing the very stable
periodicity of the pulsars.
Seven millisecond-pulsars, including PSR B1937+21, PSR J1713+0747, PSR
J0621+1002, PSR J0751+1807, PSR B1855+09, PSR J2033+1734 and PSR
J2322+2057, have been observed and investigated in the Arecibo Observatory since
1982, and their periodic change rates are respectively 1.051193 × 10
−19 s/s, 8.5314
× 10
−21 s/s, 4.732 × 10
−20 s/s, 7.7848 × 10
−21 s/s, 1.78354 × 10
−20 s/s, 1.1112
× 10
−20 s/s and 9.650 × 10
−21 s/s [20]. Obviously, the long-term stabilities of the
millisecond pulsars are higher than those of the current hydrogen atomic clocks in
laboratories.
Generally, the upper limits of pulsars’ ages are defined as the ratios of the pulse
periods to the periodic change rates, and also referred to as characteristic ages of
pulsars. For example, the pulse period and its rate of the Crab Pulsar are respectively
0.03372069749 s and 4.2277 × 10
−13 s/s on May 1, 2016, and thus it is easily
calculated that its characteristic age is 2529 years. In fact, the supernova explosion
of the Crab nebula was first observed and recorded by astronomers of the Song
Dynasty in China in 1054, and thereby calculating until 2016, its age should be
962 years. Apparently, there is a large discrepancy between the two ages. According
to the magnetic dipole model of pulsars, a modified formula of the characteristic age
is derived as follows.
τ =
P
(n − 1) ˙
P
,
(1.7)
where τ is the characteristic age of pulsars, P and ˙
P are respectively the pulse period
and its change rate, and n is a modified coefficient and usually is valued as 3.
Consequently, it is calculated by using formula (1.7) that the characteristic age
of the Crab Pulsar is 1264 years and close to the above result of 962 years. In
general, the periodic change rates of the ordinary pulsars with short periods are great
and correspondingly their characteristic ages small. It is also shown clearly that the
short period pulsars are younger. The pulse periods gradually increase with time, the
periodic change rates slow down, and the characteristic ages of the ordinary pulsars
will be older and older.
However, no all pulsars have stable rotation periods. The periods of some pulsars
are suddenly faster under the background of steady growth for a long time, and
then rapidly slow down until recovering the previous period-increasing-rate. The
phenomena, which the periods of pulsars suddenly jump, are usually called glitch.
For the younger pulsars, the glitches happen easily and the relative change rates of
periods are usually 10
–6
− 10
–10 . For example, the glitch of the Vela Pulsar happened
from February 24 to March 3, 1969; the relative change rate of the period got to 2
× 10
–7 and recovered to normal level after the following several weeks. Thereafter,