58
M. Burgay et al.
recover the pulsed signal over the whole band, obtaining a high signal-to-noise ratio
(S/N) pulse profile (Fig. 2.3, right panel).
After the discovery of a new pulsar, in order to fully exploit its potential
as an astrophysical laboratory, it is necessary to start a follow-up campaign of
observations to precisely measure its spin, astrometric and, in the case of a binary
system, orbital parameters (see Sect. 2.4). One of the basic parameters is the first
derivative of the spin period: ˙
P . This is a crucial parameter because, assuming, as the
standard electrodynamics model [16] states, 1 that the emission is due to a spinning
magneto-dipole losing rotational energy (see Eq. (2.2)), its value is directly related
to the dipolar surface magnetic field B s and the age (or an estimate of the age)
of the pulsar. The equation describing the dipole spin-down emission, obtained by
equalling the rotational energy loss to the dipole radiation power, can be written as:
− I NS ω ˙
ω =
2
3
1
c 3 ω
4 B
2
s R
6
NS sin
2 α
(2.2)
where I NS is the moment of inertia of the NS, ω = 2π/P its angular velocity, R NS
its radius and α the angle between the magnetic and the rotational axes. Rewriting
Eq. (2.2) as a function of the spin period and its derivative and using α = 90 ◦ ,
I NS = 10 45 g cm 2 and R NS = 10 6 cm, we can derive an estimate of the magnetic
field as:
B s = 3.2 × 10
19
P ˙
P
G
(2.3)
and, integrating in time, we can derive the so-called spin-down age of the pulsar as:
τ c =
P
2 ˙
P
1 −
P 2
0
P 2
∼
P
2 ˙
P
(2.4)
where P 0 is the spin period of the pulsar at birth (assumed to be negligible with
respect to the current one).
The measurement of ˙
P and all of the other parameters (e.g. position, proper
motion, Keplerian and post-Keplerian parameters) is done through the timing
technique that is fully described in Sect. 2.4.
According to the ATNF pulsar catalogue PSRcat (www.atnf.csiro.au/research/
pulsar/psrcat/ [1]), as of the end of 2017, more than 2600 pulsars have been
discovered (and published, see Fig. 2.4) in our Galaxy, including Galactic globular
clusters and in the Magellanic Clouds. The sub-set of millisecond, or recycled,
1 This is a very crude model not suitable for explaining the nature of the processes involved in
the broad band radio emission from the pulsars. However, barring the detailed physics, the energy
budget resulting from this model and the related Eqs. (2.2), (2.3), (2.4), are used as a reference for
classification of the rotational powered NSs and for comparison with more advanced and physically
sound modelling.
M. Burgay et al.
recover the pulsed signal over the whole band, obtaining a high signal-to-noise ratio
(S/N) pulse profile (Fig. 2.3, right panel).
After the discovery of a new pulsar, in order to fully exploit its potential
as an astrophysical laboratory, it is necessary to start a follow-up campaign of
observations to precisely measure its spin, astrometric and, in the case of a binary
system, orbital parameters (see Sect. 2.4). One of the basic parameters is the first
derivative of the spin period: ˙
P . This is a crucial parameter because, assuming, as the
standard electrodynamics model [16] states, 1 that the emission is due to a spinning
magneto-dipole losing rotational energy (see Eq. (2.2)), its value is directly related
to the dipolar surface magnetic field B s and the age (or an estimate of the age)
of the pulsar. The equation describing the dipole spin-down emission, obtained by
equalling the rotational energy loss to the dipole radiation power, can be written as:
− I NS ω ˙
ω =
2
3
1
c 3 ω
4 B
2
s R
6
NS sin
2 α
(2.2)
where I NS is the moment of inertia of the NS, ω = 2π/P its angular velocity, R NS
its radius and α the angle between the magnetic and the rotational axes. Rewriting
Eq. (2.2) as a function of the spin period and its derivative and using α = 90 ◦ ,
I NS = 10 45 g cm 2 and R NS = 10 6 cm, we can derive an estimate of the magnetic
field as:
B s = 3.2 × 10
19
P ˙
P
G
(2.3)
and, integrating in time, we can derive the so-called spin-down age of the pulsar as:
τ c =
P
2 ˙
P
1 −
P 2
0
P 2
∼
P
2 ˙
P
(2.4)
where P 0 is the spin period of the pulsar at birth (assumed to be negligible with
respect to the current one).
The measurement of ˙
P and all of the other parameters (e.g. position, proper
motion, Keplerian and post-Keplerian parameters) is done through the timing
technique that is fully described in Sect. 2.4.
According to the ATNF pulsar catalogue PSRcat (www.atnf.csiro.au/research/
pulsar/psrcat/ [1]), as of the end of 2017, more than 2600 pulsars have been
discovered (and published, see Fig. 2.4) in our Galaxy, including Galactic globular
clusters and in the Magellanic Clouds. The sub-set of millisecond, or recycled,
1 This is a very crude model not suitable for explaining the nature of the processes involved in
the broad band radio emission from the pulsars. However, barring the detailed physics, the energy
budget resulting from this model and the related Eqs. (2.2), (2.3), (2.4), are used as a reference for
classification of the rotational powered NSs and for comparison with more advanced and physically
sound modelling.