2 General Relativity Measurements from Pulsars
83
to emission of gravitational radiation. r and s ≡ sin i correspond to the rate and
the shape of the Shapiro delay [70], which is caused by the spacetime deformations
around the companion.
There are no extra parameters in these equations: the PK parameters only depend
on the two masses in general relativity. However in alternative theories, extra theorydependent parameters will appear in the definitions of the PK parameters (see [73,
75] for a few examples).
2.5.2.1 Double Neutron Star Binaries
Tests using PK parameters were applied for the first time to the so-called HulseTaylor pulsar, i.e. the binary system B1913+16, which was the first discovered
double neutron star (DNS) binary [92]. One of the two neutron stars is a pulsar with a
59-ms period; the orbit is highly eccentric (e = 0.61) with an orbital period of 7.8 h.
Observing this system over a number of years has allowed the precise determination
of three PK parameters: ˙
ω, γ and ˙
P int
b (the observed, intrinsic value for the orbital
decay). While the first two PK parameters ( ˙
ω and γ ) allowed the determination
of two neutron star masses [93], having a third PK parameter allows us to check
the validity of general relativity. In particular, inserting the two determined masses
into Eq. (2.16), we obtain a precise determination for ˙
P GR
b , which is the expected
value for the orbital decay according to general relativity. One can thus compare
˙
P int
b obtained from observations with ˙
P GR
b . After more than 30 years of observing
this binary pulsar, the agreement with general relativity is now at the 0.2% level
[93]. This spectacular result provided the first indirect evidence for the emission
of gravitational waves from any astrophysical system (see Fig. 2.12). It also showed
that the internal structure of the neutron stars did not affect the dynamics and energy
loss of the DNS binary system, lending more credence to the effacement of the
neutron star interiors and therefore the Strong Equivalence Principle of general
relativity [94].
We note that the intrinsic rate of orbital decay, while primarily determined from
the fitting of observed TOAs to the pulsar model, has to be corrected for a number
of factors, including vertical acceleration and differential rotation in the Galactic
potential. As far as B1913+16 is concerned, our current limited knowledge of
the shape of the Galactic potential is the largest limiting factor in improving the
accuracy of general relativity tests [95–97].
As mentioned earlier, a minimum of 3 PK parameters is necessary for providing
a test of relativistic gravity (the first 2 PK parameters help determine the 2
masses). Besides PSR B1913+16 for which 3 PK parameters were determined,
PSR B1534+12 is a 38-ms pulsar in a relativistic, DNS binary [98] for which 5 PK
parameters have been determined. Its longer orbital period and smaller eccentricity
make it less relativistic than the Hulse-Taylor pulsar, but it has a higher orbital
inclination, a stronger flux density and a narrower pulse width. An even more
interesting, relativistic system for which 5 PK parameters have been determined is
the so-called Double Pulsar PSR J0737-3039. This is the subject of the next section.
83
to emission of gravitational radiation. r and s ≡ sin i correspond to the rate and
the shape of the Shapiro delay [70], which is caused by the spacetime deformations
around the companion.
There are no extra parameters in these equations: the PK parameters only depend
on the two masses in general relativity. However in alternative theories, extra theorydependent parameters will appear in the definitions of the PK parameters (see [73,
75] for a few examples).
2.5.2.1 Double Neutron Star Binaries
Tests using PK parameters were applied for the first time to the so-called HulseTaylor pulsar, i.e. the binary system B1913+16, which was the first discovered
double neutron star (DNS) binary [92]. One of the two neutron stars is a pulsar with a
59-ms period; the orbit is highly eccentric (e = 0.61) with an orbital period of 7.8 h.
Observing this system over a number of years has allowed the precise determination
of three PK parameters: ˙
ω, γ and ˙
P int
b (the observed, intrinsic value for the orbital
decay). While the first two PK parameters ( ˙
ω and γ ) allowed the determination
of two neutron star masses [93], having a third PK parameter allows us to check
the validity of general relativity. In particular, inserting the two determined masses
into Eq. (2.16), we obtain a precise determination for ˙
P GR
b , which is the expected
value for the orbital decay according to general relativity. One can thus compare
˙
P int
b obtained from observations with ˙
P GR
b . After more than 30 years of observing
this binary pulsar, the agreement with general relativity is now at the 0.2% level
[93]. This spectacular result provided the first indirect evidence for the emission
of gravitational waves from any astrophysical system (see Fig. 2.12). It also showed
that the internal structure of the neutron stars did not affect the dynamics and energy
loss of the DNS binary system, lending more credence to the effacement of the
neutron star interiors and therefore the Strong Equivalence Principle of general
relativity [94].
We note that the intrinsic rate of orbital decay, while primarily determined from
the fitting of observed TOAs to the pulsar model, has to be corrected for a number
of factors, including vertical acceleration and differential rotation in the Galactic
potential. As far as B1913+16 is concerned, our current limited knowledge of
the shape of the Galactic potential is the largest limiting factor in improving the
accuracy of general relativity tests [95–97].
As mentioned earlier, a minimum of 3 PK parameters is necessary for providing
a test of relativistic gravity (the first 2 PK parameters help determine the 2
masses). Besides PSR B1913+16 for which 3 PK parameters were determined,
PSR B1534+12 is a 38-ms pulsar in a relativistic, DNS binary [98] for which 5 PK
parameters have been determined. Its longer orbital period and smaller eccentricity
make it less relativistic than the Hulse-Taylor pulsar, but it has a higher orbital
inclination, a stronger flux density and a narrower pulse width. An even more
interesting, relativistic system for which 5 PK parameters have been determined is
the so-called Double Pulsar PSR J0737-3039. This is the subject of the next section.