2 General Relativity Measurements from Pulsars
81
as well, for example looking at the possible “polarization” of NS–WD binaries in
the gravitational field of the Galaxy. While the orbital parameters of single NS–
WD binaries are usually not fully known, this test can instead be performed using
a statistical approach with a number of binaries. The best constraint so far of
the Nordtvedt effect was done using 21 NS–WD binaries [80], leading to a 95%
confidence upper limit of 5.6 × 10 −3 on Δ = (M gr /M in ) NS − (M gr /M in ) WD ,
where (M gr /M in ) i is the ratio between gravitational and inertial mass of the i-th
body. A more recent constraint of Δ < 4.6 × 10 −3 was placed using a sample of 27
binaries [81].
This is not the only way to test the SEP; other tests can be done to constrain various PPN parameters (a good summary of the PPN formalism can be found in [82]).
For example, a non-zero α 3 implies the existence of a preferred frame and nonconservation of momentum. An upper limit on ˆ
α 3 (the strong-field generalization of
the original PPN parameter α 3 ) is 4 × 10 −20 at the 95% confidence limit, and was
achieved using an ensemble of NS–WD binaries [80]. This constraint is especially
interesting since it is much more constraining (by 13 orders of magnitude!) than
solar system tests using the Earth and Mercury. The timing analysis of the NS–
WD binary PSR J1738+0333, coupled with the analysis of pulse profile stability
from the isolated pulsars B1937+21 and J1744-1134, has led to constraints on
the parameters ˆ
α 1 and ˆ
α 2 , which involve a violation of the Lorentz invariance:
ˆ
α 1 < (−0.4
+3.7
−3.1 ) × 10 −5 and ˆ
α 2 < 1.6 × 10 −9 , both at the 95% confidence limit
[60, 83–85]. Additionally, pulse profile stability from B1937+21 and J1744-1134
has also enabled the constraints on the parameter ˆ
ξ < 3.9 × 10 −9 (95 % CL). The
constraints on ˆ
α 1 , ˆ
α 2 , ˆ
α 3 and ˆ
ξ are all better than those achieved with solar system
tests.
Other tests however are less constraining than in the solar system. For example,
the parameter ˆ
ζ 2 , which represents non-conservation of momentum, has an upper
limit of 4 × 10 −5 using PSR B1913+16 [85]. The presence of preferred positions
and times in the universe can also lead to variations in fundamental constants such as
the gravitational constant G. The best constraint on variations of G is from a recent
timing study of the fast and extremely precise millisecond pulsar J1713+0747:
| ˙
G/G| < (−0.6 ± 1.1) × 10 −12 yr −1 at the 95% confidence limit [86].
The recent discovery of the triple system PSR J0337+1715 consisting of a white
dwarf orbiting an inner NS–WD pair [87], will lead to significant improvements
in our constraints on the SEP. The masses of all three bodies have been precisely
determined, as well as the inclination of the orbits. The gravitational field of the
outer white dwarf is larger than the Galaxy’s gravitational field by approximately
six orders of magnitude; therefore by studying the accelerations of the two inner
compact objects in the gravitational field of the outer white dwarf, we can improve
the constraint on the aforementioned parameter Δ by several orders of magnitude.
This is therefore the best system known to date for constraining the SEP.
81
as well, for example looking at the possible “polarization” of NS–WD binaries in
the gravitational field of the Galaxy. While the orbital parameters of single NS–
WD binaries are usually not fully known, this test can instead be performed using
a statistical approach with a number of binaries. The best constraint so far of
the Nordtvedt effect was done using 21 NS–WD binaries [80], leading to a 95%
confidence upper limit of 5.6 × 10 −3 on Δ = (M gr /M in ) NS − (M gr /M in ) WD ,
where (M gr /M in ) i is the ratio between gravitational and inertial mass of the i-th
body. A more recent constraint of Δ < 4.6 × 10 −3 was placed using a sample of 27
binaries [81].
This is not the only way to test the SEP; other tests can be done to constrain various PPN parameters (a good summary of the PPN formalism can be found in [82]).
For example, a non-zero α 3 implies the existence of a preferred frame and nonconservation of momentum. An upper limit on ˆ
α 3 (the strong-field generalization of
the original PPN parameter α 3 ) is 4 × 10 −20 at the 95% confidence limit, and was
achieved using an ensemble of NS–WD binaries [80]. This constraint is especially
interesting since it is much more constraining (by 13 orders of magnitude!) than
solar system tests using the Earth and Mercury. The timing analysis of the NS–
WD binary PSR J1738+0333, coupled with the analysis of pulse profile stability
from the isolated pulsars B1937+21 and J1744-1134, has led to constraints on
the parameters ˆ
α 1 and ˆ
α 2 , which involve a violation of the Lorentz invariance:
ˆ
α 1 < (−0.4
+3.7
−3.1 ) × 10 −5 and ˆ
α 2 < 1.6 × 10 −9 , both at the 95% confidence limit
[60, 83–85]. Additionally, pulse profile stability from B1937+21 and J1744-1134
has also enabled the constraints on the parameter ˆ
ξ < 3.9 × 10 −9 (95 % CL). The
constraints on ˆ
α 1 , ˆ
α 2 , ˆ
α 3 and ˆ
ξ are all better than those achieved with solar system
tests.
Other tests however are less constraining than in the solar system. For example,
the parameter ˆ
ζ 2 , which represents non-conservation of momentum, has an upper
limit of 4 × 10 −5 using PSR B1913+16 [85]. The presence of preferred positions
and times in the universe can also lead to variations in fundamental constants such as
the gravitational constant G. The best constraint on variations of G is from a recent
timing study of the fast and extremely precise millisecond pulsar J1713+0747:
| ˙
G/G| < (−0.6 ± 1.1) × 10 −12 yr −1 at the 95% confidence limit [86].
The recent discovery of the triple system PSR J0337+1715 consisting of a white
dwarf orbiting an inner NS–WD pair [87], will lead to significant improvements
in our constraints on the SEP. The masses of all three bodies have been precisely
determined, as well as the inclination of the orbits. The gravitational field of the
outer white dwarf is larger than the Galaxy’s gravitational field by approximately
six orders of magnitude; therefore by studying the accelerations of the two inner
compact objects in the gravitational field of the outer white dwarf, we can improve
the constraint on the aforementioned parameter Δ by several orders of magnitude.
This is therefore the best system known to date for constraining the SEP.