Best Limits Ever on Dipolar Gravitational Wave Emission
PSR J1738+0333 is a 5.85-ms pulsar in a binary system with an orbital
period of 8.5 hours and a companion white dwarf (WD) with a mass of
about 0.2 solar masses. This millisecond pulsar (MSP) was found with
the Parkes 64-m Radio Telescope in a 20-cm Multi-Beam search for
pulsars in intermediate Galactic latitudes ( 15° < | b | < 30°),
lead by Bryan Jacoby (then at Caltech) and Matthew Bailes (Swinburne
University).
Paulo Freire has been timing this pulsar with the Arecibo
305-m telescope for the last
3 years (project P1684) using the Wide-band Arecibo Pulsar Processors
(WAPPs). He has obtained good timing
precision, in fact this is now one of the most precisely timed pulsars
ever, the 1-hour averages of the timing residuals have a root mean
square of 200 ns per WAPP per hour. There is a small apparent
eccentricity of about 0.0000011, which indicates that the orbit, even
with a semi-major axis of 102,000 km / sin i, does not deviate from
a circle by
more than 80 µm / sin i! (and, yes, this number is correct).
However, there seem to be small dispersive delays near superior
conjunction. Taking these into account, we get an eccentricity that is
less than 0.0000005. That would imply that the orbit does not deviate
from a circle by more than 14 µm / sin i.
In a few double neutron star (DNS) systems, like PSR B1913+16 (the original
Hulse-Taylor binary pulsar), PSR B1534+12 (see related highlight), PSR J0737−3039 (the double
pulsar) and more recently PSR J1906+0746 (see related highlight), the
observation of several relativistic effects in the timing of the
neutron star (NS) observable as a pulsar (normally the object that has
been recycled, but not always) has allowed precise estimates of the
mass of the pulsar and of its NS companion. These effects, the precession
of periastron and the varying relativistic time delay at different
orbital phases (Einstein delay), can only be measured for pulsars with
eccentric orbits, that is always the case among DNSs.
Knowing the component masses,
we can predict, assuming the validity of general relativity (GR), a few
other relativistic effects, like the Shapiro delay or the rate of
orbital decay due to the emission of gravitational waves. We can test
GR if we are able to measure the latter parameters and
check if their numerical values are as predicted.
While the recycled pulsars in DNS systems spin tens of times per
second, MSPs like PSR J1738+0333 spin hundreds of times per second. They had much longer
accretion episodes, which means that their companions were much longer
lived stars of relatively low masses. These MSPs are normally found in
circular orbits with WD stars. Because of these
circular orbits, we can't measure the rate of advance of periastron nor
the Einstein delay. This makes it difficult to measure the masses of
these objects, and almost impossible to use them to test GR. This is a
pity for many reasons:
MSPs have very high timing precision, so the aforementioned
relativistic effects could be measured with extreme precision if such
pulsars were in eccentric orbits.
MSPs have accreted matter from their companions for
a very long time, so they could be substantially more massive than the
NSs found in DNS binaries. Finding how massive a
neutron star can be is important for determining how matter behaves at
very high densities, an yet unsolved problem.
Theoretically MSP-WD systems could be the best
probes for testing alternative theories of gravitation. The reason for this is the following: all
alternative theories of gravitation (but not GR), predict violation of the
Strong Equivalence Principle (SEP). The observables consequences of SEP
violation are generally proportional to the difference of
gravitational binding energies of the two components of the
binary, or a theory-specific function of them.
Therefore, DNSs that pass very precise GR tests (for the latest and
best example, see Kramer et al. 2006)
do not necessarily lead to tight constraints on SEP violation and
alternative theories of gravitation: the binding energies of the
neutron stars could be very similar, causing SEP violation to go
undetected. In a MSP-WD binary, on the other hand, the binding energy
of the WD is negligible compared to that of the MSP, so if SEP is
violated, there will be observable consequences. These would be:
If the orbital period is long, SEP violation would
cause a secular increase in the eccentricity of the orbit. This would
be due to the fact that the two components would be accelerating at
slightly different rates in the gravitational field of the Galaxy. The
Arecibo observation of several pulsar-WD systems in wide orbits and
low eccentricities has
lead to tighter limits on SEP violation (Stairs
et al. 2005).
If the orbital period is short, SEP violation could in
principle lead to observable emission of dipolar gravitational waves.
This would appear as a contribution to the orbital decay of the
system in addition to that caused by the emission of quadrupolar
gravitational waves predicted by general relativity.
Unfortunately, for most MSP-WD systems, the masses of both components
are not known, therefore we can't calculate the quadrupolar emission
predicted by GR and compare it with the observational values.
Initial timing of PSR J1738+0333 sought to determine the companion and
pulsar masses from a measurement of the Shapiro delay - this small
propagational effect allows an estimate of the pulsar and
companion masses even in the absence of any eccentricity. Generally,
high timing precision is required for a measurement, but having an
inclination close to 90° also makes the effect much easier to measure. For
1738+0333 this measurement was not possible because of the low orbital
inclination of the system. This binary system might therefore be
completely useless.
Fortunately, it was possible to determine
the masses of the components independently. This comes from recent
optical work of Marten van Kerkwijk and Bryan Jacoby. Using the
Magellan telescope on Las Campanas, Chile, they detected the companion
star and measured its spectrum accurately (see Fig. 1).
Figure 1: Spectrum of the white dwarf companion of PSR
J1738+0333. Note the sharp absorption features, these were used to
measure accurate radial velocities for this object. Image provided by
M. van Kerkwijk.
The spectrum is very similar to that of the companion of PSR
J1909−3744; which has as mass of 0.203 solar masses, measured by
Shapiro delay (Jacoby et al. 2005). The companion of
PSR J1738+0333 must therefore a very similar mass.
More recently, the radial-velocity curve was measured using Gemini
South on Cerro Pachón (see Fig. 2), from this we can derive the mass
ratio of the system, 8.1 ± 0.3. The pulsar mass is therefore about
1.6 ± 0.2 solar masses (we have assumed here a 10% uncertainty in the
mass of the companion, this still needs to be estimated more
precisely). This is an interesting value per se, if measured more
precisely it could exclude some models for the behavior of matter at
densities higher than that of the atomic nucleus. This was the
original motivation for the timing of 1738+0333.
Figure 2: Radial velocity measurements for the companion of PSR
J1738+0333 as a function of orbital phase, with best fit in blue. The
red curve represents the variation of the pulsar's orbital velocity
along the line of sight. For this binary pulsar, we have now
information on the absolute radial velocity of the center of mass,
something that is not normally available for binary pulsars. Image
provided by M. van Kerkwijk.
This is also important because it allows a calculation of the expected
rate of orbital decay due to the emission of quadrupolar gravitational
waves: −(3.4 ± 0.6) × 10−14s/s. This period
derivative is about 60 times smaller than what was measured for the
Hulse-Taylor binary pulsar; the 8.5-hour orbital period should become
approximately 1 microsecond shorter every year!
Fortunately, the timing precision for PSR J1738+0333 is so high that
we can already measure this value after only three years of timing,
although not with much significance: it is −(4.4 ±
2.9) × 10−14s/s.
What is more important is the difference between predicted and
observed values is the smallest ever measured. This introduces the
tightest constraints ever on dipolar gravitational wave emission. If
we interpret the limit on the emission of gravitational waves as a
constant "omega" in Brans-Dicke gravity, we obtain ω > 2300
(s/0.2)2 (a), the
previous pulsar limit is ω > 1300 (s/0.2)2, derived from Arecibo timing of PSR J0751+1807 (Nice
et al. 2005, see related
highlight). For GR, this
value is infinite. This is not as good as the result from the Cassini
spacecraft (ω > 40,000, Bertotti
et al. 2003), but it is obtained in the strong-field regime, the
only that can constrain all alternative theories of gravitation.
This, however, is not the main result. For 1738+0333, there is great
potential for further improvement in the test, given that the
component masses in this case are relatively well known from the
optical studies. Continued timing of PSR J1738+0333 over the next
5(10) years will increase the precision of our measurement of the
orbital period derivative by a factor of 10(40). By then, if we assume
that the measured value conforms to the prediction, the uncertainty of
the prediction itself (6 × 10−15 s/s) will be the
limiting factor in the precision of this test. This will be equivalent
to ω > 15,000 (s/0.2)2, an order of
magnitude improvement on all previous pulsar tests. If the optical
measurements can be improved, this limit could be substantially larger.
One of the advantages of the high timing precision of PSR J1738+0333
has been a precise measurement of the proper motion (6.814 ± 0.017
mas/yr in RA and 4.90 ± 0.06 mas/yr in Dec) and the parallax (1.43
± 0.10 mas). This allows a very precise correction of the kinetic
contribution to the orbital period derivative.
Furthermore, improving the mass ratio (definitely possible by averaging more
measurements) and using a precise measurement of the orbital decay
will be used to determine the mass of the pulsar and the companion
very accurately, assuming that general relativity applies. These
values might be important for the study of the equation of state for
dense matter. PSR J1738+0333 might therefore be a great physics
laboratory, relevant for the study of gravitation and the study of the
equation of state.
Figure 3: Mass constraints for the PSR J1738+0333 binary
system. The system has to be in the intersection of the companion
mass (m2) and mass ratio (R) regions. The dashed lines indicate
1-sigma limits for the measurement of the orbital decay. The solid
lines indicate constant orbital inclinations, we can see that the
orbital inclination of this binary system is slightly larger than 30
degrees. The gray bar indicates the range of precisely measured
neutron star masses.
(a) In Brans-Dicke theory, the variable "s" is the
change of the binding energy of the neutron star as a function of the
gravitational constant G, a parameter that is not fixed for that
theory. The numerical value of s depends on the equation
of state, it is predicted to range from 0.1 to 0.3.