Binary pulsars as tools to study gravity

René Breton
University of Southampton
African Institute for Mathematical Sciences
Cape Town, 17 July 2013
Binary Pulsars as Tools to Study Gravity
© Daniel Cantin / McGill University
Friday 02 August 2013

By the End You Should Remember...
Binary pulsars
• Excellent tools to test gravity
• Probe a different gravitational field regime
• System diversity = complementarity
© Daniel Cantin / McGill University

Pulsars 101

Pulsars 101
What are pulsars?
Radio pulsars are…
• Highly magnetized rapidly spinning neutron stars:
• Radius ~ 10 km
• Mass ~ 1.4 Msun
• B-field ~ 1012 Gauss
• Pspin ~ 1ms - 10 sec
• “Lighthouse effect”: radio waves emitted along the
magnetic poles.
© Michael Kramer
JBCA, University of Manchester
© Mark A. Garlick

The Pulsar Population
The P-P diagram
Fundamental parameters:
• Spin period
• Spin period derivative
Credit: Kramer and Stairs (2008)


The Binary Pulsar Population
Binary pulsars are “special”
According to the ATNF
catalogue:
• 2008 pulsars
• 186 binary pulsars
Credit: Kramer and Stairs (2008)
Binaries:
• Short spin periods
• Old
• Low magnetic fields

φ = φ0 + ν(t − t0) +
1
2
˙ν(t − t0)2
+ . . .
Binary Pulsar Timing and Gravity
Almost textbook examples
Compact objects (point mass)
Precise timing (frequency standard)
Typical TOAs precision is ~0.1% Pspin

Binary Pulsar Dynamics
&
Relativistic Effects

Newtonian orbits
Timing binary pulsars allows one to determine 5 Keplerian parameters:
• Orbital period
• Eccentricity
• Longitude of periastron
• Projected semimajor axis
• Epoch of periastron
Arpad Horvath (Wikipedia)
We measure radial Doppler shifts only…
=> The orbital inclination angle is unknown.
Binary Pulsar Timing

Post-Keplerian (PK) parameters: dynamics beyond Newton.
• PKs are phenomenological corrections (theory-independent).
• PKs are functions of Keplerian parameters, M1 and M2.
Esposito-Farese (2004)
Relativistic orbits
More than 2 PKs = test of a given relativistic theory of gravity.

• Testing gravity relies on orbital dynamics
• Ideally: pulsar + neutron star
eccentric + compact orbit
• About 12 known “relativistic” pulsar binaries
Relativistic orbits4 Weisberg & Taylor
Figure 1. Orbital decay of PSR B1913+16. The data points indicate
the observed change in the epoch of periastron with date while the
parabola illustrates the theoretically expected change in epoch for a
system emitting gravitational radiation, according to general relativity.
PSR B1913+16
• First binary pulsar discovered
(Hulse & Taylor 1975)
• First indirect evidence of gravitational wave
emission (Taylor et al. 1979)
Weisberg & Taylor (2005)

The Double Pulsar (PSR J0737-3039A/B), is the only known pulsar-pulsar system.
Pulsar A: 23 ms (Burgay et al., 2003)
Pulsar B: 2.8 s (Lyne et al., 2004)
Eccentricity: 0.08 Orbital period: 2.4 hrs !!! (vorbital ~ 0.001 c)
© John Rowe Animation
Australia Telescope National Facility, CSIRO
The Double Pulsar
A unique system

Periastron advance
Rate of precession of the
periastron: 17°yr-1 !
It takes 21 years to complete a cycle
of precession.
The Double Pulsar
Testing gravity
Kramer et al., 2006

Gravitational redshift and time dilation
Needs to climb to potential well
Clocks tick at variable rate in
gravitational potentials
The Double Pulsar
Testing gravity
Kramer et al., 2006

Orbital period decay
Gravitational wave emission
Orbit shrinks 7mm/day (coalescence
timescale ~ 85 Myrs)
The Double Pulsar
Testing gravity
Kramer et al., 2006

Orbital period decay
Gravitational wave emission
Orbit shrinks 7mm/day (coalescence
timescale ~ 85 Myrs)
Kramer et al., 2006
Double neutron star merger as seen by a theoretician
A
B
BH
The Double Pulsar
Testing gravity

Shapiro delay
Light travels in curved space-time
The Double Pulsar
Testing gravity
Kramer et al., 2006

Shapiro delay
Light travels in curved spacetime
The Double Pulsar
Testing gravity
Kramer et al., 2006

Mass ratio
Double Pulsar only:
mass ratio, R.
MA/MB = aBsin(i) / aAsin(i)
(theory-independent; at 1PN level at least)
The Double Pulsar
Testing gravity
Kramer et al., 2006

Testing GR and gravity
Mass ratio + 5 PK parameters
=> Yields 6-2=4 gravity tests
Best binary pulsar test
Shapiro delay “s” parameter
Agrees with GR within 0.05%
(Kramer et al. 2006)
Hulse-Taylor pulsar is 0.2%
The Double Pulsar
Testing gravity
Kramer et al., 2006

Precession of the spin angular momentum of a body is expected in relativistic systems.
Parallel transport in a curve space-time changes the orientation of a vector relative to distant
observers.
Known as “geodetic precession” or “de Sitter – Fokker precession”.
Relativistic Spin Precession
Spin-orbit coupling induces relativistic spin precession

Ωobs = 0.44
+0.48(4.6)
−0.16(0.24)
◦
/yr
Changes of pulse shape and polarization over time.
PSR B1913+16 (Kramer 1998, Weisberg & Taylor 2002, Clifton &
Weisberg 2008):
• Assume the predicted GR rate to map the beam
PSR B1534+12 (Stairs et al. 2004):
•
Relativistic Spin Precession
Observational evidence of precession
GEOMETRY OF PSR B1913]16 857
FIG. 1.ÈPulse proÐle of B1913]16 observed in 1995 April
At Ðrst, we measured the amplitude ratio of the leading
and trailing components using the o†-pulse rms as an
uncertainty estimator. These are presented in Figure 2,
where we also plot data from It is seen that the newWRT.
data are in good agreement with the earlier measured trend.
Performing a weighted least-squares Ðt, we obtained a ratio
change of [1.9% ^ 0.1% per year. It is interesting to note
that our Ðt is also in agreement with the component ratio
from 1978 March which was measured using the(Fig. 2),
proÐle published by & Weisberg The ampli-Taylor (1982).
tude ratio between proÐle midpoint and trailing component
seems to remain constant at a value of about 0.17 over a
time span of 20 yr within the errors.
Measuring the separation between the leading and trail-
ing components, we followed the approach of byWRT
Ðtting Gaussian curves to the central portion of each com-
ponent. The formal accuracy determined by the Ðt error can
be up to an order of magnitude better than the sampling
time, similar to a standard template matching procedure.
We note, however, that the components are asymmetric in
shape, so that the resulting centroids might be a†ected by
FIG. 2.ÈAmplitude ratio of leading and trailing components as a func-
tion of time. Filled circles were adapted from while open circlesWRT,
represent E†elsberg measurements. The dashed line represents a linear Ðt
FIG. 3.È
Closed circ
surements p
listed in Tab
the consiste
details).
the numb
In order t
tainty, we
to intensi
respective
and their
with valu
approach
1981 proÐ
levels. W
agreemen
consisten
In wha
general re
the uncer
beam exh
with inte
The Ðrst
excellent
prediction
Wh1989).
magnetic
change, t
ΩGR = 0.51◦
/yr
Kramer 1998

Pulsar A eclipsed by pulsar B for ~30 seconds at conjunction
Rapid flux changes synchronized with pulsar B’s rotation (McLaughlin et al. 2004)
A
B
Time of arrival of
B’s pulse
Double Pulsar Eclipses
Phenomenology
Breton et al. 2008

Modeling using synchrotron absorption in a truncated dipole
The “doughnut model” (Lyutikov & Thompson 2006)

Modeling using synchrotron absorption in a truncated dipole
Breton et al. 2008

Empirical evidence of dipolar magnetic field geometry.
Eclipses are a proxy to infer the orientation of pulsar B.
It works!
Breton et al. 2008
A
B

Quantitative measurement of relativistic spin precession.
Testing General Relativity in a Strong Field
General relativity passes the test once again!
Breton et al. 2008

Pulsar B disappeared in 2009... so no more “Double Pulsar”
By the way...

Pulsar B disappeared in 2009... so no more “Double Pulsar”
By the way...
2024

Testing Theories of Gravity

“Strong-field” regime:
• Still > 250 000 RSchwarzchild in separation but…
• Ebinding ~ 15% Etot
Esposito-Farese (2004)
Strong-field regime
Why are tests of gravity involving pulsars interesting?

Generalized precession rate is (Damour & Taylor, 1992, Phys. Rev. D):
In terms of a very particular choice of observable timing parameters:
Theory-Independent Test of Gravity
Unique test... for a unique double pulsar...

Test of the strong-field parameters .
Any other mixture of timing observables would
include additional strong-field parameters.

Test of the strong-field parameters .
Any other mixture of timing observables would
include additional strong-field parameters.
The Double Pulsar is the only double neutron star system in which both semi-
major axes can be measured independently!

Mass ratio from pulsar timing + white dwarf spectroscopy
Dipolar Gravitational Waves and MOND
The pulsar-white dwarf binary PSR J1738+0333
10 Freire, Wex, Esposito-Far`ese, Verbiest et al.
mc
Pb
.
Pb
.
mc
qq
Figure 5. Constraints on system masses and orbital inclination from radio and optical measurements of PSR J1738+0333 and its WD
companion. The mass ratio q and the companion mass mc are theory-independent (indicated in black), but the constraints from the
measured intrinsic orbital decay ( ˙P Int
b , in orange) are calculated assuming that GR is the correct theory of gravity. All curves intersect,
meaning that GR passes this important test. Left: cos i–mc plane. The gray region is excluded by the condition mp > 0. Right: mp–mc
Freire et al. (2012) & Antoniadis et al. (2012)
White dwarf mass from photometry + spectroscopy
Orbital period decay from pulsar timing
Freire et al. (2012) & Antoniadis et al. (2012)

˙Pxs
b = ˙P
˙M
b + ˙PT
b + ˙PD
b + ˙P
˙G
b
˙PD
b −2π nbT⊙mc
q
q + 1
κD(spsr − scomp)2
spsr,comp /Mpsr,compc2
The “excess” orbital period decay:
Constraining dipolar gravitational waves
mass loss tides dipolar gravitational
waves
variation of
gravitational constant
where

˙Pxs
b = ˙P
˙M
b + ˙PT
b + ˙PD
b + ˙P
˙G
b
˙PD
b −2π nbT⊙mc
q
q + 1
κD(spsr − scomp)2
spsr,comp /Mpsr,compc2
The “excess” orbital period decay:
mass loss tides dipolar gravitational
waves
variation of
gravitational constant
spsr = scomp
Neutron star + white dwarf binaries
have very different self-gravity
where

˙PD
b
˙P
˙G
b
The most stringe
Figure 6. Limits on ˙G/G and κD derived from the measurements
of ˙P xs
b of PSR J1738+0333 and PSR J0437−4715. The inner blue
contour level includes 68.3% and the outer contour level 95.4%
seem particu
in the comp
system make
alternative g
the emission
5 and 6, we
classes of gra
more generic
perturbative
contribution
of the bodies
does not car
ple, the well
theory falls i
Under t
change in th
radiation dam
˙PD
b −2π n
are degenerateand
Combining data from PSRs J1738+0333 and J0437-4715 breaks the degeneracy
Freire et al. (2012) and, also, Lazaridis et al. (2009)
Lunar Laser Ranging

ln A(ϕ) − ln A(ϕ0) = α0(ϕ − ϕ0) +
1
2
β0(ϕ − ϕ0)2
˜GAB ≡ G∗A2
(ϕ0) · (1 + αAαB)
γAB ≡ 1 − 2
αAαB
1 + αAαB
βA
BC ≡ 1 +
1
2
βAαBαC
(1 + αAαB)(1 + αAαC)
˜gµν ≡ A2
(ϕ)gµν
Constraining tensor-scalar theories
Freire et al. (2012)
Associated metric
A general tensor scalar field
Modify the behavior of gravitational constant
And the Eddington’s PPN parameters
t al.
e
a-
D
t
s-
s
r-
r
×
n
)
).
r
)
t
l.
t
e
n-
n
s
a
LLR
LLR
SEP
J1141–6545
B1534+12
B1913+16
J0737–3039
J1738+0333
−6 −4 −2 2 4 6
0
0
0
0|
10
10
10
10
10
Cassini
Figure 7. Solar-system and binary pulsar 1-σ constraints on the
matter-scalar coupling constants α0 and β0. Note that a log-
arithmic scale is used for the vertical axis |α0|, i.e., that GR
(α0 = β0 = 0) is sent at an inﬁnite distance down this axis.
LLR stands for lunar laser ranging, Cassini for the measure-
ment of a Shapiro time-delay variation in the Solar System, and
GR

βA
BC ≡ 1 +
1
2
βAαBαC
(1 + αAαB)(1 + αAαC)
˜g00 = A2
(ϕ)g00 ˜gij = A−2
(ϕ)gij
˜GAB = G∗(1 + αAαB)
γAB = γPPN
= 1
Constraining modified newtonian dynamics
Freire et al. (2012)
Associated metric
MOND is the non-relativistic limit of tensor-vector-scalar (TeVeS) theories
Modify the behavior of gravitational constant
And the Eddington’s PPN parameters
GR
t al.
e
a
-
s
n
,
i
0
s
5
n
w
r
e
n
σ
s
-
-
)
V
-
h
r
,
t
LLR
SEP
J1141–6545
B1534+12
B1913+16
J0737–3039
J1738+0333
10
−6 −4 −2 0 2 4 6
0
0|
100
Tuned
TeVeS
Inconsistent
TeVeS
10
10
10
Figure 8. Similar theory plane as in Fig. 7, but now for the (non-
conformal) matter-scalar coupling described in the text, general-
izing the TeVeS model. Above the upper horizontal dashed line,
the nonlinear kinetic term of the scalar ﬁeld may be a natural
function; between the two dashed lines, this function needs to
be tuned; and below the lower dashed line, it cannot exist any
and

The pulsar-white dwarf binary PSR J1738+0333
Antoniadis et al. (2013)
Antoniadis et al. (2013)
MWD MWD
P
.
b
P
.
b qq
New system discovered that provides even better constraints.
Might rule out MOND within the next few years.

|ˆα3| 5.5 × 10−20
|∆| 4.6 × 10−3
P2
orb/e2
P2
orb/(eP) P
1/3
orb /e
Pulsar + WD in low eccentricity wide orbit
Test strong equivalence principle
Test violation of momentum conservation and preferred frame-effects
More Tests of Gravity?
SEP violation, preferred-frame effects
statistical: see, e.g., Gonzalez et al. 2011, Stairs et al. 2005
individual system: see, e.g., Wex Kramer 2007

Neutron Star Equation-of-State
Probing the upper mass limit of neutron stars
PSR B1957+20
PSR J1614-2230
Lattimer 2007
van Kerkwijk, Breton
Kulkarni (2011)
Demorest et al. (2010)

The Future Is Bright
More pulsars, more photons
More pulsars: What if we know “all” pulsars from the Galaxy?
More binaries = many new oddballs
Not clear how this translates for gravity tests
More photons:
Accurate parallax for large number of pulsars
Improved timing on existing systems

Conclusions
Eccentricity
OrbitalPeriod
PSR + NS
PSR + WD
spin-orbit coupling
dipolar GW
tensor-scalar
TeVeS/MOND
NS EoS
SEP
preferred-frame effects
(individual)
preferred-frame effects
(statistical)
variation of G
consistencies of theories
relativistic effects
Binary pulsars
• Excellent tools to test gravity
• Probe a different gravitational field regime
• System diversity = complementarity
PSR + BD*

Binary pulsars as tools to study gravity

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