Measurements of binary pulsar masses and a study
on the nature of gravitational waves
Paulo C. C. Freire
Max-Planck-Institut für Radioastronomie
Bonn, Germany

2017 January 18, “Neutron Star Mergers: From Gravitational Waves to Nucleosynthesis”, Hirschegg, Austria

What are pulsars?
Neutron stars are the remnants of extremely
massive stars. Towards the end of their lives
they explode as Supernovae:•

The result is a sphere of neutrons, withdensities of several hundred million tons per
cubic cm – significantly higher than at theatomic nucleus!

•

R ~ 10-13 km•

Gravitational binding energy: about −40 000
Earth masses!

•

Some neutron stars emit radio waves
anisotropically. Their rotation then makes
them appear to pulse, like a lighthouse – apulsar!

Pulsar timing for binary pulsars

Figure: Scott Ransom•

In a binary pulsar, having a clock in thesystem allows us to measure the range
relative to the center of mass of the binary.

•

The 5 Keplerian orbital parameters derived
from pulsar timing are thousands of times
more precise than derived from Doppler
measurements – with the sameobservational data!

•

This feature is unique to pulsars, and is thefundamental reason why they are superior
astrophysical tools.

•

This is the reason why I am giving this talk
here!

•

Plus: IT’S A CLEAN EXPERIMENT!

The P-Pdot diagram and binary pulsars•

The spin period and the period
derivative tell us a lot about the pulsar– its age, magnetic field, spin-downenergy, etc.

•

Many interesting trends appear in theP- Pdot diagram:oLike the Crab, youngest pulsars
tend to be associated with SNo

The fastest pulsars are not the
youngest, but the oldest,o

Most of these are in binary
systems, where they have been
recycled.

How to recycle a pulsar
Figure from: Lorimer, D., Living Rev. Relativity 11 (2008), 8

Eccentric orbits

Circular orbits

The first binary pulsar
In 1974 Joe Taylor’s student Russel Hulse discovered PSR B1913+16, a 59-ms pulsar in theconstellation Aquila (the Eagle). First binary pulsar!

From: Hulse & Taylor, 1975, ApJ, 195, 51

PSR B1913+16

The Sun4 light seconds
Double neutron star system: PSR B1913+13(1.2 million km)

PSR B1913+16
For most binary pulsars, all we have are
the Keplerian parameters and all we canderive is the mass function:

One equation, three (known) unknowns!
LPSR B1913+16•

IF a binary pulsar is compact andeccentric – which B1913+16 certainlyis – the timing precision allows themeasurement of several relativistic
eﬀects:o The advance of periastron.
o The Einstein delay.

PSR B1913+16•

Assuming GR, 1 PN:

PSR B1913+16•

Assuming GR, 1 PN:•

3 equations for 3 unknowns!
Precise masses can be derived.

•

This was at the time the mostprecise measurement of any mass
outside the solar system.

PSR B1913+16•

A third relativistic eﬀect soon
became measurable – the orbital
decay due to GW emission!

•

Assuming GR, LO PN [(v/c)5]:•

Prediction: the orbital period
should decrease at a rate of –2.40247 × 10−12 s/s (or 75 µs per
year!)•

Eﬀect not detectable in Solar
System.

PSR B1913+16•

Rate is –2.4085(52) x 10–12 s/s.
Agreement with GR is perfect!

•

GR gives a self-consistent estimateof the component masses!

PSR B1913+16
Gravitational waves exist!

Weisberg, J.M., and Taylor, J.H., “The Relativistic Binary Pulsar B1913+16”, inBailes, M., Nice, D.J., and Thorsett, S.E., eds., Radio Pulsars: In Celebration of theContributions of Andrew Lyne, Dick Manchester and Joe Taylor – A Festschrift
Honoring their 60th Birthdays, Proceedings of a Meeting held at Mediterranean
Agronomic Institute of Chania, Crete, Greece, 26 – 29 August 2002, ASP
Conference Proceedings, vol. 302, (Astronomical Society of the Pacific, San
Francisco, 2003).

Gravitational Waves Exist!
``(…) the observation of the orbital decay in the TOAs of a binary pulsar is a direct eﬀect of theretarded propagation (at the speed of light, and with a quadrupolar structure) of the gravitational
interaction between the companion and the pulsar. In that sense, the Hulse-Taylor pulsar provides
a direct observational proof that gravity propagates at the speed of light, and has a quadrupolarstructure.’’Damour, 2014, arXiv:1411.3930v1. He adds:``The latter point is confirmed by the theoretical computation of the orbital decay in alternative
theories of gravity where the non purely quadrupolar (i.e. non purely spin 2) structure of thegravitational interaction generically induces drastic changes (….)”

The ``Double Pulsar’’: PSR J0737−3039
Discovered in the Galactic anti-center survey with
Parkes (Burgay et al. 2003, Nature, 426, 531)

DNS J0737−3039
Lucky bit #1: Orbital period of
2h 27m, it is (was) the mostrelativistic double neutron starsystem known!

B1913+16

The Sun

J0737−3039

4 light seconds

Table 2. Four independent tests of GR provided by the double pulsar. Observed PK parameters
were obtained by fitting a DDS timing model to the data. Values expected from GR take into
account the masses determined from the intersection point of the mass ratio R and the periastronadvance ẇ
w. Uncertainties refer to the last significant digits and were determined using Monte Carlo
methods.
PK parameterPṖbg (ms)sr (ms)

Observed value

Expected value from GR

Ratio of observed
to expected value

1.252(17)0.3856(26)0.99974(j39,þ16)
6.21(33)

1.24787(13)0.38418(22)0.99987(j48,þ13)
6.153(26)1.003(14)1.0036(68)0.99987(50)1.009(55)

DNS J0737−3039
A

From: Kramer et al. 2006

Residual (µs)

100

50

0

Residual (µs)

100

B

50

0
0

60

120

180
240
Longitude (deg)

300

360

Fig. 2. Measurement of a Shapiro delay demonstrating the curvature of space-time. Timing residuals(differences between observed and predicted pulse arrival times) are plotted as a function of orbital
longitude and illustrate the Shapiro delay for PSR J0737-3039A. (A) Observed timing residuals after a
fit of all model parameters given in Table 1 except the Shapiro-delay terms r and s, which were set tozero and are not included in the fit. Although a portion of the delay is absorbed in an adjustment of the
Keplerian parameters, a strong peak at 90- orbital longitude remains clearly visible. This is the orbital
phase of A’s superior conjunction (i.e., when it is positioned behind B as viewed from Earth), so that its
pulses experience a delay when moving through the curved space-time near B. The clear detection of
structure in the residuals over the whole orbit confirms the detection of the Shapiro delay, which isisolated in (B) by holding all parameters to their best-fit values given in Table 1, except the Shapiro
delay terms (which were set to zero). The red line shows the predicted delay at the center of the data
span. In both cases, residuals were averaged in 1- bins of longitude.

100

6 OCTOBER 2006

VOL 314SCIENCEIn estimating the final uncertainty of xB andhence of R, we have considered that geodetic
precession will lead to changes to the systemgeometry and hence changes to the aberration of
the rotating pulsar beam. The effects of aberration on pulsar timing are usually not separately
measurable but are absorbed into a redefinitionof the Keplerian parameters. As a result, the observed projected sizes of the semimajor axes,
xobsA,B , differ from the intrinsic sizes, xintA,B, bya factor (1 þ e AA,B ). The quantity eA depends
for each pulsar A and B on the orbital period, thespin frequency, the orientation of the pulsar spin,
and the system geometry (12). Although aberration should eventually become detectable in thetiming, allowing the determination of a further
PK parameter, at present it leads to an undetermined deviation of xobs from xint, where the latteris the relevant quantity for the mass ratio. The
parameter eAA,B scales with pulse period and istherefore expected to be two orders of magnitude
smaller for A than for B. However, because of
the high precision of the A timing parameters,
the derived value x obsA may already be significantly affected by aberration. This has (as yet) no
consequences for the mass ratio R 0 x obsB/x obsA,
as the uncertainty in R is dominated by the muchless precise x obsB. We can explore the likely
aberration corrections to x obsB for various possible geometries. Using a range of values given
by studies of the double pulsar’s emission
properties (24), we estimate eAA È 10j6 andeAB È 10j4. The contribution of aberration
therefore is at least one order of magnitude
smaller than our current timing precision. In the
future this effect may become important, possibly limiting the usefulness of R for tests of
GR. If the geometry cannot be independently
determined, we could use the observed deviations of R from the value expected within GR
to determine eAB and hence the geometry of B.
Space motion and inclination of the orbit.
Because the measured uncertainty in Ṗb decreases approximately as T j2.5, where T is thedata span, we expect to improve our test of theradiative aspect of the system to the 0.1% levelor better in about 5 years’ time. For the PSR
B1913þ16 and PSR B1534þ12 systems, theprecision of the GR test based on the orbit-

Lucky bit #2: this super-relativistic system
has a very high inclination. Shapiro delay iswell measured, providing two extra massconstraints!

www.sciencemag.org

DNS J0737−3039•

Lucky bit #3: The second NS in the system (PSR J0737−3039B) is detectable as a radio
pulsar!

R = mA / mB = xB / xA
6 mass constraints for 2 unknowns! 4 independent tests of GR!

DNS J0737−3039•

GR passes all 4 tests with flying
colors!

•There is a fifth test, fromgeodetic precession of PSR
J0737−3039B (Breton et al.
2008, Science).

Kramer et al. 2006, Science, 314, 97

DNS J0737−3039
Figure: Kramer et al., in prep.

DNS J0737−3039
0.5

Figure: Kramer et al., in prep.

0.0
-0.5

Periastron shift (s)

-1.0
-1.5
-2.0
-2.5
-3.0
-3.5
-4.0
-4.5

Newtonian Gravity
Prediction of GR for gravitational quadrupole emission-5.0
2004 2005 2006 2007 2008 2009 2010

Year

2011 2012 2013

How do pulsars compare to LIGO? I. Double
PulsarPulsar tests are complementary
to LIGO constraints!
Figure: LSC/Virgo 2016, Kramer et al. in prep.

GW150914 (v~0.4c)
GW151226 (v~0.4c)
combined
Double Pulsar (v~0.002c)(v2/c2 corrections)
Quadrupole formulaNS mass measurements. 1 - DNSs•

In GR, only the masses enter as a parameters in the description of these eﬀects to leading
PN order (Moments of inertia need higher than LO)•

It is very nice to have systems like the double pulsar to test GR / to cross-check the massmeasurement techniques – the diﬀerent combinations of PK parameters really produce very
precise (and very consistent) results.

•

But… what masses have been measured?

NS mass measurements. 1 - DNSs

An asymmetric DNS!

PSR J0453+1559 was discovered in the AO 327 MHz survey (Deneva et al. 2013, ApJ,
775, 51). It is the first asymmetric DNS! Mp = 1.559(5) M⦿, Mc = 1.174(4) M⦿, seeMartinez, Stovall, Freire et al., (2015), ApJ, 812, 143.

Another asymmetric DNS – now with a tight orbit!

Such a system has just been discovered using the ALFA receiver at the Arecibo observatory –see Lazarus, Freire et al. (2016), ApJ, 831, 150.

PSR J1913+1102•

P = 27 ms•

Pb = 4.95 hr•

e = 0.089•

Companion mass > 1 solar mass•

Double neutron star!

B1913+16

J0737−3039

4 light seconds

PSR J1913+1102

PSR J1913+1102••

Precession of periastron measured –most massive DNS ever (2.875 ±0.014 M¤).
Low-eccentricity suggests second NS
has a low mass.

oi = 30.
ωoi = 60•

System should be asymmetric!

oi = 90PSR J1913+1102••

Precession of periastron now
measured more precisely: 2.8854 ±0.0012 M¤.
Einstein delay measured! Companion
mass is 1.25 ± 0.05 M¤., thus themass of the pulsar is 1.64 ± 0.05 M¤.

PSR J1913+1102

.
ω

.
Pb

Preliminaryγ•

Orbital decay measured to 3-sigma
significance – will improve fast during
the next few years.

•

Coalescence within 0.5 Gyr.

PSR J1913+1102
PSR J1913+1102••

This could represent more than one
order of magnitude improvement insensitivity to DGW over the best
current test with J1738+0333 –provided proper motion is about 6
mas/yr.
Currently: 9 ± 3 mas / yr.

.
ω

.
Pb

PreliminaryγOld and new trends•

Total of 21 systems known might be DNSs, but three of these are doubtful. Outside globularclusters, there are now 19 systems, but two of them are doubtful.

•

They can be born with a range of masses that is wider than previously thought.

•

Two asymmetric systems have now been measured, one of them contain the least massive NS
known.

•

Emerging correlation: Low-e systems have low-mass second NS. This suggests a correlation
between NS mass and SN kick.

•

Are there any more massive NSs in DNSs? Why not?

Experiments* on the Nature of Gravitational
Radiation*These really are experiments: Nature changes the experimental setup, i.e., theorbit of the binary and the nature and masses of the components.
- our role is to make the measurements

BC

analysis of Section 4.2(1 +parameterαA αB )(1 +space
αA αCof) theories, T (α , β ), defined bybeen studied extensively in a2two1
00
ues of |β0 |. For large va
the coupling function
a quadratic
in butthe Bscalar
ϕ: higher-ordera(ϕ) =
where A,which
B, C isdenotea prioripolynomial
three bodies,= C field
isterms are r
2 relativistic periastron advance, proportional toα0 (ϕ − ϕ0 ) + βallowed.
[12, 14, 15]. The parameter α0 defines the linearFig.
matter7 with respect to th
0 (ϕ − ϕThe0 ) /2PPN
PPN+ 2γ and− ββ0 the) in
the PPNcoupling
formalism,
becomes
A comment on thescalar coupling(2constantquadraticof matterto now
two ascalar particles,
combination of the above expressions, explicitly written in
The mass
while higher-order
vertices are neglected. In this sense, this is a natural extension
of of the white deq. (9.20a) of Damour & Esposito-Farèse (1992).
optical data of Paper I,
JFBD gravity.
But the most spectacular deviation from GR is that
The diﬀerence is a neglib
In presenceofsuch
non-perturbativestrong-fielddeviations
away
from
GR,
we canscalar waves are now also emitted by any binary system,takeinto account when
• Many alternative theories of gravity predict violation of the strong equivalence principle (SEP).
have a situation
where
the eﬀective
strengthof the ofneutronstar, αA , ismatter-scalarof orderthus
contributing
to coupling
the observed
variation
the orbital
coupling cConsequences:period.
For asymmetricsystems,
notably the neutron
unity, even if thescalar-matter
coupling,
α0 , is unobservably
small in starthe Solar System§.
Figure 7 shows thbinary studied
the present
the mainquadratic
Such an eﬀect whiteleads dwarf
to a violationof SEPinthat
requirespaper,
test systems
which containa matter-scalar
3
1. Dipolar gravitational wave (DGW) emission (tight orbits, 1.5 PN, or 1/c ): whatever the value of th
neutron star. contribution comes from dipolar waves:the nonperturbative stro
The structure
dependence
1 + e2 /2gravitational2 constant GAB , has theq eﬀectiveG∗ Mofc the
DEsposito-Farèse (1993, 19(αp − αc ) ,(21)
Ṗb = −2πnb3consequence thatthe pulsar cdoes
qnot+ 1fall(1 −ine2the)5/2 same way as its companion in theare now derived either fr
gravitational fieldof a third body, which in our case is the Galaxy. One findsaPSRforJ1738+0333.
For p
where the eccentricity e is negligible in our case. [The lowestpulsar with2.a Orbital
weaklyself-gravitating
since
α0the
≪AND
1,
that
[11] IN TRIPLE
to provide
polarization
wide orbits
PULSARSYSTEM)the best cons
order expansionof(Nordtvedt(αp companion,− αceﬀect,)2 in forpowersofsensitivities

Could Einstein still be wrong?

2changed: PSR J1141−65sisdenotedasκS(12)−above.
In the present secp,cD∆p − ∆c ≃ α0 (αp − αc ) in
≃ eq.
α0 (α
α
)
.
(4)
p
0
is more constraining thation, we are numerically taking into account the full nonlinVariation
gravitational
constant
G.The
PSR J1738+0333 isWhile |α0 | 3.
< 0.003
by of
theNewton’s
Cassiniexperiment[4], αp can
be companion’sof order unity forandneutronear dependence
on thebodies’ self-gravity.]β0 > 0.7.
scalarchargeαc ≈ αtheits smallbinding energy,
0 becausestars, as outlined
above.
Althougheﬀect isofgreatly
suppressedby a small factor
α0 , The same is tr
The special case β0 = 0
while any
the ofpulsar’s
scalarwould
chargeαp GR!
may be of order 1 in
• Detecting
these eﬀects
falsify§ The quantity αln MA /∂ϕthe0 eﬀective
strengthof the coupling betweenA ≡ ∂0 measuresoryaofselfgravity) is in the r
sometheorieseven
if α0 ≈
(Damour& Esposito-Farèse
gravitating body A, with total mass MA , and the scalar field ϕ. It is equivalent to the negative
ratio
is still more sensitive. O
1993, 1996b). The orbital decay from dipolar gravitational• The
first two
dependonFor
diﬀerenceof self-gravitatingcompactness between
Therefore,of total scalarchargeto totalmass.
a weakly
body αA3members≃ α0 . of the binary.
converts into ωBD > 25
wave
emission(eq.
(21)),
which
is
of
order
O(1/c
),
is
thus
pulsar – white dwarf systems might show these eﬀects, even if they are not detectable in theof the precision of the C
genericallydoublepulsar! much larger than the usual quadrupole of ordersame constraint in the mO(1/c5 ). An observed Ṗb consistent with general relativity
considered in Alsing ettherefore strongly constrains scalar-tensor theories.
ms c2 < h/Pb = 1.35 × 1
This is illustrated in Fig. 7, where we also display the
stant), and no longer aPulsar – White dwarf systems•

For GR tests with these systems,
mass measurements are
absolutely necessary.

•

Furthermore, it is thought thatthese could be more massive,given the much longer accretion
episode!

•So, we REALLY WANT TO
MEASURE THEIR MASSES!

•

Measuring masses much morediﬃcult since generally orbits are
so circular.

Lorimer, D., Living Rev. Relativity 11 (2008), 8

Measuring MSP masses: It’s hard!
Solutions:
1) WD spectroscopy
2) Measurements of Shapiro delay
3) Find unusually eccentric systems

Relative Intensity

White dwarf spectroscopy: Sometimes we’re lucky!

0

100

200

300

400

500

Bin Number•

PSR J1738+0333 is a 5.85-ms pulsar in a
8.5-hour, low eccentricity orbit. It was
discovered in 2001 in a Parkes Multibeam high-Galactic latitude survey(Jacoby 2005, Ph.D. Thesis, Caltech).
All pictures in this section: Antoniadis et al. (2012), MNRAS, 423, 3316•

Companion WD detected at optical
wavelengths, and relatively bright!

Optical observations of PSR J1738+0333•

The WD is bright enough for a study of the spectral lines!

•

Together with WD models, these measurements allow an estimate of the WD mass:
0.181+0.007−0.005 M⦿.

Optical observations of PSR J1738+0333•

Shift in the spectral lines allows
an estimate of the mass ratio:q = 8.1 ± 0.2.

•

This allows an estimate of theorbital inclination (32.6 ± 1.0°)
and the pulsar mass:
1.46+0.07−0.06 M⦿.

•Results in Antoniadis et al. 2012,
MNRAS, 423, 3316.

and declination (see Table 1). For the intrinsic Pb , we thus
obtain= −25.9Wex,± 3.2 fs
s−1 .
8ṖbInt Freire,
Esposito-Farèse,
Verbiest et al.

rived quantities
and their uncert(5)keep a similar shape even if w
diﬀer in Section 6 below:
rections. This
just slig
3.3 Excess orbital
αA αB decay
4 would
GENERICγAB ≡ 1 − 2,(19)would also do a diﬀerent ch
1 + αA αB
From the values
mc in Paper I we can estimate thejustifies a In
posteriori
theundelowe
order to1 for q βandA αB αCA, estimate(20)of orbital≡ component
1 + causedxs• βOncemassesby
aretheknown,
we canthe rate
decay dueBC theanalysisofṖtoSectionorbitaldecay
emissionof quadrupolarGWs
in eq.4.2(7)abov
—
2
(1
+
α
α
)(1
+
α
α
)
b
A
B
A
C
quadrupolar GW emission predicted by GR (2.5 PN):
ues of |β0 —|. Forfor a low-eccentricity system, as predicted by GR:
welarge
nowvalues
discu
where A, B, C denote a priori three bodies, but B = C ishigher-order terms are resp
be contributing
192 π periastron 5/3
allowed.
The relativistic
advance,qproportional to
GR
Fig.
7
with
respect to the siṖb≃ −PPN (nb T⊙ mc )PPN
1/3
(2 + 2γ− β 5) in the PPN formalism,
becomes
now a
A comment
onṀthe com(q + 1)
xs
T
Ṗ
=
Ṗ
+
Ṗ
b
b
b
combination of the above
explicitly written in
The mass of the white dwarf+1.5 expressions,
−1
=
−27.7
fs
s
,
(6)
−1.9
eq. (9.20a) of Damour & Esposito-Farèse (1992).
optical data of Paper
Ṁ I, whi
whereṖ
b is duBut the most spectacular deviation from GR is that
The diﬀerence is a neglibible
where T⊙ ≡ GM⊙ c−3 = 4.925490947 µs (Lorimer & Kramerfromtscalarwaves
are now also
emittedby−0.86
anyμs
binarysystem,take into tribution
account whencalc…2005).
which is Subtracting
a change on the thisorbitalfrom
periodṖ
ofInt
per
year!
(eq.
(5))
we
obtainthebthus contributing to the observed variationof the orbital
mainlyby const
thematter-scalar
coupling“excess”
orbitaldecay
relativetothepredictionofGR,
period. For asymmetric systems, notably the neutron starFiguremultipole
7 shows modifthat• whiteIn xs
the presenceof dipolar
GW emission
this quantity
must
be mainlarger (in absolutevalue)matter-scalar
-Ġ
If αp
dwarf+3.7
binarystudiedin the present
paper,
thequadratic
cou
−1
Ṗ
is
a
contrib
Ṗ
=
2.0
fs
s
.
(7)
~1,
then
orbitaldecay
shouldbe~−32000
μs
per
year!
It
is
a
1.5
PN
eﬀect.
bb−3.6
contribution comes from dipolar waves:whatever the value of the lin
tions of Newton
thenonperturbativestrong-fi
2
This
is consistentzero.
1 + e As
/2 discussed2 in Section 4, thisqG∗ Mc withD
CavendishEsposito-Farèse(1993, exper
1996b(αp − αc ) ,(21)
Ṗb = −2πnb32
5/2
implies that GR
the−test
c passesq + 1 (1e ) posed by the orbital decay ofcal” terms,
the l
are now derived
either fromPSR J1738+0333. We illustrate this match in Fig. 5, where
PSR J1738+0333.
Forotherposit
of gravity
where the eccentricity e is negligible in our case. [The lowest• Can
such
a
small
changeintheorbitalperiodbedetected?
2
we seethat themass/inclination
constraints, derived fromto provide the best constrain
order
expansionof (αp − αc ) in powers of the sensitivities
Int2
eq.as(6)assuming
thatis the correct
thechanged: PSR J1141−6545
sṖp,cdenotedκD S(i.e.,in eq.
(12) above.
In GR
the present
secb is using
is 2more constraining than th
ory ofare consistent
the thetheory-independenttion,
wegravity),
are numericallytaking intowith
account
full nonlin4.1 Classicaland PSR J1738+0333
is nowear
dependence
on the bodies’
self-gravity.]
The companion’sconstraints
derivedfrom theoptical observations.
β > 0.7. The same is true f

Prediction:

Timing of PSR J1738+0333
10 years of timing with Parkes and Arecibo were necessary to measure this number precisely!

2001)
an paother.
of thedictederivedwn totion ofrtotti,

ic ame amis, for
antityth theasureindeasurehapiro
n thatals aseable,
at thes thatwe seeft plot
efactsdistances, therefore this agreement with the DM prediction
cannot be used as solid evidence that our parallax is accurate.
This distance, when combined with the known temperature and photometric properties of the white dwarf, produces an estimate for its radius that is very similar to thatderived from its the spectrum (see Paper I). This suggeststhat our value for the distance is likely to be accurate given
present
timingbetween
uncertainties.
Thisandis 55813.95899
important becauseo theNumberof rotations
52872.01692(SSB): 43 449 485 656 ± 0.
the distance (and the proper motion, also presented in Table 1) are necessary for a correct
estimate of the intrinsico Spin period (today, at 14:00, 12:00 Int
UT): 0.005850095866180740 ± 0.000000000000000005 s
orbital decay of the system Ṗb , as discussed below.
Following the analysis by Verbiest, Lorimer, &o Orbital period: 8h 30m 53.9199264 ± 0.0000003 s
McLaughlin (2010), we find that there are no significant biases aﬀecting this parallax measurement.

The (awesome) power of timingoSemi-major axis of the pulsar’s orbit, projected along the line of sight: 102957453 ± 6 m.

Intrinsic
orbitaldecay
o 3.2
Eccentricity:( 3 ± 1)× 10−7. Thismeans that the orbit deviates from a circle by (5 ± 3) μm!
The intrinsic orbital decay of the system can be obtained−1, parallax: 0.68 ± 0.05 mas.
o fromPropermotion:7.037orbital± 0.005 mas
yr−1variation, 5.073 ± 0.012
theobserved
period(Ṗb )mas
by yr
subtracting the kinematic eﬀects (Shklovskii 1970; Damour & Taylor
o 1991):
Orbital decay: −(25.9 ± 3.2) × 10−15 ss−1 (or −0.8 ± 0.1 μs yr−1!). GR Does it again!!!!
ṖbInt = Ṗb − ṖbAcc − ṖbShk .

(1)

The same equation applies to any quantity with the dimension of time, like the spin parameters (P , Ṗ and Ṗ Int ).
The first term, ṖbAcc = aT Pb /c is caused by the diﬀer-

Limit on dipolar GW emission•

Diﬀerence between orbital decay predicted by GR (quadrupolar) and observed is +0.06 ± 0.10
μs per year!

•

This represents a very serious theoretical constraint: remember prediction of −32000 μs per
year! This implies that (αp – αc)2 < 3 × 10−5.

•

Gravitational waves in the Universe really are quadrupolar, as predicted by GR!

•

This introduces stringent constraints on alternative theories of gravity that predict dipolar GW
emission.

For Scalar-Tensor theories of gravity, this is themost constraining binary pulsar test ever!
0|
LLR

See results in Freire, Wex, EspositoFarèse et al. (2012), MNRAS, 423,
3328.

100

B1534+12
SEP
J0737–3039
B1913+16

10

10
LLR
J1141–6545

Cassini

J1738+0333

10

10
−6

−4

−2

0

2

4

6

0

Also for TeVeS and friends!
0|

•

100

B1534+1210

SEP
J0737–3039•
B1913+16

Tuned
TeVeS

10
LLR
J1141–6545
J1738+0333

Inconsistent
TeVeS

10

•

10
−6

−4

−2

0

2

4

6

0

Tensor-Vector-Scalar theories(based on Bekenstein’s 2004
TeVeS theory) can also beconstrained, but in this case PSR
J1738+0333 is not enough.
Improvements in the timing
precision of the double pulsar(PSR J0737−3039) will beessential to constrain regions nearlinear coupling. To be publishedsoon (Kramer et al).
TeVeS and all non-linear friends
will soon be unnaturally finetuned theories.

Also for many others!
See e.g., ``Constraints on Einstein-Æther theory and Hořava gravity from binary pulsar
ovservations”, Kent Yagi, Diego Blas, Enrico Barausse and Nicolás Yunes, (2013) Phys. Rev. D,
89, 084067.
10-1
allowed region
stability
weak-fieldα̂, J1738+0333

c-

-2

10

10-3
10-3

10-2

10-1

100

c+
Constraints on Einstein-Æther theory from binary pulsar
observations from the observed orbital decay of PSR J1738+0333.

Does GW emission change with NS mass?

PSR J0348+0432•

This is a pulsar with a spin
period of 39 ms discovered
in a GBT 350-MHz drift-scansurvey (Lynch et al. 2013,
ApJ. 763, 81).

•

It has a WD companion and(by far) the shortest orbital
period for a pulsar-WD
system: 2h 27 min.

B1913+16

J0737−3039

PSR J0348+0432
4 light seconds

PSR J0348+0432
Optical measurements at the VLT find a
WD mass of 0.172 ± 0.003 M¤ and apulsar mass of 2.01 ± 0.04 M¤(Antoniadis, Freire, Wex, Tauris et al.
2013, Science, 340, n. 6131).
•

Most massive NS with a precise
mass measurement.

•

Confirms that such massive NSs
exist using a diﬀerent method thanthat used for J1614−2230. It also
shows that these massive NSs are
not rare.

•

Allows, for the first time, tests ofgeneral relativity with such massive
NSs! Prediction for orbital decay:−8.1 μs /year

Credit: Luis Calçada, ESO. See video at:
http://www.eso.org/public/videos/eso1319a/

This is important – system is unique!

Figure by Norbert Wex. See http://www3.mpifr-bonn.mpg.de/staﬀ/pfreire/NS_masses.html

Measurement of orbital decay

.
Pb

q

MWD

q

MWD

.
Pb

With Arecibo, GBT and Eﬀelsberg, we have now measured the orbital decay: (−8.6 ± 1.4) μs/year.
Complete agreement with GR!

Strong non-linear deviations from GR#
seriously constrained!
•

This is the first time we do a GR testwith such a massive NS: Previously,
only 1.4 M¤ NSs had been used forsuch tests!

•

This constrains the occurrence ofstrong non-linear deviations from GR,
like spontaneous scalarization (e.g.,
Damour & Esposito-Farèse, 1996, Phys.
Rev. D., 54,1474) – at least at large
PSR-WD separations!

•

Such phenomena simply just could not
be probed before.

•

NS mass absolutely necessary forinterpretation of experiment (not just for
subtracting GR quadrupolar GW term)Constraints on the equation of state

Mass measurements have direct implications for the EOS of dense matter!
Figure by Norbert Wex. See http://www3.mpifr-bonn.mpg.de/staﬀ/pfreire/NS_masses.html

Implications for GW detection•

For a NS-NS merger, only a small
fraction of a cycle can be lostwhile it is in the LIGO/Virgobands.

•… unless there are short-range,high frequency eﬀects!

How do pulsars compare to LIGO? II. LIGO
GW 150914
GR violations are limited to less than 4 %(for eﬀects that cannot be absorbed in aredefinition of parameters)

90% credible regions for the waveform
and the GW frequency. From: LSC/ Virgo

How do pulsars compare to LIGO? III. S-T
Theories•

BH-BH mergers cannot test deviations
from GR that appear only in thepresence of matter, e.g., JFBD-type
scalar-tensor theories.

•

Certain alternatives to GR predict(significant) deviations only for BHs,e.g., decoupled dymamical GaussBonnet (D2GB) gravity (see Yagi et al.
2016)

•

For certain alternatives to GR, pulsars
already provide better constraints than
expected from LIGO/Virgo observationsof NS-NS or NS-BH mergers.

•

LIGO/Virgo observations of NS-NS
mergers are essential to test shortrange phenomena, like dynamical
scalarization (Barausse et al. 2013)

Measuring MSP masses (continued)
Solutions:
1) WD spectroscopy (already discussed)
2) Measurements of Shapiro delay
3) Find unusually eccentric systems

Solution 2: Shapiro delay•

Shapiro delay (described above for double
pulsar) still measurable for circular orbits…

•

Requires good timing precision and highinclination and preferably high companion
masses - diﬃcult for MSPs with He WD
companions•

Earlly detection of Shapiro delay in binary
pulsars: PSR B1855+09 (Ryba, Taylor, 1991,
ApJ, 371, 739)•

No precise mass measurement: combination oftiming accuracy and high inclination not there
yet.

•Same for many of the early MSPs (like e.g.,
J1713+0747)

A precise MSP mass•

PSR J1909−3744 is a MSP with aspin period of 2.947 ms - and one of
the most precise timers known.

•

Pb = 1.533 d, e = 0.000000135(15)•i = 86.58(11) degrees!

•

Precise masses derived from
Shapiro delay only:
Mp = 1.438(24) M⦿
Mc = 0.2038(23) M⦿
(Jacoby et al. 2005, ApJL, 629, 113)•

Update: Pulsar mass is 1.55(3) M⦿ according to Fonseca et al. 2016, 1.54(3) M⦿ according toDesvignes et al. (2015).

•

Shapiro delay is especially prone to systematic eﬀects. Lots of TOAs needed…

A precise and large MSP mass•

PSR J1614−2230 is a MSP witha spin period of 3.15 ms.

•

Pb = 8.68 d, e = 0.00000130(4)•i = 89.17(2) degrees!

•

Precise masses derived from
Shapiro delay only:
Mp = 1.97(4) M⦿
Mc = 0.500(6) M⦿
(Demorest et al. 2010, Nature)•

Update: Mp = 1.928(17) M⦿
(Fonseca et al., 2016, arXiv:
1603.00545)

Solution 3: Triples, disrupted triples and othermonsters

From: NRAO / Cornell University Press Release

Mass for PSR J1903+0327
Precise MSP mass: 1.667 ± 0.021 M⦿ (99.7% C. L.). See Freire et al., 2011, MNRAS,412,
2763, confirmed by Fonseca et al. (2016). System formed by disruption of a triple system.

ς

h3

.
ω+/−µ’
R.+ω /−µ’

Rh3

ςWhat was surprising was that the pulsar’s motion, as measured
E\ H[TXLVLWHO\ SUHFLVH SXOVDU WLPLQJ FRXOG QRW EH FRPSOHWHO\
H[SODLQHGE\WKDWGD\RUELW:HEHJDQDPDVVLYHREVHUYing campaign with Arecibo, the GBT, and Westerbork (which obVHUYHGWKHSXOVDUHYHU\GD\RUWZRIRURYHUD\HDU WRÀJXUHRXW
where this other motion was coming from. It turns out that there
is an older, cooler, 0.4 solar mass white dwarf orbiting that inner binary every 327 days, making a hierarchical triple system.

The triple system

the pulsar’s position to better than a kilometer while
ing on orbits which are tens of millions of kilomete-XVW UHFHQWO\ ZH IXOO\ ´VROYHGµ WKH FRPSOH[ RUELWVtem using high-precision three-body integrations oftational equations of motion matched to our tim
YDWLRQV  7KH PDVVHV RI DOO WKUHH REMHFWV DUH PH
better than a part in 10,000, the inclinations of b
are measured to about a hundredth of a degree
SULVLQJO\ DUH DOPRVW SHUIHFWO\ FRSODQDU  DQG WKH
gravitational interactions are seen with h•icance
Theover
GBTtime350-MHzscalesdriftas short as a sscan survey found apulsar inthea hierarchicalIn addition,
inner white dwarf is hot
triple,PSR
J0337+1715!
cally bright, and members of our team h(Ransom
et al., 2014,
beautifulphotometricand spectroscop
Nature,505,
520)
vationsof it,
measuringits radial veloc
matches predictions from pulsar timing
gravity and temperature. We have also dewith theVLBA and a campaign is•pulsarPrecisemass
WR PHDVXUHD KLJKSUHFLVLRQ
measurements
can be SDUDOOD[ GLVWDSXOVDUZLWKLQfrom
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derivedthe 3-body
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portant calibration point for white dwar

Figure caption: A schematic of the millisecond pulsar triple-system-7KHSXOVDUVSLQQLQJHYHU\PLOOLVHFRQGVLVRUELWHGHYHU\GD\VE\DaVRODUPDVVZKLWHGZDUIDQGWKDWLQQHUV\VWHPLVRUELWHGHYHU\GD\VE\DaVRODUPDVVZKLWHGZDUI7RKHOSZLWKD
sense of scale, the distance from the Earth to the Sun is about 500 light-

systemis alreadyone of the high
•TheThissystemhas
VLRQenormous
H[DPSOHVpotential
RI D JUDYLWDWLRQDOWKUHHER
fof
NQRZQ
H[FHSW(see
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Freire, IRU WKH (DUWKsystem,which
is dramaticallycomplicate
Kramer& Wex,
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non-compactnessof the bodies), and cont
CQGra, 29, 184007)
ing observations may allow high-precisio
parts of General Relativity and inclusion i
Grav for gravitational wave detection. F
complicated evolution of the system, inv“deaths” of three main-sequence stars, w
fodder for astrophysical studies for years

Tests of the Strong Equivalence Principle
For a summary of SEP tests with pulsars, see Freire, Kramer & Wex (2012, CQGra, 29, 184007)

Lunar Laser Ranging

Damour-Schäfer test (1991), Phys. Rev. Lett. 66, 2549
Gonzalez et al. (2011), ApJ, 743, 102
de/dt test (Freire, Kramer, Wex, 2012)

Pulsar in triple test (Freire, Kramer, Wex, 2012)

A new class of binary MSPs•

There is a new class of binary
MSPs with P = 2 - 5 ms, e ~0.1 and Pb = 22-32 days (4 so
far)!

•

Formation is not understood(see discussion in Barr et al.
2016).

•

One mass measurement
submitted, two more being
prepared.

From Deneva et al. 2013, ApJ, 775, 51

90

J1946+3417
PSR J1946+3417 is a MSP with aspin period of 3.17 ms discovered
with the Eﬀelsberg telescope (Barret al. 2013, MNRAS, 435, 2234).

Position angle (deg)

•

60

30

0

-30

-60

-90

•

Pb = 27.02 d, e = 0.134(Barr, Freire et al. 2016, MNRAS, inpress, see arXiv:1611.03658)

0

30

60

90

120

150 180 210 240
Pulse longitude (deg)

270

300

330

360

J1946+3417

ς

h3

.
ω

.
ω

h3
ς

Precise masses derived from Shapiro delay and precession of periastron:
Mp = 1.828(22) M⦿, Mc = 0.2656(19) M⦿ (Barr, Freire et al. 2017, MNRAS, 465, 1711)

J1946+3417

ς

h3

.
ω

.
ω

h3
ς

Summary I – Gravity•

Double neutron stars have provided extremely precise tests of the properties of strong-field
gravity. In particular, they allowed the first detection of gravitational radiation, and showed thatbinary systems lose energy through GW emission at the rate predicted by GR.

•

Pulsar – white dwarf systems have introduced very stringent constraints on the existence ofdipolar GW emission. This introduces very stringent constraints on the nature of gravitational
waves:•o

GW emission does not change (to a measurable level) for asymmetric systems – no dipolar
component, quadrupolar to very high purityoThe purely quadrupolar nature of GW emission does not change with the compactness of
NSsWith newly discovered systems and GAIA, the future looks very promising!

Summary I – Gravity – Near future•

Until recently, DNS systems are not the best for looking for dipolar GW emission – thecomponent masses are too close to each other.

•

In MSP-WD systems, we have reached the limit of what can be done – not possible tomeasure masses more accurately.

•An asymmetric DNS – like the new system J1913+1102 – could in principle combine the bestof both worlds.

Summary II – NS mass measurements•

NSs in DNSs are now showing a wider mass distribution, with some asymmetric systems.

•

Measuring masses for MSPs is much more diﬃcult. Diverse strategies employed, all withadvantages and disadvantages: WD spectroscopy, Shapiro delay measurements, eccentric
Galactic binaries. These show thato MSP mass distribution is much wider in MSPs, with upper masses of at least 2 M⦿.
o Massive NSs are not rare!
o MSP masses might be bimodal (Antoniadis et al. 2017)

Summary II – NS mass measurements – near future•

Within 2 years, the number of NS mass measurements will double, based only on systems wealready know. One would expect that the mass distribution might grow even wider.

•

Many NSs will have much more precise masses. Masses J0437-4715 and J0751+1807 will bevery interesting in combination with NICER.

•

In the future (with MeerKAT): measurement of the moment of inertia of PSR J0737−3039A (andpossibly another system as well), which is interesting because we know the mass of that pulsar
as well.

Thank you!

For questions and suggestions, contact me at: pfreire@mpifr-bonn.mpg.de, or see my site at
http://www3.mpifr-bonn.mpg.de/staﬀ/pfreire/To stay up to date on the latest precise NS mass measurements and GR tests, check:
http://www3.mpifr-bonn.mpg.de/staﬀ/pfreire/NS_masses.html
Review on NS masses and radii: Ozel & Freire (2016), ARAA, 54, 401