Testing Gravity in a New Regime using PSR J0348+0432

J. Antoniadis, P. Freire, N. Wex, T. Tauris, R. Lynch, M. van Kerkwijk, M. Kramer, C. Bassa, V. Dhillon, T. Driebe, J. Hessels, V. Kaspi, V. Kondratiev, N. Langer, T. Marsh, M. McLaughlin, T. Pennucci, S. Ransom, I. Stairs, J. van Leeuwen,

J. Verbiest, D. Whelan

3rd BONN Workshop, 15th April 2013

Range of tested gravitational binding energies

NS-NSNS-WD

Strong field deviations from GR

↵0 = 0.0001�5 �0 �4

Note

!20 !

1

2"BD + 3

# = 1 "2!2

0

1 + !20

# 1 " 2!20

GAB/G = 1 " 2!20 (sA + sB " 2sAsB) + O(!4

0)

$AB = 3 " 4!20 (1 " sA)(1 " sB) + O(!4

0)

%AB = 1 " 8!20 sAsB + O(!4

0)

Quadratic model

Field equations

R!µ! =

8&G!

c4

!

T !µ! " 1

2T !g!µ!

"

+ 2'µ('!(

gµ!! $!

µ$!!( = "

4&G!

c4(!0 + )0()T!

and

!0 ! )0(0

Physical metric

gµ! = g!µ! exp!

2!0( + )0(2"

Various actions and action terms

Sgravity =c3

16&G!

#

d4x%"g! [R! " 2f(gµ!

! 'µ('!()]

Sgravity =c3

16&G!

#

d4x%"g! [R! " 2f(gµ!

! (,µ(,!)] + Svector

$

U[µ;!], U(µ;!), Uµ;µ, U!Uµ;! , UµUµ

%

Svector[U[µ;!]U[µ;!], U

(µ;!)U(µ;!), U"Uµ;"U#Uµ;# , Uµ;µ, UµUµ]

Svector[Uµ; g!µ! ]

Smatter[*; gµ! ]

Smatter[*; gµ! ! A2(()g!µ! + B(()UµU! ]

8

Quadratic scalar-tensor gravity of Damour & Esposito-Farèse

P = 39.1226569017806(5)ms

Pb = 2.45817750533(2) h

e . 10�6

PSR J0348+0432

[ Boyles et al. 2013, Lynch et al. 2013 ]

IAUS291. Green Bank Telescope pulsar searches 3

Figure 1. Sky cover-age of the Drift-scanand GBNCC Stage Isurveys. New pulsarsare shown as stars, andMSPs are outlined inred. The GBNCC sur-vey is currently beingextended to lower de-clinations with the goalof eventually coveringthe entire sky visible tothe GBT.

and recycled pulsars. Twenty-four pulsars from early data processing are presented inArchibald et al. (2009), Boyles et al. (2012), and Lynch et al. (2012) along with completetiming solutions. An additional 11 pulsars have been discovered since this first round ofdetailed follow-up and are still being studied. Below I provide a few highlights.• PSR J0348+0432 is a 39-ms recycled pulsar in a short, 2.4-hr orbit around a white

dwarf companion (Lynch et al. 2012). Optical imaging and spectroscopic follow-up of thecompanion have provided tight constraints on the mass of the white dwarf (Antoniadiset al., in prep), which is about 0.17 M!. The di!erent binding energies of the pulsarand white dwarf are predicted by certain tensor-vector-scalar gravitational theories tolead to strong dipolar gravitational wave emission. Timing using the Arecibo telescopeis already placing stringent limits on these theories in an as-yet unexplored strong-fieldregime (Antoniadis et al., in prep) and future timing will improve these constraints.• PSR J0337+1715 is a 2.7-ms MSP in a hierarchical triple, the first to be discovered

in the field of the Galaxy. The inner companion appears to be a white dwarf with anouter companion of undetermined nature on a much longer orbit orbit. This system wasonly recently discovered during final processing of the Drift-scan data, but early timingis already showing evidence for secular changes to the orbital parameters of the innerbinary due to three-body interactions (Ransom et al., in prep), making this system aprecision dynamical laboratory.• PSR J2222!0137 is a 33-ms recycled pulsar with a minimum companion mass of

1.1 M! (Boyles et al. 2012). The pulsar is nearby (D = 310 pc) and bright (S820 MHz "

2 mJy), and has been studied using the Very Long Baseline Array (Deller et al., in prep).The pulsar has also been the subject of a campaign to measure Shapiro delay (Boyleset al., in prep). These results will be presented in future publications.• Two high-precision MSPs discovered in the Drift-scan survey have been released

to NANOGrav and the International Pulsar Timing array.• The well-known “missing link” MSP, PSR J1023+0038 (Archibald et al. 2009) was

one of the earliest Drift-scan discoveries and has shed light on the connection betweenlow-mass X-ray binaries and MSPs.• Thirty-three RRAT candidates have been discovered in the Drift-scan, with about

six having already been confirmed. This marks a substantial increase in the size of theRRAT population (for details see the discussion by Karako-Argaman, these proceedings).

3. The Green Bank North Celestial Cap Survey

The GBNCC survey is the successor to the Drift-scan survey and was also carried outat 350 MHz, giving it excellent sensitivity to nearby, steep spectrum pulsars. It uses twice

0 0.5 1 1.5 2

Spin Phase

1170141015101610

50 48 46 44 42 3:48:40 38 36

30

33:00

30

4:32:00

30

31:00

30:30

Right Ascension (J2000)

Dec

linat

ion

(J20

00)

Figure S1: Finding chart for the PSR J0348+0432 system and the comparison star used in our analysis (seetext), created from the archived SDSS g0 image.

13

1'

The companion to PSR J0348+0432

WD companion

[ Lynch et al. 2013 ]

u' (355 nm) = 21.84 ± 0.19g' (469 nm) = 20.71 ± 0.03r' (617 nm) = 20.60 ± 0.03i' (748 nm) = 20.69 ± 0.05z' (893 nm) = 20.40 ± 0.15

SDSS

KWD = 351± 4 km s�1

KPSR = 30.008235± 0.00016 km s�1

q ⌘ MPSR/MWD = KWD/KPSR = 11.70± 0.13

Optical spectroscopy

[ Antoniadis et al. 2013 ]

Modeling the white dwarf, getting the masses

modeling the Balmer linesDataBest-Fit3σ

[ Antoniadis et al. 2013 ]

Mass of white dwarf:

0.172± 0.003M�

q

Mass of pulsar:

2.01± 0.04M�

PSR J0348+0432 and Equations-of-State

common feature of models that include the appearance of ‘exotic’hadronic matter such as hyperons4,5 or kaon condensates3 at densitiesof a few times the nuclear saturation density (ns), for example modelsGS1 and GM3 in Fig. 3. Almost all such EOSs are ruled out by ourresults. Our mass measurement does not rule out condensed quarkmatter as a component of the neutron star interior6,21, but it stronglyconstrains quark matter model parameters12. For the range of allowedEOS lines presented in Fig. 3, typical values for the physical parametersof J1614-2230 are a central baryon density of between 2ns and 5ns and aradius of between 11 and 15 km, which is only 2–3 times theSchwarzschild radius for a 1.97M[ star. It has been proposed thatthe Tolman VII EOS-independent analytic solution of Einstein’sequations marks an upper limit on the ultimate density of observablecold matter22. If this argument is correct, it follows that our mass mea-surement sets an upper limit on this maximum density of(3.74 6 0.15) 3 1015 g cm23, or ,10ns.

Evolutionary models resulting in companion masses .0.4M[ gen-erally predict that the neutron star accretes only a few hundredths of asolar mass of material, and result in a mildly recycled pulsar23, that isone with a spin period .8 ms. A few models resulting in orbital para-meters similar to those of J1614-223023,24 predict that the neutron starcould accrete up to 0.2M[, which is still significantly less than the>0.6M[ needed to bring a neutron star formed at 1.4M[ up to theobserved mass of J1614-2230. A possible explanation is that someneutron stars are formed massive (,1.9M[). Alternatively, the trans-fer of mass from the companion may be more efficient than currentmodels predict. This suggests that systems with shorter initial orbitalperiods and lower companion masses—those that produce the vastmajority of the fully recycled millisecond pulsar population23—mayexperience even greater amounts of mass transfer. In either case, ourmass measurement for J1614-2230 suggests that many other milli-second pulsars may also have masses much greater than 1.4M[.

Received 7 July; accepted 1 September 2010.

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Supplementary Information is linked to the online version of the paper atwww.nature.com/nature.

Acknowledgements P.B.D. is a Jansky Fellow of the National Radio AstronomyObservatory. J.W.T.H. is a Veni Fellow of The Netherlands Organisation for ScientificResearch. We thankJ. Lattimer for providing the EOSdataplotted inFig. 3, and P. Freire,F. Ozel and D. Psaltis for discussions. The National Radio Astronomy Observatory is afacility of the US National Science Foundation, operated under cooperative agreementby Associated Universities, Inc.

Author Contributions All authors contributed to collecting data, discussed the resultsand edited the manuscript. In addition, P.B.D. developed the MCMC code, reduced andanalysed data, and wrote the manuscript. T.P. wrote the observing proposal andcreated Fig. 3. J.W.T.H. originally discovered the pulsar. M.S.E.R. initiated the survey thatfound the pulsar. S.M.R. initiated the high-precision timing proposal.

Author Information Reprints and permissions information is available atwww.nature.com/reprints. The authors declare no competing financial interests.Readers are welcome to comment on the online version of this article atwww.nature.com/nature. Correspondence and requests for materials should beaddressed to P.B.D. (pdemores@nrao.edu).

0.07 8 9 10 11

Radius (km)12 13 14 15

0.5

1.0

1.5

2.0

AP4

J1903+0327

J1909-3744

systemsDouble neutron sDouble neutron star sysy

J1614-2230

AP3

ENG

MPA1

GM3

GS1

PAL6

FSUSQM3

SQM1

PAL1

MS0

MS2

MS1

2.5 GR

Causality

Rotation

P < !M

ass

(M(

)

Figure 3 | Neutron star mass–radius diagram. The plot shows non-rotatingmass versus physical radius for several typical EOSs27: blue, nucleons; pink,nucleons plus exotic matter; green, strange quark matter. The horizontal bandsshow the observational constraint from our J1614-2230 mass measurement of(1.97 6 0.04)M[, similar measurements for two other millisecond pulsars8,28

and the range of observed masses for double neutron star binaries2. Any EOSline that does not intersect the J1614-2230 band is ruled out by thismeasurement. In particular, most EOS curves involving exotic matter, such askaon condensates or hyperons, tend to predict maximum masses well below2.0M[ and are therefore ruled out. Including the effect of neutron star rotationincreases the maximum possible mass for each EOS. For a 3.15-ms spin period,this is a =2% correction29 and does not significantly alter our conclusions. Thegrey regions show parameter space that is ruled out by other theoretical orobservational constraints2. GR, general relativity; P, spin period.

LETTER RESEARCH

2 8 O C T O B E R 2 0 1 0 | V O L 4 6 7 | N A T U R E | 1 0 8 3

Macmillan Publishers Limited. All rights reserved©2010

[ Demorest et al. 2010, Antoniadis et al. 2013]

J0348+0432

Binding energy of PSR J0348+0432

NS-NSNS-WD

PSR J0348+0432 - a unique gravity lab

< 0.004 (Solar System)

↵p = 1 =) Pb = �110 000 µs/yr

GR =) Pb = �8.2µs/yr

Dipolar radiation in PSR J0348+0432?

|↵p(2M�)| < 0.009|↵p � ↵c| < 0.005

+

[ Antoniadis et al. 2013 ]

Pb = �8.6± 1.4µs/yr8121 accurate (few μs) pulse times-of-arrival ➞

Strong field deviations from GR

Quadratic scalar-tensor gravity of Damour & Esposito-Farèse

↵0 = 0.0001�5 �0 �4

[ Antoniadis et al. 2013 ]

nb

n2b

=mAmB

(mA +mB)296

5

⇣vc

⌘5

nb

n2b

=mAmB

(mA +mB)2

96

5

⇣vc

⌘5AB +

⇣vc

⌘3 (↵A � ↵B)2

1 + ↵A↵B

�

PSR J0348+0432 and aLIGO/Virgo

Merger of a 1.3 M⊙ and a 2.0 M⊙ neutron star ~ 104 cycles in aLIGO/Virgo band

GR

ST"ΔN"

PSR J0348+0432 ⇒ ΔΝ < 0.5

nasa.gov

[ Antoniadis et al. 2013 ]

GR template matching

norm

aliz

ed lo

g-lik

elih

ood

Simulation with αB=α0=0

Compton wavelength: �s =h

msc

Pb . �s/c

Massive scalar field

J0348+0432

[ Alsing et al. 2012, Antoniadis et al. 2013 ]

aLIGO/Virgo1.3/2.0 NS-NS

Scalar dipole radiation is emitted only when

Conclusions