DOI: 10.1126/science.1233232, (2013);340 Science

et al.John AntoniadisA Massive Pulsar in a Compact Relativistic Binary

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The list of author affi liations is available in the full article online.*Corresponding author. E-mail: jantoniadis@mpifr-bonn.mpg.de

A Massive Pulsar in a Compact Relativistic BinaryJohn Antoniadis,* Paulo C. C. Freire, Norbert Wex, Thomas M. Tauris, Ryan S. Lynch,

Marten H. van Kerkwijk, Michael Kramer, Cees Bassa, Vik S. Dhillon, Thomas Driebe,

Jason W. T. Hessels, Victoria M. Kaspi, Vladislav I. Kondratiev, Norbert Langer,

Thomas R. Marsh, Maura A. McLaughlin, Timothy T. Pennucci, Scott M. Ransom,

Ingrid H. Stairs, Joeri van Leeuwen, Joris P. W. Verbiest, David G. Whelan

Introduction: Neutron stars with masses above 1.8 solar masses (M�), possess extreme gravitational fi elds, which may give rise to phenomena outside general relativity. Hitherto, these strong-fi eld devia-tions have not been probed by experiment, because they become observable only in tight binaries containing a high-mass pulsar and where orbital decay resulting from emission of gravitational waves can be tested. Understanding the origin of such a system would also help to answer fundamental ques-tions of close-binary evolution.

Methods: We report on radio-timing observations of the pulsar J0348+0432 and phase-resolved optical spectroscopy of its white-dwarf companion, which is in a 2.46-hour orbit. We used these to derive the component masses and orbital parameters, infer the system’s motion, and constrain its age.

Results: We fi nd that the white dwarf has a mass of 0.172 ± 0.003 M�, which, combined with orbital velocity measurements, yields a pulsar mass of 2.01 ± 0.04 M�. Additionally, over a span of 2 years, we observed a signifi cant decrease in the orbital period, P�b

obs = –8.6 ± 1.4 µs year−1 in our radio-timing data.

Discussion: Pulsar J0348+0432 is only the second neutron star with a precisely determined mass of 2 M� and independently confi rms the existence of such massive neutron stars in nature. For these

masses and orbital period, general relativity predicts a significant orbital decay, which matches the observed value, P�b

obs/ P�bGR = 1.05

± 0.18.The pulsar has a gravitational binding

energy 60% higher than other known neu-tron stars in binaries where gravitational-wave damping has been detected. Because the magnitude of strong-field deviations generally depends nonlinearly on the bind-ing energy, the measurement of orbital decay transforms the system into a gravita-tional laboratory for an as-yet untested grav-ity regime. The consistency of the observed orbital decay with general relativity therefore supports its validity, even for such extreme gravity-matter couplings, and rules out strong-fi eld phenomena predicted by physi-cally well-motivated alternatives. Moreover, our result supports the use of general rela-tivity–based templates for the detection of gravitational waves from merger events with advanced ground-based detectors.

Lastly, the system provides insight into pulsar-spin evolution after mass accretion. Because of its short merging time scale of 400 megayears, the system is a direct chan-nel for the formation of an ultracompact x-ray binary, possibly leading to a pulsar-planet system or the formation of a black hole.

Artist’s impression of the PSR J0348+0432 system. The compact pulsar (with beams of radio emission) produces a strong distortion of spacetime (illustrated by the green mesh). Conversely, spacetime around its white dwarf com-panion (in light blue) is substantially less curved. According to relativistic theories of gravity, the binary system is subject to energy loss by gravitational waves.

26 APRIL 2013 VOL 340 SCIENCE www.sciencemag.org

RESEARCH ARTICLE SUMMARY

448

FIGURES AND TABLE IN THE FULL ARTICLE

Fig. 1. Radial velocities and spectrum of the

white dwarf companion to PSR J0348+0432

Fig. 2. Mass measurement of the white dwarf

companion to PSR J0348+0432

Fig. 3. System masses and orbital-inclination

constraints

Fig. 4. Probing strong fi eld gravity with PSR

J0348+0432

Fig. 5. Constraints on the phase offset in

gravitational wave cycles in the LIGO/VIRGO

bands

Fig. 6. Past and future orbital evolution of

PSR J0348+0432

Fig. 7. Possible formation channels and fi nal

fate of PSR J0348+0432

Table 1. Observed and derived parameters

for the PSR J0348+0432 system

SUPPLEMENTARY MATERIALS

Supplementary TextFigs. S1 to S11Tables S1 to S3References

ADDITIONAL RESOURCES

Fundamental Physics in Radio Astronomy group at the Max-Planck-Institut für Radioastronomie, www3.mpifr-bonn.mpg.de/div/fundamental/

The European Southern Observatory, www.eso.org/public/

D. R. Lorimer, Binary and millisecond pulsars. Living Rev. Relativ. 11, 8 (2008). http://dx.doi.org/10.12942/lrr-2008-8

T. Damour, “Binary systems as test-beds of gravity theories,” in Physics of Relativistic Objects in

Compact Binaries: From Birth to Coalescence, M. Colpi, P. Casella, V. Gorini, U. Moschella, A. Possenti, Eds. (Astrophysics and Space Science Library, Springer, Dordrecht, Netherlands, 2009), vol. 359, pp. 1–41.

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science.1233232

Cite this article as J. Antoniadis et al., Science 340, 1233232 (2013). DOI: 10.1126/science.1233232

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A Massive Pulsar in a CompactRelativistic BinaryJohn Antoniadis,1* Paulo C. C. Freire,1 Norbert Wex,1 Thomas M. Tauris,2,1 Ryan S. Lynch,3

Marten H. van Kerkwijk,4 Michael Kramer,1,5 Cees Bassa,5 Vik S. Dhillon,6 Thomas Driebe,7

Jason W. T. Hessels,8,9 Victoria M. Kaspi,3 Vladislav I. Kondratiev,8,10 Norbert Langer,2

Thomas R. Marsh,11 Maura A. McLaughlin,12 Timothy T. Pennucci,13 Scott M. Ransom,14

Ingrid H. Stairs,15 Joeri van Leeuwen,8,9 Joris P. W. Verbiest,1 David G. Whelan13

Many physically motivated extensions to general relativity (GR) predict substantial deviations inthe properties of spacetime surrounding massive neutron stars. We report the measurement ofa 2.01 T 0.04 solar mass (M◉) pulsar in a 2.46-hour orbit with a 0.172 T 0.003 M◉ white dwarf.The high pulsar mass and the compact orbit make this system a sensitive laboratory of a previouslyuntested strong-field gravity regime. Thus far, the observed orbital decay agrees with GR,supporting its validity even for the extreme conditions present in the system. The resultingconstraints on deviations support the use of GR-based templates for ground-based gravitationalwave detectors. Additionally, the system strengthens recent constraints on the properties ofdense matter and provides insight to binary stellar astrophysics and pulsar recycling.

Neutron stars (NSs) with masses above 1.8solar mass (M◉) manifested as radio pul-sars are valuable probes of fundamental

physics in extreme conditions unique in the ob-servable universe and inaccessible to terrestrialexperiments. Their highmasses are directly linkedto the equation-of-state (EOS) of matter at supra-nuclear densities (1, 2) and constrain the lowermass limit for production of astrophysical blackholes (BHs). Furthermore, they possess extremeinternal gravitational fields, which result in grav-itational binding energies substantially higher thanthose found inmore common, 1.4-M◉NSs.Modi-fications to general relativity (GR), often moti-vated by the desire for a unified model of the four

fundamental forces, can generally imprint mea-surable signatures in the gravitational waves (GWs)radiated by systems containing such objects, evenif deviations from GR vanish in the solar systemand in less-massive NSs (3–5).

However, the most massive NSs known to-day reside in long-period binaries or other sys-tems unsuitable for GWradiation tests. Identifyinga massive NS in a compact, relativistic binary isthus of key importance for understanding gravity-matter coupling under extreme conditions. Fur-thermore, the existence of a massive NS in arelativistic orbit can also be used to test currentknowledge of close binary evolution.

Results

PSR J0348+0432 and Optical Observationsof Its CompanionPSR J0348+0432, a pulsar spinning at 39 ms in a2.46-hour orbit with a low-mass companion, wasdetected by a recent survey (6, 7) conducted withthe Robert C. Byrd Green Bank Telescope (GBT).Initial timing observations of the binary yieldedan accurate astrometric position, which allowedus to identify its optical counterpart in the SloanDigital Sky Survey (SDSS) archive (8). The col-ors and flux of the counterpart are consistent witha low-mass white dwarf (WD)with a helium coreat a distance of d ∼ 2.1 kpc. Its relatively highapparent brightness (g′ = 20.71 T 0.03 mag)allowed us to resolve its spectrum by using theApache Point Optical Telescope. These observa-tions revealed deep hydrogen lines, typical of low-massWDs, confirmingourpreliminary identification.The radial velocities of the WD mirrored that ofPSR J0348+0432, also verifying that the two starsare gravitationally bound.

In December 2011, we obtained phase-resolvedspectra of the optical counterpart by using the

FORS2 spectrograph of the Very Large Telescope(VLT). For each spectrum, we measured the ra-dial velocity, which we then folded modulo thesystem’s orbital period. Our orbital fit to thevelocities constrains the semiamplitude of theirmodulation to be KWD = 351 T 4 km s−1 (1-s con-fidence interval) (Fig. 1; see also Materials andMethods). Similarly, the orbital solution fromradio-pulsar timing yields KPSR = 30.008235 T0.000016 km s−1 for the pulsar. Combined, theseconstraints imply a mass ratio, q = MPSR/MWD =KWD/KPSR = 11.70 T 0.13.

Modeling of the Balmer-series lines in a highsignal-to-noise average spectrum formed by thecoherent addition of individual spectra (Fig. 1B)shows that the WD has an effective temperatureof Teff = 10,120 T 47stat T 90sys K and a surfacegravity of log10 [g (cm s−2)] = 6.035 T 0.032stat T0.060sys dex. Here, the systematic error is anoverall estimate of uncertainties resulting from ourfitting technique and flux calibration (8). We foundno correlation of this measurement with orbitalphase and no signs of rotationally induced broad-ening in the spectral lines (8). Furthermore, wesearched for variability by using theULTRACAMinstrument (9) on the 4.2-m William-HerschelTelescope in La Palma, Spain. The light curves(fig. S3), spanning 3 hours in total, have a root-mean-square (rms) scatter of ∼0.53, 0.07, and0.08 mag in u′, g′, and r′, respectively, and showno evidence for variability over the course of theobservations. The phase-folded light curve showsno variability either. Additionally, our calibratedmagnitudes are consistent with the SDSS catalogmagnitudes, implying that the WD shone at aconstant flux over this ∼5 year time scale (8).

Mass of the White Dwarf

The surface gravity of theWD scales with its massand the inverse square of its radius (g≡GMWD/RWD

2,whereG is Newton’s gravitational constant). Thus,the observational constraints combined with atheoretical finite-temperature mass-radius rela-tion for low-massWDs yield a unique solution forthe mass of the companion (10). Numerous suchmodels exist in the literature, the most detailed ofwhich are in good agreement for very-low-massWDs (<0.17 to 0.18 M◉) but differ substantiallyfor higher masses [e.g., (11–13)]. The main reasonfor this is the difference in the predicted size ofthe hydrogen envelope, which determines wheth-er the main energy source of the star is residualhydrogen burning (for “thick” envelopes) or thelatent heat of the core (for “thin” envelopes).

In the most widely accepted scenario, WDslose their thick hydrogen envelope only if theirmass exceeds a threshold. The exact location ofthe latter is still uncertain but estimated to bearound 0.17 to 0.22M◉ [e.g., (11–13)]. Two otherpulsars with WD companions, studied in the lit-erature, strongly suggest that this transition thresh-old is indeed most likely close to 0.2M◉ (10, 14).In particular, PSR J1909−3744 has a large char-acteristic age of several gigayears (Gy) and aWD

RESEARCHARTICLE

1Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69,53121 Bonn, Germany. 2Argelander Institut für Astronomie,Auf dem Hügel 71, 53121 Bonn, Germany. 3Department ofPhysics, McGill University, 3600University Street, Montreal, QCH3A 2T8, Canada. 4Department of Astronomy and Astrophysics,University of Toronto, 50 St. George Street, Toronto, ON M5S3H4, Canada. 5Jodrell Bank Centre for Astrophysics, The Uni-versity of Manchester, Alan Turing Building, Manchester M139PL, UK. 6Department of Physics and Astronomy, University ofSheffield, Sheffield S3 7RH, UK. 7Deutsches Zentrum für Luft- undRaumfahrt e.V. (DLR), Raumfahrtmanagement, KönigswintererStr. 522-524, 53227 Bonn, Germany. 8ASTRON, the NetherlandsInstitute for Radio Astronomy, Postbus 2, 7990 AA Dwingeloo,Netherlands. 9Astronomical Institute Anton Pannekoek, Uni-versity of Amsterdam, Science Park 904, 1098 XH Amsterdam,Netherlands. 10Astro Space Center of the Lebedev PhysicalInstitute, Profsoyuznaya str. 84/32, Moscow 117997, Russia.11Department of Physics, University of Warwick, Coventry CV47AL, UK. 12Department of Physics, West Virginia University,111 White Hall, Morgantown, WV 26506, USA. 13Departmentof Astronomy, University of Virginia, Post Office Box 400325,Charlottesville, VA 22904, USA. 14National Radio AstronomyObservatory, 520 Edgemont Road, Charlottesville, VA 22903,USA. 15Department of Physics and Astronomy, University ofBritish Columbia, 6224 Agricultural Road, Vancouver, BC V6T1Z1, Canada.

*Corresponding author. E-mail: jantoniadis@mpifr-bonn.mpg.de

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Fig. 1. Radial velocities and spectrum of the white dwarf companionto PSR J0348+0432. (A) Radial velocities of the WD companion to PSRJ0348+0432 plotted against the orbital phase (shown twice for clarity). Over-plotted is the best-fit orbit of the WD (blue line) and the mirror orbit of thepulsar (green). Error bars indicate 1-s confidence intervals. (B) Details of thefit to the Balmer lines (Hb to H12) in the average spectrumof theWD companion

to PSR J0348+0432 created by the coherent addition of 26 individual spectrashifted to zero velocity. Lines from Hb (bottom) to H12 are shown. The redsolid lines are the best-fit atmospheric model (see text). Two models, one withTeff = 9900 K and log10g = 5.70 and one with Teff = 10,200 K and log10 g =6.30, each ∼ 3-s off from the best-fit central value (including systematics), areshown for comparison (dashed blue lines).

Fig. 2. Mass measurement of the white dwarf companion to PSRJ0348+0432. (A) Constraints on Teff and g for the WD companion to PSRJ0348+0432 compared with theoretical WD models. The shaded areas depictthe c2 − c2min = 2.3, 6.2, and 11.8 intervals (equivalent to 1-, 2-, and 3-s) ofour fit to the average spectrum. Dashed lines show the detailed theoretical

cooling models of (11). Continuous lines depict tracks with thick envelopes formasses up to ∼0.2M◉ that yield the most conservative constraints for the massof the WD. (B) Finite-temperature mass-radius relations for our models to-gether with the constraints imposed from modeling of the spectrum. Lowmass–high temperature points are an extrapolation from lower temperatures.

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companionwith awell-determinedmass of 0.20M◉(15) that appears to be hot (10), suggesting that itsenvelope is thick. For this reason, we base theWD mass estimate on cooling tracks with thickhydrogen atmospheres for masses up to 0.2M◉,which we constructed by using the MESA stellarevolution code (8, 16). Initial models were builtfor masses identical to the ones in (11), for whichprevious comparisons have yielded good agree-ment with observations (14), with the additionof tracks with 0.175 and 0.185 M◉ for finercoverage (Fig. 2). For masses up to 0.169M◉, ourmodels show excellent agreement with (11);however, our 0.196 M◉ model is quite different,because it has a thick envelope instead of a thinone. Being closer to the constraints for the WDcompanion to PSR J0348+0432, it yields a moreconservative mass constraint, MWD = 0.165 to0.185 at 99.73% confidence (Fig. 3 and Table 1),which we adopt. The corresponding radius isRWD = 0.046 to 0.092 R◉ at 99.73% confidence.Our models yield a cooling age of tcool ∼ 2 Gy.

Pulsar Mass

The derived WD mass and the observed massratio q imply a NSmass in the range from 1.97 to2.05M◉ at 68.27% or 1.90 to 2.18M◉ at 99.73%confidence. Hence, PSR J0348+0432 is only thesecond NS with a precisely determined massaround 2M◉, after PSR J1614−2230 (2). It has a3-s lower mass limit 0.05M◉ higher than the latterand therefore provides a verification, using a dif-ferent method, of the constraints on the EOS ofsuperdense matter present in NS interiors (2, 17).For these masses and the known orbital period,GR predicts that the orbital period should decrease

at the rate of P:GRb ¼ ð−2:58þ0:07

−0:11 Þ � 10−13 s s−1

(68.27%confidence) because of energy loss throughGW emission.

Radio Observations

Since April 2011, we have been observing PSRJ0348+0432 with the 1.4-GHz receiver of the305-m radio telescope at the Arecibo Observatoryby using its four wide-band pulsar processors (18).In order to verify the Arecibo data, we have beenindependently timing PSR J0348+0432 at 1.4 GHzby using the 100-m radio telescope in Effelsberg,Germany. The two timing data sets produce con-sistent rotational models, providing added con-fidence in both. Combining the Arecibo andEffelsberg data with the initial GBTobservations(7), we derived the timing solution presented inTable 1. To match the arrival times, the solutionrequires a significant measurement of orbital de-cay, P

:b ¼ −2:73 � 10−13 T 0:45� 10−13 s s−1

(68.27% confidence).The total proper motion and distance estimate

(Table 1) allowed us to calculate the kinematiccorrections to P

:b from its motion in the Galaxy,

plus any contribution from possible variations ofG: dP

:b ¼ 0:016� 10−13 T 0:003� 10−13 s s−1.

This is negligible compared to the measurementuncertainty. Similarly, the small rate of rotationalenergy loss of the pulsar (Table 1) excludes anysubstantial contamination resulting frommass lossfrom the system; furthermore, we can excludesubstantial contributions to P

:b from tidal effects

[see (8) for details]. Therefore, the observedP:b is

caused by GW emission, and its magnitude isentirely consistent with the one predicted by GR:P:b=P

:GRb ¼ 1:05 T 0:18 (Fig. 3).

If we assume that GR is the correct theory ofgravity, we can then derive the component massesfrom the intersection of the regions allowed byq and P

:b (Fig. 3): MWD ¼ 0:177þ0:017

−0:018 M◉ andMPSR ¼ 2:07þ0:20

−0:21 M◉ (68.27% confidence). Thesevalues are not too constraining yet. However, theuncertainty of the measurement of P

:b decreases

with T baseline−5/2 (where Tbaseline is the timing base-

line); therefore, this method will yield very precisemass measurements within a couple of years.

Discussion

PSR J0348+0432 as a Testbed for GravityThere are strong arguments for GR not to be validbeyond a (yet unknown) critical point, like itsincompatibility with quantum theory and its pre-diction of the formation of spacetime singularities.Therefore, it remains an open question whetherGR is the final description of macroscopic gravity.This strongly motivates testing gravity regimesthat have not been tested before, in particularregimes where gravity is strong and highly non-linear. Presently, binary pulsars provide the besthigh-precision experiments to probe strong-fielddeviations from GR and the best tests of theradiative properties of gravity (19–23). The orbitalperiod of PSR J0348+0432 is only 15 s longerthan that of the double pulsar system PSR J0737–3039, but it has ∼two times more fractional grav-itational binding energy than each of the double-pulsar NSs. This places it far outside the presentlytested binding energy range (Fig. 4A) (8). Be-cause the magnitude of strong-field effects gener-ally depends nonlinearly on the binding energy,the measurement of orbital decay transforms the

Fig. 3. System masses andorbital-inclination constraints.Constraints on system masses andorbital inclination from radio andoptical measurements of PSRJ0348+0432 and its WD compan-ion. Each triplet of curves corre-sponds to the most likely valueand standard deviations (68.27%confidence) of the respective pa-rameters. Of these, two (q and MWD)are independent of specific gravitytheories (in black). The contourscontain the 68.27 and 95.45% ofthe two-dimensional probabilitydistribution. The constraints fromthe measured intrinsic orbital decay(P:bint, in orange) are calculated as-

suming that GR is the correct theoryof gravity. All curves intersect inthe same region, meaning thatGR passes this radiative test (8).(Bottom left) cosi-MWD plane. Thegray region is excluded by the con-dition MPSR > 0. (Bottom right)MPSR-MWD plane. The gray regionis excluded by the condition sini ≤ 1. The lateral graphs depict the one-dimensional probability-distribution function for the WD mass (right), pulsar mass(top right), and inclination (top left) based on the mass function, MWD, and q.

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system into a gravitational laboratory for a pre-viously untested regime, qualitatively very differentfrom what was accessible in the past.

In physically consistent and extensively studiedalternatives, gravity is generally mediated by ex-tra fields (e.g., scalar) in addition to the tensorfield of GR (5). A dynamical coupling betweenmatter and these extra fields can lead to prom-inent deviations from GR that only occur at thehigh gravitational binding energies of massiveNSs. One of the prime examples is the strong-field scalarization discovered in (3). If GR is notvalid, in the PSR J0348+0432 system wheresuch an object is closely orbited by a weakly self-gravitating body, one generally expects a viola-tion of the strong equivalence principle that inturn leads to amodification in the emission ofGWs.Although in GR the lowest source multipole thatgenerates gravitational radiation is the quadrupole,alternative gravity theories generally predict thepresence of monopole and dipole radiation on topof a modification of the other multipoles (5). For abinary system, the leading change in the orbitalperiod is then given by the dipole contribution,which for a (nearly) circular orbit reads (8)

:P

dipolar

b ≃

−4p2Gc3Pb

MPSRMWD

MPSR þMWDðaPSR − aWDÞ2 ð1Þ

where aPSR is the effective coupling strengthbetween the NS and the ambient fields respon-sible for the dipole moment (e.g., scalar fields inscalar-tensor gravity) and aWD is the same pa-rameter for the WD companion. The WD com-panion to PSR J0348+0432 has a fractionalgravitational binding energy (Egrav/MWDc

2) ofjust −1.2 × 10−5 and is therefore a weakly self-gravitating object. Consequently, aWD is practi-cally identical to the linear field-matter couplinga0, which is well constrained (|a0| < 0.004) insolar system experiments (20, 24).

For aPSR, the situation is very different. Evenif a0 is vanishingly small, aPSR can have valuesclose to unity, because of a nonlinear behavior ofgravity in the interaction between matter and thegravitational fields in the strong-gravity regimeinside NSs (3, 4). A significant aPSR for NSs upto 1.47 M◉ has been excluded by various binarypulsar experiments (8, 23). The consistency ofthe observed GW damping (P

:b) with the GR

predictions for PSR J0348+0432 (Table 1) im-plies |aPSR − a0 | < 0.005 (95% confidence) andconsequently excludes significant strong-field de-viations, even for massive NSs of ∼2 M◉.

To demonstrate in some detail the implica-tions of our results for possible strong-field de-viations of gravity from Einstein’s theory, weconfront our limits on dipolar radiation with aspecific class of scalar-tensor theories, in whichgravity is mediated by a symmetric second-ranktensor field, gmn

∗, and by a long-range (massless)scalar field, ϕ. Scalar-tensor theories are well

motivated and consistent theories of gravity, ex-tensively studied in the literature [e.g., (25, 26)].For this reason, they are the most natural frame-work for us to illustrate the gravitational phenome-na that can be probed with PSR J0348+0432.

Concerning the EOS of NS matter, in ourcalculations we use the rather stiff EOS “.20” of(27) that supports (in GR) NSs of up to 2.6 M◉.We make this choice for two reasons: (i) A stifferEOSgenerally leads tomore conservative limitswhenconstraining alternative gravity theories, and (ii)

it is able to support even more massive NSs thanPSR J0348+0432, which are likely to exist (28–30).Furthermore, in most of our conclusions a specificEOS is used only for illustrative purposes, and theobtained generic results are EOS independent.

Figure 4B illustrates how PSR J0348+0432probes a nonlinear regime of gravity that has notbeen tested before. A change in EOS and gravitytheory would lead to a modified functional shapefor aPSR. However, this would not change thegeneral picture: Even in the strong gravitational

Table 1. Observed and derived parameters for the PSR J0348+0432 system. Timing parametersfor the PSR J0348+0432 system, indicated with their 1-s uncertainties as derived by tempo2 whereappropriate (numbers in parentheses refer to errors on the last digits). The timing parameters arecalculated for the reference epoch modified Julian date (MJD) 56000 and are derived from TOAs in therange MJD 54872 to 56208.

Optical parametersEffective temperature, Teff (K) 10120 T 47stat T 90sysSurface gravity, log10[g(cm s−1)] 6.035 T 0.032stat T 0.060sysSemiamplitude of orbital radial velocity, KWD (km s−1) 351 T 4Systemic radial velocity relative to the Sun, g (km s−1) −1 T 20

Timing parametersRight ascension, a (J2000) 03h 48m 43s.639000(4)Declination, d (J2000) +04° 32′ 11.′′4580(2)Proper motion in right ascension, ma (mas year−1) +4.04(16)Proper motion in declination, md (mas year

−1) +3.5(6)Parallax, pd (mas) 0.47*Spin frequency, n (Hz) 25.5606361937675(4)First derivative of n, v

:(10−15 Hz s−1) −0.15729(3)

Dispersion measure, DM (cm−3 pc) 40.46313(11)First derivative of DM, DM1 (cm−3 pc year−1) −0.00069(14)Orbital period, Pb (day) 0.102424062722(7)Time of ascending node, Tasc (MJD) 56000.084771047(11)Projected semimajor axis of the pulsar orbit, x (lt-s) 0.14097938(7)h ≡ esinw +1.9 × 10−6 T 1.0 × 10−6

k ≡ ecosw +1.4 × 10−6 T 1.0 × 10−6

First derivative of Pb, P:b (10

−12 s s−1) −0.273(45)Derived parameters

Galactic longitude, l 183.°3368Galactic latitude, b −36.°7736Distance, d (kpc) 2.1(2)Total proper motion, m (mas year−1) 5.3(4)Spin period, P (ms) 39.1226569017806(5)First derivative of P, P

:(10−18 s s−1) 0.24073(4)

Characteristic age, tc (Gy) 2.6Transverse magnetic field at the poles, B0 (10

9 G) ∼2Rate or rotational energy loss, E

:(1032 erg s−1) ∼1.6

Mass function, f (M◉) 0.000286778(4)Mass ratio, q ≡ MPSR/MWD 11.70(13)White dwarf mass, MWD (M◉) 0.172(3)Pulsar mass, MPSR (M◉) 2.01(4)“Range” parameter of Shapiro delay, r (ms) 0.84718*“Shape” parameter of Shapiro delay, s ≡ sini 0.64546*White dwarf radius, RWD (R◉) 0.065(5)Orbital separation, a (109 m) 0.832Orbital separation, a (R◉) 1.20Orbital inclination, i 40.°2(6)P:b predicted by GR, P

:bGR (10−12 s s−1) −0.258+0.008−0.011

P:b=P:bGR 1.05 T 0.18

Time until coalescence, tm (My) ∼400

*For these timing parameters, we adopted the optically derived parameters (see text for details).

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field of a 2 M◉ NS, gravity seems to be welldescribed by GR, and there is little space for anydeviations, at least in the form of long-rangefields, which influence the binary dynamics.

Short-range interactions, like massive Brans-Dickegravity (31) with a sufficiently large scalar mass(heavier than ∼10−19 eV/c2), cannot be excludedby PSR J0348+0432.

Constraints on the Phase Evolution ofNeutron Star Mergers

One of the most promising sources of GWs thatmight be detected by ground-based laser inter-ferometers like the LIGO [Laser InterferometerGravitational Wave Observatory (32)] and theVIRGO (33) projects (34) are in-spiraling com-pact binaries, consisting of NSs and BHs, whoseorbits are decaying toward a final coalescence be-cause of GW damping. As the signal sweeps infrequency through the detectors’ typical sensitivebandwidth between about 20 Hz and a few kHz,the GW signal will be deeply buried in the broad-band noise of the detectors (34). To detect it, onewill have to apply a matched filtering technique,that is, correlate the output of the detector with atemplate wave form. Consequently, it is crucial toknow the binary’s orbital phase with high accu-racy for searching and analyzing the signals fromin-spiraling compact binaries. Typically, one aimsto lose less than one GW cycle in a signal with∼104 cycles. For this reason, within GR such cal-culations have been conducted with great effortby various groups up to the 3.5 post-Newtonianorder, that is, all (nonvanishing) terms up to order(v/c)7 (where v is relative orbital velocity of the bi-nary’s components), providing sufficient accuracyfor a detection (35–37).

If the gravitational interaction between twocompact masses is different from GR, the phaseevolution over the last few thousand cycles, whichfall into the bandwidth of the detectors, might betoo different from the (GR) template to extract

Fig. 4. Probing strong field gravity with PSR J0348+0432. (A) Frac-tional gravitational binding energy as a function of the inertial mass of a NS inGR (blue curve). The dots indicate the NSs of relativistic NS-NS (in green) andNS-WD (in red) binary-pulsar systems currently used for precision gravitytests (8). (B) Effective scalar coupling as a function of the NS mass, in the“quadratic” scalar-tensor theory of (4). For the linear coupling of matter to the

scalar field, we have chosen a0 = 10−4, a value well below the sensitivity of anynear-future solar system experiment [e.g., GAIA (62)]. The solid curves cor-respond to stable NS configurations for different values of the quadraticcoupling b0: −5 to −4 (top to bottom) in steps of 0.1. The yellow area indicatesthe parameter space allowed by the best current limit on |aPSR − a0| (23),whereas only the green area is in agreement with the limit presented here.

Fig. 5. Constraints onthephaseoffset ingrav-itational wave cycles inthe LIGO/VIRGO bands.Maximum offset in GWcycles in the LIGO/VIRGOband (20 Hz to a few kHz)between the GR templateand the true phase evo-lution of the in-spiral inthe presence of dipolarradiation as a function ofthe effective coupling ofthemassive NS for two dif-ferent system configura-tions: a 2 M◉ NS with a1.25 M◉ NS (NS-NS) anda merger of a 2 M◉ NSwith a 10M◉ BH (NS-BH).In the NS-NS case, thegreen line is for aB = a0,and the gray dotted linerepresents the most con-servative, rather unphys-ical, assumptiona0=0.004and aB = 0 (8). In the NS-BH case, aB is set to zero (from the assumption that no-hair theorems hold). Theblue line is fora0 = 0.004 (solar system limit for scalar-tensor theories), and the purple line representsa0 = 0.The gray area to the right of the red line is excluded by PSR J0348+0432. In this plot, there is no assumptionconcerning the EOS.

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the signal from the noise. In scalar-tensor gravity,for instance, the evolution of the phase is drivenby radiation reaction, which is modified becausethe system loses energy to scalar GWs (38, 39).Depending on the difference between the effec-tive scalar couplings of the two bodies, aA andaB, the 1.5 post-Newtonian dipolar contributionto the phase evolution could drive the GW signalmany cycles away from the GR template. For thisreason, it is desirable that potential deviations fromGR in the interaction of two compact objects canbe tested and constrained before the start of theadvanced GW detectors. For “canonical” 1.4M◉NSs and long-range gravitational fields, this hasalready been achieved to a high degree in binarypulsar experiments, for example, (39). So far, thebest constraints on dipolar gravitational wave damp-ing in compact binaries come from the observationsof the millisecond pulsar PSR J1738+0333 (23).However, as discussed in detail above, thesetiming experiments are insensitive to strong-fielddeviations that might only become relevant in thestrong gravitational fields associated with high-massNSs. Consequently, the dynamics of amergerof a 2M◉NSwith a “canonical”NSor aBHmighthave a significant contribution from dipolar GWs.With our constraints on dipolar radiation dampingfrom the timing observations of PSR J0348+0432,given above, we can already exclude a deviationof more than ∼0.5 cycles from the GR templateduring the observable in-spiral caused by addi-tional long-range gravitational fields for thewhole range of NS masses observed in nature[see Fig. 5 and (8) for the details of the calculation].This compares to the precision of GR templatesbased on the 3.5 post-Newtonian approximation(35, 37). Furthermore, in an extension of the ar-guments in (38, 39) to massive NSs, our resultimplies that binary pulsar experiments are al-ready more sensitive for testing such deviationsthan the upcoming advanced GW detectors.

Lastly, as mentioned before, our results onPSR J0348+0432 cannot exclude dipolar radia-tion from short-range fields. Hence, if the rangeof the additional field in the gravitational inter-action happens to lie between the wavelength oftheGWs of PSR J0348+0432 and thewavelengthof the merger signal (∼109 cm; ∼10−13 eV/c2), thenthe considerations concerning the applicability ofthe GR template given here do not apply. On theother hand, in such a case the combination ofbinary pulsar and LIGO/VIRGO experiments canbe used to constrain the mass of this extra field.

Formation and Past and Future Evolutionof the System

The measured spin period, P, and spin-periodderivative P

:of PSR J0348+0432, combined with

the masses and orbital period of the system(Table 1), form a peculiar set of parameters thatgives insight to binary stellar evolution. The short2.46-hour orbital period is best understood fromevolution via a common envelope where the NSis captured in the envelope of theWD progenitor,leading to efficient removal of orbital angular

momentum on a short time scale of ∼103 years(40). This implies that the NS was born with aninitial mass close to its current mass of 2.01 M◉,because very little accretion was possible.Whereasthe slow spin period of ∼39 ms and the unusuallystrong magnetic field (8) of a few 109 G (Table 1)provide further support for this scenario, the lowWD mass contradicts the standard common-envelope hypothesis by requiring a progenitorstar mass smaller than 2.2 M◉, because moremassive stars would leave behind more massivecores (8, 41). For such low donor star masses,however, themass ratio of the binary componentsis close to unity, leading to dynamically stablemass transfer without forming a common enve-lope (42, 43). One potential solution to this massdiscrepancy for common-envelope evolution isto assume that the original mass of the WD was≥0.4M◉ and that it was subsequently evaporatedby the pulsar wind (44) when PSR J0348+0432was young and energetic, right after its recyclingphase (8). Such an evolution could also help ex-plain the formation of another puzzling system,PSR J1744−3922 (45). However, we find thatthis scenario is quite unlikely given that the ob-served spectrum of the WD in PSR J0348+0432only displays hydrogen lines, which is not ex-pected if the WD was indeed a stripped remnantof amuchmoremassive helium or carbon-oxygenWD. Furthermore, it is unclear why this evapo-ration process should have come to a completestop when the WD reached its current mass of0.17 M◉. A speculative hypothesis to circum-vent the above-mentioned problems would be acommon-envelope evolution with hypercriticalaccretion, where ∼0.6 M◉ of material was effi-ciently transferred to a 1.4 M◉ NS (8, 46).

An alternative, and more promising, forma-tion scenario is evolution via a close-orbit low-mass x-ray binary (LMXB) with a 1.0 to 1.6M◉donor star that suffered from loss of orbital an-gular momentum because of magnetic braking(43, 47, 48). This requires a finely tuned trun-cation of the mass-transfer process, which is not

yet understood in detail but which is also requiredfor other known recycled pulsars (8) with shortorbital periods of Pb ≤ 8 hours and low-mass he-lium WD companions with MWD ≈ 0.14 to0.18M◉. The interplay betweenmagnetic braking,angular momentum loss from stellar winds (pos-sibly caused by irradiation), and mass ejectedfrom the vicinity of the NS is poorly understood,and current stellar evolution models have diffi-culties reproducing these binary pulsar systems.One issue is that the converging LMXBs mostoften do not detach but keep evolving with con-tinuous mass transfer to more and more compactsystems with Pb ≤ 1 hour and ultralight donormasses smaller than 0.08 M◉.

By using the Langer stellar evolution code(8), we have attempted to model the formation ofthe PSR J0348+0432 system via LMXB evolu-tion (Fig. 6). To achieve this, we forced the donorstar to detach its Roche lobe at Pb ∼ 5 hours, suchthat the system subsequently shrinks in size to itspresent value of Pb ≅ 2.46 hours because of GWradiation within 2 Gy, the estimated cooling ageof the WD. An illustration of the past and futureevolution of PSR J0348+0432 from the two dif-ferent formation channels is shown in Fig. 7.

An abnormality of PSR J0348+0432 in viewof the LMXB model is its slow spin period ofP ∼ 39ms and, in particular, the high value for thespin period derivative, P

: ¼ 2:41� 10−19 s s−1.These values correspond to an inferred surfacemagnetic flux density of B ∼ 2 × 109 G, which ishigh compared with most other recycled pulsars(49). However, a high B value naturally explainsthe slow spin period of PSR J0348+0432 from acombination of spin-down during the Roche-lobedecoupling phase (50) and subsequent magneticdipole radiation from this high-magnetic-fieldpulsar (8, 49). Another intriguing question con-cerning this evolutionary channel is the spread inNS masses. In the five currently known NS-WDsystems with Pb ≤ 8 hours, the NS masses span alarge range of values, ranging from ∼ 1.4 up to2.0 M◉. The lower masses imply that the mass

Fig. 6. Past and futureorbital evolution of PSRJ0348+0432. Formationof PSR J0348+0432 fromour converging LMXBmod-el calculation.Theplot showsorbital period as a func-tion of time (calibrated topresent day). The progen-itordetached from itsRochelobe about 2 Gy ago (ac-cording to the estimatedcooling age of the WD)when Pb ≅ 5 hours, andsince then GW dampingreduced the orbital peri-od to its present value of2.46 hours (marked witha star). UCXB, ultracompact x-ray binary.

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transfer during the LMXB phase is extremelyinefficient: Only about 30% of the material leav-ing the donor is accreted by the NS (14, 15). Ifthis is indeed the case and if one assumes that thephysical processes that lead to the formation ofthese systems are similar, it is likely that PSRJ0348+0432 was born with an initial mass of1.7 T 0.1M◉, providing further support for a non-negligible fraction of NSs born massive (41).

Emission of GWs will continue to shrink theorbit of PSR J0348+0432, and in 400 My (whenPb ≅ 23 min) the WD will fill its Roche lobe andpossibly leave behind a planet orbiting the pulsar(51, 52). Alternatively, if PSR J0348+0432 is nearthe upper-mass limit for NSs, then a BH mightform via accretion-induced collapse of themassiveNS in a cataclysmic, g-ray burst–like event (53).

Materials and Methods

Radial Velocities and Atmospheric ParametersA detailed log of the VLT observations can befound in (8) (fig. S1 and table S1). We extractedthe spectra following closely the method used in(14) and compared them with template spectra tomeasure the radial velocities. Our best fits for theWDhad reducedc2minimumvalues of c2red, min =1.0 to 1.5 (8). Uncertainties were taken to be the

difference in velocity over which c2 increases byc2red, min to account for the fact that c2red, min isnot equal to unity (14). After transforming themeasurements to the reference frame of the solarsystem barycenter (SSB), we folded them by usingthe radio-timing ephemeris described below. Wethen fitted for the semiamplitude of the radial ve-locity modulation, KWD, and the systemic radialvelocity with respect to the SSB, g, assuming acircular orbit and keeping the time of passagethrough the ascending node, Tasc, fixed to thebest-fit value of the radio-timing ephemeris.Our solution yields KWD = 351 T 4 km s−1 andg = −1 T 20 km s−1 (8).

Details of the Balmer lines in the averagespectrum of PSR J0348+0432, created by thecoherent addition of the individual spectra shiftedto zero velocity, are shown in Fig. 1B. We mod-eled the spectrum by using a grid of detailedhydrogen atmospheres (54). These models incor-porate the improved treatment of pressure broad-ening of the absorption lines presented in (55).Asmentioned above, our fit yields Teff = 10,120 T35stat T 90sys K for the effective temperature andlog10 g = 6.042 T 0.032stat T 0.060sys for thesurface gravity (8). The c2 map shown in Fig. 2Ais inflated to take into account systematic un-certainties. The average spectrumwas also searched

for rotational broadening. By using the analyticprofile of (56) to convolve themodel atmospheres,we scanned the grid of velocities 0 ≤ vrsini ≤2000 km s−1 with a step size of 100 km s−1. Theresult is consistent with no rotation and our 1-supper limit is vr sini ≤ 430 km s−1.

Modeling of the White Dwarf Mass

Low-mass WDs are thought to form naturallywithin the age of the universe via mass transfer ina binary, either through Roche-lobe overflow orcommon-envelope evolution. In both cases, theWD forms when the envelope mass drops belowa critical limit, which depends primarily on themass of the stellar core, forcing the star to con-tract and detach from its Roche lobe. After thecontraction, the mass of the relic envelope isfixed for a given core mass, but further reductionof its size may occur shortly before the star entersthe final cooling branch because of hydrogen-shell flashes that force the star to reexpand togiant dimensions. Additional mass removal viaRoche-lobe overflow, as well as rapid hydrogen-shell burning through the CNO cycle, may thenlead to a decrease of the envelope size and affectthe cooling history and atmospheric parameters. Toinvestigate the consequence of a reduced envelopesize for the WD companion to PSR J0348+0432,we constructed WD models in which we treatthe envelope mass as a free parameter (8). For theWD companion to PSR J0348+0432, an enve-lope mass below the critical limit for hydrogenfusion is not likely for two main reasons.

First, for a pure helium composition, the ob-served surface gravity translates to aWDmass of∼0.15M◉ and a cooling age of ∼ 20My, which isanomalously small. Such a small age would alsoimply a large increase in the birth and in-spiralrate of similar relativistic NS-WD systems (57).Furthermore, postcontraction flash episodes onthe WD are not sufficient to remove the entireenvelope. Therefore, creation of a pure heliumWD requires large mass loss rates before theprogenitor contracts, which is unlikely. For smallprogenitor masses (≤1.5M◉), large mass loss pre-vents contraction, and the star evolves to a semi-degenerate companion on a nuclear time scalethat exceeds the age of the universe. For moremassive progenitors (>1.5 M◉), the core growsbeyond ∼0.17 M◉ in a short time scale and ul-timately leaves a too-massive WD.

Second, even for envelope hydrogen fractionsas low as Xavg = 10−6, the observed temperatureand surface gravity cannot be explained simulta-neously: The low surface gravity would again re-quire a small mass of ∼0.15M◉. However, in thiscase the surface hydrogen acts like an insulator,preventing the heat of the core from reaching thestellar surface. As a result, temperatures as high as10,000 K can only be reached for masses above∼0.162M◉.

Past a critical envelope mass, the pressure atthe bottom of the envelope becomes high enoughto initiate hydrogen-shell burning. The latter thenbecomes the dominant energy source, and the

Fig. 7. Possible forma-tion channels and finalfate of PSR J0348+0432.An illustration of the for-mation and evolution ofPSR J0348+0432. The zero-agemain sequence (ZAMS)mass of the NS progenitoris likely to be 20 to 25M◉,whereas the WD progeni-tor had a mass of 1.0 to1.6 M◉ (LMXB) or 2.2 to5 M◉ (common envelope,CE), depending on its for-mationchannel. In∼400My(when Pb ∼ 23 min), theWDwill fill its Roche lobe,and the system becomesanUCXB, leading to the for-mation of a BH or a pulsarwithaplanet.RLO,Roche-lobeoverflow; SN, supernova;IMXB, intermediate-massx-ray binary.

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evolutionary time scale increases; the radius ofthe star grows by ∼50% (depending on themass),expanding further for larger envelopes. The de-pendence of the surface gravity on the radius im-plies that the observed value translates to a highermass as the envelope mass increases. Therefore,the most conservative lower limit for the WDmass (and thus for PSR J0348+0432, given thefixed mass ratio) is obtained if one considersmodels with the absolute minimum envelope massrequired for hydrogen burning. In this scenario,the mass of the WD is in the range from 0.162 to0.181M◉ at 99.73% confidence (8). Despite thisconstraint being marginally consistent with ourobservations (8), it is not likely correct because ofthe high degree of fine-tuning.

For these reasons, we have adopted theassumption that the WD companion to PSRJ0348+0432 has a thick envelope, as generallyexpected for WDs with such low surface gravityand high temperature.

Radio Timing Analysis

The Arecibo observing setup (8) and data reduc-tion are similar to the well-tested ones describedin (23). Special care was taken with saving rawsearch data, which allows for iterative improve-ment of the ephemeris and eliminates orbitalphase–dependent smearing of the pulse profiles,which might contaminate the measurement ofP:b (58). From this analysis, we derived 7773 in-

dependent measurements of pulse times of arrival(TOAs) with a rms uncertainty smaller than10 ms. Similarly the Effelsberg observations yielda total of 179 TOAs with uncertainties smallerthan 20 ms.

We used the tempo2 timing package (59) and8121 available TOAs fromGBT (7), Arecibo, andEffelsberg to derive the timing solution presentedin Table 1. The motion of the radiotelescopesrelative to the barycenter of the Solar Systemwascomputed by using the DE/LE 421 solar systemephemeris (60) published by the Jet PropulsionLaboratory. The orbit of PSR J0348+0432 has avery low eccentricity; therefore, we use the ELL1orbital model (61) to describe the motion of thepulsar.

For the best fit, the reduced c2 of the timingresiduals (TOA minus model prediction) is 1.66,a result similar to what was obtained in timingobservations of other millisecond pulsars. Theoverall weighted residual rms is 4.6 ms. There areno unmodeled systematic trends in the residuals,either as a function of orbital phase or as afunction of time. Therefore c2 > 1 is most likelyproduced by underestimated TOA uncertainties.We increased our estimated TOA uncertaintiesfor each telescope and receiver to produce areduced c2 of unity on short time scales; for ourdominant data set (Arecibo), the errors were mul-tiplied by a factor of 1.3.

This produces more conservative estimates ofthe uncertainties of the timing parameters; thesehave been verified by using the Monte Carlo sta-tistical method described in (23): When all pa-

rameters are fitted, the Monte Carlo uncertaintyranges are very similar to those estimated bytempo2. As an example, tempo2 estimates P

:b =

−2.73 × 10−13 T 0.45 × 10−13 s s−1 (68.27% con-fidence), and the Monte Carlo method yieldsP:b = −2.72 × 10−13 T 0.45 × 10−13 s s−1 (68.27%

confidence), in excellent agreement. The ob-served orbital decay appears to be stable; nohigher derivatives of the orbital period aredetected (8).

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Acknowledgments: J.A. is a member of the InternationalMax Planck research school for Astronomy and Astrophysicsat the Universities of Bonn and Cologne. P.C.C.F. and J.P.W.V.gratefully acknowledge financial support by the EuropeanResearch Council for the ERC Starting Grant BEACON undercontract no. 279702. M.A.M. acknowledges support from aWest Virginia Experimental Program to Stimulate CompetitiveResearch Challenge Grant. J.W.T.H. is a Veni Fellow of theNetherlands Foundation for Scientific Research. V.M.K. holdsthe Lorne Trottier Chair in Astrophysics and Cosmology, a

Canada Research Chair, and a Killam Research Fellowshipand acknowledges additional support from a Natural Sciencesand Engineering Research Council of Canada (NSERC)Discovery Grant, from Fonds Québécois de la Recherche surla Nature et les Technologies via le Centre de RechercheAstrophysique du Québec and the Canadian Institute forAdvanced Research. M.H.v.K. and I.H.S. acknowledge supportfrom NSERC Discovery Grants. V.S.D., T.R.M., and ULTRACAMare supported by the Science and Technology Facilities Council.This work is based on data collected with the VLT of theEuropean Southern Observatory (ESO) under program088.D-0138A and observations with the 100-m Effelsbergtelescope of the Max Planck Institute for Radioastronomy. TheArecibo Observatory is operated by SRI International under acooperative agreement with the NSF (AST-1100968) and inalliance with Ana G. Méndez-Universidad Metropolitana andthe Universities Space Research Association. The NationalRadio Astronomy Observatory is a facility of the NSF operatedunder cooperative agreement by Associated Universities,Incorporated. We are grateful to D. Koester and J. Panei et al. forproviding models presented in their publications. We are obligedto J. Smoker (ESO) for his help during the VLT observationsand D. Champion for assistance with the Effelsberg observationsand useful discussions. We also thank D. Lorimer, J. Bell-Burnell,G. Esposito-Farèse, E. Keane, P. Podsiadlowski, and B. Schutzfor helpful discussions. This research made use of NASA’sAstrophysics Data System and M. T. Flanagan’s Java ScientificLibrary (www.ee.ucl.ac.uk/∼mflanaga).

Supplementary Materialswww.sciencemag.org/content/340/6131/1233232/suppl/DC1Supplementary TextFigs. S1 to S11Tables S1 to S3References (63–112)

27 November 2012; accepted 6 March 201310.1126/science.1233232

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