January26,2010 14:38 WSPC-ProceedingsTrimSize:9.75inx6.5in lazaridis 1 Precision timing of PSR J1012+5307 and strong-field GR tests KOSMASLAZARIDIS∗,NORBERTWEX,AXELJESSNER,MICHAELKRAMER∗∗, 0 J.ANTONZENSUS 1 Max-Planck-Institut fu¨r Radioastronomie 0 Auf dem Hu¨gel69, Bonn, 53121, Germany 2 ∗E-mail: [email protected] n a BENW.STAPPERS∗∗∗,GEMMAH.JANSSEN,MARKB.PURVER,ANDREWG.LYNE, J CHRISTINEA.JORDAN 6 ∗∗Jodrell Bank Centre for Astrophysics, Alan Turing Building, 2 School of Physics and Astronomy, Universityof Manchester, Manchester, M13 9PL, UK ] A ∗∗∗Stichting ASTRON, G Dwingeloo, Postbus 2, 7990 AA, the Netherlands . h p GREGORYDESVIGNES,ISMAELCOGNARD,GILLESTHEUREAU - Laboratoire de Physique et Chimie de l’Environnement, o CNRS, 3A Avenue de la Recherche Scientifique, r t Orl´eans Cedex 2, 45071, France s a [ Station de Radioastronomie de Nan¸cay, Paris Observatory, University of Orl´eans, CNRS/INSU, 18330, Nan¸cay, France 1 v 4 We report on the high precision timing analysis of the pulsar-white dwarf binary PSR 0 J1012+5307. Using 15 years of multi-telescope data from the European Pulsar Timing 7 Array(EPTA)network,asignificantmeasurementofthevariationoftheorbitalperiod 4 isobtained.Usingthisidealstrong-fieldgravitylaboratorywederivetheoryindependent . limitsforboththedipoleradiationandthevariationofthegravitational constant. 1 0 Keywords: PSRJ1012+5307; dipoleradiation;gravitational constantvariation. 0 1 : 1. Introduction v i X PSRJ1012+5307is a 5.3ms pulsarin alow eccentricitybinarysystemwith orbital r periodofPb =14.5h1 andalowmassheliumwhite dwarf(WD)companion.2 Ref.3 a compared the measured optical luminosity of the WD to the value expected from WDmodelsandcalculatedadistanceofd=840±90pc.Inadditiontheymeasured, aradialvelocitycomponentof44±8kms−1 relativeto the solarsystembarycentre (SSB),andthemassratioofthepulsaranditscompanionq =m /m =10.5±0.5. p c Finally they derived a companion mass of mc = 0.16±0.02M⊙, a pulsar mass of mp =1.64±0.22M⊙ and an orbital inclination angle of i=52◦±4◦. Ref.4 presentedthe timing analysisofPSRJ1012+5307using4yearsoftiming datafromEffelsbergand7yearsfromLovellradiotelescope.Theyderivedthespin, astrometricandbinaryparametersfor the systemandthey discussedthe prospects of future measurements of a Post-Keplerian parameter (PK) which can contribute to the derivation of stringent limits on alternative gravity theories. January26,2010 14:38 WSPC-ProceedingsTrimSize:9.75inx6.5in lazaridis 2 2. Results In this work PSR J1012+5307 has been revisited with seven more years of high- precisiontimingdataandcombineddatasetsfromtheEPTAtelescopes(Effelsberg, Lovell,Nan¸cay,Westerbork),atfivedifferentfrequencies.Thedatahavebeenanal- ysed using the timing software TEMPOa and all the astrometric, spin and binary parameters of this system have been improved. For the first time a parallax π = 1.2± 0.3mas has been measured for PSR J1012+5307.This correspondsto a distance ofd=822±178pc whichis consistent with the d=840±90 pc measured from the optical observations. As predicted by Ref. 4 a significant measurement of the change in the orbital period of the system, P˙ = 5.0(1.4)×10−14, has been obtained for the first time. b ThisiscausedbytheDopplercorrection(whichisthecombinedeffectoftheproper motion of the system5 and a correction term for the Galactic acceleration) and by a contribution due to the quadrupole term of the gravitational wave emission, as predictedbygeneralrelativity(GR).Aftersubtractingthesetwocontributionsfrom our measured value, the excess value of P˙exc = (−0.4±1.6)×10−14 confirms the b validity of GR for one more millisecond pulsar binary system. All the terms mentioned above are the ones expected to contribute by using GRas ourtheoryofgravity.However,there arealternativetheoriesofgravity,that violatethestrongequivalenceprinciple(SEP)andpredictextracontributionstothe observed orbital period variation. One is the dipole term of the gravitational wave emission, which results from the difference in gravitational binding energy of the twobodiesofabinarysystem.ThusPSRJ1012+5307,apulsar-WDsystem,isideal fortestingthestrengthofsuchemission.Forsmall-eccentricitypulsar-WDsystems, wherethesensitivitys(relatedtothegravitationalself-energyofabody)oftheWD is much smaller than the one of the pulsar, one finds P˙ dipole = −4π2 T⊙µκ s 2,6 b Pb D p where T⊙ =4.9255µs and µ is the reduced mass; sp is the sensitivity of the pulsar and κ refers to the dipole self-gravitationalcontribution. D Another term is predicted by a hypothetical variation of the locally measured gravitationalconstantastheuniverseexpands,P˙G˙ =−2G˙ 1− 1+ mc s P ,7,8 b G(cid:2) (cid:0) 2M(cid:1) p(cid:3) b whereM isthetotalmassofthesystem.Ithasbeenshownthatthereisnoneedto addtheseextracontributionstoexplainthevariationsoftheorbitalperiod,however the excess value has been used to set limits for a wide class of alternative theories of gravity. PSR J1012+5307 is an ideal lab for constraining the dipole radiation term be- cause the WD nature of the companion is affirmed optically, the mass estimates are free of any explicit strong-field effects and the mass of the pulsar is rather high, which is important in the case of strong field effects that occur only above a certain critical mass, like the spontaneous scalarisation.9 Thus, by using the G˙/G = (4 ± 9) × 10−13yr−1 limit from the Lunar Laser Ranging (LLR)10 the ahttp://www.atnf.csiro.au/research/pulsar/tempo/ January26,2010 14:38 WSPC-ProceedingsTrimSize:9.75inx6.5in lazaridis 3 G˙/G contribution has been calculated and subtracted from our excess value in order to finally obtain an improved generic limit for the dipole contribution of κ =(0.2±2.4)×10−3 (95 per cent C.L.). D A generic test for G˙ cannot be done with a single binary pulsar, since, in gen- eral, theories that predict a variation of the gravitational constant typically also predicttheexistenceofdipoleradiation.Thisdegeneracyhasbeenbrokenhereina joint analysis of PSR J1012+5307 and PSR J0437−4715,11 two binary pulsar-WD systems with tight limits for P˙ and different orbital periods. By applying Eq. 1 b P˙bexc =−2G˙ 1− 1+ mc s −4π2T⊙µκ s2 (1) P Gh (cid:16) 2M(cid:17) pi P2 D p b b to both binary pulsars, and solving in a Monte-Carlo simulation this set of two equations,stringentandgenericlimitsbasedpurelyonpulsardataandinthestrong field regime have been obtained. With a 95 per cent C.L., G˙ = (−0.7± 3.3)× G 10−12 yr−1 andκ =(0.3±2.5)×10−3.Inthefuture,moreaccuratemeasurements D of P˙ and distance of the two pulsars and WDs could constrain even more our b derived limits. AmoredetailedworkonthisstudyofPSRJ1012+5307canbefoundinRef.12. Acknowledgments We are very grateful to all staff at the Effelsberg, Westerbork, Jodrell Bank and Nan¸cay radio telescopes for their help with the observations. KL was supported for this research through a stipend from the International Max Planck Research School (IMPRS) for Astronomy and Astrophysics at the Universities of Bonn and Cologne. MP is supported by a grant from the Science and Technology Facilities Council (STFC). We are grateful to Paulo Freire for valuable discussions. References 1. L.Nicastro,A.G.Lyne,D.R.Lorimer,P.A.Harrison,M.BailesandB.D.Skidmore, MNRAS273, L68 (1995). 2. D.R. Lorimer, A.G. Lyne, L. Festin and L.Nicastro, Nat. 376, 393 (1995). 3. P. J. Callanan, P.M. Garnavich and D.Koester, MNRAS298, 207 (1998). 4. C. Lange, F. Camilo, N. Wex, M. Kramer, D. Backer, A. Lyne and O. Doroshenko, MNRAS326, 274 (2001). 5. I.S. Shklovskii,Soviet Ast. 13, 562 (1970). 6. C. 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