Pos(AASKA14)042 , 10 , Jutta 6 , 3 , Paulo C

Home , Physical Review

PoS(AASKA14)042 , 10 , Jutta 6 , http://pos.sissa.it/ 3 , Paulo C. C. 4 , Scott Ransom 9 (IHS) , Michael Kramer 4 , Adam T. Deller 3 11 , Andrea Possenti 8 [email protected] , Gemma H. Janssen , John Antoniadis 5 2 , 4 , Volker Perlick (LS); 8 , Willem van Straten 6 , Ingrid H. Stairs 1 ∗ [email protected] , Jason W. T. Hessels , Claus Lämmerzahl 3 7 Speaker. The Square Kilometre Array (SKA)gravity will effects use in pulsars pulsar to systems,ried enable which out precise yield anywhere measurements else. tests of The of strong Galacticsystems, gravitational census theories possibly of that including pulsars will cannot pulsar discover – be dozenscensorship black car- of conjecture” hole relativistic and pulsar binaries the which “no-hair canvastly theorem”. be improve the used Also, timing to the test precision SKA’s remarkabletions the of from sensitivity “cosmic millisecond will general pulsars, relativity allowing (GR). probesequivalence Aspects principles, of of gravitational potential dipole gravitation radiation, devia- to extra be ﬁelditomagnetism, components explored and of include spacetime gravitation, tests symmetries. grav- of strong ∗ Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. National Radio Astronomy Observatory, 520 EdgemontCentre Road, for Charlottesville, Astrophysics VA and 22903, Supercomputing USA and ARC Centre for All-Sky Astrophysics School of Physics, Peking University, BeijingDepartment 100871, of China Physics and Astronomy, University of British Columbia, 6224 Agricultural Rd., Max-Planck-Institut für Radioastronomie, Auf dem HügelASTRON, 69, The D-53121 Netherlands Bonn, Institute Germany for Radio Astronomy, 7990 AA Dwingeloo, The Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098Jodrell XH Bank Centre for Astrophysics, The UniversityUniversity of of Manchester, Oldenburg, M13 Department 9PL, of United Physics, Kingdom University 26111 of Oldenburg, Bremen, Germany ZARM, 28359 Bremen,INAF-Osservatorio Germany Astronomico di Cagliari, via della Scienza 5, 09047 Selargius (CA), Italy c

Advancing Astrophysics with the Square KilometreJune Array 8-13, 2014 Giardini Naxos, Italy Lijing Shao 1 2 Vancouver, BC V6T 1Z1, Canada 3 4 Netherlands 5 Amsterdam, The Netherlands 6 7 8 9 10 11 (CAASTRO), Swinburne University of Technology, PO Box 218 Hawthorn, VIC 3122, Australia E-mails: Testing Gravity with Pulsars in the SKA Era Freire Kunz Benjamin W. Stappers PoS(AASKA14)042 . The µν g Lijing Shao 2 , in addition to the canonical metric field, ϕ In November 1915, Albert Einstein published the final paper that completed his theory of Despite its success over the last century, GR still faces great challenges on the research fron- The important thing to us is that pulsar timing can be used to test some of these theories. Pulsar For example, in the Jordan-Fierz-Brans-Dicke theory (Jordan 1959; Fierz 1956; Brans & Dicke gravity and spacetime nowspacetime known for as ever. general During relativity itsone (GR), with first changing meager fifty observational our years, evidence. view Only GRfield in of was the of considered gravity 1960s experimental did a and gravity technology theoretical (Misner usher tour-de-force et inhas the al. but passed remarkable 1973; all Will 1993). experimental Overtems, tests particularly the in in subsequent binary laboratories, fifty pulsars years, in (Will 2014). GR played the Astrophysical one observations Solar of using the System radio most bands important and have measurements parts in in and the various probe history stellar into of testing the sys- tron GR, vicinity with stars of the (NSs). compact ability Particularly, to bodies, radio make namely timing precise properties black of of holes binary NSs (BHs) pulsars and, and has for neu- preciselythat probed gravitational the waves the first exist gravitational and time, that tested compactpredicted binaries the by lose radiative energy GR properties from (Hulse their of emission2010; & gravity, at Freire demonstrating Taylor the et rates 1975; al. Taylor 2012b; etof Antoniadis al. the et radiative 1979; properties al. of Kramer 2013). gravity et isof This not al. fundamental confirmation only 2006; critical physics and from Weisberg and precise the et characterisation many pointwave of al. aspects detectors, view a of of whole our astrophysics, new understanding but windowmost on it powerful the will Universe. member also The of open, Square theradio via Kilometre next timing Array gravitational generation of (SKA), pulsars of as and the radio willit telescopes, discover will dozens will play of allow a rare much unique relativistic role more binary in precise systems. many For areas this of reason experimental gravity. tiers of modern physics.Second, First, as it a non-renormalisable is field knownples. theory, to it be Reconciling appears incomplete, gravity to with since befundamental quantum it incompatible physics fails mechanics with today. quantum at stands princi- Furthermore, the outtional centre concepts challenges as for of like one our BHs. dark of understanding of matter theproposed gravity, to and great and explain modifications dark challenges these of energy of phenomena gravity pose theoriesScalar (Capozziello (TeVeS) have addi- & theory, been which de was Laurentis advanced 2011), to like explain dark the matter Tensor-Vector- (Bekenstein 2004). timing uses large radio telescopes to recordby the the times rotation of of arrival (TOAs) the ofthe pulsar. pulsed pulsar, signals, These produced dispersion TOAs depend in onradio the the telescope interstellar rotational in the and medium Solar astrometric that System. parametersdynamics If the of the of signals pulsar is the traverse, in binary, and a& binary, which the the Taylor are TOAs motion also 1981; determined depend of Damour on by the the &family the orbital Taylor of underlying 1992; TeVeS-like gravitational theories Edwards theory introduced etis (Weisberg in al. sufficiently Freire 2006). different et from Some al. GRprecise theories (2012b), to timing of result be measurements gravity, of detected in these like in orbital binarythese a the dynamics pulsars gravity timing that can theories. of constrain, or some altogether binary rule pulsars. out, some Therefore, of 1961), gravity is mediated by a scalar field, Testing gravity with pulsars in the SKA Era 1. Introduction PoS(AASKA14)042 , where 0 is the light Lijing Shao BH binaries c ϕβ

+ M 0 α 2 as ϕ Inaccessible Region GM/ac J0737•3039 J1738+0333 and radiative properties of 10 Black Holes 1 log space, non-perturbative effects, B1913+16 ) J0437•4715 0 BH, and pulsar – 10 J1903+0327 β Earth•Sun

M Binary Pulsars System Solar α ( is the gravitational constant, and 0

•10 •9 •8 •7 •6 •5 •4 •3 •2 •1

•2 •4 •6 •8 G

c 10

c •10

c /R GM log 2 (here 3 M and the existence of gravitational dipole radiation in The compactness of the gravitating companion star versus G to matter depends on the ﬁeld itself ϕ are the mass and the radius of the companion star, respectively Right: c R Pb = 1.0 d Pb = 0.1 yr Pb = 0.3 yr 2 Pb = 0.1 d and Pb = 10 d Pb = 1.0 yr c , and a total mass, a M GM/ac J0737•3039 Pb = 1.0 d 10 Pb = 0.1 yr B1913+16 log J1738+0333 J0437•4715 Parameter space for quantifying the strength of a gravitational ﬁeld (Psaltis 2008). The in spacetime introduces observable effects in gravitational experiments, like the time- J1903+0327 ϕ Earth•Sun Left: fully characterise the theory. Within some of the •8 •7 •6 •5 •4 •3 0

•22 •23 •24 •25 •26 •27 •28 10 •29 •30

Compared to the coalescence of two compact objects (that will be the main source for ground-based gravitational log [m c GM/a

] 1

and

•2 2 3 0 variation of the local gravitational constant variation of wave detectors), two componentsfield”. of a However, as binary shown pulsar bycould are explicit have well calculations, significant effects “strong-field separated, on effects” that the associated binary might with orbital be strongly dynamics prejudicially (Damour self-gravitating & NSs termed Esposito-Farèse as 1993). “weak speed). Solid and emptydwarf squares (NS-WD) are binaries, known respectively. neutron TheCircles star diamond from – large is neutron to a star small known (NS-NS) arewith neutron pulsar and their star – neutron assumed – Sgr orbital star main A* periods – BH, sequence aside. white pulsar star – binary. 5000 (Kramer et al. 2004). a binary. In a more general classthe of coupling scalar-tensor strength theories of (Damour the & scalar Esposito-Farèse field 1993, 1996), the compactness of the orbit; α Figure 1: horizontal axis measures the gravitational potential andan the orbit vertical with axis a measures semimajor the axis, spacetime curvature of Testing gravity with pulsars in the SKA Era called “spontaneous scalarisation”, may happen inFarèse compact 1993), bodies which like can NSs (Damour influenceeffects & are the also Esposito- orbital possible within dynamics an of extended familytheir a of ability TeVeS-like theories binary (Freire to system et probe al. dramatically. 2012b). strong-field With these effects, Similar binary alternative pulsars gravitational are theories. idealfrom laboratories radio with With pulsar which the timing, to binary non-detection study pulsarsthese of have theories already gravitational and severely dipole constrained provided the the radiation parameter mostgravity spaces (Freire stringent of et tests al. of 2012b; the Antoniadis strong-field et al. 2013; Stairs 2003; Wex 2014). PoS(AASKA14)042 , e.g. Lijing Shao , and SKA1-MID surveying the including the longer baselines). ◦ 5 i.e. | ≥ b | 4 (Keane et al. 2015). The SKA2 will discover even more ◦ 10 new relativistic systems with which to carry out similar and com- | ≤ b | to focus on orbital conjunction in order to measure the Shapiro delay. discover e.g. 3039 (Burgay et al. 2003; Lyne et al. 2004; Kramer et al. 2006)) and triple systems − The Square Kilometre Array will have a major impact on radio astronomy. The SKA Phase 1 This will happen through two avenues. On the one hand, SKA1-MID and SKA2 will strongly For precision pulsar timing, raw sensitivity is one of the most important factors. High cadence The SKA will also , PSR J0337+1715 (Ransom et al. 2014)), in turn dramatically improving the quality of the e.g. (SKA1) will feature roughly halfSKA1-LOW and of SKA1-MID. By its synthesising total a coherent collectingto sum deeply area of these search within elements, for a it new will densethem be relativistic possible core, with binary pulsars, in great over the precision the cases using whole of the sky, and full to SKA1-MID subsequently array time ( improve the quality of the observations of the most interesting binaries currently known ( may also be needed forTOAs some for experiments, a in particular which pulsar casecadence are sub-arraying is collected will necessary, every be few needed. weeks, though Typically, in come cases a much higher Testing gravity with pulsars in the SKA Era 1.1 The role of the Square Kilometre Array The SKA Phase 2 (SKA2)precision. will provide Both another phases major oftheories leap the to in SKA a sensitivity, new will and level significantly (Kramer thus et advance also al. experimental in 2004). tests timing of gravitational PSR J0737 ( existing tests and enabling proposed newwill tests. improve Compared the with timing the precision current forwill status southern quo, improve pulsars SKA1-MID it by by about an upments order to in of two precision, magnitude, orders and depending of SKA2 onso magnitude. their on. sky Different locations, pulsars pulse will characteristics, gain timing different stabilities, improve- and Sub-arraying can also help ifable. many sources need Though to SKA1-MID be willSKA1-LOW timed, may provide and also the if be needed reduced highest-precision to sensitivity track TOAs,influence is the regular the accept- time-variable interstellar measurements TOAs. propagation with effects In thatmaximum also all timing cases, precision and coherently accuracy. dedispersingphase Such the of timing data SKA1 observations (say, is can with essential alreadyless 50% begin for of precise in achieving the TOAs an the collecting than early area withcient, available), the while though complete for they array. others will certain naturally Forarray relativistic obtain some effects is may sources in place. only 50% become sensitivity clearly will detectable be once suffi- the full pletely novel tests. Withfinding a larger new field pulsars. of view Theneeded and to larger achieve high the sensitivity sensitivity, required of the signal to thean SKA noise assumed SKA is ratio. constant more means Consequently, in orbital efficient that an acceleration in “accelerationacceleration a (Lorimer search” in shorter an with & actual Kramer integration binary 2004), will time betelescopes the is reduced, smearing at making due the finding SKA to relativistic much varying moreof binaries. effective about than current 10,000 Simulations normal show pulsarsSKA1-LOW that and surveying the the perhaps SKA1 sky as can with manysky the discover as with Galactic a 1,800 the latitude total millisecond Galactic pulsars latitude (MSPs), with pulsars, and it is possible that among them there will be pulsar – black hole (PSR-BH) binaries PoS(AASKA14)042 for an 1 3039A/B) Lijing Shao − shows its mass- 2 3039 (Kramer et al. − shows the vast unprobed 1 5 , has “kinematic” contributions, which result from the proper for a GR-based example for PSR J0737 b , the theory must be able to describe the component masses in ˙ P 2 i.e. The current state-of-the-art binary in this area is the Double Pulsar (PSR J0737 Pulsar timing takes advantage of the tremendous rotational stability of pulsars, allowing us to Measuring two PK parameters, we can use a specific theory of gravity to determine the com- 2006; Breton et al. 2008)).should For intersect a in gravitational some theory region, toa pass self-consistent the way (Taylor test(s), & all Weisberg 1982). curves in the diagram (Burgay et al. 2003; Lyne et al. 2004), which enables five tests of GR. Figure mass diagram, where seven curves(Kramer corresponding et to al. seven 2006; mass Breton constraints etconsistent intersect al. description at 2008; of one all Kramer of point & its Wexsky 2009), timing and measurements. indicating will that The be Double GR an Pulsar provides important resides a target in self- for the the southern SKA. The timing precision of the SKA will enable tests treat them as free-falling clocks.is calculated As a which pulsar accountspulse is for TOAs. monitored A every over pulsar rotation months ephemeris always of andspin incorporates years, the derivative the accounting an spin pulsar frequency for ephemeris and and rotational generallyorbits can energy at require be least loss, a one used plus further astrometric to translationthe parameters. predict of five future reference Binary Keplerian frame, pulsar parameters accomplishedrelativistic describing for effects an most beyond binary eccentric a systems Keplerianparameters Keplerian by are orbit. orbit, introduced (Damour a & In set Deruelle order of 1986; Damour theory-independent to & “post-Keplerian” account Taylor 1992) (PK) for (see Table ponent masses of the system;cases, these to are constrain important EOS to (Watts etcan study al. be stellar tested 2015). evolution by a If theories self-consistent more and, argumentbe PK in — able parameters using some to the are masses predict measured, derived the then in“mass-mass subsequent the the diagram” first PK theory stage (see measurements. one Figure should Another way of viewing this is the so-called Testing gravity with pulsars in the SKA Era (Kramer et al. 2004; Keane etopen al. a 2015). new The era discovery of ofmic studying even censorship BH a conjecture” physics single and tight with PSR-BH the greatKopeikin system “no-hair precision, 1999; will theorem” including Kramer (Damour possible et & tests al. Esposito-Farèse of 2004;regions 1998; in Liu the the 2012; Wex “cos- & gravity Liu sector et that al. can 2012). be probed Figure with different kinds of2. PSR-BH systems. Relativistic Binaries incomplete collection of the mostcontaminated important by PK astrophysical parameters). effects other In than practice, relativisticobserved effects PK orbital due parameters to decay could gravity. parameter, be For example,motion the of the system and the differenceSystem of Barycentre. Galactic accelerations between Here that unless system otherwise andare the stated, properly Solar corrected we or assume demonstrably that negligiblemasses non-gravitational in contributions with effect. If negligible so, spin in contributions, theKeplerian the case parameters, of PK the two parameters component well-separated are masses,the functions the parameters of equation the describing of well-measured the state gravitationalconstitution (EOS) theory of of the (Damour stellar star & matters, is Taylormatter and irrelevant 1992) — to this (in a is GR, high the the “effacement” “post-Newtonian” property internal (PN) to order, be only discussed the in total section 3). masses PoS(AASKA14)042 , and on Lijing Shao 1PN ˙ x ω / , to the light speed, v 2PN ˙ ω . Simulations showed ) 5 − PN” if the suppression factor is n 10 ( 6545 (Manchester et al. 2010), O − ω s timing precision for the Double µ e b P 6 3039B (Perera et al. 2010). For PSRs B1534+12 s for the Double Pulsar we will reach the precision µ − 5 ∼ , are both at the order of 5PN . 2 b ˙ on the advance rate of periastron, namely P / 2 5PN . 3 b ˙ P time derivative of the longitude ofamplitude periastron of the Einstein delay time derivative of the orbital period range of the Shapiro delay shape of the Shapiro delay precession rate of the pulsar spin mismatch in eccentricities (see text) time derivative of the orbital eccentricity time derivative of the projected semimajorsecond axis time of derivative the of pulsar the orbit longitudesecond of time periastron derivative of the projected semimajor axis of the pulsar orbit 3039B we even have direct measurements of the precession rates, which match the − . The most important PK parameters that could be used in pulsar timing of binaries (Damour & ) SO n θ b 2 ˙ ¨ ˙ ˙ ¨ ˙ Parameter ω γ P r s Ω δ e x ω x c / Besides the orbital dynamics of two point masses, spin contributions may play an important Effects due to the PN orders are those that are suppressed by the ratio of the orbital velocity, n 2 2 v ( , compared with those due to Newtonian gravity (Will 2014). It is denoted as “ and J0737 GR predictions (Stairs et al.have 2004; comparable Fonseca sensitivity to et the al. Arecibo 2014; telescope, Breton meaning that et significant al. improvement 2008). in pre- The SKA1-MID will role in the observations ofthe spacetime pulsar produced binaries by (Barker the companion &pulsar) star, suffers O’Connell the a precession 1975). rotation with axis respect of Due tocession”. a a to freely distant Because the falling observer; of object this curvature it, effect (here of is overfrom the known time the as Earth, different “geodetic thus emitting pre- causing regions a secular ofserved change in the in some magnetosphere the tight observed will binary pulse pulsars, be profile. for1998), visible This example, B1534+12 effect in has (Stairs PSRs been B1913+16 et ob- (Weisberg al. et al. 2004; 1989; Fonseca Kramer et al. 2014), J1141 Pulsar (assuming its pulse profileprecise shape measurements can of still these be higher-order well parameters. modelled), raising the prospect of highly J1906+0746 (Lorimer et al. 2006) and J0737 c O of relativistic effects beyond their first-order PN approximationshigher-order (Kramer PN & effects Wex is 2009). important Measuring since(Barker it allows & the investigation O’Connell of the 1975; effectseffects from Damour due pulsar & to spin the Schaefer next 1988; PN Kramer order & Wex 2009). The fractional required to detect higher-order effects (Kramerscaling & from Wex 2009); current this observations. is very The likely SKA2 with SKA1-MID, will have sub- Table 1: Testing gravity with pulsars in the SKA Era Deruelle 1986; Damour & Taylor2006). 1992; In Wex practice, & for Kopeikincharacteristics a 1999; of specific Lorimer the binary pulsar & pulsar, timing Kramer experiment. only 2004; some Edwards PK et parameters al. are measured, depending on the the orbital decay, namely that by obtaining a timing variance below PoS(AASKA14)042 0). This Lijing Shao 6= x will be almost impossible to x 3039A/B, also known as the Double Pulsar (Kramer 7 − 1. The inset is an expanded view of the region of principal interest, where ≤ The mass-mass diagram of PSR J0737 For the Double Pulsar, the recycled pulsar (pulsar A) dominates the contribution to the Lense- Since in GR the total angular momentum must be conserved up to 2PN order, a change in the Thirring precession, because it is a faster rotator. The effect on ˙ spin-orbit coupling is also known assmall the effect Lense-Thirring that effect is or numerically at frame-draggingrequires 2PN effect, order a and for it high slowly is timing rotating a precision neutronsince stars, (Damour it whose & measurement offers Schaefer the 1988). potential1988; However, to measuring O’Connell it measure 2004), is the of important moment2015). great of interest inertia for of the the EOS pulsar of (Damour cold & dense Schaefer nuclear matter (Watts et al. direction of the pulsar spin mustmomentum, be compensated contributing by a a change variation in the to direction the of the projected orbital semimajor angular axis of the orbit ( ˙ et al. 2006; Breton etassumed al. to 2008) be (Kramer et GR. al., Shadedorbital in regions inclination prep.). are must In forbidden be the bythe figure the the intersection individual underlying mass of gravitational functions seven theory becauseuniqueness is curves of the at a sine solution. one of For the point more details, within see measurement Kramer et uncertainties al. proves (2006) and the Breton existence etcession al. and measurements (2008). of the pulsarsprecessing that pulsars are not in visible the toexample, Arecibo the in the sky Arecibo Double will telescope Pulsar, the await will precession theorientation rate be of of SKA2. prime the its B targets magnetosphere However, pulsar for can as be SKA1-MID. itThe measured For causes by rapidly “flickering” modelling changing the eclipses eclipse-period of flux pulsarthe density A SKA, will (Breton leading be et to al. much a 2008). better more stringent measured test by of both the phases precession of rate’s agreement with GR. Figure 2: Testing gravity with pulsars in the SKA Era PoS(AASKA14)042 ¨ ω . It 2PN 3 ˙ , the ω b ˙ can be P ˙ ω Lijing Shao software in binaries of 2 e − 1 TEMPO √ 10%. A more eccentric / , where the former is in 2 r e ∼ δ and θ δ with a magnitude comparable to that of ˙ ω 8 s are obtained per month with the SKA1. After 10 µ 1 ∼ is the eccentricity of the orbit. Therefore, we will need highly ec- e parameter can be determined to a precision θ δ from radio timing. This would impose useful constraints on the system’s geometry (Wex & http://tempo.sourceforge.net The Lense-Thirring effect also contributes to The SKA will also confirm general-relativistic orbital deformation for the first time. Damour x . In order to achieve the goal, a tight binary with good timing precision is needed. In addition, 3 , geodetic precession should be observable. This requires a relatively large “supernova kick x ) already possesses the required precision (Kramer et al. in prep.). For the other one, years of observation, the (or a more relativistic) binarydone can with the achieve Double a Pulsar better (Kramer test. & Wex 2009). These results support earlier simulations mass ratio near unity, where centric orbits to “amplify” therate to effect, break and the highly degeneracy with relativisticsouthern the orbits sky Einstein and delay. with The time large SKA it periastron is withthat likely high advance of to precision. PSR find We such B1913+16 simulate a (Hulse TOAs system & withis in Taylor orbital assumed the 1975; parameters that Weisberg similar 60 et to TOAs al. with 2010) a with precision the and ¨ Kopeikin 1999). (Damour & Schaefer 1988; Kramerextracted & from Wex the 2009). advance For rate of the periastron.very Double To precisely Pulsar, do this using this can we two in must others determine principle precise the be PK component masses parameters. One of them (the shape of Shapiro delay, principle an observable (Damour &to Taylor 1992). the TOAs However, and it the onlytransverse signal adds Doppler has a effect tiny a and periodic strong the variance gravitational correlation redshift, with its the amplitude Einstein is delay that is caused by the the misalignment angle between thei.e. pulsar spin and the orbitalvelocity” for norm the second-formed should compact be object — reasonably ininstead large, other of words, an an iron-core-collapse electron-capture supernova, supernova2013). as likely In happened such in misaligned thethe binaries, Double longitude the Pulsar of frame (Ferdman periastron dragging et and introduces al. its nonlinear projected evolution in semimajor time axis; in thus one might be able to extract & Deruelle (1986) used threerameters different were eccentricities introduced to in describe the the pulsar timing timing formula, of namely a pulsar. Two pa- Testing gravity with pulsars in the SKA Era measure, not only because in thisand case the there is spin a of closeedge-on alignment pulsar of (Kramer A the et orbital (Ferdman al. angular etsystems momentum 2006). al. (scaling from 2013), However, the but theSKA2 current also SKA (Keane population, et because Galactic al. we the 2015)), census expect and systemof will there 100 may is discover ˙ from well viewed many be the binaries almost NS-NS SKA1 that will and enable 180 the direct from measurement the orbital decay due to the emissioncarefully, of in GW order waves, to we estimate will precisely needthe the to timing kinematic estimate precision corrections the provided to distance by it. toestimated the This the precisely, SKA. can pulsar we only Again, will be if then done be this with precision. able Lense-Thirring to Because contribution estimate this to the measurement moment will of bemass, inertia done it of for will pulsar a be A pulsar a with with similar very anKramer important exquisitely & well-determined constraint Wex on 2009; the Watts et EOS al. for 2015). dense matter (Lattimer & Schutz 2005; PoS(AASKA14)042 , 2 ) 2 α − 1 0137 was α Lijing Shao − ( ∝ dipole b ˙ P and the fields associated with i 9 shows various binary systems, with the gravitational field strength 1 2) is the effective coupling strength between body , 1 = i ( i α A possible violation of the SEP could be identified by the occurrence of gravitational dipole ra- Where parameters in the timing model can be measured to high precision by other means, they One of the characteristics of GR is the property of “effacement” (Damour 1987). It states diation. The dipole radiation is at lowerby PN GR, order than thus the in canonical quadrupole principle1992, radiation it predicted 1993; can Will dominate 1993, over 2014).than the that It quadrupole in carries mode GR, away collapsing (Damour the theradiation & binary gravitational that Esposito-Farèse more energy can quickly, of be and the modifying detectedorbital orbit the by period waveform more future of of rapidly ground-based gravitational a GW binary detectors. is given The by leading the change dipolar in contribution the with a form characterised by the compactness and curvaturestar. of the orbit and the compactness of the companion 3.1 Gravitational dipole radiation and time-variation of the gravitational constant where can be restricted to ancertainties allowed for range the in remaining parameters the inof timing the external fit. information presence is of This the covariances. can estimation TheLong of lead most Baseline position, to common proper Interferometry significantly source motion (VLBI). reduced and The annual un- plied use parallax to of using pulsar Very VLBI binaries. can improve Forculate gravitational instance, the tests astrometric kinematic when information contamination ap- provided of by theimproving VLBI measured the was orbital potential used period accuracy derivative to of of cal- tests2009). the of Double gravitational In Pulsar, radiation a to second the example, 0.01% the level previously (Deller unmeasured et al. Shapiro delay for PSR J2222 that the finite extents oflong two as bodies they in are a well(SEP) binary separated. (Will are 1993). largely Effacement However, irrelevant is in tothe deeply alternative their theories rooted strong orbital of in gravitational dynamics gravity, the fields the as strongdynamics SEP associated equivalence of is with principle generally the a violated, binary NS and andFarèse may 1992, the have 1993). trajectory measurable of Figure impact light on propagation the (Will orbital 1993; Damour & Esposito- Testing gravity with pulsars in the SKA Era precisely ascertained after the position,mation proper (Deller motion, et and al. parallax 2013). were“blind fixed Since using spots” VLBI measures VLBI with motions infor- respect on topole the pulsar plane and timing; of proper the VLBI sky, motion has itmicro-arcseconds in no has for “blind different the parallax spots” and ecliptic 10 to plane. micro-arcseconds parallax(Deller per et at year With al. the for 2013). current ecliptic proper The VLBI motion SKA1timing can instruments, will precision, be allow and precisions reached a so similar of VLBI using leap 10 theproper in SKA1 VLBI motion will precision than be as able timing it to in will deliverments provide better most will in results cases be the for for very parallax and important nearby toerror pulsars subtract budget), (Paragi and the et the Shklovskii al. differential contribution Galactic 2015). (whichtial rotation, usually (which and These dominates also vertical measure- the acceleration depend in on the relativelyorbital Galactic well-constrained period poten- Galactic change models), to thus high measure precision. the intrinsic 3. Gravitational Dipole Radiation and Equivalence-Principle Tests PoS(AASKA14)042 ) = MSP M , Lijing Shao BH M ( parameter space 0 β in a NS-WD binary - 0 α WD α 6= NS α 10 parameter is negative. The reason for this is that, as showed 0 β 8; the constraints from top to bottom are based on: 10 years with a 100- . 0 ). Therefore, NS-WD binaries are the ideal laboratories for testing 1 = e 5 d, and = b P , the constraints from those two binaries are plotted in the , 3 )

M Constraints on the parameter space of scalar-tensor theories (ﬁgure courtesy of N. Wex). Coloured 4 . 1 ,

In these NS-WD binaries, the combined radio observation of the pulsar and optical observation In Figure M and the quadrupole formula in GR stringently constrains the dipolar radiation contribution, as in b 10 ˙ by Damour & Esposito-Farèse (1993), in this region NSs develop non-perturbative strong-field of the WD can give rise to2013; precise measurements Wex of 2014). two component masses Theradiation (Antoniadis et within mass al. a 2012, measurements specific can theory,of and be the this used in orbital to turn decay is caused predictprinciple confronted by the be with gravitational dominant amount the damping. over radio of the As timing gravitational P quadrupolar mentioned, observation radiation, the therefore, dipolar agreement radiation betweenthe can the cases in observed of PSRs J1738+0333 (Freire et al. 2012b) and J0348+0432 (Antoniadis et al. 2013). (see the right panel ofthese Figure theories and, if they arewhich correct, if searching detected for would falsify the GR. existence of gravitational dipole radiation, mentioned in section 1. The bestplotted. constraint from The the limits Cassini spacecraft fromtensor in theories, two the especially binary Solar when System the pulsars is stringently also constrain the parameter space of scalar- m class radio telescope, 5vertical years dashed with purple the line FAST telescope, “JFBD”grey and indicates line 5 the “GAIA” years Jordan-Fierz-Brans-Dicke indicates with gravity. the thethe The SKA limit astrometric horizontal (Liu satellite expected dashed et GAIA. from al. near-future 2014). Solar-System The experiments, foremost from the dipole moment. In(Damour the & best-studied Esposito-Farèse 1992; gravitational Will theory 1993), of we this generally have type, the scalar-tensor theory ( Figure 3: regions are excluded by2003), current PSR Solar J1738+0333 System (Freire and etchosen al. pulsar as 2012b), MPA1. experiments: and Black PSR dashed Cassini J0348+0432 lines spacecraft are (Antoniadis (Bertotti based et on et al. simulations 2013). al. for a The MSP-BH EOS system is with Testing gravity with pulsars in the SKA Era PoS(AASKA14)042 4715 − for binary Lijing Shao b ˙ P (Wex 2014). ), further improving the ˙ G 4 has to be for the spontaneous scalarisation 0 . A consequence of this is that any radiative β 8 , by the GAIA satellite 11 , and the European Extremely Large Telescope (E- e.g. 6 . b ˙ P (Antoniadis et al. 2013). 0 β , the Giant Magellan Telescope (GMT) 5 , may also significantly advance the optical observations of WDs, improving their mass and 7 http://sci.esa.int/gaia/ http://www.tmt.org/ http://www.gmto.org/ http://www.eelt.org.uk/ However, see Herdeiro & Radu (2014) for “Kerr BHs” with scalar hair after a complex, massive scalar field, In short, in the SKA era, pulsar observations will improve significantly and maintain their If any relativistic PSR-BH binaries are discovered, they will also be promising test beds for In Jordan-Fierz-Brans-Dicke theory and (from a broader viewpoint) in the generic scalar- These examples already show how important proper subtraction of the contributions from The next generation of 30-m class optical telescopes, for examples, the Thirty Meter Telescope 4 5 6 7 8 minimally coupled to GR, is included (Herdeiro & Radu 2014). distance estimates; which will soonet limit al. the 2012b). precision of some of the current gravity tests (Freire unique importance in testing alternativeputting theories other techniques of like gravity, VLBI but andextended will gravitational optical theories benefit observation. that incorporate extensively They dark will from matter be and in- dark crucial energy for as tests gravitational effects. of some gravitational dipolar radiation because the no-hairgravity; theorem this also implies applies to that scalar-tensor BHs theories have of no scalar charge ELT) tensor theories, the scalarlatter field may vary plays with the spacetime-variation role and in of time the gravitational (Damour local constant & contributes gravitational Esposito-Farèse to1988; constant, the 1992; Wex decay 2014). Will implying of 1993). The a that extra binary The the orbit contribution possible (Damour can et be al. constrained by the measurement of Galactic acceleration and the Shklovskii effectties is, in and distances how and crucial proper VLBI motions. is Furthermore,of for in the reducing the Galactic near uncertain- potential future will a also more accurate be understanding available ( (TMT) Testing gravity with pulsars in the SKA Era effects like “spontaneous scalarisation” thatSystem; are absent such in effects the would weak-fieldwaves. cause experiments The in a more massive the very the Solar pulsar large theto increase less appear. negative in For the this emissionorbit reason, where of the the dipolar orbital timing decay gravitational of has beenconstraints PSR measured on with J0348+0432, the some a allowed precision, range introduces two-solar-mass uniquely of NS stringent in a relativistic pulsars by assuming a nullgravitational contribution constant from is the accompanied dipole radiation. bythan the one In dipole general, binary radiation however, pulsar, a (Lazaridis oneradiation varying can et and also al. the time-variation conduct 2009). in a the With joint gravitationalhave constant, more constraint different utilising simultaneously the dependence fact on on that both these theconstraint the two orbital effects from dipole period pulsars of on thewhich the binary relies time-variation (Lazaridis on of et VLBI the (Deller al.and gravitational et 2009). J1738+0333, al. constant is The 2008) already (Freire and latest comparable et(Will to timing 2014). al. the (Verbiest Moreover, et best 2012b), pulsar al. constraint tests are from 2008) sensitive the of to Solar PSR strong-field System effects J0437 experiments on estimates of the kinematic corrections of PoS(AASKA14)042 , = η b P times , 4 , which

) 2 − Lijing Shao 10M ms = 10 (Liu 2012; Wex − ) BH 4 , which is 10 10 7 M − ( − O 10 ( 10 O × 4 100 such systems with MSPs . | . ∆ | directly (Damour & Esposito-Farèse (Liu et al. 2014). Five years of weekly NS 3 α , but the SKA2 will improve the timing 9 down to the order of 12 | 0 α | will therefore constrain ) angular velocity of the outer orbit (also see Eq. (8.18) in Will (1993)). BH α − NS orbital α ( 8) are depicted as dashed lines in Figure . 0 1. = e ∼ − 0 β In principle, SKA1-MID is better due to less radio frequency interference (RFI), and much wider bands than that It was estimated in Ransom et al. (2014) that there could be A possible violation of the SEP has also been investigated by tracing the orbital dynamics of The recently discovered triple system, PSR J0337+1715 (Ransom et al. 2014), provides an 9 of the Arecibo telescope. residing in the Galaxy. Since theet SKA will al. discover almost 2015), all it visible pulsars ispossible in likely that the that Galaxy the (Keane it SKA willbinary might discover and even other discover where triple a the systems triple outer like system star PSR consisting is J0337+1715, of another and an NS. it inner Such is NS-WD a close system could be (again) many orders of precision by a factor of ten, which should improve the test by a corresponding factor. Testing gravity with pulsars in the SKA Era test that constrains 1998). The constraints from simulations of a hypothetical PSR-BHobservations system with ( the SKA will constrain is the force that would “polarise”the the outer inner WD orbit in provides the a casethe “polarising” of Galactic acceleration SEP acceleration that violation. on is In the more PSR innerof than J0337+1715, pair. Damour one As & million a times Schaefer rough larger estimate, (1991),inner than we binary by use with replacing the the acceleration the in relativisticBased Eq. rate on (4) of the advance current ofpossible measurement upper periastron limit precision for of the of the SEP the violationbetter parameter orbital is than estimated, eccentricities the in currentdetectability the pulsar with triple constraint the system, (N. Arecibo Wex, a telescope,SEP-violation private observations communication). test with via SKA1-MID Due the will to accumulation mostly this of improve pulsar’s the more data small-eccentricity NS-WD binaries (Damour &the Schaefer NS 1991). and The the differential WDof free in the fall the orbital rates potential eccentricity of of vector thethe (Damour Laplace-Runge-Lenz Milky & vector Way Schaefer of will 1991). the induce The orbitusing a SEP towards characteristic statistical the violation time studies direction tends evolution of to on theassumption polarise the Galactic (Wex 2000), acceleration. eccentricity the By dimensionless distribution SEP of violation parameter NS-WD (the binaries Nordtvedt parameter), with a probabilistic opportunity to improve the SEPsystem, an test outer by WD many orbits ordersSEP an violation, of inner the NS-WD Galactic magnitude acceleration binary (Freire exerted in on et the less binary al. than is of 2012a). one the year. order In Usually, in this the tests of 5 day and et al. 2013), improving upon theunlike expected NS-WD constraint binaries, from these the tests GAIA withwith satellite. PSR-BH Worthy binaries to note will that, also constrain the parameter space 3.2 Equivalence-principle violation and its effects on orbital dynamics was constrained to a comparable magnitude2005; to Gonzalez that from et the al. teststime-variations 2011; in in the Will orbital Solar 2014). parameters System was (Stairsstatistical A also et or al. developed direct probabilistic (Freire test assumptions. et of al. SEP 2012a). with It binary does not pulsars rely that on uses the PoS(AASKA14)042 , x 2 , , ˙ inner 1 e α Lijing Shao is the coupling of the outer body is coupling in the weak field), but (Freire et al. 2012a), where 0 α ( outer 3 outer 3 0 α α α · ) ' inner 2 outer 3 α α − 13 inner 1 α ( . For such theories, the predicted SEP violation effects would be roughly 0 could, according to some alternative theories of gravity, be many orders of α outer 3 ˇ rava-Lifshitz theory. Two generic frameworks for testing deviations from GR α (Shao et al. 2013; Shao 2014), while the violation of LPI leads to spin precession of a ” times larger than their prediction for PSR J0337+1715, therefore making the system 10 0 (Damour & Esposito-Farèse 1992; Bailey & Kostelecký 2006; Shao & Wex 2012; Shao α ˙ / If there exists a preferred frame, the fixed direction will be the direction of the “absolute” velocity of the binary Besides the universality of the free fall, the other two aspects of the Einstein equivalence Generically, violation of LLI and LPI leads to modifications of the orbital dynamics of binary ω 10 NS α with respect to this preferred frame. Testing gravity with pulsars in the SKA Era magnitude more sensitive to SEPSEP violation violation effects effects are than proportional PSR to are J0337+1715. the couplings The of reason the is innerto that bodies the the scalar to field. the If scalar the fieldif outer and it body is is a a WD, NS, then then “ and 2014). The violation of LLI alsodirection leads to spin precession of asolitary solitary pulsar pulsar around with its respect “absolute” to accelerationThey a towards fixed both the change Galactic our centre view on (Shaoversus the & time emission Wex 2013). region in of the aevolution pulsar, pulse are and profiles. result related in and characteristic controlled Interestingly, changes These by modifications modifications one of set can of the be parameters orbitalon jointly in the dynamics constrained both LLI and and PPN of and spin cross-checked. gravityWex SME and 2012; frameworks. The LPI Shao of current et gravity al. best areare 2013; constraints from proportional Shao pulsar & to experiments Wex the 2013; (Stairs timingdramatically Shao et precision with 2014). al. of better 2005; It binary sensitivities. Shao was pulsars. & shownprofiles Simulations With that improves show by the these that, a SKA, constraints factor if tests ofimprove the will the 10 signal same be with factor to improved over the the noise SKA, current ratio thento best ones the of 2030). with limits solely pulse The on 10-year observations Lorentz-violating acquisition (say, from parameters of 2020 one stable profile biweekly is assumed for two MSPs in Shao et al. magnitude larger than much more sensitive to theviolation SEP in violation such predicted a in systemthat these would predict theories. such provide SEP a The violation. stringent non-detection constraint of on SEP alternative theories of3.3 gravity Local Lorentz invariance and local position invariance of gravity principle (Will 2014), namely localof Lorentz gravity, invariance can (LLI) also and berecently local tested raised position with great invariance pulsar interests (LPI) timing intheory experiments. the and gravitational Scenarios community, the with for Ho LLI examples,are violation in the have the parametrised Einstein-æther post-Newtonian (PPN)extension formalism (SME) (Will (Bailey 1993, & 2014) Kostelecký 2006), and both the of standard-model which contain parameters for LLIpulsars violation. and the spin evolution of solitary1992; pulsars Bailey in & characteristic Kostelecký ways 2006; (Damour & Wex &2014; Esposito-Farèse Kramer Shao 2007; & Shao & Wex Wex 2013). 2012;pulsar Shao introduce et The al. time-variations LLI-violating 2013; in Shao modificationscontribution the of to orbital the the orbital eccentricity periastron dynamics and advance of rate, orbital a thus inclination, binary resulting plus in an changes extra in the PK parameters, ˙ PoS(AASKA14)042 Lijing Shao star, where the former ends

M 8 50. In addition, new stable MSPs > ∼ 5. The red line is the ﬁtted model. 14 . 0 = e ). Pulsar – stellar-mass BH binaries, pulsar – intermediate- massive star and another 1

M 20 > 3 yr and the eccentricity . 0 = b P Characteristic pulsar timing residuals caused by the quadrupole moment of Sgr A* BH from BHs are predicted to be the ultimate outcome of massive stars in the theory of GR. Evidence The combination of the sensitivity and the large field of view of the SKA will inevitably mul- mass BH binaries, and pulsars orbiting theno Sgr A* other BH gravity probe different experiments new regimes are1999; of yet gravity Pfahl where able & to Loeb be 2004).mary performed binary The with composed pulsar precision of – a tests stellar-mass (Wex BH & binary Kopeikin may naturally come from a pri- simulated TOAs for three orbital phasesassumed (Liu to be et al. 2012) (figure courtesy of N. Wex). The orbital period is Figure 4: (2013). If these SKA observations(say, are from properly 2000 combined to with 2020), the the 20-year improvement pre-SKA will observations be a factor of for the existence of BHs in variousdecades, astrophysical environments and has is accumulated now during rather the past robuststill few (Narayan indirect, & and McClintock no 2013). high-precision tests However,and such of intriguing observations BHs goal are are in yet the possible. fieldsof of Testing BHs BH astronomy will physics and be physics. is achieved a The with fantastic goal the of SKA precision (Kramer tests et of al. properties 2004). tiply the number ofbinaries pulsars possible. by tens The shorter to integrationposed) hundreds, time will making in be detection pulsar beneficial of search tosystem (say, rare in discoveries a a objects of clean 10-min like environment extremely integration represents relativistic PSR-BH as arameter binaries. “holy pro- space grail” in of A terms pulsar relativistic of astronomy. A gravitational PSR-BH then vast potential, become unexplored spacetime pa- accessible curvature and (see object Figure compactness will Testing gravity with pulsars in the SKA Era from the Galactic census will be verydue helpful to in the breaking vectorial the and/or degeneracies tensorial of field2014). parameters condensations in in the the test, spacetime with such violations (Shao 4. Pulsar – Black Hole Binaries PoS(AASKA14)042 , on c is the / 2 Q Lijing Shao GM = where , should always 3 2 max M S 2 GM G / / cS Q 4 c ≡ χ ≡ q ), the spin-orbit coupling then 2 (Misner et al. 1973). If a complex, massive 2 χ − 15 = q . The dimensionless spin of a BH, M 1 (Misner et al. 1973). In alternative gravitational theories, this bound ≤ χ For a relativistic PSR – Sgr A* BH system, the pulsar can be treated as a test particle in the In the case of relativistic PSR-BH binaries, the prominent effects from gravitation will, on one . This may enable us to look into the bizarre possibility of Sgr A* BH being a boson star χ (Kleihaus et al. 2012). Withimpact a on better the periastron determination advance of from3-dimensional the the spin Sgr BH of A* spin the BH is BH mass, madeof with plausible. the the magnitude quadrupole separation This and from of further direction. timing determines the residuals An will the then extraction allow of a the quantitative test periodic of effects the “no-hair theorem”. allows an initial extraction ofinitial test an of upper the limit “cosmicof of censorship the conjecture” spin becomes magnitude available by of looking the at Sgr the A* magnitude BH. Thus an first-order approximation (Hackmann & Lämmerzahl 2008,tests 2012). of the The “cosmic strategy censorship of conjecture” performing and(2012). the the First “no-hair of theorem” all, was investigated as inthe usual Liu in measurement et pulsar al. of timing, the we periastrongeometry can advance estimate information the rate. can mass be of After thedelay. obtained that, Sgr with a A* With BH better the the through mass detection help determination of of and the the the Shapiro frame-dragging delay effects (see and section the Einstein scalar field, minimally coupled to GR,(Herdeiro is & introduced, Radu then 2014). the “no-hair theorem” could be violated hand, reinforce better measurements of existing testswave such as damping, the Shapiro and delay and on theconjecture” gravitational the and other the “no-hair hand, theorem” enableLiu (Damour & et completely Esposito-Farèse al. new 1998; 2012, tests Wex &always 2014). of Kopeikin exists 1999; the The an “cosmic “cosmic event censorship censorshippreserving horizon classical conjecture” which predictability states prevents in that us a spacetime. for from It a looking imposes realistic into a BH, maximum its spin, there central singularity, thus Testing gravity with pulsars in the SKA Era up as a BH andin the the latter centre ends of up some asenvironment globular a in clusters NS. the (Clausen The Galactic et pulsar centre, al. – there 2014;which intermediate-mass may Hessels may BH be et be binaries numerous al. detected may NSs 2015). exist as orbitingto Given radio the Sgr the pulsars Sgr A* dense (Pfahl BH A* & for BH, Loeb gravity someX-ray tests (Mori 2004). of et have al. However, been 2013; no detected Kennea pulsars yet. etit close al. Recently, is 2013) a enough not and magnetar radio close was (Eatough enough detected etBecause to through al. of the 2013) scattering observations, Sgr by however, A* the BH interstellarpulsars for medium, in in precision the general tests Galactic we of centre will (Wharton gravity needthis et (Eatough the al. will et SKA2 2012; depend al. to Wex et on 2013, detect al. these which 2015). 2013;5 bands Eatough will are et greatly al. included enhance 2015), in the although SKA1-MID,binaries, prospects the for for SKA1 example, doing will the this. start inclusion to For of contribute detecting significantly. Band the other two types of PSR-BH a rotating BH with a given mass quadrupole moment of BH, should satisfy satisfy the constraint may be slightly violated,Hilbert term, as the in Gauss-Bonnet topological the term iset Einstein-Gauss-Bonnet included al. theory, in 2011). the where, Lagrangian of The besides gravityrelates “no-hair (Kleihaus the the theorem” Einstein- higher-order states moments the of“no-hair uniqueness theorem” a of is BH valid, a exclusively the Kerr to dimensionless BH quadrupole its after of mass it a and BH, settles spin. down. For It example, if the PoS(AASKA14)042 5 . 0 ' e Lijing Shao tests of the 1800 MSPs. ∼ e.g. 1% respectively after five ∼ 3 yr and an eccentricity . 0 ' 1% and . b 0 P ∼ the “cosmic censorship conjecture” and the e.g. 16 with the Einstein delay and general-relativistic orbital e.g. for results from a simulated PSR-BH system (Liu et al. 2014). 3 for a hypothetical system with an orbital period 1% level by then (Liu et al. 2012). 4 ∼ The output of gravity tests with pulsars has two possibilities. In the first possibility, GR is By the 2020s, radio astronomy will undergo a revolution brought by the onset of the SKA1. Its Similarly, in the cases of stellar-mass BH and intermediate-mass BH binaries, the spin infor- is negative or small; see Figure 0 falsified. This will certainly providemental an interaction, important gravity, and hint the for nature ourto of further spacetime. new understanding In precision of the with the second flying funda- possibility,tool colours. GR to is This confirmed investigate will other further phenomena,of reinforce for binary our example, pulsars, confidence using in helping GR using toet effects GR deepen al. to as our make 2015). a mass understandings measurements It ofrelevant also areas, non-perturbative QCD for casts effects example, experimental (Watts to constraintstests explain of on gravitational the constructing theories nature with new great of gravitational precisionquantum dark will theories principles. matter provide in important and clues dark to reconcile energy. GR and In both cases, The most stable onesimprovement of in them the will sensitivity be ofthe used the foundation to timing of perform precision gravity. In allows a the usand number era a completely of of closer new the precision tests look SKA, gravity will at the also tests.WD existing many be tests binaries aspects will made The and of be possible NS-BH pushed with binaries. to systemsarea new including of Advances extremes, NS-NS from experimental binaries, the gravity NS- theoretical withof side novel different will tests. types also are contribute It equippedexample, to is with the the indeed different NS-NS a characteristics systems virtue to providedissipative of perform effects extremely nature in different precise orbital that tests tests dynamics pulsar with. of ( binaries GR, For in particular periodic, non- “no-hair” theorem). Tests ofprofoundly gravitational advance theories our understandings from of many fundamental facets physics. in the era of the SKA will pulsar survey will deliver a large population of pulsars, among which there will be 5. Conclusion and Outlook mation of the BHenough can (Wex & be Kopeikin extracted 1999). with Forvide the the stellar-mass much BH help better companion, of a constraints relativistic frame onfrom binary dragging the can inspiralling pro- as scalar-tensor binaries theories well (Damour than iforder & the the of Esposito-Farèse tests magnitude orbit 1998). with better is gravitational than Theseβ tight waves the constraints expected will near-future also constraint be from the an GAIA satellite when Testing gravity with pulsars in the SKA Era The timing residual from the quadrupoleFigure of Sgr A* BH has(Liu a et characteristic al. shape, 2012). as illustrated Accordingand in to the simulations quadrupole for can an beyears orbit measured of with with observations a with precisions the period of SKA. ofat Therefore, several the the months, test the of the spin “no-hair theorem” can be performed deformation), while the NS-WD and NS-BHproperty systems of are gravity suitable in to the studygravitational presence the dipole of dissipative radiative radiation asymmetry and in the gravitationalBH constancy binding binaries of energy will the ( be gravitational useful constant). to Furthermore, test PSR- the BH physics ( PoS(AASKA14)042 Lijing Shao Advancing Astrophysics with the Square 17 , PoS(AASKA14)045 As a final remark, with the better timing capability and new discoveries of stable pulsars from We thank Norbert Wex for kindly providing figures and carefully reading the manuscript. Kilometre Array tic Centre with the Square Kilometre Array”, in proc. & W. Israel, 128–198 Edwards, R. T., Hobbs, G. B.,Ferdman, & R. Manchester, D., R. Stairs, N. I. 2006, H., MNRAS, Kramer, 372, M., 1549 et al. 2013, ApJ, 767, 85 Damour, T. & Deruelle, N. 1986,Damour, Ann. T. Inst. & Henri Esposito-Farèse, Poincaré G. Phys. 1992, Théor.,—. Classical 44, 1992, and 263 Phys. Quantum Rev. Gravity, D, 9, 46, 2093 —. 4128 1993, Physical Review Letters, 70,—. 2220 1996, Phys. Rev. D, 54,—. 1474 1998, Phys. Rev. D, 58,Damour, 042001 T., Gibbons, G. W., & Taylor,Damour, J. T. H. & 1988, Schaefer, Physical G. Review 1991, Letters,—. Physical 61, 1988, Review 1151 Nuovo Letters, Cimento 66, B, 2549 101,Damour, 127 T. & Taylor, J. H. 1992,Deller, Phys. A. Rev. T., D, Bailes, 45, M., 1840 &Deller, Tingay, A. S. T., J. Boyles, 2009, J., Science, Lorimer, 323,Deller, D. 1327 A. R., T., et Verbiest, al. J. 2013, P. W., ApJ, Tingay,Eatough, 770, S. R. 145 J., P., Falcke, & H., Bailes, Karuppusamy, M. R.,Eatough, 2008, et R. ApJL, al. P., 685, Lazio, 2013, L67 T. Nature, J. 501, W., 391 Casanellas, J., et al., 2015, “Observing Radio Pulsars in the Galac- the SKA, the pulsarmentary timing to array (PTA) the projects strong-field willgravitational tests waves leap in discussed the towards here, radiative a regime PTAs new available make (Janssen era et tests as al. of 2015). well. gravitational Comple- theoriesAcknowledgement with References Antoniadis, J., Freire, P. C. C.,Antoniadis, Wex, N., J., et van al. Kerkwijk, 2013, M. Science, H.,Bailey, 340, Koester, Q. D., 448 G. et & al. Kostelecký, 2012, V. MNRAS, A.Barker, 423, 2006, B. 3316 Phys. M. Rev. & D, O’Connell, 74, R. 045001 Bekenstein, F. J. 1975, D. Phys. 2004, Rev. D, Phys. 12, Rev.Bertotti, D, 329 B., 70, Iess, 083509 L., & Tortora,Brans, P. 2003, C. Nature, & 425, Dicke, 374 R. H.Breton, 1961, R. Physical P., Review, Kaspi, 124, V. 925 M., Kramer,Burgay, M., M., et D’Amico, al. N., 2008, Possenti, Science, A.,Capozziello, 321, et S. 104 al. & 2003, de Nature, Laurentis, 426, M. 531 Clausen, 2011, D., Phys. Sigurdsson, Rep., S., 509, & 167 Chernoff,Damour, D. T. 1987, F. 2014, The problem MNRAS, of 442, motion 207 in Newtonian and Einsteinian gravity., ed. S. W. Hawking Testing gravity with pulsars in the SKA Era PoS(AASKA14)042 , Lijing Shao , PoS(AASKA14)143 , PoS(AASKA14)037 , PoS(AASKA14)047 18 Advancing Astrophysics with the Square Kilometre Array Advancing Astrophysics with the Square Kilometre Array Advancing Astrophysics with the Square Kilometre Array Advancing Astrophysics with the Square Kilometre Array SKA”, in proc. and Company) PoS(AASKA14)040 SKA”, in proc. Pulsars with the SKA”, in proc. in proc. Mori, K., Gotthelf, E. V., Zhang,Narayan, S., R. et & al. McClintock, 2013, J. ApJL, E. 770,O’Connell, 2013, L23 R. ArXiv F. e-prints, 2004, arXiv:1312.6698 Physical Review Letters,Paragi, 93, Z., 081103 Godfrey, L., Reynolds, C., et al., 2015,Perera, “Very B. Long B. P., Baseline McLaughlin, Interferometry M.Pfahl, A., with E. Kramer, the & M., Loeb, et A. al. 2004, 2010,Psaltis, ApJ, ApJ, D. 615, 721, 2008, 253 1193 Living Reviews in Relativity, 11, 9 Kennea, J. A., Burrows, D. N.,Kleihaus, Kouveliotou, B., C., Kunz, et J., al. & 2013, Radu, ApJL,Kleihaus, E. 770, B., 2011, L24 Kunz, Physical J., Review & Letters, Schneider, 106,Kramer, S. 151104 M. 2012, 1998, Phys. ApJ, Rev. 509, D, 856 85,Kramer, 024045 M., Backer, D. C., Cordes,Kramer, J. M., M., Stairs, et I. al. H., 2004, Manchester,Kramer, New R. Astron. M. N., Rev., & et 48, Wex, al. 993 N. 2006, 2009,Lattimer, Science, Classical J. 314, and M. 97 Quantum & Gravity, 26, Schutz, 073001 B.Lazaridis, F. K., 2005, Wex, ApJ, N., 629, Jessner, 979 A.,Liu, et K. al. 2012, 2009, PhD MNRAS, thesis 400, (The 805 Liu, University K., of Eatough, Manchester) R. P., Wex, N.,Liu, & K., Kramer, Wex, N., M. Kramer, 2014, M., MNRAS,Lorimer, Cordes, 445, D. J. 3115 R. M., & & Kramer, Lazio, M. T.Lorimer, 2004, J. D. Handbook W. of R., 2012, Pulsar Stairs, ApJ, Astronomy I. 747, (Cambridge H., 1 Lyne, University Freire, A. Press) P. G., C. Burgay, C., M., et Kramer, al.Manchester, M., 2006, R. et ApJ, N., al. 640, Kramer, 2004, 428 M., Science, Stairs, 303,Misner, I. 1153 C. H., W., et Thorne, al. K. 2010, S., ApJ, & 710, Wheeler, 1694 J. A. 1973, Gravitation (San Francisco: W. H. Freeman Hulse, R. A. & Taylor, J.Janssen, H. G. 1975, ApJL, H., 195, Hobbs, L51 G., McLaughlin, M., et al., 2015,Jordan, “Gravitational P. wave 1959, astronomy Zeitschrift with fur Physik, the Keane, 157, 112 E. F., Bhattacharyya, B., Kramer, M., et al., 2015, “A Cosmic Census of Radio Testing gravity with pulsars in the SKA Era Fierz, M. 1956, Helv. Phys. Acta,Fonseca, 29, E., 128 Stairs, I. H., &Freire, Thorsett, P. S. C. E. C., 2014, Kramer, ApJ, M.,Freire, 787, & P. 82 Wex, C. N. C., 2012a, Wex, Classical N., and Esposito-Farèse,Gonzalez, Quantum G., M. Gravity, et 29, E., al. 184007 Stairs, 2012b, I. MNRAS, H.,Hackmann, 423, Ferdman, E. 3328 R. & D., Lämmerzahl, et C. al. 2008,—. 2011, Physical 2012, ApJ, Review Phys. 743, Letters, Rev. 102 100, D, 171101 85,Herdeiro, 044049 C. A. R. & Radu,Hessels, E. J. 2014, W. T., Physical Possenti, Review A., Letters, Bailes, M., 112, et 221101 al., 2015, “Pulsars in Globular Clusters with the SKA”, PoS(AASKA14)042 Lijing Shao Advancing Astrophysics with the Square 19 , PoS(AASKA14)043 J. van Leeuwen, 171–176 of State of cold dense matter with the SKA”, in proc. 177: Pulsar Astronomy – 2000 and Beyond, ed. M. Kramer, N. Wex, & R. Wielebinski, 113 Kilometre Array Wharton, R. S., Chatterjee, S., Cordes,Will, J. C. M., M. Deneva, 1993, J. Theory S., and &—. Experiment Lazio, 2014, in T. Living Gravitational J. Reviews Physics W. in 2012, (Cambridge Relativity, ApJ, University 17, Press) 753, 4 108 —. 2014, ArXiv e-prints, arXiv:1402.5594 Wex, N. & Kopeikin, S. M.Wex, 1999, N. ApJ, & 514, Kramer, 388 M. 2007,Wex, MNRAS, N., 380, Liu, 455 K., Eatough, R. P., et al. 2013, in IAU Symposium, Vol. 291, IAU Symposium, ed. Testing gravity with pulsars in the SKA Era Ransom, S. M., Stairs, I. H.,Shao, Archibald, L. A. 2014, M., Physical et Review al. Letters,Shao, 2014, 112, L., Nature, 111103 Caballero, 505, R. 520 N., Kramer,Shao, M., L. et & al. Wex, 2013, N. Classical 2012,—. and Classical 2013, Quantum and Classical Gravity, Quantum 30, and Gravity, 165019 29, Quantum 215018 Gravity,Stairs, 30, I. 165020 H. 2003, Living ReviewsStairs, in I. Relativity, 6, H., 5 Faulkner, A. J.,Stairs, Lyne, I. A. H., G., Thorsett, et S. al. E., 2005,Taylor, & J. ApJ, Arzoumanian, H., 632, Z. Fowler, 1060 L. 2004, A., PhysicalTaylor, Review & J. Letters, McCulloch, H. 93, P. M. & 141101 1979, Weisberg, J. Nature, M.Verbiest, 277, J. 1982, 437 P. ApJ, W., Bailes, 253, M., 908 vanWatts, Straten, A. W., L., et Xu, al. R., 2008, Espinoza, ApJ, C., 679, et 675 al., 2015, “Probing the neutron star interior and theWeisberg, Equation J. M., Nice, D. J.,Weisberg, & J. Taylor, M., J. Romani, H. R. 2010, W., ApJ, &Weisberg, 722, J. Taylor, 1030 J. M. H. & 1989, Taylor, J. ApJ, H. 347,Wex, 1981, 1030 N. General 2000, Relativity in and Gravitation, Astronomical 13, Society 1 of the Pacific Conference Series, Vol. 202, IAU Colloq.