Electromagnetic observations of pulsars and binaries

Transcription

1 VESF SCHOOL on GRAVITATIONAL WAVES IV Edition May 2009, EGO Site - Cascina Pisa (Italy) Electromagnetic observations of pulsars and binaries ANDREA POSSENTI INAF Osservatorio Astronomico di Cagliari

2 Outline 1. Pulsar Generalities 2. Double Neutron Star Merger Rate 3. Pulsar Timing Concepts 4. Gravity Theories tests with Pulsars 28 May 2009 EGO Site Cascina (Pisa)

3 VESF SCHOOL on GRAVITATIONAL WAVES IV Edition May 2009, EGO Site - Cascina Pisa (Italy) Books Manchester & Taylor 1977 Pulsars Pulsars Lyne & Smith 2005 Pulsar Astronomy Lorimer & Kramer 2005 Handbook of Pulsar Astronomy AA.VV Physics of relativistic objects in compact binaries: from birth to coalescence, Springer Review Articles Science, April 2004 Neutron Stars, Isolated Pulsars, Binary Pulsars ARA&A, Jan 2008 The Double Pulsar Living Reviews articles: ( Stairs 2003: Testing General Relativity with pulsar timing Will,, 2006: The confrontation btw General Relativity and experiment Lorimer 2008: Binary and millisecond pulsars

4 VESF SCHOOL on GRAVITATIONAL WAVES IV Edition May 2009, EGO Site - Cascina Pisa (Italy) 1. Pulsar Generalities ELECTROMAGNETIC OBSERVATIONS OF PULSARS AND BINARIES

5 What is a Pulsar? A PULSAR is a rapidly rotating and highly magnetized neutron star, emitting a pulsed radio signal as a consequence of a light-house house

6 The rotating magnetized NS in vacuum µ = ½ B p R 3 is the magnetic moment R = NS radius B p = polar magn. field L sd Assuming that the rotational energy loss sd = d/dt (E rot ) = d/dt (IΩ 2 /2) = I Ω Ω matches the emitted power (derived from the basic electrodynamics formula): L dipole dipole = [ 2/3c 3 ] µ 2 one can infer

7 Derived parameters: age & magnetic field Actual age of pulsar is function of initial period and braking index n=(ν ν )/ ν 2 (assumed constant) For P 0 << P, P n = 3,have characteristic age If true age known,one can compute initial period From braking equation, one can derive B 0 at NS equator with R = NS radius. Value at pole is 2B 0 Typically assumed R=10 km, I=10 45 gm cm 2, n=3 (from Manchester & Taylor)

8 Pulsar Energetics Spin-down Luminosity: (from Manchester & Taylor) Radio Luminosity: (from Manchester & Taylor) 10 28

9 The B s vs P diagram Young pulsar Line A pulsar is put on it once both P and dp/dt are measured, from which B s = [ P P ]½ G. ATNF Pulsar Catalogue

10 A dichotomy in the population Young pulsar Line How to explain this group of pulsars? ATNF Pulsar Catalogue

11 Discovery of the first millisecond pulsar B (1982) [Backer et al. 1982] P = ms V = tang 0.13 c!! Extreme physical conditions occur in millisecond pulsars tangential velocity First promise of putting constraints to the Equation of State for nuclear matter!

12 The MSP vs ordinary pulsar features Short spin periods: 1.39 ms < P < 200 ms (conventional) Lower surface magnetic fields: 7.5 < log (B s (gauss)) < 10.5 (conventional) Much larger characteristic ages: τ ~ years Much higher fraction of binarity: : f bin > 70% Slower mean 3D velocity: v ~ 130 km/s (Toscano et al 1999) Half of the objects moving towards the Galactic plane (Toscano et al 1999) A tendency to wider duty cycles: W ~ P (Kramer et al 1998) Similar mean spectral index: α ~ (Kramer et al. 1998) Slightly less average radio luminosity (Kramer et al. 1998) Higher degree of polarization (Xilouris et al. 1998)

13 The MSP formation paradigm Recycling scenario: Millisecond pulsars are old neutron stars spun up by accretion of matter and angular momentum from a companion star in a multiple system [Bisnovati-Kogan & Kronberg 1974, Alpar et al. 1982]

14 1000 yr Hubble time death line A died pulsar could be spun up and rejuvenated by an evolving binary companion

15 Dana NASA A died pulsar could be spun up and rejuvenated by an evolving binary companion

16 1000 yr A newly born fast spinning pulsar Hubble time death line A recycled pulsar spins down again due to magnetodipole braking

17 [ Stairs 2004 ] Binary Evolution Binary Evolution

18 More & more pulsars: the current sample! Parkes discoveries Parkes PM = 725 Parkes SWI+SWII = Parkes PH = 18 Parkes PA > 10 Total using multibeam > 847 Parkes GC search > 34 GBT discoveries GC search > 70 Drift scan search > 20 Arecibo discoveries Galactic Plane search > 50 Until 1997: ~ 750 Now in the Atnf Catalog: ~ 1800 ~ 20 Extragalactic (LMC/SMC) ~ 150 Binary ( 140 somehow recycled) ~ 80 Young (age<10000 yr) ~ 26 Vela-like (i.e. very young) 2 Radio emitting AXPs 9 Double Neutron star binaries 1 Double pulsar TOTAL known sample 140 in 26 Globular Clusters + Rrats, Intermittent PSRs,

19 VESF SCHOOL on GRAVITATIONAL WAVES IV Edition May 2009, EGO Site - Cascina Pisa (Italy) 2. Double Neutron Stars Merger Rates ELECTROMAGNETIC OBSERVATIONS OF PULSARS AND BINARIES

20 [ from Chunglee Kim ] Coalescence rate R (empirical approach) R = Number of sources correction factor Lifetime of a system Correction factor : correction for pulsar beaming Lifetime of a system = current age + merging time of a pulsar of a system

21 Properties of pulsars in DNSs. P s (ms) (ss -1 ) P orb (hr) ecc M tot ( ) P s Galactic disk pulsars merging in less than an Hubble time B x (1.35) J x (.) J x (1.37) B x (1.39) M J x (1.24)

22 Properties of pulsars in DNSs (cont) τ c (Myr) τ merg (Myr) dω/dt (deg/yr) Galactic disk pulsars merging in less than an Hubble time B º.75 J J B º.23 J º.90

23 [ from Chunglee Kim ] Coalescence rate R (empirical approach) R = Number of sources correction factor Lifetime of a system Correction factor : correction for pulsar beaming Lifetime of a system = current age + merging time of a pulsar of a system Number of sources : number of pulsars in coalescing DNSs in the galaxy of a given type How many pulsars similar to each of the known DNSs exist in our Galaxy? It needs estimating the SCALE factor

24 Results for Double Neutron Stars [ Chunglee Kim 2008 ]

25 The Galactic coalescence rate R for Double Neutron Star Binaries For the reference model (at 95% CL): Coalescence rate R (current) (Myr -1 ) R (previous) (Myr -1 ) B1913+B1534+J0737+J1906 [ Lorimer 2008 ] B1913+B1534 Increase rate factor R peak (current) R peak (previous) ~ 5-6

26 Detection rate of Double Neutron Star inspirals [ Lorimer 2008 ] The most probable inspiral detection rates for LIGO/VIRGO R det (initial) = R det (advanced) = ~ 1 event per 8 yr (95% CL, most optimistic) ~ 600 events per yr (95% CL, most optimistic) Many uncertainties in the model Rates may be significantly higher if a substancial population of highly eccentric binary systems exists. It could escape detection due the short lifetime before GW inspiral [ Chaurasia & Bailes 2005 ] One year of observation with LISA of the Double Pulsar would detect the continuous emission at freq=0.2 mhz with a S/N 2 [ Kalogera 2004 ]

27 Results for NS-WD binaries [ Chunglee Kim 2008 ] Only 3 known coalescing systems known to date

28 The Galactic coalescence rate R for Neutron Star-White Dwarf Binaries For the reference model (at 68% CL), not corrected for beaming: Coalescence rate R (Myr -1 ) J0751+J1757+J1141 [ Chunglee Kim et al 2004 ] Coalescing frequencies are in the LISA band: but expected event rate not very encouraging [ Chunglee Kim et al 2004 ]

29 Coalescence rate calculations (other approaches) The presented approach is an empirical one The alternate option is to run extended Monte Carlo simulations of the most likely evolutionary scenario starting from a population of primordial binaries The uncertainties in the assumption for the initial state of the binaries make the range of the predicted merging rates larger than with the empirical approach [ Dewey & Cordes 1987 ] [ Lipunov et al 1996 ] [ Belczynski, Kalogera, Bulik 2002 ] [ Belczynski et al 2008 ] Combination of various observational constraints resulting from binary population synthesis code are very promising [ O Shaughnessy et al 2008 ]

30 VESF SCHOOL on GRAVITATIONAL WAVES IV Edition May 2009, EGO Site - Cascina Pisa (Italy) 3. Pulsar Timing Concepts ELECTROMAGNETIC OBSERVATIONS OF PULSARS AND BINARIES

31 Timing idea: observations Performing repeated observations of the Times of Arrival (ToAs) at the telescope of the pulsations from a given pulsar and searching the ToAs for systematic trends searching the ToAs for systematic trends on many different timescales, from minutes to decades

32 Timing idea: modeling if a physical model adequately describes the systematic trends, it is applied with the smallest number of parameters otherwise if a physical model is not adequate, it is extended (adding parameters) or rejected in favour of another model when a model finally describes accurately the observed ToAs, the values of the model s parameters shed light onto the physical properties of the pulsar and/or of its environment

33 @ Lorimer Timing of a radio pulsar

34 Getting barycentered ToAs The TOPOCENTRIC ToAs must be corrected, calculating them to infinite frequency at Solar System Barycentre (SSB) thus obtaining the BARYCENTERED ToAs: the time scale is (Tempo2) the Barycentric Coordinate Time (TCB), i.e. the proper time of an observer at SSB were the gravity field of Sun and Planets absent t SSB t obs t clk SSB : Calculated BARYCENTERED ToA at INFINITE frequency obs : Observed TOPOCENTRIC ToA : Observatory clock correction to TAI (= UTC + leap sec), via GPS D/f 2 : Dispersion term R : Roemer delay (propagation delay) to SSB (need SS ephemeris, e.g. DE405) S : Shapiro delay in Solar-System : Einstein delay at Earth E

35 Timing model: rotational terms 1. Have series of barycentered ToAs: t i 2. Model pulsar frequency evolution ν(t) by Taylor series, and then integrate to get pulse phase evolution (φ(t)(t) = 1 for t=p) 4. Form residuals r i = φ i n i 3. Choose t = 0 to be first ToA, t 0 where n i is the nearest integer to φ i 5. If pulsar model is accurate, then r i << 1 6. Corrections to model parameters are obtained by making least- squares fit to trends in r i

36 Timing model: astrometric terms Barycentric corrections depends on Pulsar POSITION, PROPER MOTION and PARALLAX Thanks to the least- square fit, one can solve for those positional and kinematic parameters from errors in SSB correction

37 Timing model: isolated pulsars From timing of an isolated pulsar over a long enough time span, one can in principle get RA & DEC: Celestian coordinates PMRA & PMDEC: Proper Motion π : Trigonometric Parallax (i.e. Distance) DM : Accurate Dispersion Measure DM1 : Time Derivative of Dispersion Measure P0: Rotational Period P1: Time derivative of P0 P2: Second time derivative of P0 P3: Third time derivative of P0

38 Since 1974 pulsars in binary systems are known

39 Correcting ToAs to the binary barycenter The PULSARCENTRIC ToAs (i.e. ToAs expressed in pulsar proper time) must be corrected, calculating them at the Pulsar System Barycenter (PSB) t PSR-BARY = T psr + R,b + E,b + S,b + A t PSR-BARY T psr R,b S,b E,b A : Time at pulsar system barycenter : Time in pulsar proper time (measured as at pulsar surface) : Roemer delay (propagation delay) from pulsar to PSB : Shapiro delay in pulsar binary : Einstein delay in pulsar binary : Aberration delay due to pulsar rotation Those terms contain various parameters of the binary system Those terms contain various parameters of the binary system and thus a least-square fit to the residuals of a model including those parameters can allow to measure them

40 For most binaries, 5 keplerian parameters are measured and are (well) enough to satisfactorily describe the data P b : Orbital period x = a p sin i : Projected semi-major axis ω : Longitude of periastron e : Eccentricity of orbit T 0 : Time of periastron Mass function: f ( m p, m c ) 4 = π G ( a p sin i) ( m c sin i) = 2 P ( m + m ) 2 orb p c for i = 90 o Minimum companion mass for i = 60 o Median companion mass

41 Pulsars as clocks Pulsar periods can sometimes be measured with unrivalled precision e.g. on Jan 16, 1999, PSR J had a period of ± ms 16 significant digits!

42 Atomic clocks vs pulsar timing [ Lorimer 2008 ] Unfortunately only a subsample of the recycled pulsars is able to achieve such a rotational stability The majority of the ordinary pulsars undergo timing irregularities es

43 VESF SCHOOL on GRAVITATIONAL WAVES IV Edition May 2009, EGO Site - Cascina Pisa (Italy) 4. Gravity Theory Tests with Pulsars ELECTROMAGNETIC OBSERVATIONS OF PULSARS AND BINARIES

44 Binary systems: the classic laws 1] Elliptical and planar orbit 2] Constant areolar velocity 3] a 3 = (G/4π 2 ) M tot P 2 Keplero (1609, 1609, 1619)

45 for some binary pulsars, the accuracy of the ToA data is so high that - by using only the keplerian description - one can obtain no acceptable timing solution! Additional physics is needed! but which physics?

46 Going beyond Kepler Even before publication of General Relativity, a blossom of alternate Gravity Theories appeared A very large class of these Theories (somehow the only ones which have some chance to be viable ) are the METRIC THEORIES OF GRAVITY [e.g Will 2006 ] - a symmetric metric exists - all test bodies follow geodesic of the metric - in local freely falling reference frames, all the NON- gravitational laws of physics are those written in the language of special relativity In metric theories, gravitation must be a phenomenon related with the occurrence of a curved spacetime

47 Going beyond Kepler In any metric theory, matter and NON-grav fields respond only to the metric Additional fields can exist, though, giving rise to - Tensor/scalar theories - Tensor/vectorial theories - Bimetric theories all of them incorporating their own parameters These additional fields prescribe how matter and NON- grav fields contribute to create the metric; once determined, the metric alone acts back on the matter

48 Going beyond Kepler The Parametrized Post Newtonian (PPN) approach A suitable and successful framework for describing the results and a constraining a very large class of METRIC theories of gravity is that of the so called Parametrized Post Newtonian formalism It describes all metric theories of gravity in WEAK-FIELD conditions, i.e. at order 1/c 2 wrt Newtonian physics [e.g Will 2006 ] Deviations from Newtonian physics are related to a set of 10 PPN-paramters, each of them associated with a specific physical effect [e.g Will 2006 ]

49 @ Will 2009 Parameter γ β ξ α 1 Going beyond Kepler What it measures, relative to general relativity How much space curvature produced by unit mass? How nonlinear is gravity? Preferred-location effects? Value in scalar tensor theory (1+w)/(2+w) 1 + L α 2 a 1 Preferred-frame effects? Value in GR ζ ζ Is momentum conserved? ζ ζ α 3 a Value in semi- conservative theories The 10 PPN-parameters and their significance g b x

50 Going beyond Kepler Tests of Gravity in the weak-field limit ε Earth = Weak in which sense? In term of the compactness parameter ε E E grav rest = GM R Earth Earthc ε Sun = E E grav rest = GM R Sun Sunc All the Solar System tests fall in this category since the experiment about the light deflection by Sun [Eddington 1919] and the observation of the Mercury advance of perihelion The PPN formalism is well tailored for describing the outcomes of these tests [e.g Will 2006 ] So far, GR has passed all these tests with full marks and cum laude

51 Going beyond Kepler But is GR still the best available theory for describing Nature also under extreme physical conditions? This is NOT an ACADEMIC question: e.g. extreme conditions are certainly those at which any long sought unified model for interactions applies [ e.g. Antoniadis 2005 ] Moreover, is enough to test alternative theories only in the weak-field limit? There exist alternative metric gravity theories (e.g. a subclass among the tensor-scalar scalar theories) which would pass ALL Solar System (weak-field limit) tests, but would be violated as soon as extreme conditions (strong-field limit) are reached [Damour & Esposito-Farese 1996]

52 Going beyond Kepler Tests of gravity in the strong-field limit Strong in which sense? In term of the compactness parameter ε the source should satisfy ε source = E E grav rest = GM R source c source Where to find a laboratory for testing GR in extreme conditions? Not on Earth or on Solar System but in the Cosmo...very interesting targets are relativistic objects in compact binaries NSs and BHs are relativistic objects compact binaries Egrav GM NS ε NS = = E R c rest NS Egrav GM BH ε BH = = E R c Gravitational radiation inspiral affects binary evolution within an Hubble time rest BH

53 Going beyond Kepler Tests of gravity in the strong-field limit Astrophysical contexts: during late stages of coalescence of a binary hosting relativistic ic object(s), the orbital velocity approaches c and the orbital separation approaches the size of the star(s), whence physical processes occur cur in strong- field conditions: wonderful targets for LIGO, VIRGO and, in future, LISA emission processes occurring in relativistic objects close to the e event horizon: e.g. spectral and timing features in the electromagnetic emission (often X- X ray) from the neighbourhood of the last stable orbit of accretion disks surrounding NS or BH hosted in a binary system: some hints from XMM- Newton and Rossi- XTE but targets for future high energy (most X- X ray) observatories: XEUS compact relativistic binary pulsars: targets for current TIMING observations in the RADIO band

54 Going beyond Kepler Tests of gravity in the strong-field limit Wait a minute! Orbits of known binary pulsars are never entering the strong-field limit... E GM grav bin psr 5 3 ε = = bin psr 5 3 bin psr Erest abin psrc c But in most alternative theories of gravity (e.g. in the tensor- scalar ones) the orbital motion and the gravitational radiation damping depend on the gravitational binding energy (i.e. self gravity, e.g. ε NS 0.2, ε BH 0.5) of the involved bodies [e.g. Esposito-Farese 2005, Will 2006] If enough accuracy in the measurements is provided, significant effects are expected to be detectable even in the weak-field limit for the orbits V

55 Going beyond Kepler Tests of gravity in the strong-field limit A suitable and successful framework for testing and constraining a very large class of gravity theories is that of the Post-Keplerian (PK) formalism [Damour & Deruelle 1986] 1 st PK parameters are operationally defined: i.e. they are phenomenological quantities, which there is a prescription to measure for 2 nd In ANY specific gravity theory (picked in a large range of metric theories), and for negligible spin contributions, the PK parameters can be written only as a function of the masses of the two stars and of the keplerian parameters of the binary system [Damour & Deruelle 1986]

56 Timing model:post-keplerian params The easiest to observe post-keplerian parameters ω : Periastron precession γ : Time dilation and gravitational redshift r : Shapiro delay range s : Shapiro delay shape P b : Orbit decay due to Gravitational Wave emission

57 Pulsar Timing: relativistic pulsars periastron precession

58 Pulsar Timing: relativistic pulsars orbital decay

59 Pulsar Timing: relativistic pulsars gravitational redshift and time dilation

60 Pulsar Timing: relativistic pulsars Shapiro delay

61 What do we learn when observing also the Post-keplerian parameters? Periastron precession Time dilation & gravitational redshift Shapiro delay (amplitude) Orbital period decay Shapiro delay (shape) e P b x m p m c M = m p + m c orbital eccentricity orbital period projected semimajor axis pulsar mass companion star mass where total system lagrangian mass Observing than 2 relativistic the values PK parameters of only 2 PK parameters Once more than are known, one derives the masses of the 2 bodies and hence predicts the further PK par on the basis of a given Gravity Theory One can measure the pulsar and companion star masses with unrivalled precision A test for Gravity Theories

62 f ( m p, m c ) = 4π G ( a p sini) ( mc sini) = 2 P ( m + m ) 2 orb p c Mass Function constraint ω& sin i = 1 NOT ALLOWED The pulsar and companion star masses are unconstrained

63 One PK-parameter: constraining mass

64 Two PK parameters: mass determined within a theory γ

65 Three PK parameters: in correct theory lines meet! γ

66 γ But not in a wrong theory!!!

67 Now the catalog contains 8/9 Double Neutron Star Binaries PULSAR Pspin DM Porb ap sin(i) Mc+Mp ecc TimeSpDwn TimeMerg [ms] [cm-3 pc] [day] [lt-s] [ Msun ] [10 8 yr] [10 8 yr] J J >T Hubble B J tbd 11.0 J >T Hubble J >1.22 < tbd >T Hubble B J NS+WD? B C

68 Now The the most catalog interesting contains 8/9 Double for Neutron GR tests Star are Binaries PULSAR Pspin DM Porb ap sin(i) Mc+Mp ecc TimeSpDwn TimeMerg [ms] [cm-3 pc] [day] [lt-s] [ Msun ] [10 8 yr] [10 8 yr] J J >T Hubble B J tbd 11.0 J >T Hubble J >1.22 < tbd >T Hubble B J NS+WD? B C

69 PSR B Discovered on 1974 [ Hulse & Taylor 75] Pulsar + Neutron Star Spin period = 59 ms Orbital period = 7.8 hrs Eccentricity = 0.61 Measured 3 PK pars: ω γ P b Most precise NS mass determination to date: (2) M sun (2) M sun sun [ Weisberg & Taylor 2004]

70 The measurements of Russell Hulse The and prediction of of Joe Taylor the Einstein s equations The (in?)direct proof of GW existence: PSR B GR provides an accurate description NOBEL of the PRIZE system as orbiting POINT MASSES: 1993 i.e. NS structure does not affect Taylor orbital & Hulse motion [ Weisberg 2007 ]

71 PSR B Discovered on 1990 [ Wolszczan 90] Pulsar + Neutron Star Spin period = 38 ms Orbital period = 10 hrs Eccentricity = 0.27 Measured 5 PK pars: ω γ P b s r Non-radiative predictions of GR tested at better than ~1% level [ Stairs 2002]

72 PSR B P b does not match! [ Stairs 2002] Affected by relative acceleration of CoM of binary pulsar system wrt Solar System barycenter [ Damour & Taylor 1991] Three terms: -vertical acc in Galactic potential -acc in the plane of the Galaxy -apparent acc due to tranverse motion [ Shklovskii 1970 ] This also limits radiative GR tests for B at current 0.2% level level [ Weisberg & Taylor 2004 ]

73 Burgay - OAC The double pulsar PSR J A/B 3039A/B

74 P. P Basic Parameters and evolution Spindown age B surf R LC B LC. E rotational Mean orb vel PSR J A 3039A 22.7 ms 1.7 x Myr 6 x 10 9 G 1,080 km 5 x 10 3 G 6 x erg s km s -1 PSR J B 3039B 2.77 s 0.88 x Myr 1.6 x G 1.32 x 10 5 km 0.7 G 1.6 x erg s km s -1 [ Burgay et al 2003; Lyne et al 2004 ]

75 Howe - ATNF The origin of the double pulsar

76 PSR J A/B 3039A/B (orb params) Discovered on 2003 [ Burgay et al 2003, Lyne et al 2004 ] Pulsar + Pulsar Spin period = 22.7 ms s Orbital period = 2.5 hrs Eccentricity = 0.09 Measured 5 PK pars: ω γ P b s r + Mass Ratio R

77 Mass-mass diagram for J A&B 3039A&B at Jan 2004

78 Mass-mass diagram for J A&B 3039A&B at Jan 2004 Mass function A

79 Mass-mass diagram for J A&B 3039A&B at Jan 2004 Mass function B

80 Mass-mass diagram for J A&B 3039A&B at Jan 2004 Mass ratio

81 The nature of the mass ratio constraint For ANY fully Conservative theories (Will 1992) e.g all Langragian-based theories including multi-scalar tensor theories (Damour & Taylor 1992) R x x B A = m m A B + O( c 4 ) Ratio is independent of strong (self-)field effects! Qualitatively different to other PK parameters, which all depend on constants like G AB, which differs from G Newton depending on strong-field effects in theory!

82 Mass-mass diagram for J A&B 3039A&B at Jan 2004 Periastron advance

83 Mass-mass diagram for J A&B 3039A&B at Jan 2004 Grav. Redshift + 2 nd order Doppler

84 Shapiro delay in PSR J A 3029A arrival times s = sin i R 1+ ecosφ ( ) g t Shap = ln c 1 sinisinψ Lyne et al 2004

85 Mass-mass diagram for J A&B 3039A&B at Jan 2004 Shapiro s

86 What is the orientation of the orbit of the system? From determination of the shape s of the Shapiro delay s= (-39,+16) it results i = 88.7( ) deg ~1 [ Possenti adapted from Lyne et al 2004 ]

87 Mass-mass diagram for J A&B 3039A&B at Jan 2004 Shapiro r

88 The unique capability of J system for General Relativity tests at June independent tests of GR! M B =1.249(1)M Observed shape of Shapiro delay in agreement with GR at 0.05% level M A =1.338(1)M Kramer

89 Expected in GR: Summary of the tests of GR Based on: R = ± & ώ= ± deg/yr Observed: [ Kramer et al 2006 ] Ratio: γ = (22) ms (26) dp b /dt= (17) (17) (17 ms (26) ms (17) 10 r =6.153(26) µs 6.21(33) µs s= ( ) (-39,+16) (68) 1.003(14) 1.009(55) (50) s s exp obs = ± Precision of 5x10-4 best in strong-field Expect to supersede solar system tests

90 Current radiative GR tests for J system are at ~1% level [ Kramer et al 2006 ] What about galactic potential and kinematic corrections? From recent interferometric determination of the distance of the system: [ Deller et al 2009 ] Radiative GR tests for J system may reach 0.01% level in a decade [ Deller et al 2009 ]

91 Time-scale of timing accuracy improvements Prospects for timing are excellent: precision ω time 1.5 P b precision γ time 1.5 P 1.3 b precision dp b /dt time 2.5 P 3 b precision r, s time 0.5 Caveats: Timing noise of B Geodetic precession may lead to changing profiles Galactic & kinematics contributions to secular changing of P b

92 The case of the Geodetic Precession The GeoPrecession rate is given by: [ Kramer ]

93 Assuming synchrotron absorpion in the closed magnetosphere of pulsar B [ Lyutikov & Thompson 2005 ] [Breton et al 2008] a nice reproduction of the eclipse of the radio signal of A was obtained

94 From the data of 63 eclipses observed at GBT: Inclination of spin axis of pulsar B wrt orbit normal Θ o ± 0.5 (1 σ) Angle between magnetic and spin axes of pulsar B α 70.9 o ± 0.5 (1 σ) [Breton et al 2008]

95 The modeling of the precession effect The best-fit geometric parameters were jointly searched for the 63 eclipses observed at GBT, keeping all the geometry constant, but allowing the longitude of the spin axis Ф to vary [Breton et al 2008]

96 The best fit parameters [Breton et al 2008] GR predicts a geodetic precession rate = ± deg/yr It is observed a geodetic precession rate = 4.77±0.66 deg/yr Agreement at 13 % level ( at 1σ 1 )

97 Constraint on spin-orbit coupling In ANY fully conservative theory σ B = spin-orbit coupling constant = generalized grav constant For the special case of the double pulsar only, we can measure getting and compare with the GR prediction Confermed GR effacement property of gravity also for SPINNING bodies: i.e. NS structure does not prevent it to behave like a spinning test particle in an external field [ Breton et al 2008 ]

98 The very last mass-mass diagram for J A/B 3039A/B jul 2008 M B =1.249(1)M 5 independent tests of GR! [Breton et al 2008] s s obs exp 0.05% M A =1.338(1)M

99 What might be feasible to measure: k Moment of Inertia of J A 3039A Total periastron advance to 2PN level: [ Damour & Schaefer 1988 ] tot = 3β 1 e T [ ] A A B B f β 2 + g β β g β β 0 0 S 0 S S 0 S 1PN 2PN Spin A Spin B Equation-of of-state for the nuclear matter!! A 10% accuracy on I would exclude most EoS [ Lattimer & Schutz 2004 ] [ Morrison et al. 2004] Neutron star dependent β = S 2 π G c 1 P I m 2

100 Constraining alternate Theories of Gravity: Tensor-Scalar [ Esposito-Farese 2004 ] General Relativity g = µν a ( ) 2 ϕ = α ϕ + β ϕ ( ) a ϕ α ϕ, β scalar field metric 1 2 Limits from J on tensor-scalar scalar theories Binary pulsars impose β 0 > due to the spontaneous scalarization effect in NSs 0 coupling field-matter coupling parameters

101 PSR J Discovered on 2000 [ Kaspi et al 2000] Pulsar + Massive WD Spin period = 394 ms Orbital period = 4.7 hrs Eccentricity = 0.17 Measured 3 PK pars: ω γ P b Radiative predictions of GR tested at better than ~6% level [ Bhat et al 2008]

102 The case of PSR J Masses of the two components are similar M NS = ( 1.27 ± 0.01 ) M sun M WD = ( 1.02 ± 0.01 ) M sun but the radii are certainly very different, leading to a significant icant difference in the degree of compactness ε (i.e. in the self-gravity ) of the two bodies: = Egrav = GM NS E R c GM grav WD 4 ε NS ε = = 10 WD 2 rest NS Erest RWDc Tensor-scalar scalar theories predicts the emission of a large amount of DIPOLAR scalar waves (as opposed to the dominant QUADRUPOLAR radiation predicted by GR) in such a very asymmetric system E

103 The case of PSR J This is the best available binary pulsar for constraining the coupling constant α 0 Whence the limits are: α 2 0, [Esposito-Farese 2005] are: [Bhat et al 2008] 0, < ⅓ Cassini limit α 2 0,B-D < Cassini limit g = µν a ϕ ( ) 2 ϕ = α ϕ + β ϕ ( ϕ ) 0 scalar field a For β 0 it holds α 0, ~ ( δ rel P b ) ½ α 0, β 0 For β 0 = 0 (i.e. Brans-Dicke) it holds α 0,B-D ~ ( In 2012 δrel P b 2% at which galactic & kin corrections become dominant, but likely a 1% determination will be achievable metric coupling field-matter coupling parameters ~ (α0, 0, )/(2 NS ) )/(2ε NS

104 some other tests on fundamental physics with binary pulsars Time derivative of G [dg/dt]/g = ( PSR J Strong Equivalence Principle = highly circular WD-MSP Momentum conservation α 3 = highly circular WD-MSP Existence of preferred frame α^ 1 = 1.4 PSR J [dg/dt]/g = (-5±18) yr -1 (about 10 times weaker than lunar ranging but much simpler and in strong-field) [ Damour & Taylor 1991, Verbiest et al 2008 ] = (weaker than solar system tests, but in strong-field regime) [ Wex 1997, Stairs et al 2005 ] ^ = (10 13 better than Earth or Mercury perhelion shifts) [ Bell & Damour 1996, Stairs et al 2005 ] = (slighlty weaker than lunar laser ranging, but in strong-field regime) [ Wex 2000 ]

105