Gravity Tests with Radio Pulsars

Transcription

1 Gravity Tests with Radio Pulsars Norbert Wex Paris, June 21 st, 2010

2 Regimes of Gravity Tests (1) Quasi-stationary weak-field regime Solar system experiments (2) Quasi-stationary strong-field regime (3) Radiative regime (4) Highly relativistic regime Binary pulsar experiments GW astronomy

3 Pulsars Extreme Objects Fast rotating: Magnetic field: up to r/min ~ G Electric field: ~ V Radius of 10 km, but 1.4 solar masses just 2½ times their Schwarzschild radius = Gravity at surface ~ g Earth

4 Pulsar Timing PSR J : 15 years of observations with EPTA P = ± s [ Lazaridis et al ] 90 billion pulses since discovery, and not lost a single count!

5 The Radio Pulsar Population ~ 2000 radio pulsars 1.40 ms (PSR J ad) 8.50 s (PSR J ) ~ 140 binary pulsars Orbital period range 95 min (PSR J R) 5.3 yr (PSR J ) Companions MSS, WD, NS, planets 1 double pulsar PSR J A/B 22.7 ms / 2.77 s P orb = 147 min e = [ Kamer & Stairs 2008, ]

6 Binary Pulsars with Neutron Star Companions Double Pulsar Hulse-Taylor Pulsar

7 Testing the Quadrupole Formalism Binary Pulsar Companion P [ms] Pb [h] L(GW) [10 27 erg/s] Precision PSR B NS % PSR B NS % PSR B C NS % PSR J WD % PSR J NS % PSR J NS %.. [ Kramer et al ] Shklovskii effect Galactic acceleration The Double Pulsar: Very small proper motion in the sky Comparably close (~ 1.2 kpc) Distance fairly well known from VLBI measurements (15%) With current uncertainties in distance and Galactic model: limit = 0.01% [ Deller et al ]

8 Testing General Relativity with Binary Pulsars PSR B

9 GR Tests with the Double Pulsar Binary parameters from timing [ Kramer et al ] Spin precession of B from eclipse observations [ Breton et al ]

10 Jordan-Fierz-Brans-Dicke (JFBD) Theory Physical metric: Effective gravitational constant in binary pulsars: γ 1 = (2.1 ± 2.3) 10-5 PPN limit: solar system experiments constrain possible deviations in binary pulsars

11 Quadratic Model by Damour & Esposito-Farèse - T 1 (α 0,β 0 ) Physical metric: Effective coupling constant α A for a mass m A : can reach unity even if α 0 is extremely small (spontaneous scalarization) [ Damour & Esposito-Farèse 1996 ]

12 Strong Field Effects in the β 0 =-6 Quadratic Model Parameters as a function of E grav /mc 2 of A and B G AB /G - 1 ω QM / ω GR solar system

13 Limits on Quadratic Tensor-Scalar Theories T 1 (α 0,β 0 ) [ Esposito-Farèse 2009 ]

14 The White-Dwarf Companion of PSR J VLT FORS1 [ Antoniadis et al ]

15 Modified EIH Formalism Modified Einstein-Infeld-Hoffmann (meih) formalism: developed by Will and Damour & Taylor provides a generic description for the motion of a compact bodies in conservative gravity theories Orbital dynamics in meih formalism for 2 (compact) bodies: Weak field limit:

16 Post-Keplerian Parameters and meih Formalism Precession of periastron Time dilation E Shapiro delay [ Damour & Taylor 1992 ]

17 Generic Tests A B [ Kramer et al ] [ Damour & Deruelle 1986, Damour 2005 ] shape s of Shapiro delay [ Kramer et al ] E [ Kramer & Wex 2009 ]

18 Semi-conservative Theories and Binary Pulsars Non-boost invariant theories of gravity predict a preferred frame for local gravitational physics non-boost invariant Lagragian for binary pulsar dynamics (in preferred frame) [ Damour & Esposito-Farèse 1992, Will 1993 ] Leads to characteristic changes in the orbital elements, like a ploarization of smalleccentricity binary orbit in direction of the projection of w e e w e 0 w Pulsar white-dwarf systems have been used to place an upper limit on α AB (1) which is well below 10-3 (90% C.L.) [ Damour & Esposito-Farèse 1992, Wex 2000 ]

19 Preferred Frame Effects in the Double Pulsar 17 deg/yr distinct signatures in timing observations with periods of 10.7 and 21.3 years (PF) (PF) preferred frame fingerprint preferred frame limit CMB [ Wex & Kramer 2007, 2010 ]

20 Relativistic Spin-Precession A General Relativity: [ Barker & O'Connell 1975 ] B Hulse-Taylor Pulsar: 1.2 deg/yr Double Pulsar (A,B): 4.7 and 5.1 deg/yr Alternative theories of gravity: [ Damour & Taylor 1992 ] Pulse profile and polarization changes due to geodetic precession seen in various binary pulsars: PSR B PSR B (changes in aberration constraints on Ω, Stairs et al. 2004) PSR J PSR J

21 Relativistic Spin Precesssion of Pulsar B Pulsar A Dec 2003 Nov 2007 [ Breton et al ]

22 The Evolution of Pulsar B Pulse profile of pulsar B at 820 MHz, Dec 2003 Mar 2008 [ Perera et al ]

23 Generic Test for Dipole Radiation Most alternative theories of gravity predict dipole radiation that dominates the energy loss of the orbital dynamcis: NS-NS binaries:? NS-WD binaries: ~1

24 Generic Test for Dipole Radiation with PSR J Pulsar P = 5.3 ms P orb =14.5 h e < years of EPTA timing Helium white dwarf optical observations m c = 0.16 ± 0.02 M sun q = m p /m c = 10.5 ± 0.5 d = 840 ± 90 pc [ Lazaridis et al ] LLR [ Callanan et al ] [ Lazaridis et al ]

25 Combined Limit for a Variation in G and Dipole Radiation PSR J Orbital period = days PSR J Orbital period = 5.75 days [ Lazaridis et al ]

26 Nano Hertz Gravitational Wave Background [ Hobbs et al ]

27 The Gravitational Wave Background h c = [ Detweiler 1979 ]

28 Pulsar Timing Array [ Hellings & Downs 1983 ] [ D. Champion ]

29 Pulsar Timing Array IPTA (International PTA) PPTA (Parkes PTA) EPTA (European PTA) NANOGrav (North American nhz Observatory for GWs) The Square Kilometre Array (SKA),

30 Testing Polarization Modes [ Lee et al ] [ Eardley et al. 1973, Will 1993 ]

31 Detecting a Massive Graviton Graviton mass (in ev) changes the shape of the cross-correlation function: Contours of 50%, 70% and 90% detection rates (0.1% false alarm): 100 log( m g [ev] ) present solar system limit [ Lee et al ]

32 The Game of Science The game of science is, in principle, without end. He who decides one day that scientific statements do not call for any further test, and that they can be regarded as finally verified, retires from the game. Karl R. Popper (Logik der Forschung 1934)