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Testing General Relativity with Relativistic Binary Pulsars Ingrid Stairs UBC GWPAW Milwaukee Jan. 29, 2011 Jodrell Bank Green Bank Telescope Parkes Arecibo Outline • Intro to pulsar timing • Equivalence principle tests - “Nordtvedt”-type tests - Orbital decay tests • Relativistic systems - Timing - Geodetic precession - Preferred-frame effects • Looking to the future Pulsars and other compact objects probe theories near objects with strong gravitational binding energy. These tests are qualitatively different from Solar-system tests! D. Page WD: 0.01% of mass NS: 10--20% of mass BH: 50% of mass is in binding energy. Pulsar Timing in a Nutshell Standard profile Measure offset Observed profile Record the start time of the observation with the observatory clock (typically a maser). The offset gives us a Time of Arrival (TOA) for the observed pulse. Then transform to Solar System Barycentre, enumerate pulses and fit the timing model. Pulsars available for GR tests Young pulsars Recycled pulsars MSPs are often very stable, nearly as good as atomic clocks on timescales of years. This should allow the use of an array of them to detect gravitational waves. This is the goal of the International Pulsar Timing Array – European, Australian and North American collaborations. Equivalence Principle Violations Pulsar timing can: set limits on the Parametrized Post-Newtonian (PPN) parameters α1, α3 (, ζ2) test for violations of the Strong Equivalence Principle (SEP) through - the Nordtvedt Effect - dipolar gravitational radiation - variations of Newton's constant (Actually, parameters modified to account for compactness of neutron stars.) (Damour & Esposito-Farèse 1992, CQG, 9, 2093; 1996, PRD, 53, 5541). SEP: Nordtvedt (Gravitational Stark) Effect Lunar Laser Ranging: Moon's orbit is not polarized toward Sun. Constraint: (4.4 4.5) 10 4 4 3 WD 10 2 2 1 1 2 1 2 3 3 3 3 (Williams et al. 2009, IJMPD, 18, 1129) pulsars: NS and WD fall Binary differently in gravitational field of Galaxy. NS m grav inertial 1 i m E grav E grav 2 1 ... m m i i Constrain Δnet = ΔNS -ΔWD Result is a polarized orbit. (Damour & Schäfer 1991, PRL, 66, 2549.) Deriving a Constraint on Δnet After Wex 1997, A&A, 317, 976. Use pulsar—white-dwarf binaries with low eccentricities ( <10-3). Eccentricity would contain a “forced” component along projection of Galactic gravitational force onto the orbit. This may partially cancel “natural” eccentricity. Constraint ∝ Pb2/e. Need to estimate orbital inclination and masses. Formerly: assume binary orbit is randomly oriented on sky. Use all similar systems to counter selection effects (Wex). Ensemble of pulsars: Δnet < 9x10-3 (Wex 1997, A&A, 317, 976; 2000, ASP Conf. Ser.). Now: use information about longitude of periastron (previously unused) and measured eccentricity and a Bayesian formulation to construct pdfs for Δnet for each appropriate pulsar, representing the full population of similar objects. Gonzalez et al., in prep. Result: |Δnet| < 0.0045 at 95% confidence (Gonzalez et al, nearly submitted, based on method used in Stairs et al. 2005). Constraints on α1 and α3 α1: Implies existence of preferred frames. Expect orbit to be polarized along projection of velocity (wrt CMB) onto orbital plane. Constraint ∝ Pb1/3/e. Ensemble of pulsars: α1 < 1.4x10-4 (Wex 2000, ASP Conf. Ser.). Comparable to LLR tests (Müller et al. 1996, PRD, 54, R5927). This test now needs updating with Bayesian approach... α3: Violates local Lorentz invariance and conservation of momentum. Expect orbit to be polarized, depending on crossproduct of system velocity and pulsar spin. Constraint ∝ Pb2/(eP), same pulsars used as for Δ test. Ensemble of pulsars: α3 < 5.5x10-20 (Gonzalez et al. in prep.; slightly worse limit than in Stairs et al. 2005, ApJ, 632, 1060, but more information used). (Cf. Perihelion shifts of Earth and Mercury: ~2x10-7 (Will 1993, “Theory & Expt. In Grav. Physics,” CUP)) Orbital Decay Tests These rely on measurement of or constraint on orbital period derivative, PÝb . This is complicated by systematic biases: PÝb PÝb PÝb PÝb PÝb PÝb Pb Observed Pb Accel Pb GÝ Pb mÝ Pb Quadrupolar Pb Dipolar PÝb PÝb PÝb Pb Accel Pb gravitational field Pb Shklovskii PÝ 2 d b c Pb Shklovskii Dipolar Gravitational Radiation Difference in gravitational binding energies of NS and WD implies dipolar gravitational radiation possible in, e.g., tensor-scalar theories. 2 2 4 G* m1m2 Ý Pb Dipole 3 c1 c 2 c Pb m1 m2 Damour & Esposito-Farèse 1996, PRD, 54, 1474. Test using pulsar—WD systems in short-period orbits. Examples: PSR B0655+64, 24.7-hour orbit: 2 cp 0 < 2.7x10-4 (Arzoumanian 2003, ASP Conf. Ser. 302, 69). PSR J1012+5307, 14.5-hour orbit: 2 cp 0 < 6x10-5 (Lazaridis et al. 2009, MNRAS 400, 805). PSR J0751+1807, 6.3-hour orbit: PÝb measurement in Nice et al. 2005 ApJ 634, 1242 has major revision with more data. PSR J1141-6545 Young pulsar with a white-dwarf companion, eccentric, 4.45-hour orbit ω, γ and PÝb measured through timing. Sin i measured by scintillation. Because of eccentricity, dipolar radiation predictions can be large. Bhat et al PRD 77, 124017 (2008) Agreement with GR here sets limits of 02 2.1105 for weakly nonlinear coupling and 02 3.4 106 for strongly nonlinear coupling (Bhat et al 2008). Orbital decay tests rely on measurement of or constraint on orbital period derivative, PÝb . This is complicated by systematic biases: PÝb PÝb PÝb PÝb PÝb PÝb Pb Observed Pb Accel Pb GÝ Pb mÝ Pb Quadrupolar Pb Dipolar PÝb PÝb PÝb Pb Accel Pb gravitational field Pb Shklovskii PÝ 2 d b c Pb Shklovskii Variation of Newton's Constant Spin: Variable G changes moment of inertia of NS. Expect PÝ GÝ depending on equation of state, PM correction... P G GÝ Various millisecond pulsars, roughly: 2 1011 yr 1 G PÝb GÝ Orbitaldecay: Expect , test with circular NS-WD binaries. Pb G GÝ (1.3 2.7) 1011 yr 1 PSR B1855+09, 12.3-day orbit: G (Kaspi, Taylor & Ryba 1994, ApJ, 428, 713; Arzoumanian 1995, PhD thesis, Princeton). PSR J1713+0747, 67.8-dayorbit: GÝ (1.5 3.8) 1012 yr 1 G (Splaver et al. 2005, ApJ, 620, 405, Nice et al. 2005, ApJ, 634, 1242). PSR J0437-4715, 5.7-day orbit: GÝ (0.5 2.6) 1012 yr 1 G (Verbiest et al 2008, ApJ 679, 675, 95% confidence, using slightly different assumptions). GÝ (4 9) 1013 yr 1 Not as constraining as LLR (Williams et al. 2004, PRL 93, 361101): G Combined Limit on GÝ and Dipolar Gravitational Radiation Lazaridis et al. 2009 (MNRAS 400, 805) combine thePÝb limits from J1012+5307 and J0437-4715 to form a combined limit on these two quantities: GÝ 12 1 (0.7 3.3) 10 yr G ( cp 0 ) 3 D (0.3 2.5) 10 2 S 2 and Relativistic Binaries Binary pulsars, especially double-neutron-star systems: measure post-Keplerian timing parameters in a theory-independent way (Damour & Deruelle 1986, AIHP, 44, 263). These predict the stellar masses in any theory of gravity. In GR: Pb 5 / 3 1 2/3 Ý 3 T0 M 1 e 2 2 Pb 1/ 3 2 / 3 4 / 3 e T0 M m2 m1 2m2 2 5 / 3 73 7 / 2 192 P 37 5/3 PÝb b 1 e 2 e 4 1 e 2 T0 m1m2 M 1/ 3 5 2 24 96 r T0 m 2 Pb 2 / 3 1/ 3 2 / 3 1 s x T0 M m2 2 M m1 m2 T0 4.925490947 s The Original System: PSR B1913+16 Highly eccentric double-NS system, 8-hour orbit. Ý and γ parameters The predict the pulsar and companion masses. The PÝb parameter is in good agreement, to ~0.2%. Galactic acceleration modeling now limits this test. Weisberg & Taylor 2003, ASP Conf. Ser. 302, 93 (Courtesy Joel Weisberg) Orbital Decay of PSR B1913+16 The accumulated shift of periastron passage time, caused by the decay of the orbit. A good match to the predictions of GR! Weisberg, Nice & Taylor, 2010 (Courtesy Joel Weisberg) Mass-mass diagram for the double pulsar J0737-3039A and B. In addition to 5 PK parameters (for A), we measure the mass ratio R. This is independent of gravitational theory ⇒ whole new constraint on gravity compared to other double-NS systems. As of July 2010; Kramer et al. in prep. Numbers reported in 2006 (Kramer et al, Science): We can use the measured values of R = 0.9336±0.0005 and Ý = 16.8995±0.0007 o/year to get the masses and then compute the other parameters as expected in GR: Expected in GR: Observed: γ = 0.38418(22) ms γ = 0.3856 ± 0.0026ms PÝ = -1.24787(13)×10-12 PÝ = (-1.252 ± 0.017)×10-12 r = 6.153(26) ms r = 6.21 ± 0.33 ms 0.00016 0.00013 s 0.99974 s 0.999870.00048 0.00039 b b PÝb 4 10 Pb Accel In particular: sobs 0.99987 0.00050 pred s Deller et al 2008, Science This was a 0.05% test of strong-field GR – now down to a ~0.02% test! Using Multiple Pulsars Strong constraints on parameters in alternate theories can be achieved by combining information from multiple pulsars plus solar-system tests (Damour & Esposito-Farese). Damour and Esposito-Farese Geodetic Precession Precession of either NS's spin axis about the total (~ orbital) angular momentum. Why would we expect this? Before the second supernova: all AM vectors aligned. Before the second supernova: all AM vectors aligned. After second supernova: orbit tilted, misalignment angle δ (shown for recycled A); B spin pointed elsewhere (defined by kick?). Geodetic Precession Precession period: 300 years for B1913+16, 700 years for B1534+12, 265 years for J1141-6545 and only ~70 years for the J0737-3039 pulsars. Observed in B1534+12 (Arzoumanian 1995) and measured by comparison to orbital aberration: spin 1 Observed in PSR B1913+16, (Weisberg et al 1989, Kramer 1998) which will disappear ~2025. Kramer 1998 0.44 0.48 o/yr 0.16 (68% confidence) cf GR prediction: 0.51 o/yr (Stairs et al 2004) What about the double pulsar? There appear to be no changes in A's profile (Manchester et al 2005, Ferdman et al 2008). This starts to put strong constraints on the misalignment angle: <37o for one-pole model, <14o for two-pole model (95.4% confidence limits, Ferdman PhD thesis, UBC 2008; plot updated to 2009). But B has changed a lot.... and has now disappeared completely! Dec. 2003 Jan. 2009 Perera et al., 2010 B's effects on A provide another avenue to precession: Eclipses of A by B occur every orbit (Lyne et al 2004, Kaspi et al 2004). A's flux is modulated by the dipolar emission from B. McLaughlin et al. 2004a See Lyutikov & Thompson 2005 for a simple geometrical model, illustrated here for April 2007 data by Breton et al. 2008. René Breton See Lyutikov & Thompson 2005 for a simple geometrical model, illustrated here for April 2007 data by Breton et al. 2008. This model makes concrete predictions if B precesses... Eclipse geometry, Breton et al 2008. If B precesses, ϕ will change with time, and the structure of the eclipse modulation should also change... and it does! Dec. 2003 Nov. 2007 Courtesy René Breton The angles α and θ stay constant, but ϕ changes at a rate of 4.77+0.66-0.65o yr-1. This is nicely consistent with the rate predicted by GR: 5.0734(7) o yr-1. And because we measure both orbital semi-major axes, this actually constrains a generalized set of gravitational strong-field theories for the first time! Breton et al 2008 Preferred-frame effects with double-NS systems Wex & Kramer 2007 Wex & Kramer showed that pulsars similar to the double pulsar are sensitive to preferred-frame effects (within semi-conservative theories) via their orbital parameters. Here they show that the double pulsar (left), a similar system at the Galactic centre (middle) and their combination can lead to strong constraints on the directionality of the preferred frame (PFE antenna). Future Telescopes The Galactic Census with the Square Kilometre Array should provide: ~30000 pulsars ~1000 millisecond pulsars ~100 relativistic binaries 1—10 pulsar – black-hole systems. With suitable PSR—BH systems, we may be able to 4 c Q c spin S measure the BH and quadrupole moment q G2 M 3 G M2 , testing 2 q the Cosmic Censorship conjecture and the No-hair theorem . Pulsar with 100 μs timing precision in 0.1-year, eccentricity 0.4 orbit around Sgr A*: weekly observations over 3 years lead to a measurement of the spin (via frame-dragging) and quadrupole moment (below) to high precision, assuming Sgr A* is an extreme Kerr BH. Wex et al., in prep. ΔS/S ~ 10-4...10-3 ΔQ/Q = 0.008 The challenge will be finding such pulsars!! Future Prospects Long-term timing of pulsar – white dwarf systems ⇒ better limits on GÝ/G and dipolar gravitational radiation, as well as PPN-type parameters ⇒ better limits on gravitational-wave background Long-term timing of relativistic systems ⇒ improved tests of strong-field GR. Ý in 0737A: we may be Potential to measure higher-order terms in able to measure the neutron-star moment of inertia! Profile changes and eclipses in relativistic binaries ⇒ better tests of precession rates, geometry determinations. Large-scale surveys, large newtelescopes... ⇒ more systems of all types... and maybe some new “holy grails” such as a pulsar—black hole system... stay tuned! ⋅ Constraints on α3 (and ζ2) α3 can also be tested by isolated pulsars. Self-acceleration and Shklovskii effect contribute to observed period derivatives: P n a self c d Ṗ pm = P 2 c Ṗ = 3 Young pulsars: α3 < 2x10-10 (Will 1993, “Theory & Expt. In Grav. Physics,”CUP). Millisecond pulsars: α3 < ~10-15 (Bell 1996, ApJ, 462, 287; Bell & Damour 1996, CQG, 13, 3121). . α3+ζ2 also accelerate the CM of a binary system ⇒ variable P in eccentric PSR B1913+16: (α3+ζ2) < 4x10-5 (Will 1992, ApJ, 393, L59). But geodetic precession and timing noise can mimic this effect, so not really a good test. PSR B1534+12 Measure same parameters as for B1913+16, plus Shapiro delay. The parameters ˙ , s and γ form a complementary test of GR. After Stairs 2005, ASP Conf. Ser. 328, 3. The measuredṖ b contains a large Shklovskii v2/d contribution. If GR is correct, the distance to the pulsar is 1.05 ± 0.05 kpc. What about the double pulsar? Geodetic precession appears not to be happening in 0737A, despite short 75-year period. No pulse shape changes over 14.5 months, plus back to discovery observation (Manchester et al 2005). But B has shown evidence of orbital (likely due to A) changes and long-term (likely precession) changes from the start. Burgay et al. 2005 See Lyutikov & Thompson 2005 for a simple geometrical model, illustrated here for April 2007 data by Breton et al. 2008.