General Relativity Tests with Pulsars

Transcription

1 General Relativity Tests with Pulsars Ingrid Stairs UBC Rencontres de Moriond La Thuile March 25, 2011 Green Bank Telescope Jodrell Bank Parkes Arecibo

2 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

3 Pulsars and other compact objects probe theories near objects with strong gravitational binding energy. These tests are qualitatively different from Solar-system tests! WD: 0.01% of mass NS: % of mass BH: 50% of mass is in binding energy.

4 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.

5 Pulsars available for GR tests Young pulsars Recycled pulsars

6 Equivalence Principle Violations Pulsar timing can: " set limits on the Parametrized Post-Newtonian (PPN) parameters α 1, α 3 (, ζ 2 ) " 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).

7 SEP: Nordtvedt (Gravitational Stark) Effect Lunar Laser Ranging: Moon's orbit is not polarized toward Sun. η = 4β γ ξ α α ζ ζ 2 η = (4.4 ± 4.5) 10 4 Constraint: (Williams et al. 2009, IJMPD, 18, 1129) WD NS Binary pulsars: NS and WD fall differently in gravitational field of Galaxy. m grav m inertial =1+ Δ i =1+ η E grav + η ʹ m i E grav m i Result is a polarized orbit. Constrain Δ net = Δ NS -Δ WD (Damour & Schäfer 1991, PRL, 66, 2549.)

8 Deriving a Constraint on Δ net 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 2 /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: Δ net < 9x10-3 (Wex 1997, A&A, 317, 976; 2000, ASP Conf. Ser.).

9 Now: use information about longitude of periastron (previously unused) and measured eccentricity and a Bayesian formulation to construct pdfs for Δ net for each appropriate pulsar, representing the full population of similar objects. Gonzalez et al., submitted. Result: Δ net < at 95% confidence (Gonzalez et al, submitted, based on method used in Stairs et al. 2005).

10 Constraints on α 1 and α 3 α 1 : Implies existence of preferred frames. Expect orbit to be polarized along projection of velocity (wrt CMB) onto orbital plane. Constraint 1/3 /e. Ensemble of pulsars: α 1 < 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... α 3 : Violates local Lorentz invariance and conservation of momentum. Expect orbit to be polarized, depending on crossproduct of system velocity and pulsar spin. Constraint 2 /(ep), same pulsars used as for Δ test. Ensemble of pulsars: α 3 < 5.5x10-20 (Gonzalez et al. submitted; 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))

11 Orbital Decay Tests These rely on measurement of or constraint on orbital period derivative, P b. This is complicated by systematic biases: Observed Accel Shklovskii = = = µ 2 d c Accel + gravitational field G + + m Shklovskii + Quadrupolar + Dipolar

12 Dipolar Gravitational Radiation Difference in gravitational binding energies of NS and WD implies dipolar gravitational radiation possible in, e.g., tensor-scalar theories. P b Dipole = 4π 2 G * m 1 m 2 ( α c 3 c1 α ) 2 c2 m 1 + m 2 Damour & Esposito-Farèse 1996, PRD, 54, Test using pulsar WD systems in short-period orbits. Examples: PSR B , 24.7-hour orbit: ( α < 2.7x10-4 cp α 0 ) 2 (Arzoumanian 2003, ASP Conf. Ser. 302, 69). PSR J , 14.5-hour orbit: ( α < 6x10-5 cp α 0 ) 2 (Lazaridis et al. 2009, MNRAS 400, 805). PSR J , 6.3-hour orbit: P b measurement in Nice et al ApJ 634, 1242 has major revision with more data.

13 PSR J Young pulsar with a white-dwarf companion, eccentric, 4.45-hour orbit. ω, γ and P b measured through timing. Sin i measured by scintillation. Because of eccentricity, dipolar radiation predictions can be large. Agreement with GR here sets limits of α 2 0 < for weakly nonlinear coupling and α 2 0 < for strongly nonlinear coupling (Bhat et al 2008, PRD 77, ).

14 Orbital decay tests rely on measurement of or constraint on orbital period derivative, P b. This is complicated by systematic biases: Observed Accel Shklovskii = = = µ 2 d c Accel + gravitational field G + + m Shklovskii + Quadrupolar + Dipolar

15 Variation of Newton's Constant Spin: Variable G changes moment of inertia of NS. Expect P depending on equation of state, PM correction... P G G G Various millisecond pulsars, roughly: G yr 1 P Orbital decay: Expect b G, test with circular NS-WD binaries. G G PSR B , 12.3-day orbit: G = ( 1.3 ± 2.7) yr 1 (Kaspi, Taylor & Ryba 1994, ApJ, 428, 713; Arzoumanian 1995, PhD thesis, Princeton). PSR J , 67.8-day orbit: (Splaver et al. 2005, ApJ, 620, 405, Nice et al. 2005, ApJ, 634, 1242). PSR J , 5.7-day orbit: G G = (1.5 ± 3.8) yr 1 G G = (0.5 ± 2.6) yr 1 (Verbiest et al 2008, ApJ 679, 675, 95% confidence, using slightly different assumptions). G Not as constraining as LLR (Williams et al. 2004, PRL 93, ): G = (4 ± 9) yr 1

16 G Combined Limit on and Dipolar Gravitational Radiation Lazaridis et al (MNRAS 400, 805) combine the from J and J to form a combined limit on these two quantities: and G G = ( 0.7 ± 3.3) yr 1 κ D (α cp α 0 ) 2 S 2 = (0.3 ± 2.5) 10 3 limits

17 ω = 3 P b 2π γ = e P b 2π 5 / 3 1/ 3 P b = π r = T 0 m 2 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: ( ) 1 ( T 0 M) 2 / 3 1 e 2 2 / T 3 0 M 4 / 3 m 2 ( m 1 + 2m 2 ) 5 / e s = x P 2 / 3 b 1/ T 3 2π 0 M 2 / 3 1 m 2 96 e4 1 e 2 ( ) 7 / 2 T 0 5 / 3 m 1 m 2 M 1/ 3 M = m 1 + m 2 T 0 = µs

18 The Original System: PSR B See Weisberg & Taylor 2003, ASP Conf. Ser. 302, 93 Highly eccentric double-ns system, 8-hour orbit. The ω and γ parameters predict the pulsar and companion masses. The parameter is in good agreement, to ~0.2%. Galactic acceleration modeling now limits this test.

19 Orbital Decay of PSR B See Weisberg, Nice & Taylor, 2010, ApJ 722, 1030 The accumulated shift of periastron passage time, caused by the decay of the orbit. A good match to the predictions of GR!

20 As of July 2010; Kramer et al. in prep. Mass-mass diagram for the double pulsar J A 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.

21 Numbers reported in 2006 (Kramer et al, Science): We can use the measured values of R = ± and ω = ± o /year to get the masses and then compute the other parameters as expected in GR: Expected in GR: Observed: γ = (22) ms γ = ± ms = (13) P = ( ± 0.017) b r = 6.153(26) ms r = 6.21 ± 0.33 ms s = s = In particular: s obs = ± pred s Accel 10 4 Deller et al 2008, Science This was a 0.05% test of strong-field GR now down to a ~0.02% test!

22 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).

23 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.

24 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?).

25 Geodetic Precession Precession period: 300 years for B , 700 years for B , 265 years for J and only ~70 years for the J pulsars. See Kramer 1998, ApJ 509, 856. Observed in PSR B , (Weisberg et al 1989, Kramer 1998) which will disappear ~2025. Observed in B (Arzoumanian 1995) and measured by comparison to orbital aberration: o /yr Ω 1 spin = (68% confidence) cf GR prediction: 0.51 o /yr (Stairs et al 2004, PRL 93, ) Kramer 1998, ApJ 509, 856

26 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: <37 o for one-pole model, <14 o for two-pole model (95.4% confidence limits, Ferdman PhD thesis, UBC 2008; plot updated to 2009).

27 Dec But B has changed a lot... and has now disappeared completely! Jan Perera et al., 2010, ApJ 721, 1193

28 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, ApJ 616, L131

29 See Lyutikov & Thompson 2005, ApJ 634, 1223 for a simple geometrical model, illustrated here for April 2007 data by Breton et al. 2008, Science 321, 104. This model makes concrete predictions if B precesses...

30 Eclipse geometry, Breton et al If B precesses, ϕ will change with time, and the structure of the eclipse modulation should also change... and it does! Breton et al. 2008, Science 321, 104 Dec Nov Courtesy René Breton

31 The angles α and θ stay constant, but ϕ changes at a rate of o yr -1. This is nicely consistent with the rate predicted by GR: (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, Science 321, 104

32 Preferred-frame effects with double-ns systems Wex & Kramer (2007, MNRAS 380, 455) 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).

33 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 measure S Q the BH spin and quadrupole moment, testing χ c G M 2 q c 4 the Cosmic Censorship conjecture and the No-hair theorem q = χ 2. G 2 M 3

34 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. Liu et al., in prep., courtesy Norbert Wex S/S ~ ΔQ/Q = The challenge will be finding such pulsars!!

35 Future Prospects Long-term timing of pulsar white dwarf systems better limits on G /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. Potential to measure higher-order terms in ω in 0737A: we may be 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 new telescopes... more systems of all types... and maybe some new holy grails such as a pulsar black hole system... stay tuned!