Ingrid StairsUBC

GWPAW Milwaukee

Jan. 29, 2011

Testing General Relativity with

Relativistic Binary Pulsars

Green BankTelescope

Parkes Arecibo

Jodrell Bank

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

D. Page

Pulsars and othercompact objects probetheories near objectswith strong gravitationalbinding energy. Thesetests are qualitativelydifferent from Solar-system tests!

WD: 0.01% of massNS: 10--20% of massBH: 50% of mass is in binding energy.

Standardprofile

Observedprofile

Measure offset

Pulsar Timing in a Nutshell

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

Recycledpulsars

MSPs are often very stable, nearly as good asatomic 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 PulsarTiming 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 forcompactness 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: (Williams et al. 2009, IJMPD, 18, 1129)

Binary pulsars: NS and WD falldifferently in gravitationalfield of Galaxy.

Constrain Δnet = ΔNS -ΔWD

(Damour & Schäfer 1991, PRL, 66, 2549.)

WD NS

Result is a polarized orbit.

€

η =4β − γ − 3−10

3ξ −α 1 +

2

3α 2 −

2

3ζ 1 −

1

3ζ 2

€

η =(4.4 ± 4.5) ×10−4

€

mgrav

m inertial

⎛

⎝ ⎜

⎞

⎠ ⎟=1+ Δ i

=1+ ηE grav

mi

⎛

⎝ ⎜

⎞

⎠ ⎟+ ′ η

E grav

mi

⎛

⎝ ⎜

⎞

⎠ ⎟

2

+ ...

Deriving a Constraint on Δnet

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.).

After Wex 1997, A&A, 317, 976.

Now: use information aboutlongitude ofperiastron (previouslyunused) and measured eccentricity and a Bayesianformulation to constructpdfs for Δnet for each

appropriate pulsar,representing the fullpopulation of similar objects.

Result: |Δnet| < 0.0045 at 95% confidence

(Gonzalez et al, nearly submitted, based on method used in Stairs et al. 2005).

Gonzalez et al., in prep.

Constraints on α1 and α3α1: Implies existence of preferred frames.

Expect orbit to be polarized along projection of velocity (wrt CMB)onto orbital plane. Constraint ∝ Pb

1/3/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 cross-product of system velocity and pulsar spin. Constraint ∝ Pb

2/(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 orconstraint on orbital period derivative, .This is complicated by systematic biases:

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˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟Observed

=˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟Accel

+˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟˙ G

+˙ P bPb

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⎝ ⎜

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⎠ ⎟˙ m

+˙ P bPb

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⎝ ⎜

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⎠ ⎟Quadrupolar

+˙ P bPb

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⎝ ⎜

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⎠ ⎟gravitational field

+˙ P bPb

⎛

⎝ ⎜

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⎠ ⎟Shklovskii

˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟Shklovskii

= μ 2 d

c

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˙ P b

Dipolar Gravitational RadiationDifference in gravitational binding energies of NS and WD impliesdipolar gravitational radiation possible in, e.g., tensor-scalar theories.

Damour & Esposito-Farèse 1996, PRD, 54, 1474.

Test using pulsar—WD systems in short-period orbits. Examples:PSR B0655+64, 24.7-hour orbit: < 2.7x10-4 (Arzoumanian 2003, ASP Conf. Ser. 302, 69).PSR J1012+5307, 14.5-hour orbit: < 6x10-5 (Lazaridis et al. 2009, MNRAS 400, 805).PSR J0751+1807, 6.3-hour orbit: measurement in Nice et al. 2005 ApJ 634, 1242 has major revision with more data.

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˙ P b Dipole =4π 2G*

c 3Pb

m1m2

m1 + m2

α c1−α c2( )

2

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α cp −α 0( )2

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α cp −α 0( )2

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˙ P b

PSR J1141-6545 Young pulsar with a white-dwarf companion, eccentric, 4.45-hour orbit

Bhat et al PRD 77, 124017 (2008)

ω, γ and measuredthrough timing. Sin i measured by scintillation.

Because of eccentricity, dipolar radiation predictions can be large.

Agreement with GR here setslimits of forweakly nonlinear coupling and for stronglynonlinear coupling (Bhat et al 2008).

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˙ P b

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α02 < 2.1×10−5

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α02 < 3.4 ×10−6

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˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟Observed

=˙ P bPb

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⎝ ⎜

⎞

⎠ ⎟Accel

+˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟˙ G

+˙ P bPb

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⎝ ⎜

⎞

⎠ ⎟˙ m

+˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟Quadrupolar

+˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟Dipolar

˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟Accel

=˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟gravitational field

+˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟Shklovskii

˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟Shklovskii

= μ 2 d

c

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˙ P bOrbital decay tests rely on measurement of orconstraint on orbital period derivative, .

This is complicated by systematic biases:

Variation of Newton's ConstantSpin: Variable G changes moment of inertia of NS. Expect depending on equation of state, PM correction...

Various millisecond pulsars, roughly:

Orbital decay: Expect , test with circular NS-WD binaries.

PSR B1855+09, 12.3-day orbit: (Kaspi, Taylor & Ryba 1994, ApJ, 428, 713; Arzoumanian 1995, PhD thesis, Princeton).

PSR J1713+0747, 67.8-day orbit: (Splaver et al. 2005, ApJ, 620, 405, Nice et al. 2005, ApJ, 634, 1242).

PSR J0437-4715, 5.7-day orbit: (Verbiest et al 2008, ApJ 679, 675, 95% confidence, using slightly different assumptions).

Not as constraining as LLR (Williams et al. 2004, PRL 93, 361101):

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˙ P

P∝

˙ G

G

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˙ G

G≤ 2 ×10−11 yr−1

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˙ P bPb

∝˙ G

G

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˙ G

G= (−1.3± 2.7) ×10−11yr−1

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˙ G

G= (1.5 ± 3.8) ×10−12 yr−1

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˙ G

G= (0.5 ± 2.6) ×10−12 yr−1

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˙ G

G= (4 ± 9) ×10−13 yr−1

Combined Limit on and Dipolar Gravitational Radiation

Lazaridis et al. 2009 (MNRAS 400, 805) combine the limits from J1012+5307 and J0437-4715 to form a combined limit on these two quantities:

and

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˙ G

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˙ G

G= (−0.7 ± 3.3) ×10−12 yr−1

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κD ≈(α cp −α 0)2

S2= (0.3± 2.5) ×10−3

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˙ P b

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˙ ω = 3Pb

2π

⎛

⎝ ⎜

⎞

⎠ ⎟−5 / 3

T0M( )2 / 3

1− e2( )

−1

γ = ePb

2π

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 3

T02 / 3M −4 / 3m2 m1 + 2m2( )

˙ P b =−192

5

Pb

2π

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⎝ ⎜

⎞

⎠ ⎟−5 / 3

1+73

24e2 +

37

96e4 ⎛

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⎠ ⎟1 − e2( )

−7 / 2T0

5 / 3m1m2M −1/ 3

r = T0m2

s = xPb

2π

⎛

⎝ ⎜

⎞

⎠ ⎟−2 / 3

T0−1/ 3M −2 / 3m2

−1

M = m1 + m2

T0 = 4.925490947μs

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:

Relativistic Binaries

The Original System: PSR B1913+16

Highly eccentric double-NSsystem, 8-hour orbit.

The and γ parameterspredict the pulsar andcompanion masses.

The parameter is ingood agreement, to ~0.2%.Galactic accelerationmodeling now limits this test.

Weisberg & Taylor 2003, ASP Conf. Ser. 302, 93(Courtesy Joel Weisberg)

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˙ ω

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˙ P b

Orbital Decay of PSR B1913+16

Weisberg, Nice & Taylor, 2010(Courtesy Joel Weisberg)

The accumulated shift ofperiastron passage time,caused by the decay of the orbit. A good match to thepredictions of GR!

Mass-mass diagram for the double pulsar J0737-3039A and B. In addition to 5 PKparameters (for A), wemeasure themass ratio R. Thisis independent ofgravitational theory⇒ whole newconstraint on gravitycompared to otherdouble-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±0.0005and = 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 = -1.24787(13)×10-12 = (-1.252 ± 0.017)×10-12

r = 6.153(26) ms r = 6.21 ± 0.33 ms

In particular:

This was a 0.05% test ofstrong-field GR – now down toa ~0.02% test!

Deller et al 2008, Science

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˙ P bPb

⎛

⎝ ⎜

⎞

⎠ ⎟Accel

≈10−4

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˙ ω

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˙ P b

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˙ P b

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s = 0.99987−0.00048+0.00013

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s = 0.99974−0.00039+0.00016

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sobs

spred= 0.99987 ± 0.00050

Using Multiple Pulsars

Damour and Esposito-Farese

Strong constraints onparameters inalternate theories can beachieved by combininginformation from multiplepulsars plus solar-systemtests (Damour & Esposito-Farese).

Geodetic Precession

Precession of either NS's spin axis aboutthe total (~ orbital) angular momentum.Why would we expect this?

Before the secondsupernova:all AM vectorsaligned.

Before the secondsupernova:all AM vectorsaligned.

After second supernova:orbit tilted, misalignment angle δ(shown for recycled A); B spin pointed elsewhere (definedby kick?).

Geodetic PrecessionPrecession 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 PSR B1913+16,(Weisberg et al 1989, Kramer 1998)

which will disappear ~2025. Kramer 1998

Observed in B1534+12(Arzoumanian 1995)

and measured bycomparison to orbital aberration: o/yr

(68% confidence)cf GR prediction: 0.51 o/yr(Stairs et al 2004)€

Ω1spin = 0.44−0.16

+0.48

What about the double pulsar?

There appear to be no changesin A's profile (Manchesteret al 2005, Ferdman et al 2008).

This starts to put strongconstraints on themisalignment 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!

Perera et al., 2010

Dec. 2003

Jan. 2009

McLaughlin et al. 2004a

B's effects on A provide another avenue to precession:

Eclipses of A by Boccur every orbit(Lyne et al 2004,Kaspi et al 2004).A's flux is modulated by thedipolar emission from B.

See Lyutikov &Thompson 2005for a simplegeometrical model,illustrated here for April 2007 databy Breton et al. 2008.

René Breton

See Lyutikov &Thompson 2005for a simplegeometrical model,illustrated here for April 2007 databy Breton et al. 2008.

This model makes concretepredictions if Bprecesses...

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

Breton et al 2008

The angles α and θ stay constant, but ϕchanges at a rate of4.77+0.66

-0.65o yr-1. This is

nicely consistent with therate predicted by GR:5.0734(7) o yr-1.

And because we measureboth orbital semi-majoraxes, this actually constrainsa generalized set ofgravitational strong-field theories for the first time!

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 TelescopesThe Galactic Census with the Square Kilometre Arrayshould provide:~30000 pulsars~1000 millisecond pulsars~100 relativistic binaries1—10 pulsar – black-hole systems.

With suitable PSR—BH systems, we may be able to measure the BH spin and quadrupole moment , testing

the Cosmic Censorship conjecture and the No-hair theorem .

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χ ≡c

G

S

M 2

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q ≡c 4

G2

Q

M 3

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q = −χ 2

ΔQ/Q = 0.008

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.

ΔS/S ~ 10-

4...10-3

Wex et al., in prep.

The challenge will be finding such pulsars!!

Future Prospects

Long-term timing of pulsar – white dwarf systems ⇒ better limits on and dipolar gravitational radiation, as well as PPN-type parameters ⇒ better limits on gravitational-wave backgroundLong-term timing of relativistic systems ⇒ improved tests of strong-field GR.Potential to measure higher-order terms in 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!

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˙ G /G

€

˙ ω

Constraints on α3 (and ζ2)

α3 can also be tested by isolated pulsars.

Self-acceleration and Shklovskii effect contribute to observed period derivatives:

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.

P 3=

Pcn⋅aself

P pm=P 2 dc

.

PSR B1534+12

Measure same parameters asfor B1913+16, plus Shapirodelay.

The parameters , s and γform a complementary testof GR.

The measured containsa large Shklovskii v2/d contribution. If GR is correct,the distance to the pulsar is1.05 ± 0.05 kpc.

After Stairs 2005, ASP Conf. Ser. 328, 3.

Pb

What about the double pulsar?

Geodetic precessionappears not to be happening in 0737A, despiteshort 75-year period.

No pulse shapechanges over 14.5months, plus back todiscovery observation(Manchester et al 2005).

But B has shown evidence oforbital (likely due to A) changes and long-term (likely precession) changes from thestart.

Burgay et al. 2005

See Lyutikov &Thompson 2005for a simplegeometrical model,illustrated here for April 2007 databy Breton et al. 2008.