testing general relativity with relativistic binary pulsars

8/13/2019 Testing General Relativity With Relativistic Binary Pulsars

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Ingrid StairsUBC

GWPAWMilwaukee

Jan. 29, 2011

Testing General Relativity withRelativistic 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 other

compact objects probetheories near objectswith strong gravitationalbinding energy. Thesetests are qualitativelydifferent from Solar-systemtests!

WD: 0.01% of massNS: 10--20% of massBH: 50% of mass

is in binding energy.



Standardprole

Observedprole

Measureoffset

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 t the timing model.



Pulsars available for GR tests

Youngpulsars

Recycledpulsars



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 todetect gravitational waves.

This is the goal of the International PulsarTiming Array – European, Australian andNorth American collaborations.



Equivalence Principle Violations

Pulsar timing can:set limits on the ParametrizedPost-Newtonian (PPN) parameters α 1, α 3 (, ζ 2)

test for violations of the Strong EquivalencePrinciple (SEP) through- the Nordtvedt Effect- dipolar gravitational radiation- variations of Newton's constant

(Actually, parameters modied 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 gravitationaleld of Galaxy.

Constrain Δ net = Δ NS -Δ WD

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

WD NS

Result is a polarized orbit.

" = 4 # $ % $ 3 $10

3& $ ' 1

+2

3' 2

$ 2

3( 1

$ 1

3( 2

" = (4.4 ± 4.5) # 10 $ 4

m grav

m inertial

"

# $

%

& ' = 1 + ( i

= 1 + ) E grav

mi

"

# $

%

& ' + * ) E grav

mi

"

# $

%

& '

2

+ ...



Deriving a Constraint on Δ net

Use pulsar—white-dwarf binarieswith low eccentricities ( <10 -3).

Eccentricity would contain a “forced”

component along projection ofGalactic gravitational force ontothe orbit. This may partiallycancel “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: Δ net < 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 measuredeccentricity and a Bayesianformulation to constructpdfs for Δ net for eachappropriate pulsar,representing the fullpopulation of similar objects.

Result: | Δ net| < 0.0045 at 95% condence (Gonzalezet al, nearly submitted, based on method used in Stairset al. 2005).

Gonzalez et al., in prep.



Constraints on α 1 and α 3α 1: 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: 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 ofmomentum. Expect orbit to be polarized, depending on cross-product of system velocity and pulsar spin. Constraint ∝ Pb

2 /(eP),

same pulsars used as forΔ

test.Ensemble of pulsars: α 3 < 5.5x10 -20 (Gonzalez et al. in prep.;slightly worse limit than in Stairs et al. 2005, ApJ, 632, 1060, butmore 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:

P b

Pb

"

# $ %

& '

Observed

= P b

Pb

"

# $ %

& '

Accel

+ P b

Pb

"

# $ %

& '

G

+ P b

Pb

"

# $ %

& '

m

+ P b

Pb

"

# $ %

& '

Quadrupolar

+ P b

Pb

"

# $ %

& '

Dipolar

Pb

Pb

"

# $

%

& '

Accel

=P

b

Pb

"

# $

%

& '

gravitational field

+P

b

Pb

"

# $

%

& '

Shklovskii

Pb

Pb

"

# $

%

& '

Shklovskii

= µ 2 d

c

˙

Pb



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

Damour & Esposito-Farèse1996, 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.

Pb Dipole

=4 "

2G*

c 3Pb

m1m

2

m1

+ m2

# c 1

$ # c 2( )

2

" cp

# " 0( )2

" cp

# " 0( )

2

˙

Pb



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

Bhat et al PRD 77, 124017 (2008)

ω , γ and measuredthrough timing. Sin imeasured by scintillation.

Because of eccentricity, dipolarradiation predictions can be large.

Agreement with GR here sets

limits of forweakly nonlinear coupling andfor strongly

nonlinear coupling (Bhat et al2008).

˙

Pb

" 0

2< 2.1 # 10 $ 5

" 0

2< 3.4 # 10 $ 6



P b

Pb

"

# $ %

& '

Observed

= P b

Pb

"

# $ %

& '

Accel

+ P b

Pb

"

# $ %

& '

G

+ P b

Pb

"

# $ %

& '

m

+ P b

Pb

"

# $ %

& '

Quadrupolar

+ P b

Pb

"

# $ %

& '

Dipolar

Pb

Pb

"

# $

%

& '

Accel

=P

b

Pb

"

# $

%

& '

gravitational field

+P

b

Pb

"

# $

%

& '

Shklovskii

Pb

Pb

"

# $

%

& '

Shklovskii

= µ 2 d

c

˙

Pb

Orbital decay tests rely on measurement of or

constraint 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% condence, using slightly different assumptions).

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

˙

PP

"

˙

GG

G

G" 2 # 10

$ 11 yr$ 1

˙

Pb

P b

"

˙

G

G

G

G= (" 1.3 ± 2.7) # 10

" 11 yr" 1

G

G= (1.5 ± 3.8) " 10 # 12 yr # 1

G

G= (0.5 ± 2.6) " 10 # 12 yr # 1

G

G=

(4±

9)"

10

# 13

yr

# 1



Combined Limit on andDipolar Gravitational Radiation

Lazaridis et al. 2009 (MNRAS 400, 805) combine the limits

from J1012+5307 and J0437-4715 to form a combined limiton these two quantities:

and

˙

G

G

G= (" 0.7 ± 3.3) # 10

" 12 yr" 1

" D

# ($ cp % $ 0 ) 2

S 2= (0.3 ± 2.5) & 10 %3

˙

Pb



˙" = 3 P

b

2 #

$

% &

'

( )

*5 / 3

T 0 M

( )2 / 3

1 * e 2

( )*1

+ = e P

b

2 #

$

% &

'

( )

1/ 3

T 0

2 / 3 M *4 / 3 m2

m1

+ 2 m2( )

Pb

=*192

5

Pb

2 #

$

% &

'

( )

*5 / 3

1 +73

24e 2

+37

96e 4$

% &

'

( ) 1 * e 2( )*

7 / 2

T 0

5 / 3 m1m

2 M *1/ 3

r = T 0 m 2

s = x P

b

2 #

$

% &

'

( )

*2 / 3

T 0

*1/ 3 M *2 / 3 m2

*1

M = m1

+ m2

T 0

= 4.925490947 µ s

Binary pulsars, especially double-neutron-star systems:

measure post-Keplerian timing parameters in atheory-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)

˙

"

˙

Pb



Orbital Decay of PSR B1913+16

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

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



Mass-mass diagram forthe 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 andthen 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-eld GR – now down to

a ~0.02% test!

Deller et al 2008, ScienceP

b

Pb

"

# $

%

& ' Accel (10 ) 4

˙

"

˙

Pb

˙

Pb

s = 0.99987" 0.00048

+ 0.00013

s = 0.99974" 0.00039

+ 0.00016

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 pointedelsewhere (defined

by 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 toorbital aberration:

o /yr

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

"1spin

= 0.44 # 0.16+ 0.48



What about the double pulsar?

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

This starts to put strongconstraints on themisalignment angle:<37 o for one-pole model,<14 o for two-pole model(95.4% condence 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 anotheravenue to precession:

Eclipses of A by Boccur every orbit(Lyne et al 2004,Kaspi et al 2004).

A's ux ismodulated by thedipolar emissionfrom B.



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



René Breton




This model makesconcretepredictions if Bprecesses...



Eclipse geometry, Breton et al 2008.If B precesses, ! will change withtime, and the structure of theeclipse modulation should alsochange... and it does!

Dec. 2003

Nov. 2007

Courtesy René Breton



Breton et al 2008

The angles α and θ stayconstant, but !

changes 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-major

axes, this actually constrainsa generalized set ofgravitational strong-eldtheories for the rst time!



Preferred-frame effects with double-NS systems

Wex & Kramer 2007

Wex & Kramer showed that pulsars similar to the double pulsar aresensitive to preferred-frame effects (within semi-conservative

theories) via their orbital parameters. Here they show that thedouble pulsar (left), a similar system at the Galactic centre (middle)and their combination can lead to strong constraints on thedirectionality of the preferred frame (PFE antenna).



Future TelescopesThe Galactic Census with theSquare 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 measurethe BH spin and quadrupole moment , testing

the Cosmic Censorship conjecture andthe No-hair theorem .

" # c

G

S

M 2

q " c

4

G2

Q M

3

q = " # 2



! Q/Q = 0.008!

Pulsar with 100 " s timing precision in 0.1-year, eccentricity 0.4orbit around Sgr A*: weekly observations over 3 years lead to ameasurement of the spin (via frame-dragging) and quadrupole

moment (below) to high precision, assuming Sgr A* is an extremeKerr BH.

Δ S/S ~ 10-4...10 -3

Wex et al., in prep.

The challengewill be ndingsuch pulsars!!



Future ProspectsLong-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 background

Long-term timing of relativistic systems⇒ improved tests of strong-eld GR.Potential to measure higher-order terms in in 0737A: we may beable to measure the neutron-star moment of inertia!

Prole 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!

G / G

˙

"



Constraints on α 3 (and ζ 2)

α 3 can also be tested by isolated pulsars.Self-acceleration and Shklovskii effect contribute to observedperiod derivatives:

Young pulsars: α 3 < 2x10 -10 (Will 1993, “Theory & Expt. In Grav.Physics,”CUP).Millisecond pulsars: α 3 < ~10 -15 (Bell 1996, ApJ, 462, 287; Bell & Damour

1996, CQG, 13, 3121) .α 3+ζ 2 also accelerate the CM of a binary system ⇒ variable Pin eccentric PSR B1913+16: (α 3+ζ 2) < 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 asfor B1913+16, plus Shapirodelay.

The parameters , s and γ form a complementary testof GR.

The measured containsa large Shklovskii v 2 /dcontribution. If GR is correct,the distance to the pulsar is1.05 ± 0.05 kpc.After Stairs 2005, ASP Conf. Ser. 328, 3.

!

P b

!



What about the double pulsar?

Geodetic precessionappears notto be happening

in 0737A, despiteshort 75-year period.

No pulse shape

changes 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 (likelyprecession) changes from thestart.

Burgay et al. 2005

testing general relativity with relativistic binary pulsars

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