Binary-pulsar tests of gravity...

Binary-pulsar testsof gravity theories

Gilles Esposito-FarèseGRεCO / IAP

Testing a theory ?Useful to contrast its predictions with alternative theories

Example: “PPN” formalism to study weak-field gravity (order Newton × ) [Eddington, Schiff, Baierlin, Nordtvedt, Will]

– g00 = 1 – 2 Gm + 2 βPPN Gm 2 + …

gij = δij 1 + 2 γPPN Gm + …

1c2

rc2 rc2

rc2

0 0.5 1 1.5 2

0.5

1

1.5

2

GeneralRelativity

Lunar Laser Ranging

Mercury perihelion shift

Mars radar ranging&

Very Long Baseline Interferometry

βPPN

γPPN

ξα1,2,3ζ1,2,3,4

GENERAL RELATIVITYis essentially the onlytheory consistent with

weak-field experiments

Solar-system experimentsin the Parametrized Post-Newtonian formalism

0.996 0.998 1 1.002 1.004

0.996

0.998

1

1.002

1.004

generalrelativity

βPPN

γPPNLLR

VLBI

0 0.5 1 1.5 2

0.5

1

1.5

2

GeneralRelativity

Lunar Laser Ranging

Mercury perihelion shift

Mars radar ranging&

Very Long Baseline Interferometry&

Time delay for Cassini spacecraft

βPPN

γPPN

ξα1,2,3ζ1,2,3,4

0.996 0.998 1 1.002 1.004

0.996

0.998

1

1.002

1.004

generalrelativity

βPPN

γPPNLLR

VLBICassini

GENERAL RELATIVITYis essentially the onlytheory consistent with

weak-field experiments

Solar-system experimentsin the Parametrized Post-Newtonian formalism

(2004)

(2003)

rc2

– g00 = 1 – 2 Gm + 2 βPPN Gm 2 + …

gij = δij 1 + 2 γPPN Gm + …

rc2 rc2[ ]

Weak-field experiments

Rc2

solar system

7×10–10 2×10–6

neutronstar

blackhole

0.2 0.5

Gmself-gravity

deviation fromflat space

[ ]0 ⇒

binary pulsars

pulsar

companion

radio waves

observer

moving clockgiving informationabout this strong-

gravity region

Strong-field tests ?

• ~ 1600 known pulsars• ~ 100 binary pulsars

Many NS-WD binaries

PSR J1141–6545 [Kaspi et al. 1999]

PSR J0407+1607PSR J2016+1947…

PSR J0751+1807 ⇒ 2.1 m NS! [Nice et al. 2005]

8 NS-NS binaries

PSR B1913+16 [Hulse-Taylor 1974]PSR B1534+12 [Wolszczan 1991]PSR J0737–3039 [Burgay et al. 2003]

PSR B2127+11C (in globular cluster)PSR J1756–2251 [Faulkner et al. 2004]PSR J1518+4904PSR J1811–1736PSR J1829+2456

PSR J1906+07 [Lorimer et al. 2005] (maybe NS-WD?)

pulsar

companion

radio waves

observer


Many NS-WD binaries

PSR J1141–6545 [Kaspi et al. 1999]

PSR J0407+1607PSR J2016+1947…


8 NS-NS binaries




pulsar

companion

radio waves

observer

Precision tests ofstrong-field gravity


Many NS-WD binaries

PSR J1141–6545 [Kaspi et al. 1999]

PSR J0407+1607PSR J2016+1947…


8 NS-NS binaries




pulsar

companion

radio waves

observer

Precision tests ofstrong-field gravity

Small-e binaries⇒ null tests of

GR’s symmetries

Tests of the “strong equivalence principle” and of preferred-frame effects

• The different accelerations (due to a thirdbody or to their absolute velocity with respectto a preferred frame) induce a polarizationof the periastron towards a precise direction

• ∃ several binary pulsars with

⇒ statistical argument to constrain PPN parameters [Damour, Schäfer, GEF, Bell, Camilo, Wex, Stairs, …]

e

B

A

C.M.

aA

aB aA

eF

e ≈ 0eR

ωR.

eF

eeR

ωR.

fixed direction

fixed direction

|eFixed| |aA – aB|

Tests of the “strong equivalence principle” and of preferred-frame effects

• The different accelerations (due to a thirdbody or to their absolute velocity with respectto a preferred frame) induce a polarizationof the periastron towards a precise direction

• ∃ several binary pulsars with

⇒ statistical argument to constrain PPN parameters [Damour, Schäfer, GEF, Bell, Camilo, Wex, Stairs, …]

e

B

A

C.M.

aA

aB aA

eF

e ≈ 0eR

ωR.

eF

eeR

ωR.

fixed direction

fixed direction

|eFixed| |aA – aB|

⇒ Constraints on PPN parameters [Stairs et al. 2005]• |α1| < 1.4×10–4 (≈ solar system bounds)• |α3| < 4×10–20 (1012 tighter than sol. syst.!)• |1 – mg/mi| < 5.6×10–3 for a neutron star

Binary-pulsar tests

pulsar

binarypulsar

= (very stable) clock

= moving clock

t

pulses

t

pulses

P

• Time of flight across orbit size of orbit (“Roemer time delay”)

– orbital period P– eccentricity e– periastron angular position ω– …

c

“Keplerian” parameters

• Redshift G mB + second order Doppler effect vA (“Einstein time delay”)

– parameter γTiming

rAB c2

“post-Keplerian” observables[PSR B1913+16 • Hulse & Taylor]

2 c2

2

• Time evolution of Keplerian parameters

– periastron advance ω (order 1 )

– gravitational radiation damping P (order 1 )

c2

c5

.

.

3observables

– 2unknown

masses mA, mB

= 1test

Plot the three curves [strips]

γTiming(mA, mB) = γTiming

ω (mA, mB) = ω

P (mA, mB) = P

theory observed

.

.

.

.

theory observed

theory observed

“ γ - ω - P test ”. .

0 0.5 1 1.5 2 2.5

companion

pulsar

⇒GR

P.

= –2.421 × 10–12

mA = 1.4408 m

mB = 1.3873 m

ω. = 4.22661°/yrγT = 4.294 ms

PSR B1913+16in general relativity

0.5

1

1.5

2

2.5Pth(mA,mB) = Pexp. .

ωth(mA,mB) = ωexp. .

intersection

γth(mA,mB) = γexpT T

mA/m

mB/m

Discovered by R. Hulse and J. Taylor in 1974

s ≤ 1

PSR B1534+12in general relativity

Discovered by A. Wolszczan in 1991

d Doppler n.a + v2

d t d PSRDoppler n.v fi ^

“Galactic” contribution to P [Damour–Taylor 1991]

.5 observables - 2 masses = 3 tests

P.

w.

gTr, s

s

r

g

w.

intersection

companion

0.5 1 1.5 2 2.5

1

1.5

0.5

2

2.5

0 mA/m

mB/m

pulsar

P.

companion

pulsar0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

mA/m

mB/m

Discovery Kaspi et al. 1999, Timing Bailes et al. 2003

PSR J1141–6545in general relativity

P.

= –4 × 10–13

Asymmetrical systemneutron star – white dwarf

(mB sin i )3

(mA+ mB)2 = 2 π 2

P

(x c)3

G

Mass function

Neutron star born after white dwarf⇒ eccentricity e = 0.17 large and nonrecycled pulsar

s ≤ 1

P.

γ

ω.

intersection

s

P.

xA/xB

r

γ

ω.

intersection

PSR J0737–3039in general relativity2nd pulsar

1st pulsar0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

mB/m

Timing Burgay et al. 2003, Double pulsar Lyne et al. 2004

ω. = 16.90°/yr

= = 1.07xBxA

mAmB

observer

pulsar A

pulsar B

P = 2 h 27 min 14.5350 s

mA/m

6 observables − 2 masses = 4 tests

S = 16 p G Ú -g {R - 2 ( mj)2 } + Smatter[matter ; gmn = e2a(j) gmn]

1 ~

Tensor-scalar theories

spin 2 spin 0 physical metric

a(j)

j

b0

a0

curvature

slope

j0

a(j) = a0 (j–j0) + 1 b0 (j–j0)2 + …2

jmatter

jj

j

j

j

...

Geff = G ( 1 + a02 )

gPPN– 1 a02

bPPN– 1 a02 b0 a0 a0

b0

a0 a0

scalargraviton -6 -4 -2 0 2 4 6b0

General Relativity

|a0|

0.025

0.030

0.035

0.010

0.015

0.020

0.005

LLR

perihelionshift

VLBI

LLR

jmatter

j

matterj

Vertical axis (b0 = 0) : Jordan–Fierz–Brans–Dicke theory a0 = 2 wBD + 32 1

Cassini

The most natural theories of gravity includea scalar field j besides the metric gmn

Deviations from general relativity due to the scalar field

• At any order in 1 , the deviations involve at least two a0 factors:cn

scalar…

a0

a0

a0 a0

a0

a0

graviton

= small deviations!

• But nonperturbative strong-field effects can occur:

a0 + a1 Gm + a2

Gm 2 + …

Rc2 Rc2deviations = a0 ¥

< 10-5

2

LARGE for Gm ª 0.2Rc2

0 0.5 1 1.5

0.5

1

1.5

ω.

γ P. General relativity

passes the test

mA/m

mB/m

0 0.5 1 1.5

0.5

1

1.5 γω.

P.

A tensor–scalar theorywhich passes the test

(β0 = –4.5, α0 small enough)

mB/m

mA/m

γ

0 0.5 1 1.5 2 2.5

0.5

1

1.5

2

2.5γ

ω.

P.

A tensor–scalar theorywhich does not pass the test

(β0 = –6, any α0)

mB/m

mA/m

PSR B1913+16in scalar-tensor theories

Vertical axis (β0 = 0) : Jordan–Fierz–Brans–Dicke theory α0 = 2 ωBD + 3Horizontal axis (α0 = 0) : perturbatively equivalent to G.R.

2 1

Solar-system & PSR B1913+16 constraintson scalar-tensor theories of gravity

a(ϕ)

ϕ

α0

β0 < 0

β0 > 0

α0

matter-scalarcoupling function

PSRB1913+16

−6 −4 −2 0 2 4 6

general relativitybinary pulsarsimpose β0 > −4.5

i.e. βPPN– 1 < 1.1

γPPN– 1[T. Damour & G.E-F 1998]

Cassini

0.025

0.050

0.030

0.035

0.040

0.045

0.010

0.015

0.020

0.005

|α0|ϕ

matter

general relativity

β0

ϕ

matter ϕ

VLBI

Vertical axis (β0 = 0) : Jordan–Fierz–Brans–Dicke theory α0 = 2 ωBD + 3

Horizontal axis (α0 = 0) : perturbatively equivalent to G.R.

2 1

Solar-system & PSR B1913+16 constraintson scalar-tensor theories of gravity

a(ϕ)

ϕ

α0

β0 < 0

β0 > 0

α0


(1993)

PSRB1913+16

(2004)

Cassini

|α0|ϕ

matter

−6 −4 −2 0 2 4 6

general relativity

β0

ϕ

matter ϕbinary pulsars

impose β0 > −4.5

i.e. βPPN– 1

< 1.1γPPN– 1

VLBI

0.025

0.050

0.035

0.040

0.045

0.010

0.015

0.020

0.005

The four accurately timedbinary pulsars in general relativity

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5 w.

mA

mB

s £ 1

P.

g

PSR B1913+16

intersection

s £ 1

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

mA

mB

P.

g

PSR J1141-6545

w.

intersections

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

mA

mB

P.

xA/xB

r

g

PSR J0737-3039

w.

intersection

s

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

r

g

mA

mB PSR B1534+12

w.

intersection

P.

Vertical axis (b0 = 0) : Jordan–Fierz–Brans–Dicke theory a0 = 2 wBD + 3Horizontal axis (a0 = 0) : perturbatively equivalent to G.R.

2 1

a(j)

j

a0

b0 < 0

b0 > 0

a0


Solar-system & best binary-pulsar constraintson scalar-tensor theories of gravity

PSRB1913+16

PSRJ1141–6545

Cassini

0.025

0.050

0.035

0.040

0.045

0.010

0.015

0.020

0.005

|a0|j

matter

-6 -4 -2 0 2 4 6

general relativity

b0

j

matterj

binary pulsarsimpose b0 > -4.5

i.e. bPPN– 1 < 1.1

gPPN– 1

VLBI

[T. Damour & G.E-F 2006]

All solar-system & binary-pulsarconstraints on tensor–scalar theories

a(j)

j

a0

b0 < 0

b0 > 0

a0

matter-scalarcoupling function LIGO/VIRGO

NS-BH

0.025

-6 -4 -2 0 2 4 6

|a0|

b0

general relativity

jmatter

j

matterj

B1534+12

J1141–6545

J0737–3039

All pulsars

0.2

0.15

0.175

0.075

0.05

0.1

0.125

B1913+16

LIGO/VIRGONS-NS

SEP


a(ϕ)

ϕ

α0

β0 < 0

β0 > 0

α0


B1913+16

J1141–6545

Cassini

−6 −4 −2 0 2 4 6β0 ϕ

matter ϕ

|α0|ϕ

matter

100

B1534+12

J0737–3039SEP

general relativity(α0 = β0 = 0)

10−2

10−3

10−4

All pulsars

10−1

LIGO/VIRGONS-BH

LIGO/VIRGONS-NS

LLR

Logarithmicscale for α0


a(ϕ)

ϕ

α0

β0 < 0

β0 > 0

α0


B1913+16

J1141–6545

Cassini

−6 −4 −2 0 2 4 6β0 ϕ

matter ϕ

|α0|ϕ

matter

100


10−2

10−3

10−4

All pulsars

10−1

Logarithmicscale for α0


a(ϕ)

ϕ

α0

β0 < 0

β0 > 0

α0


Cassini

−6 −4 −2 0 2 4 6β0 ϕ

matter ϕ

|α0|ϕ

matter

100


10−2

10−3

10−4

All pulsars

10−1


a(ϕ)

ϕ

α0

β0 < 0

β0 > 0

α0


Cassini

−6 −4 −2 0 2 4 6β0 ϕ

matter ϕ

|α0|ϕ

matter

100


10−2

10−3

10−4

All pulsars

10−1

LISANS-BH

LIGO/VIRGONS-BH


a(ϕ)

ϕ

α0

β0 < 0

β0 > 0

α0


Cassini

−6 −4 −2 0 2 4 6β0 ϕ

matter ϕ

|α0|ϕ

matter

100


10−2

10−3

10−4

All pulsars

10−1

LISANS-BH

J1141–6545+ 1% Pdot


a(ϕ)

ϕ

α0

β0 < 0

β0 > 0

α0


Cassini

−6 −4 −2 0 2 4 6β0 ϕ

matter ϕ

|α0|ϕ

matter

100


10−2

10−3

10−4

All pulsars

10−1

LISANS-BH

J1141–6545+ 1% Pdot

PSR-BH

Conclusions

• Binary pulsars are ideal tools for testing

the strong-field regime of gravity

(qualitatively different from solar-system tests)

• ⇒ GR wave templates suffice for LIGO/VIRGO/LISA.

• General relativity passes all the tests with flying colors.

• Douple pulsar PSR J0737–3039 fantastic system to test GR itself and the physics of neutron stars.

• Best systems for constraining scalar-tensor theories (large dipolar scalar waves):

asymmetrical Neutron Star–White Dwarf or Neutron Star–Black Hole

• Best known system: PSR J1141–6545

Binary-pulsar tests of gravity...

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