andrea possenti - ego-gw.it · andrea possenti inaf – osservatorio astronomico di cagliari vesf...

Electromagnetic Electromagnetic observations of observations of

pulsars and binariespulsars and binaries

ANDREA POSSENTIANDREA POSSENTIINAF INAF –– Osservatorio Astronomico di CagliariOsservatorio Astronomico di Cagliari

VESF SCHOOL on VESF SCHOOL on GRAVITATIONAL WAVESGRAVITATIONAL WAVES

IV EditionIV Edition2525--29 May 2009, EGO Site 29 May 2009, EGO Site -- Cascina Cascina –– Pisa (Italy)Pisa (Italy)

OutlineOutline

28 May 2009 28 May 2009 –– EGO Site EGO Site –– Cascina (Pisa)Cascina (Pisa)

1.1. Pulsar GeneralitiesPulsar Generalities

2.2. Double Neutron Star Merger RateDouble Neutron Star Merger Rate

3.3. Pulsar Timing ConceptsPulsar Timing Concepts

4.4. Gravity Theories tests with PulsarsGravity Theories tests with Pulsars

•• Manchester & Taylor 1977 “Manchester & Taylor 1977 “PulsarsPulsars””•• Lyne Lyne & Smith 2005 “& Smith 2005 “Pulsar AstronomyPulsar Astronomy””•• Lorimer Lorimer & Kramer 2005& Kramer 2005 ““Handbook of Pulsar Handbook of Pulsar AstronomyAstronomy””•• AA.VV. 2009 “AA.VV. 2009 “Physics of relativistic objects in compact binaries: fromPhysics of relativistic objects in compact binaries: from

birth to coalescencebirth to coalescence”, Springer”, Springer

BooksBooks

Review ArticlesReview Articles•• Science, Science, AprilApril 2004 2004 –– Neutron Stars,Neutron Stars, Isolated Pulsars, Binary Isolated Pulsars, Binary PulsarsPulsars•• ARA&A, Jan 2008ARA&A, Jan 2008 –– The Double PulsarThe Double Pulsar•• LivingLiving Reviews articles: Reviews articles: ((http://relativity.livingreviews.org/Articles)http://relativity.livingreviews.org/Articles)

•• Stairs 2003: Stairs 2003: Testing General RelativityTesting General Relativity with with pulsar timingpulsar timing•• WillWill, 2006: , 2006: The confrontation btw General Relativity and experimentThe confrontation btw General Relativity and experiment•• Lorimer 2008: Lorimer 2008: Binary and millisecond pulsarsBinary and millisecond pulsars



1.1.Pulsar GeneralitiesPulsar Generalities

ELECTROMAGNETIC OBSERVATIONS OF ELECTROMAGNETIC OBSERVATIONS OF PULSARS AND BINARIESPULSARS AND BINARIES



WhatWhat is is a Pulsar?a Pulsar?AA PULSAR PULSAR is is a a rapidlyrapidly rotatingrotating andand highlyhighly

magnetizedmagnetized neutronneutron starstar, , emittingemitting a a pulsedpulsed radio radio signalsignal as aas a consequence of consequence of aa lightlight--house effecthouse effect

@K

ram

er

The rotating magnetized NS in vacuumThe rotating magnetized NS in vacuum

Assuming that the rotational energy lossAssuming that the rotational energy loss

LLsdsd = d/dt (E= d/dt (Erotrot) = d/dt (I) = d/dt (IΩΩ22/2) = I /2) = I ΩΩ ΩΩmatches the emitted powermatches the emitted power (derived (derived

from the basic electrodynamics formula):from the basic electrodynamics formula):

LLdipole dipole = [ 2/3c= [ 2/3c33] | ] | µµ | | 22

one can inferone can infer……

··

····

µµ = ½ B= ½ Bpp RR33

is the magnetic is the magnetic momentmomentR = NS radiusR = NS radiusBBpp = polar magn. field= polar magn. field

Derived Derived parameters: age & magnetic fieldparameters: age & magnetic field

• Actual age of pulsar is function of initial periodand braking index n=(n=(νν νν )/ )/ νν 22 (assumed constant)

• For PP00 << P<< P, n = n = 33 , have “characteristic age”“characteristic age”

• If true age known,one can compute initial period

• From braking equation, one can derive B0 at NS equator with R = NS radius. Value at at polepole is 2B2B00

• Typically assumed R=10R=10 km, km, I=10I=104545 gm cmgm cm22, , n=3n=3

(from Manchester & Taylor)

·· ·

Pulsar Pulsar EnergeticsEnergetics

SpinSpin--down Luminosity: down Luminosity:


Radio Luminosity:Radio Luminosity:


1028

The BThe Bss vs P vs P diagramdiagram

A pulsar is put on it A pulsar is put on it once both P and dP/dt once both P and dP/dt

are measured, from are measured, from which which

BBs s = 3.2= 3.2··101019 19 [ P P ]½ G[ P P ]½ G..

ATNF Pulsar Catalogue

Young pulsar Line

How to explain How to explain this group of this group of

pulsars ?pulsars ?

A dichotomy A dichotomy in the in the

populationpopulation

ATNF Pulsar Catalogue

Young pulsar Line

P = 1.557 P = 1.557 msms

Extreme physical conditions Extreme physical conditions occur in millisecond pulsarsoccur in millisecond pulsars

VVtangtang = 0.13 = 0.13 cc !!!!

tangential velocity

DiscoveryDiscovery of the of the first millisecondfirst millisecond pulsar pulsar B1937+21 (1982)B1937+21 (1982) [Backer et al. 1982]

First promise of putting First promise of putting constraints to the Equation of constraints to the Equation of

State for nuclear matter !State for nuclear matter !

Short spin periods: 1.39 ms < P < 200 ms (conventional)

Lower surface magnetic fields: 7.5 < log (Bs(gauss)) < 10.5 (conventional)

Much larger characteristic ages: τ ~ 109-1010 years

Much higher fraction of binarity: fbin> 70%

Slower mean 3D velocity: v ~ 130 km/s (Toscano et al 1999)

Half of the objects moving towards the Galactic plane (Toscano et al 1999)

A tendency to wider duty cycles: W ~ 0.1-0.4 P (Kramer et al 1998)

Similar mean spectral index: α ~ - 1.7 (Kramer et al. 1998)

Slightly less average radio luminosity (Kramer et al. 1998)

Higher degree of polarization (Xilouris et al. 1998)

Short spin periods: 1.39 ms < P < 200 ms (conventional)Short spin periods: 1.39 ms < P < 200 ms (conventional)

Lower surface magnetic fields: 7.5 < log (BLower surface magnetic fields: 7.5 < log (Bss(gauss)) < 10.5 (conventional)(gauss)) < 10.5 (conventional)

Much larger characteristic agesMuch larger characteristic ages: : ττ ~ 10~ 1099--101010 10 yearsyears

Much higher fraction of binarityMuch higher fraction of binarity: f: fbinbin> 70%> 70%

Slower mean 3D velocity: v Slower mean 3D velocity: v ~ 130 km/s ~ 130 km/s (Toscano et al 1999)(Toscano et al 1999)

Half of the objects moving towards the Galactic plane Half of the objects moving towards the Galactic plane (Toscano et al 1999)(Toscano et al 1999)

A tendency to wider duty cycles: W A tendency to wider duty cycles: W ~ 0.1~ 0.1--0.4 P 0.4 P (Kramer et al 1998)(Kramer et al 1998)

Similar mean spectral index: Similar mean spectral index: αα ~ ~ -- 1.7 1.7 (Kramer et al. 1998)(Kramer et al. 1998)

Slightly less average radio luminosity Slightly less average radio luminosity (Kramer et al. 1998)(Kramer et al. 1998)

Higher degree of polarization Higher degree of polarization (Xilouris et al. 1998)(Xilouris et al. 1998)

The MSP vs ordinary pulsar features The MSP vs ordinary pulsar features

Recycling scenarioRecycling scenario: Millisecond pulsars are old neutron stars spun up by accretion of matter and angular momentum from a companion star in a

multiple system [Bisnovati-Kogan & Kronberg 1974, Alpar et al. 1982]

The MSP formation paradigm The MSP formation paradigm

A died pulsar could be spun up and rejuvenated by an A died pulsar could be spun up and rejuvenated by an evolving binary companionevolving binary companion

1000 yr

deat

hlin

e

Hubble time

A died pulsar could be spun up and rejuvenated by an A died pulsar could be spun up and rejuvenated by an evolving binary companionevolving binary companion

Dan

a B

erry

@ N

ASA

Dan

a B

erry

@ N

ASA

A newly born fast spinning pulsar

1000 yr

Hubble time

deat

hlin

e

A recycled A recycled pulsar spins down again due to pulsar spins down again due to magnetodipole brakingmagnetodipole braking

Bin

ary

Evo

luti

onB

inar

y E

volu

tion

[ St

airs

200

4 ]

the current samplethe current sample !!More & more pulsars:More & more pulsars:

Until 1997: ~ 750~ 750

Now in the Atnf Catalog: ~ ~ 18001800

~~ 2020 Extragalactic (LMC/SMC)

~~ 150150 Binary ( 140140 somehow recycled)

~~ 8080 Young (age<10000 yr)

~~ 2626 Vela-like (i.e. very young)

22 Radio emitting AXPs

99 Double Neutron star binaries

11 Double pulsar

140140 in 2626 Globular Clusters

++ Rrats, Intermittent PSRs, …

TOTALTOTAL known sampleknown sample

GC search > 70

Drift scan search > 20

GBTGBT discoveriesdiscoveries

Parkes PM = 725

Parkes SWI+SWII = 69+25

Parkes PH = 18

Parkes PA > 10

Total using multibeam > 847Parkes GC search > 34

ParkesParkes discoveriesdiscoveries

Galactic Plane search > 50

AreciboArecibo discoveriesdiscoveries

2.2.Double Neutron Stars Double Neutron Stars

Merger RatesMerger Rates




Coalescence rate R (empirical approach)Coalescence rate Coalescence rate R R (empirical approach)(empirical approach)

Lifetime of a system = current age + merging time of a pulsar of a system

Correction factor : correction for pulsar beaming

Lifetime of a systemNumber of sources × correction factorR R =

[ fr

om C

hung

lee

Kim

]

Properties of pulsars in DNSsProperties of pulsars in Properties of pulsars in DNSsDNSs

B1913+16 59.03 8.6x10-18 7.8 0.617 2.8 (1.39)

B1534+12 37.90 2.4x10 -18 10.0 0.274 2.7 (1.35)

Galactic disk Galactic disk pulsars merging in less than an Hubble timepulsars merging in less than an Hubble time

Ps (ms) (ss-1) Porb (hr) ecc Mtot ( ) Ps

.•M

J0737J0737--30393039 22.70 2.4x10 -18 2.4 0.087 2.6 (1.24)

J1756-2251 28.45 1.0x10-18 7.7 0.181 2.6 (….)

J1906+0746J1906+0746 144.10 2.0x10-14 4.1 0.085 2.6 (1.37)

Properties of pulsars in DNSs (cont)Properties of pulsars in Properties of pulsars in DNSsDNSs (cont)(cont)

B1913+16 110 320 4º.23

B1534+12 250 2500 1º.75

τc (Myr) τmerg (Myr) dω/dt (deg/yr)

J0737-3039 200 86 16º.90

Galactic disk Galactic disk pulsars merging in less than an Hubble timepulsars merging in less than an Hubble time

J1756-2251 400 15900 2°.59

J1906+0746J1906+0746 0.11 320 7°.57

Coalescence rate R (empirical approach)Coalescence rate Coalescence rate R R (empirical approach)(empirical approach)

Lifetime of a system = current age + merging time of a pulsar of a system

Correction factor : correction for pulsar beaming

Number of sources : number of pulsars in coalescing DNSs in the galaxy of a given type

Lifetime of a systemNumber of sources × correction factorR R =

How many pulsars How many pulsars ““similarsimilar”” to each of the known to each of the known DNSsDNSsexist in our exist in our Galaxy? It needs estimating the SCALE factorGalaxy? It needs estimating the SCALE factor

[ fr

om C

hung

lee

Kim

]

Results for Double Neutron StarsResults for Double Neutron StarsResults for Double Neutron Stars

[ Chunglee Kim 2008 ]

The Galactic coalescence rate R for Double Neutron Star BinariesThe The GalacticGalactic coalescence rate coalescence rate R R

for Double Neutron Star Binariesfor Double Neutron Star Binaries

118+174-79 27+80

-23

RR (current)(current) (Myr(Myr--11) R (previous) (Myr) R (previous) (Myr--11) ) Coalescence Coalescence raterate

ForFor the reference model (at 95% CL):the reference model (at 95% CL):

B1913+B1534+J0737+J1906B1913+B1534+J0737+J1906 B1913+B1534B1913+B1534[ Lorimer 2008 ]

RRpeakpeak (current)(current)

RRpeakpeak (previous)(previous)~~ 55--66

Increase rate factorIncrease rate factor

Detection rate of Double Neutron Star inspiralsDetection rate of Detection rate of Double Neutron StarDouble Neutron Star inspiralsinspirals

Rdet (advanced) =

Rdet (initial) =

TheThe most probable most probable inspiralinspiral detection rates for detection rates for LIGO/VIRGOLIGO/VIRGO

~ 1 event per 8 yr (95% CL, most optimistic)

~ 600 events per yr (95% CL, most optimistic)

Rates may be significantly higher if a substancial populationRates may be significantly higher if a substancial populationof highly eccentric binary systems exists. It could escape of highly eccentric binary systems exists. It could escape detection due the short lifetime before GW inspiraldetection due the short lifetime before GW inspiral

[ Chaurasia & Bailes 2005 ]

Many uncertainties in the modelMany uncertainties in the model

One year of observation with LISA of the Double Pulsar wouldOne year of observation with LISA of the Double Pulsar woulddetect the continuous emission at freq=0.2 mHz with a S/N detect the continuous emission at freq=0.2 mHz with a S/N ≈≈ 22

[ Kalogera 2004 ]

[ L

orim

er 2

008

]

Results for NS-WD binariesResults for NSResults for NS--WD binariesWD binaries

[ C

hung

lee

Kim

200

8 ]

Only 3 known coalescing systems known to dateOnly 3 known coalescing systems known to date

The Galactic coalescence rate R for Neutron Star-White Dwarf Binaries

The The GalacticGalactic coalescence rate coalescence rate R R for Neutron Starfor Neutron Star--White Dwarf BinariesWhite Dwarf Binaries

4+5-3

RR (Myr(Myr--11) ) Coalescence Coalescence raterate

ForFor the reference model (at the reference model (at 68%68% CL), not corrected for beaming:CL), not corrected for beaming:

J0751+J1757+J1141J0751+J1757+J1141[ Chunglee Kim et al 2004 ]

Coalescing frequencies are in the LISA band: Coalescing frequencies are in the LISA band: but expected event rate not very encouragingbut expected event rate not very encouraging

[ Chunglee Kim et al 2004 ]

Coalescence rate calculations (other approaches)

Coalescence rate calculations Coalescence rate calculations (other approaches)(other approaches)

Combination of various observational constraintsCombination of various observational constraintsresulting from binary population synthesis coderesulting from binary population synthesis codeare very promising are very promising

[ O’Shaughnessy et al 2008 ]

The presented approach is an empirical oneThe presented approach is an empirical oneThe alternate option is to run extended Monte CarloThe alternate option is to run extended Monte Carlosimulations of the most likely evolutionary scenario starting simulations of the most likely evolutionary scenario starting from a population of primordial binariesfrom a population of primordial binariesThe uncertainties in the assumption for the initial state of theThe uncertainties in the assumption for the initial state of thebinaries make the range of the predicted merging rates binaries make the range of the predicted merging rates larger than with the empirical approach larger than with the empirical approach

[ Dewey & Cordes 1987 ][ Lipunov et al 1996 ][ Belczynski, Kalogera, Bulik 2002 ] [ Belczynski et al 2008 ]

3.3.Pulsar Timing Pulsar Timing

ConceptsConcepts




Timing idea: observationsTiming idea: observationsTiming idea: observationsPerforming repeated observations of the Times of Arrivalrepeated observations of the Times of Arrival

(ToAs) at the telescope of the pulsations from a given pulsar

and

searching the ToAs for systematic trendssearching the ToAs for systematic trends on many different timescales, from minutes to decades

Timing idea: modelingTiming idea: modelingTiming idea: modelingif a physical model adequately describes the systematic trends,

it is applied with the smallest number of parameters

when a model finally describes accurately the observed ToAs, the values of the model’s parameters shed light onto the physical model’s parameters shed light onto the physical

propertiesproperties of the pulsar and/or of its environment

otherwise

if a physical model is not adequate, it is extended (adding parameters) or rejected in favour of

another model

Timing Timing of a radio pulsarof a radio pulsar

@ Lorimer

The TOPOCENTRIC ToAs must be corrected, calculating them to to infiniteinfinite frequency at Solar System frequency at Solar System BarycentreBarycentre (SSB) thus

obtaining the BARYCENTERED ToAs: the time scale is (Tempo2) the Barycentric Coordinate Time (TCB), i.e. the proper time of an observer at SSB were the gravity field of Sun and Planets absent

Getting barycentered ToAsGetting barycentered ToAs

ttSSBSSB : Calculated BARYCENTERED ToA at INFINITE frequencyttobs obs : Observed TOPOCENTRIC ToAttclk clk : Observatory clock correction to TAI (= UTC + leap sec), via GPSD/fD/f22 : Dispersion term ∆∆RR : Roemer delay (propagation delay) to SSB (need SS ephemeris, e.g. DE405) ∆∆SS : Shapiro delay in Solar-System ∆∆EE : Einstein delay at Earth

Timing model: rotational termsTiming model: rotational termsTiming model: rotational terms1. Have series of barycentered ToAs: ti

2. Model pulsar frequency evolution νν(t)(t) by Taylor series, and then integrate to get pulse phase evolution (φφ(t)(t) = 1 for t=P)

3. Choose t = 0 to be first ToA, t0

4. Form residuals residuals rrii = = φφii –– nnii where ni is the nearest integer to φi

5. If pulsar model is accurate, then ri << 16. Corrections to model parameters are obtained by making

leastleast-- squares fit to trends in squares fit to trends in rrii

Thanks to the least- square fit, one can solve for those

positional and kinematic parameters from errors in

SSB correction

Barycentric corrections depends on Pulsar

POSITION, PROPER MOTION and PARALLAX

Timing model: astrometric termsTiming model: astrometric termsTiming model: astrometric terms

Timing model: isolated pulsarsTiming model: isolated pulsarsTiming model: isolated pulsarsFrom timing of an isolated pulsar over a long enough

time span, one can in principle get

RA & DEC: Celestian coordinatesPMRA & PMDEC: Proper Motionπ : Trigonometric Parallax (i.e. Distance) DM : Accurate Dispersion MeasureDM1 : Time Derivative of Dispersion Measure P0: Rotational PeriodP1: Time derivative of P0P2: Second time derivative of P0P3: Third time derivative of P0…

Since 1974 pulsars in binary systems are known

Since 1974 pulsars in binary Since 1974 pulsars in binary systems are knownsystems are known

The PULSARCENTRIC ToAs (i.e. ToAs expressed in pulsar proper time) must be corrected, calculating them

atat the Pulsar Systemthe Pulsar System BarycenterBarycenter (PSB)

Correcting ToAs to the binary barycenter Correcting ToAs to the binary barycenter

ttPSRPSR--BARYBARY : Time at pulsar system barycenterTTpsr psr : Time in pulsar proper time (measured as at pulsar surface)∆∆R,bR,b : Roemer delay (propagation delay) from pulsar to PSB ∆∆S,bS,b : Shapiro delay in pulsar binary ∆∆E,bE,b : Einstein delay in pulsar binary∆∆AA : Aberration delay due to pulsar rotation

tPSR-BARY = Tpsr + ∆R,b + ∆E,b + ∆S,b + ∆A

Those terms contain various parameters of the binary systemThose terms contain various parameters of the binary systemand thus a least-square fit to the residuals of a model

including those parameters can allow to measure them…

( ) ( )( )2

3

2

32 sinsin4),(

cp

c

orb

pcp

mm

im

P

ia

Gmmf

+== π

Mass function:

forfor ii = 90= 90o o MinimumMinimum companion masscompanion mass

forfor ii = 60= 60o o MedianMedian companion masscompanion mass

For most binaries, 5 For most binaries, 5 kepleriankeplerian parameters are measured parameters are measured and are (well) enough to satisfactorily describe the dataand are (well) enough to satisfactorily describe the data

Pb : Orbital periodx = ap sin i : Projected semi-major axisω : Longitude of periastrone : Eccentricity of orbitT0 : Time of periastron

Pulsars as clocksPulsars as clocks

Pulsar periods can sometimes be measured with unrivalled precision

e.g. on Jan 16, 1999, PSR J0437-4715 had a period of

16 significant digits!

5.757451831072007 ± 0.000000000000008 ms

Atomic clocks vs pulsar timing Atomic clocks vs pulsar timing Atomic clocks vs pulsar timing

Unfortunately only a subsample of the recycled pulsars is able to achieve such a rotational stability

The majority of the ordinary pulsars undergo timing irregularitiThe majority of the ordinary pulsars undergo timing irregularitieses

[ L

orim

er 2

008

]

4.4.Gravity Theory Gravity Theory

Tests with PulsarsTests with Pulsars




1] 1] Elliptical and planar orbitElliptical and planar orbit

2] 2] Constant Constant areolar velocity areolar velocity

3] a3] a33 = = (G/4(G/4ππ22) ) MMtottot PP22

Keplero (1609, 1609, 1619)Keplero (1609, 1609, 1619)Keplero (1609, 1609, 1619)

Binary systems: the classic lawsBinary systems: the classic lawsBinary systems: the classic laws

……for some binary pulsars, the for some binary pulsars, the accuracy of the ToA data is so high accuracy of the ToA data is so high that that -- by using by using only the keplerianonly the keplerian

descriptiondescription -- one can obtain one can obtain no acceptable timing solutionno acceptable timing solution !!

Additional physics is needed! Additional physics is needed!

……but… which physics? but… which physics?

Going beyond Kepler…Going beyond Kepler…

Even before publication of General Relativity, a Even before publication of General Relativity, a blossom of alternate Gravity Theories appearedblossom of alternate Gravity Theories appeared

A very large class of these Theories A very large class of these Theories (somehow the only ones which have some chance to be “viable”) are the are the

METRIC THEORIES OF GRAVITYMETRIC THEORIES OF GRAVITY [e.g Will 2006 ]

- a symmetric metric exists

- all test bodies follow geodesic of the metric

- in local freely falling reference frames, all the NON- gravitational laws of physics are those written in the language of special relativity

In metric theories, gravitation must be a phenomenon In metric theories, gravitation must be a phenomenon related with the occurrence of a curved “spacetime”related with the occurrence of a curved “spacetime”


In any metric theory, matter and NONIn any metric theory, matter and NON--grav grav fields respond only to the “metric”fields respond only to the “metric”

Additional fields can exist, though, giving rise to Additional fields can exist, though, giving rise to -- Tensor/scalar theoriesTensor/scalar theories

-- Tensor/vectorial theoriesTensor/vectorial theories

-- Bimetric theoriesBimetric theories ……

all of them incorporating their own parametersall of them incorporating their own parameters

These additional fields prescribe how matter and NON-grav fields contribute to create the metric; once

determined, the metric alone acts back on the matter

These additional fields prescribe how matter and NONThese additional fields prescribe how matter and NON--grav fields contribute to create the metric; once grav fields contribute to create the metric; once

determined, the metric alone acts back on the matter determined, the metric alone acts back on the matter


The Parametrized Post Newtonian (PPN) approachThe Parametrized Post Newtonian (PPN) approach

A suitable and successful framework for describing the results aA suitable and successful framework for describing the results and nd constraining a very large class of METRIC theories of gravity isconstraining a very large class of METRIC theories of gravity is

that of the so called Parametrized Post Newtonian formalismthat of the so called Parametrized Post Newtonian formalism

Deviations from Newtonian physics are related to a set of 10 Deviations from Newtonian physics are related to a set of 10 PPNPPN--paramters, each of them associated with a specific physical paramters, each of them associated with a specific physical

effect effect [e.g Will 2006 ]

It describes all metric theories of gravity in It describes all metric theories of gravity in WEAKWEAK--FIELD FIELD conditions, i.e. at order 1/cconditions, i.e. at order 1/c22 wrt Newtonian physics wrt Newtonian physics [e.g Will 2006 ]

0

0

0

0

0

0

0

0

1 + L

(1+w)/(2+w)

Value in Value in scalarscalar

tensor theorytensor theory

00ζ4

00ζ3

00ζ2

00

Is momentum conserved?

ζ1

00α3

a20α2

a10

Preferred-frame effects?

α1

x0Preferred-location effects?ξ

b1How “nonlinear’’ is gravity?

β

g1How much space curvature produced by unit mass?

γ

Value in semiValue in semi--conservative conservative

theoriestheories

Value in Value in GRGR

What it measures, relative What it measures, relative to general relativityto general relativityParameterParameter

The 10 PPN-parameters and their significanceThe 10 PPNThe 10 PPN--parametersparameters and their and their significancesignificance

@ W

ill 2

009



Tests of Gravity in the weakTests of Gravity in the weak--field limitfield limit

The PPN formalism is well tailored for describing the outcomes The PPN formalism is well tailored for describing the outcomes of these tests of these tests [e.g Will 2006 ]

102

10−≅==cR

GM

E

E

Earth

Earth

rest

gravEarthε 6

210−≅==

cR

GM

E

E

Sun

Sun

rest

gravSunε

WeakWeak in which sensein which sense??

In term of the compactness parameter In term of the compactness parameter εε

All the Solar System tests fall in this category… since the All the Solar System tests fall in this category… since the experiment about the light deflection by Sun experiment about the light deflection by Sun [Eddington 1919]

and the observation of the Mercury advance of perihelionand the observation of the Mercury advance of perihelion

So far, So far, GR GR has passed all these tests has passed all these tests with with full marks and cum laudefull marks and cum laude

Going beyond Kepler…Going beyond Kepler…But But is GR still the bestis GR still the best available theory for describing Nature available theory for describing Nature

also under also under extremeextreme physical conditionsphysical conditions? ?

This is NOT an ACADEMIC question:This is NOT an ACADEMIC question:

e.g. e.g. extreme conditionsextreme conditions are certainly those at which any long are certainly those at which any long sought sought unified modelunified model for interactions appliesfor interactions applies [ e.g. Antoniadis 2005 ]

There exist alternative metric gravity theories (e.g. a subclassThere exist alternative metric gravity theories (e.g. a subclassamong the tensoramong the tensor--scalar theories) which would pass ALL Solar scalar theories) which would pass ALL Solar System (weakSystem (weak--field limit) tests, but would be violated as soon as field limit) tests, but would be violated as soon as

extreme conditions (strongextreme conditions (strong--field limit) are reached field limit) are reached [Damour & Esposito-Farese 1996]

Moreover, is enough to Moreover, is enough to test alternative theories only test alternative theories only in thein theweakweak--field limitfield limit? ?


Not on Earth or on Solar System…Not on Earth or on Solar System…but in the Cosmo...very interesting targets are but in the Cosmo...very interesting targets are

“relativistic objects in compact binaries”“relativistic objects in compact binaries”

Where Where to find a laboratory for testing GR in to find a laboratory for testing GR in extreme conditionsextreme conditions??

““compact” binariescompact” binariesGravitational radiation inspiral affects binary evolution within an Hubble time

NSs and BHs are NSs and BHs are “relativistic” objects“relativistic” objects

0.2εNS ≅==2cR

GM

E

E

NS

NS

rest

grav 0.5εBH ≅==2cR

GM

E

E

BH

BH

rest

grav

Tests of gravity in the strongTests of gravity in the strong--field limitfield limitStrongStrong in which sensein which sense??

In term of the compactness parameter In term of the compactness parameter εε the source should satisfythe source should satisfy

11.02

−≅==cR

GM

E

E

source

source

rest

gravsourceε


Astrophysical contextsAstrophysical contexts::•• during late stages of coalescence of a binary hosting relativistduring late stages of coalescence of a binary hosting relativistic ic object(s), the orbital velocity approaches object(s), the orbital velocity approaches cc and the orbital separation and the orbital separation approaches the size of the star(s), whence physical processes ocapproaches the size of the star(s), whence physical processes occur in cur in strongstrong-- field conditions:field conditions: wonderful targets for LIGO, VIRGO and, in wonderful targets for LIGO, VIRGO and, in future, LISAfuture, LISA

•• emission processes occurring in relativistic objects close to themission processes occurring in relativistic objects close to the event e event horizon: e.g. spectral and timing features in the electromagnetihorizon: e.g. spectral and timing features in the electromagnetic c emission (often Xemission (often X-- ray) from the neighbourhood of the last stable orbit ray) from the neighbourhood of the last stable orbit of accretion disks surrounding NS or BH hosted in a binary systeof accretion disks surrounding NS or BH hosted in a binary system: m: some hints from XMMsome hints from XMM-- Newton and RossiNewton and Rossi-- XTE but XTE but targets for future targets for future high energy (most Xhigh energy (most X-- ray) observatories: XEUSray) observatories: XEUS… …

•• compact relativistic binary pulsars: compact relativistic binary pulsars: targets for targets for currentcurrent TIMING TIMING observations in the RADIO bandobservations in the RADIO band

Tests of gravity in the strongTests of gravity in the strong--field limitfield limit


Tests of gravity in the strongTests of gravity in the strong--field limitfield limitWait a minute! Wait a minute! Orbits of known binary pulsars are never Orbits of known binary pulsars are never

entering the strongentering the strong--field limit...field limit...

But in most alternative theories of gravity (e.g. in the tensorBut in most alternative theories of gravity (e.g. in the tensor--scalar ones) the scalar ones) the orbital motion and the gravitational radiation orbital motion and the gravitational radiation damping depend on the gravitational binding energydamping depend on the gravitational binding energy (i.e. self (i.e. self

gravity, e.g. gravity, e.g. εεNSNS≈≈0.2, 0.2, εεBHBH≈≈0.5) of the involved bodies 0.5) of the involved bodies [e.g. Esposito-Farese 2005, Will 2006]

352

1010 −−

−

−− −≅==

ca

GM

E

E

psrbin

psrbin

rest

gravpsrbinε 35 1010 −−− −≅

c

V psrbin

If enough accuracy in the measurements is provided, If enough accuracy in the measurements is provided, significant significant effectseffects are expected to be detectable even are expected to be detectable even in the weakin the weak--field limit field limit

for the orbitsfor the orbits


Tests of gravity in the strongTests of gravity in the strong--field limitfield limit

A suitable and successful framework for testing and constrainingA suitable and successful framework for testing and constraininga very large class of gravity theories is that of the a very large class of gravity theories is that of the PostPost--Keplerian Keplerian

(PK) formalism(PK) formalism [Damour & Deruelle 1986]

22ndnd →→ In ANY specific gravity theory (picked in a large range of In ANY specific gravity theory (picked in a large range of metric theories), and for negligible spin contributions, the metric theories), and for negligible spin contributions, the PK PK

parametersparameters can be written only as a can be written only as a function of the masses of the function of the masses of the two stars and of the keplerian parameterstwo stars and of the keplerian parameters of the binary system of the binary system

[Damour & Deruelle 1986]

11stst →→ PK parameters are operationally definedPK parameters are operationally defined: :

i.e. they are phenomenological quantities, which there is a i.e. they are phenomenological quantities, which there is a prescription to measure forprescription to measure for

The easiest to observe post-keplerian parameters

Timing model:post-keplerian paramsTiming model:postTiming model:post--keplerian paramskeplerian params

ω : Periastron precessionγ : Time dilation and gravitational redshiftr : Shapiro delay “range”s : Shapiro delay “shape” Pb : Orbit decay due to Gravitational Wave emission

periastronperiastron precessionprecession

Pulsar Timing: relativistic pulsarsPulsar Timing: relativistic pulsars

orbital decayorbital decay


gravitational redshift and time dilationgravitational redshift and time dilation


Shapiro delayShapiro delay


What do we learn What do we learn when observing also thewhen observing also thePostPost--kepleriankeplerian parameters ?parameters ?

PeriastronPeriastron precessionprecession

Time Time dilationdilation & & gravitationalgravitational redshiftredshift

ShapiroShapiro delaydelay ((amplitudeamplitude))

ShapiroShapiro delaydelay ((shapeshape))

OrbitalOrbital periodperiod decaydecay

……where…where…

• e e orbitalorbital eccentricityeccentricity

•• PPbb orbitalorbital periodperiod

•• x x projected semimajor axisprojected semimajor axis

•• mmpp pulsar masspulsar mass

•• mmcc companioncompanion star massstar mass

•• MM == mmpp + + mmcc total system total system lagrangianlagrangian massmass

ObservingObserving the the valuesvalues of of onlyonly 2 2 PK PK parametersparameters

One can One can measuremeasure the pulsar and the pulsar and companion star companion star massesmasses withwithunrivalledunrivalled precisionprecision

Once more Once more thanthan 2 2 relativisticrelativistic PK PK parametersparametersare known, one derives the masses ofare known, one derives the masses ofthe 2 bodies and hence predicts the further the 2 bodies and hence predicts the further PK par on the basis of a given Gravity PK par on the basis of a given Gravity TheoryTheory

A test A test forfor GravityGravity TheoriesTheories

ω&

The pulsar and companion star masses are The pulsar and companion star masses are unconstrainedunconstrained

Mass Function Mass Function constraintconstraint

NOT ALLOWED

( ) ( )( )2

3

2

32 sinsin4),(

cp

c

orb

pcp

mm

im

P

ia

Gmmf

+=π=

sin sin i = 1i = 1

One PKOne PK--parameter: constraining massparameter: constraining mass

γ

Two PK parameters: mass determined Two PK parameters: mass determined withinwithin a theorya theory

Three PK parameters: in Three PK parameters: in correct theory lines meetcorrect theory lines meet !!

γ

But But not in a wrongnot in a wrong theory !!!theory !!!

γ

Now theNow the catalogcatalog contains contains 8/98/9Double Neutron Star BinariesDouble Neutron Star Binaries

J0737-3039 22.70 48.91 0.10 1.42 1.34+1.25 0.09 210 0.85J1518+4904 40.93 11.62 8.63 20.04 2.72 0.25 200 >T Hubble B1534+12 37.90 11.62 0.42 3.72 1.33+1.33 0.27 2.5 27.0J1756-2251 28.45 121.60 0.32 2.75 2.57 0.18 tbd 11.0 J1811-1736 104.18 477.00 18.78 34.78 2.57 0.82 970 >T HubbleJ1829+2456 41.00 13.90 1.18 7.24 >1.22 <1.38 0.14 tbd >T HubbleB1913+16 59.03 168.77 0.32 2.34 1.387+1.441 0.62 1.1 3.0J1906+0746 144.10 217.78 0.17 1.42 1.25+1.37 0.08 0.001 3.0 NS+WD?B2127+11C 30.53 67.13 0.34 2.52 1.36+1.34 0.68 1.0 2.2

PULSAR Pspin DM Porb ap sin(i) Mc+Mp ecc TimeSpDwn TimeMerg[ms] [cm-3 pc] [day] [lt-s] [ Msun ] [108 yr] [108 yr]

Now theNow the catalogcatalog contains contains 8/98/9Double Neutron Star BinariesDouble Neutron Star Binaries

J0737-3039 22.70 48.91 0.10 1.42 1.34+1.25 0.09 210 0.85J1518+4904 40.93 11.62 8.63 20.04 2.72 0.25 200 >T Hubble B1534+12 37.90 11.62 0.42 3.72 1.33+1.33 0.27 2.5 27.0J1756-2251 28.45 121.60 0.32 2.75 2.57 0.18 tbd 11.0 J1811-1736 104.18 477.00 18.78 34.78 2.57 0.82 970 >T HubbleJ1829+2456 41.00 13.90 1.18 7.24 >1.22 <1.38 0.14 tbd >T HubbleB1913+16 59.03 168.77 0.32 2.34 1.387+1.441 0.62 1.1 3.0J1906+0746 144.10 217.78 0.17 1.42 1.25+1.37 0.08 0.001 3.0 NS+WD?B2127+11C 30.53 67.13 0.34 2.52 1.36+1.34 0.68 1.0 2.2

PULSAR Pspin DM Porb ap sin(i) Mc+Mp ecc TimeSpDwn TimeMerg[ms] [cm-3 pc] [day] [lt-s] [ Msun ] [108 yr] [108 yr]

The most interestingThe most interestingfor GR tests are for GR tests are

Pulsar Pulsar + Neutron+ Neutron StarStarSpin period = 59 msSpin period = 59 msOrbital period = 7.8 hrsOrbital period = 7.8 hrsEccentricity = 0.61Eccentricity = 0.61

PSR B1913+16PSR B1913+16Discovered on 1974 Discovered on 1974 [ Hulse & Taylor 75]

Measured 3 PK pars: Measured 3 PK pars: ωω γγ PPbb····

Most precise NS mass determination to date:Most precise NS mass determination to date:1.4414(2) M1.4414(2) Msunsun + 1.3867(2) M+ 1.3867(2) Msun sun [ Weisberg & Taylor 2004]

[ W

eisb

erg

2007

]

The (in?)direct proof The (in?)direct proof of GW existence:of GW existence:PSRPSR B1913+16B1913+16

GR provides an accurate GR provides an accurate description of the system as description of the system as orbiting POINT MASSES: orbiting POINT MASSES: i.e. NS structure does not i.e. NS structure does not

affect orbital motionaffect orbital motion

NOBEL PRIZENOBEL PRIZE19931993

TaylorTaylor & & HulseHulse

The measurementsThe measurements of Russell Hulseof Russell Hulseandand of Joe Taylorof Joe Taylor……The prediction of theThe prediction of theEinstein’s equationsEinstein’s equations……

Pulsar Pulsar + Neutron+ Neutron StarStarSpin period = 38 msSpin period = 38 msOrbital period = 10 hrsOrbital period = 10 hrsEccentricity = 0.27Eccentricity = 0.27

PSR PSR B1534+12B1534+12Discovered on 1990 Discovered on 1990 [ Wolszczan 90]

Measured 5 PK pars: Measured 5 PK pars: ωω γγ PPb b s rs r····

NonNon--radiative predictions of GR tested at radiative predictions of GR tested at better than better than ~~1%1% levellevel [ Stairs 2002]

PSR PSR B1534+12B1534+12

Three terms:Three terms:--vertical acc in Galactic potentialvertical acc in Galactic potential--acc in the plane of the Galaxyacc in the plane of the Galaxy--apparent acc due to tranverse apparent acc due to tranverse motion motion [ Shklovskii 1970 ]

Affected by relative Affected by relative acceleration of CoM of binary acceleration of CoM of binary pulsar system wrt Solar System pulsar system wrt Solar System barycenter barycenter [ Damour & Taylor 1991]

This also limits radiative GR tests This also limits radiative GR tests for for B1913+16B1913+16 at current at current 0.2%0.2% level level [ Weisberg & Taylor 2004 ]

PPbb does not match!does not match![ Stairs 2002]

··

22.7 ms22.7 ms

1.7 x 101.7 x 10--1818

210 210 MyrMyr

6 x 106 x 1099 GG

1,080 km1,080 km

5 x 105 x 1033 GG

6 x 106 x 103333 erg serg s--11

301 km s301 km s--11

PSR J0737PSR J0737--3039A3039A

2.77 s2.77 s

0.88 x 100.88 x 10--1515

50 50 MyrMyr

1.6 x 101.6 x 101212 GG

1.32 x 101.32 x 1055 kmkm

0.7 G0.7 G

1.6 x 101.6 x 103030 erg serg s--11

323 km s323 km s--11

PSR J0737PSR J0737--3039B3039BBasic Parameters and evolutionBasic Parameters and evolution

P

P

Spindown age

Bsurf

RLC

BLC

Erotational

Mean orb vel

.

.

[ Burgay et al 2003; Lyne et al 2004 ]

Pulsar Pulsar + Pulsar+ PulsarSpin period = 22.7 ms + 2.77 sSpin period = 22.7 ms + 2.77 sOrbital period = 2.5 hrsOrbital period = 2.5 hrsEccentricity = 0.09Eccentricity = 0.09

PSR PSR J0737J0737--3039A/B 3039A/B (orb params)(orb params)

Discovered on 2003 Discovered on 2003 [ Burgay et al 2003, Lyne et al 2004 ]

Measured 5 PK pars: Measured 5 PK pars: ωω γγ PPb b s rs r····+ Mass Ratio + Mass Ratio RR

MassMass--mass diagram for J0737mass diagram for J0737--3039A&B3039A&B

at J

an 2

004

at J

an 2

004

Mass function A


at J

an 2

004

at J

an 2

004

Mass function B


at J

an 2

004

at J

an 2

004

Mass ratio


at J

an 2

004

at J

an 2

004

)( 4−+=≡ cOm

m

x

xR

B

A

A

B

The nature of the mass ratio constraintThe nature of the mass ratio constraint

e.ge.g all all LangragianLangragian--based based theories theories includingincluding multimulti--scalar tensor scalar tensor theories (Damourtheories (Damour & Taylor 1992)& Taylor 1992)

→→ ForFor ANYANY “fully Conservative”“fully Conservative” theories (Will 1992)theories (Will 1992)

→→ RatioRatio isis independent of strong (selfindependent of strong (self--)field effects!)field effects!

Qualitatively differentQualitatively different to other PK parameters, which to other PK parameters, which

allall depend on depend on “constants“constants” like G” like GABAB , which, which differs differs fromfromGGNewtonNewton depending on strongdepending on strong--field field effectseffects in theory! in theory!

Periastronadvance


at J

an 2

004

at J

an 2

004

Grav. Redshift+ 2nd order Doppler


at J

an 2

004

at J

an 2

004

Shapiro delay in Shapiro delay in PSR J0737PSR J0737--3029A3029A arrival timesarrival times

( )

= −

+∆ ψφ

sinsin1cos1

lni

ecRt g

Shap

s = sin

i

Lyn

e et

al 2

004

Shapiro s


at J

an 2

004

at J

an 2

004

What is the orientation of the orbit of What is the orientation of the orbit of the system?the system?

From determination of the “shape” s of the From determination of the “shape” s of the Shapiro delay s=0.99974(Shapiro delay s=0.99974(--39,+16)39,+16)

it results it results i = 88.7i = 88.7((--0.8+0.5) 0.8+0.5) degdeg

~1°

[ © Possenti – adapted from Lyne et al 2004 ]


Shapiro rat J

an 2

004

at J

an 2

004

The unique capability of J0737-3039 system for General Relativity tests

The unique capability of J0737The unique capability of J0737--3039 system for 3039 system for General Relativity testsGeneral Relativity tests

at June 2007at June 2007

©K

ram

er

MB=1.249(1)M

MA=1.338(1)M

Observed shape of Shapiro delay in

agreement with GR at 0.05% level

4 independent tests of GR!

•• Precision of 5x10Precision of 5x10--44 best in best in strongstrong--fieldfield•• Expect to supersede solar system testsExpect to supersede solar system tests

SummarySummary of the testsof the tests of GRof GR

Expected in GR:Expected in GR: Observed:Observed:

γγ = 0.38418= 0.38418(22)(22) msms 0.38560.3856(26)(26) msms

dPdPbb/dt/dt==--1.247871.24787(17)(17) 1010--1212 --1.2521.252(17(17)) 1010--1212

rr =6.153=6.153(26)(26) µµss 6.26.211(33)(33) µµss

ss=0.99987=0.99987((--48.+13)48.+13) 0.99970.999744((--39,+16)39,+16)

Based on: Based on: R = 1.0714R = 1.0714±±0.0011 &0.0011 & ώώ=16.89947=16.89947±±0.00068 deg/yr0.00068 deg/yr

0005.00000.1obs

exp

±=s

s

[ Kramer et al 2006 ]

1.00361.0036(68)(68)

1.0031.003(14)(14)

1.0091.009(55)(55)

0.999870.99987(50)(50)

Ratio:Ratio:

What about galactic potential and kinematic corrections?What about galactic potential and kinematic corrections?

Radiative GR tests for J0737Radiative GR tests for J0737--3039 system may 3039 system may reach 0.01% level in a decade reach 0.01% level in a decade [ Deller et al 2009 ]

From recent interferometric determination From recent interferometric determination of the distance of the system: of the distance of the system: [ Deller et al 2009 ]

Current radiative GR tests for Current radiative GR tests for J0737J0737--30393039 system system are at are at ~~1%1% level level [ Kramer et al 2006 ]

TimeTime--scale of timing accuracy improvements scale of timing accuracy improvements

Prospects for timing are Prospects for timing are excellent:excellent:

•• precision precision ωω ≈≈ timetime 1.5 1.5 PPb b

•• precision precision γγ ≈≈ time time 1.5 1.5 PPb b 1.31.3

•• precision precision dPdPbb/dt /dt ≈≈ timetime 2.5 2.5 PPbb33

•• precision precision r , s r , s ≈≈ timetime 0.5 0.5

CaveatsCaveats::

•• Timing noise of BTiming noise of B

•• Geodetic precession Geodetic precession may leadmay lead to changingto changing profilesprofiles

•• Galactic & kinematics contributions to secular Galactic & kinematics contributions to secular changing of Pchanging of Pbb

The case of the GeodeticThe case of the Geodetic PrecessionPrecession

[ ©

Kra

mer

]

The GeoPrecession rate is given by:

a nice reproduction of the eclipse of the radio a nice reproduction of the eclipse of the radio signal of A was obtained signal of A was obtained

[Bre

ton

et a

l 20

08]

Assuming synchrotron absorpion in the Assuming synchrotron absorpion in the closed magnetosphere of pulsar B… closed magnetosphere of pulsar B…

[ Lyutikov & Thompson 2005 ]

From the data of 63 eclipses observed at GBT:From the data of 63 eclipses observed at GBT:InclinationInclination of spin axis of pulsarof spin axis of pulsar B B wrtwrt orbit normal orbit normal

ΘΘ ≈≈ 130.0130.0o o ±± 0.50.5°° (1 (1 σσ))Angle Angle betweenbetween magnetic and spin magnetic and spin axesaxes of of pulsar Bpulsar B

αα ≈≈ 70.970.9o o ±± 0.50.5°° (1 (1 σσ))[Breton et al 2008]

The best-fit geometric parameters were jointly searched for the 63 eclipses observed at GBT, keeping all the geometry constant, but allowing the longitude of the spin axis longitude of the spin axis ФФ to vary to vary

[Breton et al 2008]

The modeling of the precession effect The modeling of the precession effect

[Breton et al 2008]

The best fit parameters The best fit parameters

GR predicts a geodetic precession rate = GR predicts a geodetic precession rate = 5.07345.0734±0.0007±0.0007 deg/yrdeg/yr

It is observed a geodetic precession rate = It is observed a geodetic precession rate = 4.774.77±0.66±0.66 deg/yrdeg/yr

Agreement at Agreement at 13 % level13 % level ( at 1( at 1σσ ))

Confermed GR “effacement” property of gravity also for Confermed GR “effacement” property of gravity also for SPINNING bodies: i.e. NS structure does not prevent it SPINNING bodies: i.e. NS structure does not prevent it

to behave like a spinning test particle in an external field to behave like a spinning test particle in an external field

Constraint on spinConstraint on spin--orbit coupling orbit coupling In ANY “fully conservative” In ANY “fully conservative”

theory theory

σB = spin-orbit coupling constant

= generalized grav constant

For the special case of the double pulsar only, we can measure For the special case of the double pulsar only, we can measure

……and compare with the GR prediction and compare with the GR prediction

……getting… getting…

[ B

reto

n et

al 2

008

]

The very last massThe very last mass--massmass diagram for diagram for J0737J0737--3039A/B3039A/B

jul 2008jul 2008

[Bre

ton

et a

l 20

08]

5 independent tests of GR!MB=1.249(1)M

MA=1.338(1)M

%05.0exp

obs

≈s

s

[ ]BS

BS

AS

AS

T

tot ggfe

k ββββββ00

200

20 1

1

3 −−+−

=

1PN1PN 2PN2PN Spin ASpin A Spin BSpin B

Neutron star dependentNeutron star dependent

2

12

m

I

PG

cS

πβ =

EquationEquation--ofof--StateStatefor the nuclear matter!!for the nuclear matter!!

Total Total periastronperiastron advance to 2PN level:advance to 2PN level: [ Damour & Schaefer 1988 ]

[ Lattimer & Schutz 2004 ][ Morrison et al. 2004]

A 10% accuracy on IA 10% accuracy on Iwould exclude most would exclude most EoSEoS

What might be feasible to measure:Moment of Inertia of J0737-3039AWhat What might be feasiblemight be feasible toto measure:measure:Moment of Inertia of J0737Moment of Inertia of J0737--3039A3039A

Constraining alternate Constraining alternate Theories of Gravity: TensorTheories of Gravity: Tensor--ScalarScalar

[ E

spos

ito-

Far

ese

2004

]

General RelativityGeneral Relativity

Limits from Limits from J0737J0737--3039 on3039 on

tensortensor--scalar theoriesscalar theories

( ) 200 2

1 ϕβϕαϕ +=a

metricg =µν

( )ϕa00 , βα

ϕ scalar field

coupling field-matter

coupling parameters

Binary pulsars impose Binary pulsars impose ββ00 > > -- 4.5 4.5

due to the due to the ““spontaneous spontaneous scalarizationscalarization”” effect in NSseffect in NSs

Pulsar Pulsar + Massive WD+ Massive WDSpin period = 394 msSpin period = 394 msOrbital period = 4.7 hrsOrbital period = 4.7 hrsEccentricity = 0.17Eccentricity = 0.17

PSR PSR J1141J1141--65456545Discovered on 2000 Discovered on 2000 [ Kaspi et al 2000]

Measured 3 PK pars: Measured 3 PK pars: ωω γγ PPb b ····

Radiative predictions of GR tested at Radiative predictions of GR tested at better than better than ~~6%6% levellevel [ Bhat et al 2008]

The case of PSR J1141The case of PSR J1141--65416541Masses of the two components are similarMasses of the two components are similar

MMNSNS = ( 1.27 = ( 1.27 ±± 0.01 ) M0.01 ) Msunsun

MMWDWD = ( 1.02 = ( 1.02 ±± 0.01 ) M0.01 ) Msunsun……but the radii are certainly very different, leading to a signifbut the radii are certainly very different, leading to a significant icant

difference in the degree of compactness difference in the degree of compactness εε(i.e. in the (i.e. in the selfself--gravity gravity ) of the two bodies: ) of the two bodies:

2.02

≅==cR

GM

E

E

NS

NS

rest

gravNSε 4

210−≅==

cR

GM

E

E

WD

WD

rest

gravWDε

TensorTensor--scalar scalar theories predicts the emission of a theories predicts the emission of a large large amount of DIPOLAR scalar wavesamount of DIPOLAR scalar waves (as opposed to the (as opposed to the

dominant QUADRUPOLAR radiation predicted by GR) dominant QUADRUPOLAR radiation predicted by GR) inin such a such a very asymmetric systemvery asymmetric system

( ) 200 2

1 ϕβϕαϕ +=a

metricg =µν

( )ϕa00 , βα

ϕ scalar field

coupling field-matter

coupling parameters

The case of PSR J1141The case of PSR J1141--65416541This is the best available binary This is the best available binary

pulsar for constrainingpulsar for constrainingthe coupling constant the coupling constant αα0 0

[Esposito-Farese 2005]

For For ββ0 0 = 0 (i.e. Brans= 0 (i.e. Brans--Dicke) it holds Dicke) it holds αα0,B0,B--D D ~ (~ (αα0,∞ 0,∞ )/(2)/(2εεNSNS))Whence theWhence the limits limits are: are: [Bhat et al 2008]

αα 220,∞ 0,∞ < 3.4 10< 3.4 10--6 6 ≈≈ ⅓⅓ Cassini limitCassini limit

αα 220,B0,B--D D < 2.1 10< 2.1 10--5 5 ≈ ≈ 22 Cassini limitCassini limit

For For ββ0 0 →→ ∞∞ it holds it holds αα0,0,∞∞ ~ ( ~ ( δδrel rel PPb b ))½½··

In 2012 In 2012 δδrel rel PPbb ≈≈ 2% at which galactic 2% at which galactic & kin corrections become dominant, & kin corrections become dominant,

but likely a 1% determination will be but likely a 1% determination will be achievable achievable

··

……some other tests on fundamental some other tests on fundamental physics with binary pulsarsphysics with binary pulsars

PSR J0437-4715Time derivative of GTime derivative of G [dG/dt]/G = ([dG/dt]/G = (--55±±18) 18) ·· 1010--1212 yryr--1 1

(about 10 times weaker than lunar ranging (about 10 times weaker than lunar ranging but much simpler and in strongbut much simpler and in strong--field) field) [ Damour & Taylor 1991, Verbiest et al 2008 ]

21 highly circular WD-MSPStrong Equivalence PrincipleStrong Equivalence Principle | | ∆∆ || = 5.6= 5.6 ·· 1010--33 (weaker than solar (weaker than solar

system tests, but in strongsystem tests, but in strong--field regime)field regime)[ Wex 1997, Stairs et al 2005 ]

21 highly circular WD-MSPMomentum conservation Momentum conservation | | αα33 || = 4.0= 4.0 ·· 1010--20 20 (10(101313 better than better than

Earth or Mercury perhelion shifts)Earth or Mercury perhelion shifts)[ Bell & Damour 1996, Stairs et al 2005 ]

^

PSR J1012+5307Existence of preferred frame Existence of preferred frame | | αα11 || = 1.4= 1.4 ·· 1010--44 (slighlty weaker than (slighlty weaker than

lunar laser ranging, but in stronglunar laser ranging, but in strong--field regime)field regime)[ Wex 2000 ]

^

andrea possenti - ego-gw.it · andrea possenti inaf – osservatorio astronomico di cagliari vesf...

Documents