The role of pulsars - EGO - European Gravitational Observatory

The role of pulsars’ The role of pulsars’ timing in GW timing in GW

detectiondetection

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

VESF SCHOOL on VESF SCHOOL on GRAVITATIONAL WAVESGRAVITATIONAL WAVES

V EditionV Edition2626--30 Jul 2010, SCfA 30 Jul 2010, SCfA –– Sesto Pusteria (Italy)Sesto Pusteria (Italy)

26 JULY 201026 JULY 2010

OutlineOutline1.1. Pulsar generalitiesPulsar generalities

2.2. Double neutron star merger rateDouble neutron star merger rate

3.3. Pulsar Timing conceptsPulsar Timing concepts

4. Gravitational Waves emission 4. Gravitational Waves emission constraints from binary pulsarsconstraints from binary pulsars

5. Gravitational Waves detection using pulsar 5. Gravitational Waves detection using pulsar timing arrays: the idea and the sensitivity timing arrays: the idea and the sensitivity

6. Gravitational Waves detection using pulsar 6. Gravitational Waves detection using pulsar timing arrays: ongoing experimentstiming arrays: ongoing experiments

•• 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 Relativitywith 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


V EditionV Edition2626--30 Jul 2010 30 Jul 2010 –– SCfA SCfA –– Sesto Pusteria (Italy)Sesto Pusteria (Italy)

1.1.Pulsar GeneralitiesPulsar Generalities

ELECTROMAGNETIC OBSERVATIONS OF ELECTROMAGNETIC OBSERVATIONS OF PULSARS AND BINARIESPULSARS AND BINARIES


V EditionV Edition2626--30 July 2010 30 July 2010 –– SCfA SCfA –– Sesto Pusteria (Italy)Sesto Pusteria (Italy)

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

magnetizedmagnetizedneutronneutron starstar, , emittingemitting a a pulsedpulsedradio radio signalsignal as aas aconsequence of consequence of aa lightlight --house effecthouse effect

@K

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er

The rotating magnetized NS in vacuumThe rotating magnetized NS in vacuumThe rotating magnetized NS in vacuum

Assuming that the rotational energy lossAssuming that the rotational energy loss

LL sdsd = 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):

LL dipole dipole = [ 2/3c= [ 2/3c33] | ] | µµ | | 22one 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 parameters: age & magnetic fieldDerived 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. Valueat at polepole is 2B2B00

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

(from Manchester & Taylor)

·· ·

Radio pulsar basic parametersRadio pulsar basic parametersRadio pulsar basic parameters

Radio pulsars are powered byRadio pulsars are powered byrotational energyrotational energy

SpinSpin--down age:down age:

SpinSpin--down power:down power:

Surface magnetic field: Surface magnetic field:

P P ……and allows one to place a pulsar on the basic and allows one to place a pulsar on the basic PP vs vs [ or[ or P vs BP vs Bsurfsurf ] diagram…] diagram…

LLsdsd = 3.9 · 10= 3.9 · 103131 PP--3 3 PP--1515 erg/serg/s

BBsurfsurf = 1.0 · 10= 1.0 · 101212 [ P P[ P P--1515 ]]½½ GaussGauss

ττc c = 1.6 · 10= 1.6 · 1077 P / PP / P--1515 yryr

The observation of the spin periodThe observation of the spin periodPP and of its derivativeand of its derivativeallows one to give an estimate of various physical quantities:allows one to give an estimate of various physical quantities:

P P

The Bs vs P diagram

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

Pulsar EnergeticsPulsar Pulsar EnergeticsEnergetics

SpinSpin--down Luminosity: down Luminosity:


Radio Luminosity:Radio Luminosity:


1028

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

pulsars ?pulsars ?

A dichotomy in the

population

A dichotomy A dichotomy in the in the

populationpopulation


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

Discovery of the first millisecond pulsar B1937+21 (1982)

DiscoveryDiscovery of the of the first millisecondfirst millisecond pulsar pulsar B1937+21 (1982)B1937+21 (1982) [Backer et al. 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: f bin> 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: f binbin> 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 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[Bisnovati--Kogan & Kronberg 1974, Alpar et al. 1982]Kogan & Kronberg 1974, Alpar et al. 1982]

The MSP formation paradigm 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

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A newly born fast spinning pulsar

1000 yr

Hubble time

deat

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

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

Until 1997: ~ 750~ 750

Now in the Atnf Catalog: ~ ~ 18801880

~~ 2020 Extragalactic (LMC/SMC)

~~ 150150 Binary (140140somehow recycled)

~~ 8080 Young (age<10000 yr)

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

33 Radio emitting “magnetars”

99 Double Neutron star binaries

11 Double pulsar

140140in 2626 Globular Clusters

++ Rrats, Intermittent PSRs, …

TOTALTOTAL known sampleknown sample

GC search > 70

Drift scan search > 30

GBTGBT discoveriesdiscoveries

Parkes PM = 725

Parkes SWI+SWII = 69+25

Parkes PH = 18

Parkes PA > 10

Parkes HTRU > 40

Total using multibeam >887Parkes GC search > 34

ParkesParkesdiscoveriesdiscoveries

Galactic Plane search > 50

AreciboArecibo discoveriesdiscoveries

2.2.Double neutron star Double neutron star

merger ratemerger rate




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 =

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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

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

[ Chunglee Kim 2008 ][ 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 ][ 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 ][ 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 ][ Kalogera 2004 ]

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

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

3.3.Pulsar Timing Pulsar Timing

ConceptsConcepts




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

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

++searching the ToAs for systematic trendssearching the ToAs for systematic trendson many different on many different

timescales, from minutes to decadestimescales, from minutes to decades

Timing of a radio pulsar: operations for getting a ToA

Timing Timing of a radio pulsar: operations of a radio pulsar: operations for getting a ToA for getting a ToA

@ Lorimer

The dedispersionTheThe dedispersiondedispersion

Single pulse profilevs

integrated profile

Single pulse profileSingle pulse profilevsvs

integrated profileintegrated profile

Determination of the TOPOCENTRIC Times of Arrival (ToAs)

Determination of the TOPOCENTRIC Determination of the TOPOCENTRIC TimesTimes of Arrival (ToAs)of Arrival (ToAs)

ToA uncertainty (ToA uncertainty (ωω = width of the pulse, P=pulsar period)= width of the pulse, P=pulsar period)::

Timing idea: modelingTiming idea: modelingTiming idea: modelingif a physical model adequately describes the systematic trends iif a physical model adequately describes the systematic trends in n the ToAs, it is applied with the smallest number of parametersthe ToAs, it is applied with the smallest number of parameters

when a model finally describes accurately the observed ToAs, when a model finally describes accurately the observed ToAs, the values of the 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 of the pulsar and/or of its environment

otherwiseotherwise

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

another model another model

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 scaleis (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 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 key quantity: the residualsTiming key quantity: the residualsTiming key quantity: the residualsGiven the full set of parameters (aGiven the full set of parameters (a11, a, a22, …, a, …, ann) of a model, the i) of a model, the i--th th residual rresidual rii is the difference in rotational phase is the difference in rotational phase ΦΦ (with (with --0.5<r0.5<rii<+0.5)<+0.5)

between the observed phase of arrival of the ibetween the observed phase of arrival of the i--th pulse and the th pulse and the phase of arrival of that pulse as predicted by the modelphase of arrival of that pulse as predicted by the model

rr ii = = ΦΦobserved observed ((ii --th pulseth pulse) ) –– ΦΦmodel(amodel(a11, a, a22, , ……, a, ann))((ii --th pulseth pulse))

In an iterative procedure, In an iterative procedure, one leastone least--square fitssquare fits on suitable on suitable subsets of the possible parameters (asubsets of the possible parameters (a11, a, a22, …, a, …, ann) of the model, ) of the model, in the aimin the aim to remove apparent trends and thus eventually to remove apparent trends and thus eventually toto

approach rapproach rii << 1<< 1

Thanks to the leastThanks to the least--square fit procedure, one square fit procedure, one can iterativelly solve for can iterativelly solve for

rotationalrotational ,, positional positional andand kinematickinematic

parameters, as well as parameters, as well as for other parameters, for other parameters,

when applicable when applicable

Timing analysis: removing trendsTiming analysis: removing trendsTiming analysis: removing trends

Good timing solution Good timing solution →→ no evident trend and rno evident trend and ri i << 1 for all observed pulses << 1 for all observed pulses

Timing analysis quality: rmsTiming analysis quality: rmsTiming analysis quality: rms

The quality of the timing solution is usually given in term The quality of the timing solution is usually given in term

of the root mean square of the root mean square rmsrms of the residuals:of the residuals:

the smaller rms is, the smaller physical effects the smaller rms is, the smaller physical effects can be measuredcan be measured

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 SystemBarycenterBarycenter (PSB)

Correcting ToAs to the binary barycenter 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…

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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 they are (well) enough to satisfactorily describe all and they are (well) enough to satisfactorily describe all

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

PulsarPulsar periods periods cancan sometimes besometimes bemeasured measured with unrivalled with unrivalled precisionprecision

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

16 significant digits!

5.757451831072007± 0.000000000000008 ms

Millisecond pulsars (MSPs) as clocks

Millisecond pulsars (MSPs) Millisecond pulsars (MSPs) as clocks as clocks

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 pu lsars undergo timing irregularitiThe majority of the ordinary pu lsars undergo timing irregulariti eses

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Young pulsar

Line

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Recycled Recycled pulsars: pulsars: ~ 140~ 140known objects; known objects;

NSNSageage > 10> 1088--101099 yryr

The most rapidly rotating The most rapidly rotating are known as are known as millisecond millisecond

pulsarspulsars

High precision pulsar timing: which targets?High precision pulsar timing: which targets?High precision pulsar timing: which targets?OrdinaryOrdinary pulsars: pulsars:

~ 1650~ 1650known objects; known objects; NSNSageage< few 10< few 1077 yryr

relatively long pulses relatively long pulses & &

rotational irregularitiesrotational irregularities

NOT SUITABLE FOR NOT SUITABLE FOR HIGH PRECISION HIGH PRECISION

TIMINGTIMING

The role of pulsars’ The role of pulsars’ timing in GW timing in GW

detectiondetection

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


V EditionV Edition2626--30 Jul 2010, SCfA 30 Jul 2010, SCfA –– Sesto Pusteria (Italy)Sesto Pusteria (Italy)

27 JULY 201027 JULY 2010

OutlineOutline1. Pulsar generalities1. Pulsar generalities

2. Double neutron star merger rate2. Double neutron star merger rate

3. Pulsar Timing concepts3. Pulsar Timing concepts

4.4. Gravitational Waves emission Gravitational Waves emission constraints from binary pulsarsconstraints from binary pulsars

5.5. Gravitational Waves detection using pulsar Gravitational Waves detection using pulsar timing arrays: the idea and the sensitivitytiming arrays: the idea and the sensitivity

6.6. Gravitational Waves detection using pulsar Gravitational Waves detection using pulsar timing arrays: ongoing experimentstiming arrays: ongoing experiments

4. 4. Gravitational Waves Gravitational Waves emission constraints emission constraints

in Binary Pulsarsin Binary Pulsars

GW DETECTION VIA PULSARGW DETECTION VIA PULSAR



1] 1] Elliptical and planar orbitElliptical and planar orbit

2] 2] Constant Constant areolar velocity areolar velocity

3] a3] a33 = = (G/4(G/4ππ22) ) MM tottot 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…Going beyond Kepler…

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

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

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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][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


But But is GR still the bestis GR still the bestavailable theory for describing Nature available theory for describing Nature also under also under extremeextremephysical conditionsphysical conditions? ?

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

e.g. e.g. extreme conditionsextreme conditionsare 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 ][ 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[Damour & Esposito--Farese 1996]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 theories in the strongTests of Gravity theories 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: according to the according to the BH massBH mass, they are wonderful , they are wonderful targets for targets for LIGO, VIRGOLIGO, VIRGO , for the Pulsar Timing Arrays (, for the Pulsar Timing Arrays (PTAsPTAs) and, ) and, in future, in future, LISALISA

•• 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 some hints from XMMXMM-- NewtonNewton and and RossiRossi-- XTEXTE but targets for future but targets for future high energy (most Xhigh energy (most X-- ray) observatories: ray) observatories: LOFT, XEUSLOFT, XEUS… …

•• compact relativistic binary pulsars: compact relativistic binary pulsars: targets for targets for currentcurrent TIMING TIMING observations in the observations in the RADIORADIO bandband

Tests of Gravity theories in the strongTests of Gravity theories in the strong--field limitfield limit


Tests of Gravity theories in the strongTests of Gravity theories 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[e.g. Esposito--Farese 2005, Will 2006]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 effectseffectsare 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 theories in the strongTests of Gravity theories 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][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

parametersparameterscan 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 parametersof the binary system of the binary system

[Damour & Deruelle 1986][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 pulsarsPulsar Timing: relativistic pulsars

gravitational redshift and time dilationgravitational redshift and time dilation


Shapiro delayShapiro delay


orbital decayorbital decay


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

AA test 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 the catalog contains 8/9Double Neutron Star BinariesNow 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 the catalog contains 8/9Double Neutron Star BinariesNow 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 interestingfor GR tests are:

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+16PSR B1913+16Discovered on 1974 Discovered on 1974 [ Hulse & Taylor 75][ 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][ Weisberg & Taylor 2004]

[ Wei

sber

g 20

07 ]

[ Wei

sber

g 20

07 ]

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

The (in?)direct proof of The (in?)direct proof of GW existence: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 measurementsof Russell Hulseof Russell Hulseandand of Joe Taylorof Joe Taylor……The prediction of theThe prediction of theEinstein’s equationsEinstein’s equations……

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 J0737-3039A/B (orb params)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 ][ 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 R R

++ geodetic precession rate geodetic precession rate ΩΩprec prec [ Breton et al 2008][ Breton et al 2008]

The The origin of the doubleorigin of the double pulsarpulsar

© H

owe

-A

TN

F

The double pulsar PSR J0737-3039A/BThe doubleThe double pulsar PSR J0737pulsar PSR J0737--3039A/B3039A/B

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

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 s


at J

an 2

004

at J

an 2

004


Shapiro rat J

an 2

004

at J

an 2

004

The very last mass-mass diagram for J0737-3039A/B

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

jul 2008jul 2008

[Bre

ton

et a

l [B

reto

n et

al

2008

]20

08]

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

MA=1.338(1)M

%05.0exp

obs

≈s

s

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

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 ][ Deller et al 2009 ]

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

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

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 J1141-6545PSR PSR J1141J1141--65456545

Discovered on 2000 Discovered on 2000 [ Kaspi et al 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][ Bhat et al 2008]

The case of PSR J1141-6541The case of PSR J1141The case of PSR J1141--65416541

Masses of the two components are similarMasses of the two components are similarMM NSNS = ( 1.27 = ( 1.27 ±± 0.01 ) M0.01 ) Msunsun

MM WDWD = ( 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 difference inicant difference in

the degree of compactnessthe degree of compactnessεε (i.e. in the(i.e. in theselfself--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 atheories predicts the emission of alarge large amount of DIPOLAR scalar wavesamount of DIPOLAR scalar waves(as opposed to the (as opposed to the

dominant QUADRUPOLAR radiation predicted by GRdominant QUADRUPOLAR radiation predicted by GR) ) inin such asuch avery asymmetric systemvery asymmetric system

By the 2012 By the 2012 δδrel rel PPbb ≈≈ 2% at which galactic & kin 2% at which galactic & kin corrections become dominant, but likely a 1% corrections become dominant, but likely a 1%

determination will be achievable for PSR J1141determination will be achievable for PSR J1141--6541 6541

··

5. 5. Gravitational Waves detection Gravitational Waves detection

using pulsar timing arrays: using pulsar timing arrays: the idea and the sensitivitythe idea and the sensitivity




Pulsars as GW detectorsPulsars as GW detectorsPulsars as GW detectorsThe PulsarThe Pulsar--Earth path can be used as the armEarth path can be used as the armof of

a a huge cosmichuge cosmicgravitational wavegravitational wave detectordetector

PerturbationPerturbation in spacein space--timetime can becan bedetecteddetectedin in timing residuals over a timing residuals over a suitable long observation time spansuitable long observation time span

Sensitivity (rule of thumb):Sensitivity Sensitivity (rule of thumb):(rule of thumb):

T

σ(f)~h TOA

c

Radio Radio PulsarPulsar

wherehc(f) is the dimensionless strain at freq f

σTOA is the rms uncertainty in Time of Arrival

T is the duration of the dataspan

wherewhere

hhcc(f) (f) is the dimensionless strain at freq is the dimensionless strain at freq ff

σσTOA TOA is the rms uncertainty in Time of Arrival is the rms uncertainty in Time of Arrival

T T is the duration of the dataspan is the duration of the dataspan

Source Source of GWsof GWs

EarthEarth

An instructive applicationAn instructive applicationAn instructive application

[ Jen

et e

t al 2

004

][ J

enet

et a

l 200

4 ]

[ Jen

et e

t al 2

004

]

The radio galaxy 3C66 (at The radio galaxy 3C66 (at z z = 0.02) was claimed to harbour a = 0.02) was claimed to harbour a double SMBH with a total mass of 5.4 double SMBH with a total mass of 5.4 ·· 10101010 MM sunsun and an and an

orbital period of order orbital period of order ~~yr yr [ Sudou et al 2003][ Sudou et al 2003]

Timing residuals from PSR B1855+09 Timing residuals from PSR B1855+09 exclude exclude such a massive double BH such a massive double BH at 95 c.l.at 95 c.l.

The GW background from Massive BH binaries

The GW background from Massive The GW background from Massive BH binariesBH binaries

The current paradigm is that The current paradigm is that [e.g. Ferrarese & Merrit 2000][e.g. Ferrarese & Merrit 2000]

•• mergers aremergers arean an essentialessentialpart in galaxy formation and evolutionpart in galaxy formation and evolution•• nucleinuclei of most (all?) large galaxies of most (all?) large galaxies host Massive BH(s)host Massive BH(s)(MBH:(MBH:i.e. mass larger than 10i.e. mass larger than 1066 MM sunsun))

There should There should be plenty of SMBH binariesbe plenty of SMBH binariesin the early universe, in the early universe, sinking to the their galaxy center (due to dynamical friction?) sinking to the their galaxy center (due to dynamical friction?)

The The frequency of GWfrequency of GW emitted by these systems is typicallyemitted by these systems is typically

When reaching orbital separation When reaching orbital separation less than about 1 pc, GW emission less than about 1 pc, GW emission become the dominantbecome the dominantterm in energy loss, making the MBH binary term in energy loss, making the MBH binary

to shrink faster and faster to shrink faster and faster

2/32/1

9 pc01.010 nHz3

−

a

M

Mf~

sun

[ Ses

ana,

Vec

chio

et a

l 200

8][ S

esan

a,V

ecch

io e

t al 2

008]



The expected amplitude spectrum form the ensemble of these The expected amplitude spectrum form the ensemble of these MBH binaries is MBH binaries is [ e.g. Phinney 2001; Jaffe & Backer 2003][ e.g. Phinney 2001; Jaffe & Backer 2003]

with a strain amplitude with a strain amplitude theoretically expected in the range theoretically expected in the range

[ e.g. Jaffe & Backer 2003, [ e.g. Jaffe & Backer 2003, Sesana,Vecchio et al 2008]Sesana,Vecchio et al 2008]

hhcc ≈ ≈ 1010--1616 →→ 1010--1515

3/2; =− αα(f)~fhc8 nHz

100 nHz

z~1around frequencyaround frequency ffGWBGWB = 1 = 1 yryr --11

Max contribution from BH Max contribution from BH

binaries at binaries at z z ≈ ≈ 11



An alternative representation of the results/limitsAn alternative representation of the results/limits (better for (better for cosmological backgrounds) involves cosmological backgrounds) involves

32,0

2920 g/cm102

8

3Hc h

G

H −•≅=π

ρkm/s)/Mpc(100 ,00 HhH ⋅=

critical energy density for closing the critical energy density for closing the Universe, with the Hubble constant Universe, with the Hubble constant expressed as expressed as

GWρ energy density of the GW background energy density of the GW background

fGW

cGW logd

logd1 ρρ

=Ω energy density of the GW background per energy density of the GW background per logarithmic frequency interval relative to logarithmic frequency interval relative to ρρcc

3/22,0 )( ffh GWH ∝Ω

then, the expected spectrum of the GW background goes as then, the expected spectrum of the GW background goes as

The GW background from Relic GWsThe GW background from Relic GWsThe GW background from Relic GWs

Hogan 2006

••During Phase TransitionsDuring Phase Transitions•• Bubble collisionsBubble collisions•• Topological defectsTopological defects•• Primordial turbulencePrimordial turbulence•• Magnetic fieldMagnetic field

•• InflationInflation•• quantum fluctuationsquantum fluctuations•• inflationary generated fieldsinflationary generated fields

[Hog

an 2

006]

[Hog

an 2

006]

1;1@

1010 1517

≈≈−≤ −−

βyrf

A

δβ +− ≈≈Ω 0222,0 )( fffh GWH

;β−(f)~Afhc

[ e.g. Grishchuck 2005; Boyle & Buonanno 2008][ e.g. Grishchuck 2005; Boyle & Buonanno 2008][ e.g. Grishchuck 2005; Boyle & Buonanno 2008]

The GW background from Cosmic StringsThe GW background from Cosmic StringsThe GW background from Cosmic Strings

Loops Loops are formed from strings, they are formed from strings, they oscillate and oscillate and emit GWsemit GWs++

There is a whole range of loop sizesThere is a whole range of loop sizes

↓↓this leads to a stochastic background of GWsthis leads to a stochastic background of GWs

Spa

ce.c

om

δβ −−− ≈≈Ω )3/1(222,0 )( fffh GWH

;β−(f)~Afhc 267;1@

1010 1416

→≈≈

−≤ −−

βyrf

A

[ e.g. Caldwell et al 96; Maggiore 2000; Damour & Vilenkin 2005][ e.g. Caldwell et al 96; Maggiore 2000; Damour & Vilenkin 2005][ e.g. Caldwell et al 96; Maggiore 2000; Damour & Vilenkin 2005]

The “best” case using a single pulsarThe “best” case using a single pulsarThe “best” case using a single pulsarRemembering the approx formula Remembering the approx formula

T

σ~(f)h TOA

c

one can estimate that for detecting the expected GW background fone can estimate that for detecting the expected GW background from merging rom merging of SMBHs (strain amplitude hof SMBHs (strain amplitude hcc ~ 10~ 10--1616--1010--1515) would require ) would require at least a timing at least a timing stabilitystability σσTOATOA < < 1010--100 ns over few years 100 ns over few years

The best result so far using a single source is from 8The best result so far using a single source is from 8--yr timing of PSR yr timing of PSR B1855+09 at Arecibo implying limit B1855+09 at Arecibo implying limit for for f~7 nHzf~7 nHz [ Kaspi et al 94][ Kaspi et al 94]

hhcc <<~ 10~ 10--1313

ΩΩGWGW hh0,H0,H2 2 (1/8 yr) <(1/8 yr) <~ 1.1 10~ 1.1 10--77

Extended dataset led to ΩGW h0,H2 (1/17 yr)<~ 2 10-9 [Lommen et al 2002][Lommen et al 2002]but not

confirmed yet by independent analyses[Jenet et al 2006][Jenet et al 2006]

Subject to uncontrollable timing noise effects!

A pulsar timing array (PTA)A pulsar timing array (PTA)A pulsar timing array (PTA)Using a Using a number of pulsarsnumber of pulsarsdistributed across the sky it is possible distributed across the sky it is possible

to separate the timing noise contribution from each pulsar from to separate the timing noise contribution from each pulsar from the the signature of the signature of the GW backgroundGW background, which , which manifests as a localmanifests as a local(at (at Earth) Earth) distortion in the times of arrivaldistortion in the times of arrival of the pulses which is of the pulses which is

common to the signal from all pulsarscommon to the signal from all pulsars

@ K

ram

er

The pulsar timing array conceptThe pulsar timing array conceptThe pulsar timing array conceptA(t)A(t) dimensionless amplitude of the GW at time tdimensionless amplitude of the GW at time tNNii(t)(t) intrinsic timing noise of the iintrinsic timing noise of the i--th pulsar at time tth pulsar at time tααii geometric term dependent on pulsar sky coord and GW prop&polar vgeometric term dependent on pulsar sky coord and GW prop&polar vectors ectors ννii rotation frequency of the irotation frequency of the i--th pulsarth pulsarδνδνii fractional frequency shift detected in the ifractional frequency shift detected in the i--th pulsarth pulsar

)()( tNtA iii

i +=αυδυ

By crossBy cross--correlating correlating ‹‹brackets…brackets…›› the observations of ithe observations of i--th and jth and j--th pulsars, one getsth pulsars, one gets

)()()()()()()(2 tNtNtNtAtNtAtA jiijjiji +++ αααα

Since GW amplitude and intrinsic timing noise are uncorrelated Since GW amplitude and intrinsic timing noise are uncorrelated the the latter 3 terms tend to become negligiblelatter 3 terms tend to become negligiblewhile the while the dataspandataspan(i.e. number (i.e. number

of observations) and the of observations) and the number of pulsars become large enoughnumber of pulsars become large enough

Clock errorsClock errorsAll pulsars have the same TOA All pulsars have the same TOA variations: variations: MonopoleMonopole signaturesignature

SolarSolar--System ephemeris errorsSystem ephemeris errorsDipoleDipole signaturesignature

Gravitational waves backgroundGravitational waves backgroundQuadrupoleQuadrupole signaturesignature

Can separate these effects provided there is a Can separate these effects provided there is a sufficient number of widely distributed pulsarssufficient number of widely distributed pulsars

[ adapted from Manchester ]

Idea first discussed by Idea first discussed by Romani Romani [1989][1989] and and Foster & Backer [1990]Foster & Backer [1990]

A pulsar timing array (PTA) for detecting a stocastic Background of GW (GWB)

A pulsar timing array (PTA) for detecting A pulsar timing array (PTA) for detecting a stocastic Background of GW (GWB) a stocastic Background of GW (GWB)

abababab

ab δϑϑϑθζ2

1

2

1)

2

cos1(

4

1)

2

cos1log()

2

cos1(

2

3)( ++−−−−=

θab

Pulsar Pulsar aaPulsar Pulsar bb

Hellings & Downs [1983]Hellings & Downs [1983]: correlation that an : correlation that an isotropic and stocastic GWBisotropic and stocastic GWBleaves on the leaves on the timing residuals of 2 pulsars timing residuals of 2 pulsars a andand b separeted by an anglesepareted by an angleθab in skyin sky

A too simple A too simple (interpretation of the) (interpretation of the) sensitivity curve…sensitivity curve…

Pulsar timing arrays for stocastic GWB: a typical sensitivity curve

Pulsar timing arrays for stocastic GWB: Pulsar timing arrays for stocastic GWB: a typical sensitivity curvea typical sensitivity curve

Limited by total Tspan≈ few yrs ≈ few 108 sec

Limited by interval btw observations: days→weeks ≈ 106-107 sec

For pulsar with white timing noise, best sensitivity for f ≈1/Tobs

White timing noise contribution

for the GWB due to SMBH for the GWB due to SMBH N = number of epochsN = number of epochsM = number of pulsarsM = number of pulsars)1(3/5, −•

∝MMNT

hspan

TOAGWBc

σ

Detailed simulations Detailed simulations are required for are required for more realistic more realistic sensitivity curves…sensitivity curves…

Spherical harmonic decompositionSpherical harmonic decomposition[Burke 1975, Dettweiler 1979, Jaffe & Backer 2003, Demorest et a[Burke 1975, Dettweiler 1979, Jaffe & Backer 2003, Demorest et al 2005]l 2005]

Data analysis for a stocastic GWBData analysis for a stocastic GWBData analysis for a stocastic GWB

Two point correlationTwo point correlation

Correlating the time derivative of the Correlating the time derivative of the residualsresiduals [Hellings & Downs 1983][Hellings & Downs 1983]

Directly correlating the time residualsDirectly correlating the time residuals[Jenet et al 2005][Jenet et al 2005]

Bayesian analysisBayesian analysis[van Haasteren, Levin, McDonald, Lu 2008][van Haasteren, Levin, McDonald, Lu 2008]RobustRobust: deals easily with unevenly sampled data, variable number of tracked pulsars, etc.MarginalisationMarginalisation: deals easily with all systematics of knownfunctional form, including the timing modelCapable to simultaneously measure the Capable to simultaneously measure the amplitude and the shapeamplitude and the shapeof the GWBof the GWB

Data analysis methodologiesData analysis methodologiesData analysis methodologiesBayesian analysis of the timing residuals of an ensemble of pulsBayesian analysis of the timing residuals of an ensemble of pulsars ars

[van Haasteren, Levin, McDonald, Lu 2008][van Haasteren, Levin, McDonald, Lu 2008]

Sanity check tests: Sanity check tests:

[@ v

an H

aast

eran

n 20

08]

Duration of the experiment Duration of the experiment

Typical rms of the timing data Typical rms of the timing data

Number of pulsars Number of pulsars

Rate of data taking Rate of data taking

Useful for optimizing PTA(s) experimental setupUseful for optimizing PTA(s) experimental setup [@ van Haasteren 2008]

S/N>2S/N>2

rms < 200 nsrms < 200 ns

≈≈ 2020--2525>≈ >≈ 55--10 yr10 yr

GW from discrete sources: a spiral-in binaryGW from discrete sources: a spiralGW from discrete sources: a spiral--in binaryin binaryFor a coalescing BH binaryFor a coalescing BH binary[ e.g Thorne 87 ][ e.g Thorne 87 ]

3/24

)]1([5

24 zf

Dc

GMh c

s += π5/1

213/5

21 )()( −+= MMMMMc

f = freq of GWf = freq of GWD = comoving distance of the sourceD = comoving distance of the sourcez = redshift of the sourcez = redshift of the sourceMM cc = =

The expected signature is a periodic GW signal with period twicThe expected signature is a periodic GW signal with period twice e the orbital period of the binary: well away from the last stablethe orbital period of the binary: well away from the last stableorbit it is expected a orbit it is expected a sinusoidal effectsinusoidal effecton the pulsar timing residualson the pulsar timing residuals

To give an order of magnitude estimate, at the last stable orbitTo give an order of magnitude estimate, at the last stable orbit(i.e. immediately (i.e. immediately before merging), the expected strain is before merging), the expected strain is [[Sathyaprakash & Schutz 2009Sathyaprakash & Schutz 2009]]

≈ −

DM

Mh

sun

BHLSOs

Gpc1

1010 10

13

,at a frequency at a frequency

≈

BH

sunLSO M

Mf

1010

nHz440

[ Yar

dley

et a

l 201

0 ]

[ Yar

dley

et a

l 201

0 ]

A spiral-in binary: a typical PTA sensitivity curve

A spiralA spiral--in binary: a typical in binary: a typical PTA sensitivity curve PTA sensitivity curve

Limited by total Tspan≈ few 108 sec and need to fit for spin derivative and jumps btw dataset

Limited by interval btw observations: weeks ≈ 106-107 sec

1 yr-period fitted out in fitting procedures

Ares ~ hs / freq

for inspiraling BHsfor inspiraling BHshhss = strain = strain ≈ ≈ f f 2/32/3

DDpulpul = psr distance= psr distanceΘΘ = source to psr angle= source to psr angleΦΦ = = GW polariz angleGW polariz angleffobsobs = GW freq obs= GW freq obs

−

+⋅=)cos1(2

sin)2sin()cos1(2

θω

φθπc

D

f

hA pul

obs

sresidual

[ Wen et al. 2010 ][ Wen et al. 2010 ]

[ Yar

dley

et a

l 201

0 ]

[ Yar

dley

et a

l 201

0 ]

At Virgo cluster distance (16.5 Mpc)At Virgo cluster distance (16.5 Mpc)

At least one SMBH+SMBH will induce timing At least one SMBH+SMBH will induce timing residual of order 5residual of order 5--50 nanosec 50 nanosec [ Sesana et al 2009 ][ Sesana et al 2009 ]

A spiral-in binary: some interesting cases A spiralA spiral--in binary: some interesting cases in binary: some interesting cases

GWs from discrete sources: GW bursts with memory

GWs from discrete sources: GWs from discrete sources: GW bursts with memoryGW bursts with memory

2

,,

≈

c

V

D

Rh asphejSchw

memb

hhb.,memb.,mem = burst memory strain = burst memory strain D = source distanceD = source distanceVVej,asphej,asph = vel of aspherically ejected particles = vel of aspherically ejected particles RRSchwSchw = Schwarzschild radius of source= Schwarzschild radius of source[ e.g. Braginsky & Thorne 87][ e.g. Braginsky & Thorne 87]

In generalIn general, produced when there is a net change in the time derivatives of, produced when there is a net change in the time derivatives ofmultipole multipole moments characterizing the system moments characterizing the system [e.g. Zeldovich & Polnarev 74][e.g. Zeldovich & Polnarev 74]

In astrophysicsIn astrophysics, typically occur in events which are accompanied by large amoun, typically occur in events which are accompanied by large amount of t of mass or radiation ejected in an asymmetric fashionmass or radiation ejected in an asymmetric fashion[e.g. Braginsky & Thorne 87][e.g. Braginsky & Thorne 87]

If If ejected particles are ejected particles are gravitonsgravitons, it is dubbed Christodoulou effect , it is dubbed Christodoulou effect [Payne 83; [Payne 83; Christodoulou 91; Blanchet & Damour 92] Christodoulou 91; Blanchet & Damour 92]

GW burst events characterized by a final nonGW burst events characterized by a final non--zero change in the gravitational zero change in the gravitational wave field wave field ∆∆hhijij

TTTT (burst memory)(burst memory) after a characteristic time after a characteristic time δδt (burst duration)t (burst duration)

GW bursts with memory: merging of a Super Massive BH binary

GW bursts with memory: merging GW bursts with memory: merging of a Super Massive BH binaryof a Super Massive BH binary

)cos17(sin24

22,, θθ +

∆=

D

Eh asphrad

memb

hhb.,memb.,mem = burst memory strain = burst memory strain D = source distanceD = source distance∆∆EErad,asphrad,asph = aspherically radiated energy= aspherically radiated energyθθ = l.o.s to binary angular mom angle = l.o.s to binary angular mom angle

[ Favata 2009 ] [ Favata 2009 ]

[ Fav

ata

2009

] [ F

avat

a 20

09 ]

D

Rh Schw

memb 05.0, ≈

For equal mass BHFor equal mass BH--binary at the binary at the most favourable anglemost favourable angle

This corresponds to:This corresponds to:

⋅≈ −

DM

Mh

sun

BHmemb

Gpc1

10102

8

16

,

Detecting GW bursts with memory with a PTA

Detecting GW bursts with Detecting GW bursts with memory with a PTAmemory with a PTA

The jumps in the metric is permanent and thus it produces a The jumps in the metric is permanent and thus it produces a linear increasing of pulsar timing residuals with time linear increasing of pulsar timing residuals with time [Pshirkov et al 2010 ][Pshirkov et al 2010 ]

Undistinguishable from a period glitch in a single pulsar, but Undistinguishable from a period glitch in a single pulsar, but distinguishable in a pulsar timing array. distinguishable in a pulsar timing array.

DetectableDetectablewith current facilities for SMBH binary of 10with current facilities for SMBH binary of 10 88 MM sun sun

up to ≈ 1 Gpc, or for 10up to ≈ 1 Gpc, or for 101010 MM sunsun everywhere in the Universeeverywhere in the Universe[van Haasteren and Levin 2010 ][van Haasteren and Levin 2010 ]

HoweverHowever 0.1 − 0.01 detected mergers during the current PTAs 0.1 − 0.01 detected mergers during the current PTAs lifetime of about 10 yearslifetime of about 10 years[[Sesana et al 2007 ]Sesana et al 2007 ]

LISAAdv LIGO/VIRGO

CMB-POL

Pulsar Timing array(s): the frequency spacePulsar Timing array(s): the frequency spacePulsar Timing array(s): the frequency space

Note the Note the complementarity in explored frequencies complementarity in explored frequencies with respect with respect to the current and the future GW observatories, like LIGO, to the current and the future GW observatories, like LIGO,

advLIGO, advVIRGO and LISA advLIGO, advVIRGO and LISA

PTA

6. 6. Gravitational Waves detection Gravitational Waves detection

using pulsar timing arrays: using pulsar timing arrays: ongoing experimentsongoing experiments




I. Current projects: PPTAI. Current projects: PPTAI. Current projects: PPTAParkes Pulsar Timing Array: PPTAParkes Pulsar Timing Array: PPTAAustralian based, using Parkes 64m dishAustralian based, using Parkes 64m dish

Running since Running since ~ ~ 2003 and currently achieving the 2003 and currently achieving the best results so farbest results so far

@ M

.Bu

rgay

The currently used set of observed millisecond The currently used set of observed millisecond pulsars in the PPTA australian projectpulsars in the PPTA australian project

P < 20 ms and not in globular clustersP < 20 ms and not in globular clusters

[ @D

.Man

ches

ter

]

[ Hob

bs e

t al.

Dec

200

8 ]

[ Hob

bs e

t al.

Dec

200

8 ]

For full PPTA (rms of 100 ns For full PPTA (rms of 100 ns over 5 yr for many MSPs) over 5 yr for many MSPs)

Factor >10 improvement on Factor >10 improvement on hhcc and on and on ΩΩgwgw limitslimits

hhc c [1/(1 yr)]< 1.1 [1/(1 yr)]< 1.1 ×× 1010--1414

ΩΩgwgw[1/(8 yr)]h[1/(8 yr)]h0,H0,H22 < 1.2 < 1.2 ×× 1010--88

With ~ 2 yr of useful data and 7 MSPs used (5 with a rms < 300 ns)

With ~ 2 yr of useful data and 7 MSPs used (5 with a rms < 300 ns)

North American Nanohertz Observatory for North American Nanohertz Observatory for Gravitational Waves: NANOGravGravitational Waves: NANOGrav

USA & Canada based, using the excellent Arecibo 300m USA & Canada based, using the excellent Arecibo 300m dish and GBT 101m dish and statedish and GBT 101m dish and state--ofof--art backendsart backends

Running only since Running only since ~ ~ 20082008 @ NRAO

@ Cornell

II. Current projects: NANOGravII. Current projects: NANOGravII. Current projects: NANOGrav

European Pulsar Timing Array European Pulsar Timing Array

++

Large European Array for PulsarLarge European Array for Pulsar

III. Current projects: EPTA-LEAPIII. Current projects: EPTAIII. Current projects: EPTA--LEAPLEAP

European basedEuropean based

Running since Running since ~ ~ 20062006

University of Manchester, JBO, GB ASTRON,Un.Leiden,Un.AmsterdamNL

Max-Planck Institut fur Radioastronomie, GERINAF Osservatorio Astronomico di Cagliari, ITA Nancay Observatory, FR

The partner institutionsThe partner institutions

The telescopesThe telescopes

EffelsbergEffelsberg(100 m)(100 m)--WesterborkWesterbork(96 m)(96 m)--Nancay Nancay (92 m)(92 m)--LovellLovell(76 m)(76 m)--SardiniaSardinia(64 m)(64 m)

The peopleThe people

GB GB –– FR FR –– ITA ITA –– GER GER –– NLNLBen StappersAndrew LyneMark PurverChris JordanSotirios SanidasGemma Janssen

Ismaël CognardGilles TheureauGrégory DesvignesRobert Ferdman

Andrea PossentiMarta BurgayNichi D’AmicoMaura Pilia

Michael KramerAxel JessnerKosmas Lazaridis

Jason HesselsYuri LevinRutger van Haasteren

Current limits from EPTA dataCurrent limits from EPTA dataCurrent limits from EPTA data

…and applying a Bayesian analysis [e.g. van Haasteren 2009][e.g. van Haasteren 2009]

@ v

an H

aast

eren

Using the data from 6 pulsars:J1640+22 (dataspan 12 yr ; rms=1.6µs) J1855+09 (dataspan 23 yr ; rms=1.70 µs)J1713+0747 (dataspan 11 yr ; rms=0.73 µs) J1744-1134 (dataspan 10 yr ; rms=0.55 µs)J1909-1134 (dataspan 4 yr ; rms=0.11 µs) J1918-0642 (dataspan 7 yr ; rms=2.24 µs)

hhc c [1/(1 yr)]< 1.9 [1/(1 yr)]< 1.9 ×× 1010--1414 …only a factor ≈ 1.7 worse than the current published PPTA limit

Careful analysis of the Careful analysis of the ““ redred”” component of the timing noise was performed while component of the timing noise was performed while calculating the current upper limit for a GWB signal in the Eptacalculating the current upper limit for a GWB signal in the Epta data data [van Haasteren 2009] [van Haasteren 2009]

Wes

terb

ork

Effe

lsbe

rg

@ v

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Long term advantages of EPTALong term advantages of EPTALong term advantages of EPTA

Larger total number of TOAsCommensurate scheduling will allow for improved binary

and yearly phase coverageA wide range of frequencies can be sampled and then

compared in quasi-simultaneous sessionsSimultaneous same frequency observations can be used to

check polarisation calibration and overall timing offsetsTelescope, Instrumentation, or Observatory clock based

errors can be quickly identified and corrected

++The data will be combined with those provided by

LEAP…The data will be combined with those provided by

LEAP…

Phased array of the 5 major European telescopes

Funded by the EU Research Council: 2.5 M

Phased array of the 5 major European telescopes

Funded by the EU Research Council: 2.5 M

Large European Array for Pulsars: LEAPLarge European Array for Pulsars: LEAPLarge European Array for Pulsars: LEAP

Sensitivity equivalent to illuminated AreciboSensitivity equivalent to illuminated Arecibo

But able to see much more or the skyBut able to see much more or the sky

People involved: 2 staff, 2 senior postDoc and 2 junior postDocDuration: 5 years since mid 2009People involved: 2 staff, 2 senior postDoc and 2 junior postDocDuration: 5 years since mid 2009

Expected sensitivity of EPTA+LEAP after 5 yrs of Expected sensitivity of EPTA+LEAP after 5 yrs of observations will largely improve the current best limits for observations will largely improve the current best limits for

the GW Background Amplitudethe GW Background Amplitude

Ada

pted

from

Ver

bies

t et a

l [20

09]

Ada

pted

from

Ver

bies

t et a

l [20

09]

~ a factor 10~ a factor 10~ a factor 10

[ Verbiest et al 2009 ][ Verbiest et al 2009 ]

Pulsar Timing array(s): exploring the futurePulsar Timing array(s): exploring the futurePulsar Timing array(s): exploring the futurefor the GWB due to SMBH for the GWB due to SMBH N = number of epochsN = number of epochsM = number of pulsarsM = number of pulsars)1(3/5, −•

∝MMNT

hspan

TOAGWBc

σ

Hardware Hardware and and data analysisdata analysis points required points required for for obtaining imobtaining improvements on provements on σσ

•• TelescoTelescope+Backpe+Back--end better Sensitivityend better Sensitivity

•• RealReal--time mitigation of interferencestime mitigation of interferences

•• Knowledge of the interplanetary weather (i.e. the solar wind cKnowledge of the interplanetary weather (i.e. the solar wind component) and of the omponent) and of the interstellar weatherinterstellar weather

•• Full polarimetric calibrationFull polarimetric calibration

•• Frequency dependent template pulse profilesFrequency dependent template pulse profiles

•• TimeTime--scale for stabilization of the template pulse profilescale for stabilization of the template pulse profile

•• A timing software capable to handle all the non GWA timing software capable to handle all the non GW--induced effects down to ~1 nsinduced effects down to ~1 ns

•• Improved solar system ephemerisImproved solar system ephemeris

[ Verbiest et al 2010 ][ Verbiest et al 2010 ]

Pulsar Timing array(s): exploring the futurePulsar Timing array(s): exploring the futurePulsar Timing array(s): exploring the futurefor the GWB due to SMBH for the GWB due to SMBH N = number of epochsN = number of epochsM = number of pulsarsM = number of pulsars)1(3/5, −•

∝MMNT

hspan

TOAGWBc

σ

Limits to the imLimits to the improvements onprovements on σσ/T/T5/35/3 are related are related toto two intrinsictwo intrinsic pulsar propertiespulsar properties

σσminmin : : the lowest achievable RMS residualsthe lowest achievable RMS residualstiming stabilitytiming stability :: the potential of the timing data of a given pulsarpulsarto keep constant (low) RMS residuals at all time-scales up to the time-span of a PTA project,

Pulsar Timing array(s): exploring the futurePulsar Timing array(s): exploring the futurePulsar Timing array(s): exploring the future

Nominally, σTOA should decrease linearly with 1/(S/N)1/(S/N)

these data taken on the pulsar J0437these data taken on the pulsar J0437--47154715demonstrate the potential demonstrate the potential to achieve to achieve TOA precisionsTOA precisions down to down to σσmin min ~~ 20 ns 20 ns !!

Systematic worsening of the TOA

uncertainties at high S/N, showing a

scaling with 1/sqrt(S/N) 1/sqrt(S/N)

[ Hobbs et al 2009; [ Hobbs et al 2009; Verbiest et al 2010 ]Verbiest et al 2010 ]

Pulsar Timing array(s): exploring the futurePulsar Timing array(s): exploring the futurePulsar Timing array(s): exploring the future

it therefore appears likely that the it therefore appears likely that the GWB signal will dominateGWB signal will dominate our timing our timing on on timetime--scales between 5 and 10 years,scales between 5 and 10 years,provided rms timing residuals are provided rms timing residuals are

decreased enoughdecreased enough

[ Ver

bies

t et a

l 200

9 ]

[ Ver

bies

t et a

l 200

9 ]

Using the stability parameter

σz of Matsakis et al [1997]Matsakis et al [1997]

τ = time-scalec3 = 3rd polynomial fitted to a subset of the residual of length τ

effect of a hypothetical GWB

1 µs rms

0.1 µs rms

Timing array(s): the future for GWBs detection

Timing array(s): the future for Timing array(s): the future for GWBs detectionGWBs detection

@ S

tapp

ers

Current projects are evolving in pace with predictions. Then at Current projects are evolving in pace with predictions. Then at least least very significant limits on GWB (and hopefully a detection) will very significant limits on GWB (and hopefully a detection) will be be

achieved within 5achieved within 5-- 10 years 10 years

A detailed scientific investigation of the GWBackground A detailed scientific investigation of the GWBackground is warranted with SKAis warranted with SKA

Timing array(s): the future for GWs detection of discrete sourcesTiming array(s): the future for Timing array(s): the future for

GWs detection of discrete sourcesGWs detection of discrete sources

SKA will lead to discover them and doing science (e.g. testing GSKA will lead to discover them and doing science (e.g. testing GR vs R vs alternate theories)alternate theories)

THANK YOU!

THANK YOU!

THANK YOU!

Documents

The role of pulsars - EGO - European Gravitational Observatory