Scuola nazionale de AstrofisicaRadio Pulsars 4: Precision Timing and GR

Outline

• The double pulsar PSR J0737-3039A/B• Strong-field tests of GR• Pulsar Timing Arrays - pulsar timescale and the detection of gravitational radiation

The first double pulsar!

Discovered at Parkes in 2003

One of top ten science break-throughs of 2004 - Science

PA = 22 ms, PB = 2.7 s

Orbital period 2.4 hours!

Periastron advance 16.9 deg/yr!(Burgay et al., 2003; Lyne et al. 2004)

Highly relativistic binary system!

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PSR J0730-3039A/B

John Rowe Animations/ATNF

22.7 ms

1.7 x 10-18

205 Myr

6 x 109 G

1,080 km

5 x 103 G

6 x 1033 erg s-1

A:2.77 s

0.88 x 10-15

50 Myr

1.6 x 1012 G

1.32 x 105 km

0.7 G

1.6 x 1030 erg s-1

P

P

c

BS

RLC

BLC

E

B:

Basic Parameters of PSR J0737-3039A/B

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A is a standard mildly recycled pulsar

B is a relatively young but slow pulsar whose environment is greatly affected by the presence of A

PSR J0737-3039B

• “Double-line binary” gives the mass ratio for the two stars – strong constraint on gravitational theories

• B pulsar only active for small fraction of the orbital period

0.2 pulse periods

Orb

ital p

erio

d

• MSP blows away most of B magnetosphere - dramatic effect on pulse emission

(Spitkovsky & Arons 2005)

PSR J0737-3039A/B Orbit Geometry

a1+a2 = 8.8 x 105 km

i = 88o.7 0o.6

Distance = 0.55 kpc

• We view the orbit almost edge-on

• At conjunction, pulses from A pass through the B magnetosphere

• B is bright when on near side of orbit

PSR J0737-3039A Eclipse• For orbit inclination 88.7 deg, impact parameter of A l.o.s. on B ~ 0.15 RLC,B

• B magnetosphere eclipses A - a unique probe of a pulsar magnetosphere!• Eclipse duration only ~25 sec

• Orbital velocity of A relative to B ~ 630 km s-1

• Eclipse width only ~ 16,000 km, ~ 0.12 RLC,B

• Radius of eclipsing region:

0.06 RLC,B < Reclip < 0.16 RLC,B

Eclipsing region only a small part of B magnetosphere!

• Eclipse of A is modulated with B rotational phase! • Eclipse is deeper when B radio beam is directed toward and away from us

Models: Synchrotron absorption by shock-heated wind in magnetosheath (Arons et al. 2005, Lyutikov 2004) Synchrotron absorption by relativistic plasma in closed field-line region (Rafikov & Goldreich 2005, Lyutikov & Thompson 2005)

(McLaughlin et al. 2004a)

• All models require plasma density 102 - 104 times GJ

Modulation of B radio emission by A• Sequence of ~ 400 individual pulses from B during leading bright phase

• Individual pulses from A visible in background - varying phase due to relative motion of A & B wrt observer

• On leading edge of B pulse, “drifting” effect with systematic variation of “subpulse” phase in successive pulses

• Most clearly seen between 200o and 210o

(McLaughlin et al. 2004b)

A

B

• Drift rate of 0.196 cycles/period interpreted as a beat frequency with B period

• Ratio of pulsar barycentric periods: PB/PA = 122.182

• Doppler shift from varying separation of A & B - at orbital longitude 205o, predicted beat frequency ~ 0.196 cycles/period, exactly as observed!

• Modulation is at 1/PA ~ 44 Hz

• Suggests that modulation is due to impact of A’s magnetic-dipole radiation field on B’s magnetosphere, rather than A pulses or wind energy

• Mechanism not clear - modulation of beam direction or emission intensity?

Modulation of B by A (ctd)

(McLaughlin et al. 2004b)

Orbital Modulation of PSR J0737-3039B

Secular changes are observed! Mechanism for orbital modulation not fully understood

Can’t separate effects of periastron precession and geodetic precession

(Burgay et al. 2005)

Binary pulsars and Gravity

Tests of Equivalence Principles

Limits on Parameterised Post-Newtonian (PPN) parameters

Dipolar gravitational radiation – dPb/dt

Variation of gravitational constant G – dP/dt, dPb/dt

Orbit ‘polarisation’ due to external field – orbit circularity

Binary pulsars give limits comparable to or better than Solar-system tests, but in strong-field conditions (GM/Rc2 ~ 0.1 compared to 10-5 for Solar-system tests)

Constraints on Gravitational Theories from PSR J0737-3039A/B

• Mass functions: sin i < 1 for A and B

• Mass ratio R = MA/MB Measured value: 1.0714 0.0011

Independent of theory to 1PN order

• Periastron advance : 16.8995 0.0007 deg/yr

Already gives masses of two stars (assuming GR):

MA = 1.3381 0.0007 Msun

MB = 1.2489 0.0007 Msun

Star B is a very low-mass NS!Mass Function A

Mass function B

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(Kramer et al. Science, 314, 97, 2006)

GR value Measured value Improves as

Periast. adv. (deg/yr) - 16.8995 0.0007 T1.5

Grav. Redshift (ms) 0.3842 0.386 0.003 T1.5

Pb Orbit decay -1.248 x 10-12 (-1.252 0.017) x 10-12 T2.5

r Shapiro range (s) 6.15 6.2 0.3 T0.5

s Shapiro sin i 0.99987 0.99974 T0.5

Measured Post-Keplerian Parameters for PSR J0737-3039A/B

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GR is OK! Consistent at the 0.05% level!

(Kramer et al. 2006)Non-radiative test - distinct from PSR B1913+16

+16 -39

PSR J0737-3039A/B Post-Keplerian Effects

R: Mass ratio

: periastron advance

: gravitational redshift

r & s: Shapiro delay

Pb: orbit decay

(Kramer et al. 2006)

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• Six measured parameters

• Four independent tests

• Fully consistent with general relativity (0.05%)

Orbit Decay - PSR J0737-3039A/B

• Measured Pb = (-1.252 0.017) x 10-12 in 2.5 years

• Will improve at least as T2.5

• Not limited by Galactic acceleration (as is PSR B1913+16 test)

System is closer to Sun - uncertainty in Pb,Gal ~ 10-16

• Main uncertainty is in Shklovskii term due to uncertainty in transverse velocity and distance

Scintillation gives Vperp = 66 15 km s-1

Timing gives Vperp ~10 km s-1 -- correction at 0.02% level

VLBI measurements should give improved distance

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Will surpass PSR B1913+16 in ~5 years and improve rapidly!

PSR J0737-3039: More Post-Keplerian Parameters!

• Relativistic orbit deformation: er = e (1 + r)

e = e (1 + ) ~ T2.5

Should be measurable in a few years

• Spin orbit coupling:

Geodetic precession - precession of spin axis about total angular momentum

Changes in pulse profile will give misalignment angle

Periastron precession - higher order terms

Can give measurement of NS moment of inertia

• Aberration: xobs = a1 sin i = (1 +A)xint

Will change due to geodetic precession

(Damour & Deruelle 1985)

Detection of Gravitational Waves

• Prediction of general relativity and other theories of gravity

• Generated by acceleration of massive object(s)

(K. Thorne, T. Carnahan, LISA Gallery)

• Astrophysical sources:

Inflation era

Cosmic strings

SN, BH formation in early Universe

Binary black holes in galaxies

Coalescing neutron-star binaries

Compact X-ray binaries

(NASA GSFC)

Detection of Gravitational Waves• Huge efforts over more than four decades to detect gravitational waves

• Initial efforts used bar detectors pioneered by Weber

• More recent efforts use laser interferometer systems, e.g., LIGO, LISA

• Two sites in USA• Perpendicular 4-km arms• Spectral range 10 – 500 Hz• Initial phase now commissioning• Advanced LIGO ~ 2011

LISALIGO• Orbits Sun, 20o behind the Earth• Three spacecraft in triangle• Arm length 5 million km• Spectral range 10-4 – 10-1 Hz• Planned launch ~2017

Detecting Gravitational Waves with Pulsars• Observed pulse periods affected by presence of gravitational waves in Galaxy

• For stochastic GW background, effects at pulsar and Earth are uncorrelated

• With observations of one or two pulsars, can only put limit on strength of stochastic GW background

• Best limits are obtained for GW frequencies ~ 1/T where T is length of data span

• Analysis of 8-year sequence of Arecibo observations of PSR B1855+09 gives g = GW/c < 10-7 (Kaspi et al. 1994, McHugh et al.1996)

• Extended 17-year data set gives better limit, but non-uniformity makes quantitative analysis difficult (Lommen 2001, Damour & Vilenkin 2004)

Timing residuals for PSR B1855+09

A Pulsar Timing Array• With observations of many pulsars widely distributed on the sky can in principle detect a stochastic gravitational wave background

• Gravitational waves passing over the pulsars are uncorrelated

• Gravitational waves passing over Earth produce a correlated signal in the TOA residuals for all pulsars

• Requires observations of ~20 MSPs over 5 – 10 years; could give the first direct detection of gravitational waves!

• A timing array can detect instabilities in terrestrial time standards – establish a pulsar timescale

• Can improve knowledge of Solar system properties, e.g. masses and orbits of outer planets and asteroids

Idea first discussed by Romani (1989) and Foster & Backer (1990)

Clock errors

All pulsars have the same TOA variations: monopole signature

Solar-System ephemeris errors

Dipole signature

Gravitational waves

Quadrupole signature

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

Detecting a Stochastic GW Background

Simulation using Parkes Pulsar Timing Array (PPTA) pulsars with GW background from binary black holes in galaxies

(Rick Jenet, George Hobbs)

To detect gravitational waves of astrophysical origin

To establish a pulsar-based timescale and to investigate irregularities in terrestrial timescales

To improve on the Solar System ephemeris used for barycentric correction

The PPTA Project: Goals

To achieve these goals we need ~weekly observations of ~20 MSPs over at least five years with TOA precisions of

~100 ns for ~10 pulsars and < 1 s for rest

• Modelling and detection algorithms for GW signals

• Measurement and correction for interstellar and Solar System propagation effects

• Implementation of radio-frequency interference mitigation techniques

Sky Distribution of Millisecond PulsarsP < 20 ms and not in globular clusters

A Pulsar Timescale• Terrestrial time defined by a weighted average of caesium clocks at time centres around the world

• Comparison of TAI with TT(BIPM03) shows variations of amplitude ~1 s even after trend removed

• Revisions of TT(BIPM) show variations of ~50 ns

(Petit 2004)• Pulsar timescale is not absolute, but can reveal irregularities in TAI and other terrestrial timescales

• Current best pulsars give a 10-year stability (z) comparable to TT(NIST) - TT(PTB)

• Full PPTA will define a pulsar timescale with precision of ~50 ns or better at 2-weekly intervals and model long-term trends to 5 ns or better

Current and Future Limits on the Stochastic GW Background

(Jenet et al. 2006)

10 s

Timing Residuals• Arecibo data for PSR B1855+09 (Kaspi et al. 1994) and recent PPTA data

• Monte Carlo methods used to determine detection limit for stochastic background described by hc = A(f/1yr) (where = -2/3 for SMBH, ~ -1 for relic radiation, ~ -7/6 for cosmic strings)

Current limit: gw(1/8 yr) ~ 2 10-8

For full PPTA (100ns, 5 yr): ~ 10-10

• Currently consistent with all SMBH evolutionary models (e.g., Jaffe & Backer 2003; Wyithe & Loeb 2003, Enoki et al. 2004)

• If no detection with full PPTA, all current models ruled out

• Already limiting EOS of matter in epoch of inflation (w = p/ > -1.3) and tension in cosmic strings (Grishchuk 2005; Damour & Vilenkin 2005)

The Gravitational Wave Spectrum

• Pulsars are fascinating objects whose study gives insight into extreme physical states unrealisable on Earth

• Pulsed, highly polarised and throughout our Galaxy, they are unique probes of the interstellar medium

• As precision clocks they are powerful tools for investigation of a wide range of problems, especially concerning relativity and gravitation

Summary

Grazie e Arrivederci

The PPTA Project: Methods• Using the Parkes 64-m telescope at three frequencies (680, 1400 and 3100 MHz)

• Digital filterbank system, 256 MHz bandwidth (1 GHz early 2007), 8-bit sampling, polyphase filter

• CPSR2 baseband system 2 x 64 MHz bandwidth, 2-bit sampling, coherent de-dispersion

• Developing APSR with 512 MHz bandwidth and 8-bit sampling

• Implementing real-time RFI mitigation for 50-cm band• TEMPO2: New timing analysis program, systematic errors in TOA corrections < 1 ns, graphical interfaces, predictions and simulations (Hobbs et al. 2006, Edwards et al. 2006)

• Observing 20 MSPs at 2 - 3 week intervals since mid-2004

• International collaboration and co-operation to obtain improved data sampling including pulsars at northern declinations

Dispersion Measure Variations

• DM from 10/50cm or 20/50cm observation pairs

• Variations observed in most of PPTA pulsars

• DM typically a few x 10-3 cm-3 pc

• Weak correlation of d(DM)/dt with DM, closer to linear rather than DM1/2

• Effect of Solar wind observed in pulsars with low ecliptic latitude

(You et al., in prep.)

The Parkes Pulsar Timing Array ProjectCollaborators:

Australia Telescope National Facility, CSIRO

Dick Manchester, George Hobbs, Russell Edwards, John Sarkissian, John Reynolds, Mike Kesteven, Grant Hampson, Andrew Brown

Swinburne University of TechnologyMatthew Bailes, Ramesh Bhat, Joris Verbiest, Albert Teoh

University of Texas, BrownsvilleRick Jenet, Willem van Straten

University of SydneySteve Ord

National Observatories of China, BeijingXiaopeng You

Peking University, BeijingKejia Lee

University of TasmaniaAidan Hotan