Scuola nazionale de Astrofisica Radio Pulsars 4: Precision Timing and GR Outline The double pulsar PSR J0737-3039A/B Strong-field tests of GR Pulsar Timing.
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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
.
(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)
.
.
• 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
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