Pulsar Tests of General Relativity:Status and Prospects

Ingrid Stairs UBC

10th CCGRRA May 31, 2003

(See upcoming article in Living Reviews in Relativity.)

Pulsars identified with rotating,magnetized neutron stars. B: 108 G to 1014 GP: 0.00156 s to 8.2 s

Pulsars are weak: need big telescopes

Parkes,Australia

Arecibo, Puerto Rico

Green Bank, WV

Jodrell Bank, UK

Dispersion and its Removal

Filterbank: 1/f2 law Coherent Dedispersion:much better timing precision

Pulse-to-pulse variations

Lighthouse model

Integrated profile

Cross-correlation with standard profile: Time-of-Arrival (TOA)

PSR B1534+12: between23 Aug. 1990 20:56:17.088 and15 Sept. 2002 21:38:59.712there were exactly10043172092 pulses.

High-precision timing

Pulsar Timing

Transform TOAs from telescope frame to Solar System Barycentre (~inertial relative to pulsar)

Fit P, P derivatives, position, proper motion, dispersion measure (DM), parallax...

Timing Residuals: Actual TOAs – Predicted

Ideally: no systematics in residuals

M13C – Ransom et al, in prep.

Binary Pulsars

Changing period usually quickly obvious.

Timing Binary Pulsars

All binaries: fit 5 Keplerian parameters: orbital period, projected semi-major axis, eccentricity, longitude and epoch of periastron.

Some systems: fit “Post-Keplerian” parameters:e.g., advance of periastron, orbital period derivative,time dilation/gravitational redshift, Shapiro delay.

The Pulsar Population

Equivalence Principle Violations

Pulsar timing can: set limits on the Parametrized Post-Newtonian (PPN) parameters α

1, α

3, ζ

2

test for violations of the Strong Equivalence Principle (SEP) through - the Nordtvedt Effect - dipolar gravitational radiation - variations of Newton's constant(Actually, parameters modified to account forcompactness of neutron stars.) (Damour & Esposito-Farèse 1992, CQG, 9, 2093; 1996, PRD, 53, 5541).

SEP: Nordtvedt (Gravitational Stark) Effect

Lunar Laser Ranging: Moon's orbit is not polarized toward Sun.

Constraint: |η|<0.001 e.g., Dickey et al 1994, Science, 265, 482.

Binary pulsars: NS and WD falldifferently in gravitationalfield of Galaxy.

Constrain ∆net

= ∆NS

-∆WD

(Damour & Schäfer 1991, PRL, 66, 2549.)

Deriving a Constraint on ∆net

Use pulsar—white-dwarf binaries with low eccentricities ( <10-3).Eccentricity contains a “forced” component along projection of Galactic gravitational force onto the orbit. This may partially cancel “natural” eccentricity.

Constraint α Pb

2/e. Need to estimate orbital inclination (ie masses),

and assume binary orbit is randomly oriented on sky.Ensemble of 8 pulsars: ∆

net < 9x10-3 (Wex 1997, A&A, 317, 976; 2000, ASP Conf. Ser.).

Constraints on α1 and α

3

α1: Implies existence of preferred frames.

Expect orbit to be polarized along projection of velocity (wrt CMB) onto orbital plane. Constraint α P

b

1/3/e, same statistical approach.

Ensemble of pulsars: α1 < 1.4x10-4 (Wex 2000, ASP Conf. Ser.).

Comparable to LLR tests (Müller et al. 1996, PRD, 54, R5927).

α3: Violates local Lorentz invariance and conservation of momentum.

Expect orbit to be polarized, depending on cross-product of system velocity and pulsar spin. Constraint α P

b

2/(eP), same statistical approach.

Ensemble of pulsars: α3 < 1.5x10-19 (Wex 2000, ASP Conf. Ser.).

(Cf. Perihelion shifts of Earth and Mercury: ~2x10-7 (Will 1993,

“ Theory & Expt. In Grav. Physics,” CUP))

Constraints on α3 and ζ

2

α3 can also be tested by isolated pulsars.

Self-acceleration and Shklovskii effect contribute to observed period derivatives:

Young pulsars: α3 < 2x10-10 (Will 1993, “ Theory & Expt. In Grav. Physics,” CUP).

Millisecond pulsars: α3 < ~10-15 (Bell 1996, ApJ, 462, 287; Bell & Damour 1996,

CQG, 13, 3121).

ζ2+α

3 also accelerate the CM of a binary system: variable P derivative

in eccentric PSR B1913+16: (ζ2+α

3) < 4x10-5 (Will 1992, ApJ, 393, L59).

Dipolar Gravitational Radiation

Difference in gravitational binding energies of NS and WD impliesdipolar gravitational radiation possible in, e.g., tensor-scalar theories.

Damour & Esposito-Farèse 1996, PRD, 54, 1474.

Test using pulsar—white-dwarf systems in short-period orbits.

PSR B0655+64, 24.7-hour orbit: (α

cp-α

0)2 < 2.7x10-4 (Arzoumanian 2003, ASP Conf. Ser.).

PSR J1012+5307, 14.5-hour orbit: (α

cp-α

0)2 < 4x10-4 (Lange et al. 2001, MNRAS, 326, 274).

Variation of Newton's Constant

Spin: Variable G changes moment of inertia of NS. Expect (dP/dt)/P α (dG/dt)/G Various millisecond pulsars: |(dG/dt)/G| 2x10-11 yr-1

Depends on equation of state, Shklovskii correction...

Orbital decay: Expect (dPb/dt)/P

b ~ (dG/dt)/G

Test with longer-period NS-WD binaries. PSR B1855+09, 12.3-day orbit: (dG/dt)/G = (-1.3 ± 2.7)x10-11 yr-1

(Kaspi, Taylor & Ryba 1994, ApJ, 428, 713;

Arzoumanian 1995, PhD thesis, Princeton).

(Cf. LLR/Mars laser ranging: 6x10-12 yr-1 (Dickey et al. 1994, Science, 265, 482))

Variation of Newton's Constant II

Chandrasekhar mass MCH

~(hc/G)3/2/mN

2

All measured pulsar masses cluster around M

CH, which appears not to have

changed over a Hubble time.

(dG/dt)/G = (-0.6 ± 4.2)x10-12 yr-1

(Thorsett 1996, PRL, 77, 1432).

Strong-Field Gravity

Binary pulsars, especially double-neutron-star systems:measure post-Keplerian timing parameters in a theory-independent way (Damour & Deruelle 1986, AIHP, 44, 263).These predict masses in any theory of gravity.In GR:

The Original System: PSR B1913+16

Highly eccentric double-NSsystem, 8-hour orbit.

The dω/dt and γ parameterspredict the pulsar andcompanion masses.

The dPb/dt parameter is in

good agreement.

Weisberg & Taylor 2003, ASP Conf. Ser.

Orbital Decay of PSR B1913+16

Weisberg & Taylor 2003, ASP Conf. Ser.

The accumulated shift ofperiastron passage time,caused by the decay of the orbit. A good match to thepredictions of GR!

PSR B1534+12

Measure same parameters asfor B1913+16, plus Shapirodelay.

The parameters dω/dt, s and γform a complementary testof GR.

The measured dPb/dt contains

a large Shklovskii v2/d contribution. If GR is correct,the distance to the pulsar is1.02 ± 0.05 kpc.Stairs et al. 2002, ApJ, 581, 501.

Using Multiple Pulsars

Each pulsar gives unique constraintson alternative theories of gravity.Combining the information can yield stronger tests.

Above: Constraints on coupling parameters α0 and β

0 in tensor-scalar

theories with non-linear coupling between matter and a scalar field(Damour & Esposito-Farèse 1998, PRD, 58, 042001).Pulsars disallow large negative β

0 (strong-field effects), while

Solar-system tests constrain α0.

PSR J0437-4715

Pulsar – white-dwarf binary, orbital period 5.75 days.Closest millisecond pulsar to Earth (140 pc).

The orbital inclination appears to vary, due to the Earth's orbital motion.

Use this to measure the inclination angle and predict the magnitude and shape of Shapiro delay to good accuracy (van Straten et al. 2001,

Nature, 412, 158).

First time purely geometric information predicts the Shapiro delay --good independent confirmation.

Geodetic Precession

Pulsar's spin axis is misaligned with the total angular momentum, andprecesses around it.Precession period: 300 years for B1913+16, 700 years for B1534+12.

PSR B1913+16:

Pulse peak ratio changes,and peaks draw closertogether.

The pulsar will disappearin about 2025!

Taylor & Weisberg 1989,ApJ, 345, 434.

Kramer 1998, ApJ,509, 856.

Mapping the Beam of PSR B1913+16

Weisberg & Taylor 2002, ApJ, 576, 942 Michael Kramer

Hourglass-shaped beam? Cone with off-centre core?

PSR B1534+12

1400 MHz: Arzoumanian 1995, PhD thesis, Princeton; Stairs et al., in prep.

Profile shape changesseen at a few percent ofthe pulse peak at both430 MHz and 1400 MHz.

Dipole inclination betterunderstood than forB1913+16 – easier toderive full 3-d geometry?

New Tools from Pulsar Searches

Pulsar Searches: Dispersion Periodicity Acceleration

Recent and on-goinglarge-scale searches: Parkes Multibeam

(Galaxy, flanking, high-latitude) Globular Clusters

(Parkes, Arecibo, GBT) Drift scans

(Arecibo, some GBT)

New Pulsars

Parkes surveys have found: Several ~few-day-orbit,

low-eccentricity systems (useful for α

1)

A few long-orbit systems (useful for ∆, α

3)

One very interesting short-orbit system...

Arecibo drift surveyshave found a systemwith a ~600-day orbit(useful for ∆, α

3).

(Not all shown!)

PSR J1141-6545

Young pulsar with a white-dwarf companion Discovered in Parkes Multibeam Survey (Kaspi et al 2000, ApJ, 543, 321)

Eccentric, 4.45-hour orbit Should emit lots of quadrupolar gravitational radiation Good candidate to test for dipolar gravitational radiation Highest predicted rate of geodetic precession: 1.35º/yr (265-year period) Not seen in a survey in the early 1990s: did it precess into sight recently?

Looking ahead... Long-term timing will measure or set limits on eccentricities of

new systems – ensemble tests will improve Try to derive full binary geometry for these systems to

eliminate need for some statistical arguments Coalescing (short-orbit) NS-WD should be monitored for

gravitational radiation – quadrupole and dipole Better Galactic models (for B1913+16) and a VLBI parallax

(for B1534+12) needed to improve gravitational radiation tests Try to quantify geodetic precession and determine if it will be

possible to test the prediction of precession rate Large-scale surveys: reprocessing of Parkes survey with acceleration

searching; upcoming multibeam surveys at Arecibo, GBT; SKA... Globular cluster surveys: more old pulsars, exotic binaries Keep an eye out for the Holy Grails: double pulsars,

pulsar—black-hole systems, ???...