Gravity with the SKA

Michael KramerJodrell Bank ObservatoryUniversity of Manchester

WithDon Backer, Jim Cordes, Simon Johnston,

Joe Lazio and Ben Stappers

Gravity Meeting ’06, Birmingham

Strong-field tests of gravity using Pulsars and Black Holes

Outline• Pulsars• Past and present successes• A giant leap - the power of the SKA• Transforming our knowledge offundamental physics, particularly:

- Strong-field tests of gravity- Gravitational wave astronomy

Searching & Timing: see JimGravitational Waves: see Rick

A frequently asked question, still…

Testing EinsteinExperiments made in Solar System provide accurate tests

…but only in weak gravitational field!

In strong gravitational fields, physics may be different!

Compute energy in gravitational field:

Radiative aspects need to be tested too!

Neutron stars &Black Holes:

5.015.0

≈≈

BH

NS

εε

2mcEgravity=ε

Solar system:

10000000000.00000000001.0

000001.0

≈≈≈

Moon

Earth

Sun

εεε

Pulsars are extreme objects…• Cosmic lighthouses …• Precise clocks …• Almost Black Holes …• Objects of extreme matter …

– 10x nuclear density– B ~ Bq = 4.4 x 1013 Gauss– Voltage drops ~ 1012 V– FEM = 1010-12 Fg– High-temperature & superfluid superconductor

• Massive stable flywheels superb cosmic clocks e.g. period of B1937+21:

P = 0.0015578064924327±0.0000000000000004 s

Precision tools for a wide range of fundamental physics and astrophysics

The importance of pulsar testslog(

Self-e

nerg

y)

log(Orbital energy)

Strong-field tests using pulsars…

Various approaches:

Theory-independent or phenomenological:Parameterized Post-Keplerian approach

Parameterized Post-Newtonian (PPN)

Binary pulsars

Theory-dependent:Beyond usual post-Newtonian parameters, used forclasses of tensor-scalar theories

Parametrized post-Newtonian (PPN)γ How much space

curvature per unit mass?1 γ-1<2 10-3

γ-1<3 10-4

Viking ranging (time delay)VLBI (light deflect.)

β How much “non-linearity” in the superposition law?

1 β-1<3 10-3 Perihelion shift

ξ Preferred-location effects? 0 | ξ |<3 10-3 Earth tides, Pulsars

α1Preferred-frame effects?Orbital polarization

0 α1 < 10-4

α1 < 1.2 10-4

Lunar ranging (weak) Pulsars (strong)

α2Preferred-frame effects?Spin precession

0 α2 < 4 10-7 Solar alignment

α3Preferred-frame effects?Violation of conversation of total momentum

0 α3 < 4.0 10-20 Pulsars

Will (2002), Stairs (2005)

Plus: limits on violation of SEP: |Δ|<5.5x10-3

…already a success story:The first binary pulsar

Weisberg & Taylor (2004)

• Orbit shrinks every day by 1cm• Confirmation of existence of gravitational waves

Hulse & Taylor (1974)

Tests of General RelativityElegant method to test any theory of gravity: (Damour & Taylor ’92)

• Relativistic corrections to Keplerian orbits measured

• All corrections can bewritten as function ofthe pulsar masses

• Only one true combination of mA and mB should exist

Single unique point in

a mA - mB diagram!

PK1

PK2PK3

Pass!

Tests of General RelativityElegant method to test any theory of gravity: (Damour & Taylor ’92)

• Relativistic corrections to Keplerian orbits measured

• All corrections can bewritten as function ofthe pulsar masses

• Only one true combination of mA and mB should exist

Single unique point in

a mA - mB diagram!

PK3

PK2

PK1

Fail!

Npk – 2 tests possible

…already a success story: The first double pulsar

Kramer et al. (in prep.)

Orbital Phase (deg)

Del

ay (µ

s)

s = sin(i)=0.9997±0.0002

001.0000.1obs

exp

±=ss

Kramer et al.(in prep)

Testing GR:

• most relativistic systems• most over-constrained system:

• Five PK params• Theory independentmass ratio

Double Pulsar: Tests of GRDecember 2003 (Lyne et al. 2004)

Double Pulsar: Tests of GRKramer et al. in prep.

“Scalarisation”

…already a success story: Scalar-Tensor Theories

ScalarCharge(for β0=-6)

Damour (priv. comm.)

Damour (priv. comm.)

The is more to do:

• The remaining “holy grail”: a pulsar – black hole system!• Wanted: millisecond pulsar around black hole

“…a binary pulsar with a black-hole companion has the potential of providing a superb new probe of relativistic gravity. The discriminating power of this probe might supersede all its present and foreseeable competitors…”

(Damour & Esposito-Farese 1998)

Galactic Census with the SKA• Blind survey for pulsars will discover PSR-BH systems!• Timing of discovered binary and millisecond pulsars to very high precision:

• “Find them!”• “Time them!”• “VLBI them!”

Benefiting from SKA twice:• Unique sensitivity: many pulsars, ~10,000-20,000

incl. many rare & exotic systems!• Unique timing precision and multiple beams!Not just a continuation of what has been done before

- Complete new quality of science possible!

• Galactic probes: Interstellar medium/magnetic fieldStar formation historyDynamicsPopulation via distances (ISM, VLBI)

Pulsar Science with the SKAVery wide range of applications:

Electrondistribution

Magnetic field

Galactic CentreMovement in potential

• Galactic probes• Extragalactic pulsars: Formation & Population

Turbulent magnetized IGM

Pulsar Science with the SKAVery wide range of applications:

Giant pulses

Reach the local group!

Search nearby galaxies!

• Galactic probes• Extragalactic pulsars• Relativistic plasma physics: Radio emission

Resolving magnetospheresRelation to high-energies

Pulsar Science with the SKAVery wide range of applications:

• Galactic probes• Extragalactic pulsars• Relativistic plasma physics• Extreme Dense Matter Physics: Ultra-strong B-fields

Equations-of-StateCore collapsesVariation of G

Pulsar Science with the SKAVery wide range of applications:

• Galactic probes• Extragalactic pulsars• Relativistic plasma physics• Extreme Dense Matter Physics• Multi-wavelength studies: Photonic windows

Pulsar Science with the SKAVery wide range of applications:

• Galactic probes• Extragalactic pulsars• Relativistic plasma physics• Extreme Dense Matter Physics• Multi-wavelength studies: Photonic windows

Non-photonic windows

Pulsar Science with the SKAVery wide range of applications:

• Galactic probes• Extragalactic pulsars• Relativistic plasma physics• Extreme Dense Matter Physics• Multi-wavelength studies• Exotic systems: planets

millisecond pulsarsrelativistic binariesdouble pulsarsPSR-BH systems

Pulsar Science with the SKAVery wide range of applications:

3.Holy Grail: PSR-BH

Double PulsarsPlanets

• Galactic probes• Extragalactic pulsars• Relativistic plasma physics• Extreme Dense Matter Physics• Multi-wavelength studies• Exotic systems• Gravitational physics: - Strong-field tests

- BH properties- Gravitational Waves

Pulsar Science with the SKAVery wide range of applications:

Black Hole spin:

Black Hole properties

•Astrophysical black holes are expected to rotate

2MS

Gc

≡χ S = angular momentum

• Result is relativistic spin-orbit coupling• Visible as a precession of the orbit:

Measure higher order derivatives of secularchanges in semi-major axis and longitude of periastron

• Not easy! It is not possible today!• Requires SKA sensitivity!

See Wex & Kopeikin (1999)xx ,,ω

Black Hole quadrupole moment:

Black Hole properties

•Spinning black holes are oblate

Q = quadrupole moment32

4

MQ

Gcq ≡

• Result is classical spin-orbit coupling

• Visible as transient signals in timing residuals

• Even more difficult! • Requires SKA!

Wex &

Kopeikin (1999):

• For all compact massive, BH-like objects, we’ll be able to measure spin very precisely

• In GR, for Kerr-BH we expect:

1≤χ• But if we measure

χ > 1 ⇔ Event Horizon vanishes ⇔ Naked singularity!

• Then: either GR is wrongor Censorship Conjecture is violated!

Cosmic Censorship Conjecture

No-hair theorem

2χ−≠q• If we measure

either GR is wrong, i.e. “no-hair” theoremis violated

or we have discovered a new kind of object, e.g. a Boson star with

210χ−≤q

Was Einstein right? What are the Black Hole properties? Do naked singularities exist? Do Black Holes have “hairs”?

Fundamental Physics with the SKA Pulsars discovered and observed with the SKA…

• complement studies in other windows • probe wide range of physical problems• New science possible – not just the same:

Work to be done: 2PN timing formulaCalibration techniquesMeans to handle blind surveyEfficient timing methods(LOTS of data, LOTS of pulsars)

The SKA sky!