testing gr with lisa leor barack university of southampton

Testing GR with LISA

Leor Barack University of Southampton

Birmingham, March 2006 2

Why is LISA a good lab for fundamental physics?

Sources are of high SNR and/or long duration

Lots of info in waveform (note: “signal”=amplitude, not energy!)

Sources abundant

can repeat experiment with different sources

Automatic detection of wave polarization gives precise source orientation info (thus, e.g., no “cos ” problem)

Objects detectable to cosmological distances

can probe galactic history & evolution of fund parameters

Universe transparent to GWs since first 10-43 sec

However: Bad sky resolution

Problem as sky location correlates with system parameters (and distance)

Here coordinated EM observations could help


Fundamental physics with LISA

Strong-field gravity: Mapping of BH spacetime and test of “No hair” theorem using EMRIs Test of BH area theorem by measuring mass deficits in MBH-MBH

merges.

Alternative theories of gravity: Testing scalar-tensor theories using GWs from MBH binaries Measuring speed of GWs and mass of graviton using MBH binaries Bounding the mass of graviton using eccentric binaries Bounding the mass of graviton via direct correlation of GW & EM

observations of nearby WDs and NSs

Cosmology with LISA

Improving science return by coordinating observations in EM & GW bands


Testing Strong-field gravity with LISA


inspiral Periastron precession

Spin-Orbit coupling

“Zoom-Whirl” effect

Evolution of inclination angle

Testing strong-field relativity using Extreme-Mass-Ratio-Inspiral (EMRI) probes


m= 1 M M= 106 M

efin=0.3

30 min

4 hours6 months


Sample waveform stretches


“chara

cteri

stic

am

plit

ude”,

h

c

m = 10 M

M= 106 M

D= 1 Gpc

e(plunge)=0.3

e(plunge-10yr)=0.77

Dots indicate (from left to right) state of system 5, 2, and 1 years before plunge.

Curves represent 10 yrs of source evolution

(Barack & Cutler 2003)

LISA’s noise curve



“Geodesy” of black hole geometry:

BHs have a unique multipolar structure, depending only on M and S:


),,(),,(),(

),,(),(

~

,~

rr

r

vYrdVS

YrdVM

lml

lm

lml

lm

lll

lmlm

MiSMiSM

mSM

)/(

,0for0

00

“No hair” theorem: All multipoles l >1 completely determined by M00M and S10 S

By measuring 3 multipoles only, could potentially tell between a GR black hole, and something else, perhaps even more exotic


Could LISA tell a Kerr BH from something else?

Ryan (1997): LISA could measure accurately 3-5 multipoles (if orbits are circular and equatorial, Tobs = 2 yrs):

enough to “rule out” Kerr Black hole enough to rule out a spinning Boson star (characterized by first 3 multipoles)


How would this change with full parameter space of EMRI orbits?


(For 10 M onto 106 M at 1Gpc, for various eccentricities and spins)

How well could LISA tell the EMRI parameters?

Barack and Cutler (2004)



Is it really a Kerr BH? Does is have an event horizon?

Kedsen, Gair and Kaminkowski (2005): (nonrotating) supermassive Boson stars admit stable orbits within the star, below the Schwarzschild radius

Fang & Lovelace (2005): Back reaction from tidal rising on BH horizon

Glampedakis & Babak (2005 + in progress): Kerr + generic quad. pert.

Gair et al (in progress): Do orbits in more generic spacetimes, close to Kerr, admit a 3rd integral of motion? If not, waveform will provide a smoking gun for a non-Kerr object.

If non-Kerr: is it due to failure of GR or could be explained within GR (e.g., interaction with accretion disk)? any info from EM observations could help!



Testing strong-field relativity by measuring mass deficits in MBH-MBH mergers

Hughes & Menou (2005)

Buonanno (2002) From inspiral phase (using matched filters):

get m1, m2, s1, s2

From ringdown phase (from freq. and Q):

get Mf, Sf of merger product

Calculate Mass loss in GWs

Test Hawking’s “Area Theorem”: Although Mf < m1+ m2,

we must have Af > A1 + A2 .

(Area A obtained from mass and spin)


Testing strong-field relativity by measuring mass deficits in MBH-MBH mergers

Hughes & Menou (2005)

“Golden binaries”: those with both inspiral and ringdown phases observable by LISA

Total rate for Golden Binaries:

~1 for rare MBHs scenario

~5 for abundant MBHs scenario

Total rate(rare MBHs)

Golden only(abundant MBHs)

Golden only(rare scenario)


Testing Alternative theories with LISA


Scalar-tensor theories of gravity

Variants and generalisations of Brans & Dicke (1960): Gravity described by a spacetime metric + scalar field , which may couple only to gravity (“metric” theories) or also to matter (“non-metric” theories).

Deviation from GR is parameterized by a “coupling parameter” : General Relativity is retrieved at

Best experimental bound on to date comes from solar-system gravitational time-delay measurements with Cassini spacecraft:

4104


A finite value of affects the GWs from binaries in two ways: The radiation has a component with a monopolar polarization

Monopole and dipole backreaction alters the orbital evolution; phase evolution in long-lived binaries “amplifies” this effect over time.

Advantage of method: may evolve over cosmological history. LISA could probe different cosmological epochs, which solar system measurements can’t.

Best sources: NS-MBH (have strongest dipole rad. reaction)

Given GW model and detector noise model, LISA bound on can be estimated by working out the matched filtering variance-covariance matrix and looking at the rms error 1/2

Testing scalar-tensor theoriesby measuring GWs from binaries



Will & Yunes (2004)

NS-MBH binaryNon-spinning objects, quasi-circular inspiral


SNR=10Int time= 1/2 year


Berti, Buonnanno & Will (2005)

Including non-precessional spin effects (spin vectors aligned)

Bound on degrades significantly(Parameters are highly correlated adding param’s “dilutes” available info)

Inclusion of precession effects maydecorrelate parameters and improve parameter estimation (Vecchio 2004)

Independent knowledge of some source parameters (e.g. sky location)may improve bound significantly


In alternative theories the speed of GWs could differ from c because Gravitation couples to “background” gravitational fields GWs propagate into a higher-dim space while light is confined to 3d “brane” Gravity is propagated by a massive field/particle ( dispersion)

Speed of Gravitational Waves and the mass of graviton

Ways to measure the speed of GWs & the mass of graviton:

)/exp()( 1gYUK rrrV

(“Static” Newtonian gravity) Check for violations of 1/r law:

(“Dynamic” GR) Take advantage of dispersion relation: Longer wavelengths propagate slower

22 )/(1)/( gg fccv

(“Dynamic” GR) Compare arrival times of EM/Grav waves from same event: vast distance magnifies minute differences in speed


“Static” Newtonian gravity:

“Dynamic” relativity:

Current (actual) bounds on g

From solar system planetary orbits (Talmagde et al 1988):

c > 2.8×1012 km

From galaxy clusters (Goldhaber & Nieto 1974):

c 1×1020 km ??

From rate of orbital decay in binary pulsar PSR B1534+12 (Finn & Sutton 2002):

c > 1.6×1010 km


Bounding g using LISA observations:A. Matched filtering of signals from MBH-MBH inspirals

Waves from earlier stages of the inspiral (longer wavelength) propagate slightly slower than waves from later stages – an effect coded into the GW phase evolution

Will (1998)Will & Yunes (2004)

Non-spinning objects, quasi-circular inspiral

221

21

)(

2/1

mm

mm

z

yr1obsT


Berti, Buonnanno & Will (2005)

Including non-precessional spin effects (spin vectors aligned)

Equal masses, D=3Gpc

[Dashed line: ignoring data below 10-4 Hz]

Bounding g using LISA observations:A. Matched filtering of signals from MBH-MBH inspirals


Suppose that EM is the orbital phase, measured optically, at t = t0 (with error EM)

Use LISA to measure GW. If g= , then GWEM should be consistent with 0

Given EM and EM can give experimental bound on g

“Optimal” system for this experiment: f=2.06 mHz, M1=M2=1.4M

Bounding g using LISA observations: B. Direct correlation of GW/EM observations of nearby WD or NS binaries

Larson & Hiscock (2000), Cutler, Hiscock & Larson (2003)

Assuming |EM|<<| GW| gives

For “optimal” binary source: g 1×1014 km

For “best” known binary: c 1×1013 km (LMXB 4U1820-30: f=2.909 mHz, M1=0.07M , M2=1.4M):

Constraints on orbital orientation from EM observations may improve limit significantly.


If propagation is dispersive, higher harmonics of the GWs arrive slightly earlier than lower harmonics!

22

21

min~ nncerrordisp ff

Bound on c from eccentric EMRIs:D=1 Gpc, f =1 mHz, Based on 1 year of coherent data

1017

1016

(km)minc

Bounding g using LISA observations:C. Measurements of GWs from eccentric binaries (Jones 2005)

Distribution of GW power into harmonics

e=0.7

e=0.5e=0.2


Cosmology with LISA


Chirping binaries as standard candles:

Both GW amplitude and df/dt depend on the masses through same combination: the Chirp mass,

So, from df/dt can infer GW absolute magnitude, and compare with “visual” GW magnitude to infer luminosity distance, dL. If host galaxy identified in EM [morphological evidence, accretion disks,

jets?] then given z and dL could measure the Hubble flow to high accuracy (~1%, Hughes and Holz 2005)

Conversely, if Hubble flow known to high accuracy by the time LISA flies, could use this info to help identify the host galaxy

(Caveat: uncertainties from gravitational lensing reduce quality of standard candle)

Cosmology with LISA

5/121

5/321

mmmm


Improving science return by coordinating observations in EM & GW bands

Summary

Any additional info on source parameters from EM observations (most crucially, sky location) improves parameter extraction accuracy

Complementary info on source morphology from EM observations (disks, jets?) assists interpretation of GWs

GWs contain detailed info on source orientation (e.g., cos

Comparison of GW/EM arrival times provides info on speed of gravity

Combining luminosity distance (from GW) with red-shift info (from EM) provides valuable info on cosmological evolution

Direct imaging of BH horizon via radio interferometry ?

For Sgr A* (M=4106, D=8 kpc): ~ 0.02 mas not beyond reach!

maskpc1

1105

sun

8

DM

M

testing gr with lisa leor barack university of southampton

Documents