Transcript Transparencies - Rencontres de Moriond

Gravitational waves
Opening a window on
compact objects dynamics.
Background
Detection
Sources
Prospects
Virgo @ LAL:
M Barsuglia, M-A Bizouard, V Brisson, F Cavalier, A-C Clapson, M Davier, P Hello,
S Kreckelbergh, N Leroy, M Varvella-Arnaud.
General relativity predictions
Spacetime deformation with c velocity.
Derived from quadrupolar moment of mass distribution.
5
2
6
  
 R  c 
2
P  c a  RS   v 
Weak coupling with matter.
Observable effect on test masses.
(plane wave approximation)
Wave polarisation.
L
G
c5/G ~1053 W
L + DL
Time
Detection principle
• Distance fluctuation tracking.
• Highest sensitivity with large interferometers.
Amplitude h
DL(t )
h(t ) 
L
• Antenna pattern: partial sky coverage.
Laser
Detector
•Signal analysis keys
– Noise dominated data.
– Signal extraction capability sets detectability.
(match filter statistics)
– Limited a priori knowledge of waveform
characteristics.
•Template based search.
•Minimum a priori detection methods.
Instruments status
LIGO Best detector
sensitivity in each run
Virgo
GEO 0.6
km
LIGO twice 4 km
Virgo 3 km
(plus 2 km)
S1: Sept
2002
TAMA
0.3 km
S2: March 2003
S3: Jan. 2004
6 1021 / Hz
4 1023 / Hz
LIGO-G030548-02-E
Sources: binary system
• Close binary system kinetic momentum dissipation.
• Pure celestial mechanics case:
h(t) depends on
– Chirp mass M = m3/5M2/5.
df
set by M
dt
m
M1  M 2
M 1M 2
– Eccentricity.
– Inclination angle
(binary axis, line of sight).
– Distance from Earth.
– Coalescence time.
Sources: binary system II
• Event duration
– Detection frequency band.
– System parameters.
• Catastrophic evolution:
Last Stable Orbit followed by merger.
Modelisation results just arriving.
• Candidates
– NS-NS fGW @ LSO~103 Hz
– BH-BH fGW @ LSO~102 Hz
 M Sol 

f LSO  2.2 kHz 
 M1  M 2 
fGW  2  f rot
• Close binary waveform affected by
objects’ proper motion and EOS.
Sources: binary system III
1/ 2
 m 

h  4.11021
 M Sol 
1/ 3
1/ 6
 M   10 Mpc  100 Hz 

 


 M Sol   r  f 
• Event rate (accessible volume includes Virgo Cluster)
Source
Galactic rate
(y-1)
Detection rate
(y-1)
NS-NS
~2×10-5
5x10-3 to 0.3
BH-BH
below 10-5
below 10-1
(BH-NS)
• Few direct observations to support population estimates.
Sources: core collapse
Favored case: compact object formation.
GW emission efficiency
related to
collapse asymmetry.
Realistic waveforms
from numerical relativity
(role of EOS).
SN collapse (Zwerger et al 1997)
Sources: core collapse II
Supernova to neutron star


DE
h  2.7 1023  3 GW 2 
 10  M solc 
2
1/ 2
 1 kHz   10 kpc 

 

f
r


 
• Numerical simulations convergence
Need integration of micro-physics.
f ~ 200-103 Hz , h ~ 10-22 @ 20 kpc
Burst duration < 0.1 s
• Galactic range: rate 10-2 y-1.
• Event rate 1 y-1 when reaching Virgo Cluster.
Excited compact objects
• Damping of initial departure from axi-symmetry.
(e.g. following coalescence)
• Dynamical instabilities
(Rotating liquid drop model)
• Quasi Normal Modes
– Unique Black hole de-excitation mechanism.
– Many varieties
(fundamental, pressure, rotation, gravity, spacetime)
– Mostly kHz range.
– Efficient spin-down / spin-up stalling.
2
 f
  10 kpc  a 
h ~ 6 1026  rot  
 6 
500
Hz
r

 
 10 
Quasi-periodic sources
Candidate: isolated neutron stars
• Large Galactic population.
• Mechanism for quasi-static deformation from axi-symmetry
(strong misaligned magnetic field).
GW emission
• Quasi-periodic.
• Continuous.
Most likely source type.
Crab pulsar
h ~ 10-25 @ ~ 60 Hz
Required integration > 1 year.
Multi-messenger : Supernovae
• Electromagnetic burst
– Comparison to large reference population.
– Long duration.
• Neutrino flare
– Delay of arrival / rebound.
– Constraints on neutrino mass.
• Gravitational wave
– Core dynamics at collapse & proto-NS.
– Not delayed by evolution of outer layers.
Multi-messenger : NS binary
• Expected GW detection of (terminal) spiraling stage.
=> Reconstruction of orbital parameters.
• Additional observations.
– Merger:
• GW (detectability issue)
• Neutrino burst ?
• EM counterpart ?
(possible GRB source)
– De-excitation:
• GW : Core object.
• EM : Envelop afterglow ?
Other candidates?
Any compact relativistic dynamics…
• Counterpart to observed GRB
– From current models:
• Merging => short GRB.
• Collapse => long GRB. (with neutrino flare?)
– But cosmological distances.
• Low GW energy sources
– Jet / infall
– Disk dynamics (link to micro-Quasar?)
– Accretion on compact object (e.g. LMXB models)
Prospects: network analysis
Single detection lacks:
● Confirmation.
● Waveform deconvolution.
● Sky localization.
Worldwide GW network analysis:
● Improved reconstruction.
● Complete sky coverage. (Square degree resolution)
Coincidence with other messengers
• Improve detection reliability.
• Source localization.
Prospects II
• Improve sensitivity and observable volume
– E.g. LIGO II
– Revised event rates (detection range x 10).
– Additional sources: compact objects modes.
• Low frequency band: LISA
– Other sources
Super-massive BH coalescence, early binary.
– Stochastic background.
• Theoretical / simulation work
– All-physics source models.
– New emission mechanisms.
– Inversion problem (signal to source physics)
Conclusion
• Polyvalent GW detectors on-line now.
• Sensitivities still too low for reasonable event
rates.
• Astrophysical interest of candidate sources.
• Many uncertainties remain in models.
• Complementary views of complex phenomena:
delicate connection.
Miscellaneous
Best sources are compact and relativistic
Order of magnitude approach:
(given a source of
mass M, size R, period T, asymmetry a)
© J. Weber (1974)
Which gives for a gravitational emission :
Introducing…
… we have:
•The Schwarzchild radius Rs = 2GM/c2
• A characteristic velocity v
Huge luminosity when
• R  Rs
•vc
•a1
Q  a M R2
  a M R2 / T 3
Q
2
4
PG a M R
c
T
2
5
5
6
2
6
  
 R  c 
2
c

a  RS   v 
P
G
No beaming effect
Except minimum along symmetry axis.
GW : Orders of magnitude
Source
Distance
Steel bar 5x105 kg
1m
2x10-34
10-29
H bomb 1Mton
asymmetry 10%
10 km
2x10-39
10-11
Supernova 10 M
a ~ 3%
10 Mpc
10-21
1044
Black hole binary
Coalescence 2x1 M
10 Mpc
10-20
1050
 = 2 m, L = 20 m, 5 rot./s
h
P (W)
Signal analysis:
instrument sensitivity
Order of magnitude for h: less than 10-21
Such precision is unreachable, but not sensitivity.
Ax( )  lim T1
T 
Autocorrelation of stream x(t) :
T /2
 dt x(t)x(t)
T / 2
Power Spectral Density : Sx( f ) = FT of Ax(t)
If x(t) is a noise, its PSD gives the contribution
of each frequency to the noise.
 Precision :

The sensitivity of a measure for a given signal
defines the signal to noise ratio r :

~
2
~
h( f )  t ( f ) *

df

Sh ( f )

h : measure
t : signal
2


0
S( f
x
) df
Detection principle
Mirrors as test masses
L
GW changes optical path.
● Light power changes on
photodiode.
●
P
Instrument limitations :
● seismic noise
● thermal noise
● electronic noise
● shot noise
Pdet 
P  1  C cos(D ) 
in
2
hmin 
1
L P
Detection principle
End mirror M22
Limiting factor: photon shot noise.
Table-top experiment :
hMin  10-17 Hz-1/2
Fabry-Perot 2
Virgo :
hMin  10-23 Hz-1/2
Input mirror M21
Recycling mirror Mrc
Fabry-Perot 1
Laser
Beam splitter Mbs
Input mirror M11
Photo-detector
End mirror M12
Noise identification
Seismic noise
Thermal noise


Resonances
Shot noise
VIRGO
Simulation results
Coalescence of NS binary
With unequal masses.
Density levels,
velocity vector field.
(Shibata & al 2003)
Simulation results
Supernova collapse.
Density levels ,
velocity vector
field.
(Shibata & al 2005)
ITF network
Simple signal combination
• Separate detection.
• A posteriori source direction estimation.
Angular resolution limits
• Signal strength & duration.
• Inter-instruments distance.
• Sampling rate.
Warning: very optimistic plot!
Prospects
II
References
Misner et al 1979
Thorne K.S. 1995
Cutler C. 2002
Kokkotas K. D. 1999
New K. 2003
Shibata M. et al, 2003, 2005
Zwerger et al, 1997
Arnaud N. et al 2002
Jaranowski P. et al 1998
Nutzman P. et al 2004
Kim C. et al 2004