Transcript Ricerca di onde gravitazionali

Ricerca di onde gravitazionali
 Generalita’
 Sorgenti di onde gravitazionali
 Rivelatori di o.g. (overview)
 Rivelatori (un po’ piu’ in dettaglio)
 Tecniche di rivelazione e tecnologie
 Uno sguardo al futuro: nuovi rivelatori....
M.Bassan
12 Feb 2004
1 Generalities
-Gravitational Waves (g.w.) in
General Relativity
- Features of a g.w.
Gravity is a manifestation of spacetime curvature induced by mass-energy
10 non linear equations in the unknown g
ds2=gdxdx
•
•
•
•
•
•
•
•
1915 Theory of G.R.
1916 Einstein predicts
gravitational waves (g.w.)
1960 Weber operates the first
detector
1970 Construction of
cryogenic detectors begins
1984 Taylor and Hulse find
the first indirect evidence of
g.w. (Nobel Prize 1993)
2003 First operation of large
interferometer
2004 year of discovery ???
2012 Lisa launch foreseen
Weak field approximation
o
g  g
 h
h 1
The Einstein equation in vacuum becomes
h  0
Having solutions
h t  x /c 
Spacetime perturbations, propagating
in vacuum like waves, at the speed
of light : gravitational waves
Gravitational waves are strain in space propagating with the speed of light
Main features
• 2 transversal polarization states
• Associated with massless, spin 2 particles
(gravitons)
• Emitted by time-varying quadrupole mass moment
no dipole radiation can exist (no negative mass)
2
2
dE 2G Ý
G Ý
Ý
Ý
Ý

 3 
d 

5 Q  ...


dt 3c
45c
Ý
Ý
d  i mi xi  d  0
Qij 
 x x d x
2G Ý
hij (t)  4 QÝij (t  r /c)
rc
3
i
j
GRAVITATIONAL WAVE DETECTION
• General Relativity Gravitational Waves are ripples of
space-time propagating with the speed of the light
0
g   g 
 h
metric
tensor
with
metric of
flat space
Perturbation
introduced by GW
 2
2
2
1 2 
 2  2  2  c 2 2 h  0
y
z
t 
x
•
h 1

(10-18÷ 10-20)
Equationof geodesic deviation shows how two geodesic lines, described by
two test bodies, deviate one respect to the other one by effect of gravitational
field.
2 hi

1
k k
  k Ri

0k 0 2
t2
d t2
d 2 i
k
•
A GW propagating along x axes in TT gauge produces a tiny relative
acceleration of the particles, proportional to their distance, in a plane
perpendicular to the gravitational wave direction:
d 2 x
0

0
hki  
0

0
0
0
0
0
0 h
0 hx
dt
0 

0 
hx 

 h 
y
0
2
1  y d 2 h
z d hx 
 

2
2

2
dt
dt
dt 2 
d 2 y
2
1  y d 2hx
z d h 
 

2
2

2
dt
dt
dt 2 

d 2 z
y
z
2
z
In any realistic wave is so weak that the oscillatory changes i are so small
compared to the original distance i.
1
  h ik  k
2
i
=>
Effect on test body …….
GW
L
h
L
PROPAGATION AND
POLARIZATION OF G-WAVES
The gravitational wave produce a time dependent strain h of
space. The gravitational wave detectors will measure this strain
directly. Deformation of a ring of test particles due to a
gravitational wave propagating in the direction normal to the
plane of the ring.
+ polarization
 polarization
PROPAGATION AND
POLARIZATION OF G-WAVES
The quadrupole force field of plus and cross polarization of a
gravitational wave.
• No laboratory equivalent of Hertz experiments for production of GWs
Luminosity due to a mass M and size R oscillating at frequency w~ v/R:
2 6
2G Ý
GM
v
2
Ý 
L  5 QÝ
2 5
5c
Rc
Q  MR sinw t
2
M=1000 tons, steel rotor, f = 4 Hz
L = 10-30 W
Einstein: “ .. a pratically vanishing value…”
Collapse to neutron star 1.4 Mo
L = 1052 W
h ~ W1/2d-1; source in the Galaxy h ~ 10-18 , in VIRGO cluster h ~ 10-21
Fairbank: “...a challenge for contemporary experimental physics..”
• GWs are detectable in principle
The equation for geodetic deviation is the basis for all experimental attempts to
detect GWs:
d 2l j
1  h jk k
k
2  R joko l 
2 l
dt
2 t
2
• GWs change (l) the distance (l) between freely-moving particles in empty
space.
They change the proper time taken by light to pass to and fro fixed points in
space
In a system of particles linked by non gravitational (ex.: elastic) forces, GWs
perform work and deposit energy in the system
L
h
L
L
L
Beam splitter
Photo detector
Ý(t)
Ý(t)  1xÝ(t)  w02x(t)  hÝ
xÝ
2
Gravitational radiation is a tool for astronomical observations
GWs can reveal features of their sources that cannot be learnt by
electromagnetic, cosmic rays or neutrino studies (Kip Thorne)
- GWs are emitted by coherent acceleration of large portion of matter
- GWs cannot be shielded and arrive to the detector in pristine condition
SUPERNOVAE.
If the collapse core is non-symmetrical,
the event can give off considerable
radiation in a millisecond timescale.
Information
Inner detailed dynamics of supernova
See NS and BH being formed
Nuclear physics at high density
SPINNING NEUTRON STARS.
Pulsars are rapidly spinning neutron
stars. If they have an irregular shape,
they give off a signal at constant
frequency (prec./Dpl.)
Information
Neutron star locations near the Earth
Neutron star Physics
Pulsar evolution
COALESCING BINARIES.
Two compact objects (NS or BH)
spiraling together from a binary orbit
give a chirp signal, whose shape
identifies the masses and the distance
Information
Masses of the objects
BH identification
Distance to the system
Hubble constant
Test of strong-field general relativity
STOCHASTIC BACKGROUND.
Random background, relic of the early
universe and depending on unknown
particle physics. It will look like noise
in any one detector, but two detectors
will be correlated.
Information
Confirmation of Big Bang, and inflation
Unique probe to the Planck epoch
Existence of cosmic strings
Gravitational radiation is a tool for fundamental physics
Possible fundamental observations:
• Detect GWs
WHAT WE KNOW
PSR 1913+16 (Hulse & Taylor: strong indirect evidence
WHAT WE WANT
Confirmation
• Polarization
WHAT WE KNOW
Scalar component constrained by PSR 1913+16 to 1% of the
tensor part
WHAT WE WANT
Test the six polarization states predicted by metric theories of
gravity - test of GR
• Speed of GWs (needs two detectors)
WHAT WE KNOW
Mass of graviton < 10-20 eV, from both PSR 1913+16 and validity of
Newtonian gravity in solar system
WHAT WE WANT
If both GW and EM waves come from the same source, we may compare
their speeds from the time delay (1/2 hour from Virgo Cluster for a
graviton of mass 10-20 eV)
• Early Cosmology - Planck-scale physics
After the Big Bang, photons decoupled after 13000 years, neutrinos after
1s, GWs after 10-43 s (Planck epoch).
Detecting a stochastic background of GWs is one of the most
fundamental observation possible. Detectors can measure fraction of the
closure energy density Wgw=/c
WHAT WE THINK
Models from standard inflaction, string cosmology, topological defects
WHAT WE WANT
Measure the energy density, spectrum and isotropy of the background
The search for gravitational waves
f

method
sources
10-16 Hz
109 ly
Anisotropy of CBR
- Primordial
10-9 Hz
10 ly
Timing of ms pulsars
- Primordial
- Cosmic strings
10-4 - 10-1
Hz
0.01 - 10
AU
Doppler Tracking of
spacecraft
Laser interferometers
in space
LISA
- Bynary stars
- Supermassive BH (103 -107 Mo)
formation, coalescence, inspiral
10 - 103 Hz
300 - 30000
km
Laser interferometers
on Earth
-- Inspiral of NS and BH binaries
- (1-1000 Mo)
•- Supernovae
•- Pulsars
LIGO, VIRGO, GEO,
TAMA
103 Hz
300 km
Cryogenic resonant
detectors
ALLEGRO, AURIGA,
EXPLORER, NAUTILUS,
NIOBE
- NS and BH binary coalescence
- Supernovae
- ms pulsars
Comparison with electomagnetic
waves:
Horizontal polarization
Plus polarization
Vertical polarization
Cross polarization
Einstein’s General Theory of
Relativity (1915)
Gravitation can propagate as waves in spacetime.
Actually what propagates is a ripple of space
time !
Space-time is stiff  waves have little
amplitude, even if they carry large energy
density
Hoe wordt de tijdruimte
vervormd door een gravitatie
golf ?
L
Quadrupole
field lines
L+L
Detectors of Gravitational Waves
Laser
interferometer
laser
L
h
L
Resonant
Cylinder
Resonant
Ball
Sources of Gravitational Waves
Supernova Explosion
Supernova 1987A
Sources of Gravitational Waves
Inspiraling
phase
collapse
ring
down
Sources of Gravitational Waves
Instabilities in Neutron Stars
Gravitational wave detectors
• Two different “families”:
– Massive elastic solids (cylinders or spheres)
– Michelson interferometers
• Both types are based on the mechanical coupling
between the g.w. and a test mass
• In both types the e.m. field is used as a motion
transducer
• A space interferometer (LISA) is planned to cover
the very low frequency band
Possible sources at f > 2 kHz
• Neutron stars in binary orbits: mergers, disruptions with
black holes.
• Formation of neutron stars: ringdown after initial burst.
• Neutron star vibrations, wide spectrum up to 10 kHz. Can
be excited by formation, merger or glitches.
• Stochastic background of primordial origin.
• Speculative possibilities:
– Black holes below 3 M
– Compact objects in dark matter
– Thermal spectrum at microwave frequencies, but only if inflation
did not happen!
Oscillation
frequencies of
neutron stars
• Figure from Kokkotas and
Andersson, gr-qc/0109054,
shows modes of non rotating
stars
• Modes could be excited by
violent events or by more
modest glitches
• Glitches occur often in
young pulsars, making Crab
a good target
• Glitch energy < 10-10 Mc2
Sources of Gravitational Waves
Pulsars
Very strong magnetic field
(109 Tesla)
+
Fast rotation
=
acceleration of rotation
 emission of radio, light
waves
and gravitational waves
f=10-100 Hz
The Binary Pulsar PSR 1913+16
(Hulse and Taylor’s pulsar)
• Radio pulse every T=59 ms : a pulsar rotating 17 times/s
• T varies slightly with time: T(t) with a period of 7.75 hrs
•=> Binary orbit (Doppler effect)
• From the study of T(t) derive:
• Mass of the two stars (1.4 Mo),
•inclination of orbit, eccentricity,
•orbital speed (75-300 km/s),
•semiaxis (3 Gm).
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
The Binary Pulsar PSR 1913+16 (2)
• Tight orbit => strong gravity => General Relativistic effects:
•periastron advance (4.2o /yr)
• Loss of energy for emission of gravitational waves ,
orbit shrinks (3.1 mm/orbit).
Collapse in 300 Myrs !!!