Ricerca di onde gravitazionali

M.Bassan 12 Feb 2004

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....

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=gdxdx

• 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

€

gμν =gμνo +hμν

€

hμν <<1

Weak field approximation

The Einstein equation in vacuum becomes

€

hμν =0

Having solutions

Spacetime perturbations, propagatingin vacuum like waves, at the speed of light : gravitational waves

€

hμν t−x/c( )

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)

€

−dEdt

=2G3c3

r ̇ ̇ d

⎛ ⎝ ⎜

⎞ ⎠ ⎟

2

+G

45c5˙ ̇ ̇ Q ( )

2+...

€

r d =Σimi

r x i ⇒

r ̇ ̇ d ≡0

€

Qij = ρxi∫ x jd3x

Gravitational waves are strain in space propagating with the speed of light

€

hij(t)=2Grc4

˙ ̇ Q ij(t−r /c)

• General Relativity Gravitational Waves are ripples of space-time propagating with the speed of the light

hgg += 0

metric tensor

metric of flat space

Perturbation introduced by GW

(10-18÷ 10-20)

€

hμν <<1

€

∂2

∂x 2 + ∂2

∂y 2 + ∂2

∂z2 − 1c 2

∂2

∂t 2

⎛

⎝ ⎜

⎞

⎠ ⎟hμν = 0with

•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.

k

t

ikhi

kRk

td

id ξξξ2

2

21

002

2

∂

∂=−=

kξ

GRAVITATIONAL WAVE DETECTIONGRAVITATIONAL WAVE DETECTION

•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:

02

2=

dt

d xξ

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+= +

2

2

2

2

2

2

2

1

dt

hd

dt

hd

dt

d xzyy

ξξξ

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

−

=

+

+hh

hhh

x

x

ik

00

00

0000

0000

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−= +

2

2

2

2

2

2

2

1

dt

hd

dt

hd

dt

d zxyz

ξξξ

ξy ξ y

ξ z ξ z

GW

Effect on test body …….Effect on test body …….

hLL ≈Δ

 In any realistic wave is so weak that the oscillatory changes ξi are so small compared to the original distance ξi.

kik

i h21 ξ=ξ =>

PROPAGATION AND POLARIZATION OF G-WAVESThe 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-WAVESThe 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 ~ v/R:

€

L =2G5c5

˙ ̇ ̇ Q 2 ≈GM2v6

R2c5

€

Q ≈MR2 sinωt

M=1000 tons, steel rotor, f = 4 Hz L = 10-30 WEinstein: “ .. 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:

€

d2δl j

dt2=−Rjokol

k =12

∂2hjk

∂t2 lk

• 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

Beam splitter

Photo detector

L

L

€

h=ΔLL

€

˙ ̇ x (t)+τ−1˙ x (t)+ω02x(t) =

l2

˙ ̇ h (t)

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.

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.)

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

InformationInner detailed dynamics of supernovaSee NS and BH being formedNuclear physics at high density

Information Neutron star locations near the Earth Neutron star Physics Pulsar evolution

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 noisein 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 GWsWHAT WE KNOWPSR 1913+16 (Hulse & Taylor: strong indirect evidence

WHAT WE WANTConfirmation

• PolarizationWHAT WE KNOWScalar component constrained by PSR 1913+16 to 1% of the tensor part

WHAT WE WANTTest the six polarization states predicted by metric theories of gravity - test of GR

• Speed of GWs (needs two detectors)WHAT WE KNOWMass of graviton < 10-20 eV, from both PSR 1913+16 and validity of Newtonian gravity in solar system

WHAT WE WANTIf 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 physicsAfter 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 gw=c

WHAT WE THINKModels from standard inflaction, string cosmology, topological defects

WHAT WE WANTMeasure 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

Hz0.01 - 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

LIGO, VIRGO, GEO, TAMA

-- Inspiral of NS and BH binaries

- (1-1000 Mo)

•- Supernovae•- Pulsars

103 Hz 300 km Cryogenic resonant detectorsALLEGRO, AURIGA, EXPLORER, NAUTILUS, NIOBE

- NS and BH binary coalescence

- Supernovae

- ms pulsars

Comparison with electomagnetic waves:

Horizontal polarization Vertical polarization

Plus polarization Cross polarization

Einstein’s General Theory of Relativity (1915)

Gravitation can propagate as waves in space-time.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 L+ΔL

Quadrupole field lines

Detectors of Gravitational Waves

Laserinterferometer

laser

ResonantCylinder

ResonantBall

LhLΔ=

Sources of Gravitational WavesSupernova Explosion

Supernova 1987A

Sources of Gravitational Waves

Inspiralingphase

collapse

ringdown

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 Mc2

Sources of Gravitational WavesPulsars

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 aTIFF (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 !!!