gravitational waves · 2014-10-20 · therefore, all fields including the gravitational field,...
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IIT-K, 2014 Gravitational Waves
Gravitational Waves
Physics, Technology, Astronomy and Opportunities
Unnikrishnan. C. S. Tata Institute of Fundamental Research
Mumbai
[email protected] www.tifr.res.in/~filab
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IIT-K, 2014 Gravitational Waves
The Structure of Physics:
Laws of Motion
Laws of Fundamental Forces
Conservation Laws (Constraints)
Physical Understanding
Four Fundamental Interactions and several fundamental particles
Gravity, Electromagnetism, Weak interactions and sub-nuclear strong interactions.
/a F m=
2/F GMm r= −
Conservation of momentum. Energy etc…
and Principle of relativity
Electromagnetism Weak Interaction Strong Interaction
Gravity
Matter, Fields, Space and Time
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IIT-K, 2014 Gravitational Waves
Electric Field Magnetic Field
Charges and Currents are fundamental, fields are ‘theoretical’. Current Magnetic field
Electromagnetic waves need electric AND magnetic field for generation and propagation.
0 0, ...B EE B Maxwellt t
µ ε∂ ∂− = ∇× = ∇×∂ ∂
Unobservables in Physics Fields, Wavefunction, Space and Time…
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IIT-K, 2014 Gravitational Waves
GRAVITY, ITS FIELDS and THEIR WAVES
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IIT-K, 2014 Gravitational Waves
/a F m=
2/F GMm r= −2 2/ /ga GMm r m GM r= − = −
Independent of the mass of the falling body
/a F m=
2/F kQq r=2
2/emkQ qa kQq r mr m
= =
Gravity seems to be a special interaction
Inertia turns out to be identical to the gravitational charge – Equivalence Principle (physics of gravity identical to physics in accelerated frames)
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IIT-K, 2014 Gravitational Waves
Universality of Free-Fall
12 2 1310 / 10aa m saδδ − −< → <
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IIT-K, 2014 Gravitational Waves
g
So, gravitational field ‘g’ and acceleration ’-a=g’ seem equivalent
This is called the Equivalence Principle
This is the same as saying that in free-fall, there is no gravitational field
But it does not mean that in free-fall there is no gravity!
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IIT-K, 2014 Gravitational Waves
So, tidal deviations cannot be eliminated by free-fall (description in the General Theory of Relativity)
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IIT-K, 2014 Gravitational Waves
Torsion balance: Harmonic potential Ultra-sensitive
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IIT-K, 2014 Gravitational Waves
21/Flux density R− ∝(For 3D space)
What if space is higher dimensional at some tiny scales (micrometers or less) ?
Inverse-square law for ‘g’ will change!
1 mm 0.01 gm
0.3 mm 0.3 mg
8 25 10 /g cm s−≈ ×
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IIT-K, 2014 Gravitational Waves
TIFR Gravitation Laboratory Gauribidanur, Karnataka
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IIT-K, 2014 Gravitational Waves
‘g’ of Sun ~0.6 cm/s2
14 2( ) 10 /a earth moon cm sδ −− <
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IIT-K, 2014 Gravitational Waves
Dark matter
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3% of total estimated matter: So 97% is invisible, and NOT made of ANY known particle
So, we are not sure of gravity’s behaviour at very small scales and at very large scales.
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IIT-K, 2014 Gravitational Waves
Electric Field Magnetic Field
Current Magnetic field
Electromagnetic waves need electric AND magnetic field for generation and propagation.
0 0, ...B EE B Maxwellt t
µ ε∂ ∂− = ∇× = ∇×∂ ∂
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IIT-K, 2014 Gravitational Waves
What is an electromagnetic wave?
Q
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IIT-K, 2014 Gravitational Waves
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IIT-K, 2014 Gravitational Waves
Gamma rays and galaxies
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IIT-K, 2014 Gravitational Waves
Spectral view – multi-wavelength
UV
H-α
IR
Radio
X-ray
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IIT-K, 2014 Gravitational Waves
Spectral view – multi-wavelength
Crab Nebula
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IIT-K, 2014 Gravitational Waves
Multi-wavelength galaxy
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IIT-K, 2014 Gravitational Waves
Gravity and Electromagnetism
Both have ‘electric’ and ‘magnetic’ parts Charges and currents. Mass is the ‘charge’ of gravity and Spin is its ‘gravito-magnetic moment’
One important different between the two is that while electric and magnetic fields have no electric charge, gravitational field has gravitational charge!
With m=E/c2, all forms of energy is equivalent to mass, and hence generate gravity. Therefore, all fields including the gravitational field, which carry energy, also generate gravitational fields. This is one reason why the theory of gravity (The General Theory of Relativity) is complicated to work with.
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IIT-K, 2014 Gravitational Waves
Gravity and electromagnetism
Charges (static): Coulomb force – electric fields Currents (motion): Ampere’s force – magnetic fields
What about relativistic gravity?
We know static gravitational charge (mass/energy) generates g-field. Does moving and rotating masses generate a gravito-magnetic field?!
If so, then there is a possibility of gravitational waves…
Electromagnetic Waves
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IIT-K, 2014 Gravitational Waves
03
MBrµ
=
Gravito-magnetism A natural consequence of relativistic gravity, and yet, was not detected experimentally till recently.
2 3 2 3 2gGJ GI GMBc r c r c r
Ω= = → Ω
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IIT-K, 2014 Gravitational Waves
The real gravitational field near the earth
142 5 10 /GM rad s
c rω −≈ Ω ≈ ×
Gravity Probe – B (Stanford U.)
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IIT-K, 2014 Gravitational Waves
Physics of Gravitational Waves
What is an electromagnetic wave?
Q
So, can we expect gravitational waves from oscillating (accelerated) masses?
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IIT-K, 2014 Gravitational Waves
2sin
tdqr d E
Rcθ
= → =
ct
vt
22
2 2 2
and /
sin sin
tr
r
t
E vt at aR E q RE ct c c
q aR qrER c Rc
θ θ
= ≈ = =
= =
ct
tE
rE
Since area=R2, number of flux lines/area 1/R2 So, radial Electric field (flux/area) ~ 1/R2
What about the Transverse Electric field (radiation)?
Since, circumference of a great circle on the sphere increases only as R, transverse radiation field decrease as 1/R.
Radiation
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IIT-K, 2014 Gravitational Waves
0
0
Phase diff.
2
2
2 3
3
sin
sin cos
sin cos
gtGM rE k r
RcGM r r
Rc cGMr
c R
θ
θ ω θ
ω θ θ
= × ⋅
= ×
=
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IIT-K, 2014 Gravitational Waves
+
+
The force-field of gravitational waves
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IIT-K, 2014 Gravitational Waves
The relation between spin of the field and polarization of the force field
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IIT-K, 2014 Gravitational Waves
What is the physical effect of a passing gravitational wave?
Quadrupole Radiation formula 2 2 2
4 2 2Strain L G Mr G MvhL c R c R c
ω∆= ≈ ≈
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IIT-K, 2014 Gravitational Waves
Are we confident that Gravitational Waves exist, apart from the belief in the correctness of the theory?
Jl. Franklin Inst. 1937
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Binary Pulsar 1913+16 (Hulse-Taylor)
2 6 45
32GG
dE GE M rdt c
ω= ≈
83 10ct yrs≈ ×
2 3 12/GM a Gπω ν ρ≈ → ≈
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IIT-K, 2014 Gravitational Waves
Orbital decay and speeding up of the binary pulsar:
2 6 45
32GG
dE GE M rdt c
ω= ≈
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IIT-K, 2014 Gravitational Waves
Signal Strength at Earth for neutron star spiral in milky way: Distance: 10 kpc ~ 1020 meters
With M~1030 kg, v~3x107 m/s, 19Strain 10lhl
−∆= ≈
264 2
4Strain 10G Mvh Mvc R
−≈ ≈
70.1 (3 10 m/s) for neutron stars at 100 km2
Gmv c rr
≈ = × ≈
If the event happens in another galaxy, 100 Mpc ( 1024 m away), 23Strain 10h −≈
This small strain requires the measurement of <10-20 meters in a detector of size 1 km! (almost million times smaller than the atomic nucleus).
Is it a mad venture trying to make a ‘detector’?
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1710h −≈
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A modern cryogenic resonant mechanical detector
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IIT-K, 2014 Gravitational Waves
Much less than the size of the nucleus. This is the primary device for gravitational wave detection
Michelson Interferometer
When these waves reach earth, what can they do to free masses?
( )2 11 30
2 1922 2 8 20
6.7 10 3 10Strain 0.05 10 / !3 10 10
G Mvh m mc R c
−−⋅ × ⋅
≈ → <× ×
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IIT-K, 2014 Gravitational Waves
Signal 1/R, G/c2, Random source… <<
Thermal noise, Seismic Noise, Quantum Noise Tidal Noise, All instrument Noise, Any Noise one can think of…
> or ~ Lower Limits of all these noises allowed by Physics and today’s technology…
Signal 1/R, G/c2, Random source…
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IIT-K, 2014 Gravitational Waves
I
l∆
Signal in the interferometer
/I
Mean number of photons @ intensity I= N, /N P hν=
Change in the number of photons, NN φπ∆
∆ ≈
Noise minN N= ≈ ∆
19
9minmin
With 1 W of optical power, N=10 / ,
10
sNN N
π πφ −∆∆ ≈ = ≈
The general problem of ‘fringe splitting’ (centroid, locking…)
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IIT-K, 2014 Gravitational Waves
There is another equivalent way to talk about photon shot noise that explicitly brings out the basic feature of quantum mechanics involved.
The energy-time uncertainty relation E t∆ ∆ ≥
( ) /1 11
E t N
NN N
ω φ ω
φ φ
∆ ∆ = ∆ ∆ ≈
→ ∆ ∆ ≥ → ∆ ≈ =∆
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IIT-K, 2014 Gravitational Waves
Detection of gravitational waves requires the measurement of movements 10-17 to 10-20 meters in a detector of size 1 km.
19
8 14min min
With 1 W of optical power, N=10 / , and 10 ms (100 Hz),
10 10
s
L mNπφ φ λ− −∆ ≈ ≈ → ∆ = ∆ × ≈
1) Increase Laser Power 1610 10kW L m−→ ∆ ≈
2) Increase Length up to 4 km: Not much gain, though very important (1/R).
3) Fold optical path 1710 10n m−= →
Reaching there, but not comfortable yet!
STABLE Laser
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IIT-K, 2014 Gravitational Waves
Optimal length of the Interferometer arm:
8/ 3 10 /100 750 !4 4 4
g gopt
c m HzL kmλ ν ×
≈ ≈ ≈ =
This is the optimal distance the light should travel for maximal signal. In other words light should be in the interferometer for an optimal duration of about 750 km/c seconds or a quarter of the GW period of 10 ms or so. This is achieved by multiple bounces with average time equal to about quarter of the GW period such that 4 km x nB = 750 km. So, the number of bounces is about 200.
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IIT-K, 2014 Gravitational Waves
1) Folding Fabry-Perot Cavity
Improvements:
Finesse ~ n : 300 +
16 1910 , 4 10 3 10 with 300kW km m m F− −→ → × ≈
Detection of gravitational waves requires the measurement of movements 10-17 to 10-19 meters in a detector of size several km.
Intra-cavity power > 1 MW !
Radiation Pressure Noise and Thermal Lensing are problems
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Large Interferometer VIRGO at Pisa, Italy ( 3 km)
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IIT-K, 2014 Gravitational Waves LIGO-HO
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IIT-K, 2014 Gravitational Waves
2 3 12/GM a Gπω ν ρ≈ → ≈
2 2
4Strain L G MrhL c R
ω∆= ≈
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IIT-K, 2014 Gravitational Waves
But, every bit counts… because waves strength is 1/R
If sensitivity is increased by factor X, then the distance reach increases by X, and the number of astrophysical sources increases as X3! So, a factor of 10 in sensitivity means a factor of 1000 in number of possible detections.
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IIT-K, 2014 Gravitational Waves
Laser
Mode cleaner cavity
Power recycling
FP1
FP2
Signal recycling
Scheme of the Interferometric detector
3m scale prototype being built in TIFR – can measure <10-17 m
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Schematic of Advanced LIGO detectors
Large scale Ultra high Vacuum to be fabricated in India 10 mega -litres at nano-torr
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IIT-K, 2014 Gravitational Waves
Noise from Light:
1Photon Shot Noise: sni
hP
α=
minlN
λπλ φ∆ = ∆ =
( )/ /iN P hc λ=
( )Radiation Pressure Noise = / irad
hPF N hc
λλ
=
2Movement noise due to this force: /rp rad ih F m Pω β∝ =
2 2min
1 total sn rp SQLh h h h hLf mπ
= + → = =
Standard Quantum Limit
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IIT-K, 2014 Gravitational Waves
How can we hope to measure 10-19 m when the ground vibrations are like 1 micrometer?!
Immunity to vibrations needed by a factor of 1014!
Solution:
R
Frequency
1/f2/stage 1
fres
Ground vibrations: 10-6 m at 1 Hz, 10-9 m at 30 Hz
3 stages of springs and pendulum with each resonance at around 1 Hz Response down by a factor (103)3 = 109 at 30 Hz!
Possible to isolate from vibrations at the 10-20 m level at 100 Hz with 3-4 stages.
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IIT-K, 2014 Gravitational Waves
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GEO600
Absorption/Scattering ppm level
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IIT-K, 2014 Gravitational Waves
2 2min
1 total sn rp SQLh h h h hLf mπ
= + → = =
Frequency (Hz)
1 10 100 1000
h
10-23
10-22
10-21
10-20
10-19
10-18
10-17
Shot noise
RP
Seismic
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A sample of Vacuum chambers (LIGO):
2m
< 10-8 mbar, all 4x2 km
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Quantum Noise
x p∆ ∆ ≥
Light: Energy 2 2 2 2E B p qΕ ≈ + → + Harmonic Oscillator
Main features: Zero point energy, equally quantized energy levels interpreted as number states of photons
x
p Coherent state of light - laser
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x
p Coherent state of light - laser
θ∆
A∆
Amplitude and Phase quadratures Same Heisnberg uncertainty
Amplitude Noise: AN∆
Phase Noise: Nθ∆
Therefore, if we can somehow SQUEEZE the uncertainty is amplitude or phase, we can improve measurements by the squeezing factor.
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x
p
θ∆
A∆
x
p
θ∆
A∆
x p∆ ∆ ≥
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x
p
θ∆
A∆
If the injected ‘vacuum’ is squeezed by a factor 10, then the quantum noise is reduced by the same factor, and this is equivalent to increasing the laser power by a factor 100, because noise reduces only as square root of power!
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Roman Schnabel American Jl. Physics 2013
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Why do we need more detectors?
GW detectors are not telescopes. They cannot pin-point a source.
Timing (and only timing ) can fix a direction
c t d∆ =
Need at least 3
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The LIGO-India Concept
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IIT-K, 2014 Gravitational Waves Good angular resolution Base-lines to Japan comparable
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The LIGO-India Idea and Opportunity The LIGO-India proposal envisages the hardware meant for one of the LIGO detectors (out of 3) to be given to India and Indian scientists and engineers will build and operate the detector at a suitable site in India. Thus the LIGO-India detector will be the third vertex of the LIGO network, working like a large gravitational wave telescope. The Dept. of Atomic Energy, Dept. of Science and Technology and the Planning Commission have approved the Rs.1300 Crore (15 years) proposal. A cabinet approval is required and awaited. Site selection is in progress.
www.gw-indigo.org
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Science Gain from Strategic Geographical Relocation Source localization error
Original Plan 2 +1 LIGO USA+ Virgo
LIGO-India plan 1+1 LIGO USA+ Virgo+ LIGO-India
LIGO-Aus plan 1+1 LIGO USA+ Virgo+ LIGO-Aus
S. Fairhurst arXiv:1205.6611v2
Also Polarization B. S. Sathyaprakash et al., LIGO document T1200219-v1
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4 km
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Gravitational Waves: The Indian Initiative LIGO-India Project
The IndiGO Consortium
www.gw-indigo.org
There are great possibilities and bright future for gravitational wave-based astronomy… if we manage to detect gravitational waves with these detectors