Прецизионные измерения гравитационных возмущений оптическими интерферометрами с большой базой

В.Н.Руденко (ГАИШ МГУ, Москва)

«Прецизионная физика и фундаментальные физические константы» ИТФ им.А.Ф.Иоффе, С.Петербург, 6-10 дек.2010 г.

Contents

1.Introduction

2.Setup construction 3.Objectives for observation 4.Recent results 5.Cold damping spring.

6.Advanced instrument at SQL

Global network of Detectors

Coherent Analysis: why?

-Sensitivity increase GEO 600 VIRGO Auriga Explorer determination from time of flight differences -Polarizations measurement -Test of GW Theory and GW Physical properties Astrophysical targets - Far Universe expansion rate Measurement -GW energy density in the Universe -Knowledge of Universe at times close to Planck’s time

Ligo interferometrs

Hanford 4km+2km

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 light in the large interferometer

2005-2009

First meaninful results (upper limits)

2015

Start upgraded machines first

Gravitational Waves

(GW) Gravitational waves give fundamental informations on the Universe. The four fundamental interactions coupling constants are: Strong



s =1 E.M. Weak e 2 =1/137 G F M 2 =10 -5 Gravitational GM 2 =10 -39

Some consequences of G smallness:

1)In stellar collapses Neutrinos undergo ~10 3 interactions before leaving the collapsing star,

GW<<1

.

2)After Big-Bang , electromagnetic waves decouple from hot matter after 13000 years, neutrinos after 1s, GW only after

Planck’s Time (10

-43

s) . 3) It is extremely difficult to detect them.

Detection of GW

Let’s consider two freely falling particles A and B, their separation ξ α =(x A -x B ) α satisfies the geodesic deviation equation:

d

2  

d

 2  1 2  

TT

   Riemann Force

F

  1 2

M

 

TT

  

X A ξ α X B

Consequently the receiver is a device measuring space time curvature i.e. the relative acceleration of two freely falling masses or their relative displacement.

Effect of Riemann Force Effect of 2 Polarizations L



L



L

~

L h

 10  22 h

+

h x

INTERFEROMETRIC DETECTORS

Large L High sensitivity Very Large Bandwidth 10-10000 Hz Mirrors Beam Splitter L A L B Signal



L =L A -L B Laser Displacement sensitivity can reach ~10 -19 -10 -20 measuring



L/L~10 -22 L A and L B m, then, for should be km long.

Astrophysical sources, expected amplitudes

GW- luminosity:

L

0 

c

5

G

 3 .

63  10 59

erg

/ sec

L



G

45

c

5    (

D

) 2  (

GM c

5

R

) 5

L

0 ~ (

r g R

) 5

L

0 only relativistic stars are effective radiators GW amplitude estimate for NS frequency:  

c

/

r g f

~ 150 

Hz h

~ 10  22

Hz

 1 / 2 ~ 10 ..

kHz h



r g

/

R

~ 0 .

1

h



r

g

~

R

10  18

r

g

r

 

Galaxy

   

g x

/ 

x

~ 10  16  sec  2

Hz

 1 / 2 ~ 10  7

Etv



Hz

 1 / 2 

gravity



gradient

~ 10  21 

Virgo

~ 10  23 

z

~ 1000

Virgo GW DETECTORS SENSITIVITY TAMA 300 GEO600 AURIGA, NAUTILUS, EXPLORER LIGO

Frequency Range: (50 – 1500) Hz

Blind All Sky Searching

Sources: - compact binary systems evolution (inspiral, merging, ring down) - supernova collapse events - continuous GW radiation (Pulsars) - stochastic GW background - Triggered Search ( Astro-gravity associations)

• •

Bursts

Classical sources: supernovae

–

Waveform poorly known

–

Several events/year in the Virgo cluster

• Possibly detectable only within our Galaxy

Generally, whatever can cause short ( < 1s ) GW impulses

–

Include exotic things (strings) or classical things (NS, BH ringdowns)

GW emitted 15

•

Coalescing Binaries

Source: coalescence of compact binary stars (BNS, BBH, NS/BH)

–

Waveform accurately modeled in the first and last phase

• Allows matched filtering – –

Less known in the “merger” phase

• Interesting physics here, for instance for BNS

Rate very uncertain

• A few events/year could be accessible to the LSC-Virgo network chirp 16

•

Pulsars

Distorted NS, emitting “lines” of GW radiation

–

Things greatly complicated by the Doppler effect

• Contrary to intuition, by the far the most computing intensive

search

– –

Thousands of known potential sources in our Galaxy

• Most probably below detection threshold

Many more yet unknown NS could generate a detectable signal

17

Cosmological Stochastic Background

•

Potential access to very early Universe

Relic gravitons CMBR Relic neutrinos 18

LIGO Scientific Runs (2000 – 2007) S1 – (08-09) 2000 y. ( noise 100 times projected level) S2 , S3 - during 2003 y (bad seismic isolation) S4 - (02-03) 2005 y ( duty cycle 70%, but selected 15,5 days data !) joint operation of 3 interferometers S5 - (06. 2006 - 10.2007) main results

Basic searching algorithms

Non modeled Bursts

outputs of two GW detectors: vectors

a

,

b

total energy : E =

a

2  2 2  normalized and integrated at the it is reduced to variables: Burst’s Excess Power:

E a

~

i

( /

i

 2 , 

E b

~

i E

 

C thr

Burst’s Cross Power: ( 

a

/

b

 / 

a b

( /

i

 2 , 

R



R

0

S.Klimenko, GWDAW14, January 26, 2010, Rome, LIGO-G1000033-v8 Results of the all-sky search for gravitational wave burst signals are presented for the first joint LIGO (S5) and Virgo VSR1 runs in 2006-2007.

The analysis has been performed with three different search algorithms in a wide frequency band between 50-6000 Hz.

No plausible GW candidates have been identified.

As a result, a limit on the rate of burst GW signals results from the first S5 year) has been established: (combined with the LIGO less than 2 events per year at 90% confidence level with sensitivity in the range 6-20 × 10 −22 Hz −1/2 This rate limit is increased by more than an order of magnitude compared to the previous LIGO runs.

What we known about SBGW from BBN bound ?

 gw =(1/  c )d  gw /dlog(f) h 0  gw  gw =  d log(f) [d  gw /dlog(f)] , h 0 =0.73(3) • from the balance of H and Γ at nucleosynthesis, ( H 2 =(8 π G/3) ρ) • is a bound on the total energy density, integrated over all frequencies.

f min ≈ 10 -10 Hz fixed by the horizon size at BBN • N ν = effective number of neutrino species, parametrizes any extra energy contribution • in the SM, N ν ~ (4.4 – 3.046) (due to residual interaction ν with e± QED effects). •So in order of magnitude at time of NS there were no more GWs than photons • it can be translated into a bound on the integrand 

f

5    gw < 6.9 10 -6

Results S4 , S5 , [ last run S6 (04.09 – 09.10)]

Unmodeled bursts

: upper limit → < 0.15 day -1 , h rss < 10 -20 Hz – ½

Inspiral Bursts

: upper limit → Event Rate: R R = (Number of events/ year. galaxy) 1 event per 20-300 years for NS binary for d H ~ 60 Mpc 1 event per 20-2000 years for binary ~ 5 M 0 1 event per 3 – 30 years for binary ~ 10 M 0

Pulsars

: f ~ 150 Hz , h ~ 10 -25 , ε < 10 -5

Stochastic background

: f ~(50 – 100) Hz, Ω < 6.5 10^{-5}

Существенные результаты LIGO

1. Новый

(значимый)

верхний предел на ГВ-сигнал от гамма-всплесков.

Во время серии S5 имело место событие: GRB 070201 – короткий г-всплеск (< 2 сек), положение источника отождествлено с М31 (~770 кпс) (reg. Integral, Messenger, Swift) fl.~10^{-5}erg/cm^{2}. В окне 180 сек. вокруг t arv искали сопровождающий ГВ-импульс.

С вероятностью ~95% ГВ сигнал не обнаружен. Предел на его интенсивность в модели NS, BH – “binary coalescence” оценен как E < 4.4 10^{-4} M 0 c 2 f~150 Hz

( теор. pасчет для ВС NS допускает E ~10^{-2} !)

(1M 0

2.

Перекрытие «предела замедления» на ГВ излучение пульсаров PSR BO531+21, PSR JO534-22, Crab Neb.

( ν~30 Hz, dν/dt~-3 10^{-10} Hz/s ) Теор. оценка по “spin-down rate” даёт h gw ~ 1.4 10^{-24}. Наблюдения S5, 3 мес.(~200 дн.) на частоте ν ~ 60 Hz дали h gw <3.4 10^{-25} или для степени несферичности: ε < 1.8 10^{-4}

3.

Перекрытие предела стохастического ГВ-фона по нуклеоситезу в ранней Вселенной

теория нуклеосинтеза дает ограничение на интегральную (

по частоте

) плотность ГВ фона из предположения, что гравитонов было не больше, чем фотонов; это даёт при равномерной спектральной плотности ГВ фона  gw ~ 9.7 10^{-6}. Экспериментально за время наблюдения ~ 200 дней на детекторах H1, L1 получена оценка  gw ~ 6.9 10^{-6} с достоверностью 95%

Cold Spring Damping of Thermal Noise in the LIGO setup

New Journal of Physics 11 (2009) 073032,

B Abbott

1

et.al. (LSC)

Observation of quantum effects such as

ground state cooling

,

quantum jumps

,

optical squeezing

, and

entanglement

that involve

macroscopic mechanical systems

are the subject of intense experimental effort.

The first step toward engineering a non-classical state of a mechanical oscillator is to cool it, minimizing the thermal occupation number of the mode. Any mechanical coupling to the environment admits thermal noise that randomly drives the system’s motion, as dictated by the fluctuation –dissipation theorem

, but ‘cold’ frictionless forces, such as optical or electronic feedback

, can suppress this motion, hence cooling the oscillator.

Thermal standard: Quantum standard:



x



kT m

 2 (   

r

) T  0 , Q  , (H  0) 

x



kT m

 2 

Q

  

r



x SQL



h m



m

~ 5 .

10  10 ..

kg

,...

  18 

cm

2  .

150 .

rad

/ sec

LIGO displacement sensitivity:

~ 2 .

10  16

cm

S5 scientific run



f

 150 .

Hz

..

 ~ 10  2 sec .

Quantum behaviour of macroscopic test body (?)

V.B.Braginskii. Physics Uspekhi, v.48, 595, 2005 a pendulum in gravity field, mode of acoustical resonator etc. can demonstrate quantum features under the following requirement:



E

 

kT

2  

r



kT



Q

  

instead of usual condition

kT

  

Dodonov V.V., Manko V.I., Rudenko V.N., Quantum Electronics, v.7 (№10), p.2124, 1980

«Quantum properties of macroscopic resonator with a high quality factor» -a) classical calculation mean values and a system evolution corresponds to quantum calculation with the accuracy ~ O(1/n) -b) transition probability requires only the quantum calculation; -c) observation of «energy steps» requires unrealistic measurement accuracy (Q ~ 10 18 )

n



kT

 

Realistic objective is a preparation of macroscopic system (oscillator) in the ground energetic state, i.e. with n ~ 1.

«procedure of super cooling»

in expectation of

«macroscopic quantum effects»

LIGO’s Hanford Observatory. The detector shown comprises a Michelson interferometer with a 4 km long Fabry –Perot cavity of finesse 220 placed in each arm to increase the sensitivity of the detector. Each mirror of the interferometer has mass

M

= 10.8 kg, and is suspended from a vibration isolated platform on a fine wire to form a pendulum with frequency 0.74 Hz, to shield it from external forces To minimize the effects of laser shot noise, the interferometer operates with high power levels; approximately 400W of laser power of wavelength 1064 nm is incident on the beam splitter, resulting in over 15kW of laser power circulating in each arm cavity. The present detectors are sensitive to changes in relative mirror displacements of about 10 −18 m in a 100 Hz band centered around 150 Hz (figure 2). Differential arm cavity motion, which is the degree of freedom excited by a passing gravitational wave, and hence also the most sensitive to mirror displacements. This mode corresponds to the differential motion of the centers of mass of the four mirrors,

x

c = (

x

1 −

x

2)−(

x

3 −

x

4), and has a reduced mass of

M

r = 2.7 kg.

GW интерферометр как «квадрупольный осциллятор, управляемый холодной электронно-оптической жесткостью (пружиной)»

координата ц.масс Х C = (Х2 – Х1) – (Х3 – Х4) , приведенная масса М r ~ 2.7

kg наблюдаемый сигнал Х S = X C – X N (тепловой шум зеркала + шум импульса фотонов) динамика 

M r

[  2 

j



p

( 1 /

Q

)  

p

2 

K

(  ) ]

X c M r



F N



K

(  )

X N K

(  )   2

eff M r



j



eff

эл.-опт. пружина 

eff

, 

eff

 

p

, 

p



M r

[  2 

j



eff

  2

eff

]

X c



F N



K

(  )

X N

при

K

(  )

X N



F N

осциллятор управляется электронно-оптической жесткостью

F N

 0 ,...

X C



K

(  )

M r

 2

X S T eff



M r

 2

eff



X

2

rms k B

Результаты измерений на интерферометре Н1

N eff



kT eff

 

eff



eff T eff

 140 

Гц

 1 .

4  0 .

2  

K N eff

 234  35 Advanced LIGO (2015) – планирует снижение эффективного шумового уровня в 20 – 30 раз. Это позволит вплотную приблизиться к реализации макроскопического осциллятора с флуктуациями энергии вблизи низшего энергетического состояния, т.е. эффективность искусственного охлаждения достигнет квантового предела.

Классические измерительные методы перестанут работать, потребуется практическое развитие методов т.н.«квантовых не возмущающих измерений».

GW-experiment: News

Fig. 1. Advanced Virgo sensitivity curve compared with Virgo and LIGO design and current bar sensitivity. Violin modes are not displayed for clarity