Прецизионные измерения гравитационных возмущенийоптическими 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

VIRGO

L LIGO

GEO 600

H1H2 LIGO

Coherent Analysis: why?

-Sensitivity increase

-Source direction 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

TAMA 300

Nautilus Auriga

Explorer

Ligo interferometrsHanford 4km+2km

P .R apagnani - G WDAW14 - R ome J anuary 2010 8

Virgo – Pisa:One 3km arm interferometer

LIGO – Hanford:One 4km arm interferometerOne 2km arm interferometer

LIGO – Livingston:One 4km arm interferometer

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 E.M. Weak Gravitational s=1 e2=1/137 GFM2=10-5 GM2=10-39

Some consequences of G smallness:

1)In stellar collapses Neutrinos undergo ~103interactions 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 (10-43s) .

3) It is extremely difficult to detect them.

Detection of GW

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

ξα XA

XB

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 2 Polarizations

h+ hx

TTh

d

d 2

12

2

TThMF

2

1

Riemann Force

Effect of Riemann Force

2210hLL ~

L

L

INTERFEROMETRIC DETECTORSLarge L High sensitivity

Very Large Bandwidth 10-10000 Hz

Laser

LA

LB

 

MirrorsBeam Splitter     

SignalL =LA-LB

 

Displacement sensitivity can reach ~10-19-10-20 m, then, for measuring L/L~10-22 LA and LB should be km long.

Astrophysical sources, expected amplitudes

sec/1063.3 595

0 ergG

cL

05

05

5

2

5)(~)(

45)( L

R

rL

Rc

GM

c

GL gD

only relativistic stars are effective radiators

GW- luminosity:

GW amplitude estimate for NS 1.0~/ Rrh g

1000~10~

10~

10~

23

21

18

z

Virgo

Galaxy

r

r

R

rh gg

kHzrc g ..10~/frequency:

2/12210~

150~

Hzh

Hzf

gradientgravityHzEtv

Hzxg x

2/17

2/1216

10~

sec10~/

TAMA 300

AURIGA, NAUTILUS, EXPLORER

GEO600

LIGO

Virgo

GW DETECTORS SENSITIVITY

Frequency Range: (50 – 1500) HzBlind 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)

15

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

16

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

17

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

18

Cosmological Stochastic Background• Potential access to very early Universe

Relic gravitons Relic neutrinos

CMBR

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

Non modeled Bursts outputs of two GW detectors: vectors a , b

total energy : E =

normalized and integrated at the it is reduced to variables:

Burst’s Excess Power:

Burst’s Cross Power:

bababa 2222

,)/(~ 2ii

a aE ,)/(~ 2ii

b bE

thrCE

bababa baEER /~)/( 2/10RR

Basic searching algorithms

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 (combined with the LIGO results from the first S5 year) has been established:

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.

S.Klimenko, GWDAW14, January 26, 2010, Rome, LIGO-G1000033-v8

• Nν = effective number of neutrino species, parametrizes any extra energy contribution

• in the SM, Nν ~ (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

What we known about SBGW from BBN bound ?

gw=(1/c)dgw/dlog(f) h0 gw , h0=0.73(3)

 gw = d log(f) [dgw/dlog(f)]

• from the balance of H and Γ at nucleosynthesis, (H2 =(8πG/3) ρ)

• is a bound on the total energy density, integrated over all frequencies.

fmin ≈10-10 Hz fixed by the horizon size at BBN

f

f gw Nfdfhmin

)3(106.5)(log)( 60

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

1 event per 20-300 years for NS binary

for dH ~ 60 Mpc 1 event per 20-2000 years for binary ~ 5 M0

1 event per 3 – 30 years for binary ~ 10 M0

Pulsars : f ~ 150 Hz , h ~ 10-25 , ε < 10-5

R = (Number of events/ year. galaxy)

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 tarv 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} M0c2 (1M0<m1<3M0 , 3M0<m2<40M0)

f~150 Hz (теор. pасчет для ВС NS допускает E ~10^{-2} !)

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 hgw ~ 1.4 10^{-24}. Наблюдения S5, 3 мес.(~200 дн.)

на частоте ν ~ 60 Hz дали hgw<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

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.

New Journal of Physics 11 (2009) 073032, B Abbott1 et.al. (LSC)

2m

kTx )( r

Qm

kTx

2

r

m

hxSQL

sec/.150.2,.....10 radkgm

cm1810.5~

cm1610.2~

.sec10~...150 2 Hzf

T0 , Q , (H0)

Quantum standard:

LIGO displacement sensitivity:

S5 scientific run

Thermal standard:

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:

Q

kTkTEr

2instead 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 ~ 1018 )

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»

kT

n

LIGO’s Hanford Observatory. The detector shown comprises aMichelson 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 Hzband 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 mirrordisplacements. This mode corresponds to the differential motion of the centers of mass of the four mirrors, xc = (x1 −x2)−(x3 −x4), and has a reduced mass of Mr = 2.7 kg.

GW- интерферометр как «квадрупольный осциллятор, управляемый холодной электронно-оптической жесткостью

(пружиной)»

координата ц.масс ХC = (Х2 – Х1) – (Х3 – Х4) , приведенная масса Мr ~ 2.7 kg

наблюдаемый сигнал ХS = XC – XN (тепловой шум зеркала + шум импульса фотонов)

NNcr

ppr XKFXM

KQjM )(]

)()/1([ 22

динамика

effeff

r

jM

K

2)(эл.-опт. пружина ppeffeff ,,

NNceffeffr XKFXjM )(][ 22

NN FXK )(при осциллятор управляется электронно-оптической жесткостью

Sr

CN XM

KXF

2

)(,...0

B

rmseffreff k

XMT

22

Результаты измерений на интерферометре Н1

eff

effeff

kTN

35234

2.04.1

140

eff

eff

eff

N

KT

Гц

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