Sanjeev Dhurandhar Colloqm - Indian Institute of Astrophysics

S. V. DHURANDHAR 

IUCAA 

PUNE 

12 th February 2008 Indian Institute of Astrophysics Colloquium

GRAVITATIONAL WAVES 

• Space-time warpage in the fabric of spacetime 

travels with the speed of light 

Decay in the orbit of the 

binary pulsar PSR 1913+16 

Nobel Prize to 

Hulse & Taylor 1993 

Gravitational Waves EXIST ! 


GRAVITATIONAL WAVE ASTRONOMY 

• Enormous differences between 

GW and EM 

- Produced by bulk motions of matter 

- Compact objects: 

Blackholes, neutron stars 

Binary Inspiral of NS, BH 

PROBES OF THE UNIVERSE 

GW ASTRONOMY !! 


Effect on a ring of test particles 

Metric: 

∇ 2 − 1 c 2 

∂ 

∂ t 2 

h ik = 0 

General Wave: 

h ik = h t − z/c e ¿ 

ik h ¿ 

t − z /c e ik 


Quadrupole formula : 

But h is awfully small ! 

h ~ 4G c 4 

K . E . ns 

R 

~ 

 

E kin−ns 

0 . 1 M c 2 

R 

100 Mpc −1 10 −21 

Change in arm-length: 

L ~ h L 


Interferometer 

Concept 

• Laser used to measure 

relative lengths of two 

orthogonal arms 

…causing the 

interference pattern 

to change at the 

photodiode 

Arms in LIGO are 4km 

Measure difference in length to 

one part in 10 21 or 10 -18 meters 

Suspended 

Masses 


LIGO Louisiana 4 km armlength (US) 


CURRENT DETECTOR STATUS 

• Several large scale laser interferometric detectors 

constructed: armlength of 300 m to 4 km 

- LIGO, VIRGO, GEO, TAMA, AIGO 

- LIGO, TAMA, GEO : Already taking data, S5 run of 

LIGO successfully completed: 2005 – 2007 (2 years) 

- VIRGO: Engineering runs, Science runs 

• Space based detector LISA – 5 million km 

- Launch 


TAMA Japan 

300m 

Interferometric Detectors 

LIGO Louisiana 

4000m 

Virgo Italy 

3000m 

AIGO Australia 

future 

GEO Germany 

600m 

LIGO Washington 

2000m & 4000m 


International Network of GW Interferometers 

1. Detection confidence 2. Source direction 3. Polarisation info 

LIGO-LHO: 2km, 4km 

GEO: 0.6km 

VIRGO: 3km 

TAMA: 0.3km 

LIGO-LLO: 4km 

AIGO: ()km 


Technology pushed to the limits 

Vacuum better than 10 -6 torr 

1.22 m aperture x 4000 m arms 

~9.4 x 10 3 m 3 (each site) 

~10 9 Joule of stored energy 

10 kg test masses 

0.99999 @ λ =1.024 µm 

5m 

10 W @ λ =1.024 µm 

~10 20 γ /s to split fringe to 10 -10 

Seismic isolation of 

δν/ν~10 -10 

ground motion by > 10 -6 


LIGO beam tube (January 1998 ) 


The noise floor 

• Seismic noise at low 

frequencies 

• Thermal noise at mid 

frequencies 

• Shot noise at high 

frequencies – quantum 

nature of light 

• Technical issues: alignment, 

electronics limit us to reach 

design sensitivities 


Experimental noise curves: Initial LIGO from S1 – S5 

*http://www.ligocaltech.edu/~lazz/distribution/LSC_Data 


Astrophysical Sources 

• Compact binary inspiral: “chirps” 

– NS-NS waveforms are well described 

– BH-BH need better waveforms 

– search technique: matched templates 

• Supernovae / GRBs: “bursts” 

– burst signals in coincidence with signals in 

electromagnetic radiation 

– prompt alarm (~ one hour) with neutrino detectors 

• Pulsars in our galaxy: “periodic” 

– search for observed neutron stars (frequency, doppler 

shift) 

– all sky search (computing challenge) 

• Cosmological Signals “stochastic background” 


Source Strengths 

Binary inspiral: 

h ~ 2.5 × 10 −23 [ 

M 

]5/3 

M sun 

f a 

[ 

r 

] −1[ 

100 Mpc 100 Hz 

]2/3 

Periodic: 

h ~ 1. 9 × 10 −25 [ 

I 

] 10 45 gm. cm 2 

[ 

f 

] 2 [ 500 Hz 

r 

] −1[ 

ε 

] 

10 kpc 10 −5 

Stochastic background: 

~ 

h 

f ~ 10 −26 [ 

f 

] −3/ 2 

10 Hz 

[ GW 

f 

10 −12 

]1/ 2 

Data Analysis ! 


Inspiraling compact binaries 

GW 

• Broadband source best for interferometric detectors 

• Waveform is well modeled by PN approximations 

• Numerical Relativity: great advances - merger 


Matched filtering the inspiraling binary signal 

cτ =∫ x t q t τ dt 

~ 

~ 

q f = h f 

S h 

f 


Parameter space: 1 – 30 solar masses 

Sathya & SVD (91) 

SVD & Sathya (94) 

Owen (96) 

LIGO I psd: 

Minimal match: 0 .97 

f a 

= 40 Hz 

Number of templates: ~ 10 4 

Online speed: ~ 3 GFlops 

eraFlops for MACHOS, Spins … 


Event rate, data analysis 

• Event rate (from inspiral SNR): 

~ 1 event / yr initial LIGO (20 Mpc), 10 events/day for 

advanced (350 Mpc) 

- Rate computed from survey volume, beaming fraction, 

luminosity function, short orbital period etc 

• Efficient data analysis techniques (IUCAA): 

Hierarchical search Sengupta, Dhurandhar & Lazzarini (2003) 

Interpolated search Mitra, Dhurandhar & Finn (2005) 

Coherent network search: Pai, Dhurandhar & Bose (2002), 

Indo-Japanese: Mukhopadhyay, SVD, Tagoshi, Kanda (2007) 


Breakthrough in Numerical Relativity 

Numerical Relativity 

solves 

• merger waveform 

• 3.5% of total 

restmass energy as 

compared to 1.5 % in 

inspiral waveform! 

Work in progress on stitching together waveforms 

India has the right talent/aptitude for NR 


Setting upper limits 

• Although at this early stage no detection can be announced we 

can place upper limits for example on the inspiral event rate 

For example for S2 data: 

P ρ ρ ¿ = 1 − e −ε R T 

R 90 50 y −1 MWEG −1 

A rate > than above means there is more than 90% probability 

that one inspiral event will be observed with SNR > highest SNR 

observed in the data. 

Much better event rate from S3, S4, S5 data! 


Astrophysical Results 

• Chirps 

– S2: 355 hours of coincident (2X, 3X) interferometer operation 

– Sensitive to D ~ 2 Mpc 

– R 90% < 50 events/year/MWEG (1 Msun < M1,2 < 3 Msun) 

• Bursts 

– S1: For h > 10 -18 , R90% < 2/day (limited by observation time) 

– Minimum h ~ 2 x 10 -19 

– S2: 50% detection efficiency h ~ 10 -20 

• Periodic, or “CW” 

– S2: (LIGO and GEO600) interferometers -- Targeted 28 known pulsars 

– h < 1.7 x 10 -24 (J1910-5959D) 

– e < 4.5 x 10 -6 (J2124-3358) 

– Crab limit on h within 30X of spindown rate, if spindown were due to GW emission 

• Stochastic background 

– S3: 240 hours of cross-correlation measurements for H-L, H-H 

– Sensitivity estimated to be Ω GW 

< 5 x 10 -4 50 Hz < f < 250 Hz 


The LIGO Scientific Collaboration 

500 scientists at 42 institutions 

27 US & 15 international 


Stochastic GW background: Directed search 

S.Mitra, SVD, T. Souradeep, A. Lazzarini, V. Mandic, S. Bose, S. 

Ballmer (2007) - Ligo Science Collaboration 

• Produced by unresolved gravitational wave sources 

– Blackhole mergers, r-modes, LMXBs, … 

Waveforms not well modelled 

• Statistic: : Cross-correlation between two detectors 

with a directed optimal filter Q 

¿ 

dt ∬ dt ' dt ``s rSub { size 8{1} } ` \( t' \) `s rSub { size 8{2} } } ` \( t Q 

¿ 

S = ∫¿ 

¿ 

; t , t ' − t \) } {} 


The Kernel or Point Spread Function 

LIGO detectors 

Point Source on the equator – Image not a point ! 


De-convolving the GW sky-map 

The integral equation must be inverted ! 

D = B .P + n, D = D ( W ) 

D : data 

B : known beam matrix 

P : GW power distribution over sky pixels 

i 

i 

n : noise 

Solution: 

ML estimator: 

T - 1 - 1 T -1 

P = ( B N B ) B N .D 


Solution for a broadened point source 

Source 4 pixels: 

Dirty: 

Cleaned: 


Solution for a `galactic distribution’ 

Source: 

Dirty : 

Cleaned: 


Initial 

Advanced 

• From Initial LIGO Advanced LIGO 

Next Generation LIGO (QND) 

• From 14 Mpc (NN inspiral) 200 Mpc and beyond 

• From Upper Limits Searches Detections 

• From Generic Waveforms Specified Waveforms 

• From Single Detectors Global Networks 


LISA 

• A Collaborative ESA / NASA Mission to observe lowfrequency 

gravitational waves 

• Cluster of 3 S/C in heliocentric orbit at 1 AU 

• Equilateral triangle with 5 Million km arm-length 

• Trailing the earth by 20° 

• S/C contain lasers and free-flying test masses 

• Equivalent to a Michelson interferometer 


LISA: Space based detector for detecting low 

frequency GW 


LISA sensitivity curve 

• Confusion noise – problem not faced by ground-based detectors 

• Low frequency long duration sources 


Space v/s Terrestrial 


Fundamental Physics: 

LISA SCIENCE 

• Tests of strong field GR by mergers of comparable mass BHs: 

- Area theorem – before/after measurements of M and J 

- Cosmic Censorship – is a/M > 1 after merger 

- Stellar mass BH falling into a massive BH – few per year upto 

1 Gpc (Sigurdson and Rees, Phinney) - EMRIs 

High SNR - Test no-hair theorem ~ detailed waveforms with 

10 5 cycles in the last year 10 M falling into 10 6 M BH 

• Observe GW bursts from cosmic strings or other exotic sources 


Αstrophysics: 

• Detect BH mergers in the 

range 10 5 - 10 7 M 

event rate ~ 15/yr 

• Study compact WD binaries 

- obtain mass spectrum … 

LISA SCIENCE contd 

• Detect hundreds of EMRIs – event rate ~ few hundred/yr 

- obtain spectrum of masses, spins 

• Discover unexpected sources, dark matter components 


LISA data analysis at IUCAA 

Time-delay Interferometry 

• Cancellation of laser frequency noise and other systematic 

noises – optical bench motion, clock jitter, etc, 

SVD, Vinet, Nayak, Pai (2002 – 2003) 

Polynomial vectors in delay operators: 

Module of syzygies – space of data combinations cancelling 

laser frequency noise – Algebraic geometry 

• Current Work: General relativistic model needed to account 

for all effects 

Sagnac effect, changing arm-lengths, gravitational red-shift etc 

SVD, Vinet, Chauvineau (2006 - 2008) LISA simulator 


FUTURE DIRECTIONS 

• Global Network of detectors LIGO, VIRGO, TAMA, GEO, 

AIGO 

• Sensitivity upgrades: Amplitude & bandwidth 

Advanced detectors: 2008 + 

Enhanced systems: lasers, seismic isolation, test-masses 

Event rate improvement: ~ 10 4 

• LISA will open the low frequency window: 10 -4 Hz – 1 Hz 

Many detections! High SNR 

Hopefully detections should begin soon with 

ground- based detectors

Sanjeev Dhurandhar Colloqm - Indian Institute of Astrophysics

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