Searches(for(Gravitaonal(Waves( with(ground7based ...Klimenko, September 19, SAMSI workshop, NC...

Klimenko, September 19, SAMSI workshop, NC 1 LIGO-G1200737 Credit: AEI, CCT, LSU

Searches for Gravita/onal Waves with ground-‐based Interferometers

Sergey Klimenko University of Florida for LSC Collaboration

Klimenko, September 19, SAMSI workshop, NC 2 LIGO-G1200737

Astrophysical Sources

Credit: Chandra X-ray Observatory

Casey Reed, Penn State

NS-NS

Credit: AEI, CCT, LSU

binary neutron stars

binary black holes pulsars

supernovae

gamma ray bursts

soft gamma repeaters

•  and other violent astrophysical phenomena in the Universe •  objec8ves of GW experiments: test of GR & GW astronomy


An8cipated Signals

•  “chirps” - compact binary coalescence Ø  neutron stars / black holes

•  “bursts” - Supernovae / GRBs/ BH mergers/SGRs/…. Ø  any relatively short GW transient (few minutes or less)

•  “periodic” - pulsars in our galaxy Ø  GWs from neutron stars (Doppler modulated)

•  “stochastic” - cosmological/astrophysical signals Ø  Early universe (like CMBR) and unresolved sources

use different data analysis and statistical methodologies


Detectors

�  Ini/al (1G) LIGO detectors were in opera/on for a decade Ø 6 data taking runs (~1.5 years of 2D live /me) Ø reached its design sensi/vity during the S5 run: 2005-‐2007

Virgo detector joined in May 2007 (VSR1 run) Ø run enhanced configura/on during the s6 run: 2009 – 2010 Ø decommissioned in October 2010

�  Initial LIGO data: GW strain ~ 16TB, AUX ~ 3PB

Livingston, LA (LLO)

L1: 4km x 4km

Hanford, WA (LHO) H1: 4km x 4km H2: 2km x 2km

Cacsina,Italy V1: 3km x 3km

GEO600, Germany G1: 600m x 600m


Sensi8vity of ini8al (1G) Interferometers

Hz1 102

4000)()( 23−×≈

Δ=

mfLfSstrain noise:

fermi 10~100)( 3−×Δ HzfL

150 Gm h~


Detector Antenna Sensi8vity

•  Detector response

•  Several detectors increase coverage of the sky and detection confidence

ξ = F+h+ +F×h×

L1

V1

×+ FF


Compact Binary Coalescence

LTC1rate∝

  The most efficient emiUers among expected GW sources up to 10 % of total mass à GWs

Well understood   accurate analy/cal (PN) and numerical (NR) GR models   NS-‐NS, NS-‐BH, BH-‐BH with total mass up to 500Mo are in

the sensi/ve band of ini/al detectors

inspiral: PN merger: NR ringdown


Detec8on horizon & Astrophysical rates

LIGO&Virgo rate limits

astrophysical predic/ons

horizon vs mass

PRD 85, 082002 (2012) PRD 83, 12005 (2011)

  intermediate mass compact binaries: 100<M<450Mo

  low/high mass compact binaries: M<100Mo


IMBH binaries •  Internediate Mass Black Holes – missing link between stellar mass BHs

(<100Mo) and supermassive BHs (>104 Mo) •  A single detec/on of a IMBH binary system would be first unambiguous

confirma/on of their existence. This alone is a major discovery.

100≲ M/Mo ≲450

PRD 85 (2012) 102004

Best Rate UL90% 0.13 Mpc-3 Myr-1

Average Rate UL90%

0.9 Mpc-3 Myr-1

Expected Astro Rates ~2 10-5 Mpc-3 Myr-1


advanced (2G) network

•  aLIGO (H,L), aVirgo(V) and KAGRA(j) are being constructed. •  plans for aLIGO-‐India (I) (approved by NSB)

Ø  part of aLIGO: LIGO provides instrument, India provides facility & personnel. •  x10 beUer sensi/vity than 1G

Ø  target detec/on of an/cipated NS-‐NS and possibly other sources afer 2015. Ø  extended network significantly enhances GW&mul/-‐messenger observa/ons

LIGO-‐L LCGT-‐J Virgo

LIGO-‐A

LIGO-‐H

Indigo

I,J,H,L,V – existing and planned

detector sites


Inverse Problem for GW signals

 arrival /me τ ExtTrig all-‐/me  arrival direc/on (θ,φ) ExtTrig all-‐sky  GW waveforms template unmodeled

ϕθ ,

τ2

τ1 τ3

DA scenarios: known unknown

X = [

f+f× ]

h+h×

"

#$$

%

&''+n[ ]

data = network x wave + noise

Data analysis ques/ons: 1.Detec/on: Is GW signal present in X? 2.Reconstruc/on: What can we learn about h from X?


Likelihood Method •  Likelihood ra8o (global fit to GW data)

•  Noise model: usually mul/variate Gaussian noise

•  signal model (defined by detector response)

•  find GW polariza8ons (h+,hx) at maximum of Λ •  find source sky loca8on by varia8on of Λ over θ and φ

•  Ambiguity due to a large number of free parameters

ξ [i]= h+[i]

F+ + h×[i]

F×, h+(Ω),h×(Ω), Ω− signal model

]exp[)0|( 1 TXXXp −Σ−∝

)0|()|(

XphXp

=Λ

Σ-noise covariance matrix

p(X | h)∝ exp[− X −ξ( )Σ−1 X −ξ( )T ]

Guersel&Tinto, 1998 Flannagan&Hughes, 1998 Finn, 2001 Klimenko et al. 2004, 2008 SuUon et al. 2009


Inspiral •  ξ is calculated from theore8cal

waveforms h+hx described by source parameters Ω

•  Parameter space Ω is constrained by the model

•  Sample Ω with templates (explicit template banks)

•  Find τ, θ, φ, Ω (thus ξ) from best matching template

•  Increase Ω by expanding models: spin, eccentricity, etc

•  more affected by possible discrepancy between models and nature

•  less affected by noise

Matched Filter

Burst •  Amplitudes h+[i], hx[i] are free source

parameters •  Parameter space is constrained by

signal dura8on and bandwidth •  Search through parameter space

analy8cally. •  Find τ, θ ,φ, ξ at maximum of L •  Decrease parameter space by adding

astrophysical constraints •  less affected by possible discrepancy

between models and nature •  more affected by noise

L = 2 lnΛ = 2X[i]⋅

ξ [i,h]( )

i∑ −

ξ [i,h]⋅

ξ [i,h]( )

i∑


Detec8on

  Data is non-‐sta8onary, non-‐gaussian and affected by ar8facts   Empirical background sample for es8ma8on of FA probability

Ø  constructed by 8me-‐shiding data à may be biased wrt true background Ø  need a massive background set (T observa8on x 106)

CQG 29 (2012) 155002

detec/on sta/s/c

FA ra

te

Sta/onary Gaussian noise

real noise


Detector Characteriza/on •  Along with the GW strain data LIGO records data from thousands

auxiliary monitors designed to capture environmental and instrumental disturbances Ø  Ini/al LIGO data: GW strain ~ 16TB, AUX ~ 3PB

•  First line of defense: extensive analysis of AUX and GW data to Ø  characterize detector noise and ar/facts (glitches) Ø  validate data (data quality) Ø  associate glitches with transients observed in GW data (veto analysis)

•  A mul/tude of the analysis and sta/s/cal methods Ø  Spectral density es/mators Ø  TF transforma/ons (STFT, wavelets, WDM, Hilbert-‐Huang, etc) Ø  Regression (Wiener-‐Kolmogorov, LPE & other filters) Ø  Mul/variate classifica/on, binary decision trees a lot of room for improvement


Veto analysis

H1 H2

H0:PEM-ISCT4_ACCZ

accelerometer

�  reject detected events IF they are associated with glitches. �  process TBs of AUX data �  characterize glitch sta/s/cs


coherent network analysis

•  Noise scaled network antenna patterns

•  Construct projec8ons P on f+fx plane Ø  e.g. unconstrained likelihood

ξ = [

f+,f× ]

h+h×

"

#$$

%

&''= F ⋅h

f+

f×

X

ξ u

N f+ =

F1+(θ,φ,ψ)S1

,..., FK+(θ,φ,ψ)SK

,

f× =

F1×(θ,φ,ψ)S1

,..., FK×(θ,φ,ψ)SK

network plane

L = XTPX


Network sta8s8cs

•  Detec8on sta8s8cs Ø  Likelihood (tot SNR):

Ø  coherent energy:

•  Rejec8on of glitches Ø  number of various sta8s8cs

based on residual (NULL) energy: χ2, coherent null, incoherent null, network correla8on coefficient, etc

cc = CN+ |C |

C = XTPX, Pii =0

L = XTPX

NEL −=

Wen & Shutz, 2004 Chatterji et al, PRD 74 082005 (2006) Klimenko et al, CQG 25, 114029(2008)

PRD 81 (2010) 102001

glitches injections


Detec8on Challenge

• Event has a “chirp” signature and very significant in CBC search Ø  Likely BH-‐NS system at 20-‐50 Mpc Ø  False alarm rate < 1/7000 years • Afer complete analysis the event was revealed to be a “blind injec/on”

http://www.ligo.org/news/blind-injection.php

• A candidate was iden/fied by online burst search in LIGO/Virgo data on September 16, 2010

Ø reconstructed within minutes afer data collected

Big Dog (sky location near Canis Major)


Source Reconstruc/on •  Reconstruc8on of sky coordinates

Ø  iden8fica8on of host galaxies, popula8on studies Ø  associa8on with other observa8ons (EM, ν)

à mul8-‐messenger astronomy •  Reconstruc8on of polariza8ons and waveforms

Ø  Iden8fica8on and classifica8on of sources Ø  Helps background rejec8on

•  Es8ma8on of source parameters Ø  test of GR Ø  selec8on and valida8on of source models

•  LIGO-‐India and KAGRA significantly simplify detec8on and improve source reconstruc8on


  for perfectly co-aligned detectors Α=0 – detect only one GW component

  Α - contribution to total network SNR from the second component

Network Alignment

A = | f× || f+ |

HL

IHLV

important for reconstruction of both GW polarizations and sky localization

HLV

PRD 83:102001,2011


• Median error angle in degrees (50% CL, SNRnet<30) for for reconstruc8on of ad-‐hoc burst signals

Sky Localiza8on 4 sites - IHLV

5 sites – IJHLV

3 sites – HLV

more spatially separated sites

à better sky localization


Mul/-‐messenger Astronomy

nearby galaxies

Images taken within 44 min afer the event and on subsequent nights by Zadko, SkyMapper, Swif, TAROT, ROTSE

probability skymap reconstructed with burst algorithm (cWB)

minutes afer the Big Dog event

Challenges: unambiguous associa/on of GW and other

messenger transients, low latency analysis (fast network, algorithms)

Capture source astrophysics with mul/ple messengers (EM,ν,GW) example: Big Dog event


Bayesian Coherent Analysis •  Parameter es8ma8on: X-‐data, H-‐model, θ-‐parameters

Ø  to get posterior PDF marginalize over a subset of θ

•  Model selec8on with odds ra8o •  evidence: •  hard for large θ (17 parameters for inspiral sources, could be more for burst sources) -‐ nested sampling

•  uncertain prior PDFs

Oij =p(Hi )p(H j)

p(X | Hi )p(X | H j)

p(X | H) = p(θ | H) ⋅p(X | H,

θ )∫ dθ

p(θ | X,H) = p(

θ | H) ⋅p(X | H,

θ )

p(X | H)Veitch&Vecchio, 2010 Van der Sluys et al, 2009 Skilling, 2004


Summary �  Ini/al GW interferometers

Ø  started to constrain source models (analysis of data con/nues) Ø  established conceptually new GW data analysis Ø  began integra/on of GW experiment and astronomy Ø  paved road for advanced (2G) detectors

• advanced GW interferometers Ø  target first detec/on of astrophysical GW signals Ø  LIGO-‐India and KAGRA will significantly enhance the network

• advanced data analysis Ø  challenges of confident detec/on and accurate reconstruc/on in

presence of non-‐sta/onary and non-‐Gaussian noise. Ø  about the same data volume, faster computers à can explore

promising DA & STAT methods which are prohibi/ve now Ø  demand for efficient&accurate STAT tools à beUer

communica/on between GW data analysts and experts

Searches(for(Gravitaonal(Waves( with(ground7based ...Klimenko, September 19, SAMSI workshop, NC...

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