Parameter estimation and cosmology with gravitational waves - PowerPoint PPT Presentation

. Parameter estimation and cosmology with gravitational waves Archisman Ghosh International Centre for Theoretical Sciences Chennai Mathematical Institute 2015 Mar 03 With contributions from: Walter Del Pozzo, Ajith Parameswaran Abhirup Ghosh, Siddharth Mohite T A T A I N S T I T U T E O F F U N D A M E N T A L R E S E A R C H �����������������������������������������������

. . Detection of gravitational waves round the corner! – first data from Adv-LIGO upcoming from the O1 runs . . . – first detections expected soon after. GW observations ⇒ physics / astrophysics. Estimation of parameters is a crucial step in getting any physics output from gravitational-wave observations. [Background: LIGO Hanford Observatory] 1 of 35

. Science with GW observations ✛ ✘ Gravitational-wave observations ✚ ✙ ⇋ ⇋ ⇋ Waveform Cosmological Stellar evolution, Triggered searches, Test of GR Rates, horizon modelling parameters Population / rates masses, spin, e.o.s. ✛ ✘ ✛ ✘ ✛ ✘ Physics Cosmology Astronomy ✚ ✙ ✚ ✙ ✚ ✙ 2 of 35

. Parameter estimation as a crucial step ♣ Astrophysics: “Where in the sky?” “What masses / angular momenta?” ♣ Cosmology: “What redshifts and distances?” ♣ Fundamental physics: “E.o.s. of NS?”, “Parameters of non-GR theories?” “Consistency between observed parameters?” 3 of 35

. This talk ♣ Basics Detectors, sensitivity, sources ♣ Parameter estimation Parameter estimation as a challenge Procedure, algorithms employed, some results ♣ Cosmology Cosmology motivation Prospects of cosmology with GW ♣ Future directions 4 of 35

. Basics

. Detectors Detector network and baselines ( ms ) [Source: http://www.gw-indigo.org, Pic: B. S. Sathyaprakash] LIGO detectors in Hanford, Livingston (U.S.A) and Virgo in Cascina (Italy). KAGRA (Japan) and LIGO India . . . 5 of 35

. Sensitivity 10 − 21 ♣ Ad-LIGO has 10 times more sen- AdvLIGO ZDHP Noise strain amplitude (Hz − 1 / 2 ) sitivity than initial LIGO; one can 10 − 22 survey 1000 times the volume of the sky. 10 − 23 Amplitude detectors! 10 − 24 10 1 10 2 10 3 Frequency (Hz) 10 1 1.4 Horizon distance (Gpc) Cosmological red shift 10 0 0.2 10 − 1 [ https://www.advancedligo.mit.edu ] 0.0 10 0 10 1 10 2 10 3 M z [ M � ]

. Sources Compact binary coalescences (CBCs): Mergers of binary systems of NS / BH ⇒ well-modelled “chirp” waveform. “Chirp” NS-NS: Ringdown Expected rates ∼ 40 (0 . 4 – 400) yr − 1 , BH-QNM Horizon distance ∼ 0 . 4 Gpc . Inspiral Merger Post-Newtonian Numerical Relativity NS-BH: Expected rates ∼ 20 (0 . 2 – 300) yr − 1 , [Hannam et al (2009)] Horizon distance ∼ 1 Gpc . 10 1 1.4 NS-NS: Horizon distance (Gpc) Cosmological red shift Expected rates ∼ 40 (0 . 4 – 1000) yr − 1 , Horizon distance: ∼ 8 Gpc . 10 0 0.2 [Abadie et al (2010)] Bala’s talk! 10 − 1 0.0 7 of 35 10 0 10 1 10 2 10 3 M z [ M � ]

. Parameter estimation

. What parameters to estimate? { m 1 , m 2 ,� s 1 ,� s 2 } : Intrinsic parameters. { α, δ, z , d L , ι, ψ, φ c , t c } : Extrinsic parameters. The masses are completely degenerate with the redshift and it is only possible to measure the redshifted mass, m z ≡ m (1 + z ). ( m z 1 m z 2 ) 3 / 5 redshifted chirp mass, M z ≡ phase 2 ) 1 / 5 , very accurately ⇒ ( m z 1 + m z mass ratio, q ≡ m 2 m 1 , to a reasonable degree ⇒ the combination, M z cos 2 ι amplitude , very accurately ⇒ d L amplitude d L to a reasonable degree ⇒ 8 of 35

. The challenge! {M , q ,� s 1 ,� s 2 , α, δ, d L , ι, ψ, φ c , t c } 9 parameters for non-spinning binaries. 15 parameters including spin. Additional parameters (tidal, etc. terms) for NS. Likelihood multimodal [Plot by: Siddharth Mohite] 9 of 35

. Bayesian Inference Bayesian parameter estimation: stochastic technique to sample the posterior probability on the parameters given the data and a prior. Ω | data , I ) = Prior ( � Ω | I ) L (data | � Ω , I ) Posterior ( � Evidence (data , I ) � Ω = {M , q ,� s 1 ,� s 2 , α, δ, d L , ι, ψ, φ c , t c } L (data | � Ω , I ) = P (data | signal( � data = signal( � Ω) , I ) Ω) + noise, n � �� − 1 � data − signal( � Ω) | data − signal( � = exp Ω) 2 10 − 21 AdvLIGO ZDHP ) Noise strain amplitude (Hz − 10 − 22 S ( f ) || n ( f ) || 2 � � n | n � ≡ df S 2 ( f ) 10 − 23 Gaussian noise 10 − 24 10 of 35 10 1 10 2 10 3 Frequency (Hz)

. Algorithms and software Documented in: Veitch et al (2014) The parameter estimation algorithms are implemented LIGO Algorithms Library (LAL) as LALInference . ♣ LALInferenceMCMC : Parallel tempering ♣ LALInferenceNest : Nested sampling ♣ LALInferenceBambi : Multinest ♣ pyPE : Ensemble samplers, etc. [Siddharth Mohite, AG, Walter Del Pozzo] . 11 of 35

. Estimated parameters . . . 3 detectors: HLV 5 detectors: HLVIJ M z ( M ⊙ ) 12 of 35

. Parameter estimation of high-mass BBH AG, Walter Del Pozzo, P. Ajith ♣ Uniform distribution of m 1 , 2 ∈ [20 , 50] M ⊙ . ♣ z � 0 . 5. ♣ SNR ≥ 8. LALInference ⇒ Usual (redshifted) quantities, {M z , q , m z 1 , 2 , d L } Compute: Physical (non-redshifted) quantities, {M , m 1 , 2 } NR fit formulae to compute mass and spin of final BH: � �� � η − 0 . 4333 η 2 − 0 . 4392 η 3 � M f = M 1 + 8 / 9 − 1 , √ a f 12 η − 3 . 87 η 2 + 4 . 028 η 3 . = M f [Pan et al (2011)] 13 of 35

. NR FIT Distribution of 1 − σ errors REDSHIFTED Measurement of parameters 5 det 3 det 3 det (spin) 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 ∆ m z 1 , 2 / m z ∆ M z f / M z ∆ M z / M z ∆ M z / M z 1 , 2 f Distribution of 1 − σ errors PHYSICAL 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 ∆ m 1 , 2 / m 1 , 2 ∆ M / M ∆ M / M ∆ M f / M f Distribution of 1 − σ errors UNAFFECTED 0 10 20 30 40 50 60 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 0 . 00 0 . 02 0 . 04 0 . 06 0 . 08 0 . 10 sky loc. (sq. deg.) ∆ d L / d L ∆ η / η ∆ a f / a f AG, Walter Del Pozzo, P. Ajith ( in preparation ) 14 of 35

. MASSES Parameter 3 detector 5 detector Component masses m 1 , 2 13.9% 12.9% Total mass M 11.4% 7.5% Chirp mass M 11.0% 6.5% Final mass M f 11.7% 7.6% Mass ratio q 31.6% 29.2% Symmetric mass ratio η 3.7% 3.1% Final spin a f / M f 3.1% 2.6% Luminosity distance d L 47.1% 30.0% Sky location Ω (sq. deg.) 12.50 2.39 COMPONENT FINAL SPIN

. Cosmology

. Measuring cosmological parameters Which cosmological parameters? Sriram’s talk. H 0 : Hubble parameter Ω m : Matter fraction Ω K : Curvature fraction Ω Λ : Dark energy fraction Ω r + Ω m + Ω k + Ω Λ = 1 ≈ 0 � � a ˙ a ¨ − Ω r − 1 a = H 2 a ≡ H 0 ; 2Ω m + Ω Λ 0 Expansion and acceleration of the universe. Measurable is redshift ⇒ Redshift-distance relation: � z dz ′ � Ω m (1 + z ) 3 + Ω K (1 + z ) 2 + Ω Λ d L = c (1 + z ) H ( z ′ ) , H ( z ) = H 0 15 of 35

. Standard candles ♣ Sources of known luminosity – like Supernovae of Type Ia. . Sriram’s talk. [Perlmutter, Schmidt – Measuring Cosmology [Kim et al (1997)] with Supernovae (2003)] 16 of 35

. Necessity of new input . ♣ Calibration relies on multiple steps in the cosmic distance ladder and a large amount of systematics can creep in. ♣ There is a large variability in the light-curves of SNIa and their physics is not fully understood. 0.992 72 ♣ Even the Hubble parameter is 0.984 70 not measured to a great accuracy! 0.976 0.968 68 H 0 ♣ Tension between supernova and n s 0.960 66 Planck results! 0.952 Sriram’s talk. 0.944 ♣ An independent measurement 64 0.936 will be of prime significance. 0.26 0.30 0.34 0.38 Ω m [PLANCK Collaboration (2013)] 17 of 35

. Standard sirens ♣ Gravitational wave give direct access to the luminosity distance to the event without relying on any distance ladder. ♣ They can be used as “standard sirens” “Chirp” analogous to supernovae as standard Ringdown BH-QNM candles. Inspiral ♣ Unfortunately the redshift is totally de- Merger Post-Newtonian Numerical Relativity generate with mass and cannot be inde- [Hannam et al (2009)] pendently estimated. 18 of 35

. Cosmology ⇋ Redshift Use cosmology: distance → redshift ⇒ physical masses. Use redshift information from coincident electromagnetic event: redshift + distance ⇒ cosmology. Opens up the possibility of an independent measurement of the cosmological parameters with an entirely different systematics. 19 of 35

. NS mergers ⇔ Sh-GRBs ♣ A CBC involving a NS is believed to be associated with a Sh-GRB. Resmi’s talk. [http://www.astro.caltech.edu/ avishay] ♣ Redshift of the coincident e.m. event. [Nissanke et al (2010), Nissanke et al (2013)] 0.25 Measurement error in H 0 0.2 0.15 0.1 0.05 0 0 5 10 15 20 25 Number of GW−EM NS−NS mergers 20 of 35