Credit: SXS Lensing Vivien Raymond A new beginning for transient Max Planck Institute for Gravitational-wave astrophysics Gravitational Physics CaJAGWR, Caltech, November 8th, 2016 LIGO-G1600305
Gravitational-wave astrophysics Fundamentally new way to learn about the Universe: • Is General Relativity in the correct theory of Gravity ? • What happens when matter is compressed to nuclear densities ? • What are the properties of the population(s) of compact objects ? • Is the mechanism that generates gamma-ray bursts a compact binary coalescence ? 2
The Gravitational Wave Spectrum Quantum fluctuations in the early universe Binary Supermassive Black Holes in the galactic nuclei Sources Compact Binary Coalescences Compact objects Rotating captured by Neutron Stars, Supermassive Black Supernovae Holes age of the wave period years hours sec ms universe log(frequency) -16 -14 -12 -10 -8 -6 -4 -2 0 +2 Space Ground Cosmic microwave Pulsar Timing Detectors Interferometers Interferometers background polarization [Inspired from http://science.gsfc.nasa.gov/663/research/] 3
100 years ago: General Relativity and Gravitational Waves Credit: C. Rodriguez • Before Einstein : Newtonian gravity 4
100 years ago: General Relativity and Gravitational Waves Credit: C. Rodriguez • 1915: Einstein’s General Relativity, gravitation due to spacetime curvature 5
100 years ago: General Relativity and Gravitational Waves Credit: C. Rodriguez • 1916: Albert Einstein predicts the existence of gravitational waves 6
100 years ago: General Relativity and Gravitational Waves • The wave travels at the speed of light , is transverse, and has two polarisations: � � y y � � � � x x z z • Weak coupling with matter • High-precision length measurement: Laser Interferometers • Dense masses moving fast : merging compact objects 7
~30 years ago: Laser Interferometer Gravitational-wave Observatory • Two sites 10 light-milliseconds apart • Measurement of space-time deformations with Δ L/L: ~10 -21 ! 8 LIGO Hanford and Livingston. Credit: LIGO
Inspiral Ring-down Merger GW150914: September 14, 2015 at 09:50:45 UTC 9 Credit: SXS Collaboration/Canadian Institute for Theoretical Astrophysics/SciNet
Overview (or how can we study transient GWs?) • Introduction • Compact Binary Coalescence • LIGO • Extracting astrophysics • Waveform models • Parameter Estimation • Beyond aLIGO first observing run: • Astrophysics with multiple events 10 [LIGO Scientific Collaboration ]
Compact Binary Coalescence • Intrinsic parameters: primary ˆ L and secondary masses and ~ S 1 spins (and eccentricity) ~ S 2 ˆ N H1 10 ms light • Extrinsic : time, sky-position , travel time distance, orientation , reference phase a) L1 Credit: LIGO 11
LIGO measurement technique • Very complex Test H1 Mass b) L1 instrument 10 -21 (control loops) Strain noise (Hz -1/2 ) 10 ms light travel time • Model of the H1 4 km 10 -22 noise L1 10 -23 Test 20 100 Mass Frequency (Hz) Power Beam 4 km Recycling Splitter 20 W 100 kW Circulating Power Laser Source Test Test Mass Mass Signal Recycling Photodetector 12 [LIGO-Virgo Collaboration, 2016]
Parameter Inference: GW150914 observation • How do we extract the scientific content ? 13
Gravitational waveform models • 2 models of the signal as a proxy for systematic errors: • Double-aligned-spin model ( SEOBNRv2_ROM, [Taracchini, et al., 2014; Pürrer, 2014]) • Single-precessing-spin model ( IMRPhenomPv2, [Hannam et al. Phys. 2014]) 14
Gravitational waveform models • 2 models of the signal as a proxy for systematic errors: • Double-precessing-spin model ( SEOBNRv3, [Pan et al., 2014; Babak et al., 2016]) • Single-precessing-spin model ( IMRPhenomPv2, [Hannam et al. Phys. 2014]) 15
Masses from the inspiral and ringdown 5 � 3 / 5 ( m 1 m 2 ) 3 / 5 ( m 1 + m 2 ) 1 / 5 ' c 3 • Chirp mass: • Total mass: 96 π − 8 / 3 f − 11 / 3 ˙ M = f , G ringdown • Mass ratio: q = m 1 m 2 16
ˆ L ~ Effects of spins S 1 ~ S 2 • 2 spin vectors • Magnitude: orbital hang-up • Mis-alignment: precession and modulations 17
ˆ L ~ S 1 Effects of spins • 2 spin vectors ~ S 2 • Magnitude: orbital hang-up • Mis-alignment: precession and modulations 18
Parameter Estimation • We want the posterior probability of parameters , given ~ � the data . With Bayes' theorem: ~ x x, M ) = p ( ~ x | ~ � | M ) p ( ~ � , M ) p ( ~ � | ~ p ( ~ x | M ) • Fit a model to the data ( noise and signal models) • Build a likelihood function • Specify prior knowledge • Numerically estimate the resulting distribution ( sampling algorithms) SPINSpiral [van der Sluys, Raymond , et al. 2008] , LALInference [Veitch, Raymond , et al., 2015] 19
Parameter Estimation • We want the posterior probability of parameters , given ~ � the data . With Bayes' theorem: ~ x x, M ) = p ( ~ x | ~ � | M ) p ( ~ � , M ) p ( ~ � | ~ p ( ~ x | M ) • Fit a model to the data ( noise and signal models) • Build a likelihood function • Specify prior knowledge • Numerically estimate the resulting distribution ( sampling algorithms) SPINSpiral [van der Sluys, Raymond , et al. 2008] , LALInference [Veitch, Raymond , et al., 2015] 20
Parameter Estimation • We want the posterior probability of parameters , given ~ � the data . With Bayes' theorem: ~ x x, M ) = p ( ~ x | ~ � | M ) p ( ~ � , M ) p ( ~ � | ~ p ( ~ x | M ) • Fit a model to the data ( noise and signal models) • Build a likelihood function • Specify prior knowledge • Numerically estimate the resulting distribution ( sampling algorithms) SPINSpiral [van der Sluys, Raymond , et al. 2008] , LALInference [Veitch, Raymond , et al., 2015] 21
Likelihood • How close is the remainder to the mean ? • Assumptions: gaussianity and stationarity 22
Parameter Estimation • We want the posterior probability of parameters , given ~ � the data . With Bayes' theorem: ~ x x, M ) = p ( ~ x | ~ � | M ) p ( ~ � , M ) p ( ~ � | ~ p ( ~ x | M ) • Fit a model to the data ( noise and signal models) • Build a likelihood function • Specify prior knowledge • Numerically estimate the resulting distribution ( sampling algorithms) SPINSpiral [van der Sluys, Raymond , et al. 2008] , LALInference [Veitch, Raymond , et al., 2015] 23
Parameter Estimation • We want the posterior probability of parameters , given ~ � the data . With Bayes' theorem: ~ x x, M ) = p ( ~ x | ~ � | M ) p ( ~ � , M ) p ( ~ � | ~ p ( ~ x | M ) • Fit a model to the data ( noise and signal models) • Build a likelihood function • Specify prior knowledge • Numerically estimate the resulting distribution (efficient sampling algorithms) [Raymond, et al. 2010] SPINSpiral [van der Sluys, Raymond , et al. 2008] , LALInference [Veitch, Raymond , et al., 2015] 24
25 25
Markov-Chain Monte Carlo • High dimensional parameter space • Slow waveform computation E ffi cient sampling critical (especially with precession ) [ Raymond , et al. 2010] 26
Gravitational-wave observations in the first observing run (O1) 27 [LIGO-Virgo Collaboration, 2016]
GW150914: masses • 2 models as a proxy for systematic errors: • Double-precessing-spin model ( SEOBNRv3) • Single-precessing-spin model ( IMRPhenomP) m 1 = 35 . 4 +5 . 0 � 3 . 4 M � m 2 = 28 . 9 +3 . 3 � 4 . 3 M � [LIGO-Virgo Collaboration, 2016] 28
GW150914: masses • 2 models as a proxy for systematic errors: • Double-precessing-spin model ( SEOBNRv3) • Single-precessing-spin model ( IMRPhenomP) m 1 = 35 . 4 +5 . 0 ± 0 . 1 � 3 . 4 ± 0 . 3 M � m 2 = 28 . 9 +3 . 3 ± 0 . 3 � 4 . 3 ± 0 . 3 M � [LIGO-Virgo Collaboration, 2016] 29
GW150914: masses • 2 models as a proxy for systematic errors: • Double-precessing-spin model ( SEOBNRv3) • Single-precessing-spin model ( IMRPhenomP) m 1 = 35 . 4 +5 . 0 ± 0 . 1 � 3 . 4 ± 0 . 3 M � m 2 = 28 . 9 +3 . 3 ± 0 . 3 � 4 . 3 ± 0 . 3 M � • Errors: signal strength model inaccuracies [LIGO-Virgo Collaboration, 2016] 30
2.3 GW150914: remnant black hole • Final values fitted from Numerical Relativity simulations • Final mass: M f = 62 . 2 +3 . 7 � 3 . 4 M � • Final (dimensionless) spin: a f = 0 . 68 +0 . 05 − 0 . 06 • ~ 3 solar mass radiated ! [LIGO-Virgo Collaboration, 2016] 31
GW150914: location Sun Sirius Orion Nebula Moon Large Magellanic Cloud Carina Nebula Small Magellanic Cloud [LIGO-Virgo Collaboration, 2016] 32
GW150914: location • CBC LIGO sky maps Electromagnetic counterpart Sun • Bayestar O(minutes) Sirius • LALInference-lite O(hours) Orion Nebula Moon • Includes spin e ff ects • Sub-threshold triggers in part of a network • Full LALInference O(days- Large Magellanic Cloud Carina Nebula weeks) • Sky localisation degeneracies Small Magellanic with only 2 detectors Cloud [ Raymond , et al., 2009] [LIGO-Virgo Collaboration, 2016] 33
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