Gravitational-Wave (Astro)Physics: from Theory to Data and Back

Alessandra Buonanno Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Department of Physics, University of Maryland

Spitzer Lectures, Princeton University April 26, 2018 Spitzer Lectures

•Lecture I: Basics of gravitational-wave theory and modeling

•Lecture II: Advanced methods to solve the two-body problem in General Relativity

•Lecture III: Inferring cosmology and astrophysics with gravitational- wave observations

•Lecture IV: Probing dynamical gravity and extreme matter with gravitational-wave observations

(NR simulation: Ossokine, AB & SXS @AEI)

(visualization credit: Benger @ Airborne Hydro Mapping Software & Haas @AEI) References:

• M. Maggiore’s books: “Gravitational Waves Volume 1: Theory and Experiments” (2007) & “Gravitational Waves Volume II: Astrophysics and Cosmology” (2018).

• E. Poisson & C. Will’s book: “Gravity” (2015).

• E.E. Flanagan & S.A. Hughes’ review: arXiv:0501041.

• AB’s Les Houches School Proceedings: arXiv:0709.4682.

• AB & B. Sathyaprakash’s review: arXiv:1410.7832.

• UMD/AEI graduate course on GW Physics & Astrophysics taught in Winter-Spring 2017: http://www.aei.mpg.de/2000472. Brief summary of Einstein equations and notations Brief summary of Einstein equations and notations (contd.) Brief summary of Einstein equations and notations (contd.)

Ricci scalar: Gravitational waves: signature of dynamical spacetime

• In 1916 Einstein predicted existence of gravitational waves:

Linearized gravity (weak ﬁeld):

• Distribution of mass deforms spacetime geometry in its neighborhood. Deformations propagate away at speed of light in form of waves whose oscillations reﬂect temporal variation of matter distribution.

Two radiative degrees of freedom (visualization: Dietrich @ AEI) Dietrich @ (visualization: Ripples in the curvature of spacetime First paper by Einstein on gravitational waves: 1916 Second paper by Einstein on gravitational waves: 1918

wrong by a factor 2! Linearization of Einstein equations

• We assume there is a coordinate frame in which: Linearization of Einstein equations (contd.) Lorenz gauge can always be imposed Propagation of GW in vacuum (far from source) Imposing transverse-traceless gauge Imposing transverse-traceless gauge (contd.) Linearly polarized waves in EM & GR Circularly polarized waves in EM & GR Gravitational waves have helicity 2 Newtonian description of tidal gravity Equation of geodesic deviation Interaction of GWs with free-falling particles in local Lorentz frame Geodesic deviation equation in local-Lorentz frame (LLF) Geodesic deviation equation in local-Lorentz frame (LLF) (contd.) Geodesic deviation equation in local-Lorentz frame (LLF) (contd.)

i Geodesic deviation equation in local-Lorentz frame (LLF) (contd.)

KAGRA, GWs and ring of free-falling particles GWs and ring of free-falling particles (contd.) GWs and lines of force Interaction of GWs with free-falling particles using TT gauge Equivalence between TT frame and local Lorentz frame Gravitational waves in weak-ﬁeld, slow velocity (at linear order in G)

(assuming GW source has negligible self gravity)

GW source Gravitational waves in weak-ﬁeld, slow velocity (at linear order in G)

(assuming GW source has negligible self gravity)

GW source Gravitational waves in weak-ﬁeld, slow velocity (at linear order in G)

non-negligible self-gravity:

Subdominant for binaries when computing quadrupole formula at leading order, but it needs to be included in conservation law, otherwise sources move along geodesic in ﬂat spacetime

We neglect Gravitational waves in weak-ﬁeld, slow velocity (at linear order in G)

(assuming GW source has negligible self gravity) Gravitational waves in weak-ﬁeld, slow velocity (at linear order in G)

(assuming GW source has negligible self gravity) Gravitational waves in weak-ﬁeld, slow velocity (at linear order in G)

(assuming GW source has negligible self gravity) Gravitational waves in weak-ﬁeld, slow velocity (at linear order in G) Multipolar decomposition of waves (at linear order in G)

• Multipolar expansion in terms of mass moments (IL) and mass current moments (JL) of source: D

can’t oscillate can’t oscillate can’t oscillate source GI GI˙ GI¨ GJ˙ GJ¨ h 0 + 1 + 2 + 1 + 2 + ⇠ c2D c3D c4D c4D c5D ··· • EM & GR: electric dipole moment & mass dipole moment

I : d = m x d˙ = m x = P conservation of linear 1 i i ) i i momentum i i X X • EM & GR: magnetic dipole moment & current dipole moment conservation of J1 : µ = mixi x˙ i = L ⇥ angular momentum i X The two LIGO detectors & the Virgo detector

LIGO in Hanford, WA (Abbott et al. PRL 116 (2016) 061102)

b) Test Mass

H1 10 ms light travel time = 4 km y L a) L1 Virgo in Pisa, Italy Test Mass

Power Beam L = 4 km Recycling Splitter x

Laser 20 W 100 kW Circulating Power Source Test Test Mass Mass Signal Recycling Photodetector

LIGO/Virgo measure (tiny) relative changes in separation of mirrors (phase shifts of light at beamsplitter of 10-9 rad!) How LIGO/Virgo work

LIGO Scientiﬁc Collaboration A glimpse inside the LIGO facility

LIGO Scientiﬁc Collaboration Typical noises in ground-based gravitational-wave detectors Evolution of sensitivity from Enhanced to Advanced LIGO (O1)

(Martynov et al. arXiv:1604.00439) Advanced Virgo joined Advanced LIGOs on August 1, 2017

(Abbott et al. arXiv:1709.09660)

20 10 Virgo Hanford Livingston 21 10 Hz) p

22 10 Strain (1/

23 10

100 1000 Frequency (Hz)