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

Alessandra Buonanno Max Institute for Gravitational Physics ( 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

•Lecture III: Inferring and with gravitational- wave observations

•Lecture IV: Probing dynamical and extreme 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 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

• In 1916 Einstein predicted existence of gravitational waves:

Linearized gravity (weak field):

• Distribution of deforms spacetime geometry in its neighborhood. Deformations propagate away at of 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 (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 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 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 i i X X • EM & GR: magnetic dipole moment & current dipole moment conservation of J1 : µ = mixi x˙ i = L ⇥ 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 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

LIGO Scientific Collaboration A glimpse inside the LIGO facility

LIGO Scientific Collaboration Typical noises in ground-based gravitational-wave detectors 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 (Hz)