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

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

April 26, 2018 Spitzer Lectures, Princeton University

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

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

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

• UMD/AEI graduate course on GW Physics & Astrophysics taught in Winter-Spring 2017: http://www.aei.mpg.de/2000472.

References:

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

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

• 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).

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

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:

•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.

• In 1916 Einstein predicted existence of gravitational waves:

Linearized gravity (weak field):

Ripples in the curvature of spacetime

Two radiative degrees of freedom

Gravitational waves: signature of dynamical spacetime(v

isual

izat

ion:

Die

tric

h @

AEI

)

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

(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)

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

(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)

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:

• EM & GR: electric dipole moment & mass dipole moment

• EM & GR: magnetic dipole moment & current dipole moment

conservation of linear momentum

conservation of angular momentum

J1 : µ =X

i

mixi ⇥ xi = L

I1 : d =X

i

mixi ) d =X

i

mixi = P

source

D

h ⇠ GI0c2D

+GI1c3D

+GI2c4D

+GJ1c4D

+GJ2c5D

+ · · ·

can’t oscillate can’t oscillate can’t oscillate

Photodetector

BeamSplitter

Power Recycling

Laser

Source100 kW Circulating Power

b)

a)

Signal Recycling

Test Mass

Test Mass

Test Mass

Test Mass

Lx = 4 km

20 W

H1

L1

10 ms light

travel time

L y =

4 k

m

(Abbott et al. PRL 116 (2016) 061102)

The two LIGO detectors & the Virgo detector

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

LIGO in Hanford, WA

Virgo in Pisa, Italy

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

100 1000

Frequency (Hz)

10�23

10�22

10�21

10�20

Str

ain

(1/p

Hz)

Virgo

Hanford

Livingston

(Abbott et al. arXiv:1709.09660)