Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in...
Transcript of Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in...
![Page 1: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/1.jpg)
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
![Page 2: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/2.jpg)
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)
![Page 3: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/3.jpg)
• 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.
![Page 4: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/4.jpg)
Brief summary of Einstein equations and notations
![Page 5: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/5.jpg)
Brief summary of Einstein equations and notations (contd.)
![Page 6: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/6.jpg)
Brief summary of Einstein equations and notations (contd.)
Ricci scalar:
![Page 7: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/7.jpg)
•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
)
![Page 8: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/8.jpg)
First paper by Einstein on gravitational waves: 1916
![Page 9: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/9.jpg)
Second paper by Einstein on gravitational waves: 1918
wrong by a factor 2!
![Page 10: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/10.jpg)
Linearization of Einstein equations
• We assume there is a coordinate frame in which:
![Page 11: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/11.jpg)
Linearization of Einstein equations (contd.)
![Page 12: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/12.jpg)
Lorenz gauge can always be imposed
![Page 13: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/13.jpg)
Propagation of GW in vacuum (far from source)
![Page 14: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/14.jpg)
Imposing transverse-traceless gauge
![Page 15: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/15.jpg)
Imposing transverse-traceless gauge (contd.)
![Page 16: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/16.jpg)
Linearly polarized waves in EM & GR
![Page 17: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/17.jpg)
Circularly polarized waves in EM & GR
![Page 18: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/18.jpg)
Gravitational waves have helicity 2
![Page 19: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/19.jpg)
Newtonian description of tidal gravity
![Page 20: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/20.jpg)
Equation of geodesic deviation
![Page 21: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/21.jpg)
Interaction of GWs with free-falling particles in local Lorentz frame
![Page 22: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/22.jpg)
Geodesic deviation equation in local-Lorentz frame (LLF)
![Page 23: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/23.jpg)
Geodesic deviation equation in local-Lorentz frame (LLF) (contd.)
![Page 24: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/24.jpg)
Geodesic deviation equation in local-Lorentz frame (LLF) (contd.)
i
![Page 25: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/25.jpg)
Geodesic deviation equation in local-Lorentz frame (LLF) (contd.)
KAGRA,
![Page 26: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/26.jpg)
GWs and ring of free-falling particles
![Page 27: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/27.jpg)
GWs and ring of free-falling particles (contd.)
![Page 28: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/28.jpg)
GWs and lines of force
![Page 29: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/29.jpg)
Interaction of GWs with free-falling particles using TT gauge
![Page 30: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/30.jpg)
Equivalence between TT frame and local Lorentz frame
![Page 31: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/31.jpg)
(assuming GW source has negligible self gravity)
GW source
Gravitational waves in weak-field, slow velocity (at linear order in G)
![Page 32: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/32.jpg)
(assuming GW source has negligible self gravity)
GW source
Gravitational waves in weak-field, slow velocity (at linear order in G)
![Page 33: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/33.jpg)
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
![Page 34: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/34.jpg)
(assuming GW source has negligible self gravity)
Gravitational waves in weak-field, slow velocity (at linear order in G)
![Page 35: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/35.jpg)
(assuming GW source has negligible self gravity)
Gravitational waves in weak-field, slow velocity (at linear order in G)
![Page 36: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/36.jpg)
Gravitational waves in weak-field, slow velocity (at linear order in G)
(assuming GW source has negligible self gravity)
![Page 37: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/37.jpg)
Gravitational waves in weak-field, slow velocity (at linear order in G)
![Page 38: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/38.jpg)
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
![Page 39: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/39.jpg)
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
![Page 40: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/40.jpg)
How LIGO/Virgo work
LIGO Scientific Collaboration
![Page 41: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/41.jpg)
A glimpse inside the LIGO facility
LIGO Scientific Collaboration
![Page 42: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/42.jpg)
Typical noises in ground-based gravitational-wave detectors
![Page 43: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/43.jpg)
Evolution of sensitivity from Enhanced to Advanced LIGO (O1)
(Martynov et al. arXiv:1604.00439)
![Page 44: Gravitational-Wave (Astro)Physics: from Theory to Data and ... · Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant](https://reader030.fdocuments.us/reader030/viewer/2022041016/5ec925bdd441cf3a803b349a/html5/thumbnails/44.jpg)
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)