Gravitational Waves, with Kip Thorne

Video Lectures

Displaying all 69 video lectures.
I. Overview of Gravitational-Wave Science
Lecture 1
Overview of Gravitational-Wave Science (1/4)
Play Video
Overview of Gravitational-Wave Science (1/4)
Overview of Gravitational-Wave Science (1/4)

A. The nature of gravitational waves [GW's]: Week 1, Lecture 1, slides 1 - 18
B. The GW spectrum: HF, LF, VLF, ELF bands
C. Detection techniques:
     1. Resonant-mass detectors
     2. interferometers: LIGO and its partners
Readings:
* Kip Thorne: The Scientific Case for Advanced LIGO Interferometers

Suggested Reading and Exercises:
* assignment 1
* solutions to the exercises:
   - page 1
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   - page 11
Lecture 2
Overview of Gravitational-Wave Science (2/4)
Play Video
Overview of Gravitational-Wave Science (2/4)
Overview of Gravitational-Wave Science (2/4)

C. Detection techniques:
     3. LIGO details, noise curves, technology: Week 1, Lecture 2, slides 19 - 37
     4. LISA
D. GW data analysis
E. GW sources and science
     1. Inspiral of compact body into supermassive hole
     2. Binary black hole mergers
Readings:
* Kip Thorne: The Scientific Case for Advanced LIGO Interferometers

Suggested Reading and Exercises:
* assignment 1
* solutions to the exercises:
   - page 1
   - page 2
   - page 3
   - page 4
   - page 5
   - page 6
   - page 7
   - page 8
   - page 9
   - page 10
   - page 11
Lecture 3
Overview of Gravitational-Wave Science (3/4)
Play Video
Overview of Gravitational-Wave Science (3/4)
Overview of Gravitational-Wave Science (3/4)
E. GW sources and science
     3. Neutron-star / black-hole mergers: Week 2, Lecture 3 - Part 1, slides 38 - 47
     4. Neutron-star / neutron-star inspiral
     5. Spinning neutron stars
     6. Neutron-star births
     7. Binaries in our galaxy
     8. The very early universe

Black board pictures
Kindly provided by Disa
Board 1
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Board 3
Board 4
Suggested Reading and Exercises:
* assignment 2
* solutions to the exercises:
   - page 1
   - page 2
   - page 3
   - page 4
   - page 5
   - page 6
   - page 7
   - page 8
   - page 9
   - page 10
   - page 11
Lecture 4
Overview of Gravitational-Wave Science (4/4); Introduction to General Relativity (1/5)
Play Video
Overview of Gravitational-Wave Science (4/4); Introduction to General Relativity (1/5)
Overview of GW Science (4/4)
E. GW sources and science
     8. The very early universe
Introduction to General Relativity (1/5)
A. Tidal gravity in Newtonian theory: Week 2, Lecture 3 - Part 2
    1. Motivation: tidal gravity as spacetime curvature
    2. The Newtonian tidal gravity tensor
    3. Relative acceleration of freely falling particles
II. Introduction to General Relativity
Lecture 5
Introduction to General Relativity (2/5)
Play Video
Introduction to General Relativity (2/5)
Introduction to General Relativity (2/5)
B. The mathematics underlying general relativity: Week 2, Lecture 4
     1. Vectors, tensors, tensor algebra
     2. Differentiation of tensors, connection coefficients
Lecture 6
Introduction to General Relativity (3/5)
Play Video
Introduction to General Relativity (3/5)
Introduction to General Relativity (3/5)

B. The mathematics underlying general relativity: Week 2, Lecture 4
     1. Vectors, tensors, tensor algebra
     2. Differentiation of tensors, connection coefficients
Lecture 7
Introduction to General Relativity (4/5)
Play Video
Introduction to General Relativity (4/5)
Introduction to General Relativity (4/5)

B. The mathematics underlying general relativity
     3. Commutators, coordinate and noncoordinate bases: Week 3, Lecture 5
     4. Spacetime curvature: the Riemann and Ricci tensors
     5. Relativistic tidal gravity; geodesic deviation
C. The Einstein field equations  
     1. Motivation via tidal gravity
     2. "Derivation" of the Einstein equations; number of equations and number of unknowns; contracted Bianchi identity
Lecture 8
Introduction to General Relativity (5/5)
Play Video
Introduction to General Relativity (5/5)
Introduction to General Relativity (5/5)

B. The mathematics underlying general relativity
     3. Commutators, coordinate and noncoordinate bases: Week 3, Lecture 5
     4. Spacetime curvature: the Riemann and Ricci tensors
     5. Relativistic tidal gravity; geodesic deviation
C. The Einstein field equations
     1. Motivation via tidal gravity
     2. "Derivation" of the Einstein equations; number of equations and number of unknowns; contracted Bianchi identity
III. Weak Gravitational Waves in Flat Spacetime
Lecture 9
Weak Gravitational Waves in Flat Spacetime (1/6)
Play Video
Weak Gravitational Waves in Flat Spacetime (1/6)
Weak Gravitational Waves in Flat Spacetime (1/6): Week 4, Lecture 6

A. Wave equation for Riemann tensor
B. Transverse-traceless [TT] GW field; + and x polarizations
C. A GW's tidal forces (relative motion of freely falling particles)
D. Metric perturbations; TT gauge and other gauges
Lecture 10
Weak Gravitational Waves in Flat Spacetime (2/6)
Play Video
Weak Gravitational Waves in Flat Spacetime (2/6)
Weak Gravitational Waves in Flat Spacetime (2/6): Week 4, Lecture 6

A. Wave equation for Riemann tensor
B. Transverse-traceless [TT] GW field; + and x polarizations
C. A GW's tidal forces (relative motion of freely falling particles)
D. Metric perturbations; TT gauge and other gauges
Lecture 11
Weak Gravitational Waves in Flat Spacetime (3/6)
Play Video
Weak Gravitational Waves in Flat Spacetime (3/6)
Weak Gravitational Waves in Flat Spacetime (3/6)

E. Proper reference frame of an observer: Week 4, Lecture 7
F. Physical measurements of GW's in a proper reference frame
G. Generation of GW's: The linearized Einstein field equations
H. Projecting out the TT GW field
Lecture 12
Weak Gravitational Waves in Flat Spacetime (4/6)
Play Video
Weak Gravitational Waves in Flat Spacetime (4/6)
Weak Gravitational Waves in Flat Spacetime (4/6)

E. Proper reference frame of an observer: Week 4, Lecture 7
F. Physical measurements of GW's in a proper reference frame
G. Generation of GW's: The linearized Einstein field equations
H. Projecting out the TT GW field
Lecture 13
Weak Gravitational Waves in Flat Spacetime (5/6)
Play Video
Weak Gravitational Waves in Flat Spacetime (5/6)
Weak Gravitational Waves in Flat Spacetime (5/6)

I.  Slow-motion, weak-stress approximation for GW sources: Week 5, Lecture 8
J. The quadrupole formula for GW generation
     1. Derivation in slow-motion, weak-stress approximation
     2. Validity for slow-motion sources with strong internal gravity and arbitrary stresses
Lecture 14
Weak Gravitational Waves in Flat Spacetime (6/6); Propagation of Gravitational Waves Through Curved Spacetime (1/5)
Play Video
Weak Gravitational Waves in Flat Spacetime (6/6); Propagation of Gravitational Waves Through Curved Spacetime (1/5)
Weak Gravitational Waves in Flat Spacetime (6/6)

I.  Slow-motion, weak-stress approximation for GW sources: Week 5, Lecture 8
J. The quadrupole formula for GW generation
      1. Derivation in slow-motion, weak-stress approximation
      2. Validity for slow-motion sources with strong internal gravity and arbitrary stresses
Propagation of GW's Through Curved Spacetime (1/5)

A. Short wavelength approximation; two-lenghscale expansion
B. Curved-spacetime wave equation for Riemann tensor
C. Solution of wave equation via eikonal approximation (geometric optics) - Foundations
IV. Propagation of Gravitational Waves Through Curved Spacetime
Lecture 15
Propagation of Gravitational Waves Through Curved Spacetime (2/5)
Play Video
Propagation of Gravitational Waves Through Curved Spacetime (2/5)
Propagation of GW's Through Curved Spacetime (2/5)

D. Geometric optics - Details: Week 5, Lecture 9
     1. gravitons and their propagation; graviton conservation
     2. rays as graviton world lines; propagation of + and x GW fields along rays
     3. + and x polarizations and fields, rays and transport of waves along rays
     4. gravitational focusing of GW's, e.g. by the sun; diffraction at the focus
     5. stress-energy tensor for GW's; nonlocalizability of GW energy
     6. conservation of GW energy and momentum
     7. conservation of a graviton's energy and momentum
Lecture 16
Propagation of Gravitational Waves Through Curved Spacetime (3/5)
Play Video
Propagation of Gravitational Waves Through Curved Spacetime (3/5)
Propagation of GW's Through Curved Spacetime (3/5)

D. Geometric optics - Details: Week 5, Lecture 9
      1. gravitons and their propagation; graviton conservation
      2. rays as graviton world lines; propagation of + and x GW fields along rays
      3. + and x polarizations and fields, rays and transport of waves along rays
      4. gravitational focusing of GW's, e.g. by the sun; diffraction at the focus
      5. stress-energy tensor for GW's; nonlocalizability of GW energy
      6. conservation of GW energy and momentum
      7. conservation of a graviton's energy and momentum
Lecture 17
Propagation of Gravitational Waves Through Curved Spacetime (4/5)
Play Video
Propagation of Gravitational Waves Through Curved Spacetime (4/5)
Propagation of GW's Through Curved Spacetime (4/5)

E. Propagation of GW's through homogeneous matter: Week 6, Lecture 10
     1. impact of matter on the waves is always negligible
     2. propagation through dust, perfect fluid, viscous fluid, elastic medium
     3. propagation through a cloud of neutron stars
Lecture 18
Propagation of Gravitational Waves Through Curved Spacetime (5/5)
Play Video
Propagation of Gravitational Waves Through Curved Spacetime (5/5)
Propagation of GW's Through Curved Spacetime (5/5)

E. Propagation of GW's through homogeneous matter: Week 6, Lecture 10
      1. impact of matter on the waves is always negligible
      2. propagation through dust, perfect fluid, viscous fluid, elastic medium
      3. propagation through a cloud of neutron stars
V. Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime
Lecture 19
Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (1/2)
Play Video
Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (1/2)
Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (1/2): Week 6, Lecture 11

A. Strong-field region, weak-field near zone, local wave zone, distant wave zone
B. Multipolar expansions of metric perturbation in weak-field near zone and local wave zone
      1. influence of source's mass and angular momentum
      2. mass quadrupolar component of GW's; current quadrupolar component
      3. rates of emission of energy, linear momentum, and angular momentum
C. Application to a binary star system with circular orbit
      1. inspiral rate and timescale
      2. chirp waveform; chirp mass
Lecture 20
Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (2/2)
Play Video
Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (2/2)
Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (2/2): Week 6, Lecture 11

A. Strong-field region, weak-field near zone, local wave zone, distant wave zone
B. Multipolar expansions of metric perturbation in weak-field near zone and local wave zone
      1. influence of source's mass and angular momentum
      2. mass quadrupolar component of GW's; current quadrupolar component
      3. rates of emission of energy, linear momentum, and angular momentum
C. Application to a binary star system with circular orbit
      1. inspiral rate and timescale
      2. chirp waveform; chirp mass
VI. Astrophysical Phenomenology of Binary-Star GW Sources
Lecture 21
Astrophysical Phenomenology of Binary-Star GW Sources (1/5)
Play Video
Astrophysical Phenomenology of Binary-Star GW Sources (1/5)
Sterl Phinney: Astrophysical Phenomenology of Binary-Star GW Sources (1/5)

A. GW's from Binary Star Systems: Week 7, Lecture 12 [by E. Sterl Phinney]
      1. GW-driven inspiral of a single binary [review]
      2. Inspiral evolution of a steady-sstate population of many binaries
      3. Types of stars: main-sequence stars, white dwarfs [WD], neutron stars [NS], black holes [BH]; their masses and radii
      4. Binary systems observable by LIGO (and its partners), and by LISA
B. Issues relevant to estimating numbers of binary GW sources and their merger rates
      1. Cosmology: parameters describing the universe as a whole
      2. Our Milky Way galaxy: its star-formation history, stellar populations and binary populations
      3. Use of blue light to extrapolate from rates in Milky Way to rates in the distant universe
C. Estimates of numbers of binary GW sources and inspiral/merger rates: preview of next lecture
      1. NS/NS rates based on binary-pulsar statistics and blue-light extrapol... (read more)
Lecture 22
Astrophysical Phenomenology of Binary-Star GW Sources (2/5)
Play Video
Astrophysical Phenomenology of Binary-Star GW Sources (2/5)
Sterl Phinney: Astrophysical Phenomenology of Binary-Star GW Sources (2/5)

A. GW's from Binary Star Systems: Week 7, Lecture 12 [by E. Sterl Phinney]
      1. GW-driven inspiral of a single binary [review]
      2. Inspiral evolution of a steady-sstate population of many binaries
      3. Types of stars: main-sequence stars, white dwarfs [WD], neutron stars [NS], black holes [BH]; their masses and radii
      4. Binary systems observable by LIGO (and its partners), and by LISA
B. Issues relevant to estimating numbers of binary GW sources and their merger rates
      1. Cosmology: parameters describing the universe as a whole
      2. Our Milky Way galaxy: its star-formation history, stellar populations and binary populations
      3. Use of blue light to extrapolate from rates in Milky Way to rates in the distant universe
C. Estimates of numbers of binary GW sources and inspiral/merger rates: preview of next lecture
      1. NS/NS rates based on binary-pulsar statistics and blue-light extrapol... (read more)
Lecture 23
Astrophysical Phenomenology of Binary-Star GW Sources (3/5)
Play Video
Astrophysical Phenomenology of Binary-Star GW Sources (3/5)
Sterl Phinney: Astrophysical Phenomenology of Binary-Star GW Sources (3/5)

D. Estimates of numbers of binary GW sources [for LISA] and inspiral/merger rates [for LIGO]: Week 8, Lecture 13 [by E. Sterl Phinney]

1. Estimates based on observed numbers in our galaxy
           a. pitfalls
           b. NS/NS; WD/WD, WD/NS
2. Population synthesis
           a. Foundations for population synthesis:
                i. stellar structure and evolution
                ii. binary evolution: mass transfers etc.
           b. Estimates of binary numbers for LISA
Lecture 24
Astrophysical Phenomenology of Binary-Star GW Sources (4/5)
Play Video
Astrophysical Phenomenology of Binary-Star GW Sources (4/5)
Sterl Phinney: Astrophysical Phenomenology of Binary-Star GW Sources (4/5)

D. Estimates of numbers of binary GW sources [for LISA] and inspiral/merger rates [for LIGO]: Week 8, Lecture 13 [by E. Sterl Phinney]

1. Estimates based on observed numbers in our galaxy
           a. pitfalls
           b. NS/NS; WD/WD, WD/NS
2. Population synthesis
           a. Foundations for population synthesis:
                i. stellar structure and evolution
                ii. binary evolution: mass transfers etc.
           b. Estimates of binary numbers for LISA
Lecture 25
Astrophysical Phenomenology of Binary-Star GW Sources (5/5); Post-Newtonian G-Waveforms for LIGO & Its Partners (1/2
Play Video
Astrophysical Phenomenology of Binary-Star GW Sources (5/5); Post-Newtonian G-Waveforms for LIGO & Its Partners (1/2
Kip Thorne & A. Buonanno: Astrophysical Phenomenology of Binary-Star GW Sources (5/5)

D. Estimates of numbers of binary GW sources [for LISA] and inspiral/merger rates [for LIGO]

        3. Estimates of NS/NS, NS/BH, and BH/BH numbers for LIGO -- Week 8, Lecture 14 - Part 1 [by Kip Thorne & Alessandra Buonanno]

Binary Inspiral: Post-Newtonian Gravitational Waveforms for LIGO and Its Partners (1/2)
A. Matched-filtering data analysis to detect inspiral waves
B. Foundations for post-Newtonian approximations to General Relativity
      1. Mathematical foundations
      2. Physical effects at various orders
Lecture 26
Post-Newtonian Gravitational Waveforms for LIGO & Its Partners (2/2)
Play Video
Post-Newtonian Gravitational Waveforms for LIGO & Its Partners (2/2)
Binary Inspiral: Post-Newtonian Gravitational Waveforms for LIGO and Its Partners (2/2)
C. Post-Newtonian inspiral waveforms for circular orbits and vanishing spins -- Week 8, Lecture 14 - Part 2 [by Alessandra Buonanno]
D. Expansion parameter v = (pi M f)^1/3
E. Phase evolution governed by energy balance
F. Waveform in time domain
G. Waveform in frequency domain, via stationary-phase approximation
H. Influence of spin-orbit and spin-spin coupling: Orbital and spin precession; waveform modulation
      1. NS/BH binary
      2. BH/BH binary
I. Innermost stable circular orbit (ISCO) and transition from inspiral to plunge
J. The IBBH problem: failure of post-Newtonian waveforms in late inspiral; methods to deal with this:
      1. Pade resummation
      2. Effective one-body formalism
      3. Search templates designed to deal with uncertainties in our knowledge of the waveforms
VII. Supermassive Black Holes and their Gravitational Waves
Lecture 27
Supermassive Black Holes and their Gravitational Waves (1/3)
Play Video
Supermassive Black Holes and their Gravitational Waves (1/3)
Supermassive Black Holes [SMBH's] and their Gravitational Waves [for LISA] (1/3) Week 9, Lecture 15 [by E. Sterl Phinney]

A. Astrophysical phenomenology of SMBH's in galactic nuclei
  1. Evidence for their existence
  2. Measurement of SMBH masses via cusp in stellar velocity dispersion (for masses above 10^6 Msun)
  3. Correlation of SMBH masses with velocity dispersion in galactic bulges
  4. Number of SMBH's per unit volume in universe; their distribution of masses (for masses above 10^6 Msun)
  5. Observed quasar and other electromagnetic emission from SMBH's; quiescence of most SMBH's
B. Mergers of galaxies
  1. Statistics of mergers: observational data; predictions of CDM simulations
  2. Physics of mergers
  3. Dynamical friction on SMBH's, SMBH binary formation
C. Evolution of SMBH binary
  1. Interaction with stars; loss cone
  2. Hangup and ways to overcome it: repopulation of loss cone; effect of binary motion in galaxy core; effect of ellipticity of galactic potential; interaction with gas
  3. Gravitational radiation reaction
  4. SMBH merger ...
(read more)
Lecture 28
Supermassive Black Holes and their Gravitational Waves (2/3)
Play Video
Supermassive Black Holes and their Gravitational Waves (2/3)
Supermassive Black Holes [SMBH's] and their Gravitational Waves [for LISA] (2/3) Week 9, Lecture 15 [by E. Sterl Phinney]

A. Astrophysical phenomenology of SMBH's in galactic nuclei
  1. Evidence for their existence
  2. Measurement of SMBH masses via cusp in stellar velocity dispersion (for masses above 10^6 Msun)
  3. Correlation of SMBH masses with velocity dispersion in galactic bulges
  4. Number of SMBH's per unit volume in universe; their distribution of masses (for masses above 10^6 Msun)
  5. Observed quasar and other electromagnetic emission from SMBH's; quiescence of most SMBH's
B. Mergers of galaxies
  1. Statistics of mergers: observational data; predictions of CDM simulations
  2. Physics of mergers
  3. Dynamical friction on SMBH's, SMBH binary formation
C. Evolution of SMBH binary
  1. Interaction with stars; loss cone
  2. Hangup and ways to overcome it: repopulation of loss cone; effect of binary motion in galaxy core; effect of ellipticity of galactic potential; interaction with gas
  3. Gravitational radiation reaction
  4. SMBH merger ...
(read more)
Lecture 29
Supermassive Black Holes and their Gravitational Waves (3/3); Gravitational Waves from Inflation (1/2)
Play Video
Supermassive Black Holes and their Gravitational Waves (3/3); Gravitational Waves from Inflation (1/2)
Supermassive Black Holes [SMBH's] and their Gravitational Waves [for LISA] (3/3) [by Kip Thorne]

E. Gravitational waves from SMBH binary inspiral, as measured by LISA -- Week 9, Lecture 16 [by Kip]
  1. Frequency evolution, signal-to-noise ratios
  2. Cosmological influences on waves: gravitational redshift; gravitational lensing
  3. Observables: redshifted masses, luminosity distance, inclination angle
F. GW's from inspiral of a compact star (or BH) into a SMBH
  1. Frequency evolution, signal to noise ratios
  2. Loss of signal strength due to non-optimal signal processing - caused by complexity of inspiral orbits and resulting complexity of waveforms
      a. Implications for event rates
      b. Implications for specifying the level of LISA's noise floor
Gravitational Waves from Big Bang: Amplification of Vacuum Fluctuations by Inflation (by Kip Thorne)

A. Basic idea: same as parametric amplification of classical waves
B. Mathematical details
  1. Background cosmological metric
  2. Geometric optics propagation of GW's at "late times...
(read more)
VIII. Sources of Gravitational Waves
Lecture 30
Gravitational Waves from Inflation (2/2)
Play Video
Gravitational Waves from Inflation (2/2)
Gravitational Waves from Big Bang: Amplification of Vacuum Fluctuations by Inflation (by Kip Thorne)

A. Basic idea: same as parametric amplification of classical waves
B. Mathematical details
  1. Background cosmological metric
  2. Geometric optics propagation of GW's at "late times'
  3. Wave equation for GW's at all times
  4. Frozen and decaying solutions when wavelength is much larger than background radius of curvature
  5. Matching solutions together: resulting wave amplification
Lecture 31
Gravitational Waves from Neutron-Star Rotation and Pulsation (1/2)
Play Video
Gravitational Waves from Neutron-Star Rotation and Pulsation (1/2)
Gravitational Waves from Neutron-Star Rotation and Pulsation -- Week 10, Lecture 17 [by Lee Lindblom]

A. GW's from a structurally deformed, rotating NS
  1. Deformations maintained by a solid crust
  2. Deformations maintained by stress of a strong internal magnetic field
  3. Deformations due to temperature anisotropy induced by accretion of gas onto NS [low-mass X-ray binaries; LMXB's]
  4. Magnitudes of deformation (ellipticities) detectable by LIGO-I and LIGO-II
B. GW's from pulsations in a rotating NS
  1. Types of pulsational [bar-mode] instabilities: dynamical; secular
  2. beta = T/W as diagnostic for instabilities
  3. Instabilities in uniform-density Newtonian stars [Maclaurin Spheroids]
  4. Mechanisms for forming rapidly rotating NS's:
             a. Collapse of degenerate stellar cores
             b. Accretion-induced collapse of a white dwarf
             c. Spinup by accretion
             d. Merger of a low-mass NS/NS binary

       5. NS's formed by collapse: differential rotation, values of beta,bar-mode instabilities... (read more)
Lecture 32
Gravitational Waves from Neutron-Star Rotation and Pulsation (2/2)
Play Video
Gravitational Waves from Neutron-Star Rotation and Pulsation (2/2)
Gravitational Waves from Neutron-Star Rotation and Pulsation -- Week 10, Lecture 17 [by Lee Lindblom]

A. GW's from a structurally deformed, rotating NS
  1. Deformations maintained by a solid crust
  2. Deformations maintained by stress of a strong internal magnetic field
  3. Deformations due to temperature anisotropy induced by accretion of gas onto NS [low-mass X-ray binaries; LMXB's]
  4. Magnitudes of deformation (ellipticities) detectable by LIGO-I and LIGO-II
B. GW's from pulsations in a rotating NS
  1. Types of pulsational [bar-mode] instabilities: dynamical; secular
  2. beta = T/W as diagnostic for instabilities
  3. Instabilities in uniform-density Newtonian stars [Maclaurin Spheroids]
  4. Mechanisms for forming rapidly rotating NS's:
             a. Collapse of degenerate stellar cores
             b. Accretion-induced collapse of a white dwarf
             c. Spinup by accretion
             d. Merger of a low-mass NS/NS binary
       5. NS's formed by collapse: differential rotation, values of beta,bar-mode instabilitie... (read more)
IX. Numerical Relativity as a Tool for Computing GW Generation
Lecture 33
Numerical Relativity as a Tool for Computing GW Generation (1/2)
Play Video
Numerical Relativity as a Tool for Computing GW Generation (1/2)
Numerical Relativity as a Tool for Computing GW Generation -- Week 10, Lecture 18 [by Marc Scheel]

A. Motivation: Sources that require numerical relativity for their analysis

        1. Binary black hole mergers

            a. Relevance to LIGO & partners, and to LISA
            b. Estimated event rates for LIGO-I, LIGO-II and LISA
            c. Inspiral, merger, and ringdown; estimated wave strengths from each
            d. Rich physics expected in mergers: strong, nonlinear effects; spin-spin and spin-orbit coupling; angular-momentum hangup
            e. Importance of simulating mergers as foundation for interpreting observations

       2. Tidal disruption of NS by a BH companion
             a. Estimated event rate for LIGO-II
             b. Information carried by waves: NS structure and equation of state
             c. Possible connection to gamma ray bursts
             d. Importance of simulations for interpreting observations

       3. Some other sources: NS/NS mergers, cosmic strin... (read more)
Lecture 34
Numerical Relativity as a Tool for Computing GW Generation (2/2)
Play Video
Numerical Relativity as a Tool for Computing GW Generation (2/2)
Numerical Relativity as a Tool for Computing GW Generation -- Week 10, Lecture 18 [by Marc Scheel]

A. Motivation: Sources that require numerical relativity for their analysis
  1. Binary black hole mergers
a. Relevance to LIGO & partners, and to LISA
b. Estimated event rates for LIGO-I, LIGO-II and LISA
c. Inspiral, merger, and ringdown; estimated wave strengths from each
d. Rich physics expected in mergers: strong, nonlinear effects; spin-spin and spin-orbit coupling; angular-momentum hangup
e. Importance of simulating mergers as foundation for interpreting observations
       2. Tidal disruption of NS by a BH companion
             a. Estimated event rate for LIGO-II
             b. Information carried by waves: NS structure and equation of state
             c. Possible connection to gamma ray bursts
             d. Importance of simulations for interpreting observations
       3. Some other sources: NS/NS mergers, cosmic string vibrations, brane excitations in early universe
       4. The necessi... (read more)
X. The Physics Underlying Earth-Based Gravitational Wave Interferometers
Lecture 35
The Physics Underlying Earth-Based Gravitational Wave Interferometers (1/4)
Play Video
The Physics Underlying Earth-Based Gravitational Wave Interferometers (1/4)
The Physics Underlying Earth-Based GW Interferometers - Week 11, Lecture 19 [by Kip] (1/4)

A. Idealized Interferometer: Conceptual design and crude analysis
  1. Encoding GW signal in phase shift of light
  2. Increasing signal strength via bounces in arms
  3. Limit on accuracy of phase measurement
  4. Required laser power; energetic quantum limit
  5. Power recycling
B. General relativity: Proper reference frame of an accelerated observer
  1. Foundation for analyzing earth-based interferometers
  2. GW acts solely via its tidal force on test masses; negligible coupling to light
  3. TT gauge as an alternative: GW couples solely to light and not at all to test masses
C. Optics
       1. Gaussian beams; their mathematical description
             a. Gaussian cross section and its evolutionary spreading
             b. Circular phase fronts and their evolution
             c. Eigenfunctions of optical cavity with spherical mirrors
Lecture 36
The Physics Underlying Earth-Based Gravitational Wave Interferometers (2/4)
Play Video
The Physics Underlying Earth-Based Gravitational Wave Interferometers (2/4)
The Physics Underlying Earth-Based GW Interferometers - Week 11, Lecture 19 [by Kip] (2/4)

A. Idealized Interferometer: Conceptual design and crude analysis
  1. Encoding GW signal in phase shift of light
  2. Increasing signal strength via bounces in arms
  3. Limit on accuracy of phase measurement
  4. Required laser power; energetic quantum limit
  5. Power recycling
B. General relativity: Proper reference frame of an accelerated observer
  1. Foundation for analyzing earth-based interferometers
  2. GW acts solely via its tidal force on test masses; negligible coupling to light
  3. TT gauge as an alternative: GW couples solely to light and not at all to test masses
C. Optics
       1. Gaussian beams; their mathematical description
             a. Gaussian cross section and its evolutionary spreading
             b. Circular phase fronts and their evolution
             c. Eigenfunctions of optical cavity with spherical mirrors
Lecture 37
The Physics Underlying Earth-Based Gravitational Wave Interferometers (3/4)
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The Physics Underlying Earth-Based Gravitational Wave Interferometers (3/4)
The Physics Underlying Earth-Based GW Interferometers [by Kip] (3/4)

C. Optics
       2. Paraxial Optics - Week 11, Lecture 20 [by Kip]
              a. Paraxial propagator and its use
              b. Application to derive evolution of a Gaussian beam
              c. Eigenmodes of an optical cavity with spherical mirrors
                   i. resonances as function of mirror separation; free spectral range
                   ii. mode matching of Gaussian beam into optical cavity
              d. Mirrors: reflection and transmission coefficients, losses
              e. Properties of optical cavities: finesse, mode cleaning, phase shift as function of mirror separations

D. Statistical Physics: The theory of random processes
  1. Random process; examples
  2. Fourier transforms, Parcival's theorem
  3. Spectral density; variance
  4. Filtering of random processes; influence on spectral density
  5. Shot noise in light; its spectral density
Lecture 38
The Physics Underlying Earth-Based Gravitational Wave Interferometers (4/4)
Play Video
The Physics Underlying Earth-Based Gravitational Wave Interferometers (4/4)
The Physics Underlying Earth-Based GW Interferometers [by Kip] (4/4)

C. Optics
       2. Paraxial Optics - Week 11, Lecture 20 [by Kip]
              a. Paraxial propagator and its use
              b. Application to derive evolution of a Gaussian beam
              c. Eigenmodes of an optical cavity with spherical mirrors
                   i. resonances as function of mirror separation; free spectral range
                   ii. mode matching of Gaussian beam into optical cavity
              d. Mirrors: reflection and transmission coefficients, losses
              e. Properties of optical cavities: finesse, mode cleaning, phase shift as function of mirror separations

D. Statistical Physics: The theory of random processes
  1. Random process; examples
  2. Fourier transforms, Parcival's theorem
  3. Spectral density; variance
  4. Filtering of random processes; influence on spectral density
  5. Shot noise in light; its spectral density
XI. LIGO Interferometers
Lecture 39
Overview of Real LIGO Interferometers (1/2)
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Overview of Real LIGO Interferometers (1/2)
Overview of Real LIGO Interferometers - Week 12, Lecture 21 [by Alan Weinstein]

A. Overview of noise sources & how they are controlled
B. Optics
  1. Fabry-Perot cavity theory; response of reflected light to change of cavity length
  2. Analysis of complicated, linear optical systems; response to mirror motions; Twiddle
  3. Coupling of light into arm cavities: carrier resonates; side bands do not
  4. Properties of cavities: finesse, storage time, pole frequency, gain, visibility, circulating field
  5. Power recycling
  6. Control of arm cavity lengths via Pound-Drever-Hall [PDH] reflection locking
              a. Phase modulation of input beam
              b. Demodulation; lock acquisition

       7. Schnupp Asymmetry and Schnupp locking to control the difference in distances from beam splitter to arm-cavity input mirrors (Michelson interferometer)
       8. Hermite-Gaussian modes of arm cavity; their excitation by beam and mirror imperfections and tilts
       9. Input optics for controlling input beam
             a. Mo... (read more)
Lecture 40
Overview of Real LIGO Interferometers (2/2)
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Overview of Real LIGO Interferometers (2/2)
Overview of Real LIGO Interferometers - Week 12, Lecture 21 [by Alan Weinstein]

A. Overview of noise sources & how they are controlled
B. Optics
  1. Fabry-Perot cavity theory; response of reflected light to change of cavity length
  2. Analysis of complicated, linear optical systems; response to mirror motions; Twiddle
  3. Coupling of light into arm cavities: carrier resonates; side bands do not
  4. Properties of cavities: finesse, storage time, pole frequency, gain, visibility, circulating field
  5. Power recycling
  6. Control of arm cavity lengths via Pound-Drever-Hall [PDH] reflection locking
              a. Phase modulation of input beam
              b. Demodulation; lock acquisition
       7. Schnupp Asymmetry and Schnupp locking to control the difference in distances from beam splitter to arm-cavity input mirrors (Michelson interferometer)
       8. Hermite-Gaussian modes of arm cavity; their excitation by beam and mirror imperfections and tilts
       9. Input optics for controlling input beam
             a... (read more)
Lecture 41
Thermal Noise in LIGO Interferometers and its Control (1/2)
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Thermal Noise in LIGO Interferometers and its Control (1/2)
Thermal Noise in LIGO Interferometers and its Control - Week 12, Lecture 22 [by Phil Willems]

A. Motivation: Brownian motion of a dust grain buffeted by molecules of an ideal gas
  1. dissipation, mean motion
  2. Fluctuating force as a random process; its correlation function and spectral density
  3. Solving for spectral density of particle position
B. Fluctuation-dissipation theorem
C. Damped pendulum: suspension thermal noise derived from fluctuation-dissipation theorem
D. Dissipation in a LIGO test mass or suspension described via imaginary part of generalized elastic modulus, E(f) = (applied force) / (resulting displacement) = Eo (1+i phi)
  1. Frequency-dependence of loss angle phi: viscous damping, structural damping, damping associated with an internal relaxation process
E. Dissipation/fluctuation processes for a LIGO test mass
  1. Gas molecules buffeting test mass
  2. Magnetic forces from actuator (which controls mirror)
  3. Internal processes inside the test mass itself:
             a. Analyzed via sum over normal ... (read more)
Lecture 42
Thermal Noise in LIGO Interferometers and its Control (2/2)
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Thermal Noise in LIGO Interferometers and its Control (2/2)
Thermal Noise in LIGO Interferometers and its Control - Week 12, Lecture 22 [by Phil Willems]

A. Motivation: Brownian motion of a dust grain buffeted by molecules of an ideal gas
  1. dissipation, mean motion
  2. Fluctuating force as a random process; its correlation function and spectral density
  3. Solving for spectral density of particle position
B. Fluctuation-dissipation theorem
C. Damped pendulum: suspension thermal noise derived from fluctuation-dissipation theorem
D. Dissipation in a LIGO test mass or suspension described via imaginary part of generalized elastic modulus, E(f) = (applied force) / (resulting displacement) = Eo (1+i phi)
  1. Frequency-dependence of loss angle phi: viscous damping, structural damping, damping associated with an internal relaxation process
E. Dissipation/fluctuation processes for a LIGO test mass
  1. Gas molecules buffeting test mass
  2. Magnetic forces from actuator (which controls mirror)
  3. Internal processes inside the test mass itself:
             a. Analyzed via sum over normal ... (read more)
Lecture 43
Control Systems and Laser Frequency Stabilization (1/2)
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Control Systems and Laser Frequency Stabilization (1/2)

Control Systems and Laser Frequency Stabilization - Week 13, Lecture 23  [by Erik Black]
  1. Introduction
  1. What a control system is
  2. Uses of control systems
  3. Simple control system (input, amplifier K, feedback, and output); its oscillatory instability due to time delay
General, linear control theory
  1. Laplace transforms
  2. Transfer function (Kernel) for a linear system, in time domain and in (Laplace-transform) s-space 
  3. Poles of the transfer function in s-space; their relationship to system's stability
  4. Transfer function for simple control system with s-dependent amplifier, K(s)
  1. Open-loop transfer function K(s); closed-loop transfer function K/(1+K)
  2. Nyquist diagram for analyzing stability
  3. Gain margin, phase margin
  4. Bode plot for analyzing stability; stability diagnosed via phase at unity gain point (phase margin)
  5. Bode's gain-phase relations
Laser frequency stabilization via locking to eigenmode of an optical cavity (Pound-Drever-Hall [PDH] locking): an example of linear... (read more)
Lecture 44
Control Systems and Laser Frequency Stabilization (2/2)
Play Video
Control Systems and Laser Frequency Stabilization (2/2)

Control Systems and Laser Frequency Stabilization - Week 13, Lecture 23  [by Erik Black]
  1. Introduction
  1. What a control system is
  2. Uses of control systems
  3. Simple control system (input, amplifier K, feedback, and output); its oscillatory instability due to time delay
General, linear control theory
  1. Laplace transforms
  2. Transfer function (Kernel) for a linear system, in time domain and in (Laplace-transform) s-space 
  3. Poles of the transfer function in s-space; their relationship to system's stability
  4. Transfer function for simple control system with s-dependent amplifier, K(s)
  1. Open-loop transfer function K(s); closed-loop transfer function K/(1+K)
  2. Nyquist diagram for analyzing stability
  3. Gain margin, phase margin
  4. Bode plot for analyzing stability; stability diagnosed via phase at unity gain point (phase margin)
  5. Bode's gain-phase relations
Laser frequency stabilization via locking to eigenmode of an optical cavity (Pound-Drever-Hall [PDH] locking): an example of linear ...
(read more)
Lecture 45
Interferometer Simulations and Lock Acquisition in LIGO
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Interferometer Simulations and Lock Acquisition in LIGO
Interferometer Simulations and Lock Acquisition in LIGO - Week 13, Lecture 24, Part 1  [by Matt Evans]
  1. Simulations of all or part of a LIGO interferometer
  1. What a simulation is
  2. Types of simulations:
  1. Frequency domain: fast, but limited to linear systems
  2. Time domain: slower, but necessary for nonlinearities
Example of a simulation:  Control system for a Fabry Perot cavity:
  1. Laser excites Fabry Perot cavity; returning light tapped off by Faraday isolator, detected to produce electronic signal which drives a magnetic actuator that adjusts a cavity mirror to lock the cavity to the laser.
  2. Simulation of the optics, the electronics, the mirror's mechanics, and the electromechanical transducers
  3. Linear parts of system treated via transfer functions
In complex system such as LIGO: subsystems (e.g. the above) treated as modules
Uses of simulations:
  1. Quantify things that can't be measured experimentally
  2. Selectively turn on and off noise sources
LIGO end-to-end (E2E) simulati... (read more)
Lecture 46
Seismic Isolation in Earth-Based Interferometers
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Seismic Isolation in Earth-Based Interferometers
 
Seismic Isolation in Earth-Based Interferometers - Week 13, Lecture 24, Part 2  [by Riccardo De Salvo]
  1. Seismic attenuation requirements
  2. Principals of seismic attenuation
  1. Pendulum or oscillator as an example; its transfer function
  2. Chain of oscillators; net transfer function
The Virgo isolation system as an example
The need for seismic attenuation in all six degrees of freedom:
  1. All feed into horizontal noise that interferometer measures
  2. How to achieve such attenuation
Vertical attenuation: the most serious problem
  1. A solution: cantilever blades, radially compressed
  1. Their transfer function
  2. Example in Virgo
Creep in stressed elements of isolation system
  1. Mechanism of creep
  2. Reduction of creep with time after stress was applied
  3. How to control creep: special materials; freezing dislocations; glassy materials in final attentuation stages
Mechanical resonances in isolation system
  1. Must damp them because of  interferometer's limited dynamic range
  2. Damping techn...
(read more)
Lecture 47
Quantum Optical noise in GW Interferometers (1/2)
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Quantum Optical noise in GW Interferometers (1/2)
Quantum Optical Noise in LIGO Interferometers - Week 14, Lectures 25 & 26  [by Alessandra Buonano and Yanbei Chen]
  1. Introduction: review of interferometers and their sensitivities; references on quantum optical noise; the experimental challenge: prevent quantum properties of detector and light (the "probe") from affecting the GW information we seek
  2. Quantum optical noise in conventional interferometers (LIGO-I, TAMA, VIRGO)
  1. vacuum fluctuations from dark port produce shot noise and radiation pressure fluctuations
  2. Two-photon formalism for analyzing these noises
  3. Application of this formalism to one arm cavity of the interferometer: shot noise; radiation-pressure noise
  4. Input-output relations for the full interferometer [input is vacuum fluctuation at dark port and GW force on mirrors; output is GW signal plus noise]
  5. Spectral density of quantum optical noise (shot and radiation pressure noise) deduced from input-output relations
Free-mass standard quantum limit [SQL] (for conve... (read more)
Lecture 48
Quantum Optical noise in GW Interferometers (2/2)
Play Video
Quantum Optical noise in GW Interferometers (2/2)
Quantum Optical Noise in LIGO Interferometers - Week 14, Lectures 25 & 26  [by Alessandra Buonano and Yanbei Chen]
  1. Introduction: review of interferometers and their sensitivities; references on quantum optical noise; the experimental challenge: prevent quantum properties of detector and light (the "probe") from affecting the GW information we seek
  2. Quantum optical noise in conventional interferometers (LIGO-I, TAMA, VIRGO)
  1. vacuum fluctuations from dark port produce shot noise and radiation pressure fluctuations
  2. Two-photon formalism for analyzing these noises
  3. Application of this formalism to one arm cavity of the interferometer: shot noise; radiation-pressure noise
  4. Input-output relations for the full interferometer [input is vacuum fluctuation at dark port and GW force on mirrors; output is GW signal plus noise]
  5. Spectral density of quantum optical noise (shot and radiation pressure noise) deduced from input-output relations
Free-mass standard quantum limit [SQL] (for conve... (read more)
Lecture 49
LIGO data analysis (1/2)
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LIGO data analysis (1/2)
LIGO Data Analysis - Week 15, Lecture 28  [by Albert Lazzarini]
  1. The context: LIGO-I noise curve and anticipated signal strengths
  2. LIGO data attributes
  1. Data channels: GW signal (32 kB/sec) plus many auxiliary  channels (~1 MB/sec) that monitor the state and environment of interferometer
  2. Data format: common to all interferometer projects
  3. Uses of auxiliary-channel data: reduce noise in GW channel; monitor instrument behavior
  4. The data from January 2002 observations: noise spectra; expected improvements in near future
Some signal processing theory and methods
  1. Theory of random processes: brief summary [see also Week 11, Lecture 20]
  2. Fast Fourier transforms; 90% of LIGO cpu computational time is here; their computational cost; capabilities of arrays of Pentium processors
  3. Pre-processing data to remove ugly instrumental effects
  4. Time-frequency methods: general theory; time-frequency spectrograms; time-frequency characteristics of various types of GW's (stochastic, periodic, ring...
(read more)
Lecture 50
LIGO data analysis (2/2)
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LIGO data analysis (2/2)
LIGO Data Analysis - Week 15, Lecture 28  [by Albert Lazzarini]
  1. The context: LIGO-I noise curve and anticipated signal strengths
  2. LIGO data attributes
  1. Data channels: GW signal (32 kB/sec) plus many auxiliary  channels (~1 MB/sec) that monitor the state and environment of interferometer
  2. Data format: common to all interferometer projects
  3. Uses of auxiliary-channel data: reduce noise in GW channel; monitor instrument behavior
  4. The data from January 2002 observations: noise spectra; expected improvements in near future
Some signal processing theory and methods
  1. Theory of random processes: brief summary [see also Week 11, Lecture 20]
  2. Fast Fourier transforms; 90% of LIGO cpu computational time is here; their computational cost; capabilities of arrays of Pentium processors
  3. Pre-processing data to remove ugly instrumental effects
  4. Time-frequency methods: general theory; time-frequency spectrograms; time-frequency characteristics of various types of GW's (stochastic, periodic, ring...
(read more)
Lecture 51
The Long-Term Future of LIGO: Facility Limits
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The Long-Term Future of LIGO: Facility Limits

The Long-Term Future of LIGO: Facility Limits
  1. Facilities Limits (limits on sensitivity due to the LIGO environment, vacuum system, ...) -  Week 16, Lecture 29, Part 1  [by Kip]
  1. Overview
  2. Noise due to scattering of light in the LIGO beam tube
  1. Noise mechanism
  2. Baffles to reduce the noise
  3. Random teeth on the baffles: reduce the noise and destroy coherent superposition of noise via different scattering routes
  4. Net scattering noise: from backscatter off baffles' surfaces and diffration off baffles' teeth
Noise due to fluctuating dispersion of light beam in vacuum system's residual gas
  1. Noise mechanism
  2. Magnitude of noise as function of vacuum pressure
Seismic gravitational noise (due to fluctuating gravitational pulls of density inhomogeneities caused by ambient seismic waves)
  1. Noise mechanism
  2. Modeling of the seismic waves and their noise
  3. Magnitude of noise and uncertainties
Human gravitational noise (mostly due to jerkiness of human walking)
  1. Noise mechanism
  2. Magn...
(read more)
Lecture 52
The Long-Term Future of LIGO: Techniques for Improving on LIGO-II
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The Long-Term Future of LIGO: Techniques for Improving on LIGO-II

The Long-Term Future of LIGO:  Techniques for Improving on LIGO-II
         B. Techniques for Improving on LIGO-II - Week 16, Lecture 29, Part 2  [by Ronald W.P. Drever]
  1. Beating the Standard Quantum Limit (shot noise & radiation pressure noise):  See last part of Week 14, Lecture 26 by Chen
  2. Reducing seismic noise: "straightforward" but not easy
  3. Reducing suspension thermal noise: Replace fibers by ribbons (planned for LIGO-II)
  4. Reducing internal thermal noise (the toughest problem): Cryogenically cool the test masses
                            1.  Japanese plans for LCGT (Large-scale Cryogenic Gravitational-wave Telescope); Japanese R&D
                            2.  Problem of heating the test mass by laser beam; bleading off the heat
                            3.  How cooling helps: reduced rms thermal motion; higher mechanical Q so reduced thermal fluctuations
  1. Reduce mirror heating in presence of high optical power (so power can be higher): Use diffractive opti...
(read more)
Lecture 53
Large Experimental Science and LIGO as an Example (1/2)
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Large Experimental Science and LIGO as an Example (1/2)
Quantum Optical Noise in LIGO Interferometers - Week 14, Lectures 25 & 26  [by Alessandra Buonano and Yanbei Chen]
  1. Introduction: review of interferometers and their sensitivities; references on quantum optical noise; the experimental challenge: prevent quantum properties of detector and light (the "probe") from affecting the GW information we seek
  2. Quantum optical noise in conventional interferometers (LIGO-I, TAMA, VIRGO)
  1. vacuum fluctuations from dark port produce shot noise and radiation pressure fluctuations
  2. Two-photon formalism for analyzing these noises
  3. Application of this formalism to one arm cavity of the interferometer: shot noise; radiation-pressure noise
  4. Input-output relations for the full interferometer [input is vacuum fluctuation at dark port and GW force on mirrors; output is GW signal plus noise]
  5. Spectral density of quantum optical noise (shot and radiation pressure noise) deduced from input-output relations
Free-mass standard quantum limit [SQL] (for conv... (read more)
Lecture 54
Large Experimental Science and LIGO as an Example (2/2)
Play Video
Large Experimental Science and LIGO as an Example (2/2)
Quantum Optical Noise in LIGO Interferometers - Week 14, Lectures 25 & 26  [by Alessandra Buonano and Yanbei Chen]
  1. Introduction: review of interferometers and their sensitivities; references on quantum optical noise; the experimental challenge: prevent quantum properties of detector and light (the "probe") from affecting the GW information we seek
  2. Quantum optical noise in conventional interferometers (LIGO-I, TAMA, VIRGO)
  1. vacuum fluctuations from dark port produce shot noise and radiation pressure fluctuations
  2. Two-photon formalism for analyzing these noises
  3. Application of this formalism to one arm cavity of the interferometer: shot noise; radiation-pressure noise
  4. Input-output relations for the full interferometer [input is vacuum fluctuation at dark port and GW force on mirrors; output is GW signal plus noise]
  5. Spectral density of quantum optical noise (shot and radiation pressure noise) deduced from input-output relations
Free-mass standard quantum limit [SQL] (for conve... (read more)
Lecture 55
Resonant-Mass GW Detectors for the HF Band (1/2)
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Resonant-Mass GW Detectors for the HF Band (1/2)
Resonant-Mass ("Bar") GW Detectors for the HF Band - Week 16, Lecture 30 [by William O. Hamilton (LSU)]
  1. Historical remarks; Joseph Weber's pioneering contributions; others' contributions
  2. Basic elements of a resonant-mass detector, and how it works
  1. Vacuum chamber and cryostat
  2. Seismic isolation system
  3. Bar -- fundamental end-to-end mode excited by GW
  4. Small mechanical oscillator attached to end of bar to amplify bar's mechanical motion
  5. Mechanical-electrical transducers to convert oscillator's motion into electrical signal
  1. general discussion of transducers
  2. parametric transducer: basic principle; analogy with a child pumping a swing
  3. the superconducting inductive transducer used in the LSU resonant-mass detector "Allegro"; squid amplifier and its noise
  4. back-action noise on the bar's normal mode
Thermal noise in bar
The full mechanical-electrical system for the LSU detector Allegro
  1. Equations of motion for system with noise sources
  2. Measured noise at transducer output; t...
(read more)
Lecture 56
Resonant-Mass GW Detectors for the HF Band (2/2)
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Resonant-Mass GW Detectors for the HF Band (2/2)
Resonant-Mass ("Bar") GW Detectors for the HF Band - Week 16, Lecture 30 [by William O. Hamilton (LSU)]
  1. Historical remarks; Joseph Weber's pioneering contributions; others' contributions
  2. Basic elements of a resonant-mass detector, and how it works
  1. Vacuum chamber and cryostat
  2. Seismic isolation system
  3. Bar -- fundamental end-to-end mode excited by GW
  4. Small mechanical oscillator attached to end of bar to amplify bar's mechanical motion
  5. Mechanical-electrical transducers to convert oscillator's motion into electrical signal
  1. general discussion of transducers
  2. parametric transducer: basic principle; analogy with a child pumping a swing
  3. the superconducting inductive transducer used in the LSU resonant-mass detector "Allegro"; squid amplifier and its noise
  4. back-action noise on the bar's normal mode
Thermal noise in bar
The full mechanical-electrical system for the LSU detector Allegro
  1. Equations of motion for system with noise sources
  2. Measured noise at transducer output; t...
(read more)
Lecture 57
CAJAGWR talk by W.O. Hamilton on Resonant-Mass GW Detectors
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CAJAGWR talk by W.O. Hamilton on Resonant-Mass GW Detectors
Resonant-Mass ("Bar") GW Detectors for the HF Band - Week 16 [by William O. Hamilton (LSU)]
G.                  G. IGEC: The international network of bar detectors - Week 16, CaJAGWR Seminar [by William O. Hamilton (LSU)]
  1. Data collection record since 1997
  2. Network's upper limits on Fourier transform of GW field, h(f) at resonant frequency, during 1998, as a function of time
  3. Upper limits on GW bursts during 1997 - 2000
H.                   H. Some results from the LSU detector Allegro
a.     Noise as a function of time, and noise curve
b.    Search for periodic waves (e.g. pulsars)
I.      Prospects for future improvements:
a.     Cool to lower temperatures - Auriga performance
b.    Improve SQUID amplifiers - Trento/Lignaro work
c.     Improved transducer with tighter coupling to resonant mass: broadening the frequency band of high sensitivity (in process this summer at LSU in collaboration with U. Maryland)
J.     Identifying a GW burst amidst noise: an audio analog...
(read more)
Lecture 58
Doppler tracking of spacecraft for GW detection in the low frequency band
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Doppler tracking of spacecraft for GW detection in the low frequency band
LIGO Data Analysis - Week 15, Lecture 28  [by Albert Lazzarini]
  1. The context: LIGO-I noise curve and anticipated signal strengths
  2. LIGO data attributes
  1. Data channels: GW signal (32 kB/sec) plus many auxiliary  channels (~1 MB/sec) that monitor the state and environment of interferometer
  2. Data format: common to all interferometer projects
  3. Uses of auxiliary-channel data: reduce noise in GW channel; monitor instrument behavior
  4. The data from January 2002 observations: noise spectra; expected improvements in near future
Some signal processing theory and methods
  1. Theory of random processes: brief summary [see also Week 11, Lecture 20]
  2. Fast Fourier transforms; 90% of LIGO cpu computational time is here; their computational cost; capabilities of arrays of Pentium processors
  3. Pre-processing data to remove ugly instrumental effects
  4. Time-frequency methods: general theory; time-frequency spectrograms; time-frequency characteristics of various types of GW's (stochastic, periodic, ring...
(read more)
Lecture 59
Pulsar timing for GW detection in the very low frequency band
Play Video
Pulsar timing for GW detection in the very low frequency band
LIGO Data Analysis - Week 15, Lecture 28  [by Albert Lazzarini]
  1. The context: LIGO-I noise curve and anticipated signal strengths
  2. LIGO data attributes
  1. Data channels: GW signal (32 kB/sec) plus many auxiliary  channels (~1 MB/sec) that monitor the state and environment of interferometer
  2. Data format: common to all interferometer projects
  3. Uses of auxiliary-channel data: reduce noise in GW channel; monitor instrument behavior
  4. The data from January 2002 observations: noise spectra; expected improvements in near future
Some signal processing theory and methods
  1. Theory of random processes: brief summary [see also Week 11, Lecture 20]
  2. Fast Fourier transforms; 90% of LIGO cpu computational time is here; their computational cost; capabilities of arrays of Pentium processors
  3. Pre-processing data to remove ugly instrumental effects
  4. Time-frequency methods: general theory; time-frequency spectrograms; time-frequency characteristics of various types of GW's (stochastic, periodic, ring...
(read more)
Lecture 60
LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (1/2)
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LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (1/2)

LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design -  Week 17, Lecture 31  [by William Folkner (JPL)]
  1. The context: Noise curves and GW sources for LISA and for LIGO; white-dwarf  / white-dwarf background noise for LISA.
  2. History of ideas for a LISA type GW detector: 1978 - 1998; motivations for changes of conceptual design as time passed
  3. Noise estimates for current LISA design
  1. The noise curve, in detail
  2. Shot noise and what determines it
  3. Influence of arm length
Spacecraft formation and orbits; influence of time-varying arm lengths:
  1. Time-varying separation between spacecraft; time-varying doppler shift
  2. Local frequency standard to deal with varying doppler shifts; noise in frequency standard
  3. Pointing changes to deal with spacecraft motions; pointing noise
  4. An alternative spacecraft formation that has been explored: triangle orbiting earth rather than sun; comparison with LISA's design
  5. Variation of antenna pattern with time modulat...
(read more)
Lecture 61
LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (2/2)
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LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (2/2)

LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design -  Week 17, Lecture 31  [by William Folkner (JPL)]
  1. The context: Noise curves and GW sources for LISA and for LIGO; white-dwarf  / white-dwarf background noise for LISA.
  2. History of ideas for a LISA type GW detector: 1978 - 1998; motivations for changes of conceptual design as time passed
  3. Noise estimates for current LISA design
  1. The noise curve, in detail
  2. Shot noise and what determines it
  3. Influence of arm length
Spacecraft formation and orbits; influence of time-varying arm lengths:
  1. Time-varying separation between spacecraft; time-varying doppler shift
  2. Local frequency standard to deal with varying doppler shifts; noise in frequency standard
  3. Pointing changes to deal with spacecraft motions; pointing noise
  4. An alternative spacecraft formation that has been explored: triangle orbiting earth rather than sun; comparison with LISA's design
  5. Variation of antenna pattern with time modulat...
(read more)
Lecture 62
LISA's Lasers and Optics (1/2)
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LISA's Lasers and Optics (1/2)

LISA's Lasers and Optics - Week 17, Lecture 32  [by Robert Spero (JPL)]
  1. Introduction: Comparison and contrast of LISA and LIGO
  2. LISA's light beams: 
  1. parameters; spreading (far-field limit), 
  2. why must receive, photodetect and transmit new beam back ("transpond" the light) rather than reflecting off a mirror
Detection of incoming beam: 
  1. shot noise prevents simple photodetection 
  2. reduce shot noise by beating incoming beam against local oscillator light
  3. modulation & demodulation of local oscillator light to reduce noise
  4. possible designs for transponding system: DC lock, frequency offset lock, and offset-cancelled lock (current preference)
Three-spacecraft phase-monitoring system (current baseline design):
  1. 1 master laser, three slave lasers, 4 phase measurements; 3 semi-independent 2-arm interferometers
  2. Time-delay interferometry [TDI] as an attractive alternative
Laser frequency noise and its control
  1. Analysis when GW wavelength is long compared to spacecraft sepa...
(read more)
Lecture 63
LISA's Lasers and Optics (2/2)
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LISA's Lasers and Optics (2/2)

LISA's Lasers and Optics - Week 17, Lecture 32  [by Robert Spero (JPL)]
  1. Introduction: Comparison and contrast of LISA and LIGO
  2. LISA's light beams: 
  1. parameters; spreading (far-field limit), 
  2. why must receive, photodetect and transmit new beam back ("transpond" the light) rather than reflecting off a mirror
Detection of incoming beam: 
  1. shot noise prevents simple photodetection 
  2. reduce shot noise by beating incoming beam against local oscillator light
  3. modulation & demodulation of local oscillator light to reduce noise
  4. possible designs for transponding system: DC lock, frequency offset lock, and offset-cancelled lock (current preference)
Three-spacecraft phase-monitoring system (current baseline design):
  1. 1 master laser, three slave lasers, 4 phase measurements; 3 semi-independent 2-arm interferometers
  2. Time-delay interferometry [TDI] as an attractive alternative
Laser frequency noise and its control
  1. Analysis when GW wavelength is long compared to spacecraft sepa...
(read more)
Lecture 64
Time-Delay Interferometry [TDI] for LISA (1/2)
Play Video
Time-Delay Interferometry [TDI] for LISA (1/2)
Time-Delay Interferometry [TDI] for LISA - Week 18, Lecture 34  [by John Armstrong (JPL)]
  1. The context: 
  1. Review of LISA; its main noise sources and their magnitudes
  2. Why conventional Micheson-interferometer method of cancelling laser frequency noise will not work for LISA: large, time-varying difference in arm lengths
Basic idea of TDI
  1. View unequal-arm LISA as symmetric system of 12 one-way links
  2. From 12 data channels with appropriate time delays based on estimates of arm lengths, construct TDI observables which cancel the leading noises while keeping GW signals
Details of TDI
  1. The nature of each data channel: fractional frequency shift of incoming laser light compared to local laser
  2. Noises on each channel: laser phase noise, shot noise, proof-mass acceleration noise, noise in metrology data
  3. Noise-cancelling combinations of time-delayed channel signals
  1. GW-carrying combinations
  2. Sagnac combination 
Computation of LISA sensitivity to periodic waves -- sensitivity av... (read more)
Lecture 65
Time-Delay Interferometry [TDI] for LISA (2/2)
Play Video
Time-Delay Interferometry [TDI] for LISA (2/2)
Time-Delay Interferometry [TDI] for LISA - Week 18, Lecture 34  [by John Armstrong (JPL)]
  1. The context: 
  1. Review of LISA; its main noise sources and their magnitudes
  2. Why conventional Micheson-interferometer method of cancelling laser frequency noise will not work for LISA: large, time-varying difference in arm lengths
Basic idea of TDI
  1. View unequal-arm LISA as symmetric system of 12 one-way links
  2. From 12 data channels with appropriate time delays based on estimates of arm lengths, construct TDI observables which cancel the leading noises while keeping GW signals
Details of TDI
  1. The nature of each data channel: fractional frequency shift of incoming laser light compared to local laser
  2. Noises on each channel: laser phase noise, shot noise, proof-mass acceleration noise, noise in metrology data
  3. Noise-cancelling combinations of time-delayed channel signals
  1. GW-carrying combinations
  2. Sagnac combination 
Computation of LISA sensitivity to periodic waves -- sensitivity av... (read more)
Lecture 66
LISA's Distrubance Reduction System (DRS) [Drag-Free System] (1/2)
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LISA's Distrubance Reduction System (DRS) [Drag-Free System] (1/2)

LISA's Distrubance Reduction System [DRS] (Drag-Free System) - Week 18, Lecture 33  [by Bonny Schumaker (JPL)]
  1. Review of LISA: concept, orbit, spacecraft, optics, baseline parameters that affect the DRS
  2. Requirements and general approach:
  1. Requirements on proof mass: nongravitational accelerations; centering in housing; alignment with measuring optics
  2. How these requirements arise from the science we want LISA to do, plus practical issues
  3. Acceleration requirement compared to achievements on past space missions and earth-based experiments
  4. LISA's DRS contrasted with accelerometers
The DRS control system (system to control proof-mass and spacecraft degrees of freedom)
  1. Basic design
  2. Mathematical model
  3. Solution of model to get disturbance matrix: How various disturbance sources influence proof-mass acceleration, spacecraft acceleration, and effective acceleration of proof-mass / spacecraft gap
Disturbance sources; their magnitudes; implications for DRS design and control-... (read more)
Lecture 67
LISA's Distrubance Reduction System (DRS) [Drag-Free System] (2/2)
Play Video
LISA's Distrubance Reduction System (DRS) [Drag-Free System] (2/2)
LISA's Distrubance Reduction System [DRS] (Drag-Free System) - Week 18, Lecture 33  [by Bonny Schumaker (JPL)]
  1. Review of LISA: concept, orbit, spacecraft, optics, baseline parameters that affect the DRS
  2. Requirements and general approach:
  1. Requirements on proof mass: nongravitational accelerations; centering in housing; alignment with measuring optics
  2. How these requirements arise from the science we want LISA to do, plus practical issues
  3. Acceleration requirement compared to achievements on past space missions and earth-based experiments
  4. LISA's DRS contrasted with accelerometers
The DRS control system (system to control proof-mass and spacecraft degrees of freedom)
  1. Basic design
  2. Mathematical model
  3. Solution of model to get disturbance matrix: How various disturbance sources influence proof-mass acceleration, spacecraft acceleration, and effective acceleration of proof-mass / spacecraft gap
Disturbance sources; their magnitudes; implications for DRS design and control-sys... (read more)
Lecture 68
The Big-Bang Observatory [BBO]: A Possible Follow-On Mission to LISA
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The Big-Bang Observatory [BBO]: A Possible Follow-On Mission to LISA
The Big-Bang Observatory [BBO]:  A Possible Follow-On Mission to LISA - Week 19, Lecture 35, Part 1  [by William M. Folkner (JPL)]
  1. Scientific goal for a post-LISA mission: detect and study waves from inflation and other processes in the very early universe
  1. Sensitivity goal: reach one or two orders of magnitude below predicted GW's from  standard slow-roll inflation
  2. Frequency window where foreground sources can be removed and inflationary waves are strongest: between LIGO and LISA -- f ~ 0.1 Hz = arm lengths 100 times shorter than LISA
  3. Possible noise curve for BBO; digging into the noise by cross correlating outputs of detectors (as is planned for LIGO's stochastic GW searches)
BBO conceptual design
  1. Spacecraft configuration and orbits: 
                          a.  two other LISA-type triangles, 120 degrees apart in orbit around sun; cross correlate outputs to triangulate on foreground sources and remove them; detect and remove every NS/NS, NS/BH and BH/BH merger in uni... (read more)
Lecture 69
GW's from Inflation and GW Detection in ELF Band via Anisotropy of CMB Polarization
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GW's from Inflation and GW Detection in ELF Band via Anisotropy of CMB Polarization
GW's from Inflation and GW Detection in ELF Band via Anisotropy of CMB Polarization - Week 19, Lecture 35, Part 2  [by Marc Kamionkowski]
  1. The Cosmic Microwave Background [CMB]
  1. Its nature and physical origin
  2. Surface of last scattering; size of causally connected regions
  3. Why so isotropic? only good explanation: inflation
Inflation: basic ideas
  1. Inflaton scalar field and its potential; slow roll; evolution of its vacuum energy density; influence on universal expansion: inflation
  2. Evolution of expansion factor of universe: pre-inflation, inflation, radiation-dominance, matter dominance
  3. Smoothing of universe during inflation; explanation of observed isotropy of CMB
  4. Inflation also predicts universe is spatially flat -- as has now been confirmed observationally
GW production by inflation: 
  1. Explanation as analog of Hawking radiation from a black hole
  2. Derivation as inflation's parametric amplification of vacuum fluctuations [see also Week 9, Lecture 16]
  3. Predicted rms h: pro...
(read more)