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, ringdown, bursts, chirps)
5. stacking Fourier transforms vs fully coherent transform
6. Optimal filters in general; brief overviews of applications to inspiral of compact binaries; stochastic background waves (one detector output serves as filter for other); spinning neutron stars; GW bursts

Optimal filtering for parametrizable waveforms

1. General theory; derivation of the optimal filter
2. Wave detection contrasted with parameter extraction
3. Binary inspiral: matched filtering with a family of templates

1. intrinsic vs extrinsic parameters
2. 2-parameter template family when spins are negected
3. data analysis flow
4. tests in last January's LIGO-I data 
5. setting event rate limits with 1994 LIGO prototype data

Stochastic background searches

1. General method: cross correlation of outputs of two detectors; buildup of signal to noise with integration time
2. Optimal filter when searching for background with known spectrum using detectors whose noise is correlated; effect of correlations on measured upper limits

Hypothesis testing: maximum likelihood; Baysean statistics; false alarm probability compared with detection probability

Searching for (transient) bursts of GW's

1. General theory of search strategies
2. Excess power statistic (especially useful when have limited knowledge of waveforms, e.g. today for BH/BH mergers)

Analysis of data from a network of detectors

1. LIGO network; international network
2. Coincidence analysis: rejection of uncorrelated random events
3. Event localization on the sky
4. Joint data analysis: validation of detections

1. The Nature of Gravitational Waves
2. Gravitational Waves Data Analysis
3. Gravitational Wave Sources in Neutron Stars
4. Introduction to General Relativity: Tidal Gravity
5. Mathematics of General Relativity: Tensor Algebra
6. Mathematics of General Relativity: Tensor Differentiation
7. Introduction to General Relativity (4/5)
8. Introduction to General Relativity (5/5)
9. Weak Gravitational Waves in Flat Spacetime (1/6)
10. Weak Gravitational Waves in Flat Spacetime (2/6)
11. Weak Gravitational Waves in Flat Spacetime (3/6)
12. Weak Gravitational Waves in Flat Spacetime (4/6)
13. Weak Gravitational Waves in Flat Spacetime (5/6)
14. Weak Gravitational Waves in Flat Spacetime (6/6); Propagation of Gravitational Waves Through Curved Spacetime (1/5)
15. Propagation of Gravitational Waves Through Curved Spacetime (2/5)
16. Propagation of Gravitational Waves Through Curved Spacetime (3/5)
17. Propagation of Gravitational Waves Through Curved Spacetime (4/5)
18. Propagation of Gravitational Waves Through Curved Spacetime (5/5)
19. Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (1/2)
20. Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (2/2)
21. Astrophysical Phenomenology of Binary-Star GW Sources (1/5)
22. Astrophysical Phenomenology of Binary-Star GW Sources (2/5)
23. Astrophysical Phenomenology of Binary-Star GW Sources (3/5)
24. Astrophysical Phenomenology of Binary-Star GW Sources (4/5)
25. Astrophysical Phenomenology of Binary-Star GW Sources (5/5); Post-Newtonian G-Waveforms for LIGO & Its Partners (1/2
26. Post-Newtonian Gravitational Waveforms for LIGO & Its Partners (2/2)
27. Supermassive Black Holes and their Gravitational Waves (1/3)
28. Supermassive Black Holes and their Gravitational Waves (2/3)
29. Supermassive Black Holes and their Gravitational Waves (3/3); Gravitational Waves from Inflation (1/2)
30. Gravitational Waves from Inflation (2/2)
31. Gravitational Waves from Neutron-Star Rotation and Pulsation (1/2)
32. Gravitational Waves from Neutron-Star Rotation and Pulsation (2/2)
33. Numerical Relativity as a Tool for Computing GW Generation (1/2)
34. Numerical Relativity as a Tool for Computing GW Generation (2/2)
35. The Physics Underlying Earth-Based Gravitational Wave Interferometers (1/4)
36. The Physics Underlying Earth-Based Gravitational Wave Interferometers (2/4)
37. The Physics Underlying Earth-Based Gravitational Wave Interferometers (3/4)
38. The Physics Underlying Earth-Based Gravitational Wave Interferometers (4/4)
39. Overview of Real LIGO Interferometers (1/2)
40. Overview of Real LIGO Interferometers (2/2)
41. Thermal Noise in LIGO Interferometers and its Control (1/2)
42. Thermal Noise in LIGO Interferometers and its Control (2/2)
43. Control Systems and Laser Frequency Stabilization (1/2)
44. Control Systems and Laser Frequency Stabilization (2/2)
45. Interferometer Simulations and Lock Acquisition in LIGO
46. Seismic Isolation in Earth-Based Interferometers
47. Quantum Optical noise in GW Interferometers (1/2)
48. Quantum Optical noise in GW Interferometers (2/2)
49. LIGO data analysis (1/2)
50. LIGO data analysis (2/2)
51. The Long-Term Future of LIGO: Facility Limits
52. The Long-Term Future of LIGO: Techniques for Improving on LIGO-II
53. Large Experimental Science and LIGO as an Example (1/2)
54. Large Experimental Science and LIGO as an Example (2/2)
55. Resonant-Mass GW Detectors for the HF Band (1/2)
56. Resonant-Mass GW Detectors for the HF Band (2/2)
57. CAJAGWR talk by W.O. Hamilton on Resonant-Mass GW Detectors
58. Doppler tracking of spacecraft for GW detection in the low frequency band
59. Pulsar timing for GW detection in the very low frequency band
60. LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (1/2)
61. LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (2/2)
62. LISA's Lasers and Optics (1/2)
63. LISA's Lasers and Optics (2/2)
64. Time-Delay Interferometry [TDI] for LISA (1/2)
65. Time-Delay Interferometry [TDI] for LISA (2/2)
66. LISA's Distrubance Reduction System (DRS) [Drag-Free System] (1/2)
67. LISA's Distrubance Reduction System (DRS) [Drag-Free System] (2/2)
68. The Big-Bang Observatory [BBO]: A Possible Follow-On Mission to LISA
69. GW's from Inflation and GW Detection in ELF Band via Anisotropy of CMB Polarization

Caltech's Physics 237-2002: Gravitational Waves
A Web-Based Course organized and Designed by Kip S. Thorne, Mihai Bondarescu and Yanbei Chen.

This course contains all the materials from a graduate-student-level course on Gravitational Waves taught at the California Institute of Technology, January through May of 2002. The materials include Quicktime videos of the lectures, lists of suggested and supplementary reading, copies of some of the readings, many exercises, and solutions to all exercises. The video files are so large that it may not be possible to stream them from most sites, but they can be downloaded. Alternatively, the course materials on DVD's can be borrowed via Interlibrary Loan from the Caltech Library (click on CLAS, then on Call Number, then enter QC179.T56 2002 ).

Questions and issues about this course and website can be directed to Mihai Bondarescu or Yanbei Chen.

Resources:

• - Part A - Gravitational-Wave Theory and Sources
• - Part B - Gravitational-Wave Detectors - original outline
• - Part B - Gravitational-Wave Detectors - alternative outline with the lectures reordered more logically
• - Course Materials

Credits:
Lectures by Thorne and Guest Lecturers*
Video of lectures by Bondarescu and Chen
Homework problems by Thorne and Guest Lecturers
Homework solutions by Bondarescu and Chen

*John Armstrong (JPL), Barry Barish, Erik Black, Alessandra Buonanno, Yanbei Chen, Riccardo De Salvo, Ronald Drever, Matt Evans, William Folkner (JPL), William Hamilton (LSU), Mark Kamionkowski, Albert Lazzarini, Lee Lindblom, Sterl Phinney, Mark Scheel, Bonny Schumaker (JPL), Robert Spero (JPL), Alan Weinstein, Phil Willems.