1. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 1 Summary of recent measurements of g factor changes induced by thermal loading in the H1 interferometer. Rick Savage, Malik Rakhmanov, Keita Kawabe, and Joe Betswieser

2. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 2 Measurement Technique l Dynamic resonance of light in Fabry-Perot cavities ( Rakhmanov, Savage, Reitze, Tanner 2002 Phys. Lett. A, 305 239 ). Laser frequency to PDH signal transfer function, H  (s), has cusps at multiples of FSR and features at freqs. related to the phase modulation sidebands.

3. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 3 Misaligned cavity l Features appear at frequencies related to higher-order transverse modes. Transverse mode spacing: f tm = f 01 - f 00 = (f fsr /  acos (g 1 g 2 ) 1/2 l g 1,2 = 1 - L/R 1,2 l Infer mirror curvature changes from transverse mode spacing freq. changes. l This technique proposed by F. Bondu, Aug. 2002. Rakhmanov, Debieu, Bondu, Savage, Class. Quantum Grav. 21 (2004) S487-S492.

4. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 4 H1 data – Sept. 23, 2003 Lock a single arm Mis-align input beam (MMT3) in yaw Drive VCO test input (laser freq.) Measure TF to ASPD Q mon or I mon signal Focus on phase of feature near 63 kHz 2f fsr - f tm

5. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 5 Data and (lsqcurvefit) fits. Assume metrology value for R ETMx = 7260 m Metrology value for ITMx = 14240 m ITMx TCS annulus heating  decrease in ROC (increase in curvature) R = 14337 mR = 14096 m

6. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 6 To investigate heating via 1  m light … l Lock ifo. for > 2 hours w/o TCS; P laser = 2 W l Break full lock (t = 0) and quickly lock a single arm. l Misalign input beam (MMT3) in yaw Measure temporal evolution of H  (s) l H1 Xarm data Feb. 18, 2005 l Simple exponential fit to estimate initial curvature

7. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 7 Yarm measurement Feb. 19, 2005 l Inferred curvature changes: ITMx = 293 m ITMy = 177 m Ratio:  R ITMX /  R ITMY = 293m/177m = 1.7

8. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 8 Comparison with model – Phil Willems l Xarm

9. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 9

10. 10 Comparison l Note: unlike TCS heating measurements, where only ITM was heated, 1064 nm light resonating in arm cavity heats both ITM and ETM. Time constants – simple exponential fit  ITMX = 7.7 min;  ITMY = 7.2 min (noisy data) Change in radius of curvature  R ITMX /  R ITMY = 293m/177m = 1.7 »g factor change greater in xarm by factor of 1.7 »ETM absorptions differ? »ITM absorptions differ? »If ITM bulk/surface absorption ratios differ, then absorption ratio could be larger (or smaller) »Joe Betzwieser’s POY and POX time-depentent spot size measurements

11. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 11 Calibration using TCS results l TCS calibration Xarm: 220m / 37mW = 5.9 m/mW Yarm: 190m / 45mW = 4.2 m/mW »Surface (not bulk) absorption l 1064 nm heating Xarm: 293m / 5.9 m/mW = 49mW Yarm: 177m / 4.2 m/mW = 42 mW Assumes all heating on surface and no absorption in ETMs l Surface-equivalent, ITM-only absorption calibration 14.28 km 13.71 km 14.5 km 13.9 km  ~ 220 m  ~ 190 m

12. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 12 Issues – “cold” curvature differences l “Cold” values from 1064 nm meas. ITMX: 14.226 km difference ~ 50 m ITMY: 13.615 km difference ~ 100m l Systematic errors? »Alignment drifts – sampling different areas of TM surfaces l More complex, time-dependent behavior of surface distortions? »Phil Willems studying with time- dependent model of surface distortions »g factor measurements and reduced data available in LIGO-T050030-00-W 14.28 km 13.71 km 14.5 km 13.9 km  ~ 220 m  ~ 190 m

13. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 13 P. Willems’ time-dependent Hello-Vinet model - Xarm

14. LIGO-G050111-00-W LIGO Scientific Collaboration Meeting – LLO March 2005 14 Yarm comparison