Update on O2 CO2 Calibration Uncertainty Review

Reviewing the O2 CO2 calibration uncertainty, recent updates include identifying beam clipping on the reflection photodiode, switching to the transmitted photodiode, correcting time-dependent errors, and reducing overall uncertainty budget to primarily statistical uncertainty. Data and scripts used in the review process are also detailed in the summary.

• Calibration
• Uncertainty
• Review
• Update
• Data Analysis

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1. O2 C02 Calibration Uncertainty Review / Summary / Update C. Cahillane, M. Hulko, J. Kissel, for the LSC Calibration Team G1800319-v1 1

2. Whats New In O2s C02 Release PCAL (our absolute displacement reference) was identified to have beam clipping on its reflection photodiode (RXPD) for both observatories Time-dependent systematic error C02 switched to using the transmitted photodiode (TXPD) for the entire run, therefore correcting the error C02 uncertainty budget no longer needs to include this systematic error The GDS/DCS developers in the group figured out how to apply frequency dependent time-dependent corrections to the data Can now correct for time-dependent changes in the sensing function s coupled cavity pole frequency C02 has corrected for the time-dependence of the cavity pole. C02 uncertainty budget no longer needs to include this systematic error - Note: because only LHO significantly suffers from SRC detuning, and any time-dependence in the pole frequency / Q has negligible impact on the overall uncertainty, we did not correct for it in C02 h(t), thus it remains as a systematic error This essentially reduces the uncertainty budget to only statistical uncertainty from measurements - These still contain time-dependence (i.e. from coherence of calibration lines), but it s MUCH smaller, which now means very little variation from event to event G1800319-v1 2

3. Data & Scripts Used In the Review Many thanks to Craig and Mykyta for resurrecting the O2 calibration uncertainty pipeline. I ve only used C01 data from Analysis Chucks 2&3 and used GW170104 as my comparison between C01 & C02. Need to commit C01 .tar file for Oct-06-2017_O2UncertaintyTxts that (presumably) was used in uncertainty paper (?) Should be good enough to demonstrate the differences, but I won t have exact C01 vs C02 comparisons for all events, or for All O2 comparisons. 2018_O2_LHO_GPSTime*.txt C02 Event Data is posted to EVNT aLOG 12055, but really, using ${CalSVN}/trunk/Runs/O2/${IFO}/Results/Uncertainty/ResponseFeb-26- 2018_O2UncertaintyTxts/ O2_${OBSERVATORY}_GPSTime_1186007541_C02_RelativeResponseUncertainty.tar 1-hour stride data is posted to EVNT aLOG 12056, but really, unzipped from ${CalSVN}/trunk/Runs/O2/${IFO}/Results/Uncertainty/UncertaintySpectrograms/Feb-21- Script(s) used to analyze data and produce the review: ${CalSVN}/trunk/Runs/O2/Common/Scripts/Uncertainty/ plotuncertaintyspectrograms_O2_C02_forG1800319.m plotuncertaintyspectrograms_O2a_forG1700081.m G1800319-v1 3

4. Primer: Reminder of the Process O1 C01 Response Function Systematic Error and Uncertainty At the time of GW151226, Dec 26 2015 04:37:34 1.2 (2) Do this for many times during the run during analysis ready times, with 1 hour cadence, to form spectrograms of error and uncertainty (upper and lower bounds, mag and phase) 1.18 1.16 1.14 1.12 1.1 Mangitude [ ] 1.08 1.06 1.04 1.02 0.981 0.96 0.94 0.92 H1Systematic Error L1Systematic Error H1Error and Uncertainty L1Error and Uncertainty 0.9 0.88 0.86 0.84 0.82 0.8 101 102 103 Frequency [Hz] created by plotuncertaintyspectrograms_O1_C01_forT1500576 on 13-Jun-2017 (1) Compute the uncertainty at a given time, based on a) time-independent statistical uncertainty Posteriors of MCMC fit to reference measurements b) time-independent systematic error Gaussian Process fit over residuals of all sweeps from Run c) time-dependent systematic error and uncertainty Computed from calibration lines 10 8 (3) Use percentile statistics on spectrogram data to find what is normal and how a 6 4 Phase [deg] 2 0 -2 -4 H1 O1 C01 Uncertainty Percentiles Systematic Error & Statistical Uncertainty specific time compares to it -6 -8 1.2 -10 1.16 101 102 103 1.12 Frequency [Hz] Magnitude [ ] 1.08 1.04 1 0.96 0.92 68th 95th 99.7th GW151226 0.88 0.84 0.8 101 102 103 H1 O1 C01 Uncertainty Percentiles Maximum Systematic Error & Statistical Uncertainty Frequency [Hz] created by plotuncertaintyspectrograms_O1_C01_forT1500576 on 13-Jun-2017 (4) Use percentiles to find maximum deviation from perfect, over a chosen frequency band 20 Max Magnitude Bound [%] 18 10 16 8 14 6 12 4 Phase [deg] 10 2 8 0 6 -2 4 2 -4 0 -6 101 102 103 T1500576-v7 4 -8 Frequency [Hz] created by plotuncertaintyspectrograms_O1_C01_forT1500576 on 13-Jun-2017 -10 Max within 20-100 Hz: (68th, 95th, 99.7th, GW151226) = (9.4% / 4.3 deg, 11% / 5.2 deg, 14% / 8.8 deg, 9.9% / 3.8 deg) 101 102 103 Frequency [Hz] 20 Max Phase Bound [deg] 18 68th 95th 99.7th GW151226 16 14 12 10 8 6 4 2 0 101 102 103 Frequency [Hz]

5. Case Study: GW170104, C01 vs C02 O2 C02 vs C01 Response Function Systematic Error and Uncertainty At the time of GW170104, Jan 04 2017 10:11:58 UTC H1 s systematic error is scaled closer to zero b/c PCAL clipping no longer a systematic error 1.1 1.09 1.08 1.07 1.06 1.05 Mangitude [ ] 1.04 1.03 1.02 1.01 0.991 0.98 0.97 H1 C01 Systematic Error L1 C01 Systematic Error H1 C02 Systematic Error L1 C02 Systematic Error H1 C01 Error and Uncertainty L1 C01 Error and Uncertainty H1 C02 Error and Uncertainty L1 C02 Error and Uncertainty 0.96 0.95 0.94 0.93 0.92 0.91 0.9 101 102 103 Low frequency at L1 still dominated by statistical uncertainty from less UIM and PUM measurements than H1 Frequency [Hz] created by plotuncertaintyspectrograms_O2_C02_forG1800319 on 04-Mar-2018 5 Both IFO s no longer have error from time-dependent coupled cavity pole 4 3 2 Phase [deg] 1 0 H1 larger in phase uncertainty because we didn t measure sensing function sweeps to as high a frequency -1 -2 -3 -4 -5 101 102 103 Frequency [Hz] Phase tightens up nicely also b/c removal coupled cavity pole error G1800319-v1 5

6. H1 Percentile Outliers Improve without PCAL Clipping Error H1 O2 C02 vs C01 Uncertainty, 99.7th Percentile Systematic Error & Statistical Uncertainty 1.2 1.18 1.16 All O2, C01 1.14 1.12 1.1 Magnitude [ ] 1.08 1.06 No More Cavity Pole Error! 1.04 1.02 0.981 0.96 0.94 0.92 C01 99p7th C02 99p7th C01 GW170104 C02 GW170104 0.9 0.88 0.86 No More Clipping Error! 0.84 0.82 0.8 101 102 103 Frequency [Hz] created by plotuncertaintyspectrograms_O2_C02_forG1800319 on 04-Mar-2018 5 H1 O2 C02 Uncertainty Percentiles Systematic Error & Statistical Uncertainty 4 1.1 1.08 3 1.06 2 Phase [deg] Magnitude [ ] 1.04 1 1.02 1 0 0.98 -1 0.96 68th 95th 99.7th GW170104 -2 0.94 0.92 -3 0.9 No More Cavity Pole Error! -4 101 102 103 Frequency [Hz] -5 created by plotuncertaintyspectrograms_O2_C02_forG1800319 on 04-Mar-2018 101 102 103 5 Frequency [Hz] 4 All O2, C02 3 2 Phase [deg] 1 0 Direct comparison of 99.7th percentiles between C01 (A.C. 2 & 3) vs. C02 -1 -2 -3 -4 -5 101 102 103 G1800319-v1 6 Frequency [Hz]

7. L1 Percentiles Improve at with out Cavity Pole Error L1 O2 C02 vs C01 Uncertainty, 99.7th Percentile Systematic Error & Statistical Uncertainty 1.2 All O2, C01 1.18 1.16 1.14 1.12 1.1 Magnitude [ ] 1.08 1.06 No More Cavity Pole Error! 1.04 1.02 0.981 0.96 0.94 0.92 C01 99p7th C02 99p7th C01 GW170104 C02 GW170104 0.9 0.88 0.86 0.84 0.82 0.8 101 102 103 Frequency [Hz] created by plotuncertaintyspectrograms_O2_C02_forG1800319 on 04-Mar-2018 L1 O2 C02 Uncertainty Percentiles Systematic Error & Statistical Uncertainty 1.1 5 1.08 4 1.06 3 Magnitude [ ] 1.04 1.02 2 Phase [deg] 1 1 0.98 0 0.96 68th 95th 99.7th GW170104 0.94 -1 0.92 -2 0.9 101 102 103 -3 Frequency [Hz] created by plotuncertaintyspectrograms_O2_C02_forG1800319 on 04-Mar-2018 -4 5 -5 101 102 103 4 All O2, C02 3 Frequency [Hz] 2 Phase [deg] 1 0 -1 -2 Direct comparison of 99.7th percentiles between C01 (A.C. 2 & 3) vs. C02 -3 -4 -5 101 102 103 Frequency [Hz] G1800319-v1 7

8. GW170104 and O2 Maximum Uncertainty and Error Improve! H1 O2 C02 vs C01 Uncertainty 68th Percentile Maximum Systematic Error & Statistical Uncertainty GW170104, 68th Percentile 10 Max Magnitude Bound [%] 9 C01 Result: 5.4/4.1 %, 2.1/2.2 deg (Different from Uncertainty paper 4.6/3.7 %, 1.8/1.9 deg ... I used Feb-27-2017, A.C. 2&3 results, and time *near* event, not actuatly event 8 7 6 5 4 3 2 1 0 101 102 103 Frequency [Hz] C02 Result: 2.6/3.8 %, 2.3/2.1 deg time) created by plotuncertaintyspectrograms_O2_C02_forG1800319 on 04-Mar-2018 Max within 20-2048 Hz:(C01 68th, C02 68th, C01 GW170104, C02 GW170104) = (6.1% / 2.2 deg, 2.6% / 2.4 deg, 5.4% / 2.1 deg, 2.6% / 2.3 deg) 5 L1 O2 C02 vs C01 Uncertainty 68th Percentile Maximum Systematic Error & Statistical Uncertainty Max Phase Bound [deg] C01 68th C02 68th C01 GW170104 C02 GW170104 10 Max Magnitude Bound [%] 4 9 8 3 7 6 2 5 4 1 3 2 0 101 102 103 1 0 Frequency [Hz] 101 102 103 All O2, 68th Percentile Frequency [Hz] created by plotuncertaintyspectrograms_O2_C02_forG1800319 on 04-Mar-2018 Max within 20-2048 Hz:(C01 68th, C02 68th, C01 GW170104, C02 GW170104) = (4.8% / 2.2 deg, 3.9% / 2.2 deg, 4.1% / 2.2 deg, 3.8% / 2.1 deg) 5 C01 Result: 6.1/4.8 %, 2.2/2.2 deg (Different from Uncertainty paper Isn t Quoted in paper, on figure ... I used Feb-27-2017, A.C. 2&3 results) Max Phase Bound [deg] C01 68th C02 68th C01 GW170104 C02 GW170104 4 3 2 1 0 C02 Result: 2.6/3.9 %, 2.4/2.2 deg 101 102 103 Frequency [Hz] G1800319-v1 8

9. Another C02 Result GW170817 GW170817, Aug 17 2017 12:41:04 UTC Systematic Error and Uncertainty 68th Percentile Maximum Error & Uncertainty 1.1 10 Max Magnitude Bound [%] 1.09 1.08 9 1.07 1.06 8 1.05 Mangitude [ ] 1.04 7 1.03 1.02 6 1.01 0.991 5 0.98 4 0.97 0.96 3 0.95 H1Systematic Error L1Systematic Error H1Error and Uncertainty L1Error and Uncertainty 0.94 2 0.93 0.92 1 0.91 0.9 0 101 102 103 101 102 103 Frequency [Hz] Frequency [Hz] created by plotuncertaintyspectrograms_O2_C02_forG1800319 on 04-Mar-2018 (H1 Mag / H1 Pha; L1 Mag / L1 Pha) = (2.6% / 2.3 deg; 3.9% / 2.1 deg) O2 C02, 20 - 2048Hz 5 5 Max Phase Bound [deg] 4 H1 L1 3 4 2 Phase [deg] 1 3 0 -1 2 -2 -3 1 -4 -5 0 101 102 103 101 102 103 Frequency [Hz] Frequency [Hz] G1800319-v1 9

10. New Answers! (Divided by IFO) Frequency Range: 20- 2048 Hz 68% Confidence Interval (i.e. 1-sigma) Systematic Error + Statistical Uncertainty O2 C02 H1 L1 GW170104 2.58% / 2.29 deg 3.8% / 2.13 deg GW170608 2.56% / 2.38 deg 3.89% / 2.18 deg GW170729 2.72% / 2.31 deg 3.78% / 2.13 deg GW170809 2.52% / 2.39 deg 3.79% / 2.13 deg GW170814 2.58% / 2.34 deg 3.85% / 2.16 deg GW170817 2.57% / 2.3 deg 3.85% / 2.15 deg GW170823 2.55% / 2.35 deg 3.8% / 2.15 deg GW170825 2.64% / 2.36 deg 3.86% / 2.12 deg All of O2 2.6% / 2.36 deg 3.85% / 2.15 deg G1800319-v1 10

11. New Answers! (Divided by Mag / Phase) Frequency Range: 20- 2048 Hz 68% Confidence Interval (i.e. 1-sigma) Systematic Error + Statistical Uncertainty O2 C02 H1 / L1 Mag [%] H1 / L1 Pha [deg] GW170104 2.58 / 3.8 2.29 / 2.13 2.56 / 3.89 GW170608 2.38 / 2.18 GW170729 2.72 / 3.78 2.31 / 2.13 GW170809 2.52 / 3.79 2.39 / 2.13 GW170814 2.58 / 3.85 2.34 / 2.16 GW170817 2.57 / 3.85 2.3 / 2.15 GW170823 2.55 / 3.8 2.35 / 2.15 GW170825 2.64 / 3.86 2.36 / 2.12 All of O2 2.6 / 3.85 2.36 / 2.15 G1800319-v1 11

12. Some Results for the CW Group For O1, C01 data, the uncertainty was re-analyzed for the CW group in T1500576 using these same methods, but for frequency bands 20-100 Hz, Einstein @ Home 20-475 Hz, Most Other Papers (PowerFlux, Freq. Hough, Sky Hough, and Time-domain F-Statistic, Low Frequency CW Paper 475-2000 Hz, High-Frequency CW paper Here we ve done the same (I ll skip the plots this time, but you can see from whence the numbers came on pg 10): Freq. Band [Hz] Magnitude (H1 / L1) [%] Phase (H1 / L1) [deg] 20-100 1.6 / 3.9 0.9 / 2.2 20-475 2.3 / 3.9 1.1 / 2.2 475-2000 2.4 / 2.1 2.3 / 1.7 G1800319-v1 12

13. Conclusions Removal of primary systematic errors drastically improve the error + uncertainty budget We re able to reduce maximum error + uncertainty limits Now limited by measurement uncertainty (i.e. patience, IFO time, and person power) We have some lessons learned to (potentially) get even better Craig and Mykyta are patient and awesome We are ready for O3 at ~3 % and 2 deg! G1800319-v1 13