The calculation for LIGO astronomical reach with uncertainties are updated. See the details below.
I got the updated GWINC from Nic. When I run the nomm file, the BNS range is 189.5 Mpc. The nominal value of the refractive index for nH in the code is 2.06 which is the value for the pure Ta2O5. The refractive index for Ta2O5 doped with TiO2 25% (Ta2O5:TiO2) is 2.119 (see Harry et al 2007 paper). So when I changed nH to 2.119, the BNS range became 192 Mpc due to the thinner coating.
The ring down measurements from Harry 2007 paper measure parallel loss of the coating from multilayer coating, then extract PhiH from the measurement. Again, this is done by assuming the knowledge of phiL, YL and YH. The loss angle of silica (phiL) used in the paper is 1e-4 (from Crooks 2006 paper) while the value in GWINC is 0.4e-4. In this calculation, I use phiL = 1e-4 because of a couple reasons:
- The value of 1e-4 is determined in crooks paper. Their samples and the samples used in Harry 2007 paper are for fused silica with the same heat treatment (annealing temp ~ 400-600 C). I think 0.4e-4 is from higher heat treatment (up to 700-800 C) (see Penn 2010 LVC march presentation, here).
- In Harry 2007 measurements, sample 1 is a multilayer structure of fused silica and Ta2O5: TiO2(6%). Sample6 is a single layer of Ta2O5: TiO2(6%). Sample 6 can determine the parallel loss of phiH directly without the knowledge of fused slilca's material parameters (thin form). When the loss angle of Ta2O5:TiO2(6%) as measured from sample6 is combine with the loss angle of fused silica = 1e-4, the result from the measurement from Sample1 and the calculation agree
So the value phiL = 1e-4 is only used for extracting phiH as a function of YH, while phiL = 0.4e-4 is used as a nominal value in noise budget calculation.
Running the code
The calculation is done in the code name BNS_score.m (see the attached zipped file). The file calls on IFOModel_rnd2.m that generates random material parameters by normrnd command. The plot can be made by running plot_hist.m file.
fig1: histograms and gaussian fits for coating BR noise and total noise at 100Hz.
fig2: The astronomical range for BNS, in MPC unit.The histogram is from 20k samples. The average is at 189.2 Mpc, while the mode is around 188 MPc. |