Dana, Louis

The sensing function model that is currently being used has five free parameters that we can fit for: the optical gain H_c, the coupled cavity pole frequency f_cc, the optical spring frequency f_s, the quality factor of the optical spring Q_s, and the residual time delay τ_C. However, all of the sensing function models generated to fit measured data in O4 so far have excluded the time delay term. It is unclear why this is the case/when this choice was made, so we decided to explore whether or not this term should be excluded; i.e., does excluding the time delay term cause the model to fit the data better?

Our results are summarized in the attached plots, showing the sensing function model with and without the time delay term, the measured data they were fit to, and the residuals for two sample measurements taken during O4a. The sensing function report numbers are shown in the legend, along with the fit parameters generated as part of these reports (see /ligo/groups/cal/H1/reports/) written in brackets, i.e., [H_c, f_cc, f_s, Q_s, τ_C]. The difference the time delay makes in the model is more obvious in figure 2, where τ_C is almost an order of magnitude larger than that of figure 1. Looking at the residual plots on the right, the blue markers are the measured data divided by the model with the time delay, and the orange markers are the measured data divided by the model without the time delay. Comparing these two sets of residuals, it is not immedialy obvious which one is the better fit, although perhaps the blue markers (time delay included) do fit the data slightly better. Regardless, it is clear that the choice of whether or not to include this time delay term is something that should be given more thought, and indeed it seems to fit certain measurements better than others (e.g., the model that includes the time delay seems to be a slightly worse fit compared to the model without the time delay in figure 1).

Additionally, one might think that if excluding the time delay is truly the best fit, then the MCMC which generated the fit parameters for the models shown in the two figures would simply return 0 for τ_C. However, this is not what has happened. Deeper investigation is needed to figure out why.