Fitting the 6-parameter ice model to the flasher data
Software
Get the software and processing scripts here.
Datasets were processed with fat-reader version 0.99.94.
MMC version 1.5.4 was used to simulate muon background.
A version of ppc for GPU is included in the above software archive.
Introduction
Previous work on this (see for introduction and explanation of the datasets).
Presentation given at the IceCube collaboration meeting in Berlin.
Method
For each set of ice parameters (defined by 171 x 2 scattering and absorption coefficients of the 10 m ice layers) simulate n=1-100 flasher events, each of ~ x . 2.2.1010 photons (with 11.3% glass/gel transmission, PMT efficiency, etc. at 405 nm). The numbers of photons, binned in 25 ns time steps, are compared between data and simulation via a likelihood function constructed as SUMi log2{ (1+si)/(1+di.n) } + R.
The sum is over all time bins in the range 0-2500 ns from the flasher time for those DOMs that receive on average less than 1500 p.e. (to ignore the saturation effects). The LC condition is simulated. The R in the above expression is a regularization term that smooths the table of scattering and absorption coefficients where possible (constructed in a usual way as a sum of squares of second derivatives).
Steepest descent algorithm was used to minimize the so-constructed likelihood function. The plot below shows the normalized gradient computed for several iterations (different iterations shown in different colors, black being the last one). Also shown is the likelihood value computed at 40 points along the gradient vector.
Results
New ice properties fitted to flasher data (table):
Comparison of the fitted flasher simulation and data (cf. with aha).
Comparison of the muon simulation and IC59 data (also shown for aha).
Next steps
- The method in the form presented here works well as of 10/7/9. The result above is shown after only 5 steps of the minimizer, simulating with n=1. It might be possible to achieve an even better result after a few more iterations and with more flasher events simulated per flasher. Estimated time per iteration with n=100 on 2 GPUs is 2-3 days.
- The normalization x in the likelihood function was guessed. Next, the minimization will be performed for several different values of x, allowing one to get an absolute measurement of the number of photons emitted by an average flasher.
- Get the same result starting with a different initial guess, say with bulk ice.
- Verify that the same ice table can be used to describe the 45-degree flasher set, and the standard candle data sets.
- Add the "GPU" functionality to the i3ppc icetray module, simulate a background muon set and repeat various simulation/data comparison studies.
- simulate a bulk of IC22 data, for best fit and 1-sigma away parameter sets, use that to estimate systematic errors in the unfolded IC22 neutrino spectrum.
- Come up with a name for the new ice model. How about
- MOAI (MOdified Aha Ice)
- FLASH-ICE
- EMI (Enhanced Millennium Ice)
Acknowledgments
Thanks to Martin Merck for having the insight to order, assemble, and configure the GPU computer with just the perfect timing.
Thanks to Tareq Abuzayyad for demonstrating that the GPU-accelerated photon propagation can run 100s of times faster than the CPU code.