South Pole Ice (SPICE) model Dmitry Chirkin, UW Madison

Outline Introduction: experimental setup Improved data processing: new feature extraction New features of/news from ppc Ice anisotropy Improved likelihood description and optimized binning Results

Experimental setup

Flasher dataset: SPICE Mie

Flasher dataset: new FE

Updates to the calibration and feature extraction in the fat-reader Fall 2010

waveform baseline baseline corrections to ATWD0,1,2 and FADC are gathered from the data:  from 0-bin of the waveform  from beacon launches, if available (new)  may change during run (updated in incr*step intervals, e.g., 10 sec)  performed in float numbers (new) from beaconsfrom bin #0 quality cut More plots here:

Timing of DOM launches in DAQ FADC nominal delay time: 7* *3.3=113.7 ns extra 2 clock cycles for TestDAQ 1 cycle+15 ns correction to domcal<7.2 values 15 ns correction to domcal<7.5 values sign of ATWD1 delta correct, but definition wrong?

Remaining ATWD-FADC offset DAQtestDAQ

Charge

Some new features new implementation of unfolding, based on NNLS (my translation to C of Fortran code by Lawson and Hanson); old Bayesian unfolding still there adaptive baseline calculation, uses simplified topological trigger logic:  Merge all sets of waveform values that have all of the 7 consecutive samples are within 4.5*[bin size] of each other  fit a line, use to extrapolate baseline (in the vicinity of the fit)  the waveforms are split into non-overlapping non-zero segments that are fed into the unfolding routine. This is very efficient, thus no need to resort to special treatment of simple waveforms. SLC pulses are unfolded just like any other FADC waveform for part of FADC overlapping with ATWD the saturated values are recovered by re-convolving the pulses extracted from ATWD. This improves the droop correction of the FADC waveform. droop is carried-over from the previous DOM launch  across both launches and events  checks that there was not too much droop

Channel merging new old old: exclusion window after the end of ATWD new: Subtract FADC SPE-shape-convoluted ATWD pulses from FADC waveform, then combine Launch #0Launch #1

Example in muon data

Example in flasher data

More examples here:

Example in flasher data DOM 64-30, when DOM flashing Launch #0 ATWDLaunch #0 FADC

Example in flasher data DOM 64-30, when DOM flashing Launch #1 ATWDLaunch #1 FADC

Direct photon tracking with PPC photon propagation code GPU scaling: (Graphics Processing Unit) CPU c++: Assembly: GTX 295: execution threads propagation steps photon absorbed new photon created (taken from the pool) threads complete their execution (no more photons) scattering (rotation)

News with PPC new version: in OpenCL  now written in/for 4 languages/platforms: c++, Assembly, c for CUDA, c with OpenCL  All of these agree with each other, and with i3mcml  Now confirmed that clsim agrees with ppc as well better flasher angular distribution Angular emission profile is specified with 2 rms widths: vertical=9.7 horizontal=9.8 (tilted LEDs) vertical=9.2 horizontal=10.1 (horizontal LEDs) Old: simulated a rectangle in theta, phi with rms given above New: simulate a 2d Gaussian (von Mises-Fisher distribution) with the average rms width of 9.7 degrees. Both are approximations, the 2d Gaussian is probably better. direct hole ice simulation anisotropic ice simulation Fall 2011

Direct Hole Ice simulation Hole radius = ½ nominal DOM radius Hole effective scattering ~ 50 cm Hole absorption ~ 100 m Do we need more detailed DOM simulation, including info about both the direction and point on the DOM surface? Perhaps not, if the scattering length in the hole is not much shorter than the hole radius (speculation).

Traditional “hole ice” angular sensitivity

DOM 20,20  20,19: n z =cos . nominal direct hole ice

DOM 20,20  20,21: n z =cos .

DOM 20,20  20,19: xz Ratio direct hole ice/nominal nominal hole ice deficit enhancement

DOM 20,20  20,21: xz enhancementdeficit nominal hole ice

remarks Effect of the hole ice is quite subtle: The number of photons is reduced on the side facing the emitter, and enhanced in the direction away from the emitter. The traditional “hole ice” implementation via the angular sensitivity modification reduces the number of photons in the direction into the PMT, and enhances the number of photons arriving into the back of the PMT. If the emitter is inside the hole ice, the enhancement of photons received on the same string is dramatic. Either effect is much smaller when receiver is on the different string  can decouple measurement of bulk ice properties from the hole ice

Approximation to Mie scattering f SL Simplified Liu: Henyey-Greenstein: Mie: Describes scattering on acid, mineral, salt, and soot with concentrations and radii at SP Summer 2010

Ice anisotropy? Winter 2011

Geometry around string 63

Evidence in flasher data

What is Ice anisotropy Direction of more scattering Direction of less scattering Naïve approximation: multiply the scattering coefficient by a function of photon direction, e.g., by 1 +  ( cos 2  - 1/3 ) However, this is unphysical:  (n in,n out ) =  (-n out,-n in ) (time-reversal symmetry)  (n in,n out ) =  (-n in,-n out ) (symmetry of ice)   (n in,n out ) =  (n out,n in )

A possible parameterization The scattering function we use is f(cos  ), a combination of HG and SL. How about this extension: f(cos  )= f(n in. n out )  f(An in. An out )  0 0 A = 0  0 in the basis of the 2 scattering axes and z (  are, e.g., 1.05) /  However, function f(cos  ) is well-defined for only cos  between -1 and 1. A possible modification is n in  An in /| An in |  n out  A -1 n out /| A -1 n out |. This introduces two extra parameters:  (in addition to the direction of scattering preference). The geometric scattering coefficient is constant with azimuth. However, the effective scattering coefficient receives azimuthal dependence as:

Scattering example (5% anisotropy)

Fitting for the anisotropy coefficients  1 =0.040,  2 =-0.082

Effect of anisotropy on simulation  =1.0  =1.05, b=0.93

How important is anisotropy? from SPICE paper threshold: > 0, 1, 10, 100, 400 p.e. 30% 21% so-so awesome ! threshold: > 10 p.e.

Likelihood description of data: SPICE Mie Find expectations for data and simulation by minimizing –log of Regularization terms: Measured in simulation: s and in data: d; n s and n d : number of simulated and data flasher events Sum over emitters, receivers, time bins in receiver

Likelihood description of data Two  2 functions were used:  q 2 :sum over total charges only (no time information)~ terms  t 2 :sum over total charges split in 25-ns bins~ terms Both zero and non-zero contributions contribute to the sum  however, the terms in the above sum are 0 when both d=0 and s=0. Sum over emitters, receivers, time bins in receiver

Exact description: new There is an obvious constraint which can be derived, e.g., from the normalization condition Suppose we repeat the measurement in data n d times and in simulation n s times. The  s and  d are the expectation mean values of counts per measurement in simulation and in data. With the total count in the combined set of simulation and data is s + d, the conditional probability distribution function of observing s simulation and d data counts is

Two hypotheses: If data data and simulation are unrelated and completely independent from each other, then we can maximize the likelihood for  s and  d independently, which with the above constraint yields On the other hand, we can assume that data and simulation come from the same process, i.e., We can compare the two hypotheses by forming a likelihood ratio

Derivation for multiple bins

Example To enhance the differences between the two likelihood approaches, consider that the amount of simulation is only 1/10 th of that of data

Using full range of the data and simulationSimulated exp(-x/5.0) with mean of 5.0

Optimal binning is determined by desire to: capture the changes in the rate maximize the combined statistical power of the bins The conditional probability (given the total count D) is if the bins are considered independently  i =d i. if the rate is constant across all bins,  =  i =D/L. The likelihood ratio is This never exceeds 1!  so we use 1/L! or 8. Bin size

Limiting case of near-constant rate Small bin description Single large bin of length L: We prefer a single large bin if:

Optimal binning typical

Optimal binning: flasher data -log(8) log(L!)

Initial fit to sca ~ abs Starting with homogeneous “bulk ice” properties iterate until converged  minimize  q 2 1 simulated event/flasher 4 ev/fl10 ev/fl

Correlation with dust logger data effective scattering coefficient fitted detector region

Fit to scaling coefficients  sca and  abs Both  q 2 and  t 2 have same minimum!

Absolute calibration of average flasher is obtained “for free”  no need to know absolute flasher light output beforehand  no need to know absolute DOM sensitivity 1  statistical fluctuations Minima in p y, t off, f SL

SPICE Mie [mi:]

New result

Fitting for the anisotropy coefficients  1 =0.040,  2 =-0.082

Interpretation Tilt +4% ice flow, wind -8% Direction of more scattering

Correlation of absorption vs. scattering

Examples with the new fit: 63,5

Examples with the new fit: 63,15

Examples with the new fit: 63,25

Examples with the new fit: 63,35

Examples with the new fit: 63,45

Examples with the new fit: 63,55

Conclusions and remarks Improved data processing with the new feature extraction Improved likelihood description and optimized binning Despite these substantial changes the new model is compatible with SPICE Mie! Evidence for ice anisotropy in the xy plane is presented. The quality of the fit improves substantially when anisotropy is considered in the fit:  The rms of data/simulation drops from 30% to 20%!

Other interpretations What else could cause the observed effect? difference in refractive coefficient in aligned ice crystals? n 1 =1.309, n 2 =1.313  the difference is too small does not directly affect the amount of arriving charge anyway geometry stretching?  Need more than 10 m per 1km: unlikely

What’s next Verify/refit SPICE using the new all-purpose flasher runs fit the hole ice: average detailed description eventually:  fit the color LED data