1. Photon propagation and ice properties Bootcamp 2011 @ UW Madison Dmitry Chirkin, UW Madison r air bubble photon

2. Propagation in diffusive regime absorptionscattering  r 2 =A. r 1  = = 

3. cascades near: far: combined: diffusive formula actually also gives correct limit at small distances but is difficult to compute (see icecube/201102007) muons near: far: combined: Photon propagation approximations

4. Cascades

5. Cascades: near

6. Cascades: far

7. nearby far numerical small angle merged ppc simulation ~1/r 2 ~1/r exp(-r/ p ) cascades

8. fit

9. Muons

10. nearby far merged ppc simulation ~1/r ~1/r 1/2 exp(-r/ p ) muons

11. fit

12. Mie scattering theory Continuity in E, H: boudary conditions in Maxwell equations e -ikr+i  t e -i|k||r| r

13. Mie scattering theory Analytical solution! However: Solved for spherical particles Need to know the properties of dust particles: refractive index (Re and Im) radii distributions

14. Mie scattering theory Dust concentrations have been measured elsewhere in Antarctica: the “dust core” data

15. Mie scattering - General case for scattering off particles Scattering function: approximation

16. Scattering and Absorption of Light Source is blurred Source is dimmer scattering absorption a = inverse absorption length (1/λ abs ) b = inverse scattering length (1/λ sca )

17. scattered absorbed Measuring Scattering & Absorption Install light sources in the ice Use light sensors to: - Measure how long it takes for light to travel through ice - Measure how much light is delayed - Measure how much light does not arrive Use different wavelengths Do above at many different depths

18. Embedded light sources in AMANDA 45° isotropic source (YAG laser) cos  source (N 2 lasers, blue LEDs) tilted cos  source (UV flashers)

19. Timing fits to pulsed data Fit paraboloid to  2 grid ►Scattering: e ±  e ►Absorption: a ±  a ►Correlation:  ►Fit quality:  2 min Make MC timing distributions at grid points in e - a space At each grid point, calculate  2 of comparison between data and MC timing distribution (allow for arbitrary t shift )

20. Fluence fits to DC data d1d1 d2d2 DC source In diffusive regime: N(d)  1/d exp(-d/ prop )  prop = sqrt( a e /3) c = 1/ prop d log(Nd) slope = c c1c1 c2c2 c1c1 dust No Monte Carlo!

21. Light scattering in the ice bubbles shrinking with depth dusty bands

22. Wavelength dependence of scattering

23. Light absorption in the ice LGM

24. 3-component model of absorption Ice extremely transparent between 200 nm and 500 nm Absorption determined by dust concentration in this range Wavelength dependence of dust absorption follows power law

25. A 6-parameter Plug-n-Play Ice Model b e (,d ) a(,d ) scattering absorption b e ( ,d ) Power law: -  3-component model: CM dust -  + Ae - B / T(d )T(d ) Linear correlation with dust: CM dust = D·b e (400) + E A = 6954 ± 973 B = 6618 ± 71 D = 71.4± 12.2 E = 2.57 ± 0.58  = 0.90 ± 0.03  = 1.08 ± 0.01 Temperature correction:  a = 0.01a  T id=301 id=302 id=303

26. AHA model Additionally Heterogeneous Absorption: deconvolve the smearing effect

27. Is this model perfect? Fits systematically off Points at same depth not consistent with each other! Individually fitted for each pair: best possible fit

28. Is this model perfect? Averaged scattering and absorptionFrom ice paper Measured properties not consistent with the average! Deconvolving procedure is unaware of this and is using the averages as input When replaced with the average, the data/simulation agreement will not be as good

29. SPICE: South Pole Ice model Start with the bulk ice of reasonable scattering and absorption At each step of the minimizer compare the simulation of all flasher events at all depths to the available data set do this for many ice models, varying the properties of one layer at a time  select the best one at each step converge to a solution!

30. SPICE Mie [mi:] Dmitry Chirkin, UW Madison

31. Simplified Mie Scattering Single radius particles, described better as smaller angles by SAM Also known as the Liu scattering function Introduced by Jon Miller

32. New approximation to Mie f SAM

33. Dependence on g= and f SAM g= f SAM 0.8 0 0.9 0 0.95 0 0.9 0.3 0.9 0.5 0.9 1.0 flashing 63-50  64-50

34. Dependence on and f SL cascadesmuons

35. New global fit to everything in SPICE 1. For some starting values, find best values of sca ~ abs. 2. Find best values of p y, t off, f SAM,  sca,  abs, llh tot, … p y photon yield factor t off global time offset (rising edge of the flasher pulse) f SAM fraction of SAM contribution to the scattering function  sca scaling of scattering coefficient  abs scaling of absorption coefficient 3. Repeat until converged (~3 iterations) 4. Refine the fit with sca and abs independent from each other Charge only Full likelihood with timing

36. Verification with toy simulation Input table Simulated 60 x 250 events Reconstructed table with 10 event/flasher 250 event/flasher In the dust peak

37. Correlation with dust logger With 10 events/flasher, 250 in dust peakWith 250 events/flasher everywhere

38. Plots for individual flashers SPICE Mie  AHA 

39. Plots for CORSIKA/data  SPICE Mie   AHA 

40. Plots from Anne (CORSIKA IC40)

41. Plot from Jacob Feintzeig

42. SPICE Mie: ice coefficients

43. Global scaling to ice parameters Minimum is in the same place with both likelihoods!

44. Dust logger

45. IceCube in-ice calibration devices 3 Standard candles 56880 Flashers 7 dust logs

46. Correlation with dust logger data effective scattering coefficient (from Ryan Bay) Scaling to the location of hole 50 fitted detector region

47. Improvement in simulation by Anne Schukraft by Sean Grullon Downward-going CORSIKA simulation Up-going muon neutrino simulation

48. Photon tracking with tables First, run photonics to fill space with photons, tabulate the result Create such tables for nominal light sources: cascade and uniform half-muon Simulate photon propagation by looking up photon density in tabulated distributions  Table generation is slow  Simulation suffers from a wide range of binning artifacts  Simulation is also slow! (most time is spent loading the tables)

49. Light propagation codes: two approaches (2000) PTD Photons propagated through ice with homogeneous prop. Uses average scattering No intrinsic layering: each OM sees homogeneous ice, different OMs may see different ice Fewer tables Faster Approximations Photonics Photons propagated through ice with varying properties All wavelength dependencies included Layering of ice itself: each OM sees real ice layers More tables Slower Detailed

50. photonicsBulk PTDLayered PTD PTD vs. photonics: layering average ice type 1 type 2 type 3“real” ice 3 3 3 1 1 2 2 2 2 2 2

51. Direct photon tracking with PPC simulates all photons without the need of parameterization tables using Henyey-Greenstein scattering function with =0.8 using tabulated (in 10 m depth slices) layered ice structure employing 6-parameter ice model to extrapolate in wavelength transparent folding of acceptance and efficiencies Slow execution on a CPU: needs to insert and propagate all photons Quite fast on a GPU (graphics processing unit): is used to build the SPICE model and is possible to simulate detector response in real time. photon propagation code