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Energy Determination using X2 and NFit

Energy Determination using X2 and NFit. Andrew Smith University of Maryland. Energy Determination Method - Crab. Measure event excess in 7 independent “slices” in x2 and NFit. Simulate each reconstruction epoch Use the MCAnalysis “sensi()” method to compute the number of events/day vs alpha.

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Energy Determination using X2 and NFit

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  1. Energy Determination using X2 and NFit Andrew Smith University of Maryland Andrew Smith May 2006, Milagro Collaboration Meeting

  2. Energy Determination Method - Crab • Measure event excess in 7 independent “slices” in x2 and NFit. • Simulate each reconstruction epoch • Use the MCAnalysis “sensi()” method to compute the number of events/day vs alpha. • Find minimum ChiSq for (A,alpha). • All analysis done using Geant 2.0 and “dev” version of electronic and noise simulation. • VV’s PMT simulation is included by default. • PE levels were “rescaled” to be appropriate for old calibrations. Andrew Smith May 2006, Milagro Collaboration Meeting

  3. Cuts Andrew Smith May 2006, Milagro Collaboration Meeting

  4. Energy Determination Method • Use x2/NFit slices used in weighted analysis. • Exploit energy dependence of the cuts. • Theta < 30 deg • Alpha = -2.4 spectrum Andrew Smith May 2006, Milagro Collaboration Meeting

  5. Epochs • Single layer Fitters • Epoch 1 – COM core fitter • Epoch 2 – OFF core fitter • Epoch 3 – ORCOM core fitter • Multilayer Fitters • Epoch 4 – Gaussian core fitter - 3 layer core fitter • Epoch 5 – Gaussian core fitter - 2 layer core fitter • Analysis strategy: • Combine epochs 1-3 and simulate as OFF only • Combine epochs 4-5 using “nfit_2layerEquiv” and simulate as epoch 5. Andrew Smith May 2006, Milagro Collaboration Meeting

  6. Crab Spectrum Epochs 1-3 Events/day CrabCyg Hot SpotCyg Diffuse cut Fit Spectrum: 5.70x10-7 E-2.60±0.08 c2 =6.5/5 d.o.f. Andrew Smith May 2006, Milagro Collaboration Meeting

  7. Crab Fit Results for Epochs 1-3 alpha | A,Chisq | = 2.00 | 1.35 39.89 alpha | A,Chisq | = 2.05 | 1.56 35.30 alpha | A,Chisq | = 2.10 | 1.79 30.92 alpha | A,Chisq | = 2.15 | 2.04 26.80 alpha | A,Chisq | = 2.20 | 2.33 22.96 alpha | A,Chisq | = 2.25 | 2.64 19.45 alpha | A,Chisq | = 2.30 | 2.99 16.29 alpha | A,Chisq | = 2.35 | 3.36 13.53 alpha | A,Chisq | = 2.40 | 3.77 11.19 alpha | A,Chisq | = 2.45 | 4.21 9.30 alpha | A,Chisq | = 2.50 | 4.68 7.88 alpha | A,Chisq | = 2.55 | 5.18 6.96 alpha | A,Chisq | = 2.60 | 5.70 6.54 --- minimum alpha | A,Chisq | = 2.65 | 6.25 6.64 alpha | A,Chisq | = 2.70 | 6.82 7.25 alpha | A,Chisq | = 2.75 | 7.40 8.37 alpha | A,Chisq | = 2.80 | 7.99 10.00 alpha | A,Chisq | = 2.85 | 8.58 12.12 alpha | A,Chisq | = 2.90 | 9.17 14.72 alpha | A,Chisq | = 2.95 | 9.74 17.76 alpha | A,Chisq | = 3.00 | 10.30 21.23 1395 days Ev/day Error ------ ----- 8.97 1.34 2.12 0.60 1.33 0.34 0.95 0.20 0.46 0.12 0.16 0.07 0.14 0.04 Andrew Smith May 2006, Milagro Collaboration Meeting

  8. Crab Spectrum Epochs 4-5 Events/day CrabCyg Hot SpotCyg Diffuse cut Fit Spectrum: 3.7x10-7 E-2.83±0.2 c2 =10.3/5 d.o.f. Andrew Smith May 2006, Milagro Collaboration Meeting

  9. Crab Fit Results for Epochs 4-5 alpha | A,Chisq | = 2.00 | 0.32 22.80 alpha | A,Chisq | = 2.05 | 0.38 22.04 alpha | A,Chisq | = 2.10 | 0.46 21.24 alpha | A,Chisq | = 2.15 | 0.54 20.40 alpha | A,Chisq | = 2.20 | 0.64 19.52 alpha | A,Chisq | = 2.25 | 0.76 18.62 alpha | A,Chisq | = 2.30 | 0.90 17.69 alpha | A,Chisq | = 2.35 | 1.06 16.74 alpha | A,Chisq | = 2.40 | 1.24 15.79 alpha | A,Chisq | = 2.45 | 1.44 14.84 alpha | A,Chisq | = 2.50 | 1.67 13.92 alpha | A,Chisq | = 2.55 | 1.93 13.05 alpha | A,Chisq | = 2.60 | 2.21 12.25 alpha | A,Chisq | = 2.65 | 2.51 11.55 alpha | A,Chisq | = 2.70 | 2.84 10.98 alpha | A,Chisq | = 2.75 | 3.18 10.57 alpha | A,Chisq | = 2.80 | 3.52 10.34 alpha | A,Chisq | = 2.85 | 3.87 10.33 --- Minimum alpha | A,Chisq | = 2.90 | 4.20 10.56 alpha | A,Chisq | = 2.95 | 4.51 11.03 alpha | A,Chisq | = 3.00 | 4.78 11.74 456 days Ev/day Error ------ ----- 1.59 1.94 3.90 1.15 2.02 0.68 0.28 0.42 0.90 0.27 0.39 0.13 Andrew Smith May 2006, Milagro Collaboration Meeting

  10. Cygnus Hot Spot Spectrum • Define Location of Cygnus Hot Spot as 73.5<glon<76.5 && -1.5<glat<1.5 • Also examine flux from the Cygnus region. Define the region as 65<glon<85 && -3<glat<+3 excluding the Cygnus Hot Spot contained within. Andrew Smith May 2006, Milagro Collaboration Meeting

  11. Cygnus Spectrum Epochs 1-3 Events/day CrabCyg Hot SpotCyg Diffuse cut Events/day Hot Spot: alpha<<2.0 Poor Fit Diffuse: (13.0 x 10-7) E-2.50±0.2 c2 =14.4/5dof cut Andrew Smith May 2006, Milagro Collaboration Meeting

  12. Crab Fit Results for Epochs 1-3 Hot Spot Diffuse alpha | A,Chisq | = 2.00 | 0.38 29.35 | 4.00 19.35 alpha | A,Chisq | = 2.05 | 0.41 29.78 | 4.61 18.51 alpha | A,Chisq | = 2.10 | 0.45 30.21 | 5.30 17.72 alpha | A,Chisq | = 2.15 | 0.48 30.62 | 6.06 16.97 alpha | A,Chisq | = 2.20 | 0.51 31.02 | 6.89 16.30 alpha | A,Chisq | = 2.25 | 0.54 31.41 | 7.79 15.71 alpha | A,Chisq | = 2.30 | 0.56 31.77 | 8.74 15.22 alpha | A,Chisq | = 2.35 | 0.58 32.11 | 9.76 14.83 alpha | A,Chisq | = 2.40 | 0.59 32.43 | 10.82 14.56 alpha | A,Chisq | = 2.45 | 0.60 32.71 | 11.91 14.42 alpha | A,Chisq | = 2.50 | 0.60 32.97 | 13.01 14.39 alpha | A,Chisq | = 2.55 | 0.59 33.21 | 14.12 14.50 alpha | A,Chisq | = 2.60 | 0.57 33.41 | 15.21 14.73 alpha | A,Chisq | = 2.65 | 0.55 33.58 | 16.27 15.09 alpha | A,Chisq | = 2.70 | 0.52 33.73 | 17.28 15.55 alpha | A,Chisq | = 2.75 | 0.49 33.85 | 18.21 16.12 alpha | A,Chisq | = 2.80 | 0.45 33.95 | 19.05 16.79 alpha | A,Chisq | = 2.85 | 0.41 34.03 | 19.80 17.53 alpha | A,Chisq | = 2.90 | 0.37 34.10 | 20.43 18.34 alpha | A,Chisq | = 2.95 | 0.32 34.14 | 20.94 19.20 alpha | A,Chisq | = 3.00 | 0.28 34.18 | 21.31 20.11 Ev/day Error ------ ----- Hot Spot Diffuse 2.02 2.20 | 35.29 7.61 -2.67 0.97 | 9.74 3.36 0.63 0.55 | 1.87 1.91 -0.19 0.33 | 3.65 1.12 0.11 0.19 | 1.81 0.65 0.36 0.10 | 0.40 0.36 0.20 0.06 | 0.79 0.20 Andrew Smith May 2006, Milagro Collaboration Meeting

  13. Cygnus Spectrum Epochs 4-5 Events/day CrabCyg Hot SpotCyg Diffuse cut Events/day Hot Spot: (3.4x10-7) E-2.75±0.20 c2 = 2.8/5 d.o.f. Diffuse: (11.4x10-7) E-2.85±0.25 c2 = 4.1/ 5 d.o.f. Andrew Smith May 2006, Milagro Collaboration Meeting cut

  14. Cygnus Fit Results for Epochs 4-5 Hot Spot Diffuse alpha | A,Chisq | = 2.00 | 0.42 9.97 | 1.14 10.96 alpha | A,Chisq | = 2.05 | 0.50 9.46 | 1.34 10.54 alpha | A,Chisq | = 2.10 | 0.59 8.91 | 1.58 10.10 alpha | A,Chisq | = 2.15 | 0.69 8.35 | 1.86 9.65 alpha | A,Chisq | = 2.20 | 0.80 7.77 | 2.18 9.17 alpha | A,Chisq | = 2.25 | 0.94 7.18 | 2.55 8.68 alpha | A,Chisq | = 2.30 | 1.09 6.58 | 2.97 8.17 alpha | A,Chisq | = 2.35 | 1.26 5.99 | 3.46 7.66 alpha | A,Chisq | = 2.40 | 1.45 5.40 | 4.00 7.15 alpha | A,Chisq | = 2.45 | 1.67 4.84 | 4.61 6.63 alpha | A,Chisq | = 2.50 | 1.90 4.31 | 5.28 6.14 alpha | A,Chisq | = 2.55 | 2.16 3.83 | 6.02 5.66 alpha | A,Chisq | = 2.60 | 2.44 3.43 | 6.82 5.22 alpha | A,Chisq | = 2.65 | 2.74 3.11 | 7.67 4.83 alpha | A,Chisq | = 2.70 | 3.05 2.90 | 8.57 4.50 alpha | A,Chisq | = 2.75 | 3.36 2.81 | 9.50 4.25 alpha | A,Chisq | = 2.80 | 3.68 2.87 | 10.44 4.08 alpha | A,Chisq | = 2.85 | 3.99 3.08 | 11.37 4.02 alpha | A,Chisq | = 2.90 | 4.29 3.47 | 12.26 4.06 alpha | A,Chisq | = 2.95 | 4.55 4.02 | 13.09 4.22 alpha | A,Chisq | = 3.00 | 4.79 4.73 | 13.83 4.49 456 days Ev/day Error ------ ----- Hot Spot Diffuse 8.73 3.29 | 24.23 11.32 1.54 1.83 | 12.90 6.39 2.99 1.08 | 2.85 3.74 1.01 0.67 | 3.98 2.33 0.78 0.42 | 3.62 1.46 0.50 0.26 | 1.83 0.92 0.72 0.20 | 1.58 0.68 Andrew Smith May 2006, Milagro Collaboration Meeting

  15. Potential Systematic Errors • Confirmation of A4/X2 at high end? Not enough MC data! Very few hadrons simulated with high (x2,nfit) or A4! Comparison of simulated hadrons and data. Andrew Smith May 2006, Milagro Collaboration Meeting

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