Determination of True Attenuation Lengths using SPASE-AMANDA Coincidence Data

1. Determination of True Attenuation Lengths using SPASE-AMANDA Coincidence Data Tim Miller JHU/APL

2. Introduction • Problem: • Best attenuation length fits to SPASE-AMANDA coincidence data disagree quantitatively with ice properties measured internally • Internal measurements: latt = 20-30 m • SPASE-AMANDA coincidences: latt=55-80 m • But, there is agreement on one qualitative feature: • Depth of dust layers in ice, which cause relative reduction in latt

3. Possible Explanation • Reconstructed tracks to which fits are applied are SPASE-2 event reconstructions • SPASE-2 has finite direction and position reconstruction errors: • Direction error = ??? deg • Position error = ??? m • Hit probability vs distance from module is fit with exponential to determine attenuation length, but… • Distance from module is wrong because of SPASE pointing errors • From phase space considerations, we know that reconstructed distances are more likely to be further from than nearer to true distances to modules • This results in artificially high hit probabilities at large distances, which results in artificially long attenuation lengths

4. How determine true attenuation length (1) • Use Monte Carlo approach • Assumptions • Hit probability vs distance is truly exponential • SPASE pointing error is known • SPASE position error is known • Pointing and position errors can be modeled as 2D Gaussians • SPASE position is known • AMANDA module locations are known • Sensitivity to assumptions can be checked by varying them

5. Monte Carlo Procedure (1) • for i=1:several million • Drop muon track randomly in square somewhat larger than SPASE-2 • Reconstruct hit location assuming gaussian x-y errors • Keep event if it is reconstructed inside SPASE-2 (modeled as a square) • Pick random direction for track • Reconstruct direction using random gaussian theta-phi errors • Using reconstructed landing point and direction, calculate reconstructed impact parameter for every AMANDA module • Using true landing point and direction, calculate true impact parameter for every AMANDA module • Randomly determine hit or no-hit on each AMANDA module based on true impact parameter and several assumed true attenuation lengths • Compile statistics on hit probability vs true impact parameter for each OM for each true attenuation length • Compile statistics on hit probability vs reconstructed impact parameter for each OM for each true attenuation length • End

6. Monte Carlo Procedure (2) • For I=1:(number of AMANDA OM’s) • For each true attenuation length • Fit attenuation length to true hit probability vs distance • Fit attenuation length to reconstructed hit probability vs distance • End • End • Now we know what reconstructed attenuation length corresponds to what true attenuation length for every module • Given a set of reconstructed attenuation lengths from the data we can interpolate with our results above to get the true attenuation length to which it corresponds

7. Results: True and Reconstructed Tracks • Hit Probability vs Distance Distributions • Module 302 • 5 x 106 Simulated Tracks True Latt: • True hit probability vs distance is exponential • Reconstructed hit probability vs distance levels off at short distance, as observed in data True Tracks True Latt: Reconstructed Tracks

8. Fits to True and Reconstructed Tracks • Exponential fit to true hit probability vs distance recovers the input attenuation length, as expected • Exponential fit to reconstructed hit probability vs distance gives larger attenuation length, as expected y=x

9. Fit Attenuation Length vs. Depth Data result: fit attenuation lengths vs OM depth Monte Carlo result: fit attenuation lengths vs OM z * • In data, we see that fit attenuation length generally increases with depth • Monte Carlo result reproduces this • It is apparently due to larger impact parameter errors at greater distance from SPASE-2 (i.e., deeper modules) resulting in larger apparent attenuation lengths

10. Conversion of Fit Attenuation Length to True Attenuation Length • Example of conversion from fit to true attenuation length • Single selected module = OM 301 • Red circles = fits to true and reconstructed tracks • Blue line = linear fit • Green line = 2nd order fit • Conclusion: linear interpolation sufficient for converting from fit to true attenuation length Fit attenuation length using reconstructed tracks True (MC input) attenuation length

11. Results Direction Error = 2 deg Spatial Error = 8 m True attenuation lengths = 35 to 55 m Red circles are the fit attenuation lengths seen in the real data Green circles are true attenuation lengths after we go through the procedure just described, assuming reconstruction errors given above, and convert every fit attenuation length to a “true” attenuation length via linear interpolation

12. Results Direction Error = 2.5 deg Spatial Error = 8 m • True attenuation lengths = 25 to 45 m • Direction fit error of SPASE-2 has large effect on ability to recover true attenuation length • Difference of 0.5 deg (2 vs 2.5) in assumed reconstruction accuracy changes true attenuation lengths recovered by 10 m • Conclusion: we need to know SPASE-2 reconstruction error very accurately to do this