Muons in air showers Muons on the surface

Muons in air showers Muons on the surface Muon bundles deep underground March 10, 2009 Tom Gaisser 1

Cosmic-ray cascades Extensive Air Shower (EAS) – refers to a cascade with sufficient energy ( > 100 Te. V) to reach the ground March 10, 2009 Tom Gaisser 2

Hadronic core of cascade March 10, 2009 Tom Gaisser 3

Hadronic core (p. 2) March 10, 2009 Tom Gaisser 4

Hadronic core (p. 3) March 10, 2009 Tom Gaisser 5

Hadronic core (p. 4) March 10, 2009 Tom Gaisser 6

Hadronic core (p. 5) March 10, 2009 Tom Gaisser 7

Muons in EAS (low energy) March 10, 2009 Tom Gaisser 8

High-energy muons in EAS March 10, 2009 Tom Gaisser 9

Elbert* approximation for Nm(>Em) *Phys. Rev. D 27 (1983) 1448 March 10, 2009 Tom Gaisser 10

Muons in the deep ice p 1 Nm(>Em, E 0) = A 0. 0145 Te. V Em cos q E 0 A Em x p 2 A Em E 0 1 - P 1 = 0. 76 p 2 = 5. 3 Elbert (1978), Elbert, Gaisser, Stanev (1983) --parameterization fits Monte Carlo sims for average Nm a = 2 Me. V / g/cm 2, x = 2. 5 km. w. e. Energy loss: d. Em / d. X = - a – E / x Em* = exp [ X / x ] ( Em + e ) – e , energy of muon at surface d. Nm ( X, E 0 ) d. Em March 10, 2009 = e ~ 0. 5 Te. V energy of muon at slant depth X = d / cos q d. Nm( X = 0 ) d. Em* exp [ X / x ] Tom Gaisser 11

Check for consistency Inclusive integral muon spectra (integrated over primary spectrum): Compare: 0. 186 x 25 ~ 5 840 x 66 / 104 ~ 6 March 10, 2009 Tom Gaisser 12

Visible energy in I 3 Energy in muon bundle ∫ Em d. Nm( X, E 0 ) d. Em EB(X) d. Em Energy deposited inside I 3 d. Em(X) = EB(X – 0. 5 km. w. e. ) - EB(X + 0. 5 km. w. e. ) q 0 30 o 41 o 60 o 76 o 81 o cos q 1. 0 0. 87 0. 75 0. 25 0. 15 Em* (Te. V) 0. 56 0. 69 0. 86 1. 71 8. 9 60 E 0(1 m, Te. V) 80 80 540 13800 E 0 (>2 m) / E 0(>1 m) = (2)1/p ~ 2. 5 March 10, 2009 (2. 5) -1. 7 ~ 0. 2 = fraction of ≥ 2 m at a plane Tom Gaisser 13

Muon multiplicity at depth protons Iron Total energy per nucleus March 10, 2009 Tom Gaisser 14

Muon energy spectrum at depth Nm= 7 5. 5 4. 4 2. 0 0. 2 0. 1 March 10, 2009 Nm=40 32 25 11 1. 2 0. 7 Tom Gaisser 15

Muon energy spectrum at depth Nm=230 180 145 64 7. 1 0. 4 March 10, 2009 Nm=1300 1000 830 370 41 2 Tom Gaisser 16

vertical cosq=0. 5 cosq=0. 25 March 10, 2009 Tom Gaisser 17

Note angular dependence on composition vertical cosq = 0. 5 cosq = 0. 25 March 10, 2009 Tom Gaisser 18

Concept • Measure spectrum of Evisible in I 3 muon bundles • Normalize near vertical with coincident events where primary energy can be determined by Ice. Top • Use full angular dependence – To check composition – To increase acceptance from 0. 3 to > 3 km 2 sr – To calculate background for UHE, EHE n events • Sensitivity and feasibility needs investigation and reality check with Monte Carlo March 10, 2009 Tom Gaisser 19

Energy deposit per 17 m Todor’s plot: --a single event A B March 10, 2009 Tom Gaisser 20

Radiative losses by high energy m March 10, 2009 Tom Gaisser 21

Cascades produced along m tracks Use s ( > Em/100 ) and calculate by Monte Carlo for d. Em > Em/100; Track average energy loss during propagation including low E radiative. --Lipari & Stanev, Phys. Rev. D 44 (1001) 3543 March 10, 2009 Tom Gaisser 22

Analysis procedure • Concept: like FD reconstruction in Auger – Determine trajectory with appropriate method • E. g. use core location of surface for coincident evnts • Use best LLH for in-ice – Reconstruct number of Cherenkov photons per meter along trajectory • Account for local ice properties • First pass fit gives curve A – Used curve A for estimate of energy deposit – Integral of d. E/d. X = -a –b. E gives Nm x DE • Second pass fit to estimate Nm : – Remove all DOMs (or groups) with DE > line A – Second pass gives line B • Use d. E/d. X = -a to get Nm • Need to reinterpret parameter “a” to include the “small” part of “b” –as in removal in IR divergence in bremsstrahlung • Lipari-Stanev paper shows how to do this March 10, 2009 Tom Gaisser 23