Primary Energy Reconstruction Method for Air Shower Array Experiments

Samvel Ter-Antonyan and Ali Fazely

Inverse Problem for All-particle energy spectrum

Event-by-event method Unfolding

01001 ),()()( dEEEWEFEF A

AAAA dESAEEFS )|,()()(

Advantage: general formulation

Solutions: a) regularized unfolding iterative algorithm [KASCADE Collaboration , Astropart.Phys. 24 (2005) 1]

b) parameterization of inverse problem + + a priory spectral info. [GAMMA Collaboration, Astropart.Phys. 28 (2007) 169]

Disadvantage:Pseudo solutions for elemental spectra and undefined systematic errors for unfolding algorithms (KASCADE). [S. Ter-Antonyan, Astropart.Phys. 28 (2007) 321]

Advantage: simplicity

Solution: analytical or numerical integration[J. Phys. G: Nucl. Part. Phys. 35 (2008) 115]

Disadvantage: ? The most experiments ignore the methodic errors.

A

AA EFEF )()(0

Energy estimator: 10 EE

Event-by-event analysis

),,,( cossNNe [GAMMA_09]

This work{

)cos,,( 125 S

11250 },,{ SE [ICETOP_09]

01001 ),,()()( dEAEEWEFEF

is ill-posed problem for F(E0) due to A H, He, … Fe

Redefinition of inverse problem:

a priori: ,~)( 00 EEF =2.9 0.25 for 1 PeV E0 < 500 PeV

Let ))(|)(),((L),,( 0001 ELnEEAEEW

and )(1/)( 0010 EEEE and bEaLnE )()( 00

?),,( NNe [KASCADE-GRANDE]

2

)1(exp)()(

~ 221

10

EFEF , for , - constant

where

2.0001 )()( aEE , and |a|<< 0.1

Solution for primary spectrum

Spectral errors:

2

2222

1)1()1(~

~

F

F

F

F

Statistic Errors Methodic Errors

2

)1(exp)()(

~ 221

10

EFEF 2%

Multi-parametric energy estimator for ICETOP Array:

6

54

12532

11

cos

cosaa

aSa

aaE

5

A

iiA

i E

EE

)(

)lnln(

02x

2,1,,02

i=1,…104, AH, He, O, Fe

min{2(a1,a2,…a6,(Ei)| E0,i)}

,)(

refref r

rfSrS

CORSIKA EAS SIMULATION+

ICETOP DETECTOR RESPONSE+

LDF RECONSTRUCTION

if

then

Expected biases and uncertainties of primary energy

<Ln(

E 1/E 0)>

Log(E0/GeV)

GAMMA ExperimentICETOP

Log(E0/GeV)

(Ln

(E1/

E 0))

Distribution of errors (~ Gaussian)

Verification of method

Primary energy spectra for p, He, O, Fe from GAMMA Experiment data [GAMMA Collaboration, Astropart.Phys. 28 (2007) 169]

Expected reconstructedall-particle spectrum for ICETOP

Expected (red symbols) all-particle spectrumfor ICETOP