Effect of air fluorescence properties on the reconstructed energy of UHECR

José Ramón Vázquez, María Monasor, Fernando Arqueros

Universidad Complutense de Madrid

6th Fluorescence Workshop, L’Aquila, Italy

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Summary

• Motivation• Fluorescence yield description• Comparison of experimental data sets• Humidity effect• Temperature effect• Effect on energy reconstruction• Results• Conclusions and todo

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Motivation

• The fluorescence yield Y is a relevant parameter in the determination of the primary energy of UHECRs and its uncertainty is one of the main sources of systematics in the energy reconstruction.

• Accurate measurements of this magnitude could improve our knowledge about the energy spectrum of UHECR and reduce the uncertainties.

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Fluorescence Yield• The fluorescence yield, at a given and conditions, over a

wavelength interval can be calculated as (1):

i

iYY

0 1· 1

'

i i

i

Y YP

p T

2

2

2

2

''''

1

O

O

N

N

i i

i

p

f

p

f

p

f

p

(1) Proceedings of the 5th Fluorescence Workshop. Nucl. Instrum. Meth. A 597 (2008) 1

P T

phMeV

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Comparison of experimental data sets

Three experimental data sets are widely used in UHECRs experiments based on the fluorescence technique:

1. HiRes (Kakimoto-Bunner):

• Y(P0,T0) and p’(T0) from Kakimoto (1) for 337, 357 and 391 nm lines measured at P0 = 1013 hPa and T0 = 288 K.

• The remaining spectrum is distributed according to Bunner spectrum (2).

(1) Kakimoto et al. Nuclear Instruments and Methods A 372 (1996) 527-533(2) Interpretation of Bruce Dawson in Internal Auger Note GAP 2002-067

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2. Nagano:

• Y0 and p’(T0) from his own measurements at P0 = 1013 hPa and T0 = 293 K for all wavelengths (1)

3. Auger (Nagano-Airfly):

• Y0337(800hPa, 293K) from Nagano measurements (1).

• P’(T0) and relative intensities from Airfly (2) measured at 800 hPa and 293 K.

Comparison of experimental data sets

(1) Nagano et al. Astroparticle Physics 22 (2004) 235-248(2) Ave et al. [Airfly Collaboration] Astroparticle Physics 27 (2007) 41-57(3) Keilhauer et al. Proc. 29th ICRC 7 (2005) 23

The fluorescence yield as a function of height has been evaluated for these 3 data sets using a typical atmospheric profile measured at Auger site (3).

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Comparison of experimental data sets

Average difference ~ 20% !!

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Impact of detector efficiencyHowever, the number of observed fluorescence photons depends on detector efficiency and air transmission T (X,X0) (including both molecular and aerosol effects).

X0

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Experimental data sets

Average difference ~ 7% !!

Experimental data setsIncluding Auger filter transmittance F

F

10

Average difference ~ 2% !!

Experimental data setsIncluding Auger detector efficiency

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Humidity effect

• The effect of water vapour on air can be accounted following the general equations (1):

2 2 2

2 2 2

2 2

2

1

' ' ' ' '

1 1 11 ·

' ' '

N O H Oi

ihum i N O H O

H O H O

hum dry H O

f f ff

p p p p p

p p

p p p p p

(1) Proceedings of the 5th Fluorescence Workshop. Nucl. Instrum. Meth. A 597 (2008) 1

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Temperature effect

• p’ measurements are obtained at a given T0, but its value depends on temperature T. In principle:

• However, an additional dependence due to collisional quenching cross section has been observed (1,2):

0

0 ·''T

TTpTp ii

i

T

TTpTp ii

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00 ·''

(1) Ave et al. Nucl. Instrum. and Meth. A 597 (2008) 50-54(2) Fraga et al. Nucl. Instrum. and Meth. A 597 (2008) 75-82

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Temperature effect

• The temperature dependence of p’ in dry air, considering air as 79% nitrogen and 21% oxygen, yields:

2 2

1 12 2

0 00 0

1 0.79 0.21

'' · ' ·

NN NO

N O

p T T Tp T p T

T T

In principle the T dependence for N-N quenching is different from that of N-O quenching.

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Temperature and humidity effectWe have studied different cases:• Temperature model 1:

Equal treatment of N-N and N-O quenching (1):

• Temperature model 2: Different treatment of N-N and N-O quenching:

• Humidity model:p’hum from Airfly (1)

·

AirflyNONN 22

'

21.0

'

79.0

'

1

ONair ppp

(1) AirflyNO (2) from NN

(1) Ave et al. Nucl. Instrum. and Meth. A 597 (2008) 50-54(2) Fraga et al. Nucl. Instrum. and Meth. A 597 (2008) 75-82 (3) Waldenmaier et al. Nucl. Instrum. and Meth. A 597 (2008) 67-74

(3) from ''22 ON pp

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Temperature and humidity effectAgain, typical atmospheric profiles for humidity,

temperature… measured at Auger site have been used.

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Temperature and humidity effectAgain, typical atmospheric profiles for humidity,

temperature… measured at Auger site have been used.

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Temperature and humidity effect

The humidity effect is important at low height.

Again, typical atmospheric profiles for humidity, temperature… measured at Auger site have been used.

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Temperature and humidity effectIncluding detector efficiency

The filter does not introduce any difference since these effects don’t modify significantly the spectrum (relative intensities).

Including Filter transmittance F

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Effect on energy reconstructionThe Gaisser-Hillas parameterization describes the longitudinal energy deposition :

max 00

0

max max 0

( )X X

X XX XdE X dE

edX dX X X

( )dE XE dX

dX

Typical GH profile for a shower of 1020 eV

The total calorimetric energy E will be:

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Effect on energy reconstruction• The profile of deposited energy will generate a fluorescence photon profile

according to a given Y(X):

• If this photon profile were generated by a different fluorescence yield Y’(X), the deposited energy profile would become:

)('

)(

XY

XY

dX

dE

)(·)(

XYdX

dE

dX

Xdn

dXXY

XY

dX

dEE

)('

)('

( ')diff

E EE

E

The impact on energy of using two different data sets is studied by comparing E, E’:

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Effect on energy reconstruction

The effect of the fluorescence yield on energy reconstructionwill be also dependent on:

• Detector efficiency

• Showers features:

• Zenith angle

• Primary energy and mass

• Distance shower-telescope (molecular and aerosol transmission)

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Effect on energy reconstruction

We have studied the effect of changing the fluorescence yield for three different zenith angles (0º, 30º, 60º) and three different distances shower-telescope (10, 20, 30 km) considering the Auger description as standard and comparing it with:

• Nagano

• HiRes

• Auger std + Temperature model 1

• Auger std + Temperature model 2

• Auger std + Humidity dependence

• Auger std replacing p’ from those measured by Macfly Coll.

For humidity, T and P profiles, averaged values measured at Auger site for June have been used.

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Effect on energy reconstructionComparing Auger and HiRes Y(X) profiles:

= 30º

Ediff= -20.49%

( ) ·

'( )

dE dE Y X

dX dX Y X

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Effect on energy reconstructionComparing Auger and HiRes Y(X) profiles

including detector efficiency:

= 30º

Ediff= -1.77%

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Energy reconstructionComparing Auger with Auger+humidity

dependence as a function of :

= 0º

Ediff= -7.05%

= 30º

Ediff= -3.99%

= 60º

Ediff= -0.62%

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Energy reconstructionComparing Auger with Auger+temp1

dependence as a function of :

= 0º

Ediff= -2.56%

= 30º

Ediff= -2.91%

= 60º

Ediff= -6.04%

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Preliminary Results

Auger/Nagano

Auger/Kakimoto

Auger/Temp1

Auger/Temp2

Auger/Humidity

Y(X) 1.8 -20.3 -2.6±0.7 -3.6 -6.6

Y (X)·F 0.4 -7.4 -2.6 ±0.7 -3.5 -6.9

Y (X)· 1.8 -1.8 -2.7 ±0.7 -3.6 -7.1

Y (X)· ·T(10) 1.8 -1.7 -2.7 ±0.7 -3.6 -7.1

Y (X)· ·T(20) 1.9 -1.5 -2.8 ±0.7 -3.7 -7.1

Y (X)· ·T(30) 1.9 -1.2 -2.8 ±0.7 -3.7 -7.1

Relative energy difference (%) at = 0°

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Preliminary Results

Auger/Nagano

Auger/Kakimoto

Auger/Temp1

Auger/Temp2

Auger/Humidity

Y(X) 1.7 -20.5 -2.9 ±0.7 -4.1 -3.8

Y (X)·F 0.3 -7.6 -2.9 ±0.7 -4.0 -3.9

Y (X)· 1.7 -1.8 -3.1 ±0.7 -4.1 -4.0

Y (X)· ·T(10) 1.9 -1.2 -3.1 ±0.7 -4.1 -4.0

Y (X)· ·T(20) 2.0 -0.6 -3.2 ±0.7 -4.2 -4.0

Y (X)· ·T(30) 2.1 -0.1 -3.2 ±0.7 -4.2 -4.0

Relative energy difference (%) at = 30°

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Preliminary Results

Auger/Nagano

Auger/Kakimoto

Auger/Temp1

Auger/Temp2

Auger/Humidity

Y(X) 1.1 -21.6 -6.0 ±1.5 -8.5 -0.6

Y (X)·F -0.3 -8.5 -6.0 ±1.5 -8.4 -0.6

Y (X)· 1.4 -1.4 -6.5 ±1.5 -8.7 -0.6

Y (X)· ·T(10) 1.7 -0.6 -6.6 ±1.5 -8.8 -0.6

Y (X)· ·T(20) 1.9 0.04 -6.7 ±1.5 -8.8 -0.6

Y (X)· ·T(30) 2.2 0.6 -6.8 ±1.5 -9.0 -0.6

Relative energy difference (%) at = 60°

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Conclusions

• We have developed an analytical method to study the impact of Y on the energy of UHECR showers, as a function of detector efficiency and shower geometry. No event reconstruction is needed.

• Significant differences, already pointed out, between Auger and HiRes fluorescence models have been observed. This discrepancy is strongly reduced when detector efficiency is taken into account.

• Auger and Nagano data sets don’t present significant differences (<2%).

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Conclusions• The humidity introduces a zenith angle dependent effect on energy from

7 % for 0° to 0.6% for 60°.

• Using Temperature 1 model a difference in energy of 2.7 % for 0° to 6.5 % for 60°. The separate treatment of NN and NO adds another 2% variation.

• The shower-telescope distance does not have a significant effect on the reconstructed energy.

• When p’ values from Macfly collaboration are used no significant changes in energy (<1%) are observed even when the experimental values are quite different from those obtained by Airfly collaboration.

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To do:

• Study the impact of fluorescence yield properties as a function of primary energy and mass.

• The effect of distance must be evaluated for different aerosol conditions.• Evaluate these effects under different atmopsheric conditions• Evaluate the uncertainties.