ЖЭТФ, 2022, том 161, вып. 4, стр. 544-547

THE UNREASONABLE EFFECTIVENESS

OF THE AIR-FLUORESCENCE TECHNIQUE

IN DETERMINING THE EAS SHOWER MAXIMUM

P. Sokolsky^*, R. D’Avignon

Department of Physics and Astronomy, University of Utah

84112, Salt Lake City, USA

Received September 13, 2021,

revised version December 2, 2021

Accepted for publication December 2, 2021

Contribution for the JETP special issue in honor of A. E. Chudakov’s 100th anniversary

DOI: 10.31857/S0044451022040083

an EAS is also more subject to systematic uncertainties

EDN: DPXBSA

than its energy. Detailed fits to the data distributions

to extract the CR composition thus suffer from multiple

1. Introduction. One of the great advances in

systematic issues.

the study of UHECR is the development of the air-

It is possible, however, to ask a different question.

fluorescence technique [1]. The ability to reconstruct

Whatever the components of the cosmic ray flux may

the development of an extensive air shower (EAS) pro-

be, is this composition changing as a function of en-

duced by cosmic rays at > 10¹⁷ eV in the atmosphere

ergy? Such changes may reflect propagation effects

has given us a much improved, essentially calorimetric,

from the sources, changing acceleration efficiency at

energy determination. This allows both direct mea-

the astrophysical sources, or the appearance of differ-

surement of the cosmic rays (CR) spectrum and the

ent sources. A sensitive indicator of such a change in

inter-calibration of the older surface array technique

composition is the so-called elongation plot, or the de-

where only the footprint of the EAS on the surface is

pendence of the mean X_max on log(E). For a single

sampled with scintillation or water Cherenkov coun-

component composition, it is easy to show [3] that

ters. The air-fluorescence method also gives the ability

to determine, albeit with some uncertainty, the cosmic

X_max = D ln(E/E_c),

ray composition. This is done by determining the dis-

where E_c is the critical energy and D depends on the

tribution of the depth of EAS shower maxima or X_max

particle and the hadronic model assumed.

(see [2] for an early discussion of this technique). Heavy

nuclei interact early and produce showers at smaller at-

Irrespective of the actual mixture, for a constant

composition, the slope of the elongation

mospheric depths while protons interact later and have

deeper X_max. Intermediate nuclei lie between these

d(X_max)/d(log₁₀(E))

two extremes. Thus, the fluctuations of X_max and the

actual shape of the distribution of X_max’s contain infor-

is constant. However, if the composition is changing

mation about the composition. The limitation of this

over an energy interval, then this slope, or elonga-

method is the necessity of comparing the observations

tion rate, will exhibit a corresponding change. While

with detailed simulations based on hadronic interac-

the precise correspondence of the elongation rate to

tion models. These models deal with interactions well

the composition is hadronic model dependent, the en-

beyond current accelerator data and hence have signif-

ergy dependence of interaction parameters such as to-

icant uncertainties. This is reflected in the uncertainty

tal cross section, inelasticity and multiplicity are typ-

in the inferred composition. Determining the X_max of

ically logarithmic and are not expected to produce a

rapid change in the elongation rate. Thus, a rapid

^* E-mail: ps.protopop@gmail.com

change in the rate is most simply explained in terms

544

ЖЭТФ, том 161, вып. 4, 2022

The unreasonable effectiveness of the air-fluorescence technique. . .

of a change in composition assuming no hadronic “new

physics” thresholds.

The major advantage of studying the UHECR elon-

gation rate is that one can come to certain conclu-

sions about the composition in an essentially hadronic

model independent way. However, this kind of study

is still sensitive to systematic effects inherent in the

air-fluorescence measurement technique. It is therefore

important to have multiple independent measurements

to determine how well the systematic errors are con-

trolled.

In this paper, we will compare results from all the

historic air-fluorescence experiments in the Northern

and Southern hemispheres, and look for consistency, or

lack thereof, in reported elongation rates — for evi-

dence of a change. The eight experiments considered

span a time period of 40 years and reflect a wide vari-

Fig. 1. Mean Xmax as function of energy averaged over all

ety of reconstruction techniques, calibration procedures

Northern data. Error bars are the standard deviation of the

and atmospheric corrections. As we will see, somewhat

different experiments about the mean for each energy bin

incredibly, in the energy range from 10¹⁷ to 3 · 10¹⁸ eV

there is remarkable agreement about the elongation

rate for Northern hemisphere experiments. Even the

ber of mean X_max measurements per energy bin will

absolute values of average X_max’s lie well within the

vary. We consider data from 10¹⁷ eV to 1019.2 eV only

estimated systematic errors of 20-30 g/cm². We also

to guarantee that statistical errors are smaller than

present the comparison of the mean elongation rate of

systematic errors and there is no significant statisti-

all the experiments in the Northern hemisphere with

cal sampling bias. The overall agreement as to the

the result of the Auger experiment, which is the single

elongation rate for all experiments is impressive. Un-

detector in the Southern hemisphere. We will see that

der the assumption that reversion to the mean will give

with the reversion to the mean of the seven Northern

the most reliable result, we form a mean and a standard

results, the agreement with Auger below 3 · 10¹⁸ eV is

deviation for each energy bin. Figure 1 shows the result

remarkable.

where the error bars represent the standard deviation

We briefly describe the seven experiments with elon-

of all the experiments that contribute to a particular

gation rate results in the North. All of these were based

energy bin.

in the western deserts of the state of Utah, USA. The

3. Comparison of north and south elongation

oldest and pioneering air-fluorescence experiment was

rates. The Auger collaboration [9] has constructed a

the Fly’s Eye [4]. The next generation experiment was

hybrid air-fluorescence surface detector array covering

the High Resolution Fly’s Eye (HiRes) [5] which had

∼ 3000 km² in the high desert of Argentina with sim-

smaller pixels and full stereo coverage. A prototype

ilar pixel size to TA and HiRes. The Auger elonga-

HiRes detector with a limited field of view overlook-

tion rate is in strikingly good agreement with North-

ing the CASA-MIA surface and underground muon ar-

ern measurements from 10¹⁷ to ∼ 3 · 10¹⁸ eV. There is

ray was first built [6]. The currently operating Tele-

an ∼ 25 g/cm² systematic shift between the measure-

scope Array (TA) experiment [7] consists of three air-

ments, consistent with the estimated systematic errors

fluorescence stations with 1 deg by 1 deg pixel size,

of ∼ 20 g/cm² for each experiment. Figure 2 shows

similar to HiRes, but overlooking a 700 km² surface

the world data with the Auger results shifted down by

scintillator detector array. In order to extend the air-

25 g/cm². The lower energies show a remarkable agree-

fluorescence energy range, an additional detector called

ment with elongation rate of ∼ 85 g/cm²/decade for the

TALE was added to the MD TA fluorescence station [8].

/decade for Auger. The slopes

North and 79.1 g/cm²

2. Comparison of results for northern hemi-

above 3 · 10¹⁸ eV are different, however. Auger deter-

sphere. The seven different Northern Hemisphere ex-

mines a rate of 26±2 while the average of the Northern

perimental results, here treated as independent of each

experiments gives a rate of 47.8 g/cm²/decade with a

other, have different energy thresholds so that the num-

standard deviation of 10.4.

545

P. Sokolsky, R. D’Avignon

ЖЭТФ, том 161, вып. 4, 2022

3 · 10¹⁸ eV. If we assume there are no unexplored sys-

tematic effects, then this would indicate that the com-

position of cosmic rays in the Northern and Southern

hemisphere begins to diverge at this energy, remaining

relatively light in the North and getting heavier more

rapidly in the South. The sources of the UHECR in

the North and South could be different.

5. Conclusions. The remarkable agreement in

elongation rate for eight different measurements gives

strong impetus to using the divergence above 3·10¹⁸ eV

as a tool for exploring differences in North/South com-

position. However, a consensus needs to be achieved

that there are no improperly understood systematic ef-

fects in this region. In this regard, [12] gives a historical

account of North/South measurements from a different

perspective, but comes to a similar conclusion about

the existence of a break near 3 · 10¹⁸ eV.

Fig. 2. (Color online) North and South elongation rates after

Since the important difference is in the slope, this

25 g/cm² shift. Red points are Auger data. Blue points are

systematics, if they exist, must increase with energy,

the mean Northern data. Dashed lines are linear fits with an

but only above 3 · 10¹⁸ eV. They must either increas-

assumed break at 3 · 10¹⁸ eV. Error bars have been suppressed

for clarity. Auger data points have been slightly interpolated

ingly push X_max to smaller values (the Auger case),

to correspond to the energy binning

or increasingly push X_max to larger values (the North-

ern case). Two candidates for such effects are: cuts

which increasingly throw out deep X_max, and increas-

ingly poor X_max resolution resulting in an increasing

4. Discussion. There has been a divergence of

deep X_max tail not modeled in the simulations. Neither

interpretation of X_max data at the highest energies be-

of these possibilities is supported by the work of the ex-

tween Auger and the various Northern experiments for

perimental groups. Nevertheless, the Joint TA-Auger

some time. Detailed studies of X_max distribution data

Composition Working Group should press on with fur-

shapes in the North, particularly the most recent TA

ther elucidation of such possible effects. Absent such

hybrid results [10] have been most easily understood as

effects, the divergence in composition North and South

being protonic, or nearly so, with some admixture of He

joins the emergence of different anisotropies (Cen A

and CNO possible at energies above 5 · 10¹⁸ eV. Auger

and Starburst Galaxies in the South [13]; the Hot Spot

data above 3 · 10¹⁸ eV when analyzed in a similar way

and the Perseus-Pices supercluster enhancement in the

tend to prefer a heavier composition. Until recently,

North [14]) as a strong indication of the diversity of

comparisons, done by the Joint Composition Working

cosmic ray sources at the highest energies.

Group [11] have only been made in a limited energy re-

It is remarkable that a technique that is based on

gion of 2 · 10¹⁸ to 2 · 10¹⁹ eV. Reasonable agreement in

the observation of the emission of ∼ 4 photons/par-

the X_max distributions themselves (if not the hadronic

ticle/m at distances of up to 30 km, in the presence

model dependent interpretations) could be found if one

of significant sky noise, and which has to take into

shifted either experiment’s results bin by energy bin by

account molecular and aerosol scattering in the at-

between 5 and 20 g/cm². However, the elongation rates

mosphere as well as the stability and calibration of

between the two experiments above 2·10¹⁸ eV remained

thousands of pixels can produce such reliable and

different, though the evidence for this was weakened by

reproducible experimental results. The pioneers of

the small energy range available and lack of statistics

this idea ∼ 60 years ago (Chudakov [15] in the USSR

at the highest energies.

and others in Japan and the United States) would

The present analysis using all available data paints

be pleased at what their original insight has brought

a clearer picture. At lower energies, the agreement

forth.

between North and South is highly reassuring. But

the much increased lever arm available shows a real

The full text of this paper is published in the English

difference in measured elongation rate, beginning at

version of JETP.

546

ЖЭТФ, том 161, вып. 4, 2022

The unreasonable effectiveness of the air-fluorescence technique. . .

REFERENCES

7. K. Martens, Nucl. Phys. B, Proc. Suppl. 165, 33

(2007).

1. K Greisen, Ann. Rev. Nucl. Sci. 10, 63 (1960); J. Del-

vaille, F. Kendziorski, and K. Greisen, J. Phys. Soc.

8. R. U. Abbasi, T. Abu-Zayyad, M. Allen et al., Astro-

Japan 17, Suppl. A-III, 76 (1962); K. Suga, Proc.

phys. J. 909, 178 (2021).

5th Interamerican Seminar on Cosmic Rays, La Paz,

9. A. Aab, P. Abreu, M. Aglietta et al., Nucl. Instr.

Bolivia, Vol. II, XLIX (1962); A. E. Chudakov, Proc.

Meth. A 798, 172 (2015).

5th Interamerican Seminar on Cosmic Rays, La Paz,

Bolivia, Vol. II, XLIX (1962).

10. R. U. Abbasi, M. Abe, T. Abu-Zayyad et al., Astro-

2. G. L. Cassiday, R. Cooper, S. Corbato et al., Astro-

phys. J. 858, 76 (2018).

phys. J. 356, 669 (1990).

11. V. de Souza, Proc. of 2017 ICRC, Beijing, China,

3. J. Linsley, Proc. 15th ICRC, Plovdiv, Bulgaria 8, 353

PoS(ICRC2017) 301.

(1977).

12. A. Watson, Proc. of UHECR 2018, EPJ Web Conf.

4. R. M. Baltrusaitis, G. L. Cassiday, R. Cooper et al.,

210 (2019); doi.org/10.105/ epjconf/201921000001.

Nucl. Instr. Meth. A 240, 410 (1985).

13. A. di Matteo, Proc. of 2021 ICRC, Berlin, Germany,

5. J. M. Matthews, Proc. 27th ICRC, 07-15 (2001);

PoS(ICRC2021) 308.

R. U. Abbasi, T. Abu-Zayyad, J. F. Aman et al.,

Phys. Rev. Lett. 92, 151101 (2004).

14. K. Kawata, A. di Matteo, T. Fujii et al., Proc. of 2019

ICRC, Madison, USA, PoS(ICRC2019) 310; T. Fujii,

6. T. Abu-Zayyad, K. Belov, J. Boyer et al., Nucl. Instr.

D. Ivanov, C. C. H. Jui et al., Proc. of 2021 ICRC,

Meth. A 450, 253 (2000); T. Abu-Zayyad, K. Be-

Berlin, Germany, PoS(ICRC2021) 392.

lov, D. J. Bird et al., Astrophys. J. 557, 686 (2001);

A. Borione, C. E. Couvault, J. W. Cronin et al., Nucl.

15. V. A. Belayev and A. E. Chudakov, Bull. USSR Acad.

Instr. Meth. 346, 329 (1994).

Sci., Phys. Ser. 30, 1700 (1966).

547