Fluctuation studies need to compare a parameter which is sensitive to longitudinal fluctuations against a parameter which is insensitive. Cascade calculations indicate that the shower size parameter at Haverah Park, rho (500), and the muon density are insensitive while parameters that significantly reflect the longitudinal development of a particular extensive air shower (EAS) include the muon/water Cerenkov response ratio and the muon arrival time dispersion. This paper presents conclusions based on muon fluctuation studies of EAS measured between 1976 and 1981 at Haverah Park

Blake, P. R.

Luksys, M.

Nash, W. F.

Sephton, A. J.

English

NASA Technical Reports Server

123 HE 4.3-9
MUON FLUCTUATION STUDIES OF EAS > 10 1_ eV
P. R. BLAKE, M. LUKSYS, W. F. NASH and A. J. SEPHTON
University of Nottingham, England.
I. Introduction Fluctuation studies need to compare a parameter
which is sensitive to longitudinal fluctuations against a parameter
which is insensitive. Cascade calculations indicate that the shower
size parameter at Haverah Park, p(500), and the muon density are
insensitive while parameters that significantly reflect the long±_
tudinal development of a particular EAS include the muon/water
Cerenkov response ratio and the muon arrival time dispersion. This
paper presents conclusions based on muon fluctuation studies of EAS
measured between 1976 and 1981 at Haverah Park.
2. Description of Muon Detectors Three 10 m2 shielded scintil-
lators situated at 0, 150 m and 250 m from the centre of the Haverah
Park array. Due to practical considerations the detectors had
slightly different absorber thicknesses leading to calculated
vertical muon thresholds of 317, 431 and 488 MeV respectively. Two
of the muon detectors (those at 0 m and 150 m) had immediately
neighbouring large area water Cerenkov detectors so that a local
response ratio between the two detectors could be directly measured.
The recording of the three detectors was triggered from the water
Cerenkov 500 m array by the arrival of EAS with primary energies
10 l_ eV.
3. Fluctuations in W/c Ratio The ratio of the density response of
the muon detectors to the density of the water Cerenkov detectors
(symbolised by p/c) was used to study fluctuations between EAS. For
a data set consisting of those EAS with two direct measurements of
W/c an analysis of variance (AOV) was carried out in order to
extract the between-EAS variance (OB2) from the total measured
variance (o2).
o
Number
R(m) sece of EAS OB/(W/c) F P
- 120 1.0-1.1 61 22.4% (±10) 2.44 <0.01
+220 1.1-1.2 36 19.7% (±12) 2.57 <0.01
1.2-1.3 28 24.7% (±20) 2.23 O.01<p<O.025
220 1.0-1.1 83 0.0% (-0 +15) 0.74 >0.1
+320 1.1-1.2 52 19.9% (±19) 1.46 0.05<p<0.1
1.2-1.3 37 23,4% (±12) 3.15 <0.01
320 1.0-1.1 54 0.0% (-0 +27) 0.94 >0.1
+420 1.1_1.2 36 1.1% (-I +40) 1.00 >0.1
1.2-1.3 23 4.4% (-4 +35) 1.02 >0.1
Table I Between-EAS fluctuations in W/c.
https://ntrs.nasa.gov/search.jsp?R=19850027690 2020-03-20T17:06:10+00:00Z
1.24 HE 4.3-9
Because the different energy thresholds lead to different _/c ratios
the AOV was carried out using standard residuals defined by
S.R. = [(p____/c)- (_/c)]/0, where _/c is the normalised measured
ratio, (p/c) is the average value and o the standard deviation for
the interval under consideration. The results of the AOV are
presented in Table I.
Also included in the table are the F ratio (mean square deviation
between EAS to mean square deviation within EAS) and p, the probab-
ility that random variations In the data could account for the
quoted between-EAS fluctuations. The results indicate that at core
distances -200 m the magnitude of the between-EAS fluctuations is
-20%. Such a result would be consistent wlth at least a 50% proton
primary flux at ~I0 ;_ eV [eg. Marden et al, 1971].
4. Fluctuations in Muon Rlsetlme The muon arrival tlmespread at
each of the 10 m2 muon detectors is characterlsed by the time
interval between 10% and 70% of the full pulse amplitude (T_o). The
instrumental response was found to be T_o = 32 ns. For a specific R
and e, fluctuations in T_o occur arising from fluctuations in the
longitudinal development. AOV techniques allow between-shower
fluctuations in T_o to be separated from within EAS fluctuations.
Such analysis leads to a value of aB/T_o = 10.7(±2) ns/63 ns = 17%
at 325 m, for sec8 = 1.1.
Detailed cascade model calculations relating to T_o fluctuations
remain to be carried out. As a consequence the significance of the
T_o fluctuations is treated in Section 7 in terms of fluctuations in
the height of electromagnetic maximum
5. Correlations of _/c and nn The water Cerenkov response lateral
distribution function used by the University of Leeds group to
analyse the EAS is of the form: "(nc + R/4000)
Pc = k R
It has been found that nc Is sensitive to EAS longitudinal
development. Thus a strong correlation is expected between
fluctuations in _/c and nc. Table 2 gives the.derived correlation
coefficients for the data sets from two muon detectors and also the
significance of the correlation.
Detector sece N r P
A 1.0-1.1 190 0.449 <0.001
1.1-1.2 81 0.342 <0.01
1.2-1.3 40 0.420 <0.01
1.3-1.4 20 0.598 <0.001
C 1.0"1.1 117 0.398 <0.001
1,1-1,2 52 0.595 <0.001
1.2"1.3 34 0.515 <0.01
1.3-1.4 10 0J618 <0.1
• Table 2 Correlation between fluctuation In _/c and fluctuation in
nc. r = correlation coefficient.
HE4.3-9
126
The strong correlation confirms that _/c and nc are sensitive
parameters to EAS development.
6. Correlation of U/c and T_ A small positive correlation is
found between the values of SR(u/c) and SR(T_0) at all zenith angles
(see Table 3).
Detector secO No of EAS r P
A _ U/c 1.0_1.1 20 0.032 >0.1
B _ T_o 1.1_1.2 15 -0.306 >0.1
I.2_I.3 4 0.541 >0.1
I.3_I.4 7 -0.405 >0.1
A _ U/c 1.0-1.1 32 0.016 >0.1
C _ T_o I.I_I.2 19 0.278 >0.1
I.2"I.3 25 0.172 >0.1
I.3_I.4 10 0.438 >0.1
C _ U/c 1.0_1.1 44 0.203 >0.1
A _ TTo 1.1_1.2 31 0.006 >0.1
I.2_I.3 25 0.245 >0.1
I.3-I.4 12 0.323 >0.1
C _ U/C 1.0_1.1 15 0.122 >0.1
B _ T_o 1.1-1.2 16 0.013 >0.1
I.2_I.3 12 "0.197 >0.1
I.3_I.4 9 0.382 >0.1
Table 3 Correlation between _/c and T_o fluctuations
Because of the different core distance dependences the two
correlating parameters were measured simultaneously from two
different muon detectors. The significance of the correlation
coefficients in Table 3 is statistically limited due to the small
- amount of data available for the analysis.
7. Fluctuations in Depth of Electromagnetic Maximum Fluctuations
in the depth of maximum (Xmax) are closely related to the mass
spectrum of the primary particles. It is not possible to measure
Xmax directly at Haverah Park. However the fluctuation in Xmax can
be determined indirectly from the measurement of some shower
parameters, eg. _/c which is sensitive to Xmax. Assuming
Xmax (W/c) _ (p/c)
AXmax = --
x _(_/c)/_x
and using the AOV carried out on the _/c fluctuations observed at
two detectors (for core distances 120 m < R < 220 m and sec0 < 1.3)
yields:_
N °B(g cm'2) F p
125 73.2 2.39 <0.01
HE4.3-9
128
The value of oB is the between_shower fluctuation (in g cm+2)
obtained from the AOV and gives an initial estimate of the
fluctuation in Xmax. The values of F and p show that highly
significant between-EAS fluctuations are present in the data.
Removing the spurious contribution to aB from the pressure
correction, the corrected fluctuations in depth of maximum, o(Xmax)
for EAS in the energy range 10_ _ 10_e eV is given by
a(Xmax) = (71 ± 12) g cm_). Using a similar technique the
fluctuations in T_0 yield a(Xmax) = (69 ± 28) g cm_.
Measurement of a(Xmax) at energies above 10_ eV have been reported
by other groups from a variety of studies. The values obtained
above are in good agreement with these other measurements.
8. Conclusions It was stated in section 3 that the _/c fluctuations
are consistent with at least a 50% proton primary flux at -10 _ eV.
This conclusion is supported by the o(Xmax) results. None of the
different model predictions available give such a large o(Xmax)
value based on a pure iron primary beam [eg. Gaisser et al (1982),
Chantler et al (1983)]. Since the value of a(Xmax) measured in the
present work, 71 (± 12) g cm_2, is -3.5 a above even the largest
calculated estimate for iron nuclei it is extremely unlikely that
cosmic rays in the energy range 10_ _ 1018 eV are dominantly iron
nuclei. This measurement of a(Xmax) is however consistent with a
pure proton mass composition on the basis of the calculations of
Chantler et al (1983) [a(Xmax) = 60 g cm'2].
Large fluctuations in Xmax can arise if several masses are present
in the primary beam. For a mixed composition in which
P:He:(Mg:CNO):Fe is 50:19:19:12, it is found that o(Xmax) = 57 gcm_2
based on Gaisser et al (1982).
In conclusion the fluctuation in Xmax seen at energies in the range
10I_ _ 10 18 eV can be accounted for by a mass composition in which
> 50% of the primaries are protons. Primaries at these energies
cannot be dominantly iron.
m
REFERENCES
Chantler, M. P., Craig, M. A. B., McComb, T. J. L., Orford, K. J.,
Turver, K. E. and Walley, G. M. J. Phys. G 9 L27 (1983).
Gaisser, T. K., Stanev, T., Freler, P. and Waddington, C. J. Phys.
Rev. D, 25, 2341 (1982).
Marsden, D. J., Hillas, A. M., Hollows, J. D. and Hunter, H. W.
12th Int. Cos. Ray Conf., Hobart p.I013 (1971).


Muon fluctuation studies of EAS 10(17) eV

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