Transcript Document

Variations of the high energy muon flux and space-time structure
of the temperature profile in the atmosphere
M.G. Kostyuk 1, V.B. Petkov 1, R.V. Novoseltseva 1, M.M. Boliev 1,
M.M. Berkova 2, Yu.F. Novoseltsev 1, L.V. Volkova 1, V.G. Yanke 2
1
Institute for Nuclear Research, Russian Academy of Sciences, Moscow, 115409 Russia,
2 IZMIRAN, Russian Academy of Sciences, Moscow, 142190 Russia
e-mail: [email protected]
Abstract. Temperature dependence of high energy muon flux (with energy threshold of 220 GeV) has
been investigated using experimental data of the Baksan Underground Scintillation Telescope (BUST). The
temperature radiosonde data corresponding to every 12 h and different levels of observations have been
used. The experimental data were taken during 9 years. The Correlation and Temperature Coefficients have
been obtained. Their dependencies on the altitude of the temperature measurements and muons arrival
directions are presented.
The minimum of the Correlation and Temperature Coefficients as a function of the altitude correspond
to atmosphere tropopause and maxima are related to troposphere and stratosphere. The magnitude of
temperature variation corresponding to minimum is approximately a half of the magnitude corresponding to
maxima. The values of the Correlation and Temperature Coefficients around of the minimum are
approximately a half of the corresponding values around of the maxima.
We present in this work an explanation of non-trivial behavior of the Correlation and Temperature
Coefficients as a function of the altitude of the temperature measurements. The approximate coincidence of
the minimum and maxima in the Correlation and the Temperature coefficients leads to the conclusion that
this is due not to the magnitude, but rather to the temporal behavior of the temperature in the respective
regions of the atmosphere.
Studies of past years variations in the intensity of the registration of the various components
of
the secondary cosmic radiation led to the fact that meteorological corrections, whose introduction
into the primary observational data allows us to
find variations of cosmic rays of extra atmospheric
origin. Meteorological effects on cosmic rays were possible to obtain some information about the state
of the upper atmosphere and some of the characteristics of nuclear cascade in the atmosphere.
The continuous development of our knowledge with respect to nuclear interactions, and possibilities
of computer technology makes it justified a new appeal to
these problems in order to obtain more
precise results for larger data set.
Large underground detectors as
MACRO: [ Ambrosio M. et al. (MACRO collaboration). / / Astrop.Phys. 1997. V. 24. P. 109. ];
AMANDA: [ Bouchta A. et al. (AMANDA collaboration). / / Proceedings of the ICRC99. HE.3.2.11.];
MINOS [ Grashorn E.W. et al. (MINOS collaboration. / / Proceedings of the ICRC07. (ArXiv: 0710.1616).];
LVD [ Agafonova N.J. et al / / 31-I VKKL, Moscow State University, 2010 MN / MN _14.]
as one of results have analyzed seasonal variations in the fux of high-energy muons, and it has been shown that the
period of variation is equal to one year. The maximum and minimum of the muon flux fall on July and January,
respectively (in the northern hemisphere).
Results of the BUST are presented.
The horizontal axis represents the number of 12 hour intervals from
05.02.2003.12:00 – 05.02.2012.00:00 and vertical axis represents integral (all
angles of muon arrivals are involved) daily averaged in the neighborhood of half a
day beginning 15 min counting rate of muons (CRM)
The BUST CRM depends on the threshold energy and the cosine of the zenith
angle.
Solid angles correspond intervals between seven values of cosine of zenith
angle ɵ according to formula:
cos(ɵj ) =(6-j)/6, j =0,1,2,3,4,5,6.
Index j fixes solid angles : (6-j)/6<cos(theta)<(6-j+1)/6;
Evaluation of the Temperature Coefficient
assumption that CRM variations

was carried out at the
Vi  100%  Ii / I
is described as
Vi  Ti ,
Correlation and Temperature Coefficients C and  were calculated as
 T I
C 
 T I 
i
2
i
i
2 1/ 2
i
,
Ti  Ti  T  ti ,
 
 T V
 T
i
i
2
(% K ),
i
I i  I i  I ,
Ti are the values of the temperature of the a half of the day beginning, the
values Ii is one day averaged quantity, T and I are corresponding mean
values for period 05.02.2003.12:00 – 05.02.2012.00:00. Index I is the
number of 12 hour interval.
The horizontal axis represents the number 12 hour intervals from 05.02.2003.12:00 –
05.02.2012.00:00 and vertical axis represents daily averaged in the neighborhood of half
a day beginning 15 min counting rate of muons (CRM) for different solid angles of muon
arrivals.
The figure presents the dependence of different directions muons arrival
Temperature
Coefficients
(data
correspond
to
05.02.2003.12:00
–
05.02.2012.00:00 ) on altitude of the point near Mineralnye Vody where
temperature was measured. Temperature Coefficients change nonmonotonically as a function of altitude.
The well-pronounced minimum is observed in the region of 15–20 km, and the
well-pronounced maxima correspond to 14 and 21 km.
The figure presents the dependence of different directions muons arrival Correlation
Coefficients (data correspond to 05.02.2003.12:00 – 05.02.2012.00:00 ) on altitude of
the point near Mineralnye Vody where temperature was measured. Temperature
Coefficients change non-monotonically as a function of altitude.
The well-pronounced minimum is observed in the region of 15–20 km, and the wellpronounced maxima correspond to 14 and 21 km.
The Figure shows the “saturation” effect: if observation time increases
(horisontal axes), Integral CRM Temperature Coefficient corresponding different
altitude (where the temperature was measured) exhibits any tendency to
stabilisation.
Space-time variation of temperature (at three different heights) for period
05.02.2003.12:00 – 05.02.2012.00:00. The horizontal axis represents
number 12 hour interval the vertical axis represents temperature
variations corresponding to the beginning of each half of a day.
IntCRM, spase-time temperature structure (for 05.02.2008.12:00 – 05 02 2009.00:00)
and sine fit. Correlation and Temperature coefficients being overlapping of functions of
different variation rate are small.
Conclusions
The behavior of the Correlation and Temperature Coefficients as a function of the
atmosphere point altitude
(where the temperature was measured)
has been
presented for different muons arrival directions to BUST (with equal solid angles)
for period 05.02.2003.12:00–05.02.2012.00:00.
The minimum of the Correlation and Temperature Coefficients as a function of
the height corresponds to atmosphere tropopause and maxima are related
to troposphere and stratosphere correspondingly.
“Saturation” effect: if observation time increases Integral CRM Temperature
Coefficient corresponding different altitude (where the temperature was measured)
exhibits any tendency to stabilisation.
The approximate coincidence of the minima and maxima of the Correlation and
Temperature Coefficients leads to the conclusion that this is not due to magnitude,
but rather the nature of the temporal behaviour of temperature in the respective
regions of the atmosphere, because the Correlation Coefficient does not change if
the temperature or CRM will be multiplied by any value. The difference in periods of
temporal change in CRM and the tropopause temperature is the only
reason for having
a minimum for the Correlation and Temperature Coefficients.