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, Russia, 2 IZMIRAN, Russian Academy of Sciences, Moscow, Russia 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 V. 24. P ]; AMANDA: [ Bouchta A. et al. (AMANDA collaboration). / / Proceedings of the ICRC99. HE ]; MINOS [ Grashorn E.W. et al. (MINOS collaboration. / / Proceedings of the ICRC07. (ArXiv: ).]; 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 :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( ɵ j ) =(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  was carried out at the assumption that CRM variations is described as Correlation and Temperature Coefficients C and  were calculated as T i are the values of the temperature of the a half of the day beginning, the values I i is one day averaged quantity, T and I are corresponding mean values for period :00 – :00. Index I is the number of 12 hour interval.

The horizontal axis represents the number 12 hour intervals from :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 :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 well-pronounced maxima correspond to 14 and 21 km.

The figure presents the dependence of different directions muons arrival Correlation Coefficients (data correspond to :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 well- pronounced 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 :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 :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 :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.