Seasonal variation of atmospheric muons in IceCube
Serap Tilav, Thomas K. Gaisser, Dennis Soldin, Paolo Desiati
SSeasonal variation of atmospheric muons inIceCube
The IceCube Collaboration ∗ http://icecube.wisc.edu/collaboration/authors/icrc19_icecubeE-mail: [email protected], [email protected] After more than seven years of data taking with the full IceCube detector triggering at an averagerate of 2.15 kHz, a sample of half a trillion muon events is available for analysis. The extremetemperature variations in the stratosphere together with the high data rate reveal features on bothlong and short time scales with unprecedented precision. In this paper we report an analysis interms of the atmospheric profile for production of muons from decay of charged pions and kaons.We comment on the implications for seasonal variations of neutrinos, which are presented in aseparate paper at this conference.
Corresponding authors:
Serap Tilav † , Thomas K. Gaisser , Dennis Soldin , Paolo Desiati Bartol Research Institute, Dept. of Physics and Astronomy, University of Delaware, Newark,DE 19716 USA Wisconsin Institute for Particle Astrophysics and Cosmology, University of Wisconsin, Madison,WI 53706 USA36th International Cosmic Ray Conference -ICRC2019-July 24th - August 1st, 2019Madison, WI, U.S.A. ∗ For collaboration list, see PoS(ICRC2019) 1177. † Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ a r X i v : . [ a s t r o - ph . H E ] S e p uon seasonal variations Serap Tilav
1. Introduction
Measurements of seasonal variations of the muon flux in deep underground detectors havea long history, starting with a detector in a deep cavity near Cornell University [1]. The papersreporting the results from the MINOS far [2] and near [3] detectors review data from several ex-periments in terms of minimum muon energy needed to reach the detector (e.g. 0 .
73 TeV at theMINOS far detector at Soudan and ∼ / cos θ GeV for the near detector at Fermilab). The vari-ations are characterized by a correlation coefficient α T ( E µ ) obtained by fitting a straight line torate vs. effective temperature at the energy of each detector. The correlation coefficient and theeffective temperature are defined respectively as δ R (cid:104) R (cid:105) = α T × δ T (cid:104) T (cid:105) (1.1)and T eff ( θ ) = (cid:82) d E µ (cid:82) dX P µ ( E µ , θ , X ) A eff ( E µ , θ ) T ( X ) (cid:82) d E µ (cid:82) dX P µ ( E µ , θ , X ) A eff ( E µ , θ ) . (1.2)For compact underground tracking detectors, A eff is simply the projected fiducial area of thedetector coupled with the selection efficiency of single tracks. For IceCube, with its widely spaceddetectors the effective area requires a Monte Carlo simulation of the detector response to the classof events used for the analysis. A significant technical difference is that the MINOS analysis isdone in terms of integral quantities that refer to all muons above a minimum energy, while theIceCube analysis is differential in muon energy. Thus for IceCube the muon production spectrum P µ ( E µ , θ , X ) in Eq. 1.2 is number of muons produced per logarithmic bin of energy per g/cm ofslant depth X along a trajectory at zenith angle θ .The basic physics responsible for the seasonal variation of the muon flux and its dependenceon energy in the region ∼
50 GeV to 5 TeV is the competition between interaction and decay forthe charged pions and kaons that are the dominant source of muons (and muon neutrinos) in thisenergy region. As temperature increases, the atmosphere expands and decay to muons becomesmore likely compared to re-interaction of the parent meson. The critical energy of a hadron isthe energy at which decay and interaction have equal probability at a slant depth comparable tothe interaction length. The relation between density and atmospheric depth (pressure) depends ontemperature through the ideal gas law, leading to the expression for the critical energy parameteras a function of temperature at depth X Vertical = X / cos ( θ ) : ε i ( X ) = R T ( X ) Mg m i c c τ i , (1.3)where M = . − for dry air, g is the acceleration of gravity and R = . − mol − . For T = ◦ K, ε π =
115 GeV and ε K =
857 GeV.Although there is some uncertainty in relating the theoretical formalism for inclusive fluxes ofsingle muons that we use to the IceCube data sample described in the next section, we demonstratein this paper that the high event rate of 190 million events per day allows unprecedented resolutionof features in the muon flux. The large size of IceCube also makes possible a measurement ofseasonal variations of ν µ [4, 5]. In the concluding section of this paper, we comment on thecomplementarity provided by these two measurements, in particular in connection with the ratio ofkaons to pions in the secondary cosmic radiation.2 uon seasonal variations Serap Tilav
Figure 1:
IceCube Muon Rate (black line) overlaid with the temperature profile of the South Pole atmo-sphere at different pressure heights. The plot illustrates the behavior of the seasonal cycles as well as theshort-term (day to week time scales) variations in rate with respect to the temperature variations in thestratosphere.
2. Measurement of muons in IceCube
The IceCube Neutrino Observatory, located at the geographical South Pole, records high-energy muons at depths of 1450-2450m in the Antarctic ice. While the sensors look for rare astro-physical neutrinos as signal, downgoing muons with energies above 400 GeV are able to penetrateand trigger the detector at a rate of 2.15 kHz on average with ±
8% seasonal variation.Events that pass the InIce-SMT8 trigger criterion in IceCube (a simple multiplicity triggerof 8 or more sensors with local coincidence in 5 µ sec) are used for this analysis. A previousdiscussion of the analysis based on data from IceCube during construction from 2007 to 2011(IC22, IC40, IC59 and IC79) was presented in [6]. Here we use seven years of data taken with thefully completed detector since May 2011 (IC86). The daily rate is obtained by using only the runslonger than 30 minutes with complete detector configuration. Fig. 1 illustrates the IceCube muonrate correlation with the temperature profile of the South Pole atmosphere over 7 years. The SouthPole atmospheric temperature profile is extracted from data supplied by the AIRS [7] (AtmosphericInfra Red Sounder) instrument aboard NASA’s Aqua satellite.3 uon seasonal variations Serap Tilav
3. Muon production profile and effective temperature
The effective temperature for each day is obtained by weighting the temperature profile in theatmosphere with the muon production spectrum along the trajectory at zenith angle θ and integrat-ing over angle. Low- and high-energy forms for the production spectrum are respectively [8] P µ ( E µ , θ , X ) ≈ N ( E µ ) e − X / Λ N λ N × (cid:2) Z N π Z πµ ( γ ) + . Z NK Z K µ ( γ ) (cid:3) (3.1)and P µ ( E µ , θ , X ) ≈ N ( E µ ) (cid:26) ε π X cos θ E µ Z πµ ( γ + ) Z N π − Z NN Λ π Λ π − Λ N × (cid:16) e − X / Λ π − e − X / Λ N (cid:17) + . ε K X cos θ E µ Z K µ ( γ + ) Z NK − Z NN Λ K Λ K − Λ N × (cid:16) e − X / Λ K − e − X / Λ N (cid:17)(cid:111) . (3.2)Each equation has one term for muons from decay of charged pions (branching ratio ≈
1) andanother for charged kaons (branching ratio ≈ . ) . The nucleon interaction and attenuationlengths are related as λ N = Λ N ( − Z NN ) . The spectrum weighted moments have the form Z ab = (cid:82) x γ d n ab d x d x for a → b . The moments for production of pions and kaons depend on the model ofhadronic interactions used to describe production of pions and kaons by interactions of cosmic-ray nucleons in the atmosphere, while the decay moments depend only on the two-body decaykinematics of pion and kaon decay. In particular, Z πµ ( γ ) = ( − r γ + π )( γ + )( − r π ) = (cid:90) r π x γ d n µ d x d x (3.3)and Z πµ ( γ + ) = ( − r γ + π )( γ + )( − r π ) , (3.4)where x = E µ / E π , γ is the integral spectral index of the cosmic-ray spectrum and r π = ( m µ / m π ) ≈ . r K = ( m µ / m K ) ≈ . P µ ( E µ , θ , X ) = P π , low + P π , low / P π , high + P K , low + P K , low / P K , high (3.5)and integrated using Eq. 1.2 to obtain the effective temperature for each direction. The denominatorof Eq. 1.2 is the rate of events, which normalizes the effective temperature. Finally, the weightedsum over zenith angle gives the effective temperature. The dependence on temperature comesentirely from the temperature dependence of the critical energies shown in Eq. 1.3.4 uon seasonal variations Serap Tilav
4. Correlation with effective temperature
Temperature profiles at the South Pole are obtained from the AIRS satellite system at 21 atmo-spheric depths from 1 to 800 hecto-pascals in quasi logarithmic intervals. We use these temperatureprofiles to calculate event rate and T eff for each day. As an example, we show in Fig. 2 the compar- Figure 2:
Comparison of measured muon rate with calculated rate for 2012. ison of the measured and the calculated rate for 2012. The calculated rate depends on the primaryspectrum of nucleons evaluated at the energy of the muon ( N ( E µ ) ) and on A eff and is normalizedhere to the observed rate. The calculation matches the features well, but is off by a factor of twoin absolute rate. The normalization is directly proportional to the primary spectrum of nucleons,so a revised calculation starting with direct measurement to normalize the primary spectrum is un-derway. The calculated amplitude of the seasonal variation (maximum rate divided by minimumrate) is ≈
2% greater in the calculation than measured, but the short-term features agree remarkablywell. The observed sudden rate jump by 5.4% in 5 days during 5-10/Oct/2012 is reproduced in thecalculated rate as 5.9% increase, which is caused by the 7.2% increase in T eff during the same days.Sudden rate jumps of this magnitude are not uncommon during the early October period of eachyear, as seen in Fig. 1, although the increase in 2012 is exceptionally sharp. Figure 3:
Correlation coefficient between (a): the measured rate and T eff (b): the calculated rate and T eff forInIce-SMT8 muon events of IceCube 2012 data. uon seasonal variations Serap Tilav
Fig. 3(a) gives the correlation between the measured rate and the calculated T eff for 2012showing the % variation of the measured muon rate R µ over the average rate vs the % variation of T eff with respect to (cid:104) T eff (cid:105) for 2012. From Eq. 1.1, the slope indicated by the line in the figure isthe correlation coefficient α T . The experimental value of the correlation coefficient is 0.75, whichis about what is expected for the ∼ TeV muons that dominate the InIce-SMT8 trigger. To illustratethe non-linearity of the relation between muon rate and effective temperature we show in Fig. 3(b)the calculated δ R µ / (cid:104) R µ (cid:105) vs the same δ T eff / (cid:104) T eff (cid:105) used in Fig. 3(a) for the measured rate. Thecalculated rate shows a qualitatively similar, though slightly smaller, hysteresis than the measuredrate. The observed hysteresis exhibits a characteristic behavior for the South Pole related to thequalitatively different temperature profile in the Austral Spring. The upper atmosphere warmsquickly while deeper in the atmosphere the air remains cold. The calculated slope corresponds toan α T ≈ .
84. Its larger value corresponds to the slightly larger annual modulation of the calculatedrate in Fig. 2. What is new here is that the high precision of the IceCube rates with statisticalfluctuations at the level of 10 − × (cid:104) R µ (cid:105) , makes visible for the first time the non-linearity of therelation between rate and effective temperature.To illustrate the origin of this non-linearity it is helpful to go through the analysis explicitlyat fixed muon energy where A eff and primary flux cancel. We use an energy of 1 TeV, which ischaracteristic of muons in IceCube at 2 km depth in ice. For fixed energy the muon flux at zenithangle θ and atmospheric depth X is φ µ ( E µ , θ ) = N ( E µ ) (cid:90) X / cos θ (cid:26) A πµ ( X ) + B πµ ( X ) E µ cos θ / ε π + A K µ ( X ) + B K µ ( X ) E µ cos θ / ε K (cid:27) d X , (4.1)where A M µ = R M µ Z NM Z M µ ( γ ) exp ( − X / Λ N ) λ N (4.2)and B M µ = Z M µ ( γ ) Z M µ ( γ + ) Λ M − Λ N Λ M Λ N X e − X / Λ N e − X / Λ M − e − X / Λ N . (4.3)Here R M µ is the branching ratio of meson M = π or K to muons. The dependence on temperatureis contained entirely in the critical energies in Eq. 4.1 as defined in Eq. 1.3. From its definition inEq. 1.1, the correlation coefficient can be calculated from the derivative with respect to T of therate R as α T ( E , θ ) = (cid:104) T (cid:105)(cid:104) R (cid:105) d R d T . (4.4)The rate R is proportional to Eq. 4.1, sod R d T = N ( E µ ) (cid:90) (cid:26) A πµ B πµ E µ cos θ / ε π ( (cid:104) T (cid:105) )( + B πµ E µ cos θ / ε π ) + A K µ B K µ E µ cos θ / ε K ( (cid:104) T (cid:105) )( + B K µ E µ cos θ / ε K ) (cid:27) (cid:104) T (cid:105) T ( X ) d X . (4.5)Multiplying by (cid:104) T (cid:105) / (cid:104) R (cid:105) , the flux N ( E µ ) cancels, and α T ( E , θ ) follows from Eq. 4.4.The result of the calculation is shown in the Fig. 4. The correlation coefficient in the left plotis the slope of Rate vs. T eff and should be compared with Fig. 3. The correlation coefficient foreach day is the convolution of the muon production profile and the temperature profile. The fourdays shown in the right panel of Fig. 4 are chosen to illustrate seasonal differences. In particular,the October temperature profile with its high value in the upper atmosphere leads to a lower ratefor the same T eff compared to April. 6 uon seasonal variations Serap Tilav
Figure 4:
Left: Rate and correlation coefficient for TeV muons at cos θ = .
85. Right: muon productionand temperature profiles for 4 days at the beginning of each quarter of 2012.
5. Discussion
Production spectra for ν µ + ν µ have the same form as for muons. The only difference comesfrom the decay factors for the parent mesons. For the neutrino from meson M ( π ± or K ± ), Z M ν ( γ ) = ( − r M ) γ + ( γ + )( − r M ) (5.1)and Z M ν ( γ + ) = ( − r M ) γ + ( γ + )( − r M ) . (5.2)Because r π is large, the muon carries most of the energy in pion decay, while in kaon decay theenergy is shared almost equally between the muon and the neutrino. As a consequence, the kaonchannel becomes the dominant source of ν µ above ∼
100 GeV where Eq. 5.2 applies. This featuremeans that the study of seasonal variations of muons and neutrinos in the same framework shouldbe most sensitive to features like the kaon to pion ratio.To illustrate this possibility we calculate the correlation coefficient for muons and neutrinos at1 TeV, an energy that is typical for data samples for seasonal variations of neutrinos as well as formuons in IceCube. Analysis of seasonal variations of neutrinos in IceCube [4, 5] is done with adata sample of upgoing neutrino-induced muons from the Southern sky with zenith angles 90 ◦ to120 ◦ . The temperatures relevant for the neutrinos cover a much larger portion of the sky than for thedownward muons at the South Pole, for which the zenith angle range is ≈ ◦ to 60 ◦ . For simplicitytherefore we estimate the correlation coefficients by making the calculation at fixed T = ◦ K.The angular dependence of the correlation coefficients at 1 TeV are compared for muon neutrinosand for muons in Fig. 5. The atmospheric neutrino flux is largest near the horizon. The importantregion for downward muons is near the vertical cos θ ≥ . Summary:
The large volume of IceCube allows study of seasonal variations of neutrinos aswell as muons. The high rate of muons in IceCube provides a statistical precision of the data thatreveals significant variations on short time scales, as illustrated in Fig. 2. The high precision alsoreveals the non-linearity in the relation between rate and effective temperature illustrated in Fig. 3.7 uon seasonal variations
Serap Tilav
Figure 5:
Zenith angle dependence of the calculated correlation coefficient.
Work in progress includes updating the primary spectrum and revisiting the calculation of effectivearea to account for details of the data selection, for accidental coincident events and for the smallcontribution of multiple muons to the signal.
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