Zenith Angle Distribution Research Articles

Measurement of the Flux and Zenith-Angle Distribution of Upward Throughgoing Muons by Super-Kamiokande

A total of 614 upward throughgoing muons of minimum energy 1.6thinspthinspGeV are observed by Super-Kamiokande during 537 detector live days. The measured muon flux is [1.74{plus_minus}0.07(stat){plus_minus} 0.02(sys)]{times}10{sup {minus}13} cm{sup {minus}2}thinsps{sup {minus}1}thinspsr{sup {minus}1} compared to an expected flux of [1.97{plus_minus}0.44(theor)]{times} 10{sup {minus}13} cm{sup {minus}2}thinsps{sup {minus}1}thinspsr{sup {minus}1} . The absolute measured flux is in agreement with the prediction within the errors. However, the zenith-angle dependence of the observed upward throughgoing muon flux does not agree with no-oscillation predictions. The observed distortion in shape is consistent with the {nu}{sub {mu}}{leftrightarrow}{nu}{sub {tau}} oscillation hypothesis with sin{sup 2}thinsp2{theta} {gt}0.4 and 1{times}10{sup {minus}3}{lt}{Delta}m{sup 2}{lt}1{times}1 0{sup {minus}1} eV{sup 2} at 90{percent} confidence level. {copyright} {ital 1999} {ital The American Physical Society}

Statistical tests for zenith angle dependences of up-going μ-like neutrino events for multi-GeV region

At the Neutrino 98 conference the Super Kamiokande collaboration presented a reduction of up-going μ-like events compared to down-going μ -like events by a factor of 0.54 −0.05 +0.06 for an exposure of 33 kton-years. Also, the zenith angle distribution observed by MACRO for -1 ≤ cos Θ ≤ −0.1 does not fit well for the no oscillation expectation. On the basis of x 2 tested results (shape, absolute value), however, their claim for neutrino oscillations cannot be considered to be firmly established from the standpoint of statistical evidence.

Active-active and active-sterile neutrino oscillation solutions to the atmospheric neutrino anomaly

We perform a fit to the full data set corresponding to 33.0 kt-yr of data of the Super-Kamiokande experiment as well as to all other experiments in order to compare the two most likely solutions to the atmospheric neutrino anomaly in terms of oscillations in the ν μ → ν τ and ν μ → ν s channels. Using state-of-the-art atmospheric neutrino fluxes we have determined the allowed regions of oscillation parameters for both channels. We find that the Δm 2 values for the active-sterile oscillations (both for positive and negative Δm 2) are higher than for the ν μ → ν τ case, and that the increased Super-Kamiokande sample slightly favours ν μ → ν τ oscillations over oscillations into a sterile species ν s , ν μ → ν s , and disfavours ν μ → ν e . We also give the zenith angle distributions predicted for the best fit points in each of the possible oscillation channels. Finally we compare our determinations of the atmospheric neutrino oscillation parameters with the expected sensitivities of future long-baseline experiments K2K, MINOS, ICARUS, OPERA and NOE.

Super-Kamiokande atmospheric neutrino data, zenith distributions, and three-flavor oscillations

We present a detailed analysis of the zenith angle distributions of atmospheric neutrino events observed in the Super-Kamiokande (SK) underground experiment, assuming two-flavor and three-flavor oscillations (with one dominant mass scale) among active neutrinos. In particular, we calculate the five angular distributions associated with sub-GeV and multi-GeV \ensuremath{\mu}-like and e-like events and to upward through-going muons, for a total of 30 accurately computed observables (zenith bins). First we study how such observables vary with the oscillation parameters, and then we perform a fit to the experimental data as measured in SK for an exposure of 33 kTy (535 days). In the two-flavor mixing case, we confirm the results of the SK Collaboration analysis, namely, that ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ oscillations are preferred over ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{e},$ and that the no oscillation case is excluded with high confidence. In the three-flavor mixing case, we perform our analysis with and without the additional constraints imposed by the CHOOZ reactor experiment. In both cases, the analysis favors a dominance of the ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ channel. Without the CHOOZ constraints, the amplitudes of the subdominant ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{e}$ and ${\ensuremath{\nu}}_{e}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ transitions can also be relatively large, indicating that, at present, current SK data do not exclude sizable ${\ensuremath{\nu}}_{e}$ mixing by themselves. After combining the CHOOZ and SK data, the amplitudes of the subdominant transitions are constrained to be smaller, but they can still play a non-negligible role both in atmospheric and other neutrino oscillation searches. In particular, we find that the ${\ensuremath{\nu}}_{e}$ appearance probability expected in long baseline experiments can reach the testable level of \ensuremath{\sim}15%. We also discuss Earth matter effects, theoretical uncertainties, and various aspects of the statistical analysis.

Study of the atmospheric neutrino flux in the multi-GeV energy range

The flavor ratio of the atmospheric neutrino flux and its zenith angle dependence have been studied in the multi-GeV energy range using an exposure of 25.5 kiloton-years of the Super-Kamiokande detector. By comparing the data to a detailed Monte Carlo simulation, the ratio ( μ/ e) DATA/( μ/ e) MC was measured to be 0.66±0.06(stat.)±0.08(sys.). In addition, a strong distortion in the shape of the μ-like event zenith angle distribution was observed. The ratio of the number of upward to downward μ-like events was found to be 0.52 +0.07 −0.06(stat.)±0.01(sys.), with an expected value of 0.98±0.03(stat.)±0.02(sys.), while the same ratio for the e-like events was consistent with unity.

Geomagnetic effects on atmospheric neutrinos

Geomagnetic effects distort the zenith angle distribution of sub--GeV and few--GeV atmospheric neutrinos, breaking the up--down symmetry that would be present in the absence of neutrino oscillations and without a geomagnetic field. The geomagnetic effects also produce a characteristic azimuthal dependence of the $\nu$--fluxes, related to the well known east--west effect, that should be detectable in neutrino experiments of sufficiently large mass. We discuss these effects quantitatively. Because the azimuthal dependence is in first order independent of any oscillation effect, it is a useful diagnostic tool for studying possible systematic effects in the search for neutrino oscillations.

Energy and zenith angle distribution of upward going muons and neutrino oscillations

The energy and zenith angle distribution of neutrino induced, upward going muons can give direct information on the presence of $\nu$--oscillations in precisely the range of parameters suggested as a solution of the atmospheric neutrino problem. We discuss here the uncertainties in the theoretical prediction. The shape of the zenith angle distribution of the muon flux is quite insensitive to modifications of the theoretical input and is a good probe for the existence of neutrino oscillations. We conclude that the existing data sample on $\nu$--induced muons has the statistical power to confirm or refute the $\nu$--oscillation solution of the atmospheric neutrino problem.

Does the Sun appear brighter at night in neutrinos?

We calculate accurately the number of solar neutrino events expected as a function of solar zenith angle, with and without neutrino oscillations, for detectors at the locations of Super-Kamiokande, SNO, and the Gran Sasso National Laboratory. Using different Earth models to estimate geophysical uncertainties, and different solar models to estimate solar uncertainties, we evaluate distortions predicted by the Mikheyev-Smirnov-Wolfenstein (MSW) effect in the zenith angle distributions of solar neutrino events. The distortions are caused by oscillations and by $\ensuremath{\nu}$-$e$ interactions in the Earth that regenerate ${\ensuremath{\nu}}_{e}$ from ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ or ${\ensuremath{\nu}}_{\ensuremath{\tau}}.$ We show that the first two moments of the zenith-angle distribution are more sensitive to the small mixing angle MSW solution than the conventionally studied day-night asymmetry. We present iso-$\ensuremath{\sigma}$ contours that illustrate the potential of Super-Kamiokande, SNO, BOREXINO, ICARUS, and HERON/HELLAZ for detecting the Earth regeneration effect at their actual locations (and at the equator). MSW solutions favored by the four pioneering solar neutrino experiments predict characteristic distortions for Super-Kamiokande, SNO, BOREXINO, and ICARUS that range from being unmeasurably small to $g5\ensuremath{\sigma}$ (stat) after only a few years of observations.

The search for cosmic strangelets with the supersonic concorde and with JACEE's circumpolar balloon flight in Antarctica

The search for cosmic strangelet nuclei was carried out by two experiments with emulsion chambers. A balloon-borne JACEE emulsion chamber was flown at 3.5 g/cm2 for 200 h in Antarctica (JACEE-10 experiment) and the Concorde flights were made by ECHOS at an atmospheric depth of 110 g/cm2 between Paris and New York. No nuclei withZ⩾30 survived after traversing 60–120 g/cm2 of the detector materials in the JACEE instruments. No evidence for a long mean free path were found in the zenith angle distribution forZ/β⩾26 nuclei. The exposure factor used by the JACEE was 72 m2hsr. The intensity upperbounds,I⩽(2.2–9.7)×10−2/m2h sr, were obtained for strangelets having an atmospheric attenuation length of 220−50 g/cm2, which corresponds to the case for mass numberA=100–10000 andZ/β > 13. Concorde experiments (ECHOS) used both a thin and a thick emulsion chamber. The total exposure was 209 m2 h sr and no candidates with chargeZ⩾30 were found. The largest track hadZ/β=28.6±1.29 withβ ∼ 1. Nuclei observed with charge 13⩽Z⩽30 were consistent with the survival intensity of ordinary nuclei. The flux bounds from the ECHOS experiments were I⩽(2.1–5.0) x 10−2/m2h for strangelets with mass number 100⩽A⩽1000.

Remote sensing reflectance and its relationship to optical properties of natural waters

Abstract Monte Carlo simulations of photon propagation through natural water have been utilized to determine the sub-surface remote sensing reflectance, R RSW (the sub-surface value of the ratio of upwelling radiance from the nadir to the downwelling irradiance) as a function of water type (defined by the ratio of the backscattering coefficient to the absorption coefficient Bb/a), solar zenith angle, and incident radiation distribution (direct or diffuse). R RSW, as opposed to volume reflectance, R V (the sub-surface value of the ratio of upwelling to downwelling vector irradiance), is directly applicable to remotely sensed data collected over natural waters. It is shown that, for a nadir viewing direction, (a) R RSW is essentially independent of solar zenith angle and incident radiation distribution and (b) the dominant factor in determining R RSW is the optical nature of the water body itself (expressed as Bb/a). A relationship between the sub-surface remote sensing reflectance averaged over solar zenit...

A preliminary analysis of atomic oxygen dayglow using solar EUV measurements from ASSI

On 30 September 1988 a sounding rocket experiment was conducted to characterize the extreme and far ultraviolet (EUV and FUV) oxygen dayglow emissions at high spectral resolution (1.5 Å). The wavelength coverage of the spectrometer was chosen to include 989, 1027, 1304, and 1356 Å lines, four prominent atomic oxygen features in the terrestrial dayglow. The instrument, Berkeley EUV Airglow Rocket Spectrometer (BEARS), pointed approximately 110° from the rocket's axis en route to an apogee of 963 km. The data obtained by BEARS will enable us to investigate the mechanisms governing the interactions between two of the fundamental components of the solar-terrestrial system: solar ionizing radiation and the Earth's upper atmosphere. The goal of this study is to characterize the physical parameters of the EUV emissions resulting from these interactions so that EUV remote sensing can gainfully be employed as a quantitative diagnostic of the terrestrial atmosphere and plasma environment. Since the solar spectrometer aboard the BEARS payload failed, our analysis will use the solar flux measurements of the Airglow and Solar Spectrometer Instrument (ASSI) on board the San Marco D/L satellite at the time of our flight. However, at the present time, the ASSI measurements for the day of the BEARS experiment are not available. We are therefore currently using a model of solar EUV irradiance in our analysis. Preliminary modeling results of the altitude and zenith angle distribution of these emissions are presented along with the data.

Re-analysis of the primary mass composition in the 'knee region' on the basis of the Tien Shan data and the independent-nucleon model of A-A interactions

Experimental results on EAS muon and electron size fluctuations obtained in the Tien Shan experiment are reanalysed using a more realistic model of nucleus-nucleus collision and taking into account the influence of the zenith angle distribution on the width of fluctuations and the difference in the shape of muon lateral distributions in EAS initiated by different primary nuclei. The corrected primary mass composition in the 'knee region' is likely to be heavier than at lower energies.

Prompt leptons in cosmic rays

Energy spectra and zenith-angle distributions of cosmic-ray muons, neutrinos and antineutrinos of prompt generation for energy interval (1÷106) TeV are calculated. For calculations of differential cross-sections of D±, D0,\(\bar D\)0 and Λc production inNN and πN interactions the recombination quark-parton model (RQPM) is used. Accounting of nuclear effects is done by using the additive quark model and the optical model of nucleus. Detailed comparison of results obtained in RQPM with corresponding predictions of quark-gluon string model (MQGS) is carried out. Dynamics of semi-leptonic D- and Λc and energy losses of muons in the atmosphere are taken into account. Calculations of hadronic cascades in the atmosphere are done with accounting of growth with energy of total inelastic hadron-nucleus cross-sections, steepening of primary cosmic-ray spectrum and processes of pion regeneration. The comparison of our calculations with experimental data and with calculations of other authors is given.

The zenith angle distribution of extensive air showers at sea level: a measure of shower development

Measurements and computer simulations have been made of the zenith angle distribution of extensive air showers at sea level. The observed distribution is found to be sensitive to the properties of the primary particle interactions and, with present modelling, is not compatible with a purely heavy particle primary composition.

Penetration of sunlight into a canopy: Explicit models based on vertical and horizontal leaf projections

The projections of leaf areas onto a horizontal plane and onto a vertical plane are examined for their utility in characterizing canopies for sunlight penetration (direct beam only) models. These projections exactly specify the penetration if the projections on the principal plane of the normals to the top surfaces of the leaves are in the same quadrant as the Sun. Inferring the total leaf area from these projections (and therefore the penetration as a function of the total leaf area) is possible only with a large uncertainty (up to ±32%) because the projections are a specific measure of the total leaf area only if the leaf angle distribution is known. It is expected that this uncertainty could be reduced to more acceptable levels by making an approximate assessment of whether the zenith angle distribution is that of an extremophile canopy. An extremophile canopy would have the maximum leaf area possible for given set of projections. Simple leaf projection measurements would then become a practical substitute for detailed measurements of the leaf angle distribution. This is not true if for a fraction of the canopy, the leaf normal projections fall in the non-solar quadrant. In this case, accurate and detailed information about the leaf orientation is required for assessing the penetration; the horizontal and vertical projections are inadequate for this purpose.

Diurnal CO variations in the Venus mesophere from CO microwave spectra

Microwave spectra of carbon monoxide (12CO) in the mesosphere of Venus were measured in December 1978, May and December 1980, and January, September, and November 1982. These spectra are analyzed to provide mixing profiles of CO in the Venus mesosphere and best constrain the mixing profile of CO between ∼ 100 and 80 km altitude. From the January 1982 measurement (which, of all our spectra, best constrains the abundance of CO below 80 km altitude) we find an upper limit for the CO mixing ratio below 80 km altitude that is two to three times smaller than the stratospheric (∼65 km) value of 4.5 ± 1.0 × 10−5 determined by P. Connes, J. Connes, L.D. Kaplan, and W. S. Benedict (1968, Astrophys. J. 152, 731–743) in 1967, indicating a possible long-term change in the lower atmospheric concentration of CO. Intercomparison among the individual CO profiles derived from our spectra indicates considerable short-term temporal and/or spatial variation in the profile of CO mixing in the Venus mesosphere above 80 km. A more complete comparison with previously published CO microwave spectra from a number of authors specifies the basic diurnal nature of mesospheric CO variability. CO abundance above ∼ 95 km in the Venus atmosphere shows approximately a factor of 2–4 enhancement on the nightside relative to the dayside of Venus. Peak nightside CO abundance above ∼95 km occurs very near to the antisolar point on Venus (local time of peak CO abundance above ∼95 km occurs at 0.6−0.6+0.7 hr after midnight on Venus), strongly suggesting that retrograde zonal flow is substantially reduced at an altitude of 100 km in the Venus mesosphere. In contrast, CO abundances between 80 and 90 km altitude show a maximum that is shifted from the antisolar point toward the morningside of Venus (local time of peak CO abundance between 80 and 90 km occurs at 8.5 ± 1.0 hr past midnight on Venus). The magnitude of the diurnal variation of CO abundance between 80 and 90 km is again, approximately a factor of 2–4. Disk-averaged spectra of Venus do not determine the exact form for the diurnal distribution of CO in the Venus mesosphere as indicated by comparison of synthetic spectra, based upon model distributions, and the measured spectra. However, the offset in phase for the diurnal variation for the >95 km and 80–90-km-altitude regions requires an asymmetric (in solar zenith angle) distribution.

Diurnal CO variations in the Venus mesophere from CO microwave spectra

Microwave spectra of carbon monoxide ( 12CO) in the mesosphere of Venus were measured in December 1978, May and December 1980, and January, September, and November 1982. These spectra are analyzed to provide mixing profiles of CO in the Venus mesosphere and best constrain the mixing profile of CO between ∼ 100 and 80 km altitude. From the January 1982 measurement (which, of all our spectra, best constrains the abundance of CO below 80 km altitude) we find an upper limit for the CO mixing ratio below 80 km altitude that is two to three times smaller than the stratospheric (∼65 km) value of 4.5 ± 1.0 × 10 −5 determined by P. Connes, J. Connes, L.D. Kaplan, and W. S. Benedict (1968, Astrophys. J. 152, 731–743) in 1967, indicating a possible long-term change in the lower atmospheric concentration of CO. Intercomparison among the individual CO profiles derived from our spectra indicates considerable short-term temporal and/or spatial variation in the profile of CO mixing in the Venus mesosphere above 80 km. A more complete comparison with previously published CO microwave spectra from a number of authors specifies the basic diurnal nature of mesospheric CO variability. CO abundance above ∼ 95 km in the Venus atmosphere shows approximately a factor of 2–4 enhancement on the nightside relative to the dayside of Venus. Peak nightside CO abundance above ∼95 km occurs very near to the antisolar point on Venus (local time of peak CO abundance above ∼95 km occurs at 0.6 −0.6 +0.7 hr after midnight on Venus), strongly suggesting that retrograde zonal flow is substantially reduced at an altitude of 100 km in the Venus mesosphere. In contrast, CO abundances between 80 and 90 km altitude show a maximum that is shifted from the antisolar point toward the morningside of Venus (local time of peak CO abundance between 80 and 90 km occurs at 8.5 ± 1.0 hr past midnight on Venus). The magnitude of the diurnal variation of CO abundance between 80 and 90 km is again, approximately a factor of 2–4. Disk-averaged spectra of Venus do not determine the exact form for the diurnal distribution of CO in the Venus mesosphere as indicated by comparison of synthetic spectra, based upon model distributions, and the measured spectra. However, the offset in phase for the diurnal variation for the >95 km and 80–90-km-altitude regions requires an asymmetric (in solar zenith angle) distribution.

Observation of horizontal air showers with energies of 1 to 100 TeV

An observation of horizontal air showers of sizes from 103 to 105 particles (1 to 100 TeV in energy) has been performed. For showers of sizes up to ∼2.104, the size spectrum and zenith angle distributions are observed to be consistent with expectation. Some deviation appears in both the size spectrum and angle distributions for showers above ∼2.104, which suggests that they may be due to a short-lived muon parent particle.

Atmospheric gamma ray angle and energy distributions from sea level to 3.5 g/cm² and 2 to 25 MeV

Angle and energy distributions are reported here for gamma rays from ground level to 3.5 g/cm² residual atmosphere at energies of 2 to 25 MeV and zenith angles of 0° to 50° and 180° to 130°. They complement the previous results of Ryan et al. (1977) for altitudes above 100 g/cm². The observations were made with the University of California, Riverside (UCR), double Compton scatter telescope from a balloon launched from Palestine, Texas, geomagnetic cut‐off of 4.5 GV, on May 13, 1975. The ground level measurements were made at Riverside, California, at 1000‐g/cm² residual atmosphere, geomagnetic cut‐off of 5.4 GV, on July 21, 1977. Growth curves for downward‐moving gamma rays have pronounced maxima at 160±30 g/cm² residual atmosphere, while those for upward‐moving gamma rays are essentially constant at altitudes above the Pfotzer maximum. Below about 300 g/cm² both the downward and the upward fluxes decrease with average e‐folding depths of 192±15 and 179±12 g/cm², respectively. The ratio of the downward‐ to upward‐moving gamma rays near the vertical is 17±5, independent of depth below the Pfotzer maximum. The energy variation, E−1.1, of the downward‐moving gamma rays is flatter than the E−1.8 of the upward moving ones at all depths below 100 g/cm². All zenith angle distributions show peaks toward the horizon. Above the Pfotzer maximum the downward flux decreases more rapidly away from the horizon than the upward flux, while below the converse is true. The azimuth angle distributions at 4.0 g/cm² show northward anisotropies that increase with energy from 3.9±0.9% at 2–10 MeV to 7.0±2.3% at 10–25 MeV.

Measurements of the energy spectrum of cosmic-ray muons at sea-level with emulsion chambers

The energy spectrum of cosmic-ray muons at sea-level has been measured in the energy range of 1 TeV to 10 TeV with the emulsion chambers exposed at shallow depth underground. The total amount of exposure is 61.6 tons of lead/year. On the vertical muon intensity, it is shown that the index of the spectrum is 2.70±0.10, when it is expressed with a single power law. The zenith angle distributions in the energies around several TeV are not inconsistent with those expected from the muons of pion and kaon decay.