Elsevier

Advances in Space Research

Volume 55, Issue 1, 1 January 2015, Pages 363-389
Advances in Space Research

Neutron monitors and muon detectors for solar modulation studies: Interstellar flux, yield function, and assessment of critical parameters in count rate calculations

https://doi.org/10.1016/j.asr.2014.06.021Get rights and content

Abstract

Particles count rates at given Earth location and altitude result from the convolution of (i) the interstellar (IS) cosmic-ray fluxes outside the solar cavity, (ii) the time-dependent modulation of IS into Top-of-Atmosphere (TOA) fluxes, (iii) the rigidity cut-off (or geomagnetic transmission function) and grammage at the counter location, (iv) the atmosphere response to incoming TOA cosmic rays (shower development), and (v) the counter response to the various particles/energies in the shower. Count rates from neutron monitors or muon counters are therefore a proxy to solar activity. In this paper, we review all ingredients, discuss how their uncertainties impact count rate calculations, and how they translate into variation/uncertainties on the level of solar modulation ϕ (in the simple Force-Field approximation). The main uncertainty for neutron monitors is related to the yield function. However, many other effects have a significant impact, at the 5–10% level on ϕ values. We find no clear ranking of the dominant effects, as some depend on the station position and/or the weather and/or the season. An abacus to translate any variation of count rates (for neutron and μ detectors) to a variation of the solar modulation ϕ is provided.

Introduction

After the discovery of cosmic rays (CR) by Hess in 1912, ground-based CR detectors located at various latitudes, longitudes and altitudes, played a major role to determine the CR composition and spectrum (see Stoker (2009) for a historical perspective). From the 50’s, networks of neutron monitors (Simpson, 2000) and muon telescopes (Duldig, 2000) were developed. They provide today one of the most valuable data to inspect time variations of the integrated CR flux in the 10–100 GeV/n range.

The formal link between these variations and the Sun activity was established in the mid-fifties, by means of a transport equation of CR fluxes in the solar cavity (Parker, 1965, Jokipii, 1966). In the 80’s, the effect of particle drift was shown to be responsible to a charge-sign dependent modulation (Potgieter, 2013), following the Sun polarity cycle.1 However, the Force-Field approximation (Gleeson and Axford, 1967, Gleeson and Axford, 1968) has remained widely used thanks to its simplicity: this approximation, used in this work, has only one parameter ϕ(t).

Several strategies have been developed for time series reconstruction of the modulation level ϕ(t), and/or CR TOA fluxes at any time (of interest for many applications):

  • Using spacecraft measurements (e.g., Davis et al., 2001, Buchvarova et al., 2011, Buchvarova and Draganov, 2013): it is the most direct approach, but the time coverage is limited to a few decades with a poor sampling;

  • Comparison of calculated and measured count rates in ground-based detectors (Usoskin et al., 1999, Usoskin et al., 2002, Usoskin et al., 2005, Usoskin et al., 2011): it covers a larger period (60 years), with a very good time resolution (a few minutes)2;

  • Extracting relationships between the modulation level and solar activity proxies, based on empirical (Badhwar and O’Neill, 1994, Badhwar and O’Neill, 1996, O’Neill, 2006, O’Neill, 2010) or semi-empirical (Nymmik et al., 1992, Nymmik et al., 1994, Nymmik et al., 1996, Nymmik, 2007, Tylka et al., 1997, Ahluwalia, 2013) approaches.

All these strategies provide a satisfactory description of CR fluxes, though some fare better than others (for comparisons, see Buchvarova and Velinov, 2010, Mrigakshi et al., 2012, Zhao and Qin, 2013, Matthia et al., 2013). Note also that empirical methods are expected to provide effective and less meaningful values for ϕ (O’Neill, 2006).

In this paper, we focus on the second strategy, for a systematic study of the main uncertainties affecting the calculation of expected count rates in NM and muon detectors. This requires the description of the atmosphere and of the ground-based detector responses to incoming CRs (e.g., Clem and Dorman, 2000). The various uncertainties, described in the Dorman, 1974, Dorman, 2004, Dorman, 2009 textbooks, are generally discussed separately in research articles (uncertainty on the yield function, geomagnetic rigidity cutoff, seasonal effects…), and not propagated to the modulation parameter. For this reason, we believe it is useful to recap and gather them in a single study, re-assess which ones are the most important, and link these uncertainties to the expected level of variation/uncertainty they imply on the modulation level ϕ(t). The complementarity (different uncertainties and time coverage) of NM count rates and TOA CR flux measurements to obtain time-series of the solar modulation parameters is left to a second study.3

The paper is organised as follows: we start with a general presentation of the ingredients involved in the count rate calculations (Section 2), and discuss a new fit for the IS fluxes (Section 3). We then detail the calculation of the propagation in the atmosphere, providing a new yield function parametrisation (Section 4). Combining these inputs allows us to link the count rate variation with the solar modulation parameter, and to study the various sources of uncertainties (Section 5). The final ranking of the uncertainties in terms of both count rates and ϕ concludes this study (Section 6).

Section snippets

From IS fluxes to ground-based detector count rates

A ground-based detector D at geographical coordinate r=(φ,λ,h) measures, at time t, a count rate per unit interval ND(r,t), from the production (from CRs) of secondary particles in the atmosphere (atmospheric shower):ND(r,t)=0T(R,r,t)×i=CRsYiD(R,h)dJiTOAdR(R,t)dR,with R=pc/Ze, and i running on CR species:

  • T(R,r,t) is the transmission function in the geomagnetic field, which depends on the detector location and can vary with time (Section 5.2.2);

  • YiD(R,h) is the yield function at altitude h

Determination of IS fluxes: from H to Ni

Due to the interplay between the CR relative abundances and the yield function, the most important primary CR contributors to the count rates are protons, heliums, and heavier nuclei (in a small but non negligible fraction). In recent studies, in addition to proton and helium, the contribution of species heavier than He is accounted for as an effective enhancement of the He flux (Webber and Higbie, 2003, Usoskin et al., 2011).

In order to assess the uncertainties (on count rate calculations)

Atmospheric propagation, yield function, and detectors

When entering the Earth atmosphere, CRs initiate cascades of nuclear reactions involving primary energetic particles (mainly hydrogen and helium but also heavier nuclei) and atmospheric nuclei such as oxygen or nitrogen. The so-called Extensive Air Showers (EAS) generate secondary particles along their path, to be detected by ground-based instruments.

In this section, we discuss the generation of secondary particles (Section 4.1) as an input to provide a new yield function parametrisation

Count rates: variations and uncertainties

In this section, count rates are calculated from Eq. (1), which involves the yield function YiD(h,R), the modulated fluxes JiTOA(t) for all CR species i, and the geomagnetic transmission T(R,r,t). To validate our code, we compare count rate variations (vs Rc) to existing latitude surveys (Section 5.1). We then propagate, on count rates, IS flux and yield function uncertainties (Section 5.2.1), and geomagnetic transmission function uncertainties (Section 5.2.2). We conclude the section with

Conclusions: count rate variation and uncertainty iso-contours in the (Rc,ϕ) plane

We have made a detailed study of count rates (and uncertainties) for neutron monitors and μ detectors, as a function of the rigidity cut-off and the modulation level ϕ, in the context of the force-field approximation.

Acknowledgements

D. M. thanks K. Louedec for useful discussions on the Auger scaler data, A. L. Mishev and I. G. Usoskin for clarifications on their yield function, and P. M. O’Neill for providing his BO11 flux model. We thank the anonymous referee for her/his careful reading that helped correcting several mistakes in the text.

References (179)

  • L.I. Dorman et al.

    Effective non-vertical and apparent cutoff rigidities for a cosmic ray latitude survey from Antarctica to Italy in minimum of solar activity

    Adv. Space Res.

    (2008)
  • F. James et al.

    Minuit – a system for function minimization and analysis of the parameter errors and correlations

    Comput. Phys. Commun.

    (1975)
  • K.C. Kim et al.

    Cosmic ray 2H/1H ratio measured from BESS in 2000 during solar maximum

    Adv. Space Res.

    (2013)
  • H. Krüger et al.

    A calibration neutron monitor: Statistical accuracy and environmental sensitivity

    Adv. Space Res.

    (2010)
  • K. Kudela et al.

    On transmissivity of low energy cosmic rays in disturbed magnetosphere

    Adv. Space Res.

    (2008)
  • D. Matthiä et al.

    A ready-to-use galactic cosmic ray model

    Adv. Space Res.

    (2013)
  • A.L. Mishev et al.

    Normalized ionization yield function for various nuclei obtained with full Monte Carlo simulations

    Adv. Space Res.

    (2011)
  • H.S. Ahn et al.

    Discrepant Hardening Observed in Cosmic-ray Elemental Spectra

    ApJ

    (2010)
  • AMS Collaboration et al.

    Cosmic protons

    Phys. Lett. B

    (2000)
  • AMS Collaboration et al.

    Helium in near Earth orbit

    Phys. Lett. B

    (2000)
  • AMS Collaboration et al.

    The Alpha Magnetic Spectrometer (AMS) on the International Space Station: Part I – results from the test flight on the space shuttle

    Phys. Rep.

    (2002)
  • AMS Collaboration et al.

    Isotopic composition of light nuclei in cosmic rays: results from AMS-01

    ApJ

    (2011)
  • H.W. Babcock

    The topology of the Sun’s magnetic field and the 22-year cycle

    ApJ

    (1961)
  • G.A. Bazilevskaya et al.

    Cosmic ray induced ion production in the atmosphere

    Space Sci. Rev.

    (2008)
  • Bercovitch, M., Robertson, B.C., 1965. Meteorological factors affecting the counting rate of neutron monitors. In:...
  • M. Berkova et al.

    Temperature effect of muon component and practical questions of how to take into account in real time

    Astrophys. Space Sci. Trans

    (2012)
  • M.D. Berkova et al.

    Temperature effect of the muon component and practical questions for considering it in real time

    Bull. Russ. Acad. Sci. Phys.

    (2011)
  • J. Bieber et al.

    Continued decline of South Pole neutron monitor counting rate

    J. Geophys. Res. (Space Phys.)

    (2013)
  • J.W. Bieber et al.

    Spaceship Earth – An Optimized Network of Neutron Monitors

  • J.W. Bieber et al.

    Efficient computation of apparent cutoffs

  • J.W. Bieber et al.

    Long-term decline of south pole neutron rates

    J. Geophys. Res. (Space Phys.)

    (2007)
  • W.R. Binns et al.

    Abundances of ultraheavy elements in the cosmic radiation – Results from HEAO 3

    ApJ

    (1989)
  • P. Bobik et al.

    Magnetospheric transmission function approach to disentangle primary from secondary cosmic ray fluxes in the penumbra region

    J. Geophys. Res. (Space Phys.)

    (2006)
  • M. Boezio et al.

    The Cosmic-Ray Proton and Helium Spectra between 0.4 and 200 GV

    ApJ

    (1999)
  • M. Buchvarova et al.

    Cosmic-Ray Spectrum Approximation Model: Experimental Results and Comparison with Other Models

    Sol. Phys.

    (2013)
  • R.A. Burger et al.

    Rigidity dependence of cosmic ray proton latitudinal gradients measured by the Ulysses spacecraft: implications for the diffusion tensor

    J. Geophys. Res.

    (2000)
  • Bütikofer, R., Flückiger, E.O., Desorgher, L. 2008.. Characteristics of near real-time cutoff calculations on a local...
  • R.A. Caballero-Lopez et al.

    Limitations of the force field equation to describe cosmic ray modulation

    J. Geophys. Res. (Space Phys.)

    (Januray 2004)
  • R.A. Caballero-Lopez et al.

    Cosmic-ray yield and response functions in the atmosphere

    J. Geophys. Res. (Space Phys.)

    (2012)
  • H. Carmichael et al.

    Latitude survey in North America

  • S. Cecchini et al.

    Atmospheric muons: experimental aspects

    Geoscientific Instrumentation, Methods and Data Systems

    (2012)
  • R.L. Chasson et al.

    Atmospheric water vapor and attenuation of the cosmic-ray nucleonic component

    J. Geophys. Res.

    (1966)
  • A. Cheminet et al.

    Characterization of the IRSN neutron multisphere spectrometer (HERMEIS) at European standard calibration fields

    J. Instrum.

    (2012)
  • A. Cheminet et al.

    Experimental measurements of the cosmic-ray induced neutron spectra at various mountain altitudes with HERMEIS

    IEEE Trans. Nucl. Sci.

    (2012)
  • A. Cheminet et al.

    Measurements and Monte Carlo Simulations of the spectral variations of the cosmic-ray induced neutrons at the Pic du Midi over a two-year period

    Radiat. Prot. Dosimetry.

    (2013)
  • A. Cheminet et al.

    Cosmic ray solar modulation and Forbush decrease analyses based on atmospheric neutron spectrometry at mountain altitude and GEANT4 simulations of extensive air showers

    J. Geophys. Res. (Space Phys.)

    (2013)
  • A. Cheminet et al.

    Characterization of the neutron environment and SEE investigations at the CERN-EU high energy reference field and at the pic du midi

    IEEE Trans. Nucl. Sci.

    (2013)
  • J. Clem

    Atmospheric yield functions and the response to secondary particles of neutron monitors

  • J.M. Clem et al.

    Neutron monitor response functions

    Space Sci. Rev.

    (2000)
  • J.M. Clem et al.

    Contribution of obliquely incident particles to neutron monitor counting rate

    J. Geophys. Res.

    (1997)
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