The muon charge asymmetry and the directional distribution of thunderstorm events observed by the GRAPES-3 muon telescope

Abstract

The electric fields inside thunderstorms can significantly modify the intensity of secondary cosmic ray muons at the ground level, producing measurable variations in their intensity ($Δ$I$_μ$). By utilizing the decade-long observations of thunderstorms (April 2011-December 2020) by the GRAPES-3 muon telescope (G3MT), a directional asymmetry in $Δ$I$_μ$ is observed, with nearly six times more events being detected from the east than the west directions. Using detailed CORSIKA Monte Carlo simulations, it is shown that this asymmetry is caused by the variations of the muon charge ratio R$_μ$ (N$_{μ^+}$/N$_{μ^-}$). The anisotropic R$_μ$ in turn, is caused by the systematic changes in geomagnetic cutoff rigidities, and subsequent selective filtering of predominantly positively charged primary cosmic rays. As a consequence, the R$_μ$ increases systematically from west to east across the G3MT field of view, enhancing the sensitivity of east directions to positively charged thunderstorm top. Monte Carlo simulations with constant R$_μ$ show that the directional asymmetry disappears, demonstrating the muon charge imbalance to be the dominant driver of the observed asymmetry. The dependence of R$_μ$ on the hadronic interaction is also studied by comparing seven combinations high-, and low-energy hadronic interaction generators, which show a $\lesssim$7% spread in R$_μ$, and $\lesssim$14% variation in the derived thunderstorm potentials. These results provide the first quantitative link between the muon charge asymmetry caused by the geomagnetic field, and the directional distribution of thunderstorms, reinforcing the role of muon observations as a probe of gigavolt potentials in atmospheric electrical structures.

Figures (6)

• Figure 1: Representation of (a) muon angle reconstruction in a single projection using PRC hits, and (b) solid angle coverage of G3MT in 169-direction configuration shown as dotted lines, excluding outermost overflow bins. Solid lines represent coarser 9-direction configuration.
• Figure 2: Locations of electric field mills installed in GRAPES-3 and other places, labeled 1 to 4.
• Figure 3: Distribution of 487 thunderstorm recorded by G3MT during April 2011 to December 2020 based on observed muon intensity variation ($\Delta I_{\mu}$). Since events are selected based on condition $\mid\Delta I_{\mu}\mid>$0.3%, bins in band --0.3 to 0.3% are empty. Dotted line is a Gaussian fit to guide the eye, and indicate that event distribution follows a normal distribution. The fits yields a mean = --0.33%, and rms = 0.4% -- negative mean implies that most thunderstorms cause muon deficit due to dominant positive thunderstorm potential in the nature.
• Figure 4: Map of muon charge ratio R$_\mu$ (N$_{\mu^+}$/N$_{\mu^-}$) derived by using CORSIKA with SIBYLL-FLUKA combination in 169-direction configuration of G3MT FOV. A sample of 10$^6$ simulated muons yields a statistical error of $\sim$0.1%. R$_\mu$ = 1.251 for full FOV of G3MT, and has values of 1.136, 1.254, 1.374 for vertical groups in west (W$_{G}$), vertical (V$_{G}$), east (E$_{G}$), respectively. Similarly, R$_\mu$ has values of 1.258, 1.245, 1.261 for horizontal groups in north (N$_{G}$), horizontal (H$_{G}$), south (S$_{G}$), respectively. The mean values of R$_\mu$ of 1.255$\pm$0.119, and 1.255$\pm$0.008 for vertical, and horizontal groups, respectively are nearly same but the large difference in their rms indicates presence of a stronger muon charge asymmetry in E-W (rms = 0.119) than N-S (rms = 0.008) directions.
• Figure 5: Variation of muon charge ratio (R$_\mu$=N$_{\mu^+}$/N$_{\mu^-}$) as a function of applied thunderstorm potential derived for GRAPES-3 total field of view using CORSIKA with SIBYLL-FLUKA hadronic interaction generators in the thunderstorm potential range of --3 GV to +3 GV with a step size of 0.25 GV. Each potential step contains R$_\mu$ generated using about 169$\times$10$^6$ muons. R$_\mu$ is 1.251 at zero thunderstorm potential.