Azimuthal asymmetry in the risetime of the surface detector signals of the Pierre Auger Observatory

The azimuthal asymmetry in the risetime of signals in Auger surface detector stations is a source of information on shower development. The azimuthal asymmetry is due to a combination of the longitudinal evolution of the shower and geometrical effects related to the angles of incidence of the particles into the detectors. The magnitude of the effect depends upon the zenith angle and state of development of the shower and thus provides a novel observable, $(\sec \theta {)}_{\max }$, sensitive to the mass composition of cosmic rays above $3\times {10}^{18}\mathrm{eV}$. By comparing measurements with predictions from shower simulations, we find for both of our adopted models of hadronic physics (QGSJETII-04 and EPOS-LHC) an indication that the mean cosmic-ray mass increases slowly with energy, as has been inferred from other studies. However, the mass estimates are dependent on the shower model and on the range of distance from the shower core selected. Thus the method has uncovered further deficiencies in our understanding of shower modeling that must be resolved before the mass composition can be inferred from $(\sec \theta {)}_{\max }$.

Figure 1

Schematic view of the shower geometry. The incoming direction of the primary particle defines two regions, “early” ($|\zeta |<\pi /2$) and “late” region ($|\zeta |>\pi /2$). Note the different amount of atmosphere traversed by the particles reaching the detectors in each region.

Figure 2

Top: two stations in an event of 16.9 EeV and 15.7° in zenith. Bottom: two stations in an event of 7.7 EeV and 52° in zenith. Left panels correspond to early stations while right panels correspond to late stations.

Figure 3

Example of risetime vs core distance for stations in events between energies ${10}^{19.2}–{10}^{19.6}\mathrm{eV}$ and zenith angle 42°–48°. Top: scatter distribution of the risetime values for individual stations. Bottom: bin-by-bin averages of the risetime. Vertical bars represent the root-mean-square of the corresponding distributions.

Figure 4

Dependence of $⟨t_{1/2}/r⟩$ on the polar angle $\zeta$ in the shower plane for primary energy $\log (E/\mathrm{eV})=18.55–18.70$ (top) and 19.20–19.50 (bottom) at different zenith angles bands. Each data point represents an average (with the corresponding uncertainty) over all stations surviving the selection criteria (see text).

Figure 5

Dependence of $⟨t_{1/2}/r⟩$ on $\zeta$ for two chosen core distance intervals for data. Results of the fitted parameters (see text) are shown for each core distance interval.

Figure 6

Asymmetry longitudinal development in bins of $\log (E/\mathrm{eV})$ at the interval 500–1000 m. From left to right and top to bottom: 18.55–18.70,18.70–18.85,18.85–19.00,19.00–19.20,19.20–19.50 and above 19.50.

Figure 7

Asymmetry longitudinal development in bins of $\log (E/\mathrm{eV})$ at the interval 1000–2000 m. From left to right and top to bottom: 18.55–18.70,18.70–18.85,18.85–19.00,19.00–19.20,19.20–19.50 and above 19.50.

Figure 8

Energy dependence of $(\sec \theta {)}_{\max }$ for both intervals of core distance 500–1000 m and 1000–2000 m. Brackets represent the systematic uncertainty and the vertical lines the statistical uncertainties. The number of stations used for the analysis are indicated.

Figure 9

Comparison between $(\sec \theta {)}_{\max }$, for both data and Monte Carlo predictions in the 500–1000 m interval (top) and in the 1000–2000 m interval (bottom) using both hadronic models EPOS-LHC (solid lines) and QGSJETII-04 (dashed lines), for both primaries, proton (red) and iron (blue).

Figure 10

Comparison of $⟨\ln A⟩$ as a function of energy for both core distance intervals predicted by EPOS-LHC (top panel) and QGSJETII-04 (bottom panel).

Figure 11

$⟨\ln A⟩$ as a function of energy as predicted by EPOS-LHC and QGSJETII-04. Results from the asymmetry analysis in both $r$ intervals are shown and compared with those from the elongation curve [5] and the MPD method [13].