Limit Cycles of Polynomially Integrable Piecewise Differential Systems

In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonian. Under this assumption, piecewise differential systems have no more than one limit cycle. This study characterizes linear differential systems with polynomial first integrals

Search for Spatial Correlations of Neutrinos with Ultra-high-energy Cosmic Rays

For several decades, the origin of ultra-high-energy cosmic rays (UHECRs) has been an unsolved question of high-energy astrophysics. One approach for solving this puzzle is to correlate UHECRs with high-energy neutrinos, since neutrinos are a direct probe of hadronic interactions of cosmic rays and are not deflected by magnetic fields. In this paper, we present three different approaches for correlating the arrival directions of neutrinos with the arrival directions of UHECRs. The neutrino data are provided by the IceCube Neutrino Observatory and ANTARES, while the UHECR data with energies above ∼50 EeV are provided by the Pierre Auger Observatory and the Telescope Array. All experiments provide increased statistics and improved reconstructions with respect to our previous results reported in 2015. The first analysis uses a high-statistics neutrino sample optimized for point-source searches to search for excesses of neutrino clustering in the vicinity of UHECR directions. The second analysis searches for an excess of UHECRs in the direction of the highest-energy neutrinos. The third analysis searches for an excess of pairs of UHECRs and highest-energy neutrinos on different angular scales. None of the analyses have found a significant excess, and previously reported overfluctuations are reduced in significance. Based on these results, we further constrain the neutrino flux spatially correlated with UHECRs

Cosmological implications of photon-flux upper limits at ultra-high energies in scenarios of Planckian-interacting massive particles for dark matter

We present a thorough search for signatures that would be suggestive of super-heavy $X$ particles decaying in the Galactic halo, in the data of the Pierre Auger Observatory. From the lack of signal, we derive upper limits for different energy thresholds above ${\gtrsim}10^8$\,GeV on the expected secondary by-product fluxes from $X$-particle decay. Assuming that the energy density of these super-heavy particles matches that of dark matter observed today, we translate the upper bounds on the particle fluxes into tight constraints on the couplings governing the decay process as a function of the particle mass. We show that instanton-induced decay processes allow us to derive a bound on the reduced coupling constant of gauge interactions in the dark sector: \alpha_X \alt 0.09, for 10^{9} \alt M_X/\text{GeV} < 10^{19}. This upper limit on $\alpha_X$ is complementary to the non-observation of tensor modes in the cosmic microwave background in the context of Planckian-interacting massive particles for dark matter produced during the reheating epoch. Viable regions for this scenario to explain dark matter are delineated in several planes of the multidimensional parameter space that involves, in addition to $M_X$ and $\alpha_X$, the Hubble rate at the end of inflation, the reheating efficiency, and the non-minimal coupling of the Higgs with curvature.Comment: 15 pages, 8 figures, Accompanying paper of arXiv:2203.0885

Arrival Directions of Cosmic Rays above 32 EeV from Phase One of the Pierre Auger Observatory

A promising energy range to look for angular correlations between cosmic rays of extragalactic origin and their sources is at the highest energies, above a few tens of EeV (1 EeV ≡ 10¹⁸ eV). Despite the flux of these particles being extremely low, the area of ∼3000 km² covered at the Pierre Auger Observatory, and the 17 yr data-taking period of the Phase 1 of its operations, have enabled us to measure the arrival directions of more than 2600 ultra-high-energy cosmic rays above 32 EeV. We publish this data set, the largest available at such energies from an integrated exposure of 122,000 km² sr yr, and search it for anisotropies over the 3.4π steradians covered with the Observatory. Evidence for a deviation in excess of isotropy at intermediate angular scales, with ∼15° Gaussian spread or ∼25° top-hat radius, is obtained at the 4σ significance level for cosmic-ray energies above ∼40 EeV

Design and implementation of the AMIGA embedded system for data acquisition

The Auger Muon Infill Ground Array (AMIGA) is part of the AugerPrime upgrade of the Pierre Auger Observatory. It consists of particle counters buried 2.3 m underground next to the water-Cherenkov stations that form the 23.5 km$^2$ large infilled array. The reduced distance between detectors in this denser area allows the lowering of the energy threshold for primary cosmic ray reconstruction down to about 10$^{17}$ eV. At the depth of 2.3 m the electromagnetic component of cosmic ray showers is almost entirely absorbed so that the buried scintillators provide an independent and direct measurement of the air showers muon content. This work describes the design and implementation of the AMIGA embedded system, which provides centralized control, data acquisition and environment monitoring to its detectors. The presented system was firstly tested in the engineering array phase ended in 2017, and lately selected as the final design to be installed in all new detectors of the production phase. The system was proven to be robust and reliable and has worked in a stable manner since its first deployment.Comment: Accepted for publication at JINST. Published version, 34 pages, 15 figures, 4 table

Joint analysis of the energy spectrum of ultra-high-energy cosmic rays measured at the Pierre Auger Observatory and the Telescope Array

The measurement of the energy spectrum of ultra-high-energy cosmic rays (UHECRs) is of crucial importance to clarify their origin and acceleration mechanisms. The Pierre Auger Observatory in Argentina and the Telescope Array (TA) in the US have reported their measurements of UHECR energy spectra observed in the southern and northern hemisphere, respectively. The region of the sky accessible to both Observatories ([−15,+24] degrees in declination) can be used to cross-calibrate the two spectra. The Auger-TA energy spectrum working group was organized in 2012 and has been working to understand the uncertainties in energy scale in both experiments, their systematic differences, and differences in the shape of the spectra. In previous works, we reported that there was an overall agreement of the energy spectra measured by the two observatories below 10 EeV while at higher energies, a remaining significant difference was observed in the common declination band. We revisit this issue to understand its origin by examining the systematic uncertainties, statistical effects, and other possibilities. We will also discuss the differences in the spectra in different declination bands and a new feature in the spectrum recently reported by the Auger Collaboration

UHECR arrival directions in the latest data from the original Auger and TA surface detectors and nearby galaxies

The distribution of ultra-high-energy cosmic-ray arrival directions appears to be nearly isotropic except for a dipole moment of order $6 \times (E/10~\mathrm{EeV})$ per cent. Nonetheless, at the highest energies, as the number of possible candidate sources within the propagation horizon and the magnetic deflections both shrink, smaller-scale anisotropies might be expected to emerge. On the other hand, the flux suppression reduces the statistics available for searching for such anisotropies. In this work, we consider two different lists of candidate sources: a sample of nearby starburst galaxies and the 2MRS catalog tracing stellar mass within 250 Mpc. We combine surface-detector data collected at the Pierre Auger Observatory until 2020 and the Telescope Array until 2019, and use them to test models in which UHECRs comprise an isotropic background and a foreground originating from the candidate sources and randomly deflected by magnetic fields. The free parameters of these models are the energy threshold, the signal fraction, and the search angular scale. We find a correlation between the arrival directions of $11.8\%_{-3.1\%}^{+5.0\%}$ of cosmic rays detected with $E \ge 38~\mathrm{EeV}$ by Auger or with $E \gtrsim 49~\mathrm{EeV}$ by TA and the position of nearby starburst galaxies on a ${15.5^\circ}_{-3.2^\circ}^{+5.3^\circ}$ angular scale, with a 4.2σ post-trial significance, as well as a weaker correlation with the overall galaxy distribution

The UHECR dipole and quadrupole in the latest data from the original Auger and TA surface detectors

The sources of ultra-high-energy cosmic rays are still unknown, but assuming standard physics, they are expected to lie within a few hundred megaparsecs from us. Indeed, over cosmological distances cosmic rays lose energy to interactions with background photons, at a rate depending on their mass number and energy and properties of photonuclear interactions and photon backgrounds. The universe is not homogeneous at such scales, hence the distribution of the arrival directions of cosmic rays is expected to reflect the inhomogeneities in the distribution of galaxies; the shorter the energy loss lengths, the stronger the expected anisotropies. Galactic and intergalactic magnetic fields can blur and distort the picture, but the magnitudes of the largest-scale anisotropies, namely the dipole and quadrupole moments, are the most robust to their effects. Measuring them with no bias regardless of any higher-order multipoles is not possible except with full-sky coverage. In this work, we achieve this in three energy ranges (approximately 8--16 EeV, 16--32 EeV, and 32--∞ EeV) by combining surface-detector data collected at the Pierre Auger Observatory until 2020 and at the Telescope Array (TA) until 2019, before the completion of the upgrades of the arrays with new scintillator detectors. We find that the full-sky coverage achieved by combining Auger and TA data reduces the uncertainties on the north-south components of the dipole and quadrupole in half compared to Auger-only results

The UHECR dipole and quadrupole in the latest data from the original Auger and TA surface detectors

The sources of ultra-high-energy cosmic rays are still unknown, but assuming standard physics, they are expected to lie within a few hundred megaparsecs from us. Indeed, over cosmological distances cosmic rays lose energy to interactions with background photons, at a rate depending on their mass number and energy and properties of photonuclear interactions and photon backgrounds. The universe is not homogeneous at such scales, hence the distribution of the arrival directions of cosmic rays is expected to reflect the inhomogeneities in the distribution of galaxies; the shorter the energy loss lengths, the stronger the expected anisotropies. Galactic and intergalactic magnetic fields can blur and distort the picture, but the magnitudes of the largest-scale anisotropies, namely the dipole and quadrupole moments, are the most robust to their effects. Measuring them with no bias regardless of any higher-order multipoles is not possible except with full-sky coverage. In this work, we achieve this in three energy ranges (approximately 8--16 EeV, 16--32 EeV, and 32--∞ EeV) by combining surface-detector data collected at the Pierre Auger Observatory until 2020 and at the Telescope Array (TA) until 2019, before the completion of the upgrades of the arrays with new scintillator detectors. We find that the full-sky coverage achieved by combining Auger and TA data reduces the uncertainties on the north-south components of the dipole and quadrupole in half compared to Auger-only results