On Anisotropy of Ultra-High Energy Cosmic-Rays
📝 Abstract
We briefly summarize our study on anisotropy of Ultra-High Energy Cosmic-Rays (UHECRs), in which we define a statistics that measures the correlation between UHECRs and Large Scale Structure (LSS). We also comment here on recently published paper by Koers and Tinyakov that compared our statistics to improved KS statistics.
💡 Analysis
We briefly summarize our study on anisotropy of Ultra-High Energy Cosmic-Rays (UHECRs), in which we define a statistics that measures the correlation between UHECRs and Large Scale Structure (LSS). We also comment here on recently published paper by Koers and Tinyakov that compared our statistics to improved KS statistics.
📄 Content
arXiv:0901.2256v2 [astro-ph.HE] 29 Jan 2009 On Anisotropy of Ultra-High Energy Cosmic-Rays Tamar Kashti Weizmann Institute of Science, Israel Abstract We briefly summarize our study on anisotropy of Ultra-High Energy Cosmic-Rays (UHECRs), in which we define a statistics that measures the correlation between UHECRs and Large Scale Structure (LSS). We also comment here on recently published paper by Koers and Tinyakov that compared our statistics to improved KS statistics. Key words: ultra high energy cosmic rays, cosmic rays, large scale structure PACS: 95.85.Ry, 98.65.-r The origin of cosmic rays of energies > 1019 eV is a puzzle [1,2,3]. The arrival di- rection of UHECRs show no correlation with the galactic disk, which point towards extra-galactic origan. A suppression of the spectrum at ∼5 × 1019 eV is expected due to the GZK suppression [4,5]. The suppression was observed by HIRES [6] and the new Auger Observatory [7], see fig. 1(a). Thus, cosmic-rays with energies above ∼5×1019 eV can reach us only from sources with distance below ∼100 Mpc. In these distances, the Universe is not isotropic, implying that correlation with LSS can give us information on the origin of UHECRs. There are few leading candidates as the sources of UHECRs. Assuming that UHECRs are protons, the large magnetic fields needed for acceleration requires source luminosity of L ≳1012L⊙Γ2/β for protons with 1020 eV, where L⊙is the Sun luminosity and Γ is Lorentz factor of the magnetized plasma [3]. Therefore, the only known astrophysical sources that reaches these energies are Active Galactic Nuclei (AGNs) and sources of Gamma-ray bursts. The anisotropy of UHECRs from these sources should be correlated with LSS. Another possible source of UHECRs is the decay of new heavy particles coming from top-down models [1], which predict isotropic signal. In [8], we derive the expected all sky angular distribution of the UHECR intensity, and defined a statistics XC,UB that measures the correlation between the predicted and observed UHECR arrival direction distribution. Following [9], we consider a model where the UHECR flux is produced by cosmological sources of protons tracing the large scale Preprint submitted to Elsevier 30 October 2018 100 10 1 10 E [EeV] J× E2.61 [1016eV1.61/m2 sr s]
Xgal. model Auger HiRes Fig. 1. (a) The spectrum of HIRES and Auger after a shift of ∆E/E = +23% in the calibration of the absolute energy scale of the Auger experiment. The solid line is the spectrum that would be generated by a cosmological distribution of sources of protons, with intrinsic spectrum d log n/d log E = −2. (b) The positions of the 27 Auger events with energy exceeding 5.7 × 1019 eV, overlaid on the intensity map obtained in the biased model, in galactic coordinates. galaxy distribution. We assume that the sources are intrinsically identical and that the number density of sources is drawn from a Poisson distribution with an average given by b[δ]¯s(z), where ¯s(z) is the average comoving number density of sources at redshift z and b is some bias functional of the local fractional galaxy over density, δ ≡δρ/¯ρ. The LSS galaxy density field is derived from the PSCz catalogue [10]. For the bias functional we consider three models: an isotropic (I) model, b[δ] = 1; an unbiased (UB) model where the source distribution traces the galaxy distribution with b[δ] = 1 + δ; and a biased (B) model, b[δ] = 1 + δ for δ > 0 and b[δ] = 0 otherwise. The statistics we defined in [8], which measures the correlation between predicted and observed UHECR arrival direction distributions, is: XC,M = X {i} (Ni −Ni,iso)(Ni,M −Ni,iso) Ni,iso . Here {i} is a set of angular bins, Ni is the number of events detected in bin i, and Ni,M is the average number of events expected to be detected in the M (e.g. isotropic, unbiased, biased) model. In order to avoid sensitivity to the possible distortion of the UHECR inten- sity map by magnetic fields, we used 6◦×6◦angular bins and excluded the Galactic plane region, |b| < 12◦. The value of XC,UB can be straight forwardly calculated using the nu- merical representations of the UHECR maps at http://www.weizmann.ac.il/~waxman/criso . The XC statistics is more sensitive to expected anisotropy signature than the com- monly used power spectrum, Cℓ= 1 2ℓ+1 Pm=ℓ m=−ℓa2 ℓm (e.g. [11]), and the two-point corre- lation function, W(D) = PN i P j<i Θ(D −Dij) (e.g. [12]). This can be seen from table 1(a). The anisotropy signal is stronger at lower energy: Although the contrast of the fluctuations in the UHECR intensity is higher at high energy, the signal becomes weaker at higher energies since the number of observed UHECR drops rapidly with energy, see table 1(b). In [8] we also show that a few fold increase of the Auger exposure is likely to increase the significance to > 99% CL, but not to > 99.9% CL (unless the UHECR source density is comparable or larger than that of galaxies). 2 E > 40 EeV, 100 events P(I/UB) P(I/B) P(UB/B) XC,UB 23% 79% 42% XW ({D =
This content is AI-processed based on ArXiv data.