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Register a new userCosmic Ray Small-Scale Anisotropies in Quasi-Linear Theory
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Philipp Mertsch
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The distribution of arrival directions of cosmic rays is remarkably isotropic, which is a consequence of their repeated scattering in magnetic fields. Yet, high-statistics observatories like IceCube and HAWC have revealed the presence of small-scale structures at levels of 1 part in 10,000 at hundreds of TeV, which are not expected in typical diffusion models of cosmic rays. We follow up on the suggestion that these small-scale anisotropies are a result of cosmic ray streaming in a particular realisation of the turbulent magnetic field within a few scattering lengths in our local Galactic neighbourhood. So far, this hypothesis has been investigated mostly numerically, by tracking test particles through turbulent magnetic fields. For the first time, we present an analytical computation that through a perturbative approach allows predicting the angular power spectrum of cosmic ray arrival directions for a given model of turbulence. We illustrate this method for a simple, isotropic turbulence model and we find remarkable agreement with the results of numerical studies.
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The arrival directions of Galactic cosmic rays (CRs) are highly isotropic. This is expected from the presence of turbulent magnetic fields in our Galactic environment that repeatedly scatter charged CRs during propagation. However, various CR observatories have identified weak anisotropies of various angular sizes and with relative intensities of up to a level of 1 part in 1,000. Whereas large-scale anisotropies are generally predicted by standard diffusion models, the appearance of small-scale anisotropies down to an angular size of 10 degrees is surprising. In this review, we summarise the current experimental situation for both the large-scale and small-scale anisotropies. We address some of the issues in comparing different experimental results and remaining questions in interpreting the observed large-scale anisotropies. We then review the standard diffusive picture and its difficulty in producing the small-scale anisotropies. Having set the stage, we review the various ideas and models put forward for explaining the small-scale anisotropies.
We have performed the first measurement of the angular power spectrum in the large-scale diffuse emission at energies from 1-50 GeV. We compared results from data and a simulated model in order to identify significant differences in anisotropy properties. We found angular power above the photon noise level in the data at multipoles greater than ~ 100 for energies 1< E <10 GeV. The excess power in the data suggests a contribution from a point source population not present in the model.
We present a detailed study of the large-scale anisotropies of cosmic rays with energies above 4 EeV measured using the Pierre Auger Observatory. For the energy bins [4,8] EeV and $Egeq 8$ EeV, the most significant signal is a dipolar modulation in right ascension at energies above 8 EeV, as previously reported. In this paper we further scrutinize the highest-energy bin by splitting it into three energy ranges. We find that the amplitude of the dipole increases with energy above 4 EeV. The growth can be fitted with a power law with index $beta=0.79pm 0.19$. The directions of the dipoles are consistent with an extragalactic origin of these anisotropies at all the energies considered. Additionally we have estimated the quadrupolar components of the anisotropy: they are not statistically significant. We discuss the results in the context of the predictions from different models for the distribution of ultrahigh-energy sources and cosmic magnetic fields.
The gyro-resonant cosmic-ray (CR) streaming instability is believed to play a crucial role in CR transport, leading to growth of Alfven waves at small scales that scatter CRs, and impacts the interaction of CRs with the ISM on large scales. However, extreme scale separation ($lambda ll rm pc$), low cosmic ray number density ($n_{rm CR}/n_{rm ISM} sim 10^{-9}$), and weak CR anisotropy ($sim v_A/c$) pose strong challenges for proper numerical studies of this instability on a microphysical level. Employing the recently developed magnetohydrodynamic-particle-in-cell (MHD-PIC) method, which has unique advantages to alleviate these issues, we conduct one-dimensional simulations that quantitatively demonstrate the growth and saturation of the instability in the parameter regime consistent with realistic CR streaming in the large-scale ISM. Our implementation of the $delta f$ method dramatically reduces Poisson noise and enables us to accurately capture wave growth over a broad spectrum, equally shared between left and right handed Alfven modes. We are also able to accurately follow the quasi-linear diffusion of CRs subsequent to wave growth, which is achieved by employing phase randomization across periodic boundaries. Full isotropization of the CRs in the wave frame requires pitch angles of most CRs to efficiently cross $90^circ$, and can be captured in simulations with relatively high wave amplitude and/or high spatial resolution. We attribute this crossing to non-linear wave-particle interaction (rather than mirror reflection) by investigating individual CR trajectories. We anticipate our methodology will open up opportunities for future investigations that incorporate additional physics.
The small angular scale fluctuations of the (on large scale) isotropic gamma-ray background (IGRB) carry information about the presence of unresolved source classes. A guaranteed contribution to the IGRB is expected from the unresolved gamma-ray AGN while other extragalactic sources, Galactic gamma-ray source populations and dark matter Galactic and extragalactic structures (and sub-structures) are candidate contributors. The IGRB was measured with unprecedented precision by the Large Area Telescope (LAT) on-board of the Fermi gamma-ray observatory, and these data were used for measuring the IGRB angular power spectrum (APS). Detailed Monte Carlo simulations of Fermi-LAT all-sky observations were performed to provide a reference against which to compare the results obtained for the real data set. The Monte Carlo simulations are also a method for performing those detailed studies of the APS contributions of single source populations, which are required in order to identify the actual IGRB contributors. We present preliminary results of an anisotropy search in the IGRB. At angular scales <2deg (e.g. above multipole 155), angular power above the photon noise level is detected, at energies between 1 and 10 GeV in each energy bin, with statistical significance between 7.2 and 4.1 sigmas. The energy not dependence of the fluctuation anisotropy is pointing to the presence of one or more unclustered source populations, while the energy dependence of the intensity anisotropy is consistent with source populations having average photon index 2.40pm0.07.
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