A New Method for Calculating Arrival Distribution of Ultra-High Energy Cosmic Rays above 10^19 eV with Modifications by the Galactic Magnetic Field

We present a new method for calculating arrival distribution of UHECRs including modifications by the galactic magnetic field. We perform numerical simulations of UHE anti-protons, which are injected isotropically at the earth, in the Galaxy and record the directions of velocities at the earth and outside the Galaxy for all of the trajectories. We then select some of them so that the resultant mapping of the velocity directions outside the Galaxy of the selected trajectories corresponds to a given source location scenario, applying Liouville's theorem. We also consider energy loss processes of UHE protons in the intergalactic space. Applying this method to our source location scenario which is adopted in our recent study and can explain the AGASA observation above 4 \times 10^{19} eV, we calculate the arrival distribution of UHECRs including lower energy (E>10^19 eV) ones. We find that our source model can reproduce the large-scale isotropy and the small-scale anisotropy on UHECR arrival distribution above 10^19 eV observed by the AGASA. We also demonstrate the UHECR arrival distribution above 10^19 eV with the event number expected by future experiments in the next few years. The interesting feature of the resultant arrival distribution is the arrangement of the clustered events in the order of their energies, reflecting the directions of the galactic magnetic field. This is also pointed out by Alvarez-Muniz et al.(2002). This feature will allow us to obtain some kind of information about the composition of UHECRs and the magnetic field with increasing amount of data.Comment: 10 pages, 8 figures, to appear in the Astrophysical Journa

Revision of the Selection Function of the Optical Redshift Survey using the Sloan Digital Sky Survey Early Data Release: Toward an Accurate Estimate of Source Number Density of Ultra-High Energy Cosmic Rays

If Ultra-High Energy Cosmic Rays (UHECRs) are originated from nearby galaxies, modeling of the distribution of nearby galaxies is important to an accurate estimate the source number density of UHECRs. We investigate uncertainty of the selection function of the Optical Redshift Survey (ORS), which we used to construct a source model of UHECRs. The investigation is based on a comparison of numbe counts of ORS galaxies with those of the spectroscopic sample of the Sloan Digital Sky Survey (SDSS) Early Data Release (EDR). We carefully count galaxies in the same absolute magnitude bin from the two samples. We find a slight systematic overestimate of the ORS counts outside 5000 km s$^{-1}$ by about a factor of 2. We revise the selection function of the ORS assuming that the SDSS counts are correct. Our revision is based on the absorption given in the ORS catalog as well as that computed from Schlegel et al. (1998), which is systematically larger than the former by $A_B \sim 0.1$ mag in the region of low absorption. It is found that introduction of Schlegel et al.'s absorption changes one of the parameters of the ORS selection function by more than 10%. The revision should be taken into account in the future analysis of the source number density of UHECRs based on the ORS. Using the revised selection function, we determine the global structure of the Local Supercluster (LSC) with a source model of UHECRs, that is, a number-density model consisting of a uniform spherical halo and an exponential disk. We find that the revision is insignificant in terms of the structure of the LSC. However, the revised selection function will be useful to other studies such as peculiar velocity and correlation function.Comment: 22 pages, 13 figures. accepted for publication in PAS

Statistical Significance of Small Scale Anisotropy in Arrival Directions of Ultra-High Energy Cosmic Rays

Recently, the High Resolution Fly's Eye (HiRes) experiment claims that there is no small scale anisotropy in the arrival distribution of ultra-high energy cosmic rays (UHECRs) above $E>10^{19}$ eV contrary to the Akeno Giant Air Shower Array (AGASA) observation. In this paper, we discuss the statistical significance of this discrepancy between the two experiments. We calculate arrival distribution of UHECRs above $10^{19}$ eV predicted by the source models constructed using the Optical Redshift Survey galaxy sample. We apply the new method developed by us for calculating arrival distribution in the presence of the galactic magnetic field. The great advantage of this method is that it enables us to calculate UHECR arrival distribution with lower energy ($\sim 10^{19}$ eV) than previous studies within reasonable time by following only the trajectories of UHECRs actually reaching the earth. It has been realized that the small scale anisotropy observed by the AGASA can be explained with the source number density $\sim 10^{-5 \sim -6}$ Mpc$^{-3}$ assuming weak extragalactic magnetic field ($B \le 1$ nG). We find that the predicted small scale anisotropy for this source number density is also consistent with the current HiRes data. We thus conclude that the statement by the HiRes experiment that they do not find small scale anisotropy in UHECR arrival distribution is not statistically significant at present. We also show future prospect of determining the source number density with increasing amount of observed data.Comment: 8 pages, 7 figure

Arrival Distribution of Ultra-High Energy Cosmic Rays: Prospects for the Future

We predict the arrival distribution of UHECRs above $4 \times 10^{19}$ eV with the event number expected by future experiments in the next few years. We perform event simulations with the source model which is adopted in our recent study and can explain the current AGASA observation. At first, we calculate the harmonic amplitude and the two point correlation function for the simulated event sets. We find that significant anisotropy on large angle scale will be observed when $\sim 10^3$ cosmic rays above $4 \times 10^{19}$ eV are detected by future experiments. The statistics of the two point correlation function will also increase. The angle scale at which the events have strong correlation with each other corresponds to deflection angle of UHECR in propagating in the EGMF, which in turn can be determined by the future observations. We further investigate the relation between the number of events clustered at a direction and the distance of their sources. Despite the limited amount of data, we find that the C2 triplet events observed by the AGASA may originate from the source within 100 Mpc. Merger galaxy Arp 299 (NGC 3690 + IC 694) is the best candidate for their source. If data accumulate, the UHECR sources within $\sim 100$ Mpc can be identified from observed event clusterings significantly. This will provide some kinds of information about poorly known parameters which influence the propagation of UHECRs, such as extragalactic and galactic magnetic field, chemical composition of observed cosmic rays. Also, we will reveal their origin with our method to identify the sources of UHECR. Finally, we predict the arrival distribution of UHECRs above $10^{20}$ eV, which is expected to be observed if the current HiRes spectrum is correct, and discuss their statistical features and implications.Comment: 11 pages, 9 figures. accepted version for publication in Ap

Dynamical Stability of Six-dimensional Warped Flux Compactification

We show the dynamical stability of a six-dimensional braneworld solution with warped flux compactification recently found by the authors. We consider linear perturbations around this background spacetime, assuming the axisymmetry in the extra dimensions. The perturbations are expanded by scalar-, vector- and tensor-type harmonics of the four-dimensional Minkoswki spacetime and we analyze each type separately. It is found that there is no unstable mode in each sector and that there are zero modes only in the tensor sector, corresponding to the four-dimensional gravitons. We also obtain the first few Kaluza-Klein modes in each sector.Comment: 46 pages, 8 figures. Version to appear in JCA

Cross-Correlation between UHECR Arrival Distribution and Large-Scale Structure

We investigate correlation between the arrival directions of ultra-high-energy cosmic rays (UHECRs) and the large-scale structure (LSS) of the Universe by using statistical quantities which can find the angular scale of the correlation. The Infrared Astronomical Satellite Point Source Redshift Survey (IRAS PSCz) catalog of galaxies is adopted for LSS. We find a positive correlation of the highest energy events detected by the Pierre Auger Observatory (PAO) with the IRAS galaxies inside $z=0.018$ within the angular scale of $\sim 15^{\circ}$. This positive correlation observed in the southern sky implies that a significant fraction of the highest energy events comes from nearby extragalactic objects. We also analyze the data of the Akeno Giant Air Shower Array (AGASA) which observed the northern hemisphere, but the obvious signals of positive correlation with the galaxy distribution are not found. Since the exposure of the AGASA is smaller than the PAO, the cross-correlation in the northern sky should be tested using a larger number of events detected in the future. We also discuss the correlation using the all-sky combined data sets of both the PAO and AGASA, and find a significant correlation within $\sim 8^{\circ}$. These angular scales can constrain several models of intergalactic magnetic field. These cross-correlation signals can be well reproduced by a source model in which the distribution of UHECR sources is related to the IRAS galaxies.Comment: 21 pages,7 figure

Codimension Two Branes and Distributional Curvature

In general relativity, there is a well-developed formalism for working with the approximation that a gravitational source is concentrated on a shell, or codimension one surface. By contrast, there are obstacles to concentrating sources on surfaces that have a higher codimension, for example, a string in a spacetime with dimension greater than or equal to four. Here it is shown that, by giving up some of the generality of the codimension one case, curvature can be concentrated on submanifolds that have codimension two. A class of metrics is identified such that (1) the scalar curvature and Ricci densities exist as distributions with support on a co-dimension two submanifold, and (2) using the Einstein equation, the distributional curvature corresponds to a concentrated stress-energy with equation of state p equals minus the energy density, where p is the isotropic pressure tangent to the submanifold. This is the appropriate stress-energy to describe a self-gravitating brane that is governed by an area action, or a brane world deSitter cosmology. The possibility of having a different equation of state arise from a wider class of metrics is discussed.Comment: 18 pages; v2 references added; typos corrected, references added; additional references adde

Volume stabilization in a warped flux compactification model

We investigate the stability of the extra dimensions in a warped, codimension two braneworld that is based upon an Einstein-Maxwell-dilaton theory with a non-vanishing scalar field potential. The braneworld solution has two 3-branes, which are located at the positions of the conical singularities. For this type of brane solution the relative positions of the branes (the shape modulus) is determined via the tension-deficit relations, if the brane tensions are fixed. However, the volume of the extra dimensions (the volume modulus) is not fixed in the context of the classical theory, implying we should take quantum corrections into account. Hence, we discuss the one-loop effective potential of the volume modulus for a massless, minimally coupled scalar field.Comment: 25 pages, 8 figures, typos correcte

Ultrahigh Energy Nuclei in the Galactic Magnetic Field

Observations are consistent with a significant fraction of heavy nuclei in the cosmic ray flux above a few times 10^19 eV. Such nuclei can be deflected considerably in the Galactic magnetic field, with important implications for the search of their sources. We perform detailed simulations of heavy nuclei propagation within recent Galactic magnetic field models. While such models are not yet sufficiently constrained to predict deflection maps in detail, we find general features of the distribution of (de-) magnified flux from sources. Since in most theoretical models sources of heavy nuclei are located in the local large scale structure of galaxies, we show examples of images of several nearby galaxy clusters and of the supergalactic plane. Such general features may be useful to develop efficient methods for source reconstruction from observed ultrahigh energy cosmic ray arrival directions.Comment: 17 pages, 11 figures. Published in JCA

A doubly covariant formula of deficit angle and its application to six-dimensional braneworld

We reformulate boundary conditions for axisymmetric codimension-2 braneworlds in a way which is applicable to linear perturbation with various gauge conditions. Our interest is in the thin brane limit and thus this scheme assumes that the perturbations are also axisymmetric and that the surface energy-momentum tensor of the brane is proportional to its induced metric. An advantage of our scheme is that it allows much more freedom for convenient coordinate choices than the other methods. This is because in our scheme, the coordinate system in the bulk and that on the brane are completely disentangled. Therefore, the latter does not need to be a subset of the former and the brane does not need to stay at a fixed bulk coordinate position. The boundary condition is manifestly doubly covariant: it is invariant under gauge transformations in the bulk and at the same time covariant under those on the brane. We take advantage of the double covariance when we analyze the linear perturbation of a particular model of six-dimensional braneworld with warped flux compactification.Comment: 25 pages, REVTeX4; published in CQ