1. Propagation of Ultra-high Energy Cosmic Rays in Local Magnetic Fields Hajime Takami (Univ. of Tokyo) Collaborator: Katsuhiko Sato (Univ. of Tokyo, RESCEU) 4th Korean Astrophysics Workshop @ KASI, Korea Ref. H.Takami, H. Yoshiguchi, & K. Sato ApJ, 639, 803 (2006) H. Yoshiguchi, S. Nagataki, & K. Sato ApJ, 596, 1044 (2003)

2. Index 1. Introduction 2. Models of Magnetic Fields 3. Our Method for the UHECR Propagation 4. Results 5. Summary

3. Ultra-high Energy Cosmic Rays (UHECRs) Extragalactic origin Extragalactic origin ( larger than thickness of Galaxy ) ( larger than thickness of Galaxy ) Light composition(?) Light composition(?) Expected to have small deflection angles in cosmic magnetic fields. Expected to have small deflection angles in cosmic magnetic fields. Expected to have the spectral cutoff due to photopion production with the CMB (GZK cutoff). Expected to have the spectral cutoff due to photopion production with the CMB (GZK cutoff). UHECRs above 10 19 eV are highest energy cosmic rays. ( Observed energy spectrum ) Whether there is the spectral cutoff or not is one of problems Auger and TA will solve this problem.

4. E>4×10 19 eV 57 events (>10 20 eV 8 events) Isotropic at large angle scale Arrival Distribution of UHECRs AGASA observation showed the arrival distribution is isotropic at large angle scale, but has strong correlation at small angle scale. However, HiRes observation showed the distribution has no small scale anisotropy. But this discrepancy between the two observations is not statistically significant at present observed event number (yoshiguchi et al. 2004). Two Point correlation N(θ) strong correlation at small angle （～ 3 deg ）

5. UHECR propagation in the Universe Energy loss processes (only in intergalactic space) Energy loss processes (only in intergalactic space) Interaction with the CMB Interaction with the CMB Pair creation ( Chodorowski et al. 1992 ) Pair creation ( Chodorowski et al. 1992 ) Photopion production ( Mucke et al. 2000 ) Photopion production ( Mucke et al. 2000 ) Adiabatic energy loss (due to the cosmic expansion) Adiabatic energy loss (due to the cosmic expansion) Magnetic deflections Magnetic deflections Due to extragalactic magnetic field (EGMF) Due to extragalactic magnetic field (EGMF) Due to Galactic magnetic field (GMF) Due to Galactic magnetic field (GMF) UHECRs experience energy losses and deflections due to cosmic magnetic field during the propagation in space. So the propagation processes are very important in order to simulate their arrival distribution and their energy spectrum at Earth. We consider

6. Our Study We have performed numerical simulations of the propagation of UHECRs in a structured extragalactic magnetic field (EGMF) and Galactic magnetic field (GMF). We have performed numerical simulations of the propagation of UHECRs in a structured extragalactic magnetic field (EGMF) and Galactic magnetic field (GMF). A new method for the calculation of the propagation in magnetic field is developed. A new method for the calculation of the propagation in magnetic field is developed. Our models of EGMF and distribution of UHECR sources reflect structures observed around the Milky Way. Our models of EGMF and distribution of UHECR sources reflect structures observed around the Milky Way. We assume that UHECRs are protons above 10 19 eV. We assume that UHECRs are protons above 10 19 eV. The arrival distribution of UHECRs at the Earth is simulated and is compared with AGASA observation statistically. The arrival distribution of UHECRs at the Earth is simulated and is compared with AGASA observation statistically. From the comparison, we find number density of UHECR sources that reproduces the observation. From the comparison, we find number density of UHECR sources that reproduces the observation.

7. Index 1. Introduction 2. Models of Magnetic Fields 3. Our Method for the UHECR Propagation 4. Results 5. Summary

8. Observation of Magnetic Field Magnetic fields are little known theoretically and observationally. EGMF EGMF There are observations of MFs from only clusters of galaxies. The Faraday rotation measurement The Faraday rotation measurement some evidence for the presence of MFs of a few uG ( Vogt et al. 2003 etc. ) Hard X-ray emission Hard X-ray emission average strength of intracluster MF within the emitting volume is 0.2-0.4 uG (Fusco-Femiano et al. 1999, Rephaeli et al. 1999) GMF GMF There are many observations with the Faraday rotation, of which most in Galactic plane. (Beck 2000) Models of magnetic fields should reflect these observational results.

9. Magnetic Fields expected by simulations Some groups have obtained local magnetic field by their cosmological simulations. Dolag et al. (2005) Sigl et al. (2004) We also construct EGMF model in order to calculate the propagation. Matter density reproduces observed local structures. So Magnetic field is also thought to reproduce local structure. But they didn’t calculate the propagation. Magnetic field generated from their simulation. They calculated the UHECR propagation. But observed local structures are not reproduced.

10. IRAS PSCz Catalog of galaxies We use the IRAS PSCz Catalog of galaxies to construct our structured EGMF model and models of sources of UHECRs. Large sky coverage Source model We select some of all the galaxies in this sample. The probability that a given galaxy is selected is proportional to its absolute luminosities. Only parameter is number density of galaxies.

11. Our structured EGMF model We assumedensity distribution from the IRAS catalog E=10 19.6 eVE=10 20 eV Strength of EGMF is normalized in the center of the Virgo cluster : 0.4 uG Deflection angles when CRs with fixed energies are propagated from the Earth to 100 Mpc. These figures show that our EGMF model reflects the distribution of the IRAS galaxies.

12. Model of Galactic Magnetic Field dipole + spiral We adopt the same GMF model by Alvarez-Muniz et al. (2002). At the Solar system ～ 0.3uG ～ 1.5uG Top view of our Galaxy Side view of our Galaxy Top view of our Galaxy

13. Index 1. Introduction 2. Models of Magnetic Fields 3. Our Method for the UHECR Propagation 4. Results 5. Summary

14. A problem with the calculation If UHECR sources emit huge number of CRs, only very small fraction of CRs can reach the Earth due to magnetic deflections, but most of CRs cannot arrive at the Earth. Earth Source Our Galaxy Intergalactic Space (with EGMF) This calculation takes a long CPU time to gather enough number of event at the Earth.

15. 1. CRs with a charge of -1 are ejected isotropically from the Earth 2. We then record their directions of velocities at ejection and r=40kpc (boundary between Galactic space and extragalactic space). 3. Finally, we select some of these trajectories so that the resulting mapping of velocity directions outside our galaxy corresponds to our source model. 40kpc G.C Earth A Solution of the Problem (1) Without EGMF, a method had been developed to solve the difficulty. ( Yoshiguchi et al., ApJ, 596, 1044 ) In this method, we can consider only UHECRs that reach the Earth. How can one calculate arrival distribution of UHE proton for a given source location scenario in detail ? Galactic space extragalactic space

16. When we consider anisotropic source distribution, we multiply its effect to this probability distribution. Arrival distribution of UHE protons at the earth is obtained. one to one correspondence This map can be regarded as probability distribution for proton to be able to reach the earth in the case of isotropic source distribution. 2,000,000 “anti-protons” are ejected from Earth isotropically and their trajectories are recorded until 40 kpc.

17. A Solution of the Problem (2) Trajectories of CRs (Charge=-1) in Galactic space expand those in intergalactic space with EGMF. Earth Source Our Galaxy Intergalactic Space (with EGMF) 1.The trajectories in intergalactic space are recorded. 2.When each trajectory passes galaxies (sources), the proton has a certain contribution to the “real”--- positive arriving--- CRs. 3.We regard the contribution factors of each CR as probabilities that the CR is a “real” event observed at Earth. 4.We select trajectories corresponding to the probabilities. This method gives us a natural expansion of our previous method. This method enables us to save the CPU time greatly. The arrival distribution !

18. Index 1. Introduction 2. Models of Magnetic Fields 3. Our Method for the UHECR Propagation 4. Results 5. Summary

19. Examples of trajectories in GMF Top view Side view Trajectories of “anti-protons” (E=10 18.5 eV) ejected from the earth in the direction b=0°(=protons arriving at Earth ) Only dipole fieldOnly spiral field B B The spiral field: deflect CRs in the direction dependent on the direction of GMF near the Solar system. The dipole field: exclude CRs from Galactic Center region. E=10 18.5 eV Earth

20. Effect of GMF We can see the deflections about UHECRs above 10 19 eV. Spiral field Dipole field We eject cosmic rays above 10 19 eV with a charge of -1 from the Earth isotropically and follow them at 40 kpc from Galactic center. Injection direction of CRs Velocity direction at 40kpc from GC Points in the right figure show source directions of them if extragalactic magnetic field is neglected. GMF

21. An Arrival Distribution We simulate an arrival distribution in several conditions of MF. UHECRs are arranged in the order of their energies, reflecting the directions of GMF. On the other hand, EGMF diffuse the arrival directions of UHECRs. The arrangement will allow us to obtain some kind of information about the composition of UHECRs and the GMF ( future works ) n s ~10 -5 Mpc -3

22. Two-point Correlation Functions 49 events ( 4×10 19 -10 20 eV ) n s ~10 -5 Mpc -3 From comparison between panels, MFs, especially EGMF, makes the small-scale anisotropy be weaken. In many cases of source number density, we calculate the two-point correlation functions. The comparison to the observed results enables us to estimate source number density that best reproduces the observations. Histograms : observational result by AGASA. Histograms : observational result by AGASA. Error bars : 1 sigma error due to finite event selections Error bars : 1 sigma error due to finite event selections Shade : 1 sigma total error including cosmic variance (source selection) Shade : 1 sigma total error including cosmic variance (source selection)

23. Chi-square fitting with obs. data Black : normal source model (NS) (power of each source independent of its luminosity ) Black : normal source model (NS) (power of each source independent of its luminosity ) Red : luminosity weighted source model (LS) Red : luminosity weighted source model (LS) Error bars : cosmic variance at fixed source number density Error bars : cosmic variance at fixed source number density No MF case NS model : ~10 -5 Mpc -3 LS model : ~10 -4 Mpc -3 NS model : ~10 -6 -10 -5 Mpc -3 LS model : ~10 -5 -10 -4 Mpc -3 GMF + EGMF case The most appropreate source number density that reproduces the observation

24. Energy Spectrum Both cases reproduce observed spectra below 10 20 eV. UHECRs above 10 20 eV cannot be explained by our source model and are expected to have other origins. In the case of LS model, the same tendencies can be seen. GMF: Yes EGMF=0.0 uG EGMF=0.4 uG NS model@ 10 -5 Mpc -3

25. Index 1. Introduction 2. Models of Magnetic Fields 3. Our Method for the UHECR Propagation 4. Results 5. Summary

26. Summary We performed numerical simulations of the propagation of UHECRs above 10 19 eV, considering a structured EGMF and GMF. We performed numerical simulations of the propagation of UHECRs above 10 19 eV, considering a structured EGMF and GMF. We developed a new method of simulations of the arrival distribution of UHECRs, applying to an inverse process, and simulated the distribution at Earth We developed a new method of simulations of the arrival distribution of UHECRs, applying to an inverse process, and simulated the distribution at Earth Our EGMF model and source distribution that is constructed from the IRAS galaxies reflect the structures observed. Our EGMF model and source distribution that is constructed from the IRAS galaxies reflect the structures observed. We estimate number density of UHECR source that best reproduces the AGASA observation. We estimate number density of UHECR source that best reproduces the AGASA observation. Our source models reproduce observed spectra below 10 20 eV. Our source models reproduce observed spectra below 10 20 eV.