propagation of ultra-high energy cosmic rays in local magnetic fields

Propagation of Ultra-high Energy Propagation of Ultra-high Energy Cosmic Rays in Local Magnetic Cosmic Rays in Local Magnetic

FieldsFields

Hajime Takami (Univ. of Tokyo)Hajime Takami (Univ. of Tokyo)Collaborator: Katsuhiko Sato (Univ. of Tokyo, RESCEU)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)

IndexIndex1. Introduction1. Introduction

2. Models of Magnetic Fields2. Models of Magnetic Fields

3. Our Method for the UHECR 3. Our Method for the UHECR PropagationPropagation

4. Results4. Results

5. Summary5. Summary

Ultra-high Energy Cosmic Rays (UHECRs) Ultra-high Energy Cosmic Rays (UHECRs)

Extragalactic originExtragalactic origin

( larger than thickness of Galaxy )( larger than thickness of Galaxy )

Light composition(?)Light composition(?) Expected to have small defExpected to have small def

lection angles in cosmic mlection angles in cosmic magnetic fields.agnetic fields.

Expected to have the spectExpected to have the spectral cutoff due to photopion ral cutoff due to photopion production with the CMB (Gproduction with the CMB (GZK cutoff).ZK cutoff).

UHECRs above 1019eV 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.

E>4×1019eV 57 events (>1020eV 8 events)

Isotropic at large angle scale

Arrival Distribution of UHECRsArrival Distribution of UHECRsAGASA 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 correlationat small angle（～ 3 deg ）

UHECR propagation in the UHECR propagation in the UniverseUniverse

Energy loss processes (only in intergalactic space)Energy loss processes (only in intergalactic space) Interaction with the CMBInteraction 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 deflectionsMagnetic 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

Our StudyOur Study We have performed numerical simulations of the propagaWe have performed numerical simulations of the propaga

tion of UHECRs in a structured extragalactic magnetic fieltion of UHECRs in a structured extragalactic magnetic field (EGMF) and Galactic magnetic field (GMF).d (EGMF) and Galactic magnetic field (GMF).

A new method for the calculation of the propagation in mA new method for the calculation of the propagation in magnetic field is developed. agnetic field is developed.

Our models of EGMF and distribution of UHECR sources rOur models of EGMF and distribution of UHECR sources reflect structures observed around the Milky Way. eflect structures observed around the Milky Way.

We assume that UHECRs are protons above 10We assume that UHECRs are protons above 101919eV. eV. The arrival distribution of UHECRs at the Earth is simulatThe arrival distribution of UHECRs at the Earth is simulat

ed and is compared with AGASA observation statistically.ed and is compared with AGASA observation statistically. From the comparison, we find number density of UHECR From the comparison, we find number density of UHECR

sources that reproduces the observation.sources that reproduces the observation.

Observation of Magnetic FieldObservation of Magnetic FieldMagnetic fields are little known theoretically and observationally.

EGMFEGMFThere are observations of MFs from only clusters of galaxies.There are observations of MFs from only clusters of galaxies.

The Faraday rotation measurementThe Faraday rotation measurementsome evidence for the presence of MFs of a few uG ( Vogt et al. 2003 etc. )some evidence for the presence of MFs of a few uG ( Vogt et al. 2003 etc. )

Hard X-ray emissionHard X-ray emissionaverage strength of intracluster MF within the emitting volume is 0.2-0.4 uG average strength of intracluster MF within the emitting volume is 0.2-0.4 uG (Fusco-Femiano et al. 1999, Rephaeli et al. 1999)(Fusco-Femiano et al. 1999, Rephaeli et al. 1999)

GMFGMFThere are many observations with the Faraday rotation, of which most in GaThere are many observations with the Faraday rotation, of which most in Ga

lactic plane.lactic plane.

(Beck 2000)

Models of magnetic fields should reflect these observational results.

Magnetic Fields expected by Magnetic Fields expected by simulationssimulations

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.

IRAS PSCz Catalog of galaxiesIRAS PSCz Catalog of galaxiesWe use the IRAS PSCz Catalog of galaxies to construct our structured EGMF model and models of sources of UHECRs.

Large sky coverage

Source modelWe 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.

Our structured EGMF modelOur structured EGMF modelWe assume density distribution from the IRAS

catalog

E=1019.6eV E=1020eV

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.

Model of Galactic Magnetic Model of Galactic Magnetic FieldField

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

A problem with the calculationA problem with the calculationIf 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.

1. CRs with a charge of -1 are ejected isotropically from the Earth2. 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)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

When we consider anisotropic source distribution,we multiply its effect to this probability distribution.

Arrival distribution of UHEprotons at the earth is obtained.

one to one correspondence

This map can be regarded as probability distribution for protonto 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.

A Solution of the Problem (2)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 !

Examples of trajectories in GMFExamples of trajectories in GMF

Top view

Side view

Trajectories of “anti-protons” (E=1018.5eV) ejected from the earth in the direction b=0°(=protons arriving at Earth )

Only dipole field Only 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=1018.5eV

Earth

Effect of GMFEffect of GMFWe can see the deflections about UHECRs above 1019eV.

Spiral field

Dipole field

We eject cosmic rays above 1019eV with a charge of -1 from the Earth isotropically and follow them at 40 kpc from Galactic center.

Injection direction of CRsVelocity direction at 40kpc from GC

Points in the right figure show source directions of them if extragalactic magnetic field is neglected.

GMF

An Arrival DistributionAn Arrival DistributionWe 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 )

ns~10-5Mpc-

3

Two-point Correlation Two-point Correlation FunctionsFunctions

49 events ( 4×1019-1020eV )

ns~10-5Mpc-

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 Histograms : observational result by AGASA.result by AGASA.

Error bars : 1 sigma error due Error bars : 1 sigma error due to finite event selectionsto finite event selections

Shade : 1 sigma total error Shade : 1 sigma total error including cosmic variance including cosmic variance (source selection)(source selection)

Chi-square fitting with obs. dataChi-square fitting with obs. data

Black : normal source model Black : normal source model (NS) (power of each source (NS) (power of each source independent of its luminosity )independent of its luminosity )

Red : luminosity weighted source Red : luminosity weighted source model (LS)model (LS)

Error bars : cosmic variance at Error bars : cosmic variance at fixed source number densityfixed source number density

No MF caseNS 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

Energy SpectrumEnergy Spectrum

Both cases reproduce observed spectra below 1020eV. UHECRs above 1020eV 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

SummarySummary We performed numerical simulations of the propagation oWe performed numerical simulations of the propagation o

f UHECRs above 10f UHECRs above 101919eV, considering a structured EGMF aeV, considering a structured EGMF and GMF.nd GMF.

We developed a new method of simulations of the arrival We developed a new method of simulations of the arrival distribution of UHECRs, applying to an inverse process, adistribution of UHECRs, applying to an inverse process, and simulated the distribution at Earthnd simulated the distribution at Earth

Our EGMF model and source distribution that is constructOur EGMF model and source distribution that is constructed from the IRAS galaxies reflect the structures observeed from the IRAS galaxies reflect the structures observed.d.

We estimate number density of UHECR source that best rWe estimate number density of UHECR source that best reproduces the AGASA observation.eproduces the AGASA observation.

Our source models reproduce observed spectra below 10Our source models reproduce observed spectra below 102020eV.eV.

propagation of ultra-high energy cosmic rays in local magnetic fields

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