4th Korean Astrophysics Workshop @ KASI, Korea
Propagation of Ultra-high Energy
Cosmic Rays in Local Magnetic Fields
Hajime Takami (Univ. of Tokyo)
Collaborator: Katsuhiko Sato (Univ. of Tokyo, RESCEU)
Ref. H.Takami, H. Yoshiguchi, & K. Sato ApJ, 639, 803 (2006)
H. Yoshiguchi, S. Nagataki, & K. Sato ApJ, 596, 1044 (2003)
Index
1.
2.
3.
4.
5.
Introduction
Models of Magnetic Fields
Our Method for the UHECR Propagation
Results
Summary
Ultra-high Energy Cosmic Rays (UHECRs)
UHECRs above 1019eV are highest energy cosmic rays.

Extragalactic origin
( larger than thickness of Galaxy )



( Observed energy spectrum )
Light composition(?)
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).
Whether there is the spectral cutoff or not is one of problems
Auger and TA will solve this problem.
Arrival Distribution of UHECRs
AGASA observation showed the arrival distribution is isotropic at
large angle scale, but has strong correlation at small angle scale.
E>4×1019eV 57 events (>1020eV 8 events)
Two Point correlation N(θ)
strong correlation
at small angle
（～ 3 deg）
Isotropic at large 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).
UHECR propagation in the Universe
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

Energy loss processes (only in intergalactic space)

Interaction with the CMB
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Pair creation ( Chodorowski et al. 1992 )
Photopion production ( Mucke et al. 2000 )
Adiabatic energy loss (due to the cosmic expansion)
Magnetic deflections


Due to extragalactic magnetic field (EGMF)
Due to Galactic magnetic field (GMF)
Our Study
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
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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.
Our models of EGMF and distribution of UHECR sources
reflect structures observed around the Milky Way.
We assume that UHECRs are protons above 1019eV.
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.
Index
1.
2.
3.
4.
5.
Introduction
Models of Magnetic Fields
Our Method for the UHECR Propagation
Results
Summary
Observation of Magnetic Field
Magnetic fields are little known theoretically and observationally.

EGMF
There are observations of MFs from only clusters of galaxies.
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
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The Faraday rotation measurement
some evidence for the presence of MFs of a few uG ( Vogt et al. 2003 etc. )
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
There are many observations with the Faraday rotation, of which most in
Galactic plane.
Models of magnetic fields should
reflect these observational results.
(Beck 2000)
Magnetic Fields expected by simulations
Some groups have obtained local magnetic field by their
cosmological simulations.
Magnetic field generated from their
simulation. They calculated the
UHECR propagation.
But observed local structures are
not reproduced.
Sigl et al. (2004)
Matter density reproduces
observed local structures. So
Magnetic field is also thought to
reproduce local structure.
But they didn’t calculate the
propagation.
Dolag et al. (2005)
We also construct EGMF model in order to calculate the propagation.
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.
Our structured EGMF model
We assume
density distribution from the IRAS catalog
Strength of EGMF is normalized in the center of the Virgo cluster : 0.4 uG
E=1019.6eV
E=1020eV
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 Field
We adopt the same GMF model by Alvarez-Muniz et al. (2002) .
dipole
At the Solar system ～0.3uG
+
spiral
～1.5uG
Top view of our Galaxy
Top view of our Galaxy
Side view of our Galaxy
Index
1.
2.
3.
4.
5.
Introduction
Models of Magnetic Fields
Our Method for the UHECR Propagation
Results
Summary
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.
Intergalactic Space
(with EGMF)
Our Galaxy
Earth
Source
This calculation takes a long
CPU time to gather enough
number of event at the Earth.
A Solution of the Problem (1)
Without EGMF, a method had been developed to solve the
difficulty. ( Yoshiguchi et al., ApJ, 596, 1044 )
1. CRs with a charge of -1 are
ejected isotropically from the Earth
Galactic space
2. We then record their directions of
40kpc
velocities at ejection and r=40kpc
(boundary between Galactic space
Earth
G.C
and extragalactic space).
3. Finally, we select some of these
trajectories so that the resulting
mapping of velocity directions
outside our galaxy corresponds to
extragalactic space
our source model.
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 ?
2,000,000 “anti-protons” are ejected from Earth isotropically and their
trajectories are recorded until 40 kpc.
This map can be regarded as probability distribution for proton
to be able to reach the earth in the case of isotropic source distribution.
When we consider anisotropic source distribution,
we multiply its effect to this probability distribution.
one to one correspondence
Arrival distribution of UHE
protons at the earth is obtained.
A Solution of the Problem (2)
Trajectories of CRs (Charge=-1) in Galactic space expand those in
intergalactic space with EGMF.
1. The trajectories in intergalactic space
are recorded.
Intergalactic Space
(with EGMF)
Source
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.
Our Galaxy
Earth
4. We select trajectories corresponding
to the probabilities.
The arrival distribution !
This method gives us a natural expansion of our previous method.
This method enables us to save the CPU time greatly.
Index
1.
2.
3.
4.
5.
Introduction
Models of Magnetic Fields
Our Method for the UHECR Propagation
Results
Summary
Examples of trajectories in GMF
Trajectories of “anti-protons” (E=1018.5eV) ejected from the
earth in the direction b=0°(=protons arriving at Earth )
Only dipole field
E=1018.5eV
Only spiral field
B
Side view
Earth
B
Top view
The dipole field: exclude CRs from Galactic Center region.
The spiral field: deflect CRs in the direction dependent on
the direction of GMF near the Solar system.
Effect of GMF
We can see the deflections about UHECRs above 1019eV.
We eject cosmic rays above 1019eV with a charge of -1 from the Earth
isotropically and follow them at 40 kpc from Galactic center.
GMF
Dipole field
Injection direction of CRs
Spiral field
Velocity direction at 40kpc from GC
Points in the right figure show source directions of them
if extragalactic magnetic field is neglected.
An Arrival Distribution
We simulate an arrival distribution in several conditions of MF.
ns~10-5Mpc-3
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 )
Two-point Correlation Functions
49 events ( 4×1019-1020eV )
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
ns~10-5Mpc-3
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Histograms : observational result
by AGASA.
Error bars : 1 sigma error due to
finite event selections
Shade : 1 sigma total error
including cosmic variance (source
selection)
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.
Chi-square fitting with obs. data
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Black : normal source model
(NS) (power of each source
independent of its luminosity )
Red : luminosity weighted source
model (LS)
Error bars : cosmic variance at
fixed source number density
The most appropreate source number density that reproduces the observation
GMF + EGMF case
No MF case
NS model : ~10-5 Mpc-3
NS model : ~10-6-10-5 Mpc-3
LS model : ~10-4 Mpc-3
LS model : ~10-5-10-4 Mpc-3
Energy Spectrum
GMF: Yes
EGMF=0.0 uG
EGMF=0.4 uG
NS model@ 10-5 Mpc-3
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.
Index
1.
2.
3.
4.
5.
Introduction
Models of Magnetic Fields
Our Method for the UHECR Propagation
Results
Summary
Summary





We performed numerical simulations of the propagation
of UHECRs above 1019eV, 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
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.
Our source models reproduce observed spectra below
1020eV.