1. Haoning He(RIKEN/UCLA/PMO)
Monte Carlo Bayesian search for the plausible source of the Telescope Array hotspot
Haoning He(RIKEN/UCLA/PMO)
Collaborators: Alexander Kusenko(UCLA,IPMU), Nagataki Shigehiro(RIKEN), Binbin Zhang(CSPAR, IAA-CSIC), Ruizhi Yang(MPIK), Yizhong Fan(PMO)

2. The Hotspot of UHECRs observed by the Telescope Array
The first time
(Data between 2008 May 11 and 2013 May 4, The TA Collaboration, 2014)

3. The possible sources of UHECRs at the TA hotspot
Assumption: Pure composition from a single point source
The time delay due to deflections —The duration and energy budget of the source
Acceleration capability—Type of the source
The GZK suppression—Distance of the source
The event distribution due to deflections—Direction of the source

4. The effect of the magnetic field, the time delay
The time delay between photons and the deflected cosmic rays ?
CR1
The time delay between cosmic rays with different deflected angles
CR2
The high-energy gamma-rays, cosmic rays and neutirnos are three new messengers to approach the properties of the high energy universe.
As propagating in the universe, the high-energy gamma-rays and cosmic rays will interact with the background photons and the intersteller medium, set a horizon on the univers we learn about.
Also the high energy cosmic rays will be deflected by the magnetic field in the universe, therefore the original information of the sources location are missing.
Howerve, a nearly massless sub-atomic particle called the neutrino, barely interact with matter, will propagate in a line, and almost no information are lost when propagating, can help us to study the sources directly.
Due to the low reation efficiency, neutrino are hard to be observed.
Observer
(Finley, C. B. 2006, Ph.D. Thesis)

5. The time delay —The duration and energy budget of sources
A single long-term-active source
A single transient source
A past GRB with an extremely high kinetic energy at a distance ~ Mpc could produce the observed Hotspot.
A groups of transient sources in one galaxy
The requisite total isotropic injected energy
of the single transient source

6. + GRBs in Star-forming Galaxy + + + The far-infrared luminosity
At least 19 GRBs occurred during a delayed time
a beaming correction factor for the GRB rate +
GRB rate in the star-forming galaxy + + +
The far-infrared luminosity

7. The source candidates Within the distance of 200Mpc
Massive galaxy clusters
Ackermann, M., Ajello, M., Albert, A., et al. 2014, Astrophys.J., 787, 18
BL Lac objects
M. Ackermann, M. Ajello, W. Atwood et al., Astrophys. J.810, 14 (2015);
Horan, D., & Wakely, S. 2008, AAS/High Energy Astrophysics Division #10, 10, #41.06
Radio galaxies
Starburst galaxies
Nolan, P. L., Abdo, A. A., Ackermann, M., et al. 2012, Astrophys. J. Suppl. Ser., 199, 31
Starforming galaxies
M. Ackermann, M. Ajello, A. Allafort et al., Astrophys. J.755, 164 (2012).

8. Magnetic Bending Effects
Assumption：Pure composition from a single source
Systematic Shift by regular magnetic field:
Deflections by random magnetic field:
Probability of Bending Angle:

9. Three simulated cases

10. The distribution of TA hotspot events
Blue: Events with > 75EeV
(High Rigidity).
Red: Events with < 75EeV
(Low Rigidity).
Squares represent the weighted
centers of the events.
Probability: 0.2% random realizations would produce a similar hotspot detection, implying the probability of 99.8% that the magnetic-selected structure of the TA
hotspot is not from a fluctuation.

11. A Monte Carlo Bayesian Search
Coordinates of the original source
(R.A., Dec.)
The magnetic field & composition
The diffusion angle
The probability for i-th TA hotspot event
The log-likelihood function with 5 parameters

12. Parameters constraints by fitting the model to the observation data using MC approach （Bin-Bin Zhang
Zhang et al.15; Feroz & Hobson 08

13. The 1,2,3-sigma error Contours
Best fit
Galactic
Plane
SGP

14. Sources in 1-sigma contour and constraints on magnetic fields
Random Field:
GMF (～1kpc): 25μG/z EGMF (～1Mpc): 25nG/z.
Regular Field:
~ For M82.
GMF (～1kpc): 35μG/z EGMF (～1Mpc): 35nG/z.

15. Reduced error with increasing statistics

16. Summary and Discussion
The MCB method can be adopted for future increasing statistics
Compositions of hotspot events & Magnetic fields
Spectrum of hotspot events (GZK cutoff?)
EeV Neutrinos
For sources with distance about 200 Mpc, assuming a pure proton composition, 90% UHECRs are strongly attenuated by photo-meson interactions with CMB photons, and produce neutrinos.
Thank you!

17. Summary
We have explored the hypothesis of a single source for the TA hotspot, and studied a universal model that cosmic rays from a single source are deflected by magnetic fields.
Our analysis reveals that the distribution of the TA hotspot events is diffused strongly by the random magnetic field, consistent with the single source hypothesis, and the chance probability of this distribution is 0.2%.
The MCB method can be used to find out the best-fit source coordinates and magnetic field parameters.
The MCB method can be adopted to other magnetic-selected hotspots possibly observed in the future, and constrain the magnetic field.
Thank you!

18. Telescope Array Experiment (Japan-US)

19. The Hotspot of UHECRs observed by the Telescope Array
Five years
(Data between 2008 May 11 and 2013 May 4, The TA Collaboration, 2014)

20. The GZK suppression—Distances of sources
200Mpc
Kotera & Olinto 2011

21. Acceleration capability
Lamor Radius=Typical scale of sources
Emax=ZBL
Based on the simple condition that the larmor radius sould be larger than the typical scale of source, the maximu accelerated energy is in proportional to the strength of the magnetic field and the typical scale of source.
As shown in the hillas plot, GRBs can accelerate protons to a energy up to larger than 10 to 20 eV.
sources among the long-term active sources from Fermi LAT catalogue and TeV catalogue (
including massive galaxy clusters [19], BL Lac objects [20], radio galax-
ies and starburst galaxies [21].