1. A. Uryson Lebedev Physical Institute RAS, Moscow
Ultra-high energy cosmic rays (UHECRs) from supermassive black holes (SMBHs)
A. Uryson
Lebedev Physical Institute RAS, Moscow

2. COSMIC RAYS
Cosmic rays (CRs) are emission that comes to the Earth from the space.
The most part of cosmic rays is particles (protons).
The CR energy range is wide: ~10 MeV - ~3×1020 eV.
The interval of energies E>4×1019 eV is called ultra-high energies (UHE).

3. The main problem is: what are UHECR sources?
GZK-effect
Propagating in the extragalactic space, a cosmic particle interacts with relic (and radio) background, and the particle energy decreases.
Due to this particles which start at energies E>4×1019 eV reach the Earth at lower energies,
if particle sources are located at distances greater than ~50 Mpc.
Greisen 1966; Zatsepin and Kuzmin 1966 (GZK-effect).
The main problem is: what are UHECR sources?

4. CR data Data on UHECRs are obtained at giant ground-based arrays:
the Pierre Auger Observatory and the Telescope Array
CR arrival directions, composition, anisotropy, the energy spectrum.
The energy spectrum
due to GZK-effect its shape differs from that of an injection spectrum.
It is possible to estimate distances to sources analyzing CR energy spectra measured.

6. Obviously CRs at ultra-high energies E>4×1019 eV are accelerated in extragalactic point-like sources (but still they are not revealed).
CR arrival directions can be used to identify sources if CRs propagate in straight lines.
Source identification by particle arrival directions was not effective mainly due to two reasons:
errors in CR arrivals of ~ 10 that are too large to select a source among astrophysical objects falling in the error-box around arrival direction, and
to CR deflection in extragalactic magnetic fields which are studied insufficiently at present.

7. extragalactic electromagnetic cascades
Another manifestation of GZK-effect:
extragalactic electromagnetic cascades
In space, UHECRs interact with cosmic microwave background
and extragalactic background light:
p+γb p+π0, p+γb n+π+.
π0  γ +γ, π+μ+ +νµ , μ+ e+ +νe+ν ̅µ
γ+γb e+ + e-
e+ γb e'+ γ' .
As a result electromagnetic cascades are initiated
by UHECRs in extragalactic space.
Consequently UHECRs contribute to the isotropic gamma-ray background and to the astrophysical neutrino flux.

8. Isotropic gamma-ray background (IGRB) is measured by the Fermi LAT (the gamma-ray telescope LAT onboard the space observatory Fermi). Fermi LAT data are used for UHECR study as follows. 1) Different classes of objects which are possible UHECR sources are considered; UHECR spectra at the Earth are calculated to fit the measured spectrum. 2) Gamma-ray emission I cascade g generated by UHECRs in extragalactic space is calculated. 3) The calculated gamma-ray intensity is compared with the Fermi LAT IGRB, and models of UHECR sources in which I cascade g > Fermi LAT IGRB are excluded. See e.g. Giachinti et al. 2015; Gavish, Eichler 2016; Berezinsky, Gazizov, Kalashev 2016, where possible UHECR sources are active galactic nuclei (AGN); to fit spectra measured injection spectra are exponential: index a≥2.2, or around 2.6 depending on cosmological evolution of AGN.

9. Neutrino fluxes are generated during UHECR propagation.
The neutrino intensity is obtained:
1) at the neutrino observatory IceCube in the energy range
of about (100 – 3×106) GeV,
2) at the PAO in the range of (2×108 – 2×1010) GeV.

10. Thus two conditions on CR models arises:
in addition to
Icascade γ < Fermi LAT IGRB (gamma-ray test)
cascade neutrino intensity Icascade υ
should be less than the intensity of astrophysics neutrino measured I υ measured,
Icascade υ< I υ measured (neutrino test)

11. THE MODEL CR sources are pointlike. (They are SMBHs
THE MODEL CR sources are pointlike. (They are SMBHs. ) UHECRs are protons. Other assumptions concern three points: 1) CR sources – injection spectra and evolution 2) Extragalactic background emission 3) Extragalactic magnetic fields

12. The injection spectra in sources assumed to be exponential, ∝E-α,
with the spectral index equals to a=2.2, 1.8, 1, 0.5, 0
where 0 corresponds to equiprobable generation of particles at any UHE.
The spectra are harder than those discussed previously in literature
due to another acceleration mechanism:
here electric fields accelerate CRs (see e.g. [Haswell, Tajima, Sakai, ApJ. 1992])
rather than shock fronts.

13. We suppose that UHECR sources are located at distances z≥0.05.
Source evolution
We suppose that UHECR sources are located at distances z≥0.05.
Source evolution influences on the CR spectrum measured
(e.g. Uryson 1998, 2018; Berezinsky et al. 2016; Gavish, Eichler 2016).
In the model we use a scenario of BL Lac evolution
(Di Mauro et al., 2014; Kalashev, Kido 2015).

14. Extragalactic background emission Cosmic microwave background: Planck distribution, <εr> =6.7∙10-4 eV, <nr >=400 сm-3. Extragalactic background light: Inoue et al Extragalactic radio background: Protheroe, Biermann 1996.

15. Extragalactic magnetic fields
seem to be inhomogeneous: 1∙10−17Gs < B <3∙10−6 Gs
(Kronberg 2005; Essey, Ando and Kusenko 2011; Dzhatdoev et al. 2017).
Fields of B<≈10-9 –10-8 Gs do not break cascades.
Fields of B∼10−6 Gs disturb cascades due to electron synchrotron emission.
We suppose that regions where extragalactic fields are of∼10−6 Gs occupy a small part of extragalactic space and neglect them.
We assume that extragalactic fields do not break cascades.

16. the public available code TransportCR (Kalashev, Kido 2015)
COMPUTING
the public available code TransportCR (Kalashev, Kido 2015)
for CR propagation in the extragalactic space

18. Model spectra are several orders lower than the PAO and TA spectra and differ strongly in shape. So CR sources with hard injection spectra contribute negligibly to the CR flux detected by ground arrays. What is the UHECR contribution to the diffuse gamma-ray emission?

19. Fermi LAT IGRB = unresolved sources + extragalactic diffuse emission Contribution of unresolved sources at E>50 GeV: 86 (+16, -14) % (Di Mauro 2016) Fermi LAT IGRB (E>50 GeV)=1.325·10-9 (cm-2 s-1 sr-1) Deducting contribution of unresolved sources of 86% IGRB without blazars (E>50 GeV) =1.855∙10-10 (cm-2 s-1 sr -1). (1)

20. IGRB without blazars (E>50 GeV) =1.855×10-10 (cm-2 s-1 sr-1). (1)
In the model for the set of spectral index values a=2.2, 1.8, 1, 0.5, 0
the cascade integral gamma-ray intensity is:
Icascade γ(E>50 GeV)≈ ( ) ×10-10 (cm-2 s-1 sr-1) (2)
The model cascade gamma-ray emission Icascade γ(E>50 GeV) is less than the value (1) in all cases of spectral indices considered.
Thus the model under consideration satisfies the gamma-ray test.

21. We do not discuss cascade gamma-ray spectra because they depend negligibly on CR injection spectra (Berezinsky, Kalashev 2016; Dzhatdoev et al. 2017).

22. Neutrino fluxes are also generated during UHECR propagation, whereupon the neutrino test on CR models arises. Astrophysics neutrino fluxes measured are:
E2dΦ/dE = (1.84×10-4 – 1.44×10-8) GeV sr-1 s-1 cm-2 at
E=( ×106) GeV [PAO],
E2dΦ/dE < 1.3×10-7 GeV sr-1 s-1 cm-2 at (2×1017 – 2×1019)eV [IceCube].

24. At energies E >1019 eV neutrino spectra depends
on injection spectra.

25. All calculated spectra of cascade neutrinos are lower than those measured.
So the model satisfies the neutrino test.

26. CONCLUSION
Here particle injection spectra are assumed to be harder than those discussed previously in cosmic-ray literature.
1. In this case particle flux on the Earth is too low for detection.
2. But particles produce in the space a noticeable flux of diffuse gamma-ray emission
via electromagnetic cascades.
3. It should be accounted for analyzing other source models and dark matter models.
4. Neutrinos are produced in cascades, and at energies E >1019 eV neutrino spectra
depends on injection spectra.
5. So data on gamma-ray and neutrino emission can be used to study the model.

27. Remarks
In the study presented it is important that injection spectra are hard.
It is no matter where they are formed.
The idea about hard injection particle spectra in sources arises
from (Haswell, Tajima and Sakai, Astrophys. J. 1992)
where particle acceleration by electric fields in accretion discs around SMBHs
is analyzed.
Another approach to the Universe structure (without SMBHs) exist
(e.g. V. Olyeynik, this conference).
2. The first attempt to study extragalactic EM-cascades using CR data:
Uryson JETP 1998.

28. Thank you!