2.5. Remnants of quasars
2.5.1. What is a quasar remnant and how would they accelerate particles?
Interestingly, the absence of powerful radio emitting objects in the direction of several UHECRs led some colleagues to think that dead, faint objects, yet ones sufficiently active as to accelerate particles up to relativistic energies, are responsible for the UHECRs observed. Such is the idea behind the concept of quasar remnants (QRs) as UHECR emitters [282, 283]: a spinning supermassive black hole, threaded by magnetic fields generated by currents flowing in a disc or torus, induces an emf which, if vaccum breakdown is prevented and in the absence of severe energy losses, accelerate a particle near the full voltage.
Although in the present epoch there is a paucity of luminous quasars (L 1047 ergs s-1), those which appear at large redshifts, the expected local number of dead quasars associated with the same parent population is expected to be large [284, 285, 286]. Supermassive black holes are now to be found in the relatively dormant nuclei of giant elliptical galaxies, generally regarded as QRs. (21) The compact dynamo model has been proposed as a natural mechanism for accelerating CRs in such environments . In this model , if B is the ordered poloidal field near the hole, V ~ aB, where a is the hole's specific angular momentum (e.g., a = M for an extreme Kerr hole of mass M). In an appropriate astrophysical scaling 
where B4 B / (104 G) and M9 M / (109 M). Assuming that the energy density of the magnetic field near the event horizon is in equipartition with the rest mass energy density of accreting matter , it is possible to introduce the accretion rate in the voltage expression. In terms of an Advection Dominated Accretion Flow (ADAF) model (e.g., Ref. ), for example,
where is the accretion rate dM / dt in M yr-1, and then, the maximum emf (a / M ~ 1) is
This potential is not, however, the maximum obtainable energy.
The rate of energy loss through curvature radiation by a particle of energy E = mc2 can then be expressed as
see  for a detailed explanation. Here, is the average curvature radius of an accelerating ion, assumed to be independent of the ion energy. The energy change per unit length of an accelerating ion having charge Z and mass mi = µ mp is given by
where h is the gap height. After integration from s = 0 to h, the maximum acceleration energy is obtained
Consequently, only a fraction
of the potential energy available will be released as UHECRs; the rest will be radiated in the form of curvature photons.
For a proton, the suppression ratio is E / [e(V)] [(50M9)-1/2 B4-3/4]r1/2, where r denotes the magnetic field curvature in units of the Schwarzschild radius (h ~ Rg) . For r 1 and (0.1 - 10) M yr-1, and using the previous equations,
Heavier nuclei would reach higher energies, but are subject to photo-disintegration. For highly energetic protons, energy losses due to photo-pion production in collisions with ambient photons also becomes a relatively important effect. A lower limit to the radiation length (min) for the proton energy loss associated with photo-pion production is estimated by considering the population of target photons within the source region [R(source radius) 2GM / c2] at radio frequencies 360( / 1011)-1 GHz is given by 
where p , µ b p / 10-30 cm2, RS is the Schwarzschild radius (twice the gravitational radius Rg = GM), K <E(loss)> / E(initial) is the inelasticity in a single collision  and Q is the core emission rate (photons s-1) for electromagnetic radiation at > 360 GHz, given by Q = h-1 -1 L d where h is the Planck constant and L = 4 D2 F for a source of spectral density F at distance D. A useful approximation is that  <K p , µ b> [(K p , µ b(dQ / d) d)] / Q < 120 µb. Those quasar remnants with min > R are expected to successfully accelerate protons up to ~ Emax. Noteworthy, the observed flux of CRs would apparently drain only a negligible amount of energy from the black hole dynamo, since replenishing the particles ejected at high energies (> 1020 eV) would only require a minimal mass input: a CR luminosity of 1042 ergs/s in such particles (if protons) corresponds to a rest mass loss rate of less than 10-5 M in a Hubble time.
2.5.2. Correlations of UHECRs with QRs
The first analysis of possible correlations between UHECRs and QRs was carried out in Ref. , where, imposing very restrictive selection criteria -those necessary for obtaining candidate objects providing the most favorable setting for a black hole based compact dynamo model of UHECR production- a group of galaxies from the Nearby Optical Galaxy (NOG) catalog of Giuricin et al.  was a priori selected as individual plausible sources of CRs. (22) It was found that nearby QR candidates present an above-random positional correlation with the sample of UHECRs. Surprisingly, this correlation appears on closer angular scales than that expected when taking into account the deflection caused by typically assumed intergalactic or Galactic magnetic fields. (23)
As one can see using Eq. (8), scattering in large scale magnetic irregularities (nG) are enough to bend the orbits of super-GZK protons by about 4 deg in a 50 Mpc traversal. The CR angular offsets observed for the quasar remnants in Ref.  are much smaller than whereas, for a variety of assumed magnetic field scenarios, is often substantially larger than the estimated AGASA measurement error of 1.6 degrees. Should the apparent clustering of correlated pairs be supported by future data, perhaps a viable scenario under which this could occur is that in which the intergalactic medium between Earth and the three apparently `clustered' quasar remnants is sufficiently different from the intergalactic medium in front of the remaining nine objects that are much more uniformly distributed on the accessible sky. This appears at least plausible judging from the 100 micron map of the region shown in Fig. 7.
Figure 7. IRAS 100 micron view of the North Galactic Pole (white=high flux, dark blue=low flux), towards the region of several QRs that appear coinciding with UHECRs. Small circles mark the 12 galaxies (candidate quasar remnants) in the sample of Ref. . Red circles mark galaxies perhaps associated with UHECRs; white circles mark galaxies without associated UHECRs. Note that the palusible UHECR sources tend to be found in directions of lower 100 micron flux, [UHECR-coinciding source directions present IRAS fluxes 0.614 ± 0.022 MJy/sr whereas the directions towards those galaxies non-coinciding with UHECRs presnet 1.68 ± 0.63 MJy/sr.] To the extent that the 100 micron flux traces the Galactic dust and magnetic field, then CRs are likely to be better aligned with their sources in directions of low flux. Figure courtesy of Tim Hamilton.
For the deflection of an energetic (60 EeV) proton in traversing 34 Mpc (the mean of the QRs distances in Table 3 of ) to be less than a degree, the magnetic field must fulfill B < 2 × 10-10 -1/2 G, which appears to be not drastically different from the canonical nano-Gauss B field and usually assumed coherence lengths ~ 1 Mpc. Also, in some directions, the magnetic field of our own galaxy could well lead to a deflection of up to several degrees for primaries with energies below 60 EeV; see, for instance, Table 1 of Ref. . A recent study of this issue was presented by Alvarez-Muñiz et al. . However, a possible filamentary topology of the Galaxy's magnetic field would likely allow some directional windows, albeit narrow, where the deflection of an UHECR could be much less than typical.
In a very recent paper, Isola et al.  have studied predictions for large and small scale UHECR arrival direction anisotropies in a scenario where the particles are injected with a mono-energetic spectrum (all particles coming from a source are emitted with the maximal energy of acceleration for that source as derived in that same paper) by a distribution of QRs. They find that the sample of (37) QRs they considered is distributed too anisotropically to explain the isotropic ultra high energy CR flux except in the case where extragalactic magnetic fields of 0.1µG extend over many Mpc. As statistical quantities for this analysis were used spherical multi-poles and the autocorrelation function. For a weak magnetic field, of order of 1 nG, the predictions appear to be inconsistent with the observed distribution of arrival directions of UHECRs, because the magnetic field is too weak to isotropize the distribution coming from a limited number of non-uniformly distributed sources, as already pointed out in Ref. . Isola et al. also found that the contribution from the farthest sources is completely negligible even for this weak magnetic field. None of the objects that were found close to UHECR positions in the Torres et al. previous set were included in the Isola et al. sample. Little further progress regarding possible correlation of sources can be made until a much more larger set of UHECRs is recorded, something that will have to wait to the operation of PAO.
2.5.3. TeV emission from QRs
A concomitant effect of UHECR emission from QRs is that, as shown by Levinson , the dominant fraction of the rotational energy extracted from the black hole is radiated in the TeV band. He showed that the spectrum produced by the curvature radiation of a single ion will peak at an energy
and is a power law I(E) (E)1/3 below the cutoff. The overall spectrum of curvature photons would depend on the energy distribution of the accelerating particles, and is expected to be somewhat softer below the peak. For Emax = 3 × 1020 eV and h ~ Rg, E max 50µ-1 (Z B4)1/2 TeV. Then, provided that vaccum breakdown does not occur, and that TeV photons can escape the system, QRs should emit -rays.
Indeed, it was recently noted by Neronov et al.  that the concomitant TeV radiation would be at a level sufficiently high as to be (for many combination of the system parameters) ruled out by bounds imposed HEGRA/AIROBICC.
Recent numerical simulations additionally suggest that the accretion process and magnetic field structure in the vicinity of the horizon can be non-stationary, owing to rapid magnetic field reconnection . This would probably lead to appreciable complications of the model, as the location of the gap, the injection of seed particles into the gap, and, perhaps, the voltage drop across it might change with time. How should this affect the picture described above is unclear at present.
21 Indeed, the term "quasar remnants" was introduced by Chokshi and Turner  to describe the present-epoch population of dead quasars harboring supermassive black hole nuclei. Back.
22 The latter catalog is a complete magnitude-limited (corrected blue total magnitude B 14), distance-limited (redshift z 0.02) sample of several thousand galaxies of latitude |b| > 20°. Back.
23 Deflections due to the magnetic fields would of course be avoided if the primary were a photon, generated in the neighborhood of the QR via an accelerated charged particle interaction. Back.