Central accumulation of magnetic flux in massive Seyfert galaxies as a possible engine to trigger ultrahigh energy cosmic rays

In the present paper we investigate the production of ultrahigh energy cosmic rays (UHECRs) from Seyferts. We discuss the UHECR luminosities obtained by two possible engine trigger models: pure radiative transfer and the energy extraction from poloidal magnetic flux. The first case is modeled by Kerr slim disk or Bondi accretion mechanisms. Since it is assumed that the broadband spectra of Seyferts indicate that at least the outer portions of their accretion disks are cold and geometrically thin, and since our results point that the consequent radiative energy transfer is inefficient, we build the second approach based on massive Seyferts with sufficient central poloidal magnetic field to trigger an outflow of magnetically driven charged particles capable to explain the observed UHECRs and gamma rays in Earth experiments from a given Seyfert source.

Figure 1

Model of a Seyfert accretion disk, that is slim, cold and presenting an inefficient accretion flow due to the great distance from the central black hole. The role of the central poloidal magnetic field is to produce a jet of magnetically driven charged particles, triggering the emission of UHECRs. An approximately spherical accretion symmetry could be modeled for such a system, privileging a Bondi accretion.

Figure 2

Comparison between ${\eta }_{pr}^{UL}$ and $\log (M_{\mathrm{BH}}/M_{\odot })$ using three different models of accretion: Bondi, Kerr slim disk and Eddington. (See the study of the stability of such systems at [76, 77].) The ${\eta }_{pr}^{UL}$ is calculated using the method presented in [50, 51] neglecting the radiation losses during acceleration of UHECR. The original method uses the mass of the galaxy to calculate the UHECR upper limit flux and here the model was adapted to use the black hole mass. For the Seyfert case, since the accretion is inefficient, ${\eta }_{pr}^{UL}$ will have values between the Kerr slim model (triangles) and the Bondi model (stars). Note that at the Bondi threshold, the ${\eta }_{pr}^{UL}$ values are larger than in the Kerr slim disk threshold case, indicating that the radiative system should transfer more energy to accelerate cosmic rays when the accretion mechanism is inefficient as that found in Seyferts and therefore only massive Seyferts $(>10^{8.2}{M}_{\odot })$ are sources capable of accelerating cosmic rays. In the figure, each point corresponds to one of the Seyferts presented at Table 1.

Figure 3

Maximal energy for nuclei of iron, proton and carbon as a function of the $M_{\mathrm{BH}}$. The arrows indicate the upper limit on the proton energy to Seyfert galaxies MCG-01-24-012, NGC 985 and NGC 1142. The BH masses for the mentioned Seyferts come from [54, 55].