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Astron. Astrophys. 364, 552-556 (2000)

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4. Magnetized black hole model

Kerr-Newman isolated black holes are interesting candidates for the production of variable gamma-ray sources in the Galaxy (Punsly 1998a, 1998b). The configuration of a simple axisymmetric magnetosphere around a maximally rotating black hole attains a minimum energy configuration when the hole and the magnetosphere have equal and opposite charge. Punsly (1998a) has shown that the magnetospheric charge can be supported in a stationary orbiting ring or disk. The entire magnetized system is stable only in an isolated environment, otherwise accretion into the black hole would disrupt the ring and its fields. Kerr-Newman black holes are charged similarly to neutron stars in pulsars. However, unlike neutron stars, black holes have no solid surface and consequently no thermal X-ray emission is expected. These objects can support strong magnetized bipolar winds in the form of jets, where gamma-ray emission is originated by the inverse Compton mechanism (Punsly 1998a). Since both magnetic and rotation axes are always aligned therein, their emission is nonpulsating (NP) and for such a reason they have been called NP black holes (Punsly 1999).

We propose that 3EG J1828+0142 could be a NP black hole created by the same supernova explosion that produced the nearby SNR. In the following, we present a specific model that reproduces the steep gamma-ray spectrum observed at EGRET energies. The model takes into account electron-positron annihilations in the inner jet, self-Compton cooling of the relativistic leptons, and synchrotron emission of the outer jet, in such a way that it provides concrete predictions for different wavebands that can be tested in the near future.

We shall follow the treatment given by Punsly (1998a), considering a black hole of mass [FORMULA] [FORMULA] and a polar magnetic field strength [FORMULA] G. The inner jet begins at the inner light cylinder (located at a cylindrical radius [FORMULA] from the symmetry axis):

[EQUATION]

this is at a distance [FORMULA] from the event horizon:

[EQUATION]

The radius of the jet r is given in terms of the axial displacement from the black hole, R, as:

[EQUATION]

Thus, the inner jet is tightly collimated. Its length is given by:

[EQUATION]

The Doppler enhancement factor is constant and assumed to be:

[EQUATION]

The magnetic field and the particle number density vary with R as:

[EQUATION]

and

[EQUATION]

where

[EQUATION]

The maximum thermal Lorentz factor, [FORMULA], is:

[EQUATION]

Gamma-rays are produced in this inner jet by electron-positron annihilations and self-Compton emission. The annihilation luminosity is enhanced by Doppler boosting in the jet as:

[EQUATION]

where

[EQUATION]

(see Roland & Hermsen 1995, noticing the wrong exponent in their Eq. 4, where it should be no dependency on [FORMULA]). In the above Eq. (13), n is the number density of electron-positron pairs, V is the volume where the annihilations occur, and [FORMULA] is the Thomson cross section. The peak of the annihilation line will be at an energy:

[EQUATION]

which in our model corresponds to 6.4 MeV, assuming [FORMULA]. The spectral shape of the annihilation line is as in Böttcher & Schlickeiser (1996). Notice, however, that these authors consider an external source of photons for the inverse Compton radiation and, consequently, their conclusions on the minimum leptonic number density in the jet do not apply to our case.

The outer jet, which is responsible for the bulk of the synchrotron emission, can be parameterized as a direct extrapolation of the inner jet:

[EQUATION]

[EQUATION]

[EQUATION]

[EQUATION]

[EQUATION]

[EQUATION]

[EQUATION]

[EQUATION]

[EQUATION]

The bulk of the gamma-ray emission originates in the inner jet. We have computed its emissivity using the synchrotron self-Compton (SSC) formalism developed for AGNs by Ghisellini et al. (1985) and adapted to magnetized black holes by Punsly (1998b). The computed spectral energy distribution (SED) is shown in Fig. 2. Notice that the radio luminosity is low, so no strong point-like counterpart is expected at centimeter wavelengths. The radio jets and the terminal radio lobes should appear as a weak ([FORMULA] mJy at 5 GHz) source with an angular size of a few arcseconds. Any of the sources in Table 2, then, are potential counterparts.

[FIGURE] Fig. 2. Spectral energy distribution for the magnetized black hole model.

At a few MeV, the gamma-ray annihilation luminosity exceeds the SSC emission and the spectrum presents a broad peak. The pair annihilation contribution produces a steepening in the spectrum, which presents an index [FORMULA] in the EGRET energy band, consistent with the observations.

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
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