Astron. Astrophys. 331, L57-L60 (1998)

3. Comparisons to the Centaurus A X-ray spectrum

3.1. The parameters of the model

The free parameters used in this model are:

• The angle between the observer and the jet axis, .
• The mass of the central object M (in solar masses ), which mainly controls the radius of the jet, taken to be .
• The accretion rate (in ).
• The particle distribution index s, related to the X-ray energy spectral index .
• The opacity parameter .

In fact, the high energy spectrum is not very sensitive to variations of the accretion rate and hence to the disk luminosity (see MHP for explanations). The spectral index is constrained by the the observations below the spectral break, and the parameter is found to take limited values around 0.1. This leads to only two real free parameters; the angle and the radius of the jet (or equivalently the central mass with the above assumption). It is important to realize that other important parameters, as the particle density, the distance from the center, the plasma velocity, are not free but are linked to the above quantities through the differential equations and their boundary conditions.

We apply our model to the 1991 simultaneous OSSE/COMPTEL (VP 12) observations, together with EGRET results from Thompson et al. (1995). The best fit for a cylindrical jet is given in Fig. 1.

Fig. 1. Comparison between the high state of emission in 1991 and our model (solid line). The dotted line represents the annihilation component. The parameters are defined in the text. OSSE data are from Kinzer et al. (1995), COMPTEL data from Steinle et al. (1996) and EGRET data from Thompson et al. (1995) (dashed lines).

For a Schwarzschild black hole we used the following set of parameters: , , , , , where denotes the Eddington accretion rate. The internal radius of the disk is and the external one is . The emission zone is found to be located around 100 .

The derived angle confirms the misaligned nature of the Centaurus A jet and is in agreement with the previous derivations of the direction of the line of sight inferred from HII distributions studies (Graham (1979)), which is a little smaller.

3.2. A red-shifted spectral break

For the high state, the spectral break verifies well the relation . Such a value is explained by the strong (exponential) absorption of the soft photons in the Thomson optically thick plasma at where the pair density reaches values of order of for Centaurus A.
As pointed before, this strong absorption zone also corresponds to the gamma-ray photosphere of 0.511 MeV in the pair plasma rest frame. In the observer frame a Lorentz transformation shifts the energy of this optically thin region to MeV, where is the Doppler factor at the emission zone.

If the soft photon source is a standard accretion disk the bulk Lorentz factor of the beam, for , scales as (see Eq. (36) in MHP)

In the present case, the infered angles between the jet and the line of sight directions give , the Doppler factor at the emission zone is lower than 1, and the spectral break is red-shifted for an external observer. For a spectral break at keV depending of the state of the object we obtain . This corresponds well to the value expected around 100 The annihilation line, which plays a minor role here, is also red-shifted down to an energy of MeV (see Eq. (67) in MHP).

3.3. Low states of activity

The 1992-1994 low state of activity shows a spectral softening located at a higher energy ( keV). Below the break, the energy spectral index () does not seem to depend on the intensity level. Only the higher energy data from OSSE, COMPTEL and EGRET can constrain value of the spectral break. Unfortunatly the OSSE-EGRET (VP 316) and COMPTEL (1992-1993) observations are not simultaneous, and precise value of the break can not be deduced. We argue that in our scheme the low state of activity can be associated with a less efficient pair formation process. This effect can be quantified by relaxing the "type I" opacity conditions used in our simulations (see Eq. (2)). The pair plasma is taken now to have a longitudinal (instead of transverse) Thomson optical depth of 1 at a distance where the corresponding opacity to pair production is . The "type II" opacity conditions now read:

There is no simple relation between the two systems , and , due to the non-linear factor containing (see Eq. (52) in MHP) in the continuity equations. In particular, low density solutions cannot be described by type I conditions. The soft photon and the particle densities with type II conditions are derived in the same way as for the type I.

The best fit of the low state is given in Fig. 2, with the parameters , , , , . The model predicts .

Fig. 2. Comparison between the 1992-1994 low state of emission and the model. The parameters are defined in the text. EGRET data are derived from Thompson et al. (1995) summing all phase 2 observations (P2).

© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998
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