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Astron. Astrophys. 362, 646-654 (2000)

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4. Consequences for gamma-ray escape from Cen X-3

In the previous section we investigated general features of the [FORMULA]-ray spectra escaping from the radiation field of a massive star. In order to have results of calculations which can be directly compared with the observations we compute the [FORMULA]-ray light curves expected from the Cen X-3 system assuming that the compact object in this binary system injects [FORMULA]-ray photons or electrons with a power law spectrum. The parameters of the Cen X-3 system, used in computations, are mentioned in the Introduction. Note that the orbit of the compact object is almost circular, so then the expected light curve should be symmetrical. Therefore we compute only the photon fluxes for the phases from 0 to 0.5, where the phase is measured from the side of the observer.

The [FORMULA]-ray light curves of photons escaping from the system in the case of isotropic injection of electrons (or positrons) with a power law spectrum and spectral index -2 are shown in Figs. 7a,b for photons with energies above 100 MeV, i.e. the EGRET energy range (a), and above 300 GeV, i.e. Cherenkov technique energy range (b). The results are shown for the cut-offs in the spectrum of electrons at [FORMULA] MeV (full histogram) and at [FORMULA] MeV (dashed histogram). Note however, that the case with a cut-off at [FORMULA] MeV is shown only for comparison since it may not be completely right. Our assumption of the isotropization of secondary [FORMULA] pairs with the Lorentz factors [FORMULA] may not be justified in this case(see Eq. 3). The light curves show that the [FORMULA]-ray flux should change drastically during the [FORMULA] day orbital period of the system by at least an order of magnitude. However the [FORMULA]-ray light curves observed at different energy ranges behave completely differently. When the photon flux above 100 MeV increases from the phase 0 up to the eclipse of the compact object by the massive star, which occurs for the phase [FORMULA], the photon flux above 300 GeV decreases. This is the result of the propagation of photons in the anisotropic radiation of a massive star as discussed in details in Sect. 3. In Fig. 8, we show the spectra of [FORMULA]-rays which should be seen by the observer for different phases of the compact object: 0 (full histogram), 0.15 (dotted), 0.35 (dashed), and 0.5 (dot-dashed). The photon spectra above 100 MeV have similar shapes but different intensities. The spectra above 300 GeV differ significantly not only in the intensities but also in shape.

[FIGURE] Fig. 7a and b. The light curves observed in [FORMULA]-rays at inclination angle of the orbital plane of Cen X-3 system equal to [FORMULA] at energies above 100 MeV a , and 300 GeV b in the case of isotropic injection of electrons with a power law spectrum with exponent -2. Specific histograms show the number of primary photons which escaped without interaction (dotted), secondary photons (dashed) and all photons (full).

[FIGURE] Fig. 8. Gamma-ray spectra observed from the Cen X-3 system at the inclination angle [FORMULA] for four different phases of the binary system 0. (full histogram), 0.15 (dotted), 0.35 (dashed), and 0.5 (dot-dashed) within the bin width equal to 0.1. The primary electrons, with a power law spectrum, exponent -2, and a cut-off at [FORMULA] MeV (a) and [FORMULA] MeV (b), are injected isotropically by the compact object.

We have also computed the [FORMULA]-ray light curves in the case of isotropic injection of primary photons with the power law spectrum and index -2 (see Fig. 9a,b). Specific histograms in these figures show the light curves for all escaping [FORMULA]-ray photons (full histograms), primary photons which escape without cascading (dotted), and secondary photons produced in cascades (dashed). As expected the light curves for secondary photons in the case of injection of primary photons and electrons are very similar. However the contribution of escaping primary photons to the [FORMULA]-ray light curves with energies above 100 MeV dominates the secondary photons. Altogether, the [FORMULA]-ray light curves at energies above 100 MeV are very flat with a strong decrease for phases between [FORMULA] resulting from the eclipse condition. During the eclipse, the observer may only detect secondary photons produced in cascades (dashed histogram in Fig. 9b), but on the level of about an order of magnitude lower. The [FORMULA]-ray light curves above 300 GeV do not differ significantly for the case of injection of primary photons or electrons (compare Figs 7b and 9b). The contribution of primary non-cascading photons dominates only for small values of the phase (dotted histogram in Fig. 9b). From these computations it becomes clear that investigation of the [FORMULA]-ray light curves at photon energies above 100 MeV (but not above 300 GeV) should allow the determination between types of primary particles dominantly produced by the compact object, photons or electrons (positrons), provided that these particles are injected isotropically with a power law spectrum.

[FIGURE] Fig. 9a and b. The [FORMULA]-ray photon light curves observed at the inclination angle [FORMULA] to the orbital plane in Cen X-3 system at two energy ranges: above 100 MeV a , and above 300 GeV b . The primary [FORMULA]-rays, with the power law spectrum with exponent -2 are injected by the compact object isotropically. Specific histograms show: the number of primary photons which escaped without interaction (dotted); the secondary photons (dashed); and all photons (full).

We also show in Figs. 10a,b the spectra of escaping photons for different phases of the compact object, separately for secondary cascade photons and for primary photons which escape without interaction. The photon spectral index below [FORMULA] GeV for all escaping photons (primary plus secondary) varies with phase only over a relatively small range, from -1.8 to -2. The observed photon fluxes are almost constant. At TeV energies the spectra change drastically with the phase of the compact object, similarly to the above discussed case of the injection of primary electrons. Note that for phase 0.5 (corresponding to the total eclipse of the compact object by the massive star), only secondary photons at energies below [FORMULA] GeV can be observed (Figs. 10a and b).

[FIGURE] Fig. 10a and b. Gamma-ray spectra of secondary a and primary b photons escaping from the Cen X-3 system at the inclination angle [FORMULA] for four different locations of the compact source defined by the phase of the binary system: 0. (full histogram), 0.15 (dotted), 0.35 (dashed), and 0.5 within the bin width equal to 0.1. The primary gamma-rays are injected isotropically and have the power law spectrum with exponent equal to -2.

As we have discussed in the Introduction, Cen X-3 has been detected in the GeV and TeV energy range. The emission in the GeV energy range can be fitted by a power law with spectral index [FORMULA] (Vestrand et al. 1997). This index is consistent with our results for both discussed models of isotropic injection of primary photons or electrons with a power law spectrum and spectral index -2. However, the EGRET observations indicate modulation of the GeV emission with the pulsar's spin period, which should not be observed in the case of injection of primary electrons since the escaping photons at these energies were produced in the cascade process and the information on the pulsar period should disappear. Therefore the model with injection of primary electrons by the compact object seems not to work. The modulation with the pulsar period might be observed in the case of injection of primary photons from the compact object, provided that the secondary photons do not completely dominate the primary escaping photons. In fact, this is evident from our simulations (see Figs. 10a,b). However, as is seen in Fig. 9a, the photon flux, although constant through most of the phase range, should drop drastically during the eclipse of the compact object by the massive star. This feature has not been observed but also can not be rejected by the EGRET observations (Vestrand et al. 1997).

Cen X-3 has also been reported as a source of TeV photons modulated with the orbital period of the binary system by earlier, less sensitive Cherenkov observations (Brazier et al. 1990, North et al. 1990). Recent observations report that Cen X-3 is a source of steady emission above [FORMULA] GeV (Chadwick et al. 1998). However modulation with the pulsar and orbital periods has not been found (Chadwick et al. 1999b). Our calculations show that in both models, injection of primary photons and injection of primary electrons by the compact object, the modulation of the signal with the orbital period should be very clear. On the other hand, the modulation with the pulsar period should not be observed because the secondary cascade photons determine the light curve in the case of injection of primary electrons and dominate or give a similar contribution to the light curve in the case of injection of primary photons (see dotted histogram in Fig. 9b).

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© European Southern Observatory (ESO) 2000

Online publication: October 24, 2000
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