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Departament d'Astronomia i Meteorologia, Universitat de Barcelona, Av. Diagonal 647, E-08028 Barcelona, Spain
Cir X-1 is the only periodic radio emitting X-ray source detected in the Southern Hemisphere. This object has a wide range of emission in all spectral windows, and multi-wavelength observations have been reported at X-ray Kaluzienski, et al. (1976), optical Haynes et al. (1978), infrared Glass, (1978) and radio Haynes et al. (1978). Such studies suggest that we are dealing with an eccentric binary system with a 16.6 d orbital period, the same period of both X-ray and radio outbursts. Radio outbursts usually occur after X-ray outbursts, and may exhibit multi-peaked structure. Based on HI absorption measurements Goss & Mebold (1977) a distance of 8-10 kpc is adopted.
The compact object is probably a neutron star of 1.1 to 1.4 Tennant et al. (1986). The optical counterpart is not well known because the location in a highly obscured region, where three faint stars are within of the radio position Argue, et al. (1984). The soft X-ray properties seem to indicate some few solar masses for the primary star Stewart et al. (1991). However, its X-ray and radio properties do not fit easily into the high mass or low mass classification.
Another remarkable peculiarity is the existence of a radio nebula surrounding this source Haynes et al. (1986) with jet-like structure observed inside Stewart et al. (1993). It has been suggested that Cir X-1 may be a runaway binary Clark, et al. (1975) ejected from the SNR G321.9-0.3.
In the present model, it is considered that a Cir X-1 radio outburst takes place due to the bipolar ejection of a cloud of synchrotron-emitting relativistic electrons (plasmon), mixed with ionized thermal gas, following a transitory supercritical accretion event onto the compact star.
During this process, fresh relativistic electrons can be injected into the plasmon, which is assumed to be in adiabatic expansion.
In the course of the expansion, assumed to occur at a constant velocity , the electrons will be subjected to adiabatic, synchrotron and inverse Compton energy losses, that are given by:
where is a constant depending on the geometry and the expansion velocity.
where (cgs) and represents the radiation energy density.
Let be the energy distribution function of relativistic particles. Its time evolution is controlled by the following continuity equation:
where includes all the energy loss mechanisms and is the source term (number of particles injected per unit time and per unit energy interval).
It is assumed that injected particles have an energy power law spectrum of index p, with energy limits , and that the injection process takes place, at a constant rate, during a finite interval . Thus, the source term is:
By integrating over the energy limits, the relationship between the mass of relativistic particles injected per unit of time, , and the parameter , is:
being the mass of the electron and has been assumed.
Assuming magnetic flux conservation, the evolution of the magnetic field can be written as:
where the subscript zero indicates initial values at t=0.
On the other hand, for the radiation energy density is used the approximation of Paredes et al. (1991):
At this point, the calculation of synchrotron emission and absorption coefficients, as well as that of radio flux density, follows a treatment parallel to that of Paredes et al. (1991).
The model described above has been applied to the radio light curves of Cir X-1 as observed by Haynes et al. (1978) at 1.4, 2.3, 5.0 and 8.4 GHz. The main features of this outburst were:
has been subtracted from all of them.
I have carried out numerical calculations for the flux density at these four frequencies during the outburst. Two plasmon ejection events have been considered to account for the double-peaked flare observed. The computed radio light curves take into account the overlapping of both plasmons. The best fit parameters of each plasmon are given in Table 1. In Figure 1, we can see that the present model reproduces acceptably well the observed data at several frequencies simultaneously.
Table 1: Physical parameters of the plasmons.
Figure 1: Observed data of Cir X-1 for the 1977 May double-peaked radio outbursts at the frequencies of 8.4, 5.0, 2.3 and 1.4 GHz. The continuous line is the model fit carried out using the parameters of Table 1.
A possible improvement of the present model could be achieved by using a time dependent injection term in the following way:
The time dependence of the injection function could be specially important for X-ray binary systems where the accretion rate changes significantly along the orbital phase. In particular, when the accretion is due to a stellar wind, it can be shown that the function exhibits two well defined peaks for orbits of high eccentricity Taylor et al. (1992). Those peaks could be related to the double peaked radio outbursts in objects such as Cir X-1.