5. The X-Ray Spectrum

Figure 5 shows a typical X-ray spectrum of Cen X-3 observed with the EXOSAT GSPC (see Chapter 6). The data have been unfolded from the instrument response. The pulse-phase averaged spectrum between 1 and 20 keV is fitted by a power law with photon index $\sim$ 1, modified by interstellar absorption and an exponential roll off to higher energies. There is also an iron emission feature between 6 and 7 keV (White et al. (1983) and references therein) which has been found to pulsate with an amplitude $\sim$ 50% of the mean intensity (Day et al. (1993); Takalo et al. (1990)). The energy of this feature varies with pulse phase and from observation to observation. Nagase et al. (1992) modeled the iron line as a blend of 6.4 keV and 6.7 keV lines. They found that the 6.4 keV line underwent an abrupt eclipse, implying that the size of its emission region was $$D_{6.4}\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$<$}}}3\times10^{10}{\rm\ cm}\approx1{\rm\ light\mbox{-}second}.$$
The 6.7 keV line had a much broader partial eclipse which means that $$D_{6.7}\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$>$}}}8\times10^{11}{\rm\ cm}\approx27{\rm\ light\mbox{-}second}.$$
Comparing these values with Figure 2.2 it is clear that D_6.7 is comparable to the radius of the companion. The constraint on D_6.4 is satisfied comfortably by the Alfvén radius ( R_A $\sim$ 3 x 10⁸ cm from Equation 1.61). Day et al. (1993) consider back illumination of an incomplete Alfvén shell by one pole of the neutron star to be the most likely source of the pulsed 6.4 keV line.

Figure 3: Typical pulse-phase averaged X-ray spectrum of Cen X-3 observed with the EXOSAT GSPC. The data have been unfolded from the instrument response. The spectrum is a power law with photon index $\sim$ 1 which falls off to low energies due to interstellar absorption and has an exponential roll off above 10 keV. The prominent feature between 6 and 7 keV is due to Fe K$\alpha$ emission.

In order to explain the observed properties of the iron lines in Cen X-3 we must be able to specify where the radiation is emitted, how is it reprocessed and what the physical conditions in those places are. Because of the intense X-ray flux one might expect that all the matter close to the neutron star should be completely ionized. However the results of Nagase et al. (1992) show relatively un-ionized iron emission within 1 light-second of the neutron star. This is possible because the accretion disk is not fully ionized. It is dense enough for recombination to keep the ionization parameter $\xi$ = ${L_{\rm x}\over n_e r^2}$ low. The time required for local thermodynamic equilibrium (LTE) to be attained is proportional to the inverse of the electron density n_e. For a 10⁴ K plasma with n_e $\sim$ 10¹⁶cm^-3 LTE is established in less than 1 $\mu$s (Thorne (1988)). This suggests that matter entering the accretion disk will quickly recombine. I have calculated the radial dependence of the properties of an accretion disk based on the model of Shakura and Sunyaev (1973). The results are shown in Figure 5. The luminosity has been assumed to be 10³⁷ erg s^-1. The radial dependence of $\xi$ is calculated for normal incidence of the X-ray flux on the disk and thus describes an upper limit to $\xi$. From Equation 1.61 the inner disk is truncated at r = r_A $\approx$ 3 x 10⁸ cm and the disk parameters have been calculated for radii greater than this. This means that the disk can contribute a fraction R_x/r_A $\sim$ 10^-2 of the total luminosity. Thus the only observable X-rays from the disk will be reflected. The low calculated value of the ionization parameter $\xi$ suggests that photoionization will not be important for iron in the disk. This model does not include the effects of X-ray heating by radiation from the neutron star. The radiation temperature will be

$$\over {1\over2}$$ (85)

assuming a face-on disk.

Figure 4: Radial dependence of the properties of an accretion disk based on the model of Shakura and Sunyaev (1973) with $\alpha$ = 1. This calculation assumes M₁ = M_x/M_$\odot$ = 1.1, R₆ = 1, and L₃₇ = 1. The parameters shown, from top to bottom, are the disk mass per unit area $\Sigma$, the disk scale height H, the disk density $\rho$, the central temperature T_c (in the midplane of the disk) , the radial drift speed v_r, the electron density n_e, and the ionization parameter $\xi$.

Figure 5 shows that that the inner accretion disk is a plausible emission site for the 6.4 keV fluorescent iron line. If this is the case the physical width of the line may place an upper limit on the temperature of the fluorescing matter and the Keplerian rotation speed of the magnetosphere.