Question

b) Figure 1 shows light curves of a particular X-ray binary obtained from an observation made by XMM-Newton. The light curves have different energy ranges: the top curve uses only 0.3 keV–4 keV photons, while the bottom curve uses 4 keV–10 keV photons. The horizontal axis is time, measured in seconds; only a portion of the observation is shown. The peak 0.3 keV–10 keV flux, seen at time t ≈ 2.7 × 104 s is (7.4 ± 0.5) × 10−12 W m−2; the spectrum of the X-ray emission at this time is well described by a black body with a temperature given by kT = (1.94 ± 0.17) keV. (i) Determine from these light curves whether this system contains a 1.4 M neutron star or a 10 M black hole, explaining, in a few sentences, any steps in your deduction. For the calculations in (ii)–(v) below, you should use the value chosen in (i) for the mass of the compact object in the system. (ii) By making an assumption about the nature of the event that produces the peak flux at t ≈ 2.7 × 104 s, calculate the distance to the system with appropriate uncertainty limits. Carry out your calculations based on theoretical considerations of the maximum luminosity expected of this phenomenon (the Eddington luminosity), You should explain whether you have calculated a maximum or minimum distance for the source. A B Figure 1 Light curves of an X-ray binary observed by the XMM-Newton X-ray observatory. (iii) Assuming the source of the black body spectrum at t ≈ 2.7 × 104 s is spherical, show that the black body temperature is around 20 million kelvin and calculate the radius of the emitting sphere. Carry out your calculations for the assumption you used in (ii). (iv) Compare the depths of dips in the 0.3 keV–4 keV and 4 keV–10 keV light curves. Explain in a few sentences, what this tells us about the nature of the dips and the inclination angle i at which the system is viewed. (v) Estimate the orbital period of the X-ray binary with reasonable uncertainties. Explain your reasoning.

2.5x10 3x10 3.5x10 4x10 4.5x10 Time (s) Figure 1 Light curves of an X-ray binary observed by the XMM-Newton X-ray observatory.