Is it possible to calculate the masses of the stars in an x-ray binary system when all i know of the system is that; one of the stars is a main sequences star of spectral type K5 measured from optical spectroscopy. The companion star is believed to be a neutron star with no distinct pulsations, however the x-ray emission has exhibited erratic and dramatic changes over long periods of time, the last outburst was in 1979 when the luminosity in the x-ray band was estimated to be 4 x 10^30 J s^-1.?
a) If it is not possible to calculate the masses of the stars, what would be a reasonable assumed mass for the neutron star? How did you deduce this?
b) By considering the energy released in one second, calculate the rate (Q) at which mass would have to be transferred (in Kg s^-1) to the neutron star in order to provide the luminosity that was observed in the 1979 outburst. Clearly state any assumption made in your calculations.
The energy released in one second was 4 x 10^30 J. This is from a conversion of the mass of the main sequence star into x-ray photons. Using the relativistic expression E = mc^2 m can be found as 4 x 10 ^30 J/ c^2 = 4/9 x10^(30-16) = 4/9 x 10^14 Kg
Q = 4/9 x 10 ^14 kg/sec Assuming all mas is converted to photons in transfer process.
a) yes it is possible to calculate the masses of the stars composing the system using the Doppler shift data available from the x-ray and main sequence star spectra.
· We determine the mass of the Sun by making measurements of the orbital parameters of a planet, and using Kepler's Harmonic Law to deduce the Mass of the Sun. Actually, Kepler's Laws will give you the sum of the masses of the Sun and the planet, but the mass of the planet is so much smaller than the Solar mass that we can take that number as the mass of the Sun.
· The only way to directly measure the mass of stars is to measure the mass of stars that are part of binary systems, two stars that orbit one another.
By observing a binary system, it is fairly straightforward to measure the period of revolution.
The other piece of information ...
The solution assists with calculating the masses of the stars in an x-ray binary system.