An Introduction to Modern Astrophysics · Problem 17.24

Close Binary Star Systems — Carroll & Ostlie

Physics — Astrophysics · black-holes-x-ray-binary

Problem

In the X-ray binary system A0620

-

00, the radial orbital velocities for the normal star and the compact object are

v_{s,r} = 457

km s

^{-1}

and

v_{c,r} = 43

km s

^{-1}

, respectively. The orbital period is 0.3226 day. (a) Calculate the mass function (the right-hand side of Eq. 7.7),

\frac{m_c^3}{(m_s + m_c)^2}\,\sin^3 i,

where

m_s

is the mass of the normal star,

m_c

is the mass of its compact companion, and

i

is the angle of inclination of the orbit. What does this result say about the mass of the compact object? (Note that the value of

v_{c,r}

was not needed to obtain this result.) (b) Now use the value of the orbital radial velocity of the compact object to determine its mass, assuming

i = 90°

. What does this result say about the mass of the compact object? (c) The X-rays are not eclipsed in this system, so the angle of inclination must be less than approximately

85°

. Suppose that the angle of inclination were

45°

. What would the mass of the compact object be then?

Related theory

Primordial Black Holes

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