Spectroscopy of the X-ray transient GRO J1655 40 gives an orbital period

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Celestial mechanics and planetary systems · Stellar death and compact objects

Stars from the Inside, Ch Accretion power: mass transfer, discs and the weighing of black holes

Problem

Spectroscopy of the X-ray transient GRO J1655

-

40 gives an orbital period

P = 2.62\,\mathrm{d}

, a radial-velocity semi-amplitude of the visible donor star

K_2 = 228\,\mathrm{km\,s^{-1}}

, an orbital inclination

i = 70.2^\circ

from ellipsoidal light-curve modelling, and a mass ratio

q = M_2/M_1 = 0.334

(donor mass over compact-object mass) from rotational broadening of the donor's absorption lines (Orosz & Bailyn 1997, ApJ 477, 876; van der Hooft et al. 1998, ApJ 494, 275). The maximum mass a neutron star's equation of state can support is taken as

M_{\max,\rm NS} \approx 3\,M_\odot

(Chapter 13). ((a)) Compute the mass function of the compact object,

f(M_1) = PK_2^3/2\pi G

, and state what can be concluded about the nature of the compact object from this number alone, without using

i

q

. ((b)) Using

M_1\sin^3i/(1+q)^2 = f(M_1)

, combine

f(M_1)

with the quoted

i

and

q

to obtain the compact object's mass

M_1

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