Australia Telescope National Facility

Atmospheric Modelling of the Companion Star in
GRO J1655-40
Michelle Buxton , Stephane Vennes, PASA, 18 (1), in press.

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Measuring the Mass of the Compact Object from Companion Star Data

The mass of the compact object in GRO J1655-40 has been derived via the radial velocity curves of the secondary star (Bailyn et al. 1995b, Orosz & Bailyn 1997, Phillips, Shahbaz & Podsiadlowski 1999) and accretion disk (Soria et al. 1998), and modelling of optical light curves (van der Hooft et al. 1997, van der Hooft et al. 1998). The results of these are given in Table 1. Since the theoretical mass limit of a rotating neutron star is 3.18 M $_\odot$ (Friedman, Ipser & Parker 1986) these results place GRO J1655-40 as one of the best black-hole candidates. We will concentrate here on another method based on the rotational velocity of the companion star.

Table 1: Compact object and companion star mass estimates derived for GRO J1655-40.

Compact Object Mass (M $_\odot$ )	Companion Star Mass (M $_\odot$ )	Reference
> 3.16 $\pm$ 0.15		Bailyn et al. 1995b
7.02 $\pm$ 0.22	2.34 $\pm$ 0.12	Orosz & Bailyn 1997
5.85 $\pm$ 0.95	1.38 $\pm$ 0.42	van der Hooft et al. 1997
> 5.1		Soria et al. 1998
6.95 $\pm$ 0.65	2.35 $\pm$ 0.75	van der Hooft et al. 1998
5.35 $\pm$ 1.25		Phillips, Shahbaz & Podsiadlowski 1999
6.70 $\pm$ 1.20	2.50 $\pm$ 0.80	Shahbaz et al. 1999

The rotational velocity enables us to calculate the mass of the compact object in the following way:

Let M₁ be the mass of the compact object and M₂ the mass of the companion star. The mass ratio of the binary is given by q = M₂/M₁. It is assumed that the companion star has filled its Roche lobe, given by:

$\begin{displaymath} \frac{r_L}{a}=\frac{0.49 q^{2/3}}{0.6 q^{2/3}+\ln(1+q^{1/3})}, 0<q<\infty \end{displaymath}$

(1)

(Eggleton 1983), where r_L is the effective Roche lobe radius, a the binary separation. We also assume that the rotation of the companion star is synchronous with the orbital velocity of the binary (Paczynski 1971), leading to the following equation:

$\begin{displaymath} v_{rot}\sin i = (K_2 + K_1)\frac{r_L}{a} = K_2(1+q)\frac{r_L}{a} \end{displaymath}$

(2)

where K₁ and K₂ are the semi-amplitude of the radial velocity curves of the compact object and companion star, respectively, and i is the inclination of the binary. If we know K₂ and $v_{rot}\sin i$ , then using equations (1) and (2) we may calculate q.

The mass function of the companion star, derived from Kepler's Third Law, is given by:

$\begin{displaymath} f(M_{1},M_{2}) \equiv \frac{(M_{1}\sin i)^{3}}{(M_{2}+M_{1})^{2}} \equiv \frac{PK_2^3}{2\pi G} = \frac{M_1\sin^3i}{(1+q)^2} \end{displaymath}$

(3)

where P is the orbital period of the binary and can be found from the radial velocity curve of the companion (optical light curves can also be used to measure P). Together with K₂, i and q, M₁ can then be evaluated from equation (3) and M₂ is found via q.

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