What else may we presume?

Since we know virtually nothing in advance of our star, it makes no solid sense to make any further presumptions. We cannot safely say that the orbit is either circular or elliptical, until we examine the shape of radial velocity curves. We cannot be sure about the temperatures until we examine light curves and measure the color index. We have no idea about the parameters that influence the shape of synthetic curves, such as the inclination, mass ratio or the semi-major axis; we definitely have no clues about the secular changes (time derivatives of the period and the periastron); these are of such perturbative order that it is rarely obvious how to change these values. As the fit brings you closer to the solution, more of the star's nature will be revealed; take it one step at the time.