Detail Discuss on How to Obtain Binary Fractions

1. Detail Discuss on How to Obtain Binary Fractions

2. Introduction • Without photometric errors, existence of blending and binaries, the observed stars of a star cluster will exactly lie on their theoretic isochrone on CMD. • Photometric errors broaden isochrone symmetrically on CMD, while the blending and binaries affect it asymmetrically in the same way, to redward. • It is not enough to obtain binaries from photometric results unless artificial star experiments are applied.

3. Completeness • In compact environment, blending is a major reason for incompleteness. Add stars randomly on the images and count the recovered stars, completeness factor can be obtained. • However, the star s added can be either a single or a binary. This is the key idea for the method introduced as following.

4. Method • To study binary fraction of star clusters, the key step is that to generate synthetic artificial star catalogs, in which the artificial stars must have the similar level of crowding (so similar blending probabilities) and errors as the observed companies. Then we can adjust the two parameters (binary fraction and mass ratio distribution) of input artificial stars, and compared with the observation • See Rubenstein & Bailyn (1997), Bellazzini et al (2002) and Zhao & Bailyn (2005) for more detail discuss.

9. Method discuss • Artificial stars are made to blend with observed stars rather than let them blend with each other. The advantage is that we have no need to know the spatial distribution of stars, but the chance of superposition of the fake star is automatically included. • MSRL (main-sequence ridgeline) is defined as the mode of each magnitude bin. So it is not model-dependent as the theoretical isochrone do. The results are sensitive to which line to compare as reference.