Photometric Determination of Unresolved Main-sequence Binaries in the Pleiades: Binary Fraction and Mass Ratio Distribution

Accurate determination of binary fractions ($f_{\rm b}$) and mass ratio ($q$) distributions is crucial for understanding the dynamical evolution of open clusters. We present an improved multiband fitting technique to enhance the analysis of binary properties. This approach enables an accurate photometric determination of $f_{\rm b}$ and $q$ distribution in a cluster. The detectable mass ratio can be down to the $q_{\rm lim}$, limited by the minimum stellar mass in theoretical models. First, we derived an empirical model for magnitudes of Gaia DR3 and 2MASS bands that match the photometry of single stars in the Pleiades. We then performed a multiband fitting for each cluster member, deriving the probability density function (PDF) of its primary mass ($\mathcal{M}_1$) and $q$ in the Bayesian framework. 1154 main-sequence (MS) single stars or unresolved MS+MS binaries are identified as members of the Pleiades. By stacking their PDFs, we conducted a detailed analysis of binary properties of the cluster. We found the $f_{\rm b}$ of this sample is $0.34 \pm 0.02$. The $q$ distribution exhibits a three-segment power-law profile: an initial increase, followed by a decrease, and then another increase. This distribution can be interpreted as a fiducial power-law profile with an exponent of -1.0 that is determined in the range of $0.3 < q < 0.8$, but with a deficiency of binaries at lower $q$ and an excess at higher $q$. The variations of $f_{\rm b}$ and $q$ with $\mathcal{M}_1$ reveal a complex binary distribution within the Pleiades, which might be attributed to a combination of primordial binary formation mechanisms, dynamical interactions, and the observational limit of photometric binaries imposed by $q_{\rm lim} (\mathcal{M}_1)$.