Unresolved multiple stars and Galactic clusters' mass estimates

If not properly accounted for, unresolved binary stars can induce a bias in the photometric determination of star cluster masses inferred from star counts and the luminosity function. A correction factor close to 1.15 (for a binary fraction of 0.35) was found in \citep{Boro19}, which needs to be applied to blind photometric mass estimates. This value for the correction factor was found to be smaller than literature values. In an attempt to lift this discrepancy, in this work the focus is on higher order multiple stars with the goal of investigating the effect of triple and quadruple systems adopting the same methodology and data-set as in the quoted work. Then the result is found that when triple and quadruple together with binary systems are properly accounted for, the actual cluster mass (computed as all stars were single) should be incremented by a factor of 1.18$-$1.27, depending on the cluster and when the binary fraction $\alpha$ is 0.35. Fitting formulae are provided to derive the increment factor for different binary star percentages.