All Tables

Table 1: The distribution of stars over main-sequence spectral type for the Kroupa and Salpeter mass distributions (BD = brown dwarfs).
Table 2: The mass ratio distribution resulting from different pairing functions, for different samples, as compared to the generating mass ratio distribution h_q(q).
Table 3: The specific binary fraction $\mathcal{B}_{M_1}(M_1)$ as compared to the generating binary fraction $\mathcal{B}$ , for different the pairing functions.
Table 4: Do the properties of a population resulting from a certain pairing function depend on its generating properties? The three generating properties f_M(M), f_q(q) and $\mathcal{B}$ are listed in the top row. For each of the ten quantities listed in the left-most column, we list whether or not they depend on the choice of f_M(M), f_q(q) and $\mathcal{B}$ . We indicate dependence and independence with the symbols $\surd$ and $\times$ , respectively. The results for f_q;M₁(q) and $\mathcal{B}_{M_1}(M_1)$ are valid only for a population of binaries with identical primary mass M₁. The distribution over total system mass $f_{M_{\rm T}}$ includes both binary systems and single stars.
Table 5: Suppose that a stellar population has an observed mass ratio distribution $f_{q,{\rm obs}}(q) =1$ for $q_{\rm min}< q \leq 1$ . What is the pairing function and the generating mass distribution f_q(q)? This table lists the exponent $\gamma _q$ of the generating mass distribution $f_q(q)\propto q^{\gamma _q}$ that is most compatible with the synthetic observations.
Table A.1: The specific mass ratio distribution f_q(q) for pairing function SCP-I, resulting from a power-law generating mass distribution f_m(m) and a uniform generating mass ratio distribution h_q(q). See Appendix A.4.3 for details.
Table A.2: The specific mass ratio distribution f_q(q) for pairing function SCP-II, resulting from a power-law generating mass distribution $f_{\rm m}(m)$ and a uniform generating mass ratio distribution h_q(q). See Appendix A.4.3 for details.
Table A.3: The specific binary fraction $\mathcal{B}_{M_1}(M_1)$ for the nine pairing functions described in this paper, resulting from a power-law mass distribution f_M(M) and a uniform mass ratio distribution h_q(q). See Appendices A.1-A.4 for a detailed description, and Fig. 7 for a visualisation.