Binding energy & binary separation vs. stellar mass of VLM binaries

(a) System Binding Energy versus Total Mass (primary + secondary) and (b) Binary Separation versus Total Mass is shown. The newly discovered binary system LP 1033-31 AB (shown as LP1) has been indicated with red solid circle. Another detected binary system LP 877-72 AB (shown as LP8) and indicated with blue solid triangle. The estimated uncertainties have also shown for both the systems. For LP 1033-31 AB, the uncertainties are clearly visible, whereas for LP 877-72 AB, the uncertainties are smaller than the size of the symbols.

Figure legend: [1]: Fischer & Marcy (1992) and Reid & Gizis (1997); [2]: VML archive, Burgasser et al. (2007b) and Siegler et al. (2005); [3]: Caballero et al. (2006) and Caballero (2007a, b, 2009); [4]: Luhman et al. (2009), Luhman (2012), Dhital et al. (2010), and Mužić et al. (2012); [5]: Burningham et al. (2010); [6]: Faherty et al. (2010) and Baron et al. (2015); [7]: Ross 458 AB, Beuzit et al. (2004) and Goldman et al. (2010); [8]: HIP 78530 AB, Lafrenière et al. (2011); [9]: Janson et al. (2012); [10]: Deacon et al. (2014); and [11]: Gálvez-Ortiz et al. (2017).

In the panel (a), we have overplotted the minimum binding energy line from Zuckerman & Song (2009) (red solid line) and the two lines showing the Jeans length criteria for mass ratio q = 1.0 (blue dot–dashed line) and q = 0.1 (blue–dashed line) adopted from Faherty et al. (2010).

In the panel (b), the empirical limit for stability stated by Reid et al. (2001) (black dot–dashed line) and by Burgasser et al. (2003) (red solid line) has been shown. We also overplot the lifetime isochrones suggested by Dhital et al. (2010) with data of Close et al. (2007) and Weinberg et al. (1987) equations for dissipation times of 1, 2, and 10 Gyr (blue dashed lines). Both the systems LP 1033-31 AB and LP 877-72 AB being well above the minimum-binding energy lines in (a) as well as the stability limits in (b) signify that both systems are stable.

[Image Credit: Karmakar et al. (2020)]