# Study of the Mass-Ratio Distribution of Spectroscopic Binaries. II. The Boundaries of the Brown-Dwarf Desert as Seen with the APOGEE Spectroscopic Binaries

## TL;DR

This study confirms the existence of the Brown-Dwarf Desert in spectroscopic binaries and delineates its boundaries using APOGEE data, revealing a mass ratio distribution that varies with orbital period and suggesting different formation scenarios.

## Contribution

It introduces a new algorithm to analyze the mass-ratio distribution of spectroscopic binaries and refines the boundaries of the Brown-Dwarf Desert based on APOGEE observations.

## Key findings

- The Brown-Dwarf Desert exists for short-period binaries with companion masses 0.02-0.2 M_sun.
- Long-period binaries show a linear increase in low-q systems, indicating no dearth.
- The boundaries of the desert may have a wedged or trapezoidal shape, not matching traditional mass limits.

## Abstract

Analysis of APOGEE DR12 stellar radial-velocities by Troup et al. (2016) affirmed the existence of the well-known Brown-Dwarf Desert (BDD). They detected a dearth of spectroscopic binaries (SB) with periods shorter than $\sim 10$ - $30$ days and secondaries with masses in the range of $\sim0.01$ - $0.1\, M_{\odot}$. We reconsider here their sample of binaries, focusing on 116 systems on the main sequence of the Gaia color-magnitude diagram, with mostly K-dwarf primaries. Using our recently devised algorithm to analyze the mass-ratio distribution of a sample of SBs we confirm the BDD existence and delineate its boundaries. For the K-dwarf APOGEE $1$ - $25$ days binaries, the companion-mass range of the BDD is $\sim0.02$ - $0.2\, M_{\odot}$. The mass ratio distribution of the long-period ($25$ - $500$ days) binaries does not show any dearth at the $q$-range studied. Instead, their distribution displays a linear increase in $\log q$, implying a tendency towards low-$q$ values. The limits of the BDD do not coincide with the frequently used mass limits of the brown-dwarf population, sometimes defined as $0.013$ and $0.08\, M_{\odot}$, based on theoretically derived stellar minimum masses for burning deuterium and hydrogen in their cores. Trying to draw the boundaries of the desert, we suggest either a wedged or trapezoidal shape. We discuss briefly different scenarios that can account for the formation of the BDD, in terms of differentiating between stellar secondaries and planets in particular, and compare this desert to the Neptunian desert that can distinguish between Jovian planets and super Earths of short periods.