BEBOP VIII. SOPHIE radial velocities reveal an eccentric, circumbinary brown dwarf

Circumbinary configurations offer a test of planet formation in an altered environment, where the inner binary has perturbed a protoplanetary disc. Comparisons of the physical and orbital parameters between the circumbinary planet population and the population of exoplanets orbiting single stars will reveal how these disc perturbations affect the assembly of planets. Circumbinary exoplanets detected thus far typically have masses $< 3 \,\rm M_{jup}$ raising the question of whether high-mass circumbinary planets are possible, and also whether population features such as the brown dwarf desert would appear in circumbinary configurations like for single star systems. Here, we report observations taken with the SOPHIE high-resolution spectrograph. These observations reveal an $m_{\rm b}\,\sin i_{\rm b} = 20.9 \,\rm M_{jup}$ outer companion, on an eccentric ($e = 0.43$), $1800\,\rm d$ orbit, which we call BEBOP-4 (AB) b. Using dynamical arguments we constrain the true mass $m_{\rm b}< 26.3 \,\rm M_{jup}$. The inner binary's two eclipsing stellar components have masses $M_{\rm A} = 1.51\,\rm M_\odot$, and $M_{\rm B} = 0.46\,\rm M_\odot$. Their orbital period is $72\,\rm d$, and their eccentricity is $0.27$. This system contains the longest period binary surveyed by the BEBOP project. BEBOP-4b is expected to be detectable using Gaia DR4 single epoch astrometric measurements. Despite a large period ratio of $\sim 25:1$, the substantial eccentricities of both orbits mean that the outer orbit is on the edge of orbital stability, and located in between two destabilising secular resonances. Should the outer companion survive, the BEBOP-4 system appears like a precursor to several post-common envelope binaries exhibiting eclipse timing variations where very massive circumbinary companions have been proposed.