The 19th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun Edited by G. A. Feiden Relation between Brown Dwarfs and Exoplanets Lauren Melissa Flor Torres1, Roger Coziol1, Klauss-Peter Schröeder1, César A. Caretta1 and Dennis Jack1 1 Departamento de Astronomía, Universidad de Guanajuato, Guanajuato, México Abstract One of the most debated subjects in Astronomy since the discovery of exoplanets is how can we distinguish the most massive of such objects from very-low mass stars like Brown Dwarfs (BDs)? We have been looking for evidences of a diﬀerence in physical characteristics that could be related to diﬀerent formation processes. Using a new diagnostic diagram that compares the baryonic gravitational potential (BGP) with the distances from their host stars, we have classiﬁed a sample of 355 well- studied exoplanets according to their possible structures. We have then compared the exoplanets to a sample of 87 conﬁrmed BDs, identifying a range in BGP that could be common to both objects. By analyzing the mass-radius relations (MRR) of the exoplanets and BDs in those diﬀerent BGP ranges, we were able to distinguish diﬀerent characteristic behaviors. By comparing with models in the literature, our results suggest that BDs and massive exoplanets might have similar structures dominated by liquid metallic hydrogen (LMH). 1 Introduction The most accepted interpretation of Brown Dwarfs (BDs) is that they are failed stars (Cushing, 2014), because, although it is assumed they formed like stars, their masses are too small to permit the fusion of hydrogen in their nucleus. This characteristic allows to separate BDs from main sequence stars based on their masses: because a star must reach a crit- ical mass to be able to burn its hydrogen, which varies from 0.07 M⊙for solar metallicity to 0.09 M⊙for lower metal- licities (Burrows et al., 2001), any star with a mass < 70 MJ (where MJ is the mass of Jupiter) is a BD (Bate, 2006). However, determining a lower mass limit for a BD is more diﬃcult. In practice, the consensus to adopt the critical mass for the fusion of deuterium, which is around 13 MJ (Bate, 2006), is arbitrary, because theoretically the lowest mass a BD could have may be just a few MJ (Larson, 1969; Rees, 1976; Silk, 1977a,b; Boss, 1988). Interestingly, this mass is also typical of massive exoplanets, and, since there is no obvious upper-mass limit for an exoplanet, hence, persists the prob- lem of distinguishing between to two objects. In this poster, using a large sample of “well-studied” exo- planets, and comparing with a large sample of “conﬁrmed” BDs available in the literature, we probe a mass range com- mon to both classes of objects, looking for evidence of a dif- ference between their respective physical structures, as re- ﬂected by their mass-radius relations (hereafter MRRs). Our study concentrates on two questions: 1) At what mass boundary should we expect to see a variation in the MRR that would be consistent with a diﬀerence of structure be- tween exoplanets and BDs? 2) Is there a special intermedi- ate mass range where these two classes of objects are likely to overlap in mass? In particular, we propose a lower-mass limit for BDs based on the Self-Gravitating (SG) limit, which marks the moment the self-gravity of matter begins to aﬀect signiﬁcantly the structure of a body (Padmanabhan, 1993). In addition to the MRR, the distance of a planet from its host star could also reveal something about its formation pro- cess (Lissauer, 1993). For the exoplanets, this last parame- ter is fundamental to identify Hot Jupiters (Johnson, 2009), while for the BDs, this parameter can be used to test the “BD’s desert” hypothesis, which according to some authors (e.g., Grether & Lineweaver, 2006) might be related to diﬀer- ent formation processes for exoplanets and BDs. 2 Samples Our sample of exoplanets consists of 355 entries in the lat- est issue of the transiting planets catalog available at TEP- Cat1, and can be co