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What do these apparent discontinuities in the IMF and the CMF tell us about the validity of several proposed scenarios of VLM star and brown dwarf formation? We review the principal formation scenarios following the discussion in the review article of Luhman (2012), and then evaluate how well each of these scenarios explains the general properties of the IMF and the CMF noted above.

Core Fragmentation. In this scenario, collapsing gas in a molecular cloud forms denser cores that then fragment into multiple cores of different masses. Subsequent accretion is dominated by the more massive cores and the less massive cores eventually form brown dwarfs (Bonnell et al. 2008).

Core Ejection. Some protostellar objects are ejected from a star forming region via dynamical interactions with other objects or due to the natural velocity dispersion within a cluster. The ejection stops the accretion process (Reipurth & Clarke 2001).

Photoionization. Radiation from a nearby hot O or B star dissipates the inter-stellar medium in the vicinity of a low mass accreting core, thus halting the accretion process (Hester et al. 1996; Whitworth & Zinnecker 2004).

Disk Instability. In a manner similar to planet formation, localized instabilities in an accretion disk around a star cause some gas to collapse and form a proto-stellar core (e.g., Thies et al. 2010; Stamatellos et al. 2011)

In addition to these four processes, Bate (2011) notes that hydrodynamic cloud collapse simulations (Bate 2009, 2011) are in good agreement with the stellar IMF and stellar CMF, but overproduce the number of brown dwarfs unless radiative feedback is incorporated into the model (Bate 2011). The last model produces a cluster of stars and brown dwarfs whose statistical properties are very similar to those of observed young clusters, suggesting that radiative feedback is indeed an important mechanism in brown dwarf formation. A significant problem with this idea is the lack of a clear mechanism through which feedback is ignited only in stellar objects. At ages of a few Myr, the vast majority of an object’s luminosity comes from the release of internal gravitational energy, so the onset of hydrogen burning would have a negligible effect on overall luminosity (Chabrier & Baraffe 1997). Also, while studies such as those by Jayawardhana et al. (2003), Bouy et al. (2008), and Comer´on et al. (2010) show that there is some evidence for late accretion that is still happening at the time of hydrogen

ignition around 3−5 Myr (Chabrier & Baraffe 1997), the bulk of accretion happens in the

first million years, where stellar and substellar objects are virtually indistinguishable.

4.6.1, and Chapter 2 can be summarized as follows: 1. Stars significantly outnumber brown dwarfs.

2. There is evidence for a discontinuity in the IMF, CMF and other companion properties at masses close to the HBMM.

3. Stellar/substellar binaries are rare regardless of the characteristics of the more massive component.

4. Substellar binaries tend to have high mass ratios. 5. Wide separation substellar binaries are rare.

Core fragmentation has the potential of producing objects over a wide range of masses, both stellar and substellar. If accretion continues after the initial fragmentation and is then halted by radiative feedback, as proposed by Bate (2011), it could explain why there exist more stars than brown dwarfs. However, core fragmentation offers limited insights into the binary properties, with no apparent mechanism for favoring high mass ratio binaries and preventing the creation of stellar/substellar pairs. Disk instability is generally thought to produce lower mass companions in the planetary mass range. Because the matter available in an accretion disk is roughly proportional to the mass of the accreting star, brown dwarf formation through disk instability would imply that high mass stars are more likely to have brown dwarf companions. This assertion is refuted by the invariability of the brown

dwarf desert argued in §4.4. Core ejection and photoionization are both mechanisms where

would explain why high mass ratio binaries are more common amongst brown dwarfs, as the mechanism halting accretion would have the same effect on both components of the binary. The potential for dynamical disruption during core ejection would also explain why close separation binaries with higher binding energies are more common. However, the ideas of core fragmentation and core ejection have problems of their own. There is no evidence for the spatial segregation of brown dwarfs that would happen as a consequence of core ejection. Luhman (2012) also note that the mass function of brown dwarfs in young clusters does not appear to be altered by the presence of hot O stars, thus providing evidence against the photoionization scenario.

The above discussion shows that while the binary properties of VLM stars and brown dwarfs may be explained by formation through core ejection or photoionization, a look at the broader implications of the proposed mechanisms of VLM star and brown dwarf formation still leads to largely inconclusive results. The results discussed in this chapter place constraints in the theory in the sense that any viable candidate theory of star and brown dwarf formation must now explain the existence of a brown dwarf desert that exists even at relatively high mass ratios in the case of M star primaries. However, substantial questions regarding formation still exist, and the available data are still not sufficient to clearly differentiate amongst the proposed models for brown dwarf and VLM star formation.

The HLIMIT Survey − Overview and Observations

This chapter as well as Chapter 6 are based on “The Solar Neighborhood XXXII: The

Hydrogen Burning Limit” (Dieterich et al. 2014).

5.1 Introduction

The first comprehensive stellar structure and evolution models for the low mass end of the

main sequence were published in the late 20th_{century (e.g., Burrows et al. 1993; Baraffe et al.}

1995, §2.3). While the predictions of these models are widely accepted today, they remain

largely unconstrained by observations. The problem is particularly noteworthy when it comes to the issue of distinguishing the smallest stars from the substellar brown dwarfs. While the internal physics of stars and brown dwarfs is different, their atmospheric properties overlap in the late M and early L spectral types, thus making them difficult to distinguish based on photometric and spectroscopic features alone. One test used to identify substellar

objects − the lithium test (Rebolo et al. 1992)− relies on the fact that lithium undergoes

nuclear burning at temperatures slightly lower than hydrogen, and therefore should be totally consumed in fully convective hydrogen burning objects at time scales much less than their

evolutionary time scales. Detection of the LiIλ6708 line would therefore signal the substellar

nature of an object. This is a powerful test, but it fails us when we most need it. While

evolutionary models predict the minimal stellar mass to be anywhere from 0.07M⊙to 0.08M⊙

(§6.7.3), the lithium test only works for masses .0.06M⊙ due to the lower mass at which

The models for low mass stars and brown dwarfs in current usage (Burrows et al. 1993, 1997; Baraffe et al. 1998; Chabrier et al. 2000; Baraffe et al. 2003) predict the end of the

stellar main sequence at temperatures ranging from 1550−1750K, corresponding roughly

to spectral type L4. These models have achieved varying degrees of success, but as we

discuss in §6.7.3, are mutually inconsistent when it comes to determining the properties

of the smallest possible star. The inconsistency is not surprising given that none of these decade-old evolutionary models incorporates the state-of-the-art in atmospheric models, nor do they account for the recent 22% downward revision in solar abundances (Caffau et al.

2011), which are in agreement with the results of solar astero-seismology1_.

Over the last ten years, few changes were made to evolutionary models for VLM stars and brown dwarfs in large part because the models provide predictions that are not directly observable. Whereas an atmospheric model can be fully tested against an observed spectrum, testing an evolutionary model requires accurate knowledge of mass, age, and metallicity as well as an accurate atmospheric model that serves as a boundary condition.

The problem of understanding the stellar/substellar boundary can essentially be formu-

lated by posing two questions. The first one is: “What do objects close to either side of the

stellar/substellar boundary look like to an observer?” The second question is: “What are the masses and other structural parameters of objects on either side of the stellar/substellar boundary?” While it is the second question that usually gets the most attention, we note that any attempt to determine masses at the stellar/substellar boundary assumes an inher-

1_{A review of the history of revisions to solar abundances, including issues related to solar astero-}

ently model dependent (and therefore possibly flawed) answer to the first question. What is needed is an observational test that relies as little on evolutionary models as possible. Prior to describing the methods used to attack the problem in this study, we describe several pos- sible ways of addressing the first question with minimal reliance on modeling, and highlight each test’s strengths and weaknesses.