Intrinsic Properties of Brown Dwarfs Brown Dwarf Evolution

Stars and brown dwarfs form through the collapse of gaseous material (mainly hydrogen) in giant molecular clouds. As the gas collapses, energy is released leading to increased temperatures in the protostellar core. At the same time, the core density, pC, rises and the material becomes partially degenerate. As the protostar collapses further, degeneracy acts as an energy sink, slowing and eventually curtailing the rise in core temperature, TC. Hydrostatic equilibrium is achieved, and the collapse stops, when the sum of the normal gas pressure and degeneracy pressure is sufficient to balance the gravitational potential. The significant role played by degeneracy in low mass objects ensures that very low-mass stars, brown dwarfs and gas giant exoplanets all have diameters similar to that of Jupiter, Rjup.

The energy released during collapse, and hence TC(max), depends primarily on the protostellar mass, M. Theoretical models predict that objects with solar abundance and M > 0.078 solar masses (M©) become stars; their cores are partially degenerate, but the energy released during collapse is sufficient to achieve central temperatures TC(max) > Tcrit, leading to sustained hydrogen fusion. Objects with solar abundance and total mass M < 0.074M© never reach core temperatures that exceed Tcrit; these objects are brown dwarfs. Protostars with slightly higher masses, in the range 0.074 < < 0.078, achieve temporary core fusion (for ~ 109 to > 1010 years) before degeneracy absorbs sufficient energy to push the temperature below Tcrit. The latter objects are known as transition objects, spending their initial years as stars, but ending their lives as brown dwarfs.

Chemical abundance has a secondary role in defining MBDcrit, the mass threshold that separates brown dwarfs and stars (Burrows et al, 2001). Higher helium abundance, Y, leads to a higher mean molecular weight, smaller radii and higher TC and pC for the same mass; consequently, MBDcrit decreases with increasing Y. Lower metallicity leads to smaller atmospheric opacities, which in turn produces shallower temperature gradients and higher luminosities (less efficient energy retention), and correspondingly lower TC; thus, decreasing [M/H] leads to increased MBDcrit and higher luminosities and temperatures at the H-burning limit. As a specific example, at zero metallicity, MBDcrit ~ 0.092M©, and the H-burning limit lies at Teff ~ 3600K or ~ 1900K hotter than the brown dwarf limit at solar abundances (Burrows et al, 2001).

Lacking a long-lived central energy source, brown dwarfs fade and cool on astronomically rapid timescales. The weak dependence of radius on gravity (mass) and temperature leads to all brown dwarfs following similar trajectories in the (L, Teff) plane. The rate of evolution depends on mass, with higher mass brown dwarfs cooling less rapidly than lower mass objects. Burrows et al (2001) give the approximate relations

where g is gravity and t, age.

Main-sequence stars obey a mass-luminosity relation: higher mass stars are more luminous, with L « M4 5 for M > 1M© and L « M2 5 at lower masses. The similarity in brown dwarf evolutionary tracks means that we cannot estimate the mass of a brown dwarf unless we know its age: in essence, all brown dwarfs have the same luminosity - just at different stages in their careers. However, the longer cooling times for higher-mass brown dwarfs make it likely that most field dwarfs have masses between 0.06M© and the hydrogen-burning limit.

Figures 5.1 and 5.2 illustrate the evolution of solar-abundance low-mass stars and brown dwarfs; the predictions are based on theoretical models computed by the

Low-mass star/brown dwarf models

Low-mass star/brown dwarf models

Brown Dwarf Evolution

Fig. 5.1. Luminosity evolution of brown dwarfs: the evolutionary tracks are from the model calculations by Burrows et al (1993, 1997). The masses range from 0.10 M© (uppermost solid line) to 0.009 Mq (lowest solid line); the latter object is not capable of sustaining deuterium burning, and therefore fades more rapidly over the initial 108 years. The higher mass objects (stars) achieve equilibrium, and constant luminosity, after ~ 300 Myrs; the dotted cyan line and solid green line (0.075M© and 0.070 Mq, respectively) are transition objects that are only capable of sustaining hydrogen fusion for a few billion years.

Fig. 5.1. Luminosity evolution of brown dwarfs: the evolutionary tracks are from the model calculations by Burrows et al (1993, 1997). The masses range from 0.10 M© (uppermost solid line) to 0.009 Mq (lowest solid line); the latter object is not capable of sustaining deuterium burning, and therefore fades more rapidly over the initial 108 years. The higher mass objects (stars) achieve equilibrium, and constant luminosity, after ~ 300 Myrs; the dotted cyan line and solid green line (0.075M© and 0.070 Mq, respectively) are transition objects that are only capable of sustaining hydrogen fusion for a few billion years.

Brown Dwarf Evolution

Age Gyrs

Fig. 5.2. Temperature evolution of brown dwarfs - the models are identical to those shown in Fig. 5.1. The horizontal hatched lines mark the temperatures at the transitions between spectral types M, L, T and (more speculatively) the yet-to-be discovered class Y.

Age Gyrs

Fig. 5.2. Temperature evolution of brown dwarfs - the models are identical to those shown in Fig. 5.1. The horizontal hatched lines mark the temperatures at the transitions between spectral types M, L, T and (more speculatively) the yet-to-be discovered class Y.

Tucson group (Burrows et al., 1993; 1997). Figure 5.1 shows that a brown dwarf with L ~ 10~4Lq could be a 1 Gyr-year old transition object, or a 107-year old planetary-mass brown dwarf. There are spectral indicators that can be employed as crude age/mass discriminators for isolated brown dwarfs, as discussed in the following section.

Three features of the tracks plotted in Figs 5.1 and 5.2 deserve comment: first, the slow decline in Teff and L for ages t < 107 years and masses exceeding ~ 0.013Mq is a consequence of fusion of primordial deuterium, which require TC > 2 x 105K (Salpeter, 1954); second, the 0.075Mq dwarf is a transition object, and the shallower slope between ~ 109 and 1010 years reflects the presence of temporary hydrogen fusion; and, finally, the increasing separation between the M > 0.08Mq models and lower-mass models at t > few x 109 years marks the division between fusion-supported stars and passively cooling brown dwarfs.

120 I. Neill Reid and Stanimir A. Metchev 5.2.2 Observed Characteristics

As a brown dwarf ages and cools, the spectral energy distribution goes through significant changes. The initial temperature 3,000K) corresponds to a mid-type M dwarf, with a spectrum dominated by TiO, VO and metal hydride (MgH, CaH) absorption at optical wavelengths, and water bands in the near infrared. As the surface temperature falls below 2,500K, silicate dust particles condense in the atmosphere, removing TiO and, eventually, VO as significant opacity sources. Metal hydrides (MgH, CaH, FeH) and alkaline absorption lines (Na, K, Cs, Rb) become the most prominent features in the optical and far red, replacing TiO and VO. These objects are L dwarfs (Kirkpatrick et al, 1999), with temperatures cooler than ~ 2, 000K. As the temperature cools below ~ 1, 700K, methane forms in the outer atmosphere, becoming a prominent source of near-IR absorption at temperatures below ~ 1, 300K; these are T dwarfs (Burgasser et al, 2002). At temperatures below ~ 500K, ammonia (NH3) is predicted to make a significant contribution to the near-and mid-IR spectrum (Kirkpatrick, 2005). While no brown dwarf this cool has yet been identified, they have already been assigned a new spectral class, type Y. The spectral changes are illustrated in Figs 5.3 and 5.4 using representative spectra.

The flux distribution of a 2000K black body peaks at ~ 1.5^m. M, L and T dwarfs are far from black bodies, but the bulk of the energy is emitted at near-infrared wavelengths. The presence of strong absorption bands due to water and,

Brown Wavelength

Wavelength (Angstroms)

Fig. 5.3. Optical spectra of L and T-type brown dwarfs. The effective temperature ranges from ~ 2100K at L0 to ~ 900K at T5; the most prominent spectral features are labelled.

Wavelength (Angstroms)

Fig. 5.3. Optical spectra of L and T-type brown dwarfs. The effective temperature ranges from ~ 2100K at L0 to ~ 900K at T5; the most prominent spectral features are labelled.

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Fig. 5.4. Near-infrared spectra of L and T-type brown dwarfs. As in Fig. 5.3, the most prominent spectral features are labelled. Note, in particular, the onset of methane absorption bands that define spectral type T.

at cooler temperatures, methane favours emission in low opacity windows in the spectrum, notably the 1.2^m J band. As a guide, typical mid-type L dwarfs are ~ 10 magnitudes (a factor of 104) brighter at Mj than at visual wavelengths; mid-type T dwarfs, like Gl 229B, are at least ~ 13 magnitudes brighter at Mj than My.

Figure 5.5 shows the empirical (Mj, spectral type) and (Mj, (J-K)) colour-magnitude distributions outlined by low-mass stars and brown dwarfs with accurate parallax measurements. Late-type L dwarfs are exceptionally red at near-infrared wavelengths, rivaled only by carbon stars. The rapid blueward evolution in (J-K) between spectral types L and T reflects the onset of methane absorption, and the consequent suppression of flux in the 2.2^m K passband. The lowest luminosity T dwarfs currently known have Mj ~ 17, 14 magnitudes (or a factor of 400,000) fainter than the Sun at that wavelength. At visual wavelengths, T dwarfs are even fainter, with My ~ 30, or 1010 less luminous than the Sun.

The coolest T dwarfs known have Tef f ~ 700K, while the hottest 'hot Jupiters' are predicted to have temperatures Teff from 1200 to 1500K. Stellar irradiation is likely to affect the temperature/density atmosphere profiles for the latter objects. Nonetheless, there are likely to be substantial similarities in the spectral appearances of late-L and T dwarfs, and gas giants in sub-Mercurian orbits around solar-type stars.

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Spectral Types

Fig. 5.5. The (Mj, (J-K)) and (MJ, spectral type) diagrams defined by low mass stars and brown dwarfs. M dwarfs are plotted as crosses, L dwarfs as solid points and T dwarfs as 5-point stars. M and then L dwarfs become progressively redder in (J-K) as the luminosity and temperature decrease. The onset of methane absorption at spectral type T reduces the flux emitted in the 2.2^m K band and leads to blue colours, comparable with hot A stars (the optical-IR colours for T dwarfs are much redder than A stars). The flux emitted in the J band is enhanced in early-type T dwarfs, leading to significant overlap in Mj with the later-type L dwarfs.

Fig. 5.5. The (Mj, (J-K)) and (MJ, spectral type) diagrams defined by low mass stars and brown dwarfs. M dwarfs are plotted as crosses, L dwarfs as solid points and T dwarfs as 5-point stars. M and then L dwarfs become progressively redder in (J-K) as the luminosity and temperature decrease. The onset of methane absorption at spectral type T reduces the flux emitted in the 2.2^m K band and leads to blue colours, comparable with hot A stars (the optical-IR colours for T dwarfs are much redder than A stars). The flux emitted in the J band is enhanced in early-type T dwarfs, leading to significant overlap in Mj with the later-type L dwarfs.

We can anticipate some spectral differences, however. Most known hot Jupiters have masses less than ~ 2 Jupiter masses3, MJup, while most field brown dwarfs have masses between 60 to 75MJup. Since all of these dwarfs have the same radius, ~ lRJup, the surface gravities differ by factors of 30 to 60. Recent observations of field brown dwarfs have identified a small number with systematically different spectral features: specifically, the objects have unusually strong VO absorption, weaker alkaline atomic lines and weaker hydride bands, and they tend to be redder than average in (J-K) (Kirkpatrick, 2008; Cruz et al, 2008). Spectroscopically, these dwarfs show a greater resemblance to cool giants, strongly suggesting that the anomalous features are indicative of lower gravities, lower masses and relatively young ages. To date, most of these unusual objects are L dwarfs, lying at the upper temperature limit for even hot Jupiters. However, these observations are starting to provide clues about the likely appearance of gas giant exoplanets.

5 The Brown Dwarf - Exoplanet Connection 123 5.2.3 Classifying Brown Dwarfs and Exoplanets

Brown dwarfs have observational properties that overlap with low-mass stars at one extreme and with exoplanets at the other. Brown dwarfs are formally distinguished from stars on the basis that they cannot support long-term sustained core hydrogen fusion. Recently, there have been suggestions that similar criteria should be used to separate brown dwarfs and exoplanets; specifically, Basri (2000) and Oppenheimer et al (2000) have proposed setting the break at the mass threshold for deuterium burning, or ~ 0.013M© for solar abundance objects (Grossman & Graboske, 1973; Saumon et al, 1996).

In principle, the deuterium-burning divisor appears to offer the advantage of a unified classification scheme. However, it is based on a property that is not directly observable, save in systems with multiple objects in known orbits. On the other hand, one might argue that the same arguments apply to hydrogen fusion: while the presence of primordial lithium is a key test for low mass brown dwarfs (Rebolo et al, 1992), in most cases the status of an object as a brown dwarf or a star is based on its observed temperature and luminosity, and there can be ambiguities in classification.

The Basri/Oppenheimer proposal, however, sets aside the traditional approach of classifying objects based on how they form: stars and brown dwarfs through core collapse in molecular clouds (Bodenheimer et al, 1980; Padoan & Nordlund, 2004); planets through core accretion (Lissauer & Stewart, 1993) or gravitational instabilities (Boss, 2002) within circumstellar disks. This difference in origin is likely to lead to significant differences in chemical composition, as can be seen in the Solar System, where the non-solar composition of Jupiter and Saturn is radically different from the ice giants, Uranus and Neptune. Corresponding changes in the emergent spectral energy distribution may be subtle, but the higher mean molecular weights lead to significant variations in the mean density and the mass-radius relation. The latter effects are already evident in the range of intrinsic properties deduced for transiting exoplanets (Fortney, Marley & Barnes, 2007).

Thus, formation within a disk does have observable consequences. Indeed, there are likely to be fewer ambiguities under this classification system than relying on an arbitrary, and essentially unmeasureable, mass limit that applies to all very low-mass objects. Moreover, identifying isolated < 0.013M© objects as "planets" or even "exoplanets" is likely to add further unnecessary post-Pluto confusion about that term among the lay public. We prefer to preserve the traditional terminology, and distinguish brown dwarfs and planets on the basis of their formation mechanism. We therefore choose to classify objects such as the recently discovered 2MASSW J1207334-393254B (2M1207-39B), AB Pic B, GQ Lup B and SCRF 1845B as low mass brown dwarfs, not exoplanets.

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