The Evolution of L and T Dwarfs in Color‐Magnitude Diagrams

“We use the elemental abundances of Lodders (2003).”

“Figures 2 and 3 compare our cloudless sequence with the COND03models of Baraffe et al. (2003) and our cloudy fsed ¼ 2 sequence with the DUSTY00 models of Chabrier et al. (2000b) and Baraffe et al. (2002), respectively.”

“3Heþ : ð5Þ We use the nuclear reaction cross sections from the NACRE database (Angulo et al. 1999) and apply the screening corrections developed by Chabrier, which include both ionic and electronic screening (Saumon et al. 1996; Chabrier & Baraffe 1997; G. Chabrier 1999, private communication).”

“…of isolated brown dwarfs—a relatively simple case of stellar evolution—has been studied extensively for the past 20 years and is well understood (D’Antona & Mazzitelli 1985; Nelson et al. 1986; Burrows et al. 1989, 1997; Burrows & Liebert 1993; Chabrier et al. 2000a, 2000b; Baraffe et al. 2002).”

“For these evolution sequences with solar metallicity atmospheres, the minimum hydrogen-burning mass, defined by objects that reach stable H burning at an age of 10 Gyr, is 0.075M , where TeA ¼ 1910 K for the cloudless sequence.”

“Our chemical equilibrium grid of molecular, atomic, and ionic abundances as a function of temperature, pressure, and metallicity is based on the work of Fegley & Lodders (1994,1996), Lodders (1999, 2002), and Lodders & Fegley (2002, 2006).”

“For a 10 Gyr old brown dwarf of 0.06 M , we find a luminosity that is 0.104 dex lower than that of Baraffe et al. (2003), which is in perfect agreement with the value given in Chabrier et al. (2000b) for the change in luminosity brought by introducing conduction in the evolution.”

“Our thermal radiative transfer follows the source function technique of Toon et al. (1989) allowing inclusion of arbitrary Mie scattering particles in the opacity of each layer.”

“Our baseline cloud model (Ackerman & Marley 2001) parameterizes the efficiency of sedimentation of cloud particles through an efficiency factor, fsed.”

“Baraffe et al. (2002) have shown that the evolution of brown dwarfs is quite sensitive to the choice of initial state for ages under 1Myr.”

“The agreement is not as good as we found with the COND03models (Fig.”

“The availability of parallaxes for brown dwarfs (Dahn et al. 2002; Tinney et al. 2003; Vrba et al. 2004) provides absolutemagnitudes and spectral fluxes that can be compared with a combination of evolution models and synthetic spectra and colors.”

“Tsuji & Nakajima (2003), Knapp et al. (2004), and Burrows et al. (2006) have suggested that variations in gravity (i.e., a spread in mass and age) account for the broadening.”

“The model has been very successful when applied to the atmospheres of brown dwarfs and Jupiter (Ackerman &Marley 2001; Knapp et al. 2004; Golimowski et al. 2004).”

“Our atmosphere models have been described previously (McKay et al. 1989; Marley et al. 1996, 2002; Burrows et al. 1997; Marley & McKay 1999) and used in several detailed comparisons with data (Marley et al. 1996, 2002; Roellig et al. 2004; Saumon et al. 2006, 2007; Leggett et al. 2007b; Mainzer et…”

“Our opacity database, accounting for all important absorbers, is described in Freedman et al. (2008).”

“Our chemical equilibrium grid of molecular, atomic, and ionic abundances as a function of temperature, pressure, and metallicity is based on the work of Fegley & Lodders (1994,1996), Lodders (1999, 2002), and Lodders & Fegley (2002, 2006).”

“The breadth of the late-M and early-L distribution is comparable to the scatter caused by variations in gravity, supporting the idea that the latter is indeed the second parameter of the sequence (Tsuji & Nakajima 2003; Burrows et al. 2006).”

“While the observational evidence is consistent with a roughly flat SFR over the age of the Galaxy (Allen et al. 2005), we consider an exponentially decreasing SFRwith a characteristic timescale of ¼ 5 Gyr (Miller & Scalo 1979).”

“…(McKay et al. 1989; Marley et al. 1996, 2002; Burrows et al. 1997; Marley & McKay 1999) and used in several detailed comparisons with data (Marley et al. 1996, 2002; Roellig et al. 2004; Saumon et al. 2006, 2007; Leggett et al. 2007b; Mainzer et al. 2007; Blake et al. 2007; Cushing et al.…”

“The availability of parallaxes for brown dwarfs (Dahn et al. 2002; Tinney et al. 2003; Vrba et al. 2004) provides absolutemagnitudes and spectral fluxes that can be compared with a combination of evolution models and synthetic spectra and colors.”

“…number of gas and condensate species (Allard et al. 2001; Lodders 2002), increasingly complete molecular opacity databases (Freedman et al. 2008; Sharp & Burrows 2007), extreme resonance line broadening (Burrows et al. 2000; Allard et al. 2005), and particulate cloud models (Allard et al. 2001;…”

“…of the role of the K i and Na i resonance doublets at optical wavelengths (Burrows et al. 2000), (2) improved H2 CIA opacity (Borysow et al. 2001; Borysow 2002), (3) a new line list for TiO (Allard et al. 2000; Freedman et al. 2008), (4) improved modeling of the condensation chem- istry (Lodders…”

“Particularly significant changes in cloudless models since the work of Marley et al. (1996) are (1) the recognition of the role of the K i and Na i resonance doublets at optical wavelengths (Burrows et al. 2000), (2) improved H2 CIA opacity (Borysow et al. 2001; Borysow 2002), (3) a new line list…”

“Detailed spectral analysis of brown dwarfs with unusual J K colors for their spectral types have more extreme cloud parameters (Burgasser et al. 2008; Cushing et al. 2008; Stephens et al. 2008), which strongly suggests that cloudiness is the second parameter.”

“Our chemical equilibrium grid of molecular, atomic, and ionic abundances as a function of temperature, pressure, and metallicity is based on the work of Fegley & Lodders (1994,1996), Lodders (1999, 2002), and Lodders & Fegley (2002, 2006).”

“Here we have recomputed the cooling with the hybrid boundary condition which results in features in the evolution that could not occur within the Chabrier (2002) and Burgasser et al. (2002) schemes.”

“Our chemical equilibrium grid of molecular, atomic, and ionic abundances as a function of temperature, pressure, and metallicity is based on the work of Fegley & Lodders (1994,1996), Lodders (1999, 2002), and Lodders & Fegley (2002, 2006).”

“The effect of atmospheric opacity on the cooling of brown dwarfs is also well known (Burrows et al. 1993; Burrows & Liebert 1993; Chabrier & Baraffe 2000; Chabrier et al. 2000b), and a comparison of the cloudy and cloudless sequences shows the expected trends.”

“Themodel atmospheres used in B97 are the nongray cloudless models of Marley et al. (1996) complemented with gray cloudless models at the higher TeA (Saumon et al. 1996).”

“This was confirmed by the discovery of binary brown dwarfs with (coeval) components spanning the L/T transition and showing the J-band flux reversal (Burgasser et al. 2006; Liu et al. 2006).”

“Our atmosphere models have been described previously (McKay et al. 1989; Marley et al. 1996, 2002; Burrows et al. 1997; Marley & McKay 1999) and used in several detailed comparisons with data (Marley et al. 1996, 2002; Roellig et al. 2004; Saumon et al. 2006, 2007; Leggett et al. 2007b; Mainzer et…”

“The screening correction (Graboske et al. 1973) is more crude, but this only affects models at the edge of the main sequence.”

“It is supported by the lowTeA found for two transition brown dwarf companions of young main-sequence stars, HD 203030B (Metchev & Hillenbrand 2006) and HN Peg B (Luhman et al. 2007).”

“99+011613.0, whose SED favors a model with fsed ¼ 4 (Stephens et al. 2008).”

“The importance of binaries in brown dwarf population synthesis has been pointed out by Chabrier (2002) and Burgasser (2007).”

“The relevant parameters of the cluster are its distance (134 3 pc; Percival et al. 2005), age ( 100Y120 Myr; Martı́n et al. 1998), metallicity (½Fe/H ¼ 0:034 0:024; Boesgaard & Friel 1990), and extinction [E(V I ) ¼ 0:06; Stauffer & Hartmann 1987].”

“Lithium burning is a useful age/mass diagnostic of brown dwarfs (Rebolo et al. 1992; Basri 2000) but contributes negligibly to nuclear energy production and is not included in our code.”

“The relevant parameters of the cluster are its distance (134 3 pc; Percival et al. 2005), age ( 100Y120 Myr; Martı́n et al. 1998), metallicity (½Fe/H ¼ 0:034 0:024; Boesgaard & Friel 1990), and extinction [E(V I ) ¼ 0:06; Stauffer & Hartmann 1987].”

“Our chemical equilibrium grid of molecular, atomic, and ionic abundances as a function of temperature, pressure, and metallicity is based on the work of Fegley & Lodders (1994,1996), Lodders (1999, 2002), and Lodders & Fegley (2002, 2006).”

“Our chemical equilibrium grid of molecular, atomic, and ionic abundances as a function of temperature, pressure, and metallicity is based on the work of Fegley & Lodders (1994,1996), Lodders (1999, 2002), and Lodders & Fegley (2002, 2006).”

“…2001; Lodders 2002), increasingly complete molecular opacity databases (Freedman et al. 2008; Sharp & Burrows 2007), extreme resonance line broadening (Burrows et al. 2000; Allard et al. 2005), and particulate cloud models (Allard et al. 2001; Ackerman&Marley 2001; Tsuji 2002; Helling et al. 2008).”

“Nuclear Energy Generation Nuclear energy generation in low-mass stars and brown dwarfs is quite simple and is reduced to one branch of the p-p chain (Burrows & Liebert 1993): pþ p ! d þ eþ þ e; ð4Þ pþ d !”

“In addition to the input mass and age distributions, the synthetic population is drawn from the observed distribution inmetallicity of 253Mdwarfs (Casagrande et al. 2008) spanning 0:9 ½M/H 0:3 with an average of 0:20 0:22.”

“…(1) the recognition of the role of the K i and Na i resonance doublets at optical wavelengths (Burrows et al. 2000), (2) improved H2 CIA opacity (Borysow et al. 2001; Borysow 2002), (3) a new line list for TiO (Allard et al. 2000; Freedman et al. 2008), (4) improved modeling of the condensation…”

“The rather simplistic cloud models developed so far are not adequate for understanding the cause of the transition, and the complex dust formation model of Helling et al. (2008) has not been applied to modeling the L/T transition.”

“This is confirmed by detailed spectral analysis of unusually red and blue J K colors with our synthetic spectra, showing that L dwarfs span a range of fsed ¼ 1Y3 (Burgasser et al. 2008; Cushing et al. 2008; Stephens et al. 2008), with the redder dwarfs having lower values of fsed.”

“The importance of using realistic, nongray atmosphere models for the surface boundary condition of very low mass stars and brown dwarfs has been emphasized for some time (Saumon et al. 1994; Chabrier & Baraffe 1997).”

“Finally, there are indications that the nearby field brown dwarfs may be a relatively young population (Allen et al. 2005; Metchev & Hillenbrand 2006; Liu et al. 2008; Cruz et al. 2008), which would decrease the typical gravity compared to our simulation, increase the effect of clouds, and move the…”

“Deep surveys have established that its low-mass stellar and substellar population can be reproduced by a power-law IMF with an index of 0:6 (Moraux et al. 2003; Bihain et al. 2006).”

“This was confirmed by the discovery of binary brown dwarfs with (coeval) components spanning the L/T transition and showing the J-band flux reversal (Burgasser et al. 2006; Liu et al. 2006).”

“Lithium burning is a useful age/mass diagnostic of brown dwarfs (Rebolo et al. 1992; Basri 2000) but contributes negligibly to nuclear energy production and is not included in our code.”

“The pioneering work of Chabrier (2002) and the extensive studies of Burgasser (2004) and Allen et al. (2003, 2005) show how variations in the IMF and SFR affect one-dimensional distribution functions (such as the luminosity function) of field brown dwarfs.”

“The importance of binaries in brown dwarf population synthesis has been pointed out by Chabrier (2002) and Burgasser (2007).”

“Since there is evidence that the local BD population has a younger average age than solar-type stars (Allen et al. 2005;Metchev&Hillenbrand 2006; Zapatero Osorio et al. 2007; Liu et al. 2008; Cruz et al. 2008), we consider a SFR where all BDs were formed at a constant rate in the past 5 Gyr (Fig.”

“99+011613.0, whose SED favors a model with fsed ¼ 4 (Stephens et al. 2008).”

“The pioneering work of Chabrier (2002) and the extensive studies of Burgasser (2004) and Allen et al. (2003, 2005) show how variations in the IMF and SFR affect one-dimensional distribution functions (such as the luminosity function) of field brown dwarfs.”

“These evolution sequences have already been applied extensively to the analysis of brown dwarf observations (Roellig et al. 2004; Saumon et al. 2006, 2007; Leggett et al. 2007a, 2007b; Cushing et al. 2008) but have not been discussed in any detail.”

“…of isolated brown dwarfs—a relatively simple case of stellar evolution—has been studied extensively for the past 20 years and is well understood (D’Antona & Mazzitelli 1985; Nelson et al. 1986; Burrows et al. 1989, 1997; Burrows & Liebert 1993; Chabrier et al. 2000a, 2000b; Baraffe et al.…”

“Our chemical equilibrium grid of molecular, atomic, and ionic abundances as a function of temperature, pressure, and metallicity is based on the work of Fegley & Lodders (1994,1996), Lodders (1999, 2002), and Lodders & Fegley (2002, 2006).”

“These evolution sequences have already been applied extensively to the analysis of brown dwarf observations (Roellig et al. 2004; Saumon et al. 2006, 2007; Leggett et al. 2007a, 2007b; Cushing et al. 2008) but have not been discussed in any detail.”

“These evolution sequences have already been applied extensively to the analysis of brown dwarf observations (Roellig et al. 2004; Saumon et al. 2006, 2007; Leggett et al. 2007a, 2007b; Cushing et al. 2008) but have not been discussed in any detail.”

“…of isolated brown dwarfs—a relatively simple case of stellar evolution—has been studied extensively for the past 20 years and is well understood (D’Antona & Mazzitelli 1985; Nelson et al. 1986; Burrows et al. 1989, 1997; Burrows & Liebert 1993; Chabrier et al. 2000a, 2000b; Baraffe et al. 2002).”

“To obtain a boundary condition for TeA < 500 K, we define T10 as the temperature at P ¼ 10 bar that gives the same entropy S as the atmosphere model (Lunine et al. 1989).”

“For a 10 Gyr old brown dwarf of 0.06 M , we find a luminosity that is 0.104 dex lower than that of Baraffe et al. (2003), which is in perfect agreement with the value given in Chabrier et al. (2000b) for the change in luminosity brought by introducing conduction in the evolution.”

“…models down to 0.096M (Chabrier & Baraffe 2000), but there is growing evidence that models of late-L dwarfs are systematically underluminous for a given mass and age, as revealed by the first few dynamical mass measurements below the stellar mass limit ( Ireland et al. 2008; Dupuy et al. 2008).”

“Since there is evidence that the local BD population has a younger average age than solar-type stars (Allen et al. 2005;Metchev&Hillenbrand 2006; Zapatero Osorio et al. 2007; Liu et al. 2008; Cruz et al. 2008), we consider a SFR where all BDs were formed at a constant rate in the past 5 Gyr (Fig.”

“…(McKay et al. 1989; Marley et al. 1996, 2002; Burrows et al. 1997; Marley & McKay 1999) and used in several detailed comparisons with data (Marley et al. 1996, 2002; Roellig et al. 2004; Saumon et al. 2006, 2007; Leggett et al. 2007b; Mainzer et al. 2007; Blake et al. 2007; Cushing et al. 2008).”

“The breadth of the late-M and early-L distribution is comparable to the scatter caused by variations in gravity, supporting the idea that the latter is indeed the second parameter of the sequence (Tsuji & Nakajima 2003; Burrows et al. 2006).”

“This value of is typical for Galactic clusters (Moraux et al. 2003; Bouvier et al. 2003; Barrado y Navascués et al. 2002, 2004), although a recent study suggests that the IMF of young clusters is decreasing in the substellar regime (Andersen et al. 2008).”

“The Casewell et al. (2007) survey goes k1 mag fainter and shows a tighter L dwarf sequence.”

“Deep surveys have established that its low-mass stellar and substellar population can be reproduced by a power-law IMF with an index of 0:6 (Moraux et al. 2003; Bihain et al. 2006).”

“…of isolated brown dwarfs—a relatively simple case of stellar evolution—has been studied extensively for the past 20 years and is well understood (D’Antona & Mazzitelli 1985; Nelson et al. 1986; Burrows et al. 1989, 1997; Burrows & Liebert 1993; Chabrier et al. 2000a, 2000b; Baraffe et al. 2002).”

“…2001; Lodders 2002), increasingly complete molecular opacity databases (Freedman et al. 2008; Sharp & Burrows 2007), extreme resonance line broadening (Burrows et al. 2000; Allard et al. 2005), and particulate cloud models (Allard et al. 2001; Ackerman&Marley 2001; Tsuji 2002; Helling et al. 2008).”

“The relevant parameters of the cluster are its distance (134 3 pc; Percival et al. 2005), age ( 100Y120 Myr; Martı́n et al. 1998), metallicity (½Fe/H ¼ 0:034 0:024; Boesgaard & Friel 1990), and extinction [E(V I ) ¼ 0:06; Stauffer & Hartmann 1987].”

“…(McKay et al. 1989; Marley et al. 1996, 2002; Burrows et al. 1997; Marley & McKay 1999) and used in several detailed comparisons with data (Marley et al. 1996, 2002; Roellig et al. 2004; Saumon et al. 2006, 2007; Leggett et al. 2007b; Mainzer et al. 2007; Blake et al. 2007; Cushing et al. 2008).”

“The pioneering work of Chabrier (2002) and the extensive studies of Burgasser (2004) and Allen et al. (2003, 2005) show how variations in the IMF and SFR affect one-dimensional distribution functions (such as the luminosity function) of field brown dwarfs.”

“This value of is typical for Galactic clusters (Moraux et al. 2003; Bouvier et al. 2003; Barrado y Navascués et al. 2002, 2004), although a recent study suggests that the IMF of young clusters is decreasing in the substellar regime (Andersen et al. 2008).”

“From stellar modeling, estimates of the minimum mass for hydrogen burning range from 0.07Me to 0.09Me (Burrows et al. 1993, 1997; Baraffe et al. 1998, 2003; Chabrier et al. 2000; Saumon & Marley 2008).”

“Although the CMDs most directly probe the color evolution of brown dwarfs (i.e., cloud dispersal), in the theoretical perspective of Saumon & Marley (2008) this pileup and gap are inextricably tied to luminosity evolution as well.”

“We first fit the observed J and H band spectra using standard cloud-free equilibrium-chemistry models, constrained to have radii for a given mass as given by evolutionary tracks, similar to those in ( 35 ).”