The Sonora Substellar Atmosphere Models VI. Red Diamondback: Extending Diamondback with SPHINX for Brown Dwarf Early Evolution

TL;DR

The study extends the Sonora Diamondback brown dwarf evolution framework to higher effective temperatures by coupling SPHINX M-dwarf atmospheres (2000–4000 K) with the Diamondback grid via a weighted 2000–2400 K transition, enabling 1 Myr–15 Gyr evolutionary tracks across a broad mass and metallicity range. The approach yields hotter early-time boundaries and significant metallicity effects on cooling, radius, and luminosity compared to extrapolated older models, and reveals Hayashi-track behavior and revised deuterium burning characteristics for young brown dwarfs. The resulting tracks, isochrones, and synthetic photometry offer a cohesive tool for interpreting young substellar populations and benchmarking JWST-era observations, with data and boundary-condition tables publicly available. This work highlights the critical role of atmospheric boundary conditions in shaping the early evolution of substellar objects and provides a framework for future improvements in high-$T_{ ext{eff}}$ opacities and cloud treatments.

Abstract

We extend the Sonora Diamondback brown dwarf evolution models to higher effective temperatures to treat the evolution of younger, higher mass objects. Due to an upper temperature limit of $T_\mathrm{eff}=$2400 K in the original Sonora Diamondback model grid, high mass objects ($M\geq$ 0.05 $M_\mathrm{\odot}=$ 52.4 $M_\mathrm{J}$) were limited to ages of $\gtrsim$ 100 Myr. To include the early evolution of brown dwarfs at $T_\mathrm{eff}>$ 2400 K, we use existing and new SPHINX cloud-free model atmosphere calculations of temperature structures of M-type atmospheres. These atmospheres range from $T_\mathrm{eff}$ 2000--4000 K, log($g$) 3.0--5.5, and metallicity [M/H] $-$0.5 to $+$0.5. This combination of Diamondback and SPHINX atmospheres, with a transition across $T_\mathrm{eff}$ 2000--2400 K, allows us to calculate evolution tracks, and infrared photometry and colors, for ages $>$ 1 Myr and masses from above the hydrogen burning minimum mass down to planetary masses. The Hayashi phase of massive brown dwarf evolution (ages $<$ 10--100 Myr) at low surface gravity leads to nearly constant $T_\mathrm{eff}$ values, at effective temperatures much lower than would be obtained from simply extrapolating backwards from evolution tracks at older ages.

Figures (9)

• Figure 1: Selected $P$--$T$ profiles from Iyer:2023_SphinxMdwarfAtm (thin solid line) and Morely:2024_SonoraDiamondback (thick dot-dashed line) for two effective temperatures and three surface gravities. The left panel shows atmospheres with $T_\mathrm{eff}$$=$ 2400 K, while the right panel shows those with $T_\mathrm{eff}$$=$ 3000 K. We show the interpolated/extrapolated $T_{10}$ values from Morely:2024_SonoraDiamondback along the $P=$ 10 bar isobar (horizontal grey dotted line). At 2400 K, the Morely:2024_SonoraDiamondback atmospheres are hotter at lower pressures than the Iyer:2023_SphinxMdwarfAtm atmospheres due to the inclusion of clouds that add opacity, although this has minimal impact on $T_{10}$. The Iyer:2023_SphinxMdwarfAtm atmospheres start to become hotter at log($g$) $\lesssim$ 4 due to the inclusion of a range of atomic opacities not found in Morely:2024_SonoraDiamondback. By $T_\mathrm{eff}$$=$ 3000 K, the Iyer:2023_SphinxMdwarfAtm atmospheres are hotter at each surface gravity than the extrapolated $T_{10}$ values from Morely:2024_SonoraDiamondback, with the discrepancy widening dramatically as one goes to lower surface gravities ($\gtrsim$ 3000 K at log($g$) $=$ 3.5).
• Figure 2: The solar metallicity ([M/H]$=+$0.0) $T_\mathrm{eff}$--log($g$)--$T_{10}$ table used as a boundary condition in our thermal evolution model. The $T_{10}$ values are tabulated for the Sonora DiamondbackMorely:2024_SonoraDiamondback and SPHINXIyer:2023_SphinxMdwarfAtm atmospheres as indicated in the plot. The process used to determine the boundary condition in the "'weighted transition" region, where these two atmosphere grids overlap in $T_\mathrm{eff}$, is described in § \ref{['sec:methods:t10']}. A structure model with a particular $T_{10}$ and surface gravity determines its $T_\mathrm{eff}$ by interpolating within this table.
• Figure 3: Luminosity evolution tracks of selected models from our work (thin solid lines) compared to the Morely:2024_SonoraDiamondback tracks (thick dot-dashed lines) and the recent Chabrier:2023_CD21newHBMM models (thin dotted lines). Models are labeled by their mass in $M_\mathrm{J}$. The bottom panel shows the logarithmic ratios of the Morely:2024_SonoraDiamondback and Chabrier:2023_CD21newHBMM models to those of this work, (i.e. a value of 0.25 means the model is $\sim$1.78x as luminous as our models at that age.) Our luminosity tracks are typically within 1% of the Morely:2024_SonoraDiamondback luminosities at late ages ($\gtrsim$ 1 Gyr), but are more luminous at young ages due to higher initial entropy and the inclusion of Iyer:2023_SphinxMdwarfAtm atmospheric boundary conditions. As the Chabrier:2023_CD21newHBMM models do not account for the L--T transition, they tend to be more luminous before and less luminous after the L--T transition than our models except for the very lowest mass cases, which are less luminous at all young ages and more luminous beyond several Gyr.
• Figure 4: Luminosity evolution tracks (top panel) of selected solar metallicity ([M/H]$=+$0.0, thick solid lines), metal-rich ([M/H]$=+$0.5, thin dashed lines) and metal-poor ([M/H] $=-$0.5, thin dotted lines). Models are labeled by their mass in $M_\mathrm{J}$. We show the logarithmic ratios of the metal-rich (middle panel) and metal-poor (bottom panel) models to the solar metallicity models, (i.e. a value of 0.125 means the model is $\sim$1.33x as luminous as its solar metallicity counterpart at that age.) Higher mass objects are less luminous the more metal rich they are until $\sim$10 Myr, where they become more luminous.
• Figure 5: Evolution tracks of $T_\mathrm{eff}$ (top panel), radius (middle panel), and surface gravity (bottom panel) of selected solar metallicity (thick solid lines), metal-rich (thin dashed lines) and metal-poor (thin dotted lines) model objects. Models are labeled by their mass in $M_\mathrm{J}$. In general, the objects tend to be hotter, smaller, and of higher surface gravity as metallicity decreases, with these patterns becoming more apparent at higher masses and younger ages. Most of the modeled properties here become less sensitive to metallicity as these objects age, but objects that are close to or above the hydrogen-burning limit ($M\gtrsim$ 0.06$M_\mathrm{\odot}$$=$ 62.9 $M_\mathrm{J}$) retain differences due to metallicity well after a few Gyr.