Pink Dwarfs and the Paths to Stardom: How Brown Dwarfs Pushed Above the Hydrogen Burning Limit Evolve

TL;DR

This paper investigates brown dwarfs that gain mass via binary interactions and cross the hydrogen burning limit (HBL). Using MESA simulations of three-stage runs (pre-accretion brown dwarf, mass accretion to various final masses at fast or slow rates, then post-accretion evolution), the authors classify outcomes into beige dwarfs, pink dwarfs (with or without a frozen core or luminosity plateau), and maroon dwarfs. They find a distinct luminosity plateau and a frozen-core phase in pink dwarfs, whose duration is governed by the core heating time $t_{\mathrm{core\, heating}} = \dfrac{1}{L_{\mathrm{nuc}}} \int_0^{m_{\mathrm{ref}}} (S - S_{\mathrm{ref}}) C_V T \, dm$, linking energy input to the re-establishment of convection and a near-constant-entropy interior. This work provides observable predictions and a framework to constrain binary mass-transfer physics via locating pink/beige dwarfs, e.g., as faint companions to white dwarfs, and motivates companion studies for candidate identifications.

Abstract

Brown dwarfs that gain mass through binary interactions may be pushed above the boundary that divides brown dwarfs from low-mass stars: the hydrogen burning limit (HBL). Some of these objects will make their way to the main sequence and may eventually be indistinguishable from ordinary low-mass stars, while others will remain brown dwarf-like, unable to burn hydrogen at a high enough rate to power their surface luminosity. We study the evolution of both types of object to provide a taxonomy and testable observational predictions for these objects depending on their evolutionary path. Using MESA simulations, we find that a subset of the objects that will eventually become stars experience an extended luminosity plateau, where their surface luminosity remains nearly constant on 100 Myr - Gyr timescales. We find that the plateau timescale is set by the amount of energy required to re-heat the cores of these objects to a level sufficient to sustain convection. The timescales required for the cores of these objects to "unfreeze" and arrive at the main sequence is long enough that surveys may be able to find objects in this evolutionary stage. These objects, along with those that never reach the main sequence, occupy a unique space in a mass-luminosity diagram, and would provide a unique constraint on binary mass transfer physics.

Figures (9)

• Figure 1: A schematic diagram. The coloured arrows represent the paths the different stellar and substellar objects take as they evolve on a plot of mass against $\psi$, the thermal energy per particle in units of the Fermi energy in the star's core. Lower values of $\psi$ indicate colder and more degenerate cores. The separately coloured regions and their corresponding outline arrows indicate what direction an object would move. In the pink region within the parabola, objects have a nuclear luminosity, $L_{\mathrm{nuc}}$, greater than their surface luminosity, $L_{\mathrm{surf}}$ and they evolve to the right as their cores heat up. In the blue region, $L_{\mathrm{surf}} > L_{\mathrm{nuc}}$, so objects evolve to the left as they radiate more energy than they generate. The black parabola is where $L_{\mathrm{nuc}}=L_{\mathrm{surf}}$. The solid right-hand side of the parabola represents the main sequence; it is stable to perturbations in $\psi$. The dashed left-hand side is unstable. The lowest mass on the parabola is the hydrogen burning limit, M$_\mathrm{HBL}$. The arrows for the red dwarf and brown dwarf are horizontal as these objects do not change their mass throughout their lives without an outside influence. Maroon, pink, and beige dwarfs begin as brown dwarfs and evolve leftwards until an episode of mass accretion results in them splitting off from the brown dwarf arrow vertically, at least in the case of fast accretion. When accretion has stopped, they then evolve horizontally to the left or right. Maroon dwarfs, like red dwarfs, evolve left and settle on the main sequence. Beige dwarfs end up above the hydrogen burning limit, but outside of the parabola, and so evolve left like a brown dwarf, never reaching the main sequence. A pink dwarf is located inside the parabola when mass has stopped accreting and then evolves to the right to settle on the main sequence. The 'frozen cores/plateaus' region in the parabola is the area in which a subset of our pink dwarf models have a frozen core or luminosity plateau (see Section \ref{['sec:results']}).
• Figure 2: The MESA runs. In each run, the first key parameter is the time at which a brown dwarf begins a mass accretion phase, measured relative to its formation (the x-axis, which is reversed so that the brown dwarf moves leftward just like in Figure \ref{['fig:schematic']}). The second parameter is the final mass of the brown dwarf after its accretion phase, which in all cases begins as a $0.065\ M_\odot$ ordinary brown dwarf. Note that for each point in this figure we run a case where the accretion is fast, taking $10^7$ years, and a case where the accretion is slow, taking $10^9$ years.
• Figure 3: MESA models in the $M-\psi$ diagram. MESA models at the end of their accretion phase are plotted in the same space as the schematic diagram (Figure \ref{['fig:schematic']}): mass versus the core temperature in units of the Fermi energy, which is 1/center_degeneracy in terms of MESA outputs. Models are assigned colours and symbols according to their final fates. Models that never reach the main sequence are yellow circles (beige dwarfs). Models that approach the main sequence from the right are maroon pentagons (maroon dwarfs). Pink dwarfs that have a frozen core (see text) are squares; pink dwarfs that have luminosity plateaus (see text) are diamonds, and pink dwarfs that have neither are pink stars. We also show several isochrones for the ordinary evolution of low-mass stars and brown dwarfs at 0.1, 1, and 10 Gyr from right to left, which show the presence of the main sequence and the continuous cooling of ordinary brown dwarfs. Isochrones for several versions of these models are shown: the red lines have altered atmospheric boundary conditions, and the blue lines are models with lower metallicities.
• Figure 4: Luminosity over time of an example set of objects. The top five rows show examples of brown dwarfs to which mass was added, while the bottom two panels show a brown dwarf and a star with constant masses ($0.065 M_\odot$ and $0.085 M_\odot$ respectively). The luminosity produced by nuclear reactions $L_\mathrm{nuc}$ is shown as the gray curve, while the luminosity radiated at the surface $L_\mathrm{surf}$ is shown in red. The x-axis shows time elapsed, with $t=0$ corresponding to the birth of the original brown dwarf to which mass is later added. The plots begin at the start of the accretion phase. The end of the accretion phase is marked by a pair of circles on each line, and is either $10^7$ or $10^9$ years after the start of the accretion phase, or at $t=0$ in the case of the ordinary brown dwarf and star. Time periods during which an object has a frozen core or luminosity plateau (see text) are marked as blue and light blue lines respectively. Brown dwarf-like objects, namely the beige dwarfs in the first column and the brown dwarf, have surface luminosities that exceed the nuclear luminosity in the long run, while the pink and maroon dwarfs (right 3 columns) and the star arrive at an equilibrium where $L_\mathrm{surf}=L_\mathrm{nuc}$, often after multiple Gyr.
• Figure 5: The entropy profiles of the various example objects. The x-axis is the Lagrangian mass coordinate $m(<r)$ of the star normalised by the mass of the object $M$. The y-axis is the specific entropy divided by the product of Avogadro's number $N_A$ and Boltzmann's constant $k_B$, yielding a dimensionless number. Blue lines correspond to snapshots which are classified as having a frozen core, namely that the convective core mass is $<0.95\ M$. Red lines correspond to snapshots where this is not true, i.e. the object is fully convective. Within the red or blue lines, darker lines correspond to later times. Snapshots are only shown after the end of the accretion phase. These models are the same as those shown in Figure \ref{['fig:gallery_Lt']}.