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We have been using Keck laser guide star adaptive optics to monitor the orbits of ultracool binaries, providing dynamical masses at lower luminosities and temperatures than previously available and enabling strong tests of theoretical models. We have identified three specific problems with theory: (1) We find that model color-magnitude diagrams cannot be reliably used to infer masses as they do not accurately reproduce the colors of ultracool dwarfs of known mass. (2) Effective temperatures inferred from evolutionary model radii are typically inconsistent with temperatures derived from fitting atmospheric models to observed spectra by 100-300 K. (3) For the only known pair of field brown dwarfs with a precise mass (3%) and age determination (~25%), the measured luminosities are ~2-3x higher than predicted by model cooling rates (i.e., masses inferred from Lbol and age are 20-30% larger than measured). To make progress in understanding the observed discrepancies, more mass measurements spanning a wide range of luminosity, temperature, and age are needed, along with more accurate age determinations (e.g., via asteroseismology) for primary stars with brown dwarf binary companions. Also, resolved optical and infrared spectroscopy are needed to measure lithium depletion and to characterize the atmospheres of binary components in order to better assess model deficiencies.
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We present the current status of the analytic theory of brown dwarf evolution and the lower mass limit of the hydrogen burning main sequence stars. In the spirit of a simplified analytic theory we also introduce some modifications to the existing models. We give an exact expression for the pressure of an ideal non-relativistic Fermi gas at a finite temperature, therefore allowing for non-zero values of the degeneracy parameter ($psi = frac{kT}{mu_{F}}$, where $mu_{F}$ is the Fermi energy). We review the derivation of surface luminosity using an entropy matching condition and the first-order phase transition between the molecular hydrogen in the outer envelope and the partially-ionized hydrogen in the inner region. We also discuss the results of modern simulations of the plasma phase transition, which illustrate the uncertainties in determining its critical temperature. Based on the existing models and with some simple modification we find the maximum mass for a brown dwarf to be in the range $0.064M_odot-0.087M_odot$. An analytic formula for the luminosity evolution allows us to estimate the time period of the non-steady state (i.e., non-main sequence) nuclear burning for substellar objects. Standard models also predict that stars that are just above the substellar mass limit can reach an extremely low luminosity main sequence after at least a few million years of evolution, and sometimes much longer. We estimate that $simeq 11 %$ of stars take longer than $10^7$ yr to reach the main-sequence, and $simeq 5 %$ of stars take longer than $10^8$ yr.
The abundance of brown dwarfs (BDs) in young clusters is a diagnostic of star formation theory. Here we revisit the issue of determining the substellar initial mass function (IMF), based on a comparison between NGC1333 and IC348, two clusters in the Perseus star-forming region. We derive their mass distributions for a range of model isochrones, varying distances, extinction laws and ages, with comprehensive assessments of the uncertainties. We find that the choice of isochrone and other parameters have significant effects on the results, thus we caution against comparing IMFs obtained using different approaches. For NGC1333, we find that the star/BD ratio R is between 1.9 and 2.4, for all plausible scenarios, consistent with our previous work. For IC348, R is between 2.9 and 4.0, suggesting that previous studies have overestimated this value. Thus, the star forming process generates about 2.5-5 substellar objects per 10 stars. The derived star/BD ratios correspond to a slope of the power-law mass function of alpha=0.7-1.0 for the 0.03-1.0Msol mass range. The median mass in these clusters - the typical stellar mass - is between 0.13-0.30Msol. Assuming that NGC1333 is at a shorter distance than IC348, we find a significant difference in the cumulative distribution of masses between the two clusters, resulting from an overabundance of very low mass objects in NGC1333. Gaia astrometry will constrain the cluster distances better and will lead to a more definitive conclusion. Furthermore, ratio R is somewhat larger in IC348 compared with NGC1333, although this difference is still within the margins of error. Our results indicate that environments with higher object density may produce a larger fraction of very low mass objects, in line with predictions for brown dwarf formation through gravitational fragmentation of filaments falling into a cluster potential.
We present new evidence for a problem with cooling rates predicted by substellar evolutionary models that implies model-derived masses in the literature for brown dwarfs and directly imaged planets may be too high. Based on our dynamical mass for Gl 417BC (L4.5+L6) and a gyrochronology system age from its young, solar-type host star, commonly used models predict luminosities 0.2$-$0.4 dex lower than we observe. This corroborates a similar luminosity$-$age discrepancy identified in our previous work on the L4+L4 binary HD 130948BC, which coincidentally has nearly identical component masses ($approx$50$-$55 $M_{rm Jup}$) and age ($approx$800 Myr) as Gl 417BC. Such a luminosity offset would cause systematic errors of 15%$-$25% in model-derived masses at this age. After comparing different models, including cloudless models that should not be appropriate for mid-L dwarfs like Gl 417BC and HD 130948BC but actually match their luminosities better, we speculate the observed over-luminosity could be caused by opacity holes (i.e., patchy clouds) in these objects. Moreover, from hybrid substellar evolutionary models that account for cloud disappearance we infer the corresponding phase of over-luminosity may extend from a few hundred Myr up to a few Gyr and cause masses to to be over-estimated by up to 25%, even well after clouds disappear from view entirely. Thus, the range of of ages and spectral types affected by this potential systematic shift in luminosity evolution would encompass most known directly imaged gas-giants and field brown dwarfs.
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The cosmic expansion is computed for various dynamical vacuum models $Lambda(H)$ and confronted to the Cosmic Microwave Background (CMB) power spectrum from Planck. We also combined CMB in a joint analysis with other probes in order to place constraints on the cosmological parameters of the dynamical vacuum models. We find that all $Lambda(H)$ models are very efficient and in very good agreement with the data. Considering that the interaction term of the dark sector is given in terms of matter and radiation densities, we find that the corresponding $Lambda(H)$ model shows a small but non-zero deviation from $Lambda$ cosmology, nevertheless the confidence level is close to $sim 2.5sigma$.
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