Training Big Random Forests with Little Resources

Without access to large compute clusters, building random forests on large datasets is still a challenging problem. This is, in particular, the case if fully-grown trees are desired. We propose a simple yet effective framework that allows to efficiently construct ensembles of huge trees for hundreds of millions or even billions of training instances using a cheap desktop computer with commodity hardware. The basic idea is to consider a multi-level construction scheme, which builds top trees for small random subsets of the available data and which subsequently distributes all training instances to the top trees' leaves for further processing. While being conceptually simple, the overall efficiency crucially depends on the particular implementation of the different phases. The practical merits of our approach are demonstrated using dense datasets with hundreds of millions of training instances.Comment: 9 pages, 9 Figure

The Dependence of Brown Dwarf Radii on Atmospheric Metallicity and Clouds: Theory and Comparison with Observations

Employing realistic and consistent atmosphere boundary conditions, we have generated evolutionary models for brown dwarfs and very-low-mass stars (VLMs) for different metallicities ([Fe/H]), with and without clouds. We find that the spread in radius at a given mass and age can be as large as $\sim$10% to $\sim$25%, with higher-metallicity, higher-cloud-thickness atmospheres resulting quite naturally in larger radii. For each 0.1 dex increase in [Fe/H], radii increase by $\sim$1% to $\sim$2.5%, depending upon age and mass. We also find that, while for smaller masses and older ages brown dwarf radii decrease with increasing helium fraction ($Y$) (as expected), for more massive brown dwarfs and a wide range of ages they increase with helium fraction. The increase in radius in going from $Y=0.25$ to $Y=0.28$ can be as large as $\sim$0.025 \rj\ ($\sim$2.5%). Furthermore, we find that for VLMs an increase in atmospheric metallicity from 0.0 to 0.5 dex, increases radii by $\sim$4%, and from -0.5 to 0.5 dex by $\sim$10%. Therefore, we suggest that opacity due to higher metallicity might naturally account for the apparent radius anomalies in some eclipsing VLM systems. Ten to twenty-five percent variations in radius exceed errors stemming from uncertainities in the equation of state alone. This serves to emphasize that transit and eclipse measurements of brown dwarf radii constrain numerous effects collectively, importantly including the atmosphere and condensate cloud models, and not just the equation of state. At all times, one is testing a multi-parameter theory, and not a universal radius$-$mass relation.Comment: Accepted to the Astrophysical Journal, May 3, 201

Chemical Equilibrium Abundances in Brown Dwarf and Extrasolar Giant Planet Atmospheres

We calculate detailed chemical abundance profiles for a variety of brown dwarf and extrasolar giant planet atmosphere models, focusing in particular on Gliese 229B, and derive the systematics of the changes in the dominant reservoirs of the major elements with altitude and temperature. We assume an Anders and Grevesse (1989) solar composition of 27 chemical elements and track 330 gas--phase species, including the monatomic forms of the elements, as well as about 120 condensates. We address the issue of the formation and composition of clouds in the cool atmospheres of substellar objects and explore the rain out and depletion of refractories. We conclude that the opacity of clouds of low--temperature ($\le$900 K), small--radius condensibles (specific chlorides and sulfides), may be responsible for the steep spectrum of Gliese 229B observed in the near infrared below 1 \mic. Furthermore, we assemble a temperature sequence of chemical transitions in substellar atmospheres that may be used to anchor and define a sequence of spectral types for substellar objects with T$_{eff}$s from $\sim$2200 K to $\sim$100 K.Comment: 57 pages total, LaTeX, 14 figures, 5 tables, also available in uuencoded, gzipped, and tarred form via anonymous ftp at www.astrophysics.arizona.edu (cd to pub/burrows/chem), submitted to Ap.

NASA Ares I Launch Vehicle Roll and Reaction Control Systems Design Status

This paper provides an update of design status following the preliminary design review of NASA s Ares I first stage roll and upper stage reaction control systems. The Ares I launch vehicle has been chosen to return humans to the moon, mars, and beyond. It consists of a first stage five segment solid rocket booster and an upper stage liquid bi-propellant J-2X engine. Similar to many launch vehicles, the Ares I has reaction control systems used to provide the vehicle with three degrees of freedom stabilization during the mission. During launch, the first stage roll control system will provide the Ares I with the ability to counteract induced roll torque. After first stage booster separation, the upper stage reaction control system will provide the upper stage element with three degrees of freedom control as needed. Trade studies and design assessments conducted on the roll and reaction control systems include: propellant selection, thruster arrangement, pressurization system configuration, and system component trades. Since successful completion of the preliminary design review, work has progressed towards the critical design review with accomplishments made in the following areas: pressurant / propellant tank, thruster assembly, and other component configurations, as well as thruster module design, and waterhammer mitigation approach. Also, results from early development testing are discussed along with plans for upcoming system testing. This paper concludes by summarizing the process of down selecting to the current baseline configuration for the Ares I roll and reaction control systems

Model atmospheres for massive gas giants with thick clouds: Application to the HR 8799 planets and predictions for future detections

We have generated an extensive new suite of massive giant planet atmosphere models and used it to obtain fits to photometric data for the planets HR 8799b, c, and d. We consider a wide range of cloudy and cloud-free models. The cloudy models incorporate different geometrical and optical thicknesses, modal particle sizes, and metallicities. For each planet and set of cloud parameters, we explore grids in gravity and effective temperature, with which we determine constraints on the planet's mass and age. Our new models yield statistically significant fits to the data, and conclusively confirm that the HR 8799 planets have much thicker clouds than those required to explain data for typical L and T dwarfs. Both models with 1) physically thick forsterite clouds and a 60-micron modal particle size and 2) clouds made of 1 micron-sized pure iron droplets and 1% supersaturation fit the data. Current data are insufficient to accurately constrain the microscopic cloud properties, such as composition and particle size. The range of best-estimated masses for HR 8799b, HR 8799c, and HR 8799d conservatively span 2-12 M_J, 6-13 M_J, and 3-11 M_J, respectively and imply coeval ages between ~10 and ~150 Myr, consistent with previously reported stellar age. The best-fit temperatures and gravities are slightly lower than values obtained by Currie et al. (2011) using even thicker cloud models. Finally, we use these models to predict the near-to-mid IR colors of soon-to-be imaged planets. Our models predict that planet-mass objects follow a locus in some near-to-mid IR color-magnitude diagrams that is clearly separable from the standard L/T dwarf locus for field brown dwarfs.Comment: Accepted for publication in Ap

Line Intensities and Molecular Opacities of the FeH F4Δi−X4ΔiF^4\Delta_i-X^4\Delta_i Transition

We calculate new line lists and opacities for the $F^4\Delta_i-X^4\Delta_i$ transition of FeH. The 0-0 band of this transition is responsible for the Wing-Ford band seen in M-type stars, sunspots and brown dwarfs. The new Einstein A values for each line are based on a high level ab initio calculation of the electronic transition dipole moment. The necessary rotational line strength factors (H\"onl-London factors) are derived for both the Hund's case (a) and (b) coupling limits. A new set of spectroscopic constants were derived from the existing FeH term values for v=0, 1 and 2 levels of the $X$ and $F$ states. Using these constants extrapolated term values were generated for v=3 and 4 and for $J$ values up to 50.5. The line lists (including Einstein A values) for the 25 vibrational bands with v$\leq$4 were generated using a merged list of experimental and extrapolated term values. The FeH line lists were use to compute the molecular opacities for a range of temperatures and pressures encountered in L and M dwarf atmospheres. Good agreement was found between the computed and observed spectral energy distribution of the L5 dwarf 2MASS-1507.Comment: 52 pages, 3 figures, many tables, accepted for publication in the Astrophysical Journal Supplement

Ks-band detection of thermal emission and color constraints to CoRoT-1b: A low-albedo planet with inefficient atmospheric energy redistribution and a temperature inversion

We report the detection in Ks-band of the secondary eclipse of the hot Jupiter CoRoT-1b, from time series photometry with the ARC 3.5-m telescope at Apache Point Observatory. The eclipse shows a depth of 0.336+/-0.042 percent and is centered at phase 0.5022 (+0.0023,-0.0027), consistent with a zero eccentricity orbit ecos{\omega} = 0.0035 (+0.0036,-0.0042). We perform the first optical to near-infrared multi-band photometric analysis of an exoplanet's atmosphere and constrain the reflected and thermal emissions by combining our result with the recent 0.6, 0.71, and 2.09 micron secondary eclipse detections by Snellen et al. (2009), Gillon et al. (2009), and Alonso et al. (2009a). Comparing the multi-wavelength detections to state-of-the-art radiative-convective chemical-equilibrium atmosphere models, we find the near-infrared fluxes difficult to reproduce. The closest blackbody-based and physical models provide the following atmosphere parameters: a temperature T = 2454 (+84,-170) K, a very low Bond albedo A_B = 0.000 (+0.087,-0.000), and an energy redistribution parameter P_n = 0.1, indicating a small but nonzero amount of heat transfer from the day- to night-side. The best physical model suggests a thermal inversion layer with an extra optical absorber of opacity kappa_e =0.05cm^2g^-1, placed near the 0.1-bar atmospheric pressure level. This inversion layer is located ten times deeper in the atmosphere than the absorbers used in models to fit mid-infrared Spitzer detections of other irradiated hot Jupiters.Comment: accepted for publication on Ap

Theoretical Transit Spectra for GJ 1214b and Other "Super-Earths"

We present new calculations of transit spectra of super-Earths that allow for atmospheres with arbitrary proportions of common molecular species and haze. We test this method with generic spectra, reproducing the expected systematics and absorption features, then apply it to the nearby super-Earth GJ 1214b, which has produced conflicting observational data, leaving the questions of a hydrogen-rich versus hydrogen-poor atmosphere and the water content of the atmosphere ambiguous. We present representative transit spectra for a range of classes of atmosphere models for GJ 1214b. Our analysis supports a hydrogen-rich atmosphere with a cloud or haze layer, although a hydrogen-poor model with less than 10% water is not ruled out. Several classes of models are ruled out, however, including hydrogen-rich atmospheres with no haze, hydrogen-rich atmospheres with a haze of about 0.01-micron tholin particles, and hydrogen-poor atmospheres with major sources of absorption other than water. We propose an observational test to distinguish hydrogen-rich from hydrogen-poor atmospheres. Finally, we provide a library of theoretical transit spectra for super-Earths with a broad range of parameters to facilitate future comparison with anticipated data.Comment: 33 pages, 21 figures, 3 table

The Deuterium-Burning Mass Limit for Brown Dwarfs and Giant Planets

There is no universally acknowledged criterion to distinguish brown dwarfs from planets. Numerous studies have used or suggested a definition based on an object's mass, taking the ~13-Jupiter mass (M_J) limit for the ignition of deuterium. Here, we investigate various deuterium-burning masses for a range of models. We find that, while 13 M_J is generally a reasonable rule of thumb, the deuterium fusion mass depends on the helium abundance, the initial deuterium abundance, the metallicity of the model, and on what fraction of an object's initial deuterium abundance must combust in order for the object to qualify as having burned deuterium. Even though, for most proto-brown dwarf conditions, 50% of the initial deuterium will burn if the object's mass is ~(13.0 +/- 0.8)M_J, the full range of possibilities is significantly broader. For models ranging from zero-metallicity to more than three times solar metallicity, the deuterium burning mass ranges from ~11.0 M_J (for 3-times solar metallicity, 10% of initial deuterium burned) to ~16.3 M_J (for zero metallicity, 90% of initial deuterium burned).Comment: "Models" section expanded, references added, accepted by Ap