1,124 research outputs found
Most 1.6 Earth-Radius Planets are not Rocky
The Kepler Mission, combined with ground based radial velocity (RV) follow-up
and dynamical analyses of transit timing variations, has revolutionized the
observational constraints on sub-Neptune-size planet compositions. The results
of an extensive Kepler follow-up program including multiple Doppler
measurements for 22 planet-hosting stars more than doubles the population of
sub-Neptune-sized transiting planets that have RV mass constraints. This
unprecedentedly large and homogeneous sample of planets with both mass and
radius constraints opens the possibility of a statistical study of the
underlying population of planet compositions. We focus on the intriguing
transition between rocky exoplanets (comprised of iron and silicates) and
planets with voluminous layers of volatiles (H/He and astrophysical ices).
Applying a hierarchical Bayesian statistical approach to the sample of Kepler
transiting sub-Neptune planets with Keck RV follow-up, we constrain the
fraction of close-in planets (with orbital periods less than ~50 days) that are
sufficiently dense to be rocky, as a function of planet radius. We show that
the majority of 1.6 Earth-radius planets are too low density to be comprised of
Fe and silicates alone. At larger radii, the constraints on the fraction of
rocky planets are even more stringent. These insights into the size
demographics of rocky and volatile-rich planets offer empirical constraints to
planet formation theories, and guide the range of planet radii to be considered
in studies of the occurrence rate of "Earth-like" planets, .Comment: Accepted to ApJ, In pres
Evolutionary Analysis of Gaseous Sub-Neptune-Mass Planets with MESA
Sub-Neptune-sized exoplanets represent one of the most common types of
planets in the Milky Way, yet many of their properties are unknown. Here, we
present a prescription to adapt the capabilities of the stellar evolution
toolkit Modules for Experiments in Stellar Astrophysics (MESA) to model
sub-Neptune mass planets with H/He envelopes. With the addition of routines
treating the planet core luminosity, heavy element enrichment, atmospheric
boundary condition, and mass loss due to hydrodynamic winds, the evolutionary
pathways of planets with diverse starting conditions are more accurately
constrained. Using these dynamical models, we construct mass-composition
relationships of planets from 1 to 400 and investigate how
mass-loss impacts their composition and evolution history. We demonstrate that
planet radii are typically insensitive to the evolution pathway that brought
the planet to its instantaneous mass, composition and age, with variations from
hysteresis. We find that planet envelope mass loss timescales, , vary non-monotonically with H/He envelope mass fractions (at fixed
planet mass). In our simulations of young (100~Myr) low-mass
() planets with rocky cores, is
maximized at to . The resulting convergent mass loss
evolution could potentially imprint itself on the close-in planet population as
a preferred H/He mass fraction of . Looking ahead, we anticipate
that this numerical code will see widespread applications complementing both
3-D models and observational exoplanet surveys.Comment: 18 pages, 9 figures, and 4 tables. Accepted to the Astrophysical
Journal on August 29th, 201
Transit Light Curves with Finite Integration Time: Fisher Information Analysis
Kepler has revolutionized the study of transiting planets with its
unprecedented photometric precision on more than 150,000 target stars. Most of
the transiting planet candidates detected by Kepler have been observed as
long-cadence targets with 30 minute integration times, and the upcoming
Transiting Exoplanet Survey Satellite (TESS) will record full frame images with
a similar integration time. Integrations of 30 minutes affect the transit
shape, particularly for small planets and in cases of low signal-to-noise.
Using the Fisher information matrix technique, we derive analytic
approximations for the variances and covariances on the transit parameters
obtained from fitting light curve photometry collected with a finite
integration time. We find that binning the light curve can significantly
increase the uncertainties and covariances on the inferred parameters when
comparing scenarios with constant total signal-to-noise (constant total
integration time in the absence of read noise). Uncertainties on the transit
ingress/egress time increase by a factor of 34 for Earth-size planets and 3.4
for Jupiter-size planets around Sun-like stars for integration times of 30
minutes compared to instantaneously-sampled light curves. Similarly,
uncertainties on the mid-transit time for Earth and Jupiter-size planets
increase by factors of 3.9 and 1.4. Uncertainties on the transit depth are
largely unaffected by finite integration times. While correlations among the
transit depth, ingress duration, and transit duration all increase in magnitude
with longer integration times, the mid-transit time remains uncorrelated with
the other parameters. We provide code in Python and Mathematica for predicting
the variances and covariances at www.its.caltech.edu/~eprice
Probabilistic Mass-Radius Relationship for Sub-Neptune-Sized Planets
The Kepler Mission has discovered thousands of planets with radii $<4\
R_\oplusM/M_\oplus=2.7(R/R_\oplus)^{1.3}1.9\ M_\oplusR_{pl}<4\ R_\oplus$). More broadly, this work provides a
framework for further analyses of the M-R relation and its probable
dependencies on period and stellar properties.Comment: 14 pages, 5 figures, 2 tables. Accepted to the Astrophysical Journal
on April 28, 2016. Select posterior samples and code to use them to compute
the posterior predictive mass distribution are available at
https://github.com/dawolfgang/MRrelatio
Regrouping for Instruction in Reading: Effective Practices
It is the intent of this project to create a handbook providing information about a plan for regrouping for instruction in reading at Long Beach Elementary School. It will be presented to parents, teachers and administrators at workshops concerning regrouping for instruction in reading. The handbook will provide practical applications of curricular adaptation and instructional techniques that may be used to facilitate improvement in reading for students. The policies and procedures described in the manual will provide the following information:
β’ Assessment
β’ Placement
β’ Transitions
β’ Pace and Skill Levels
β’ Curricular Adaptations
β’ Teacher Collaboration and Consultation
β’ Ongoing Student Evaluation
β’ Flexibility of Grouping
β’ Instructional Teaching Technique
Comparison of multivariate methods for measuring change from pretest to posttest
Three multivariate methods for measuring change from pretest to posttest are compared with respect to statistical power over various levels and combinations of effect size, alpha level, sample size, number of dependent variables, number of significantly different dependent variables, correlation between corresponding pretest and posttest scores, and correlation between unrelated pretest and posttest scores. The method utilizing posttests as the dependent variables and pretests as covariates was found to have superior statistical power in the majority of the scenarios examined. However, there were scenarios where the method utilizing change scores as dependent variables and the method utilizing only posttests as the dependent variables displayed greater power. Using results from the Monte Carlo simulations, comparisons are presented that reveal the conditions under which each of the three multivariate methods displayed greater statistical power than the other two. In addition to the immediate implications of the current study, suggested future avenues of research that could expand upon the current findings are discussed
Festschrift for Dean Simon
We write together about our dear friend Michelle Simon because of her enormous contribution to our professional and personal lives. Working with someone who becomes more than a colleague, but a friend as well, is a special gift. Michelle not only paved our path, she became a trail blazer in legal education. The professional trajectory of Michelle Simon speaks volumes to her talent, tenacity, and consensus building skills
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