Saving Planetary Systems: Dead Zones & Planetary Migration

The tidal interaction between a disk and a planet leads to the planet's migration. A long-standing question regarding this mechanism is how to stop the migration before planets plunge into their central stars. In this paper, we propose a new, simple mechanism to significantly slow down planet migration, and test the possibility by using a hybrid numerical integrator to simulate the disk-planet interaction. The key component of the scenario is the role of low viscosity regions in protostellar disks known as dead zones, which affect planetary migration in two ways. First of all, it allows a smaller-mass planet to open a gap, and hence switch the faster type I migration to the slower type II migration. Secondly, a low viscosity slows down type II migration itself, because type II migration is directly proportional to the viscosity. We present numerical simulations of planetary migration by using a hybrid symplectic integrator-gas dynamics code. Assuming that the disk viscosity parameter inside the dead zone is (alpha=1e-4-1e-5), we find that, when a low-mass planet (e.g. 1-10 Earth masses) migrates from outside the dead zone, its migration is stopped due to the mass accumulation inside the dead zone. When a low-mass planet migrates from inside the dead zone, it opens a gap and slows down its migration. A massive planet like Jupiter, on the other hand, opens a gap and slows down inside the dead zone, independent of its initial orbital radius. The final orbital radius of a Jupiter mass planet depends on the dead zone's viscosity. For the range of alpha's noted above, this can vary anywhere from 7 AU, to an orbital radius of 0.1 AU that is characteristic of the hot Jupiters.Comment: 38 pages, 14 figures, some changes in text and figures, accepted for publication in Ap

Principals' sensemaking of coaching for ambitious reading instruction in a high-stakes accountability policy environment

In the present exploratory qualitative study we examine the contextual factors that influenced the implementation of a multi-year comprehensive literacy-coaching program (Content- Focused Coaching, CFC). We argue that principals' sensemaking of the dialogic instructional strategies promoted by the program in light of high-stakes accountability policies influenced coaches' work with teachers. Principals' views of the efficacy of the teaching strategies promoted by CFC for meeting accountability targets influenced how principals socially positioned coaches in schools (i.e., the degree to which they promoted coaches as sources of expertise to teachers), and the extent to which the coaching received by teachers focused on implementing dialogic teaching practices. Our results also suggest that principals' sensemaking of the program was for the most part consistent across years, even in the face of shifting accountability status and changes in district leadership. Implications of our findings for improving the implementation of coaching programs are discussed

About multiplicities and applications to Bezout numbers

Let $(A,\mathfrak{m},\Bbbk)$ denote a local Noetherian ring and $\mathfrak{q}$ an ideal such that $\ell_A(M/\mathfrak{q}M) < \infty$ for a finitely generated $A$-module $M$. Let \au = a_1,\ldots,a_d denote a system of parameters of $M$ such that $a_i \in \mathfrak{q}^{c_i} \setminus \mathfrak{q}^{c_i+1}$ for $i=1,\ldots,d$. It follows that \chi := e_0(\au;M) - c \cdot e_0(\mathfrak{q};M) \geq 0, where $c = c_1\cdot \ldots \cdot c_d$. The main results of the report are a discussion when $\chi = 0$ resp. to describe the value of $\chi$ in some particular cases. Applications concern results on the multiplicity e_0(\au;M) and applications to Bezout numbers.Comment: 11 pages, to appear Springer INdAM-Series, Vol. 20 (2017

Evolutionary Tracks of Trapped, Accreting Protoplanets: the Origin of the Observed Mass-Period Relation

The large number of observed exoplanets ($\gtrsim$ 700) provides important constraints on their origin as deduced from the mass-period diagram of planets. The most surprising features in the diagram are 1) the (apparent) pile up of gas giants at a period of $\sim 500$ days ($\sim1$ AU) and 2) the so-called mass-period relation which indicates that planetary mass is an increasing function of orbital period. We construct the evolutionary tracks of growing planets at planet traps in evolving protoplanetary disks and show that they provide a good physical understanding of how these observational properties arise. The fundamental feature of our model is that inhomogeneities in protoplanetary disks give rise to multiple (up to 3) trapping sites for rapid (type I) planetary migration of planetary cores. The viscous evolution of disks results in the slow radial movement of the traps and their cores from large to small orbital periods. In our model, the slow inward motion of planet traps is coupled with the standard core accretion scenario for planetary growth. As planets grow, type II migration takes over. Planet growth and radial movement are ultimately stalled by the dispersal of gas disks via photoevaporation. Our model makes a number of important predictions: that distinct sub-populations of planets that reflect the properties of planet traps where they have grown result in the mass-period relation; that the presence of these sub-populations naturally explains a pile-up of planets at $\sim 1$ AU; and that evolutionary tracks from the ice line do put planets at short periods and fill an earlier claimed "planet desert" - sparse population of planets in the mass-semi-major axis diagram.Comment: 20 pages, 11 figures, 9 tables; accepted for publication in ApJ. No change in our conclusions while more discussion is added for supporting the importance of planet trap

ICB Nutrisolo Trichoderma® as growth promoter in soybean crops

Soybean is the most important crop in the world due to growing external demand. Nevertheless, its production requires a high use of pesticides. Trichoderma is a fungal genus with the potential to promote plant growth because of its broad metabolic arsenal. Because it increases efficiency in several cultures, Trichoderma spp. have the potential to be used as an alternative to chemicals. Given this context, this study aimed to evaluate the performance of the ICB Nutrisolo Trichoderma® inoculant on parameters related to soybean growth and production. Crops with five different soil and climate conditions were evaluated in Rio Grande do Sul State (southern Brazil) using parameters such as average plant height, average plant population, average number of grains/pod, number of pods/plant average, and average weight of one thousand grains, which revealed the results of productivity. The ICB Nutrisolo Trichoderma® increased plant height, number of pods, and grain weight, consequently increasing productivity in soybean plants. In this way, it was possible to characterize the product ICB Nutrisolo Trichoderma® as a growth-promoting inoculant for the soybean crop, increasing the scope of product registration

Dead Zones and the Origin of Planetary Masses

Protoplanets accrete material from their natal protostellar disks until they are sufficiently massive to open a gap in the face of the disk's viscosity that arises from the magneto-rotational instability (MRI). By computing the ionization structure within observationally well-constrained disk models, we demonstrate that poorly ionized, low viscosity "dead zones" stretch out to 12 AU within typical disks. We find that planets of terrestrial mass robustly form within the dead zones while massive Jovian planets form beyond. Dead zones will also halt the rapid migration of planets into their central stars. Finally, we argue that the gravitational scattering of low mass planets formed in the dead zone, to larger radii by a rapidly accreting Jupiter beyond, can explain the distribution of planetary masses in our solar system.Comment: 10 pages, 4 figures, accepted for publication in ApJ

The Growth & Migration of Jovian Planets in Evolving Protostellar Disks with Dead Zones

The growth of Jovian mass planets during migration in their protoplanetary disks is one of the most important problems that needs to be solved in light of observations of the exosolar planets. Studies of the migration of planets in standard gas disk models routinely show that migration is too fast to form Jovian planets, and that such migrating planetary cores generally plunge into the central stars in less than a Myr. In previous work, we have shown that a poorly ionized, less viscous region in a protoplanetary disk called a dead zone slows down the migration of fixed-mass planets. In this paper, we extend our numerical calculations to include dead zone evolution along with the disk, as well as planet formation via accretion of rocky and gaseous materials. Using our symplectic-integrator-gas dynamics code, we find that dead zones, even in evolving disks wherein migrating planets grow by accretion, still play a fundamental role in saving planetary systems. We demonstrate that Jovian planets form within 2.5 Myr for disks that are ten times more massive than a minimum mass solar nebula (MMSN) with an opacity reduction and without slowing down migration artificially. Our simulations indicate that protoplanetary disks with an initial mass comparable to the MMSN only produce Neptunian mass planets. We also find that planet migration does not help core accretion as much in the oligarchic planetesimal accretion scenario as it was expected in the runaway accretion scenario. Therefore we expect that an opacity reduction (or some other mechanisms) is needed to solve the formation timescale problem even for migrating protoplanets, as long as we consider the oligarchic growth. We also point out a possible role of a dead zone in explaining long-lived, strongly accreting gas disks.Comment: 16 pages, 15 figures, accepted for publication in Ap

Assessing students' skills at writing analytically in response to texts

Despite the importance of writing analytically in response to texts, there are few assessments measuring students' mastery of this skill. This manuscript describes the development of a response-to-text assessment (RTA) intended for use in research. In a subsequent validity investigation we examined whether the RTA distinguished among classrooms in students' ability to write analytically in response to text and whether measures of teaching predicted this variation. We demonstrate that the RTA was correlated with the state standardized assessment, but did not overlap with this accountability test completely and, additionally, that more variation between classrooms existed on the RTA. Students' opportunities for reasoning and extended writing in the classroom were significantly associated with RTA scores. The findings suggest that the RTA can be a valuable tool for conducting research on students' attainment of analytic writing skills and for understanding how teaching relates to student achievement on these skills. © 2013 by The University of Chicago. All rights reserved

Combining Multiple Measures of Students' Opportunities to Develop Analytic, Text-Based Writing Skills

Guided by evidence that teachers contribute to student achievement outcomes, researchers have been reexamining how to study instruction and the classroom opportunities teachers create for students. We describe our experience measuring students' opportunities to develop analytic, text-based writing skills. Utilizing multiple methods of data collection-writing assignment tasks, daily logs, and an annual survey-we generated a composite that was used in prediction models to examine multivariate outcomes, including scores on a state accountability test and a project-developed response-to-text assessment. Our findings demonstrate that students' opportunities to develop analytic, text-based writing skills predicted classroom performance on the project-developed response-to-text assessment. We discuss the importance of considering the measure(s) of learning when examining teaching-learning associations as well as implications for combining multiple measures for purposes of better construct representation. © 2012 Copyright Taylor and Francis Group, LLC