Homi Bhabha Centre for Science Education

In addition to its search for extrasolar planets, the NASA Kepler mission provides exquisite data on stellar oscillations. We report the detections of oscillations in 500 solar-type stars in the Kepler field of view, an ensemble that is large enough to allow statistical studies of intrinsic stellar properties (such as mass, radius, and age) and to test theories of stellar evolution. We find that the distribution of observed masses of these stars shows intriguing differences to predictions from models of synthetic stellar populations in the Galaxy.

Let G be a compact <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -adic Lie group, with no element of order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> , and having a closed normal subgroup H such that G/H is isomorphic to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>𝐙</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:math> . We prove the existence of a canonical Ore set <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>S</mml:mi> <mml:mo>*</mml:mo> </mml:msup> </mml:math> of non-zero divisors in the Iwasawa algebra <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Λ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>S</mml:mi> <mml:mo>*</mml:mo> </mml:msup> </mml:math> , we are able to define a characteristic element for every finitely generated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Λ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -module M which has the property that the quotient of M by its <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -primary submodule is finitely generated over the Iwasawa algebra of H. We discuss the evaluation of this characteristic element at Artin representations of G, and its relation to the G-Euler characteristics of the twists of M by such representations. Finally, we illustrate the arithmetic applications of these ideas by formulating a precise version of the main conjecture of Iwasawa theory for an elliptic curve E over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>𝐐</mml:mi> </mml:math> , without complex multiplication, over the field F generated by the coordinates of all its p-power division points; here <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> is a prime at least 5 where E has good ordinary reduction, and G is the Galois group of F over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>𝐐</mml:mi> </mml:math> .

Teachers' questions in the inquiry classroom not only explore and make student thinking explicit in the class but also serve to guide and scaffold it. Several studies analysing teachers' questions and their categories have been reported; however the need for a fine-grained analysis has been felt, especially in the inquiry setting. This study attempts a fine-grained analysis of the rich variety of teachers' questions and their roles in an inquiry science classroom, which are illustrated with vignettes from our classes. We present a sequential typology of teachers' questions that emerged from this empirical study, one that brings out their progression in an inquiry class. We juxtapose them with the ones asked during traditional teaching. We also examine, through teachers' self-reports, their motivations for questioning. This work leads towards a characterisation of the complex process of teaching science as an inquiry that teachers interested in moving towards more constructivist teaching practices in their classrooms may find helpful.

Recently the number of main-sequence and subgiant stars exhibiting solar-like oscillations that are resolved into individual mode frequencies has increased dramatically. While only a few such data sets were available for detailed modeling just a decade ago, the Kepler mission has produced suitable observations for hundreds of new targets. This rapid expansion in observational capacity has been accompanied by a shift in analysis and modeling strategies to yield uniform sets of derived stellar properties more quickly and easily. We use previously published asteroseismic and spectroscopic data sets to provide a uniform analysis of 42 solar-type Kepler targets from the Asteroseismic Modeling Portal. We find that fitting the individual frequencies typically doubles the precision of the asteroseismic radius, mass, and age compared to grid-based modeling of the global oscillation properties, and improves the precision of the radius and mass by about a factor of three over empirical scaling relations. We demonstrate the utility of the derived properties with several applications.

Abstract While there is a growing body of work that examines disciplinary identity development, unlike qualitative work in this area, quantitative research has not fully incorporated the importance of different contexts, nor has it uniquely focused on underrepresented groups (in this case, women in physics). This study examines how the constructs posited by prior work as important for physics identity, as well as an additional theorized construct, may interrelate and affect female students' physics identity differently depending on the context. Context in this study refers to two different experiential levels in college. The constructs examined include performance/competence, recognition, and interest, as well as sense of belonging. In particular, we used structural equation modeling to examine the effect that these constructs have on the physics identity of two groups of female physics undergraduates: first year students and senior year students. The results reveal that the relationship of the theorized constructs with physics identity vary between the two groups as well as compared to prior research with broad college student populations (not just physics majors). Unlike broad college student populations, for our sample of female physics undergraduates, interest did not have a direct effect on physics identity while sense of belonging was significant only for senior year students. These results exemplify the importance of examining context or different types of student experiences when studying disciplinary identity development rather than generalizing previous frameworks to all contexts.

The previously proposed molecular tailoring approached (MTA) [Deshmukh, M. M.; Gadre, S. R.; Bartolotti, L. J. J. Phys. Chem. A 2006, 110, 12519] for the estimation of intramolecular O-H...O hydrogen bond energy is extended to that for the N-H...O=C bond within polypeptides. The methodology is initially tested on a tetrapeptide containing two types of N-H...O=C hydrogen bonds and is found to distinguish between them. The estimated values are in good agreement with the trends predicted by the geometrical parameters. Furthermore, this methodology is applied to partially as well as fully substituted, capped polyglycines that contain five glycine residues (acetyl-(gly)(5)-NH(2)) to check the effect of substituents on the energetics of hydrogen bonds. The estimated N-H...O=C bond energy values lie in the range of 4-6 kcal/mol. These estimated values are not only in concurrence with the geometric parameters but also able to reflect the subtle effects of substituents for the substituted polypeptides studied in the present work.

For the very best and brightest asteroseismic solar-type targets observed by Kepler, the frequency precision is sufficient to determine the acoustic depths of the surface convective layer and the helium ionization zone. Such sharp features inside the acoustic cavity of the star, which we call acoustic glitches, create small oscillatory deviations from the uniform spacing of frequencies in a sequence of oscillation modes with the same spherical harmonic degree. We use these oscillatory signals to determine the acoustic locations of such features in 19 solar-type stars observed by the Kepler mission. Four independent groups of researchers utilized the oscillation frequencies themselves, the second differences of the frequencies and the ratio of the small and large separation to locate the base of the convection zone and the second helium ionization zone. Despite the significantly different methods of analysis, good agreement was found between the results of these four groups, barring a few cases. These results also agree reasonably well with the locations of these layers in representative models of the stars. These results firmly establish the presence of the oscillatory signals in the asteroseismic data and the viability of several techniques to determine the location of acoustic glitches inside stars.

Abstract This paper surveys some major trends from research on visual and spatial thinking coming from cognitive science, developmental psychology, science literacy, and science studies. It explores the role of visualisation in creativity, in building mental models, and in the communication of scientific ideas, in order to place these findings in the context of science education research and practice. Keywords: Science educationTransformational reasoningVisual and spatial learning Notes The original version of this paper is a part of epiSTEME‐2 reviews, edited by B. Choksi and C. Natarajan and published in 2008 by Macmillan India Ltd. Visual presentation at epiSTEME‐2 held at the Homi Bhabha Centre for Science Education, TIFR, Mumbai, in February 2007. See http://www.hbcse.tifr.res.in/ep2visual-presentation.pdf.

We present the discovery of HD 221416 b, the first transiting planet identified by the Transiting Exoplanet Survey Satellite (TESS) for which asteroseismology of the host star is possible. HD 221416 b (HIP 116158, TOI-197) is a bright (V = 8.2 mag), spectroscopically classified subgiant that oscillates with an average frequency of about 430 μHz and displays a clear signature of mixed modes. The oscillation amplitude confirms that the redder TESS bandpass compared to Kepler has a small effect on the oscillations, supporting the expected yield of thousands of solar-like oscillators with TESS 2 minute cadence observations. Asteroseismic modeling yields a robust determination of the host star radius (R ⋆ = 2.943 ± 0.064 R ⊙), mass (M ⋆ = 1.212 ± 0.074 M ⊙), and age (4.9 ± 1.1 Gyr), and demonstrates that it has just started ascending the red-giant branch. Combining asteroseismology with transit modeling and radial-velocity observations, we show that the planet is a “hot Saturn” (R p = 9.17 ± 0.33 R ⊕) with an orbital period of ∼14.3 days, irradiance of F = 343 ± 24 F ⊕, and moderate mass (M p = 60.5 ± 5.7 M ⊕) and density (ρ p = 0.431 ± 0.062 g cm‑3). The properties of HD 221416 b show that the host-star metallicity–planet mass correlation found in sub-Saturns (4–8 R ⊕) does not extend to larger radii, indicating that planets in the transition between sub-Saturns and Jupiters follow a relatively narrow range of densities. With a density measured to ∼15%, HD 221416 b is one of the best characterized Saturn-size planets to date, augmenting the small number of known transiting planets around evolved stars and demonstrating the power of TESS to characterize exoplanets and their host stars using asteroseismology.

The structural stratification of a solar-type main-sequence star primarily depends on its mass and chemical composition. The surface heavy element abundances of the solar-type stars are reasonably well determined using conventional spectroscopy; however, the second most abundant element helium is not. This is due to the fact that the envelope temperature of such stars is not high enough to excite helium. Since the helium abundance of a star affects its structure and subsequent evolution, the uncertainty in the helium abundance of a star makes estimates of its global properties (mass, radius, age etc.) uncertain as well. The detections of the signatures of the acoustic glitches from the precisely measured stellar oscillation frequencies provide an indirect way to estimate the envelope helium content. We use the glitch signature caused by the ionization of helium to determine the envelope helium abundance of 38 stars in the Kepler seismic LEGACY sample. Our results confirm that atomic diffusion does indeed take place in solar-type stars. We use the measured surface abundances in combination with the settling predicted by the stellar models to determine the initial abundances. The initial helium and metal mass fractions have subsequently been used to get the preliminary estimates of the primordial helium abundance, Y p = 0.244 0.019, and the Galactic enrichment ratio, Y/ Z = 1.226 0.849. Although the current estimates have large errorbars due to the limited sample size, this method holds great promises to determine these parameters precisely in the era of upcoming space missions.

Multiple external representations (MERs) are central to the practice and learning of science, mathematics and engineering, as the phenomena and entities investigated and controlled in these domains are often not available for perception and action. MERs therefore play a twofold constitutive role in reasoning in these domains. Firstly, MERs stand in for the phenomena and entities that are imagined, and thus make possible scientific investigations. Secondly, related to the above, sensorimotor and imagination-based interactions with the MERs make possible focused cognitive operations involving these phenomena and entities, such as mental rotation and analogical transformations. These two constitutive roles suggest that acquiring expertise in science, mathematics and engineering requires developing the ability to transform and integrate the MERs in that field, in tandem with running operations in imagination on the phenomena and entities the MERs stand for. This core ability to integrate external and internal representations and operations on them – termed representational competence (RC) – is therefore critical to learning in science, mathematics and engineering. However, no general account of this core process is currently available. We argue that, given the above two constitutive roles played by MERs, a theoretical account of representational competence requires an explicit model of how the cognitive system interacts with external representations, and how imagination abilities develop through this process. At the applied level, this account is required to develop design guidelines for new media interventions for learning science and mathematics, particularly emerging ones that are based on embodied interactions. As a first step to developing such a theoretical account, we review the literature on learning with MERs, as well as acquiring RC, in chemistry, biology, physics, mathematics and engineering, from two perspectives. First, we focus on the important theoretical accounts and related empirical studies, and examine what is common about them. Second, we summarise the major trends in each discipline, and then bring together these trends. The results show that most models and empirical studies of RC are framed within the classical information processing approach, and do not take a constitutive view of external representations. To develop an account compatible with the constitutive view of external representations, we outline an interaction-based theoretical account of RC, extending recent advances in distributed and embodied cognition.

Over the course of its history, the Milky Way has ingested multiple smaller satellite galaxies1. Although these accreted stellar populations can be forensically identified as kinematically distinct structures within the Galaxy, it is difficult in general to date precisely the age at which any one merger occurred. Recent results have revealed a population of stars that were accreted via the collision of a dwarf galaxy, called Gaia–Enceladus1, leading to substantial pollution of the chemical and dynamical properties of the Milky Way. Here we identify the very bright, naked-eye star ν Indi as an indicator of the age of the early in situ population of the Galaxy. We combine asteroseismic, spectroscopic, astrometric and kinematic observations to show that this metal-poor, alpha-element-rich star was an indigenous member of the halo, and we measure its age to be $$11.0\pm 0.7$$ (stat) $$\pm 0.8$$ (sys) billion years. The star bears hallmarks consistent with having been kinematically heated by the Gaia–Enceladus collision. Its age implies that the earliest the merger could have begun was 11.6 and 13.2 billion years ago, at 68% and 95% confidence, respectively. Computations based on hierarchical cosmological models slightly reduce the above limits. Bright star $$\nu$$ Indi shows elevated levels of alpha-process elements, suggesting great age, and is kinematically heated, probably from the merger of a dwarf galaxy with the Milky Way. Chaplin et al. make a case for $$\nu$$ Indi being an accurate indicator of the timing for the Gaia–Enceladus merger.

The complete and incomplete fusion cross sections for $^{9}\mathrm{Be}+^{124}\mathrm{Sn}$ reaction have been deduced using the online $\ensuremath{\gamma}$-ray measurement technique. Complete fusion at energies above the Coulomb barrier was found to be suppressed by $~28%$ compared to the coupled-channels calculations and is in agreement with the systematics of L. R. Gasques et al. [Phys. Rev. C 79, 034605 (2009)]. Study of the projectile dependence for fusion on a $^{124}\mathrm{Sn}$ target shows that, for $^{9}\mathrm{Be}$ nuclei, the enhancement at below-barrier energies is substantial compared to that of tightly bound nuclei.

Novel computational representations, such as simulation models of complex systems and video games for scientific discovery (Foldit, EteRNA etc.), are dramatically changing the way discoveries emerge in science and engineering. The cognitive roles played by such computational representations in discovery are not well understood. We present a theoretical analysis of the cognitive roles such representations play, based on an ethnographic study of the building of computational models in a systems biology laboratory. Specifically, we focus on a case of model-building by an engineer that led to a remarkable discovery in basic bioscience. Accounting for such discoveries requires a distributed cognition (DC) analysis, as DC focuses on the roles played by external representations in cognitive processes. However, DC analyses by and large have not examined scientific discovery, and they mostly focus on memory offloading, particularly how the use of existing external representations changes the nature of cognitive tasks. In contrast, we study discovery processes and argue that discoveries emerge from the processes of building the computational representation. The building process integrates manipulations in imagination and in the representation, creating a coupled cognitive system of model and modeler, where the model is incorporated into the modeler's imagination. This account extends DC significantly, and we present some of the theoretical and application implications of this extended account.

16 Cyg A and B are among the brightest stars observed by Kepler. What makes these stars more interesting is that they are solar analogs. 16 Cyg A and B exhibit solar-like oscillations. In this work we use oscillation frequencies obtained using 2.5 years of Kepler data to determine the current helium abundance of these stars. For this we use the fact that the helium ionization zone leaves a signature on the oscillation frequencies and that this signature can be calibrated to determine the helium abundance of that layer. By calibrating the signature of the helium ionization zone against models of known helium abundance, the helium abundance in the envelope of 16 Cyg A is found to lie in the range 0.231 to 0.251 and that of 16 Cyg B lies in the range 0.218 to 0.266.

About 1% of giant stars have been shown to have large surface Li abundances, which is unexpected according to standard stellar evolution models. Several scenarios for lithium production have been proposed, but it is still unclear why these Li-rich giants exist. A missing piece in this puzzle is the knowledge of the exact stage of evolution of these stars. Using low-and-high-resolution spectroscopic observations, we have undertaken a survey of lithium-rich giants in the Kepler field. In this Letter, we report the finding of the first confirmed Li-rich core-helium-burning giant, as revealed by asteroseismic analysis. The evolutionary timescales constrained by its mass suggest that Li production most likely took place through non-canonical mixing at the RGB tip, possibly during the helium flash.

In this study, we examine how subjects set up, transform, and reason with models that they establish on the basis of known facts as they seek to explain a familiar everyday phenomenon—the phases of the moon. An interview schedule was designed to elicit subjects’ reasoning, and in the case where explanations were mistaken, to induce a change in explanation. Detailed interviews of eight participants were videotaped and their reasoning analysed to highlight the difficulties encountered, the interaction between physical and geometrical aspects, simplification and idealisation processes, interplay between facts, concepts and visualisation, and the use of external visualisations through gestures and diagrams. We suggest that visualisation is an important process in science learning, and point to the importance of developing among students the ability to work with diagrams.

Context. With the advent of space-based asteroseismology, determining accurate properties of red-giant stars using their observed oscillations has become the focus of many investigations due to their implications in a variety of fields in astrophysics. Stellar models are fundamental in predicting quantities such as stellar age, and their reliability critically depends on the numerical implementation of the physics at play in this evolutionary phase. Aims. We introduce the Aarhus red giants challenge, a series of detailed comparisons between widely used stellar evolution and oscillation codes that aim to establish the minimum level of uncertainties in properties of red giants arising solely from numerical implementations. We present the first set of results focusing on stellar evolution tracks and structures in the red-giant-branch (RGB) phase. Methods. Using nine state-of-the-art stellar evolution codes, we defined a set of input physics and physical constants for our calculations and calibrated the convective efficiency to a specific point on the main sequence. We produced evolutionary tracks and stellar structure models at a fixed radius along the red-giant branch for masses of 1.0 M ⊙ , 1.5 M ⊙ , 2.0 M ⊙ , and 2.5 M ⊙ , and compared the predicted stellar properties. Results. Once models have been calibrated on the main sequence, we find a residual spread in the predicted effective temperatures across all codes of ∼20 K at solar radius and ∼30–40 K in the RGB regardless of the considered stellar mass. The predicted ages show variations of 2–5% (increasing with stellar mass), which we attribute to differences in the numerical implementation of energy generation. The luminosity of the RGB-bump shows a spread of about 10% for the considered codes, which translates into magnitude differences of ∼0.1 mag in the optical V -band. We also compare the predicted [C/N] abundance ratio and find a spread of 0.1 dex or more for all considered masses. Conclusions. Our comparisons show that differences at the level of a few percent still remain in evolutionary calculations of red giants branch stars despite the use of the same input physics. These are mostly due to differences in the energy generation routines and interpolation across opacities, and they call for further investigation on these matters in the context of using properties of red giants as benchmarks for astrophysical studies.

Abstract Acoustic glitches are regions inside a star where the sound speed or its derivatives change abruptly. These leave a small characteristic oscillatory signature in the stellar oscillation frequencies. With the precision achieved by Kepler seismic data, it is now possible to extract these small amplitude oscillatory signatures, and infer the locations of the glitches. We perform glitch analysis for all the 66 stars in the Kepler seismic LEGACY sample to derive the locations of the base of the envelope convection zone (CZ) and the helium ionization zone. The signature from helium ionization zone is found to be robust for all stars in the sample, whereas the CZ signature is found to be weak and problematic, particularly for relatively massive stars with large errorbars on the oscillation frequencies. We demonstrate that the helium glitch signature can be used to constrain the properties of the helium ionization layers and the helium abundance.

We have considered nonuniversal gaugino mass models of supergravity, arising from a mixture of two superfield contributions to the gauge kinetic term, belonging to a singlet and a nonsinglet representation of the grand unified theory group. In particular we analyze two models, where the contributing superfields belong to the singlet and the 75-dimensional, and the singlet and the 200-dimensional representations of $SU(5)$. The resulting lightest superparticle is a mixed bino-Higgsino state in the first case and a mixed bino-wino-Higgsino state in the second. In both cases one obtains cosmologically compatible dark matter relic density over broad regions of the parameter space. We predict promising signals in direct dark matter detection experiments as well as in indirect detection experiments via high energy neutrinos coming from their pair annihilation in the Sun. Besides, we find interesting $\ensuremath{\gamma}$-ray signal rates that will be probed in the Fermi gamma-ray space telescope. We also expect promising collider signals at LHC in both cases.