Design and Development of a Learning Progression about Stellar Structure and Evolution

[This paper is part of the Focused Collection on Astronomy Education Research.] In this paper we discuss the design and development of a learning progression (LP) to describe and interpret students' understanding about stellar structure and evolution (SSE). The LP is built upon three content dimensions: hydrostatic equilibrium; composition and aggregation state; functioning and evolution. The data to build up the levels of the hypothetical LP (LP1) came from a 45-minute, seven-question interview, with 33 high school students previously taught about the topic. The questions were adapted from an existing multiple-choice instrument. Data were analyzed using Minstrell's "facets" approach. To assess the validity of LP1, we designed a twelve-hour teaching module featuring paper-and-pencil tasks and practical activities to estimate the stellar structure and evolution parameters. Twenty high school students were interviewed before and after the activities using the same interview protocol. Results informed a revision of LP1 (LP2) and, in parallel, of the module. The revised module included supplementary activities corresponding to changes made to LP1. We then assessed LP2 with 30 high school students through the same interview, submitted before and after the teaching intervention. A final version of the LP (LP3) was then developed drawing on students' emerging reasoning strategies. This paper contributes to research in science education by providing an example of the iterative development of the instruction required to support the student thinking that LPs' levels describe. Concerning astronomy education research, our findings can inform suitable instructional activities more responsive to students' reasoning strategies about stellar structure and evolution

Developing the use of visual representations to explain basic astronomy phenomena

Several decades of research have contributed to our understanding of students’ reasoning about astronomical phenomena. Some authors have pointed out the difficulty in reading and interpreting images used in school textbooks as factors that may justify the persistence of misconceptions. However, only a few studies have investigated to what extent usual textbook images influence students’ understanding of such phenomena. This study examines this issue exploring 13-14 years old students’ explanations, drawings and conceptions about three familiar phenomena: change of seasons, Moon phases and solar/lunar eclipses. The research questions that guided the study were: RQ1) How are students’ explanations and visual representations about familiar astronomical phenomena affected by different imagesupport conditions? RQ2) How are students’ conceptions about familiar astronomical phenomena affected by different image-support conditions? RQ3) Which features of the used images most affected the students’ visual representations and explanations of familiar astronomical phenomena? To answer our research questions, we designed three instructional contexts under increasing support conditions: textbook images and text; teaching booklets with specially designed images and text; only text. To analyze students’ drawings, we used exploratory factor analysis to deconstruct drawings into their most salient elements. To analyze students’ explanations, we adopted a constant comparison method identifying different levels of increasing knowledge. To investigate students’ conceptions, we used a mixed multiple choice/true false baseline questionnaire. For RQ1, results show that the specially designed images condition was effective in helping students producing informed drawings in comparison to text-only condition for all phenomena, and more effective than textbook images condition when one considers seasonal change drawings. Concerning RQ2, the specially designed images condition was the most effective for all phenomena. Concerning RQ3, prevalent elements of astronomy images that affected students’ explanations and visual representations were: elliptical Earth's orbit, position of the Sun with respect to the Moon orbit, Sun, Moon and Earth alignment. Our findings confirm concerns about textbook astronomy images, whose features may interfere with the identification of the relevant factors underlying the phenomena. Moreover, findings of this study suggest that affordances of the specially designed images may play an essential role in scaffolding meaningful understanding of the targeted phenomena. Implications for teaching through and learning from visual representations in astronomy education are briefly discussed

Updated theoretical Period-Age and Period-Age-Color relations for Galactic Classical Cepheids: an application to the Gaia DR2 sample

Updated evolutionary and pulsational model predictions are combined in order to interpret the properties of Galactic Classical Cepheids in the Gaia Data Release 2. In particular, the location of the instability strip boundaries and the analytical relations connecting pulsation periods to the intrinsic stellar parameters are combined with evolutionary tracks to derive reliable and accurate period-age, and the first theoretical period-age-color relations in the Gaia bands for a solar chemical abundance pattern ($Z$=$0.02$, $Y$=$0.28$). The adopted theoretical framework takes into account possible variations in the mass-luminosity relation for the core helium-burning stage as due to changes in the core convective overshooting and/or mass loss efficiency, as well as the impact on the instability strip boundaries due to different assumptions for superadiabatic convection efficiency. The inferred period-age and period-age-color relations are applied to a selected sample of both fundamental and first overtone Gaia Cepheids, and individual ages for the various adopted theoretical scenarios are derived. The retrieved age distributions confirm that a variation in the efficiency of superadiabatic convection in the pulsational model computations has a negligible effect, whereas a brighter Mass-Luminosity relation, as produced by mild overshooting, rotation or mass loss, implies significantly older age predictions. Moreover, older Cepheids are found at larger Galactocentric distances, while first overtone Cepheids are found to be systematically older than the fundamental ones. The comparison with independent age distribution analysis in literature supports the predictive capability of current theoretical framework.Comment: 14 pages, 11 figures, 8 tables, accepted for publication in MNRA

Detection of solar-like oscillations in the G5 subgiant mu-Herculis

A clear detection of excess of power, providing a substantial evidence for solar-like oscillations in the G5 subgiant \muher{}, is presented. This star was observed over seven nights with the SARG echelle spectrograph operating with the 3.6-m Italian TNG Telescope, using an iodine absorption cell as a velocity reference. A clear excess of power centered at 1.2 mHz, with peak amplitudes of about 0.9 \ms in the amplitude spectrum is present. Fitting the asymptotic relation to the power spectrum, a mode identification for the $\ell=0,1,2,3$ modes in the frequency range 900-1600 \muHz is derived. The most likely value for the large separation turns out to be 56.5 \muHz, consistent with theoretical expectations. The mean amplitude per mode ($l=0,1$) at peak power results to be $0.63 \rm m s^{-1}$, almost three times larger than the solar one.Comment: 8 pages, 6 figures, ApJ to appea

The Hertzsprung progression of Classical Cepheids in the Gaia era

A new fine grid of nonlinear convective pulsation models for the so-called "bump Cepheids" is presented to investigate the Hertzprung progression (HP) phenomenon shown by their light and radial pulsation velocity curves. The period corresponding to the center of the HP is investigated as a function of various model assumptions, such as the efficiency of super-adiabatic convection, the mass-luminosity relation, and the metal and helium abundances. The assumed mass-luminosity relation is found to significantly affect the phenomenon but variations in the chemical composition as well as in the stellar mass (at fixed mass-luminosity relation) also play a key role in determining the value of the HP center period. Finally, the predictive capability of the presented theoretical scenario is tested against observed light curves of bump Cepheids in the ESA Gaia database, also considering the variation of the pulsation amplitudes and of the Fourier parameters $R_{21}$ and $\Phi_{21}$ with the pulsation period. A qualitative agreement between theory and observations is found for what concerns the evolution of the light curve morphology as the period moves across the HP center, as well for the pattern in period-amplitude, period-$R21$ and period-$\Phi_{21}$ planes. A larger sample of observed Cepheids with accurate light curves and metallicities is required in order to derive more quantitative conclusions.Comment: Accepted for publication on MNRA

Standard candles from the Gaia perspective

The ESA Gaia mission will bring a new era to the domain of standard candles. Progresses in this domain will be achieved thanks to unprecedented astrometric precision, whole-sky coverage and the combination of photometric, spectrophotometric and spectroscopic measurements. The fundamental outcome of the mission will be the Gaia catalogue produced by the Gaia Data Analysis and Processing Consortium (DPAC), which will contain a variable source classification and specific properties for stars of specific variability types. We review what will be produced for Cepheids, RR Lyrae, Long Period Variable stars and eclipsing binarie

Predicted Masses of Galactic Cepheids in the Gaia Data Release 2

On the basis of recently computed nonlinear convective pulsation models of Galactic Cepheids, spanning wide ranges of input stellar parameters, we derive theoretical mass-dependent Period-Wesenheit relations in the Gaia bands, namely, G, G BP, and G BR, that are found to be almost independent of the assumed efficiency of superadiabatic convection. The application to a selected subsample of the Gaia Data Release 2 Galactic Cepheids database allows us to derive mass-dependent estimates of their individual distances. By imposing their match with the astrometric values inferred from Gaia, we are able to evaluate the individual mass of each pulsator. The inferred mass distribution is peaked around 5.6M o˙ and 5.4M o˙ for the F and FO pulsators, respectively. If the estimated Gaia parallax offset «Δϖ» mas is applied to Gaia parallaxes before imposing their coincidence with the theoretical ones, the inferred mass distribution is found to shift toward lower masses, namely, ∼5.2M o˙ and 5.1M o˙ for the F and FO pulsators, respectively. The comparison with independent evaluations of the stellar masses, for a subset of binary Cepheids in our sample, seems to support the predictive capability of the current theoretical scenario. By forcing the coincidence of our mass determinations with these literature values we derive an independent estimate of the mean offset to be applied to Gaia DR2 parallaxes, «Δϖ» = 0.053 ± 0.029 mas, slightly higher but in agreement within the errors with the Riess et al. value

Period-Age-Metallicity and Period-Age-Color-Metallicity relations for Classical Cepheids: an application to the Gaia EDR3 sample

Based on updated pulsation models for Classical Cepheids, computed for various assumptions about the metallicity and helium abundance, roughly representative of pulsators in the Small Magellanic Cloud ($Z$=$0.004$ and $Y$=$0.25$), Large Magellanic Cloud ($Z$=$0.008$ and $Y$=$0.25$), and M31 ($Z$=$0.03$ and $Y$=$0.28$), and self-consistent updated evolutionary predictions, we derived Period-Age and multi-band Period-Age-Color relations that also take into account variations in the Mass-Luminosity relation. These results, combined with those previously derived for Galactic Cepheids, were used to investigate the metallicity effect when using these variables as age indicators. In particular, we found that a variation in the metal abundance affects both the slope and the zero point of the above-mentioned relations. The new relations were applied to a sample of Gaia Early Data Release 3 Classical Cepheids. The retrieved distribution of the individual ages confirms that a brighter Mass-Luminosity relation produces older ages and that First Overtone pulsators are found to be concentrated towards older ages with respect to the Fundamental ones at a fixed Mass-Luminosity relation. Moreover, the inclusion of a metallicity term in the Period-Age and Period-Age-Color relations slightly modifies the predicted ages. In particular, the age distribution of the selected sample of Galactic Cepheids is found to be shifted towards slightly older values, when the F-mode canonical relations are considered, with respect to the case at a fixed solar chemical composition. A marginally opposite dependence can be found in the noncanonical F-mode and canonical FO-mode cases

A theoretical scenario for Galactic RR Lyrae in the Gaia data base: constraints on the parallax offset

On the basis of an extended set of non-linear convective RR Lyrae pulsation models we derive the first theoretical light curves in the Gaia bands G, GBP, and GRP and the corresponding intensity-weighted mean magnitudes and pulsation amplitudes. The effects of chemical composition on the derived Bailey diagrams in the Gaia filters are discussed for both Fundamental and first overtone mode pulsators. The inferred mean magnitudes and colours are used to derive the first theoretical Period-Wesenheit relations for RR Lyrae in the Gaia filters. The application of the theoretical Period-Wesenheit relations for both the Fundamental and first overtone mode to Galactic RR Lyrae in the Gaia Data Release 2 data base and complementary information on individual metal abundances allows us to derive theoretical estimates of their individual parallaxes. These results are compared with the astrometric solutions to conclude that a very small offset, consistent with zero, is required in order to reconcile the predicted distances with Gaia results