Evidence for coupling of evolved star atmospheres and spiral arms of the milky way

It is imperative to map the strength and distribution of feedback in galaxies to understand how feedback affects galactic ecosystems. H2O masers act as indicators of energy injection into the interstellar medium. Our goal is to measure the strength and distribution of feedback traced by water masers in the Milky Way. We identify optical counterparts to H2O masers discovered by the HOPS survey. The distribution and luminosities of H2O masers in the Milky Way are determined using parallax measurements derived from the second Gaia Data Release. We provide evidence of a correlation between evolved stars, as traced by H2O masers, and the spiral structure of the Milky Way, suggesting a link between evolved stars and the Galactic environment

Structural parameters for globular clusters in M31 and generalizations for the fundamental plane

The structures of globular clusters (GCs) reflect their dynamical states and past histories. High-resolution imaging allows the exploration of morphologies of clusters in other galaxies. Surface brightness profiles from new Hubble Space Telescope observations of 34 globular clusters in M31 are presented, together with fits of several different structural models to each cluster. M31 clusters appear to be adequately fit by standard King models, and do not obviously require alternate descriptions with relatively stronger halos, such as are needed to fit many GCs in other nearby galaxies. The derived structural parameters are combined with corrected versions of those measured in an earlier survey to construct a comprehensive catalog of structural and dynamical parameters for M31 GCs with a sample size similar to that for the Milky Way. Clusters in M31, the Milky Way, Magellanic Clouds, Fornax dwarf spheroidal and NGC 5128 define a very tight fundamental plane with identical slopes. The combined evidence for these widely different galaxies strongly reinforces the view that old globular clusters have near-universal structural properties regardless of host environment.Comment: AJ in press; 59 pages including 16 figure

Understanding Linear Function: A Comparison of Selected Textbooks from England and Shanghai

This study describes a comparison of how worked examples in selected textbooks from England and Shanghai presented possible learning trajectories towards understanding linear function. Six selected English textbooks and one Shanghai compulsory textbook were analysed with regards to the understanding required for pure mathematics knowledge in linear function. Understanding was defined as being at five levels: Dependent Relationship, Connecting Representations, Local Properties Noticing, Object Analysis and Inventising. These levels were developed by examining the most prominent theories from the existing literature on understanding function. Findings suggested that the English textbooks constrained the structural aspect of understanding linear function due to a point-to-point view of function, while the Shanghai textbook which focussed on a variable view of function overemphasised the algebraic approach. The discussion explored the drawbacks to each approach and what teachers or textbook writers could do to balance these two approaches in order to facilitate students’ understanding towards a structural view of linear function

Developing the use of diagrammatic representations in primary mathematics through professional development

Background: The research on diagrammatic representations highlights their importance for the teaching and learning of mathematics. However, the empirical evidence to support their use in the classroom is mixed and somewhat lacking. Purpose: The aim of this study was to develop the use of diagrammatic representations of mathematical concepts in primary classrooms, through introducing primary teachers to the research literature in this area, and researching the subsequent impact on children and teachers. A professional development programme was designed, involving three one-day training sessions for mathematics co-ordinators. They were asked to implement the ideas from the training back in their schools. Sample: Mathematics co-ordinators from eight primary schools attended the professional development programme. The study focussed on Year 3 pupils (aged seven–eight) and Year 5 pupils (aged nine–10). Design and methods: In this paper, we report the qualitative findings from the larger project looking at the overall impact of the professional development programme. The paper focuses on semi-structured interviews carried out with the mathematics co-ordinators attending the professional development sessions, and the Year 3 and Year 5 class teachers who subsequently worked with the co-ordinators on their use of diagrammatic representations in their teaching of mathematics. Lesson observations involving the class teachers were also carried out in order to explore further the possible impact of the project on classroom practice. Results: The qualitative results identified the impact of the project on mathematics co-ordinators and class teachers’ knowledge and practice. However, the nature of this impact was complex, with a variety of facilitating and hindering factors identified for the transfer of the professional development ideas on the use of diagrammatic representations. In addition, different levels of sophistication of class teachers’ use of diagrammatic representations were identified. Conclusions: Implications for the development of professional development programmes to facilitate the transfer of research into practice were identified. Recommendations for the use of diagrammatic representations are also put forward

Compact Star Clusters in the M31 Disk

We have carried out a survey of compact star clusters (apparent size <3 arcsec) in the southwest part of the M31 galaxy, based on the high-resolution Suprime-Cam images (17.5 arcmin x 28.5 arcmin), covering ~15% of the deprojected galaxy disk area. The UBVRI photometry of 285 cluster candidates (V < 20.5 mag) was performed using frames of the Local Group Galaxies Survey. The final sample, containing 238 high probability star cluster candidates (typical half-light radius r_h ~ 1.5 pc), was selected by specifying a lower limit of r_h > 0.15 arcsec (>0.6 pc). We derived cluster parameters based on the photometric data and multiband images by employing simple stellar population models. The clusters have a wide range of ages from ~5 Myr (young objects associated with 24 um and/or Ha emission) to ~10 Gyr (globular cluster candidates), and possess mass in a range of 3.0 < log(m/M_sol) < 4.3 peaking at m ~ 4000 M_sol. Typical age of these intermediate-mass clusters is in the range of 30 Myr < t < 3 Gyr, with a prominent peak at ~70 Myr. These findings suggest a rich intermediate-mass star cluster population in M31, which appears to be scarce in the Milky Way galaxy.Comment: 16 pages, 8 figures, 1 table, accepted for publication in Ap

Age Estimations of M31 Globular Clusters from Their Spectral Energy Distributions

This paper presents accurate spectral energy distributions (SEDs) of 16 M31 globular clusters (GCs) confirmed by spectroscopy and/or high spatial-resolution imaging, as well as 30 M31 globular cluster candidates detected by Mochejska et al. Most of these candidates have m_V > 18, deeper than previous searches, and these candidates have not yet been confirmed to be globular clusters. The SEDs of these clusters and candidates are obtained as part of the BATC Multicolor Survey of the Sky, in which the spectrophotometrically-calibrated CCD images of M31 in 13 intermediate-band filters from 4000 to 10000 A were observed. These filters are specifically designed to exclude most of the bright and variable night-sky emission lines including the OH forest. In comparison to the SEDs of true GCs, we find that some of the candidate objects are not GCs in M31. SED fits show that theoretical simple stellar population (SSP) models can fit the true GCs very well. We estimate the ages of these GCs by comparing with SSP models. We find that, the M31 clusters range in age from a few ten Myr to a few Gyr old, as well as old GCs, confirming the conclusion that has been found by Barmby et a, Williams & Hodge, Beasley et al., Burstein et al. and Puzia et al. in their investigations of the SEDs of M31 globular clusters.Comment: Accepted for Publication in A&Ap, 13 pages, 6 figure