Ordered groupoids and the holomorph of an inverse semigroup

We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap operation on an inverse semigroup: for groups these two constructions coincide. We present detailed calculations for semilattices of groups and for the polycyclic monoids.Comment: 16 page

Radial Structure in the TW Hya Circumstellar Disk

We present new near-infrared interferometric data from the CHARA array and the Keck Interferometer on the circumstellar disk of the young star, TW Hya, a proposed "transition disk." We use these data, as well as previously published, spatially resolved data at 10 μm and 7 mm, to constrain disk models based on a standard flared disk structure. We find that we can match the interferometry data sets and the overall spectral energy distribution with a three-component model, which combines elements at spatial scales proposed by previous studies: optically thin, emission nearest the star, an inner optically thick ring of emission at roughly 0.5 AU followed by an opacity gap and, finally, an outer optically thick disk starting at ~4 AU. The model demonstrates that the constraints imposed by the spatially resolved data can be met with a physically plausible disk but this requires a disk containing not only an inner gap in the optically thick disk as previously suggested, but also a gap between the inner and outer optically thick disks. Our model is consistent with the suggestion by Calvet et al. of a planet with an orbital radius of a few AU. We discuss the implications of an opacity gap within the optically thick disk

A Spectroscopic Orbit for Regulus

We present a radial velocity study of the rapidly rotating B-star Regulus that indicates the star is a single-lined spectroscopic binary. The orbital period (40.11 d) and probable semimajor axis (0.35 AU) are large enough that the system is not interacting at present. However, the mass function suggests that the secondary has a low mass (M_2 > 0.30 M_sun), and we argue that the companion may be a white dwarf. Such a star would be the remnant of a former mass donor that was the source of the large spin angular momentum of Regulus itself.Comment: 18 pages, 2 figures, ApJL in pres

The Evidence Chamber: Playful Science Communication and Research Through Digital Storytelling

In a courtroom, it is essential that the scientific evidence is both understandable and understood, so that the strengths and limitations of that evidence, within the context of a legal case, can inform decision making. The Evidence Chamber brings together entertainment, public engagement with science and research into a public performance activity that is centred around digital storytelling and science communication. This experience engages public audiences with science and allows a better understanding of how people interpret scientific evidence. In this paper, we discuss how we created this experience as an in-person and fully virtual performance through successful collaboration between forensic science research, public audiences, public engagement professionals, the legal profession, and digital performance artists

Multiplicity of Galactic Cepheids from long-baseline interferometry~III. Sub-percent limits on the relative brightness of a close companion of δ\delta~Cephei

We report new CHARA/MIRC interferometric observations of the Cepheid archetype $\delta$ Cep, which aimed at detecting the newly discovered spectroscopic companion. We reached a maximum dynamic range $\Delta H$ = 6.4, 5.8, and 5.2 mag, respectively within the relative distance to the Cepheid $r < 25$ mas, $25 < r < 50$ mas and $50 < r < 100$ mas. Our observations did not show strong evidence of a companion. We have a marginal detection at $3\sigma$ with a flux ratio of 0.21\%, but nothing convincing as we found other possible probable locations. We ruled out the presence of companion with a spectral type earlier than F0V, A1V and B9V, respectively for the previously cited ranges $r$. From our estimated sensitivity limits and the Cepheid light curve, we derived lower-limit magnitudes in the $H$ band for this possible companion to be $H_\mathrm{comp} > 9.15, 8.31$ and 7.77 mag, respectively for $r < 25$ mas, $25 < r < 50$ mas and $50 < r < 100$ mas. We also found that to be consistent with the predicted orbital period, the companion has to be located at a projected separation $< 24$ mas with a spectral type later than a F0V star.Comment: Accepted for publication in MNRA

Interferometric radii of bright Kepler stars with the CHARA Array: {\theta} Cygni and 16 Cygni A and B

We present the results of long-baseline optical interferometry observations using the Precision Astronomical Visual Observations (PAVO) beam combiner at the Center for High Angular Resolution Astronomy (CHARA) Array to measure the angular sizes of three bright Kepler stars: {\theta} Cygni, and both components of the binary system 16 Cygni. Supporting infrared observations were made with the Michigan Infrared Combiner (MIRC) and Classic beam combiner, also at the CHARA Array. We find limb-darkened angular diameters of 0.753+/-0.009 mas for {\theta} Cyg, 0.539+/-0.007 mas for 16 Cyg A and 0.490+/-0.006 mas for 16 Cyg B. The Kepler Mission has observed these stars with outstanding photometric precision, revealing the presence of solar-like oscillations. Due to the brightness of these stars the oscillations have exceptional signal-to-noise, allowing for detailed study through asteroseismology, and are well constrained by other observations. We have combined our interferometric diameters with Hipparcos parallaxes, spectrophotometric bolometric fluxes and the asteroseismic large frequency separation to measure linear radii ({\theta} Cyg: 1.48+/-0.02 Rsun, 16 Cyg A: 1.22+/-0.02 Rsun, 16 Cyg B: 1.12+/-0.02 Rsun), effective temperatures ({\theta} Cyg: 6749+/-44 K, 16 Cyg A: 5839+/-42 K, 16 Cyg B: 5809+/-39 K), and masses ({\theta} Cyg: 1.37+/-0.04 Msun, 16 Cyg A: 1.07+/-0.05 Msun, 16 Cyg B: 1.05+/-0.04 Msun) for each star with very little model dependence. The measurements presented here will provide strong constraints for future stellar modelling efforts.Comment: 9 pages, 4 figures, and 5 tables, accepted for publication in Monthly Notices of the Royal Astronomical Societ

Imaging the Algol Triple System in H Band with the CHARA Interferometer

Algol (Beta Per) is an extensively studied hierarchical triple system whose inner pair is a prototype semi-detached binary with mass transfer occurring from the sub-giant secondary to the main-sequence primary. We present here the results of our Algol observations made between 2006 and 2010 at the CHARA interferometer with the Michigan Infrared Combiner in the H band. The use of four telescopes with long baselines allows us to achieve better than 0.5 mas resolution and to unambiguously resolve the three stars. The inner and outer orbital elements, as well as the angular sizes and mass ratios for the three components are determined independently from previous studies. We report a significantly improved orbit for the inner stellar pair with the consequence of a 15% change in the primary mass compared to previous studies. We also determine the mutual inclination of the orbits to be much closer to perpendicularity than previously established. State-of-the-art image reconstruction algorithms are used to image the full triple system. In particular an image sequence of 55 distinct phases of the inner pair orbit is reconstructed, clearly showing the Roche-lobe-filling secondary revolving around the primary, with several epochs corresponding to the primary and secondary eclipses

Improving the surface brightness-color relation for early-type stars using optical interferometry

The aim of this work is to improve the SBC relation for early-type stars in the $-1 \leq V-K \leq 0$ color domain, using optical interferometry. Observations of eight B- and A-type stars were secured with the VEGA/CHARA instrument in the visible. The derived uniform disk angular diameters were converted into limb darkened angular diameters and included in a larger sample of 24 stars, already observed by interferometry, in order to derive a revised empirical relation for O, B, A spectral type stars with a V-K color index ranging from -1 to 0. We also took the opportunity to check the consistency of the SBC relation up to $V-K \simeq 4$ using 100 additional measurements. We determined the uniform disk angular diameter for the eight following stars: $\gamma$ Ori, $\zeta$ Per, $8$ Cyg, $\iota$ Her, $\lambda$ Aql, $\zeta$ Peg, $\gamma$ Lyr, and $\delta$ Cyg with V-K color ranging from -0.70 to 0.02 and typical precision of about $1.5\%$. Using our total sample of 132 stars with $V-K$ colors index ranging from about $-1$ to $4$, we provide a revised SBC relation. For late-type stars ($0 \leq V-K \leq 4$), the results are consistent with previous studies. For early-type stars ($-1 \leq V-K \leq 0$), our new VEGA/CHARA measurements combined with a careful selection of the stars (rejecting stars with environment or stars with a strong variability), allows us to reach an unprecedented precision of about 0.16 magnitude or $\simeq 7\%$ in terms of angular diameter.Comment: 13 pages, 5 figures, accepted for publication in A&