Investigating the spectroscopic, magnetic and circumstellar variability of the O9 subgiant star HD 57682

The O9IV star HD 57682, discovered to be magnetic within the context of the MiMeS survey in 2009, is one of only eight convincingly detected magnetic O-type stars. Among this select group, it stands out due to its sharp-lined photospheric spectrum. Since its discovery, the MiMeS Collaboration has continued to obtain spectroscopic and magnetic observations in order to refine our knowledge of its magnetic field strength and geometry, rotational period, and spectral properties and variability. In this paper we report new ESPaDOnS spectropolarimetric observations of HD 57682, which are combined with previously published ESPaDOnS data and archival H{\alpha} spectroscopy. This dataset is used to determine the rotational period (63.5708 \pm 0.0057 d), refine the longitudinal magnetic field variation and magnetic geometry (dipole surface field strength of 880\pm50 G and magnetic obliquity of 79\pm4\circ as measured from the magnetic longitudinal field variations, assuming an inclination of 60\circ), and examine the phase variation of various lines. In particular, we demonstrate that the H{\alpha} equivalent width undergoes a double-wave variation during a single rotation of the star, consistent with the derived magnetic geometry. We group the variable lines into two classes: those that, like H{\alpha}, exhibit non-sinusoidal variability, often with multiple maxima during the rotation cycle, and those that vary essentially sinusoidally. Based on our modelling of the H{\alpha} emission, we show that the variability is consistent with emission being generated from an optically thick, flattened distribution of magnetically-confined plasma that is roughly distributed about the magnetic equator. Finally, we discuss our findings in the magnetospheric framework proposed in our earlier study.Comment: 21 pages, 19 figures, Accepted for publication in MNRA

Host control and nutrient trading in a photosynthetic symbiosis

Photosymbiosis is one of the most important evolutionary trajectories, resulting in the chloroplast and the subsequent development of all complex photosynthetic organisms. The ciliate Paramecium bursaria and the alga Chlorella have a well established and well studied light dependent endosymbiotic relationship. Despite its prominence, there remain many unanswered questions regarding the exact mechanisms of the photosymbiosis. Of particular interest is how a host maintains and manages its symbiont load in response to the allocation of nutrients between itself and its symbionts. Here we construct a detailed mathematical model, parameterised from the literature, that explicitly incorporates nutrient trading within a deterministic model of both partners. The model demonstrates how the symbiotic relationship can manifest as parasitism of the host by the symbionts, mutualism, wherein both partners benefit, or exploitation of the symbionts by the hosts. We show that the precise nature of the photosymbiosis is determined by both environmental conditions (how much light is available for photosynthesis) and the level of control a host has over its symbiont load. Our model provides a framework within which it is possible to pose detailed questions regarding the evolutionary behaviour of this important example of an established light dependent endosymbiosis; we focus on one question in particular, namely the evolution of host control, and show using an adaptive dynamics approach that a moderate level of host control may evolve provided the associated costs are not prohibitive