Jon O. Sundqvist

A magnetic confinement versus rotation classification of massive-star magnetospheres

Building on results from the Magnetism in Massive Stars (MiMeS) project, this paper shows how a two-parameter classification of massive-star magnetospheres in terms of the magnetic wind confinement (which sets the Alfv´ en radius RA) and stellar rotation (which sets the Kepler co-rotation radius RK) provides a useful organization of both observational signatures and theoretical predictions. We compile the first comprehensive study of inferred and observed values for relevant stellar and magnetic parameters of 64 confirmed magnetic OB stars with Teff 16 kK. Using these parameters, we locate the stars in the magnetic confinement–rotation diagram, a log–log plot of RK versus RA. This diagram can be subdivided into regimes of centrifugal magnetospheres (CM), with RA > RK ,v ersusdynamical magnetospheres (DM), with RK > RA. We show how key observational diagnostics, like the presence and characteristics of Hα emission, depend on a star’s position within the diagram, as well as other parameters, especially the expected wind mass-loss rates. In particular, we identify two distinct populations of magnetic stars with Hα emission: namely, slowly rotating O-type stars with narrow emission consistent with a DM, and more rapidly rotating B-type stars with broader emission associated with a CM. For O-type stars, the high mass-loss rates are sufficient to accumulate enough material for line emission even within the relatively short free-fall time-scale associated with a DM: this high mass-loss rate also leads to a rapid magnetic spindown of the stellar rotation. For the B-type stars, the longer confinement of a CM is required to accumulate sufficient emitting material from their relatively weak winds, which also lead to much longer spindown time-scales. Finally, we discuss how other observational diagnostics, e.g. variability of UV wind lines or X-ray emission, relate to the inferred magnetic properties of these stars, and summarize prospects for future developments in our understanding of massive-star magnetospheres.

Mass loss from inhomogeneous hot star winds - I. Resonance line formation in 2D models

Context. The mass-loss rate is a key parameter of hot, massive stars. Small-scale inhomogeneities (clumping) in the winds of these stars are conventionally included in spectral analyses by assuming optically thin clumps, a void inter-clump medium, and a smooth velocity field. To reconcile investigations of different diagnostics (in particular, unsaturated UV resonance lines vs. Hα/radio emission) within such models, a highly clumped wind with very low mass-loss rates needs to be invoked, where the resonance lines seem to indicate rates an order of magnitude (or even more) lower than previously accepted values. If found to be realistic, this would challenge the radiative line-driven wind theory and have dramatic consequences for the evolution of massive stars. Aims. We investigate basic properties of the formation of resonance lines in small-scale inhomogeneous hot star winds with nonmonotonic velocity fields. Methods. We study inhomogeneous wind structures by means of 2D stochastic and pseudo-2D radiation-hydrodynamic wind models, constructed by assembling 1D snapshots in radially independent slices. A Monte-Carlo radiative transfer code, which treats the resonance line formation in an axially symmetric spherical wind (without resorting to the Sobolev approximation), is presented and used to produce synthetic line spectra. Results. The optically thin clumping limit is only valid for very weak lines. The detailed density structure, the inter-clump medium, and the non-monotonic velocity field are all important for the line formation. We confirm previous findings that radiationhydrodynamic wind models reproduce observed characteristics of strong lines (e.g., the black troughs) without applying the highly supersonic “microturbulence” needed in smooth models. For intermediate strong lines, the velocity spans of the clumps are of central importance. Current radiation-hydrodynamic models predict spans that are too large to reproduce observed profiles unless a very low mass-loss rate is invoked. By simulating lower spans in 2D stochastic models, the profile strengths become drastically reduced, and are consistent with higher mass-loss rates. To simultaneously meet the constraints from strong lines, the inter-clump medium must be non-void. A first comparison to the observed Phosphorus V doublet in the O6 supergiant λ Cep confirms that line profiles calculated from a stochastic 2D model reproduce observations with a mass-loss rate approximately ten times higher than that derived from the same lines but assuming optically thin clumping. Tentatively this may resolve discrepancies between theoretical predictions, evolutionary constraints, and recent derived mass-loss rates, and suggests a re-investigation of the clump structure predicted by current radiation-hydrodynamic models.

Mass loss from inhomogeneous hot star winds - II. Constraints from a combined optical/UV study

Context. Mass loss is essential for massive star evolution, thus also for the variety of astrophysical applications relying on it s predictions. However, mass-loss rates currently in use for hot, massive stars have recently been seriously questioned, mainl y because of the effects of wind clumping. Aims. We investigate the impact of clumping on diagnostic ultraviolet resonance and optical recombination lines often used to derive empirical mass-loss rates of hot stars. Optically thick clu mps, a non-void interclump medium, and a non-monotonic velocity field are all accounted for in a single model. The line formation is firs t theoretically studied, after which an exemplary multi-di agnostic study of an O-supergiant is performed. Methods. We used 2D and 3D stochastic and radiation-hydrodynamic wind models, constructed by assembling 1D snapshots in radially independent slices. To compute synthetic spectra, we developed and used detailed radiative transfer codes for both recombination lines (solving the ‘formal integral’) and resonance lines ( using a Monte-Carlo approach). In addition, we propose an analytic method to model these lines in clumpy winds, which does not rely on optically thin clumping. Results. The importance of the ‘vorosity’ effect for line formation in clumpy winds is emphasized. Resonance lines are generally more affected by optically thick clumping than recombination lines. Synthetic spectra calculated directly from current radia tionhydrodynamic wind models of the line-driven instability are unable to in parallel reproduce strategic optical and ultr aviolet lines for

Clumping in the inner winds of hot, massive stars from hydrodynamical line-driven instability simulations

We investigate the eects of stellar limb-darkening and photospheric perturbations for the onset of wind structure arising from the strong, intrinsic line-deshadowing instability (LDI) of a line-driven stellar wind. A linear perturbation analysis shows that including limb-darkening reduces the stabilizing eect of the diuse radiation, leading to a net instability growth rate even at the wind base. Numerical radiationhydrodynamics simulations of the non-linear evolution of this instability then show that, in comparison with previous models assuming a uniformly bright star without base perturbations, wind structure now develops much closer (r . 1:1R?) to the photosphere. This is in much better agreement with observations of O-type stars, which typically indicate the presence of strong clumping quite near the wind base.

A dynamical magnetosphere model for periodic Hα emission from the slowly rotating magnetic O star HD 191612

The magnetic O star HD 191612 exhibits strongly variable, cyclic Balmer line emission on a 538-d period. We show here that its variable Hα emission can be well reproduced by the rotational phase variation of synthetic spectra computed directly from full radiation magnetohydrodynamical simulations of a magnetically confined wind. In slow rotators such as HD 191612, wind material on closed magnetic field loops falls back to the star, but the transient suspension of material within the loops leads to a statistically overdense, low-velocity region around the magnetic equator, causing the spectral variations. We contrast such ‘dynamical magnetospheres’ (DMs) with the more steady-state ‘centrifugal magnetospheres’ of stars with rapid rotation, and discuss the prospects of using this DM paradigm to explain periodic line emission from also other non-rapidly rotating magnetic massive stars.

Discovery of a magnetic field in the rapidly rotating O-type secondary of the colliding-wind binary HD 47129 (Plaskett's star)

We report the detection of a strong, organized magnetic field in the secondary component of the massive O8III/I+O7.5V/III double-lined spectroscopic binary system HD 47129 (Plas- ketts star), in the context of the Magnetism in Massive Star s (MiMeS) survey. Eight inde- pendent Stokes V observations were acquired using the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope and the Narval spectropolarimeter at the Telescope Bernard Lyot. Using Least-Squares Deconvolution we obtain definite detections of signal in Stokes V in 3 observations. No significant signal is detected in the di agnostic null (N) spectra. The Zeeman signatures are broad and track the radial velocity of the secondary component; we therefore conclude that the rapidly-rotating secondary co mponent is the magnetized star. Cor- recting the polarized spectra for the line and continuum of the (sharp-lined) primary, we mea- sured the longitudinal magnetic field from each observation . The longitudinal field of the secondary is variable and exhibits extreme values of−810± 150 G and +680± 190 G, im- plying a minimum surface dipole polar strength of 2850± 500 G. In contrast, we derive an upper limit (3σ) to the primarys surface magnetic field of 230 G. The combina tion of a strong magnetic field and rapid rotation leads us to conclude that th e secondary hosts a centrifugal magnetosphere fed through a magnetically confined wind. We r evisit the properties of the op- tical line profiles and X-ray emission - previously interpre ted as a consequence of colliding stellar winds - in this context. We conclude that HD 47129 represents a heretofore unique stellar system - a close, massive binary with a rapidly rotat ing, magnetized component - that will be a rich target for further study.

Measuring mass-loss rates and constraining shock physics using X-ray line profiles of O stars from the Chandra archive

We quantitatively investigate the extent of wind absorption signatures in the X-ray grating spectra of all non-magnetic, effectively single O stars in the Chandra archive via line profile fitting. Under the usual assumption of a spherically symmetric wind with embedded shocks, we confirm previous claims that some objects show little or no wind absorption. However, many other objects do show asymmetric and blueshifted line profiles, indicative of wind absorption. For these stars, we are able to derive wind mass-loss rates from the ensemble of line profiles, and find values lower by an average factor of 3 than those predicted by current theoretical models, and consistent with Hα if clumping factors of fcl ≈ 20 are assumed. The same profile fitting indicates an onset radius of X-rays typically at r ≈ 1.5R*, and terminal velocities for the X-ray emitting wind component that are consistent with that of the bulk wind. We explore the likelihood that the stars in the sample that do not show significant wind absorption signatures in their line profiles have at least some X-ray emission that arises from colliding wind shocks with a close binary companion. The one clear exception is ζ Oph, a weak-wind star that appears to simply have a very low mass-loss rate. We also reanalyse the results from the canonical O supergiant ζ Pup, using a solar-metallicity wind opacity model and find M^˙=1.8×10−6 M_ ⊙yr^−1, consistent with recent multiwavelength determinations.

Mass loss from inhomogeneous hot star winds - III. An effective-opacity formalism for line radiative transfer in accelerating, clumped two-component media, and first results on theory and diagnostics

[Abridged] We develop and benchmark a fast and easy-to-use effective-opacity formalism for line and continuum radiative transfer in an accelerating two-component clumpy medium. The formalism bridges the limits of optically thin and thick clumps, and is here used to i) design a simple vorosity-modified Sobolev with exact integration (vmSEI) method for analyzing UV wind resonance lines in hot, massive stars, and ii) derive simple correction factors to the line force driving the outflows of such stars. We show that (for a given ionization factor) UV resonance doublets may be used to analytically predict the upward corrections in empirically inferred mass-loss rates associated with porosity in velocity space (a.k.a. velocity-porosity, or vorosity), but that severe solution degeneracies exist. For an inter-clump density set to 1 % of the mean density, we for O and B supergiants derive upward empirical mass-loss corrections of typically factors of either ~5 or ~50, depending on which of the two applicable solutions is chosen. Overall, our results indicate this solution dichotomy severely limits the use of UV resonance lines as direct mass-loss indicators of clumped hot stellar winds. We next apply the effective-opacity formalism to the standard CAK theory of line-driven winds. By analytic and numerical hydrodynamics calculations, we show that in cases where vorosity is important at the critical point setting the mass-loss rate, the reduced line-force leads to a lower theoretical mass loss, by a factor scaling with the normalized velocity filling factor fvel. On the other hand, if vorosity is important only above this critical point, the predicted mass loss is not affected, but the wind terminal speed is reduced. This shows that porosity in velocity space can have a significant impact not only on the diagnostics, but also on the dynamics and theory of radiatively driven winds.

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 Magnetism in Massive Stars (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 Echelle SpectroPolarimetric Device for the Observation of Stars (ESPaDOnS) spectropolarimetric observations of HD 57682, which are combined with previously published ESPaDOnS data and archival Hα spectroscopy. This data set is used to determine the rotational period (63.5708 ± 0.0057 d), refine the longitudinal magnetic field variation and magnetic geometry (dipole surface field strength of 880 ± 50 G and magnetic obliquity of 79° ± 4° as measured from the magnetic longitudinal field variations, assuming an inclination of 60°) and examine the phase variation of various lines. In particular, we demonstrate that the Hα 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 Hα, exhibit non-sinusoidal variability, often with multiple maxima during the rotation cycle, and those that vary essentially sinusoidally. Based on our modelling of the Hα 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.

First 3DMHD simulation of a massive-star magnetosphere with application to Hα emission from θ1 Ori C

We present the first fully 3D magnetohydrodynamic (MHD) simulation for magnetic channelling and confinement of a radiatively driven, massive-star wind. The specific parameters are chosen to represent the prototypical slowly rotating magnetic O star θ 1 Ori C, for which centrifugal and other dynamical effects of rotation are negligible. The computed global structure in latitude and radius resembles that found in previous 2D simulations, with unimpeded outflow along open field lines near the magnetic poles, and a complex equatorial belt of inner wind trapping by closed loops near the stellar surface, giving way to outflow above the Alfv´ en radius. In contrast to this previous 2D work, the 3D simulation described here now also shows how this complex structure fragments in azimuth, forming distinct clumps of closed loop infall within the Alfv´ en radius, transitioning in the outer wind to radial spokes of enhanced density with characteristic azimuthal separation of 15 ◦ –20 ◦ . Applying these results in a 3D code for line radiative transfer, we show that emission from the associated 3D ‘dynamical magnetosphere’ matches well the observed Hα emission seen from θ 1 Ori C, fitting both its dynamic spectrum over rotational phase and the observed level of cycle-to-cycle stochastic variation. Comparison with previously developed 2D models for the Balmer emission from a dynamical magnetosphere generally confirms that time averaging over 2D snapshots can be a good proxy for the spatial averaging over 3D azimuthal wind structure. Nevertheless, fully 3D simulations will still be needed to model the emission from magnetospheres with non-dipole field components, such as suggested by asymmetric features seen in the Hα equivalent-width curve of θ 1 Ori C.