Wind Theory Research Articles

High-energy emission from the pulsar striped wind: a synchrotron model for gamma-ray pulsars

(abridged) Gamma-ray pulsars constitute a class of high and very high-energy emitters for which the known population is steadily increasing thanks to the Fermi/Large Area Telescope. In this paper, their gamma-ray luminosity and spectral features are explained in the framework of synchrotron radiation from particles located in the stripe of the pulsar wind. Apart from radiative losses, particles are also subject to a constant re-acceleration and reheating for instance by a magnetic reconnection induced electric field. The high-energy luminosity scales as $L_\gamma \approx 2\times10^{26} \textrm{W} \, (L_{\rm sd}/10^{28} \textrm{W})^{1/2} \, (P/1 \textrm{s})^{-1/2}$ where $L_{\rm sd}$ is the pulsar spindown luminosity and $P$ its period. From this relation, we derive important parameters of pulsar magnetosphere and wind theories. Indeed, we find bulk Lorentz factor of the wind scaling as $\Gamma_{\rm v} \approx 10 \, \tau_{\rm rec}^{1/5} \, (L_{\rm sd}/10^{28} \textrm{W})^{1/2}$, pair multiplicity $\kappa$ related to the magnetization parameter $\sigma$ by $\kappa\,\sigma \, \tau_{\rm rec}^{1/5} \approx 10^8$, and efficiency $\eta$ of spin-down luminosity conversion into particle kinetic energy according to the relation $\eta\,\sigma\approx1$. A good guess for the associated reconnection rate is then $\tau_{\rm rec} \approx 0.5 \, (L_{\rm sd}/10^{28} \textrm{W})^{-5/12}$. Finally, pulses in gamma-rays are visible only if $L_{\rm sd}/P\gtrsim 10^{27} \textrm{W/s}$. This model differs from other high-energy emission mechanisms because it makes allowance not only for rotational kinetic energy release but also for an additional reservoir of energy anchored to the magnetic field of the stripe and released for instance by some magnetic reconnection processes.

A peculiar Of star in the Local Group galaxy IC 1613

Context. Results from the theory of radiatively driven winds are incorporated in stellar evolutionary and population synthesis models, and used in our interpretation of the observations of the deep Universe. Yet, the theory has been confirmed only until Small Magellanic Cloud metallicities. Analyses of O-stars at lower metallicities are needed to prove the theory. Aims. We have observed GHV-62024, an O6.5 IIIf star in the low-metallicity galaxy IC1613. According to a previous preliminary analysis this star could challenge the radiatively driven wind theory at low metallicities. Methods. Our observations were obtained with VIMOS at VLT, at R~2000 and were analysed using the latest version of the model atmosphere code FASTWIND, which includes N III Results. We obtain the stellar parameters and conclude that the star follows the average wind momentum-luminosity relationship (WLR) expected for its metallicity, but with a high value for the exponent of the wind velocity law, beta. We suggest that this high value may be reached because GHV-62024 could be a fast rotator seen at a low inclination angle. While the derived beta value does not change by adopting a lower wind terminal velocity, a wrong $V_\infty$ has a clear impact on the position of the star in the WLR diagram. The N and He abundances are very high, consistent with strong CNO mixing that could have been caused by the fast rotation, although we cannot discard a different origin. We find again the well-known mass-discrepancy. Conclusions. We conclude that the star follows the WLR expected for its metallicity. The results are consistent with GHV-62024 being a fast rotator seen close to pole-on, contaminated at the surface with CNO products and with a wind structure altered by the fast rotation without modifying the global WLR. We suggest that this could be a general property of fast rotators.

Magnetic fields during the early stages of massive star formation - II. A generalized outflow criterion

Numerical simulations of outflows formed during the collapse of 100-M⊙ cloud cores are presented. We derive a generalized criterion from magnetohydrodynamical wind theory to analyse the launching mechanism of these outflows. The criterion is successfully applied to the whole outflow structure and cases with sub-Keplerian disc rotation. It allows us to decide whether an outflow is driven centrifugally or by the toroidal magnetic pressure. We show that quantities such as the magnetic field line inclination or the ratio of the toroidal to poloidal magnetic field alone are insufficient to determine the driving mechanism of outflows. By performing 12 simulations with variable initial rotational and magnetic energies, we are able to study the influence of the initial conditions on the properties of outflows and jets around massive protostars in detail. Our simulations reveal a strong effect of the magnetic field strength on the morphology of outflows. In runs with weak fields or high rotational energies, well-collimated, fast jets are observed, whereas for strong fields poorly collimated, low-velocity outflows are found. We show that the occurrence of a fast jet is coupled to the existence of a Keplerian protostellar disc. Despite the very different morphologies, all outflows are launched from the discs by centrifugal acceleration with the toroidal magnetic field increasingly contributing to the gas acceleration further away from the discs. The poor collimation of the outflows in runs with strong magnetic fields is a consequence of the weak hoop stresses. This in turn is caused by the slow build-up of a toroidal magnetic field due to strongly sub-Keplerian disc rotation. The mass and momentum outflow rates are of the order of 10−4 M⊙ yr−1 and 10−4 M⊙ km s−1 yr−1, respectively. The mass ejection/accretion ratios scatter around a mean of 0.3 in accordance with observational and analytical results. Based on our results, we suggest an evolutionary scenario for the earliest stage of massive star formation in which initially poorly collimated outflows develop, which successively get better collimated during their evolution due to the generation of fast jets.

Clumped stellar winds in supergiant high-mass X-ray binaries: X-ray variability and photoionization

The clumping of massive star winds is an established paradigm, which is confirmed by multiple lines of evidence and is supported by stellar wind theory. The purpose of this paper is to bridge the gap between detailed models of inhomogeneous stellar winds in single stars and the phenomenological description of donor winds in supergiant high‐mass X‐ray binaries (HMXBs). We use the results from time‐dependent hydrodynamical models of the instability in the line‐driven wind of a massive supergiant star to derive the time‐dependent accretion rate on to a compact object in the Bondi–Hoyle–Lyttleton approximation. The strong density and velocity fluctuations in the wind result in strong variability of the synthetic X‐ray light curves. The model predicts a large‐scale X‐ray variability, up to eight orders of magnitude, on relatively short time‐scales. The apparent lack of evidence for such strong variability in the observed HMXBs indicates that the details of the accretion process act to reduce the variability resulting from the stellar wind velocity and density jumps. We study the absorption of X‐rays in the clumped stellar wind by means of a two‐dimensional stochastic wind model. The monochromatic absorption in the cool stellar wind, depending on the orbital phase, is computed for realistic stellar wind opacity. We find that the absorption of X‐rays changes strongly at different orbital phases. The degree of the variability resulting from the absorption in the wind depends on the shape of the wind clumps, and this is stronger for oblate clumps. We address the photoionization in the clumped wind, and we show that the degree of ionization is affected by the wind clumping. We derive a correction factor for the photoionization parameter, and we show that the photoionization parameter is reduced by a factor compared to the smooth wind models with the same mass‐loss rate, where is the wind inhomogeneity parameter. We conclude that wind clumping must also be taken into account when comparing the observed and model spectra of the photoionized stellar wind.

Rain-Wind-Induced Vibration Control for Long Span Transmission Tower

In this paper, multiple tuned liquid dampers control for rain-wind-induced response of long span transmission tower is investigated. Equations of motion for a structure-TLD system are derived. According to the mechanism of vibration control, rain-wind-induced vibration control for tower model with multiple tuned liquid dampers is carried out by using numerical simulation. Three-dimensional finite element model of tower based on a real project is established. Rain-wind load time history is simulated based on wind and rain theory. Time history curves and the maximum responses without and with tuned liquid damper under rain-wind excitation are analyzed and discussed. The results show that the tuned liquid damper could decrease the rain-wind-induced response of long span transmission tower, and the device could be installed in tower when the response too large.

Wind - terrain effects on the propagation of wildfires in rugged terrain: fire channelling

The interaction of wind, terrain and a fire burning in a landscape can produce a variety of unusual yet significant effects on fire propagation. One such example, in which a fire exhibits rapid spread in a direction transverse to the synoptic winds as well as in the usual downwind direction, is considered in this paper. This type of fire spread, which is referred to as ‘fire channelling’, is characterised by intense lateral and downwind spotting and production of extensive flaming zones. The dependence of fire channelling on wind and terrain is analysed using wind, terrain and multispectral fire data collected during the January 2003 Alpine fires over south-eastern Australia. As part of the analysis, a simple terrain-filter model is utilised to confirm a quantitative link between instances of fire channelling and parts of the terrain that are sufficiently steep and lee-facing. By appealing to the theory of wind–terrain interaction and the available evidence, several processes that could produce the atypical fire spread are considered and some discounted. Based on the processes that could not be discounted, and a previous analysis of wind regimes in rugged terrain, a likely explanation for the fire channelling phenomenon is hypothesised. Implications of fire channelling for bushfire risk management are also discussed.

L-band spectroscopy of Galactic OB-stars

Context. Mass-loss, occurring through radiation driven supersonic winds, is a key issue throughout the evolution of massive stars. Two outstanding problems are currently challenging the theory of radiation-driven winds: wind clumping and the weak-wind problem. Aims. We seek to obtain accurate mass-loss rates of OB stars at different evolutionary stages to constrain the impact of both problems in our current understanding of massive star winds. Methods. We perform a multi-wavelength quantitative analysis of a sample of ten Galactic OB-stars by means of the atmospheric code CMFGEN, with special emphasis on the L-band window. A detailed investigation is carried out on the potential of Br\alpha\ and Pf\gamma\ as mass-loss and clumping diagnostics. Results. For objects with dense winds, Br\alpha\ samples the intermediate wind while Pf\gamma\ maps the inner one. In combination with other indicators (UV, H\alpha, Br\gamma) these lines enable us to constrain the wind clumping structure and to obtain "true" mass-loss rates. For objects with weak winds, Br\alpha\ emerges as a reliable diagnostic tool to constrain the mass-loss rates. The emission component at the line Doppler-core superimposed on the rather shallow Stark absorption wings reacts very sensitively to mass loss already at very low mass-loss values. On the other hand, the line wings display similar sensitivity to mass loss as H\alpha, the classical optical mass loss diagnostics. Conclusions. Our investigation reveals the great diagnostic potential of L-band spectroscopy to derive clumping properties and mass-loss rates of hot star winds. We are confident that Br\alpha\ will become the primary diagnostic tool to measure very low mass-loss rates with unprecedented accuracy

Design and Analysis of Star–Delta Hybrid Windings for High-Voltage Induction Motors

In this paper, a Y-Δ hybrid connection for a high-voltage induction motor is described. Low winding harmonic content is achieved by careful consideration of the interaction between the Y- and Δ-connected three-phase winding sets so that the magnetomotive force (MMF) in the air gap is close to sinusoid. Essentially, the two winding sets operate in a six-phase mode. This paper goes on to verify that the fundamental distribution coefficient for the stator MMF is enhanced compared to a standard three-phase winding set. The design method for converting a conventional double-layer lap winding in a high-voltage induction motor into a Y-Δ hybrid lap winding is described using standard winding theory as often applied to small- and medium-sized motors. The main parameters addressed when designing the winding are the conductor wire gauge, coil turns, and parallel winding branches in the Y and Δ connections. A winding design scheme for a 1250-kW 6-kV induction motor is put forward and experimentally validated; the results show that the efficiency can be raised effectively without increasing the cost.

Toward a nonlinear theory of katabatic winds

The classic Prandtl slope flow model is generalized to include nonlinear turbulent friction and rotation. Several general regularities are established. In particular, a universal expression for the mass flux along the slope and a relationship between the surface velocity components, both independent of the friction law, are obtained. The applicability of the model to describing katabatic winds on fairly large horizontal scales is discussed.

Disk wind in the radiation of young intermediate-mass stars

We consider the role of the disk wind in the formation of hydrogen emission spectra of young intermediate-mass Herbig Ae stars. The assumed parameters for the kinematic characteristics of the wind region are typical of the theory of magnetocentrifugal disk winds. Our computations of the excitation and ionization states for atoms in the emitting region are based on the Sobolev approximation for a medium with a large velocity gradient. The calculations show that hydrogen-line emission profiles can have a complex structure that depends on the disk-wind parameters, as well as on the system’s orientation relative to the line of sight. The model proposed is able to explain most types of Hα profiles observed for Herbig Ae stars.

Winding Function 이론을 이용한 동기형 릴럭턴스 전동기의 토크 특성 해석

In this paper, torque characteristics analysis of Synchronous Reluctance Motor with the cylindrical rotor type by winding function theory(WFT) is described. The stator is same as one of the induction motor. From the d-axis, q-axis flux density distribution, to calculate self and mutual inductances needed to calculate the torque of the machine by using winding function theory the new equivalent geometry of rotor was proposed. D-axis, q-axis flux densities, self inductance and torque characteristics were obtained. From the comparison with results of finite element analysis the proposed method was verified.

SLOW RADIATION-DRIVEN WIND SOLUTIONS OF A-TYPE SUPERGIANTS

The theory of radiation-driven winds succeeded in describing terminal velocities and mass loss rates of massive stars. However, for A-type supergiants the standard m-CAK solution predicts values of mass loss and terminal velocity higher than the observed values. Based on the existence of a slow wind solution in fast rotating massive stars, we explore numerically the parameter space of radiation-driven flows to search for new wind solutions in slowly rotating stars, that could explain the origin of these discrepancies. We solve the 1-D hydrodynamical equation of rotating radiation-driven winds at different stellar latitudes and explore the influence of ionization's changes throughout the wind in the velocity profile. We have found that for particular sets of stellar and line-force parameters, a new slow solution exists over the entire star when the rotational speed is slow or even zero. In the case of slow rotating A-type supergiant stars the presence of this novel slow solution at all latitudes leads to mass losses and wind terminal velocities which are in agreement with the observed values. The theoretical Wind Momentum-Luminosity Relationship derived with these slow solutions shows very good agreement with the empirical relationship. In addition, the ratio between the terminal and escape velocities, which provides a simple way to predict stellar wind energy and momentum input into the interstellar medium, is also properly traced.

Analysis of the Concentric Planetary Magnetic Gear With Strengthened Stator and Interior Permanent Magnet Inner Rotor

Magnetic gears have been proposed as a means of increasing torque density within electromechanical systems, while avoiding problems associated with traditional mechanical gears. While the idea behind magnetic gears goes back to early patents, their study and use in industry has been very limited to date. This study looks into variations of the concentric planetary magnetic gear which could lead to further use. It also investigates applying winding function theory (WFT) to aid in analysis of the gear. The new application of winding function theory is verified with the use of finite element analysis (FEA) as well as a prototype which has been fabricated.

Mass loss from inhomogeneous hot star winds

Mass-loss rates currently in use for hot, massive stars have recently been seriously questioned, mainly because of the effects of wind clumping. We investigate the impact of clumping on diagnostic ultraviolet resonance and optical recombination lines. Optically thick clumps, a non-void interclump medium, and a non-monotonic velocity field are all accounted for in a single model. We used 2D and 3D stochastic and radiation-hydrodynamic (RH) 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: Synthetic spectra calculated directly from current RH wind models of the line-driven instability are unable to in parallel reproduce strategic optical and ultraviolet lines for the Galactic O-supergiant LCep. Using our stochastic wind models, we obtain consistent fits essentially by increasing the clumping in the inner wind. A mass-loss rate is derived that is approximately two times lower than predicted by the line-driven wind theory, but much higher than the corresponding rate derived from spectra when assuming optically thin clumps. Our analytic formulation for line formation is used to demonstrate the potential impact of optically thick clumping in weak-winded stars and to confirm recent results that resonance doublets may be used as tracers of wind structure and optically thick clumping. (Abridged)

The theory of stellar winds

We present a brief overview of the theory of stellar winds with a strong emphasis on the radiation-driven outflows from massive stars. The resulting implications for the evolution and fate of massive stars are also discussed. Furthermore, we relate the effects of mass loss to the angular momentum evolution, which is particularly relevant for the production of long and soft gamma-ray bursts. Mass-loss rates are not only a function of the metallicity, but are also found to depend on temperature, particularly in the region of the bi-stability jump at 21 000 Kelvin. We highlight the role of the bi-stability jump for Luminous Blue Variable (LBV) stars, and discuss suggestions that LBVs might be direct progenitors of supernovae. We emphasize that radiation-driven wind studies rely heavily on the input opacity data and linelists, and that these are thus of fundamental importance to both the mass-loss predictions themselves, as well as to our overall understanding of the lives and deaths of massive stars.

Ion fractions and the weak wind problem

AbstractSome late-type O stars display anomalously weak winds, possibly due to decoupling of the main driving ions from the bulk plasma. This issue and the uncertainty about the nature of wind clumping are a challenge to line-driven wind theory and need resolving in order to fully understand hot stars. We describe the results from the computation of ion fractions for the various elements in O star winds using non-LTE code CMFGEN, including parameterisation of microclumping and X-rays.

Large scale magnetic fields in viscous resistive accretion disks

<i>Aims. <i/>Cold steady-state disk wind theory from near Keplerian accretion disks requires a large scale magnetic field at near equipartition strength. However the minimum magnetization has never been tested with time dependent simulations. We investigate the time evolution of a Shakura-Sunyaev accretion disk threaded by a weak vertical magnetic field. The strength of the field is such that the disk magnetization falls off rapidly with radius.<i>Methods. <i/>Four 2.5D numerical simulations of viscous resistive accretion disk are performed using the magnetohydrodynamic code PLUTO. In these simulations, a mean field approach is used and turbulence is assumed to give rise to anomalous transport coefficients (alpha prescription). <i>Results. <i/>The large scale magnetic field introduces only a small perturbation to the disk structure, with accretion driven by the dominant viscous torque. However, a super fast magnetosonic jet is observed to be launched from the innermost regions and remains stationary over more than 953 Keplerian orbits. This is the longest accretion-ejection simulation ever carried out. The self-confined jet is launched from a finite radial zone in the disk which remains constant over time. Ejection is made possible because the magnetization reaches unity at the disk surface, due to the steep density decrease. However, no ejection is reported when the midplane magnetization becomes too small. The asymptotic jet velocity remains nevertheless too low to explain observed jets. This is because of the negligible power carried away by the jet.<i>Conclusions. <i/>Astrophysical disks with superheated surface layers could drive analogous outflows even if their midplane magnetization is low. Sufficient angular momentum would be extracted by the turbulent viscosity to allow the accretion process to continue. The magnetized outflows would be no more than byproducts, rather than a fundamental driver of accretion. However, if the midplane magnetization increases towards the center, a natural transition to an inner jet dominated disk could be achieved.

Accreting white dwarfs as supersoft X‐ray sources

AbstractI review various phenomena associated with mass‐accreting white dwarfs (WDs) in the view of supersoft X‐ray sources. When the mass‐accretion rate is low (Ṁacc &lt; a few × 10–7 M⊙yr–1), hydrogen nuclear burning is unstable and nova outbursts occur. A nova is a transient supersoft X‐ray source (SSS) in its later phase which timescale depends strongly on the WD mass. The X‐ray turn on/off time is a good indicator of the WD mass. At an intermediate mass‐accretion rate an accreting WD becomes a persistent SSS with steady hydrogen burning. For a higher mass‐accretion rate, the WD undergoes “accretion wind evolution” in which the WD accretes matter from the equatorial plane and loses mass by optically thick winds from the other directions. Two SSS, namely RX J0513‐6951 and V Sge, are corresponding objects to this accretion wind evolution. We can specify mass increasing WDs from light‐curve analysis based on the optically thick wind theory using multiwavelength observational data including optical, IR, and supersoft X‐rays. Mass estimates of individual objects give important information for the binary evolution scenario of type Ia supernovae (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Mass loss from inhomogeneous hot star winds

<i>Context. <i/>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. /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. <i>Aims. <i/>We investigate basic properties of the formation of resonance lines in small-scale inhomogeneous hot star winds with non-monotonic velocity fields.<i>Methods. <i/>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.<i>Results. <i/>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 radiation-hydrodynamic 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 <i>λ<i/> 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.

A UNIVERSAL DECLINE LAW OF CLASSICAL NOVAE. IV. V838 HER (1991): A VERY MASSIVE WHITE DWARF

We present a unified model of optical and ultraviolet (UV) light curves for one of the fastest classical novae, V838 Herculis (Nova Herculis 1991), and estimate its white dwarf (WD) mass. Based on an optically thick wind theory of nova outbursts, we model the optical light curves with free-free emission and the UV 1455 \AA light curves with blackbody emission. Our models of 1.35 \pm 0.02 M_\sun WD reproduce simultaneously the optical and UV 1455 \AA observations. The mass lost by the wind is \Delta M_{wind} \sim 2 \times 10^{-6} M_\sun. We provide new determinations of the reddening, E(B-V) = 0.53 \pm 0.05, and of the distance, 2.7 \pm 0.5 kpc.