Line-driven Winds Research Articles

New mass-loss rates of B supergiants from global wind models

Massive stars lose a significant fraction of mass during their evolution. However, the corresponding mass-loss rates are rather uncertain, especially for evolved stars. To improve this, we calculated global line-driven wind models for Galactic B supergiants. Our models predict radial wind structure and particularly the mass-loss rates and terminal velocities directly from basic stellar parameters. The hydrodynamic structure of the flow is consistently determined from the photosphere in nearly hydrostatic equilibrium to supersonically expanding wind. The radiative force is derived from the solution of the radiative transfer equation in the comoving frame. We provide a simple formula that predicts theoretical mass-loss rates as a function of stellar luminosity and effective temperature. The mass-loss rate of B supergiants slightly decreases with temperature down to about 22.5 kK, where the region of recombination of Fe IV to Fe III starts to appear. In this region, which is about 5 kK wide, the mass-loss rate gradually increases by a factor of about 6. The increase of the mass-loss rate is associated with a gradual decrease of terminal velocities by a factor of about 2. We compared the predicted wind parameters with observations. While the observed wind terminal velocities are reasonably reproduced by the models, the situation with mass-loss rates is less clear. The mass-loss rates derived from observations that are uncorrected for clumping are by a factor of 3 to 9 higher than our predictions on cool and hot sides of the studied sample, respectively. These observations can be reconciled with theory assuming a temperature-dependent clumping factor that is decreasing toward lower effective temperatures. On the other hand, the mass-loss rate estimates that are not sensitive to clumping agree with our predictions much better. Our predictions are by a factor of about 10 lower than the values currently used in evolutionary models appealing for reconsideration of the role of winds in the stellar evolution.

Conditions for accretion disc formation and observability of wind-accreting X-ray binaries

Abstract We explore the effect of anisotropic wind driving on the properties of accretion onto black holes (BHs) in close binaries. We specifically focus on line-driven winds, which are common in high-mass X-ray binaries (HMXBs). In close binary systems, the tidal force from the companion star can modify the wind structure in two different ways. One is the reduction of wind terminal velocity due to the weaker effective surface gravity. The other is the reduction in mass flux due to gravity darkening (GD). We incorporate these effects into the so-called CAK theory in a simple way and investigate the wind flow around the accretor on the orbital scale. We find that a focused accretion stream is naturally formed when the Roche lobe filling factor is ${\gtrsim}0.8$ –0.9, analogous to that of wind Roche lobe overflow, but only when the velocity reduction is taken into account. The formation of a stream is necessary to bring in sufficient angular momentum to form an accretion disc around the BH. GD effects reduce the amount of accreted angular momentum, but not enough to prevent the formation of a disc. Based on these results, we expect there to be a discrete step in the observability of HMXBs depending on whether the donor Roche lobe filling factor is below or above ${\sim}$ 0.8–0.9.

Getting started: How a supersonic stellar wind is initiated from a hydrostatic surface

AbstractMost of a star’s mass is bound in a hydrostatic equilibrium in which pressure balances gravity. But if at some near-surface layer additional outward forces overcome gravity, this can transition to a supersonic, outflowing wind, with the sonic point, where the outward force cancels gravity, marking the division between hydrostatic atmosphere and wind outflow. This talk will review general issues with such transonic initiation of a stellar wind outflow, and how this helps set the wind mass loss rate. The main discussion contrasts the flow initiation in four prominent classes of steady-state winds: (1) the pressure-driven coronal wind of the sun and other cool stars; (2) line-driven winds from OB stars; (3) a two-stage initiation model for the much denser winds from Wolf-Rayet (WR) stars; and (4) the slow “overflow” mass loss from highly evolved giant stars. A follow on discussion briefly reviews eruptive mass loss, with particular focus on the giant eruption of η Carinae.

The Zwicky Transient Facility Bright Transient Survey. II. A Public Statistical Sample for Exploring Supernova Demographics*

Abstract We present a public catalog of transients from the Zwicky Transient Facility (ZTF) Bright Transient Survey, a magnitude-limited (m < 19 mag in either the g or r filter) survey for extragalactic transients in the ZTF public stream. We introduce cuts on survey coverage, sky visibility around peak light, and other properties unconnected to the nature of the transient, and show that the resulting statistical sample is spectroscopically 97% complete at <18 mag, 93% complete at <18.5 mag, and 75% complete at <19 mag. We summarize the fundamental properties of this population, identifying distinct duration–luminosity correlations in a variety of supernova (SN) classes and associating the majority of fast optical transients with well-established spectroscopic SN types (primarily SN Ibn and II/IIb). We measure the Type Ia SN and core-collapse (CC) SN rates and luminosity functions, which show good consistency with recent work. About 7% of CC SNe explode in very low-luminosity galaxies (M i > −16 mag), 10% in red-sequence galaxies, and 1% in massive ellipticals. We find no significant difference in the luminosity or color distributions between the host galaxies of SNe Type II and SNe Type Ib/c, suggesting that line-driven wind stripping does not play a major role in the loss of the hydrogen envelope from their progenitors. Future large-scale classification efforts with ZTF and other wide-area surveys will provide high-quality measurements of the rates, properties, and environments of all known types of optical transients and limits on the existence of theoretically predicted but as yet unobserved explosions.

Line-drag damping of Alfvén waves in radiatively driven winds of magnetic massive stars

ABSTRACT Line-driven stellar winds from massive (OB) stars are subject to a strong line-deshadowing instability. Recently, spectropolarimetric surveys have collected ample evidence that a subset of Galactic massive stars hosts strong surface magnetic fields. We investigate here the propagation and stability of magnetoradiative waves in such a magnetized, line-driven wind. Our analytic, linear stability analysis includes line-scattering from the stellar radiation, and accounts for both radial and non-radial perturbations. We establish a bridging law for arbitrary perturbation wavelength after which we analyse separately the long- and short-wavelength limits. While long-wavelength radiative and magnetic waves are found to be completely decoupled, a key result is that short-wavelength, radially propagating Alfvén waves couple to the scattered radiation field and are strongly damped due to the line-drag effect. This damping of magnetic waves in a scattering-line-driven flow could have important effects on regulating the non-linear wind dynamics, and so might also have strong influence on observational diagnostics of the wind structure and clumping of magnetic line-driven winds.

Detecting Pair-instability Supernovae at z ≲ 5 with the James Webb Space Telescope

Abstract Pair-instability supernovae (PISNe) are the ultimate cosmic lighthouses, capable of being observed at z ≳ 25 and revealing the properties of primordial stars at cosmic dawn. But it is now understood that the spectra and light curves of these events evolved with redshift as the universe became polluted with heavy elements because chemically enriched stars in this mass range typically lose most of their hydrogen envelopes and explode as bare helium cores. The light curves of such transients can be considerably dimmer in the near-infrared today than those of primordial PISNe of equal energy and progenitor mass. Here, we calculate detection rates for PISNe whose progenitors lost their outer layers to either line-driven winds or rotation at z ≲ 10, their detection limit in redshift for the James Webb Space Telescope (JWST). We find that JWST may be able to detect only Population II (metal-poor) PISNe over the redshift range of z ≲ 4, but not their Population III (metal-free) counterparts.

Q wind code release: a non-hydrodynamical approach to modelling line-driven winds in active galactic nuclei

ABSTRACT Ultraviolet (UV) line-driven winds may be an important part of the active galactic nucleus (AGN) feedback process, but understanding their impact is hindered by the complex nature of the radiation hydrodynamics. Instead, we have taken the approach pioneered by Risaliti & Elvis, calculating only ballistic trajectories from radiation forces and gravity but neglecting gas pressure. We have completely rewritten their Qwind code using more robust algorithms and can now quickly model the acceleration phase of these winds for any AGN spectral energy distribution spanning UV and X-ray wavebands. We demonstrate the code using an AGN with black hole mass $10^8\, \text{M}_\odot$ emitting at half the Eddington rate and show that this can effectively eject a wind with velocities ${\simeq}(0.1-0.2)\, c$. The mass loss rates can be up to ≃0.3M⊙ per year, consistent with more computationally expensive hydrodynamical simulations, though we highlight the importance of future improvements in radiation transfer along the multiple different lines of sight illuminating the wind. The code is fully public and can be used to quickly explore the conditions under which AGN feedback can be dominated by accretion disc winds.

Line-driven disc wind in near-Eddington active galactic nuclei: decrease of mass accretion rate due to powerful outflow

ABSTRACT Based on recent X-ray observations, ultrafast outflows from supermassive black holes are expected to have enough energy to dramatically affect their host galaxy but their launch and acceleration mechanisms are not well understood. We perform two-dimensional radiation hydrodynamics simulations of UV line-driven disc winds in order to calculate the mass-loss rates and kinetic power in these models. We develop a new iterative technique that reduces the mass accretion rate through the inner disc in response to the wind mass-loss. This makes the inner disc less UV bright, reducing the wind power compared to previous simulations which assumed a constant accretion rate with radius. The line-driven winds in our simulations are still extremely powerful, with around half the supplied mass accretion rate being ejected in the wind for black holes with mass 108–$10^{10}\, \mathrm{ M}_\odot$ accreting at L/LEdd = 0.5–0.9. Our results open up the way for estimating the growth rate of supermassive black hole and evaluating the kinetic energy ejected into the interstellar medium (active galactic nuclei feedback) based on a physical model of line-driven disc winds.

Stellar wind models of central stars of planetary nebulae

Context. Fast line-driven stellar winds play an important role in the evolution of planetary nebulae, even though they are relatively weak. Aims. We provide global (unified) hot star wind models of central stars of planetary nebulae. The models predict wind structure including the mass-loss rates, terminal velocities, and emergent fluxes from basic stellar parameters. Methods. We applied our wind code for parameters corresponding to evolutionary stages between the asymptotic giant branch and white dwarf phases for a star with a final mass of 0.569 M⊙. We study the influence of metallicity and wind inhomogeneities (clumping) on the wind properties. Results. Line-driven winds appear very early after the star leaves the asymptotic giant branch (at the latest for Teff ≈ 10 kK) and fade away at the white dwarf cooling track (below Teff = 105 kK). Their mass-loss rate mostly scales with the stellar luminosity and, consequently, the mass-loss rate only varies slightly during the transition from the red to the blue part of the Hertzsprung–Russell diagram. There are the following two exceptions to the monotonic behavior: a bistability jump at around 20 kK, where the mass-loss rate decreases by a factor of a few (during evolution) due to a change in iron ionization, and an additional maximum at about Teff = 40−50 kK. On the other hand, the terminal velocity increases from about a few hundreds of km s−1 to a few thousands of km s−1 during the transition as a result of stellar radius decrease. The wind terminal velocity also significantly increases at the bistability jump. Derived wind parameters reasonably agree with observations. The effect of clumping is stronger at the hot side of the bistability jump than at the cool side. Conclusions. Derived fits to wind parameters can be used in evolutionary models and in studies of planetary nebula formation. A predicted bistability jump in mass-loss rates can cause the appearance of an additional shell of planetary nebula.

The WISSH quasars project

Hyper-luminous quasars (Lbol ≳ 1047 erg s−1) are ideal laboratories to study the interaction and impact of the extreme radiative field and the most powerful winds in the active galactic nuclei (AGN) nuclear regions. They typically exhibit low coronal X-ray luminosity (LX) compared to the ultraviolet (UV) and mid-infrared (MIR) radiative outputs (LUV and LUV); a non-negligible fraction of them report even ∼1 dex weaker LX compared to the prediction of the well established LX–LUV and LX–LUV relations followed by the bulk of the AGN population. In our WISE/SDSS-selected Hyper-luminous (WISSH) z = 2 − 4 broad-line quasar sample, we report on the discovery of a dependence between the intrinsic 2–10 keV luminosity (L2 − 10) and the blueshifted velocity of the CIV emission line (vCIV) that is indicative of accretion disc winds. In particular, sources with the fastest winds (vCIV ≳ 3000 km s−1) possess ∼0.5–1 dex lower L2 − 10 than sources with negligible vCIV. No similar dependence is found on LUV, LUV, Lbol, the photon index, or the absorption column density. We interpret these findings in the context of accretion disc wind models. Both magnetohydrodynamic and line-driven models can qualitatively explain the reported relations as a consequence of X-ray shielding from the inner wind regions. In case of line-driven winds, the launch of fast winds is favoured by a reduced X-ray emission, and we speculate that these winds may play a role in directly limiting the coronal hard X-ray production.

The stellar and wind parameters of six prototypical HMXBs and their evolutionary status

Context.High-mass X-ray binaries (HMXBs) are exceptional astrophysical laboratories that offer a rare glimpse into the physical processes that govern accretion on compact objects, massive-star winds, and stellar evolution. In a subset of the HMXBs, the compact objects accrete matter solely from winds of massive donor stars. These so-called wind-fed HMXBs are divided in persistent (classical) HMXBs and supergiant fast X-ray transients (SFXTs) according to their X-ray properties. While it has been suggested that this dichotomy depends on the characteristics of stellar winds, they have been poorly studied.Aims.With this investigation, we aim to remedy this situation by systematically analyzing donor stars of wind-fed HMXBs that are observable in the UV, concentrating on those with neutron star (NS) companions.Methods.We obtainedSwiftX-ray data, HST UV spectra, and additional optical spectra for all our targets. The spectral analysis of our program stars was carried out with the Potsdam Wolf–Rayet model atmosphere code.Results.Our multi-wavelength approach allows us to provide stellar and wind parameters for six donor stars (four wind-fed systems and two OBe X-ray binaries). The wind properties are in line with the predictions of the line-driven wind theory. Based on the abundances, three of the donor stars are in an advanced evolutionary stage, while for some of the stars, the abundance pattern indicates that processed material might have been accreted. When passing by the NS in its tight orbit, the donor star wind has not yet reached its terminal velocity but it is still significantly slower; its speed is comparable with the orbital velocity of the NS companion. There are no systematic differences between the two types of wind-fed HMXBs (persistent versus transients) with respect to the donor stars. For the SFXTs in our sample, the orbital eccentricity is decisive for their transient X-ray nature. The dichotomy of wind-fed HMXBs studied in this work is primarily a result of the orbital configuration, while in general it is likely that it reflects a complex interplay between the donor-star parameters, the orbital configuration, and the NS properties. Based on the orbital parameters and the further evolution of the donor stars, the investigated HMXBs will presumably form Thorne–Żytkow objects in the future.

Self-consistent Solutions for Line-driven Winds of Hot Massive Stars: The m-CAK Procedure

Abstract Massive stars present strong stellar winds that are described by the radiation driven wind theory. Accurate mass-loss rates are necessary to properly describe the stellar evolution across the Hertzsprung–Russel Diagram. We present a self-consistent procedure that coupled the hydrodynamics with calculations of the line-force, giving as results the line-force parameters, the velocity field, and the mass-loss rate. Our calculations contemplate the contribution to the line-force multiplier from more than ∼900,000 atomic transitions, an NLTE radiation flux from the photosphere and a quasi-LTE approximation for the occupational numbers. A full set of line-force parameters for T eff ≥ 32,000 K, surface gravities higher than 3.4 dex for two different metallicities are presented, with their corresponding wind parameters (terminal velocities and mass-loss rates). The already known dependence of line-force parameters on effective temperature is enhanced by the dependence on . The terminal velocities present a stepper scaling relation with respect to the escape velocity, this might explain the scatter values observed in the hot side of the bistability jump. Moreover, a comparison of self-consistent mass-loss rates with empirical values shows a good agreement. Self-consistent wind solutions are used as input in FASTWIND to calculate synthetic spectra. We show, comparing with the observed spectra for three stars, that varying the clumping factor, the synthetic spectra rapidly converge into the neighborhood region of the solution. It is important to stress that our self-consistent procedure significantly reduces the number of free parameters needed to obtain a synthetic spectrum.

The properties of broad absorption line outflows based on a large sample of quasars

Quasar outflows carry mass, momentum and energy into the surrounding environment, and have long been considered a potential key factor in regulating the growth of supermassive black holes and the evolution of their host galaxies. A crucial parameter for understanding the origin of these outflows and measuring their influence on their host galaxies is the distance (R) between the outflow gas and the galaxy center. While R has been measured in a number of individual galaxies, its distribution remains unknown. Here we report the distributions of R and the kinetic luminosities of quasars outflows, using the statistical properties of broad absorption line variability in a sample of 915 quasars from the Sloan Digital Sky Surveys. The mean and standard deviation of the distribution of R are 10^{1.4+/-0.5} parsecs. The typical outflow distance in this sample is tens of parsec, which is beyond the theoretically predicted location (0.01 ~ 0.1 parsecs) where the accretion disc line-driven wind is launched, but is smaller than the scales of most outflows that are derived using the excited state absorption lines. The typical value of the mass-flow rate is of tens to a hundred solar masses per year, or several times the accretion rate. The typical kinetic-to-bolometric luminosity ratio is a few per cent, indicating that outflows are energetic enough to influence the evolution of their host galaxies.

Light variations due to the line-driven wind instability and wind blanketing in O stars

A small fraction of the radiative flux emitted by hot stars is absorbed by their winds and redistributed towards longer wavelengths. This effect, which leads also to the heating of the stellar photosphere, is termed wind blanketing. For stars with variable winds, the effect of wind blanketing may lead to the photometric variability. We have studied the consequences of line driven wind instability and wind blanketing for the light variability of O stars. We combined the results of wind hydrodynamic simulations and of global wind models to predict the light variability of hot stars due to the wind blanketing and instability. The wind instability causes stochastic light variability with amplitude of the order of tens of millimagnitudes and a typical timescale of the order of hours for spatially coherent wind structure. The amplitude is of the order of millimagnitudes when assuming that the wind consists of large number of independent concentric cones. The variability with such amplitude is observable using present space borne photometers. We show that the simulated light curve is similar to the light curves of O stars obtained using BRITE and CoRoT satellites.

Expanding CO Shells in the Orion A Molecular Cloud

Abstract We present the discovery of expanding spherical shells around low- to intermediate-mass young stars in the Orion A giant molecular cloud using observations of 12 CO (1–0) and 13 CO (1–0) from the Nobeyama Radio Observatory 45 m telescope. The shells have radii from 0.05 to 0.85 pc and expand outward at 0.8–5 km s−1. The total energy in the expanding shells is comparable to protostellar outflows in the region. Together, shells and outflows inject enough energy and momentum to maintain the cloud turbulence. The mass-loss rates required to power the observed shells are two to three orders of magnitude higher than predicted for line-driven stellar winds from intermediate-mass stars. This discrepancy may be resolved by invoking accretion-driven wind variability. We describe in detail several shells in this paper and present the full sample in the online journal.

Non-axisymmetric line-driven disc winds II - full velocity gradient

We study non-axisymetric features of 3D line driven winds in the Sobolev approximation, where the optical depth is calculated using the full velocity gradient. We find that non-axisymmetric density features, so called clumps, form primarily at the base of the wind on super-Sobolev length scales. The density of clumps differs by a factor of $\sim 3$ from the azimuthal average, the magnitude of their velocity dispersion is comparable to the flow velocity and they produce $\sim 20\%$ variations in the column density. Clumps may be observable because differences in density produce enhancements in emission and absorption profiles or through their velocity dispersion which enhances line broadening.

Non-axisymmetric line-driven disc winds – I. Disc perturbations

We study mass outflows driven from accretion discs by radiation pressure due to spectral lines. To investigate non-axisymmetric effects, we use the Athena++ code and develop a new module to account for radiation pressure driving. In 2D, our new simulations are consistent with previous 2D axisymmetric solutions by Proga et al. who used the Zeus 2D code. Specifically, we find that the disc winds are time dependent, characterized by a dense stream confined to $\sim 45^{\circ}$ relative to the disc midplane and bounded on the polar side by a less dense, fast stream. Introducing a vertical, $\phi$-dependent, subsonic velocity perturbation in the disc midplane does not change the overall character of the solution but global outflow properties such as the mass, momentum and kinetic energy fluxes are altered by up to 100%. Non-axisymmetric density structures develop and persist mainly at the base of the wind. They are relatively small, and their densities can be a few times higher that the azimuthal average. The structure of the non-axisymmetric and axisymmetric solutions differ also in other ways. Perhaps most importantly from the observational point of view are the differences in the so called clumping factors, that serve as a proxy for emissivity due to two body processes. In particular, the spatially averaged clumping factor over the entire fast stream, while it is of a comparable value in both solutions, it varies about 10 times faster in the non-axisymmetric case.

Accretion from a clumpy massive-star wind in supergiant X-ray binaries

Supergiant X-ray Binaries (SgXB) host a compact object, often a neutron star (NS), orbiting an evolved O/B star. Mass transfer proceeds through the intense line-driven wind of the stellar donor, a fraction of which is captured by the gravitational field of the NS. The subsequent accretion process onto the NS is responsible for the abundant X-ray emission from SgXB. They also display peak-to-peak variability of the X-ray flux by a factor of a few 10 to 100, along with changes in the hardness ratios possibly due to varying absorption along the line-of-sight. We use recent radiation-hydrodynamic simulations of inhomogeneities (aka clumps) in the non-stationary wind of massive hot stars to evaluate their impact on the time-variable accretion process. For this, we run 3D hydrodynamic simulations of the wind in the vicinity of the accretor to investigate the formation of the bow shock and follow the inhomogeneous flow over several spatial orders of magnitude, down to the NS magnetosphere. In particular, we show that the impact of the wind clumps on the time-variability of the intrinsic mass accretion rate is severely tempered by the crossing of the shock, compared to the purely ballistic Bondi-Hoyle-Lyttleton estimation. We also account for the variable absorption due to clumps passing by the line-of-sight and estimate the final effective variability of the column density and mass accretion rate for different orbital separations. Finally, we compare our results to the most recent analysis of the X-ray flux and the hardness ratio in Vela X-1.

The WISSH quasars project

We perform a survey of the X-ray properties of 41 objects from the WISE/SDSS selected Hyper-luminous (WISSH) quasars sample, composed by 86 broad-line quasars (QSOs) with bolometric luminosity $L_{Bol}\geq 2\times 10^{47}\,erg\, s^{-1}$, at z~2-4. All but 3 QSOs show unabsorbed 2-10 keV luminosities $L_{2-10}\geq10^{45} \,erg \,s^{-1}$. Thanks to their extreme radiative output across the Mid-IR-to-X-ray range, WISSH QSOs offer the opportunity to significantly extend and validate the existing relations involving $L_{2-10}$. We study $L_{2-10}$ as a function of (i) X-ray-to-Optical (X/O) flux ratio, (ii) mid-IR luminosity ($L_{MIR}$), (iii) $L_{Bol}$ as well as (iv) $\alpha_{OX}$ vs. the 2500$\mathring{A}$ luminosity. We find that WISSH QSOs show very low X/O(<0.1) compared to typical AGN values; $L_{2-10}/L_{MIR}$ ratios significantly smaller than those derived for AGN with lower luminosity; large X-ray bolometric corrections $k_{\rm Bol,X}\sim$ 100-1000; and steep $-2<\alpha_{OX}<-1.7$. These results lead to a scenario where the X-ray emission of hyper-luminous quasars is relatively weaker compared to lower-luminosity AGN. Models predict that such an X-ray weakness can be relevant for the acceleration of powerful high-ionization emission line-driven winds, commonly detected in the UV spectra of WISSH QSOs, which can in turn perturb the X-ray corona and weaken its emission. Accordingly, hyper-luminous QSOs represent the ideal laboratory to study the link between the AGN energy output and wind acceleration. Additionally, WISSH QSOs show very large BH masses ($\log[M_{\rm BH}/M_{\odot}]$>9.5). This enables a more robust modeling of the $\Gamma-M_{BH}$ relation by increasing the statistics at high masses. We derive a flatter $\Gamma$ dependence than previously found over the broad range 5 <$\log(M_{\rm BH}/M_{\odot})$ < 11.

A Semi-analytical Model for Wind-fed Black Hole High-mass X-Ray Binaries: State Transition Triggered by Magnetic Fields from the Companion Star

Abstract We propose a mechanism of state transition in wind-fed black hole (BH) binaries (high-mass X-ray binaries) such as Cyg X-1 and LMC X-1. Modeling a line-driven stellar wind from the companion by two-dimensional hydrodynamical calculations, we investigate the processes of wind capture by, and accretion onto, the BH. We assume that the wind acceleration is terminated at the He ii ionization front because ions responsible for line-driven acceleration are ionized within the front, i.e., the He iii region. It is found that the mass accretion rate inferred from the luminosity is remarkably smaller than the capture rate. Considering the difference, we construct a model for the state transition based on the accretion flow being controlled by magnetorotational instability. The outer flow is torus-like, and plays an important role to trigger the transition. The model can explain why state transition does occur in Cyg X-1, while not in LMC X-1. Cyg X-1 exhibits a relatively low luminosity, and then the He ii ionization front is located and can move between the companion and BH, depending on its ionizing photon flux. On the other hand, LMC X-1 exhibits too high luminosity for the front to move considerably; the front is too close to the companion atmosphere. The model also predicts that each state of high-soft or low-hard would last fairly long because the luminosity depends weakly on the wind velocity. In the context of the model, the state transition is triggered by a fluctuation of the magnetic field when its amplitude becomes comparable to the field strength in the torus-like outer flow.