Decretion Disk Research Articles

Populations of Be stars: stellar evolution of extreme stars

AbstractAmong the emission-line stars, the classical Be stars known for their extreme properties are remarkable. The Be stars are B-type main sequence stars that have displayed at least once in their life emission lines in their spectrum. Beyond this phenomenological approach some progresses were made on the understanding of this class of stars. With high-technology techniques (interferometry, adaptive optics, multi-objects spectroscopy, spectropolarimetry, high-resolution photometry, etc) from different instruments and space mission such as the VLTI, CHARA, FLAMES, ESPADONS-NARVAL, COROT, MOST, SPITZER, etc, some discoveries were performed allowing to constrain the modeling of the Be stars stellar evolution but also their circumstellar decretion disks. In particular, the confrontation between theory and observations about the effects of the stellar formation and evolution on the main sequence, the metallicity, the magnetic fields, the stellar pulsations, the rotational velocity, and the binarity (including the X-rays binaries) on the Be phenomenon appearance is discussed. The disks observations and the efforts made on their modeling is mentioned. As the life of a star does not finish at the end of the main sequence, we also mention their stellar evolution post main sequence including the gamma-ray bursts. Finally, the different new results and remaining questions about the main physical properties of the Be stars are summarized and possible ways of investigations proposed. The recent and future facilities (XSHOOTER, ALMA, E-ELT, TMT, GMT, JWST, GAIA, etc) and their instruments that may help to improve the knowledge of Be stars are also briefly introduced.

On Be/X-ray binaries with an intermediate-mass black hole

We adopt the tidal truncation model proposed by Negueruela and Okazaki for Be/X-ray binaries to investigate the influence of intermediate-mass black holes (IMBHs) on Be-star disks. We show that the viscous decretion disks around Be stars are generally truncated ineffectively under the tidal force of IMBHs. Combining this with observations of Be/X-ray binaries, we suggest that Be/IMBH X-ray binaries may appear as recurrent luminous X-ray transients with quasi-periodic X-ray outbursts.

STAR FORMATION HISTORY AND X-RAY BINARY POPULATIONS: THE CASE OF THE SMALL MAGELLANIC CLOUD

Using Chandra, XMM-Newton, and optical photometric catalogs we study the young X-ray binary (XRB) populations of the Small Magellanic Cloud. We find that the Be/X-ray binaries (Be-XRBs) are observed in regions with star formation rate bursts ~25-60 Myr ago. The similarity of this age with the age of maximum occurrence of the Be phenomenon (~40 Myr) indicates that the presence of a circumstellar decretion disk plays a significant role in the number of observed XRBs in the 10-100 Myr age range. We also find that regions with strong but more recent star formation (e.g., the Wing) are deficient in Be-XRBs. By correlating the number of observed Be-XRBs with the formation rate of their parent populations, we measure a Be-XRB production rate of ~1 system per 3 x 10^(-3) M$_{\odot}$/yr. Finally, we use the strong localization of the Be-XRB systems in order to set limits on the kicks imparted on the neutron star during the supernova explosion.

Mass and angular momentum loss of first stars via decretion disks

AbstractAlthough the first stars were likely very hot and luminous, their low or zero metallicity implies that any mass loss through winds driven by line-scattering of radiation in metal ions was likely small or non-existent. Here we examine the potential role of another possible mechanism for mass loss in these first stars, namely via decretion disks associated with near-critical rotation induced from evolution of the stellar interior. In this case the mass loss is set by the angular momentum needed to keep the stellar rotation at or below the critical rate. In present evolutionary models, that mass loss is estimated by assuming effective release from a spherical shell at the surface. Here we examine the potentially important role of viscous coupling of the decretion disk in outward angular momentum transport, emphasizing that the specific angular momentum at the outer edge of the disk can be much larger than at the stellar surface. The net result is that, for a given stellar interior angular momentum excess, the mass loss required from a decretion disk can be significantly less than invoked in previous models assuming a direct, near-surface release.

Evolution and appearance of Be stars in SMC clusters

AbstractStar clusters are privileged laboratories for studying the evolution of massive stars (OB stars). One particularly interesting question concerns the phases during which the classical Be stars occur, which—unlike HAe/Be stars—are not pre-main-sequence objects, nor supergiants. Rather, they are extremely rapidly rotating B-type stars with a circumstellar decretion disk formed by episodic ejections of matter from the central star. To study the impact of mass, metallicity, and age on the Be phase, we observed Small Magellanic Cloud (SMC) open clusters with two different techniques: (i) with the ESO–WFI in slitless mode, which allowed us to find the brighter Be and other emission-line stars in 84 SMC open clusters, and (ii) with the VLT–FLAMES multifiber spectrograph to determine accurately the evolutionary phases of Be stars in the Be-star-rich SMC open cluster NGC 330. Based on a comparison to the Milky Way, a model of Be stellar evolution, appearance as a function of metallicity and mass, and spectral type is developed, involving the fractional critical rotation rate as a key parameter.

Nonradial pulsations in the open cluster NGC 3766

AbstractNonradial pulsations (NRPs) are a proposed mechanism for the formation of decretion disks around Be stars. They are important tools to study the internal structure of stars. NGC 3766 has an unusually large fraction of transient Be stars, so it is an excellent location to study the formation mechanism of Be-star disks. High-resolution spectroscopy can reveal line-profile variations from NRPs, allowing measurements of both the degree, l, and azimuthal order, m. However, spectroscopic studies require large amounts of time with large telescopes to achieve the necessary high signal-to-noise ratio and time-domain coverage. On the other hand, multicolor photometry can be performed more easily with small telescopes to measure l only. Here, we present representative light curves of Be stars and nonemitting B stars in NGC 3766 from the CTIO 0.9m telescope in an effort to study NRPs in this cluster.

Cyclic variability of the circumstellar disk of the Be starζ Tauri

Emission lines formed in decretion disks of Be stars often undergo long-term cyclic variations, especially in the violet-to-red (V/R) ratio of their primary components. From observations of the bright Be-shell star zeta Tau, the possibly broadest and longest data set illustrating the prototype of this behaviour was compiled from our own and archival observations. It comprises optical and infrared spectra, broad-band polarimetry, and interferometric observations. From 3 V/R cycles between 1997 and 2008, a mean cycle length in H alpha of 1400-1430 days was derived. After each minimum in V/R, the shell absorption weakens and splits into two components, leading to 3 emission peaks. This phase makes the strongest contribution to the variability in cycle length. V/R curves of different lines are shifted in phase. Lines formed on average closer to the central star are ahead of the others. The shell absorption lines fall into 2 categories differing in line width, ionization/excitation potential, and variability of the equivalent width. The interferometry has resolved the continuum and the line emission in Br gamma and He I 2.06. The phasing of the Br gamma emission shows that the photocenter of the line-emitting region lies within the plane of the disk but is offset from the continuum source. The plane of the disk is constant throughout the observed V/R cycles. The self-consistent, one-armed, disk-oscillation model is developed in Paper II.

Cyclic variability of the circumstellar disk of the Be starζTauri

<i>Context. <i/>About 2/3 of the Be stars present the so-called variations, a phenomenon characterized by the quasi-cyclic variation in the ratio between the violet and red emission peaks of the emission lines. These variations are generally explained by global oscillations in the circumstellar disk forming a one-armed spiral density pattern that precesses around the star with a period of a few years.<i>Aims. <i/>This paper presents self-consistent models of polarimetric, photometric, spectrophotometric, and interferometric observations of the classical Be star <i>ζ<i/> Tauri. The primary goal is to conduct a critical quantitative test of the global oscillation scenario.<i>Methods. <i/>Detailed three-dimensional, NLTE radiative transfer calculations were carried out using the radiative transfer code HDUST. The most up-to-date research on Be stars was used as input for the code in order to include a physically realistic description for the central star and the circumstellar disk. The model adopts a rotationally deformed, gravity darkened central star, surrounded by a disk whose unperturbed state is given by a steady-state viscous decretion disk model. It is further assumed that this disk is in vertical hydrostatic equilibrium.<i>Results. <i/>By adopting a viscous decretion disk model for <i>ζ<i/> Tauri and a rigorous solution of the radiative transfer, a very good fit of the time-average properties of the disk was obtained. This provides strong theoretical evidence that the viscous decretion disk model is the mechanism responsible for disk formation. The global oscillation model successfully fitted spatially resolved VLTI/AMBER observations and the temporal variations in the H<i>α<i/> and Br<i>γ<i/> lines. This result convincingly demonstrates that the oscillation pattern in the disk is a one-armed spiral. Possible model shortcomings, as well as suggestions for future improvements, are also discussed.

MINIMUM MASS SOLAR NEBULAE AND PLANETARY MIGRATION

The Minimum Mass Solar Nebula (MMSN) is a protoplanetary disk that contains the minimum amount of solids necessary to build the planets of the Solar System. Assuming that the giant planets formed in the compact configuration they have at the beginning of the "Nice model", Desch (2007) built a new MMSN. He finds a decretion disk, about ten times denser than the well-known Hayashi MMSN. The disk profile is almost stationary for about ten million years. However, a planet in a protoplanetary disk migrates. In a massive, long-lived disk, this question has to be addressed. With numerical simulations, we show that the four giant planets of the Solar System could not survive in this disk. In particular, Jupiter enters the type III, runaway regime, and falls into the Sun like a stone. Known planet-planet interaction mechanisms to prevent migration, fail in this nebula, in contrast to the Hayashi MMSN. Planetary migration constrains the construction of a MMSN. We show how this should be done self-consistently.

Periodicities in the high-mass X-ray binary system RX J0146.9+6121/LS I+61°235

The high-mass X-ray binary RX J0146.9+6121, with optical counterpart LS I+61 ◦ 235 (V831 Cas), is an intriguing system on the outskirts of the open cluster NGC 663. It contains the slowest Be type X-ray pulsar known with a pulse period of around 1400 s and, primarily from the study of variation in the emission line profile of Hα, it is known to have a Be decretion disc with a one-armed density wave period of approximately 1240 d. Here we present the results of an extensive photometric campaign, supplemented with optical spectroscopy, aimed at measuring short time-scale periodicities. We find three significant periodicities in the photometric data at, in order of statistical significance, 0.34, 0.67 and 0.10 d. We give arguments to support the interpretation that the 0.34 and 0.10 d periods could be due to stellar oscillations of the B-type primary star and that the 0.67 d period is the spin period of the Be star with a spin axis inclination of 23 +10 −8 degrees. We measured a systemic velocity of −37.0 ± 4.3 km s −1 confirming that LS I+61 ◦ 235 has a high probability of membership in the young cluster NGC 663 from which the system’s age can be estimated as 20–25 Myr. From archival RXTE All Sky Monitor (ASM) data we further find ‘super’ X-ray outbursts roughly every 450 d. If these super outbursts are caused by the alignment of the compact star with the one-armed decretion disc enhancement, then the orbital period is approximately 330 d.

Non-LTE Calculation for the Be Star Decretion Disk

Abstract The non-LTE state of the hydrogen gas in isothermal transonic decretion disks around a B1V star has been calculated by an iterative method in order to explore the basic physical process in the disk. This dynamical model is characterized by a density law in the equatorial plane of $\rho(R) \propto R^{-3.5}$. The continuous radiation was calculated with the $\Lambda$ iteration in the integral form, while we adopted a single-flight escape probability for lines. We describe the non-LTE state, the radiation flow and conversion in the disk. We conclude that the stellar Balmer continuum plays a key role in the non-LTE state of the disk. An examination of the local energy gain and loss suggests that the disk temperature has double minima along the equatorial plane in the optically thick case: the intermediate region caused by deficient ultraviolet radiation and the outer Lyman $\alpha$ cooling region. We also calculated some observable quantities, such as the spectral energy distribution, the $UBV$ colors, the infrared excess and the Balmer line profiles. Our calculations with a mass-loss rate less than $10^{-10}M_{\odot}\ {\rm yr}^{-1}$ reproduce the observed continuum quantities. However, we could not obtain the large H$\alpha$ emission strength observed in Be stars. We suggest that the density gradient of the Be star disk is slower than that of an isothermal decretion disk.

Mass Distribution and Planet Formation in the Solar Nebula

The surface density profile Σ(r) of the solar nebula protoplanetary disk is a fundamental input to all models of disk processes and evolution. Traditionally it is estimated by spreading out the augmented masses of the planets over the annuli in which the planets orbit today, the so-called minimum-mass solar nebula. Doing so implicitly assumes that the planets completely accreted all planetesimals in their feeding zones, but this assumption has not been tested. Indeed, models of the growth of Uranus and Neptune predict that these planets could not have grown to ~10 M⊕ within the lifetime of the disk, even though they must have, to accrete H/He atmospheres. In this paper we adopt the starting positions of the planets in the model of planetary dynamics (Tsiganis and coworkers), in which the solar system started in a much more compact configuration. We derive a surface density profile that is well approximated by the power law Σ(r) = 343(fp/0.5)-1(r/10 AU)-2.168 g cm-2, where fp is the fraction of the solid mass in the form of planetesimals. We show that this profile is inconsistent with a steady state accretion disk but is consistent with a steady state decretion disk that is being photoevaporated. We calculate the growth of planets in the context of this disk model and demonstrate for the first time that all of the giant planets can achieve their isolation masses and begin to accrete H/He atmospheres within the lifetime of the disk. The fit of our inferred Σ(r) to the augmented masses of the planets is excellent (<10%), but only if Uranus and Neptune swtiched places early in the solar system's evolution, a possibility predicted by the Nice model.

Formation and evolution of Ae and Be stars

Several scenarios for the formation of accretion and decretion disks in single and binary Ae and Be stars are proposed. It is shown that, in order for a rapidly rotating main-sequence Be star to lose mass via a disk, the star’s rotation must be quasi-rigid-body. Estimates show that such rotation can be maintained by the star’s magnetic field, which is probably a relict field. The evolution of single Be main-sequence stars is numerically simulated allowing for mass loss via the stellar wind and rotational mass loss assuming rigid-body rotation. The stellar wind is the factor that determines the maximum mass of Be stars, which is close to 30M ⊙. The evolution of Be stars in close binaries is analyzed in the approximation adopted in our scenario. Long gamma-ray bursts can be obtained as a result of the collapse of rapidly rotating oxygen—neon degenerate dwarfs—the accreting companions of Be stars—into neutron stars.

Accretion vs. colliding wind models for the gamma-ray binary LS I +61 303: an assessment

Context. LS I +61 303 is a puzzling Be/X-ray binary with variable gamma-ray emission up to TeV energies. The nature of the compact object and the origin of the high-energy emission are unclear. One family of models invokes particle acceleration in shocks from the collision between the B-star wind and a relativistic pulsar wind, whereas another centers on a relativistic jet powered by accretion from the Be star decretion disc onto a black hole. Recent high-resolution radio observations showing a putative “cometary tail” pointing away from the Be star near periastron have been cited as support for the pulsar-wind model. Aims. We wish to carry out a quantitative assessment of these competing models. Methods. We apply a “Smoothed Particle Hydrodynamics” (SPH) code in 3D dynamical simulations for both the pulsar-windinteraction and accretion-jet models. The former yields a dynamical description of the shape of the wind-wind interaction surface. The latter provides a dynamical estimation of the accretion rate under a variety of conditions, and how this varies with orbital phase. Results. The results allow critical evaluation of how the two distinct models confront the data in various wavebands. When one accounts for the 3D dynamical wind interaction under realistic constraints for the relative strength of the B-star and pulsar winds, the resulting form of the interaction front does not match the putative “cometary tail” claimed from radio observations. On the other hand, dynamical simulations of the accretion-jet model indicate that the orbital phase variation of accretion power includes a secondary broad peak well away from periastron, thus providing a plausible way to explain the observed TeV gamma ray emission toward apastron. Conclusions. Contrary to previous claims, the colliding-wind model is not clearly established for LS I +61 303, whereas the accretionjet model can reproduce many key characteristics, such as required energy budget, lightcurve, and spectrum of the observed TeV gamma-ray emission.

High-energy gamma-ray emission from the inner jet of LS I +61 303: the hadronic contribution revisited

LS I +61 303 has been detected by the Cherenkov telescope MAGIC at very high energies, presenting a variable flux along the orbital motion with a maximum clearly separated from the periastron passage. In the light of the new observational constraints, we revisit the discussion of the production of high-energy gamma rays from particle interactions in the inner jet of this system. The hadronic contribution could represent a major fraction of the TeV emission detected from this source. The spectral energy distribution resulting from pp interactions is recalculated. Opacity effects introduced by the photon fields of the primary star and the stellar decretion disk are shown to be essential in shaping the high-energy gamma-ray light curve at energies close to 200 GeV. We also present results of Monte Carlo simulations of the electromagnetic cascades developed very close to the periastron passage. We conclude that a hadronic microquasar model for the gamma-ray emission in LS I +61 303 can reproduce the main features of its observed high-energy γ-ray flux.

Viscous overstability and eccentricity evolution in three-dimensional gaseous discs

We investigate the growth or decay rate of the fundamental mode of even symmetry in a viscous accretion disc. This mode occurs in eccentric discs and is known to be potentially overstable. We determine the vertical structure of the disc and its modes, treating radiative energy transport in the diffusion approximation. In the limit of very long radial wavelength, an analytical criterion for viscous overstability is obtained, which involves the effective shear and bulk viscosity, the adiabatic exponent, and the opacity law of the disc. This differs from the prediction of a two-dimensional model. On shorter wavelengths (a few times the disc thickness), the criterion for overstability is more difficult to satisfy because of the different vertical structure of the mode. In a low-viscosity disc a third regime of intermediate wavelengths appears, in which the overstability is suppressed as the horizontal velocity perturbations develop significant vertical shear. We suggest that this effect determines the damping rate of eccentricity in protoplanetary discs, for which the long-wavelength analysis is inapplicable and overstability is unlikely to occur on any scale. In thinner accretion discs and in decretion discs around Be stars overstability may occur only on the longest wavelengths, leading to the preferential excitation of global eccentric modes.

R modes of slowly pulsating B stars

Slowly pulsating B (SPB) stars are g-mode pulsators in main-sequence stages with mass ranging from M∼ 3 to ∼8 M⊙. In this paper, we examine pulsational stability of low-m r modes in SPB stars by calculating fully non-adiabatic oscillations of uniformly rotating stars, where m is an integer representing the azimuthal wavenumber around the rotation axis. r modes are rotationally induced, non-axisymmetric, oscillation modes, whose oscillation frequency strongly depends on the rotation frequency Ω of the star. They are conveniently classified by using two integer indices m and l′≥ ∼m∼ that define the asymptotic oscillation frequency 2mΩ/[l′(l′+ 1)] in the limit of Ω→ 0. We confirm Savonije's and Townsend's finding that low-m, high-radial order, odd r modes with l′=m in SPB stars are excited by the same iron opacity bump mechanism that excites low-frequency g modes of the variables, when the rotation frequency Ω is sufficiently high. No even r modes with low m are found to be pulsationally unstable. Since the surface pattern of the temperature perturbation of odd modes is antisymmetric about the equator of the star, observed photometric amplitudes caused by the unstable odd r modes with l′=m are strongly dependent on the inclination angle between the axis of rotation and the line of sight. Applying the wave-meanflow interaction formalism to non-adiabatic r modes in rapidly rotating SPB models, we find that because of the r φ component of the Reynolds stress and the radial transport of the eddy fluctuation of density in the rotating star, the surface rotation is accelerated by the forcing due to the low l′=m unstable r modes. We suggest that the amount of angular momentum redistribution in the surface region of the stars can be comparable to that needed to sustain decretion discs found in Be systems. We make a brief comparison between non-adiabatic r-mode calculations done with and without the traditional approximation. In the traditional approximation, the local horizontal component of the rotation vector Ω is ignored in the momentum conservation equation, which makes it possible to represent the angular dependence of an oscillation mode using a single Hough function. We find that the oscillation frequencies of low-m r modes computed with and without the traditional approximation are qualitatively in good agreement. We also find that the pulsational instability of r modes in the traditional approximation appears weaker than that without the approximation.

Models of astrophysical decretion-accretion diffusional disks

The formation of gaseous diffusional accretion-decretion disks is an important stage in the evolution of numerous astronomical objects. Matter is accreted onto the object in the accretion part of these disks, while the angular momentum of the accreted matter is transported from the central region to the periphery in the decretion part. Here, we consider general questions connected with the formation and evolution of diffusive accretion-decretion disks in various astrophysical objects. Such disks can be described using nonstationary diffusion models. The phenomenological parameters of these models are the coefficients in the relations for the characteristic turbulent velocity and mean free path of diffusion elements in the disk. We have developed a numerical technique to compute the disk evolution for a number of models (a massive disk, a disk with continuous accretion, a purely decretion disk). Analytical expressions estimating the basic parameters of accretion-decretion disks are presented. We discuss the relationship between the models considered and the classical α model of an accretion disk.

Discovery of the optical counterpart to the X-ray pulsar SAX J2103.5+4545

We report optical and infrared photometric and spectroscopic observations that identify the counterpart to the 358.6-s X-ray transient pulsar SAX J2103.5+4545 with a moderately reddened V=14.2 B0Ve star. This identification makes SAX J2103.5+4545 the Be/X-ray binary with the shortest orbital period known, Porb= 12.7 days. The amount of absorption to the system has been estimated to be Av=4.2+-0.3, which for such an early-type star implies a distance of about 6.5 kpc. The optical spectra reveal major and rapid changes in the strength and shape of the Halpha line. The Halpha line was initially observed as a double peak profile with the ratio of the intensities of the blue over the red peak greater than one (V/R > 1). Two weeks later this ratio reversed (V/R< 1). Subsequently, in less than a month, the emission ceased and Halpha appeared in absorption. This fast spectral variability is interpreted within the viscous decretion disc model and demonstrates the significant role of the neutron star on the evolution of the circumstellar disc around the Be star. The implications of the small orbit and moderate eccentricity on the spin period of the neutron star are discussed.

Formation and Dissipation of Viscous Disks around Be Stars

Based on the viscous decretion disk model for Be Stars, we study the effect of the torque from the star on the Be star disk, using a 3-D smoothed particle hydrodynamics code and turning on and off the mass ejection from the star. We find that, after the mass ejection is shut off, the innermost part of the disk begins to accrete and the accreting part gradually propagates outward. We also find that the Be disk in misaligned binaries precesses in a retrograde sense when no mass is supplied from the star. If the mass supply is resumed for such a disk, an inner disk is formed with its rotation axis misaligned with that of the outer disk. By the interaction between the inner and outer disks, the outer disk rapidly changes its direction to that of the inner disk.