Line-force Parameters Research Articles

Estimation of Physical Stellar Parameters from Spectral Models Using Deep Learning Techniques

This article presents a new algorithm that uses techniques from the field of artificial intelligence to automatically estimate the physical parameters of massive stars from a grid of stellar spectral models. This is the first grid to consider hydrodynamic solutions for stellar winds and radiative transport, containing more than 573 thousand synthetic spectra. The methodology involves grouping spectral models using deep learning and clustering techniques. The goal is to delineate the search regions and differentiate the “species” of spectra based on the shapes of the spectral line profiles. Synthetic spectra close to an observed stellar spectrum are selected using deep learning and unsupervised clustering algorithms. As a result, for each spectrum, we found the effective temperature, surface gravity, micro-turbulence velocity, and abundance of elements, such as helium and silicon. In addition, the values of the line force parameters were obtained. The developed algorithm was tested with 40 observed spectra, achieving 85% of the expected results according to the scientific literature. The execution time ranged from 6 to 13 min per spectrum, which represents less than 5% of the total time required for a one-to-one comparison search under the same conditions.

The wind of rotating B supergiants – II. The δ-slow hydrodynamic regime

ABSTRACT The theory of line-driven winds can explain many observed spectral features in early-type stars, though our understanding the winds of B supergiants remains incomplete. The hydrodynamic equations for slowly rotating stellar winds predict two regimes based on the line-force parameter δ: the fast and the δ-slow solution. In this paper, we aim to explore the capability of the latter to explain the observed properties of B supergiant winds. We calculate Hα line profiles, the most sensitive wind diagnostics in the optical, for both fast and δ-slow wind models. We fit them to observed data from a well-studied sample of B supergiants, by adapting the line-force parameters (k, α, and δ) of the hydrodynamic model. Unexpectedly, the observed Hα spectra can be reproduced by both hydrodynamic wind regimes with similar precision. We argue that this similarity results from the similar shape of the normalized velocity law produced by both regimes in the lower, Hα-forming wind region. Our findings raise a dichotomy, because mass-loss rates and terminal velocities (v∞) for each solution are quite different. The δ-slow solution predicts maximum values for v∞ that are systematically lower than those measured in the ultraviolet, whereas the v∞ values of the fast solution are closer, and probably more appropriate. However, our results also indicate that the δ-slow solution might better describe the dense winds of B hypergiants. Multiwavelength analyses and a larger sample of stars are needed to reach a definitive conclusion.

Evolution of rotating massive stars with new hydrodynamic wind models

Context. Mass loss due to radiatively line-driven winds is central to our understanding of the evolution of massive stars in both single and multiple systems. This mass loss plays a key role in modulating the stellar evolution at different metallicities, particularly in the case of massive stars with M* ≥ 25 M⊙. Aims. We extend the evolution models introduced in Paper I, where the mass-loss recipe is based on the simultaneous calculation of the wind hydrodynamics and the line acceleration, by incorporating the effects of stellar rotation. Methods. As in Paper I, we introduce a grid of self-consistent line-force parameters (k, α, δ) for a set of standard evolutionary tracks using GENEC. Based on this grid, we analysed the effects of stellar rotation, CNO abundances, and He/H ratio on the wind solutions to derive additional terms for the recipe with which we predict the self-consistent mass-loss rate, Ṁsc. With this, we generated a new set of evolutionary tracks with rotation for MZAMS = 25, 40, 70, and 120 M⊙, and for metallicities Z = 0.014 (Galactic) and 0.006 (Large Magellanic Cloud). Results. In addition to the expected correction factor due to rotation, the mass-loss rate decreases when the surface becomes more helium rich, especially in the later moments of the main-sequence phase. The self-consistent approach gives lower mass-loss rates than the standard values adopted in previous GENEC evolution models. This decrease strongly affects the tracks of the most massive models. Weaker winds allow the star to retain more mass, but also more angular momentum. As a consequence, weaker wind models rotate faster and show a less efficient mixing in their inner stellar structure at a given age. Conclusions. The self-consistent tracks predict an evolution of the rotational velocities through the main sequence that closely agrees with the range of v sin i values found by recent surveys of Galactic O-type stars. As subsequent implications, the weaker winds from self-consistent models also suggest a reduction of the contribution of the isotope 26Al to the interstellar medium due to stellar winds of massive stars during the MS phase. Moreover, the higher luminosities found for the self-consistent evolutionary models suggest that some populations of massive stars might be less massive than previously thought, as in the case of Ofpe stars at the Galactic centre. Therefore, this study opens a wide range of consequences for further research based on the evolution of massive stars.

Revisiting viscous transonic decretion disks of Be stars

Aims. In the context of Be stars, we re-studied the viscous transonic decretion disk model of these stars. This model is driven by a radiative force due to an ensemble of optically thin lines and viscosity considering the Shakura–Sunyaev prescription. Methods. The nonlinear equation of motion presents a singularity (sonic point) and an eigenvalue, which is also the initial condition at the stellar surface. Then, to obtain this eigenvalue, we set it as a radial quantity and performed a detailed topological analysis. We describe a numerical method for solving either nodal or saddle transonic solutions. Results. The value of the viscosity α barely determines the location of the sonic point, but it determines the topology of the solution. We found two nodal solutions, which are almost indistinguishable. Saddle solutions were found for lower values of α than required for the nodal solutions. In addition, rotational velocity does not play a determinate role in the velocity (and density) profile, because the viscosity effects collapse all the solutions to almost a unique one in a small region above the stellar surface. Conclusions. A suitable combination of line-force parameters and/or disk temperature gives the location of the sonic point lower than 50 stellar radii, describing a truncated disk. This could explain the SED turn-down observed in Be stars without needing a binary companion.

New self-consistent wind parameters to fit optical spectra of O-type stars observed with the HERMES spectrograph

Aims. We performed a spectral fitting for a set of O-type stars based on self-consistent wind solutions, which provide mass-loss rate and velocity profiles directly derived from the initial stellar parameters. The great advantage of this self-consistent spectral fitting is therefore the reduction of the number of free parameters to be tuned. Methods. Self-consistent values for the line-force parameters (k, α, δ)sc and subsequently for the mass-loss rate, Msc, and terminal velocity, υ∞‚sc, are provided by the m-CAK prescription introduced in Paper I, which is updated in this work with improvements such as a temperature structure T(r) for the wind that are self-consistently evaluated from the line-acceleration. Synthetic spectra were calculated using the radiative transfer code FASTWIND, replacing the classical β-law for our new calculated velocity profiles v(r) and therefore making clumping the only free parameter for the stellar wind. Results. We found that self-consistent m-CAK solutions provide values for theoretical mass-loss rates of the order of the most recent predictions of other studies. From here, we generate synthetic spectra with self-consistent hydrodynamics to fit and obtain a new set of stellar and wind parameters for our sample of O-type stars (HD 192639, 9 Sge, HD 57682, HD 218915, HD 195592, and HD 210809), whose spectra were taken with the high-resolution echelle spectrograph HERMES (R = 85 000). We find a satisfactory global fit for our observations, with a good accuracy for photospheric He I and He II lines and a quite acceptable fit for H lines. Although this self-consistent spectral analysis is currently constrained in the optical wavelength range alone, this is an important step towards the determination of stellar and wind parameters without using a β-law. Based on the variance of the line-force parameters, we establish that our method is valid for O-type stars with Teff ≥ 30 kK and log g ≥ 3.2. Given these results, we expect that the values introduced here are helpful for future studies of the stars constituting this sample, together with the prospect that the m-CAK self-consistent prescription may be extended to numerous studies of massive stars in the future.

ISOSCELES: Grid of stellar atmosphere and hydrodynamic models of massive stars. The first results

AbstractIn this work we seek to derive simultaneously the stellar and wind parameters of massive stars, mainly A and B type supergiant stars. Our stellar properties encompass the effective temperature, the surface gravity, the micro-turbulence velocity and, silicon abundance. For wind properties we consider the line–force parameters (α, k and δ) obtained from the standard line-driven wind theory. To model the data we use the radiative transport code Fastwind considering the hydrodynamic solutions derived with the stationary code Hydwind. Then, ISOSCELES, a grid of stellar atmosphere and hydrodynamic models of massive stars is created. Together with the observed spectra and a semi-automatic tool the physical properties from these stars are determined through spectral line fittings. This quantitative spectroscopic analysis provide an estimation about the line–force parameters. In addition, we confirm that the hydrodynamic solutions, called δ-slow solutions, describe quite reliable the radiation line-driven winds of B supergiant stars.

Analytical solutions for radiation-driven winds in massive stars – II. The δ-slow regime

ABSTRACT Accurate mass-loss rates and terminal velocities from massive stars winds are essential to obtain synthetic spectra from radiative transfer calculations and to determine the evolutionary path of massive stars. From a theoretical point of view, analytical expressions for the wind parameters and velocity profile would have many advantages over numerical calculations that solve the complex non-linear set of hydrodynamic equations. In a previous work, we obtained an analytical description for the fast wind regime. Now, we propose an approximate expression for the line-force in terms of new parameters and obtain a velocity profile closed-form solution (in terms of the Lambert W function) for the δ-slow regime. Using this analytical velocity profile, we were able to obtain the mass-loss rates based on the m-CAK theory. Moreover, we established a relation between this new set of line-force parameters with the known stellar and m-CAK line-force parameters. To this purpose, we calculated a grid of numerical hydrodynamical models and performed a multivariate multiple regression. The numerical and our descriptions lead to good agreement between their values.

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.

Ω-slow Solutions and Be Star Disks

Abstract As the disk formation mechanism(s) in Be stars is(are) as yet unknown, we investigate the role of rapidly rotating radiation-driven winds in this process. We implemented the effects of high stellar rotation on m-CAK models accounting for the shape of the star, the oblate finite disk correction factor, and gravity darkening. For a fast rotating star, we obtain a two-component wind model, i.e., a fast, thin wind in the polar latitudes and an Ω-slow, dense wind in the equatorial regions. We use the equatorial mass densities to explore Hα emission profiles for the following scenarios: (1) a spherically symmetric star, (2) an oblate star with constant temperature, and (3) an oblate star with gravity darkening. One result of this work is that we have developed a novel method for solving the gravity-darkened, oblate m-CAK equation of motion. Furthermore, from our modeling we find that (a) the oblate finite disk correction factor, for the scenario considering the gravity darkening, can vary by at least a factor of two between the equatorial and polar directions, influencing the velocity profile and mass-loss rate accordingly, (b) the Hα profiles predicted by our model are in agreement with those predicted by a standard power-law model for following values of the line-force parameters: , and , and (c) the contribution of the fast wind component to the Hα emission line profile is negligible; therefore, the line profiles arise mainly from the equatorial disks of Be stars.

Stellar and wind parameters of massive stars from spectral analysis

AbstractThe only way to deduce information from stars is to decode the radiation it emits in an appropriate way. Spectroscopy can solve this and derive many properties of stars. In this work we seek to derive simultaneously the stellar and wind characteristics of a wide range of massive stars. Our stellar properties encompass the effective temperature, the surface gravity, the stellar radius, the micro-turbulence velocity, the rotational velocity and the Si abundance. For wind properties we consider the mass-loss rate, the terminal velocity and the line–force parameters α, k and δ (from the line–driven wind theory). To model the data we use the radiative transport code Fastwind considering the newest hydrodynamical solutions derived with Hydwind code, which needs stellar and line–force parameters to obtain a wind solution. A grid of spectral models of massive stars is created and together with the observed spectra their physical properties are determined through spectral line fittings. These fittings provide an estimation about the line–force parameters, whose theoretical calculations are extremely complex. Furthermore, we expect to confirm that the hydrodynamical solutions obtained with a value of δ slightly larger than ~ 0.25, called δ-slow solutions, describe quite reliable the radiation line-driven winds of A and late B supergiant stars and at the same time explain disagreements between observational data and theoretical models for the Wind–Momentum Luminosity Relationship (WLR).

New Solutions to Line-Driven Winds of Hot Massive Stars

AbstractIn the frame of radiation driven wind theory (Castor et al.1975), we present self-consistent hydrodynamical solutions to the line-force parameters (k, α, δ) under LTE conditions. Hydrodynamic models are provided by HydWind (Curé 2004). We evaluate these results with those ones previously found in literature, focusing in different regions of the optical depth to be used to perform the calculations. The values for mass-loss rate and terminal velocity obtained from our calculations are also presented.We also examine the line-force parameters for the case when large changes in ionization throughout the wind occurs (δ-slow solutions, Curé et al.2011).

THE WIND OF ROTATING B SUPERGIANTS. I. DOMAINS OF SLOW AND FAST SOLUTION REGIMES

ABSTRACT In the scenario of rotating radiation-driven wind theory for massive stars, three types of stationary hydrodynamic solutions are currently known: the classical (fast) m-CAK solution, the Ω-slow solution that arises for fast rotators, and the so-called δ-slow solution if high values of the δ line-force parameter are allowed independently of the rotation speed. Compared to the fast solution, both “slow solutions” have lower terminal velocities. As the study of the parameter domain for the slow solution is still incomplete, we perform a comprehensive analysis of the distinctive flow regimes for B supergiants that emerge from a fine grid of rotation values, Ω, and various ionization conditions in the wind (δ) parameter. The wind ionization defines two domains: one for fast outflowing winds and the other for slow expanding flows. Both domains are clear-cut by a gap, where a kink/plateau structure of the velocity law could exist for a finite interval of δ. The location and width of the gap depend on T eff and Ω. There is a smooth and continuous transition between the Ω-slow and δ-slow regimes, a single Ω δ-slow regime. We discuss different situations where the slow solutions can be found and the possibility of a switch between fast and slow solutions in B supergiant winds. We compare the theoretical terminal velocity with observations of B and A supergiants and find that the fast regime prevails mostly for early B supergiants while the slow wind regime matches better for A and B mid- and late-type supergiants.

LINE-DRIVEN WINDS REVISITED IN THE CONTEXT OF Be STARS: Ω-SLOW SOLUTIONS WITH HIGHkVALUES

The standard, or fast, solutions of m-CAK line-driven wind theory cannot account for slowly outflowing disks like the ones that surround Be stars. It has been previously shown that there exists another family of solutions --- the $\Omega$-slow solutions --- that is characterized by much slower terminal velocities and higher mass-loss rates. We have solved the one-dimensional m-CAK hydrodynamical equation of rotating radiation-driven winds for this latter solution, starting from standard values of the line force parameters ($\alpha$, $k$, and $\delta$), and then systematically varying the values of $\alpha$ and $k$. Terminal velocities and mass-loss rates that are in good agreement with those found in Be stars are obtained from the solutions with lower $\alpha$ and higher $k$ values. Furthermore, the equatorial densities of such solutions are comparable to those that are typically assumed in ad hoc models. For very high values of $k$, we find that the wind solutions exhibit a new kind of behavior.

ON LOCAL IONIZATION EQUILIBRIUM AND DISK WINDS IN QSOs

We present theoretical C iv λλ1548,1550 absorption line profiles for QSOs calculated assuming the accretion disk wind (ADW) scenario. The results suggest that the multiple absorption troughs seen in many QSOs may be due to the discontinuities in the ion balance of the wind (caused by X-rays), rather than discontinuities in the density/velocity structure. The profiles are calculated from a 2.5-dimensional time-dependent hydrodynamic simulation of a line-driven disk wind for a typical QSO black hole mass, a typical QSO luminosity, and for a standard Shakura–Sunyaev disk. We include the effects of ionizing X-rays originating from within the inner disk radius by assuming that the wind is shielded from the X-rays from a certain viewing angle up to 90° ("edge on"). In the shielded region, we assume constant ionization equilibrium, and thus constant line-force parameters. In the non-shielded region, we assume that both the line-force and the C iv populations are nonexistent. The model can account for P-Cygni absorption troughs (produced at edge on viewing angles), multiple absorption troughs (produced at viewing angles close to the angle that separates the shielded region and the non-shielded region), and for detached absorption troughs (produced at an angle in between the first two absorption line types); that is, the model can account for the general types of broad absorption lines seen in QSOs as a viewing angle effect. The steady nature of ADWs, in turn, may account for the steady nature of the absorption structure observed in multiple-trough broad absorption line QSOs. The model parameters are Mbh = 109 M☉ and Ldisk = 1047 erg s−1.

JET FORMATION FROM MASSIVE YOUNG STARS: MAGNETOHYDRODYNAMICS VERSUS RADIATION PRESSURE

Observations indicate that outflows from massive young stars are more collimated during their early evolution compared to later stages. Our paper investigates various physical processes that impacts the outflow dynamics, i.e. its acceleration and collimation. We perform axisymmetric MHD simulations particularly considering the radiation pressure exerted by the star and the disk. We have modified the PLUTO code to include radiative forces in the line-driving approximation. We launch the outflow from the innermost disk region (r < 50 AU) by magneto-centrifugal acceleration. In order to disentangle MHD effects from radiative forces, we start the simulation in pure MHD, and later switch on the radiation force. We perform a parameter study considering different stellar masses (thus luminosity), magnetic flux, and line-force strength. For our reference simulation - assuming a 30 Msun star, we find substantial de-collimation of 35 % due to radiation forces. The opening angle increases from 20 deg to 32 deg for stellar masses from 20 Msun to 60 Msun. A small change in the line-force parameter 'alpha' from 0.60 to 0.55 changes the opening angle by ~ 8 deg. We find that it is mainly the stellar radiation which affects the jet dynamics. Unless the disk extends very close to the star, its pressure is too small to have much impact. Essentially, our parameter runs with different stellar mass can be understood as a proxy for the time evolution of the star-outflow system. Thus, we have shown that when the stellar mass (thus luminosity) increases (with age), the outflows become less collimated.

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.

The slow winds of A-type supergiants

AbstractThe line driven- and rotation modulated-wind theory predicts an alternative slow solution, besides from the standard m-CAK solution, when the rotational velocity is close to the critical velocity. We study the behaviour of the winds of A-type supergiants (Asg) and show that under particular conditions, e.g., when the δ line-force parameter is about 0.25, the slow solution could exist over the whole star, even for the cases when the rotational speed is slow or zero. We discuss density and velocity profiles as well as possible observational conterparts.

O stars with weak winds: the Galactic case

We study the stellar and wind properties of a sample of Galactic O dwarfs to track the conditions under which weak winds (i.e mass loss rates lower than � 10 −8 M⊙ yr −1 ) appear. The sample is composed of low and high luminosity dwarfs including Vz stars and stars known to display qualitatively weak winds. Atmosphere models including non-LTE treatment, spherical expansion and line blanketing are computed with the code CMFGEN (Hillier & Miller 1998). Both UV and Hlines are used to derive wind properties while optical H and He lines give the stellar parameters. We find that the stars of our sample are usually 1 to 4 Myr old. Mass loss rates of all stars are found to be lower than expected from the hydrodynamical predictions of Vink et al. (2001). For stars with log L L⊙ > 5.2, the reduction is by less than a factor 5 and is mainly due to the inclusion of clumping in the models. For stars with log L L⊙ < 5.2 the reduction can be as high as a factor 100. The inclusion of X-ray emission (possibly due to magnetic mechanisms) in models with low density is crucial to derive accurate mass loss rates from UV lines, while it is found to be unimportant for high density winds. The modified wind momentum - luminosity relation shows a significant change of slope around this transition luminosity. Terminal velocities of low luminosity stars are also found to be low. Both mass loss rates and terminal velocities of low L stars are consistent with a reduced line force parameter �. However, the physical reason for such a reduction is still not clear although the finding of weak winds in Galactic stars excludes the role of a reduced metallicity. There may be a link between an early evolutionary state and a weak wind, but this has to be confirmed by further studies of Vz stars. X-rays, through the change in the ionisation structure they imply, may be at the origin of a reduction of the radiative acceleration, leading to lower mass loss rates. A better understanding of the origin of X-rays is of crucial importance for the study of the physics of weak winds

Critical line force measurements for liquid drops on optical surfaces

A short review of the physics of a liquid drop on an inclined solid surface is presented and related to the problem of shedding water droplets from optical surfaces. A simple experimental method of quantitatively evaluating the water shedding properties for coatings for optical surfaces is described and data are presented for distilled water and seawater droplets on clean acrylic surfaces and acrylic surfaces treated with two silicon-based hydrophobic surface coatings. These results are presented in terms of critical line force parameters that are independent of drop size. The efficacy of one silicon-based hydrophobic surface coating is demonstrated by measuring the intensity of laser light returned through coated and uncoated acrylic slides sprayed with seawater.