Envelope inflation in massive stars near the Eddington limit

Massive stars, i.e. those stars with masses more than about 10 times that of the Sun, are important agents for the chemical and dynamical evolution of galaxies. Because of the steep mass-luminosity relation, massive stars are extremely luminous objects. Therefore, increasingly massive stars approach their so-called Eddington luminosity, i.e., the maximum luminosity they can radiate at. It is usually believed that when the Eddington limit is reached, strong outflows are initiated. We present state-of-the-art stellar evolutionary models of massive stars, and the detailed analyses of their interior structures. After investigating model grids with five different initial chemical compositions, we find that stars reach the Eddington limit in their envelope already at masses of ~30 Solar masses and above. Furthermore, instead of showing any violent behaviour upon reaching the Eddington limit, the models develop inflated envelopes, which are extended low-density regions beneath the surface. This phenomenon is mediated by the opacity and convective energy transport in the models. Luminous Blue Variables (LBVs) like S Doradus which show strong variability on a timescale of a decades have been previously suggested to be connected to the Eddington limit, although little was known about their evolutionary stage or interior structure. We find that the hot edge of the S Doradus variability strip coincides with a line beyond which our models show strong envelope inflation, indicating a possible connection between the two. Furthermore, the inflated envelope mass in our coolest models reach several Solar masses. They provide the first physical model which could explain the large mass ejected by LBVs during the so-called Giant Eruptions, like the one observed for Eta Carinae in the 19th century. To further explore the observational consequences of envelope inflation, we follow the evolution of massive hydrogen-free models through the post main-sequence phase and predict that when these inflated stars explode as supernovae, it will lead to extended rise times of the shock breakout signal. Our model closely matches the properties of SN 2008D, the only observation of a shock breakout from a supernova so far. We conclude that envelope inflation affects the evolution of massive stars from the zero-age main-sequence up to the point of explosion, and may invoke observational instabilities in the envelope that might manifest themselves as pulsations and atmospheric macroturbulence

Extended supernova shock breakout signals from inflated stellar envelopes

Stars close to the Eddington luminosity can have large low-density inflated envelopes. We show that the rise times of shock breakout signals from supernovae can be extended significantly if supernova progenitors have an inflated stellar envelope. If the shock breakout occurs in such inflated envelopes, the shock breakout signals diffuse in them, and their rise time can be significantly extended. Then, the rise times of the shock breakout signals are dominated by the diffusion time in the inflated envelope rather than the light-crossing time of the progenitors. We show that our inflated Wolf-Rayet star models whose radii are of the order of the solar radius can have shock breakout signals which are longer than ~100 sec. The existence of inflated envelopes in Wolf-Rayet supernova progenitors may be related to the mysterious long shock breakout signal observed in Type Ib SN 2008D. Extended shock breakout signals may provide evidence for the existence of inflated stellar envelopes and can be used to constrain the physical properties of these enigmatic structures.Comment: 5 pages, 3 figures, 1 table, accepted by Astronomy & Astrophysics Letters, proofed in v

Evolution towards and beyond accretion-induced collapse of massive white dwarfs and formation of millisecond pulsars

Millisecond pulsars (MSPs) are generally believed to be old neutron stars (NSs), formed via type Ib/c core-collapse supernovae (SNe), which have been spun up to high rotation rates via accretion from a companion star in a low-mass X-ray binary (LMXB). In an alternative formation channel, NSs are produced via the accretion-induced collapse (AIC) of a massive white dwarf (WD) in a close binary. Here we investigate binary evolution leading to AIC and examine if NSs formed in this way can subsequently be recycled to form MSPs and, if so, how they can observationally be distinguished from pulsars formed via the standard core-collapse SN channel in terms of their masses, spins, orbital periods and space velocities. Numerical calculations with a detailed stellar evolution code were used for the first time to study the combined pre- and post-AIC evolution of close binaries. We investigated the mass transfer onto a massive WD in 240 systems with three different types of non-degenerate donor stars: main-sequence stars, red giants, and helium stars. When the WD is able to accrete sufficient mass (depending on the mass-transfer rate and the duration of the accretion phase) we assumed it collapses to form a NS and we studied the dynamical effects of this implosion on the binary orbit. Subsequently, we followed the mass-transfer epoch which resumes once the donor star refills its Roche lobe and calculated the continued LMXB evolution until the end. We demonstrate that the final properties of these MSPs are, in general, remarkably similar to those of MSPs formed via the standard core-collapse SN channel. However, the resultant MSPs created via the AIC channel preferentially form in certain orbital period intervals. Finally, we discuss the link between AIC and young NSs in globular clusters. Our calculations are also applicable to progenitor binaries of SNe Ia under certain conditions. [Abridged]Comment: 26 pages, 20 figures, 2 tables. A few references added. A&A in pres

Metallicity dependence of turbulent pressure and macroturbulence in stellar envelopes

Macroturbulence, introduced as a fudge to reproduce the width and shape of stellar absorption lines, reflects gas motions in stellar atmospheres. While in cool stars, it is thought to be caused by convection zones immediately beneath the stellar surface, the origin of macroturbulence in hot stars is still under discussion. Recent works established a correlation between the turbulent-to-total pressure ratio inside the envelope of stellar models and the macroturbulent velocities observed in corresponding Galactic stars. To probe this connection further, we evaluated the turbulent pressure that arises in the envelope convective zones of stellar models in the mass range 1-125 Msun based on the mixing-length theory and computed for metallicities of the Large and Small Magellanic Cloud. We find that the turbulent pressure contributions in models with these metallicities located in the hot high-luminosity part of the Hertzsprung-Russel (HR) diagram is lower than in similar models with solar metallicity, whereas the turbulent pressure in low-metallicity models populating the cool part of the HR-diagram is not reduced. Based on our models, we find that the currently available observations of hot massive stars in the Magellanic Clouds appear to support a connection between macroturbulence and the turbulent pressure in stellar envelopes. Multidimensional simulations of sub-surface convection zones and a larger number of high-quality observations are necessary to test this idea more rigorously.Comment: Accepted A&A, 8 p

Diagnostic of the unstable envelopes of Wolf-Rayet stars

The envelopes of stars near the Eddington limit are prone to various instabilities. A high Eddington factor in connection with the Fe opacity peak leads to convective instability, and a corresponding envelope inflation may induce pulsational instability. Here, we investigate the occurrence and consequences of both instabilities in models of Wolf-Rayet stars. We determine the convective velocities in the sub-surface convective zones to estimate the amplitude of the turbulent velocity at the base of the wind that potentially leads to the formation of small-scale wind structures, as observed in several WR stars. We also investigate the effect of mass loss on the pulsations of our models. We approximated solar metallicity WR stars by models of mass-losing helium stars, and we characterized the properties of convection in the envelope adopting the standard MLT. Our results show the occurrence of sub-surface convective regions in all studied models. Small surface velocity amplitudes are predicted for models with masses below 10Msun. For models with M>10Msun, the surface velocity amplitudes are of the order of 10km/s. Moreover we find the occurrence of pulsations for stars in the mass range 9-14Msun, while mass loss appears to stabilize the more massive WR stars. We confront our results with observationally derived line variabilities of 17 WN stars. The data suggest variability to occur for stars above 10Msun, which is increasing linearly with mass above this value, in agreement with our results. We further find some of our models to be unstable to radial pulsations, and predict local magnetic fields of the order of hundreds of Gauss in WR stars more massive than 10Msun. Our study relates the surface velocity fluctuations induced by sub-surface convection to the formation of clumping in the inner part of the wind. From this mechanism, we expect a stronger variability in more massive WR stars.Comment: A&A, accepte

Thermal averaging in quantum many-body systems: a non-perturbative thermal cluster cumulant approach

We present here a non-perturbative cluster cumulant approach for effecting thermal averaging in quantum-mechanical observables. We introduce a new representation of thermo field dynamics (TFD), with the associated thermal normal order and Wick expansion, and replace the thermal averaging by a quantum mechanical one involving a thermal "base state" |0β. Unlike the traditional TFD, only the physical variables appear in our formulation. The imaginary time evolution of the statistical operator is treated by our recently developed time-dependent coupled cluster theory. The partition function Z is evaluated as a completely contracted quantity involving |0β. We have computed Z for an anharmonic oscillator with quartic perturbation as an illustrative application. We also demonstrate numerically the validity of the Kohn-Luttinger theorem