Context. The Hertzsprung-Russell diagram is an essential diagnostic diagram for stellar structure and evolution, which has now been in use for more than 100 years. Aims. We introduce a new diagram ...based on the gravity-effective temperature diagram, which has various advantages. Methods. Our spectroscopic Hertzsprung-Russell (sHR) diagram shows the inverse of the flux-mean gravity versus the effective temperature. Observed stars whose spectra have been quantitatively analyzed can be entered in this diagram without the knowledge of the stellar distance or absolute brightness. Results. Observed stars can be as conveniently compared to stellar evolution calculations in the sHR diagram as in the Hertzsprung-Russell diagram. However, at the same time, our ordinate is proportional to the stellar mass-to-luminosity ratio, which can thus be directly determined. For intermediate- and low-mass star evolution at constant mass, we show that the shape of an evolutionary track in the sHR diagram is identical to that in the Hertzsprung-Russell diagram. We also demonstrate that for hot stars, their stellar Eddington factor can be directly read off the sHR diagram. For stars near their Eddington limit, we argue that a version of the sHR diagram may be useful where the gravity is exchanged by the effective gravity. Conclusions. We discuss the advantages and limitations of the sHR diagram, and show that it can be fruitfully applied to Galactic stars, but also to stars with known distance, e.g., in the LMC or in galaxies beyond the Local Group.
Context. The majority of the Wolf–Rayet (WR) stars represent the stripped cores of evolved massive stars who lost most of their hydrogen envelope. Wind stripping in single stars is expected to be ...inefficient in producing WR stars in metal-poor environments such as the Small Magellanic Cloud (SMC). While binary interaction can also produce WR stars at low metallicity, it is puzzling that the fraction of WR binaries appears to be about 40%, independent of the metallicity. Aim. We aim to use the recently determined physical properties of the twelve known SMC WR stars to explore their possible formation channels through comparisons with stellar models. Methods. We used the MESA stellar evolution code to construct two grids of stellar models with SMC metallicity. One of these consists of models of rapidly rotating single stars, which evolve in part or completely chemically homogeneously. In a second grid, we analyzed core helium burning stellar models assuming constant hydrogen and helium gradients in their envelopes. Results. We find that chemically homogeneous evolution is not able to account for the majority of the WR stars in the SMC. However, in particular the apparently single WR star SMC AB12, and the double WR system SMC AB5 (HD 5980) appear consistent with this channel. We further find a dichotomy in the envelope hydrogen gradients required to explain the observed temperatures of the SMC WR stars. Shallow gradients are found for the WR stars with O star companions, while much steeper hydrogen gradients are required to understand the group of hot apparently single WR stars. Conclusions. The derived shallow hydrogen gradients in the WR component of the WR+O star binaries are consistent with predictions from binary models where mass transfer occurs early, in agreement with their binary properties. Since the hydrogen profiles in evolutionary models of massive stars become steeper with time after the main sequence, we conclude that most of the hot (Teff > 60 kK ) apparently single WR stars lost their envelope after a phase of strong expansion, e.g., as the result of common envelope evolution with a lower mass companion. The so far undetected companions, either main sequence stars or compact objects, are then expected to still be present. A corresponding search might identify the first immediate double black hole binary progenitor with masses as high as those detected in GW150914.
We study supernova ejecta-companion interactions in a sample of realistic semidetached binary systems representative of Type Ia supernova progenitor binaries in a single-degenerate scenario. We model ...the interaction process with the help of a high-resolution hydrodynamic code assuming cylindrical symmetry. We find that the ejecta hole has a half-opening angle of 40-50 degree with the density by a factor of 2-4 lower, in good agreement with the previous studies. Quantitative differences from the past results in the amounts and kinematics of the stripped companion material and levels of contamination of the companion with the ejecta material can be explained by different model assumptions and effects due to numerical diffusion. We analyse and, for the first time, provide simulation-based estimates of the amounts and of the thermal characteristics of the shock-heated material responsible for producing a prompt, soft X-ray emission. Besides the shocked ejecta material, considered in the original model by Kasen, we also account for the stripped, shock-heated envelope material of stellar companions, which we predict partially contributes to the prompt emission. The amount of the energy deposited in the envelope is comparable to the energy stored in the ejecta. The total energy budget available for the prompt emission is by a factor of about 2-4 smaller than originally predicted by Kasen. Although the shocked envelope has a higher characteristic temperature than the shocked ejecta, the temperature estimates of the shocked material are in good agreement with the Kasen's model. The hottest shocked plasma is produced in the subgiant companion case.
Context. The evolution of massive stars is strongly influenced by internal mixing processes such as semiconvection, convective core overshooting, and rotationally induced mixing. None of these ...processes are currently well constrained. Aims. We investigate models for massive stars in the Small Magellanic Cloud (SMC), for which stellar-wind mass loss is less important than for their metal-rich counterparts. We aim to constrain the various mixing efficiencies by comparing model results to observations. Methods. For this purpose, we use the stellar-evolution code MESA to compute more than 60 grids of detailed evolutionary models for stars with initial masses of 9…100 M⊙, assuming different combinations of mixing efficiencies of the various processes in each grid. Our models evolve through core hydrogen and helium burning, such that they can be compared with the massive main sequence and supergiant population of the SMC. Results. We find that for most of the combinations of the mixing efficiencies, models in a wide mass range spend core-helium burning either only as blue supergiants, or only as red supergiants. The latter case corresponds to models that maintain a shallow slope of the hydrogen/helium (H/He) gradient separating the core and the envelope of the models. Only a small part of the mixing parameter space leads to models that produce a significant number of blue and red supergiants, which are both in abundance in the SMC. Some of our grids also predict a cut-off in the number of red supergiants above log L/L⊙ = 5…5.5. Interestingly, these models contain steep H/He gradients, as is required to understand the hot, hydrogen-rich Wolf-Rayet stars in the SMC. We find that unless it is very fast, rotation has a limited effect on the H/He profiles in our models. Conclusions. While we use specific implementations of the considered mixing processes, they comprehensively probe the two first-order structural parameters, the core mass and the H/He gradient in the core-envelope interface. Our results imply that in massive stars, mixing during the main-sequence evolution leads to a moderate increase in the helium core masses, and also that the H/He gradients above the helium cores become very steep. Our model grids can be used to further refine the various mixing efficiencies with the help of future observational surveys of the massive stars in the SMC, and thereby help to considerably reduce the uncertainties in models of massive star evolution.
Because the majority of massive stars are born as members of close binary systems, populations of massive main-sequence stars contain stellar mergers and products of binary mass transfer. We simulate ...populations of massive stars accounting for all major binary evolution effects based on the most recent binary parameter statistics and extensively evaluate the effect of model uncertainties. Assuming constant star formation, we find that 8 super(+9) sub(-4)% of a sample of early-type stars are the products of a merger resulting from a close binary system. In total we find that 30 super(+10) sub(-15)% of massive main-sequence stars are the products of binary interaction. We show that the commonly adopted approach to minimize the effects of binaries on an observed sample by excluding systems detected as binaries through radial velocity campaigns can be counterproductive. Systems with significant radial velocity variations are mostly pre-interaction systems. Excluding them substantially enhances the relative incidence of mergers and binary products in the non-radial velocity variable sample. This poses a challenge for testing single stellar evolutionary models. It also raises the question of whether certain peculiar classes of stars, such as magnetic O stars, are the result of binary interaction and it emphasizes the need to further study the effect of binarity on the diagnostics that are used to derive the fundamental properties (star-formation history, initial mass function, mass-to-light ratio) of stellar populations nearby and at high redshift.
A large number of extremely low-mass helium white dwarfs (ELM WDs) have been discovered in recent years. The majority of them are found in close binary systems suggesting they are formed either ...through a common-envelope phase or via stable mass transfer in a low-mass X-ray binary (LMXB) or a cataclysmic variable (CV) system. Here, we investigate the formation of these objects through the LMXB channel with emphasis on the proto-WD evolution in environments with different metallicities. We study for the first time the combined effects of rotational mixing and element diffusion (e.g. gravitational settling, thermal and chemical diffusion) on the evolution of proto-WDs and on the cooling properties of the resulting WDs. We present state-of-the-art binary stellar evolution models computed with MESA for metallicities of Z = 0.02, 0.01, 0.001 and 0.0002, producing WDs with masses between ~ 0.16−0.45 M⊙. Our results confirm that element diffusion plays a significant role in the evolution of proto-WDs that experience hydrogen shell flashes. The occurrence of these flashes produces a clear dichotomy in the cooling timescales of ELM WDs, which has important consequences e.g. for the age determination of binary millisecond pulsars. In addition, we confirm that the threshold mass at which this dichotomy occurs depends on metallicity. Rotational mixing is found to counteract the effect of gravitational settling in the surface layers of young, bloated ELM proto-WDs and therefore plays a key role in determining their surface chemical abundances, i.e. the observed presence of metals in their atmospheres. We predict that these proto-WDs have helium-rich envelopes through a significant part of their lifetime. This is of great importance as helium is a crucial ingredient in the driving of the κ-mechanism suggested for the newly observed ELM proto-WD pulsators. However, we find that the number of hydrogen shell flashes and, as a result, the hydrogen envelope mass at the beginning of the cooling track, are not influenced significantly by rotational mixing. In addition to being dependent on proto-WD mass and metallicity, the hydrogen envelope mass of the newly formed proto-WDs depends on whether or not the donor star experiences a temporary contraction when the H-burning shell crosses the hydrogen discontinuity left behind by the convective envelope. The hydrogen envelope at detachment, although small compared to the total mass of the WD, contains enough angular momentum such that the spin frequency of the resulting WD on the cooling track is well above the orbital frequency.
ABSTRACT
During the first three observing runs of the Advanced gravitational-wave detector network, the LIGO/Virgo collaboration detected several black hole binary (BHBH) mergers. As the population ...of detected BHBH mergers grows, it will become possible to constrain different channels for their formation. Here we consider the chemically homogeneous evolution (CHE) channel in close binaries, by performing population synthesis simulations that combine realistic binary models with detailed cosmological calculations of the chemical and star-formation history of the Universe. This allows us to constrain population properties, as well as cosmological and aLIGO/aVirgo detection rates of BHBH mergers formed through this pathway. We predict a BHBH merger rate at redshift zero of $5.8 \textrm {Gpc}^{-3} \textrm {yr}^{-1}$ through the CHE channel, to be compared with aLIGO/aVirgo’s measured rate of ${53.2}_{-28.2}^{+55.8} \text{Gpc}^{-3}\text{yr}^{-1}$, and find that eventual merger systems have BH masses in the range $17{-}43 \,\textrm {M}_{\odot }$ below the pair-instability supernova (PISN) gap, and ${\gt}124 \textrm {M}_{\odot }$ above the PISN gap. We investigate effects of momentum kicks during black hole formation, and calculate cosmological and magnitude limited PISN rates. We also study the effects of high-redshift deviations in the star formation rate. We find that momentum kicks tend to increase delay times of BHBH systems, and our magnitude limited PISN rate estimates indicate that current deep surveys should be able to detect such events. Lastly, we find that our cosmological merger rate estimates change by at most ${\sim}8{{\ \rm per\ cent}}$ for mild deviations of the star formation rate in the early Universe, and by up to ${\sim}40\,\text{per cent}$ for extreme deviations.
Rotation is thought to be a major factor in the evolution of massive stars-especially at low metallicity-with consequences for their chemical yields, ionizing flux, and final fate. We investigate how ...this affects the distribution of rotation rates, through stellar winds, expansion, tides, mass transfer, and mergers. For this purpose, we simulate a massive binary-star population typical for our Galaxy assuming continuous star formation. We find that, because of binary interaction, 20 super(+5) sub(-10)% of all massive main-sequence stars have projected rotational velocities in excess of 200 km s super(-1). The fraction of rapid rotators we derive is similar to that observed. If indeed mass transfer and mergers are the main cause for rapid rotation in massive stars, little room remains for rapidly rotating stars that are born single. Furthermore, our results allow for the possibility that all early-type Be stars result from binary interactions and suggest that evidence for rotation in explosions, such as long gamma-ray bursts, points to a binary origin.
Context.
Steady-state currents, so-called Eddington–Sweet circulation, result in the mixing of chemical elements in rotating stars, and in extreme cases lead to a homogeneous composition. Such ...circulation currents are also predicted in tidally deformed binary stars, which are thought to be progenitors of double black-hole merger events.
Aims.
This work aims to quantitatively characterise the steady-state circulation currents in components of a tidally locked binary system and to explore the effects of such currents on numerical models.
Methods.
Previous results describing the circulation velocity in a single rotating star and a tidally and rotationally distorted binary star are used to deduce a new prescription for the internal circulation in tidally locked binaries. We explore the effect of this prescription numerically with a detailed stellar evolution code for binary systems with initial orbital periods between 0.5 and 2.0 days, primary masses between 25 and 100
M
⊙
and initial mass-ratios
q
i
= 0.5, 0.7, 0.9, 1.0 at metallicity
Z
=
Z
⊙
/50.
Results.
When comparing circulation velocities in the radial direction for the cases of a single rotating star and a binary star, it is found that the average circulation velocity in the binary star may be described as an enhancement to the circulation velocity in a single rotating star. This velocity enhancement is a simple function depending on the masses of the binary components and amounts to a factor of approximately two when the components have equal masses. After applying this enhancement to stellar models, it is found that the formation of double helium stars through efficient mixing occurs for systems with higher initial orbital periods, lower primary masses and lower mass ratios, compared to the standard circulation scenario. Taking into account appropriate distributions for primary mass, initial period and mass ratio, models with enhanced mixing predict 2.4 times more double helium stars being produced in the parameter space than models without.
Conclusions.
We conclude that the effects of companion-induced circulation have strong implications for the formation of close binary black holes through the chemically homogeneous evolution channel. Not only do the predicted detection rates increase but double black-hole systems with mass ratios as low as 0.8 may be formed when companion-induced circulation is taken into account.
The presence of a nearby companion alters the evolution of massive stars in binary systems, leading to phenomena such as stellar mergers, x-ray binaries, and gamma-ray bursts. Unambiguous constraints ...on the fraction of massive stars affected by binary interaction were lacking. We simultaneously measured all relevant binary characteristics in a sample of Galactic massive O stars and quantified the frequency and nature of binary interactions. More than 70% of all massive stars will exchange mass with a companion, leading to a binary merger in one-third of the cases. These numbers greatly exceed previous estimates and imply that binary interaction dominates the evolution of massive stars, with implications for populations of massive stars and their supernovae.
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