Final Orbital Separation Research Articles

SCATTER: A New Common Envelope Formalism

One of the most mysterious astrophysical states is the common envelope (CE) phase of binary evolution, in which two stars are enshrouded by the envelope shed by one of them. Interactions between the stars and the envelope shrinks the orbit. The CE can lead to mergers or to a subsequent phase of interactions. Mergers may involve any combination of two compact objects and/or stars. Some involving white dwarfs may produce Type Ia supernovae, while merging neutron stars may yield gamma-ray bursts, and merging compact objects of all kinds produce gravitational radiation. Since CEs can arise from a variety of different initial conditions, and due to the complexity of the processes involved, it is difficult to predict their end states. When many systems are being considered, as in population synthesis calculations, conservation principles are generally employed. Here we use angular momentum in a new way to derive a simple expression for the final orbital separation. This method provides advantages for the study of binaries and is particularly well suited to higher-order multiples, now considered to be important in the genesis of potential mergers. Here we focus on CEs in binaries, and the follow-up paper extends our formalism to multiple-star systems within which a CE occurs.

Rejuvenated Accretors Have Less Bound Envelopes: Impact of Roche Lobe Overflow on Subsequent Common Envelope Events

Common envelope (CE) evolution is an outstanding open problem in stellar evolution, critical to the formation of compact binaries including gravitational-wave sources. In the “classical” isolated binary evolution scenario for double compact objects, the CE is usually the second mass transfer phase. Thus, the donor star of the CE is the product of a previous binary interaction, often stable Roche lobe overflow (RLOF). Because of the accretion of mass during the first RLOF, the main-sequence core of the accretor star grows and is “rejuvenated.” This modifies the core-envelope boundary region and decreases significantly the envelope binding energy for the remaining evolution. Comparing accretor stars from self-consistent binary models to stars evolved as single, we demonstrate that the rejuvenation can lower the energy required to eject a CE by ∼42%–96% for both black hole and neutron star progenitors, depending on the evolutionary stage and final orbital separation. Therefore, binaries experiencing first stable mass transfer may more easily survive subsequent CE events and result in possibly wider final separations compared to current predictions. Despite their high mass, our accretors also experience extended “blue loops,” which may have observational consequences for low-metallicity stellar populations and asteroseismology.

The final orbital separation in common envelope evolution

In the majority of population synthesis calculations of close binary stars, the common envelope (CE) phase is modeled using a standard prescription based upon the conservation of energy, known as the alpha prescription. In this prescription, the orbital separation of the secondary and giant core at the end of the CE phase is taken to be the orbital separation when the envelope becomes unbound. However, recent observations of planetary nebulae with binary cores (BPNe), believed to be the immediate products of CE evolution, indicate orbital periods that are significantly shorter than predicted by population synthesis models using the alpha prescription. We argue that unbinding the envelope provides a necessary, but not sufficient, condition to escape a merger during CE evolution. The spiral-in of the secondary must also be halted. This requires the additional dynamical constraint that the frictional torque on the secondary be reduced to approximately zero. In this paper, we undertake a preliminary examination of the effect of adding this dynamical constraint in population synthesis calculations of BPNe. We assume that the frictional torque will be sufficiently reduced when the secondary enters a region within the giant where the mass-radius profile is flat. We crudely estimate the location of this region as a function of the core mass based upon existing stellar models of AGB stars between 1 and 7 M⊙. We calculate a theoretical orbital period distribution of BPNe using a population synthesis code that incorporates this dynamical constraint along with the alpha prescription.

Common-envelope evolution with an asymptotic giant branch star

Common-envelope phases are decisive for the evolution of many binary systems. Cases with asymptotic giant branch (AGB) primary stars are of particular interest because they are thought to be progenitors of various astrophysical transients. In three-dimensional hydrodynamic simulations with the moving-mesh code AREPO, we study the common-envelope evolution of a 1.0 M⊙ early-AGB star with companions of different masses. Although the stellar envelope of an AGB star is less tightly bound than that of a red giant, we find that the release of orbital energy of the core binary is insufficient to eject more than about twenty percent of the envelope mass. Ionization energy that is released in the expanding envelope, however, can lead to complete envelope ejection. Because recombination proceeds largely at high optical depths in our simulations, it is likely that this effect indeed plays a significant role in the considered systems. The efficiency of mass loss and the final orbital separation of the core binary system depend on the mass ratio between the companion and the primary star. Our results suggest a linear relation between the ratio of final to initial orbital separation and this parameter.

The impact of recombination energy on simulations of the common-envelope binary interaction

ABSTRACT During the common-envelope binary interaction, the expanding layers of the gaseous common envelope recombine and the resulting recombination energy has been suggested as a contributing factor to the ejection of the envelope. In this paper, we perform a comparative study between simulations with and without the inclusion of recombination energy. We use two distinct setups, comprising a 0.88- and 1.8-M⊙ giants, that have been studied before and can serve as benchmarks. In so doing, we conclude that (i) the final orbital separation is not affected by the choice of equation of state (EoS). In other words, simulations that unbind but a small fraction of the envelope result in similar final separations to those that, thanks to recombination energy, unbind a far larger fraction. (ii) The adoption of a tabulated EoS results in a much greater fraction of unbound envelope and we demonstrate the cause of this to be the release of recombination energy. (iii) The fraction of hydrogen recombination energy that is allowed to do work should be about half of that which our adiabatic simulations use. (iv) However, for the heavier star simulation, we conclude that it is helium and not hydrogen recombination energy that unbinds the gas and we determine that all helium recombination energy is thermalized in the envelope and does work. (v) The outer regions of the expanding common envelope are likely to see the formation of dust. This dust would promote additional unbinding and shaping of the ejected envelope into axisymmetric morphologies.

Speaking with one voice: simulations and observations discuss the common envelope α parameter

ABSTRACT We present a comparative study between the results of most hydrodynamic simulations of the common envelope binary interaction to date and observations of post-common envelope binaries. The goal is to evaluate whether this data set indicates the existence of a formula that may predict final separations of post-common envelope systems as a function of pre-common envelope parameters. Some of our conclusions are not surprising while others are more subtle. We find that: (i) Values of the final orbital separation derived from common envelope simulations must at this time be considered upper limits. Simulations that include recombination energy do not seem to have systematically different final separations; these and other simulations imply αCE < 0.6–1.0. At least one simulation, applicable to double-degenerate systems, implies αCE < 0.2. (ii) Despite large reconstruction errors, the post-RGB observations reconstructed parameters are in agreement with some of the simulations. The post-AGB observations behave instead as if they had a systematically lower value of αCE. The lack of common envelope simulations with low-mass AGB stars leaves us with no insight as to why this is the case. (iii) The smallest mass companion that survives the common envelope with intermediate mass giants is 0.05–0.1 M⊙. (iv) Observations of binaries with separations larger than ∼10 R⊙, tend to have high M2/M1 mass ratios and may go through a relatively long phase of unstable Roche lobe mass transfer followed by a weakened common envelope (or with no common envelope at all). (v) The effect of the spatial resolution and of the softening length on simulation results remains poorly quantified.

Common envelope evolution on a moving mesh

AbstractWe outline the methodology of simulating common envelope evolution (CEE) with the moving-mesh code manga. We extend manga to include multiple time-steps. This provides substantial speedups for problems with large dynamic range. We describe the implementation of realistic equations of state relevant in stellar structure and the generation of suitable initial conditions. We then carry out two example simulations of a 2 M⊙ red giant with a 0.36 M⊙ core and a 1 M⊙ companion undergoing CEE for 240 days. In one simulation the red giant is set into corotation with the orbital motion and in the other it is non-rotating. We find that the separation between the companion and red giant core shrinks from 52 R⊙ to 3.6 R⊙ and 3.2 R⊙, respectively, ending with an eccentricity of 0.1. We also find that 66 and 63 per cent of the envelope mass is ejected. This is higher than in many previous works. Several reasons for this are discussed. These include our inclusion of recombination energy. Our simulations show that putting giants in corotation increases the fraction of mass ejected from the system and results in a larger final orbital separation. We conclude that the entire envelope of the red giant might be ejected during the plunge phase of CEE in this region of parameter space.

The number of progenitors in the core-degenerate scenario for Type Ia supernovae

We calculate the expected number of type Ia supernovae (SN Ia) in the core-degenerate (CD) scenario and find it to match observations within the uncertainties of the code. In the CD scenario the super-Chandrasekhar mass white dwarf (WD) is formed at the termination of the common envelope phase from a merger of a WD companion with the hot core of a massive asymptotic giant branch (AGB) star. We use a simple population synthesis code that avoids the large uncertainties involved in estimating the final orbital separation of the common envelope evolution. Instead, we assume that systems where the core of the secondary AGB star is more massive than the WD remnant of the primary star merge at the termination of the common envelope phase. We also use a simple prescription to count systems that have strong interaction during the AGB phase, but not during the earlier red giant branch (RGB) phase. That a very simple population synthesis code that uses the basics of stellar evolution ingredients can match the observed rate of SN Ia might suggest that the CD-scenario plays a major role in forming SN Ia.

Merger by migration at the final phase of common envelope evolution

I find the common envelope (CE) energy formalism, the CE α-prescription, to be inadequate to predict the final orbital separation of the CE evolution in massive envelopes. I find that when the orbital separation decreases to ∼10 times the final orbital separation predicted by the CE α-prescription, the companion has not enough mass in its vicinity to carry away its angular momentum. The core-secondary binary system must get rid of its angular momentum by interacting with mass further out. The binary system interacts gravitationally with a rapidly-rotating flat envelope, in a situation that resembles planet-migration in protoplanetary disks. The envelope convection of the giant carries energy and angular momentum outward. The basic assumption of the CE α-prescription, that the binary system’s gravitational energy goes to unbind the envelope, breaks down. Based on that, I claim that merger is a common outcome of the CE evolution of AGB and red super-giants stars with an envelope to secondary mass ratio of Menv/M2≳5. I discuss some other puzzling observations that might be explained by the migration and merger processes.

Tides and tidal engulfment in post-main-sequence binaries: period gaps for planets and brown dwarfs around white dwarfs

The presence of a close, low-mass companion is thought to play a substantial and perhaps necessary role in shaping post-asymptotic giant branch and planetary nebula outflows. During post-main-sequence evolution, radial expansion of the primary star, accompanied by intense winds, can significantly alter the binary orbit via tidal dissipation and mass-loss. To investigate this, we couple stellar evolution models (from the zero-age main sequence through the end of the post-MS) to a tidal evolution code. The binary's fate is determined by the initial masses of the primary and the companion, the initial orbit (taken to be circular), and the Reimers mass-loss parameter. For a range of these parameters, we determine whether the orbit expands due to mass-loss or decays due to tidal torques. Where a common envelope (CE) phase ensues, we estimate the final orbital separation based on the energy required to unbind the envelope. These calculations predict period gaps for planetary and brown dwarf companions to white dwarfs. The upper end of the gap is the shortest period at which a CE phase is avoided. The lower end is the longest period at which companions survive their CE phase. For binary systems with 1 M⊙ progenitors, we predict no Jupiter-mass companions with periods ≲270 d. Once engulfed, Jupiter-mass companions do not survive a CE phase. For binary systems consisting of a 1 M⊙ progenitor with a companion 10 times the mass of Jupiter, we predict a period gap between ∼0.1 and ∼380 d. These results are consistent with both the detection of a ∼50MJ brown dwarf in a ∼0.003 au (∼0.08 d) orbit around the white dwarf WD 0137−349 and the tentative detection of a ∼2MJ planet in a ≳2.7 au (≳4 yr) orbit around the white dwarf GD66.

ADIABATIC MASS LOSS AND THE OUTCOME OF THE COMMON ENVELOPE PHASE OF BINARY EVOLUTION

We have developed a new method for calculating common envelope (CE) events based on explicit consideration of the donor star's structural response to adiabatic mass loss. In contrast to existing CE prescriptions, which specify a priori the donor's remnant mass, we determine this quantity self-consistently and find it depends on binary and CE parameters. This aspect of our model is particularly important to realistic modeling for upper main sequence star donors without strongly degenerate cores (and hence without a clear core/envelope boundary). We illustrate the central features of our method by considering CE events involving 10 solar mass donors on or before their red giant branch. For such donors, the remnant core mass can be as much as 30% larger than the star's He-core mass. Applied across a population of such binaries, our methodology results in a significantly broader remnant mass and final orbital separation distribution and a 20% increase in CE survival rates as compared to previous prescriptions for the CE phase.

Comments on the final orbital separation in common envelope evolution

I study some aspects of common envelope evolution, where a compact star enters the envelope of a giant star. I show that in some binary systems under a narrow range of parameters, a substantial fraction of the giant stellar envelope is lost before the onset of the common envelope. The reduced envelope mass at the onset of the common envelope implies that the binary system emerges from the common envelope with a relatively large orbital separation. I therefore caution against a simple treatment, which omits this process, in the study of systems that evolved through a common envelope phase and ended with a relatively large orbital separation, e.g., PG1115+166. A fraction of the envelope that is lost while the companion is still outside the giant stellar envelope is accreted by the companion. The companion may form an accretion disk and blow two jets. I propose this scenario for the formation of the bipolar planetary nebula NGC 2346, which has a binary nucleus with an orbital period longer than that of any other known binary system in planetary nebulae. Because this scenario, of a late common envelope phase, occurs for a narrow range of parameters, I expect it to be applicable to a small, but non-negligible, number of systems.