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.
ABSTRACT
We investigate the common envelope binary interaction, that leads to the formation of compact binaries, such as the progenitors of Type Ia supernovae or of mergers that emit detectable ...gravitational waves. In this work, we diverge from the classic numerical approach that models the dynamic inspiral. We focus instead on the asymptotic behaviour of the common envelope expansion after the dynamic inspiral terminates. We use the SPH code phantom to simulate one of the set-ups from Passy et al., with a 0.88 M⊙, 83 R⊙ RGB primary and a 0.6 M⊙ companion, then we follow the ejecta expansion for 50 yr. Additionally, we utilize a tabulated equation of state including the envelope recombination energy in the simulation (Reichardt et al.), achieving a full unbinding. We show that, as time passes, the envelope’s radial velocities dominate over the tangential ones, hence allowing us to apply an homologous expansion kinematic model to the ejecta. The external layers of the envelope become homologous as soon as they are ejected, but it takes 5000 d (14 yr) for the bulk of the unbound gas to achieve the homologously expanding regime. We observe that the complex distribution generated by the dynamic inspiral evolves into a more ordered, shell-like shaped one in the asymptotic regime. We show that the thermodynamics of the expanding envelope are in very good agreement with those expected for an adiabatically expanding sphere under the homologous condition and give a prediction for the location and temperature of the photosphere assuming dust to be the main source of opacity. This technique ploughs the way to determining the long-term light behaviour of common envelope transients.
ABSTRACT
We study the formation of dust in the expanding gas ejected as a result of a common envelope binary interaction. In our novel approach, we apply the dust formation model of Nozawa et al. to ...the outputs of the 3D hydrodynamic SPH simulation performed by Iaconi et al. that involves a giant of 0.88 M⊙ and 83 R⊙, with a companion of 0.6 M⊙ placed on the surface of the giant in circular orbit. After simulating the dynamic in-spiral phase, we follow the expansion of the ejecta for $\simeq 18\, 000$ d. During this period, the gas is able to cool down enough to reach dust formation temperatures. Our results show that dust forms efficiently in the window between ≃ 300 d (the end of the dynamic in-spiral) and ≃ 5000 d. The dust forms in two separate populations; an outer one in the material ejected during the first few orbits of the companion inside the primary’s envelope and an inner one in the rest of the ejected material. We are able to fit the grain-size distribution at the end of the simulation with a double power law. The slope of the power law for smaller grains is flatter than that for larger grains, creating a knee-shaped distribution. The power-law indexes are, however, different from the classical values determined for the interstellar medium. We also estimate that the contribution to cosmic dust by common envelope events is not negligible and comparable to that of novae and supernovae.
A multiple input multiple output (MIMO) power line communication (PLC) model for industrial facilities was developed that uses the physics of a bottom-up model but can be calibrated like top-down ...models. The PLC model considers 4-conductor cables (three-phase conductors and a ground conductor) and has several load types, including motor loads. The model is calibrated to data using mean field variational inference with a sensitivity analysis to reduce the parameter space. The results show that the inference method can accurately identify many of the model parameters, and the model is accurate even when the network is modified.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
Bayesian inference is used to calibrate a bottom-up home PLC network model with unknown loads and wires at frequencies up to 30 MHz. A network topology with over 50 parameters is calibrated using ...global sensitivity analysis and transitional Markov Chain Monte Carlo (TMCMC). The sensitivity-informed Bayesian inference computes Sobol indices for each network parameter and applies TMCMC to calibrate the most sensitive parameters for a given network topology. A greedy random search with TMCMC is used to refine the discrete random variables of the network. This results in a model that can accurately compute the transfer function despite noisy training data and a high dimensional parameter space. The model is able to infer some parameters of the network used to produce the training data, and accurately computes the transfer function under extrapolative scenarios.
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•An Artificial Neural Network (ANN) was trained to invert the Merkel model to calculate the outlet water temperature of a forced-air evaporative cooling tower.•Calculation efficiency improved by ...approximately four orders of magnitude compared to inverting the Merkel model via simplex-based optimization.•Three case studies are provided to demonstrate the capability of improved computational speed.
Real-time monitoring of a research nuclear reactor, a system in which all generated power is dissipated to the environment, can be performed via analysis of the heat rejection from the cooling system. Given an inlet water temperature and flow rate, the reactor power can be well-approximated from the outlet water temperature; however, the instrumentation to measure outlet conditions may not be robust or accurate. If we know how a cooling tower performs from historical data, but cannot measure the outlet temperature, a mathematical representation of the system can be inverted to obtain the outlet water temperature that describes the cooling capacity. Unfortunately, model inversion processes are computationally expensive. To address this, an artificial neural network (ANN) is implemented to assess the performance of a multi-cell cooling tower for a nuclear reactor. This approach leverages the Merkel model to obtain an extensive data set describing performance of the cooling tower cells throughout a wide array of potential operating conditions. The Merkel model is expressed as a function of four parameters: the inlet and outlet water temperatures, inlet air wet bulb temperature, and ratio of liquid-to-gas mass flow rates (L/G), which together provide a non-dimensional number indicative of cooling tower performance, called the Merkel integral. Computing a 4-dimensional data structure that describes finite combinations of the Merkel integral, an inverse model is then generated using an ANN to determine the cell outlet water temperature from the other three model parameters along with the computed Merkel integral. Compared to traditional model inversion methods, the ANN reduces the computational time by approximately 4 orders of magnitude, with effectively no sacrifice to solution accuracy, and could be applied for different cooling towers in the event the performance curve is known. Three use cases of the ANN are then reviewed: (1) determining the cell outlet water temperatures when gas flow at rated conditions (GFRC) is known, (2) performing the prior case without knowledge of the GRFC, and (3) assessing performance differences between the individual tower cells.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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