本文通过对比不同氦质量和速度分布的双爆轰模型辐射转移模拟,揭示He I 10830 Å光谱特征在Ia型超新星中的显著多样性,为利用氦信号检验双爆轰参数空间提供依据。
摘要:
亚钱德拉塞卡质量双爆轰的Ia型超新星(SNe Ia)模型表明,该情景的一个显著特征是外层抛射物中存在未燃烧的氦。然而,现代爆炸模拟表明,其质量和速度分布可能存在显著变化。我们最近针对双爆轰情景的一个实现进行了NLTE(非局部热力学平衡)辐射转移模拟,其中抛射物中存在适度的氦质量(0.018 M⊙),且速度相对较高(约18000 km/s)。该模拟预测在Mg II 10927 Å蓝侧出现He I 10830 Å特征,这与“过渡型”SNe Ia的近红外观测结果一致。为了展示氦信号预期的多样性,我们在此给出一个双爆轰模型的计算结果,该模型具有更高的氦质量(约0.04 M⊙),且以较低速度(约13000 km/s)抛射。尽管我们的模拟未预测到清晰的光学或2微米氦特征,但存在一个强且持续的He I 10830 Å吸收。该特征出现的波长与观测中有时出现的Mg II 10927 Å特征的扩展蓝翼一致,表明这是一个氦的光谱信号(尽管对于这个特定模型而言,该特征过强且过于持续,无法与正常SNe Ia一致)。两个模拟预测的He I 10830 Å存在显著差异,表明氦光谱信号可能在SNe Ia群体中表现出显著变化。这促使进一步开展利用该可观测信号来检验双爆轰模型参数空间的工作。
英文摘要:
Models of sub-Chandrasekhar mass double detonations for Type Ia supernovae (SNe Ia) suggest a distinguishing property of this scenario is unburnt helium in the outer ejecta. However, modern explosion simulations suggest there may be significant variations in its mass and velocity distribution. We recently presented a NLTE (non local thermodynamic equilibrium) radiative transfer simulation for one realisation of the double detonation scenario with a modest He mass (0.018 M${\odot}$) present in the ejecta at relatively high velocities (${\sim}18000\,\mathrm{km}\,\mathrm{s}^{-1}$). That simulation predicted a He I 10830$\,Å$ feature blueward of Mg II 10927$\,Å$ consistent with near-infrared observations of "transitional" SNe Ia. To demonstrate the expected diversity in the helium signature, here we present a calculation for a double detonation model with a higher He mass (${\sim}$0.04 M${\odot}$) ejected at lower velocities (${\sim}13000\,\mathrm{km}\,\mathrm{s}^{-1}$). Despite our simulation predicting no clear optical or 2 micron helium features, a strong and persistent He I 10830$\,Å$ absorption is present. The feature appears at wavelengths consistent with the extended blue wing of the Mg II 10927$\,Å$ feature sometimes present in observations, suggesting this is a helium spectral signature (although for this particular model it is too strong and persistent to be consistent with normal SNe Ia). The significant differences in He I 10830$\,Å$ predicted by the two simulations suggests helium spectral signatures likely show significant variation throughout the SNe Ia population. This motivates further work to use this observable signature to test the parameter space for double detonation models.
Detonations in helium-rich envelopes surrounding white dwarfs have garnered attention as triggers of faint thermonuclear ".Ia" supernovae and double detonation Type Ia supernovae. However, recent studies have found that the minimum size of a hotspot that can lead to a helium detonation is comparable to, or even larger than, the white dwarf's pressure scale height, casting doubt on the successful ignition of helium detonations in these systems. In this paper, we examine the previously neglected effects of C/O pollution and a full nuclear reaction network, and we consider hotspots with spatially…
Accreted helium layers on white dwarfs have been highlighted for many decades as a possible site for a detonation triggered by a thermonuclear runaway. In this paper, we find the minimum helium layer thickness that will sustain a steady laterally propagating detonation and show that it depends on the density and composition of the helium layer, specifically C12 and O16. Detonations in these thin helium layers have speeds slower than the Chapman-Jouget (CJ) speed from complete helium burning, v_cj=1.5e9 cm/s. Though gravitationally unbound, the ashes still have unburned helium (~ 80% in the thi…
Using 2D and 3D simulation, we study the "robustness" of the double detonation scenario for Type Ia supernovae, in which a detonation in the helium shell of a carbon-oxygen white dwarf induces a secondary detonation in the underlying core. We find that a helium detonation cannot easily descend into the core unless it commences (artificially) well above the hottest layer calculated for the helium shell in current presupernova models. Compressional waves induced by the sliding helium detonation, however, robustly generate hot spots which trigger a detonation in the core. Our simulations show tha…
The origins of type Ia supernovae (SNe Ia) are still debated. Some of the leading scenarios involve a double detonation in double white dwarf (WD) systems. In these scenarios, helium shell detonation occurs on top of a carbon-oxygen (CO) WD, which then drives the detonation of the CO-core, producing a SN Ia. Extensive studies have been done on the possibility of a double helium detonation, following a dynamical helium mass-transfer phase onto a CO-WD. However, 3D self-consistent modeling of the double-WD system, the mass transfer, and the helium shell detonation have been little studied. Here …
The double-detonation explosion model has been considered a candidate for explaining astrophysical transients with a wide range of luminosities. In this model, a carbon-oxygen white dwarf star explodes following detonation of a surface layer of helium. One potential signature of this explosion mechanism is the presence of unburned helium in the outer ejecta, left over from the surface helium layer. In this paper we present simple approximations to estimate the optical depths of important He I lines in the ejecta of double-detonation models. We use these approximations to compute synthetic spec…
The double-detonation explosion scenario of Type Ia supernovae has gained increased support from the SN Ia community as a viable progenitor model, making it a promising candidate alongside the well-known single degenerate and double degenerate scenarios. We present delay times of double-detonation SNe, in which a sub-Chandrasekhar mass carbon-oxygen white dwarf accretes non-dynamically from a helium-rich companion. One of the main uncertainties in quantifying SN rates from double-detonations is the (assumed) retention efficiency of He-rich matter. Therefore, we implement a new prescription for…
In order for a double-detonation model to be viable for normal type Ia supernovae, the adverse impact of helium-burning ash on early-time observables has to be avoided, which requires that the helium envelope mass should be at most 0.02 solar mass. Most of the previous studies introduced detonation by artificial hot spots, and therefore the robustness of the spontaneous helium detonation remains uncertain. In the present work, we conduct a self-consistent hydrodynamic study on the spontaneous ignition of the helium envelope in the context of the double-degenerate channel, by applying an ideali…
Calculations of synthetic spectropolarimetry are one means to test multi-dimensional explosion models for Type Ia supernovae. In a recent paper, we demonstrated that the violent merger of a 1.1 and 0.9 M$_{\odot}$ white dwarf binary system is too asymmetric to explain the low polarization levels commonly observed in normal Type Ia supernovae. Here, we present polarization simulations for two alternative scenarios: the sub-Chandrasekhar mass double-detonation and the Chandrasekhar mass delayed-detonation model. Specifically, we study a two-dimensional double-detonation model and a three-dimensi…
It has been proposed that Type Ia supernovae (SNe Ia) that are normal in their spectra and brightness can be explained by a double detonation that ignites first in a helium shell on the surface of the white dwarf (WD). This proposition is supported by the satisfactory match between simulated explosions of sub-Chandrasekhar-mass WDs with no surface He layer and observations of normal SNe Ia. However, previous calculations of He-ignited double detonations have required either artificial removal of the He shell ashes or extreme enrichment of the surface He layer in order to obtain normal SNe Ia. …
We study a new mechanism for deflagration to detonation transition in thermonuclear supernovae (SNe Ia), based on the formation of shocks by amplification of sound waves in the steep density gradients of white dwarfs envelopes. Given a large enough jump in density a small pressure and velocity perturbation, produced by the turbulent deflagration, turns into a shock down of the gradient, where it will dissipate and heat up the media. With the right frequency and amplitude the heating can be enough to initiate a detonation, which can propagate backward and up the density gradient. We studied pla…
The detonation of a helium shell on a white dwarf has been proposed as a possible explosion triggering mechanism for Type Ia supernovae. Here, we report ZTF 18aaqeasu (SN 2018byg/ATLAS 18pqq), a peculiar Type I supernova, consistent with being a helium-shell double-detonation. With a rise time of $\approx 18$ days from explosion, the transient reached a peak absolute magnitude of $M_R \approx -18.2$ mag, exhibiting a light curve akin to sub-luminous SN 1991bg-like Type Ia supernovae, albeit with an unusually steep increase in brightness within a week from explosion. Spectra taken near peak lig…
Study of the double detonation Type Ia supernova scenario, in which a helium shell detonation triggers a carbon core detonation in a sub-Chandrasekhar-mass white dwarf, has experienced a resurgence in the past decade. New evolutionary scenarios and a better understanding of which nuclear reactions are essential have allowed for successful explosions in white dwarfs with much thinner helium shells than in the original, decades-old incarnation of the double detonation scenario. In this paper, we present the first suite of light curves and spectra from multi-dimensional radiative transfer calcula…
Several models for type Ia-like supernovae events rely on the production of a self-sustained detonation powered by nuclear reactions. In the absence of hydrogen, the fuel that powers these detonations typically consists of either pure helium (He) or a mixture of carbon and oxygen (C/O). Studies that systematically determine the conditions required to initiate detonations in C/O material exist, but until now no analogous investigation of He matter has been conducted. We perform one-dimensional reactive hydrodynamical simulations at a variety of initial density and temperature combinations and f…
We present theoretical delay times and rates of thermonuclear explosions that are thought to produce Type Ia supernovae, including the double-detonation sub-Chandrasekhar mass model, using the population synthesis binary evolution code StarTrack. If detonations of sub-Chandrasekhar mass carbon-oxygen white dwarfs following a detonation in an accumulated layer of helium on the white dwarf's surface ("double-detonation" models) are able to produce thermonuclear explosions which are characteristically similar to those of SNe Ia, then these sub-Chandrasekhar mass explosions may account for at leas…
Upon formation, degenerate He core white dwarfs are surrounded by a radiative H-rich layer primarily supported by ideal gas pressure. In this Letter, we examine the effect of this H-rich layer on mass transfer in He+C/O double white dwarf binaries that will eventually merge and possibly yield a Type Ia supernova (SN Ia) in the double detonation scenario. Because its thermal profile and equation of state differ from the underlying He core, the H-rich layer is transferred stably onto the C/O white dwarf prior to the He core's tidal disruption. We find that this material is ejected from the binar…
We describe the detonation mechanism comprising the "Pulsationally Assisted" Gravitationally Confined Detonation (GCD) model of Type Ia supernovae SNe Ia. This model is analogous to the previous GCD model reported in Jordan et al.(2008); however, the chosen initial conditions produce a substantively different detonation mechanism, resulting from a larger energy release during the deflagration phase. The resulting final kinetic energy and nickel-56 yields conform better to observational values than is the case for the "classical" GCD models. In the present class of models, the ignition of a def…
Models for supernovae (SNe) arising from thermonuclear explosions of white dwarfs (WDs) have been extensively studied over the last few decades, mostly focusing on the single degenerate (accretion of material of a WD) and double degenerate (WD-WD merger) scenarios. In recent years it was suggested that WD-WD direct collisions provide an additional channel for such explosions. Here we extend the studies of such explosions, and explore the role of Helium-shells in affecting the thermonuclear explosions. We study both the impact of low-mass helium ($\sim0.01$ M$_{\odot})$ shells, as well as high …
During the early evolution of an AM CVn system, helium is accreted onto the surface of a white dwarf under conditions suitable for unstable thermonuclear ignition. The turbulent motions induced by the convective burning phase in the He envelope become strong enough to influence the propagation of burning fronts and may result in the onset of a detonation. Such an outcome would yield radioactive isotopes and a faint rapidly rising thermonuclear ".Ia" supernova. In this paper, we present hydrodynamic explosion models and observable outcomes of these He shell detonations for a range of initial co…
The detonation of a sub-Chandrasekhar-mass white dwarf (WD) has emerged as one of the most promising Type Ia supernova (SN Ia) progenitor scenarios. Recent studies have suggested that the rapid transfer of a very small amount of helium from one WD to another is sufficient to ignite a helium shell detonation that subsequently triggers a carbon core detonation, yielding a "dynamically-driven double degenerate double detonation" SN Ia. Because the helium shell that surrounds the core explosion is so minimal, this scenario approaches the limiting case of a bare C/O WD detonation. Motivated by disc…
Over the past decades, many explosion scenarios for Type Ia supernovae have been proposed and investigated including various combinations of deflagrations and detonations in white dwarfs of different masses up to the Chandrasekhar mass. One of these is the gravitationally confined detonation model. In this case a weak deflagration burns to the surface, wraps around the bound core, and collides at the antipode. A subsequent detonation is then initiated in the collision area. Since the parameter space for this scenario, that is, varying central densities and ignition geometries, has not been stu…
Sub-Chandrasekhar CO white dwarfs accreting helium have been considered as candidates for Type Ia supernova(SNIa) progenitors since the early 1980s (helium shell mass $> 0.1 M_\odot $). These models, once detonated did not fit the observed spectra and light curve of typical SNIa observations. New theoretical work examined detonations on much less massive ($< 0.05 M_\odot $) envelopes. They find stable detonations that lead to light curves, spectra and abundances that compare relatively well with the observational data. The exact mechanism leading to the ignition of helium detonation is a key i…
The progenitor systems and explosion mechanism of Type Ia supernovae are still unknown. Currently favoured progenitors include double-degenerate systems consisting of two carbon-oxygen white dwarfs with thin helium shells. In the double-detonation scenario, violent accretion leads to a helium detonation on the more massive primary white dwarf that turns into a carbon detonation in its core and explodes it. We investigate the fate of the secondary white dwarf, focusing on changes of the ejecta and observables of the explosion if the secondary explodes as well rather than survives. We simulate a…
The precise nature of Type Ia supernova (SN Ia) progenitors remains a mystery, but the detonation of a sub-Chandrasekhar-mass white dwarf (WD) has become a promising candidate. There is a growing body of work suggesting that the carbon core detonation of a sub-Chandrasekhar-mass WD can be triggered by the detonation of a helium shell accreted from a companion WD, through either inward shock convergence near the center or direct edge-lit detonation. This "double-detonation" SN Ia can be triggered by a small helium shell and is therefore well approximated by the detonation of a bare carbon-oxyge…
The progenitors of Type Ia Supernovae (SNe Ia) are still unknown, despite significant progress during the last years in theory and observations. Violent mergers of two carbon--oxygen (CO) white dwarfs (WDs) are one candidate suggested to be responsible for at least a significant fraction of normal SNe Ia. Here, we simulate the merger of two CO WDs using a moving-mesh code that allows for the inclusion of thin helium (He) shells (0.01\,\msun) on top of the WDs, at an unprecedented numerical resolution. The accretion of He onto the primary WD leads to the formation of a detonation in its He shel…
Evolution of binaries containing a hot subdwarf and a white dwarf to double white dwarfs, and double detonation supernovae with hypervelocity runaway stars
Max Planck Institut für Astrophysik(马克斯·普朗克天体物理学研究所);Center for Astrophysics | Harvard & Smithsonian(哈佛-史密森尼天体物理中心)
We demonstrate tidal detonation during a tidal disruption event (TDE) of a helium (He) white dwarf (WD) with $0.45M_\odot$ by an intermediate mass black hole (IMBH) by extremely high-resolution simulations. Tanikawa et al. (2017) have showed tidal detonation in previous studies results from unphysical heating due to low-resolution simulations, and such unphysical heating occurs in 3-dimensional (3D) smoothed particle hydrodynamics (SPH) simulations even with $10$ million SPH particles. In order to avoid such unphysical heating, we perform 3D SPH simulations up to $300$ million SPH particles, a…
Type Ia supernovae (SNe Ia) originate from the thermonuclear explosions of carbon-oxygen (C-O) white dwarfs (WDs). The single-degenerate scenario is a well-explored model of SNe Ia where unstable thermonuclear burning initiates in an accreting, Chandrasekhar-mass WD and forms an advancing flame. By several proposed physical processes the rising, burning material triggers a detonation, which subsequently consumes and unbinds the WD. However, if a detonation is not triggered and the deflagration is too weak to unbind the star, a completely different scenario unfolds. We explore the failure of th…
Collisions of white dwarfs (WDs) have recently been invoked as a possible mechanism for type Ia supernovae (SNIa). A pivotal feature for the viability of WD collisions as SNIa progenitors is that a significant fraction of the mass is highly compressed to the densities required for efficient $^{56}$Ni production before the ignition of the detonation wave. Previous studies have predominantly employed model WDs composed entirely of carbon-oxygen (CO), whereas WDs are expected to have a non-negligible helium envelope. Given that helium is more susceptible to explosive burning than CO under the con…
Nowadays the number of models aimed at explaining the Type Ia supernova phenomenon is high and discriminating between them is a must-do. In this work we explore the influence of rotation in the evolution of the nuclear flame which drives the explosion in the so called gravitational confined detonation models. Assuming that the flame starts in a point-like region slightly above the center of the white dwarf (WD) and adding a moderate amount of angular velocity to the star we follow the evolution of the deflagration using a smoothed particle hydrodynamics code. We find that the results are very …
The feasibility of the Double Detonation mechanism, -a surface Helium-detonation followed by the complete carbon detonation of the core-, in a rotating white dwarf with a mass $\simeq 1 M_{\odot}$ is studied using three-dimensional hydrodynamic simulations. Assuming rigid rotation, the rotational speed is taken high enough as to considerably distort the initial spherical geometry of the white dwarf. Unlike spherically symmetric models, we found that when helium ignition is located far from the spinning axis the detonation fronts converge asynchronically at the antipodes of the igniting point. …
Multidimensional Nebular-Phase Calculations of Dynamically-Driven Double-Degenerate Double-Detonation Models for Type Ia Supernovae
Queen’s University Belfast(贝尔法斯特女王大学);Cosmic Dawn Center (DAWN)(宇宙黎明中心);Niels Bohr Institute, University of Copenhagen(哥本哈根大学尼尔斯·玻尔研究所);GSI Helmholtzzentrum für Schwerionenforschung(重离子研究中心);Max-Planck-Institut für Astrophysik(马克斯·普朗克天体物理研究所);School of Physics, Trinity College Dublin, The University of Dublin(都柏林三一学院物理系);Heidelberger Institut für Theoretische Studien(海德堡理论研究所)
We have studied double-detonation explosions in double-degenerate (DD) systems with different companion white dwarfs (WD) for modeling type Ia supernovae (SNe Ia) by means of high-resolution smoothed particle hydrodynamics (SPH) simulations. We have found that only the primary WDs explode in some of the DD systems, while the explosions of the primary WDs induce the explosions of the companion WDs in the other DD systems. The former case is so-called Dynamically-Driven Double-Degenerate Double-Detonation (D$^6$) explosion, or helium-ignited violent merger explosion. The supernova ejecta of the …
Type Ia supernovae (SNe Ia) are likely the thermonuclear explosions of carbon-oxygen (CO) white-dwarf (WD) stars, but their progenitor systems remain elusive. Recently, Sharon & Kushnir (2022) used The Zwicky Transient Facility Bright Transient Survey to construct a synthesized $^{56}$Ni mass, $M_\text{Ni56}$, distribution of SNe Ia. They found that the rate of low-luminosity ($M_\text{Ni56}\approx0.15\,M_{\odot}$) SNe Ia is lower by a factor of $\sim10$ than the more common $M_\text{Ni56}\approx0.7\,M_{\odot}$ events. We here show that in order for the double-detonation model (DDM, in which a…
The detonation of a helium shell on top of a carbon-oxygen white dwarf has been argued as a potential explosion mechanism for type Ia supernovae (SNe~Ia). The ash produced during helium shell burning can lead to light curves and spectra that are inconsistent with normal SNe~Ia, but may be viable for some objects showing a light curve bump within the days following explosion. We present a series of radiative transfer models designed to mimic predictions from double detonation explosion models. We consider a range of core and shell masses, and systematically explore multiple post-explosion compo…
The observed sub-class of "superluminous" Type Ia supernovae lacks a convincing theoretical explanation. If the emission of such objects were powered exclusively by radioactive decay of 56Ni formed in the explosion, a progenitor mass close to or even above the Chandrasekhar limit for a non-rotating white dwarf star would be required. Masses significantly exceeding this limit can be supported by differential rotation. We, therefore, explore explosions and predict observables for various scenarios resulting from differentially rotating carbon-oxygen white dwarfs close to their respective limit o…
Despite the importance of Type Ia supernovae (SNe Ia) throughout astronomy, the precise progenitor systems and explosion mechanisms that drive SNe Ia are still unknown. An explosion scenario that has gained traction recently is the double detonation in which an accreted shell of He detonates and triggers a secondary detonation in the underlying white dwarf. Our research presents a number of high resolution, multi-dimensional, full star simulations of thin-He-shell, sub-Chandrasekhar-mass white dwarf progenitors that undergo a double detonation. This suite of thin-shell progenitors incorporates…
Thermonuclear supernovae are the result of the violent unbinding of a white dwarf, but the precise nature of the explosion mechanism(s) is a matter of active debate. To this end, several specific scenarios have been proposed to explain the observable traits of SNe Ia. A promising pathway is the double-detonation scenario, where a white dwarf accretes a shell of helium-rich material from a companion and a detonation in the resulting helium shell is the primary cause of the explosion. Through a set of two-dimensional grid-based simulations of this scenario we clearly distinguish three phases of …
Merging carbon-oxygen (CO) white dwarfs are a promising progenitor system for Type Ia supernovae (SN Ia), but the underlying physics and timing of the detonation are still debated. If an explosion occurs after the secondary star is fully disrupted, the exploding primary will expand into a dense CO medium that may still have a disk-like structure. This interaction will decelerate and distort the ejecta. Here we carry out multi-dimensional simulations of ``tamped" SN Ia models, using both particle and grid-based codes to study the merger and explosion dynamics, and a radiative transfer code to c…
We present results for a suite of fourteen three-dimensional, high resolution hydrodynamical simulations of delayed-detonation modelsof Type Ia supernova (SN Ia) explosions. This model suite comprises the first set of three-dimensional SN Ia simulations with detailed isotopic yield information. As such, it may serve as a database for Chandrasekhar-mass delayed-detonation model nucleosynthetic yields and for deriving synthetic observables such as spectra and light curves. We employ a physically motivated, stochastic model based on turbulent velocity fluctuations and fuel density to calculate in…
The progenitor system(s) and the explosion mechanism(s) of Type Ia supernovae (SNe Ia) are still under debate. Non-electromagnetic observables, in particular gravitational waves and neutrino emission, of thermonuclear supernovae are a complementary window to light curves and spectra for studying these enigmatic objects. A leading model for SNe Ia is the thermonuclear incineration of a near-Chandrasekhar mass carbon-oxygen white dwarf star in a "delayed-detonation". We calculate a three-dimensional hydrodynamic explosion for the N100 delayed-detonation model extensively discussed in the literat…
Merging white dwarfs are a possible progenitor of Type Ia supernovae (SNe Ia). While it is not entirely clear if and when an explosion is triggered in such systems, numerical models suggest that a detonation might be initiated before the stars have coalesced to form a single compact object. Here we study such "peri-merger" detonations by means of numerical simulations, modeling the disruption and nucleosynthesis of the stars until the ejecta reach the coasting phase. Synthetic light curves and spectra are generated for comparison with observations. Three models are considered with primary mass…
The structure of a thermonuclear detonation wave can be solved accurately and, thus, may serve as a test bed for studying different approximations that are included in multidimensional hydrodynamical simulations of supernova. We present the structure of thermonuclear detonations for the equal mass fraction of $^{12}$C and $^{16}$O (CO) and for pure $^{4}$He (He) over a wide range of upstream plasma conditions. The lists of isotopes we constructed allow us to determine the detonation speeds, as well as the final states for these detonations, with an uncertainty of the percent level (obtained he…
The recently proposed "dynamically driven double-degenerate double-detonation" (D6) scenario posits that Type Ia supernovae (SNe) may occur during dynamically unstable mass transfer between two white dwarfs (WDs) in a binary. This scenario predicts that the donor WD may then survive the explosion and be released as a hypervelocity runaway, opening up the exciting possibility of identifying remnant stars from D6 SNe and using them to study the physics of detonations that produce Type Ia SNe. Three candidate D6 runaway objects have been identified in Gaia data. The observable runaway velocity of…
Helium accretion induced explosions in CO white dwarfs (WDs) are considered promising candidates for a number of observed types of stellar transients, including supernovae (SNe) of Type Ia and Type Iax. However, a clear favorite outcome has not yet emerged. We explore the conditions of helium ignition in the white dwarf and the final fates of helium star-WD binaries as function of their initial orbital periods and component masses. We compute 274 model binary systems with the Binary Evolution Code (BEC), where both components are fully resolved. Stellar and orbital evolution is computed simult…