Simulating a binary system that experiences the grazing envelope evolution
MMNRAS , 1–15 (2017) Preprint 3 May 2018 Compiled using MNRAS L A TEX style file v3.0
Simulating a binary system that experiences the grazingenvelope evolution
Sagiv Shiber, (cid:63) Noam Soker † Physics Department, Technion – Israel Institute of Technology, Technion City – Haifa 3200003, Israel
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We conduct three-dimensional hydrodynamical simulations, and show that when asecondary star launches jets while performing spiral-in motion into the envelope of agiant star, the envelope is inflated, some mass is ejected by the jets, and the commonenvelope phase is postponed. We simulate this grazing envelope evolution (GEE) un-der the assumption that the secondary star accretes mass from the envelope of theasymptotic giant branch (AGB) star and launches jets. In these simulations we do notyet include the gravitational energy that is released by the spiraling-in binary system.Neither do we include the spinning of the envelope. Considering these omissions, weconclude that our results support the idea that jets might play a crucial role in thecommon envelope evolution, or in preventing it.
Key words: binaries: close — stars: AGB and post-AGB — stars: winds, outflows— ISM: jets and outflows
Jets that are launched by a compact object that accretesmass from an extended ambient gas play significant rolesin influencing back the ambient gas in many types of as-trophysical objects. In most cases the system operates in anegative feedback cycle, the jet feedback mechanism (JFM;Soker 2016a).One such case might be the common envelope evolution.Armitage & Livio (2000) and Chevalier (2012) discuss theejection of the common envelope by jets that are launchedfrom a neutron star that is spiraling-in inside a giant enve-lope. They, however, do not consider jets to play a role whenthe compact companion of the common envelope evolutionis not a neutron star. We here follow earlier suggestions thatjets play a significant role in removing the common envelopewhen other compact companions are considered as well, inparticular main sequence companions (e.g., Soker 2004; Pa-pish et al. 2015; Soker 2015, 2016a; Moreno M´endez et al.2017).We do note that in a recent paper Murguia-Berthier etal. (2017) argue that disk formation in common envelopeevolution is rare, and so is the JFM in common envelopeevolution. On the other hand, there are arguments that theaccreted gas can launch jets even when the angular mo-mentum is below the Keplerian angular momentum on the (cid:63)
E-mail: [email protected] † E-mail: [email protected] surface of the mass-accreting compact companion (Shiber etal. 2016; Schreier & Soker 2016). In addition, Blackman &Lucchini (2014) study the momenta of the outflow of bipolarpre-planetary nebulae, and conclude that strongly interact-ing binary systems launch energetic jets, probably through acommon envelope evolution. In any case, Murguia-Berthieret al. (2017) find that an accretion disk is likely to be formedin the partial ionization zones in the giant envelope. Thesezones are located in the outer envelope. Therefore, even ifthe companion does penetrate somewhat into the envelope,it might still launch jets.Numerical simulations of the common envelope evolu-tion that employ no other energy source beside the gravi-tational energy of the in-spiraling binary system failed toachieve the expected ejection of the common envelope (e.g.,Taam & Ricker 2010; De Marco et al. 2011; Passy et al.2012; Ricker & Taam 2012; Nandez et al. 2014; Ohlmannet al. 2016; Staff et al. 2016b; Nandez & Ivanova 2016; Ku-ruwita et al. 2016; Ivanova & Nandez 2016; Iaconi et al.2017b; De Marco & Izzard 2017; Galaviz et al. 2017; Iaconiet al. 2017a). In light of this results we insert the JFM tothe common envelope evolution.Another extra energy source (see some discussion byKruckow et al. 2016) that has been suggested to eject thecommon envelope is the recombination energy of hydrogenand helium (e.g., Nandez et al. 2015; Ivanova & Nandez2016; Clayton et al. 2017). However, Harpaz (1998), Soker& Harpaz (2003), and Sabach et al. (2017) question the ef- c (cid:13) a r X i v : . [ a s t r o - ph . S R ] M a y S. Shiber and N. Soker ficiency by which the recombination energy can be used toeject the envelope.Along side the negative JFM, where the jets removeenvelope mass and hence reduce accretion rate, there is apositive component. The jets remove high entropy gas andenergy from the close surroundings of the accreting compactcompanion, hence reducing the pressure in that region andenabling high accretion rate (Shiber et al. 2016; Staff et al.2016a). Without this effect accretion rate would be reducedby the development of high pressure in the close surround-ings of accreting compact companion (e.g. Ricker & Taam2012; MacLeod & Ramirez-Ruiz 2015). More on the dynam-ics of jets in the common envelope can be found in the paperby Moreno M´endez et al. (2017).If jets manage to eject the envelope outside the orbitof the companion from the onset of the contact between thecompact companion and the giant envelope, the system willnot enter a common envelope phase. Instead, the systemwill enter the grazing envelope evolution (GEE; Sabach &Soker 2015; Soker 2015; Shiber et al. 2017). In this case,the system might enter a common envelope evolution onlyat a later stage. The jets might carry more energy thanthe gravitational energy that is released by the in-spiralingbinary system (the core of the giant and the companion).In some cases the orbital separation will not decrease much,or possibly even increase while the jets remove the giantenvelope (Soker 2017).In the present study we conduct our second set of simu-lations of the GEE. In the previous study (Shiber et al. 2017)we set a constant orbital separation (without spiraling-in),while here we set the system to spiral-in. We describe thenumerical setting in section 2 and the results in section 3.Our short summary is in section 4.
We follow the routine as described in (Shiber et al. 2017).We run the stellar evolution code
MESA (Paxton et al. 2011,2013, 2015) and follow the evolution of a star of initial mass M ZAMS = 3 . M (cid:12) to obtain an asymptotic giant branch(AGB) model with a mass of M AGB (cid:39) . (cid:12) and radius of R AGB (cid:39)
FLASH (Fryxell et al. 2000). The grid is a uni-form Cartesian three-dimensional cube with side length of1 . × cm. The size of each cell in the grid is 4 . × cmin all runs except the higher resolution run, where the gridhas a smaller cell size of 2 . × cm . We position thestellar giant center at the center of the grid. The gravity ofthe primary star is taken as constant and spherically sym-metric during the simulations. Namely, the influence of massloss from the envelope and of envelope distortion on gravityis neglected.We do not include the gravity of the secondary star.This omission can be partially justified. First, the secondaryis a low mass star. Second, the jets interact with the envelopein regions relatively far from the secondary star, where thebinding energy is mostly affected by the gravity of the AGBprimary star.We neglect cooling by radiation and treat the gas asan ideal gas with adiabatic index of γ = 5 /
3. At the outerlayers where the density is lower, radiation can be important and we will address it in our results. To save computationaltime the inner 0 .
33 AU sphere of the AGB star is replacedwith a constant density and pressure sphere, as we havedone in Shiber et al. (2017). In a test run the giant modelstays stable, and develops only a weak outflow with a kineticenergy that is negligible compared with the energy of the jetsin our simulations.We start at t = 0 by placing a low-mass main sequencesecondary star at the surface of the AGB star on its equa-tor, at a ( x, y, z ) = (1 . × cm , , z = 0, while performinga spiraling-in motion inside the AGB envelope. During itsspiraling-in motion the secondary star launches bipolar jetswith a half-opening angle of θ jet and a velocity of v jet .For the one high-resolution simulation we take θ jet =30 ◦ and v jet = 400 km s − , about 0 . θ jet = 30 ◦ , v jet = 400 km s − , while in the others we take θ jet = 60 ◦ and v jet = 700 km s − , about 1 . R (cid:12) with a velocity of 473 km s − .When outside the AGB envelope the secondary star ac-cretes mass through an accretion disk (e.g. Chen et al. 2017)that is likely to launch jets. We assume that when the sec-ondary star enters the envelope it already has an accretiondisk that launches jets. We let the secondary star to con-tinuously launch two opposite jets from its momentary lo-cation. To the initial velocity of the jets relative to the sec-ondary star, v jet , we add the momentary orbital velocity ofthe secondary star (both azimuthal and radial components).We numerically inject the jets on the two sides of the sec-ondary star in a cone of a length about the size of two gridcells. Namely, 1 × cm in the low resolution runs and0 . × cm in the high resolution run.The inward radial velocity component of the spiraling-in motion is constant and is determined in such a way thatin a time of t sp the secondary spirals-in to 2 / t sp was setto 595 day, equal to 3 Keplerian orbits around the AGBsurface, but due to the spiraling-in motion the secondarycompleted almost four rounds. This inward motion was de-rived based on the spiraling-in orbits that were obtainedin former CEE numerical simulations (e.g. Ricker & Taam2012; MacLeod & Ramirez-Ruiz 2015). We also performtwo additional runs, one in which we double the spiraling-intime and one where we took half the spiraling-in time.The mass injection rate into the two jets in the simula-tions is ˙ M jet = 10 − M (cid:12) yr − . This rate is based on Bondi- MNRAS000
33 AU sphere of the AGB star is replacedwith a constant density and pressure sphere, as we havedone in Shiber et al. (2017). In a test run the giant modelstays stable, and develops only a weak outflow with a kineticenergy that is negligible compared with the energy of the jetsin our simulations.We start at t = 0 by placing a low-mass main sequencesecondary star at the surface of the AGB star on its equa-tor, at a ( x, y, z ) = (1 . × cm , , z = 0, while performinga spiraling-in motion inside the AGB envelope. During itsspiraling-in motion the secondary star launches bipolar jetswith a half-opening angle of θ jet and a velocity of v jet .For the one high-resolution simulation we take θ jet =30 ◦ and v jet = 400 km s − , about 0 . θ jet = 30 ◦ , v jet = 400 km s − , while in the others we take θ jet = 60 ◦ and v jet = 700 km s − , about 1 . R (cid:12) with a velocity of 473 km s − .When outside the AGB envelope the secondary star ac-cretes mass through an accretion disk (e.g. Chen et al. 2017)that is likely to launch jets. We assume that when the sec-ondary star enters the envelope it already has an accretiondisk that launches jets. We let the secondary star to con-tinuously launch two opposite jets from its momentary lo-cation. To the initial velocity of the jets relative to the sec-ondary star, v jet , we add the momentary orbital velocity ofthe secondary star (both azimuthal and radial components).We numerically inject the jets on the two sides of the sec-ondary star in a cone of a length about the size of two gridcells. Namely, 1 × cm in the low resolution runs and0 . × cm in the high resolution run.The inward radial velocity component of the spiraling-in motion is constant and is determined in such a way thatin a time of t sp the secondary spirals-in to 2 / t sp was setto 595 day, equal to 3 Keplerian orbits around the AGBsurface, but due to the spiraling-in motion the secondarycompleted almost four rounds. This inward motion was de-rived based on the spiraling-in orbits that were obtainedin former CEE numerical simulations (e.g. Ricker & Taam2012; MacLeod & Ramirez-Ruiz 2015). We also performtwo additional runs, one in which we double the spiraling-intime and one where we took half the spiraling-in time.The mass injection rate into the two jets in the simula-tions is ˙ M jet = 10 − M (cid:12) yr − . This rate is based on Bondi- MNRAS000 , 1–15 (2017)
D simulations of GEE Hoyle-Lyttleton (BHL) accretion rate and was discussed inthe previous paper (Shiber et al. 2017). A suppression of theaccretion rate relative to the BHL value is expected in thesecases due to the pressure built around the accreting objectand due to asymmetric accretion flows. However, the sup-pression is moderate because the jets carry gas and energyout and reduce the pressure (Shiber et al. 2016).In calculating the BHL accretion rate we consider thegiant steep density profile around the companion and notonly the local surface density. The BHL accretion rate isthen divided by two factors to obtain the mass injectionrate into the jets. The first reduction factor of value of tenis the suppression that was discussed above due to pressurearound the secondary star. The second reduction factor is atypical ratio of jets mass outflow rate to the accretion rate,which we also take to be ten. On the other hand, we expectan enhancement of about a factor of 15 in the accretion rateas the secondary star spirals-in to the inner denser regionsof the envelope. However, we take a conservative approachand keep the mass injection rate at its initial low value of˙ M jet = 10 − M (cid:12) yr − . In a forthcoming study the secondarygravity will be included and we will deal with the modulationof the accretion rate as the secondary star dives into theenvelope. We set the secondary star to spiral-in, and explore the dis-tortion of the envelope and the outflow. In section 3.1 weconcentrate on the distortion of the envelope, and in sec-tion 3.2 we describe the outflow. In these two subsectionswe describe a numerical run with one set of parameters, thehigh-resolution fiducial run and we compare it to a lowerresolution run for a resolution study. In section 3.3 we willpresent the effects of varying the opening angle of the jetsand their velocity, as well as of the spiraling-in time.
In Fig. 1 we present the density of the fiducial run (seesection 2) in the equatorial plane at twelve times, as indi-cated in each panel in days. The location of the companion ismarked by an ‘X’, and it orbits counterclockwise. We notethe following features. As can be best seen at late times,the secondary penetrates into the envelope, and expels thegas outside its orbit. The expelled gas is seen as envelopeinflation trailing the companion. Note that the gravity ofthe companion is not included, and the effect is solely dueto the jets that are launched by the companion. As can beseen by following the low density contours, the outer enve-lope is heavily distorted and flows outward. By removing thegas, the companion continues to graze the envelope ratherthan entering a common envelope evolution. By the timewe terminate the simulation there is an indication that thecompanion enters a common envelope, as there is a densegas outside its orbit. But by this stage the mass accretionrate is likely to increase and so is the energy of the jets. Inaddition, the release of gravitational energy by the in-spiralorbit should be included by that time. That energy will in-flate the envelope and ease its removal by jets. These effectsare the tasks of a forthcoming paper. In fig. 2 we present the temperature in the equatorialplane at the same times as in Fig. 1. The two arc-like hightemperature regions in red are post-shock regions movingaround the star. There is a transitory period when theseshock waves cross the grid. They are numerically formed bythe sudden injection of the jets, but as they propagate invery low density regions they do not influence much the re-sults. After about 200 days their signature disappear, and aspiral pattern appears to trail the secondary star. The hightemperature gas emits X-ray. However, we expect that thedense wind from the giant will absorb the X-ray. The ob-servational signature will be a transient in the visible andin the infra-red band, i.e., an intermediate luminosity opti-cal transient (ILOT), as expected in the formation of somebipolar planetary nebulae (Soker & Kashi 2012), in the GEE(Soker 2016b), and in the common envelope (e.g., Retter &Marom 2003; Retter et al. 2006; Tylenda et al. 2011, 2013;Nandez et al. 2014; Zhu et al. 2016; Galaviz et al. 2017).To further present the formation of a common envelopeat the end of our simulation, in Fig. 3 we present the flow inmeridional planes. In the onset of the GEE, when the sec-ondary orbits on the initial giant surface, the jets expel thelow density gas at high velocities. As the secondary spiralsin, the jets are deflected by the denser inner regions of thegiant and bend towards the equatorial plane. The bendingof jets inside a common envelope can be seen in earlier sim-ulations (Soker et al. 2013; Moreno M´endez et al. 2017), aswell as in the GEE (Shiber et al. 2017). When the secondaryspirals-in even deeper the jets are halt by the giant envelope,and escape only behind the companion in a trailing flow asdiscussed above. The result is that the secondary enters acommon envelope phase. Again, the entrance to a commonenvelope phase might be avoided in full simulations that in-clude the increase in the accretion rate, hence in the powerof the jets, and include also the gravitational energy that isreleased by the in-spiraling companion. This might be thecase for relatively more massive companions. We will studythe upper limit on the secondary mass for the formation ofa common envelope in the future.Fig. 4 and 5 show the flow properties at the end oftwo simulations after the secondary has completed about 4rounds. One run is the fiducial run (right column), and theother run has identical parameters but with a lower resolu-tion of twice the cells size (left column). Fig. 4 presents theflow in the equatorial plane. A spiral arm structure is clearlyseen, mainly in the temperature maps (lower panels). Theflow structure is similar in both resolutions, but the higherresolution run reveals finer details.In the upper panels of Fig. 5 we present the densitymap in a meridional plane as in Fig. 3. The outer contoursof the density maps show a distorted envelope lifted by theenergetic jets. In the lower panel we present the density mapin the plane perpendicular to the momentary radius vectorof the secondary star (a plane tangential to the φ direction)and perpendicular to the equatorial plane. In these panelsthe secondary is at the center. The jets are strongly bentbackward, as seen in the two narrow light-brown stripes tothe left of the secondary star. Over all, the jets that arelaunched from the spiraling-in secondary star lead to anasymmetric and complicated flow structure.To summarized this subsection we emphasize the fol-lowing. (1) The jets expel mass efficiently at the beginning MNRAS , 1–15 (2017)
S. Shiber and N. Soker
100 km/sec − − − y ( AU ) − − − y ( AU ) − − − y ( AU ) − − − − − − y ( AU ) − − − − − − − − − − − − D e n s i t y (cid:0) g c m (cid:1) Figure 1.
Density maps and velocity vectors in the equatorial plane z = 0 of our fiducial run, the only one with the high resolution,with jets’ velocity of v jet = 400 km s − , and a jets’ half opening angle of θ jet = 30 ◦ , at twelve different times given in days. Thecompanion orbits counterclockwise, and its momentary location is marked with ’X’. Its initial and final orbital radii are 1 AU and0 .
67 AU, respectively. The orbital period at the surface is 198 . − as indicated with the arrow above the first panel. We can clearly see how the jets leave a low density trailingbehind the secondary star as they lift and remove envelope mass. MNRAS000
67 AU, respectively. The orbital period at the surface is 198 . − as indicated with the arrow above the first panel. We can clearly see how the jets leave a low density trailingbehind the secondary star as they lift and remove envelope mass. MNRAS000 , 1–15 (2017) D simulations of GEE − − − y ( AU ) − − − y ( AU ) − − − y ( AU ) − − − − − − y ( AU ) − − − − − − T e m p e r a t u r e ( K ) Figure 2.
Like Fig. 1 but presenting the temperature maps. The two red arcs moving around the star in two opposite directions areshocks that are formed by the sudden injection of the jets. They are propagating in very low-density regions, and do not affect much theresults. Their signature completely disappear after about 200 days. One should only treat them as a numerical feature. After this initialphase a spiral structure trailing the secondary star is clearly seen.MNRAS , 1–15 (2017)
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100 km/sec − − − z ( AU ) − − − ρ (AU) − − − z ( AU ) − − − ρ (AU) − − − − − − D e n s i t y (cid:0) g c m (cid:1) Figure 3.
Density maps and velocity vectors for the fiducial run at four times given in days as indicated, in meridional planes thatcontains the center of the giant and the momentary location of the secondary star. The horizontal axis is ρ = ± (cid:112) x + y . The companionlocation is marked with ’X’. The different patterns of the flow as the secondary moves inward is clearly seen. The jets proceed out easilywhen the secondary is in the low density outskirts of the giant, while the jets are halt and bend when the secondary is in the more densinner regions. of the simulation when the secondary star orbits the giantoutskirts. (2) Deeper in the envelope the jets expel mass lessefficiently and the outflow is directed mainly to the equato-rial plane in a narrow region trailing the companion. Thecommon envelope evolution then commences. (3) We notethough that in our simulations we do not include the grav-itational energy that is released by the in-spiraling process.The inclusion of the orbital energy that is released will delaythe onset of the common envelope, or will avoid it altogether.The later is expected for relatively massive companions. We start by presenting some average properties of the massejected from the binary system. In Fig. 6 we show the evolu-tion of the total mass that is ejected from the system in bluesolid line, and the part that is unbound, i.e., has a positivetotal energy, in dotted green line. We compare these twoquantities to the mass that is injected into the jets (dashed orange line). The amount of ejected mass is calculated asmass leaving a sphere of radius 4 AU. The thick lines arefor the high resolution fiducial run and the thin lines are forthe lower resolution run with identical jet parameters. Weemphasize again that the only extra energy that is includedis that of the jets, and in this paper we do not yet includethe gravitational energy released by the in-spiraling binarysystem. We note that at late times, when the secondary stardives into the envelope the increase in ejected unbound massdecreases.We see from Fig. 6 that more mass is ejected and be-comes unbound in the lower resolution run, by about 16%at the end of the runs. Although the runs have the iden-tical physical jet parameters, i.e., the jet velocity and thejet opening angle, they differ in their numeric parameters.Mainly, the cone length in which the jets are numerically in-jected is different. In the high resolution run the cone lengthis half of the cone length in the low resolution. Although thejets have the same injection rate in both cases, in the high
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D simulations of GEE
100 km/sec − − − y ( AU ) − − − − − − y ( AU ) − − − − − − − − − D e n s i t y (cid:0) g c m (cid:1) T e m p e r a t u r e ( K ) Figure 4.
The hydrodynamic properties in the equatorial (orbital) plane z = 0 of our fiducial run (right column) and a low resolutionrun (left column) with identical jet parameters. All panels are at t = 595 days, amounts to almost 4 orbital rounds, and when the orbitalseparation has reduced to 0 .
67 AU. The upper panels show density and velocity maps, and the lower panels show the temperature maps. resolution run the jets are injected inside a smaller volume.The low resolution run where the jets are numerically in-jected inside a larger volume yields higher mass ejection.In Fig. 7 we present the mass per unit solid angle, dm/d
Ω, that left a sphere of radius 4 AU over 595 days(about 4 orbits), as a function of the angle from the equa-torial ( θ = 0 ◦ is the equatorial plane and θ = 90 ◦ is thepoles). The quantity dm/d Ω is calculated by summing overthe azimuthal angle φ at each angle θ , and combining thetwo hemispheres. We also show the value of the root meansquare of the velocity (cid:112) (cid:104) v (cid:105) ≡ (cid:112) dE k ( θ ) /dM ( θ ), where dE k ( θ ) and dM ( θ ) are the kinetic energy and mass, respec-tively, that left the 4 AU sphere. The thick lines show re-sults for the fiducial run while the thin lines are for the lowresolution run with identical jets parameters. The outflowis concentrated around the equatorial plane in both cases,although it is not monotonic with θ . What we find moreinteresting, is that the maximum outflow velocity is at mid-latitude (see also Shiber et al. 2017). In the high resolution run the maximal velocity is higher with a more pronouncedpick. The outflow is faster in this case but less massive.In Fig. 8, we show the specific angular momentum ofthe outflowing gas about the axis perpendicular to the or-bital plane j z in the fiducial run (thick line) and in the lowresolution run (thin line). This is similar to the mass perunit solid angle and the velocity of the outflowing gas asfunction of θ that we presented in Fig. 7, but for specificangular momentum. We show the specific angular momen-tum of the outflowing gas relative to the specific angularmomentum of a body performing Keplerian motion on theinitial surface of the AGB star j orb ,iz = (cid:112) GM AGB R AGB,i .We find the total average specific angular momentum of theejected mass in both cases to be j z (total) (cid:39) − . j orb ,i . Thenegative values imply that the ejected mass carries angularmomentum opposite to that of the secondary star. This isbecause the jets are bent backward and push gas in the op-posite direction. The jets can actually spin-up the envelope,but not by much.In Fig 9 we present the ejected mass per unit solid an-gle over different times of the fiducial run, as function of MNRAS , 1–15 (2017)
S. Shiber and N. Soker − − − ρ (AU) − − − z ( AU ) − − − ρ (AU) − − − z ( AU ) − − − ρ (AU) − − − z ( AU ) − − − ρ (AU) − − − z ( AU ) − − − − − − D e n s i t y (cid:0) g c m (cid:1) Figure 5.
Like upper panels of Fig. 4, but for different planes. Again, our fiducial run is on the right column and the low resolution runwith identical jet parameters is on the left column. The upper row shows the density and velocity in the ρ − z meridional plane thatcontains the center of the giant and the momentary location of the secondary star (the same plane as depicted in Fig 3; ρ = ± (cid:112) x + y ).The lower row shows the density and velocity in the ¯ ρ − z plane that is perpendicular to the momentary radius vector of the secondarystar and perpendicular to the equatorial plane. ¯ ρ = ± (cid:112) ( x − x s ) + ( y − y s ) in these panels, where ( x s , y s ,
0) is the momentary threedimensional position of the secondary. ( θ, φ ) as Hammer projection of a sphere of radius 4 AU.The evolution of the ejected mass geometry clearly showsthe highly asymmetrical mass ejection and its concentra-tion near the equatorial plane. These maps also show thepronounced clumpy nature of the outflow. At later timesthe concentration of outflow toward the equatorial plane in-creases. This results from a stronger bending backward ofthe jets as the secondary dives deeper into the envelope.The location of the strongest outflow moves around becausethe ejection has a spiral morphology (see Figs. 1 and 2).To further present the morphology of the outflowinggas, in Fig. 10 we present constant-density surfaces at theend of the fiducial run. Each row is for a different densityvalue, and the two columns are for two different viewingangles as explain in the caption. The red color depicts theentire constant-density surface. The green areas are the un-bound regions, i.e., have positive total energy. The green color areas further present the concentrated of ejected massnear the equatorial plane.We emphasize that even though the jet are launchedin directions perpendicular to the equatorial plane, most ofthe mass is ejected from the system in the equatorial planedirections. We can see it in two ways. One, as mentionedbefore, the jets are diverted towards the equatorial plane bythe dense envelope. The denser the area around the compan-ion the stronger bending of the jets will be. The other way isto realize that the jets create high-temperature low-densitybubbles which escapes buoyantly outward, i.e., in and nearthe equatorial plane. These bubbles push and entrain enve-lope gas outward.The angular momentum in our simulations is affectedsolely by the jets as they are launched with the momentaryvelocity of the secondary star, and as we do not includeneither the secondary gravity that can spin up the primary,nor initial giant rotation. The bending of the jets and the MNRAS000
0) is the momentary threedimensional position of the secondary. ( θ, φ ) as Hammer projection of a sphere of radius 4 AU.The evolution of the ejected mass geometry clearly showsthe highly asymmetrical mass ejection and its concentra-tion near the equatorial plane. These maps also show thepronounced clumpy nature of the outflow. At later timesthe concentration of outflow toward the equatorial plane in-creases. This results from a stronger bending backward ofthe jets as the secondary dives deeper into the envelope.The location of the strongest outflow moves around becausethe ejection has a spiral morphology (see Figs. 1 and 2).To further present the morphology of the outflowinggas, in Fig. 10 we present constant-density surfaces at theend of the fiducial run. Each row is for a different densityvalue, and the two columns are for two different viewingangles as explain in the caption. The red color depicts theentire constant-density surface. The green areas are the un-bound regions, i.e., have positive total energy. The green color areas further present the concentrated of ejected massnear the equatorial plane.We emphasize that even though the jet are launchedin directions perpendicular to the equatorial plane, most ofthe mass is ejected from the system in the equatorial planedirections. We can see it in two ways. One, as mentionedbefore, the jets are diverted towards the equatorial plane bythe dense envelope. The denser the area around the compan-ion the stronger bending of the jets will be. The other way isto realize that the jets create high-temperature low-densitybubbles which escapes buoyantly outward, i.e., in and nearthe equatorial plane. These bubbles push and entrain enve-lope gas outward.The angular momentum in our simulations is affectedsolely by the jets as they are launched with the momentaryvelocity of the secondary star, and as we do not includeneither the secondary gravity that can spin up the primary,nor initial giant rotation. The bending of the jets and the MNRAS000 , 1–15 (2017)
D simulations of GEE Time (days) . . . . M a ss ( M ⊙ ) total - ltotal - hjetsunbound - lunbound - h Figure 6.
The total mass (solid blue line) that crosses outthrough a spherical shell of radius 4 AU, the unbound (dottedgreen line) mass that crosses out the same sphere, and the injectedmass into the jets (dashed orange line) as function of time. Theamount of mass flowing outward is more than ten times higherthan the mass injected in the jets. The unbound mass percentageof the total mass decreases as the secondary spirals-in. The thicklines are for the high resolution run while the thin lines are forthe low resolution run. θ (degrees) . . . . . . d M / d Ω ( M ⊙ s r − ) p h V i ( k m / s ec ) Figure 7.
The total mass crosses out through a spherical shellof radius 4 AU per unit solid angle (green line) and the rootmean square of the outflow velocities that crossed the same sphere(dashed blue line) as a function of the angle from the equatorialplane θ , after 595 day of the fiducial Run. The equator is at θ = 0 ◦ and the poles are at θ = 90 ◦ . The amount of mass lost isthat from the two hemispheres combined. Although the mass lossis concentrated near the equatorial plane, the highest averageoutflow velocity is at mid-latitude. The thick lines are for thehigh resolution fiducial run while the thin lines are for the lowresolution run with identical jet parameters. bubbles motion in our simulations distribute the angularmomentum among the envelope parts they interact with. The parameter space of the type of simulations we performis huge. Below we describe the results of a limited numberof simulations with varying values of some parameters, allwith the low resolution numerical grid. θ (degrees) − . − . − . − . . . . . j z / j o r b , i z jz - ljz - h Figure 8.
The z component of the specific angular momentum ofthe ejected mass, as function of angle from the equatorial plane θ , and relative to the specific angular momentum of a body per-forming Keplerian motion on the initial surface of the AGB star.The thick line is from the high resolution run while the thin lineis from the low resolution run. In Fig. 11 we present density and velocity maps in theequatorial plane at the end of the simulations, when theorbital separation has been reduced to 0 .
67 AU, for foursimulations differ in the jet velocity and jet half-openingangle. The left upper panel shows the equatorial of a runwhere we set the jet velocity to be v jet = 400 km s − andthe half-opening angle to be θ jet = 30 ◦ . As we noted in sub-sections 3.1 and 3.2, the structure of the flow has a spiralshape and the envelope is inflated outside the secondary or-bit. The upper-right panel corresponds to a simulation withthe same jet velocity and outflow mass rate but for wider jetsof θ jet = 60 ◦ . The spiral shape is more pronounced in thiscase, the ejected envelope flows faster, and more pronouncedclumps of gas are ripped from the envelope (seen on the leftpart of the panel). The lower-left panel show the flow for thecase of v jet = 700 km s − and θ jet = 30 ◦ . As expected for ahigher jet velocity which implies three times the jets’ power,the envelope outer to the secondary orbit is more extended.In the lower-right panel the values are v jet = 700 km s − and θ jet = 60 ◦ . As with the cases for a lower jet velocity,clumps of ejected envelope gas reach larger distances andvelocities for the wider jets. In all panels we note the highlyasymmetrical mass ejection.In Fig. 12 we compare the same four runs at the sametime but present the density and velocity maps on a planethat is perpendicular to the momentary radius vector of thesecondary star (the same plane that is shown in the lowerpanels in Fig. 5). Asymmetrical pattern emanates from allthe runs. The narrow trail behind the jets widens and es-capes to larger distances with higher jet velocity and largerjet opening angle. The low density elongated structure start-ing from the center and extending to the left in each panelis the jets’ material. Higher energy jets more easily escapefrom the envelope, and hence the higher energy simulationsenter a common envelope phase at a later time.Fig. 13 shows the meridional plane that contains themomentary position of the secondary star and the centerof the AGB star for the same runs and at the same timeas in the previous two figures. Loops are seen on the right MNRAS , 1–15 (2017) S. Shiber and N. Soker − ◦ − ◦ − ◦ − ◦ − ◦ ◦ +15 ◦ +30 ◦ +45 ◦ +60 ◦ +75 ◦ ◦ ◦ ◦ ◦ ◦ ◦ − . − . − . − . − . − . − . − . − . − . M ejected ( M ⊙ sr − ) − ◦ − ◦ − ◦ − ◦ − ◦ ◦ +15 ◦ +30 ◦ +45 ◦ +60 ◦ +75 ◦ ◦ ◦ ◦ ◦ ◦ ◦ − . − . − . − . − . − . − . M ejected ( M ⊙ sr − ) − ◦ − ◦ − ◦ − ◦ − ◦ ◦ +15 ◦ +30 ◦ +45 ◦ +60 ◦ +75 ◦ ◦ ◦ ◦ ◦ ◦ ◦ − . − . − . − . − . − . − . − . − . M ejected ( M ⊙ sr − ) − ◦ − ◦ − ◦ − ◦ − ◦ ◦ +15 ◦ +30 ◦ +45 ◦ +60 ◦ +75 ◦ ◦ ◦ ◦ ◦ ◦ ◦ − . − . − . − . − . − . − . − . − . M ejected ( M ⊙ sr − ) − ◦ − ◦ − ◦ − ◦ − ◦ ◦ +15 ◦ +30 ◦ +45 ◦ +60 ◦ +75 ◦ ◦ ◦ ◦ ◦ ◦ ◦ − . − . − . − . − . − . − . − . M ejected ( M ⊙ sr − ) Figure 9.
The total mass outflow from a spherical shell of radius 4 AU per unit solid angle during five time periods. The four smallermaps correspond to the time periods of 0 − .
8, 29 . − − .
9, and 267 . − . −
595 day. Zero latitude is the equatorial plane and zero longitude(at the center) is the initial location of the companion. The companion is moving towards higher angles, namely from the right to theleft. We can see a concentration of clumpy mass ejection near the equatorial. side of each panel. They are larger for higher velocity andhigher jets’ opening angles. These loops are part of the spiraloutflow.We present temperature maps from the same runs andat the same time as in previous three figures in Fig. 14. Thepost-shock material of the ejected gas forms a spiral patterntrailing the secondary star. A higher velocity yields largerregions of high temperature gas, and a wider opening angleof the jets results in a more complicated pattern and a widerspread of the spiral pattern. As discussed in relation to Fig. 2, the hot gas suffers a radiatively cooling in addition to theadiabatic cooling, and might lead to an ILOT event.We also study the effect of the spiraling-in time. In Fig.15 we show plots of three runs differ in the spiral-in time t sp from a = 1 AU to a = 0 .
67 AU. The left column isfor t sp = 1190 day equals to 6 Keplerian orbits around theAGB surface, but due to the spiraling-in motion the sec-ondary completes almost 8 rounds. The middle column isfor t sp = 595 day, our fiducial run. In the right column t sp = 298 day equals to 1.5 Keplerian orbits around theAGB surface, but with the spiraling-in motion the com- MNRAS000
67 AU. The left column isfor t sp = 1190 day equals to 6 Keplerian orbits around theAGB surface, but due to the spiraling-in motion the sec-ondary completes almost 8 rounds. The middle column isfor t sp = 595 day, our fiducial run. In the right column t sp = 298 day equals to 1.5 Keplerian orbits around theAGB surface, but with the spiraling-in motion the com- MNRAS000 , 1–15 (2017)
D simulations of GEE Figure 10.
3D maps of constant-density surfaces, each row for a different density surface, at the end of our fiducial run at t = 595 day.The densities from top to bottom are 5 × − , × − and 10 − g cm − , respectively. Axes run from − × cm to 7 × cm.In the left column the equatorial plane is along the line of sight in a horizontal plane through z = 0, while in the right column the line ofsight is perpendicular to the equatorial plane. The red color is the entire constant density surface, while the green color depicts unboundmaterial, i.e., material which its sum of the kinetic, gravitational and internal energy is positive. The arrows depict velocity vectors, withthe magnitude of the velocity proportional to the length of the arrow and to the brightness of the arrow as given in the gray bar on theleft of each panel, and in the range of 1 −
80 km s − . panion completes around 2 rounds. In all the runs we set v jet = 400 km s − and θ jet = 30 ◦ , and we end the simula-tion when the orbital separation has shrank to a = 0 .
67 AU.In the figure we present density and velocity maps in threeplanes, the equatorial plane (top), the perpendicular plane(second row), and the meridional plane (third row), as ex-plained in the caption. In the bottom row we present thetemperature maps in the equatorial plane.As expected, when the spiraling-in time scale increasesand more energy is injected in the jets by the time the sec-ondary star reaches a = 0 .
67 AU, the envelope suffers morepronounced inflation. Also expected is that for a longer in-spiral time the geometry of the envelope ejection will be more isotropic. The temperature maps, for example, showthe more sharply appearing spiral shape in the rapid plunge-in case relative to the slower spiraling-in where the arms aremore extended.The main conclusion from the six different simulationswe have described above in figs. 11 - 15 is that in all casesthe jets manage to inflate the envelope and eject some enve-lope gas. We imply from this conclusion that the GEE is apromising process to help in removing the envelope, as longas the secondary star launches energetic jets.
MNRAS , 1–15 (2017) S. Shiber and N. Soker
100 km/sec − − − y ( AU ) − − − − − − y ( AU ) − − − − − − − − − D e n s i t y (cid:0) g c m (cid:1) Figure 11.
Density and velocity maps in the orbital plane z = 0 comparing four different runs after 589 days when the orbital separationhas been reduced to 0 .
67 AU. We label each panel by the value taken for the jets initial velocity relative to the secondary star v jet , andby the jets initial half-opening angle θ jet. The first three digits stand for the jet velocity in km s − , and the last two digits are the halfopening angle in degrees. The upper left panel is the fiducial run whose flow structure is described in previous figures. The symbol ’X’in the outer part of the AGB star marks the location of the secondary star that rotates counterclockwise. The tail behind the secondarystar in all panels show that as the secondary star dives into the envelope the jets remove mass from the outer part of the envelope. We simulated a secondary star that spirals-in from the sur-face of an AGB star at an orbital separation of a = R AGB =1 AU, to a radius of a = 0 .
67 AU. We assumed that thesecondary star launches jets continuously as it spirals-in,with a power that is several percents of that expected fromthe Bondy-Hoyle-Lyttleton accretion rate. The jet velocityis about equal to the escape velocity from the secondarystar. Our goal is to explore the effect of jets, without yetintroducing the orbital energy and the rotation of the enve-lope.We revealed the structure of the outflow that resultssolely from the jets (figs. 1-4). The jets inflate the enve-lope outside the orbit, and eject some of the mass. Thesecondary star spiraled-in through an envelope layer with amass of 0 . M (cid:12) , and ejected 0 . M (cid:12) . The very low ejectedmass fraction is explained because the gravitational energyof the binary system and initial envelope rotation were not included. More efficient mass removal occurs when the sec-ondary star orbits the outskirts of the envelope.Due to the bending of the jets by the AGB envelope,the mass outflow concentrates around the equatorial plane.The geometry is of an outflowing spiral pattern trailing thesecondary star. Overall the flow is highly asymmetric andclumpy. Although most of the mass outflows from near theequatorial plane, the highest velocity of the outflow is atmid-latitude (fig. 7).We examined the parameter space with additional fiveruns differ in the jets’ velocity and the jets’ half-opening an-gle (Figs. 9-14), and in the in-spiral time (Fig. 15). We findoutflow in all cases. We conclude that the GEE is a promis-ing process. In some cases it might substantially postponeand even prevent the spiraling-in process. However, to de-termine whether the jets play a significant role, the grav-itational energy of the binary system and the spinning of MNRAS000
67 AU. We assumed that thesecondary star launches jets continuously as it spirals-in,with a power that is several percents of that expected fromthe Bondy-Hoyle-Lyttleton accretion rate. The jet velocityis about equal to the escape velocity from the secondarystar. Our goal is to explore the effect of jets, without yetintroducing the orbital energy and the rotation of the enve-lope.We revealed the structure of the outflow that resultssolely from the jets (figs. 1-4). The jets inflate the enve-lope outside the orbit, and eject some of the mass. Thesecondary star spiraled-in through an envelope layer with amass of 0 . M (cid:12) , and ejected 0 . M (cid:12) . The very low ejectedmass fraction is explained because the gravitational energyof the binary system and initial envelope rotation were not included. More efficient mass removal occurs when the sec-ondary star orbits the outskirts of the envelope.Due to the bending of the jets by the AGB envelope,the mass outflow concentrates around the equatorial plane.The geometry is of an outflowing spiral pattern trailing thesecondary star. Overall the flow is highly asymmetric andclumpy. Although most of the mass outflows from near theequatorial plane, the highest velocity of the outflow is atmid-latitude (fig. 7).We examined the parameter space with additional fiveruns differ in the jets’ velocity and the jets’ half-opening an-gle (Figs. 9-14), and in the in-spiral time (Fig. 15). We findoutflow in all cases. We conclude that the GEE is a promis-ing process. In some cases it might substantially postponeand even prevent the spiraling-in process. However, to de-termine whether the jets play a significant role, the grav-itational energy of the binary system and the spinning of MNRAS000 , 1–15 (2017)
D simulations of GEE
100 km/sec − z ( AU ) − − − ρ (AU) − z ( AU ) − − − ρ (AU) − − − − − − D e n s i t y (cid:0) g c m (cid:1) Figure 12.
Like Fig. 11, but for the ¯ ρ − z plane that is perpendicular to the momentary radius vector of the secondary star andperpendicular to the equatorial plane. The center of the AGB star is at a distance of 0 .
67 AU from this plane and projected onto thecenter of each panel. These plots emphasize the highly asymmetrical mass ejection. the AGB envelope must be included. These are the tasks offuture studies.
ACKNOWLEDGMENTS
We thank an anonymous referee for comments that im-proved the presentation of our results. This work was sup-ported by the Cy-Tera Project, which is co-funded by theEuropean Regional Development Fund and the Republic ofCyprus through the Research Promotion Foundation. Wethank Thekla Loizou from the Cyprus HPC Facility for herkind technical assistance. FLASH was developed largely bythe DOE-supported ASC/Alliances Center for Astrophysi-cal Thermonuclear Flashes at the University of Chicago. Inproducing the images in this paper we used VisIt which issupported by the Department of Energy with funding fromthe Advanced Simulation and Computing Program and theScientific Discovery through Advanced Computing Program.This work also required the use and integration of a Pythonpackage for astronomy, yt (http://yt-project.org, Turk et al. 2011). We acknowledge support from the Israel ScienceFoundation and a grant from the Asher Space Research In-stitute at the Technion.
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Like Fig. 11, but for the ρ − z meridional plane that contains the center of the giant and the momentary location of thesecondary star. Again, the asymmetrical mass ejection is clearly seen.Iaconi, R., De Marco, O., Passy, J.-C., & Staff, J., et al. 2017a,arXiv:1706.09786Iaconi, R., Reichardt, T., Staff, J., De Marco, O., Passy, J.-C.,Price, D., Wurster, J., & Herwig, F. 2017b, MNRAS, 464,4028Ivanova, N., & Nandez, J. L. A. 2016, MNRAS, 462, 362Kruckow, M. U., Tauris, T. M., Langer, N., Szecsi, D., Marchant,P., & Podsiadlowski, Ph. 2016, A&A, 596, A58Kuruwita, R. L., Staff, J., & De Marco, O. 2016, MNRAS, 461,486MacLeod, M., & Ramirez-Ruiz, E. 2015, ApJ, 803, 41Moreno M´endez, E., L´opez-C´amara, D., & De Colle, F. 2017,MNRAS, 470, 2929Murguia-Berthier, A., MacLeod, M., Ramirez-Ruiz, E., Antoni,A., & Macias, P. 2017, ApJ, 845, 173Nandez, J. L. A., & Ivanova, N. 2016, MNRAS, 460, 3992Nandez, J. L. A., Ivanova, N., & Lombardi, J. C., Jr. 2014, ApJ,786, 39Nandez, J. L. A., Ivanova, N., & Lombardi, J. C. 2015, MNRAS,450, L39Ohlmann, S. T., R¨opke, F. K., Pakmor, R., & Springel, V. 2016,ApJ, 816, L9Papish, O., Soker, N., & Bukay, I. 2015, MNRAS, 449, 288Passy, J.-C., De Marco, O., Fryer, C. L., et al. 2012, ApJ, 744, 52 Paxton, B., Bildsten, L., Dotter, A., et al. 2011, ApJS, 192, 3Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208, 4Paxton, B., Marchant, P., Schwab, J., et al. 2015, ApJS, 220, 15Retter, A., & Marom, A. 2003, MNRAS, 345, L25Retter, A., Zhang, B., Siess, L., & Levinson, A. 2006, MNRAS,370, 1573Ricker, P. M., & Taam, R. E. 2012, ApJ, 746, 74Sabach, E., Hillel, S., Schreier, R., & Soker, N. 2017, MNRAS,472, 4361Sabach, E., & Soker, N. 2015, MNRAS, 450, 1716Schreier, R., & Soker, N. 2016, Research in Astronomy and As-trophysics, 16, 001Shiber, S., Kashi, A., & Soker, N. 2017, MNRAS, 465, L54Shiber, S., Schreier, R., & Soker, N. 2016, Research in Astronomyand Astrophysics, 16, 117Soker, N. 2004, New Astron., 9, 399Soker, N. 2015, ApJ, 800, 114Soker, N. 2016a, New Astron. Rev., 75, 1Soker, N. 2016b, New Astron., 47, 16Soker, N. 2017, MNRAS, 470, L102Soker, N., Akashi, M., Gilkis, A., Hillel, S., Papish, O.,Refaelovich, M., & Tsebrenko, D. 2013, AstronomischeNachrichten, 334, 402Soker, N., & Harpaz, A. 2003, MNRAS, 343, 456MNRAS000 , 1–15 (2017) D simulations of GEE − − − y ( AU ) − − − − − − y ( AU ) − − − T e m p e r a t u r e ( K ) Figure 14.
Like Fig. 11 but showing the temperature maps. Wider jets result in wider tails trailing behind the secondary star. Jets withhigher velocity expel the envelope mass more vigorously.Soker, N., & Kashi, A. 2012, ApJ, 746, 100Staff, J. E., De Marco, O., Macdonald, D., Galaviz, P., Passy, J.C.,Iaconi, R., & Mac Low, M.-M 2016a, MNRAS, 455, 3511Staff, J. E., De Marco, O., Wood, P., Galaviz, P., & Passy, J.-C.2016b, MNRAS, 458, 832Taam, R. E., & Ricker, P. M. 2010, New Astron. Rev., 54, 65Turk, M. J., Smith, B. D., Oishi, J. S., et al. 2011, ApJS, 192, 9Tylenda, R., Hajduk, M., Kami´nski, T., et al. 2011, A&A, 528,A114Tylenda, R., Kami´nski, T., Udalski, A., et al. 2013, A&A, 555,A16Zhu, L.-Y., Zhao, E.-G., & Zhou, X. 2016, Research in Astronomyand Astrophysics, 16, 68MNRAS , 1–15 (2017) S. Shiber and N. Soker − − − y ( AU )
100 km/sec − − − z ( AU ) − − − z ( AU ) − − − − − − y ( AU ) − − − − − − − − − − − − D e n s i t y (cid:0) g c m (cid:1) − − − − − − D e n s i t y (cid:0) g c m (cid:1) − − − − − − D e n s i t y (cid:0) g c m (cid:1) T e m p e r a t u r e ( K ) Figure 15.
Comparison of the hydrodynamic properties of three runs at a final orbital separation of a = 0 .
67 AU, that are differ inthe in-spiral time t sp . All the other parameters are as in the fiducial run. The left column is for t sp = 1190 day, the middle columncontains plots of the fiducial run for which t sp = 595 day, and the right column presents plots for a simulation with t sp = 298 day. Thetop three rows show density and velocity maps in the orbital plane z = 0 (top row), in a plane that is perpendicular to the momentaryradius vector of the secondary star and perpendicular to the equatorial plane (second row), and in the meridional plane that containsthe center of the giant and the momentary location of the secondary star (third row). The bottom row shows temperature maps in theorbital plane. MNRAS000