Wind morphology around cool evolved stars in binaries: the case of slowly accelerating oxygen-rich outflows
AAstronomy & Astrophysics manuscript no. aa c (cid:13)
ESO 2020January 15, 2020
Wind morphology around cool evolved stars in binaries
The case of slowly accelerating oxygen-rich outflows
I. El Mellah , , J. Bolte , L. Decin , W. Homan , and R. Keppens Centre for mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven,Belgium Institute of Astronomy, KU Leuven, Celestijnenlaan 200D B2401, 3001 Leuven, Belgium e-mail: [email protected] Received ...; accepted ...
ABSTRACT
Context.
The late evolutionary phase of low and intermediate-mass stars is strongly constrained by their mass-loss rate, which is ordersof magnitude higher than during the main sequence. The wind surrounding these cool expanded stars frequently shows non-sphericalsymmetry, thought to be due to an unseen companion orbiting the donor star. The imprints left in the outflow carry information on thecompanion but also on the launching mechanism of these dust-driven winds.
Aims.
We study the morphology of the circumbinary envelope and identify the conditions of formation of a wind-captured diskaround the companion. Long-term orbital changes induced by mass-loss and mass transfer to the secondary are also investigated.We pay particular attention to oxygen-rich i.e. slowly accelerating outflows, in order to look for systematic di ff erences between thedynamics of the wind around carbon and oxygen-rich asymptotic giant branch (AGB) stars. Methods.
We present a model based on a reduced number of dimensionless parameters to connect the wind morphology to theproperties of the underlying binary system. Thanks to the high performance code
MPI-AMRVAC , we run an extensive set of 70 three-dimensional hydrodynamics simulations of a progressively accelerating wind propagating in the Roche potential formed by a mass-loosing evolved star in orbit with a main sequence companion. The highly adaptive mesh refinement we use enables us to resolve theflow structure both in the immediate vicinity of the secondary, where bow shocks, outflows and wind-captured disks form, and up to40 orbital separations, where spiral arms, arcs and equatorial density enhancements develop.
Results.
When the companion is deeply engulfed in the wind, the lower terminal wind speeds and more progressive wind accelerationaround oxygen-rich AGB stars make them more prone than carbon-rich AGB stars to display more disturbed outflows, a disk-likestructure around the companion and a wind concentrated in the orbital plane. In these configurations, a large fraction of the wind iscaptured by the companion which leads to a significant shrinking of the orbit over the mass-loss timescale, if the donor star is at leasta few times more massive than its companion. In the other cases, an increase of the orbital separation is to be expected, though at arate lower than the mass-loss rate of the donor star. Provided the companion has a mass of at least a tenth of the mass of the donorstar, it can compress the wind in the orbital plane up to large distances.
Conclusions.
The grid of models we compute covers a wide scope of configurations in function of the dust chemical content, theterminal wind speed relative to the orbital speed, the extension of the dust condensation region around the cool evolved star and themass ratio. It provides a convenient frame of reference to interpret high-resolution maps of the outflows surrounding cool evolvedstars.
Key words. stars: AGB and post-AGB binaries – (stars:) binaries: general – stars: winds, outflows – stars: evolution – accretion,accretion discs – methods: numerical
1. Introduction
As they evolve beyond the main sequence, low and intermediate-mass stars of initial masses ranging from 0.8 to 8 M (cid:12) are boundto expand and cool down. Along the red giant branch (RGB),the e ff ective gravity in the outermost layers drops and the mass-loss rate increases (Groenewegen 2012). During the subsequentasymptotic giant branch (AGB) phase, the mass-loss rate peaksat 10 − to 10 − M (cid:12) yr − , with terminal wind speeds of 5 to 20 kms − (Knapp et al. 1998; Habing & Olofsson 2003; Herwig 2005;Ramstedt et al. 2009). By the time they eventually become whitedwarfs, AGB stars lost 35 to 85% of their mass (Marshall et al.2004). The stars with an initial mass above ∼ M (cid:12) undergo aphase where they manifest as red supergiants (RSG, Levesque2010). Through their winds, cool evolved stars represent a ma-jor source of dust and molecular enrichment for the interstellarmedium (Groenewegen et al. 2002). Although the wind launch-ing mechanism remains largely unknown for RSGs, a dust-driven model proved successful for AGB stars (see Höfner &Olofsson 2018, for a recent and comprehensive review). The κ -mechanism excites radial pulsations which shoot out materialand provoke the formation of internal shocks within a coupleof stellar radii. The compressed gas cools down downstreamthe shocks until it reaches temperatures of 1 500 to 1 800K, lowenough to trigger the condensation of gaseous species into dustgrains which absorb the stellar radiation, accelerate and drag theambient gas (Liljegren et al. 2016; Freytag et al. 2017). Dur-ing their post-main sequence evolution, low and intermediate-mass stars experience several dredge-up events which bringfreshly formed carbon to the outer envelope and can turn orig- Article number, page 1 of 15 a r X i v : . [ a s t r o - ph . S R ] J a n & A proofs: manuscript no. aa inally oxygen-rich (O-rich) stars into carbon-rich (C-rich) stars(Straniero et al. 1997; Herwig & Austin 2004) with dramaticconsequences on the dust chemical content. Since the latter setsthe dust opacity, the wind acceleration profile strongly di ff ersaround O-rich and C-rich AGB stars: the low opacity of dustgrains formed from O-rich gaseous environments leads to amuch more progressive wind acceleration around O-rich AGBstars, where the wind reaches its terminal speed several tens ofstellar radii away from the donor star (Decin et al. 2010, 2018). Afull understanding of dust-driven winds emitted by cool evolvedstars requires a radiative hydro-chemical model of dust grainsgrowth in an environment generally out of thermodynamic equi-librium (Boulangier et al. 2019b).High spatial and spectral resolution instruments have shedan unprecedented light on the complexity of the astrochemistryat work in these cool winds. While the Hubble space telescopeushered in a new era of high-resolution imaging in the opticalwavelength range, the infrared space telescope Spitzer revealedhow diverse the wind properties can be around cool evolved starsin the Galaxy but also in the nearby small and large Magellanicclouds (Dell’Agli et al. 2015; Yang et al. 2018). The Hubblespace telescope captures the light scattered by the dust presentin large quantities in the inner regions of the wind but molecularline emission also contains invaluable information. The power-ful spectrometers aboard Herschel and the (sub)millimeter inter-ferometer ALMA granted us access to a plethora of rotationaland vibrational lines originating up to several thousands of as-tronomical units (au) away from the cool evolved star. Thanks tomulti-channel molecular emission maps, the kinematic structureof the circumstellar flow can be characterized, opening the doorto a full 3D reconstruction of the wind (Decin et al. 2018; Decin& Al. 2020).Significant non-spherical features in the wind of coolevolved stars have been identified thanks to these instruments,but also in the shape of planetary nebulae, which are thought tobe the descendants of RGB and AGB stars (Shklovsky 1956).Recurrent axisymmetric patterns appear around cool evolvedstars such as compressed structures (disks or tori, Bujarrabalet al. 2016; Kamath et al. 2016), polar cavities and spirals(Homan et al. 2018), but also arcs (Decin & Al. 2020). Al-though alternative explanations have been proposed (Nordhaus& Blackman 2006; Chi¸tˇa et al. 2008), the community has beenprogressively more inclined to attribute these features to thepresence of an unseen companion. The reason of this shift inopinion stems from observations as well as new population syn-thesis results (Moe & Di Stefano 2017). In a few systems wherenon-spherical imprints are observed in the circumstellar environ-ments, robust hints in favor of the presence of a companion haveemerged. In these systems, it is still questioned though whetherthe companion is close enough to be responsible for producingthese non-spherical features or if there is a third undetected ob-ject on a close orbit with the donor star. Around RGB stars withperiodically modulated luminosities, simultaneous monitoringof the Doppler shift and of the light curve proved that these vari-ations were due to the ellipsoidal deformation of the star due tothe presence of a companion on a close orbit (sequence E longperiod variables, Nicholls et al. 2010). Furthermore, the complexmorphology of the AGB wind in the Mira AB system has beenshown to be partly due to a companion on a ∼
500 years orbit(Ramstedt et al. 2014).The impact of binarity on stellar evolution can not be over-stated. Interactions in a close binary system modify the chemicalstratification within the star and alter the evolution of its spin viamass and angular momentum exchanges with the orbiting com- panion (De Marco & Izzard 2017). It has been shown to be akey-ingredient to understand Barium stars (Bidelman & Keenan1951), SNe Ia as descendants of symbiotic binaries (Claeys et al.2014), Carbon and s-process enhanced metal-poor stars (Abateet al. 2013) and blue stragglers in old open clusters (Jofré et al.2016). Classic Roche lobe overflow (RLOF) and wind accretionhave been shown to be the two limit mass transfer mechanismsof generally more complex configurations. Numerical hydrody-namics simulations enabled hybrid regimes such as wind-RLOFto be identified (Mohamed & Podsiadlowski 2007), which turnedout to be decisive to reconcile models and observations. They re-vealed enhanced mass transfer rates between the donor star, alsocalled the primary, and the accretor, also called the secondary(Abate et al. 2013), and the formation of wind-captured disksaround the secondary (Huarte-Espinosa et al. 2013; de Val-Borroet al. 2017).Grid-based and smooth particle hydrodynamics numericalsimulations also reproduced large scale features left by the sec-ondary in the wind of the donor star, such as arcs, spirals andcircumbinary disks, and evaluated the impact of the inclinationof the orbit with the line-of-sight (Mastrodemos & Morris 1999;Liu et al. 2017; Chen et al. 2018; Saladino et al. 2019; Kim et al.2019). However, the slow acceleration of O-rich outflows provedto be a challenging ingredient to account for, along with control-ling the amount of kinetic energy per unit mass provided to theflow by the radiative pressure on dust grains. Resolving both thewind launching scale and the whole circumbinary outflow re-quires highly adaptive grids whose geometry matches the oneof the outflow. As noted by Chen et al. (2017), spherical gridsrepresent good candidates to move forwards. This is why in thiswork, we developed a numerical framework based on a radiallystretched spherical mesh centered on the donor star. It highlyfacilitates the treatment of the wind launching, guarantees theconservation of angular momentum and limits numerical arti-facts introduced by the discretization of the equations (e.g. nu-merical di ff usivity). It also enables us to capture both the initialdeviation of the wind by the secondary and the shaping of thecircumbinary envelope up to several 10 orbital separations at acomputational cost so low that we can cover a wide range of real-istic sets of parameters. With the dimensionless parametrizationwe introduce, we can parametrically explore how the propertiesof the dust-driven acceleration and of the accreting companiondetermines the morphology of the outflow.In Section 2, we present a model based on an empirical windacceleration so as to reproduce a predefined velocity profile. Wealso identify the dimensionless parameters which determine theshape of the hydrodynamics solutions we solve in our numericalsetup. In Section 3, we report on the main results of our compre-hensive exploration of 70 configurations representative of C-richand O-rich AGB stars with an orbiting companion. It providesa grid of models spanning all the possible configurations whosemain properties are summarized and discussed in Section 4.
2. Model β -wind In this section, we describe how the wind is accelerated fromthe donor star. The wind launching does not depend on time andstellar pulsations are not included in the present model (see Chenet al. 2017, for a model with periodic modulations of the mass-loss rate through the radial outflow velocity). We use the classic β -wind velocity profile as a parametrization to compute the cor-responding radiative acceleration term for an isolated star. This Article number, page 2 of 15. El Mellah et al.: Wind morphology around cool evolved stars in binaries method guarantees that we control both the terminal speed andhow quickly the wind reaches it, contrary to previously used ap-proaches which parametrize directly the acceleration term: al-ternatives include winds undergoing reverted gravity (Kim et al.2019) or the free-wind model where radiation counterbalancesexactly gravity, leading to a constant wind speed (Liu et al. 2017)or a thermally-driven wind when thermal pressure is included(Saladino et al. 2019). An enforced β velocity profile alleviatesthe full radiative-hydrochemical computation required to deter-mine the acceleration profile, allowing us to explore the impactof a wide range of realistic acceleration profiles at an a ff ordablecomputational cost. We first validate our approach in the simplemost context: a pres-sureless purely radial wind in spherical geometry undergoinggravity and an outwards radiative force whose large amplitudejustifies that we neglect the pressure force which drives ther-mal winds (Lamers & Cassinelli 1999). These radiatively-drivenwinds are well described by a velocity profile called the β -law(Puls et al. 2008): v β ( r ) = v ∞ (1 − R / r ) β (1)where R is the distance to the stellar center where accelerationtriggers, v ∞ is the terminal wind speed and β is a positive expo-nent whose value determines how quickly the wind reaches itsterminal speed, with a more progressive acceleration for a largervalue of β . Around hot stars, Lucy & Solomon (1970) and Castoret al. (1975) designed a model which describes how the resonantline absorption of the many UV photons available by partly ion-ized metal ions provides momentum to the outer envelopes ofthe stellar atmosphere. These winds are said to be line-drivenand a physically-motivated analysis leads to the velocity profilein equation (1). Around AGB stars, wind launching is believedto be made possible thanks to pulsations which lift up materialup to a distance, the dust condensation radius R d , where the tem-perature is low enough and the density high enough owing to theshocks for dust to form. The subsequent radiative pressure forceof the continuum on the dust grains accelerate them and oncethey redistribute their momentum to the ambient gas throughdrag, a wind is launched (Höfner & Olofsson 2018). Aroundother types of cool evolved stars such as RSGs, the wind launch-ing mechanism remains largely unknown, although the observedvelocity profiles still reasonably match the aforementioned β -law(Decin et al. 2006).The terminal wind speed of radiatively-driven winds in-creases with the escape speed, which leads to much larger ter-minal speeds for hot stars ( ∼ − ) than cool evolvedstars ( ∼
10 km s − ). The acceleration starts very close from thephotosphere around hot stars while it only starts at the dust con-densation radius for winds of AGB stars. Depending on the stel-lar metallicity, the β exponent ranges between 0.5 and 2.5 forhot stars (Sander et al. 2017) while it varies much more for AGBstars depending on the chemical content. C-rich AGB stars leadto dust grains of high opacity, strongly accelerated by the stellarradiative field. The terminal speed is reached within a few stel-lar radii, which yields a β exponent as low as 0.1 (Decin et al.2015a). Due to the low opacity of the dust grains formed in theirmidst, winds surrounding O-rich AGB stars accelerate in a muchmore progressive way, with β exponents as high as 5 (Khouriet al. 2014).The implementation of this configuration in a uni-dimensional numerical setup leads to the stable profile repre- sented in Figure 1 (blue solid line). The initial condition is a flatdensity profile with zero-speed and the analytic solution is set atthe inner boundary condition located at 1.01 R . The accelerationsource term is given by v β d v β . This preliminary benchmark con-firms the validity of the solving schemes used later on in the full3D setup described in 2.3. β -wind A specific di ffi culty for numerical simulations of winds aroundO-rich AGB stars arises from the low wind speed up to largedistances. For C-rich AGB stars, the sonic point at radius R s isvery close from the dust condensation radius which ensures thatthe wind can safely be injected from r = R d at the sound speed orslightly above, as it has been done in previous simulations (Kimet al. 2019). It prevents spurious reflections of acoustic waves atthe injection border of the simulation box. For O-rich AGB starsthough, such a procedure requires more caution since the windmight remain subsonic up to several stellar radii.In case the β -law in equation (1) gives a subsonic wind speedat the inner edge of the simulation space, set at 1.2 R d , we need tomodify the β velocity profile such as the wind starts a few 0.01%above the local sound speed c s , s : v β, mod ( r ) = c s , s + ( v ∞ − c s , s )(1 − R d / r ) β (cid:48) (2)where β (cid:48) is computed such that the terminal radius remains un-changed. This fix is generally needed for O-rich stars but notfor C-rich stars. We compute the local sound speed assuming aradial temperature profile T ∝ r − . , in agreement with the obser-vations, a temperature at the dust condensation radius of 1,500Kand a fiducial mean molecular weight of 1 proton mass. An addi-tional argument in favor of the legitimacy of this approach comesFig. 1: Velocity profiles for a C-rich AGB star (solid blue line, β = .
1) and for an O-rich AGB star (solid red line, β = β -law such as the wind is launched at avelocity slightly above the sound speed at the inner edge of thesimulation space ( β (cid:48) ∼ . Article number, page 3 of 15 & A proofs: manuscript no. aa from simulations of the flow structure in the innermost parts, be-tween the stellar photosphere and the dust condensation radius.For instance, Freytag et al. (2017) performed simulations of theouter envelopes of AGB stars and found characteristic turbulentspeeds associated with Mach numbers of 2 to 3. A modified β ve-locity profile is represented in Figure 1 (red dashed line) whereit can be seen that even for very slowly accelerating winds, thediscrepancy with the classic β -law (red solid line) remains mod-erate. Hereafter, we write v β both for the standard and modified β -law, depending on whether a correction is needed or not. The aforementioned launching procedure guarantees that theright amount of kinetic energy per unit mass is progressivelyinjected into the wind, given a certain predefined velocity pro-file. The modeling of the full binary can now be described. Wework in the frame co-rotating with the two bodies, at the or-bital angular speed Ω , neglecting any eccentricity of the orbit. Tolimit the number of parameters, the star is assumed to have nospin since its significant radial expansion leads to a spin angularspeed much lower than the orbital angular speed Ω . Moreover,Saladino et al. (2019) studied the secular evolution of the spinof the AGB donors in binaries due to mass-loss and tidal inter-actions and concluded that the stellar spin was negligible in theAGB phase for orbital separations larger than 5 au. The strongdependency of the synchronization timescale on the ratio of thestellar radius to the orbital separation might, however, lead to fastspinning-up of the donor star when it gets close to fill its Rochelobe (Zahn 1977). We also discard gas self-gravity and the feed-back of the wind on the stellar masses and orbits, negligible overthe duration of our simulations.The fundamental equations of hydrodynamics which deter-mine the evolution of the stellar wind are the continuity equationand the conservation of linear momentum: ∂ t ρ + ∇ · ( ρ v ) = ∂ t ( ρ v ) + ∇ · ( ρ v ⊗ v + P ) = − ρ GM r r − ρ Ω ∧ ( Ω ∧ r ) − Ω ∧ ρ v + ρ v β d r v β r r (4)where ρ , v and P are the mass density, the velocity vector andthe pressure respectively, while G is the gravitational constant. is the diagonal unity 3 by 3 matrix, ⊗ is the dyadic product and ∧ is the cross product. The subscripts 1 and 2 refer to the donorstar and to the secondary object respectively, with M i the mass ofbody i and r i the position vector with respect to body i . Finally, r is the position vector with respect to the center of mass of the2 bodies. The first term on the right hand side of equation (4)represents the gravitational influence of the secondary object andthe second and third terms are the centrifugal and Coriolis forces.The last term includes the gravitational attraction of the donorstar and the radiative acceleration, as described in Section 2.1,with v β given by equation (1) or (2). The orbital angular speed Ω is related to M , M and the orbital separation a via Kepler’s 3 rd law. The coupling of the gas with the dust is encapsulated in thisradiative acceleration term.We need an additional equation to determine the evolution ofthe pressure entering equation (4). Ideally, this equation would account for the full thermodynamics of the problem and in par-ticular, for the heating by the stellar radiative field and re-emitingdust grains (Boulangier et al. 2019a,b) and for the electron andmolecular cooling mechanisms. Instead, we will rely on the fol-lowing polytropic prescription to close the system of equations: P = S ρ γ (5)where γ is the polytropic index and S is a constant which can berelated to the sound speed at the sonic point c s , s and the densityat the sonic point ρ s through S = c s , s / (cid:16) γρ γ − s (cid:17) .Physically, a polytropic index of 5 / / cooling (adiabatic hypothesis) while apolytropic index of 1 would mean that heating and cooling aree ffi cient enough to counterbalance any change of internal en-ergy due to expansion or compression respectively (isothermalhypothesis). To determine the suitable polytropic index to repro-duce the observed temperature profile of T ∝ r − . , we followthis reasoning: due to the polytropic assumption and the ideal gaslaw, T ∝ ρ γ − . In addition, due to mass conservation in sphericalgeometry, when the wind speed has reached the terminal speed, ρ ∝ r − . Consequently, a polytropic index γ = . R in = . R d with a density set by the sonic radius R s with respect to R in anda radial velocity given by the β -law, modified if needed. Thetoroidal component of the velocity vector is set by the absenceof spin of the donor star in the inertial frame of the observer.We rely on the following normalization, which reduces thenumber of parameters, needed to numerically compute the shapeof the solutions, to 5: – length: the condensation radius R d , – speed: the orbital speed a Ω , – density: the sonic point density ρ s , linked to the mass-lossrate.The 5 fundamental dimensionless shape parameters whichappear in the equations after normalization and entirely deter-mine all possible numerical solutions are: – the mass ratio q = M / M , – the dust condensation radius filling factor f = R d / R R , , with R R , the Roche lobe radius of the primary given by Eggleton(1983), – the ratio of the terminal to the orbital speed η = v ∞ / ( a Ω ), – the β exponent which sets the steepness of the velocity pro-file, – the ratio of the terminal speed to the sound speed at the dustcondensation radius v ∞ / c s , d .To identify the main dependencies of the wind morphologyon these parameters, we consider di ff erent values for these pa-rameters, representative of AGB binaries. We take mass ratiosof 1 and 10, for respectively an AGB star in orbit with a mainsequence solar-type companion and with a low-mass star or abrown dwarf companion. The filling factor varies much fromone system to another since both RGB and AGB donor starscan be large enough and / or the orbital separation can be smallenough such that the dust condensation region (or even the staritself) might fill the Roche lobe. We work with a filling factorof 5%, 20% and 80% to study the impact of the stellar expan-sion and / or the secular evolution of the orbital parameters on the Article number, page 4 of 15. El Mellah et al.: Wind morphology around cool evolved stars in binaries wind dynamics. To distinguish between the quickly acceleratedwinds of C-rich AGB stars and the slowly accelerating winds ofO-rich AGB stars, we consider β exponents of 0.1 and 5 respec-tively. The terminal wind speed compared to the orbital speedtakes 6 di ff erent values, 0.5, 0.8, 1.2, 2, 4 and 8. Given the lim-ited influence of the flow temperature quantified through the lastparameter, we set it to a realistic value and use c s , d = v ∞ / R (cid:63) ∼ ∼ ∼ − R (cid:63) exist (Sargent et al. 2011). The orbitalspeed a Ω varies widely, from 3 km s − for wide binaries contain-ing an AGB donor with orbital periods of the order of a few 1 000years and a binary mass of the order of 1 M (cid:12) , up to 15 km s − fora binary mass of 5 M (cid:12) and an orbital period as low as 50 years(for CW Leo, Decin et al. 2015b). For a particular class of RGBstars which manifest themselves as sequence E long period vari-ables, a companion is believed to be on a close orbit with typicalorbital periods of 100 days and orbital speeds a Ω of ∼
50 km s − (Nicholls et al. 2010). Finally, the stellar mass-loss rate ˙ M < ρ s = (cid:12)(cid:12)(cid:12) ˙ M (cid:12)(cid:12)(cid:12) π c s , s R s = (cid:12)(cid:12)(cid:12) ˙ M (cid:12)(cid:12)(cid:12) π c s , d R d (cid:32) R d R s (cid:33) . (6)where the last factor accounts for the radial temperature profileand ranges between 0.75 and 1 since R s ranges from R d (for aquickly accelerating wind) to 1.2 R d (for a slowly acceleratingwind corrected with the modified β -wind profile described inSection 2.1.2). The exponent 1.7 comes from the assumed radialtemperature profiles. For a realistic sound speed at the dust con-densation radius of ∼ − , a mass-loss rate from 10 − M (cid:12) yr − to 10 − M (cid:12) yr − and a dust condensation radius between2 and 5 times the typical stellar radius R (cid:63) ∼ · − g cm − and2 · − g cm − . As a reference, we report in Table 1 the physi-cal parameters deduced from observations for the classic C-richAGB star CW Leo (a.k.a. IRC + We solve the equations presented in the previous section usingthe finite volume code
MPI-AMRVAC (Xia et al. 2018). Our sim-ulation box is a spherical grid centered on the donor star andextending from 1 . R d up to 40 orbital separations, a distance atwhich ALMA can easily characterize the wind morphology forobjects up to several 100 parsecs. The polar axis of the meshis aligned with the orbital angular momentum vector and mirror-symmetry with respect to the orbital plane enables us to computethe solution only in the upper half of the spherical grid. Thanks tothe geometric increase of the radial size of the cells, we can uni-formly resolve the flow over a wide range of scales at an a ff ord-able computational cost (El Mellah et al. 2018). The coupling of Table 1: Parameters of the C-rich star CW Leo and its compan-ion. In the top part of the table, the results from Decin et al.(2015b) and Cernicharo et al. (2015) are reported, where bothteams essentially disagreed on the orbital period P, leading todi ff erent orbital speeds. In the second part, we give the corre-sponding normalization units in cgs. In the last part, we computethe corresponding dimensionless parameters.Decin +
15 Cernicharo + (cid:12) (cid:12) M (cid:12) (cid:12) R d ˙ M -1.5 · − M (cid:12) yr − -2 · − M (cid:12) yr − v ∞ − P 55 years 800 yearsa 25 au 100 auR d · cma Ω · cm s − · cm s − ρ s · − g cm − · − g cm − q 7 1 f ∼ β η ∼ ∼ cells. On the coarsest AMR level, we work with 64 cells in theazimuthal direction, from 0 to 2 π , and with 16 cells in the North-South direction, from 0 to π/
2. The number of cells in the radialdirection depends on the filling factor and mass ratios which setthe position of the outer boundary of the simulation space, at 40orbital separations. It typically ranges from 48 to 80 cells, whichguarantees an approximate aspect ratio of one-to-one in the or-bital plane.The initial conditions are the ones for an isolated donor starderived from the 1D case (see Section 2.1). To determine thephysical duration of each simulation, we compute the time re-quired for a purely radial wind to cross the simulation box, from1.2 dust condensation radii to 40 orbital separations, given thevelocity profile and notwithstanding the presence of the sec-ondary. The simulation duration is then set to 1.5 times this valuewhich typically amounts to 4 to 20 orbital periods. Notice that asimulation duration as low as 4 is enough for the wind to crossthe simulation space when the wind speed is much higher thanthe orbital speed. For winds with a lower terminal speed and amore progressive acceleration, a longer integration time is re-quired to enable the wind to develop and reach the permanentregime.We work with a minimum number of AMR levels of 4 andthe number of levels of refinement is set by the requirement thatthe accretion radius R acc is resolved with at least ∼
10 cells alongeach direction. The accretion radius characterizes the extent ofthe bow shock formed ahead of the secondary as it gravitation-ally focuses the supersonic wind from the primary (Edgar 2004).
Article number, page 5 of 15 & A proofs: manuscript no. aa
Since it is the critical region where the subsequent disks andlarge scale structures originate, we need to ensure that we re-solve it whatever the set of parameters we use. In the currentproblem, the accretion radius is given by: R acc = GM v β ( r = a ) (7)and its normalized value with respect to the dust condensationradius depends only on the 4 first shape parameters given atthe end of Section 2.2. The maximum number of AMR levelsneeded, typically for a low mass of the secondary ( q =
10) anda large terminal wind speed ( η = ff ect of thepresence of the secondary on the AGB wind morphology. Be-sides their expensive computational cost and the absence of largescale structures, these configurations do not lead to the formationof a wind-captured disk around the secondary due to the lowamount of angular momentum in the wind when it reaches thesecondary. These configurations yield very similar flow struc-tures than the planar Bondi-Hoyle-Lyttleton problem (Blondin& Raymer 2012; El Mellah & Casse 2015). Consequently, welower by a factor of 10 the duration of the 13 simulations out of72 which require strictly more than 6 levels of AMR. These sim-ulations do not lead to the formation of visible patterns, exceptin the immediate vicinity of the secondary, well within its Rochelobe, where a tail appears but becomes quickly indistinguishablefrom the ambient essentially spherical wind. Among the remain-ing 59 simulations, the coupled use of the radially stretched gridwith 4 to 6 levels of AMR leads to a wide dynamic range, witha ratio between the size of the lowest and highest resolution cellcorresponding to 8 to 11 levels of AMR if we had used a Carte-sian mesh.In order to solve the aforementioned equations of hydrody-namics, we use a 3 rd order HLL solver (Toro et al. 1994) with aKoren slope limiter (Vreugdenhil & Koren 1993). The equationshave been discretized such that angular-momentum is preservedto machine precision, as described in El Mellah et al. (2019a).The gravitational softening radius is set by the size of the higherresolution cells. Doing so, we ensure that the wind-captured diskformed around the secondary is well resolved, at least along itsradial extent and its outer regions.
3. Results
How does the presence of a companion star or brown dwarf al-ter the structure of the stellar wind from the donor star? Theinfluence of the secondary object is twofold. On one hand, itsgravitational influence induces an orbital motion for the primarywhich itself can generate a spiral shock in the wind (Kim & Taam2012b). And on the other hand, the gravitational pull of the sec-ondary on the wind focuses it and leads to the formation of adetached bow shock around the secondary. Depending on theamount of specific kinetic energy deposited in the wind com-pared to the Roche potential, the flow structure around the sec-ondary will either be essentially planar (Blondin et al. 1991) orwill embrace the more complex wind-RLOF configuration (Mo-hamed & Podsiadlowski 2011). Let us first examine the diversityof features which can emerge at large scale, in the circumbinarywind morphology. Fig. 2: 3D iso-density contours of a simulation of a C-rich donorstar with q = f =
80% and η = .
8. If R d = M = · − M (cid:12) yr − , the semi-transparent yellow surface sur-rounds a region where density is larger than 3 · − g cm − andwith a diameter of approximately 800 au. The arrow indicatesthe direction of the orbital angular momentum. A zoom-in onthe innermost region is provided in Figure 8. In the co-rotating frame where these simulations are ran, the or-bital motion of the primary around the center of mass manifestsitself through the centrifugal force. When the wind speed is lowenough compared to the orbital speed (i.e. for low values of the η parameter), the wind is significantly beamed into the orbitalplane. Without eccentricity, the flow remains essentially axisym-metric with respect to the donor star but a low density environ-ment develops o ff -plane.In Figure 2, three 3D iso-density contours have been repre-sented at a scale extending up to 40 times the orbital separation(with a zoomed-in version in Figure 8). Most of the wind is con-centrated in the orbital plane as shown by the semi-transparentyellow surface which represents an intermediate density. In red,within the black frame, the flow departs from axisymmetry dueto the gravitational influence of the secondary. It is the scale ofthe orbital separation, at which wind-RLOF mass transfer takesplace, and it is described in more detail in Section 3.2 where azoomed-in figure can be found.Recently, Decin et al. (2019) suggested that the measuredmass-loss rates of O-rich intermediate mass AGB stars coinedas OH / IR-stars could have been significantly overestimated be-cause of the underlying assumption that the wind was sphericallydistributed. This preliminary estimate relied on ballistic and hy-drodynamic simulations with prescribed acceleration profiles toreproduce di ff erent velocity laws (Kim & Taam 2012b; El Mel-lah & Casse 2017). Here, we introduce a factor to quantify theequatorial density enhancement (EDE) based on a subdivisionof the flow in 3 regions each spanning a range of co-latitudes of π/ – region A: within a co-latitude of π/ – region C: within a co-latitude of π/ – region B: in-between the twoOnce the flow has reached numerical equilibrium, we averagethe density in regions A and C (and over the 2 π longitudinal an-gles). Then, for each radius, we divide the obtained mean densitynear the orbital plane by the one near the axis and take the me-dian to obtain the EDE factor, represented in Figure 3. In order Article number, page 6 of 15. El Mellah et al.: Wind morphology around cool evolved stars in binaries
Fig. 3: EDE factors for each simulation as a function of η , theratio of the terminal wind speed to the orbital speed, for a dustcondensation radius filling factor of 5% (top) and 80% (bot-tom). The EDE factors as defined in the text evaluate how thewind is compressed in the orbital plane, with a value of 1 for aspherically symmetric flow. Di ff erent mass ratios (resp. β expo-nents) are represented with di ff erent marker shapes (resp. col-ors). The solid lines connect the points corresponding to O-richAGB donor stars. The top axis indicates the corresponding or-bital separation for a donor mass of 4 M (cid:12) , a terminal wind speedof 10 km s − (with a ∝ M / v ∞ ) and a mass ratio of 1 (in blue)and 10 (in orange).to relate this factor to the overestimation of the mass-loss rate,we compute the ratio between the column density of an isotropicwind with a density equal to the one computed in the region C,and the column density of a wind subdivided in the 3 uniformregions described above. The results are reported in Figure 4 anddepend on the inclination of the system with respect to the line-of-sight. The wind speed is assumed to be constant so as thedensity decays as r − and then, when the environment is opti-cally thin, the ratio of column densities is a good proxy for theratio of the measured mass-loss rate assuming spherical symme-try to the real mass-loss rate. We perform this computation forsystems seen face-on (in green) and edge-on (in red), and inte-grating along a line-of-sight either passing by the donor star oro ff set such as it intercepts the orbital plane (if face-on) or the Fig. 4: Ratio of the mass-loss rate deduced from assuming spher-ical symmetry to the real mass-loss rate, as a function of the EDEfactor for a system seen face-on (resp. edge-on) in green (resp.red). The solid and dashed lines are for an integration along aline-of-sight passing by the donor star and o ff set respectively.orbital axis (if edge-on) with an impact parameter of ∼
10 dustcondensation radii.In Figure 4, we retrieve that a EDE factor of unity is asso-ciated to a ratio of 1 (i.e. no overestimation, the real value ofthe mass-loss rate is obtained). The error remains under a fac-tor of 3 if the system is seen face-on. The error increases muchfaster with the EDE factor for systems seen edge-on (approxi-mately proportionally). This computation shows that significantoverestimates can occur even for EDE factors as low as a few.The detailed evaluation of the actual overestimation depends onthe density profile assumed (Homan et al. 2015, 2016) and onthe diagnostics used (either molecular lines or dust emission).As expected, for circumbinary envelopes essentially spheri-cal, the EDE factor is close to 1. However, the EDE factor can bemuch larger when most of the mass is concentrated in the orbitalplane. The latter case does occur for realistic parameters. Themost direct conclusion we can draw from Figure 3 is the quickincrease in the compression of the flow as soon as the termi-nal wind speed gets slightly smaller than the orbital speed. Theexact position of the threshold in η depends on the other param-eters: the transition occurs at larger values of η for a lower massratio and a larger filling factor. While the former evolution cor-responds to a larger gravitational influence of the secondary, thelatter yields less room for the wind to accelerate which makes thewind more prone to be shaped by the orbital motion. For a massratio of 10 and a filling factor of 5%, the wind remains sphericalwith a compression factor below 10 for a terminal wind speedas low as half of the orbital speed (orange markers in top panelin Figure 3). Notice however that such a low ratio η can onlybe reached in extreme cases, when the orbital period is shorterthan a few years (for instance sequence E long period variablesNicholls et al. 2010) or when the wind is anomalously slow.A general trend to keep in mind is that once the terminalwind speed is slow enough compared to the orbital speed, thecompression in the orbital plane is much more e ffi cient for adust condensation filling factor of 80% (bottom panel) than 5%(top panel). This is due to the fact that the wind speed at theorbital separation can be very low for large filling factors sincethe acceleration only starts shortly before the wind reaches the Article number, page 7 of 15 & A proofs: manuscript no. aa secondary. But once η (cid:38)
2, the compression of the flow is in-sensitive to the filling factor and to the chemical content of thedust.Furthermore, these results show that when the filling factorof the dust condensation radius is lower than 10%, little di ff er-ence should be expected between the compression of the windaround C-rich and O-rich AGB stars. Indeed, by the time itreached the secondary, the dust-driven wind had time to almostfully reach its terminal wind speed. In this configuration, pro-vided a C-rich and an O-rich AGB stars have the same ratio η of the terminal wind speed to the orbital speed, the morphologyof their circumbinary envelope should be similar and no system-atic di ff erence should exist. Biases could only be due to di ff erentmass ratios between the donor star and the secondary compan-ion. On the contrary, at low η and for a dust condensation ra-dius which extends up to 80% of the Roche lobe radius of theprimary (bottom panel in Figure 3), the circumbinary envelopearound an O-rich star is more prone to be compressed in the or-bital plane than for a C-rich star due to the slow acceleration ofO-rich winds.Eventually, it must be noticed that up to a parameter η of 2, aEDE factor of 3 to 8 can subsist when the secondary is massiveenough ( q (cid:46)
10) and / or when the filling factor is large enough.This implies that mass-loss rate estimates assuming a 1D geom-etry might significantly overestimate the actual mass-loss rateif the used diagnostic is sensitive to the equatorial density en-hancement. As discussed by Decin et al. (2019), mass-loss ratesbased on dust diagnostics are sensitive to the EDE, while low-excitation CO lines observed with large beams are more reliabletracers of the mass-loss rate even in the case of binary interac-tion. An additional concern is that the accretion of a fractionof the outflow by the secondary might lower the mass-loss ratemeasured at larger distance (up to ∼ Spiral arms are a recurrent pattern around cool evolved starssuch as the C-rich AGB stars R Sculptoris (Maercker et al. 2012;Homan et al. 2015) and AFGL3068 (Kim et al. 2017). Arcs havealso been observed as broken rings in protoplanetary nebulae byRamos-Larios et al. (2016) for instance. They have been pro-posed to originate from expanding outflows collimated in the or- bital plane and could be the manifestation of spiral arms seenedge-on (Kim et al. 2019).The numerous 3D simulations we performed bring a uniqueopportunity to disentangle between the intrinsic characteristicsand the apparent di ff erences induced by the random inclinationof the system with respect to the line-of-sight. In these simu-lations, the spiral shocks in the wind are always seeded in thevicinity of the secondary. However, at large scale, the details ofthe flow structure around the secondary do not impact the shapeof the circumbinary envelope which is determined by the dimen-sionless parameters listed in Section 2.2.A spiral shock is defined by its density enhancement, pitchangle and vertical extension. The pitch angle is the angle be-tween the spiral and the local direction of the circular orbit,with larger pitch angles for more radial spirals (see angle rep-resented in the right panel in Figure 5). The larger the pitch an-gle, the larger the ratio of the inter-arm separation to the orbitalseparation. When the terminal wind speed is larger than the or-bital speed, the pitch angle increases quickly with η (see Kim& Taam 2012a, for a semi-analytic formula of the locus of thespiral) although the density contrast and vertical extent eventu-ally vanish. In Figure 5, we represented slices in the orbital planeof the density of 3 simulations with a large terminal wind speedcompared to the orbital speed, similar to what Cernicharo et al.(2015) found for CW Leo ( η = β exponent. However, the more progressive acceleration of theO-rich AGB star (central panel) blurs the spiral shock which be-comes less visible. On the other hand, a C-rich AGB donor star(left panel) can feature a sharp hollow spiral. In the right panel,we represented a zoom-in on the region where the shock firstforms, for a simulation with a large filling factor C-rich donorstar and a higher resolution than the two other panels. A stronginstability sets in which propagates along the shock up to largescales. The stability of the Bondi-Hoyle-Lyttleton flow in 3D hasbeen a long-debated question (see Foglizzo et al. 2005, for anoverview of the numerical simulations). Di ff erent types of insta-bilities which can be triggered have been identified such as (i)the flip-flop instability, susceptible to produce alternatively coand counter-rotating wind-captured disks but seemingly absentFig. 5: Logarithmic density maps in the orbital plane for 3 simulations with q = η =
4. (left panel) C-rich donor star with f = f = f = Article number, page 8 of 15. El Mellah et al.: Wind morphology around cool evolved stars in binaries from 3D simulations (Ru ff ert 1999; Blondin & Raymer 2012),and (ii) the advective-acoustic instability (Foglizzo et al. 2006),extensively studied in spherical geometry. Here, we do not carryout the detailed analysis of the origin of this instability but no-tice its quick growth and its capacity to perturb the flow at largescale.When the terminal wind speed becomes lower than the or-bital speed, the pitch angle significantly decreases as the spiralgrows: the wind is not provided enough kinetic energy per unitmass by the stellar radiative field to overcome the attraction ofthe Roche potential ( η (cid:46) η =
1, with respect to the zero-speed slice in themolecular line emission maps of CW Leo by Cernicharo et al.(2015). In contrast, using η = ff erence comes from our sim-plified treatment of the cooling, based on a polytropic prescrip-tion, which does not capture the enhanced cooling e ffi ciency inthe highest density regions, contrary to the more physically real-istic cooling mechanism Chen et al. (2017) rely on.The flow structure is largely di ff erent when seen edge-on.Since its compression in the orbital plane has been describedin detail in Section 3.1.1, let us focus here on the arcs whichemerge as the η parameter decreases. In Figure 7, we show thedensity map of the same simulation as the right panel in Fig-ure 5 but seen from another viewpoint. It is a slice containing theorbital angular momentum vector and the axis joining the twobodies, with the secondary lying on the left of the primary. Witha EDE factor of ∼
3, the wind compression in the orbital planeis hardly visible by eye in the density distribution. However, themonitoring of the local mass-loss rate (i.e. per unit solid angle)and its comparison with the isotropic one reveals alternating ex-cesses and deficit (respectively white and green dashed lines) ofmore than 20%. They are essentially due to an enhanced den-sity and have opposite phase on the two sides of the secondary.If non-linear e ff ects are triggered in these regions such as dustcondensation (Boulangier et al. 2019b), these regions might stillbe visible for an η parameter as large as 4. Otherwise, we haveto turn towards lower values of η such as in the bottom panel inFigure 9. It represents only the inner region but arcs appear inthe flow as slices of a spiral propagating outwards (see top panelin the same figure) and spreads to much larger distances. Fig. 6: Slice in the orbital plane of the gas density (logarithmicscale), after 20 orbital periods. This simulation is for a C-richdonor star with q = f =
20% and η = .
8. An animatedversion can be found in the supplementary material.Fig. 7: Edge-on view of the simulation in the right panel in Fig-ure 5. The green and white dashed contours represent respec-tively 20% deficit and excesses in the local mass-loss rate withrespect to the isotropic case.
Roche lobe overflow is a well-known mass transfer mechanismwhich leads to the formation of a narrow stream of material flow-ing through the inner Lagrangian point. As the material falls to-wards the secondary object, it acquires enough angular momen-tum to form a large and permanent disk within its Roche lobe(see e.g. Frank et al. 1986). Here, we look at a somewhat lessextreme case since most cool evolved stars with undetected peri-odic velocity modulation along the line-of-sight are expected tohave an orbital separation large enough to currently not fill theirRoche lobe. At the other end of the possible mass transfer mech-anisms lies wind accretion, based on the theory of planar accre-tion of a supersonic flow by a point-mass (section 8.1 in El Mel-lah 2016). In our simulations, this regime is an accurate represen-
Article number, page 9 of 15 & A proofs: manuscript no. aa tation of the configurations when the wind speed is much higherthan the orbital speed when the wind reaches the secondary (i.e.low f and high η ). But for wind speeds of the order of the orbitalvelocity, the wind is strongly beamed towards the secondary andwe find a third type of mass transfer called wind-RLOF (Mo-hamed & Podsiadlowski 2007). Due to the large stellar mass-loss rate and to the focusing of the wind in the orbital plane, asignificant mass transfer enhancement can take place comparedto the two other regimes. It has been suggested to explain theorigin of the excess in barium of some carbon-enhanced metal-poor stars (Abate et al. 2013) but also for the high mass accretionrates needed to reproduce the luminosity of some ultra-luminousX-ray sources (El Mellah et al. 2019b).Our simulations reproduce the main features associated tothe wind-RLOF mechanism: the enhanced mass transfer and theformation of a wind-captured disk around the accretor. In Fig-ure 9, we show how the wind is strongly shaped by the grav-itational potential of the two orbiting bodies in the innermostregions of a wind emitted by an O-rich AGB star. In this config-uration, the wind is so slow when it reaches the secondary thatthe accretion radius is of the order of the Roche lobe radius ofthe secondary, a clear signature of wind-RLOF. The top panelis a slice in the orbital plane, associated to a face-on view, whilethe bottom panel represents a transverse slice containing the sec-ondary object (on the right of the primary). The velocity field,like in all figures in this paper, is the one in the inertial observerframe. While it remains essentially radial around the donor starbeyond a few orbital separations, a high vorticity indicative ofa wind-captured disk arises in the vicinity of the secondary, onthe right of the AGB donor in the top panel in Figure 9. Noticethe di ff erences between the flow structure in the top panel of thisfigure or in the zoom in 3D representation in Figure 8, and in theright panel in Figure 5 where the wind was much faster with re-spect to the orbital speed: for the slower wind in Figures 8 and9, the accretion radius gets larger than the Roche lobe radius.The flow gains enough angular momentum to form a permanentwind-captured disk of maximal extension (Paczynski 1977) anda wide spiral with a low pitch angle in the wake of the accretor.Furthermore, the wind is now strongly beamed into the or-bital plane as visible in the bottom panel in Figure 9. O ff theplane, the wind fails to take o ff and falls back, leading to a sig-nificant increase in the density scale compared to the configu-rations where the wind remains essentially isotropic (e.g. Fig-ure 7). Within this compressed flow, the spiral visible in the up-per panel deploys and seen edge-on, it manifests with alternatingarcs of higher and lower density.The presence or not of a wind-captured disk around thesecondary shares another connection with observations. Indeed,provided the secondary has a magnetic field large enough, theaccretion of matter might not only change the spin of the sec-ondary but also lead to significant outflows (Zanni & Ferreira2013). Depending on how collimated they are and on the incli-nation of the magnetic field with respect to the orbital angularmomentum axis, it could participate in the shaping of the lowdensity o ff -plane environment. In this part, we report on the fraction of wind which eventuallymanages to escape the binary system. Due to the preliminary ex-pansion of the donor star, we neglect its spin compared to themuch larger orbital angular momentum but Chen et al. (2018)carried out a detailed analysis of the orbital shrinking / wideningwhere they also account for spin-orbit synchronisation. The sec- Fig. 8: Zoom in on the central region in Figure 2 (black frame)where the donor is a C-rich star and q = f =
80% and η = . R d = M = − M (cid:12) yr − , in semi-transparent yellowis represented the 3D iso-density surface ρ = · − g cm − andin red, the surface ρ = · − g cm − . The inner boundary of thesimulation space is visible in dark red in the right part and thevelocity field in the orbital plane has been represented.ular change of orbital angular momentum induced by the mass-loss of the primary can only provoke a widening or a shrinkingof the orbit, sometimes at a rate much higher than the mass-lossitself. Constraining the angular momentum loss is a necessarystep to perform binary population synthesis and evaluate whichfraction of the systems will undergo a common envelope phase(Ricker & Taam 2012) or produce a Type Ia supernova (Iben,I. & Tutukov 1984; Webbink 1984). Here, given the large stellarmass-loss rate and the large orbital separation, additional sourcesof orbital angular momentum loss or gain (e.g. magnetic braking,gravitational waves and stellar expansion) are believed to be mi-nor. If we assume that all the wind either leaves the system oris accreted by the secondary, we have the following evolution ofthe orbital period P (Tauris & van den Heuvel 2003):˙ PP = ˙ M M (cid:34) α + q + q (1 − (cid:15) )1 + q − − (cid:15) q ) (cid:35) = ˙ M M (cid:34) q (1 − α ) − α q − − α )1 + q (cid:35) (8)where α is the fraction of the wind which escapes the systemwhile (cid:15) is the fraction of wind captured by the secondary (a.k.a.the accretion e ffi ciency). The last expression is obtained using α + (cid:15) =
1. Since ˙ M is always negative (the donor star loosesmass), the sign of the term within brackets decides whether theorbit shrinks (if positive) or widens (if negative). In Figure 10,we represented the opposite of the term within bracket which,sign apart, stands for the ratio of two characteristic time scales:the amount of time for the star to loose a given fraction of itsmass to the amount of time for the orbital separation to be mod-ified by the same fraction. In Appendix A and for comparisonwith other numerical results, we provide the reader with the samegraphics for the orbital period and the orbital speed. Article number, page 10 of 15. El Mellah et al.: Wind morphology around cool evolved stars in binaries
Fig. 9: (top panel) Logarithmic density map in the orbital plane of the innermost region of the wind. The arrows in white representthe velocity field while the black lines indicate the streamlines in the vicinity of the secondary where a wind-captured disk develops.In solid white is the contour of the Roche potential with the value at the innermost Lagrangian point. (bottom panel) Side-view ofthe same density map, with the secondary object on the right of the inner boundary (the red sphere of radius 1.2 dust condensationradius). The velocity field has been represented in the upper half while the mesh and its di ff erent levels of refinement are visible inthe bottom half. This simulation is for an O-rich donor star with q = f =
80% and η = . Article number, page 11 of 15 & A proofs: manuscript no. aa
The mass-loss rate ˙ M is highly variable during the evolutionof AGB stars, with short episodes of enhanced mass-loss, up to10 − M (cid:12) yr − , separated by quiescent phases where the mass-lossrate is of the order of 10 − M (cid:12) yr − (Bloecker 1995). In this con-text, the reader should keep in mind that the time scales involvedin the ratio represented in Figure 10 are bound to change by or-der of magnitudes during the AGB phase and should be thoughtas instantaneous rates of change. Within the grey shaded region,the rate of change of the orbital separation is lower than the rateof change of the mass of the donor star while elsewhere, for agiven relative change of the donor mass by a certain fraction,the orbital separation changes by more than this fraction (i.e.the orbital separation evolves "faster" than the donor mass). Notsurprisingly, for a mass ratio q = M / M lower than unity, theorbital separation evolves slowly. Indeed, since most of the massis now in the secondary, the total mass remains fairly constant asthe primary looses mass and the impact of the mass-loss on theorbit is limited.The two asymptotic cases are the black dotted line (RLOF, (cid:15) =
1) and the solid blue line (free wind, α = q ∼
1, a purely conservative masstransfer (i.e. (cid:15) = α =
0) is prone to provoke a faster contrac-tion of the Roche lobe radius than of the stellar radius (D’Souzaet al. 2005). The positive feedback loop provokes the quick in-spiral of the two bodies and the system enters a common enve-lope phase, although properly accounting for the stellar internalstructure pushes the critical mass ratio to a few (Pavlovskii et al.2017; Quast et al. 2019). These results are consistent with thepresent framework when mass transfer is only partly conserva-tive ( α <
1, black dotted line, red and green solid lines in Fig-ure 10): we retrieve in Figure 10 that there is always a criticalmass ratio beyond which the mass transfer yields a quick inspi-ral of the system (compared to the mass-loss time scale). Theless conservative the mass transfer, the larger this critical massratio.We measure α by computing the mass-loss rate at 10 orbitalseparations and comparing it to the mass-loss rate at the inneredge of the simulation space, representative of the stellar mass-loss rate. In Figure 11, we plotted (cid:15) = − α as a function ofthe main parameter, the ratio η of the terminal wind speed to theorbital speed. Beyond η =
1, the accretion e ffi ciency remainsinvariably smaller than 5%. Negative values are due to unsteadi-ness and uncertainties in the numerical computation, of the orderof a few percent. This uncertainty precludes any quantitative pre-diction, but relying on Figure 10 provides insightful predictions.According to these results, for a mass ratio inferior to 10, a ter-minal wind speed larger than the orbital speed means that theorbital separation remains essentially unchanged over the mass-loss time scale M / ˙ M (although the orbital period might in-crease significantly, see upper panel in Figure A.1). In the sameway, even for η <
1, the orbital evolution of binaries where thedonor star is a C-rich AGB stars ten times more massive thanthe secondary (orange squares) can only be modest, and so is theorbital evolution of O-rich AGB stars with q =
10 provided thedust condensation filling factor is smaller than ∼
20% (orangecircles in the upper panel). For f = η < ffi ciency ofseveral 10%. Provided the mass ratio is large ( q larger than afew), the orbital separation quickly decays until the mass ratiois low enough to enter the gray shaded region in Figure 10. Theassociated quick increase of the orbital speed, still for q largerthan a few, will enhance the phenomenon by lowering η and in- Fig. 10: Rate of orbital separation change compared to the rateof stellar mass change. In the grey shaded region, the mass ofthe donor star changes faster than the orbital separation whileabove (resp. below) the orbit expands (resp. contracts). The twolimit cases are conservative mass transfer (dotted line, RLOF)and pure mass-loss without accretion by the secondary (solidblue line). In-between, the green and red solid lines are for anaccretion e ffi ciency by the secondary of 5% and 50% respec-tively. The arrows indicate that as mass transfer proceeds, themass ratio can only decrease.creasing the accretion e ffi ciency (cid:15) . In the same way, even for alow filling factor, a massive secondary object ( q =
1) will cap-ture a significant fraction of the stellar wind but due to the lowmass ratio, Figure 10 indicates that the orbit will only marginallychange over a mass-loss characteristic time scale.
4. Discussion & summary
With our numerical setup, we recover a wide variety of observedcircumstellar morphologies produced by the presence of a lowermass companion around a mass loosing cool evolved star. Weshow that the main parameter driving the wind dynamics is theratio η of the terminal wind speed to the orbital speed, althoughsignificant di ff erences can arise between C-rich and O-rich starsfor η ∼ η of 0.5 realistic only if theorbital period is lower than a decade. Assuming the orbital an-gular momentum changes only due to the outflow from the cool Article number, page 12 of 15. El Mellah et al.: Wind morphology around cool evolved stars in binaries
Fig. 11: Fraction (cid:15) of the wind captured by the secondary (accre-tion e ffi ciency) as a function of the ratio η of the terminal windspeed to the orbital speed for a dust condensation radius fillingfactor of 5% (upper panel) and 80% (lower panel). Square (resp.circular) markers are for C-rich (resp. O-rich) AGB stars. Blue(resp. orange) markers are for mass ratios q = q = – a terminal wind speed smaller than the orbital speed – a mass ratio larger than a few – a dust condensation region which extends up to several 10%of the primary Roche lobe radiusIn the other cases, the system will undergo a variation of theorbital separation of lower relative change than the stellar masschange, either an orbit widening or shrinking depending on themass ratio and on the fraction of stellar wind captured by thesecondary. Accounting for eccentricity will likely modify theseconclusions. Eccentric orbits have been commonly observed forsystems with large orbital separations (i.e. large values of η ),in agreement with the long circularization time scales expected(Zahn 1977). Its e ff ect on the wind morphology has been thor-oughly reported on in Kim et al. (2015), Kim et al. (2017) and Kim et al. (2019) but to our knowledge, its impact on the orbitalangular momentum remains to be investigated.In the configurations where q ∼ η (cid:46) η soa slice in the orbital plane of the simulation should be represen-tative of a face-on view. Interestingly enough, these successivearcs in the orbital plane appear in spite of the steadiness of themass-loss rate, without any burst nor pulsation. The spacing be-tween them is of the order of a few orbital separations at the outeredge of our simulation box and expands self-similarly with thedistance to the donor star in the outer regions.Unfortunately, the long orbital periods of binaries contain-ing a cool evolved star preclude any monitoring of the rate ofchange of the orbital period. But in systems with shorter orbitalperiods such as supergiant X-ray binaries and ultra-luminous X-ray sources, this rate has been measured (see e.g. Falanga et al.2015). The mass ratio can then be constrained using the wob-bling motion of the two bodies projected along the line-of-sight(see e.g. Quaintrell et al. 2003) or the timing of the neutron starpulses (Fürst et al. 2018). Together, they bring strong constraintson the wind fraction (cid:15) captured by the secondary and can beconfronted to the mass accretion rates deduced from the X-rayluminosity.This paper introduces a convenient framework to imple-ment new e ff ects. In particular, the spherical mesh centeredon the donor star opens the door to the addition of a key-ingredient: matter-radiation interaction. In this paper, we sim-ply parametrized the wind acceleration to identify archetypalconfigurations. A subset of configurations can now serve as thebedrock for more realistic simulations where additional physi-cal e ff ects are introduced such as the growth of dust grains andtheir coupling with the stellar radiative field. Thanks to the lowcomputational cost of each simulation and to innovative schemesto treat parabolic and elliptic equations recently implemented in MPI-AMRVAC (Teunissen & Keppens 2019), we can start to ex-plore radiative e ff ects.Radiation is not only a decisive actor in the launching andsubsequent carving of the wind but also our main source of infor-mation on these systems. The advent of high-resolution imageryin (sub)millimeter wavelengths brought up the pressing need toproduce synthetic observables to be confronted with. Each ofthe simulations we performed, which contain the information onthe temperature, gas density and velocity 3D distribution, cannow be post-processed to produce dust infrared and molecular-line emission maps for di ff erent inclinations, either with Monte-Carlo radiative transfer code such as SKIRT (Baes et al. 2011;Camps & Baes 2015), RADMC-3D (Dullemond et al. 2012)or SPARX (Kim et al. 2013), but also with new-generation raysolvers such as Magritte (De Ceuster et al. 2019). Acknowledgements.
The authors wish to thank the atomium
ALMA Large Pro-gramme collaboration (2018.1.00659, PI. L. Decin) for the observational con-sequences of the present analysis. IEM has received funding from the ResearchFoundation Flanders (FWO) and the European Union’s Horizon 2020 researchand innovation program under the Marie Skłodowska-Curie grant agreement No665501. LD, JB and WD acknowledge support from the ERC consolidator grant646758 AEROSOL. The simulations were conducted on the Tier-1 VSC (Flem-ish Supercomputer Center funded by Hercules foundation and Flemish gov-
Article number, page 13 of 15 & A proofs: manuscript no. aa ernment). RK is supported by Internal Funds KU Leuven, project C14 / / References
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Appendix A: Appendix A: orbital separationchanges due to mass-loss
If the orbital separation increases as the system looses mass, theorbital period increases, and if the orbital period decreases asthe system looses mass, the orbital separation decreases. How-ever, mixed cases can occur. Since the total mass of the sys-tem diminishes, if the orbital separation decreases slowly, theorbital period can increase. Comparing Figure 10 and the upperpanel in Figure A.1 confirms that when the mass ratio is such that(˙ a / a ) / ( − ˙ M / M ) is negative (i.e. the orbit is shrinking) but closeto zero, the orbital period can still be increasing. The net e ff ecton the orbital speed is visible in the bottom panel in Figure A.1. Fig. A.1: Rate of change of the orbital period (upper panel) andorbital speed a Ω (bottom panel) compared to the rate of stellarmass change. In the grey shaded region, the mass of the donorstar changes faster than the orbital period or speed. The two limitcases are conservative mass transfer (dotted line, RLOF) andpure mass-loss without accretion by the secondary (solid blueline). In-between, the green and red solid lines are for an accre-tion e ffi ciency by the secondary of 5% and 50% respectively. Thearrows indicate that as mass transfer proceeds, the mass ratio canonly decrease.ciency by the secondary of 5% and 50% respectively. Thearrows indicate that as mass transfer proceeds, the mass ratio canonly decrease.