Three-dimensional simulations of the interaction between the nova ejecta, the accretion disk, and the companion star
Joana Figueira, Jordi Jose, Enrique Garcia-Berro, Simon W. Campbell, Domingo Garcia-Senz, Shazrene Mohamed
aa r X i v : . [ a s t r o - ph . S R ] D ec Astronomy&Astrophysicsmanuscript no. 31545 c (cid:13)
ESO 2018August 21, 2018
Three-dimensional simulations of the interaction between the novaejecta, the accretion disk, and the companion star
Joana Figueira , , Jordi Jos´e , , Enrique Garc´ıa-Berro , , Simon W. Campbell , , , Domingo Garc´ıa-Senz , , andShazrene Mohamed , , Departament de F´ısica, EEBE, Universitat Polit`ecnica de Catalunya, c / Eduard Maristany 10, E-08930 Barcelona, Spain Institut d’Estudis Espacials de Catalunya, c / Gran Capit`a 2-4, Ed. Nexus-201, E-08034 Barcelona, Spain Departament de F´ısica, Universitat Polit`ecnica de Catalunya, c / Esteve Terrades 5, E-08860 Castelldefels, Spain Max-Planck-Institut f¨ur Astrophysik, Karl-Schwarzschild-Strasse 1, D-85748 Garching bei M¨unchen, Germany School of Physics and Astronomy, Monash University, Clayton 3800, Victoria, Australia Monash Centre for Astrophysics (MoCA), Monash University, Clayton 3800, Victoria, Australia South African Astronomical Observatory, PO Box 9, Observatory Rd., 7935 Cape Town, South Africa Astronomy Department, University of Cape Town, 7701 Rodenbosch, South Africa South Africa National Institute for Theoretical Physics, Private Bag X1, Matieland, 7602 Stellenbosch, South Africae-mail: [email protected]
August 21, 2018
ABSTRACT
Context.
Classical novae are thermonuclear explosions hosted by accreting white dwarfs in stellar binary systems. Material pilesup on top of the white dwarf star under mildly degenerate conditions, driving a thermonuclear runaway. The energy released bythe suite of nuclear processes operating at the envelope (mostly proton-capture reactions and β + -decays) heats the material up topeak temperatures ranging from 100 to 400 MK. In these events, about 10 − − − M ⊙ , enriched in CNO and, sometimes, otherintermediate-mass elements (e.g., Ne, Na, Mg, Al), are ejected into the interstellar medium. Aims.
To date, most of the e ff orts undertaken in the modeling of classical nova outbursts have focused on the early stages of theexplosion and ejection, ignoring the interaction of the ejecta, first with the accretion disk orbiting the white dwarf, and ultimately withthe secondary star. Methods.
A suite of three-dimensional, SPH simulations of the interaction between the nova ejecta, the accretion disk, and the stellarcompanion have been performed to fill this gap, aimed at testing the influence of the di ff erent parameters (i.e., mass and velocity ofthe ejecta, mass and geometry of the accretion disk) on the dynamical and chemical properties of the system. Results.
We discuss the conditions that lead to the disruption of the accretion disk and to mass loss from the binary system. Inaddition, we discuss the likelihood of chemical contamination of the stellar secondary induced by the impact with the nova ejecta andits potential e ff ect on the next nova cycle. Key words. (Stars:) novae, cataclysmic variables — nuclear reactions, nucleosynthesis, abundances — hydrodynamics
1. Introduction
The coupling of spectroscopic determinations of chemical abun-dances, photometric studies of light curves, and hydrodynamicsimulations of the accretion, expansion and ejection stages, hasbeen instrumental in our understanding of the nova phenomenon.The scenario envisaged assumes a white dwarf star hosting theexplosion in a close binary system (see, e.g., Sanford 1949, Joy1954, and Kraft 1964, for some of the first systematic observa-tions that revealed the binary nature of novae). The low-mass,main sequence stellar companion (frequently, a K-M dwarf, al-though observations increasingly support the presence of moreevolved companions in some systems) overfills its Roche lobe,and matter flows through the inner Lagrangian point of the sys-tem. A fraction of this hydrogen-rich matter lost by the sec-ondary spirals in via an accretion disk and ultimately piles upon top of the white dwarf (typically, at a rate ∼ − − − M ⊙ yr − ). The accreted envelope layers get gradually compressedby the continuous matter infall under mildly degenerate con-ditions. Compressional heating initiates nuclear reactions and Send o ff print requests to : J. Jos´e a thermonuclear runaway ensues. The thermonuclear origin ofnova explosions was first theorized by Schatzman (1949, 1951).This was followed by a number of significant contributions inthe 1950s and 1960s (see, e.g., Cameron 1959, Gurevitch &Lebedinsky 1957), including pioneering attempts to mimic theexplosion through the coupling of radiative transfer in an opti-cally thick expanding shell with hydrodynamics (Giannone &Weigert 1967, Rose 1968, Sparks 1969).To date, most of the e ff orts undertaken in the modeling ofnova outbursts have focused on the early stages of the explo-sion and ejection (see Starrfield, Iliadis & Hix 2008, 2016, Jos´e& Shore 2008, and Jos´e 2016, for recent reviews). Therefore,key aspects of the evolution of these systems, associated withthe interaction of the ejecta, first with the accretion disk orbit-ing the white dwarf, and ultimately with the secondary star, havebeen largely unexplored . Shortly after the outer layers of thewhite dwarf expand and achieve escape velocity, a fraction of the Note, however, that a similar scenario, the interaction between thematerial ejected in a type Ia supernova and the companion star, has beenaddressed in a number of papers (see, e.g., Marietta, Burrows & Fryxell2000, and Garc´ıa-Senz, Badenes & Serichol 2012). J. Figueira et al.: 3D simulations of the interaction between the nova ejecta and the binary system ejected material is expected to collide with the secondary star. Asa result, part of the nova ejecta will mix with the outermost lay-ers of the secondary. The resulting chemical contamination mayhave potential implications for the next nova cycle, once masstransfer from the secondary resumes.Novae are also prolific dust producers. Infrared (Evans &Rawlings 2008, Gehrz 1998, 2008) and ultraviolet observations(Shore et al. 1994) have unambiguously revealed dust formingepisodes in the ejected shells accompanying some nova out-bursts, about ∼
100 days after the explosion. In fact, it hasbeen suggested that novae may have contributed to the in-ventory of presolar grains isolated from meteorites. A majorbreakthrough in the identification of nova candidate grains wasachieved by Amari et al. (2001, 2002), who reported severalSiC and graphite grains, isolated from the Murchison and Acfer094 meteorites, with abundance patterns qualitatively similar tothose predicted by models of nova outbursts: low C / C and N / N ratios, high Si / Si and close-to-solar Si / Si ratios,and high Al / Al and Ne / Ne ratios. However, to quantita-tively match the grain data, mixing between material synthesizedin the explosion and more than ten times as much unprocessed,isotopically close-to-solar material was required. The collisionof the ejecta, either with the accretion disk or with the secondarystar, may naturally provide the required chemical dilution to ex-plain the reported grain data.Moreover, the unexpected discovery of very high-energyemission ( >
100 MeV), first observed in the symbiotic binaryV407 Cygni (Abdo et al. 2010), and subsequently detected ina number of novae (e.g., V407 Cyg, V1324 Sco, V959 Mon,V339 Del, V1369 Cen), by the Large Area Telescope on boardthe Fermi γ -ray space observatory (Fermi LAT), has also beenlinked to shock acceleration in the ejected shells after interac-tion with a wind from the secondary . This has confirmed novaeas a distinct class of γ -ray sources (Ackermann et al. 2014).All the abovementioned aspects stress the need for a thor-ough description of the dynamics of the system after the novaexplosion, following the collision of the ejecta with the accre-tion disk, and subsequently, with the secondary star. The presentpaper aims at filling this gap. The manuscript is organized as fol-lows. The method of computation, the input physics, and the ini-tial conditions adopted are described in Sect. 2. A full accountof the di ff erent 3D simulations of the interaction of the ejectawith the accretion disk, and ultimately with the main sequencecompanion, is presented in Sect. 3. The e ff ect of the di ff erent pa-rameters on the stability of the accretion disk as well as on theamount of mass lost from the system is also analyzed in Sect. 3.Discussion on the expected level of chemical contamination ofthe outer layers of the secondary star is given in Sect. 4. A sum-mary of the most relevant conclusions of this paper is presentedin Sect. 5. Di ff usive shock acceleration of electrons and protons, with a max-imum energy of a few TeV, was predicted by Tatische ff & Hernanz(2007), in the framework of the 2006 outburst of the recurrent nova RSOphiuchi. See also Shore et al. (2013) for an explanation of the originof X-ray emission in Nova Mon 2012 based on internal shocks drivenby the collision of filaments that freeze out during expansion.
2. Model and input physics
The 3D computational domain of the simulations discussed inthis paper includes the white dwarf that hosts the nova explo-sion, the expanding nova ejecta, the accretion disk, and the mainsequence companion. The white dwarf is modelled as a 0.6 M ⊙ point-like mass, whichis enough to account for its gravitational pull on the system. Theexpanding ejecta, which at the beginning of the 3D simulationsis located between 0.65 R ⊙ (inner edge) and 0.72 R ⊙ (outer edge)from the underlying white dwarf, has a mean metallicity of Z = .
54, and a mass, density and velocity profiles corresponding tothe values computed with the 1D code
SHIVA (see Sect. 2.2, fordetails).
A 1 M ⊙ , solar metallicity, main sequence companion is adoptedas the secondary. The star has spherical symmetry and is builtin hydrostatic equilibrium conditions. A polytropic equation ofstate with γ = / ∼ R ⊙ of the secondary, the outermost ∼ R ⊙ (0.15 M ⊙ ) of the star have been taken into account. Therest of the star has been replaced by a point-like mass located atits center. To generate the initial 3D particle distribution of theouter main sequence layers, the initial 1D density profile is slicedinto several shells of equal radius. For each shell, a ‘glass’ tech-nique has been implemented (White 1996): in essence, a cube isfilled with a random number of particles until a uniform distri-bution is achieved, from which a shell with constant density isextracted. The same procedure is used for each shell at di ff erentdensities and has also been adopted for the accretion disk and theejecta (assuming in this case axial symmetry). The initial den-sity profile for the outer main sequence layers is shown in Fig.1. For convenience, and to guarantee good accuracy in the inter-polated functions, all SPH particles used in this work have thesame mass, ∼ − M ⊙ . One can easily infer the number of SPHparticles within each mass shell from its total mass. About 3.8million SPH particles have been used to model the outer ∼ . R ⊙ (0.15 M ⊙ ) of the secondary. To guarantee that the resulting3D structure is in hydrostatic equilibrium, the stellar secondaryis relaxed for a total time of the order of 20 orbital periods. The accretion disk that orbits the point-like white dwarfin Keplerian rotation is modeled according to the Shakura- The presence of a disk, and its key role in the simulations reportedin this paper, does not allow us to rely on SPH axisymmetric codesto increase resolution of the models, in constrast to other astrophysicalscenarios such as type Ia supernovae (see, e.g., Garc´ıa-Senz, Badenes& Serichol 2012).. Figueira et al.: 3D simulations of the interaction between the nova ejecta and the binary system 3
Table 1: Models computed.
Model M ejecta M disk V maxejecta H / R Disk( M ⊙ ) ( M ⊙ ) (km s − ) disruptionA 5 . × − . × − .
03 YesA hres a . × − . × − .
03 YesB 5 . × − . × −
800 0 .
03 YesC 5 . × − . × − .
03 NoD 5 . × − . × −
800 0 .
03 NoE 1 . × − . × − .
03 YesF 1 . × − . × −
800 0 .
03 YesG 5 . × − . × − .
06 NoH 1 . × − . × − .
06 YesI 5 . × − . × − .
03 NoJ 5 . × − . × − .
06 YesK 5 . × − . × − .
06 Yes a Model computed with twice the number of particles than Model A. −4 −3 −2 −1 ρ [ g c m − ] MS R [ R ⊙ ]10 −7 −⊙ −5 −4 −3 ρ [ g c m − ] Accretion Disk
Fig. 1: Initial density profiles for the outer main sequence layers (after relaxation) and the accretion disk.Sunyaev, V-shaped disk solution (Shakura & Sunyaev 1973,Frank, King & Raine 2002). In the fiducial model reported inthis paper (hereafter, Model A; see Table 1) a solar-compositiondisk, with a mass of 2 × − M ⊙ , and a geometry given by a ratioof height to radius of H / R = .
03, has been assumed (see Sects.3.4 and 3.5, for the e ff ect of these parameters on the simulations).Other models of accretion disks (e.g., flared disks) and inclusionof alternative assumptions (smaller extended disks; see Warner2003) will be addressed in a future paper —see Puebla, Diaz &Hubeny (2007), for a comparison between current disk modelsand observational data. In this work, the accretion disk containsonly a few thousand SPH particles, being the truly limiting fac-tor of the simulations (the nova ejecta contains up to 19,000 SPHparticles). The sound-crossing time throughout the disk is ∼ ∼ The first stages of the evolution of the nova outbursts, throughaccretion, expansion, and ejection, have been modeled by meansof the 1D, spherically symmetric, Lagrangian, hydrodynamiccode
SHIVA (see Jos´e & Hernanz 1998, and Jos´e 2016, fordetails). When the inner edge of the ejecta reached a size of0.65 R ⊙ , the structure was mapped onto a 3D domain, thatincluded as well the white dwarf that hosts the nova explo-sion, the accretion disk, and the main sequence companion.The evolution of the system was subsequently followed withthe 3D smoothed-particle hydrodynamics (SPH) code GADGET-2 (Springel, Yoshida & White 2001, Springel & Hernquist 2002,Springel 2005). This parallelized, explicit, Lagrangian, mesh-free code describes fluids in terms of a set of discrete elements(hereafter, particles). Their continuous properties (e.g., density,temperature, velocity) are obtained through kernel interpolationand summation over all neighboring particles. In the simula-tions presented in this paper, a cubic spline kernel has beenadopted. To handle shocks,
GADGET-2 uses the artificial viscos-ity prescription developed by Monaghan (1997), together witha viscosity-limiter for pure shear flows (Balsara 1995). In addi-
J. Figueira et al.: 3D simulations of the interaction between the nova ejecta and the binary system
Table 2: Mass (ejecta plus disk) gravitationally bound to the secondary star, ∆ M MS , and to the white dwarf, ∆ M WD , and total massleaving the binary system, ∆ M esc , together with their fractions (in %) over the total ejecta plus disk masses, after collision with thenova ejecta. ∆ M MS , lost is the mass lost by the main sequence star in the interaction with the nova ejecta. Model ∆ M MS ( M ⊙ ) ∆ M WD ( M ⊙ ) ∆ M esc ( M ⊙ ) ∆ M MS ( M ejecta + M disk ) ∆ M WD ( M ejecta + M disk ) ∆ M esc ( M ejecta + M disk ) ∆ M MS , lost ( M ⊙ )A 1 . × − . × − . × − × − A hres . × − . × − . × − . × − B 2 . × − . × − . × − . × − . × − . × − . × − D 6 . × − . × − . × − . × − E 5 . × − . × − . × − . × − F 9 . × − . × − . × − . × − G 5 . × − . × − . × − × − H 6 . × − . × − . × − . × − I 2 . × − . × − . × − . × − J 1 . × − . × − . × − . × − K 5 . × − . × − . × − tion, the code computes gravitational interactions using a hier-archical oct-tree algorithm (Barnes & Hut 1986). Time steps arecontrolled by means of a Courant factor taken as 0.15. The grav-itational softening of the SPH particles has been approximatedby their smoothing lengths. It is worth noting that GADGET-2 en-ables density contrasts since it o ff ers adaptive smoothing lengths(Springel & Hernquist 2002).The characteristic size of the overall binary system, for agiven set of values of the masses of the primary and secondarystars, is determined by the orbital period. In the simulations re-ported in this work, a value of P orb = . P orb > ∼
12 times longer than the timeit takes for the ejecta to reach and hit the main sequence com-panion. The e ff ect of the Coriolis and centrifugal forces has alsonot been considered. They introduce angular momentum andviscous-shear dissipation, which may a ff ect the trajectories ofsome of the ejecta particles as they travel toward the secondary.Such e ff ects will be addressed in a future manuscript.
3. Results: Disk stability and mass loss
Observations suggest that the accretion disk does not always getdisrupted by a nova outburst . Indeed, in some systems, the pres-ence of a disk has been confirmed only a few months / years afterthe explosion (see, e.g., Leibowitz, Mendelson, & Mashal 1992,Retter, Leibowitz, & Kovo-Kariti 1998, Retter, Leibowitz, &Ofek 1997, Skillman et al. 1997, Hernanz & Sala 2002), whichis clearly at odds with the typical timescales required for a diskto assemble (of the order of decades). It has been suggested thatthe accretion disk is only disrupted if the system is an interme-diate polar (Retter 2003). In those systems, the magnetic fieldcould truncate the inner regions of the disk, which would be lessmassive than in non-magnetic systems, and therefore, prone tobe disrupted by a nova explosion. However, it is worth notingthat the mass and the mean density of such disks are also poorlyconstrained quantities from an observational viewpoint.To elucidate the possible e ff ect of the nova outburst on theaccretion disk, a suite of models aimed at testing the influence See, however, Drake & Orlando (2010), for simulations of recurrentnova systems leading always to full disruption of the accretion disks. of the di ff erent parameters of the system (i.e., mass and velocityof the ejecta, mass and geometry of the accretion disk) have beenconsidered (see Table 1). Model A describes the interaction between M ejecta = . × − M ⊙ , ejected from a 0.6 M ⊙ white dwarf during a nova outburst(with a maximum velocity of the ejecta of V maxejecta = − ), and a 2 × − M ⊙ accretion disk (with H / R = M ⊙ main sequencecompanion (see Table 1). Snapshots of the evolution of thismodel, in terms of density, are displayed in Fig. 2. Movies show-ing the full evolution of this model are available online and at .The ejecta hits the disk a few seconds after the beginningof the simulation (Fig. 2, upper panels). The energy releasedduring the collision heats the disk, which achieves a maximumtemperature of h T maxdisk i ∼ . × K, with only a handful of SPHparticles ( ∼
20) reaching T max ∼ . × K. This suggests thatnuclear reactions do not play a relevant role in the interaction .Only a small fraction of the nova ejecta hits the disk ( m ′ ejecta ∼ M ejecta ), with a mean kinetic energy, K = m ′ ejecta V ∼ × ergs. A crude estimate of the gravitational binding energy ofthe disk can be obtained from U ∼ GM WD M disk / r mean , where G is the gravitational constant, M WD is the mass of the underlyingwhite dwarf, and M disk and r mean are the mass of the disk and themean distance between the white dwarf and the disk. Estimatesfor Model A yield U ∼ × ergs, which is similar to thekinetic energy of the impinging ejecta. In Model A, simulationsreveal the total disruption of the disk (middle left panel), whichgets totally swept up and mixed with the ejecta. However, othermodels with di ff erent choices for the geometry ( H / R ), mass, andvelocity of the disk, and mass of the ejecta, may yield di ff erentoutcomes (see below).At about t ∼
17 min (middle panels), a mixture of ejectaand disk material impinges on the main sequence companion.The temperature increases slightly in the outermost layers ofthe secondary, but not enough to spark nuclear reactions. In thecollision, a subset of the ejecta / disk particles penetrate throughthe outer layers of the secondary, reaching a maximum depth of ∼ . × − M ⊙ from the surface. The energy released in the The same conclusion applies to all models reported in this paper.. Figueira et al.: 3D simulations of the interaction between the nova ejecta and the binary system 5
MS WDEjectaAccretionDisk-6 -4 -2log density [g/cm ] Fig. 2: Cross-sectional slice in the binary orbital plane (XY) showing the density of Model A at di ff erent stages ofthe interaction between the nova ejecta and the accretion disk, subsequently followed by a collision with the main se-quence companion. A movie showing the full evolution of this model, modelA-XY.mov , is available online and at . See also modelA-YZ.mov , for a movie depicting the evolutionof the system from a side view (YZ plane). Snapshots and movies have been generated by means of the visualisation softwareSPLASH (Price 2007).collision drives a moderate expansion of the outer layers of thestar (lower panels). Since the secondary overfills its Roche lobe,part of the material incorporated into the main sequence star willbe later re-accreted by the white dwarf, as soon as mass-transferresumes and the accretion disk is re-established.About ∼ . × − M ⊙ (i.e., 88% of the mixture of diskand nova ejecta) leave the binary system in Model A. In con-trast, only ∼ × − M ⊙ (3.7%; mostly nova ejecta) remaingravitationally bound to the main sequence companion, while ∼ . × − M ⊙ (8.7%) are bound to the white dwarf (see Table2). A small amount of mass, 2 × − M ⊙ , involving only a hand-ful of SPH particles, is expelled from the outer main sequencelayers in the interaction with the nova ejecta. Figure 3 shows thetime evolution of the mass leaving the binary system in ModelA, and for all models reported in this paper. The early and sharpincrease in mass loss ( t ≤
10 min) results from the interactionbetween the nova ejecta and the disk, when the latter gets totallyswept up and mixed with the former. Most of the ejecta and diskmixture leaves the binary system. The longer-term evolution of the mass loss plot ( t >
10 min) reveals that little is expelled fromthe outer main sequence layers as a result of the impact with thenova ejecta.To test the feasibility of these results, a higher resolutionrun with twice the number of particles than Model A (here-after, Model A hres ) was also performed. As shown in Table2 (see also Fig. 3), both models A and A hres yield similarresults, which suggests that the overall number of particlesadopted in this paper was appropriate. Movies showing thefull evolution of Model A hres are also available online and at . Two values for the mass of the nova ejecta, M ejecta , have beenconsidered to analyze the e ff ect of this parameter. As shown inTable 2, a comparison between our fiducial Model A (character-ized by M ejecta = . × − M ⊙ ) and Model E (with M ejecta = . × − M ⊙ ) reveals that, as expected, increasing the mass of J. Figueira et al.: 3D simulations of the interaction between the nova ejecta and the binary system
Fig. 3: Time evolution of the mass leaving the binary system for the di ff erent models reported in this paper.the ejecta translates into larger masses gravitationally bound tothe white dwarf ( ∆ M WD ) and to the main sequence companion( ∆ M MS ), at the end of the simulations. In turn, the total amountof mass lost from the system, ∆ M esc , also increases. An identicalpattern is found when comparing Models B and F (for which amaximum velocity of the nova ejecta of V maxejecta =
800 km s − hasbeen assumed) and Models G and H ( V maxejecta = − , buttwice the mass of the disk compared to Model A), with an excep-tion: whereas the accretion disk gets fully disrupted in Models A,B, E, F, and H, it survives the collision with the ejecta in ModelG (Fig. 4). This can be understood from the ratios M ejecta / M disk adopted in the di ff erent models: the lowest value, M ejecta / M disk ∼
13, corresponds to Model G, which suggests that only disks withmasses much lower than the ejecta undergo total disruption. Thefact that the disk gets disrupted in Model H but not in Model Ga ff ects the dynamics of the system and results in a moderatelylarger amount of mass that remains bound to the white dwarfin the former. Except for such peculiar case, the fraction of theoverall mass available (i.e., ejecta plus disk) that escapes the bi-nary system (or remains bound to the main sequence or to thewhite dwarf) does not depend much on the choice of the mass ofthe nova ejecta (see Table 2). Note, indeed, that the fraction ofmass leaving the system increases from 59% to 89%, while thefraction that remains bound to the white dwarf drops from 31%to 8%, when comparing Models G and H. As reported for ModelA, small amounts of mass, up to 1 . × − M ⊙ , involving only afew SPH particles, are expelled (if any) from the outer main se-quence layers in the interaction with the nova ejecta, with valuesincreasing for larger nova ejected masses. Three values for the maximum velocity of the ejecta, V maxejecta , rep-resentative of classical nova systems (Gehrz et al. 1998), havebeen adopted to analyze the influence of this parameter: 800 kms − , 1200 km s − , and 3000 km s − . Comparison between ModelsA and B reveals that an increase in the velocity of the ejectayields larger ejected masses from the binary system, while re- ducing the amount of mass that remains gravitationally bound,either to the white dwarf or to the main sequence companion.The fraction of nova ejecta plus disk mass that escapes thebinary system (or remains bound to the main sequence or to thewhite dwarf) follows exactly the same trend. However, in sharpcontrast to the results reported in Section 3.2, the specific frac-tions depend significantly on the values adopted for the velocityof the ejecta (Table 2). For instance, the fraction of mass leavingthe system increases from 60% to 89%, while the fractions thatremain bound to the white dwarf or to the main sequence dropfrom 30% to 8%, and from 10% to 4%, respectively, when com-paring Models D and I. Similar patterns are observed regardlessof whether the disk gets disrupted or not (see, e.g., Models C,D and I, Models E and F, and Models G and J, for which dif-ferent combinations of masses of the ejecta and disk have beenadopted). Larger velocities for the nova ejecta drive, as expected,larger (but always tiny) amounts of mass lost by the main se-quence companion, with a maximum value of 2 . × − M ⊙ achieved in Model I.It is worth mentioning that while the accretion disk isdisrupted in Models A, B, E and F, it survives the impactwith the ejecta in all models characterized by moderatelylow M ejecta / M disk ratios (e.g., Models C, D, I, and G, with M ejecta / M disk ranging between 5.5 and 13). Note, however, thatModel J, characterized by M ejecta / M disk =
13, results in disk dis-ruption too. This is caused by the large kinetic energy and mo-mentum carried by the impinging ejecta, which in this particularmodel expands with a maximum velocity of 3000 km s − . The mass of the accretion disk that orbits around the whitedwarf is a poorly constrained quantity. Accordingly, a series ofdisks with di ff erent masses, constructed in the framework of theShakura & Sunyaev model, have been considered. Comparisonbetween Models A and C, for which two di ff erent values of themass of the disk, M disk , have been adopted (2 × − and 10 − M ⊙ , respectively) reveals, as mentioned before, that the lower themass of the disk, the larger the probability of disruption. Hence, . Figueira et al.: 3D simulations of the interaction between the nova ejecta and the binary system 7 -6 -4 -2log density [g/cm ] Fig. 4: Same as Fig. 2, but for density plots corresponding to Model G at di ff erent times. Note that in this model the accretiondisk does not get totally swept up in the impact with the nova ejecta. Snapshots and movies have been generated by means of thevisualisation software SPLASH (Price 2007).while the disk in Model A gets disrupted by the nova blast, itsurvives the impact in Model C. The same pattern is found forModels B and D, characterized by a lower expansion velocity ofthe nova ejecta (800 km s − ), and Models K and G, for which adi ff erent geometry of the disk, with a larger H / R ratio, was as-sumed. Increasing the mass of the accretion disk reduces in turnthe amount of mass lost by the binary system (and conversely,increases the amount of mass that remains gravitationally boundto the white dwarf and to the main sequence companion) .The fraction of nova ejecta plus disk mass that escapes thebinary system (or remains bound to the main sequence or to thewhite dwarf) follows the same pattern, with values showing aclear dependence on the accretion disk mass. Note, however, that Models K and G result in nearly identicalejected masses from the binary systems. This may partially result fromthe di ff erent geometry of the disks adopted and from the smaller rangeof values for the masses (a factor of 2 in Models G - K, versus a factorof 5 in Models A - C and B - D). So far, we have analyzed the interaction of the nova ejectawith accretion disks characterized by a height to radius ratio of H / R = .
03. However, observations increasingly support a dis-persion in the value of H / R , within the range 0.03 – 0.1 (seeMaccarone 2014; Shafter & Misselt 2006; Knigge et al. 2000).The influence of this parameter on the dynamical properties ofthe system has been analyzed by means of Model K, in whicha ratio of H / R = .
06 has been adopted for the accretion disk.Comparison between Model K and our fiducial Model A sug-gests that an increase in H / R has a similar e ff ect as a reduc-tion in the velocity of the expanding nova ejecta: here, a larger H / R results in an increase of the e ff ective impact cross-sectionbetween disk and ejecta. This decelerates a larger fraction ofthe ejecta, and as a result, the amount of mass gravitationallybound to the white dwarf and to the main sequence companionincreases, while the overall mass lost from the binary system de-creases. The fraction of nova ejecta plus disk mass that escapesthe binary system (or remains bound to the main sequence orto the white dwarf) follows exactly the same trend. A thoroughcomparison between Models A and K reveals that the specific J. Figueira et al.: 3D simulations of the interaction between the nova ejecta and the binary system fractions depend significantly on the adopted H / R ratio (Table2).
4. Chemical pollution of the secondary star
One of the possible outcomes of the dynamical interaction be-tween the nova ejecta and the main sequence companion is thepollution of the secondary, enhancing the metal content of itsouter layers. The degree of contamination induced by the impactwith the nova ejecta can be estimated from the overall numberof particles gravitationally bound to the main sequence star (see,e.g., Lombardi et al. 2006). But this is by no means straight for-ward. On the one hand, the models presented in this work fol-low the evolution of the binary system for about 3000 s, whichcorresponds to ∼ . P orb . At this stage, a large number of par-ticles gravitationally bound to the secondary are still orbitingaround in a corona that surrounds the star. Even though such par-ticles will eventually fall into the star, it is di ffi cult to anticipatehow deep these particles will penetrate into its envelope. Self-consistent calculations of these advanced stages would requirea prohibitively intense computational e ff ort for many orbital pe-riods to compute the corresponding infalling trajectories. Andeven if such numerical simulations would be feasible, a detailedaccount of the chemical profiles of the outer layers of the sec-ondary would require the use of more realistic initial models forthe main sequence star (see, e.g., Sills & Lombardi 1997) and theinclusion of important physical mechanisms that would be op-erating simultaneously (i.e., chemical di ff usion, convection...).This is clearly out of the scope of the present paper. However, toillustrate the expected levels of chemical pollution, we have pro-vide some crude estimates of the compositional changes in theouter layers of the secondary at di ff erent mass depths, for ModelA. Assuming that all the gravitationally bound particles still inorbit will be incorporated and mixed with the outer 10 − M ⊙ ofthe main sequence companion, a mean metallicity of Z ∼ . Z ∼ .
036 for 10 − M ⊙ ,and Z ∼ .
019 for 10 − M ⊙ ).A final issue involves the relevance of these results in theframework of systems with low-mass secondaries ( M ≤ M ⊙ ),in which the presence of a convective envelope may wash outany trace of chemical pollution induced by the impact with thenova ejecta. This aspect has been addressed by Marks & Sarna(1998) and Marks, Sarna & Prialnik (1997), who analyzed thee ff ect of re-accretion of material ejected during nova outburstson the chemical evolution of the secondary, for binary systemswith similar orbital periods and masses to those reported in thismanuscript. The low-mass main sequence stars were evolvedtaking into account all major processes that may a ff ect their sur-face composition: nuclear reactions, mass loss, convection, ther-mohaline mixing, and contamination with the nova ejecta. Usinga control model, where no nova ejecta was incorporated into thesecondary, they reported elemental (e.g., C and N) and isotopicdi ff erences ( C / C, N / N, O / O) on the surface layersof the secondary stars induced by the impact with the ejecta.Therefore, one may expect some e ff ect on the next nova cycle,once mass transfer onto the white dwarf component resumes,even in binaries with low-mass secondaries. This aspect, how-ever, deserves in-depth analysis.
5. Conclusions
Eleven 3D SPH simulations of the interaction between the novaejecta, the accretion disk, and the stellar companion have beencomputed, aimed at testing the influence of the di ff erent param-eters (i.e., mass and velocity of the ejecta, mass and geometryof the accretion disk) on the dynamical and chemical propertiesof the binary system. The main conclusions reached in this workare summarized as follows: – We have investigated the conditions leading to the disruptionof the accretion disk that orbits the white dwarf star. In 7out of the 11 models computed, the disk gets fully disruptedand swept up. In all these models, the disks are character-ized by masses much smaller than that of the ejecta. Oursimulations show that in models with V-shaped disks withheight-to-radius ratios of H / R = .
03 and M ejecta / M disk ≤ . M ejecta / M disk ≤
13, for H / R = .
06) the disk survives theimpact with the nova blast. – Small amounts of mass, up to 1 . × − M ⊙ are expelledfrom the outer main sequence layers in the interaction withthe nova ejecta. No ejection is reported from 2 out of the 11models computed. – An increase of the mass of the nova ejecta yields, in general,larger amounts of mass lost by the binary system, and largermasses gravitationally bound to the white dwarf and to themain sequence companion. The fraction of the overall massavailable (i.e., ejecta plus disk) that escapes the binary sys-tem (or remains bound to the main sequence or to the whitedwarf) does not depend much on the choice of the mass ofthe nova ejecta. However, the dynamics of the system is in-fluenced by disk disruption when the increase of the mass ofthe nova ejecta modifies the stability of the disk, moderatelya ff ecting the distribution of masses that remain gravitation-ally bound to the white dwarf or to the main sequence, aswell as the amount of mass lost from the system. For in-stance, when comparing Models G (disk partially disrupted)and H (disk fully disrupted and swept up by the ejecta), thefraction of mass that leaves the binary system increases from59% to 89%, while the fraction that remains bound to thewhite dwarf drops from 31% to 8%. – An increase in the velocity of the ejecta results in largerejected masses from the binary system, while reducing theamount of mass that remains gravitationally bound, eitherto the white dwarf or to the main sequence, regardless ofwhether the disk gets disrupted or not. This results from thelarger kinetic energy and momentum carried by the imping-ing ejecta when its velocity is increased. The fraction of novaejecta plus disk mass that escapes the binary system (or re-mains bound to the main sequence or to the white dwarf)follows exactly the same trend. The specific fractions dependmuch on the values adopted for the velocity of the ejecta. Thelarge kinetic energy and momentum carried by the ejecta inmodels with V max e jecta = − can lead to disk disruptioneven for models characterized by relatively low M ejecta / M disk ratios, as in Model J. – An increase of the mass of the accretion disk reduces theamount of mass lost by the binary system, and conversely,increases the amount of mass gravitationally bound to thewhite dwarf and to the main sequence companion. For in-stance, when comparing Models A ( M disk = . × − M ⊙ )and C ( M disk = . × − M ⊙ ), the fraction of mass thatleaves the binary system decreases from 88% to 67%, whilethe fractions that remain bound to the white dwarf and to themain sequence star increase from 9% to 25%, and from 4% . Figueira et al.: 3D simulations of the interaction between the nova ejecta and the binary system 9 to 8%, respectively. This results from the smaller kinetic en-ergy and momentum transferred to the disk particles per unitmass when the mass of the disk is increased, which in turnreduces the probability of disk disruption by the nova blast. – An increase in the height-to-radius ratio of the disk has sim-ilar e ff ects to a reduction of the velocity of the expandingejecta: the larger e ff ective impact cross-section between diskand ejecta slows down a larger fraction of the nova ejecta,which in turn increases the mass gravitationally bound to thewhite dwarf and to the main sequence star, while reducingthe overall mass lost by the binary system. – A certain level of chemical contamination of the stellar sec-ondary is induced by the impact with the nova ejecta (witha mean metallicity of Z ∼ .
18 estimated at the outer 10 − M ⊙ layers in the hemisphere hit by the ejecta, for Model A).This may have potential e ff ects on the next nova cycle.Since the problem is intrinsically three-dimensional we can-not rely on 2D or axisymmetric approximations. A possible wayto increase the resolution is to use a conical 3D computationaldomain, with the point-like white dwarf located at the vertex ofthe cone, so that only a fraction of the ejecta and disk, togetherwith the full stellar secondary, are taken into account. The ex-pected gain in resolution could reach a factor of ∼
2, with ∼ Acknowledgements.
The authors would like to thank RubenM. Cabez´on, for many fruitful discussions and exchanges. Thiswork has been partially supported by the Spanish MINECOgrant AYA2014–59084–P, and by the AGAUR / Generalitat deCatalunya grant SGR0038 / References
Abdo, A. A., Ackermann, M., Ajello, M., et al., 2010, Science, 329, 817Ackermann, M., Ajello, M., Albert, A., et al., 2014, Science, 345, 554Amari, S., Gao, X., Nittler, L. R., et al., 2001, ApJ, 551, 1065Amari, S., 2002, NewAR, 46, 519Barnes, J., & Hut, P., 1986, Nature, 324, 446Balsara, D. S., 1995, J. Comput. Phys., 121, 357Cameron, A. G. W., 1959, ApJ, 130, 916Drake, J. J., & Orlando, S., 2010, ApJL, 720, L195Evans, A., & Rawlings, M. C., 2008, in
Classical Novae , 2nd Ed., ed. M. F.Bode, and A. Evans (Cambridge Univ. Press: Cambridge, UK), 308Frank, J., King, A., & Raine, D., 2002,
Accretion Power in Astrophysics , 3 rd Ed.(Cambridge Univ. Press: Cambridge, UK)Garc´ıa-Senz, D., Badenes, C., & Serichol, N., 2012, ApJ, 745, 75Gehrz, R., 2008, in
Classical Novae , 2nd Ed., ed. M. F. Bode, and A. Evans(Cambridge Univ. Press: Cambridge, UK), 167Gehrz, R.D., Truran, J.W., Williams, R.E., & Starrfield, S., 1998, PASP, 110, 3Giannone, P., & Weigert, A., 1967, Z. Astrophys., 67, 41Gurevitch, L. E., & Lebedinsky, A. I., 1957, in
Non-Stable Stars , ed. G. H.Herbig (Cambridge Univ. Press: Cambridge, UK), 77Hernanz, M., & Sala, G., 2002, Science, 298, 393Jos´e, J., 2016,
Stellar Explosions: Hydrodynamics and Nucleosynthesis (CRC / Taylor and Francis: Boca Raton, FL)Jos´e, J. & Hernanz, M., 1998, ApJ, 494, 680Jos´e, J. & Shore, S., 2008, in
Classical Novae , 2nd Ed., ed. M.F. Bode and A.Evans (Cambridge Univ. Press: Cambridge, UK), 121Joy, A. H., 1954, ApJ, 120, 377Knigge, C., Long, K. S., Hoard, D. W., Szkody, P., & Dhillon, V. S., 2000, ApJL,539, L49Kraft, R. P., 1964, ApJ, 139, 457Leibowitz, E. M., Mendelson, H., Mashal, E., Prialnik, D., & Seitter, W. C.,1992, ApJ, 385, 49Lombardi, J. C., Jr., Proulx, Z. F., Dooley, K. L., et al., 2006, ApJ, 640, 441 Maccarone, T. J., 2014, Space Sci. Revs., 183, 101Marietta, E., Burrows, A., & Fryxell, B., 2000, ApJS, 128, 615Marks, P. B., & Sarna, M. J., 1998, MNRAS, 301, 699Marks, P. B., Sarna, M. J., & Prialnik, D., 1997, MNRAS, 290, 283Monaghan, J. J., 1997, J. Comput. Phys., 136, 298Price, D. J., 2007, Publ. Astron. Soc. Australia, 24, 159Puebla, R. E., Diaz, M. P., & Hubeny, I., 2007, AJ, 134, 1923Retter, A., 2003, in
Symbiotic Stars Probing Stellar Evolution , ed. R. L. M.Corradi, R. Mikolajewska, & T. J. Mahoney (Astronomical Society of thePacific: San Francisco, CA), 232Retter, A., Leibowitz, E. M., and Kovo-Kariti, O., 1998, MNRAS, 293, 145Retter, A., Leibowitz, E. M., and Ofek, E. O., 1997, MNRAS, 286, 745Rose, W. K., 1968,ApJ, 152, 245Sanford, R. F., 1949, ApJ, 109, 81Schatzman, E., 1949, Ann. Astrophys., 12, 281Schatzman, E., 1951, Ann. Astrophys., 14, 294Shafter, A. W., & Misselt, K. A., 2006, ApJ, 644, 1104Shakura, N., & Sunyaev, R., 1973, A&A, 24, 337Shore, S. N., De Gennaro Aquino, I., Schwarz, G. J., et al., 2013, A&A, 553,A123Shore, S. N., Starrfield, S., Gonzalez-Riestra, R., Hauschildt, P. H., & Sonneborn,G., 1994, Nature, 369, 539Skillman, D. R., Harvey, D., Patterson, J., & Vanmunster, T., 1997, PASP, 109,114Sparks, W. M., 1969, ApJ, 156, 569Springel, V., 2005, MNRAS, 364, 1105Springel, V., & Hernquist, L., 2002, MNRAS, 333, 649Springel, V., Yoshida, N., & White, S. D. M., 2001, New Astr., 6, 79Starrfield, S., Iliadis, C., & Hix, W.R., 2008, in
Classical Novae , 2nd Ed., ed.M.F. Bode and A. Evans (Cambridge Univ. Press: Cambridge, UK), 77Starrfield, S., Iliadis, C., & Hix, W.R., 2016, PASP, 128, 051001Tappert, C., Schmidtobreick, L., Vogt, N., & Ederoclite, A., 2013, MNRAS, 436,2412Tatische ff , V., & Hernanz, M., 2007, ApJL, 663, L101Warner, B., 2003, Cataclysmic variable Stars (Cambridge Univ. Press:Cambridge, UK)White S. D. M., 1996, in