MNRAS 497, 3166–3179 (2020)

doi:10.1093/mnras/staa2169

Advance Access publication 2020 July 25

Properties of the post in-spiral common envelope ejecta II: dust formation
Roberto Iaconi,1‹ † Keiichi Maeda,1 Takaya Nozawa,2 Orsola De Marco3,4 and Thomas Reichardt

3,4

1 Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
3 Department of Physics & Astronomy, Macquarie University, Sydney, NSW 2109, Australia
4 Astronomy, Astrophysics and Astrophotonics Research Centre, Macquarie University, Sydney, NSW 2109, Australia

Accepted 2020 July 20. Received 2020 June 26; in original form 2020 March 13

ABSTRACT

We study the formation of dust in the expanding gas ejected as a result of a common envelope binary interaction. In our novel
approach, we apply the dust formation model of Nozawa et al. to the outputs of the 3D hydrodynamic SPH simulation performed
by Iaconi et al. that involves a giant of 0.88 M and 83 R , with a companion of 0.6 M placed on the surface of the giant incircular orbit. After simulating the dynamic in-spiral phase, we follow the expansion of the ejecta for  18 000 d. During thisperiod, the gas is able to cool down enough to reach dust formation temperatures. Our results show that dust forms efficiently
in the window between  300 d (the end of the dynamic in-spiral) and  5000 d. The dust forms in two separate populations;an outer one in the material ejected during the first few orbits of the companion inside the primary’s envelope and an inner one
in the rest of the ejected material. We are able to fit the grain-size distribution at the end of the simulation with a double powerlaw. The slope of the power law for smaller grains is flatter than that for larger grains, creating a knee-shaped distribution. The
power-law indexes are, however, different from the classical values determined for the interstellar medium. We also estimate thatthe contribution to cosmic dust by common envelope events is not negligible and comparable to that of novae and supernovae.
Key words: hydrodynamics – methods: analytic – methods: numerical – binaries: close – stars: evolution – dust, extinction.

1 I N T RO D U C T I O N
The common envelope interaction (Paczynski 1976; Ivanova et al.
2013b, hereafter CE) is a binary interaction process that leads to a
reduction in a binary’s orbital separation resulting in a merger orin the formation of compact evolved binaries, which in turn canbecome Type Ia supernovae, gamma-ray bursts, merging double
black holes/neutron stars emitting detectable gravitational waves.
A typical common envelope configuration is a giant primary and amore compact companion, such as a main-sequence star or a whitedwarf, but other configurations are possible.
Given its intrinsic three-dimensional (3D) structure and physicalcomplexity, research on CE has been mainly carried out throughhydrodynamic simulations. Several simulations have been performed
with different codes (e.g. Sandquist et al. 1998; Passy et al. 2012;
Ricker & Taam 2012; Ohlmann et al. 2016a, to cite a few; see table A3of Iaconi & De Marco 2019 for a more detailed list). Different
physical mechanisms and their impact on the final outcome have been
considered: H and He recombination energy injected in the gas whenthe envelope expands and cools down (Nandez, Ivanova & Lombardi
2015; Ivanova & Nandez 2016; Nandez & Ivanova 2016; and Ivanova
2018 support the idea that the energy released by recombination
has a major contribution in the envelope unbinding process, while
Grichener, Sabach & Soker 2018 and Soker, Grichener & Sabach2018 support the idea that such energy is mostly radiated away

 E-mail: robertoiaconi1@gmail.com† JSPS International Research Fellow (Graduate School of Science, Kyoto
University)and does not affect strongly the envelope unbinding process); themagnetic field generated by the companion star (Ohlmann et al.
2016b); jets from the companion star (Shiber, Kashi & Soker 2017;
Shiber & Soker 2018; López-Cámara, De Colle & Moreno Méndez
2019; Schreier, Hillel & Soker 2019; Shiber et al. 2019); pre-CE
Roche lobe overflow (Reichardt et al. 2019); envelope fall-back(Kuruwita, Staff & De Marco 2016); high orbital eccentricities (Staff
et al. 2016); dust-driven winds (e.g. Glanz & Perets 2018); stellar
pulsations (e.g. Clayton et al. 2017); and convection (Wilson &Nordhaus 2019). CE wind tunnel simulations have also been carriedout by MacLeod et al. (2017), Murguia-Berthier et al. (2017), andDe et al. (2019). All of these works analyse the dynamic in-spiralphase, during which the two stars quickly approach each other in atime-scale comparable to the dynamical time-scale of the primary,i.e. from months to years (but see e.g. Soker 1993 and Soker 2017
for studies on the post-dynamic in-spiral phase).
This paper follows on from Iaconi et al. (2019), where we analysed
the behaviour of the CE ejecta after the dynamic in-spiral. We carriedout a 3D SPH simulation almost identical to those of Iaconi et al.
(2018), but we ran the simulation for longer, 18 434 d ( 50 yr)
after the end of the dynamic in-spiral and analysed the dynamic
and thermodynamic properties of the extended envelope gas. In
that paper, we showed that the evolution of the CE ejecta, after
the termination of the dynamic in-spiral, can be approximated byhomologous expansion after  5000 d from the beginning of thesimulation (the end of in-spiral is at  300 d). We also observed
the formation of ring-like features expanding self-similarly. If the
post-dynamic in-spiral CE evolution is homologous, then it can be
fully calculated analytically by applying the homologous expansion
equations to any simulation data dump chosen as initial conditions.

C 2020 The Author(s)Published by Oxford University Press on behalf of the Royal Astronomical Society

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2 Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan

Dust formation in common envelope ejecta

and what are the effects our numerical choices on it; in Section 3, we
describe the process of dust formation; in Section 4, we show the main
characteristics of the dust grains that form in the ejected envelope(grains size, location, mass, size distribution, and contribution to thecosmic dust); and in Section 5, we compare our results with theobservations of dust in the post-CE system V1309 Sco. Finally, thesummary and conclusions are given in Section 6.

2 D U S T F O R M AT I O N M O D E L
In this section, we give an explanation of the dust formation modeland how we applied it to our data. For a full description of the model,
see Nozawa & Kozasa (2013).

2.1 Oxygen and carbon-based dust chemistries
Nozawa & Kozasa (2013) formulated the non-steady-state dust
formation process involving nucleation and grain growth and applied
it to two grain species: pyroxene-type silicates (MgSiO3 ) and carbon(C). The choice is based on the fact that these are considered to be
the most representative species of dust grains in interstellar space.
Whether C or MgSiO3 grains are formed is determined by the number
ratio of carbon and oxygen atoms in the gas phase (hereafter referred
to as the C/O ratio). The abundances of gaseous C and O atoms aremainly controlled by the formation of CO molecules, because CO
molecules efficiently form at relatively high temperatures and cantrap almost completely either C or O atoms prior to dust formation,
depending on which of the two has a lower number density. Let us
consider the conditions required for the formation of the two typesof dust separately.
MgSiO3 grains are the most expected type of dust in oxygen-richenvelopes of RGB CE we simulate here, because these stars have
not yet undergone the third dredge up and have solar abundances(Asplund et al. 2009; where the number fractions of the elements
forming the grains considered are ordered in the following way: nO> nC > nMg > nSi ). Thus, the fact that the C/O ratio is smaller thanunit results in all the C atoms to be locked up in CO molecules. This
prevents the formation of C grains, leaving the MgSiO3 grains as
the main dust species formed. Indeed, a C/O ratio <1 is observedin several low-mass red novae objects (e.g. V1309 Sco; Tylenda &Kamiński 2016).
Nevertheless, we still consider the formation of C grains in our
CE ejecta. There have been suggestions that CO molecules can beeasily destroyed by energetic electrons, which enables, even for
C/O <1, the condensation of C grains from gas-phase C atoms thatare not bound in CO molecules (Clayton, Liu & Dalgarno 1999). In
addition, observations of classic novae have revealed the concurrent
formation of silicate and carbon grains in their ejecta (Evans et al.
2005; Sakon et al. 2016). These works indicate that the formation of
CO molecules is not always complete, and that C grains can condensein the ejected gas with C/O <1. Hence, we also address the formationof C grains under the extreme assumption that no CO molecule isformed. Finally, investigating the formation of C grains is applicableto the CE ejecta of asymptotic giant branch (AGB) stars.
For both of the grain species, the amount of dust that forms depends
on the abundance of elements that can solidify into dust. Generally
for MgSiO3 grains, Si atoms are assumed to combine with O to form
SiO molecules, whose abundance is equal to that of the Si atoms.
Therefore, the amount of MgSiO3 grains formed is proportional to
the least abundant element between Mg and Si. In our case, it is Si,
which we will use as the key species for all the calculations related
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We showed the power of this approach by building a toy model forthe calculation of the photosphere where the ejecta expand following
the homologous dynamics and the main contribution to opacity isprovided by dust formed in the cooling envelope gas. The determination of the photosphere location and temperature carried in Iaconi
et al. (2019) did not explain in detail how the calculations of the dust
formation were performed, something that we concentrate on here.
The number of common envelope events observed is multiplying
quickly, with most of the observational counterparts of CE events
being associated with red nova outbursts (Ivanova et al. 2013a).
Moreover, a new class of infrared transients has been discovered andclassified by Jencson et al. (2019), which shows similarities to otherevents that, in the optical, have been interpreted as common envelope
mergers. It is also clear that in both of these types of transients,
dust is often present, with many red novae being fully or partiallyembedded in dust (e.g.: V4332 Sgr, Banerjee et al. 2007, 2015; BLG360, Tylenda et al. 2013, Kaminski – private communication; NN
Ser, Hardy et al. 2016; and V1309 Sco, Tylenda & Kamiński 2016)
and several of the new transients showing distinctive dust signatures(Jencson et al. 2019; Pastorello et al. 2019). Therefore, it is essential
to study the formation and evolution of dust in the CE environment
to fully understand the evolution of these observational counterparts.
Another reason to include dust in CE interactions is that a dusty
common envelope may be ejected more readily by radiation pressure.
The question of what forces play a role in ejecting the CE is still open
(e.g. Reichardt et al. 2020) and dust driving remains a candidate atleast for some of the cases. While in this paper we do not calculate
the radiative forces, determining the location, timing, and type ofdust that forms is a necessary calculation.
A model for dust formation in CE ejecta was previously carriedout by Lü, Zhu & Podsiadlowski (2013). Their model presents some
substantial differences with respect to ours. First, they assume that
the CE ejecta expand following the kinematics of a stellar windwith spherical symmetry. Secondly, they considered olivine-typesilicates, pyroxene-type silicates, and iron grains, while we utilize
the pyroxene-type silicate MgSiO3 and carbon grains. Finally, Lü
et al. (2013) adopted the dust formation model by Ferrarotti & Gail(2006), who specify the number of seed nuclei by hand, while we use
the dust formation model by Nozawa & Kozasa (2013), which treats
seed formation and dust growth self-consistently. Dust formation incommon envelopes was also considered analytically by Soker (1998)
and Glanz & Perets (2018). Soker (1998) proposes the formation ofdust taking place in cold spots of the envelope ejecta, following the
CE between an AGB star and a Jupiter-sized object. Glanz & Perets(2018) explore instead the idea that dust-driven winds taking place
after the dynamic in-spiral might help to unbind the envelope. Our
study, on the other hand, is the first that presents a detailed modelof dust formation in CE ejecta based on the outputs of 3D SPH
hydrodynamic simulations (we also highlight that, even in otherastrophysical contexts, e.g. supernovae, only a few studies of dust
formation applied to 3D simulations have been performed). Dust
formation does not happen at fixed locations but is achieved in theflow of the gas parcels. Therefore, grid-based hydrodynamic codes,
which use Eulerian schemes, can be coupled to dust formation models
only by introducing a large number of test particles. Such approach
results in approximations due to the fact that no matter how many
test particles one introduces, they will not be able to track accurately
all the locations of the gas parcels. On the other hand, this study uses
an SPH code, based on a Lagrangian formalism, which allows us tofollow every moving element of the fluid without any approximation.
This paper is structured as follows: in Section 2, we describe
the dust formation model we use, how we applied it to our data,

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to MgSiO3 grains. For C grains, the key species is simply C, which
we will use as the key species for the related calculations.
2.2 Application of the dust model to the common envelope
simulation outputs

MNRAS 497, 3166–3179 (2020)

2.3 Impact of the numerical setup on the dust formation model
In this section, we discuss different numerical factors and assumptions that could affect the results of our dust formation calculation.

2.3.1 Recombination energy and bound portion of the ejecta
Our simulation does not include radiative heating or cooling; therefore, the gas heats and cools adiabatically. However, the hot plasmaof the giant’s envelope recombines after the ejection and can be an
important source of radiative cooling. In this work, we model therecombination of the ejecta’s gas by using a tabulated equation ofstate, taken from the MESA code (Paxton et al. 2011), which allows
the gas of the envelope to recombine when it reaches sufficiently low
temperatures. The full payload of the recombination energy released
is instantly thermalized and added to the internal energy of the gas,increasing its pressure and allowing it to do work. This results inthe unbinding of 94 per cent of the stellar envelope. Whether an
SPH particle is unbound is determined by checking if the sum of its
kinetic, potential, and thermal energies is larger than zero (Ekin +Epot + Etherm > 0).
Here, we do not argue on the merits of recombination energy inunbinding the stellar envelope (for that, see references in Section 1).
Rather, we use a CE simulation where the gas becomes almost
completely unbound as must be the case in at least some casesin Nature. The latent recombination energy in our stellar envelope
is in principle sufficient to fully unbind the gian’s envelope, if it
is fully utilized to do work and does not escape, something thatis not the case for similar but even slightly more massive giants(see the calculations in section 7.2 of Iaconi et al. 2018). Including
recombination energy without including radiation transfer results inthe portion of energy that should be radiated away to stay in the gas,increasing its temperature and possibly affecting the timing of dust
formation and the size of dust formed (both depending on the gas
temperature; see Nozawa & Kozasa 2013).
Reichardt et al. (2020) carry out a detailed analysis of theavailability of recombination energy to do work in their numericalsetup and conclude that  50 per cent of the hydrogen recombinationenergy and  95 per cent of the helium recombination energy are
effectively available to do work. Helium recombination is very
efficient in driving the envelope because it is released deep in the

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The condensation of dust takes place in the cooling gas, where theunsaturated state turns into the supersaturated state determined by
the condition S > 1, where S is the supersaturation ratio of the gas(equation 56 of Nozawa & Kozasa 2013). Thus, to determine if dust
condensation takes place, we need to follow the supersaturation ratio,
which depends on the temperature and partial pressure of condensable gaseous atoms (Nozawa & Kozasa 2013). Our hydrodynamic
simulations of the CE ejecta record the density and pressure (which
can be converted to temperature) as a function of time for each SPH
particle. Hence, the feasibility of dust formation can be assessed,
based on the evolution of S calculated from the simulation outputs.
Nozawa & Kozasa (2013) found that the formation of MgSiO3
and C grains in the expanding gas can be achieved when the
non-dimensional quantity on = τ sat (ton )/τ coll (ton ) is higher thanunity, where τ sat is the time-scale in which the supersaturation ratio
increases, τ coll is the time-scale on which the gas particles collide,and ton is the onset time of dust formation; on represents the ratioof time-scales between the seed nuclei formation and grain growth at
ton . Note that the supersaturation ratio increases with decreasing gas
temperature: ln S ∝ T−1 . Hence, S is sensitive to gas temperature T,
and τ sat = |dln S/dt|−1 is approximately proportional to the coolingtime of the gas.
Nozawa & Kozasa (2013) also showed that the typical radius of
newly formed dust can be determined by the value of on . In thisstudy, we examine the possibility of dust formation and estimate
the size and mass of dust by calculating on for each SPH particle
and for the entire duration of the simulation. In our calculations, theonset time of dust formation ton is defined as the time when S reaches
10. The gas temperatures when S = 10 are 1200–1600 K and1700–2100 K for MgSiO3 and C grains, respectively, dependingon the number density of the key gas species. Since the time-scaleof dust formation (a few days) is much shorter than the dynamical
time-scale of the ejecta, ton can be regarded as the condensation
time of dust. Dust destruction by sputtering in shocks is not taken
into account in the current model, and one might argue that shocks
produced during the dynamic in-spiral could potentially destroy partof the dust. However, the erosion of dust by sputtering requires thepresence of shocks travelling in the medium at velocities 100 km
s−1 (Nozawa, Kozasa & Habe 2006; Nozawa et al. 2007). Shocksof such magnitude are not present in our CE environment, which
exhibits only weak shocks with velocities of a few tens km s−1 . In
addition, we do not see any shock heating after the termination of
the dynamic in-spiral, with the ejecta steadily cooling down once theinitial interaction is completed [see panel (b) of fig. 6 in Iaconi et al.
2019]. Therefore, shock-driven dust destruction should be negligible.
The formula used by Iaconi et al. (2019) to calculate on assumed
homologous evolution of the density and temperature of the gas.
This assumption affects the value of on , since the time-scale of gas
cooling is regulated by the time-scale of gas expansion. However, oursimulation reveals that the evolution of the ejecta can be describedby a homologous model only after  5000 d. Here, we remove theassumption of homologous expansion for the evolution of density andtemperature, and we derive on directly and independently for each
SPH particle on the basis of the time-scale of gas cooling obtained
from the temperature derivative between one code dump and thefollowing one (referred to as non-homologous case).

A comparison between homologous and non-homologous cases
reveals as expected a shorter cooling time-scale, on average, in the
non-homologous case between  2500 d and  5000 d, due to thefaster temperature decrease (panel b of fig. 6 in Iaconi et al. 2019).
At its maximum, the difference in cooling time-scale between thetwo cases is about a factor of 2. This mainly leads to the formationof a larger number of smaller dust grains in the non-homologous
case. Nevertheless, we would not expect a large difference in thelocation of the photosphere because the radius and temperature of
the photosphere do not depend greatly on the grain radius so long as
it is less than 0.1 μm (Iaconi et al. 2019).
We also stress here that the dust model we use is not limited
only to the physical environments of supernovae. It was shown thatthe model can be applied to dust-forming environments expanding
slower than supernova ejecta, such as stellar winds (Nozawa et al.
2014). In summary, the dust formation model used here has alreadybeen validated in a wide range of physical environments (density
and temperature of the gas), which also fully cover the physicalconditions of the CE ejecta.

Dust formation in common envelope ejecta

2.3.2 The temperature of dust and gas
Being unable to calculate the dust temperature, we have assumed that
it is the same as the gas: Tdust = Tgas . Here, we consider the validityof this assumption for the formation of the seed grains and for grain
growth.
We started by estimating the collisional heating rate, Rcoll , theradiative heating rate, Rheat , and the radiative cooling rate, Rcool , byapplying the prescription of Nozawa et al. [2008, their equation (1)]to our CE ejecta during the dust formation period. The three rates
determine Tdust via the balance equation:
Rcoll + Rheat = Rcool .

(1)

The values we obtain are Rcoll  7 × (102 –104 )χ er g cm−2 s−1 ,Rheat  3.5 × (105 –106 )χ er g cm−2 s−1 , and Rcool  1.1 × (107 –108 )χ er g cm−2 s−1 , where χ is the geometrical cross-section of
the dust particles. With the typical physical quantities of the postCE ejecta considered here, the energy involved in collisional heating
between dust and gas is negligible compared to that involved inradiative heating/cooling of dust. The temperature of dust is higher orlower than that of the gas, respectively, if radiative heating dominates
or if radiative cooling dominates. In particular, small dust grains are
susceptible to rapid temperature fluctuations.
In terms of the formation of seed grains, we can safely assume
that Tdust = Tgas . In fact, the seed grains are very small (<30 atoms)
and can be regarded as large molecules, therefore, sharing a similar
temperature to that of the gas where they form. That said, Keith &Lazzati (2011) claim that the formation rate of seed grains canbe enhanced by temperature fluctuations. However, they consider
physical conditions very different from those present in astronomical
environments (very high temperatures and very high gas densities);
therefore, the results of their study cannot simply be included in
the dust formation model we used here. If temperature fluctuations
were present and resulted in variations of the formation rate of seedgrains, we would expect the onset of dust formation to be shifted atearlier/later times. Moreover, Paquette & Nuth (2011) systematicallyanalysed the effects of the formation rate of seed grains on their
final size and found that a substantial increase in the former results
only in a small increase in the latter. Therefore, even if temperaturefluctuations would affect the formation rate of seed grains, it would
not have significant effects on our results for the grain size.
Our assumption that dust and gas temperatures are the same could
be more of an issue for grain growth. Dust temperatures higher thangas temperatures due to radiative heating might lead to evaporation of
the grains and effectively quench grain growth. We can observe that ingeneral, Rheat < Rcool by one order of magnitude, and a more accurate
calculation showed that this is true for all the SPH particles forboth C and MgSiO3 grains. This is more easily satisfied by MgSiO3
because the opacity (absorption efficiency) of MgSiO3 is lower at theblackody peak wavelength of the central object. Therefore, radiative
heating falls below radiative cooling, meaning that dust temperaturemust be always lower than gas temperature. This may lead to anincrease in grain growth rate, but in our model, we assume thesticking probability to be constant. Therefore, in our formalism,
as the temperature of dust decreases, the grain growth rate does notincrease. It is difficult to model grain growth by accounting for theeffect of temperature fluctuations and to predict what the behaviour
would be under the present circumstances if such effects were taken
into account. We leave such an investigation to future work.
We additionally note that since Rheat < Rcool , the radiation fromthe central object has a negligible effect on dust destruction and thatthe radiation pressure generated would accelerate the dust to only a
few tens km s−1 ; therefore, the effect on the ejecta dynamics would
be small.
3 D U S T F O R M AT I O N P RO C E S S
In Fig. 1, we plot on as a function of the distance from the centre ofmass (CoM) of the system and for both types of dust considered inthis work. The particles shown in each panel are only those that haveachieved the condition for the onset of dust formation (S ≥ 10) before
the time at which each snapshot is taken. We plot these quantities atfour different times: the end of the dynamic in-spiral ( 300 d), theend of the formation of the outer dust population ( 900 d; see below
and Section 4.2), the onset of homologous expansion in the ejecta( 5000 d), and the end of the simulation (18 434 d). Additionally,
we show as a colour gradient the onset time of dust formation, ton ,of the SPH particles.
For the great majority of the particles, the values of on we record
at ton are larger than unity (in Fig. 1, all the SPH particles for C grains
and most of them for MgSiO3 grains, respectively, reside above theblack horizontal line). This means that, for the great majority of theparticles, the nucleated seed clusters can grow stably through theaccretion of the key gas species. Therefore, nearly the maximum
possible amount of dust is formed in our simulation. The differencein the values of on between the two dust types mainly stems fromthe difference in condensation temperature and number abundanceof the key gas species.
We observe two distinct populations for on : an outer population
represented by the diagonal strip formed between  300 and  900 din the outer layer and an inner population formed by the clump that
forms in the inner layers starting from  900 d. We will analyse thetwo populations in detail in Sections 4.2 and 4.3, when discussing
the locations where dust forms and the grain-size distribution.
In the outer dust population, the formation of grains mostly
proceeds from the outside-in. We notice, however, that for a given
distance, dust forms at different times. For example, by picking a
distance of 800 AU in Fig. 1 [panel (d)], we can see that the colourchanges from blue in the upper part of the distribution of each dust
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star. We therefore expect that the unbound mass in our simulation
is approximately correct, since only 50 per cent of the energy fromrecombined hydrogen may be radiated away.
According to our model, dust formation takes place in neutral,
unbound shells. Assuming all unbound ejecta to be neutral, we canestimate the average total energy of a single unbound SPH particle
as Ekin + Epot + Etherm  1.65 × 1041 erg, where Etherm includes therecombination energy contributions to the internal energy from H
and He (again, see Reichardt et al. 2020 for details). Note that suchcontributions are the recombination energies values before having
subtracted the estimated amounts that have been radiated away. By
using the numbers provided by Reichardt et al. (2020) at 359 d fromthe beginning of the simulation ( 50 d after the end of the dynamic
in-spiral), we estimate the energy lost via radiative cooling of a single
unbound SPH particle to be  4.2 × 1040 erg. If we compare the two
numbers, we can see that about 25 per cent of the total energy would
be lost via radiative cooling. Without including it, the ejecta will
therefore reach dust formation temperatures later, at lower densities,
and our dust model might be producing dust grains slightly smaller
than those obtained in a model including radiation transfer.
The bound portion of the envelope is very small and, except fora few SPH particles that remain close to the central binary, theremaining ones are mixed up with the unbound ejecta. These particles
are very loosely bound and behave similarly to their unboundneighbours, therefore exhibiting a similar pattern of dust formation.

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type to green in the lower part, which corresponds to a spread intime of  900 d. In the inner dust population, we observe insteada much larger spread of ton at a fixed distance. For example, if we
consider a distance of 400 AU in Fig. 1 [panel (d)], the range of ton
is of the order of several thousands of days. Therefore, especiallyfor the inner dust population, regions that are equidistant from the
CoM see the coexistence of dusty and dust-free gas. This is due tothe complex dynamic and thermodynamic interactions taking placein the inner portions of the ejecta even after the dynamic in-spiral(Iaconi et al. 2019).
To clarify how ton depends on the location, we plot in Fig. 2 theprojection of SPH particles that formed C grains at 18 434 d on thex–y [panel (a)] and x–z [panel (b)] planes, where the colour scale
represents ton . The results for MgSiO3 are very similar to those for
C and we do not show them. In the projections, it is clear that theouter portion of the ejecta has a more evident ton gradient, while theinner region has a more mixed ton distribution.
The process of dust formation, which starts right after the completion of the dynamic in-spiral, lasts until  5000 d. This corresponds
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to the time required for the ejecta to achieve homologous expansion(Iaconi et al. 2019). At  5000 d  96 per cent and  97 per centof the particles, for MgSiO3 and C, respectively, have formed dust.
Most of the remaining particles slowly form dust over the remaining 15 000 d of the simulation. The fact that the dust formation process
starts at the end of the dynamic in-spiral and terminates when theejecta achieve homologous expansion is purely coincidental.

4 C H A R AC T E R I S T I C S O F T H E D U S T
The model proposed by Nozawa & Kozasa (2013) allows us toevaluate several properties of the newly formed dust. In this section,
we will analyse these properties and their implications.

4.1 Average grain size
Let us first consider the evolution of the average grain radius, aave ,as a function of time (Fig. 3). For both MgSiO3 and C grains, we

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Figure 1. on for the particles that have achieved the condition S ≥ 10 as a function of the distance from the CoM of the system, at  300 d (a),  900 d (b),
 5000 d (c), and 18434 d (d) for C and MgSiO3 grains. The colour scale represents ton , while the black horizontal line represents on = 1.

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5000 d reduces the value of aave and produces the small bump weobserve after the initial steady increase.
The difference in average radius between C and MgSiO3 grains is
instead dictated by the different number densities of the key elementsof the two dust types, C and MgSiO3 , respectively. The former hasa higher number density, resulting in a final aave  4 × 10−2 μm,
while the latter has a lower one, and a final aave  5 × 10−3 μm.

4.2 Location of the grains

Figure 3. Average grain size, aave , for MgSiO3 and C dust as a function oftime.

observe a general increase in aave during the first  2500 d of thesimulation. This is followed by a small decrease up to  5000 d,
when all the possible dust grains have formed (Section 3) and aave
becomes constant.
Larger grains form on average at later times. In the model we use,aave is roughly proportional to on ∝ ρon Ton3/2 [but see equation (64)of Nozawa & Kozasa 2013 for the correct relationship], where ρ on isthe density of an SPH particle at the onset of dust formation and Ton
is its temperature (equations 63 and 64 of Nozawa & Kozasa 2013).
Hence, an increase in the average grain size means that dust grains
form in denser layers of the ejecta at later times. In Fig. 1 [panel(d)], we observe that within 600 AU from the CoM of the system,
the maximum value of on is approximately constant. This region
becomes populated between 900 and 5000 d. A constant maximum
on results in a constant maximum grain size. As a result, the valuesof aave change depending only on the amount and size of smaller dust
grains. The increase in number of smaller grains between 900 and

By looking at the distribution of grains with respect to the CoM of thesystem (Fig. 4), we can see two distinct populations. The outer dust
population is composed by the grains that form earlier and shows adecreasing grain size at increasing distance from the CoM. In Fig. 4,
the outer population can be identified with the blue-to-green points
that occupy the area between  600 AU and  1600 AU from the
CoM. The inner dust population is instead formed by the grains
residing at distances <600 AU. The two populations form from 
300 to  900 d (outer population) and  900 to  5000 d (inner
population) and can be correlated with the shapes of the profiles oftemperature and density of the ejecta. At the end of the simulation,
we in fact observe that the region between  600 AU and  1600 AU
corresponds to a region where temperature and density decrease atincreasing distance from the CoM (for the density plot, see fig. 3 ofIaconi et al. 2019).
The formation of two populations is due to the envelope ejection
dynamics. The SPH particles that produce the outer dust population
amount to  10 per cent of the ejecta mass and coincide to the part ofthe ejecta that is unbound purely by being accelerated above escapevelocity by the deposited orbital energy (Iaconi et al. 2017; Iaconi
et al. 2018). This part of the ejecta cools down almost adiabaticallyafter being unbound, because it is free to expand into the empty space.
As a result, the gas temperature decreases until it reaches values
suitable for dust formation at earlier times than in the remaining partof the ejecta.
The inner layers of the ejecta interact with each other in the courseof the first  5000 d of the simulation (Iaconi et al. 2019). This results
in a more complex evolution and produces the inner dust population
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Figure 2. Projections on the x−y (panel a) and x−z (panel b) planes of the SPH particles that formed C grains; ton is represented by the colour scale. The
projections are taken at 18434 d, the end of the simulation. The results for MgSiO3 grains are very similar to those showed here.

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whose formation time and size are diverse. For both populations, butmore so for the second one, grains of different sizes form at different
times for a given distance from the centre. This is reminiscent of
the behaviour of on . In fact, in accordance to the formulation of
Nozawa & Kozasa (2013), aave ∝ on ∝ τ sat (ton )/τ coll (ton ). Therefore,
the size of the grains that form in a specific SPH particle depends
MNRAS 497, 3166–3179 (2020)

on the balance between how fast the new seed nuclei form (τ sat )and how fast the gas particles can collide with the seed nuclei andpre-formed grains to grow them (τ coll ). The combination of large τ sat
and small τ coll results in a rapid buildup of large grains. As a result,
we observe that, at the same distance from the CoM, SPH particles
form larger grains at earlier times as well as smaller grains at later

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Figure 4. Grain radius, a, as a function of the distance from the CoM of the system for C (a) and MgSiO3 (b) grains at the end of the simulation. On the upper
x-axis, we plot the mass coordinate with respect to the total ejecta mass. The colour scale represents ton .

Dust formation in common envelope ejecta

3173

times (see also Section 4.1). This process takes place roughly in twophases. First, a front of dust formation, starting from the outskirts ofthe ejecta, moves inwards and forms the larger grains. At this point,in the inner layers of the ejecta, we have SPH particles where larger
dust grains have already formed and SPH particles where the gas has
not yet met the physical conditions for dust formation. The latter are
where the smaller dust grains are gradually formed. This process isclear by looking at the distribution of the colours in Fig. 4.
When dust starts forming after the dynamic in-spiral, at  300 d,
the first grains form at  20 AU from the CoM of the binary. By 
5000 d, the dust stops forming. The last grains form at  100 AU.
Therefore, we observe dust forming roughly in a 100 AU shell aroundthe binary system. Previous results on dust formation in CE (Lüet al. 2013), using a 1D model, estimated a range between  7 and7 × 104 AU, much larger than the one we obtain here, implying that
their ejecta rarefy and cool down more slowly in the 1D model thanin our 3D model.

4.3 Grain-size distribution
For both the dust types considered, the size distributions are weighted
towards small grains. They peak at  3 × 10−3 μm for C and 1.8 × 10−3 μm for MgSiO3 grains. Moreover, we can see thatthe size of the grains spans a relatively broad range, between 
3 × 10−3 and  9 × 10−1 μm for C and between  1.4 × 10−3 and 7 × 10−2 μm for MgSiO3 . This is shown in Fig. 5, where we plot
the number of dust grains versus the grain radius, a, for C [panel (a)]and MgSiO3 [panel (b)].
We observe that the distributions have a distinct shape, with a netchange of slope at  5 × 10−2 μm and  5 × 10−3 μm for C andMgSiO3 grains, respectively. This turnover point, in terms of how
much ejecta mass is contained in a single a bin, represents theaverage grain size. In other words, the a bins around the turnover
point are those that contain the highest amount of gas mass pernumber of dust grains. We can match the turnover point in grain
size with the maximum in the density distribution of SPH particles(Fig. 6), located at  7 × 10−16 g·cm−3 . By looking at the dottedlines in the two panels of Fig. 5, which represent constant masses, it
is possible to see that on the left of the turnover points, the magentalines move closer to the constant mass lines, while on the right of theturnover points, the cyan lines move closer to the constant mass lines.
A similar behaviour can be observed for the maximum of the density
distribution in Fig. 6. This informs us of the fact that a turnover point
in density results in a turnover point in the grain-size distribution.
We are able to fit two power laws through the data, marked by
the magenta and cyan lines in Fig. 5. The two power laws have been
fit through the data between the vertical dashed lines and the fitting
parameters are shown in Table 1, where for the power law, we use
the nomenclature n(a) = Ca−q , the same as that of Nozawa (2016).
Let us now consider separately the three areas of Fig. 5 separated by
the vertical dashed lines.
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Figure 5. Number of dust grains as a function of the grain radius, a, at the end of the simulation for C grains (a) and MgSiO3 grains (b). In panel (a), themagenta line represents the best fit to a power law in the range 3 × 10−3 ≤ a < 5 × 10−2 μm, the cyan line in the range 5 × 10−2 ≤ a ≤ 9 × 10−1 μm. In
panel (b), the magenta line represents the best fit to a power law in the range 1.4 × 10−3 ≤ a < 5 × 10−3 μm, the cyan line in the range 5 × 10−3 ≤ a ≤7 × 10−2 μm. The boundaries of the fitting are marked by the vertical dashed lines, while the dotted line represents a line at constant mass for reference. We
overplot the distribution for the outer dust population (i.e. at 900 d) in cyan (a) and pink (b), for C and MgSiO3 , respectively. Note that the bin size use for theouter dust population is smaller than that used for the data at the end of the simulation.

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Table 1. Parameters of the fits in Fig. 5. Note that the nomenclature for the parameters has been chosen to be the sameas that of Nozawa (2016), who expresses the power law as n(a) = Ca−q ; see Nozawa (2016) for further details.
Dust typeC
MgSiO3

MagentaCyan

Parameters

Std deviation

Parameters

C = 3.88 × 10−4

6.71 × 10−5

C = 1.65 × 10−10

q = 1.62
C = 6.92 × 10−4
q = 1.43±±±±

3.87 × 10−2

4.14 × 10−4
10−1

The left side of the distribution, with the smallest grains formed
at very low densities in the late stages of the dust formation (seee.g. Fig. 4), does not display any particular trend. The gas wherethese grains are located achieves homologous expansion after dust
is formed, i.e. after  5000 d from the beginning of the simulation.
We highlight that, even though the number of dust grains in thispart of the distribution is large, the mass of the gas where they
reside, and hence the dust mass, is quite low. Its mass corresponds
to  0.44 per cent and  1.32 per cent of the ejecta mass for C andMgSiO3 , respectively. This is in line with the results obtained by
Iaconi et al. (2019), who showed that most of the ejecta has achieved
homologous expansion by the  5000-d mark.
The middle part of the distributions contains the majority of theejecta mass,  67 per cent in the case of C grains and 61 per cent in
the case of MgSiO3 grains. The power-law slopes representing the
distribution are −1.62 and −1.43, for C and MgSiO3 , respectively.
All of these dust grains form in areas where the gas has alreadyachieved homologous expansion. We highlight here that we performed the fit in logarithmic space, i.e. on the distribution obtainedas n(a) = dn/dlog a, where n is the number of dust grains. As a result,the slopes of the power-law fits decrease by 1 if the distribution isfitted in linear space,1 resulting in exponents of −2.62 and −2.43.
The linear slopes we obtain differ from the typical values estimatedfor interstellar dust grains, which are in the range −3.5  −q  −4(e.g. Nozawa & Fukugita 2013).
The right part of the distributions corresponds to the cusps pointing
upwards visible in Fig. 4 and also in this case the dust grains form
in regions where the gas has achieved homologous expansion. The
cusps are located between  300 and  600 AU for both C and1 Let us define the distribution derived in linear space as dn . This distributiondaand the one derived in logarithmic space are connected by the relation dn
da =
dn
1
.
If
the
distribution
derivedinlogarithmic
space
is
a
power
law
of
a ln 10 d log aCa −(q+1)
the type Ca−q , we obtain dn
=
.
da
ln 10

MNRAS 497, 3166–3179 (2020)

q = 6.56
C = 5.81 × 10−16
q = 6.67

Std deviation±±±±

5.55 × 10−11
1.92 × 10−1
3.92 × 10−16
1.68 × 10−1

MgSiO3 and contain, respectively,  32 per cent and  37 per centof the ejecta mass. This part of the distributions is fitted by power laws
whose slopes are steeper than for smaller grains with exponents of−6.56 and −6.67, for C and MgSiO3 , respectively. These exponents
correspond to −7.56 and −7.67 for a linear fit. Also in this case,the linear slopes we obtain differ from the typical values estimatedfor interstellar dust grains. The presence of a steeper power law
at larger grain size is a feature that appears also in other dust
formation environments. For example, Nozawa et al. (2003) observe acrossover point between smaller and larger grain sizes, with a steeper
slope for larger grain sizes, for dust formed in supernova ejecta. As
mentioned in Section 4.2, the radius of newly formed grains is mainly
determined by the gas density at the onset of dust formation; larger
dust grains form in denser gas and vice versa. Hence, the grain-size
distributions given here reflect more or less the density distribution of
SPH particles. This implies that different dynamical models would
result in different power-law indices.
We also overplot the distribution for the outer dust in the case of C
in cyan [Fig. 5, panel (a)] and in the case of MgSiO3 in pink [Fig. 5,
panel (b)] to those of the distribution at the end of the simulation
for comparison. The inner dust population dominates the grain-size
distribution at the end of the simulation. This is particularly true
for large grain sizes. Larger grains are in fact mostly formed in the
inner dust population, so the outer population misses that part of thestatistic.

4.4 The shape of the dusty ejecta
The two dust populations discussed in Section 4.2 differ mainly
because the former, exterior one is more ordered, with smaller grains
residing at larger distances. The latter population is instead morechaotic, with a range of grain sizes at all distances. This is visible
in the shape of the dusty ejecta, which we show in Fig. 7 for the
C grains, where the top row are slices on the x−y and x−z planesat  900 d and the bottom row are the same slices at the end of

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Figure 6. Number of SPH particles as a function of density at the end of the simulation. The dotted line represents a line at constant mass for reference.

Dust formation in common envelope ejecta

3175

the simulation. We have chosen 900 d and 18 434 d because theyhighlight well the separation between the two dust populations.
At  900 d, we observe that the dusty part of the ejecta is only
the external one, leaving a dust-free cavity around the central binary.
Such cavity has an elliptic shape and spans an area between 20 and
30 AU just before the inner population starts forming and fillingthe dust-free space. In agreement with Fig. 4, from the outside to theinside, we observe a trend of increasing grain size as a function of the
distance. In the innermost area of the dusty gas, there is a layer where
the largest grains form (clearly visible as a mostly orange-coloured
area in panels a and b of Fig. 7). This results from the compression
generated by the first orbit of the companion inside the primary’s
envelope. When the gas belonging to the compressed layer cools
down to dust formation temperatures, its higher density prompts theformation of larger grains. Moreover, the dust we observe in panels(a) and (b) of Fig. 7 is mostly made up of unbound gas as it forms

in the portion of the ejecta that is accelerated above escape velocity
during the first orbit of the companion (see also Section 4.2).
At the end of the simulation, the gas has rarefied and cooled enoughto form dust over the entire ejecta. In panels (c) and (d) of Fig. 7, we
crop the slices to a distance of 700 AU, roughly corresponding to thetransition distance between the outer and inner dust populations. In
panel (c), we observe that the outermost area shows a greater numberof larger grains; these are concentrated on the equatorial plane andcorrespond to those in the cusp between 400 and 600 AU in Fig. 4.
We also observe the presence of small grains in the most internal
region of the ejecta. The remaining portion of the ejecta is occupied
by a mixture of different grain sizes. There is a ring-shaped feature
between  300 and  400 AU showing larger grain sizes. Since dust
has formed over the entire ejecta, the patterns of the dusty ejecta are
the same of those of the density distribution, which presents a higher
density ring as shown in figs 4 and 5 of Iaconi et al. (2019). A similar

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Figure 7. Slices on the x−y [panels (a) and (c)] and x − z [panels (b) and (d)] planes of the SPH particles that formed C grains; the dust size is represented by
the colour scale. The slices are taken at  900 d (top) and at 18 434 d (bottom) to clearly show the location of the two dust populations discussed in Section 4.2.
Note that panels (c) and (d) are cropped at 700 AU to include only the SPH particles belonging to the inner dust population, formed in the inner regions of theejecta. We do not plot the map of the MgSiO3 grains because it is very similar to the one of the C grains, only with different grain sizes.

3176

R. Iaconi et al.
and 4.2, we observe the layers of the ejecta gradually forming dust
as they expand and cool down. From this, it follows straight awaythat the total dust mass is steadily increasing.
4.6 Contribution of CE to cosmic dust

behaviour is present in the simulation of Reichardt et al. (2020), whocarried out a common envelope simulation that did not include theeffects of dust but which, by virtue of using a tabulated equation ofstate, could map the opacity in the envelope as a function of time. In
their fig. 10, top panels, we see a thick high-opacity ring at ∼100 AU
from the centre. This ring compares directly to the ring observedin the outer population dust in Fig. 7, which sits at ∼30 AU. The
different ring sizes are due to the fact that the snapshot presented by
Reichardt et al. (2020) is taken at 1840 d, while those in Fig. 7 aretaken at 900 d. Finally, the dust distribution in the two perpendicular
cuts also matches what is seen in the opacity maps of Reichardt
et al. (2020). Equatorially concentrated dust formation will propel
different layers of the ejecta at different speeds contributing to their
shaping in addition to what the geometry of the common envelope
interaction has already imparted to the ejecta.

5 O B S E RVAT I O N A L C O U N T E R PA RT S
4.5 Dust mass
In our simulation, every particle forms the same mass of either C or
MgSiO3 grains. This is because the amount of dust formed depends
only on the key element number density and on the total mass of the
SPH particle, with all the SPH particles in the simulation having thesame mass. We show the evolution of the dust mass formed in Fig. 8.
The mass of C grains at the end of the simulation amounts to2.22 × 10−3 M , while that of MgSiO3 amounts to 9.39 × 10−4 M .
These values correspond to  0.5 per cent and  0.2 per cent of theejected envelope mass, respectively. These values are in the samerange to those estimated by Lü et al. (2013), who calculated dust
masses ranging between  10−4 M and 5 × 10−2 M for the bulk of
their models. In the models of Reichardt et al. (2020), approximately
0.06 M of gas reside in the high-opacity shell where we presume
that dust is forming, implying a dust mass of ∼6 × 10−4 M , usinga gas-to-dust ratio of 100, a value that is in line with what we findhere.
In Fig. 8, the shape of the curves for C and MgSiO3 is similar.
This is due to the fact that the supersaturation ratio reaches its criticalvalue, S = 10, at the same time for both dust types, and when thishappens, the vast majority of the SPH particles have on > 1, forming
the maximum amount of dust possible (see Section 3). As a result,
the timing of the production of dust is similar.
The dust mass increases monotonically up to  5000 d, so new
grains are constantly formed. As discussed previously in Sections 4.1
MNRAS 497, 3166–3179 (2020)

The presence of dust is a very important feature frequently identified
in the observed counterparts of CE events (see Section 1). However,the detailed study of the properties of the newly formed dust grains
has been limited to the CE merger V1309 Sco, between a solar mass
subgiant star and a much less massive companion (Nicholls et al.
2013; Tylenda & Kamiński 2016).
Nicholls et al. (2013) analysed the dust formation between  547 dand  700 d after the outburst by constructing a simple dust model
based on their data. Their model considers a couple of dust species,
grain sizes between 0.1 and 4.0 μm, and temperatures between 200
and 1500 K. Within these ranges, they selected the dust type and sizethat best fit the observational data. They concluded that the continuum
was well represented by amorphous silicates dust at 400 K, while themain absorption line could be fitted by amorphous pyroxene dust of
3 μm at 800 K. The warm temperature and large grain size indicatedby the line feature led them to conclude that the dust had recently
formed and was processed in the circumstellar environment, rather
than inside the stellar envelope, thus confirming its CE origin.
Tylenda & Kamiński (2016) created instead a model aimed todetermine general parameters of the dust ejected and study its
interaction with the central object, rather than to determine thechemical composition of the dust. Their main assumptions were
therefore that the dust was composed of silicates and that its spatial
distribution was that of a shell cut in the polar direction, so to
simulate dust concentrated around the orbital plane. Their radiation

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Figure 8. Dust mass formed as a function of time for MgSiO3 and C grains.

In this section, we estimate the CE contribution to the Galactic dust
budget. To do so, we need to estimate the number of CE events
per year and multiply it by the dust yield of each as determined in
Section 4.5 ( 10−3 M for both C and MgSiO3 grains).
We can estimate the number of CE events per year for the Milky
Way by assuming that they are the same as the rate of luminous
red novae, namely 0.1−0.2 events per year (Kochanek, Adams &Belczynski 2014; Howitt et al. 2020). We note that this might be an
overestimate, because we do not know what percentage of red novae
is indeed the result of a CE event. With these numbers, we obtain an
injection of dust in the ISM by CE events of 1−2 × 10−4 M yr−1 .
The dust injected in the ISM by sources other than supernovae or novae, namely all stellar winds, is estimated to be ∼4.5 × 10−3 M yr−1
for the Milky Way (Draine 2009). The CE contribution to the Galactic
dust can therefore be estimated to be up to 5 per cent of the dust
produced by other known sources. The estimate provided here gives
an idea of the fact that the injection of dust into the ISM by CE does
not dominate the cosmic dust production but might not be negligible
and could be comparable to other dust sources such as novae andSNe (see e.g. table 1 of Draine 2009).
Lü et al. (2013) also considered the Galactic dust production fromCE events over the Galaxy’s lifetime using an analytical estimate ofthe dust production and a population synthesis code to determine therate of CE occurrences. They use a dust yield per event similar toours, and an estimated 20 per cent of all systems that go through a
CE interaction, which corresponds to a rate up to 0.8 events per year.
As a result of their four times higher frequency of CE interactions,they obtain a larger yield of dust by CE events.

Dust formation in common envelope ejecta(i) The formation of large dust particles usually requires extreme
environments and/or special physical processes (e.g. coagulation via
grain–grain collisions). In the current calculation, we do not include
such processes and, therefore, even if a population of larger grains
could be formed, we would not be able to reproduce it. Nevertheless,given the typical densities and temperatures of our gas, it seems
unlikely that larger grains would be able to form.
(ii) Grain sizes derived from IR-SED fitting tend to be large(1 μm). This is known for the case of nova ejecta, Type II SN,
AGB stars, and PN (Meixner et al. 2002; Wesson et al. 2010; Sakon
et al. 2016). Therefore, the study of Nicholls et al. (2013) might haveobtained systematically large grain sizes for V1309 Sco.
(iii) Nicholls et al. (2013) concluded that the dust was formed in
the post-dynamic in-spiral phase. However, there is another possible
scenario for the dust formation in V1309 Sco. As can be seen in
fig. 1 of Nicholls et al. (2013), the optical light curve quickly declines
during the year 2007, roughly 1 yr before the outburst. In the phase
before the outburst, dust has formed in gas lost from the binaryprior to the dynamic in-spiral (Tylenda & Kamiński 2016). These
dust grains could then have been swept up by the material ejectedduring the dynamic in-spiral and heated up to temperatures highenough to emit in the IR band. In such a scenario, dust can form inphysical conditions more suitable for the formations of grains withsizes 1 μm.
(iv) The mass of the dust we obtain is similar to that of Tylenda &Kamiński (2016); this gives a good indication that the dust formed
after the dynamic in-spiral is stable and does not get destroyed during
the subsequent expansion of the ejecta (see also our argument on
shocks in Section 2.2).
(v) The distribution of the dust we obtain reflects the overall
geometry of the ejecta. This leaves not only a more rarefied layer ofdust towards the polar direction, because the CE ejecta are naturally
concentrated along the equatorial plane, but also thinner layers ofdust in certain directions along the equatorial plane itself [see, forexample, the bottom right section of the dusty ejecta in panel (c)of Fig. 7]. This could allow the radiation from the central object toescape from these spots, similarly to what was observed by Tylenda &Kamiński (2016).
A more adequate comparison would require more observationsof dust in post-CE systems together with more theoretical dust
formation models based on CE simulations. These are both missingin the current literature.
6 S U M M A RY A N D C O N C L U S I O N S
In this paper, we presented the first work on dust formation based on a
3D hydrodynamic simulation of the CE interaction. We extended thework carried out by Iaconi et al. (2019) by applying the dust formation
model of Nozawa & Kozasa (2013) to the simulation outputs of the
3D SPH hydrodynamic simulation of the CE binary interaction of
Iaconi et al. (2019). In this simulation, the system has been evolvedfor 18 434 d ( 50 yr) after the termination of the dynamic in-spiralto assess the dynamic and thermodynamic behaviour of the ejecta.
This allows us to investigate the details of the formation of dust,
its spatial and size distributions, and to estimate the contribution of
the CE interaction to the production of cosmic dust. We consider
two types of dust, carbon dust (C) and pyroxene-type silicates dust
(MgSiO3 ), that represent the most common types of grains present
in the interstellar medium. Our main results are the following:(i) In both cases of C and MgSiO3 , dust grains are produced allover the ejected envelope (i.e. in 99 per cent of the SPH particles).
The dust formation starts right after the end of the dynamic in-spiral( 300 d) and terminates at  5000 d.
(ii) The dust formed can be divided into two populations, an outerone formed between  300 and  900 d, and an inner one formed
between  900 and  5000 d from the rest of the ejecta. In the outer
population, dust is formed in a more ordered way with respect to theinner population, starting at larger distances and with smaller grains
and terminating at smaller distances with larger grains. The inner
population is more complex, with multiple grain sizes forming in thesame layers at different times. The formation of two populations is theresult of different envelope ejection dynamics. The outer population
is formed in the gas that belongs to the outer layers of the primary,which are rapidly unbound during the first orbit of the companion
inside the CE and expand with negligible self-interaction in the empty
space around the binary. The inner population is formed in the gasthat belongs to the inner layers of the primary; such layers interact
with one another, achieving the conditions for dust formation under
different combinations of physical parameters inside the same layer.
(iii) On average, the size of dust grains formed increases as time
passes. At the end of the dust formation process, the average radiusof the grains is  4 × 10−2 μm for C and  5 × 10−3 μm for
MgSiO3 .
(iv) For both C and MgSiO3 , the size distribution of the dust
formed is weighted towards small grains and spans a relatively broad
range. The distributions can be fitted with a double power law, witha turnover point where the slope of the fitting power law changes.
The power law fitting the smaller grain sizes is flatter than the one
for the larger grain sizes, a feature present also in other astrophysicalenvironments, such as supernovae (Nozawa et al. 2003). However,
the indices of the two power laws differ from the canonical value
expected for the interstellar dust grains. To clarify what is happening,
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transfer calculation allowed them to estimate a total dust mass of 
10−3 M , which reproduced well the observed spectrum. They also
noted that the observations showed evidence of light penetrating theejecta in certain directions without interacting significantly with thedust.
Our dust formation model is based on a system where theprimary has a mass similar to the primary star of V1309 Sco, but
is substantially larger, and our companion is ∼4 times more massive(for a range of possible parameters of this system, see e.g. Tylenda
et al. 2011). Despite these differences, we carry out a comparison.
The V1309 Sco merger took place during the very early RGB
phase of the primary, so we will be looking at the MgSiO3 grains
for a comparison, a silicate mineral such as the one contemplatedby Nicholls et al. (2013). According to our model, dust would form
between  300 and  5000 d from the beginning of the simulation,
where  300 d marks the end of the dynamic in-spiral phase. During
this period, both temperature and density decrease by one orderof magnitude in the inner parts of the ejecta to several orders ofmagnitude in the outskirts. We observe that dust forms as soon as
the gas decreases to temperatures ∼1000 K. Therefore, we predictthat dust forms in warm environments, similar to the conclusionof Nicholls et al. (2013). On the other hand, the entire MgSiO3
dust population in our simulation has sizes smaller than 0.1 μm. It
is therefore possible that in our case, dust forms at densities low
enough to counterbalance the warm temperatures and still produce
small grains.
Given the differences and the approximations in our model andin the observation-derived quantities, it is impossible to perform
an accurate quantitative comparison. However, we can make a few
points:

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This is the first work on dust formation based on a 3D hydrodynamic simulation of the CE interaction. We hope that in the future,
more work of this kind will be performed with different stellar
masses, orbital parameters, dust formation models, and numericalcodes to achieve a deeper understanding of the dust formation processduring the CE evolution. It would be important to also assess the
dynamic effect that the presence of dust has on the ejecta.
AC K N OW L E D G E M E N T S
RI is grateful for the financial support provided by the Postodoctoral
Research Fellowship of the Japan Society for the Promotion of
Science (JSPS P18753). KM acknowledges the support provided
by the JSPS KAKENHI grants 17H02864, 18H04585, 18H05223,
20H00174, and 20H04737. TN acknowledges the support provided
by the JSPS KAKENHI grant 18K03707. We are grateful to thereferee for the useful comments and for helping to improve the paper.
We also thank Noam Soker and Tomasz Kaminski for their feedback
after posting this work on astro-ph, which significantly contributed todeepening the arguments proposed in this work. We acknowledge thecomputational facilities of the Department of Physics and Astronomyof Macquarie University, on which the simulations have been carriedout. The computations described in this work were performed using
the PHANTOM code (https://phantomsph.bitbucket.io/), which is the
product of a collaborative effort of scientists under the lead of A/Prof.
Daniel Price (Monash University, Melbourne, VIC, Australia).
DATA AVA I L A B I L I T Y
All simulation outputs are available upon request by e-mailingroberto.iaconi@kusastro.kyoto-u.ac.jp.
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