Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries

Draft version June 17, 2020 Typeset using LATEX twocolumn style in AASTeX62

Ryan M. Lau,1 J.J. Eldridge,2 Matthew J. Hankins,3 Astrid Lamberts,4 Itsuki Sakon,5 and Peredur M. Williams6

1Institute of Space & Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan 2Department of Physics, University of Auckland, Private Bag 92019, Auckland 1010, New Zealand 3Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA 4UniversitéCôted’Azur, Observatoire de la Côted’Azur, CNRS, Laboratoire Lagrange, Laboratoire ARTEMIS, France 5Department of Astronomy, School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 6Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ

(Accepted June 12, 2020) Submitted to ApJ

ABSTRACT We present a dust spectral energy distribution (SED) and binary stellar population analysis revisiting the dust production rates (DPRs) in the winds of carbon-rich Wolf-Rayet (WC) binaries and their impact on galactic dust budgets. DustEM SED models of 19 Galactic WC “dustars” reveal DPRs of −10 −6 −1 M˙ d ∼ 10 − 10 M yr and carbon dust condensation fractions, χC , between 0.002 − 40%. A large (0.1 − 1.0 µm) dust grain size composition is favored for eﬃcient dustars where χC & 1%. Results for dustars with known orbital periods verify a power-law relation between χC , orbital period, WC mass-loss rate, and wind velocity consistent with predictions from theoretical models of dust formation in colliding-wind binaries. We incorporated dust production into Binary Population and Spectral Synthesis (BPASS) models to analyze dust production rates from WC dustars, asymptotic giant branch stars (AGBs), red supergiants (RSGs), and core-collapse supernovae (SNe). BPASS 6 models assuming constant star formation (SF) and a co-eval 10 M stellar population were performed at low, Large Magellanic Cloud (LMC)-like, and solar metallicities (Z = 0.001, 0.008, and 0.020). Both constant SF and co-eval models show that SNe are net dust destroyers at all metallicities. Constant SF models at LMC-like metallicities show that AGB stars slightly outproduce WC binaries and RSGs by factors of 2 − 3, whereas at solar metallicites WC binaries are the dominant source of dust for ∼ 60 Myr until the onset of AGBs, which match the dust input of WC binaries. Co-eval population models show that for “bursty” SF, AGB stars dominate dust production at late times (t & 70 Myr).

Keywords: infrared: ISM — stars: Wolf-Rayet — (stars:) circumstellar matter — (ISM:) dust, extinction

1. INTRODUCTION 2007). All of the known dust-forming WR stars, here- arXiv:2006.08695v1 [astro-ph.SR] 15 Jun 2020 Dust formation can surprisingly occur in the hostile after referred to as “dustars” (Marchenko & Moffat circumstellar environment of Wolf-Rayet (WR) stars, 2007), are of the carbon-rich (WC) sub-type. These WC which are descendants of massive O-stars character- dustars typically exhibit late spectral sub-types (WC7 −1 - WC9), which are characterized by relatively cool WR ized by fast winds (& 1000 km s ), hot photospheres 5 photospheres (T∗ ∼ 40000−70000 K; Sander et al. 2019). (T∗ & 40000 K), and high luminosities (L∗ ∼ 10 L ; Gehrz & Hackwell 1974; Williams et al. 1987; Crowther In order to explain the observed dust formation in the hostile environment of WC dustars, the binary nature is believed to play a key role: strong winds from the WC Corresponding author: Ryan Lau star collide with weaker winds from an OB-star compan- [email protected] ion and create dense regions in the wake of the compan- 2 Lau et al. ion’s orbit that allow for dust to condense (Williams et due to the shocks they drive into the surrounding ISM al. 1990; Usov 1991; Cherchneff 2015). (Temim et al. 2015). The density enhancements in the wind collision region There are, however, major challenges in addressing the facilitates rapid radiative cooling that lead to dust for- dust contribution from WC dustars in the ISM of galax- mation in addition to shielding newly formed dust grains ies across cosmic time. The measured dust production from UV photons emitted by the central binary. Unam- rates of WC dustars show a wide range of conflicting biguous evidence of dust formation regulated by binary values in literature throughout the past several decades. influence was presented in high spatial resolution near- This is due in part to uncertainties in distance estimates IR images of the WC9 binary WR104 by Tuthill et al. and the different techniques used to model dust emis- (1999) that revealed a remarkable dust “pinwheel.” sion, which is also difficult given the complex dust mor- The binary orbital parameters such as the semi-major phology observed around WC dustars. Another chal- axis/orbital period and eccentricity modulate the dust lenge is that binary stellar evolution tracks are complex formation in WC dustars. For example, systems with and much more difficult to model than single star evo- low eccentricity and short orbital periods (∼ yr) like lution. WR104 exhibit persistent dust formation in continuous In this paper we study the dust production from WC pinwheel plumes resembling an Archimedean spiral that dustars by conducting a consistent dust spectral energy change in position angle as the WC star and its binary distribution (SED) analysis utilizing archival IR pho- companion move in their orbit (Tuthill et al. 2008). Al- tometry and spectroscopy of a sample of 19 Galactic ternatively, WC dustars with high orbital eccentricity dustars with distance estimates from Gaia DR2 (Bailer- and longer orbital periods (& 5 yr) like WR140 exhibit Jones et al. 2018; Rate & Crowther 2020). Based on periodic dust formation, where the onset of dust for- the results of our SED analysis, we incorporate dust mation corresponds to periapse when the WC star and production in Binary Population and Spectral Synthe- its companion are near their closest orbital separation sis (BPASS; Eldridge et al. 2017; Stanway & Eldridge (Williams et al. 2009a). 2018) models to investigate the dust input from WC Despite the fact that WC dustars can produce copious dustars relative to AGB stars, red supergiants (RSGs), −8 −6 −1 amounts of dust (M˙ d ∼ 10 − 10 M yr ; Williams and core-collapse SNe at difference metallicities repre- et al. 1987; Hankins et al. 2016; Hendrix et al. 2016) they sentative of different epochs in cosmic time. We also have been commonly overlooked as significant sources of model the dust input in the well-studied Large Mag- dust in the ISM of galaxies in the local and early Uni- ellanic Cloud (LMC), where AGB stars are claimed to verse. The input from WC dustars compared to lead- be a significant source of dust and SN are likely net ing dust producers like asymptotic giant branch (AGB; dust destroyers (Riebel et al. 2012; Temim et al. 2015). Boyer et al. 2012) stars and core-collapse supernovae This work presents the first implementation of BPASS (SNe; Dwek & Cherchneff 2011) is thought to be low to investigate dust production from binary stellar pop- given their relative rarity as products of only the most ulations. massive O-stars. Additionally, at low metallicities it is The paper is organized as follows. First, we describe difficult to form a WR star in the context of single star the sample selection and the IR photometric and spec- evolution (Conti 1975) due to a lack of metals that drive troscopic data sets and extinction correction utilized for mass-loss and the expulsion of the hydrogen envelope. the SED modelling (Sec.2). In Sec.3, we detail our However, the influence of their binary nature on the dust SED modeling approach with DustEM, present the formation of WR stars and their dust formation is not results of our analysis with descriptions of selected WC well-understood, especially given observations that re- dustars, and compare our result with previous stud- veal a majority (& 70%) of massive stars are in binaries ies and the theoretical dust formation model by Usov that will eventually interact with their companion over (1991). In Sec.4, we describe the BPASS dust models their lifetimes (Sana et al. 2012). Such binary interac- and present the results of constant star formation and tion enables the formation of WR stars through mech- co-eval population models in environments correspond- anisms such as envelope stripping via Roche-Lobe over- ing to low (Z = 0.001), LMC-like (Z = 0.008), and solar flow (Mauerhan et al. 2015; De Marco, & Izzard 2017). (Z = 0.020) metallicites. We also provide a compari- This provides formation channels of WC binaries even son between BPASS model results and the LMC that at low metallicities. Revisiting the impact of WC dus- highlight the importance of star formation history in tars is motivated by the need for additional dust input modeling the dust input from massive stars. Lastly, we sources since SNe may in fact be net dust destroyers discuss the astrophysical implications of our study on the dust production from WC dustars (Sec.5). Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 3

2. WC DUSTAR SAMPLE AND OBSERVATIONS ration was used with 20” chop and nod amplitudes. The 2.1. Dustar Sample Selection total integration time on WR48a was 15 minutes. Raw images were accessed and downloaded from the ESO The goal of this analysis is to fit dust spectral en- Science Archive Facility and processed using the Modest ergy distribution (SED) models to the mid-IR emis- Image Analysis and Reduction (MIRA) software written sion from WC dustars incorporating distance informa- by Terry Herter (See Herter et al. 2013). tion from Gaia DR2 (Rate & Crowther 2020) to de- The NeII 2 imaging observations of WR48a achieved rive the dust “shell” radii, mass, production rates, and near diffraction-limited imaging with a measured Gaus- condensation fraction. Dust SED models require spec- sian full-width at half maximum (FWHM) of 0.45”. troscopy or well-sampled photometry between ∼ 2 − 30 µm where the thermal emission from circumstellar dust 2.2.2. Space-Based Mid-IR Spectroscopy and Photometry dominates over the photosphere and free-free emission from ISO, Spitzer, and WISE from ionized winds in the WC system (e.g. Williams et ISO/SWS. Five WC dustars in this sample have al. 1987). Beyond ∼ 30 µm, background emission from archival 2.2 - 40 µm medium resolution (R ≈ 250 − 600) cooler ISM dust may start to contaminate the IR SED. spectra taken by the Short Wavelength Spectrometer Dustar distances are adopted from the recent study by (SWS; de Graauw et al. 1996) on the Infrared Space Ob- Rate & Crowther(2020), who perform a Bayesian anal- servatory (ISO; Kessler et al. 1996) that were obtained ysis on Gaia DR2 parallaxes to 383 Galactic WR stars in the WRSTARS program (PI - van der Hucht; van with priors based on HII regions and dust extinction. der Hucht et al. 1996). Archival ISO/SWS spectra of Since a non-negligible fraction of known WC dustars these five dustars (WR48a, WR70, WR98a, WR104, and exhibit variability on . 1 yr timescales (Williams 2019), WR118) were downloaded from the database of SWS the known variables in this sample are restricted to those spectra processed and hosted by Sloan et al.(2003) 2. that have contemporaneous mid-IR observations or mid- The “sws” files, which are the final versions of the SWS IR spectroscopy out to at least ∼ 20 µm taken in a single spectra corrected for segment discontinuities and over- epoch. The dustars with no observed variability in this laps, were used for the SED analysis. sample have ∼ 10 − 20 µm spectroscopic or photomet- In order to verify the quality of the SWS data ric coverage with sufficiently high spatial resolution at and identify possible normalization issues between longer wavelengths (FWHM. 6”) to distinguish possi- SWS bands, the “pws” files that show the spectra ble contamination from surrounding IR sources or ISM prior segment-to-segment normalization were inspected. emission. All five dustars with ISO/SWS data did not exhibit Out of the 88 currently known WC dustars in V 1.23 segment-to-segment discontinuities larger than ∼ 10% (July 2019) of the Galactic Wolf Rayet Catalogue (Ross- 1 below 27.5 µm, which is the wavelength where the 3E lowe & Crowther 2015) , our sample consists of 19 dus- band of the long wavelength section starts. Due to the tars shown in Table1 that meet the above criteria. flux discontinuities and larger flux uncertainties beyond 2.2. Observations and Archival Data 27.5 µm , only the 2.2 - 27.5 µm data were used for the SED fitting. The spectra of WR48a, WR98a, WR104, 2.2.1. Mid-IR Imaging of WR48a with VLT/VISIR and WR118 were smoothed by a median filter with a Mid-IR imaging observations of WR48a (PID: 097.D- 51-element kernel, and the spectrum of WR70, which 0707(A); PI - Lau) were performed on the Very Large had an “sws” file with wavelengths sampled a factor Telescope (VLT) at the ESO Paranal observatory using of 4 higher times higher than the other 4 sources, was the VLT spectrometer and imager for the mid-infrared smoothed with a 201-element kernel. (VISIR, Lagage et al. 2004) at the Cassegrain focus of Spitzer/IRS. Six WC dustars have archival mid- UT3 on 2016 June 15. Images of WR48a presented in IR spectra taken by the Infrared Spectrograph (IRS; this work were taken with the NeII 2 filter (λc=13.04 Houck et al. 2004) on the Spitzer Space Telescope µm, ∆λ = 0.22) and obtained using chopping and nod- (Werner et al. 2004) across multiple programs through- ding to remove the sky and telescope thermal back- out the Spitzer “cold mission” (2004 - 2009). Hi-Res ground emission. (R∼ 600) Spitzer/IRS spectra of WR140 (PID - 124; PI Given the size of the field of view with VISIR of - Gehrz), WR19, WR103, and WR53 (all 3 PID 199; PI 00 38×38 in comparison to the extent of the dust emission - Houck) were downloaded from the Combined Atlas of from WR48a (∼ 500), an on-detector chop-nod configu-

2 https://users.physics.unc.edu/∼gcsloan/library/swsatlas/ 1 http://pacrowther.staﬀ.shef.ac.uk/WRcat/ atlas.html 4 Lau et al.

Sources with Spitzer IRS Spectra (CASSIS; Lebouteiller The Spitzer, WISE, and ground-based 2MASS pho- et al. 2015)3. The spectrum of WR19 was published in tometry provided in the MIPSGAL 24 µm point source the WC dust chemistry study by Marchenko & Moffat catalog (Gutermuth & Heyer 2015) were primarily uti- (2017), and the spectrum of WR103 was published by lized for the non-variable dustars without ISO spec- Crowther et al.(2006) in their UV to mid-IR spectral troscopy. analysis comparing WC9 and [WC9] stars. Ardila et al. 2.2.3. Ground-based IR Photometry (2010) also included the spectra of WR53 and WR103 in their atlas of Spitzer stellar spectra. Broad emission line Given their brightness in the mid-IR (& Jy), WC features from WR103, WR140, and WR19 were masked, dustars have been targeted by ground-based observa- and the lower signal-to-noise ratio spectra of WR140 tories in the IR for many decades (e.g. Williams et al. and WR19 were smoothed by a median filter with an 1987). In the near-IR, JHK fluxes from 2MASS (Skrut- 11-element kernel. skie et al. 2006) were incorporated in the SED model- In order to verify the photometric accuracy of the long ing for the following dustars without ISO/SWS cover- wavelength (> 20 µm) IRS spectra of WR140, the flux age: WR48b, WR53, WR59, WR95, WR96, WR103, was checked against 24 µm photometry from the Multi- WR106, WR119, WR121, and WR124-22. Mid-IR L- band Imaging Photometer for Spitzer (MIPS; Rieke et ,M-,N-, and Q-band photometry published by Williams al. 2004) taken in the same program and within ∼ 1 et al.(1987) taken by the ESO 3.6-m and the United month of the IRS observations (PID - 124; PI - Gehrz). Kingdom Infra-Red Telescope (UKIRT) was used for The 24 µm Spitzer/MIPS photometry of WR140 ex- WR103, WR106, and WR119. tracted with a 35”-radius aperture and a 40 - 50” back- For WR137, one of the known periodic dust-makers, 4 the SED is composed of contemporaneous J, H, K, ground annulus is F24,MIPS = 1.07±0.05 This is consis- L, M, N, and Q photometry taken in 1985.47 from tent with the IRS spectrum at 24 µm (F24,IRS ≈ 0.8±0.4 Jy). UKIRT and published by Williams et al.(2001). Near- The dustars WR48a and WR98a had coverage from contemporaneous JHKLMNQ photometry taken by both Spitzer/IRS (PID - 40285, PI - Waters) and UKIRT in 1993.5 was also adopted for the SED of ISO/SWS, but the ISO spectra were adopted in this the periodic dust-maker WR125 (Williams et al. 1994). work for SED modeling due to its extended wavelength In the unique case of the periodic dust-maker WR140, coverage and the sufficiently high signal-to-noise detec- ground-based mid-IR observations with UKIRT by tion. Williams et al.(2009a) were linked with the space- Spitzer/IRAC and MIPS. For the non-variable based spectroscopic observations by Spitzer/IRS. Al- dustars, mid-IR Spitzer photometry were adopted from though near-IR photometry of WR140 was not ob- the Galactic Legacy Infrared Mid-Plane Survey Extraor- tained around the same time as the mid-IR UKIRT dinaire (GLIMPSE; Churchwell et al. 2009) taken by the and IRS observations, JHK measurements were taken Infrared Array Camera (IRAC; Fazio et al. 2004) at 3.6, during the previous dust formation epoch at an iden- 4.5, 5.8, and 8.0 µm in addition to 24 µm photome- tical orbital phase (φ = 0.43; Williams et al. 2009a). try from the MIPS Galactic Plane Survey (MIPSGAL; Importantly, the epoch-to-epoch stability of the near- Carey, et al. 2009). IR light curve is consistent to within 0.1 mag. The WISE. For dustars without any significant contami- semi-contemporaneous and phase-consistent coverage of nation or confusion from background emission or nearby WR140 from 1.2 - 35 µm therefore enabled the dust 00 SED analysis of this system. sources with . 10 , four band mid-IR photometry (3.4, 4.6, 12.1, and 22.0 µm) from the Wide-field In- Table2 provides a summary of the archival dataset frared Survey Explorer (WISE; Wright et al. 2010) in used for each of the 19 dustars. the ALLWISE program (Cutri & et al. 2013) were 2.2.4. IR Extinction Correction adopted. WISE W3 (12.1 µm) photometry is notably Many of the WC dustars in this sample are heavily valuable since it bridges the wavelength gap between extinguished (A 5) along the line of sight by the the Spitzer/IRAC Ch4 (8.0 µm) and MIPS 24 µm mea- V & ISM, which is apparent from deep silicate absorption in surements. their IR SEDs at 9.7 µm (e.g. Chiar & Tielens 2001). This silicate-dominated extinction is interstellar in na- 3 https://cassis.sirtf.com/ ture since the circumstellar dust formed by the WC dus- 4 An aperture correction factor of 1.08 was included in this flux tars is carbon-rich (Roche & Aitken 1984). In order calculation in accordance with Table 4.13 of the MIPS Instrument to correct for interstellar extinction, the dustar SEDs Handbook for the aperture and background annulus radii used. were dereddened with the “Local ISM” extinction curve Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 5 from Chiar & Tielens(2006) and adopting the visual • Single component dustar models are assumed to extinction, Av (= 1.1AV), derived by Rate & Crowther have a single geometrically thin dust shell centered (2020)5 except for WR98a due to its large distance and on the WC+OB binary. extinction uncertainties. The visual extinction towards WR98a is instead based on the value from van der Hucht • Double component dustars are modeled with two geometrically thin dust ring components with dif- (2001). The v filter (λC = 5160 A˚) is on the narrow-band system introduced by Smith(1968) specifically to study ferent radii from the central binary utilizing the technique described below in Sec. 3.2 in greater WR stars. The adopted Av for each dustar is shown in Tab.3. The selection of the local ISM extinction curve detail. by Chiar & Tielens(2006) was motivated by their use of Note that in the single component model, the morphol- WC dustar spectra to define the shape of the 1.25 - 25 ogy of the dust shell (e.g. torus vs. spherical shell) does µm extinction. Since several of the dustar spectra ex- −2 not affect the dust emission spectrum. tended beyond 25 µm, a consistent λ power-law was In addition to circumstellar dust, the IR excess from used in this work to extrapolate the extinction curve. WC dustars can originate from free-free emission in their ionized winds (Cohen et al. 1975). The IR excess due to free-free emission can be characterized by a power- 3. WC DUSTAR SED MODELING RESULTS AND −0.96 law Fff ∝ λ (Morris et al. 1993) and may there- ANALYSIS fore dominate at shorter IR wavelengths such as the J- 3.1. WC Dustar SED Modeling Overview band (λ = 1.25 µm). In order to remove contamination from free-free emission in the SEDs, we subtract this The complex “pinwheel” morphology of the spatially free-free emission power-law model normalized at the J- resolved circumstellar dust observed around several well- band flux for dustars where the J-band flux is 10% of studied dustars such as WR104 (Tuthill et al. 1999; & the mid-IR flux peak associated with circumstellar dust. Soulain et al. 2018) and WR98a (Monnier et al. 1999) In the unique case of WR140 where the emission from presents a complicated scenario for radiative transfer the central system has been spatially resolved from ex- modeling. For example, Hendrix et al.(2016) performed tended circumstellar dust, an interpolation is performed radiative transfer dust models on 3D hydrodynamic sim- between the IR photometry of the stellar wind contin- ulations fitting the observed emission and morphology of uum measured by Williams et al.(2009a) to characterize the dust plume around WR98a. Alternatively, Williams and subtract this component. et al.(1987) had fit simple analytic dust shell models to dustar SEDs assuming their dust emission is optically 3.2. Two-component Dust Model thin. Zubko(1998) provided an updated SED analysis using a detailed theoretical model of dust shells that In this section we describe the framework of the two account for grain formation physics and dynamics on a component dust model. The “pinwheel” dust morphol- sample of Galactic WC dustars with photometry from ogy from these systems are approximated as two concen- Williams et al.(1987). Although the Zubko(1998) SED tric dust rings. Figure1 presents a schematic illustra- models were performed before the circumstellar emission tion of the different components in this model and the from WC dustars were spatially resolved, the derived comparison to the pinwheel dust, where the first dust dust production rates and carbon condensation fraction component corresponds to the first dust spiral “coil” and provide valuable benchmarks for comparison. the second component corresponds to the second contin- We performed dust SED fits to the 19 WC dustars in uation of this coil. In these models, the inner dust ring our sample with the tool DustEM (Compiègneet al. 2011) attenuates the radiation impinging on the outer ring and with single or double dust component models. DustEM is is described as follows. a numerical tool that computes the dust emission in the The incident stellar radiative flux on dust components optically thin limit heated by an input radiation field 1 and 2 at distances r1 and r2 (where r1 < r2) from the with no radiative transfer. Single dust component mod- central heating source, respectively, can be described as els were attempted for all dustars initially, and double −τ L∗ L∗e components models were used for SEDs with unsatis- F = and F = , (1) 1 4πr2 2 4πr2 factory single component fits. The two different SED 1 2 modeling methods are described as follows: where τ is the optical depth through component 1. De- riving the radiative heating of component 1 is therefore straightforward since it only requires information of the 5 WR Av is referred to as Av in Rate & Crowther(2020) heating source radiation field and its distance to the 6 Lau et al.

regions within the ﬁrst two pinwheel arcs (e.g. Tuthill Component 2 et al. 2008). This implies that

L + L Ω = IR,1 IR,2 , (4) L∗

from which it follows from Eq.3 that F2 can be re- expressed as WC+OB L∗ 1 F2 = 2 1 − −1 , (5) Component 1 4πr2 1 + f Edge-on Cross Section where f ≡ LIR,1/LIR,2. With equations1&5, we have therefore arrived at a simplified 2-component pseudo- radiative transfer model with L∗, f, r1, and r2 as the Component 2 model parameters. Component 1 In a test for limit cases, it is apparent that when component 1 absorbs all of the stellar flux (f→∞), F2 = 0. Conversely, when component 1 does not absorb any of L∗ the stellar flux (f→0), F2 = 2 . 4πr2 WC+OB This two component dust model is used for four dustars: WR48a, WR98a, WR104, and WR118.

3.3. Adopted and Derived SED Model Parameters In our DustEM SED modeling, we input the luminosity Face-on “Pinwheel” and radiation field of the heating source, the distance to the dust components, dust composition, and the dust Figure 1. (Top) Two component dust model cross-section grain size distribution as model inputs. For the two schematic (Bottom) Face-on “pinwheel” dust morphology component models, we also input the IR luminosity ratio schematic of continuous WC dustars overlaid with the approximated position of the two dust components in this of the two dust components, f (see Eq.5). model. We adopt the appropriate radiation field that is rep- resentative of the spectral sub-type of each WC dus- heating source. However, the radiative heating of com- tar from the Potsdam Wolf-Rayet Star (PoWR) model ponent 2 requires information on the attenuated stellar atmospheres (Gräfeneret al. 2002; Sander et al. 2012, flux through component 1. This attenuation can be re- 2019). The radiation field is then scaled by the lumi- lated to the total IR luminosity radiated by component nosity of the heating source and the distance to the dust components assuming the incident flux decreases 1, LIR,1: as F ∝ r−2 (Eq.1). While the radiation field and lumi- −τ nosity are adopted from previous studies, we performed LIR,1 = L∗(1 − e )Ω, (2) a logarithmic grid search for the dust component dis- where Ω is the geometric coverage fraction of compo- tances and (for the two component cases) the IR lumi- nents 1 and 2 around the central heating source and it is nosity ratio of the two dust components. The grid search assumed both components have the same coverage frac- range and intervals for the different free parameters of tion (Fig.1). From Eq.2, it follows that e−τ = 1− LIR,1 , L∗ Ω each dustar model is provided in Table2. Table2 also and the incident flux on component 2 can then be ex- lists the observatories from which the IR archival data pressed as were obtained for each dustar in the sample. The dust grain size distribution in WC dustars is still 1 L F = L − IR,1 . (3) disputed and is one of the issues addressed by this work. 2 4πr2 ∗ Ω 2 Theoretical studies on WC dustars winds by Zubko We assume that 100% of the stellar flux impinging on (1998) predict that dust grains only grow up to sizes components 1 and 2 is absorbed and re-radiated into of a ∼ 0.01 µm, which has been corroborated by dust the IR by the two components. This assumption is mo- SED analysis of observed IR emission from the dustar tivated by spatially resolved observations that reveal the WR140 (Williams et al. 2009a). However, IR dust emis- IR emission from WC dustars are dominated by emitting sion and extinction studies of WC dustars by different Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 7 groups suggest the presence of large a & 0.5 µm dust continuous dust makers, the instantaneous dust produc- grains (Chiar & Tielens 2001; Marchenko et al. 2002; tion rate calculation will vary depending on the phase Rajagopal et al. 2007). the observations. The orbital period-averaged dust pro- In order to address this grain size discrepancy, we test duction rate calculation (Eq.7) is therefore applied to both small and large grain size distributions for the WC the periodic, non-continuous dustars WR 140, WR 137, dustars in our sample that have been spatially resolved. WR125, and WR 19, while Eq.6 is applied to the other Since heat capacity increases with increasing grain size, 15 dustars. Note that for continuous dust makers, the large grains need to be at a closer distance to the ra- dust production rate averaged over an orbital period will diative heating source than small grains in order to ex- be the same as the instantaneous dust production rate. hibit a similar temperature and spectral shape. There- In the 2-component dust models, we take a conserva- fore, we can compare which grain size distribution in tive approach and estimate the dust production rates our SED models provides dust shell distances consis- based only on the dust mass and the distance to the 1st tent with the observed circumstellar dust morphology dust component since cooler and more extended dust constraints. The small (large) grain size distributions may contribute to the dust mass determined for the 2nd includes dust grains ranging from a = 0.01 − 0.1 µm component. (0.1 − 1.0 µm) with a number density distribution pro- Lastly, the fraction of carbon in the WC winds that −3 portional to n(a) ∝ a . We note that the grain size condense into dust, χC , is estimated based on the dust has a minimal effect on the derived dust mass since this production rate, the adopted mass-loss rate for the WC quantity is fit from the longer wavelength IR emission wind, and an assumption that the WC wind is com- (& 10 µm) in the SED where the dust opacity is not posed of 40% carbon by mass (Sander et al. 2019). The as sensitive to grain size as the shorter wavelength IR adopted WC dustar properties are summarized in Ta- emission (e.g. Harries et al. 2004). ble3. We assume that the dust grains are composed purely 3.4. WC Dustar SED Modeling Results of amorphous carbon, which is consistent with their fea- tureless IR spectra and the C-rich environment in the In this section we present the results of our DustEM SED vicinity of the WC star (Williams et al. 1987; van der models for the 19 WC dustars in our sample. First, as a Hucht et al. 1996). We adopt the DustEM amorphous verification of our modeling approach we highlight the carbon (“amCBEx”) grains with refractive indices de- results on the well-studied periodic dust-maker WR140, rived by Zubko et al.(1996) and Compiègneet al.(2011) the continuous “pinwheel” dust-maker WR104, and −3 and assume a bulk density of ρb = 2.0 g cm . the 32.5-yr orbital period dustar WR48a. Then we By performing a least-squares fit of the DustEM model present and describe the results on the remaining IR- to the WC dustar SEDs, we derive the dust mass (Md), luminous (LIR/L∗ & 0.1) dustars, a selection of the dust temperature (Td), and distances between the dust single component dustars, and additional systems with components and central system (r). For the continuous angular size constraints. Lastly, we discuss the over- dust-makers with a dust expansion velocity of vexp, the all results on dust formation and grain size properties, dust production rate can then be approximated by compare results from previous studies, and test our results against the theoretical model of dust formation in Md vexp colliding winds by Usov(1991). The results from the (continuous) M˙ d ∼ , (6) r DustEM SED models are summarized in Table4. where v is assumed to be comparable to the stellar exp 3.4.1. The Archetypal Periodic Dust-Maker WR140 wind velocity v∗ or is derived directly from dust proper motion measurements in multi-epoch imaging. WR140 is a WC7+O5 system with a well-defined 7.94 For the periodic, non-continuous dust-makers with a yr orbital period, a high orbital eccentricity of e = 0.90, 6 recurring dust formation timescale P associated with the and a total luminosity of L∗ ∼ 1 × 10 L (Williams et orbital period of the central binary (e.g. Williams et al. al. 2009a; Monnier et al. 2011). The distance to WR140 +110 2009a; Monnier et al. 2011), we approximate the dust measured by Gaia parallax is d = 1640−90 pc (Rate & production rate by Crowther 2020), which is consistent with previous distance estimates (Dougherty et al. 2005; Monnier et al. Md 2011). (periodic) M˙ d ∼ . (7) P Dust formation in WR140 only occurs when the bi- Eq.7 effectively calculates the dust production rate nary system is at periapse. The proper motion of the averaged over the orbital period, whereas Eq.6 is an “in- resulting dust “arc” formed during periapse has been stantaneous” dust production rate. For periodic, non- characterized by multi-epoch, spatially resolved mid-IR 8 Lau et al. 2.5 WR140 (2003 December) WR140 IR Phot (Gemini/Michelle - 12.5 m) Spitzer/IRS 2.0 Comp 1 (r1 = 1170 AU)

1.5

1.0 Flux (Jy)

0.5

0.0 2" 0 5 10 15 20 25 30 35 40 Wavelength ( m)

Figure 2. (Left) Mid-IR 12.5 µm image of WR140 taken by Gemini/Michelle (Williams et al. 2009a) in 2003 Dec overlaid with circles centered on WR140 representing the fitted distances of emitting dust for the large (solid) and small (dashed) grain size distribution models. The small grain dust model best matches the observed location of the dust plume. (Right) Best-fit DustEM SED model of WR140 using the small grain size distribution fit to UKIRT L- and M-band photometry taken in 2004 Jun (Williams et al. 2009a) and Spitzer/IRS spectroscopy taken in 2004 May. Gray bars correspond to the 1σ flux uncertainty. imaging as the arc propagates away from the central timescales in WR140. SED fits from ground-based ob- binary (Fig.2, Left; Williams et al. 2009a). These im- servations by Williams et al.(2009a) indicate a total −8 ages allows us to verify our SED model-derived separa- dust mass of less than 2 × 10 M at a phase of 0.56 tion distances between the dust component and central around WR140, which consistently constrains our de- heating source. For the line-of-sight extinction we adopt rived dust mass. Adopting a total mass-loss rate of −5 −1 Av = 2.21 (Rate & Crowther 2020). M˙ ≈ 2 × 10 M yr derived by X-ray monitoring We perform single component DustEM models to the observations of shocked gas in the wind collision region stellar wind-subtracted 5 - 37 µm Spitzer/IRS spectrum between the WC and O stars (Sugawara et al. 2015) taken on 2004 May, UKIRT L- and M-band imaging and assuming a 40% carbon composition by mass, the taken on 2004 Jun, and JHK imaging taken on 1996 carbon dust condensation fraction is χC ≈ 0.01%. Aug where WR140 was at a nearly identical orbital phase (φ = 0.43) as the UKIRT and Spitzer observations 3.4.2. The Continuous “Pinwheel” Dust-Maker WR104 (Fig.2, Right). This orbital phase corresponds to 3.4 yr WR104 is the prototypical, continuous dust-maker after IR maximum and periastron passage. The small that exhibits a nearly face-on pinwheel (Fig.3, Left) (large) dust grain distribution SED fit provides a sepa- with an orbital period of 242 days Tuthill et al.(1999, ration distance between the dust component and central 2008). The central binary is composed of a WC9+OB +310 +160 +720 heating source of r = 1170−340 AU (360−100 AU). Spa- star and has a Gaia-derived distance of d = 2740−550 pc. tially resolved mid-IR imaging observations of WR140 This is consistent with the well-defined distance deter- at this orbital phase show that the extended dust arc is mined from the location of its possible stellar association 700 - 900 mas from the central source (Williams et al. host, Sgr OB1, and observations of the proper motion 2009a), which is closely consistent with the separation of its circumstellar dust (d = 2580 ± 120 pc; Soulain et distance derived from our small grain dust distribution al. 2018). Given the tighter constraints from their high model, 1170 AU ≈ 700 mas (Fig.2, Left). This small spatial resolution imaging, we adopt the Soulain et al. grain distribution is also consistent with the dust emis- (2018) distance for the dust SED model. The line-of- sion analysis by Williams et al.(2009a) who deduced a sight extinction towards WR104 is Av = 6.67 (Rate & characteristic grain size of 0.01 µm. Crowther 2020). We adopt a total system luminosity of 5 From the small grain dust SED, we derive a total dust L∗ = 2.5×10 L , consistent with Monnier et al.(2007) +3.84 −9 mass of Md = (6.44−3.30) × 10 M , which implies a and the mean WC9 luminosity derived by Sander et al. ˙ +4.8 −10 (2019). dust production rate of Md = (8.1−4.2) × 10 M yr−1 (Eq.7) given the periodic 7.94 yr dust formation Since single dust component models fail to fit the ISO/SWS spectrum of WR104 between 2 - 27.5 µm, we Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 9 800 WR104 (LG) ISO/SWS 700 Comp 1 (r1 = 70 AU) Comp 2 (r2 = 460 AU) 100 600 Combined Dust Emission 500

0 400

Flux (Jy) 300

Milliarcseconds 200 -100 100 0 -100 0 100 0 5 10 15 20 25 30 35 40 Milliarcseconds Wavelength ( m)

Figure 3. (Left) Near-IR reconstructed interferometric image of WR104 taken with the CH4 (λc = 2.27 µm) filter on the Keck I Telescope reproduced from Figure 1 in Tuthill et al.(2008) centered on the origin of their best-fit Archimedean spiral model (dotted line) and overlaid with red circles representing the location of the fitted dust component 1 for the large (solid) and small (dashed) grain models. Contour levels are 0.4%, 1%, 2%, 5%, 10%, and 50% of the peak emission. The large grain dust model best matches the observed location of the centralized peak dust emission. (Right) Best-fit 2-component DustEM SED model of WR104 using the large grain size distribution fit to ISO/SWS spectroscopy. revGray bars correspond to the 1σ flux uncertainty. apply the double component SED models (Fig.3, Right) • The large grain size distribution we adopt vs. the and derive separation distances between the central bi- small grain distribution used by Harries et al. +60 +20 nary and dust components of r1 = 240−80 AU (70−10 (2004) implies a closer/shorter distance of the dust +1130 +110 AU) and r2 = 1300−740 AU (460−90 AU) for the small component to the central binary and thus a higher (large) dust distribution models. High spatial resolution dust production rate (see Eq.6). IR imaging by Tuthill et al.(2008) show that the distance between the central binary and the onset of the When applying a small grain dust model and adopting spiral dust plume where the IR emission peaks is ∼ 15 a distance of 1600 pc we arrive at a consistent dust pro- ˙ −7 −1 mas (40 AU). Figure3 (Left) shows the approximate lo- duction rate of Md ≈ 6 × 10 M yr . cation of the first dust component for small and large The dust production rate from our large grain SED grain models compared to the observed dust morphol- model shows that WR104 is producing the most dust ogy. Given the closer agreement of the first dust compo- out of the all the dustars in our sample and is likely nent, we favor the large grain distribution for WR104. the highest dust maker amongst all known WC dustars −5 From our large grain dust SED model, we derive dust (Tab.4). Assuming a WC mass-loss rate of 3 ×10 M −1 +0.70 −6 yr (Crowther 1997; Harries et al. 2004) and a 40% car- masses of Md1 = (1.19−0.44) × 10 M and Md2 = +3.09 −5 bon mass fraction, we infer a carbon dust condensation (6.06−2.06) × 10 M for the two dust components. fraction of χC ≈ 40%. This carbon dust condensation Adopting a dust expansion velocity of vexp = 1220 km s−1 (Howarth & Schmutz 1992), the dust production efficiency is notably higher than the ∼few percent de- ˙ +1.27 −6 rived by Harries et al.(2004) and implies that a sub- rate based on component 1 is Md = (4.39−0.97) × 10 −1 stantial fraction of the available carbon in the WC wind M yr . This dust production rate is a factor of ∼ 5 higher forms dust. than the M˙ = 8 ± 1 × 10−7 M yr−1 value derived d 3.4.3. The Longest Period (32.5-yr) Dustar WR48a by Harries et al.(2004) from 3D dust radiative transfer models. However, we can reconcile this discrepancy WR48a is a continuous but variable dust-maker host- based on the following points: ing a WC8 star with a proposed O-star companion. WR48a is the longest period dustar known with an IR • Harries et al.(2004) adopt a distance to WR104 of light curve-derived period of 32.5 yr and also exhibits 1600 pc as opposed to our value of 2580 pc, which episodes of brief dust-formation (Williams et al. 2012). 2 5 accounts for a factor of (2580/1600) ≈ 2.6 higher The total luminosity of the system is L∗ ∼ 4 × 10 +920 for our derived dust mass. L , and its Gaia-derived distance of d = 2270−570 pc is 10 Lau et al.

WR48a (2004 March 15) this dust arc in the VISIR images and its extended na- (Gemini/TReCS - 12.3 m) ture we assume position uncertainty of 0.23”, which is 0.5× the PSF FWHM (0.4500). Adopting the Gaia distance of 2270 pc, the dust expansion velocity of WR48a +390 −1 is vexp = 1000−240 ± 200 km s , where the first and second uncertainties are from the distance and proper motion, respectively. The derived expansion velocity is consistent with the 1200±170 km s−1 wind velocity measured for WR48a from its 10830-A˚ emission line width (Williams et al. 2012). We apply the 2-component dust SED model to fit the ISO/SWS spectrum of WR48a between 2 - 27.5 2" µm (Fig.5). From the 2-component model, we derive separation distances between the central system and +100 +70 WR48a (2016 June 15) dust components of r1 = 350−130 AU (110−40 AU) and +640 +440 (VLT/VISIR - 13.04 m) r2 = 2370−900 AU (720−150 AU) for the small (large) dust distribution models. Historic mid-IR light curves show an IR brightening consistent with enhanced dust formation around 1994.5 (Williams et al. 2012). Using the estimated dust expansion velocity of 1000 km s−1, this dust formed in 1994.5 would be located at ∼ 340 AU from the central binary at time of the ISO/SWS observation (1996 Feb). This distance estimate is consistent with the small grain distribution, which we therefore infer for the dust composition. 2" Based on our small grain distribution SED model (Fig.5), we derive dust masses for components 1 and 2 of +1.12 −7 +5.84 Md1 = (1.42−0.99) × 10 M and Md2 = (9.82−5.93) × Figure 4. (Top) Mid-IR 12.3 µm image of WR48a taken by −6 10 M . Using the component 1 distance and mass and Gemini/TReCS on 2004 Mar 15 overlaid with a dashed arc a dust expansion velocity of v = 1000 km s−1, we esti- showing the location of a prominent dust arc plume. (Bot- exp ˙ +3.48 −8 tom) 13.04 µm image of WR48a taken by VLT/VISIR on mate a dust production rate of Md = (8.46−4.38) × 10 −1 2016 Jun 15 overlaid with the 2004 dust arc position (dashed) M yr . The carbon dust condensation fraction is as above and its new position (dot-dashed) at the date of the therefore χC ≈ 0.1% assuming the radio-derived mass- −4 −1 VISIR observation. loss rate of 1.7×10 M yr (Zhekov et al. 2014) and a 40% carbon mass composition. slightly less than previous distance estimates based on its suggested association with galactic clusters Danks 1 and 2 (∼ 3.3−4.6 kpc, Danks et al. 1984). However, van 3.4.4. IR Luminous Dustars der Hucht(2001) determine a distance of 1200 pc based on its WC8 spectral type. We therefore adopt the Gaia WR98a. WR98a is a WC8 or WC9+OB dustar distance for our dust models since it falls between the exhibiting continuous dust formation and appears like two distance estimates. We also adopt a line-of-sight in- a “rotating pinwheel” that “revolves” with a 1.54 period (Monnier et al. 1999). The Gaia distance to- terstellar extinction towards WR48a of Av = 8.28 (Rate wards WR98a derived by Rate & Crowther(2020) is & Crowther 2020). +870 In Figure4, we present mid-IR imaging observa- d = 1260−410 pc. Despite its close distance, WR98a is tions taken by Gemini-South/TReCS (Marchenko & buried behind over 10 magnitudes of visual extinction Moffat 2007; PID - GS-2004A-Q-63, PI - A. Moffat) from the ISM along the line-of-sight based on a deep sil- and VLT/VISIR at similar N-band wavelengths at 2004 icate absorption feature (Chiar & Tielens 2006). Rate & March 15 and 2016 June 15, respectively. The overlaid Crowther(2020) derive a much lower visual extinction arc segment in Fig.4 shows the ∼ 1.100 proper motion of Av = 1.25, but assign it with a ‘b’ flag that denotes it of eastern dust arc over the 12.3 years separating the as highly implausible. Additionally, they note that the two observations. Given the low signal-to-noise ratio of Gaia parallax measurement of WR98a exhibits large astrometric noise (> 1 mas). Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 11

Due to the uncertainties in the Rate & Crowther 120 WR48a ISO/SWS (2020) interstellar extinction and distance measure- Comp 1 (r1 = 350 AU) ments, we adopt Av = 13.79 from van der Hucht(2001) 100 Comp 2 (r2 = 2370 AU) and a distance of d = 1900 pc derived by Monnier et Combined Dust Emission al.(1999) that is consistent with the upper distance 80 uncertainties from Gaia. Monnier et al.(1999) derive this distance to WR98a based on its dust proper mo- 60 −1

tion and adopting an expansion velocity of 900 km s Flux (Jy) (Williams et al. 1995). The stellar luminosity of WR98a 40 is not well-characterized given the high extinction. We 5 20 therefore adopt a system luminosity of L∗ = 1.5 × 10 L that is consistent with the value adopted in the 0 WR98a models by Hendrix et al.(2016). Given its 0 5 10 15 20 25 30 35 40 lower wind velocity, WC9 stellar properties are assumed Wavelength ( m) for WR98a. We fit double component dust SED models to the Figure 5. Best-fit two-component DustEM model of WR48a ISO/SWS spectrum of WR98a between 2 - 27.5 µm using the small grain size distribution fit to ISO/SWS spectroscopy taken in 1996 Feb. (Fig.6, Top Left) and derive dust component distances +50 +10 +1120 of r1 = 200−70 AU (60−10 AU) and r2 = 860−400 AU +190 WR118. WR118 is a continuous WC9 dust-maker (370−130 AU) for the small (large) grain size distribution models. Spatially resolved images of the circumstellar with a possible pinwheel morphology (Millour et al. dust around WR98a demonstrate that the majority of 2009). The Gaia distance towards WR118 determined +780 the mid-IR dust emission is concentrated in the central by Rate & Crowther(2020) is d = 2490−680 pc, which ∼ 70 mas, or ∼ 100 AU, of the central binary (Monnier exhibited astrometric noise in excess > 1 mas and large et al. 1999, 2007) with no prominent extended emission parallax uncertainty. However, this distance is consis- beyond ∼ 150 mas, or ∼ 200 AU. Similar to WR104, we tent with previous estimates based on photometry and prefer the large grain size distribution for WR98a. No- spectral type (d = 3130 pc, van der Hucht 2001). We tably, based on the dust component distances derived therefore adopt the Gaia distance for the dust SED mod- from the large grain SED model and adopting a dust els. WR118 is also heavily reddened by interstellar ex- expansion velocity of 900 km s−1 (Williams et al. 1995), tinction, where Av = 13.68 (Rate & Crowther 2020). We 5 the expansion timescale between the two components is adopt a combined stellar luminosity of L∗ = 2.5 × 10 ∼ 1.6 yr, which is consistent with the 1.54 yr orbital L , consistent with the mean WC9 luminosity derived period. The separation between the two dust compo- by Sander et al.(2019). nents is therefore consistent with the distance between We fit double component dust SED models to the the dust spirals in WR98a. ISO/SWS spectrum of WR118 between 2 - 27.5 µm From the large grain dust SED model, we derive dust (Fig.6, Top Right) and derive separation distances for +1.08 components 1 and 2 of r = 120+30 AU (30+10 AU) and masses for components 1 and 2 of Md1 = (1.82 ) × 1 −50 −10 −0.68 +320 +120 −7 +11.73 −6 r2 = 680 AU (260 AU) for the small (large) 10 M and Md2 = (9.25−5.29 ) × 10 M . Using the −300 −80 distance and mass of component 1, the dust production grain size distributions. High spatial resolution inter- ˙ +1.77 −7 −1 ferometric IR observations of WR118 indicate that dust rate is Md = (6.10−1.38) × 10 M yr . Adopting −4.66 is located with ∼ 15 mas (∼ 40 AU) of the central bi- the mean WC9 star mass-loss rate of M˙ = 10 M yr−1 and a carbon mass fraction of 40% (Sander et al. nary (Yudin et al. 2001; Monnier et al. 2007; Millour et 2019) for WR98a, we estimate a carbon dust condensa- al. 2009), which is comparable to size of component 1 in the large grain model. We therefore favor the large tion fraction of χC ≈ 7%. We note that there is a discrepancy between our de- grain models for WR118, which is also consistent with rived dust production rate and the value determined the large grain composition trend for the other IR lumi- from the hydrodynamic simulations by Hendrix et al. nous WC9 dustars in our sample. (2016), who obtain a dust production rate of ∼ 10−8 From the large grain SED models of WR118, we de- +6.24 −8 M yr−1. This discrepancy is primarily due to their termine dust masses of Md1 = (5.58−2.95) × 10 M +6.99 −6 assumption of a fixed value of 0.2% for the dust conden- and Md2 = (6.61−3.42) × 10 M for the components 1 sation fraction of the total WC mass loss rate. and 2. Adopting an expansion velocity consistent with −1 WC9 stars of vexp = 1390 km s , a WC9 mass-loss 12 Lau et al. 200 200 WR98a (LG) ISO/SWS WR118 (LG) ISO/SWS 175 Comp 1 (r1 = 60 AU) 175 Comp 1 (r1 = 30 AU) Comp 2 (r2 = 370 AU) Comp 2 (r2 = 260 AU) 150 Combined Dust Emission 150 Combined Dust Emission 125 125 100 100

Flux (Jy) 75 Flux (Jy) 75 50 50 25 25 0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Wavelength ( m) Wavelength ( m) 0.12 20.0 WR19 Spitzer/IRS WR70 ISO/SWS Comp 1 (r1 = 6870 AU) 17.5 Comp 1 (r1 = 550 AU) 0.10 15.0 0.08 12.5 0.06 10.0

Flux (Jy) Flux (Jy) 7.5 0.04 5.0 0.02 2.5 0.00 0.0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Wavelength ( m) Wavelength ( m) 4.0 7 WR137 IR Phot WR125 IR Phot 3.5 Comp 1 (r1 = 660 AU) 6 Comp 1 (r1 = 490 AU) 3.0 5 2.5 4 2.0 3

Flux (Jy) 1.5 Flux (Jy) 1.0 2 0.5 1 0.0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Wavelength ( m) Wavelength ( m)

Figure 6. Best-ﬁt DustEM models of WR98a, WR118, WR19, WR70, WR137, and WR125. A large grain size distribution 2-component dust model was used for the WR98a and WR118, and a small grain size distribution 1-component dust model was used for the other four dustars. −4.66 −1 rate of M˙ = 10 M yr (Sander et al. 2019), and 3.4.5. Selected Single Component Dustars a 40% carbon fraction by mass, we ﬁnd that the dust WR19. WR19 is a periodic WC5+O9 dustar with an production rate and carbon dust condensation fraction orbital period of 10.1 yr and an eccentricity of e = 0.8 is M˙ = (6.27+2.78) × 10−7 M yr−1 and χ ≈ 7%, d −1.94 C (Williams et al. 2009b). This system hosts one of the respectively. earliest type WC stars amongst the known WC dus- +780 tars. The Gaia distance to WR19 is d = 4330−580 pc Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 13

(Rate & Crowther 2020), which is slightly larger than yet been resolved, so it is difficult to distinguish be- previous distance estimates based on optical photom- tween a small or large grain size distribution. However, etry and spectral type (d ∼ 3300 pc, van der Hucht we choose to adopt the small grain size distribution to 2001). However, since Gaia observations of WR19 were be consistent with the WC dust formation analysis by taken before the onset of dust formation in 2017, it ex- Zubko(1998). hibited a mostly dust-free environment which likely con- The small grain SED models of WR70 provide a dust +2.40 −8 tributed to the well-constrained distance. We therefore mass of Md = (6.60−1.78) × 10 M . Adopting the adopt the Gaia-derived distance for our dust SED mod- mean WC9 mass-loss rate and velocity of M˙ = 10−4.66 −1 −1 eling. WR19 is also affected by line-of-sight interstellar M yr and vexp = 1390 km s (Sander et al. 2019), extinction, where Av = 5.19 (Rate & Crowther 2020). we derive a dust production rate and carbon dust con- 5 ˙ +0.65 −8 −1 We adopt a combined stellar luminosity of L∗ = 4 × 10 densation fraction of Md = (3.51−0.56) × 10 M yr L , the mean luminosity for WC5 stars as derived by and χC ≈ 0.4%, where we have assumed the winds are Sander et al.(2019). composed of 40% carbon by mass. We fit single component dust SED models to the stel- WR137. WR137 is a periodic WC7+O9 dustar with lar wind-subtracted 5-37 µm Spitzer/IRS spectrum of an orbital period of 13.05 yr derived from both ra- WR19 (Fig.6, Center Left) and derive a dust separa- dial velocity measurements and IR light curve variations +3130 tion distance from the central binary of r = 6870−3630 (Williams et al. 2001; Lefèvreet al. 2005). The Gaia- +2030 +180 AU (2680−1530 AU) for the small (large) grain size mod- derived distance of d = 2100−160 pc is consistent with els. Based on the orbital phase of WR19 when Spitzer previous distance estimates towards the system (e.g. observed it (2005 Jun, φ ≈ 0.84), we can estimate the d ≈ 1820 pc; Nugis & Lamers 2000). We therefore adopt extent of dust formed at periastron passage in early 1997 the Gaia distances for our dust SED models of WR137. (Williams et al. 2009b). Adopting the mean WC5 wind We also adopt an interstellar extinction and heating −1 velocity from Sander et al.(2019) of vexp = 2780 km s source luminosity of Av = 1.70 (Rate & Crowther 2020) 5 for the dust expansion velocity, the dust formed in the and L∗ = 5.4 × 10 L , respectively, where the stellar 1997 periastron passage should be located ∼ 5000 AU luminosity was derived by a spectral pseudo fit from the away in 2005 Jun. We therefore favor the small grain PoWR models by Sander et al.(2012). composition given the consistency with the dust expan- We fit single component dust SED models to the stel- sion distance estimate. lar wind-subtracted contemporaneous 1.2 - 20 µm pho- For the small grain SED models of WR19, we derive a tometry taken in 1985 May by Williams et al.(2001) +3.76 −8 dust mass of Md = (3.98−2.84)×10 M , which implies (Fig.6, Bottom Left) and derive a separation distance ˙ +3.72 −9 +240 a dust production rate of Md = (3.94−2.81) × 10 M between dust and the central binary of r = 660−220 AU −1 +110 yr (Eq.7) given its orbital period of 10.1 yr. Adopting (210−70 AU) for small (large) grain size models. The −4.39 −1 the mean WC5 mass-loss rate of M˙ = 10 M yr mid-IR emission from dust formation in WR137 peaked (Sander et al. 2019) and a 40% carbon mass fraction, in mid-1984 (Williams et al. 2001); therefore, assuming −1 the carbon dust condensation fraction is χC ≈ 0.02%. the expansion velocity of 2000 km s (Sander et al. WR70. WR70 is a continuous but variable WC9+B0I 2012), we expect the dust to be located ∼ 400 AU at dustar with a proposed period of 2.8 yr derived from its the time of the WR137 observations. Since dust forma- IR light curve (Niemela 1995; Williams et al. 2013a). tion from WR137 started several years before the mid- +440 The Gaia-derived distance to WR70 is d = 3010−340 pc, 1984 peak and may therefore have propagated further, which is consistent with the recently revised extinction- we suggest that the dust is most likely composed of small based distance estimate of d ≈ 3500 pc (Williams et al. grains. We therefore favor the small grain model. This 2013a). We therefore adopt the Gaia distance for our is also supported by WR137’s similarity in both orbital dust SED models. The adopted line-of-sight extinction properties and spectral sub-type to WR140, which ex- and combined stellar luminosity of the WR70 system hibits dust consistent with small grains. 5 is Av = 5.20 and 7 × 10 L , respectively (Rate & Based on the small grain SED models and the 13.05 Crowther 2020; Williams et al. 2013a). yr dust formation/orbital period of WR137, we derive a +0.64 −8 We fit single component dust SED models to the stel- dust mass of Md = (1.20−0.57) × 10 M and a dust ˙ +4.90 −10 −1 lar wind-subtracted 2-27.5 µm ISO/SWS spectrum of production rate of Md = (9.21−4.36) × 10 M yr WR70 (Fig.6, Center Right) and determine a separa- (Eq.7). Adopting the mean WC7 mass-loss of M˙ = −5 −1 tion distance between dust and the central binary of 2.7 × 10 M yr and a 40% carbon composition by +80 +80 r = 550−70 AU (150−50 AU) for the small (large) grain mass, the carbon dust condensation fraction is χC = size models. Extended emission around WR70 has not 0.009%. 14 Lau et al. 20.0 40 WR95 (LG) IR Phot WR106 (LG) IR Phot 17.5 Comp 1 (r1 = 40 AU) 35 Comp 1 (r1 = 50 AU) 15.0 30 12.5 25 10.0 20

Flux (Jy) 7.5 Flux (Jy) 15 5.0 10 2.5 5 0.0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Wavelength ( m) Wavelength ( m)

Figure 7. Best-fit DustEM models of WR95 and WR106 with the large grain size distribution. −7 WR125. WR125 is a WC7+O9III system (Williams is roughly consistent with the Md = 1.64 × 10 M et al. 1994; Midooka et al. 2019) that recently exhibited derived from the isothermal dust model by Williams et a second observed IR re-brightening implying a 28.3 yr al.(1994) after correcting for different distance assump- 5 −1 period (Williams 2019). The Gaia-derived distance to- tions. We adopt a mass-loss rate of 1.6 × 10 M yr +990 wards WR125 is 3360−650 pc (Rate & Crowther 2020), from the spectral model fit by Sander et al.(2012) and a which is closer than the previous distance estimate of 40% carbon mass fraction and determine a carbon dust 4700 pc (Williams et al. 1992) based on a near-IR flux condensation fraction of χC ≈ 0.03%. comparison to the similar system WR140 and its well- defined distance. Given the distance uncertainties aris- 3.4.6. Additional WC Dustars with Angular Size ing from a relative comparison to WR140, we use the Constraints Gaia distance for our dust SED models of WR125. The adopted line-of sight extinction and combined stellar lu- WR95 and WR106 are continuous WC9 dustars (van der Hucht 2001) that have constraints on their extended minosity of WR125 is Av = 6.48 (Rate & Crowther 5 dust emission from IR high spatial resolution obser- 2020) and L∗ = 1.6 × 10 L , respectively, where the stellar luminosity was derived by a spectral pseudo fit vations (Monnier et al. 2007; Rajagopal et al. 2007). from the PoWR models by Sander et al.(2012). The Gaia-derived distances towards WR95 and WR106 +430 +560 We fit single component dust SED models to the stel- are 2070−310 pc and 3070−430 pc, respectively (Rate & lar wind-subtracted 1.2 - 20 µm photometry of WR125 Crowther 2020). The dust separation distances deter- +110 +70 taken in 1993.47-1993.5 (Fig.6, Bottom Right), sev- mined from our SED models are r = 130−40 AU (40−20 +220 +120 eral years after the onset of observed dust formation AU) for WR95 and r = 170−60 AU (50−20 AU) for between 1990 - 91 (Williams et al. 1994), and determine WR106 assuming small (large) grains. a dust separation distance between the central binary Rajagopal et al.(2007) measure a 28.4 and 45.0 mas +170 +70 Gaussian FWHM at 10.5 µm for WR95 and WR106, of r = 490−100 AU (170−40 AU) assuming small (large) grains. Assuming a dust expansion velocity of 2000 km respectively, which is consistent with the FWHM mea- s−1, consistent with the mean WC7 wind velocity de- sured by Monnier et al.(2007) for these systems at rived by Sander et al.(2019), the dynamical timescale shorter IR wavelengths (2.2 and 3.08 µm) near the emis- of the modeled dust is 1.2 yr (0.4 yr) for the small (large) sion peaks in the SEDs (Fig.7). These angular sizes cor- dust grains distributions. Since the small grain model respond to a linear size of 60 AU for WR 95 and 100 AU timescale is consistent with formation during the ob- for WR106. Assuming a circular morphology, the extent served peak IR emission in mid 1992 (Williams et al. of the dust shells should be ∼half of these linear sizes: 1994), we favor the small grain dust model. ∼ 30 AU for WR 95 and ∼ 50 AU for WR106. This is For the small grain SED models, we derive a dust mass consistent with our large grain size models, which agrees +0.61 −7 with the interpretation from Rajagopal et al.(2007) who of Md = (1.00 ) × 10 M and a dust production −0.35 also favor dust models with larger (∼ 1 µm) grains for rate of M˙ = (3.54+2.15)×10−9 M yr−1 (Eq.7) assum- d −1.22 WR95 and WR106 and determine dust shell radii of a ing an orbital period of 28.3 yr. Our derived dust mass few tens of AU from the stars. Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 15

C vs LIR DPR vs LIR WC9 (Large Grains) WC9 (Large Grains) 2 10 WC9 5 WC9 WC8 10 WC8

1 WR48a ) WR48a 10 WC7 (WR140, WR137, WR125) 1 WC7 (WR140, WR137, WR125)

WC5 (WR19) r WC5 (WR19) y 7 ) 0 10 PL Fit ( 1.21 ± 0.06)

% 10 (

M C ( 1

10 R

P 9

D 10 2 10

3 10 11 0 1 2 3 4 5 10 0 1 2 3 4 5 10 10 10 10 10 10 10 10 10 10 10 10 L (L ) LIR (L ) IR

Figure 8. (Left) Distribution of derived dustar values for χC vs LIR. The markers with thick border represent the dustars where the large grain model was favored, markers with thin borders represent dustars where the small grain model was favored, and markers without borders show the dustars where the small grain model was adopted by default. Open, unfilled markers show the highly variable or periodic dustars WR19, WR48a, WR125, WR137, and WR140. (Right) Distribution of DPR vs 1.21±0.06 LIR overlaid with the best-fit power-law relation DPR ∝ LIR . The highly variable or periodic dustars (WR19, WR48a, WR125, WR137, and WR140) were excluded from the fit since. Assuming the large grain SED models, the dust pro- overlap with ours. Zubko(1998), however, modelled ˙ +2.00 −8 −1 duction rates are Md = (9.36−3.36) × 10 M yr the dust formation physics and dynamics under the as- ˙ +1.14 −7 −1 and Md = (2.97−1.01) × 10 M yr for WR95 and sumption of spherically symmetric winds since the com- WR106, respectively. Given the adopted mass-loss rates plex, colliding-wind morphology of WC dustars was not from PoWR models by Sander et al.(2012) (Tab.3) and known at that time. Despite the difference in analytical assuming a 40% carbon composition in the winds by techniques, Zubko(1998) derive a range mass loss rates mass, the carbon dust condensation fraction is ∼ 1.2% and carbon dust fractions consistent with our results. for WR95 and ∼ 4.6% for WR106. They determine condensed carbon fractions of 0.002 - For the dustars without dust radius constraints 20% and dust production rates of 5 × 10−10 - 6 × 10−6 −1 (e.g. WR70), we assume a small grain size distribu- M yr . tion. In addition to WR70, the 8 other dustars that fall into this category are WR48b, WR53, WR59, WR96, 3.4.8. IR Luminosity, Dust Production Rate, and Grain WR103, WR119, WR121, and WR124-22. DustEM SED Size models of these 8 dustars are shown in Figures 11 and 12. The distribution of LIR and the DPR of WC dustars provides a valuable empirical relation for estimating 3.4.7. Dust Properties and Comparison to Previous Studies DPRs from IR luminosities that can be directly mea- The results of the DustEM SED models to the 19 WC sured from IR observations. Excluding the periodic and dustars are presented in Table4. In Figure8, the dust highly variable dustars, the DPR vs LIR (Fig.8, Right) condensation fraction χC and the DPR is plotted against relation can be characterized by the following power-law the total IR luminosity of each dustar. Both plots show fit: that χC and the DPR increase with increasing with IR luminosity. The periodic or highly variable dust pro- ˙ ! ducers (WR19, WR48a, WR125, WR137, and WR 140) Md +0.06 LIR +0.32 Log −1 = 1.21−0.06 Log − 11.55−0.18. show slight discrepancies from this trend since their IR M yr L luminosity varies depending on the orbital phase. These (8) results demonstrate that WC dustars exhibit a range of In Fig.8 (Left) it is apparent that the efficient dust −10 −6 DPRs and χC values ranging from 1 × 10 - 4 × 10 makers, where χC & 1%, are consistent with large grain −1 M yr and ∼ 0.002 − 40%, respectively. dust models. This suggests that there is no homoge- The most recent and relevant study to compare our neous grain size distribution exhibited by all WC dus- results to is that of Zubko(1998), who conducted a tars, but rather that larger grain sizes (& 0.1 µm) are homogeneous modelling analysis of the SEDs and dust produced by dustars with higher dust condensation frac- shells of 17 Galactic WC dustars incorporating grain tions. However, if the WC subtype influences the grain physics and dynamics. A majority of their sample size, it is possible that WC9 dustars preferentially form 16 Lau et al. large grains. Regardless, the results suggest that effi- Colliding Wind Dust Condensation Relation

2 1 cient WC9 dustars form larger dust grain that will be 10 ) 4

more robust against destruction and sputtering via SN 0 R

1 0 R W 10 W shocks and survive longer in the ISM. M M

( 1 10 6

3.5. Investigating the Colliding Wind Dust Formation ) 4

0 2 R 1 R Model W 10 v W

v WC9 (LG; WR104, WR98a)

( 3 10 WC9 (WR70)

Usov(1991) investigated a theoretical model of dust )

4 WC8 (WR48a) 0

1 4

formation in the wind collision between WR and OB R

C WC7 (WR140, WR137, WR125)

W 10 , WC5 (WR19) binaries. They derived an analytical relation for the C 5 PL Fit ( ) ( 1.2 ± 0.4 fraction of the WR wind which is strongly cooled and 10 0 1 compressed in the shock layer between the two stars: 10 10 Orbital Period (yr)

2 1/2 2 ˙ 2 −6 −2 ˙ −2 6 α ∝ η (1 + η ) MWR vWR D , (9) Figure 9. χC MWR vWR normalized to the χC , velocity, mass-loss rate of WR104 plotted against Porb for the 8 where η is the wind momentum ratio between the OB dustars in our sample with orbital periods. The dashed ˙ MOBvOB ˙ ˙ −2 6 and WR stars η = , MWR/OB is the mass- line shows the best-ﬁt power-law relation χC M vWR ∝ M˙ WRvWR WR P −1.2±0.4, where the 32.5 yr orbital period dustar WR48a is loss rate of the WR/OB star, vWR/OB is the terminal orb wind velocity of the WR/OB star, and D is the separa- the outlier. tion distance between the WR and OB star. Usov(1991) assume that most of the carbon from the WC wind in Usov(1991) colliding-wind model (Eq.9), they should this cold, compressed shock layer condenses into dust, exhibit the following relation with our assumptions: which implies that ˙ −2 6 −4/3 χC MWR vWR ∝ Porb . (11)

α ∝ χC . (10) ˙ −2 6 In Fig.9 we plot χC MWR vWR vs Porb for the 8 dustars normalized to the carbon dust condensation effi- We can therefore test the theoretical model from Usov ciency, wind velocity, and mass-loss rate of WR104. (1991) by investigating the relation between χ and the C M˙ , v , and P are provided from Tab.3 and χ is WC binary mass-loss rates, wind velocities, and orbital WR WR orb C provided from Tab.4. We note that the power-law rela- separation. tion is insensitive to the dustar system used to provide We focus on the 8 WC dustars in our sample with the normalization factors. We determine a P −1.2±0.4 known orbital periods (P ): WR19, WR48a, WR70, orb orb power-law fit, where WR48a is excluded as an outlier WR98a, WR104, WR125, WR137, and WR140. Us- since it exhibits a higher mass-loss rate than the other ing Kepler’s Third Law and assuming a similar total systems (See Tab.3). This derived power-law fit is con- mass for each dustar system, it follows that the orbital 2/3 sistent with the theoretical power-law relation from the separation D is proportional to P . Eccentricity is orb Usov(1991) model with our assumption of constant η also an important parameter that regulates the dust across the dustars (Eq. 11). The consistency of the ob- formation and orbital separation for the periodic, non- servational results and theoretical model supports the continuous dustars (e.g. WR19, WR125, WR137, and colliding-wind interpretation of WC dustars and demon- WR140); however, their dust production rates and thus strates the effect of the binary orbital parameters on their carbon condensation efficiencies were calculated as dust formation efficiency. an average over the orbital period (Eq.7). Since the 2 time-averaged separation distance is a (1 + e /2) (See 4. BPASS DUST PRODUCTION MODEL RESULTS Williams 2003), where a is the semi-major axis and e is the eccentricity of the system, the eccentricity should 4.1. Binary Population and Spectra Synthesis Models only contribute variations from a by a factor of 1.5 at The Binary Population and Spectral Synthesis most. Given the minor effect of eccentricity in this re- (BPASS; Eldridge et al. 2017) suite of binary stellar lation and the eccentricity uncertainty in most dustars, evolution and stellar population models provides a valu- 2/3 we assume that D ∝ Porb for all 8 systems. able tool for investigating dust production from stellar Due to uncertainties in the mass-loss rate and wind populations. The presence of a binary companion is a velocity of the binary OB companions of the WC stars, key factor that influences both the formation of WC we make the assumption that η is similar for the dustars. stars and their dust production via colliding winds, If the observed dustar properties are consistent with the which underscores the utility of the binary evolution Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 17 tracks utilized in BPASS for modeling the dust contribu- terminal explosion is considered a Type II SN. tion from WC binaries in stellar populations. Notably, A 10% dust condensation efficiency by mass is BPASS evolutionary models may also be used to study adopted for the dust-forming elements in the SN the formation history of individual WC binary system ejecta (Dwek et al. 2014; Sarangi et al. 2018). Dust (e.g. Thomas et al., in preparation). This work presents forming elements include carbon, oxygen, magne- the first use of BPASS to model dust production from sium, silicon, and iron. The hydrogen, helium, stellar populations. nitrogen, and neon synthesized in the SN ejecta We use the BPASS v2.2.1 binary models as de- are not considered as dust-forming elements. scribed in Stanway & Eldridge(2018) with the default “135 300” BPASS initial mass function (IMF). This • Type II SNe Dust Destruction. When a SN ex- IMF is based on Kroupa et al.(1993) with a power-law plodes its shock interacts with the surrounding ISM and destroys the ISM dust grains. Given a slope from 0.1 to 1.0 M of -1.30 that steepens to -2.35 total ISM mass that the SN clears of dust, mg, above this to an upper stellar mass of 300 M . Stellar mass-loss is determined by the difference between the the destroyed quantity of dust per SN explosion stellar mass in the current and previous timesteps. can be estimated as In addition to the WC binaries, three more sources of dust are considered in our BPASS models based on the md = mg χd/g, (12) current understanding of leading dust producers: dust condensation in type II supernova (SN) ejecta and in where χd/g is the gas-to-dust mass ratio of the ISM stellar winds of AGB and RSG stars (Matsuura et al. (Dwek et al. 2014; Temim et al. 2015). Note that 2009; Dwek & Cherchneff 2011; Boyer et al. 2012; Temim this does not include destruction of SN ejecta dust et al. 2015; Srinivasan et al. 2016). We do not include by the reverse shock, which is not considered in the dust input from H-poor type Ia or Ib/c SNe since our work. The following fitting formula derived by type II SNe are considered to be the most efficient and Yamasawa et al.(2011) is adopted for determining prolific source of SN dust (e.g. Sarangi et al. 2018 and mg: ref. therein). Luminous Blue Variables (LBVs), massive evolved −0.202 −0.298 stars that exhibit giant outbursts of extreme mass-loss mg = 1535 nISM ((Z/Z ) + 0.039) M , (Humphreys & Davidson 1994; Smith 2014), may also (13) be important sources of dust. Based on observations of where nISM is the density of the surrounding ISM their circumstellar dusty nebulae, LBVs are capable of and Z is the solar metallciity (Z = 0.02). Given forming between ∼ 0.001 − 0.1 M of dust (Kochanek the weak dependence on nISM, an ISM density of 2011 and ref. therein). This corresponds to a DPR of −3 nISM = 1 g cm is assumed for all BPASS mod- −7 −5 −1 ∼ 10 − 10 M yr for an LBV assuming a lifetime els. Total SN dust input rates are determined with 4 of ∼ 10 yr (Smith 2014), which is comparable to the and without incorporating this dust destruction upper DPR range of WC dustars. However, given their prescription. rarity, the evolutionary formation pathways for LBVs and the physics of their eruptive mass-loss is not well • AGBs. An AGB star is identified as a star with an understood. Due to these uncertainties it is difficult to effective temperature less than 103.66 K, a lumi- 4.4 identify LBVs and quantify their dust contribution via nosity less than 10 L , a CO core mass greater eruptive mass-loss in current BPASS models (Eldridge than 0.5 M , and a difference between the He and et al. 2017). We therefore we omit them from the BPASS CO core masses less than 0.1 M . This luminosity models in this study but acknowledge their potential as cut off is consistent with the most luminous AGB important dust producers that warrant further investi- in the Large Magellanic Cloud (Riebel et al. 2012). gation. The AGB dust production is calculated assuming The dust formation prescriptions and the assumed pa- a 0.5% condensation fraction of the total mass-loss rameters for identifying the four dust inputs sources and is scaled by the metallicity ratio of the model (type II SNe, AGBs, RSGs, and WC binaries) in the and the solar metallicity, Z/Z (van Loon 2000). BPASS models are described as follows: • RSGs. A star is identified as an RSG if its effective • Type II SNe. For stars with a final mass greater temperature is less than 103.66 K and its luminos- 4.4 than 2 M , CO core mass greater than 1.38 M , ity is greater than 10 L . The empirically de- and H surface mass fraction greater than 1%, the rived Mbol-DPR relation from Massey et al.(2005) 18 Lau et al.

is adopted and scaled by the metallicity ratio of the Since the shocks from end-of-life SN explosions may model and the solar metallicity, Z/Z , to quantify destroy the newly formed circumstellar dust from RSGs the dust input from the RSGs. An upper limit was and WC binaries, their dust input is not included if they set on the RSG dust production requiring the dust end their lives as SNe. It is assumed that RSGs and WC input of each time step to be less than the total stars end their lives as explosive SNe if their remnant metals in the mass-loss. core mass is less than 3 M , whereas a core with a mass greater than 3 M leads to a direct collapse into a black • WC Binaries. WC+OB binaries are identified as hole with minimal ejecta energy and circumstellar dust systems where the WC star has no hydrogen, a survival. combined C and O mass fraction higher than N, a He mass fraction higher than 40%, a C mass 4.2. BPASS Dust Models at Z = 0.001, 0.008, and fraction higher than 25%, and a companion with 0.020 an effective temperature greater than 104.38 K. BPASS dust models were run at low (Z = 0.001), The metallicity dependence for the total mass-loss LMC-like (Z = 0.008), and solar (Z = 0.020) metallici- rates from WR stars in BPASS are described as a ties in order to explore the relative dust contribution of power-law relation M˙ ∝ Zα, where α = 0.5 (El- WC binaries, AGBs, RSGs, and SNe at different epochs dridge et al. 2017). The dust production rate from in cosmic time as characterized by different metallicities. ˙ ˙ WC binaries is Md = MXC χC , where XC is the The star formation history will impact the stellar popu- surface mass fraction of carbon that is output from lations and their dust input. For example, in a scenario BPASS. The χC relation (Eq. 11) that we verified with constant star formation (SF), the dust sources as- in Sec. 3.5 is adopted and scaled to the properties sociated with massive stars have short lifetimes but will of WR104: be continuously replenished by on-going star formation. Two star formation scenarios were therefore considered for the BPASS models at each metallicity: a co-eval !2 106 M stellar population and constant SF. These two M˙ v −6 P −4/3 χ ≈ 40% ∞ orb . different star formation scenarios represent contrasting C ˙ MWR104 vWR104 PWR104 star forming histories, i.e. a single starburst event vs. (14) continuous star formation. The dust condensation fraction is therefore treated The dust-to-gas mass ratios, which are relevant for the as a function of the mass-loss rate and terminal SN destruction rates, are assumed to be χd/g = 0.0008, wind velocity of the primary star (i.e. the WC 0.0018, and 0.007 (Zubko et al. 2004) for the Z = 0.001, star) and the orbital period of the system. The 0.008, and 0.020 metallicity models, respectively. The low-Z and LMC-like dust-to-gas mass ratios are adopted terminal wind velocity (v∞) is defined by the stel- from the values derived for the SMC and LMC, respec- lar mass-loss rate (M˙ ), luminosity (L∗), and the tively, by Temim et al.(2015). Based on Eq. 13, the momentum transfer efficiency (ηmom) from the re- total ISM mass swept up by SNe in the low-Z, LMC- lation ηmom = Mv˙ ∞/(L∗/c), where c is the speed like, and solar metallicity models is mg = 3088, 1947, of light. M˙ and L∗ are output parameters from and 1518 M , respectively. BPASS, and we adopt a fixed value of ηmom = 5.3, the median value of the 11 Galactic dusty WC The cumulative dust production rates in for the con- 6 stars from the optical spectroscopic analysis by stant SF and co-eval 10 M stellar population models Sander et al.(2019). In the BPASS models, we are shown in Fig. 10. Results from the constant SF and 6 only consider the dust input from WC binaries 10 M stellar population models at a time t = 1.0 Gyr with orbital periods consistent with the range of are provided in Tab.5 and6, respectively. orbital periods in our sample: P = 0.66 − 32.5 orb 4.2.1. Constant SF Models yr. Lastly, since not all WC binaries are dust producers, we conservatively assume that 28% of The results from the constant SF models are shown in the BPASS WC systems that meet these crite- Fig. 10 (Left Column) and Tab.5. In order to check the ria are dustars, which is based on the observed DPR prescriptions of the four dust sources, we compare WC-dustar/WC ratio in the Galaxy (Rosslowe & the model results against observationally measured val- Crowther 2015). This is percentage is likely an ues and previous studies. The average DPRs for AGB underestimate given the recent mid-IR variability and RSG stars in the LMC-like metallicity model are D E −9 −1 D E analysis by Williams(2019). M˙ d,AGB = 1.1 × 10 M yr and M˙ d,RSG = Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 19

Constant SF BPASS Dust Model Co-eval 106 M Population 8 10 Z = 0.020 4 10 Z = 0.020 )

6 ) 10 2 M

4 M 10 ( (

10 s s s s a

2 a 0

M 10 10 M

t t s

0 s u 10 u 2 D D

l 2 l

a RSG RSG a t

10 t o AGB o 4 AGB T 4 T 10 10 WC Binary WC Binary SNe (Type II) SNe (Type II) 6 6 10 6 7 8 9 10 11 10 6 7 8 9 10 11 Log(Age/yr) Log(Age/yr)

8 Z = 0.008 4 Z = 0.008 10 10 6 ) 10 ) 2 10

M 4 M ( (

10 s s s s

a 2 a 0 10 10 M M

t t

s 0 s u 10 u 2 D D

10 l l

a 2 a t 10 RSG t RSG o o 4 T AGB T AGB 4 10 10 WC Binary WC Binary SNe (Type II) SNe (Type II) 6 6 10 6 7 8 9 10 11 10 6 7 8 9 10 11 Log(Age/yr) Log(Age/yr)

8 Z = 0.001 4 10 10 Z = 0.001 6 ) 10 ) 2 10

M 4 M ( (

10 s s s s

a 2 a 0 10 10 M M

t t

s 0 s u 10 u 2 D D

10 l l

a 2 a t 10 RSG t RSG o o 4 T AGB T AGB 4 10 10 WC Binary WC Binary SNe (Type II) SNe (Type II) 6 6 10 6 7 8 9 10 11 10 6 7 8 9 10 11 Log(Age/yr) Log(Age/yr)

Figure 10. (Left Column) Constant SF BPASS models at low (Z = 0.001), LMC-like (Z = 0.008), and solar (Z = 0.020) metallicities showing the cumulative dust mass input as a function of time. The SNe models with dust destruction do not 6 appear in any of the plots since SNe are net destroyers of dust at all timesteps. (Right Column) Co-eval 10 M stellar population BPASS models at low, LMC-like, and solar metallicities showing the total cumulative dust mass input (solid lines) as a function of time. The dotted lines show the dust input in a single time bin for each dust source. The SNe + dust destruction model does not appear for the same reason as described above.

−9 −1 1.7 × 10 M yr , which are consistent within factors calculate a theoretical IMF-averaged SN dust yield of of a few to the average DPRs measured from mid-IR ob- 0.65 M for a 100% dust condensation efficiency in SNe. servations of the LMC (Riebel et al. 2012; Srinivasan et A 10% condensation efficiency, which we adopt for the D E −10 −1 al. 2016), where M˙ d,AGB = 6.9 × 10 M yr and BPASS models, applied to the Temim et al.(2015) SN dust yields is therefore consistent within a factor of two D E −10 −1 M˙ d,RSG = 4.0 × 10 M yr . Temim et al.(2015) 20 Lau et al. to the BPASS SN dust yields (∼ 0.1 M ). The aver- from the solar metallicity model. AGB stars lead the age dust mass destroyed per SN in the LMC measured dust production in the LMC-like metallicity models but by Temim et al.(2015) is 6 .1 ± 2.6 M for silicates and only by factors of 2 − 3 over RSGs and WC binaries. 1.6±0.7 M for carbon grains, which is consistent within WC binaries notably form within the first 2 Myr after factors of a few to the average dust mass destroyed per the onset of star formation and are the first sources of SN in the LMC-like BPASS models (3.5 M ). We dis- dust in the LMC-like (and solar) models. cuss the comparisons to the LMC in further detail in In the low Z models, RSGs, AGBs, and WC binaries Sec. 4.3. show smaller populations and form dust at a much lower The average dust production rate from WC binaries rate than the LMC-like and solar models. WC binaries D E −7 in the solar metallicity models is M˙ d,W C = 9.9×10 exhibit the most substantial decrease in dust production −1 and population. This is because only the most massive M yr , which is slightly greater than the average DPR D E and luminous stars evolve to the WC phase at lower from our sample of 19 Galactic dustars M˙ = d,W C metallicities. Such luminous stars drive faster winds −7 −1 3.3 × 10 M yr . However, we find that the WC bi- and therefore form dust much less efficiently given the nary dust production from the BPASS models is largely sensitivity of χC to wind velocity (Eq.9). At low Z, if dominated by systems with the shortest orbital period: SNe are indeed net dust destroyers, AGBs and RSGs are ∼ 50% of the total WC binary dust input in the solar likely the dominant dust sources with dust input rates metallicity model originates from 3 systems with Porb exceeding WC binaries by over 3 orders of magnitude. between 0.66 and 1.0 yr. These 3 systems have an aver- −6 −1 age DPR of 3.7×10 M yr , which is consistent with 6 our measured DPR of the Porb = 0.66 yr system WR104, 4.2.2. Co-Eval 10 M Stellar Population Models −6 −1 M˙ d = 4.4 × 10 M yr . We therefore conclude that our BPASS dust prescriptions provide reasonable esti- Figure 10 (Right Column) shows the dust mass input mates for the dust input from the four sources. in each time bin and the cumulative dust mass input The constant SF BPASS models show that dust pro- as a function of time for WC binaries, AGBs, RSGs, duction from SNe without dust destruction dominates and SNe. The most notable difference in the dust pro- AGBs, RSGs, and WC binaries by over an order of mag- duction between the co-eval population and the con- nitude for all 3 metallicities. However, SNe are consis- stant SF models is the relatively higher dust contribu- tently net dust destroyers at all time steps when incor- tion by AGBs. For example, the total dust mass from porating SN dust destruction, and the SN dust destruc- AGB stars at a time t = 1.0 Gyr is over an order of tion rate exceeds the production rate by over an order magnitude greater than the total dust mass input from of magnitude. The average dust produced per SN is RSGs and WC binaries in all three metallicity models (Tab.6). Similar to the constant SF models, SNe are ∼ 0.1 M for all 3 metallicities. We note that dust formation in SN ejecta is still uncertain and measurements consistently net dust destroyers at all 3 metallicites. The −6 RSG dust input shows two peaks, where the secondary range from ∼ 10 − 1 M of dust per SN (Temim et al. 2015; Gall & Hjorth 2018; Sarangi et al. 2018), but peak around ∼ 100 Myr is consistent with the onset of SNe would have to form dust beyond the highest mass AGBs. This secondary, late-time peak arises due to the range of the observed values in order to compensate for difficulties in distinguishing the population of luminous the dust destruction rate. AGB stars from faint RSGs (Eldridge et al. 2017). SN In the solar metallicity models, WC binaries are the models with dust destruction show that the AGBs dom- dominant source of dust for ∼ 60 Myr until the onset of inate the dust input at all three metallicities. the AGB star population that forms dust at a similar The dust production timescales, which we define as rate to the WC binaries. We note that the WC binaries the length of time the sources are forming dust, are are significant dust producers in the solar metallicity provided in Tab.6 and shows that WC binaries only model despite almost half of the WC stars ending their produce dust for ∆tWC = 0.5 − 4.3 Myr. Note that lives as SNe with their dust input removed (Tab.5). the RSG and WC binary timescales in Tab.6 only in- The LMC-like metallicity model shows slightly re- clude sources that do not end their lives as SNe. When duced dust input from AGB and RSG stars compared including sources that end their lives as SNe, the first to the solar metallicity models. The WC binaries show RSG peak is broader and bridges the second peak in all a much greater reduction in dust production due to a 3 metallicity models, and the WC binary dust forma- smaller population by a factor two and a lower aver- tion timescale in the solar metallicity model is broader age dust production rate by over an order of magnitude by factor of ∼ 2 (∆tWC = 5.4 Myr) than the 2.5 Myr timescale reported in Tab.6. Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 21

As expected, the WC dust production timescale ues measured from mid-IR observations of the LMC by is substantially shorter than the dust production Riebel et al.(2012); Srinivasan et al.(2016) and the timescales of AGB stars, where ∆tAGB = 1.5 − 2.4 Gyr. Magellanic Cloud SN remnant analysis by Temim et al. The short dust production timescale of WC binaries (2015). The total dust input rate from the AGB stars at explains the difference in their cumulative dust input time t = 12.6 Gyr is closely consistent to the observed rate relative to the longer-lived AGB stars between the rate. However, the SN rate and the total WC binary constant SF and co-eval population models. Given their and RSG dust input rates from the models are larger short timescales, the presence of WC binaries should than the observed values. also reflect the intensity of recent star formation. Both the BPASS models and results from previous 6 The results from the co-eval 10 M stellar popula- studies show an agreement that the dust production tion BPASS models indicates that for a “bursty” SFH, from SNe without dust destruction dominates the other AGB stars will dominate the dust budget at late times three sources by over an order of magnitude. However, (t & 70 Myr) over WC binaries and RSGs with SNe when incorporating the effects of ISM dust destruction as net dust destroyers. However, the LMC-like and from SN shocks, SNe are net destroyers of dust (Temim solar models show that WC binaries are the first and et al. 2015). dominant source of dust for ∼ 1 Myr before the RSG It is apparent that the population of sources associ- dust production starts to increase. Notably, in the solar ated with massive stars is over-predicted by the con- metallicity mode, the WC binaries are the leading dust stant SF BPASS models: the total number of RSGs at source until the onset of AGB stars. t = 12.6 Gyr (NRSG = 11887), which includes RSGs that eventually will explode as SNe and not input dust, 4.3. LMC BPASS Dust Model and Massive Star is a factor of ∼ 3 greater than the observed number of Population Discrepancy RSGs, and both the SN rate and the number of dust- producing WC binaries exceed the observed value by The well-studied dust and supernova remnant proper- over an order of magnitude. ties of the nearby LMC (d ∼ 50 kpc) highlights its util- For the WC binaries, there are only 2 currently known ity as a laboratory to test dust input rates in its ISM dust producers in the LMC as opposed to the 52 pre- (e.g. Matsuura et al. 2009; Temim et al. 2015). Im- dicted by the models. These two systems, HD 36402 and portantly, the stellar populations and dust input from HD 38030, both host WC4 stars and exhibit dust forma- AGBs, RSGs, and SNe have been previously measured tion periods of 5.1 and > 20 yr, respectively (Williams or estimated observationally and thus provide a compar- 2019). The estimated lower limit on the current ob- ison for the BPASS model output (Sec. 4.2.1). In this served WC binary dust input rate in the LMC, 3 × 10−8 section, we apply the Z = 0.008 constant star forma- M yr−1 (Tab.7) is derived by the measured amor- tion BPASS models to the LMC and demonstrate the phous carbon dust mass of M ∼ 1.5 × 10−7 M around discrepancy in the massive star populations due to its d HD 36402 by Williams(2011) divided by its 5.1 yr or- complex and variable star formation history (SFH; Har- bital period. Interestingly, the DPR of HD 36402 is ris & Zaritsky 2009). The LMC dust-to-gas mass ratio, consistent within a factor of two to the mean dust input which is relevant for the SN dust destruction rates, is rate for the WC binaries in the BPASS model where assumed to be χ = 0.0018 (Temim et al. 2015). The D E d/g M˙ = 6.2 × 10−8 M yr−1. The dust input total ISM mass swept up per SN adopted in the BPASS d,W C rate from the longer period HD 38030 WC system is models based on Eq. 13 is m = 1947 M and is con- g not yet known since it was only recently identified as sistent with the LMC value measured by Temim et al. a periodic/episodic dust former. However, given their (2015) of m ∼ 2000 M . g longer orbital period (> 5 yr) and lower IR luminosi- In order to model the dust input the LMC, the dust ties (Williams et al. 2013), these two LMC WC systems production and stellar population output from the con- are unlikely to be significant dust producers like WR104 stant SF BPASS models at a metallicity of Z = 0.008 where M˙ ∼ 10−6 M yr−1 (Tab.4). were scaled by a constant factor such that the total d We attribute the number discrepancy of the massive number of AGB stars at a time t = 12.6 Gyr matches star population to the assumption of a constant SF in the current observed number of AGBs in the LMC, the BPASS models since the SFH of the LMC is com- N ≈ 20000 (Riebel et al. 2012; Zhukovska & Hen- AGB plex and variable (Harris & Zaritsky 2009). Analysis of ning 2013; Srinivasan et al. 2016). The current age of the SFH in the LMC by Harris & Zaritsky(2009) indi- the LMC is assumed to be t = 12.6 Gyr. cates that the current total stellar mass is significantly In Table7, we compare the dust input, populations, composed of stars formed in an initial epoch of star for- and SN rates from the LMC BPASS models with val- 22 Lau et al. mation that ceased 10 Gyr ago; this was followed by a significant fraction of the ISM was composed of dust quiescent period until 5 Gyr ago with recent star forma- from WC binaries. tion peaks occurring 12 Myr, 100 Myr, 500 Myr, and 2 In the context of cosmochemistry, the formation of Gyr ago. Normalizing the number of sources from the large dust grains supports the hypothesis of WR stars constant SF BPASS models to the observed AGB stars as source of short-lived radionuclides (SLRs) in the So- in the LMC would therefore over-predict the number of lar System. The longer destruction timescales of larger RSGs and WC binaries and SN rates, all of which are grains suggest WR winds were able to transport and products of shorter-lived massive stars. Notably, the seed SLRs like Al26 in the pre-solar nebula (Dwarkadas lifetime of the WC binary dust producers in the BPASS et al. 2017). models is < 5 × 106 Myr and is shorter than one of Given the impact of WC dustars on the ISM, it is the most recent star formation peaks in the LMC that important to understand their dust chemistry and the occurred 12 Myr ago (Harris & Zaritsky 2009). grain formation physics in their hostile wind collision en- The results from this LMC analysis highlight the im- vironment. The C-rich dust that forms in the H-deficient −1 portance of considering the SFH in modeling the dust and fast winds (& 1000 km s ) of WC binaries likely input rates, especially from massive stars. Although this follows a different chemical formation pathway than that is beyond the scope of the work presented here, future of C- and H-rich AGBs (Le Teuff & Cherchneff 1998; work with BPASS dust models incorporating variable Cherchneff et al. 2000). Distinguishing emission features SFH is crucial for obtaining a more complete under- of the molecular precursors of C-rich dust condensed in standing of galactic dust production rates. WC binaries from other sources could provide a means of observationally tracing their contribution to galactic 5. DISCUSSION AND CONCLUSIONS ISM. Interestingly, the ISO/SWS spectroscopy of WC 5.1. Astrophysical Implications dustars re-analyzed in this work also show evidence of hydrocarbon features (Marchenko & Moffat 2017). The WC dustar SED analysis and the predicted dust Our analysis of the carbon dust condensation fraction input from BPASS models indicate that WC binaries (Sec. 3.5) strengthens our understanding of dust forma- are leading sources of dust, comparable to AGB stars, tion in colliding-wind binaries; however, it is important in environments with constant star formation at solar to consider that not all WC+OB binaries form dust. For metallicities if SNe are indeed net dust destroyers. For example, the well-studied colliding-wind system γ2 Velo- a stellar population formed in an instantaneous star- rum (a.k.a WR11) hosts a WC8+O7.5III binary with a burst at solar metallicities, WC binaries will dominate 78.5-day orbital period and does not exhibit any dust the dust contribution until the onset of AGBs. WC bi- formation (Schmutz et al. 1997; Lamberts et al. 2017). naries are also among the earliest sources of dust in LMC Systems with shorter orbital periods and thus shorter and solar metallicities, which implies they are an early orbital separations may be affected by “sudden radia- reservoir of carbon-rich dust. tive braking” of the WR winds due to deceleration as Due to the net dust destruction rates from SNe, ad- winds approach the luminous OB companion (Gayley ditional dust input is still necessary to account for the et al. 1997). In their analysis, Gayley et al.(1997) in- observed dust in galactic ISM (Dwek et al. 2014). For deed suggest that the wind-wind collision γ2 Velorum is example, in the LMC an additional dust source with an significantly affected by radiative braking. Tuthill et al. input rate more than an order of magnitude greater than (2008) also explore the impact of radiative braking in the combined input from AGB stars and SNe is needed WR104 and find that it may be play an important role to balance out the SN dust destruction (Temim et al. in the wind-wind interaction and shock cone geometry, 2015). The net SN dust destruction rate for all three which are both related to the dust formation. Continued metallicity models also shows that the dust destruction high spatial-resolution observations combined with hy- exceeds the input from AGBs, RSGs, and WC binaries drodynamic simulations of the wind-wind collisions are by several orders of magnitude. therefore crucial for understanding the conditions lead- Although WC dustars may not provide enough dust ing to dust formation in colliding-wind systems. to account for this deficit, the large 0.1 - 1.0 µm-sized From a dust chemistry perspective, it is interesting to grains produced by the heavy WR104-like dust mak- consider why dust formation via colliding winds has only ers would be more robust against destruction from SN been observed for carbon-rich WRs but not for nitrogen- shocks. Such large grains would exhibit grain lifetimes rich WR (WN) stars. As pointed out by Mauerhan et a factor of ∼ 3 longer relative to small ∼ 100 A˚-sized al.(2015), a C-rich chemistry is not a requirement for grains (Jones et al. 1996). Therefore, the destruction dust formation in a colliding-wind binary. For example, timescales of the ISM grains would be lengthened if a Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 23 the N-rich LBV system η Car exhibits episodic dust for- ulation. Both the constant SF and co-eval models show mation via colliding winds similar to WR140, but dust that SNe produce the most dust out of all the sources, around η Car is likely composed of metal-rich silicates, but are net dust destroyers at all metallicities when con- corundum (Al2O3), and/or iron as opposed to amor- sidering the ISM dust destruction from SN shocks. At phous carbon (Smith 2010; Morris et al. 2017). How- low (Z = 0.001) metallicities, AGB stars input a compa- −3 −1 ever, the high mass-loss rate of ∼ 10 M yr from rable amount of dust to RSGs and outproduce WC bi- the primary star in η Car (Hillier et al. 2001) exceeds the naries by over 3 orders of magnitude. At LMC-like (Z = mass-loss rates of WN and WC stars by over an order of 0.008) metallicities, the AGB stars slightly outproduce magnitude. We therefore speculate that the density of WC binaries and RSGs by factors of 2-3, whereas at so- refractory elements such as Al and O may be too low in lar metallicities WC binaries are the dominant source colliding-wind WN binaries to facilitate dust formation, of dust until the onset of AGBs, which form dust at a whereas C in WC winds is readily abundant (40% by comparable rate (Fig. 10, Tab.5). mass; Sander et al. 2019). Results from the co-eval population models indicate that for a “bursty” star formation history, AGB stars 5.2. Conclusions become significant sources of dust at late times after their onset (t > 100 Myr) but still do not produce as We conducted an SED analysis of a sample of much dust as SNe without considering dust destruc- 19 Galactic WC dustars with archival ground- and tion. However, at LMC-like and solar metallicities, the space-based IR photometry and spectroscopy obtained AGBs dominate the dust production over WC binaries over the past several decades and revised Gaia distance and RSGs as well as SNe if they are indeed net dust estimates by Rate & Crowther(2020). The SEDs were destroyers at these metallicities (Fig. 10, Tab.6). modeled using with single or double dust com- DustEM Constant star formation BPASS models of the LMC ponent models. (Z = 0.008) and comparisons to the observationally de- Results from the SED modeling show that WC dustars rived populations of AGBs, RSGs, WC binaries, and can produce small (0.01−0.1 µm) or large (0.1−1.0 µm) SNe demonstrated the inconsistencies between the ob- dust grains, where large grains are favored for the effi- served and model massive star populations. The SN cient (χ 1%) dust makers WR 95, WR98a, WR104, C & rates and the population of WC binaries and RSGs from WR106, and WR118. We find that WC dustars exhibit the constant SF BPASS model over-predicted the ob- a range of dust production rates and carbon dust con- served values, which we attribute to the complex and densation fractions, which increases with increasing IR variable star forming history of the LMC (Harris & luminosity (Sec. 3.4.8). We also fit the empirical rela- Zaritsky 2009). tion between the DPR and IR luminosity that applies Lastly, our conclusions on WC binaries as important to the non-periodic dustars (Eq.8). For the WC dus- but overlooked dust sources strongly motivates further tars with known periods and under the assumption of pursuits of BPASS dust models with variable SFH and consistent wind momentum ratios (η), we successfully future studies addressing the open questions on WC dust demonstrate the predicted power-law relation between formation physics and dust chemistry. With the combi- χ , M˙ , v , and P (Fig.9) for theoretical mod- C WR WR orb nation of high sensitivity and spatial resolution in the els of dust-forming colliding wind WR systems by Usov mid-IR, observations with the upcoming James Webb (1991). Space Telescope will transform our understanding of WC In order to study the dust contribution of WC dustars dustars and dust formation in hostile environments. in comparison to other leading stellar dust producers (AGBs, RSGs, SNe), we performed binary population synthesis models using BPASS incorporating dust pro- Acknowledgements. We thank T. Onaka, I. Endo, duction perscriptions for the four sources in addition to T. Bakx, M. Buragohain, E. Lagadec, T. Nozawa, dust destruction from SNe. For the WC binaries, the A. Soulain, T. Takeuchi, and M. Corcoran for the en- dust production rate in the BPASS models was defined lightening discussions on dust, SNe, AGBs, RSGs, and from the verified dust condensation relation in Eq. 11 WR binaries. We also thank Greg Sloan for the guid- from the SED analysis results and scaled to the proper- ance on assessing the quality of ISO/SWS data. We ties of WR104. would also like to thank the anonymous referee for We performed two sets of BPASS dust models at three their careful review and insightful comments that have different metallicities Z = 0.001, 0.008, and 0.020 rep- improved the focus and clarity of our work. PMW resenting different phases of cosmic time assuming con- thanks the Institute for Astronomy for continued hos- 6 stant star formation and a co-eval 10 M stellar pop- pitality and access to the facilities of the Royal Ob- 24 Lau et al. servatory. RML acknowledges the Japan Aerospace the Netherlands and the United Kingdom) and with Exploration Agency’s International Top Young Fellow- the participation of ISAS and NASA. This publication ship. This work is based in part on observations made makes use of data products from the Wide-field Infrared with the Spitzer Space Telescope, obtained from the Survey Explorer, which is a joint project of the Univer- NASA/IPAC Infrared Science Archive, both of which sity of California, Los Angeles, and the Jet Propulsion are operated by the Jet Propulsion Laboratory, Cal- Laboratory/California Institute of Technology, funded ifornia Institute of Technology under a contract with by the National Aeronautics and Space Administration the National Aeronautics and Space Administration. Based in part on observations collected at the Euro- pean Organisation for Astronomical Research in the Facilities: Spitzer(IRS, IRAC, and MIPS), WISE, Southern Hemisphere under ESO programme 097.D- ISO(SWS), VLT(VISIR) 0707(A). Based in part on observations with ISO, an Software: BPASS, DustEM, MIRA ESA project with instruments funded by ESA Member States (especially the PI countries: France, Germany,

REFERENCES

Allen, D. A., Swings, J. P., & Harvey, P. M. 1972, A&A, Danks, A. C., Wamsteker, W., Shaver, P. A., & Retallack, 20, 333 D. S. 1984, A&A, 132, 301 Ardila, D. R., Van Dyk, S. D., Makowiecki, W., et al. 2010, De Marco, O., & Izzard, R. G. 2017, PASA, 34, e001 ApJS, 191, 301 Dougherty, S. M., Beasley, A. J., Claussen, M. J., et al. Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., 2005, ApJ, 623, 447 Mantelet, G., & Andrae, R. 2018, AJ, 156, 58 Dwarkadas, V. V., Dauphas, N., Meyer, B., et al. 2017, Boyer, M. L., Srinivasan, S., Riebel, D., et al. 2012, ApJ, ApJ, 851, 147 748, 40 Dwek, E., & Cherchneff, I. 2011, ApJ, 727, 63 Carey S. J., et al., 2009, PASP, 121, 76 Dwek, E., Staguhn, J., Arendt, R. G., et al. 2014, ApJL, Cherchneff, I., Le Teuff, Y. H., Williams, P. M., et al. 2000, 788, L30 A&A, 357, 572 Eldridge, J. J., Stanway, E. R., Xiao, L., et al. 2017, PASA, Cherchneff, I. 2015, Wolf-rayet Stars, 269 34, e058 Fazio, G. G., Hora, J. L., Allen, L. E., et al. 2004, ApJS, Chiar, J. E., & Tielens, A. G. G. M. 2001, ApJL, 550, L207 154, 10 Chiar, J. E., & Tielens, A. G. G. M. 2006, ApJ, 637, 774 Gall, C., & Hjorth, J. 2018, ApJ, 868, 62 Churchwell, E., Babler, B. L., Meade, M. R., et al. 2009, Gayley, K. G., Owocki, S. P., & Cranmer, S. R. 1997, ApJ, PASP, 121, 213 475, 786 Cohen, M., Barlow, M. J., & Kuhi, L. V. 1975, A&A, 40, Gehrz, R. D., & Hackwell, J. A. 1974, ApJ, 194, 619 291 de Graauw, T., Haser, L. N., Beintema, D. A., et al. 1996, Compiègne,M., Verstraete, L., Jones, A., et al. 2011, A&A, A&A, 315, L49 525, A103 Gräfener,G., Koesterke, L., & Hamann, W.-R. 2002, A&A, Conti, P. S. 1975, Memoires of the Societe Royale des 387, 244 Sciences de Liege, 9, 193 Gutermuth, R. A., & Heyer, M. 2015, AJ, 149, 64 Conti, P. S., & Vacca, W. D. 1990, AJ, 100, 431 Hackwell, J. A., Gehrz, R. D., & Grasdalen, G. L. 1979, Crowther, P. A. 1997, MNRAS, 290, L59 ApJ, 234, 133 Crowther, P. A., De Marco, O., & Barlow, M. J. 1998, Hankins, M. J., Lau, R. M., Morris, M. R., et al. 2016, MNRAS, 296, 367 ApJ, 827, 136 Crowther, P. A., Morris, P. W., & Smith, J. D. 2006, ApJ, Harries, T. J., Monnier, J. D., Symington, N. H., & 636, 1033 Kurosawa, R. 2004, MNRAS, 350, 565 Crowther, P. A. 2007, ARA&A, 45, 177 Harris, J., & Zaritsky, D. 2009, AJ, 138, 1243 Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, Herter, T. L., Vacca, W. D., Adams, J. D., et al. 2013, VizieR Online Data Catalog, 2246, PASP, 125, 1393 Cutri, R. M., & et al. 2013, VizieR Online Data Catalog, Hendrix, T., Keppens, R., van Marle, A. J., et al. 2016, II/328 MNRAS, 460, 3975 Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 25

Hillier, D. J., Davidson, K., Ishibashi, K., et al. 2001, ApJ, Monnier, J. D., Tuthill, P. G., & Danchi, W. C. 1999, 553, 837 ApJL, 525, L97 Houck, J. R., Roellig, T. L., van Cleve, J., et al. 2004, Monnier, J. D., Tuthill, P. G., Danchi, W. C., et al. 2007, ApJS, 154, 18 ApJ, 655, 1033 Howarth, I. D., & Schmutz, W. 1992, A&A, 261, 503 Monnier, J. D., Zhao, M., Pedretti, E., et al. 2011, ApJL, van der Hucht, K. A., Hidayat, B., Admiranto, A. G., et al. 742, L1 1988, A&A, 199, 217 Morris, P. W., Brownsberger, K. R., Conti, P. S., Massey, van der Hucht, K. A., Morris, P. W., Williams, P. M., et al. P., & Vacca, W. D. 1993, ApJ, 412, 324 1996, A&A, 315, L193 Morris, P. W., Gull, T. R., Hillier, D. J., et al. 2017, ApJ, van der Hucht, K. A. 2001, NewAR, 45, 135 842, 79 Humphreys, R. M., & Davidson, K. 1994, PASP, 106, 1025 Niemela, V. S. 1995, Wolf-Rayet Stars: Binaries; Colliding Kanarek, G., Shara, M., Faherty, J., et al. 2015, MNRAS, Winds; Evolution, 163, 223 452, 2858 Nugis, T., & Lamers, H. J. G. L. M. 2000, A&A, 360, 227 Jones, A. P., Tielens, A. G. G. M., & Hollenbach, D. J. Pittard, J. M. 2007, ApJL, 660, L141 1996, ApJ, 469, 740 Rajagopal, J., Menut, J.-L., Wallace, D., et al. 2007, ApJ, Kessler, M. F., Steinz, J. A., Anderegg, M. E., et al. 1996, 671, 2017 A&A, 315, L27 Rate, G., & Crowther, P. A. 2020, MNRAS, 493, 1512 Kochanek, C. S. 2011, ApJ, 743, 73 Riebel, D., Srinivasan, S., Sargent, B., et al. 2012, ApJ, Kroupa, P., Tout, C. A., & Gilmore, G. 1993, MNRAS, 262, 753, 71 545 Rieke, G. H., Young, E. T., Engelbracht, C. W., et al. 2004, Lagage, P. O., Pel, J. W., Authier, M., et al. 2004, The ApJS, 154, 25 Messenger, 117, 12 Roche, P. F., & Aitken, D. K. 1984, MNRAS, 208, 481 Lamberts, A., Millour, F., Liermann, A., et al. 2017, Rosslowe, C. K., & Crowther, P. A. 2015, MNRAS, 447, MNRAS, 468, 2655 2322 Lau, R. M., Hankins, M. J., Schödel,R., et al. 2017, ApJL, Rosslowe, C. K., & Crowther, P. A. 2018, MNRAS, 473, 835, L31 2853 Lebouteiller, V., Barry, D. J., Goes, C., et al. 2015, ApJS, Sana, H., de Mink, S. E., de Koter, A., et al. 2012, Science, 218, 21 337, 444 Lefèvre,L., Marchenko, S. V., Lépine,S., et al. 2005, MNRAS, 360, 141 Sander, A., Hamann, W.-R., & Todt, H. 2012, A&A, 540, Le Teuff, Y. H., & Cherchneff, I. 1998, Abundance Profiles: A144 Diagnostic Tools for Galaxy History, 188 Sander, A. A. C., Hamann, W.-R., Todt, H., et al. 2019, van Loon, J. T. 2000, A&A, 354, 125 A&A, 621, A92 Lundstrom, I., & Stenholm, B. 1984, A&AS, 58, 163 Sarangi, A., Matsuura, M., & Micelotta, E. R. 2018, SSRv, Marchenko, S. V., Moffat, A. F. J., Vacca, W. D., et al. 214, 63 2002, ApJL, 565, L59 Schmutz, W., Schweickhardt, J., Stahl, O., et al. 1997, Marchenko, S. V., & Moffat, A. F. J. 2007, Massive Stars in A&A, 328, 219 Interactive Binaries, 367, 213 Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, Marchenko, S. V., & Moffat, A. F. J. 2017, MNRAS, 468, 131, 1163 2416 Shara, M. M., Moffat, A. F. J., Smith, L. F., et al. 1999, Massey, P., Plez, B., Levesque, E. M., et al. 2005, ApJ, 634, AJ, 118, 390 1286 Sloan, G. C., Kraemer, K. E., Price, S. D., & Shipman, Matsuura, M., Barlow, M. J., Zijlstra, A. A., et al. 2009, R. F. 2003, ApJS, 147, 379 MNRAS, 396, 918 Smith, L. F., Shara, M. M., & Moffat, A. F. J. 1990, ApJ, Mauerhan, J., Smith, N., Van Dyk, S. D., et al. 2015, 358, 229 MNRAS, 450, 2551 Smith, L. F. 1968, MNRAS, 140, 409 Midooka, T., Sugawara, Y., & Ebisawa, K. 2019, MNRAS, Smith, N. 2010, MNRAS, 402, 145 484, 2229 Smith, N. 2014, ARA&A, 52, 487 Millour, F., Driebe, T., Chesneau, O., et al. 2009, A&A, Soulain, A., Millour, F., Lopez, B., et al. 2018, A&A, 618, 506, L49 A108 26 Lau et al.

Srinivasan, S., Boyer, M. L., Kemper, F., et al. 2016, Williams, D. M. 2003, American Journal of Physics, 71, MNRAS, 457, 2814 1198 Stanway, E. R., & Eldridge, J. J. 2018, MNRAS, 479, 75 Williams, P. M., Marchenko, S. V., Marston, A. P., et al. Sugawara, Y., Maeda, Y., Tsuboi, Y., et al. 2015, PASJ, 67, 2009, MNRAS, 395, 1749 121 Williams, P. M., Rauw, G., & van der Hucht, K. A. 2009, Temim, T., Dwek, E., Tchernyshyov, K., et al. 2015, ApJ, MNRAS, 395, 2221 799, 158 Williams, P. M. 2011, Bulletin de la Societe Royale des Tuthill, P. G., Monnier, J. D., & Danchi, W. C. 1999, Sciences de Liege, 80, 195 Nature, 398, 487 Williams, P. M., van der Hucht, K. A., van Wyk, F., et al. Tuthill, P. G., Monnier, J. D., Lawrance, N., et al. 2008, 2012, MNRAS, 420, 2526 ApJ, 675, 698 Williams, P. M., van der Hucht, K. A., van Wyk, F., et al. Usov, V. V. 1991, MNRAS, 252, 49 2013, MNRAS, 429, 494 Werner, M. W., Roellig, T. L., Low, F. J., et al. 2004, Williams, P. M., Chu, Y.-H., Gruendl, R. A., et al. 2013, ApJS, 154, 1 Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. MNRAS, 431, 1160 2010, AJ, 140, 1868 Williams, P. M. 2019, MNRAS, 488, 1282 Williams, P. M., van der Hucht, K. A., & The, P. S. 1987, Yamasawa, D., Habe, A., Kozasa, T., et al. 2011, ApJ, 735, A&A, 182, 91 44 Williams, P. M., van der Hucht, K. A., Pollock, A. M. T., Yudin, B., Balega, Y., Bl¨ocker, T., et al. 2001, A&A, 379, et al. 1990, MNRAS, 243, 662 229 Williams, P. M., van der Hucht, K. A., Bouchet, P., et al. Zhekov, S. A., Gagn´e,M., & Skinner, S. L. 2011, ApJL, 1992, MNRAS, 258, 461 727, L17 Williams, P. M., van der Hucht, K. A., Kidger, M. R., et al. Zhekov, S. A., Tomov, T., Gawronski, M. P., et al. 2014, 1994, MNRAS, 266, 247 MNRAS, 445, 1663 Williams, P. M., Cohen, M., van der Hucht, K. A., Zhukovska, S., & Henning, T. 2013, A&A, 555, A99 Bouchet, P., & Vacca, W. D. 1995, MNRAS, 275, 889 Zubko, V. G., Mennella, V., Colangeli, L., et al. 1996, Williams, P. M., & van der Hucht, K. A. 2000, MNRAS, MNRAS, 282, 1321 314, 23 Zubko, V. G. 1998, MNRAS, 295, 109 Williams, P. M., Kidger, M. R., van der Hucht, K. A., et al. Zubko, V., Dwek, E., & Arendt, R. G. 2004, ApJS, 152, 211 2001, MNRAS, 324, 156 Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 27 0.6 2.00 WR48b IR Phot WR53 IR Phot Comp 1 (r1 = 180 AU) 1.75 Spitzer/IRS 0.5 Comp 1 (r1 = 240 AU) 1.50 0.4 1.25 0.3 1.00

Flux (Jy) 0.2 Flux (Jy) 0.75 0.1 0.50 0.25 0.0 0.00 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Wavelength ( m) Wavelength ( m) 2.5 7 WR59 IR Phot WR96 IR Phot Comp 1 (r1 = 210 AU) 6 Comp 1 (r1 = 180 AU) 2.0 5 1.5 4

1.0 3 Flux (Jy) Flux (Jy) 2 0.5 1 0.0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Wavelength ( m) Wavelength ( m) 2.00 2.00 WR103 IR Phot WR119 IR Phot 1.75 Spitzer/IRS 1.75 Comp 1 (r1 = 70 AU) Comp 1 (r1 = 240 AU) 1.50 1.50 1.25 1.25 1.00 1.00

Flux (Jy) 0.75 Flux (Jy) 0.75 0.50 0.50 0.25 0.25 0.00 0.00 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Wavelength ( m) Wavelength ( m)

Figure 11. Best-ﬁt DustEM models of WR48b, WR53, WR59, WR96, WR103, and WR119. 28 Lau et al. 10 0.20 WR121 IR Phot WR124-22 IR Phot Comp 1 (r1 = 130 AU) Comp 1 (r1 = 190 AU) 8 0.15

6 0.10

4 0.05 Flux (Jy) Flux (Jy)

2 0.00

0 0.05 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Wavelength ( m) Wavelength ( m)

Figure 12. Best-ﬁt DustEM models of WR121 and WR124-22.

Table 1. WC Dustar Table

WR Num Ref Alt Name RA Dec Spec. Type Spec. Ref 19 VII LS 3 10 18 05.02 -58 16 25.90 WC5d CDB98, W09b 48b VII SMSNPL 8 13 11 27.45 -63 46 00.80 WC9d SMS99, VII 48a VII D83 1 13 12 39.65 -62 42 55.80 WC8vd+WN8 Z14 53 VII HD 117297 13 30 53.26 -62 04 51.80 WC8d WH00 59 VII GSC 9004-3553 13 49 32.66 -61 31 42.20 WC9d HH88, VII 70 VII HIP 75863 15 29 44.70 -58 34 51.20 WC9vd+B0I N95, W13a 95 VII He3-1434 17 36 19.76 -33 26 10.90 WC9d VII 96 VII LSS 4265 17 36 24.20 -32 54 29.00 WC9d HH88, VII 98a VII IRAS 17380-3031 17 41 12.90 -30 32 29.00 WC8-9vd W95 103 VII HIP 88287 18 01 43.14 -32 42 55.20 WC9d VII 104 VII Ve2-45 18 02 04.07 -23 37 41.20 WC9d+B0.5V WH00 106 VII IC14-8 18 04 43.66 -21 09 30.70 WC9d VII 118 VII GL 2179 18 31 42.30 -09 59 15.00 WC9d CV90, VII 119 VII The 2 18 39 17.91 -10 05 31.10 WC9d WH00 121 VII AS 320 18 44 13.15 -03 47 57.80 WC9d VII 125 VII V378 Vul 19 28 15.61 +19 33 21.4 WC7ed+O9III W94, W19 137 VII HIP 99769 20 14 31.77 +36 39 39.60 WC7pd+O9 SS90, W01 140 VII HIP 100287 20 20 27.98 +43 51 16.30 WC7pd+O5 W90, W09a 124-22 KSF15 1695-2B7 19 27 17.98 16 05 24.6 WC9d KSF15, W19 Note—Name, coordinates, and spectral sub-type of the 19 WC dustars in our sample obtained from V 1.23 of the Galactic Wolf-Rayet Catalogue. The references correspond to the following: VII - van der Hucht(2001), KSF15 - Kanarek et al.(2015), RC18 - Rosslowe & Crowther(2018), CDB98 - Crowther et al.(1998), W09b - Williams et al.(2009b), SMS99 - Shara et al.(1999), Z14 - Zhekov et al.(2014), WH00 - Williams & van der Hucht(2000), HH88 - van der Hucht et al.(1988), N95 - Niemela(1995), W13a - Williams et al.(2013a), W95 - Williams et al.(1995), CV90 - Conti & Vacca(1990), SS90 - Smith et al.(1990), W01 - Williams et al.(2001), W90 - Williams et al.(1990), W94 - Williams et al.(1994), W09a - Williams et al.(2009a), W19 - Williams(2019) Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 29

Table 2. WC Dustar SED Model Details

WR Num r1 range (AU) r1 intervals IR Archival Data Ref. 19 (100, 10000) 50 Spitzer/IRS MM17 48b (50, 3000) 30 2MASS, WISE, Spitzer/IRAC+MIPS Cu03, Cu13,Ch09, Ca09 48a (10, 3000) 25 ISO/SWS vdH96 53 (50, 3000) 30 2MASS, Spitzer/IRAC+IRS Cu03, Ch09, Ar10 59 (50, 3000) 30 2MASS, WISE,Spitzer/IRAC Cu03,Cu13, Ca09 70 (50, 3000) 30 ISO/SWS S03 95 (10, 1000) 30 2MASS, ESO-3.8m, Spitzer/MIPS Cu03, W87, Ca09 96 (50, 3000) 30 2MASS, WISE, Spitzer/IRAC+MIPS Cu03, Cu13,Ch09, Ca09 98a (20, 3000) 25 ISO/SWS vdH96 103 (10, 1000) 30 2MASS, ESO-3.8m, Spitzer/IRS Cu03, W87, Ar10 104 (20, 3000) 25 ISO/SWS vdH96 106 (10, 1000) 30 2MASS, ESO-3.8m, Spitzer/MIPS Cu03, W87, Ca09 118 (10, 1000) 25 ISO/SWS vdH96 119 (50, 1000) 30 2MASS, ESO-3.8m, WISE Cu03, W87, Cu13 121 (10, 1000) 30 2MASS, WISE, Spitzer/IRAC+MIPS Cu03, Cu13, Ch09, Ca09 125 (50, 1000) 30 UKIRT W94 124-22 (20, 3000) 30 2MASS, WISE, Spitzer/IRAC+MIPS Cu03, Cu13, Ch09, Ca09 137 (50, 1000) 30 UKIRT W01 140 (100, 3000) 30 TCS, UKIRT, Spitzer/IRS* W09a

Note—The range of r1 values (in AU) and number of logarithmic intervals is shown for each dustar model. For the two-component dust models, the r2 ﬁtting parameters is the same as that of r1, and f ( = LIR,1/LIR,2) is searched in 20 logarithmic intervals between (0.1, 100). Archival IR photometry taken by 2MASS, WISE, and Spitzer were adopted from the MIPSGAL 24 µm point source catalog (Gutermuth & Heyer 2015). The following references are associated with the archival data of each dustar and is indicated in the rightmost column: MM17 - Marchenko & Moﬀat(2017), Cu03 - Cutri et al.(2003), Cu13 - Cutri & et al.(2013), Ch09 - Churchwell et al.(2009), Ca09 - Carey, et al.(2009), vdH96 - van der Hucht et al.(1996), Ar10 - Ardila et al. (2010), S03 - Sloan et al.(2003), W87 - Williams et al.(1987), W94 - Williams et al.(1994), W01 - Williams et al.(2001), W09a - Williams et al.(2009a). * Spitzer/IRS spectroscopy of WR140 is unpublished. 30 Lau et al.

Table 3. Adopted Dustar Parameters

WR L∗ Ref T∗ Log(Rt) vexp Ref Av M˙ Ref d Ref Porb Ref −1 −1 (L ) (K) (R ) (km s ) (M yr ) (kpc) (yr) 5 −5 +0.78 19 4 × 10 S19 79400 0.3 2780 S19 5.19 4.1 × 10 S19 4.33−0.58 RC20 10.1 W09b 5 −4 a +0.92 48a 4 × 10 W12 50000 0.9 1000 this work 8.28 1.7 × 10 Z14 2.27−0.57 RC20 32.5 W12 5 −5 +1.25 48b 2.5 × 10 S19 40000 1 1390 S19 5.73 2.2 × 10 S19 5.12−0.92 RC20 5 −5 +0.74 53* 3.3 × 10 S19 50000 0.9 1800 S12 3.25 2.2 × 10 S19 4.14−0.56 RC20 5 −5 +0.69 59* 5.8 × 10 S19 40000 1 1300 S12 6.43 3.3 × 10 S19 3.57−0.51 RC20 5 −5 +0.44 70 7 × 10 W13a 40000 1 1390 S19 5.20 2.2 × 10 S19 3.01−0.34 RC20 ∼ 2.8 W13a 5 −5 +0.43 95* 1.7 × 10 S19 45000 0.9 1900 S12 6.63 1.9 × 10 S19 2.07−0.31 RC20 5 −5 +0.58 96* 2.5 × 10 S19 40000 1 1390 S19 5.48 2.2 × 10 S19 2.64−0.43 RC20 5 −5 +0.58 98a 1.5 × 10 H16 45000 0.9 900 W95 13.79 2.2 × 10 S19 1.9−0.35 M99 1.54 M99 5 −5 +1.28 103* 3.2 × 10 S19 45000 0.8 1190 S12 1.40 2.8 × 10 S19 3.46−0.77 RC20 5 −5 +0.12 104 2.5 × 10 S19,M07 40000 1 1220 HS92 6.67 3 × 10 C97 2.58−0.12 So18 0.66 T08 5 −5 +0.56 106* 1.7 × 10 S19 45000 0.8 1100 S12 4.61 1.6 × 10 S19 3.07−0.43 RC20 5 −5 +0.78 118 2.5 × 10 S19 40000 1 1390 S19 13.68 2.2 × 10 S19 2.49−0.68† RC20 5 −5 +1.24 119* 0.5 × 10 S19 45000 0.8 1300 S12 3.91 0.7 × 10 S19 3.22−0.73 RC20 5 −5 +0.30 121* 1.4 × 10 S19 45000 0.8 1100 S12 5.31 1.4 × 10 S19 2.23−0.24 RC20 5 −5 +0.99 125* 1.6 × 10 S12 55000 1.1 2000 S12 6.48 2.7 × 10 S19 3.36−0.65 RC20 28.3 W19 5 −5 +0.18 137* 5.4 × 10 S12 56000 1 2000 S12 1.70 2.7 × 10 S19 2.10−0.16 RC20 13.05 L05 6 −5 +0.11 140 1 × 10 W09a 56000 1 ∼ 2400 W09a 2.21 2 × 10 Su15 1.64−0.09 RC20 7.94 M11 5 b −5 +1.07 124-22 2.5 × 10 S19 40000 1 1390 S19 14.77 2.2 × 10 S19 1.91−0.72† RC20 Note—PoWR models are used for the radiation field of the dust heating source with the following parameters: the stellar heating source luminosity, L∗, the effecting temperature of the heating source, T∗, the “transformed radius” of the WC star (Sander et al. 2012, 2019), Rt in Log units of R . Additional model parameters are the wind velocity/dust expansion velocity, vexp, the visual extinction towards the dustar, Av, the mass-loss rate of the WC star, M˙ , the distance towards the dustar, d, and the dustar orbital period, Porb. All of the visual extinctions were adopted from Rate & Crowther(2020) except for WR98a whose extinction value is from van der Hucht(2001). WR names with *’s indicate systems whose stellar spectra were explicitly modeled with the PoWR grid by Sander et al.(2012), which provides L ∗, T∗,Rt, vexp, and M˙ . The † symbol indicates distance values that were flagged for astrometric excess noise > 1 mas and large parallax uncertainty by RC20. The provided references correspond to the following: S19 - Sander et al.(2019), W12 - Williams et al.(2012), Z14 - Zhekov et al.(2014), W13a - Williams et al.(2013a), H16 - Hendrix et al.(2016), M07 - Monnier et al.(2007), So18 - Soulain et al. (2018), S12 - Sander et al.(2012), W95 - Williams et al.(1995), HS92 - Howarth & Schmutz(1992), W09b - Williams et al.(2009b), W19 - Williams(2019), C97 - Crowther(1997), Su15 - Sugawara et al.(2015), RC20 - Rate & Crowther(2020), M99 - Monnier et al.(1999), T08 - Tuthill et al.(2008), L05 - Lefèvreet al.(2005), M11 - Monnier et al.(2011). (a) WR48a mass-loss rate from Z14 was adjusted for the revised RC20 distance. −1 (b) Derived from AKs = 1.58 (RC20) and assuming Av = (0.107) AKs. , 1 d 0004 0003 55 ,M . . . 110 011 004 005 076 011 013 001 017 063 005 07 586 443 026 022 020 005 006 006 012 001 023 074 104 263 005 780 003 ∗ 0 ...... 20 06 57 16 05 02 0 0 0 0 0 0 0 0 0 0 0 8 1 0 0 ...... +0 − 2 0 1 /L − +0 +0 − +0 − +0 − +0 − − +0 − +10 − − +0 +1 +0 − +0 − +0 − +0 − +0 − +0 − − +0 +3 − − +2 Revisiting the(%) Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 31 57 IR . 319 033 009 010 0017 13 350 635 053 152 039 024 12 399 232 054 168 93 C ...... ,L χ ∗ ) 89 0 10 0 0 10 0 10 0 9 0 98 0 9 0 0 98 0 0 8 0 7 7 8 1 96 0 7 36 4 87 0 6 1 − − − − − − − − − − − − − − − − − − − − , the fraction of stellar )e )e )e )e )e )e )e )e )e )e )e )e )e )e )e )e )e )e )e yr IR 62 22 36 15 35 38 94 14 97 01 38 96 11 19 81 56 36 52 23 13 15 90 83 26 78 90 27 14 56 11 14 48 72 65 00 56 03 77 ......

0 1 4 4 0 1 2 0 1 0 0 0 2 4 0 3 0 0 1 − − − − − +0 +2 +4 +4 +0 +2 − − +2 − +1 − − − +0 +0 +0 − +3 − − +3 +0 − − +1 − +2 +0 − − +0 +1 uncertainties from the model (M values correspond to the dust 79 54 21 11 49 80 71 33 10 46 27 94 51 39 36 10 97 48 10 d ...... σ d ˙ 1 M T ± 6 (6 6 (6 5 (4 6 (8 − − − − )e )e )e )e ) 73 . 93 42 06 29

84 99 09 ...... 5 3 2 5 − − +5 +6 − +3 +11 − (M 2 61 82 06 25 d . . . . Factor” column which applies to L unc 8 (2 d 978911 (1 (3 (9 (8 (1 9 (9 999 (4 (1 (5 87 (9 8 (3 (3 8 (6 896 (6 (9 (6 97 (9 (1 − − − − − − − − − − − − − − − − − − − )e for component 2 are ﬁt. )e )e )e )e )e )e )e )e )e )e )e )e )e )e )e )e )e )e )M 69 2 . 36 73 35 57 30 60 95 38 29 44 87 67 69 84 99 78 63 97 68

61 64 84 49 90 52 24 70 81 96 68 40 76 12 18 63 67 08 ...... 4 0 0 3 4 2 1 0 3 1 1 0 2 0 1 0 1 3 0 IR, − +0 − +0 − +3 − +6 − +9 − +3 − +6 +23 − − +1 − − +1 +0 − − +2 − +3 +1 +2 − − +0 − +1 +6 − +1 − (M /L 1 00 20 44 67 92 43 89 91 60 50 98 42 58 93 19 83 39 09 82 1 d ...... (1 (1 (6 (9 (8 (7 (2 (3 (2 (3 M (1 (5 (1 (6 (5 (1 (6 (0 (9 , the total IR luminosity of emitting dust, L IR, 1 , and the mass fraction of carbon in the WC wind condensed into dust, d d 2 ˙ M IR, 95 66 66 66 80 39 39 83 ...... 0 1 1 1 /L 1 +0 − +2 − +2 − +5 − 46 83 46 46 IR, . . . . 5 1 5 5 m for the small and large distributions, respectively. µ 06943 00652 00019 00071 00011 02005 00686 00002 00049 00037 ...... 1 0 0 0 0 0 . (%) L 04 48 46 37 71 32 ...... +0 − +0 − +0 − +0 − +0 − 38 24 58 01 03 01 01 03 57 18 01 07 29 42 01 03 02 01 18 28 12 01 1 1 0 ∗ ...... ), and luminosity ratio L 0 0 2 0 0 0 0 0 0 0 0 +1 − +1 − +0 − 2 +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − /L d 48 01 63 . . . 22 61148 03704 00640 00412 14 14 34 74 79 00128 63 01 35 43 15 IR ...... m and 0 µ , the dust production rate, 1 d 01 WC Dustar SED Model Results . )e+2 0 )e+2 0 )e+1 0 )e+1 0 )e+3 0 )e+2 0 )e+4 16 )e+3 4 )e+2 0 )e+2 0 )e+2 0 )e+3 0 )e+0 0 )e+4 2 )e+3 1 )e+3 0 )e+2 0 )e+5 49 )e+4 11 = 0 )L 11 35 19 20 54 19 26 39 29 87 79 07 43 01 96 45 33 04 07 32 37 02 10 09 45 34 71 34 96 07 66 48 48 07 29 04 38 05 ......

a 1 0 0 0 0 1 0 4 0 0 0 0 0 0 0 0 0 0 0 +0 − +0 − +0 − +0 − +0 − +1 − +0 − +0 − +0 − +0 − +0 − +1 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − (L ), dust mass (M , the dust temperature of component 1, T 2 27 84 36 78 02 40 03 43 04 93 13 72 05 40 12 08 23 92 74 1 d Table 4...... r IR 55) (3 68) (9 18) (2 14) (6 43) (1 92) (3 29) (1 40) (7 72) (4 10) (1 88) (4 39) (7 42) (7 31) (2 39) (5 46) (1 97) (1 49) (1 70) (1 ...... 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 , , , , , , , , , , , , , , , , , , , Factor L 65 85 89 39 80 75 67 73 79 60 75 72 56 74 53 91 70 60 67 ...... unc (0 (0 (0 (0 (0 (0 (0 (0 (0 d (0 (0 (0 (0 (0 (0 (0 (0 (0 (0 ), temperature (T 2 r are independent of the adopted dustar distance. The WR names with “(LG)” or “(SG)” indicate models where the large or small grain 40 80 40 80 uncertainties in the adopted distance are provided as multiplicative factors in the “ (K) +90 − +50 − +90 − +80 − 2 , the dust mass in component 1, M 2 σ d ∗ d 1 420 340 310 340 ± /L IR , and T 50 340 370 170 1 60 70 50 110 240 200 40 130 40 30 70 70 170 50 70 +60 − +300 − +200 − +190 − (K) T d +50 − +110 − +80 − +140 − +180 − +220 − +40 − +150 − +40 − +80 − +150 − +80 − +150 − +50 − +70 − 1 d ,T 570 630 570 900 930 960 860 910 1010 730 250 1110 770 1020 970 1370 910 860 960 2 r , 1 r 900 90 80 130 +640 − +110 − +120 − +190 − (AU) T 2 2370 460 260 370 SED models provide the radius of component 1, . Note that 340 3630 60 100 220 60 50 40 30 30 70 130 60 C +310 − +3130 − 30 20 10 20 10 10 +170 − +240 − +80 − +150 − +30 − +90 − +30 − +80 − +100 − +130 − +40 − χ DustEM (AU) r +60 − +70 − +20 − +120 − +10 − +10 − 1 , and d ˙ M —Best-ﬁt , 2 . For the 2-component dust models, the radius ( d C luminosity re-radiated in theχ IR by dust, L size distribution were favored based on spatial size constraints. All other dustars SED models used the small grain size distribution. temperature of the smallestﬁtting are grain shown component for inM each the derived parameter. grain size distribution: 125 (SG)137 490 (SG)140 660 (SG)124-22 1170 190 119121 70 130 118 (LG) 30 53 240 48b59 180 70 210 550 WR19 (SG)48a r (SG) 6870 350 95 (LG) 40 104 (LG)106 70 (LG) 50 96103 180 240 98a (LG) 60 Note 32 Lau et al.

Table 5. BPASS Constant SF Dust Models (at t = 1.0 Gyr)

Low-Z LMC-like Solar Z = 0.001 Z = 0.008 Z = 0.020

χd/g 0.0008 0.0018 0.007

mg (M ) 3088 1947 1518

NAGB 1739 (100%) 5465 (100%) 6613 (100%)

NRSG 2332 (65%) 6070 (30%) 6900 (28%)

NWC 3 (100%) 27 (100%) 47 (56%) −1 −2 −2 −2 RSN (yr ) 2.6 × 10 1.7 × 10 1.2 × 10 −1 −7 −10 −6 −9 −5 −9 M˙ d,AGB (M yr ) 4.4 × 10 [2.5 × 10 ] 5.7 × 10 [1.1 × 10 ] 1.9 × 10 [2.9 × 10 ] −1 −7 −10 −6 −9 −6 −9 M˙ d,RSG (M yr ) 3.1 × 10 [2.0 × 10 ] 3.0 × 10 [1.7 × 10 ] 7.4 × 10 [3.8 × 10 ] −1 −10 −11 −6 −8 −5 −7 M˙ d,W C (M yr ) 1.7 × 10 [6.5 × 10 ] 1.7 × 10 [6.2 × 10 ] 2.6 × 10 [9.9 × 10 ] −1 −3 −3 −3 M˙ d,SN (M yr ) 3.1 × 10 [0.12 M ] 1.8 × 10 [0.10 M ] 1.1 × 10 [0.10 M ] −1 −2 −2 −2 M˙ SN,dest (M yr ) −6.5 × 10 [−2.5 M ] −5.9 × 10 [−3.5 M ] −8.2 × 10 [−10.6 M ]

Log(t0,AGB ) 7.9 7.9 7.8

Log(t0,RSG) 6.3 6.4 6.5

Log(t0,W C ) 6.3 6.3 6.4

Log(t0,SN ) 6.5 6.6 6.7 Note—Dust source populations from the constant SFR BPASS dust model for AGBs, RSGs, and WC binaries, the SN rate (RSN ), the total and average (in brackets) DPR for each source at time t = 1.0 Gyr. χd/g is the adopted dust-to-gas mass ratio and mg is the total ISM mass swept up by each SN as determined by Eq. 13 at each metallicity. N shows the total numbers of sources present at this time and the percentage indicates the fraction contribute to the dust input and do not end their lives as SN. The AGB, RSG, and WC binary DPRs are determined from the population that do not end their lives as SN. The SN DPR value in brackets is the average mass of dust formed/destroyed per SN. The time, t0 (yr), corresponds to the onset time of each dust source. Revisiting the Impact of Dust Production from Carbon-Rich Wolf-Rayet Binaries 33

6 Table 6. BPASS 10 M Stellar Population Dust Mod- els (at t = 1.0 Gyr)

Low-Z LMC-like Solar Z = 0.001 Z = 0.008 Z = 0.020 1 2 2 Md,AGB (M ) 1.0 × 10 1.0 × 10 2.7 × 10 −1 0 0 Md,RSG (M ) 2.9 × 10 2.1 × 10 4.3 × 10 −5 −1 0 Md,W C (M ) 1.9 × 10 2.3 × 10 3.7 × 10 3 2 2 Md,SN (M ) 1.4 × 10 9.1 × 10 5.4 × 10 9 9 9 ∆tAGB (yr) 1.5 × 10 1.9 × 10 2.4 × 10 8 8 8 ∆tRSG (yr) 2.0 × 10 1.6 × 10 2.5 × 10 5 6 6 ∆tWC (yr) 5.2 × 10 4.3 × 10 2.5 × 10 7 7 7 ∆tSN (yr) 9.7 × 10 7.5 × 10 5.8 × 10 Note—Model results show the cumulative dust mass, Md, produced by each source and the timescale, ∆t that each source is actively forming dust. These are results show the population of RSG and WC stars that do not end their lives as SNe 34 Lau et al.

Table 7. BPASS LMC Dust Model Table

BPASS (t = 12.6 Gyr) From Obs.

NAGB 20000 (100%) 20040

NRSG 11887 (30%) 3589

NWC 52 (100%) 2 −1 −2 −3 RSN (yr ) 3.3 × 10 2.6 × 10 −1 −5 −10 −5 −10 M˙ d,AGB (M yr ) 1.4 × 10 [7.1 × 10 ] 1.4 × 10 [6.9 × 10 ] −1 −6 −9 −6 −10 M˙ d,RSG (M yr ) 5.9 × 10 [1.6 × 10 ] 1.4 × 10 [4.0 × 10 ] ˙ −1 −6 −8 −8 Md,W C (M yr ) 3.3 × 10 [6.2 × 10 ] & 3 × 10 −1 −3 −3 M˙ d,SN (M yr ) 3.4 × 10 [0.10 M ] 1.7 × 10 [0.65 M ]* −1 −1 −2 M˙ SN,dest (M yr ) −1.1 × 10 [−3.5 M ] ∼ −3 × 10 [∼ −8 M ]

Log(t0,AGB ) 7.9 -

Log(t0,RSG) 6.4 -

Log(t0,W C ) 6.3 -

Log(t0,SN ) 6.6 - Note—Results from the LMC BPASS dust models at time t = 12.6 Gyr compared to observationally derived values (Temim et al. 2015; Srinivasan et al. 2016; Williams 2019). Values in this table are presented in the same format as Tab.5. Note that the observed value of NWC corresponds to the number of known dust forming WC systems in the LMC. For the SN dust destruction in the BPASS model, it is assumed that the dust-to-gas mass ratio in the LMC is χd/g = 0.0018 and that the SN shock clears dust from a total surrounding ISM mass of mg = 1947 M . The dust destruction rates in the right column are from Temim et al.(2015), who derive mg ∼ 2000 M . *Temim et al.(2015) estimate the SN dust production rate in the LMC assuming 100% dust condensation eﬃciency and present these as absolute upper limits on the injected dust mass.