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

Mid-IR imaging observations of WR48a (PID: 097.D-0707(A); PI—Lau) were performed on the Very Large Telescope (VLT) at the ESO Paranal observatory using the VLT spectrometer and imager for the mid-infrared (VISIR; Lagage et al. 2004) at the Cassegrain focus of UT3 on 2016 June 15. Images of WR48a presented in this work were taken with the NeII_2 filter (λ_c = 13.04 μm, Δλ = 0.22) and obtained using chopping and nodding to remove the sky and telescope thermal background emission.

Given the size of the field of view with VISIR of 38'' × 38'' in comparison to the extent of the dust emission from WR48a (∼5''), an on-detector chop-nod configuration was used with 20'' chop and nod amplitudes. The total integration time on WR48a was 15 minutes. Raw images were accessed and downloaded from the ESO Science Archive Facility and processed using the Modest Image Analysis and Reduction (MIRA) software written by Terry Herter (see Herter et al. 2013).

The NeII_2 imaging observations of WR48a achieved near-diffraction-limited imaging with a measured Gaussian full width at half maximum (FWHM) of 045.

ISO/SWS. Five WC dustars in this sample have archival 2.2–40 μm medium-resolution ($R\approx 250\mbox{--}600$) spectra taken by the Short Wavelength Spectrometer (SWS; de Graauw et al. 1996) on the Infrared Space Observatory (ISO; Kessler et al. 1996) that were obtained in the WRSTARS program (PI—van der Hucht; van der Hucht et al. 1996). Archival ISO/SWS spectra of these five dustars (WR48a, WR70, WR98a, WR104, and WR118) were downloaded from the database of SWS spectra processed and hosted by Sloan et al. (2003).⁸ The "sws" files, which are the final versions of the SWS spectra corrected for segment discontinuities and overlaps, were used for the SED analysis.

In order to verify the quality of the SWS data and identify possible normalization issues between SWS bands, the "pws" files that show the spectra prior segment-to-segment normalization were inspected. None of the five dustars with ISO/SWS data exhibit segment-to-segment discontinuities larger than ∼10% below 27.5 μm, which is the wavelength where the 3E band of the long-wavelength section starts. Due to the flux discontinuities and larger flux uncertainties beyond 27.5 μm, only the 2.2–27.5 μm data were used for the SED fitting. The spectra of WR48a, WR98a, WR104, and WR118 were smoothed by a median filter with a 51-element kernel, and the spectrum of WR70, which had an "sws" file with wavelengths sampled a factor of four times higher than the other four sources, was smoothed with a 201-element kernel.

Spitzer/IRS. Six WC dustars have archival mid-IR spectra taken by the Infrared Spectrograph (IRS; Houck et al. 2004) on the Spitzer Space Telescope (Werner et al. 2004) across multiple programs throughout the Spitzer "cold mission" (2004–2009). Hi-Res (R ∼ 600) Spitzer/IRS spectra of WR140 (PID—124; PI—Gehrz), WR19, WR103, and WR53 (all three from PID 199; PI—Houck) were downloaded from the Combined Atlas of Sources with Spitzer IRS Spectra (CASSIS; Lebouteiller et al. 2015).⁹ The spectrum of WR19 was published in the WC dust chemistry study by Marchenko & Moffat (2017), and the spectrum of WR103 was published by Crowther et al. (2006) in their UV to mid-IR spectral analysis comparing WC9 and [WC9] stars. Ardila et al. (2010) also included the spectra of WR53 and WR103 in their atlas of Spitzer stellar spectra. Broad emission line features from WR103, WR140, and WR19 were masked, and the spectra of WR140 and WR19 with lower signal-to-noise ratios were smoothed by a median filter with an 11-element kernel.

In order to verify the photometric accuracy of the long-wavelength (>20 μm) IRS spectra of WR140, the flux was checked against 24 μm photometry from the Multiband Imaging Photometer for Spitzer (MIPS; Rieke et al. 2004) taken in the same program and within ∼1 month of the IRS observations (PID—124; PI—Gehrz). The 24 μm Spitzer/MIPS photometry of WR140 extracted with a 35''-radius aperture and a 40''–50'' background annulus is ${F}_{24,\mathrm{MIPS}}\,=1.07\pm 0.05$.¹⁰ This is consistent with the IRS spectrum at 24 μm (${F}_{24,\mathrm{IRS}}\approx 0.8\pm 0.4$ Jy).

The dustars WR48a and WR98a had coverage from both Spitzer/IRS (PID—40285; PI—Waters) and ISO/SWS, but the ISO spectra were adopted in this work for SED modeling due to its extended wavelength coverage and the sufficiently high signal-to-noise detection.

Spitzer/IRAC and MIPS. For the nonvariable dustars, mid-IR Spitzer photometry was adopted from the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE; Churchwell et al. 2009) taken by the Infrared Array Camera (IRAC; Fazio et al. 2004) at 3.6, 4.5, 5.8, and 8.0 μm in addition to 24 μm photometry from the MIPS Galactic Plane Survey (MIPSGAL; Carey et al. 2009).

WISE. For dustars without any significant contamination or confusion from background emission or nearby sources with ≲10'', four-band mid-IR photometry (3.4, 4.6, 12.1, and 22.0 μm) from the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) in the ALLWISE program (Cutri 2013) were adopted. WISE W3 (12.1 μm) photometry is notably valuable since it bridges the wavelength gap between the Spitzer/IRAC Ch4 (8.0 μm) and MIPS 24 μm measurements.

The Spitzer, WISE, and ground-based 2MASS photometry provided in the MIPSGAL 24 μm point source catalog (Gutermuth & Heyer 2015) were primarily utilized for the nonvariable dustars without ISO spectroscopy.

Given their brightness in the mid-IR (≳Jy), WC dustars have been targeted by ground-based observatories in the IR for many decades (e.g., Williams et al. 1987). In the near-IR, JHK fluxes from 2MASS (Skrutskie et al. 2006) were incorporated in the SED modeling for the following dustars without ISO/SWS coverage: WR48b, WR53, WR59, WR95, WR96, WR103, WR106, WR119, WR121, and WR124-22. Mid-IR L-, M-, N-, and Q-band photometry published by Williams et al. (1987) taken by the ESO 3.6 m and the United Kingdom Infra-Red Telescope (UKIRT) was used for WR103, WR106, and WR119.

For WR137, one of the known periodic dust-makers, the SED is composed of contemporaneous J, H, K, L, M, N, and Q photometry taken in 1985.47 from UKIRT and published by Williams et al. (2001). Near-contemporaneous JHKLMNQ photometry taken by UKIRT in 1993.5 was also adopted for the SED of the periodic dust-maker WR125 (Williams et al. 1994).

In the unique case of the periodic dust-maker WR140, ground-based mid-IR observations with UKIRT by Williams et al. (2009a) were linked with the space-based spectroscopic observations by Spitzer/IRS. Although near-IR photometry of WR140 was not obtained around the same time as the mid-IR UKIRT and IRS observations, JHK measurements were taken during the previous dust formation epoch at an identical orbital phase (ϕ = 0.43; Williams et al. 2009a). Importantly, the epoch-to-epoch stability of the near-IR light curve is consistent to within 0.1 mag. The semi-contemporaneous and phase-consistent coverage of WR140 from 1.2 to 35 μm therefore enabled the dust SED analysis of this system.

Table 2 provides a summary of the archival data set used for each of the 19 dustars.

Many of the WC dustars in this sample are heavily extinguished (A_V ≳ 5) along the line of sight by the ISM, which is apparent from deep silicate absorption in their IR SEDs at 9.7 μm (e.g., Chiar & Tielens 2001). This silicate-dominated extinction is interstellar in nature because the circumstellar dust formed by the WC dustars is carbon-rich (Roche & Aitken 1984). In order to correct for interstellar extinction, the dustar SEDs were dereddened with the "Local ISM" extinction curve from Chiar & Tielens (2006) and adopting the visual extinction, A_v (=1.1A_V), derived by Rate & Crowther (2020)¹¹ except for WR98a due to its large distance and extinction uncertainties. The visual extinction toward WR98a is instead based on the value from van der Hucht (2001). The v filter (λ_C = 5160 Å) is on the narrowband system introduced by Smith (1968) specifically to study WR stars. The adopted A_v for each dustar is shown in Table 3. The selection of the local ISM extinction curve by Chiar & Tielens (2006) was motivated by their use of WC dustar spectra to define the shape of the 1.25–25 μm extinction. Since several of the dustar spectra extended beyond 25 μm, a consistent λ⁻² power law was used in this work to extrapolate the extinction curve.

WR140 is a WC7+O5 system with a well-defined 7.94 yr orbital period, a high orbital eccentricity of e = 0.90, and a total luminosity of L_* ∼ 1 × 10⁶ L_⊙ (Williams et al. 2009a; Monnier et al. 2011). The distance to WR140 measured by Gaia parallax is $d={1640}_{-90}^{+110}$ pc (Rate & Crowther 2020), which is consistent with previous distance estimates (Dougherty et al. 2005; Monnier et al. 2011).

Dust formation in WR140 only occurs when the binary system is at periapse. The proper motion of the resulting dust "arc" formed during periapse has been characterized by multi-epoch, spatially resolved mid-IR imaging as the arc propagates away from the central binary (Figure 2, Left; Williams et al. 2009a). These images allows us to verify our SED model-derived separation distances between the dust component and central heating source. For the line-of-sight extinction, we adopt A_v = 2.21 (Rate & Crowther 2020).

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We perform single-component DustEM models to the stellar wind-subtracted 5–37 μm Spitzer/IRS spectrum taken on 2004 May, UKIRT L- and M-band imaging taken on 2004 June, and JHK imaging taken on 1996 August where WR140 was at an orbital phase (ϕ = 0.43) nearly identical to that of the UKIRT and Spitzer observations (Figure 2, right). This orbital phase corresponds to 3.4 yr after IR maximum and periastron passage. The small (large) dust grain distribution SED fit provides a separation distance between the dust component and central heating source of $r={1170}_{-340}^{+310}$ au (${360}_{-100}^{+160}$ au). Spatially resolved mid-IR imaging observations of WR140 at this orbital phase show that the extended dust arc is 700–900 mas from the central source (Williams et al. 2009a), which is closely consistent with the separation distance derived from our small grain dust distribution model, 1170 au ≈ 700 mas (Figure 2, left). This small grain distribution is also consistent with the dust emission analysis by Williams et al. (2009a), who deduced a characteristic grain size of 0.01 μm.

From the small grain dust SED, we derive a total dust mass of ${M}_{d}=({6.44}_{-3.30}^{+3.84})\times {10}^{-9}$ M_⊙, which implies a dust production rate of ${\dot{M}}_{d}=({8.1}_{-4.2}^{+4.8})\times {10}^{-10}$ M_⊙ yr⁻¹ (Equation (7)), given the periodic 7.94 yr dust formation timescales in WR140. SED fits from ground-based observations by Williams et al. (2009a) indicate a total dust mass of less than 2 × 10⁻⁸ M_⊙ at a phase of 0.56 around WR140, which consistently constrains our derived dust mass. Adopting a total mass-loss rate of $\dot{M}\approx 2\times {10}^{-5}$ M_⊙ yr⁻¹ derived by X-ray monitoring observations of shocked gas in the wind collision region between the WC and O stars (Sugawara et al. 2015) and assuming a 40% carbon composition by mass, the carbon dust condensation fraction is χ_C ≈ 0.01%.

WR104 is the prototypical, continuous dust-maker that exhibits a nearly face-on pinwheel (Figure 3, left) with an orbital period of 242 days (Tuthill et al. 1999, 2008). The central binary is composed of a WC9+OB star and has a Gaia-derived distance of $d={2740}_{-550}^{+720}$ pc. This is consistent with the well-defined distance determined from the location of its possible stellar association host, Sgr OB1, and observations of the proper motion of its circumstellar dust (d = 2580 ± 120 pc; Soulain et al. 2018). Given the tighter constraints from their high spatial resolution imaging, we adopt the Soulain et al. (2018) distance for the dust SED model. The line-of-sight extinction toward WR104 is A_v = 6.67 (Rate & Crowther 2020). We adopt a total system luminosity of L_* = 2.5 × 10⁵ L_⊙, consistent with Monnier et al. (2007) and the mean WC9 luminosity derived by Sander et al. (2019) .

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Since single-component models fail to fit the ISO/SWS spectrum of WR104 between 2 and 27.5 μm, we apply the double-component SED models (Figure 3, Right) and derive separation distances between the central binary and dust components of ${r}_{1}={240}_{-80}^{+60}$ au (${70}_{-10}^{+20}$ au) and ${r}_{2}={1300}_{-740}^{+1130}$ au (${460}_{-90}^{+110}$ au) for the small (large) dust distribution models. High spatial resolution IR imaging by Tuthill et al. (2008) shows that the distance between the central binary and the onset of the spiral dust plume where the IR emission peaks is ∼15 mas (40 au). Figure 3 (left) shows the approximate location of the first dust component for small and large grain models compared to the observed dust morphology. Given the closer agreement of the first dust component, we favor the large grain distribution for WR104.

From our large grain dust SED model, we derive dust masses of ${M}_{d1}=({1.19}_{-0.44}^{+0.70})\times {10}^{-6}$ M_⊙ and ${M}_{d2}=({6.06}_{-2.06}^{+3.09})\,\times {10}^{-5}$ M_⊙ for the two dust components. Adopting a dust expansion velocity of v_exp = 1220 km s⁻¹ (Howarth & Schmutz 1992), the dust production rate based on component 1 is ${\dot{M}}_{d}\,=({4.39}_{-0.97}^{+1.27})\times {10}^{-6}$ M_⊙ yr⁻¹.

This dust production rate is a factor of ∼5 higher than the ${\dot{M}}_{d}=8\pm 1\times {10}^{-7}$ M_⊙ yr⁻¹ value derived by Harries et al. (2004) from 3D dust radiative transfer models. However, we can reconcile this discrepancy based on the following points:

• 1.  
  Harries et al. (2004) adopt a distance to WR104 of 1600 pc as opposed to our value of 2580 pc, which accounts for a factor of (2580/1600)² ≈ 2.6 higher for our derived dust mass.
• 2.  
  The large grain size distribution we adopt versus the small grain distribution used by Harries et al. (2004) implies a closer/shorter distance of the dust component from the central binary—and thus a higher dust production rate (see Equation (6)).

When applying a small grain dust model and adopting a distance of 1600 pc we arrive at a consistent dust production rate of ${\dot{M}}_{d}\approx 6\times {10}^{-7}$ M_⊙ yr⁻¹.

The dust production rate from our large grain SED model shows that WR104 is producing the most dust out of the all the dustars in our sample and is likely the highest dust-maker among all known WC dustars (Table 4). Assuming a WC mass-loss rate of 3 × 10⁻⁵ M_⊙ yr⁻¹ (Crowther 1997; Harries et al. 2004) and a 40% carbon mass fraction, we infer a carbon dust condensation fraction of χ_C ≈ 40%. This carbon dust condensation efficiency is notably higher than the ∼few percent derived by Harries et al. (2004) and implies that a substantial fraction of the available carbon in the WC wind forms dust.

WR48a is a continuous but variable dust-maker hosting a WC8 star with a proposed O-star companion. WR48a is the longest-period dustar known, with an IR light curve–derived period of 32.5 yr, and also exhibits episodes of brief dust formation (Williams et al. 2012). The total luminosity of the system is L_* ∼ 4×10⁵ L_⊙, and its Gaia-derived distance of $d={2270}_{-570}^{+920}$ pc is 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 der Hucht (2001) determine a distance of 1200 pc based on its WC8 spectral type. We therefore adopt the Gaia distance for our dust models, because it falls between the two distance estimates. We also adopt a line-of-sight interstellar extinction toward WR48a of A_v = 8.28 (Rate & Crowther 2020).

In Figure 4, we present mid-IR imaging observations taken by Gemini-South/TReCS (Marchenko & Moffat 2007; PID—GS-2004A-Q-63, PI—A. Moffat) and VLT/VISIR at similar N-band wavelengths at 2004 March 15 and 2016 June 15, respectively. The overlaid arc segment in Figure 4 shows the ∼11 proper motion of eastern dust arc over the 12.3 years separating the two observations. Given the low signal-to-noise ratio of this dust arc in the VISIR images, as well as its extended nature, we assume position uncertainty of 023, which is 0.5× the PSF FWHM (045). Adopting the Gaia distance of 2270 pc, the dust expansion velocity of WR48a is ${v}_{\exp }={1000}_{-240}^{+390}\pm 200$ km s⁻¹, 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 Å emission line width (Williams et al. 2012).

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We apply the two-component dust SED model to fit the ISO/SWS spectrum of WR48a between 2 and 27.5 μm (Figure 5). From the two-component model, we derive separation distances between the central system and dust components of ${r}_{1}={350}_{-130}^{+100}$ au (${110}_{-40}^{+70}$ au) and ${r}_{2}={2370}_{-900}^{+640}$ au (${720}_{-150}^{+440}$ 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 February). This distance estimate is consistent with the small grain distribution, which we therefore infer for the dust composition.

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Based on our small grain distribution SED model (Figure 5), we derive dust masses for components 1 and 2 of ${M}_{d1}\,=({1.42}_{-0.99}^{+1.12})\times {10}^{-7}$ M_⊙ and ${M}_{d2}=({9.82}_{-5.93}^{+5.84})\times {10}^{-6}$ M_⊙. Using the component 1 distance and mass and a dust expansion velocity of v_exp = 1000 km s⁻¹, we estimate a dust production rate of ${\dot{M}}_{d}=({8.46}_{-4.38}^{+3.48})\times {10}^{-8}$ M_⊙ yr⁻¹. The carbon dust condensation fraction is therefore χ_C ≈ 0.1%, assuming the radio-derived mass-loss rate of 1.7 × 10⁻⁴ M_⊙ yr⁻¹ (Zhekov et al. 2014) and a 40% carbon mass composition.

WR98a. WR98a is a WC8 or WC9+OB dustar exhibiting continuous dust formation and appears like a "rotating pinwheel" that "revolves" with a 1.54 period (Monnier et al. 1999). The Gaia distance toward WR98a derived by Rate & Crowther (2020) is $d={1260}_{-410}^{+870}$ pc. Despite its close distance, WR98a is buried behind over 10 mag of visual extinction from the ISM along the line of sight based on a deep silicate absorption feature (Chiar & Tielens 2006). Rate & Crowther (2020) derive a much lower visual extinction of A_v = 1.25, but assign it a "b" flag that denotes it as highly implausible. Additionally, they note that the Gaia parallax measurement of WR98a exhibits large astrometric noise (>1 mas).

Due to the uncertainties in the Rate & Crowther (2020) interstellar extinction and distance measurements, we adopt A_v = 13.79 from van der Hucht (2001) and a distance of d = 1900 pc derived by Monnier et al. (1999) that is consistent with the upper distance uncertainties from Gaia. Monnier et al. (1999) derive this distance to WR98a based on its dust proper motion and adopting an expansion velocity of 900 km s⁻¹ (Williams et al. 1995). The stellar luminosity of WR98a is not well-characterized given the high extinction. We therefore adopt a system luminosity of L_* = 1.5 × 10⁵ L_⊙ that is consistent with the value adopted in the WR98a models by Hendrix et al. (2016). Given its lower wind velocity, WC9 stellar properties are assumed for WR98a.

We fit double-component dust SED models to the ISO/SWS spectrum of WR98a between 2 and 27.5 μm (Figure 6, top left) and derive dust component distances of ${r}_{1}={200}_{-70}^{+50}$ au (${60}_{-10}^{+10}$ au) and ${r}_{2}={860}_{-400}^{+1120}$ au (${370}_{-130}^{+190}$ au) for the small (large) grain size distribution models. Spatially resolved images of the circumstellar dust around WR98a demonstrate that the majority of the mid-IR dust emission is concentrated in the central ∼70 mas, or ∼100 au, of the central binary (Monnier et al. 1999, 2007), with no prominent extended emission beyond ∼150 mas, or ∼200 au. As with WR104, we prefer the large grain size distribution for WR98a. Notably, based on the dust component distances derived from the large grain SED model and adopting a dust expansion velocity of 900 km s⁻¹ (Williams et al. 1995), the expansion timescale between the two components is ∼1.6 yr, which is consistent with the 1.54 yr orbital period. The separation between the two dust components is therefore consistent with the distance between the dust spirals in WR98a.

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From the large grain dust SED model, we derive dust masses for components 1 and 2 of ${M}_{d1}=({1.82}_{-0.68}^{+1.08})\times {10}^{-7}$ M_⊙ and ${M}_{d2}=({9.25}_{-5.29}^{+11.73})\times {10}^{-6}$ M_⊙. Using the distance and mass of component 1, the dust production rate is ${\dot{M}}_{d}=({6.10}_{-1.38}^{+1.77})\,\times {10}^{-7}$ M_⊙ yr⁻¹. Adopting the mean WC9 star mass-loss rate of $\dot{M}={10}^{-4.66}$ M_⊙ yr⁻¹ and a carbon mass fraction of 40% (Sander et al. 2019) for WR98a, we estimate a carbon dust condensation fraction of χ_C ≈ 7%.

We note that there is a discrepancy between our derived dust production rate and the value determined from the hydrodynamic simulations by Hendrix et al. (2016), who obtain a dust production rate of ∼10⁻⁸ M_⊙ yr⁻¹. This discrepancy is primarily due to their assumption of a fixed value of 0.2% for the dust condensation fraction of the total WC mass-loss rate.

WR118. WR118 is a continuous WC9 dust-maker with a possible pinwheel morphology (Millour et al. 2009). The Gaia distance toward WR118 determined by Rate & Crowther (2020) is $d={2490}_{-680}^{+780}$ pc, which exhibited astrometric noise in excess >1 mas and large parallax uncertainty. However, this distance is consistent with previous estimates based on photometry and spectral type (d = 3130 pc; van der Hucht 2001). We therefore adopt the Gaia distance for the dust SED models. WR118 is also heavily reddened by interstellar extinction, where A_v = 13.68 (Rate & Crowther 2020). We adopt a combined stellar luminosity of L_* = 2.5 × 10⁵ L_⊙, consistent with the mean WC9 luminosity derived by Sander et al. (2019).

We fit double-component dust SED models to the ISO/SWS spectrum of WR118 between 2 and 27.5 μm (Figure 6, top right) and derive separation distances for components 1 and 2 of ${r}_{1}={120}_{-50}^{+30}$ au (${30}_{-10}^{+10}$ au) and ${r}_{2}={680}_{-300}^{+320}$ au (${260}_{-80}^{+120}$ au) for the small (large) grain size distributions. High spatial resolution interferometric IR observations of WR118 indicate that dust is located with ∼15 mas (∼40 au) of the central binary (Yudin et al. 2001; Monnier et al. 2007; Millour et al. 2009), which is comparable to the size of component 1 in the large grain model. We therefore favor the large grain model for WR118, which is also consistent with the large grain composition trend for the other IR-luminous WC9 dustars in our sample.

From the large grain SED models of WR118, we determine dust masses of ${M}_{d1}=({5.58}_{-2.95}^{+6.24})\times {10}^{-8}$ M_⊙ and ${M}_{d2}\,=({6.61}_{-3.42}^{+6.99})\times {10}^{-6}$ M_⊙ for components 1 and 2. Adopting an expansion velocity consistent with WC9 stars of v_exp = 1390 km s⁻¹, a WC9 mass-loss rate of $\dot{M}={10}^{-4.66}$ M_⊙ yr⁻¹ (Sander et al. 2019), and a 40% carbon fraction by mass, we find that the dust production rate and carbon dust condensation fraction are ${\dot{M}}_{d}=({6.27}_{-1.94}^{+2.78})\times {10}^{-7}$ M_⊙ yr⁻¹ and χ_C ≈ 7%, respectively.

WR19. WR19 is a periodic WC5+O9 dustar with an orbital period of 10.1 yr and an eccentricity of e = 0.8 (Williams et al. 2009b). This system hosts one of the earliest-type WC stars among the known WC dustars. The Gaia distance to WR19 is $d={4330}_{-580}^{+780}$ pc (Rate & Crowther 2020), which is slightly larger than previous distance estimates based on optical photometry and spectral type (d ∼ 3300 pc; van der Hucht 2001). However, because Gaia observations of WR19 were taken before the onset of dust formation in 2017, it exhibited a mostly dust-free environment that likely contributed to the well-constrained distance. We therefore adopt the Gaia-derived distance for our dust SED modeling. WR19 is also affected by line-of-sight interstellar extinction, where A_v = 5.19 (Rate & Crowther 2020). We adopt a combined stellar luminosity of L_* = 4 × 10⁵ L_⊙, the mean luminosity for WC5 stars as derived by Sander et al. (2019).

We fit single-component dust SED models to the stellar wind-subtracted 5–37 μm Spitzer/IRS spectrum of WR19 (Figure 6, center left) and derive a dust separation distance from the central binary of $r={6870}_{-3630}^{+3130}$ au (${2680}_{-1530}^{+2030}$ au) for the small (large) grain size models. Based on the orbital phase of WR19 when Spitzer observed it (2005 June, ϕ ≈ 0.84), we can estimate the extent of dust formed at periastron passage in early 1997 (Williams et al. 2009b). Adopting the mean WC5 wind velocity from Sander et al. (2019) of v_exp = 2780 km s⁻¹ for the dust expansion velocity, the dust formed in the 1997 periastron passage should be located ∼5000 au away in 2005 June. We therefore favor the small grain composition given the consistency with the dust expansion distance estimate.

For the small grain SED models of WR19, we derive a dust mass of ${M}_{d}=({3.98}_{-2.84}^{+3.76})\times {10}^{-8}$ M_⊙, which implies a dust production rate of ${\dot{M}}_{d}=({3.94}_{-2.81}^{+3.72})\times {10}^{-9}$ M_⊙ yr⁻¹ (Equation (7)) given its orbital period of 10.1 yr. Adopting the mean WC5 mass-loss rate of $\dot{M}={10}^{-4.39}$ M_⊙ yr⁻¹ (Sander et al. 2019) and a 40% carbon mass fraction, the carbon dust condensation fraction is χ_C ≈ 0.02%.

WR70. WR70 is a continuous but variable WC9+B0I dustar with a proposed period of 2.8 yr derived from its IR light curve (Niemela 1995; Williams et al. 2013b). The Gaia-derived distance to WR70 is $d={3010}_{-340}^{+440}$ pc, which is consistent with the recently revised extinction-based distance estimate of d ≈ 3500 pc (Williams et al. 2013b). We therefore adopt the Gaia distance for our dust SED models. The adopted line-of-sight extinction and combined stellar luminosity of the WR70 system are A_v = 5.20 and 7 × 10⁵ L_⊙, respectively (Williams et al. 2013b; Rate & Crowther 2020).

We fit single-component dust SED models to the stellar wind-subtracted 2–27.5 μm ISO/SWS spectrum of WR70 (Figure 6, center right) and determine a separation distance between dust and the central binary of $r={550}_{-70}^{+80}$ au (${150}_{-50}^{+80}$ au) for the small (large) grain size models. Extended emission around WR70 has not yet been resolved, so it is difficult to distinguish between a small or large grain size distribution. However, we choose to adopt the small grain size distribution in order to be consistent with the WC dust formation analysis by Zubko (1998).

The small grain SED models of WR70 provide a dust mass of ${M}_{d}=({6.60}_{-1.78}^{+2.40})\times {10}^{-8}$ M_⊙. Adopting the mean WC9 mass-loss rate and velocity of $\dot{M}={10}^{-4.66}$ M_⊙ yr⁻¹ and ${v}_{\exp }=1390$ km s⁻¹ (Sander et al. 2019), we derive a dust production rate and carbon dust condensation fraction of ${\dot{M}}_{d}=({3.51}_{-0.56}^{+0.65})\times {10}^{-8}$ M_⊙ yr⁻¹ and χ_C ≈ 0.4%, where we have assumed the winds are composed of 40% carbon by mass.

WR137. WR137 is a periodic WC7+O9 dustar with an orbital period of 13.05 yr derived from both radial velocity measurements and IR light curve variations (Williams et al. 2001; Lefèvre et al. 2005). The Gaia-derived distance of $d={2100}_{-160}^{+180}$ pc is consistent with previous distance estimates toward the system (e.g., d ≈ 1820 pc; Nugis & Lamers 2000). We therefore adopt the Gaia distances for our dust SED models of WR137. We also adopt an interstellar extinction and a heating source luminosity of A_v = 1.70 (Rate & Crowther 2020) and L_* = 5.4 × 10⁵ L_⊙, respectively, where the stellar luminosity was derived by a pseudo-spectral fit from the PoWR models by Sander et al. (2012).

We fit single-component dust SED models to the stellar wind-subtracted contemporaneous 1.2–20 μm photometry taken in 1985 May by Williams et al. (2001) (Figure 6, bottom left) and derive a separation distance between dust and the central binary of $r={660}_{-220}^{+240}$ au (${210}_{-70}^{+110}$ au) for small (large) grain size models. The mid-IR emission from dust formation in WR137 peaked in mid-1984 (Williams et al. 2001); therefore, assuming the expansion velocity of 2000 km s⁻¹ (Sander et al. 2012), we expect the dust to be located ∼400 au at the time of the WR137 observations. Since dust formation from WR137 started several years before the mid-1984 peak and may therefore have propagated further, we suggest that the dust is most likely composed of small grains. We therefore favor the small grain model. This is also supported by WR137's similarity in both orbital properties and spectral subtype to WR140, which exhibits dust consistent with small grains.

Based on the small grain SED models and the 13.05 yr dust formation/orbital period of WR137, we derive a dust mass of ${M}_{d}=({1.20}_{-0.57}^{+0.64})\times {10}^{-8}$ M_⊙ and a dust production rate of ${\dot{M}}_{d}=({9.21}_{-4.36}^{+4.90})\times {10}^{-10}$ M_⊙ yr⁻¹ (Equation (7)). Adopting the mean WC7 mass loss of $\dot{M}=2.7\times {10}^{-5}$ M_⊙ yr⁻¹ and a 40% carbon composition by mass, the carbon dust condensation fraction is χ_C = 0.009%.

WR125. WR125 is a WC7+O9III system (Williams et al. 1994; Midooka et al. 2019) that recently exhibited a second observed IR rebrightening, implying a 28.3 yr period (Williams 2019). The Gaia-derived distance toward WR125 is ${3360}_{-650}^{+990}$ pc (Rate & Crowther 2020), which is closer than the previous distance estimate of 4700 pc (Williams et al. 1992) based on a near-IR flux comparison to the similar system WR140 and its well-defined distance. Given the distance uncertainties arising from a relative comparison to WR140, we use the Gaia distance for our dust SED models of WR125. The adopted line-of-sight extinction and combined stellar luminosity of WR125 are A_v = 6.48 (Rate & Crowther 2020) and L_* = 1.6 × 10⁵ L_⊙, respectively, where the stellar luminosity was derived by a pseudo-spectral fit from the PoWR models by Sander et al. (2012).

We fit single-component dust SED models to the stellar wind-subtracted 1.2–20 μm photometry of WR125 taken in 1993.47–1993.5 (Figure 6, bottom right), several years after the onset of observed dust formation between 1990 and 91 (Williams et al. 1994), and determine a dust separation distance between the central binary of $r={490}_{-100}^{+170}$ au (${170}_{-40}^{+70}$ au) assuming small (large) grains. Assuming a dust expansion velocity of 2000 km s⁻¹, consistent with the mean WC7 wind velocity derived by Sander et al. (2019), the dynamical timescale of the modeled dust is 1.2 yr (0.4 yr) for the small (large) dust grains distributions. Because the small grain model timescale is consistent with formation during the observed peak IR emission in mid-1992 (Williams et al. 1994), we favor the small grain dust model.

For the small grain SED models, we derive a dust mass of ${M}_{d}=({1.00}_{-0.35}^{+0.61})\times {10}^{-7}$ M_⊙ and a dust production rate of ${\dot{M}}_{d}=({3.54}_{-1.22}^{+2.15})\times {10}^{-9}$ M_⊙ yr⁻¹ (Equation (7)), assuming an orbital period of 28.3 yr. Our derived dust mass is roughly consistent with the M_d = 1.64 × 10⁻⁷ M_⊙ derived from the isothermal dust model by Williams et al. (1994) after correcting for different distance assumptions. We adopt a mass-loss rate of 1.6 × 10⁵ M_⊙ yr⁻¹ from the spectral model fit by Sander et al. (2012), and a 40% carbon mass fraction. We then determine a carbon dust condensation fraction of χ_C ≈ 0.03%.

WR95 and WR106 are continuous WC9 dustars (van der Hucht 2001) that have constraints on their extended dust emission from IR high spatial resolution observations (Monnier et al. 2007; Rajagopal et al. 2007). The Gaia-derived distances toward WR95 and WR106 are ${2070}_{-310}^{+430}$ pc and ${3070}_{-430}^{+560}$ pc, respectively (Rate & Crowther 2020). The dust separation distances determined from our SED models are $r={130}_{-40}^{+110}$ au (${40}_{-20}^{+70}$ au) for WR95 and $r={170}_{-60}^{+220}$ au (${50}_{-20}^{+120}$ au) for WR106, assuming small (large) grains.

Rajagopal et al. (2007) measure a 28.4 and a 45.0 mas Gaussian FWHM at 10.5 μm for WR95 and WR106, respectively, consistent with the FWHM measured by Monnier et al. (2007) for these systems at shorter IR wavelengths (2.2 and 3.08 μm) near the emission peaks in the SEDs (Figure 7). These angular sizes correspond to a linear size of 60 au for WR 95 and 100 au for WR106. Assuming a circular morphology, the extent of the dust shells should be approximately half of these linear sizes: ∼30 au for WR 95 and ∼50 au for WR106. This is consistent with our large grain size models, and agrees with the interpretation from Rajagopal et al. (2007). Those authors also favor dust models with larger (∼1 μm) grains for WR95 and WR106, and determine dust shell radii of a few tens of astronomical unit from the stars.

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Assuming the large grain SED models, the dust production rates are ${\dot{M}}_{d}=({9.36}_{-3.36}^{+2.00})\times {10}^{-8}$ M_⊙ yr⁻¹ and ${\dot{M}}_{d}=({2.97}_{-1.01}^{+1.14})\,\times {10}^{-7}$ M_⊙ yr⁻¹ for WR95 and WR106, respectively. Given the adopted mass-loss rates (Table 3) from PoWR models by Sander et al. (2012) and assuming a 40% carbon composition in the winds by mass, the carbon dust condensation fraction is ∼1.2% for WR95 and ∼4.6% for WR106.

For the dustars without dust radius constraints (e.g., WR70), we assume a small grain size distribution. In addition to WR70, the eight other dustars that fall into this category are WR48b, WR53, WR59, WR96, WR103, WR119, WR121, and WR124-22. DustEM SED models of these eight dustars are shown in Figures 8 and 9.

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The results of the DustEM SED models to the 19 WC dustars are presented in Table 4. In Figure 10, the dust condensation fraction χ_C and the DPR are plotted against the total IR luminosity of each dustar. Both plots show that χ_C and the DPR increase with increasing with IR luminosity. The periodic or highly variable dust producers (WR19, WR48a, WR125, WR137, and WR 140) show slight discrepancies from this trend because their IR luminosity varies depending on the orbital phase. These results demonstrate that WC dustars exhibit a range of DPRs and χ_C values ranging from 1 × 10⁻¹⁰–4 × 10⁻⁶ M_⊙ yr⁻¹ and ∼0.002%–40%, respectively.

The most recent and relevant study to compare our results to is that of Zubko (1998), who conducted a homogeneous modeling analysis of the SEDs and dust shells of 17 Galactic WC dustars incorporating grain physics and dynamics. A majority of their sample overlaps with ours. Zubko (1998), however, modeled the dust formation physics and dynamics under the assumption of spherically symmetric winds, because the complex, colliding-wind morphology of WC dustars was not known at that time. Despite the difference in analytical techniques, Zubko (1998) derive a range of mass-loss rates and carbon dust fractions consistent with our results. They determine condensed carbon fractions of 0.002%–20% and dust production rates of 5 × 10⁻¹⁰–6 × 10⁻⁶ M_⊙ yr⁻¹.

The distribution of L_IR and the DPR of WC dustars provides a valuable empirical relation for estimating DPRs from IR luminosities that can be directly measured from IR observations. Excluding the periodic and highly variable dustars, the DPR versus L_IR (Figure 10, right) relation can be characterized by the following power-law fit:

$$\begin{eqnarray}&&\mathrm{Log}\left(\displaystyle \frac{\dot{{M}_{d}}}{{M}_{\odot }\,{\mathrm{yr}}^{-1}}\right)={1.21}_{-0.06}^{+0.06}\,\mathrm{Log}\left(\displaystyle \frac{{L}_{\mathrm{IR}}}{{L}_{\odot }}\right)-{11.55}_{-0.18}^{+0.32}.\end{eqnarray} \tag{ 8 }$$

In Figure 10 (left), it is apparent that the efficient dust-makers, where χ_C ≳ 1%, are consistent with large grain dust models. This suggests that there is no homogeneous grain size distribution exhibited by all WC dustars, but rather that larger grain sizes (≳0.1 μm) are produced by dustars with higher dust condensation fractions. However, if the WC subtype influences the grain size, it is possible that WC9 dustars preferentially form large grains. Regardless, the results suggest that efficient WC9 dustars form larger dust grains that will be more robust against destruction and sputtering via SN shocks and survive longer in the ISM.

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The results from the constant SF models are shown in Figure 12 (left column) and Table 5. In order to check the DPR prescriptions of the four dust sources, we compare the model results against observationally measured values and previous studies. The average DPRs for AGB and RSG stars in the LMC-like metallicity model are $\left\langle {\dot{M}}_{d,\mathrm{AGB}}\right\rangle =1.1\times {10}^{-9}$ M_⊙ yr⁻¹ and $\left\langle {\dot{M}}_{d,\mathrm{RSG}}\right\rangle =1.7\times {10}^{-9}$ M_⊙ yr⁻¹, which are consistent within factors of a few to the average DPRs measured from mid-IR observations of the LMC (Riebel et al. 2012; Srinivasan et al. 2016), where $\left\langle {\dot{M}}_{d,\mathrm{AGB}}\right\rangle =6.9\times {10}^{-10}$ M_⊙ yr⁻¹ and $\left\langle {\dot{M}}_{d,\mathrm{RSG}}\right\rangle =4.0\times {10}^{-10}$ M_⊙ yr⁻¹. Temim et al. (2015) calculate a theoretical IMF-averaged SN dust yield of 0.65 M_⊙ for a 100% dust condensation efficiency in SNe. A 10% condensation efficiency, which we adopt for the BPASS models, applied to the Temim et al. (2015) SN dust yields is therefore consistent within a factor of two to the BPASS SN dust yields (∼0.1 M_⊙). The average dust mass destroyed per SN in the LMC measured by Temim et al. (2015) is 6.1 ± 2.6 M_⊙ for silicates and 1.6 ± 0.7 M_⊙ for carbon grains, which is consistent within factors of a few to the average dust mass destroyed per SN in the LMC-like BPASS models (3.5 M_⊙). We discuss the comparisons to the LMC in further detail in Section 4.3.

The average dust production rate from WC binaries in the solar metallicity models is $\left\langle {\dot{M}}_{d,\mathrm{WC}}\right\rangle =9.9\times {10}^{-7}$ M_⊙ yr⁻¹, which is slightly greater than the average DPR from our sample of 19 Galactic dustars $\left\langle {\dot{M}}_{d,\mathrm{WC}}\right\rangle =3.3\times {10}^{-7}$ M_⊙ yr⁻¹. However, we find that the WC binary dust production from the BPASS models is largely dominated by systems with the shortest orbital period: ∼50% of the total WC binary dust input in the solar metallicity model originates from three systems with P_orb between 0.66 and 1.0 yr. These three systems have an average DPR of 3.7 × 10⁻⁶ M_⊙ yr⁻¹, which is consistent with our measured DPR of the P_orb = 0.66 yr system WR104, ${\dot{M}}_{d}=4.4\times {10}^{-6}$ M_⊙ yr⁻¹. We therefore conclude that our BPASS dust prescriptions provide reasonable estimates for the dust input from the four sources.

The constant SF BPASS models show that dust production from SNe without dust destruction dominates AGBs, RSGs, and WC binaries by over an order of magnitude for all three metallicities. However, SNe are consistently net dust destroyers at all time steps when incorporating SN dust destruction, and the SN dust destruction rate exceeds the production rate by over an order of magnitude. The average dust produced per SN is ∼0.1 M_⊙ for all three metallicities. We note that dust formation in SN ejecta is still uncertain and measurements range from ∼10⁻⁶ to 1 M_⊙ of dust per SN (Temim et al. 2015; Gall & Hjorth 2018; Sarangi et al. 2018), but SNe would have to form dust beyond the highest mass range of the observed values in order to compensate for the dust destruction rate.

In the solar metallicity models, WC binaries are the dominant source of dust for ∼60 Myr until the onset of the AGB star population that forms dust at a similar rate to the WC binaries. We note that the WC binaries are significant dust producers in the solar metallicity model despite almost half of the WC stars ending their lives as SNe with their dust input removed (Table 5).

The LMC-like metallicity model shows slightly reduced dust input from AGB and RSG stars compared to the solar metallicity models. The WC binaries show a much greater reduction in dust production due to having a smaller population (by a factor of two) and a lower average dust production rate (by over an order of magnitude) versus those of the solar metallicity model. AGB stars lead the dust production in the LMC-like metallicity models, but only by factors of 2–3 over RSGs and WC binaries. WC binaries notably form within the first 2 Myr after the onset of star formation and are the first sources of dust in the LMC-like (and solar) models.

In the low-Z models, RSGs, AGBs, and WC binaries show smaller populations and form dust at a much lower rate than the LMC-like and solar models. WC binaries exhibit the most substantial decrease in dust production and population. This is because only the most massive and luminous stars evolve to the WC phase at lower metallicities. Such luminous stars drive faster winds and therefore form dust much less efficiently, given the sensitivity of χ_C to wind velocity (Equation (9)). At low Z, if SNe are indeed net dust destroyers, AGBs and RSGs are likely the dominant dust sources, with dust input rates exceeding WC binaries by over three orders of magnitude.

Figure 12 (right column) shows the dust mass input in each time bin and the cumulative dust mass input as a function of time for WC binaries, AGBs, RSGs, and SNe. The most notable difference in the dust production between the coeval population and the constant SF models is the relatively higher dust contribution by AGBs. For example, the total dust mass from AGB stars at a time t = 1.0 Gyr is over an order of magnitude greater than the total dust mass input from RSGs and WC binaries in all three metallicity models (Table 6). Like the constant SF models, SNe are consistently net dust destroyers at all three metallicities. The RSG dust input shows two peaks, where the secondary peak around ∼100 Myr is consistent with the onset of AGBs. This secondary, late-time peak arises due to the difficulties in distinguishing the population of luminous AGB stars from faint RSGs (Eldridge et al. 2017). SN models with dust destruction show that the AGBs dominate the dust input at all three metallicities.

The dust production timescales, which we define as the length of time during which the sources are forming dust, are provided in Table 6 and show that WC binaries only produce dust for ${\rm{\Delta }}{t}_{\mathrm{WC}}=0.5\mbox{--}4.3\,\mathrm{Myr}$. Note that the RSG and WC binary timescales in Table 6 only include sources that do not end their lives as SNe. When including sources that end their lives as SNe, the first RSG peak is broader and bridges the second peak in all three metallicity models, and the WC binary dust formation timescale in the solar metallicity model is broader by factor of ∼2 (Δt_WC = 5.4 Myr) than the 2.5 Myr timescale reported in Table 6.

As expected, the WC dust production timescale is substantially shorter than the dust production timescales of AGB stars, where ${\rm{\Delta }}{t}_{\mathrm{AGB}}=1.\mbox{--}2.4\,\mathrm{Gyr}$. The short dust production timescale of WC binaries explains the difference in their cumulative dust input rate relative to the longer-lived AGB stars between the constant SF and coeval population models. Given their short timescales, the presence of WC binaries should also reflect the intensity of recent star formation.

The results from the coeval 10⁶ M_⊙ stellar population BPASS models indicate that, for a "bursty" SFH, AGB stars will dominate the dust budget at late times (t ≳ 70 Myr) over WC binaries and RSGs with SNe as net dust destroyers. However, the LMC-like and solar models show that WC binaries are the first and the dominant source of dust for ∼1 Myr before the RSG dust production starts to increase. Notably, in the solar metallicity mode, the WC binaries are the leading dust source until the onset of AGB stars.