RISING FROM THE ASHES: MID-INFRARED RE-BRIGHTENING OF THE IMPOSTOR SN 2010da IN NGC 300

The outburst of a new OT in NGC 300 was discovered by Monard (2010) with his 0.3 m telescope at the Bronberg Observatory and an unfiltered ST7-XME CCD camera. The initial detection was made on 2010 May 23.16, during a morning session of SN searching in nearby galaxies. A confirmation image was obtained on 2010 May 24.14 with the same instrumentation. These were the first Bronberg observations of NGC 300 of the season, following its solar conjunction, showing that the eruption was already underway. The discovery light curve is shown in Figure 2 and the data are provided in Table 1. Throughout the paper, the "peak" date (t_d = 0) corresponds to the date of the optical outburst (JD = 2455343.66).

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On 2010 May 25, we began photometric monitoring of this event with the ANDICAM CCD camera on the SMARTS Consortium¹⁴ 1.3 m telescope at Cerro Tololo Inter-American Observatory (CTIO). This monitoring continued until 2010 September 5, after which the OT became too faint for useful observations. A re-brightening of the object was detected on 2011 October 21.16 by Chornock et al. (2011). We resumed the 1.3 m coverage on 2011 November 12, and continued until 2011 December 20, after which the OT was again too faint for further observations.

The SMARTS monitoring was carried out by service personnel at CTIO, using BVRI filters in the Johnson–Kron–Cousins system. The ANDICAM frames were bias-subtracted and flat-fielded in the SMARTS pipeline at Yale University. We then determined differential magnitudes between the OT and a nearby comparison star, using standard aperture-photometry tasks in IRAF.¹⁵ Absolute photometry of the comparison star (J2000: 00:55:06.47, −37:42:58.2) was determined from aperture photometry on 11 sets of BVRI frames obtained on four photometric nights, calibrated to standard stars of Landolt (1992). This calibration yielded V = 13.710, B − V = 0.596, $V-R=0.346$, and $V-I=0.675$, with mean errors of about ±0.003–0.007 mag.

The resulting calibrated magnitudes of the OT from the SMARTS monitoring are listed in Table 2 and are shown in Figures 3(B), 4(A), and (B). The tabulated uncertainties are based only on photon statistics; the systematic errors due to the zero-point uncertainty and instrumental effects are likely of the order of ±0.01–0.02 mag. In addition, the OT lies in a small cluster (Binder et al. 2016), only marginally resolved in the 1.3 m images, which contaminates the photometry at the OT's faintest level; we have not attempted to correct for this effect.

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The g-, r-, and i-band follow-up images were taken between 2014 May 17 to 2015 November 13 with the 1m-Swope telescope, at Las Campanas Observatory, using a recently installed e2v CCD, 4 K × 4 K pixels array of 0435/pix. The observations, the standard data reduction procedure (bias subtraction, flat fielding, and linearity correction) and the photometry calibration was performed by Carnegie Supernova Project collaborators in a similar way as detailed in Hamuy et al. (2006). The field was calibrated in two photometric nights: 2014 August 1 and 2014 December 20. The PSF photometry of SN 2010da were converted from the Natural system of Swope (Contreras et al. 2010) to AB magnitudes based on the transformations provided by Equations (A5)–(A7) in Stritzinger et al. (2011). The following color terms (CT) were adopted in these transformations: CT_g = −0.010, CT_r = −0.014, and CT_i = +0.018. Since the transformed AB magnitudes of SN 2010da were consistent within <0.01 mag of the Natural system photometry, the Natural magnitudes were treated as AB magnitudes when ultimately converting to the Vega system presented in Table 2. The gri photometry is shown in Figures 3(B) and 4(C).

The full mid-IR light curve of SN 2010da taken by Spitzer/IRAC before, during, and after the optical and X-ray outburst is shown in Figure 3(A), where t_d = 0 corresponds to the day of the optical peak (JD = 2455343.66). The optical light curve (Figure 3(B)) and X-ray observations (Figure 3(C)) from Binder et al. (2016, and references therein) are plotted on the same time axis as the mid-IR light curve. On day −156, the 3.6 μm emission increased by ∼50% of the progenitor flux as measured from day −2379 and −880 observations. This flux increase is significant given that the source has remained constant to within a few percent at 3.6 and within ∼10% at 4.5 μm between days −2379 and −880. Within 23 days of the initial brightening on day −156, the 3.6 μm flux increased to its highest measured mid-IR value of 0.27 mJy, a factor of ∼2.5 times the progenitor flux. At day 60, after the initial optical outburst, the source exhibited a similar 3.6 μm flux as on day −133. The sharp increase and immediate decrease in brightness at 3.6 μm indicates that an outburst in the mid-IR occurred between days −133 and 81, which is consistent with the timing of the X-ray and optical emission peaks.

By day 460, the 3.6 and 4.5 μm flux decreased to values slightly higher and lower than the progenitor flux at respective wavelengths. The following measurement made on day 806 indicated a gradual re-brightening in the mid-IR with similar fluxes observed on day 1386. Between days 1386 and 1602, there is evidence of rapid re-brightening given the sharp increase in flux from day 1386 to 1562 followed by a steep decrease. At day 1936, the mid-IR flux increased by ∼25% from day 1602 and decreased slightly in the subsequent observation on day 1943. This is suggestive of another re-brightening event in the mid-IR between days 1602 and 1936 and, as in the case of the initial outburst, appears to coincide with the re-brightening X-ray and optical emission (blue dashed and green dot–dashed lines in Figure 3, respectively). The following two observations on days 1951 and 1965 show a rapid increase to the peak measured brightness at late-times, almost a factor of approximately two greater than the progenitor flux. The most recent two mid-IR observations made on days 2097 and 2104 show a sharp decrease in flux ∼10% lower than on day 1965, which suggests that another peak in the mid-IR emission occurred between days 1965 and 2097.

Detailed BVRI light curves of SN 2010da taken at "early" (day ∼0–100) and "intermediate" (day ∼500) epochs and the gri light curve taken at a "late" (day ∼1300–2000) epoch are shown in Figures 4(A)–(C), respectively. Prior to its discovery as an OT (Monard 2010), archival optical imaging of NGC 300 from Magellan/Megacam reveal non-detections of r- and i-band counterparts to a deep limit of 24 AB mag (Berger & Chornock 2010). The early epoch observations capture a peak in the optical emission occurring 4.2 days after its discovery followed by a rapid decline in brightness by a factor of ∼20 from the peak flux within 50 days, and a factor of ∼60 within 100 days. Given the peak V-band flux of 16.17 ± 0.02 mag and a distance modulus of μ = 26.5 (Dalcanton et al. 2009), the absolute visual magnitude of the optical peak is M_V = −10.3, consistent with the value reported from the initial discovery (Khan et al. 2010; Monard 2010).

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The intermediate epoch BVRI light curve (Figure 4(B)) reveals a re-brightening of the optical counterpart to V = 19.27 ± 0.04 mag, which is ∼3.0 mag fainter than the peak brightness but ∼1.5 mag brighter than the final V magnitude measured in the early epoch. The timing and brightness of this re-brightening is consistent with the 6.5 m Magellan/Clay telescope optical observations of SN 2010da reported by Chornock et al. (2011). As in the case of the initial outburst, the intermediate outburst exhibits a steep decline in brightness in the following ∼50 days.

The late-time gri light curve (Figure 4(C)) exhibits a gradual re-brightening between days 1530 and 1833 by ∼0.5 mag in all three bands. Only the r band, however, exceeds the lowest measured brightness in the earlier epochs assuming r ≈ R, g ≈ V, and i ≈ I. The late epoch optical re-brightening is consistent with the timing of the re-brightening X-ray emission observed on day 1635. In the ∼70 days following the apparent optical peak at day 1833, the optical brightness does not vary significantly. However, the final gri measurements made on day 1996, which is ∼30 days after the final mid-IR observation, show a ∼0.2 mag decrease from the peak brightness.

The evolution of the optical colors (B − V, V − I, and g − i) from the outbursts at early, intermediate, and late epochs is shown in Figures 4(D), (E), and (F), respectively. In the early epoch, the V − I color becomes significantly redder within ∼20 days of the initial outburst, increasing from V − I ≈ 0.6 to 1.0. The B − V color does not exhibit the same evolution and only increases from $B-V\approx 0.38$ at the outburst to 0.45 after 20 days. The optical colors measured at the peak of the intermediate epoch are consistent with the colors in the early epoch after day 40; however, there are less than 10 observations between days 40 and 530. At the final B- and V-band measurements of the decreasing brightness after the outburst, the B − V color shows a rapid red-ward change from $B-V\approx 0.48$–0.92 within a short 10-day timescale. Late-time g − i colors are consistent with the V − I colors at intermediate times ($g-i\sim 1.1$).

The detection of the progenitor in the mid-IR and non-detection at optical wavelengths are consistent with a central source that was enshrouded by dense and dusty circumstellar material. This mid-IR emission likely originates from hot (T_d ≳ 500 K) circumstellar material in the vicinity of SN 2010da and its progenitor and can therefore be used to trace the properties of the emitting dust. The temporal evolution of the dust temperature (T_d), total IR luminosity (L_IR), and mass (M_d) and the equilibrium temperature radius (R_Eq) are shown in Figures 5(A)–(D), respectively, and provided in Table 3.

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Dust temperatures were derived by fitting the 3.6 and 4.5 μm fluxes to a single-temperature modified blackbody, a Planck function multiplied by a grain emissivity model assuming a composition of carbonaceous a = 0.1 μm sized grains (Zubko et al. 2004). The progenitor dust exhibited temperatures of 650–750 K. At the first detection made with at both 3.6 and 4.5 μm after the outburst (day 460), the dust temperature increased to 850 ± 70 K and showed an increasing trend up until it peaked at day 1386–1020 ± 90 K. The following measurement taken 175 days after the temperature peak revealed that the temperature quickly decreased to 910 ± 50 K. No significant deviations from ∼900 K were measured.

The total infrared luminosity of the emitting dust was estimated by integrating over the temperature-fitted modified blackbody and assuming a distance of 2.0 Mpc toward NGC 300 (Dalcanton et al. 2009). The evolution of L_IR closely resembles the mid-IR light curve with a gradual post-outburst increase followed by a decrease measured at day 2097. Prior to the eruption, the progenitor exhibited an IR luminosity of L_IR ≈ 1.4 ± 0.1 × 10⁴ L_⊙, consistent with the mid-IR progenitor luminosity determined by Prieto et al. (2010). On day 1936, where measured IR luminosity peaked, L_IR increased by over a factor of two from the progenitor levels to 3.5 ± 0.3 × 10⁴ L_⊙. The final measurements made on days 2097 and 2104 show a decrease from the peak luminosity to ∼2.5 ± 0.3 × 10⁴ L_⊙.

Dust masses were derived from the mid-IR fluxes and temperature-fitted modified blackbodies as indicated in Equation (1):

$$\begin{eqnarray}&&{M}_{d}=\displaystyle \frac{(4/3)a\,{\rho }_{b}\,{F}_{\lambda }\,{d}^{2}}{{Q}_{C}(\lambda ,a){B}_{\lambda }({T}_{d})},\end{eqnarray} \tag{ 1 }$$

where a is the adopted grain size, ${\rho }_{b}$ is the bulk density of the dust grains, F_λ is the measured flux, d is the distance to the source, ${Q}_{C}(\lambda ,a)$ is the grain emissivity model for carbonaceous grains, and ${B}_{\lambda }({T}_{d})$ is the Planck function. A bulk density of ${\rho }_{b}=2.2\,\mathrm{gm}\,{\mathrm{cm}}^{-3}$ (e.g., Draine & Li 2007) is assumed for the emitting carbonaceous grains. The estimated dust mass of the progenitor averaged over the first three observations (${M}_{d}=2.6\pm 1.0\times {10}^{-7}\,{M}_{\odot }$) decreased by over a factor of approximately two at the first 3.6 and 4.5 μm measurements made after the outburst at day 460, where M_d = 0.9 ± 0.3 × 10⁻⁷ M_⊙. In the following ∼930 days, the dust mass gradually decreased to a minimum of 0.5 ± 0.1 × 10⁻⁷ M_⊙. Between days 1386 and 1562, the dust mass increased significantly by 0.7 × 10⁻⁷ M_⊙, which implies that dust was formed at a rate of ${\dot{M}}_{D}\approx 1.4\,\times {10}^{-7}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. The timing of this increased dust production is consistent with the late-time re-brightening in the X-ray, optical, and mid-IR as well as the decrease in dust temperature. The final mid-IR measurements taken around day ∼2000 reveal a 20%–40% (1–2σ) increase in dust mass from day 1602.

The equilibrium temperature radius, R_Eq, is determined from the distance where the absorbed power from the radiation field of the heating source is equal to the power emitted by the dust grain of temperature T_d. The equilibrium temperature radius provides an estimate of the physical size of the hot, circumstellar dust and is given by

$$\begin{eqnarray}&&{R}_{\mathrm{Eq}}\approx {\left(\displaystyle \frac{{Q}_{\mathrm{abs}}}{{Q}_{{\rm{e}}}}\displaystyle \frac{{L}_{\mathrm{IR}}}{16\pi \sigma {T}_{D}^{4}}\right)}^{1/2},\end{eqnarray} \tag{ 2 }$$

where Q_abs and Q_e are the grain absorption and emission Planck mean cross sections (see Gilman 1974), respectively, and σ is the Stefan–Boltzmann constant. A typical value of $({Q}_{\mathrm{abs}}/{Q}_{{\rm{e}}})\approx 0.3$ (e.g., Smith et al. 2016) is assumed for the calculation. Note that if the heating of the mid-IR emitting dust is instead dominated locally by collisions with hot electrons in a post-shock environment (e.g., Dwek 1987; Dwek et al. 2008), R_Eq will not reflect the physical size of the system. However, it is unlikely that the mid-IR emitting dust is dominantly heated by a shock driven from the initial outburst since the observed mass of an illuminated shell of shock-heated dust should increase rapidly as a function of time as it propagates outward radially (${M}_{{\rm{d}}}\propto {t}^{2};$ Fox et al. 2011). This is inconsistent with the "step-function"-like evolution of the dust mass.

Before the outburst, the progenitor exhibited an equilibrium temperature radius of ∼10–12 au. After the outburst on day 460, the radius decreased from the progenitor size to 7.3 ± 1.4 au and did not change significantly in the following measurements made on days 806 and 1386. At late times coincident with the multi-wavelength outbursts and dust mass increase, the radius grew to 9 ± 1 au and did not deviate significantly throughout the final observations.

The evolution of the temperature and luminosity of the dereddened SN 2010da optical counterpart is shown in Figures 6(A) and (B), respectively, and are provided in Table 2. Optical photometry was corrected for foreground extinction (A_V = 0.26) and the differential extinction internal to NGC 300 along the line of sight toward SN 2010da (A_V ∼ 0.4; Binder et al. 2016).

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Temperatures were derived by fitting a single-temperature blackbody to the BVI and gi photometry, where the R and r bands are purposely ignored due to potential contamination from prominent Hα line emission detected from the outburst (Chornock & Berger 2010). Temperatures peak at ∼9500 K for several days around the initial optical peak and decrease rapidly to ∼6500 K in the 40 days following the peak. At the intermediate epoch, the temperature peaks at ∼6700 K on day 534 and decreases to ∼6200 K within eight days. Temperatures derived in the late epoch have large error bars due to the faintness of the optical counterpart; however, they exhibit a range of temperature ∼6000–8000 K consistent with values estimated during the previous epochs.

Luminosities of the optical counterpart to SN 2010da were estimated by integrating over the temperature-fitted blackbodies. The highest measured luminosity is 3 × 10⁶ L_⊙ and is consistent with the initial optical brightness peak. After the peak, the luminosity rapidly decreased by over two orders of magnitude to ∼4 × 10⁴ L_⊙ at the end of the early epoch (t_d = 101 days). At the intermediate-time re-brightening on day ∼530, the luminosity peaked at ∼1.4 × 10⁵ L_⊙ and decreased by a factor of approximately two in the following 40 days. In the late epoch, the optical counterpart exhibited luminosities ranging from ∼5–10 × 10⁴ L_⊙, which is consistent with the luminosity minimum of the intermediate epoch.

The significant decrease in reddening and optical depth toward SN 2010da during and after the outburst (Bond 2010; Brown 2010) imply the destruction of the circumstellar dust that heavily enshrouded the progenitor. The decrease in the derived mass between the progenitor and post-outburst DUSTY models (Table 4) is suggestive of dust destruction as well. Given the luminosity of the optical flash from the initial outburst (L ≈ 3 × 10⁶ L_⊙), we can estimate the radius, r_sub, out to where the optical/UV flux will evaporate dust by heating it beyond the sublimation temperature (T_sub ∼ 1700 K; e.g., Gall et al. 2011). The sublimation radius can be estimated from Equation (2) to be r_sub ≈ 4×10¹⁴ cm (∼27 au). Since r_sub is greater than the pre-outburst equilibrium temperature radius shown in Figure 5(D), we conclude that a significant amount of circumstellar dust was evaporated in the initial optical flash. The lower post-outburst dust mass estimates at early and intermediate times relative to the progenitor dust mass despite higher post-outburst luminosities strengthens this claim.

The prominent post-outburst re-brightening across IR, optical, and X-ray wavelengths at around day ∼1600 (Figure 3) implicates the survival of the progenitor. However, we must consider the alternative explanation where the re-brightening arises from interactions between a shock driven by the initial outburst with shells or clumps of circumstellar material. We claim that this is unlikely due to the hardness variability of the post-outburst X-ray emission reported by Binder et al. (2016): high luminosity measurements taken on days 120 and 1635 exhibit harder X-ray emission than the low-luminosity emission observed on day 1450 (see Figure 3(C)). The hardening and increasing X-ray energetics between days 1450 and 1635 are indicative of continued outburst activity from a surviving central system. Such variability is difficult to reconcile with a terminal outburst. Given the apparent survival of the progenitor, we propose that the late-time (days ∼1500–2100) re-brightening of the IR luminosity by over a factor of two times the progenitor (Figure 5(B)) is due to an increase in the luminosity of the central system and on-going dust formation.

At intermediate times (days ∼460–1390), the dust temperature exhibits a similar increasing trend as the IR luminosity, whereas the late-time temperature shows a sudden drop while the luminosity continues to increase until day ∼2000. The intermediate-time temperature–luminosity correlation is consistent with the scenario where a fixed quantity of emitting dust is at a constant distance (i.e., the dust formation radius) from a heating source increasing in brightness: T_d ∝ L^1/4 (Equation (2)). Constant dust masses estimated at intermediate times (Figures 5(C) and (D)) strengthen this interpretation. Ultimately, we are not sensitive to changes in the luminosity from possible warm and/or cold dust distributions and therefore require far-IR photometry to conclusively claim that the heating source is increasing in luminosity. However, it is apparent from the evolution of the mid-IR dust properties and variability of the temperature and luminosity of the optical counterpart (Figure 6) that the energetics of the system is significantly changing many years after the initial eruption.

Mid-IR emission observed after the outburst must be associated with dust that either survived the initial optical/UV flash, reformed in the supersaturated vapor of the previously evaporated grains, and/or reformed in the outflow from the central source. Alternatively, the emitting dust could be interstellar in nature and illuminated by the optical flash (i.e., an "IR echo"). We first test the IR echo scenario by using Equation (2) to estimate the predicted temperature of dust at a distance of $c\,t/2$, which is where the hottest dust is located if heated by the optical/UV flash (e.g., Fox et al. 2011, 2015). At t ≈ 460 days and given an optical/UV outburst luminosity of L ≈ 3×10⁶ L_⊙, the predicted dust temperature is 43 K, significantly less than the temperature estimated at day 460 (T_d ≈ 850 ± 73 K). It is therefore unlikely that the post-outburst mid-IR emission is due to an IR echo.

The unchanging equilibrium temperature radius of the emitting dust at intermediate times (∼8 au, Figure 5(D)) over ∼2.5 years suggests that the mid-IR emission is not associated with dust reformation in the progenitor winds nor survival from the optical/UV flash. Dust formed through either channel would unlikely be located at radii that are smaller than the radii estimated for the progenitor dust, especially given an approximate shock velocity of ∼660 km s⁻¹ based on the FWHM of the Hα emission line observed from SN 2010da during the outburst (Chornock & Berger 2010). Given a shock velocity of 660 km s⁻¹, the shock that would sweep up reformed or surviving dust (e.g., Kochanek 2011) will propagate ∼300 au over 2.5 year and is over an order of magnitude larger than the estimated dust radius. Although we cannot rule out the presence of surviving or reformed cold dust due to the lack of far-IR measurements, we claim that the post-outburst emission in the mid-IR is primarily associated with newly formed dust from the surviving central system.

The growth in IR luminosity from SN 2010da directly contrasts with the late-time mid-IR light curves of SN 2008S and OT2008-1 that decrease to over a magnitude below the mid-IR flux from the respective progenitors (Figure 8). Notably, SN 2008S and OT2008-1 did not have any detections of X-ray emission, whereas the peak X-ray luminosity from SN 2010da was L_x ∼ 4.5 × 10³⁸ erg s⁻¹ (Immler et al. 2010). Subsequent X-ray and optical outbursts like those observed from SN 2010da may be hidden by substantial quantities of circumstellar dust still present around SN 2008S and OT2008-1 (τ_V ≳ 100 assuming surviving stars with similar luminosity as their progenitor; Adams et al. 2015); however, this high value of τ_V is also in disagreement with the moderate optical depth estimated from the post-outburst SED of SN 2010da (τ_V ∼ 1; Figure 7(B)). One may argue that differences in viewing angles or dust shell morphology may explain the non-detection of X-ray emission; however, it is difficult to invoke geometry as a means to reconcile the contrasting evolution of the late-time IR luminosity. Given the evidence we presented, we claim that SN 2010da does not fall within the class of SN 2008S-like transients.

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Low-luminosity SNe have been proposed as the mechanism for 2008S-like events and may provide an alternative explanation for the SN 2010da outburst. In this scenario, SN 2010da's late-time increase in luminosity may be due to energy input from the shock driven into the circumstellar material by the initial outburst. Interestingly, the high X-ray luminosity detected from the initial outburst is consistent with the total integrated luminosity of the system at late times (see Figures 7(B) and 8). However, the SN-interpretation is highly unlikely given the re-brightening events at mid-IR, optical, and X-ray wavelengths and the hardness variability of the X-ray emission (Binder et al. 2016) that imply the survival of the progenitor system.

The prospect of SN 2010da corresponding to a merger event is interesting given the increasing attention on stellar mergers (e.g., Smith et al. 2016); however, this interpretation is unlikely due to the SN 2010da's high X-ray luminosity and late-time re-brightening. Additionally, the smoothly declining optical light curve following the initial outburst of SN 2010da (Figure 4) is not consistent with the almost periodic peaks exhibited from merger candidates V838 Mon and NGC 4490 OT.

Interestingly, V838 Mon, the prototypical system believed to be representative of a stellar merger, exhibited a peak absolute V-band magnitude of about −9.8 (Sparks et al. 2008), similar to the SN 2010da peak (M_V ∼ −10.3). Antonini et al. (2010) report variable X-ray emission from V838 Mon ∼6 with luminosities of ∼10^32-33 erg s⁻¹ ∼ 6 years after the initial outburst that is believed to be a consequence of interaction between its ejecta and early-type companion. It is difficult to reconcile the discrepancy in the X-ray energetics between V838 Mon and SN 2010da given the ≳3 orders of magnitude difference in X-ray luminosity; therefore, we rule out the merger scenario for SN 2010da.

The high X-ray luminosity of the initial outburst and subsequent re-brightening present strong evidence for an HMXB interpretation (Binder et al. 2016) since stellar wind-driven mechanisms have not been observed to reach such high luminosity. For example, the highest X-ray luminosity from a known LBV is ∼10³⁴ erg s⁻¹ (Nazé et al. 2012), which is four orders of magnitude less than the peak X-ray luminosity from SN 2010da. Interestingly, optical spectra taken around the initial optical peak reveal emission lines indicative of an LBV-like outburst (e.g., Hα, He i, Fe ii, and [N ii]; Chornock & Berger 2010; Elias-Rosa et al. 2010). Binder et al. (2016) therefore suggest that SN 2010da is associated with an eruption from an LBV-HMXB system. They substantiate this claim from the ≲5 Myr age estimate for the population of nearby stars inferred from the CMD. LBVs, however, are not found to exhibit luminosities lower than ≲2.5 × 10⁵ L_⊙ (Smith et al. 2004), which is over a factor of four greater than the progenitor luminosity estimated from the SED model (Figure 7(A)). We propose that the optical companion of the HMXB is instead an sgB[e]-star.

SgB[e]-stars resemble LBVs spectroscopically and share a similar region in the HR diagram; however, sgB[e]-stars can be less luminous than LBVs and do not exhibit giant eruptions. The significant increase of the luminosity during the optical outburst (∼3 × 10⁶ L_⊙) is therefore the strongest evidence against the sgB[e] hypothesis. Although individual sgB[e] stars do not exhibit significant variability, increases in the luminosity of the optical continuum concurrent with X-ray outbursts have been observed from sgB[e]-HMXB systems. For example, optical observations of the April 1998 X-ray outburst (L_X ∼ 3 × 10³⁸ erg s⁻¹) of the galactic sgB[e]-HMXB CI Cam revealed lower limits on the optical outburst amplitude of a factor of two to five times the continuum level of the progenitor¹⁸ (Hynes et al. 2002). This is still over an order of magnitude less than the amplitude of the initial optical outburst from SN 2010da, but is consistent with the intermediate and late-time re-brightening events (Figure 6). Analogous to CI Cam, the optical variability from SN 2010da is likely due to interactions between the sgB[e]-star and its compact companion.

The process(es) driving the optical outburst in sgB[e]-HMXBs can be the heating of the sgB[e] star, reprocessing of the X-ray emission, direct emission from ejecta, and/or interaction between ejecta and existing circumstellar material (e.g., Hynes et al. 2002). For SN 2010da, heating of the optical companion is unlikely since the B − V color remains roughly constant following the outburst (Figure 4(D)) and the effective temperature only exhibits a range of ∼6000–10,000 K (Figure 6(A)). Reprocessing of X-ray emission is also unlikely given the analysis of the archival Swift data by Villar et al. (2016), who show the X-ray emission taken within 40 days of the initial outburst decays at a faster rate than the optical emission. The most plausible explanation for the optical outburst is therefore the direct emission from ejecta and/or interactions of the ejecta with circumstellar material. This is identical to the interpretation of the optical outburst from CI Cam (Hynes et al. 2002).

A comparison of the mid-IR color and magnitudes of known sgB[e] stars and bona-fide LBVs in the Large Magellanic Cloud (Bonanos et al. 2009) to the SN 2010da progenitor (in "quiescence") and after the eruption ("post-outburst") are shown in Figure 9. The mid-IR color and absolute magnitude of the progenitor most resemble the sgB[e] stars. Similar to the progenitor, the sgB[e] stars presented by Bonanos et al. (2009) exhibit mid-IR excesses consistent with hot ∼600 K circumstellar dust. Interestingly, SN 2010da migrated to bluer colors during and following the eruption, which places it in between the sgB[e] and LBV population in the CMD.

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Although there are few known, bona-fide sgB[e]-HMXB systems (CI Cam, Hynes et al. 2002; IGR J16318-4848, Filliatre & Chaty 2004), the observed luminosities and mass in circumstellar material from the literature (Filliatre & Chaty 2004; Thureau et al. 2009; Chaty & Rahoui 2012) are similar to what we derive for SN 2010da. From DUSTY models fit to the pre- and post-outburst SED of CI Cam, Thureau et al. (2009) derive a pre-outburst luminosity and dust mass of 2 × 10⁵ L_⊙ and 3 × 10⁻⁶ M_⊙, and a post-outburst luminosity and dust mass of 6 × 10⁴ L_⊙ and 8 × 10⁻⁷ M_⊙. Chaty & Rahoui (2012) estimate a dust mass of 1.4 × 10⁻⁸ M_⊙ by fitting a T_d ∼ 800 disk model to the near- to mid-IR spectra of IGR J16318-4848 and assuming a distance of 1.6 kpc to the system. The stellar luminosity of the optical companion at a distance of 1.6 kpc is ∼6 × 10⁴ L_⊙. However, Chaty & Rahoui (2012) mention the system may be further away out to ∼4 kpc, which would imply a dust mass of ∼9 × 10⁻⁸ M_⊙ and a luminosity of ∼4 × 10⁵ L_⊙. The late-time optical luminosity (∼10⁵ L_⊙) and hot dust mass (1.4 × 10⁻⁷ M_⊙) we estimate for SN 2010da are therefore comparable to that of the other sgB[e]-HMXB systems. Notably, infrared spectroscopy of IGR J16318-4848 reveal significant intrinsic optical absorption (${A}_{V}\sim 6;$ Chaty & Rahoui 2012), which is consistent with the local extinction estimated for the SN 2010da progenitor (Figure 7(A)).

Based on the similar properties to other systems and the mid-IR color of the progenitor, we argue that SN 2010da is likely an sgB[e]-HMXB. Ages of sgB[e] stars are also comparable to the ≲5 Myr age inferred from the CMD of stars in the vicinity of SN 2010da (Binder et al. 2016). However, since there are no confirmed LBV-HMXB systems, there is not enough information to conclusively rule out the LBV-HMXB hypothesis.

It is important to discuss the possible non-supergiant BeXB interpretation of SN 2010da as proposed by Binder et al. (2011) since they are more common than sgB[e]-HMXBs and also exhibit X-ray outbursts with luminosities exceeding ∼10³⁸ erg s⁻¹. The most significant difference between sgB[e] and Be stars is the lack of hot circumstellar dust around Be stars (e.g., Zickgraf 1999). Given the clear presence of hot dust around SN 2010da and its progenitor, it is highly unlikely to be a non-supergiant Be star.

In this section, we assume that SN 2010da is a sgB[e]-HMXB system with a neutron star (NS) companion and derive constraints on its orbital parameters based on the observed outburst properties. High X-ray luminosity of the outbursts from sgB[e]-HMXB systems are powered by accretion onto the NS. If the NS accretes material from the sgB[e] star's winds, the large amplitude variation of the X-ray luminosity by over two orders of magnitude suggests that the NS is in a highly eccentric orbit. We can then place constraints on the orbital eccentricity, e, period, P_orb, and semimajor axis, a, of the system given the measurements of the varying X-ray luminosity. We note that the X-ray emission may also be due to mass transfer via RLOF; however, X-ray emission from HMXBs is typically dominated by accretion from stellar winds. Additionally, sgB[e] stars are not known to exhibit significant changes in radius given their unvarying spectral profile.

Under the assumption of Bondi–Hoyle accretion, the X-ray luminosity from the NS in a HMXB can be expressed as

$$\begin{eqnarray}&&{L}_{{\rm{X}}}=\eta \,{\dot{M}}_{\mathrm{acc}}\,{c}^{2},\end{eqnarray} \tag{ 4 }$$

where η is a constant that depends on the physics of the accretion for which we adopt a value of ∼0.1 (Oskinova et al. 2012), ${\dot{M}}_{\mathrm{acc}}$ is the mass accretion rate of the NS, and c is the speed of light. For accretion fed by stellar winds of mass-loss rate ${\dot{M}}_{{\rm{w}}}$ and velocity v_w regulated by the orbital motion of the NS, ${\dot{M}}_{\mathrm{acc}}$ is

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{acc}}=4\pi \,\xi \displaystyle \frac{{(G{M}_{\mathrm{NS}})}^{2}}{{v}_{\mathrm{rel}}^{3}}\displaystyle \frac{{\dot{M}}_{{\rm{w}}}}{4\pi \,{r}^{2}\,{v}_{{\rm{w}}}},\end{eqnarray} \tag{ 5 }$$

where ξ is a factor accounting for radiation pressure and the finite cooling time of the gas for which we assume is ∼1 (e.g., Oskinova et al. 2012), M_NS is the mass of the NS, v_rel is the velocity of the NS relative to the winds, and r is the orbital separation between the stellar wind source and the NS. The relative velocity is simply related to the wind velocity and the orbital velocity of the NS, v_orb, as follows.

$$\begin{eqnarray}&&{v}_{\mathrm{rel}}=\sqrt{{v}_{\mathrm{orb}}^{2}+{v}_{{\rm{w}}}^{2}}.\end{eqnarray} \tag{ 6 }$$

Using the vis-viva equation, v_orb can be re-expressed as

$$\begin{eqnarray}&&{v}_{\mathrm{orb}}=\sqrt{G\,{M}_{* }\left(\displaystyle \frac{2}{r}-\displaystyle \frac{1}{a}\right)},\end{eqnarray} \tag{ 7 }$$

where M_* is the mass of the sgB[e] star and G is the gravitational constant.

The eccentricity of the system can be constrained assuming that the observed X-ray luminosity peak, ${L}_{{\rm{X}},{\rm{p}}}$, occurs during periapse ($r=a(1-e)$) and that the lowest measured X-ray luminosity, ${L}_{{\rm{X}},{\rm{a}}}$, occurs during apoapse ($r=a(1+e)$). The ratio between the peak and minimum measured X-ray luminosity is ∼100 (Binder et al. 2016), which implies ${L}_{{\rm{X}},{\rm{p}}}/{L}_{{\rm{X}},{\rm{a}}}\gt 100$. It then follows from Equations (4)–(6) that

$$\begin{eqnarray}&&\displaystyle \frac{{L}_{{\rm{X}},{\rm{p}}}}{{L}_{{\rm{X}},{\rm{a}}}}=\displaystyle \frac{{({v}_{\mathrm{orb},{\rm{a}}}^{2}+{v}_{{\rm{w}}}^{2})}^{3/2}{(1+e)}^{2}}{{({v}_{\mathrm{orb},{\rm{p}}}^{2}+{v}_{{\rm{w}}}^{2})}^{3/2}{(1-e)}^{2}}\gt 100,\end{eqnarray} \tag{ 8 }$$

where ${v}_{\mathrm{orb},{\rm{a}}}$ and ${v}_{\mathrm{orb},{\rm{p}}}$ are the orbital velocities of the NS during apoapse and periapse, respectively. We assume that ${v}_{\mathrm{orb}}\lt {v}_{w}$ at apoapse and periapse, which implies

$$\begin{eqnarray}&&\displaystyle \frac{{({v}_{\mathrm{orb},{\rm{a}}}^{2}+{v}_{{\rm{w}}}^{2})}^{3/2}{(1+e)}^{2}}{{({v}_{\mathrm{orb},{\rm{p}}}^{2}+{v}_{{\rm{w}}}^{2})}^{3/2}{(1-e)}^{2}}\approx \displaystyle \frac{{(1+e)}^{2}}{{(1-e)}^{2}}\gt 100.\end{eqnarray} \tag{ 9 }$$

The lower limit on the eccentricity is therefore

$$\begin{eqnarray}&&e\gt 0.82.\end{eqnarray} \tag{ 10 }$$

By combining Equations (4)–(7), we can constrain the semimajor axis and orbital period from the limits on the orbital eccentricity from the X-ray luminosity at periapse:

$$\begin{eqnarray}{L}_{{\rm{X}},{\rm{p}}} & \approx & 0.1\,{c}^{2}\displaystyle \frac{{\dot{M}}_{{\rm{w}}}}{{(a(1-e))}^{2}\,{v}_{{\rm{w}}}}\\ & & \times \displaystyle \frac{{(G{M}_{\mathrm{NS}})}^{2}}{{\left(G{M}_{* }\left(\frac{2}{a(1-e)}-\frac{1}{a}\right)+{v}_{{\rm{w}}}^{2}\right)}^{3/2}}.\end{eqnarray} \tag{ 11 }$$

At the late-time X-ray luminosity peak around day ∼1600, where ${L}_{{\rm{X}},{\rm{p}}}\sim 4\times {10}^{37}$ erg s⁻¹ (Binder et al. 2016), we infer a stellar wind mass-loss rate of ${\dot{M}}_{{\rm{w}}}\sim 1.4\times {10}^{-5}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ from our analysis in Section 3.2.1 and adopt a gas-to-dust mass ratio of 100. We assume a wind velocity of v_w ∼ 660 km s⁻¹ based on the widths of the emission lines observed during the optical re-brightening at intermediate times (Chornock & Berger 2010; Elias-Rosa et al. 2010; Chornock et al. 2011). Adopting ${M}_{* }\sim 40\,{M}_{\odot }$ for the sgB[e] star and ${M}_{\mathrm{NS}}\sim 1.5\,{M}_{\odot }$ for the NS, we can show from Equation (11) that

$$\begin{eqnarray}&&a\gtrsim 0.26\,\mathrm{au}\,\mathrm{and}\,{P}_{\mathrm{orb}}\gtrsim 8\,\mathrm{days}.\end{eqnarray} \tag{ 12 }$$

Based on the ∼400 day timespan between the apparent local maxima at days 1562 and 1965 in the late-time mid-IR light curve (see Figure 3(A)), we place upper limits on the orbital period and semimajor axis assuming the IR peaks correspond to the periastron passage of the NS:

$$\begin{eqnarray}&&{P}_{\mathrm{orb}}\lesssim 400\,\mathrm{days}\,\mathrm{and}\,a\lesssim 3.6\,\mathrm{au}.\end{eqnarray} \tag{ 13 }$$

Known sgHMXBs typically exhibit orbital periods of 10 days or less with low eccentricities (e ≲ 0.3; Reig 2011) due to short circularization timescales. The long orbital periods and high eccentricities inferred for the system are therefore consistent with the Binder et al. (2016) interpretation of SN 2010da as a newly formed HMXB. Circularization timescales estimated for known sgHMXBs range from ∼10⁴–10⁷ years (Stoyanov & Zamanov 2009), which suggests that the presumed HMXB associated with SN 2010da is less than 10⁴ years old.

We can glean insight on the orbital and disk/shell configuration of the system from the upper limit derived for the semimajor axis of the binary. Estimates of the dust shell/disk radius indicate sizes greater than 7 au (see Figure 5(D)), which implies the disk/shell likely surrounds the entire binary system. Interactions between the sgB[e] star and compact companion may, therefore, be linked to the formation of the circumbinary disk/shell. Notably, the rapid increase of the observed mass of hot dust on day 1562 that occurred within ∼100 days of the late-time X-ray outburst (Figure 5(C)) is consistent with this claim. It is plausible that ejecta from the late-time outburst interacted with and swept-up the older dust distribution observed at intermediate times, thereby driving the material out further from the central system (day ∼1500 in Figure 5(D)). The interaction of ejecta with existing circumstellar material is also consistent with the proposed mechanism driving the optical counterpart of the outburst for this system and CI Cam (Hynes et al. 2002). Additional multi-wavelength and spectroscopic follow-up observations will be required to further substantiate our claim.