SPIRITS 16tn in NGC 3556: A Heavily Obscured and Low-luminosity Supernova at 8.8 Mpc

SPIRITS 16tn was discovered at a right ascension and declination of 11^h11^m2040, +55°40'173 (J2000). Located 899  from the center of the star-forming galaxy NGC 3556, the position of SPIRITS 16tn is coincident with a dust lane in the disk.

NED¹⁵ lists 17 individual distance estimates to NGC 3556, with a median value of μ = 29.71 mag and standard deviation of 0.67 mag. Throughout this work, we adopt the most recent value from Sorce et al. (2014) of μ = 29.72 ± 0.41 mag (D ≈ 8.8 Mpc). This estimate is based on the mid-IR Tully–Fisher relation using the [3.6] micron flux with color and selection bias corrections. The redshift of NGC 3556 is z = 0.002332 (v = 699 km s⁻¹; Shostak 1975).

We assume Galactic extinction along the line of sight to NGC 3556 of A_V = 0.046 mag from the Schlafly & Finkbeiner (2011) recalibration of the Schlegel et al. (1998) IR-based dust map assuming a Fitzpatrick (1999) extinction law with R_V = 3.1. Furthermore, for all other considerations of the possible extinction to SPIRITS 16tn throughout this work, including any foreground host extinction, we assume the Fitzpatrick (1999) Milky Way extinction curve with R_V = 3.1 unless otherwise noted.

Since its discovery, we continued to monitor SPIRITS 16tn with Spitzer/IRAC at [3.6] and [4.5] as part of the SPIRITS program. Image subtraction was performed on all subsequent epochs, as described in Section 2.1. Photometry was performed on the reference-subtracted images using a 4 mosaicked pixel (24) aperture and a background annulus from 4 to 12 pixels (24–72). The extracted flux was multiplied by aperture corrections of 1.215 and 1.233 for [3.6] and [4.5], respectively, as described in the IRAC instrument handbook.¹⁶ Fluxes then were converted to Vega system magnitudes using the handbook-defined zero-magnitude fluxes for each IRAC channel. At discovery, our photometry gives [4.5] = 13.04 ± 0.05 mag (M_[4.5] = −16.7 mag; λL_λ = 1.3 × 10⁷ L_⊙).

We triggered observations with the Ultra-violet/Optical Telescope (UVOT; Roming et al. 2005) on board the Neil Gehrels Swift Observatory (Gehrels et al. 2004; Nousek 2004) on 2016 August 29.1. No source was detected in the U-, B-, and V-band images with integration times of 540, 580, and 540 s, respectively (Adams et al. 2016a). We derived 5σ limiting magnitudes of V > 19.9 mag, B > 20.2 mag, and U > 19.9 mag. The extreme V − [4.5] ≳ 6.9 mag color indicates that SPIRITS 16tn is likely highly obscured.

We observed SPIRITS 16tn on 2016 September 25, t = 42 days, with the Wide Field Camera 3 (WFC3) on the HST in the UVIS channel with the F814W filter and the IR channel with the F110W and F160W filters. These observations were part of our Cycle 23 Target of Opportunity program to observe SPIRITS transients (GO-14258; PI: H. Bond). All three images are shown in the bottom row of Figure 1. The photometry and limits from our space-based follow-up effort are listed in Table 1 and shown in Figure 2.

Zoom In Zoom Out Reset image size

At the time of its discovery, SPIRITS 16tn was inaccessible for ground-based observing except at high latitudes. We began ground-based follow-up of SPIRITS 16tn from Palomar Observatory in 2016 October, approximately 2 months after discovery. We obtained near-IR images of SPIRITS 16tn in JHK_s with the Wide Field Infrared Camera (WIRC; Wilson et al. 2003) on the Palomar 200-inch Hale telescope (P200) at several epochs, employing large dithers approximately every minute to allow for accurate subtraction of the bright near-IR sky background. Flat-fielding, background subtraction, astrometric alignment, and final stacking of images in each filter were performed using a custom pipeline.

Additional near-IR H- and K_s-band imaging was obtained with the Wide Field Camera (WFCAM; Casali et al. 2007) on the United Kingdom Infrared Telescope (UKIRT) at Mauna Kea Observatories. We obtained simultaneous optical/near-IR rizYJH with the Reionization and Transients InfraRed camera (RATIR; Butler et al. 2012) on the 1.5 m Johnson Telescope at the Mexican Observatorio Astronomico Nacional on the Sierra San Pedro Martir in Baja California, Mexico (Watson et al. 2012).

We obtained one epoch of optical (i-band) imaging with the Spectral Energy Distribution Machine (SEDM; Blagorodnova et al. 2018) on the fully automated Palomar 60-inch telescope (P60; Cenko et al. 2006) and an epoch of g- and I-band imaging with the Low-Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) on the Keck I Telescope on Maunakea.

Photometry was performed by simultaneously fitting the point-spread function of the transient, measured using field stars, and background, modeled using low-order polynomials. The photometric zero-point in each image was obtained by performing photometry on stars of known magnitude in the field. For the near-IR JHK images we selected 10 bright, isolated Two Micron All Sky Survey (2MASS) stars, and for Y band we adopt the conversion from 2MASS used for WFCAM/UKIRT from Hodgkin et al. (2009). For optical images, we used 12 SDSS stars, adopting the conversions of Jordi et al. (2006) to convert from the Sloan ugriz system to UBVRI magnitudes where necessary.

We examined the location of SPIRITS 16tn in a deep z-band image of NGC 3556 from 2017 May 25.0, taken with the CCD Mosaic imager on the 4 m Mayall Telescope at Kitt Peak National Observatory (KPNO) as part of the Mayall z-band Legacy Survey (MzLS). We derive a limit on the flux from the transient of z > 22.5 mag, providing our most stringent constraint on the explosion date of SPIRITS 16tn at 82.0 days before the first detection.

We list all of our photometry of SPIRITS 16tn in Table 1. For nondetections we list 5σ upper limits, where we estimated σ as the standard deviation of the pixel values near the transient position to account for uncertain variations in the background flux from the host galaxy. Our light curves of SPIRITS 16tn are shown in Figure 2. Additionally, Shappee et al. (2016) reported pre-discovery limits from nondetections of SPIRITS 16tn in the All-Sky Automated Survey for Supernovae (ASAS-SN) between UT 2016 May 16.3 and 2016 June 10.3, constraining optical emission from SPIRITS 16tn to V > 17.81 mag at t = −65.7 days. Vinko et al. (2016) also reported observations in the Sloan i filter of SPIRITS 16tn on 2016 September 1.8, placing a limit on the flux from the transient of i > 18.7 mag at t = 17.8 days. We show these limits along with our own photometry in Figure 2. As reported, these limits do not further constrain the extinction or explosion date beyond the data newly presented here.

The Palomar Cosmic Web Imager (PCWI; Matuszewski et al. 2010) is an integral field spectrograph mounted on the Cassegrain focus of the 200-inch Hale telescope at Palomar Observatory. The instrument has a field of view of 40'' × 60'' divided across 24 slices with dimensions of 40'' × 25 each. The spectrograph uses an R ∼ 5000 volume phase holographic grating (in the red filter) to achieve an instantaneous bandwidth of ≈550 Å. A complete description of the instrument, observing approach, and data analysis methodology can be found in Martin et al. (2014).

We observed the host region of SPIRITS 16tn with PCWI (centered at the location of the transient) on 2017 October 18 in order to characterize the star formation rate in the transient environment. The instrument was configured to a central wavelength of 6630 Å, covering the wavelength range from approximately 6400 to 6900 Å. We obtained one 600 s exposure of the transient region with the instrument oriented to a position angle of 270^◦ (slices oriented in the north–south direction) followed by one 600 s background sky exposure of a nearby field with no bright sources.

We also obtained calibration images including arc lamp spectra, dome flats, and a standard-star spectrum. The 2D spectra were sliced, rectified, spatially aligned, and wavelength-calibrated using the calibration images to produce data cubes for each sky exposure, sampled at (R.A., decl., λ) intervals of (26, 06, 0.22 Å). The sky background cube was subtracted from the source cube to remove the sky emission lines, followed by flux calibration using the standard star Feige 15. This produces the final flux-calibrated spectral cube of the 40'' × 60'' region centered at the location of the transient.

The observed SED at t = 41.9 days is remarkably red. It is likely that SPIRITS 16tn suffers from a high degree of host extinction given its location along an obvious dust lane in a highly inclined, late-type host galaxy. The photometry of SPIRITS 16tn cannot directly constrain the extinction parameters without some assumptions about the intrinsic SED of the source. We attempt to estimate the extinction to SPIRITS 16tn by comparing the optical/near-IR SEDs to the SEDs of well-studied SNe.

Type II-Plateau SNe (SNe IIP) are the most common of all CCSN subtypes, and we use the IJH light curves of the SN IIP SN 2004et from Maguire et al. (2010) as a template for comparison. Following Maguire et al. (2010), we adopt an explosion date of UT 2004 September 22.0 (MJD = 53,270. 0), a distance of D = 5.9 Mpc, and a total (Galactic and host) extinction parameterized by E(B − V) = 0.41 mag for SN 2004et. The light curves of SN 2004et are well sampled during each of the canonical phases of SN IIP light-curve evolution: the ≈100-day photospheric plateau phase, the rapid fall-off of the plateau, and the subsequent radioactive decline phase. The absolute phase of SPIRITS 16tn is highly uncertain, as our most constraining pre-explosion upper limit is at 82 days before discovery. Using a linear interpolation of the light curves, we find the host extinction parameter E(B − V) that best reproduces the I − J color of SN 2004et between 50 and 150 days in increments of 1 day. Even across this wide range of possible phases, the color evolution of SN 2004et is such that we find a range of 2.6 mag < E(B − V) < 2.95 mag, with a mean value of E(B − V) = 2.8 mag.

In the top left panel of Figure 6, we show the observed SED of SPIRITS 16tn at t = 41.9 days (maximum age of 123.9 days) compared to the SED of SN 2004et at 150 days post explosion, just after the start of radioactive decline phase, but scaled down by a factor of 4.2 × 10⁻². Applying E(B − V) = 2.7 mag then provides a good match between the I-, J-, and H-band measurements to those of SPIRITS 16tn.

We performed a similar analysis using the light curves of SN 2005cs in nearby galaxy M51, a prototypical and well-observed low-luminosity SN IIP explosion (Pastorello et al. 2006, 2009). With a peak bolometric luminosity of ≈6 × 10⁴² erg s⁻¹, SN 2005cs was ∼10 times fainter than SN 2004et. We adopt a distance to SN 2005cs of 7.1 Mpc (Takáts & Vinkó 2006), a total foreground extinction (Milky Way and host) of E(B − V) = 0.05 mag (Baron et al. 2007), and an explosion date of UT 2005 June 27.5 (MJD = 53,548.5) as in Pastorello et al. (2009). While the I-band light curve is well sampled throughout the plateau, fall-off, and decline tail, the available near-IR J- and H-band photometry is more limited. We compare the SED of SN 2005cs at a phase of 270 days to the late-time SED of SPIRITS 16tn at t = 184.7 days (maximum age of 266.7 days) in the top right panel of Figure 6. We find a suitable match with E(B − V) = 2.5 mag and scaling the SED of SN 2005cs by a factor of 0.76.

We find that assuming an SN II-like SED for SPIRITS 16tn indicates a high degree of foreground host extinction in the range of E(B − V) ≈ 2.5–3.0 mag (A_V ≈ 7.8–9.3 mag assuming R_V = 3.1), regardless of the absolute phase since explosion. This estimate is high compared to interstellar extinction for typical lines of sight in disk galaxies (A_V ≈ 1–2 mag kpc⁻¹), but given high inclination of NGC 3556 and the coincidence of SPIRITS 16tn with a clear dust lane, it is not unreasonable. A direct comparison of the luminosity of SPIRITS 16tn is not possible in this analysis because of the large uncertainty in absolute phase. The inferred luminosity of SPIRITS 16tn at t = 184.7 days is comparable, however, to a late-phase, low-luminosity, SN 2005cs-like explosion, suggesting that SPIRITS 16tn is likely both heavily obscured and intrinsically faint.

The bright IR emission associated with SPIRITS 16tn likely indicates the presence of warm dust. To model the dust emission, we assume an optically thin distribution of dust of total mass M_d, composed of spherical grains of radius a, radiating thermally at a single, equilibrium temperature T_d. This idealized model is described in more detail by, e.g., Hildebrand (1983), Dwek (1985), and Fox et al. (2010).

The expected flux from the warm dust is

$$\begin{eqnarray}&&{F}_{\nu }={M}_{{\rm{d}}}\displaystyle \frac{{\kappa }_{\nu }(a){B}_{\nu }({T}_{{\rm{d}}})}{{D}^{2}},\end{eqnarray} \tag{ 1 }$$

where B_ν(T_d) is the Planck blackbody function, D is the distance from the source, and κ_ν(a) is the dust mass absorption coefficient. In what follows, we assume a grain size of a = 0.1 μm and use broken power-law approximations to the dust mass absorption coefficients for dust composed entirely of either graphite or silicate (derived from Mie theory; see Figure 4 of Fox et al. 2010). To account for host extinction, we assume E(B − V) = 2.5 mag based on our comparison with SN 2005cs above.²²

We fit the IR photometric data for the Spitzer discovery epoch (t = 0 days) with this simple dust model for both graphite and silicate compositions to infer T_d and M_d. Under the assumption of optically thin dust, the IR luminosity is not sensitive to the size of the dust cloud. In the optically thick case, however, the radius corresponding to blackbody emission provides a lower bound on the dust radius, R_d. We repeat the procedure for the quasi-contemporaneous optical–IR SEDs at t = 41.9 and 187.4 days, including an additional, hotter blackbody component of temperature T_* and radius R_*. We note that for E(B − V) = 2.5 our optical/near-IR data do not cover the peak of the hotter SED component, and furthermore, the values inferred for T_* and R_* strongly depend on the choice of extinction. We do not attempt to make strong statements about the properties of the hotter component of the SED for these reasons, and we focus our analysis on the properties of the dust component. The results are shown in the bottom left panel of Figure 6 and summarized in Table 3.

At t = 0 days, our best-fitting results to the IR SED give T_dust ≈ 680 K (880 K) and M_dust ≈ 1. 1 × 10⁻⁴ M_⊙ (1.5 × 10⁻⁴ M_⊙) for graphite (silicate) dust. The blackbody fit to the data gives a higher temperature of T_d ≈ 1100 K and sets a lower bound on the dust radius of R_d ≳ 4. 0 × 10¹⁵ cm.

At t = 41.9 days, we find similar results for the dust temperature for each model, but we infer a somewhat lower mass of M_dust ≈ 0. 4 × 10⁻⁴ M_⊙ (0.7 × 10⁻⁴ M_⊙) for graphite (silicate) dust and a smaller bound on the dust radius from the blackbody fit of R_d ≳ 2. 5 × 10¹⁵ cm. We note, however, that the uncertainties in interpolating the [4.5] and K_s-band light curves to construct the SED t = 41.9 days may have artificially lowered these values.

At t = 187.4 days, the data are no longer well fit by a hot source component and warm dust. The best-fitting results find T_d ≈ 700–1000 K but are notably inconsistent with the upper limit at [3.6]. The blackbody dust radius is smaller by a factor of 3–5 compared to the earlier epochs, and the inferred dust masses are lower by at least a factor of 10. As discussed below in the context of a CCSN, the flux at [4.5] at this phase is likely enhanced by emission from the fundamental vibrational transition of CO and is not attributable solely to thermal emission from warm dust. The lack of evidence for a warm dust component at this phase may indicate that the dust has cooled, shifting the flux to longer wavelengths not probed by our data. Alternatively, as discussed below in Section 4.2.2, the early presence and subsequent disappearance of the warm dust component may be interpreted as evidence for an IR echo, i.e., the reprocessing of the UV/optical emission from the luminosity peak of the transient into the thermal IR by a shell of preexisting circumstellar dust.

In addition to the simple dust models described above, we modeled the SED of SPIRITS 16tn using the dust radiative transfer code dusty (Ivezic & Elitzur 1997; Ivezic et al. 1999; Elitzur & Ivezić 2001). To find best-fitting models and allowed parameter ranges, we use a Markov chain Monte Carlo (MCMC) wrapper around dusty. Here we use a spherically symmetric distribution of graphite dust from Draine & Lee (1984) with a standard MRN grain size distribution (dn/da ∝ a^−3.5, 0.005 < a < 0.25 μm; Mathis et al. 1977). For the central luminosity source, we assume a simple blackbody spectrum and allow the model to find best-fitting values for the source temperature T_* and luminosity L_*, the optical depth in V band due to circumstellar dust τ_V, the dust temperature T_d, and the inner dust radius R_d. The source temperature and luminosity depend strongly on the assumed foreground extinction, but for simplicity, we again fix the extinction at E(B − V) = 2.5 mag as above. Our implementation of dusty uses a Cardelli et al. (1989) extinction law with R_V = 3.1, but the differences from the Fitzpatrick (1999) law assumed throughout the majority of this work are small at the wavelengths of interest in the optical and near-IR.

In this model, the dust is heated by the central source, i.e., the inferred properties of the dust are not independent of L_* and R_*. As T_d is constrained strongly by the shape of the IR SED, we do not expect it to vary strongly with the other model parameters. Furthermore, it is fairly robust to the choice of extinction, as the effects of reddening are small in the IR. We expect, however, R_d and τ_V to vary strongly with the central source properties, namely, a hotter, more luminous central source will force dust at a given temperature to larger radii and correspondingly lower optical depths. This model also does not account for light-travel time effects inherent to dust at large radii from an evolving, transient source.

The results of our dusty modeling at both epochs are given in Table 4, including both the values for each parameter for the best-fitting model, i.e., the model that minimizes χ², and the median value and 90% confidence interval limits from the MCMC posterior distributions. We note that the best-fitting values are sometimes near the extrema of the posterior distributions. The best-fitting SEDs are also shown in the bottom right panel of Figure 6 in comparison to the observations.

Table 4.  Results of SED Modeling with Dusty^a

Phaseb	log L*/L⊙		T*		τV		Td		log Rd/cm
(days)			(K)				(K)
41.9	7.4	${7.1}_{-0.2}^{+0.3}$	15200	${10900}_{-2700}^{+4500}$	0.06	${0.2}_{-0.1}^{+0.2}$	840	${810}_{-90}^{+80}$	16.8	${16.7}_{-0.2}^{+0.2}$
187.4	8.6	${6.2}_{-0.5}^{+2.0}$	40200	${5800}_{-2600}^{+24100}$	4.9	${0.9}_{-0.8}^{+4.5}$	190	${370}_{-170}^{+400}$	19.1	${16.9}_{-1.1}^{+1.8}$
187.4c	6.0	${6.4}_{-0.7}^{+1.6}$	48100	${7600}_{-4100}^{+23800}$	⋯	⋯	⋯	⋯	⋯	⋯

Notes.

^aFor each parameter, we give the value for the best-fitting model that minimizes χ² and the median value from the MCMC with the 90% confidence interval limits. ^bPhase is number of days since the earliest detection of this event on 2016 August 15.0 (MJD = 57,615.0). ^cResults for t = 187.4 days when [4.5] flux is treated as an upper limit including only a single blackbody component.

Download table as:  ASCIITypeset image

At t = 41.9 days, there is a clear IR excess requiring a warm dust component in addition to the interior, hotter source component. The MCMC results for this model have a dust temperature of ${T}_{{\rm{d}}}={810}_{-90}^{+80}$ K, consistent with the best-fitting value from our simple, optically thin graphite dust model at this epoch in Section 3.3.2, and an inner dust radius of ${R}_{{\rm{d}}}={5.0}_{-1.9}^{+2.9}\times {10}^{16}$ cm at 90% confidence. As expected, T_d is well constrained by the K_s-band and [4.5] fluxes and does not vary strongly with the other parameters of the model. While producing a significant IR excess, the dust is optically thin at ${\tau }_{V}={0.2}_{-0.1}^{+0.2}$. Because our photometry does not cover the peak of the hot blackbody component, our measurements can only place a lower limit on the temperature and luminosity of the source, and the upper confidence limits found by the MCMC are not physically meaningful. We infer T_* ≳ 8200 K and L_* ≳ 7.9 × 10⁶ L_⊙, but note that these limits are highly dependent on our choice of foreground host extinction, i.e., for E(B − V)_host < 2.5 mag, a lower blackbody temperature and luminosity would be consistent with the data.

At t = 187.4 days, the hot component has faded by a factor of ≈2.7 in the J and H bands. Again, our photometric measurements do not cover the peak of this component, and thus the results of the MCMC modeling only allow us to estimate a lower limit on the source temperature of T_* > 3200 K. The flux in the redder bands, however, has faded more quickly. The dusty model fits a dust component to the excess flux at [4.5] with constraints from the MCMC at ${T}_{{\rm{d}}}={370}_{-170}^{+400}$ K, but there is a strong degeneracy between the cooler dust temperatures at smaller radii ($\approx 6\,\times {10}^{15}$ cm) and warmer dust at large radii (≈5 × 10¹⁹ cm). Again, it is likely that the flux at [4.5] is enhanced by emission from the fundamental vibrational mode of CO, and therefore it is probably not attributable to thermal emission from dust. Treating the measurement at [4.5] instead as an upper limit, we find that the SED of SPIRITS 16tn at t = 187.4 days can be adequately modeled with a single blackbody component with T_* > 4500 K and L_* > 5.0 × 10⁵ L_⊙.

In Figure 10, we show our limits on the radio luminosity of SPIRITS 16tn as a function of phase compared to the peak radio luminosities and times to peak for CCSNe. Radio emission is produced in CCSNe when the fastest SN ejecta interact with and shock the slow-moving pre-explosion CSM from the pre-explosion stellar wind of the progenitor. As the shock wave propagates through the CSM, turbulent instabilities amplify magnetic fields and accelerate relativistic electrons (Chevalier 1982). The resultant radio emission is characterized by slowly declining, optically thin, nonthermal synchrotron and early, optically thick absorption at low frequencies. Proposed absorption mechanisms include synchrotron self-absorption (SSA) or internal free–free absorption in the emitting region and free–free absorption by the external, ionized CSM (e.g., Chevalier 1982, 1998).

Zoom In Zoom Out Reset image size

If one assumes that SSA is dominant, for an electron population with an energy spectral index of p = 3, the size of the radio-emitting region at the time of the SSA peak can be calculated as (Chevalier 1998)

$$\begin{eqnarray}{R}_{{\rm{s}}} & = & 4.0\times {10}^{14}{\alpha }^{-1/19}{\left(\displaystyle \frac{f}{0.5}\right)}^{-1/19}{\left(\displaystyle \frac{{F}_{{\rm{p}}}}{\mathrm{mJy}}\right)}^{9/19}\\ & & \times {\left(\displaystyle \frac{D}{\mathrm{Mpc}}\right)}^{18/19}{\left(\displaystyle \frac{\nu }{5\mathrm{GHz}}\right)}^{-1}\mathrm{cm},\end{eqnarray} \tag{ 2 }$$

where α ≡ _e/_B is the ratio of the energy density in relativistic electrons to that in the magnetic field, f is the fraction of the spherical volume filled by the radio-emitting region, F_p is the peak flux at frequency ν, and D is the distance to the source. If additional absorption mechanisms are important, this radius must be even larger. The shock wave velocities, v_s, inferred for α = 1 (assuming equipartition) and f = 0.5 (as estimated in Chevalier & Fransson 2006) are shown as the dashed lines in Figure 10. We the note weak dependence in Equation (2) of the shock radius on these parameters.

For a steady, pre-SN stellar wind, the density profile of the CSM as a function of radius, r, is ${\rho }_{{\rm{w}}}=A/{r}^{2}\equiv \dot{M}/(4\pi {r}^{2}{v}_{{\rm{w}}})$, where $\dot{M}$ is the mass-loss rate and v_w is the wind velocity. $A\equiv \dot{M}/(4\pi {v}_{{\rm{w}}})$ is the normalization of the CSM density profile as in Chevalier (1982). As calculated by Chevalier & Fransson (2006), the radio emission at time t since explosion of a CCSN is sensitive to the density profile of the CSM as

$$\begin{eqnarray}&&{A}_{\star }{\epsilon }_{B-1}{\alpha }^{8/19}=1.0{\left(\displaystyle \frac{f}{0.5}\right)}^{-8/19}{\left(\displaystyle \frac{{F}_{{\rm{p}}}}{\mathrm{mJy}}\right)}^{-4/19}\\ &&\times \,{\left(\displaystyle \frac{D}{\mathrm{Mpc}}\right)}^{-8/19}{\left(\displaystyle \frac{\nu }{5\mathrm{GHz}}\right)}^{2}{\left(\displaystyle \frac{t}{10\mathrm{days}}\right)}^{2},\end{eqnarray} \tag{ 3 }$$

where _B−1 ≡ _B/0.1 and A_⋆ ≡ A/(5 × 10¹¹ g cm⁻¹) is a dimensionless proxy for A. We show lines of constant A_⋆ in Figure 10, determined largely by the strong dependence of this parameter on t_peak.

Our deep nondetections of SPIRITS 16tn indicate either that this event is an intrinsically weak radio source or that the emission is heavily absorbed. Though we do not rule out radio emission arising at very late times, characteristic of strongly interacting SNe IIn with a dense CSM, this scenario is unlikely given the lack of prominent interaction features in the optical/near-IR spectra. Our observations are inconsistent with most varieties of stripped-envelope events, which tend to be more luminous radio sources. A high-velocity (v_s ≳ 50,000 km s⁻¹) SN Ic with a fast-evolving radio light curve, however, is not explicitly ruled out (cf. SN 2007gr, Soderberg et al. 2010; and PTF12gzk, Horesh et al. 2013a). Our optical–IR SED analysis and comparisons with well-studied SNe II indicate that SPIRITS 16tn falls at the low end of the SN luminosity function, and a weak SN II radio counterpart is consistent with our observations. Using Equation (3), for typical SN II shock velocities of v_s ≈ few × 10³ km s⁻¹, our nondetections can constrain A_{⋆ B−1} α^8/19 ≲ 24. For a steady pre-SN wind, we then infer a limit on the pre-SN mass-loss rate of $\dot{M}\lesssim 2.4\times {10}^{-6}{\left(\tfrac{{\epsilon }_{B}}{0.1}\right)}^{-1}{\alpha }^{-8/19}\left(\tfrac{{v}_{{\rm{w}}}}{10\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right)\,{M}_{\odot }$ yr⁻¹.

Such mass-loss rate is consistent with a low-luminosity RSG (L ≈ 10^4.5–10⁵ L_⊙) based on the standard observational prescriptions of de Jager et al. (1988; see, e.g., Figure 3 of Smith 2014). This supports the picture of SPIRITS 16tn as a low-luminosity SN II arising from the explosion of a low-mass (M ≈ 10–15 M_⊙) RSG progenitor. We note that, depending on the assumed explosion date of SPIRITS 16tn, for v_s = 10,000 km s⁻¹ and v_w = 10 km s⁻¹, the timing of our radio observations probes the mass-loss history of the progenitor only in the final ≈50–600 yr before the explosion.

Concurrent panchromatic observations spanning the radio to the X-ray have indicated deviations from energy equipartition in some SNe. For example, for SN 2011dh Soderberg et al. (2012) find α = 30 and _B = 0.01. Adopting such values results in only a modest decrease in the shock velocity (using Equation (2)) by a factor of 1.2 and an increase in our limit on the mass-loss rate by a factor of 2.4. Alternatively for SN 2011dh, Horesh et al. (2013b) find α ≈ 500–1700, adopting a value of 1000 as a reasonable average, and _B = 3 × 10⁻⁴. This still results in only a modest decrease in the inferred shock velocity by a factor of 1.4, and for a fixed wind velocity, the limit on the mass-loss rate increases by a factor of 20.

In Section 3.3, our modeling of the SED of SPIRITS 16tn at t = 0 and 41.9 days suggests the presence of an IR component (T_d ≈ 700–900 K) powered by thermal emission by at least M_d ≈ (1.0–1.5) × 10⁻⁴ M_⊙ of warm dust (our observations are not sensitive to any additional dust at cooler temperatures). By t = 187.4 days, we no longer see evidence for this warm dust component, indicating that either it has faded or the dust has cooled, shifting the flux to longer wavelengths.

The dust emission may arise from either preexisting circumstellar dust formed in the pre-SN wind of the progenitor or newly formed dust in the dense, rapidly cooling ejecta behind the SN shock. For a shock velocity of v_s = 10,000 km s⁻¹, the radius of the shock at a phase of 82.0 days (the maximum age of SPIRITS 16tn at t = 0 days) is ${R}_{s}\,=7.1\times {10}^{15}({v}_{s}/{10}^{4}\,\mathrm{km}\,{{\rm{s}}}^{-1})$ cm. As we infer a lower limit on the dust radius (blackbody radius from Section 3.3.2) of R_d ≳ 4.0 × 10¹⁵ cm that is smaller than the shock radius, it is plausible that the emitting dust is located in the post-shock cooling zone. Given the low observed dust temperatures, however, it is unlikely that the early dust component is due to newly formed dust in the ejecta. We would expect newly formed dust to be near the evaporation temperature, as, given sufficiently high densities, dust grains will begin to condense as soon as the drop in temperature of the radiation environment allows. Typical values for astrophysical dust are T_evap ≈ 1900 K for graphite and T_evap ≈ 1500 K for silicate, significantly hotter than the observed dust component.

For preexisting dust, we can interpret the observed IR excess as an IR echo. In this scenario, a preexisting shell of dust is heated by the peak luminosity of the explosion and reradiates this energy thermally in the IR. The duration of the echo is related to the size of the dust shell from geometrical arguments as Δt ∼ 2R_d/c. The observations of the warm dust component between t = 0 and 41.9 days, and subsequent fading by t = 187.4 days, when the maximum age of SPIRITS 16tn is 269.4 days, would then require 5.4 × 10¹⁶ cm ≲ R_d ≲ 3. 5 × 10¹⁷ cm.

As a consistency check, we can estimate the peak luminosity, L_peak, of the transient required to heat spherical dust grains of radius a within this range of distances to the observed temperatures. The energy absorbed by a dust grain is balanced by the energy it radiates as

$$\begin{eqnarray}&&\displaystyle \frac{{L}_{\mathrm{peak}}}{4\pi {R}_{{\rm{d}}}^{2}}\pi {a}^{2}{Q}_{\mathrm{abs}}=4\pi {a}^{2}{\sigma }_{\mathrm{SB}}{T}_{{\rm{d}}}^{4}{Q}_{\mathrm{em}}.\end{eqnarray} \tag{ 4 }$$

The peak luminosity of the transient is then given by

$$\begin{eqnarray}&&{L}_{\mathrm{peak}}=16\pi {R}_{{\rm{d}}}^{2}{\sigma }_{\mathrm{SB}}{T}_{{\rm{d}}}^{4}\displaystyle \frac{{Q}_{\mathrm{em}}}{{Q}_{\mathrm{abs}}},\end{eqnarray} \tag{ 5 }$$

where Q_em and Q_abs are Planck-averaged emission and absorption efficiencies for Laor & Draine (1993) dust grains. For the temperature of the incident radiation field we assume values T_rad = 10,000 K and T_rad = 6000 K, characteristic of an SN at peak. We use a value of σ_SB = 5.67 × 10⁻⁵ erg cm⁻² K⁻⁴ s⁻¹ for the Stefan–Boltzmann constant. For graphite grains of size a = 0.1 μm at T_d = 680 K, we find 4.7 × 10⁴⁰ erg s⁻¹ ≲ L_peak ≲ 1.9 × 10⁴² erg s⁻¹ for T_rad =10,000 K and similar values of 5.7 × 10⁴⁰ erg s⁻¹ ≲ L_peak ≲2.3 × 10⁴² erg s⁻¹ for T_rad = 6000 K. Alternatively, for grains of silicate composition at T_d = 880 K, we find a somewhat higher values of 9.9 × 10⁴¹ erg s⁻¹ ≲ L_peak ≲ 4.0 × 10⁴³ erg s⁻¹ for T_rad = 10,000 K, or 2.6 × 10⁴¹ erg s⁻¹ ≲ L_peak ≲ 1.0 ×10⁴³ erg s⁻¹ for T_rad = 6000 K.

While these estimates are crude, we can still compare them to the observed range of peak luminosities for SNe II. Faran et al. (2018), for example, estimate the bolometric luminosities of 29 SNe II and find peak values spanning at least two orders of magnitude and ranging from L_bol ≈ 2.4 × 10⁴¹ erg s⁻¹ to 2.4 × 10⁴³ erg s⁻¹. Similarly, the pseudo-bolometric (from ∼U to I band) light curves of the sample of SNe II from Valenti et al. (2016) span L_bol ≈ 1.0 × 10⁴¹ erg s⁻¹ to 5 × 10⁴² erg s⁻¹. Among the faintest SNe II known, the quasi-bolometric UBVRI light curve of SN 1999br peaked at only 4.5 × 10⁴⁰ erg s⁻¹ (Pastorello et al. 2004, 2009). The observed range of peak luminosities for SNe II is similar to the range of luminosities estimated above to explain the IR excess of SPIRITS 16tn as a dust echo.

We can also estimate the pre-SN mass-loss rate of the progenitor star necessary to support such an echo. We assume that the dust is concentrated in a thin shell with Δr/R_d = 0.1, a dust-to-gas ratio of M_d/M_g = 0.01, and again a pre-SN wind velocity of v_w = 10 km s⁻¹ and find $\dot{M}\approx 9\times {10}^{-6}\mbox{--}6\times {10}^{-5}$ $\left(\tfrac{{M}_{{\rm{d}}}}{{10}^{-4}{M}_{\odot }}\right){\left(\tfrac{{M}_{{\rm{d}}}/{M}_{{\rm{g}}}}{0.01}\right)}^{-1}$ ${\left(\tfrac{{\rm{\Delta }}r/{R}_{{\rm{d}}}}{0.1}\right)}^{-1}\left(\tfrac{{v}_{{\rm{w}}}}{10\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right){M}_{\odot }$ yr⁻¹ for the range of R_d allowed by the observations. These estimates are a factor of ≈4–25 higher than that in Section 4.2.1 based on the radio observations, but they probe an earlier time in the mass-loss history of the progenitor of somewhere between ≈1700 and 11,000 yr before explosion. While such mass-loss rates would imply a more luminous and massive RSG progenitor (L ≈ 10^5.2–10^5.5 L_⊙, again assuming standard de Jager et al. 1988 prescriptions), if the dust is confined to a shell, this could indicate a relatively brief episode of enhanced mass loss.

SN 2008S and the luminous 2008 optical transient in NGC 300 (NGC 300 OT2008-1) are the prototypes of a distinct class of transients. They have optically obscured progenitors but bright mid-IR pre-explosion counterparts (M_[4.5] < −10 mag), suggested to be extreme asymptotic giant branch stars of intermediate mass (≈10–15 M_⊙) self-obscured by a dense, dusty wind (Prieto et al. 2008; Bond et al. 2009; Thompson et al. 2009). They are less luminous than typical CCSNe at peak (L_bol ≈ 10⁴¹ erg s⁻¹ for SN 2008S; Botticella et al. 2009). Emission lines in their spectra indicate slow expansion velocities of 70–80 km s⁻¹ (e.g., Bond et al. 2009; Humphreys et al. 2011). A proposed physical scenario is a weak explosion, possibly an electron-capture SN, or massive stellar eruption that destroys most of the obscuring dust, allowing the transient to be optically luminous. The development of a late-time IR excess, however, suggests that the dust reforms, obscuring the optical transient at late times (e.g., Thompson et al. 2009; Kochanek 2011; Szczygiełet al. 2012). Both events are now fainter than their progenitor luminosities at [3.6] and [4.5], suggesting that the transients were terminal events (Adams et al. 2016b).

The [4.5] light curve of SN 2008S is shown as the blue squares in Figure 7 compared to SPIRITS 16tn and several SNe II. The peak luminosity at [4.5] is similar to SPIRITS 16tn. Furthermore, the peak bolometric luminosity of SN 2008S-like events is sufficient to power the IR dust echo discussed in Section 4.2.2. The IR luminosity of SPIRITS 16tn declines more rapidly, and we do not observe a late-time IR excess powered by newly formed dust, inconsistent with the characteristic evolution of SN 2008S-like events.

The 2011 transient in NGC 4490 (hereafter NGC 4490-OT; Smith et al. 2016) and M101 2015OT-1 (Blagorodnova et al. 2017) are proposed massive analogs of the galactic contact binary merger V1309 Sco (Tylenda et al. 2011) and the B-type stellar merger V838 Mon (Bond et al. 2003; Sparks et al. 2008). These events typically have unobscured, optical progenitors; irregular, multipeaked light curves, increasingly red colors with time; and significant late-time IR excesses powered by copious dust formation. Their spectra show relatively narrow emission features of H i indicating low velocities of ∼100 km s⁻¹.

In the IR, NGC 4490-OT peaked at M_[4.5] ≈ −15 mag, ≈1.7 mag fainter than SPIRITS 16tn. The inferred mass for the progenitor system of NGC 4490-OT was 20–30 M_⊙, and thus a merger origin for the more luminous SPIRITS 16tn would likely require an exceptionally massive progenitor. Furthermore, the IR light curve of NGC 4490-OT is long-lived, remaining too luminous at phases ≳800 days to be powered by an IR echo (Smith et al. 2016). The relatively short-lived IR excess of SPIRITS 16tn, interpreted here as an IR echo, is generally inconsistent with the observed IR evolution typical of massive star mergers.

Given the low inferred luminosity and lack of radio detection for SPIRITS 16tn, an "SN impostor" may also be a plausible explanation for the observed characteristics of SPIRITS 16tn. SN impostors are nonterminal, massive star outbursts (typically an M ≳ 20–25 M_⊙ luminous blue variable [LBV]) that mimics the appearance of a true SN (e.g., Smith et al. 2011; Van Dyk & Matheson 2012). These events are are typically fainter in the optical fainter than true SNe (M_V ≲ −14 mag). Impostors have in some cases been mistakenly classified as SNe IIn, due to the presence of "narrow" hydrogen emission lines on top of an "intermediate-width" base (v ∼ 1500–2000 km s⁻¹). Some impostor outbursts have been observed to directly precede the death of the progenitor in the final years before the SN explosion, e.g., SN 2006jc (Pastorello et al. 2007) and SN 2009ip (Mauerhan et al. 2013; Pastorello et al. 2013). An impostor may be distinguished from a terminal SN explosion by the identification of a surviving progenitor star, or the detection of subsequent outbursts, also indicating that the progenitor has survived.

We detect no clear spectroscopic signatures of an SN or impostor in SPIRITS 16tn and see no evidence of a subsequent outburst or variability in 1.5 yr of continued monitoring with Spitzer post discovery. We also cannot directly test for the survival of the progenitor with currently available data. Deep, high-resolution, near-IR imaging may be able to constrain the presence of a surviving star after the light from the transient completely fades.