SN 2010MB: DIRECT EVIDENCE FOR A SUPERNOVA INTERACTING WITH A LARGE AMOUNT OF HYDROGEN-FREE CIRCUMSTELLAR MATERIAL

On 2010 April 10 UT (MJD 55296.76) the Palomar Transient Factory (PTF; Law et al. 2009, Rau et al. 2009) detected SN 2010mb at R.A. $=16^{\mathrm{h}}00^{\mathrm{m}}23\buildrel{\mathrm{s}}\over{.}103$ and decl. =37°44'57'' (detection magnitude 21.47  ±  0.2 in r band) using the CFH12K survey camera mounted on the 48'' Oschin Schmidt telescope at the Palomar observatory (P48). Analysis of previous images showed the SN was visible on 2010 March 18 UT (MJD 55273.96), at a magnitude of 22.2  ±  0.54 in the r band. The object is located on the edge of the galaxy SDSS J160023.23+374454.8 at a redshift z = 0.1325. Figure 1 shows detection, reference, and subtracted images of the SN.

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Prior to 2010 March 18 UT, the galaxy was imaged 10 times by the PTF survey between 2009 May 18 and August 21 UT (MJD 54969-55064), with no evidence for the SN or any activity in its vicinity.

We classified SN 2010mb as a Type Ic SN based on a spectrum lacking signatures of either hydrogen or helium taken on 2010 June 8 UT (MJD 55355. Figures 2 and 3; Ben-Ami et al. 2012).

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SN 2010mb, discovered near the P48 detection limit, was intermittently detected during the first 50 days after its discovery, ¹⁷ until it became continuously visible on 2010 May 31 UT (MJD 55347.71) at an apparent magnitude of 20.85  ±  0.12 in the r band.

Photometry of SN 2010mb was obtained by the P48 (Law et al. 2009; Rau et al. 2009), the gamma-ray burst camera (Cenko et al. 2006) mounted on the Palomar 60'' telescope (P60), the Large Format Camera mounted on the Palomar 200'' Hale telescope (P200), and the Low Resolution Imaging Spectrograph (LRIS) mounted on the 10 m Keck-I telescope (Oke et al. 1995). Data were reduced using the MKDIFFLC photometry routine (Gal-Yam et al. 2004, 2008), except for P48 data reduced using point-spread function (PSF) photometry on image subtractions. ¹⁸ The PTF data processing is discussed in Laher (2014 ¹⁹ ), while the photometric calibration is discussed in Ofek et al. (2012a; 2012b). We adopt a distance modulus of 39.07 mag, based on measured redshift from the SN spectrum (assuming H₀ = 67.3 km s⁻¹Mpc⁻¹ and Ω_m = 0.315; Planck Collaboration et al. 2013), corresponding to a luminosity distance of ≈650.46 Mpc, a Galactic extinction correction of E(B − V) = 0.013 mag (A_r = 0.033 mag; Schlafly & Finkbeiner 2011; see NED, ²⁰ as well as Section 3.6.) Photometric results are given in Table 1 and plotted in Figure 4. No correction for the host extinction is applied. The lack of strong interstellar medium (ISM) absorption and the blue spectral energy distribution (SED) measured at late times (see Section 3) argue against a substantial host extinction.

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The light curve (LC) displayed a long plateau in r band lasting ∼180 days, followed by a slow decline at a rate of 0.004 mag day⁻¹, while the g band and B band LCs are slowly rising during the first ∼250 days (Figure 4). The total amount of energy emitted in the r band over a period of ∼600 days is ∼1.2 × 10⁵⁰ erg (an average flux of 1.8 × 10⁻¹³ erg s⁻¹ cm⁻²). Assuming a bolometric correction of 10% at early times and 50% at later times based on our spectral decomposition (see Section 3.2), we estimate a total energy emission of 3.7  ±  0.4 × 10⁵⁰ erg over a period of ∼600 days.

Six spectra of SN 2010mb were obtained (Table 2 and Figure 2). Data were reduced using standard IRAF and IDL routines (e.g., Matheson et al. 2000b, Gal-Yam et al. 2007) and were smoothed with a three-pixel boxcar. The observed spectra are deredshifted by z = 0.1325, where the redshift was determined using a χ² minimization with an absorption-line template (Howell et al. 2005; Galactic lines identification in later spectra, e.g., 2012 February 20 spectrum, confirms our redshift determination). Spectra are calibrated to the gri P48/P60 photometry (2010 June 8, July 8, and November 1 UT), to an extrapolation of the gri P48/P60 photometry (2010 September 5 UT), and to LFC r band photometry (2011 March 4 and July 5 UT). A spectrum of the host galaxy nucleus was taken on 2012 February 20 UT using LRIS (see Section 3.6).

Table 2. Spectroscopy Log

Date (MJD)	Telescope	Instrument	Exposure Time	Grism/Grating	Slit
			(sec)	(lpm)
2010 Jun 8 (55355) a	Keck-I	LRIS	600	400/400 b	1''
2010 Jul 8 (55385)	Keck-I	LRIS	750	400/400	1''
2010 Sep 5 (55444)	Keck-I	LRIS	750	400/400	1''
2010 Nov 1 (55501)	Keck-I	LRIS	750	400/400	1''
2011 Mar 4 (55624)	Keck-I	LRIS	900	400/400	1''
2011 Jul 5 (55747)	Keck-II	DEIMOS c	1200	600	07
2012 Feb 20 (55977) d	Keck-I	LRIS	1200	400/400	1''
Date (MJD)	Resolution	Airmass	Paralactic Angle	Position Angle	Spec. Standard
	(Å)
2010 Jun 8 (55355)	1.09/1.16	1.38	−75°	27°	BD+28 4211
2010 Jul 8 (55385)	1.09/1.16	1.01	134°	270°	BD+26 2606
2010 Sep 5 (55444)	1.09/1.16	1.24	−90°	19°	BD+28 4211
2010 Nov 1 (55501)	1.09/1.16	1.55	−90°	−8°	BD+28 4211
2011 Mar 4 (55624)	1.09/1.16	1.29	14°	270°	BD+28 4211
2011 Jul 5 (55747)	0.65	1.07	42°	256°	BD+28 4211
2012 Feb 20 (55977)	1.09/1.16	1.18	238°	328°	BD+26 2606

Notes. ^aThe CBET classifying this object (Ben-Ami et al. 2012) erroneously lists the Palomar 200'' Hale telescope as that used for the spectrum taken on 2010 June 8 UT. The details here supersede this publication. ^bThe Low Resolution Imaging Spectrograph has two arms (blue and red). Each arm is equipped with a different grating and, therefore, a different resolution. ^cDeep Imaging Multi-Object Spectrograph Faber et al. (2003); filter: GG455. ^dHost Galaxy spectrum.

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The first three spectra of SN 2010mb (2010 June 8, July 8, and September 5 UT) resemble a Type Ic SN at the transition between photospheric and nebular phase as late as ∼170 days after discovery (i.e., photospheric features observed in the spectrum taken on 2010 September 5 UT, Figure 2). Automatic classification using Superfit (Howell et al. 2005) of the spectra taken on 2010 June 8 and July 8 UT suggests that the best match is to the late-time spectra of SN 1997ef 89 days after peak magnitude (an energetic Type Ic SN showing late transition from photospheric phase to nebular phase; Mazzali et al. 2004), and SN 1995F 90 days after discovery (a Type Ic SN; Matheson et al. 2001), while automatic classification using SNID (Blondin & Tonry 2011) suggests that the best match is to SN 2007gr at 54 days after peak magnitude (a "normal" Type Ic; Hunter et al. 2009), Figure 3. This highlights the slow evolution of SN 2010mb, similar to SN 1997ef, and much slower than a "normal" Type Ic SN like SN 2007gr. The spectra also resemble nebular spectra of SN 2007bi (PISN; Gal-Yam et al. 2009). Based on the resemblance between SN 2010mb spectrum taken on 2010 June 8 UT, and SN 1997ef spectrum taken 89 days after peak magnitude, and assuming a rise time of 20 days (Mazzali et al. 2004), we assume SN 2010mb exploded around 2010 February 23 UT, though this number is highly uncertain.

Early and intermediate spectra (i.e., 2010 June 8 until November 1 UT) are dominated by blended lines of Ca ii λλ3933, 3968 and [S ii] λ4069, Mg i] λ4571 and [S i] λ4589, [O iii] λλ4959, 5007, Fe ii blended lines (5200–5400 Å), [O i] and Fe ii blended lines (6300–6400 Å), O i λ7773 and [S i] λ7728, and Ca ii λλ8498, 8542, 8662, and [C i] λ8727. The Na i D line, [Si i] λ6527, and [Ca ii] λλ7291, 7324 are clearly observed in the spectra as well (line identification is based on the models described in Section 3.2; Wavelengths are given in rest frame); see Figure 3. Some of the lines, such as the Mg i] λ4571 line, seem to have an internal structure, while others, such as the [Ca ii] λλ7291, 7324 seem to have narrow cores, an indication for a different spatial distribution of these elements and, therefore, for a non-spherical geometry; see Figure 5. Late-time spectra (2011 March 4 and July 5 UT; Figure 2) are dominated by a blue quasi-continuum component, also reflected in g band and B band photometry that is slowly rising during the first ∼250 days, a behavior inconsistent with that of a purely hydrodynamic radioactive explosion that would show a monotonic decrease in temperature with time. We therefore conclude that another energy source other than radioactive ⁵⁶Ni decay, the common energy source powering Type Ic SNe, is driving the optical display of SN 2010mb at late times.

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We model the spectra obtained on 2010 June 8, July 8, September 5, and 2011 March 4 UT. We start by modeling the blue quasi-continuum, ²¹ which seems to be the strongest component in late-time spectra (2011 March 4 and July 5 UT). An attempt to fit blackbody profiles at temperatures between 5000–10, 000 K to the observed blue quasi-continuum gave unsatisfactory results. We conclude that the quasi-continuum is nonthermal in the sense that it is not described well by a blackbody of any temperature, a behavior also known for Type IIn SNe (e.g., Kiewe et al. 2012). We therefore use the spectral continuum derived from observations of SN 2005cl, a hydrogen-rich Type IIn SN, with prominent blue quasi-continuum associated with CSM–ejecta interaction. We use the spectrum taken on 2005 August 13 UT, in which the CSM–ejecta interaction seems to be the strongest. The spectrum is dominated by overlapping Fe ii lines, some of which are partially resolved (Kiewe et al. 2012). After removing the Balmer lines and fitting a smooth curve to the continuum, we scale the resulting curve to fit the continuum seen in each of the SN 2010mb observed spectra. The match between the SN 2010mb blue quasi-continuum at late times when the blue quasi-continuum is more prominent, and the model based on the SN 2005cl spectrum, lends credence to this approach.

After removing the blue quasi-continuum from the four spectra, we compose a photospheric model to match the observed spectra. SN 1997ef and SN 2010mb both show an extended LC and a late transition from photospheric to nebular emission (Figures 2, 3, and 6). We therefore use photospheric models based on SN 1997ef (Iwamoto et al. 2000; Mazzali et al. 2000) for SN 2010mb. After removing the photospheric component and following the methodology of Mazzali et al. (2004), we are left with nebular spectra.

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To model the nebular component of SN 2010mb, we construct custom models, using nebular models of SN 1997ef (Mazzali et al. 2000, 2004; Mazzali & Lucy 1993; Lucy 1999; Mazzali et al. 2007) as a starting point with adjustments to each element mass, so that the nebular line strengths agree with the observations. We assume that the emitting nebula is spherical and has a sharp outer boundary, defined by the width of the emission lines. We adopt a boundary velocity of 5000 km s⁻¹, in agreement with the nebular O i lines, the Na i D line, the Ca ii/[C i] blend near 8600 Å, and the Fe II/Na i D emission near 5200 Å, which is a blend of many different lines of different strength. The flat topped lines observed in some of the cases (e.g., Mg i] shown in Figure 5) indicate additional complexity, possibly a nonuniform spatial abundance structure. Based on the evolution of the LC and the spectra, e.g., the large flux fraction at late times from the blue quasi-continuum, we introduce an external energy source to the nebular model that increases with time, which we associate with high energy photons coming from interaction of the SN ejecta with hydrogen-free CSM.

The good match between the models and the observed spectra confirms our assumption regarding the three components that comprise SN 2010mb observed spectra, as well as the use of SN 2005cl spectra and SN 1997ef models as starting points. The decomposition results are shown in Figure 6, while Table 3 gives our results for the chemical composition and emitting mass from the nebular phase at each epoch. The mass of each element is scaled linearly with the line strengths, and from the match quality, we derive a ⩽50% uncertainty in the derived masses for most of the elements.

The derived masses indicate we have observed the explosion of a massive stripped-envelope star (for comparison, the ejecta mass in an average Type Ic SN is 1.7 M_☉; Drout et al. 2011). This is further supported by the long transition phase from photospheric to nebular emission; delayed disappearance of photospheric (optically thick) emission indicates a large total mass (Mazzali et al. 2004). The simultaneous detection of photospheric/nebular SN emission and radiation from the ejecta–CSM interaction suggests either that the outer hydrogen-free material is clumpy, or a non-spherical geometry of the CSM (e.g., in a disk or torus). Such a geometry allows us to observe the ejecta directly, in addition to ongoing interaction in the inner circumference of the CSM structure. The mass estimates based on the nebular model should be increased, correcting for the covering fraction of the CSM.

Based on our spectral decomposition, we estimate for each point in the LC the fraction of SN flux (photospheric+nebular), as well as that coming from the ejecta–CSM interaction. We thus produce two synthetic LCs—one representing the SN and the second representing the ejecta–CSM interaction, plotted in Figure 7. The synthetic SN LC decline is in agreement with that expected from ⁵⁶Ni decay, assuming full trapping of the gamma-rays as was observed for SN 1987A, indicating a large ejecta mass (the estimated ejecta mass for SN 1987A is 15 M_☉; e.g., de Freitas Pacheco 1989). The amount of radioactive nickel (0.1  ±  0.01 M_☉) suggested by the model is also consistent with the nickel mass–peak magnitude relation for SNe (Perets et al. 2010), predicting ∼0.1–0.15 M_☉ of ⁵⁶Ni, using our photometry. The synthetic LC for the interaction component shows a maximum at around 2010 September 1 UT (MJD 55440) and a much slower decline; and it is dominating the optical display from around 2010 November 20 UT (MJD 55520).

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Some of the spectra show a prominent emission line on top of the [O i] λ5577 nebular feature, Figure 8. We detected and measured this emission line flux by fitting a function to the line profile using the standard IRAF procedure splot, as well as a custom MATLAB script, which removes nearby continuum by using a spline function at an area of ±100 Å around the line peak. We verified that the line is not sensitive to varying the parameters in the nebular modeling code (i.e., changing the amount of radiating mass in the nebular phase) and the blue quasi-continuum flux, and we found a variability of ∼5% for the line flux. We ran Cloudy, a spectral synthesis code designed to predict the physical properties in the ISM under a broad range of conditions ²² (Ferland et al. 1998). We modeled slabs of optically thin and collisional gas, in order to compute the emission-line intensities associated with specific elements, as functions of the gas temperature and density. Two models are presented in Figure 9, both with parameters chosen so that the flux of the [O i] λ5577 line is similar to/greater than that of the [O i] λλ6300, 6363 lines, as observed: (1) a composition of S, C, O, Si, Ca, and Fe, with ratios in accordance with the 2011 March 4 UT nebular model results (Table 3) in order to check whether the [O i] λ5577 line is coming from the SN ejecta (i.e., a slow component in the nebular matter); and (2) a composition of 90% He, 5% C, 5% O, and traces of iron—the expected shell composition from a PPI event (Chatzopoulos & Wheeler 2012). Comparing to the observed spectra, we rule out the nebular model, which would lead to strong lines of Ca ii that are not seen. The presence of only [O i] lines is consistent with the PPI model. The property of the [O i] λ5577 line as a tracer of high densities of oxygen is shown in Figure 9, bottom panel. Only at densities ∼10⁷ cm⁻³ does the [O i] λ5577 line have a flux similar to the flux in the [O i] λλ6300, 6363 lines. For the [O i] λ5577 to be the dominant line among the [O i] lines as observed, a density of ∼10⁹ cm⁻³ is required. Further examination of the data show that the [O i] λ5577 line is blueshifted by 800 km s⁻¹ and has a velocity dispersion of 600 km s⁻¹, while the [O i] λλ6300, 6363 lines have the same redshift as the host galaxy, and a velocity dispersion of ∼300 km s⁻¹, i.e., they are instrumentally unresolved. We therefore identify the [O i] λ5577 high density line with the CSM interaction and the [O i] λλ6300, 6363 lines as the host galaxy emission.

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We find that the line at [O i] λ5577 reaches peak intensity between 2010 September 5 and November 1 UT (integrated intensity of 7  ±  0.4, 7.8  ±  0.3 × 10⁻¹⁷ erg s⁻¹ cm⁻², respectively), while the [O i] λλ6300, 6363 lines are clearly seen in the host galaxy spectrum taken on 2012 February 20 UT. The observed evolution of the [O i] λ5577 line seems to be responding to the blue quasi-continuum. This behavior, as well as the resemblance of the blue quasi-continuum model to the spectral continuum of SN 2010mb (e.g., the 2011 March 4 UT spectrum, Figure 6), shows that at late times the observed LC is powered by interaction of the SN ejecta with hydrogen-free CSM.

We can estimate the amount of CSM needed to convert the SN ejecta kinetic energy to radiation through interaction. From the LC, we estimate the amount of energy radiated between consecutive data points ΔE, and from the line width in the observed spectra, we get the ejecta velocity, v ≈ 5000 km s⁻¹. Next, using the relation (1/2)ΔMv² = ΔE, where is the conversion efficiency and is determined in an iterative way using the relation = ΔM_CSM/M_ej + ΔM_CSM (Murase et al. 2011), we derive the mass needed for energy conversion ΔM. We estimate the radius at which interaction takes place at any given time by assuming an expansion of the SN ejecta at a constant velocity of 5000 km s⁻¹. We then derive a lower limit on the density by dividing the CSM mass by the shell volume swept by the ejecta between two consecutive points in the LC. We get a total CSM mass of ∼3.3 M_☉ distributed around the progenitor with a density profile ∝r^−2.6, (Figure 10, left panel). The derived densities (∼10⁹ cm⁻³ peak density) are in agreement with the observed evolution of the [O i] λ5577 recombination line.

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Based on this analysis, we conclude the following: (1) ∼3 M_☉ of hydrogen-free CSM is present at the vicinity of the progenitor, with a mass loss rate higher than those associated with standard winds from Wolf–Rayet (WR) stars (i.e., Ø(1) M_☉ year⁻¹ compared to Ø(10⁻⁵) M_☉ year⁻¹). (2) Assuming bremsstrahlung is the main cooling mechanism of this plasma, the cooling time is orders of magnitude shorter than the time gap between adjacent points in the LC, i.e., Ø(10³ s) at the derived densities versus Ø(10⁶ s) between adjacent measurements on the LC, and so the CSM–ejecta interaction energy is radiated promptly. (3) SN 2010mb was imaged with the Swift X-ray telescope (Burrows et al. 2005) on 2011 April 22 UT. Using an exposure of 5435 s, we derive a 3σ upper limit of 5 × 10⁻¹⁴ erg s⁻¹ cm⁻² for the 0.3–10 keV band assuming a photon index of 2. The column density is high enough to explain why X-ray photons have not been detected (Figure 10, right panel).

The host galaxy spectrum taken on 2012 February 20 UT (taken at the galaxy nucleus 13 E and 22 S from the SN location; Figure 11) shows narrow Balmer emission lines filling slightly wider Balmer absorption features. This is typical to galaxies with a dominant population of older stars (∼1 Gyr), mixed with a population of younger hotter stars (Dressler & Gunn 1983; Covino et al. 2006), which in turn indicates that star formation is still present in the galaxy. The spectrum is dominated by lines of Hα/β λλ6563, 4861, [N ii] λλ6548, 6583, [O iii] lines λλ4959, 5007, as well as [O ii] λ3727. The difference between the SEDs of the host galaxy (black curve) and SN 2010mb (blue and red curves), also evident from color comparison of the host (g − r = 0.45; Sloan Digital Sky Survey, SDSS) and the SN (g − r = −0.93 on 2010 July 10 UT and g − r = −2.73 on 2011 January 12 UT), shows that the blue quasi-continuum is not a result of residual contamination from the host galaxy.

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Host galaxy analysis was performed using two different spectra: for the SN position using the spectrum taken on 2010 September 5 UT, and for the galaxy nucleus, using the spectrum taken on 2012 February 20 UT. The SN offset from the host galaxy center is 255 or 5.9 kpc in the radial direction at the redshift of the host (see Section 2.2). We detected and measured the emission line fluxes of Hα, Hβ [O ii], [O iii], and [N ii] using the standard IRAF procedure splot. We find that the host galaxy properties derived from the nucleus and from the SN position agree with each other within the error bars, with the SN position values having larger errors because of the lower signal-to-noise ratio at the SN position. We estimate a reddening of E(B − V) = 0.19  ±  0.03 mag for the nucleus and E(B − V)  ⩽  0.09 mag for the SN site, having used the observed ratio of the Balmer lines, and assuming the Cardelli et al. (1989) extinction law with R_V  = 3.1, as well as case B recombination with a Balmer decrement of Hα/Hβ = 2.86. In the following, we correct the detected emission line fluxes for reddening. To compute the oxygen abundance from these H ii region emission lines, we follow Modjaz et al. (2011 and references therein) and employ the scales of Pettini & Pagel (2004; PP04-O3N2) and of Kewley & Dopita (2002, hereafter KD02), to obtain oxygen abundance values for the host galaxy nucleus of 12 + log (O/H)_{PP04 − O3N2} = 8.39  ±  0.01 and 12 + log (O/H)_KD02 = 8.60  ±  0.05, respectively, where we consider only statistical uncertainties. The oxygen abundance at the SN site is consistent with that of the host galaxy nucleus within the error bars. We conclude that the metallicity of the SN host galaxy is $0.5^{+0.42}_{-0.19}$ Z_☉, having used the scale of Pettini & Pagel (2004) and a solar oxygen abundance value of 12 + log (O/H) =8.69 (Asplund et al. 2009). The total star formation rate that we measured using the Hα luminosity (Kennicutt 1998) is ∼0.32 M_☉ yr⁻¹.

The observed data are consistently explained by a PPI event followed by a CC SN. During the first ∼150 days after discovery, ∼90% of the optical display is coming from the SN explosion. At later times, as the ejecta reach the hydrogen-free CSM, a shock wave is generated at the interface between the two media, and X-ray photons generated at the shock front are exciting both the CSM and the ejecta, thus introducing a new source of energy. Eventually, this new source dominates the optical radiation—as can be seen from the long-lasting optical display compared to other Type Ic SNe, the change in the SED, and the evolution of the forbidden [O i] line. If we assume a non-spherical geometry for the CSM, the high energy photons will excite mostly the ejecta in the plane of the torus, thus perhaps generating the observed internal structure in the nebular lines (Figure 5). Mazzali et al. (2007) suggest that a flat-topped profile might be the result of a disk observed edge-on (leading to a double peak line profile), where the inner component of the disk would contain more mass, so that its emission could fill the valley between the two peaks.

A recent model of a 110 M_☉ star in a low metallicity environment produces a stripped C/O core when encountering the pair instability for the first time (Chatzopoulos & Wheeler 2012). The period of pair instability will result in the ejection of a ∼3 M_☉ shell that is significantly enhanced in He, C, and O. Subsequent pulses may be even richer in carbon and oxygen, as they probe inner regions of the progenitor. Later, the progenitor will return to the normal evolution track, until it ends its life in an iron-CC SN. In the case of SN 2010mb, we estimate the time gap between the last pulse and the CC event was ∼2.2 yr, if we assume a velocity of 800 km s⁻¹ for the matter ejected in the final pulse based on the observed [O i] λ5577 recombination line blueshift, again in accordance with models (Woosley et al. 2007). While in the past PISNe and PPI events were assumed to happen only in very low metallicity environments, recent works (Langer et al. 2007; Chatzopoulos & Wheeler 2012; Yusof et al. 2013) predict these explosions can also occur in local dwarf galaxies with metallicity values which are well within the errors of those measured for SN 2010mb, i.e., metallicities as high as Z = Z_☉/3.

Interaction of SN ejecta with hydrogen-free material is also observed in Type Ibn SNe (Pastorello et al. 2008a; Smith et al. 2012). These events are defined by strong He i emission lines, with a blue quasi-continuum, which are suggested to be the result of a blend of Fe ii lines that are observed in at least two cases (SN 1999cq, Matheson et al. 2000a; SN 2006jc, Foley et al. 2007). Type Ibn SNe are associated with the explosion of WR progenitors embedded in a helium-rich hydrogen-diluted CSM. The interacting material composition is consistent with that of WR winds, i.e., hydrogen and helium for WN progenitors, and helium for WC/WO progenitors (Pastorello et al. 2008b). The main differences between Type Ibn SNe and SN 2010mb are as follows: (1) Type Ibn SNe have much shorter timescales than that of SN 2010mb; therefore, ⁵⁶Ni/⁵⁶Co mixing in the outer shells is not a possible explanation for the blue quasi-continuum in our case as it decays too fast (a half-life of 8/77 days, respectively). Scattering from interstellar dust Matheson et al. (2000a) as echoes also cannot explain the plateau because the integrated flux during the plateau is higher than the flux from the peak in the case of SN 2010mb. (2) In Type Ibn SNe, B band and g band magnitudes decrease with time. (3) While in Type Ibn the interaction has a modest influence on the observed LC and a fairly modest amount of CSM is involved (less than ∼0.3 M_☉; Pastorello et al. 2008a), in the case of SN 2010mb, CSM interaction is the dominant power source at late times, and it probably involves a much higher mass of CSM (>3 M_☉). We conclude that a similar scenario to the one generating Type Ibn SNe is not adequate for SN 2010mb.

The presence of a large amount of CSM can also be attributed to wave excitation by vigorous convection in the late stages of stellar evolution (Si nuclear burning phase; Quataert & Shiode 2012). In this scenario, convective motions excite internal gravity waves that in some cases are converted to sound waves as they tunnel toward the stellar surface. As the sound waves dissipate while crossing through the star envelope, they release a large amount of energy that can unbind up to several solar masses of the stellar envelope. In case of SN 2010mb, the interaction goes for long time, indicating the CSM must extend over large distances, and it was ejected at an earlier phase than the Si nuclear burning phase of the progenitor. It remains to be demonstrated that high mass loss rates can be produced during earlier nuclear burning stages in order to explain the optical display of SN 2010mb.

Luminous blue variable stars (Humphreys & Davidson 1994, Meynet et al. 2011) are also associated with strong eruptions. Maeder (1992) has shown that in the outer shells of these stars, the free fall time becomes longer than the thermal diffusion time, leading to super-Eddington luminosity, and the ejection of a large amount of material. In cases where this process sets in after the progenitor lost its hydrogen and helium outer shells, the ejected material will be comprised from intermediate mass elements, mainly O and C, as seen in our case. This option is speculative at this time and needs to be further explored.

Finally, another event where interaction of SN ejecta with H-free CSM was suggested as a way to explain an increased, short lived luminosity is SN 2009dc, an SN interpreted as a 'Super Chandrasekhar' Type Ia SN. Hachinger et al. (2012) suggest that a non-violent white dwarf merger can culminate in a Type Ia SN interacting with H-/He-free CSM, causing an increase in the observed flux with respect to the flux of a typical Type Ia SN. In such a case, if the emitting CSM is concentrated in clumps or in a torus, the observed emission will be a sum of two components: one from the SN explosion, and the other from the ejecta-CSM interaction, as is the case for SN 2010mb. However, the total amount of radiation that can be added by interaction with white dwarf debris is much smaller than seen for SN 2010mb.

4.3.1. Photon Diffusion

Type II-P SNe also exhibit a plateau in their LCs. The mechanism driving this plateau is photon diffusion through the expanding ejecta. We analyze the SN 2010mb LC in the context of the recombination front model Popov (1993). In this model, the opacity is approximated by a step function and is constant above the ionization temperature, T_ion, and equals zero below that. We assume that above the ionization temperature the opacity is dominated by Thomson scattering, and since the envelope contains mainly metals, we take k = 0.2 cm² g⁻¹. This approximation to the opacity is an upper bound on the real opacity, which is already smaller than 0.2 cm² g⁻¹ at temperatures of T_ion ≈ 3 × 10⁴ K Rabinak & Waxman (2011). We assume the effective temperature of the radiation is ≈5, 000 K from the models described in Section 3.2, and we get an ion temperature of T_ion ≈ (T_eff/2^1/4) ≈ 4170 K. Based on this analytic model, we get the following estimation for the ejecta mass, explosion energy, and progenitor radius:

$M_{ej}\sim 1160\, t^4_{185}T^4_{4170}v^3_{5}L_{41}^{-1}\kappa _{0.2}^{-1}\,\,{M}_{\odot }$

$E\sim 8.4\times 10^{52}t^4_{185}T^4_{4170}v^5_{5}L_{41}^{-1}\kappa _{0.2}^{-1}\,\mathrm{erg}$

$R_s\sim 2.3\times 10^{11}t^{-2}_{185}T^{-4}_{4170}v^{-4}_{5}L_{41}^2 \kappa _{0.2}\,\mathrm{cm,}$

where t₁₈₅ = t_p /185 days, T₄₁₇₀ = T_ion/4170 K, L₄₁ = L/10⁴¹ erg s⁻¹, v₅ = v_ph /5 × 10⁸ cm s⁻¹, and κ_0.2 = κ/0.2 cm² g⁻¹. Even when considering the uncertainties in the measurements, the model suggests an unrealistically large ejecta mass (several hundred solar masses of He, C, and O), and therefore, we pursue it no more.

4.3.2. Magnetar

Magnetars, very highly magnetic (B > 10¹⁴ G) and rapidly rotating (P_s ≈ 2–5 ms) NSs, generated at the time of SN explosion, can have a large impact on SN LCs (Mazzali et al. 2006; Maeda et al. 2007; Kasen & Bildsten 2010; Woosley 2010; Inserra et al. 2013). These magnetars spin down in a few months (comparable to the radiative diffusion time in SN ejecta, t_d ), depositing enough energy to power the rare superluminous (L > 10⁴⁴ erg s⁻¹) hydrogen poor SLSN-I Quimby et al. (2011); Gal-Yam (2012); Inserra et al. (2013). The much lower (and nearly constant) luminosity, L_SN ≈ 10⁴² erg s⁻¹, of SN 2010mb over a prolonged (>500 days) period requires a different interpretation. Specifically, a young NS with a magnetic dipole spin-down luminosity L_p ≈ 10⁴² erg s⁻¹, and a spin-down timescale, t_p , longer than 10 yr, so that L_p is approximately constant over the 500 days, is needed. Such a power source (Kasen & Bildsten 2010) would overwhelm the adiabatic losses from the initial explosion, and reset the SN luminosity to L_p . Setting L_p = 10⁴² erg s⁻¹ gives the relation B ≈ 3 × 10¹³G(P_s /8 ms)², and requiring a spin-down timescale longer than 10 yr implies that P_s < 8 ms. Though more rapidly rotating than the fastest known young pulsar, PSR J0537-6910 (Marshall et al. 1998) (at P_s = 16 ms), such an initial spin and magnetic field are certainly allowed (e.g., the implied B ≈ 4 × 10¹² G for an initial spin of 3 ms is entirely reasonable). In this scenario, the young NS spin-down luminosity is reprocessed by the SN ejecta, allowing for a long, visible event. Though we remain unsure as to the form (i.e., Poynting flux, particles, or radiation) of the spin-down power, L_p , we will assume that the thinning of the ejecta due to expansion will eventually lead to an inefficient coupling and, hence, a reduction in the optical brightness of the event. For an ejecta mass of M_ej ≈ 5 M_☉ moving at an average velocity fixed by E = M_ej V²/2, the column depth in the ejecta will evolve with time as

$\begin{equation} {M_{\rm ej} \over 4\pi (Vt)^2}= 2 {\rm g \over cm^{2}}\left(500\, {\rm days}\over t\right)^2\left(10^{51} \ {\rm erg}\over E\right)\left(M_{\rm ej}\over 5\, M_\odot \right)^2, \end{equation} \tag{ 1 }$

implying thinning to fast energetic ions and hard radiation at about the time where the SN faded.

The magnetar model can explain the LC timescale but fails to explain the color evolution of SN 2010mb, the high density narrow O lines, and the presence of strong nebular lines that require an optically thin medium, while the reprocessing of the radiation emitted by the magnetar requires a thick medium.