A LUMINOUS AND FAST-EXPANDING TYPE Ib SUPERNOVA SN 2012au

We first correct the Galactic extinction of E(B − V)_MW = 0.048 mag (Schlegel et al. 1998). For the extinction within the host galaxy, we place a limit as E(B − V)_host ⩽ 0.035 mag from the upper limit of the equivalent width (EW) of the Na i D absorption line (Poznanski et al. 2012) in the averaged spectra. The extinctions in the host galaxy are thus negligibly small (≲ 0.1 mag in V band).⁸ Therefore, we adopt the total extinction toward SN 2012au as E(B − V)_total = 0.048 mag.

The light curves (LCs) and color curves are shown in Figure 1. The SN reached peak brightness R_max = 13.1 ± 0.1 mag on March 21.0 ± 1.0 (which is set to be t = 0 day), corresponding to the absolute magnitude M_R, max = −18.7 ± 0.2 mag. A compilation by the Lick Observatory Supernova Search (LOSS) indicates that the mean absolute magnitude of SNe Ib/c is 〈M_R, max〉 = −16.1 ± 1.2 mag (Li et al. 2011). Another systematic study suggests that 〈M_R, max〉 = −17.9 ± 0.9 mag for SNe Ib (and −18.3 ± 0.6 mag and −19.0 ± 1.1 mag for SNe Ic and SNe Ic-BL, respectively; Drout et al. 2011). SN 2012au belongs to a very luminous group among SNe Ib. The post-maximum decline within 15 days is estimated to be Δm₁₅(R) = 0.57 ± 0.06 mag, which is located near the center of the cluster of Drout et al.'s samples, which range from ∼0.4 to ∼0.8 mag. After t ∼ 30 days, the SN showed a slow decline with the rate 0.017 mag day⁻¹ (average in 34–111 days) in R band.

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In the upper panel of Figure 2, we show a comparison of R-band LC with other CC-SNe, SN 2008ax (Ib/IIb), SN 2009jf (Ib), SN 1998bw (Ic-BL), and SN 1993J (IIb) and also with the LOSS averages. Around maximum, the LC of SN 2012au is very similar to those of SN 1998bw and the LOSS average, showing a slightly slower evolution than LCs of SNe 2008ax and SN 1993J. On the other hand, in the tail of LC (t ≳ 30 days), SN 2012au shows slower evolution than these SNe except for the slowly evolving SN Ib 2009jf. These facts suggest that the trapping efficiencies of optical and γ-ray photons within the ejecta are larger than the typical.

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The color evolution is shown in the lower panel of Figure 1. It becomes progressively redder until ∼20 days and then its slopes becomes rather flat, which is similar to those seen in other SNe Ib/c. Drout et al. (2011) suggested that the intrinsic V−R colors fall in a relatively narrow range 0.26 ± 0.06 mag around 10 days. In the case of SN 2012au, V − R = 0.36 ± 0.02 mag at 10 days, which is slightly redder than the mean value.

We show the spectral evolution from −6 days to +138 days in Figure 3. Around maximum, the absorption line of He i λ5876 is conspicuous as in other SNe Ib. We can see other He i lines (λλ6678, 7065), Fe ii λ5169, and Ca ii IR triplet. After +110 days, nebular emission lines, [O i] λλ6300, 6364 and [Ca ii] λλ7291, 7323, appear. A comparison of the spectra around maximum and +35 days are shown in the bottom panels of Figure 3. It is clear that the blueshift of He i and other lines in SN 2012au is larger than other SNe, which is discussed in Section 4.2.

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From our BVRI photometry, we calculated quasi-bolometric luminosity, assuming that the BVRI bands occupy about 60% of the bolometric one around the peak (Tomita et al. 2006). Because of this simple assumption, this bolometric luminosity may well have a large systematic error (∼20%). The derived quasi-bolometric LC is shown in the bottom panel of Figure 2. It reaches (6.7 ± 1.3) × 10⁴² erg s⁻¹ at maximum. This is clearly larger than those of SN 2009jf (3.2 × 10⁴² erg s⁻¹; Sahu et al. 2011) and SN 2008ax (2.4 × 10⁴² erg s⁻¹; Taubenberger et al. 2011; cf. 1.0 × 10⁴³ erg s⁻¹ for luminous SN 1998bw; Nakamura et al. 2001; see below).

A general interpretation of the radiation source of SNe Ib/c around maximum is that the energy generated by the decay of ⁵⁶Ni and ⁵⁶Co emerges out of the photosphere as optical radiation (Arnett 1982). Therefore, the ⁵⁶Ni mass, M(⁵⁶Ni), can be derived from the peak bolometric luminosity L_max and the rising time t_r (Stritzinger et al. 2006) as

$$\begin{equation} L_{\rm max} = ( 6.45\times e^{-\frac{t_r}{8.8}} + 1.45\times e^{-\frac{t_r}{111.3}} ) \times \left (\!\frac{M(^{56}{\rm Ni})}{M_{\odot }} \!\right) \times 10^{43}\ {\rm erg\ s}^{-1} {.} \end{equation} \tag{ 1 }$$

With t_r = 16.5 ± 1.0 days (Milisavljevic et al. 2013b) and L_max = 6.7 × 10⁴² erg s⁻¹, we obtain M(⁵⁶Ni) = 0.30 M_☉. This ⁵⁶Ni mass is larger than that in other SNe Ib (e.g., 0.07–0.15 M_☉ in SN 2008ax and 0.14–0.20 M_☉ in SN 2009jf; see also Drout et al. 2011).

Next, we try to constrain the ⁵⁶Ni mass from the tail component of the quasi-bolometric LC (t = 30–70 days) using a simple one-zone model (Maeda et al. 2003) as shown in Figure 2. At first, with a simplified assumption that γ-rays are fully trapped and deposit their energy in the ejecta, this model gives ⁵⁶Ni masses of 0.30 M_☉ for the peak bolometric luminosity (as is equivalent to Equation (1)). For a more realistic treatment where the γ-rays can only be partly absorbed, we need to provide the optical depth to γ-ray within the ejecta, τ. In this case, the bolometric luminosity in the later phase (t ≳ 30 days) can be written as⁹

$$\begin{equation} L = M(^{56}{\rm Ni}) e^{(-t_d/113\ \scriptsize {\mbox{days}})} [ \epsilon _{\gamma }(1-e^{-\tau })+\epsilon _{e^{+}} ] \end{equation} \tag{ 2 }$$

and

$$\begin{equation} \tau = 1000 \times \frac{(M_{\rm ej}/M_{\odot })^2}{E_{51}} t_{d}^{-2} \mbox{,} \end{equation} \tag{ 3 }$$

where t_d is the time after the explosion in days (≡ t_r + t), _γ = 6.8 × 10⁹ erg s⁻¹ g⁻¹ and $\epsilon _{e^{+}} = 2.4\times 10^8\ {\rm erg\ s^{-1}\ g^{-1}}$ are energy deposits by γ-ray and positrons, respectively, and (M_ej/M_☉) is the ejecta mass in solar mass unit. By changing these parameters, however, it turns out that we are unable to reproduce the peak and tail simultaneously with a single component (for example, the case of M(⁵⁶Ni) = 0.26 M_☉ and [(M_ej/M_☉)²/E₅₁] = 4 is shown in Figure 2). The tail luminosity requires a small value of τ, while tail slope requires a large value of τ instead.

Therefore, we introduce a two-component model similar to Maeda et al. (2003), consisting of an inner region having large optical thickness τ_in and an outer region having small τ_out. The luminosity is then expressed as

$$\begin{eqnarray} L_{\rm opt} &=& M_{\rm in}(^{56}{\rm Ni}) e^{(-t_d/113\ \rm {d{\rm ays}})} [ \epsilon _{\gamma }(1-e^{-\tau _{\rm in}}) + \epsilon _{e^{+}} ] \nonumber\\ && + M_{\rm out}(^{56}{\rm Ni}) e^{(-t_d/113\ \rm {d{\rm ays}})} [ \epsilon _{\gamma }(1-e^{-\tau _{\rm out}})+\epsilon _{e^{+}} ] \mbox{,} \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} \tau _{\rm in} &=& 1000 \times \left [ \frac{(M_{\rm ej}/M_{\odot })^2}{E_{51}} \right ]_{\rm in} t_{d}^{-2} \mbox{, and} \end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray} \tau _{\rm out} &=& 1000 \times \left [ \frac{(M_{\rm ej}/M_{\odot })^2}{E_{51}} \right ]_{\rm out} t_{d}^{-2} \mbox{.} \end{eqnarray} \tag{ 6 }$$

The observation is reproduced reasonably well using this model with M_in(⁵⁶Ni) = 0.14 M_☉, [(M_ej/M_☉)²/E₅₁]_in = 20, M_out(⁵⁶Ni) = 0.12 M_☉, and [(M_ej/M_☉)²/E₅₁]_out = 2 (bottom panel of Figure 2). This result favors that a dense core exists in their inner region. It is interesting that a similar density contrast has also been derived for the luminous SN Ic-BL 1998bw which possibly produced a jet-like asymmetric ejection (Maeda et al. 2003); M_in(⁵⁶Ni) = 0.11 M_☉, [(M_ej/M_☉)²/E₅₁]_in = 26, M_out(⁵⁶Ni) = 0.44 M_☉, and [(M_ej/M_☉)²/E₅₁]_out = 1. The fraction of ⁵⁶Ni in the high-velocity component is smaller in SN 2012au, which might suggest either a difference in details of the explosion or a different viewing direction (see also Milisavljevic et al. 2013b).

In this two-component model, the sum of the ⁵⁶Ni mass is 0.26 M_☉. The difference from 0.30 M_☉ derived from the peak luminosity suggests that the ratio of peak bolometric to radioactive luminosities, α, is not unity, but α ≃ 1.2 (e.g., Howell et al. 2006). Therefore, the ⁵⁶Ni mass of 0.26 M_☉ is likely a better estimation. However, to provide a better comparison to other SNe (where α ∼ 1 is typically assumed), we adopt 0.30 M_☉ throughout this Letter.

We derived the line velocities of He i λ5876, Ca ii IR triplet (assumed to the absorption peak at 8571 Å), and Fe ii λ5169 by fitting a quadratic function to each absorption feature (Figure 4). Around maximum, the He velocity of SN 2012au is ∼15,000 km s⁻¹, which is significantly larger than those of the SNe Ib samples in Branch et al. (2002) that clustered around ∼11,000 km s⁻¹. After 30 days, the He velocities in most SNe Ib decrease and tend to converge at 7000–8000 km s⁻¹ (Figure 4; see also Branch et al. 2002). On the other hand, SN 2012au exhibits large He velocity, ∼10,000 km s⁻¹ even at +50 days. We also derived the line velocities at He i λ6678 and λ7065 up to +10 days and confirmed that their velocities are consistent with that of He i λ5876 within 1000 km s⁻¹, suggesting that the contamination by Na i D to He i λ5876 is negligible during the period. The line velocities of Ca ii IR triplet and Fe ii λ5169 are also as large as that of He i at −6 days (Figure 4). The Fe velocity shows a steep decrease from 12,500 km s⁻¹ around maximum to an asymptotic value of ∼4000 km s⁻¹ after +50 days. This trend is also seen in other SNe Ib, while the velocity in other SNe Ib is lower than 9000 km s⁻¹ at maximum (Branch et al. 2002). This may suggest that the distribution of iron is rather widespread, up to the outermost region, in the ejecta.

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We show the EW of He i λ5876 absorption line in Figure 4. It is about 80 Å at −6 days, which is larger than that of SN 2008D at similar phase. This might be related with the He envelope mass and/or the distribution of ⁵⁶Ni.

We estimate the ejecta mass, M_ej, and kinetic energy, E_k, using scaling relations. The relevant basic equations are

$$\begin{eqnarray} t_r &\propto & \kappa ^{1/2} M_{\rm ej}^{3/4} E_k^{-1/4} \mbox{} \mbox{ and} \end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray} v &\propto & E_k^{1/2} M_{\rm ej}^{-1/2} \mbox{,} \end{eqnarray} \tag{ 8 }$$

where κ is absorption coefficient for optical photons, and v is a typical expansion velocity (Arnett 1982). We apply this relation to the case of SN 2012au using the parameters derived for well-studied SN 2008D (Tanaka et al. 2009) as the scaling template. We derive the parameters of SN 2012au as M_ej = 5–7 M_☉ and E_k = (7–18) × 10⁵¹ erg, where we adopt the He i line velocities around maximum as the expansion velocities.¹⁰

In Figure 5, we plot the peak R-band absolute magnitude M_{R, max} versus the He i λ5876 line velocity v_He around maximum (left panel) and the ⁵⁶Ni mass versus the kinetic energy (right panel) in SN 2012au with those of other SNe Ib (and also SNe Ic in the right panel) for comparison. We see weak positive correlations in both v_He–M_{R, max} and E_k–M(⁵⁶Ni) except for very peculiar SN 2005bf. To our knowledge, the former correlation has not been pointed out so far; the data point of SN Ib 2012au makes it much clearer. Also in the right panel, the point of SN 2012au is apart from the average of SNe Ib and Ic, and rather near of the average of GRB-associated SNe. These results may indicate that SN 2012au have observational properties similar to hypernova.

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