A LUMINOUS PECULIAR TYPE IA SUPERNOVA SN 2011HR: MORE LIKE SN 1991T OR SN 2007if?

The photometric observations of SN 2011hr were performed in broad UBVRI bands with the Tsinghua-NAOC 0.8 m telescope (hereafter TNT; Wang et al. 2008; Huang et al. 2012) at Xing-Long Observatory of NAOC. This telescope is equipped with a 1340 × 1300 CCD (PI VersArray: 1300B), providing a field of view (FOV) of $11\buildrel{\,\prime}\over{.} 5\;\times \;11\buildrel{\,\prime}\over{.} 2$ with a spatial resolution of ∼ 052 pixel⁻¹. The typical exposure times are 180 s in the BVRI bands and 300 s in the U band when taking images of SN 2011hr. These images have typical FWHM of about 25. The CCD images were reduced using standard IRAF routines. The data collections started from $t\approx -14$ days and lasted until $t\approx +70$ days relative to the B-band maximum light. All CCD images were reduced using the IRAF¹³ standard procedure.

Since SN 2011hr exploded near the center of its host galaxy, the step of subtracting the galaxy template from the SN images is necessary for accurate photometry, in particular when the SN became faint and/or the images were taken under poor seeing conditions. Higher-quality template images were obtained with the TNT on 2013 May 11, when the SN was sufficiently faint. Using the galaxy-subtracted images, we measured the instrumental magnitudes of the SN and the local standard stars (labeled in Figure 1) by aperture photometry, performed using the IRAF DAOPHOT package (Stetson 1987). The radius for the photometric aperture is set as 2.0 times the FWHM; the sky background light was determined from the median counts at a radius that is 5.0 times the FWHM. Twelve local standard stars in the field of SN 2011hr are labeled in Figure 1. We transformed the instrumental magnitudes of these reference stars to the standard Johnson UBV (Johnson et al. 1966) and Kron–Cousins RI (Cousins 1981) systems through the following transforming equations (Huang et al. 2012):

$$\begin{eqnarray}&&U\;=\;u+0.22(U-B),\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&B\;=\;b+0.15(B-V),\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&V\;=\;v-0.06(B-V),\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&R\;=\;r-0.10(V-R),\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&I\;=\;i+0.02(V-I),\end{eqnarray} \tag{ 5 }$$

where UBVRI represent the magnitudes in the standard system and ubvri represent the instrumental magnitudes. The color term coefficient was determined by observing Landolt (1992) standards on photometric nights. The magnitudes of these reference stars are listed in Table 1, and they are then used to convert the photometry of SN 2011hr to the standard UBVRI magnitudes as shown in Table 2.

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Figure 2 displays the UBVRI-band light curves of SN 2011hr (see details in Table 2). Some basic photometric parameters such as the maximum-light dates, peak magnitudes, and magnitude decline rates (Δm₁₅; Phillips 1993) can be derived from a polynomial fit to the observed light curves, which are listed in Table 3. We find that SN 2011hr reached a B-band maximum brightness of $14.95\pm 0.03$ mag on JD 2,455,889.62 ± 0.30 (2011 November 23.12), with a decline rate ${\rm{\Delta }}{m}_{15}$(B) = 0.92 ± 0.03 mag. The slower decline rate suggests that SN 2011hr should be intrinsically luminous if it follows the WLR (e.g., Phillips 1993; Riess et al. 1996; Goldhaber et al. 2001; Guy et al. 2005); see also Table 3 and detailed discussion in Section 2.5. After correcting for a Galactic reddening of $E(B\;-\;V)$ = 0.02 mag (Schlegel et al. 1998), the color index B_max − V_max becomes 0.23 ± 0.04 mag. On the other hand, the corresponding color index is about 0.13 ± 0.03 mag for SN 1991T. This suggests that both SN 2011hr and SN 1991T suffer a significant host-galaxy reddening assuming that their intrinsic colors are comparable to that established for normal SNe Ia (e.g., Phillips et al. 1999; Wang et al. 2009b); see also Sections 2.3 and 2.4.

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Table 3.  Light-curve Parameters of SN 2011hr

Band	${\lambda }_{{mid}}$	tmaxa	mpeakb	Δm15b	Mpeakb
	(Å)	(−2455000.5)	(mag)	(mag)	(mag)
U	3650	887.39(50)	14.63(03)	1.04(05)	−20.34(45)
B	4450	889.12(30)	14.95(02)	0.92(03)	−19.84(40)
V	5500	889.95(30)	14.70(03)	0.59(03)	−19.87(35)
R	6450	890.01(30)	14.62(02)	0.53(05)	−19.81(30)
I	7870	890.10(40)	14.70(03)	0.45(05)	−19.57(30)

Notes.

^a1σ uncertainties, in units of 0.01 days. ^b1σ uncertainties, in units of 0.01 mag.

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Overplotted in Figure 2 are the light curves of other well-observed SNe, including overluminous SN Ia SN 1991T (Δm₁₅ = 0.94 mag; Sasdelli et al. 2014 and therein), SN 1999aa (Δm₁₅(B) = 0.83 mag; Jha et al. 2006), the "golden standard" SN Ia SN 2005cf (Δm₁₅(B) = 1.05 mag; Wang et al. 2009b), the superluminous SN 2007if (Δm₁₅(B) = 0.71; Scalzo et al. 2010) and SN 2009dc (Δm₁₅(B) = 0.71; Taubenberger et al. 2010). In general, SN 2011hr shows a close resemblance to SN 1991T in UBVRI-band photometry. Compared to SN 2011hr/SN 1991T, the superluminous object SN 2009dc shows apparently broader light curves, especially in the redder bands, where its secondary maximum/shoulder feature is more prominent. Note that another so-called superluminous SN Ia, SN 2007if, is found to be more similar in morphology to SN 2011hr/SN 1991T.

Figure 3 shows the color curves of SN 2011hr. Overplotted are the color curves of SN 1991T, SN 1999aa, SN 2005cf, SN 2007if, and SN 2009dc. All of these color curves (including those of SN 2011hr) are corrected for the reddening of the Milky Way and the host galaxy. The reddening of SN 2011hr is discussed in the following section.

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At early time, the $U\;-\;B$ colors of the luminous/superluminous SNe Ia (including SN 2011hr) show distinct behavior compared to the normal SN 2005cf. The former group tends to become progressively redder after explosion, while SN 2005cf shows a "red–blue–red" evolutionary trend at a similar phase. At around maximum light, the B − V color of SN 2011hr and SN 1991T is redder than that of other comparison SNe Ia. SN 2011hr and SN 1991T are also found to be redder by 0.1–0.2 mag than predicted by the Lira–Phillips relation (Phillips et al. 1999; see solid line in Figure 3). Among our comparison sample, SN 2009dc shows the bluest U − B and B − V colors at t < +35 days, while it (and SN 2007if) shows redder V − R and V − I colors. Large scatter can be seen in the V − I color, where the strength of the Ca ii near-IR (NIR) triplet could have a dominant effect. In general, SN 2011hr shows a color evolution that is quite similar to that of SN 1991T and SN 2007if at all phases.

The Milky Way reddening of SN 2011hr is $E{(B-V)}_{\mathrm{Gal}}$ = 0.02 mag (Schlegel et al. 1998), corresponding to an extinction of 0.06 mag adopting the standard Galactic reddening law (i.e., R_V = 3.1; Cardelli et al. 1989). The reddening due to the host galaxy can be estimated by several empirical methods. For instance, a comparison of the late-time B − V color with that predicted by the Lira–Phillips relation (Phillips et al. 1999) gives a host-galaxy reddening of $E{(B-V)}_{\mathrm{host}}$ = 0.29 ± 0.07 mag for SN 2011hr. The peak ${B}_{\mathrm{max}}-$V_max color has also been used as a better reddening indicator for SNe Ia (Phillips et al. 1999; Wang et al. 2009b), based on its dependence on Δm₁₅(B). For SN 2011hr, the observed peak B − V color is 0.23 ± 0.04 mag, which suggests a host-galaxy reddening of E(B – V) = 0.32 ± 0.06 mag. However, a scatter of about 0.1 mag might exist for the above estimates considering that such overluminous SNe Ia may have intrinsically different colors relative to the normal SNe Ia.

The low-resolution spectra of SN 2011hr show prominent signatures of Na i D absorption, for which the equivalent width (EW) of this absorption can be derived by using a double-Gaussian fit as shown in Figure 4. The best fit yields EW(Na i D) = 1.42 $\pm \;0.02$ Å with ${\mathrm{EW}}_{{\rm{D}}1}$ = 0.84 $\pm \;0.01$ Å and ${\mathrm{EW}}_{{\rm{D}}2}$ = 0.58 $\pm \;0.01$ Å. Based on an empirical correlation between reddening and the EW of Na i D, namely, $E(B-V)\;=\;0.16\;\mathrm{EW}-0.01$ [Å] (Turatto et al. 2003), we estimate $E{(B-V)}_{\mathrm{host}}$ to be 0.22 ± 0.10 mag for SN 2011hr, which is consistent with the result derived from the photometric B − V color within 1σ error.

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Combining the results from both photometry and Na i D absorption, a host-galaxy reddening of $E{(B-V)}_{\mathrm{host}}$ =0.25 ± 0.10 can be obtained for SN 2011hr. On the other hand, the spectral modeling presented in Section 4.3 suggests a moderate host-galaxy reddening, i.e., $E{(B-V)}_{\mathrm{host}}$ = 0.15 mag, which seems to be more reasonable as it matches the observed colors. Therefore, a mean value $E{(B-V)}_{\mathrm{total}}=0.22\pm 0.05$ mag is adopted as the total reddening of SN 2011hr in this paper.

The actual luminosity of SN 2011hr is affected by the uncertainty in the distance to the SN. Table 4 lists the measurements obtained using different methods. One can see that these measurements show significant dispersion. For example, the distance derived from the redshift of the host galaxy NGC 2691 and the Hubble flow is 59.3 ± 4.0 Mpc (Mould et al. 2000), which agrees with the result from the Tully–Fisher relation (60.2 ± 10.0 Mpc; Theureau et al. 2007). These two values are larger than the luminosity distance derived for the SN using the original Phillips (1993) relation but close to that derived from the modified relation for 91T-like events in Blondin et al. (2012), as listed in Table 4.

Table 4.  Distances to SN 2011hr and NGC 2691

Method	Details	Results (Mpc)
Hubble flowa	4269 km s−1	59.3 ± 4
Tully–Fisherb	JHK bands	60.2 ± 10
Phillips relationc	$E(B-V)$ = 0.17	48.24 ± 8
Phillips relationd	$E(B-V)$ = 0.17	56.58 ± 4
NIR luminouse	H band	43.7 ± 5

Notes.

^aCorrected for Virgo infall, GA, and Shapley (Mould et al. 2000), on the scale of H₀ = 72 km s⁻¹ Mpc⁻¹. ^bMean distance from estimates in the JHK bands (Theureau et al. 2007; Tully et al. 2009). ^cΔm₁₅(B) = 0.92; Phillips (1993). ^dModified Phillips (1993) relation in Figure 13 of Blondin et al. (2012) for 91T-like events. ^eWeyant et al. (2014).

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On the other hand, we can also estimate the distance to SN 2011hr based on its NIR magnitude, since the JHK-band luminosities of SNe Ia are relatively insensitive to the reddening and are more uniform around the peak compared to the corresponding values in the optical bands (Meikle 2000; Krisciunas et al. 2004; Barone-Nugent et al. 2012). Additionally, some peculiar SNe Ia such as SN 1999aa, SN 1999ac, and SN 1999aw are found to have normal luminosities in the NIR bands (Krisciunas et al. 2004), though they appear somewhat peculiar in optical bands. Based on the NIR photometry of 13 SNe Ia (including SN 2011hr), Weyant et al. (2014) estimated their mean absolute peak magnitude as −18.31 ± 0.02 mag in the H band. Taking the observed H-band peak magnitude of 15.02 $\pm \;0.20$ mag for SN 2011hr (Weyant et al. 2014) and assuming that it has a similar absolute H-band magnitude, we get a distance modulus $m-M=33.20\pm 0.20$ mag or $D=43.7\pm 5.0$ Mpc. This estimate is much smaller than the Tully–Fisher distance and that inferred from the Hubble flow. Note, however, that the dispersion of the sample from Weyant et al. (2014) will decrease significantly from ${\sigma }_{{\rm{H}}}$ = 0.23 mag to ∼0.18 mag if SN 2011hr was excluded in the analysis. This is due to the fact that SN 2011hr is actually more luminous than normal SNe Ia by ∼0.7 mag in the H band.

As the distance derived from Hubble expansion is independent of corrections for reddening and agrees well with the estimate from the Tully–Fisher relation, a distance of D = 60.0 ± 6.0 Mpc is thus adopted for SN 2011hr in this paper.

A journal of spectroscopic observation of SN 2011hr is given in Table 5. A total of 11 low-resolution spectra were obtained with the LJT, the Yunnan Faint Object Spectrograph and Camera (YFOSC; Zhang et al. 2014), the Xing-Long 2.16 m telescope (hereafter XLT), and the Beijing Faint Object Spectrograph and Camera (BFOSC). During our spectral observations, the typical FWHM was about $1\buildrel{\prime\prime}\over{.} 5$ at Lijiang Observatory and about $2\buildrel{\prime\prime}\over{.} 5$ at Xinglong Observatory. All spectra were reduced using standard IRAF routines. Flux calibration was done using spectrophotometric flux standard stars observed at a similar airmass on the same night. The spectra were further corrected for the atmospheric absorption and telluric lines at the site. Synthetic photometry computed using Bessell (1992) passbands was introduced to check the spectroscopic flux calibration, while the spectral fluxes were adjusted to match the contemporaneous photometry. Figure 4 shows the complete spectral evolution of SN 2011hr.

The spectra of SN 2011hr are described in more detail and compared to those of SN 1991T, SN 1999aa, SN 2005cf, SN 2007if, and SN 2009dc at different epochs in this section; see Figures 5, 6, and 7. All of these spectra have been corrected for redshift and reddening. The line identifications labeled in these figures are based on the modeling results for SN 1991T (Mazzali et al. 1995). The spectra of SN 2011hr have been corrected for the contamination of host-galaxy emission lines by using the spectrum taken at the site of SN 2011hr (with the LJT and YFOSC) at ∼500 days after maximum light.

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3.2.1. The Early Phase

Figure 5 displays the spectra at t < −7 days. At this phase, the spectra usually carry the signature of the ejecta materials in the outermost layers and show mainly lines of IMEs for normal SNe Ia. The spectra of SN 2011hr are rather similar to those of 91T-like events, which are characterized by a blue continuum and prominent Fe iii/Fe ii lines. Two main absorption features in SN 2011hr and SN 1991T are multiplets of Fe iii or Fe ii lines at 4404 and 5129 Å. By contrast, lines from IMEs (e.g., Si ii, S ii, and O i) are very weak, which is a common characteristic of 91T-like SNe Ia. Lines of Si iii are also present in the spectra. This peculiar phenomenon is due to a combination of high photospheric temperature and low abundance of light elements in the ejecta (Mazzali et al. 1995; Sasdelli et al. 2014).

A notable difference between SN 2011hr and SN 1991T is the absorption near 3900 Å at $t\approx -10$ and −8 days. Such a feature could be a blend of Fe iii λ4006 and Ni ii λ4067. The spectrum of SN 1999aa at $t\approx -9$ days shows both strong Fe iii lines and also a strong Ca ii H&K feature, while the absorption of Si ii λ6355 is weaker in this object. Spectral databases of SNe Ia (e.g., Blondin et al. 2012; Silverman et al. 2012) indicate that most SNe show strong Ca ii absorption from very early phases to 4–5 months after explosion. However, as shown in Figure 8, the Ca ii lines in the spectra of SN 2011hr are even weaker than those of SN 1991T at some phases after maximum light.

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At $t\lt -7$ days, the spectrum of SN 2007if is also featureless and dominated by lines of doubly ionized Fe and Si. Ca ii absorptions are also very weak at this phase. Note that the Fe iii lines are weaker in SN 2007if compared to those in SN 2011hr at this phase. In SN 2007if, a weak absorption on the red side of the weak Si ii λ6355 could be due to absorption from C ii λ6580. The spectrum of SN 2009dc at $t\approx -9$ days is characterized by prominent C ii λ6580 absorption, which is comparable in strength to the Si ii λ6355. However, there is no evidence that such a strong C ii feature is present in the early-time spectra of SN 2011hr, which shows differences from superluminous SNe Ia.

Figure 9 compares the Fe iii features of SN 2011hr, SN 1991T, and SN 1999aa. Some Fe lines, identified by modeling performed in Section 4.3, are marked at a velocity of ∼12,000 km s⁻¹. The absorption feature shown in the left panel of the plot is a blend of Fe iii λ4397, λ4421, and λ4432 and is represented as Fe iii (A). The feature shown in the right panel is a multiplet of Fe iii λ5082, λ5129, and λ5158 and is represented as Fe iii (B). For the Fe iii (A) feature, the three SNe Ia show similarities in the line strength, velocity, and shape at $t\approx -13$ days. For the Fe iii (B) feature, SN 2011hr appears weaker than SN 1991T and SN 1999aa on the blue side of the absorption, which is more significant at earlier phases. It is unlikely that this difference is due to the absorption of Fe iii λ5082 alone.

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3.2.2. The Maximum-light Phase

Figure 6 shows the spectra at around maximum light. At $t\approx -4$ days, the Fe ii/Fe iii lines appear shallower and wider in SN 2011hr compared to SN 1991T. At this phase, the S ii features at ∼5300 Å and ∼5450 Å start to emerge in the spectra of SN 2011hr and SN 1991T. These lines are useful to follow the shift of the ionization state of IMEs from doubly to singly ionized species. S ii features in the spectra of SN 2011hr and SN 1991T are weaker than in SN 1999aa, suggesting a relatively lower ionization state for the latter. Moreover, the Fe iii (B) absorption in SN 1999aa may be blended with the Fe ii lines, suggesting a lower ionization. In SN 2011hr, the weak absorption near 6150 Å is likely to be Si ii λ6355, which may indicate a lower ejecta velocity (see also Figure 10). In other SNe Ia, this Si ii feature is stronger at similar phases.

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At $t\;\approx \;0$ days, Si ii λ6355 finally develops in SN 2011hr, but it does not become as strong as normal SNe Ia. The EW of this line is ∼34 Å for SN 2011hr, which is only slightly larger than SN 2007if (i.e., ∼25 Å) and smaller than SN 1991T (i.e., ∼48 Å), SN 1999aa (i.e., ∼56 Å), SN 2005cf (i.e., ∼85 Å), and SN 2009dc (i.e., ∼51 Å) at similar phases. At this phase, the "W"-shaped feature of S ii lines becomes noticeable in SN 2011hr. The presence of the S ii lines indicates that SN 2011hr originated from a thermonuclear runaway. Inspection of Figure 6 reveals that there is no clear signature of O i λ7773 absorption in SN 2011hr and SN 1991T near maximum light. However, this feature becomes obvious in the spectra of other SNe Ia at this phase.

3.2.3. The Postmaximum Phase

The postmaximum spectra of SN 2011hr are compared with those of other SNe Ia in Figure 7. At about 2 weeks after maximum light, the spectrum of SN 2011hr is dominated by lines of iron and sodium, and the Si ii λ6355 absorption is still very weak and the O i λ7773 line is almost undetectable at this phase. SN 2007if exhibits similar features in the comparable-phase spectra, while SN 2009dc shows stronger absorptions of Si ii λ6355 and O i λ7773 but has lower expansion velocities. Moreover, the Ca ii NIR triplets of SN 2011hr, SN 2007if, and SN 2009dc are all weak compared to SN 1991T.

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At $t\;\approx \;+26$ days, the spectra of SN 2011hr and SN 2007if become more similar. For normal SNe Ia at this phase, the absorption of the Ca ii NIR triplet usually evolves to become the strongest feature in the spectra. However, such a line feature is still rather weak in SN 2011hr, SN 2007if, and SN 2009dc. At this phase, SN 1991T and SN 1999aa show absorption of the Ca ii NIR triplet that is as strong as that seen in normal SNe Ia. At 2–3 months later, absorption of the Ca ii NIR triplet grows in strength in SN 2011hr, SN 2007if, and SN 2009dc, but it is still significantly weaker compared to that seen in SN 1991T and SN 1999aa. The postmaximum spectra of SN 2011hr show distinct behavior relative to normal SNe Ia but are overall very similar to those of SN 2007if, including the velocity and strength of different species.

Figure 10 shows the ejecta velocity of SN 2011hr measured via the absorption feature of Fe iii before maximum light and Si ii λ6355 after the peak. The absorption near 4300 and 5000 Å is produced by blends of Fe iii lines, with rest wavelengths marked in Figure 5. A mean wavelength is adopted for each feature in the velocity estimation. The position of the blueshifted absorption minimum was measured using both the Gaussian fit and the direct measurement of the center of the absorption, and the results are averaged. The results for the two groups of Fe iii lines are also averaged in this figure. The first two points of Si ii λ6355 of SN 2011hr are derived from center of the minor absorption around 6200 Å, which are ∼1000 km s⁻¹ lower than the measurement at $t\approx +0$ days. This might suggest that this feature is not due to Si ii λ6355, but it is more likely that the Si ii line grows in strength and velocity owing to recombination and that its optical depth at higher velocities increases with time in spite of decreasing density. The Si ii λ6355 velocity near maximum light is estimated as $v=10.88\;\pm$ 0.15 ×  10³ km s⁻¹ for SN 2011hr, which is closer to that of SN 1991T and SN 1999aa. SN 2007if and SN 2009dc have lower velocities, which suggests that they may have different ejecta structures.

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The velocity gradient of SN 2011hr, derived from absorption of Si ii λ6355 during the period from $t\;\approx \;+0$ to $t\;\approx$ +15 days, is $9\;\pm 10$ km s⁻¹day⁻¹. This is comparable to that of SN 1999aa, SN 1991T, and SN 2007if, which places SN 2011hr in the low-velocity gradient (LVG) category of SNe Ia according to the classification scheme of Benetti (2005). After maximum light, SN 2011hr shows a higher Si ii velocity relative to the comparison SNe Ia, indicating that the inner boundary of the Si shell is located at higher velocities. If the inner layers are dominated by Fe-group elements (Mazzali et al. 2007), this implies that SN 2011hr produced more ⁵⁶Ni than the normal SNe Ia.

Figure 11 displays the quasi-bolometric light curves of SN 2011hr derived from the UBVRI photometry, compared to those of SN 1991T (Sasdelli et al. 2014), SN 1999aa (Jha et al. 2006), SN 2005cf (Wang et al. 2009b), SN 2007if (Scalzo et al. 2010), and SN 2009dc (Taubenberger et al. 2010). Note that the brightness of SN 2011hr is located at the middle of SN 1991T/SN 1999aa and SN 2007if/SN 2009dc. However, the bolometric light curve of SN 2011hr is similar to that of SN 1991T and SN 1999aa in morphology. The superluminous SN 2007if and SN 2009dc show apparently wider light curves. These suggest that SN 2011hr may have a somewhat different explosion mechanism from these superluminous SNe Ia, although it shares some spectroscopic properties with SN 2007if.

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To estimate the ⁵⁶Ni mass synthesized in the explosion of SN 2011hr, we need to calculate its generic bolometric luminosity at maximum light. The UV emission of SN 2011hr was estimated by assuming that it has a similar ratio of UV to B-band flux as the well-sampled 99aa-like event iPTF14bdn (Smitka et al. 2015), while the NIR contribution was extrapolated based on its $J\;\&amp;\;H$-band photometry published by Weyant et al. (2014). The peak "uvoir" bolometric luminosity is thus estimated to be $(2.30\pm 0.90)\times {10}^{43}$ erg s⁻¹. Applying a t² model to the observed R-band light curve yields an explosion time of MJD = 55,869.7 ± 1.0 and a rise time of 19.4 ± 1.0 days in B band, which is close to the estimate derived from the spectral modeling (i.e., ∼20 days in the B band; see discussions in Section 4.1). Considering the UV contribution, the bolometric curve of SN 2011hr reaches its peak at about 1.4 days earlier than in B band; a rise time of 18.0 ± 1.0 days is thus adopted for SN 2011hr in the following analysis. Based on these parameters, we estimate that the ⁵⁶Ni mass synthesized in the explosion of SN 2011hr is M(⁵⁶Ni) = $1.11\pm 0.43\;{M}_{\odot }$ according to the Arnett law (Arnett 1982; Stritzinger & Leibundgut 2005). This value is larger than that obtained for SN 1991T (M(⁵⁶Ni) = 0.82 ${M}_{\odot }$), SN 1999aa (M(⁵⁶Ni) = 0.72 ${M}_{\odot }$), and SN 2005cf (M(⁵⁶Ni) = 0.75 ${M}_{\odot }$). The ⁵⁶Ni masses inferred for SN 2007if and SN 2009dc (with a similar method) are much larger, which are close to 2.0 ${M}_{\odot }$. An accurate determination of the ⁵⁶Ni mass could be also obtained using nebular spectra (Mazzali et al. 2007), but no late-time spectra are available for SN 2011hr.

Our observations indicate that SN 2011hr is an overluminous SN Ia. Both the SC-mass and the Chandrasekhar-mass scenario have been proposed to explain observational features of overluminous SNe Ia. Yoon & Langer (2005) suggested that the WDs may accrete mass from a nondegenerate or another WD companion star and grow in mass to values exceeding the Chandrasekhar-mass limit (which can reach a mass of $\gtrsim 2.0\;{M}_{\odot }$ if the WD is in differential rotation). Thermonuclear explosions of rapidly rotating WDs have been suggested to account for production of superluminous SNe Ia in terms of both burning products and explosion kinematics by Pfannes et al. (2010a, 2010b). Also, they find that a rotating WD that detonates has an ejecta velocity compatible with that of a normal SN Ia. Meanwhile, Pfannes et al. (2010a, 2010b) also showed that a significant amount of IMEs are produced for rotating SC-mass WDs. Inspection of Figure 6 reveals that SN 2011hr has rather weak absorption features of Si ii, Ca ii, and O i, unlike the 91T-like and normal SNe  Ia. These results indicate that the IMEs (especially Ca) are apparently less abundant in SN 2011hr, which seems to be inconsistent with the predictions of rotating SC-mass WDs (see Pfannes et al. 2010a, 2010b).

Alternatively, SN 2011hr may be an energetic explosion of a Chandrasekhar-mass WD. For instance, the Chandrasekhar-mass model with a high kinetic energy in Iwamoto et al. (1999) may be a good candidate for producing overluminous SNe Ia, which will be addressed in Section 4.3. The gravitationally confined detonation (GCD) of near-Chandrasekhar-mass WDs may be an alternative scenario to explain the overluminous SNe Ia. The GCD model has been studied by different groups (e.g., Plewa et al. 2004, 2007; Meakin et al. 2009; Jordan et al. 2012). On one hand, it has been shown that the GCD model may provide explanations for overluminous SN 1991T-like events because it can produce a large mass of ${}^{56}\mathrm{Ni}$ that can even exceed 1.0 ${M}_{\odot }$. On the other hand, GCD models naturally produce chemically mixed compositions and thus are proposed to explain the high-velocity Fe-group elements observed in early-time spectra of some overluminous 91T-like SNe. Unfortunately, to date, no detailed radiative transfer calculations have yet been performed to compare with the observations of overluminous SNe Ia.

Finally, we point out that the absence of C and O lines in the early-time spectra of SN 2011hr suggests that SN 2011hr is unlikely to be the result of the merger of two WDs (i.e., the so-called violent merger model within the double-degenerate scenario).

To set further constraints on the possible progenitor scenario, we modeled the early spectra of SN 2011hr using a well-tested Monte Carlo code that was initially developed by Mazzali & Lucy (1993) and later improved by Lucy (1999) and Mazzali (2000) by including the photon branching. The code assumes a photosphere with a scaled blackbody emission. This approximation is valid when the inner part of the ejecta that encloses most of the radioactive materials is optically thick. To model the spectra, we adopt a technique called "abundance tomography" (Stehle et al. 2005; Mazzali et al. 2008; Tanaka et al. 2011; Ashall et al. 2014; Sasdelli et al. 2014). As shown in previous sections, there are some uncertainties in determinations of the distance and host-galaxy reddening for SN 2011hr. A higher luminosity may require an SC-mass progenitor, e.g., M(⁵⁶Ni) = 1.61 ${M}_{\odot }$ if $E(B-V)\;=\;0.27$ and D = 66 Mpc. We want to investigate whether a Chandrasekhar-mass scenario is still viable for SN 2011hr, or whether it can only be explained with an SC-mass model. For our investigation, we use the density profile of the energetic WDD3 model from Iwamoto et al. (1999). This should be a good choice for SN 2011hr, which shows lines with relatively higher velocities.

We fit the luminosity of SN 2011hr from spectral modeling. This is an independent estimate of the distance and the extinction. We follow the same method as that described in Sasdelli et al. (2014) to study the luminosity of SN 1991T, which is an ideal SN for a comparative study with SN 2011hr. Similarly to SN 1991T, the time at which the recombination from Si iii into Si ii happens can place a tight constraint on the luminosity. For SN 2011hr, this transition happens at a couple of days later than SN 1991T. Figure 12 displays the comparison of the modeled spectra of SN 2011hr at $t\approx -13$ days and −4 days, respectively. The observed and modeled spectra of SN 1991T are also shown as references. The distance adopted for SN 2011hr is D = 60 Mpc (i.e., $m-M\;=\;33.89$). In addition to the Milky Way reddening of $E(B-V)\;=\;0.02$, we use a reddening $E(B-V)\;=\;0.15$ for the host galaxy. A larger reddening is disfavored by the synthetic color from the model spectrum.

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Compared to SN 1991T, the Fe iii features at 4200 and 4900 Å are less pronounced in SN 2011hr. The modeling analysis shows that this can be explained with an ionization effect, as a consequence of the fact that the temperature of SN 2011hr is higher than that of SN 1991T. The Si ii line at 6100 Å first appears at around the B-band maximum light, ∼4 days later than in SN 1991T. Again, this can also be due to an ionization effect caused by the higher luminosity of SN 2011hr. On the other hand, the Si iii λ4450 line is weaker than in SN 1991T despite a larger fraction of Si iii because of a lower Si abundance. Si is the dominant element only within 11,500 and 12,000 km s⁻¹. SN 2011hr has an abundance profile qualitatively similar to SN 1991T, but likely representing a more extreme case (i.e., Figure 13). The interface between the ⁵⁶Ni-dominated interior and the layer dominated by IMEs is thinner in SN 2011hr compared to that seen in SN 1991T. The ⁵⁶Ni fraction exceeds 90% up to velocities as high as ∼11,500 km s⁻¹. This matches the lowest velocities of Si ii measured in the spectra. The layer dominated by Si and other IMEs is also thinner than in SN 1991T, and their total mass is just $0.07\;{M}_{\odot }$, while in SN 1991T the IME mass is $0.18\;{M}_{\odot }$ (Sasdelli et al. 2014). We could recap the properties of SN 2011hr as "more 91T-like than SN 1991T itself."

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The modeling result shows that the luminosity of SN 2011hr is higher than SN 1991T by about 20%. This requires a ⁵⁶Ni mass of about $0.94\ {M}_{\odot }$. The luminosity of SN 2011hr is at the brightest end of SNe Ia, which requires a large amount of ⁵⁶Ni, but this is balanced by a lower mass of IMEs. The model does not require a mass larger than the Chandrasekhar mass, and instead it suggests that a scenario with an efficiently burned Chandrasekhar mass is also possible to produce such an overluminous SN Ia.