THE HIGHLY ENERGETIC EXPANSION OF SN 2010bh ASSOCIATED WITH GRB 100316D

UBVRI photometry of SN 2010bh was obtained with the FOcal Reducer and low dispersion Spectrograph (FORS2; field of view (FOV) 68 × 68; scale 025 pixel⁻¹; Appenzeller et al. 1998) at the ESO VLT UT1 and with the 0.41 m Panchromatic Robotic Optical Monitoring and Polarimetry Telescopes (PROMPTs) 1 and 5 located at CTIO (FOV 10' × 10', 06 pixel⁻¹; Reichart et al. 2005). The R-band images from the X-shooter Acquisition Camera (FOV 147 × 147; 0173 pixel⁻¹; D'Odorico et al. 2006) were also used to cover the early evolution. The data were reduced with standard techniques using IRAF⁴⁰ tasks. Since the SN exploded in a region with a complex background, a template subtraction method, based on the ISIS package (Alard & Lupton 1998; Alard 2000), was applied to remove contamination from the host-galaxy light. As no pre-explosion observations were available of SN 2010bh, we used images obtained with VLT/FORS2 on September 17 (about 185 days past explosion; see Table 1), assuming that the SN flux contribution was negligible at this epoch (see Section 3). For PROMPT observations, template images were acquired on 2011 February 2, with the exception of the I band at PROMPT5, for which the template image was acquired on 2011 January 26 (see Table 1).

A point-spread-function (PSF) fitting method was applied to measure the SN magnitudes in the difference images. In particular, the PSF was derived from field stars measured on either the template or target image, whichever had the worst seeing. The kernel size was scaled according to the seeing to avoid truncation of the wings. We also performed aperture photometry on the subtracted images, obtaining very similar results. The uncertainties were estimated by means of artificial stars with the same magnitude as the SN: we first placed them close to the SN position (within few pixels) and then in the opposite side of the galaxy, where the background residuals were similar. The two approaches, intended to test for the effect of different background contributions, gave similar results. By observing several photometric standard fields, from Landolt (1992) for the U band and from Stetson (2000) for the BVRI filters, we obtained the color equations for each night and instrument, and used them to transform instrumental magnitudes to the standard photometric system. We calibrated the magnitudes of a local sequence of stars in the SN 2010bh field over four photometric nights (April 3, 5, 8 and 11) and used them to obtain the photometric zero points for the non-photometric nights (Figure 1 and Table 2). Because of the significant color term, we applied a calibration correction (S-correction) to the PROMPTs instrumental SN magnitudes to transform them into a standard photometric system following Pignata et al. (2008). Finally, a K-correction based on the nearly simultaneous spectra was applied to the observed BVRI magnitudes. For the U-band magnitudes, the signal-to-noise ratio (S/N) was too low to measure a reliable K-correction from the spectra. UBVRI magnitudes of the SN are reported in Table 3 and plotted in Figure 2. We computed upper limit magnitudes (Table 3 and Figure 2) placing an artificial star at the SN position on the background-subtracted images and decreasing its magnitude down to the point of detectability over the background level. At template images epochs, limiting magnitudes were measured directly over the host-galaxy level, reported in Table 3 but not in Figure 2 because they do not set tight limits to the late-phase decline.

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We followed the spectroscopic evolution of SN 2010bh with VLT/X-shooter (12 epochs) and VLT/FORS2 (8 epochs), as reported in Table 4. When possible, the spectra were acquired with the slit positioned along the north–south direction to minimize the host-galaxy contamination. For both instruments, the effects of atmospheric dispersion (Filippenko 1982) at high airmass have been reduced by using an atmospheric dispersion corrector. Simultaneous UV, VIS, and NIR spectra (∼3000–24800 Å) were taken with X-shooter using slit widths of 10, 09, and 09 for each arm, respectively (D'Odorico et al. 2006). We used a nodding throw along the slit (nodding lengths of 2''  and 4'') to obtain better sky subtraction. The data were reduced using version 0.9.4 of the ESO X-shooter pipeline (Goldoni et al. 2006) with the calibration frames (biases, darks, arc lamps, and flat fields) taken during daytime. After reducing the data using more advanced versions of the software, no relevant changes were found. With FORS2, we used the 300V grism (3300–9000 Å) and a slit width of 1''.

Both X-shooter and FORS2 spectra were extracted using standard IRAF tasks. Spectrophotometric and telluric standard-star exposures taken on the same night as the SN 2010bh observations were used to flux-calibrate the extracted spectra and to remove telluric absorption features. We checked the absolute flux calibration of the spectra by using the nearly simultaneous R-band magnitudes. Figure 5 shows the spectral sequence after correcting for both Galactic and host-galaxy reddening; both the wavelength scale and epochs are reported in the host-galaxy rest frame (see Sections 3.1 and 3.3). The most prominent emission lines of the host galaxy have been removed. Figure 6 is a zoom-in of the spectral sequence in the optical range. The three spectra taken in the nebular phase (2010 September 28 to October 1; see Table 4) have been combined to improve the S/N. The co-added spectrum is shown in Figure 9 (see Section 3.4).

SN 2010bh exploded at $\alpha = 07^{\rm h}10^{\rm m}30\mbox{$.\!\!^{\mathrm s}$}53$ and δ = −56°15'1978 (J2000; Starling et al. 2011) in a bright anonymous galaxy. We measured the host-galaxy redshift by calculating the average shift of the central wavelengths of its strongest emission lines ([O ii] λ3727, Ne iii λ3869, [O iii] λλ4959, 5007, H i Balmer lines, He i λ5876, [O i] λ6300, [N ii] λ6584, and [Si ii] λλ6716, 6731) in each of the 12 X-shooter spectra and correcting it for the radial component of Earth's heliocentric motion. The weighted mean of the resulting heliocentric redshifts is z = 0.0592 ± 0.0001. The high precision of the redshift estimate was possible thanks to the accuracy of the wavelength solution over the whole wavelength range of the X-shooter spectra (2 km s⁻¹ for the UV and VIS arms). This value is in good agreement with the values presented in previous works (z ≈ 0.059, Vergani et al. 2010; z = 0.0591 ± 0.0001, Starling et al. 2011; z = 0.0593, Chornock et al. 2010a). For a concordance cosmology (Hubble constant H₀ = 73   km s⁻¹ Mpc⁻¹, Ω_Λ = 0.73, and Ω_m = 0.27), we obtained a luminosity distance of about 254 Mpc (i.e., distance modulus μ = 37.02 mag).

We estimated the host-galaxy extinction by measuring the total equivalent width (EW) of the interstellar Na i D absorption doublet (λλ5890.0, 5895.9) with the assumption of a gas-to-dust ratio similar to the average ratio in our Galaxy. Measurements were performed on a spectrum obtained combining the almost featureless early-epoch X-shooter spectra (phases 2.4 days, 3.3 days, and 4.2 days, see Table 4). We found EW(λ5890.0)_host = 0.59 ± 0.05 Å and EW(λ5895.9)_host = 0.30 ± 0.02 Å, giving a total EW(Na i D)_host = 0.89 ± 0.07 Å (Figure 3). Applying the relation by Turatto et al. (2003), $E(B-V)= 0.16 \times {\rm EW({\rm Na}\,{\mathsc i}\,D)}$, we obtained E(B − V)_host = 0.14 ± 0.01 mag, which is the value we adopt throughout this work. For the Milky Way extinction, we measured EW(λ5890.0)_MW = 0.40 ± 0.10 Å, while the second doublet component was not detectable (Figure 3). Assuming a flux ratio 2:1 between the two absorption lines, we obtained a total EW(Na i D)_MW = 0.60 ± 0.15 Å, implying E(B − V)_MW = 0.10 ± 0.03 mag. This value is in agreement with that found by Schlegel et al. (1998), E(B − V)_MW = 0.12 mag. We decided to adopt the latter because of the large uncertainty in our estimate of EW(Na i D)_MW.

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Recently, Poznanski et al. (2011) and Olivares et al. (2010) claimed that Na i D absorption may be a bad proxy for the extinction, especially if one uses low-resolution spectra where the two doublet lines cannot be resolved. Although we have a higher dispersion in the X-shooter spectra that allows us to separate the two components, we checked our result by estimating the reddening inside the host galaxy (along the line of sight) from the Balmer-line intensity ratios of the H ii region coincident with the SN. First, we corrected both X-shooter and FORS2 spectra for the Milky Way extinction, then, assuming Case B recombination (T = 10⁴ K; Osterbrock 1989), we measured the Hα/Hβ ratios from each spectrum. We obtained an average value of E(B − V)_host = 0.18 ± 0.06 mag, in agreement with that used in this work (E(B − V)_host = 0.14 mag).

An independent and consistent estimate of the reddening has been given by Cano et al. (2011b), who found a host-galaxy color excess E(B − V)_host = 0.18 ± 0.08 mag comparing the SN 2010bh colors with those of the Type Ibc SN sample studied by Drout et al. (2011). A higher value for the host-galaxy reddening (E(B − V)_host = 0.39 ± 0.03 mag) has been found by Olivares et al. (2012), by fitting a broadband spectral energy distribution (SED) constructed using GROND and Swift/XRT data. While Cano et al. (2011b) and Olivares et al. (2012) have estimated E(B − V)_host from indirect methods (statistics of Type Ic SNe and SED modeling, respectively), our procedure is based on a direct estimate of the dust amount in the line of sight of the SN from the optical spectra, the only necessary underlying assumption being that the dust-to-gas ratio is constant and equal to the Galactic one.

We also used the 12 X-shooter spectra to estimate the metallicity of the bright region underlying SN 2010bh. We measured both the N2 and O3N2 diagnostic ratios (Pettini et al. 2004), obtaining an average oxygen abundance 12 + log(O/H) = 8.20 ± 0.24, where the error is dominated by the uncertainties associated with the adopted linear relationships. The values of ∼8.2 reported by Chornock et al. (2010a) at the SN location, which is based on a spectrum at +3.3 days after the explosion, and 8.2 ± 0.1 by Levesque et al. (2011), which is based on a spectrum at +52 days, are in excellent agreement with our estimate. From the spectrum of the H ii region located close to the SN, Starling et al. (2011) found an oxygen abundance of 8.23 ± 0.15.

Figure 2 illustrates the SN 2010bh light curves. Our R-band light curve traces well the early evolutionary stages; the SN reaches maximum light (M_R ≈ −18.5 mag) at 8.0 ± 1.0 rest-frame days past the explosion, confirming the rise time independently found by Cano et al. (2011b) and Olivares et al. (2012). This is the steepest rise to maximum brightness ever found among both SNe associated with GRBs and broad-lined (BL) SNe for which explosion dates have been well constrained (e.g., SN 2002ap: R_max at 12 days; Mazzali et al. 2007b; Foley et al. 2003; SN 2003jd: R_max at ∼16 days; Valenti et al. 2008a; SN 2005nc: R_max at ∼12 days; Della Valle et al. 2006).

A decline of 0.056 ± 0.015 mag day⁻¹ is measured between 0 and 15 days after R-band maximum. Good sampling of the post-maximum phases was also obtained in the UBVI bands (Figure 2). In Figure 4, we compare the R-band light curve of SN 2010bh with those of two previous well-sampled GRB–SNe: SN 1998bw (Galama et al. 1998; Patat et al. 2001) and SN 2006aj (Sollerman et al. 2006; Pian et al. 2006; Ferrero et al. 2006). The light curve of a more typical Type Ic SN (SN 1994I; Richmond et al. 1996) is also shown.

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After maximum brightness, SN 2010bh and SN 1998bw have a similar behavior, but the decay rate of SN 2010bh between the last two R-band points corresponds to ∼0.03 mag day⁻¹ in the rest frame, to be compared with that of SN 1998bw (0.013 mag day⁻¹). Using the decline rates found by Patat et al. (2001) for SN 1998bw, we estimate the magnitudes of SN 2010bh at the epoch when the VLT subtraction images were acquired (+166.5 rest-frame days from maximum; see Table 1): V ≈ 25.0, R ≈ 23.8, and I ≈ 23.6 mag. Considering this as an upper limit, if it was indeed the flux level of SN 2010bh, it would cause an oversubtraction and an underestimate of the SN fluxes in the V, R, and I bands by less than 0.03 mag around maximum and 0.15 mag in the latest epochs. For each epoch, the corresponding inferred possible contamination by a residual SN flux has been included in the error estimate (Table 3).

SN 2010bh is less luminous than the other two GRB–SNe (Figure 4), which suggests a smaller amount of ejected ⁵⁶Ni mass. Moreover, since the width of a light curve scales with the ratio between the total ejected mass M_ej and the total explosion kinetic energy E_k (Arnett 1982, 1996), the fast evolution of SN 2010bh likely reveals a relatively highly energetic explosion and/or a small M_ej. On the other hand, a highly asymmetric explosion may also result in a faster expansion in the polar direction, leading to a short diffusion time and a fast rise time (Maeda et al. 2006).

We note that our R-band photometry (neither corrected for Galactic or host extinction) at 0.5 days is ∼1 mag and ∼0.6 mag fainter than those of Cano et al. (2011b) and Olivares et al. (2012), respectively. This implies that we observe in our data the smooth rise in flux typical of an SN, and no evidence of the extra early component that they interpret as shock breakout. While we processed all raw data in a homogeneous way and consider this first flux point and its uncertainty formally correct, we caution that at these low-flux levels the X-Shooter acquisition camera imaging data may depend very critically on the assumed background.

The spectral sequence of SN 2010bh (Figures 5 and 6) is unique among BL–SNe and HNe for its detailed temporal coverage and extended wavelength range (3000–24800 Å). At early epochs, the SED can be fit with a blackbody spectrum with T_bb ≈ 8500 K. Thereafter, the continuum, shaped by broad bumps and absorptions, becomes redder with time because of expansion and cooling. The two main minima at ∼5500 Å and ∼7500 Å (Figure 6) can be identified with the blueshifted Si ii (λ6355) and Ca ii NIR triplet (gf-weighted line centroid λ8579) absorption lines, respectively. These lines are the most representative of the stratification of the expanding ejecta: their expansion velocities and evolution with time are shown in Figure 7. All velocities have been determined by fitting a Gaussian profile to the absorption features in the rest-frame spectra and measuring the blueshift of the minimum. The uncertainty that affects each line velocity has been taken to be equal to three times the standard deviation of the measured minimum positions. The velocity of Si ii λ6355 ranges from ∼36,000  km s⁻¹ at about seven days from the explosion to ∼25,500 km s⁻¹ at the last epoch. Ca ii velocities are systematically about 20% higher than those of Si ii. In Figure 7, we note that the velocity of the Si ii λ6355 line in SN 2010bh is higher than in SNe 1998bw and 2006aj, while it is similar to that of SN 2003dh, although with a shallower drop.

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Considering its importance in constraining the nature and the evolutionary state of the progenitor star, we have searched for the spectroscopic signature of helium in our spectra. We observe weak absorption features in the optical and NIR that may be compatible with He i λ5876 and He i 1.083 μm blueshifted by ∼20,000–30,000 km s⁻¹ and ∼28,000–38,000 km s⁻¹, respectively (see Figure 6). The latter is in agreement with the velocities measured for Si ii and Ca ii. However, He i features may be blended with other species, like Na i in the optical and C i or Si i in the NIR (Mazzali & Lucy 1998; Millard et al. 1999; Sauer et al. 2006; Taubenberger et al. 2006). In particular, the contribution of C i cannot be ruled out. Indeed, by comparing the spectra of SN 2010bh to those of SNe 1998bw (Patat et al. 2001) and 2007gr (Valenti et al. 2008b) at similar epochs, we can identify the broad absorption at ∼1.6 μm with the C i λ16,890 line. Such absorption becomes more prominent starting eight days after explosion. A detection of the He i 2.058 μm line, typically not blended with other species, in the spectra of SN 2010bh is not possible, since the line, possibly blueshifted at any velocity up to 35,000 km s⁻¹, would lie in the observed range 1.9–1.95 μm, which is heavily affected by telluric absorptions. Consequently, we cannot confirm the identification of He i λ5876 and He i 1.083 μm. Spectral modeling may help in recognizing the different ions contributing to the spectral line formation. This will be the scope of a future paper.

In Bufano et al. (2010), based on the spectrum taken on March 23, we reported the presence of a significant flux deficit in the range 4500–5500 Å. The flux density also seems low at wavelengths shorter than ∼3500 Å. From the spectral evolution (Figure 5), we can see that such deficits are seen only at this epoch. A careful analysis of the X-shooter spectrum has not identified any instrumental cause of these features. However, their time scale is too short to be explained physically, and therefore we will regard them as spurious.

In Figure 8, we compare the spectra of SN 2010bh with those of SNe 1998bw (Patat et al. 2001) and 2006aj (Mazzali et al. 2006a) at similar phases after explosion. At ∼4 days from the burst, both SNe 2006aj and 2010bh present a featureless spectrum, with the exception in the latter SN of a weak and broad (∼47,000 km s⁻¹) P-Cygni feature due to the Ca ii NIR triplet. This line becomes more prominent at later phases and displays a decreasing velocity (see also Figure 7). The Ca ii triplet velocity remains significantly higher than in SN 2006aj, for which Mazzali et al. (2006a) measured ∼25,000 km s⁻¹ roughly constant with time. In SN 1998bw spectra, Patat et al. (2001) found that the main contribution to the absorptions at ∼7000 Å was given by O i (Figure 8), which is not obvious in our spectra of SN 2010bh. Absorptions at ∼3500 Å and ∼4500 Å in SN 2010bh spectra are likely due to Fe ii and Ti ii, as found for SN 2006aj through spectral modeling (Mazzali et al. 2006a).

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In the upper panel of Figure 9, we show the FORS2 nebular spectrum (∼186 days after explosion in the rest frame). At this time, no significant continuum flux contribution from the supernova photosphere is expected. Therefore, since the SN exploded on a bright region of the host galaxy, we fit the spectral continuum with a polynomial function to obtain and subtract the background flux. The final continuum-subtracted nebular spectrum in the range 5500–7000 Å is plotted in the lower left panel of Figure 9. It shows the [O i] narrow emission lines at 6300 Å and 6363 Å from the underlying galaxy region, and a broad but faint component, which, when fitted with a Gaussian function, peaks at 6340 Å with a total flux of 1.3 × 10⁻¹⁶ erg cm⁻² s⁻¹.

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From the comparison of SN 2010bh with SN 1998bw and SN 2006aj at similar rest-frame phases after the burst (214 and 206 days, respectively; Patat et al. 2001; Mazzali et al. 2007a; the lower right panel in Figure 9), we find that the [O i] bump is very weak in SN 2010bh. The signal in the continuum-subtracted spectrum is too low to guarantee a secure measurement of the [O i] abundance and to perform spectral modeling. However, taking into account the lack of strong evidence of O i lines in SN 2010bh spectra at early epochs, this could indicate a very small amount of ejected oxygen, and, consequently, a less massive progenitor than for SNe 1998bw and 2006aj. On the other hand, it could also be explained as a lower nebular flux, providing an indirect additional support for the M_Ni, M_ej, and E_k values we found and discuss in the next section (see also Table 5). Indeed, considering that the energy input scales roughly as M_Ni × (τ_γ + 0.035), where τ_γ is the optical depth to radioactive gamma rays (τ_γ ≈ 10³ M²_ej E⁻¹_k t⁻²: see, e.g., Maeda et al. 2003) and 0.035 is the positron contribution, we obtain a late-time flux in SN 2010bh which is about a factor of ∼7 and a factor of ∼2.5 smaller than that in SN 1998bw and SN 2006aj, respectively (for the same distance and reddening).

Since photometry in the individual bands is affected by possible spectral lines and their time evolution, it is important to construct a bolometric light curve to estimate reliably the SN physical parameters. As a first approximation, we obtained a quasi-bolometric BVRI light curve using FORS2 photometry and the synthetic BVRI magnitudes obtained from X-shooter spectra. To this aim, BVRI magnitudes were first corrected for extinction and converted to flux density at the effective wavelength of the Johnson–Cousins filters. The SED was then integrated over the entire wavelength range and, finally, the integrated flux was converted into luminosity using the adopted distance (Section 3.1). The error bars of the bolometric luminosities obtained using X-shooter spectra are equal to the typical uncertainty of 10% that affects spectra flux calibration.

In Figure 10, the pseudo-bolometric luminosity of SN 2010bh is compared to those of the GRB–SNe 1998bw and 2006aj. It displays an evolution similar to that of SN 2006aj, although with a fainter peak by about 0.2 dex (L_{bol, 10bh} ≈ 3 × 10⁴² erg s⁻¹).

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For the bolometric light curve fitting, we used a simple model, that assumes, for the photometric phases, a concentration of the radioactive nickel (⁵⁶Ni) in the core, a homologous expansion of the ejecta, and a spherical symmetry, following the prescriptions of Arnett (1982), and, for the nebular phases, includes the energy contribution from the ⁵⁶Ni−⁵⁶Co−⁵⁶Fe decay (Sutherland & Wheeler 1984; Cappellaro et al. 1997). For a detailed description of the model see Valenti et al. (2008a). The bolometric light curve model suggests a total ejected mass of radioactive ⁵⁶Ni of M_Ni = 0.12 ± 0.02 M_☉. The lack of measurements during the nebular phase prevents us from verifying this value through the radioactive tail.

Although a direct comparison with the quasi-bolometric curves created by Cano et al. (2011b) and Olivares et al. (2012) is not possible because of the difference in the wavelength ranges used to construct them, our M_Ni estimate is in good agreement with that of Cano et al. (2011b) who found a ⁵⁶Ni mass of M_Ni = 0.10 ± 0.01 M_☉. Olivares et al. (2012) derived a higher value (M_Ni = 0.21 ± 0.03 M_☉), likely because of the higher extinction correction.