SUPERNOVA 2008bk AND ITS RED SUPERGIANT PROGENITOR

We obtained BVRI images of SN 2008bk, at eight epochs late in its evolution: four at the Calar Alto 2.2 m telescope + the CAFOS SiTe (scale 053 pixel⁻¹, field of view 9' × 9'), two at the 2.5 m Nordic Optical Telescope (NOT; Roque de los Muchachos Observatory, La Palma, Spain) + ALFOSC (019 pixel⁻¹, field of view 65 × 65), and two using the SMARTS 1.3 m telescope + ANDICAM at CTIO. These images were processed using standard IRAF¹² procedures for image trimming, bias subtraction, and flat-field corrections. Additionally, we add several relatively early-time epochs at V, with an image obtained at the Las Campanas Observatory (LCO) 2.5 m duPont telescope on 2008 April 13 and six images obtained with the Global Rent-A-Scope (GRAS) 0.32 m and 0.41 m telescopes at epochs spanning the plateau to early on the exponential tail. We have also included BV data, obtained by the CHilean Automatic Supernova sEarch (CHASE; Pignata et al. 2008) with PROMPT 2.

We extracted instrumental photometry for the SN and reference stars from these images, generally, via point-spread function (PSF) fitting using DAOPHOT (Stetson 1987) within IRAF. When the shapes of the stars in images deviated substantially from a "well-behaved" PSF, we relied only on aperture photometry. For this reason, we calibrated the SN and reference star instrumental photometry from all of the images to existing photometry for the star field around the host galaxy. NGC 7793 was observed by Larsen & Richtler (1999) in UBVRI with the Danish 1.54 m telescope + the Danish Faint Object Spectrograph and Camera on 1997 September 6. We obtained these images, posted for public distribution in FITS format, from the NASA/IPAC Extragalactic Database (NED¹³). We extracted instrumental magnitudes from the images using IRAF, first with a 4'' aperture and then with a PSF for each band. Calibration was established using photometry of a number of isolated reference stars through a 20'' aperture, which matches the aperture used to establish the calibration through standard-star observations by Larsen (1999, his Table 1); see Figure 1 and Table 1 for the locations and magnitudes of these stars. We also applied the appropriate extinction corrections (S. S. Larsen 2010, private communication).

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We can compare our BVR photometry with those magnitudes provided in NOMAD;¹⁴ however, the uncertainties in these latter magnitudes are substantial, resulting in large scatter in the comparison: for B, NOMAD − Ours =−0.32 ± 0.20; for V, −0.51 ± 0.15; and for R, −0.39 ± 0.19. A far better comparison can be made at I with the more reliable photometry from the DENIS database (The DENIS Consortium 2005): DENIS − Ours =0.02 ± 0.05 mag. The good agreement in the I magnitudes provides us with some confidence, overall, in the calibration of our photometry.

As many reference stars as possible were generally adopted for the calibration; however, for the shallowest images, we had to use a combination of the magnitudes of star K (the brightest star in Table 1) and the less precise BV photometry from the bright NOMAD stars seen in these images. The resulting photometry of SN 2008bk is given in Table 2. The uncertainties in the SN photometry in all four bands arise from the measurement uncertainties from DAOPHOT, the uncertainties in the absolute calibration given by Larsen (1999), and the uncertainties in transforming the instrumental magnitudes to standard magnitudes, based on the reference stars, all added in quadrature.

The BVRI light curves for SN 2008bk are shown in Figure 2. As we have noted, many of the multi-band points are beyond the plateau phase and on the exponential tail. However, the V photometry at earlier times provides us with adequate leverage on the overall photometric evolution of SN 2008bk, from soon after explosion through the onset of this tail. The lone early-time B − V data point provides us with some leverage on the initial color of the SN.

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For comparison, we also show in Figure 2 the V light curves for both the "normal" SN II-P 1999em (Hamuy et al. 2001; Leonard et al. 2002; Elmhamdi et al. 2003) and the subluminous SN II-P 2005cs in M51 (Pastorello et al. 2009), and, for all bands, the subluminous SN II-P 1999br (Pastorello et al. 2004). We have attempted to match, by eye, the brightnesses of these comparison SNe with SN 2008bk toward the end of the plateau phase at V. Although we have very limited coverage at the end of the plateau, it appears that this phase ended very near JD 2,454,651 (i.e., 2008 July 3), implying that the plateau lasted ∼100 days after discovery. (Additionally, the end of the plateau phase for SN 1999br is not well defined; Pastorello et al. 2004.) The SN 2008bk light curves are shown in Figure 2 relative to that epoch.

In Figure 3, we show the absolute V light curve for SN 2008bk, which results from correcting for the assumed extinction (see Section 4.1) and distance modulus (see Section 4.2) to the SN. We also show for comparison the absolute V light curves for SN 1999em, corrected for the total extinction, A_V = 0.31 mag (e.g., Hamuy et al. 2001), and the Cepheid distance modulus to its host galaxy (Leonard et al. 2003); SN 2005cs, corrected for the extinction from Pastorello et al. (2009) and the distance modulus from Tonry et al. (2001); and SN 1999br (extinction and distance modulus from Pastorello et al. 2004). We estimate that SN 2008bk had an absolute magnitude near maximum brightness during the plateau phase of M⁰_V = −14.8 mag, which is ∼2.1 mag less luminous than SN 1999em. Although the plateau brightness for SN 2008bk is very similar to the M⁰_V = −14.9 mag for the low-luminosity SN II-P 2005cs (Pastorello et al. 2009), SN 2008bk did not decline nearly as rapidly, post-maximum, nor is it nearly as subluminous on the tail as SN 2005cs. One can see from Figure 2 that SN 2008bk exhibits a striking photometric resemblance to SN 1999br at all bands. However, a noticeable offset exists between the absolute brightnesses of SNe 2008bk and 1999br; we comment on this more in Section 5. We will demonstrate in Section 2.2 that SN 2008bk also spectroscopically most closely resembles SN 1999br. We therefore consider SN 2008bk to be a low-luminosity SN II-P, quite similar to SN 1999br.

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The photometric comparison with SN 1999br (assuming the explosion date for SN 1999br is JD 2,451,278; Pastorello et al. 2004) indicates that the explosion epoch for SN 2008bk was ∼JD 2,454,550, or ∼2008 March 24. Monard, therefore, likely discovered the SN ≲  1 day after explosion.

We obtained several spectra of SN 2008bk at late times, using the Blanco 4 m telescope at CTIO with the RC-Spectrograph in 2008 July and using the Calar Alto 2.2 m telescope with the CAFOS SiTe imaging spectrograph in 2008 September. The details of these observations are given in Table 3. The spectra were reduced using standard IRAF routines. The preprocessing of the spectroscopic data (trimming, bias, overscan, and flat-field correction) were the same as for the images (see Section 2.1). The one-dimensional spectra were wavelength calibrated by comparison with arc-lamp spectra obtained during the same night and with the same instrumental configuration, and flux calibrated using spectrophotometric standard stars. The zero point of the wavelength calibration was verified against the bright night-sky emission lines. The standard-star spectra were also used to model and remove the telluric absorption (e.g., Matheson et al. 2000).

The resulting spectra are shown in Figure 4. Since the spectra obtained at CTIO are only spaced in time each by a day, the features in the spectra had varied little in that time interval. Thus, we show only a representative spectrum from July 24. The same is true for the two spectra obtained at Calar Alto in mid-September; we display only the spectrum from September 16. The July 24 spectrum is ∼21 days past the plateau phase, while the September 16 and 30 spectra are during the nebular phase, at ∼75 and ∼89 days past the plateau. In Figure 5, we show the SN 2008bk spectrum from July 24, and also spectra of the normal SN II-P 1999em (Leonard et al. 2002) at 1 day and 29 days past the plateau phase, as well as a spectrum of the subluminous SN II-P 1999br in NGC 4900 (Pastorello et al. 2004) at essentially the end of the plateau. The spectra for SN 1999em were obtained from the SUSPECT SN database.¹⁵ A. Pastorello kindly provided the spectrum from the Padova SN data archive of SN 1999br from 1999 July 20.

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Both the strength and width of the various spectral lines, and the overall continuum shape, for SN 2008bk compare rather poorly with SN 1999em. A far better comparison, overall, can be made with SN 1999br. The relative strength of, for example, the [Ca ii] λλ7291, 7324 feature in the SN 2008bk spectrum, compared with that in the SN 1999br spectrum, again indicates that SN 2008bk is also a low-luminosity SN II-P.

Here we estimate the extinction to the SN. The startlingly good agreement, seen in Figure 2, between the light curves of both SN 2008bk and SN 1999br in all observed bands (the SN 1999br curves have all been uniformly adjusted by −4.6 mag to match, by eye, those of SN 2008bk) implies that the extinction toward SN 2008bk is quite similar to that of SN 1999br. Smartt et al. (2009) assume only the Galactic foreground contribution to the extinction toward SN 1999br: A_V = 0.065 mag. We can then logically infer that the extinction toward SN 2008bk is comparably quite low; we assume A_V = 0.065 mag. Interestingly, the estimate for the Galactic line-of-sight extinction toward the SN is, in fact, A_V = 0.065 mag (Schlegel et al. 1998), which would imply that the extinction in the immediate galactic environment of SN 2008bk is negligible. From a preliminary analysis of the photospheric spectra for SN 2008bk, no sign exists of Na i D absorption due to the host galaxy. Additionally, the average internal extinction in NGC 7793 is generally quite low (A_B = 0.12 mag; Pierce & Tully 1992). The low-extinction value is consistent with the lack of emission at 8.0 μm (normally attributed to emission from polycyclic aromatic hydrocarbons in interstellar dust clouds) detected at the position of SN 2008bk in archival images of NGC 7793 obtained using the InfraRed Array Camera (IRAC) on the Spitzer Space Telescope. It is also consistent with the fact that the SN is within what appears to be a nebular, possibly evacuated, bubble (see Figure 7).

We also require an estimate of the distance modulus to the SN. Puche & Carignan (1988) calculated a mean distance modulus, 27.64  ±  0.19 mag, to NGC 7793 from several distance indicators, including the Tully–Fisher relation. Karachentsev et al. (2003) measured a distance modulus of 27.96 ± 0.24 Mpc (somewhat more distant, but in good agreement with the Puche & Carignan value), using HST images of the host galaxy to estimate the "tip of the red giant branch" (TRGB) brightness to be I = 23.95 ± 0.22 mag. (These HST images, unfortunately, did not cover the SN site; furthermore, we note that Mould & Sakai (2008), using the TRGB calibration of M⁰_I = −4.05 mag by Rizzi et al. (2007), found μ⁰ = 27.78 mag; however, their assumed I-band extinction, A_I = 0.22 mag, is almost certainly too large.)

The distance modulus has been recently determined using Cepheids in the host galaxy by Pietrzyński et al. (2010) to be μ⁰ = 27.68 ± 0.05 mag (random) ±0.08 mag (systematic). Those authors note that their distance modulus also agrees very well with a recent TRGB measurement, μ⁰ = 27.72  ±  0.08 mag, by Jacobs et al. (2009). Hereafter, we adopt the Cepheid distance modulus and, conservatively, assume the (larger) systematic uncertainty in that estimate.

Furthermore, we need to know the metallicity in the SN environment, since we are comparing the progenitor's observed characteristics with estimates from models that are generated assuming a particular metallicity.

We consider the metallicity to be equivalent to the local oxygen abundance. The most accurate estimate of the metallicity ideally would be from the immediate SN environment itself, or failing that, from regions of the host galaxy in the general vicinity of the SN. We show several such H ii regions in Figure 7, which is a continuum-subtracted Hα (+ [N ii]) image of NGC 7793, released as an ancillary data product by the Spitzer SINGS Legacy project¹⁶ (Kennicutt et al. 2003). In the spectroscopic observations of the SN obtained on 2008 September 30 at Calar Alto, light from two H ii regions, "A" and "B," approximately to the south of the SN also fell within the CAFOS slit.

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Pettini & Pagel (2004) calibrate relations between the O abundance and the strong-intensity line indices N2 = log [N ii] λ6584/Hα (see, e.g., Terlevich et al. 1991; Storchi-Bergmann et al. 1994; Denicoló et al. 2002) and O3N2 = log (([O iii] λ5007/Hβ)/([N ii] λ6584/Hα)). These two indices are relatively unaffected by extinction, since they depend on ratios of intensities for two spectral lines essentially contiguous in wavelength. The 1σ uncertainties in the O abundance from these two indices are ±0.18 and ±0.14 dex, respectively (Pettini & Pagel 2004). We measured the intensities for these various emission lines, using standard routines in IRAF, and estimate these line indices for these two H ii regions.

The resulting values of the indices and the computed abundances are given in Table 5. We estimate that our measurement errors lead to uncertainties in the abundances of, conservatively, ±0.05 dex. Additionally, we can consider the measurements for the H ii regions #27 from Bibby & Crowther (2010) and W13 from McCall et al. (1985). These two regions are labeled in Figure 7 and listed in Table 5. We also include in the table the deprojected angular distance of each H ii region from the SN, assuming the values of the host-galaxy inclination and position angle from Bibby & Crowther (2010) and references therein. The linear distances in the table are assuming a distance to the host galaxy of 3.4 Mpc (see Section 4.2).

One can see that the O abundances of these H ii regions are all consistent with an approximate range of 8.4–8.5 dex. The region nearest to (∼200 pc from) the SN, in particular, has 12 + log(O/H) = 8.45. Assuming the solar photospheric abundance is 12 + log(O/H) =8.66 ± 0.05 (Asplund et al. 2004), we can infer that the metallicity in the SN environment is ≈0.6 solar. The mean O abundance of H ii regions in the LMC is 12 + log(O/H) =8.37 ± 0.22 (Russell & Dopita 1990) or ∼0.5 solar. Therefore, the metallicity at the SN site is most likely not solar, but also is likely not quite as low as the mean LMC nebular metallicity. However, with the level of uncertainties in the Pettini & Pagel (2004) calibration relations, in our measurements, and in the assumed solar and LMC O abundances, we analyze the progenitor photometry considering a range of metallicities. We will show that the inferred intrinsic properties for the progenitor, nonetheless, are most consistent with subsolar metallicity in the SN environment.

We have assumed a relatively low extinction toward SN 2008bk, based on the comparison with SN 1999br (Section 2.1). We further assume that this extinction (Section 4.1) is also appropriate to apply to the progenitor star. From the Gemini optical data, this star, therefore, had an absolute magnitude M⁰_V = −4.94 and a dereddened color (V − I)₀ ≈ 2.19 mag, which imply that the progenitor was a lower-luminosity (class Ib), early M-type RSG (e.g., Humphreys & McElroy 1984).

From the observed optical and near-IR photometry in Table 4, we show the SED of the star in Figure 8. For comparison we show synthetic SEDs, generated using SYNPHOT applied to the MARCS¹⁷ model stellar atmospheres (Gustafsson et al. 2008) for RSGs with effective temperature T_eff = 3600 K and surface gravity log g = 0.0, assuming spherical geometry and subsolar metallicity ([M/H] = −0.25, where [M/H] denotes the ratio of the general metal abundance to H, relative to the Sun). We also show the models at solar metallicity ([M/H] = 0) for this temperature, and one can see little difference with the subsolar models. The MARCS models are for stars with initial masses 5 and 15 M_☉ (we will show that the initial mass of the SN 2008bk progenitor was between these two values) and have microturbulence velocities spanning from 1 to 5 km s⁻¹. The models were all reddened by the assumed value for the progenitor, following the Cardelli et al. (1989) reddening law, and were normalized to the observed V magnitude. The agreement of all of these models with the observed SED is quite good, to within the uncertainties in the photometry of the progenitor. (However, the models do diverge by ≳ 1σ from the observation at R, and compare less well with the observations at H.) We therefore consider the effective temperature of the star to be T_eff = 3600 K, with a conservative uncertainty of ±50 K.

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This effective temperature corresponds to spectral type M2–M2.5 at LMC metallicity (Levesque et al. 2006, their Table 4) and M3 at solar metallicity (Levesque et al. 2005, their Table 5). The metallicity in the SN 2008bk environment is likely somewhere in between (Section 4.3). From Levesque et al. (2005, their Table 6) for Galactic (solar metallicity) RSGs, the V and K bolometric corrections at T_eff = 3600 K are BC_V = −1.75 and BC_K = 2.84 mag, respectively. At LMC metallicity, the bolometric corrections vary little from the solar values at this T_eff: BC_V = −1.78 and BC_K = 2.84 mag (Levesque et al. 2006). The absolute bolometric magnitude of the star, therefore, from V is M_bol = −6.70 ± 0.12 mag, and from K it is M_bol = −6.67 ± 0.13 mag. The total uncertainties arise from the uncertainties in the measured photometry for the star and in the distance modulus (see Section 4.2), and at V, in the range in BC_V. That these two estimates of M_bol, established from the two different photometric measurements, agree so well to within the uncertainties, instills us with considerable confidence in the star's photometry and in our estimates of the extinction and the star's effective temperature. Assuming M_bol(☉) = 4.74 mag, the bolometric luminosity relative to the Sun is then log (L_bol/L_☉) = 4.57 ± 0.06 from both V and K. The luminosity and effective temperature together indicate that the RSG's radius, at ∼6 months prior to explosion, is R_⋆ = 496 ± 34 R_☉.

The inferred intrinsic properties of the progenitor of SN 2008bk are shown in the HRD in Figure 9. We can also compare the star's locus in the HRD with massive-star evolutionary tracks of various initial masses, and, given the uncertainties mentioned in Section 4.3, we take into consideration tracks at several metallicities. In panel (a) of the figure, we compare to tracks at solar metallicity (Z = 0.02), i.e., the Cambridge STARS tracks from Eldridge & Tout (2004) and the Geneva tracks from Hirschi et al. (2004), which include either stellar equatorial rotation, at v_ini = 300 km s⁻¹, or no rotation. One can see that these tracks would imply that the initial mass of the progenitor is in the range of ∼10–12 M_☉. However, these tracks all terminate at cooler effective temperatures and higher luminosities (and larger stellar radii) than is the case for the progenitor. In total, the solar metallicity tracks compare rather poorly with the progenitor's inferred properties, and we consider it unlikely that the larger initial masses implied by these tracks apply to the SN 2008bk progenitor.

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In Figure 9, panel (b), we show a comparison with the STARS tracks at Z = 0.01 (i.e., at Z/Z_☉ = 0.5; the Geneva tracks have not been published at subsolar metallicity in this mass range). The 8 and 8.5 M_☉ model tracks both terminate with T_eff = 3567 K, and with log (L_bol/L_☉) = 4.59 and 4.63 (respectively) and R_⋆ = 514 and 541 R_☉ (respectively), which are essentially consistent, to within the uncertainties, with those properties of the progenitor. Note that the 9 M_☉ model terminates at a luminosity that is higher than the range we have inferred for the progenitor's luminosity. Note also that the 7.5 M_☉ track terminates at a much cooler temperature and much higher luminosity, and therefore we can discount it entirely. In panel (c), we compare with the STARS models for Z = 0.008 (i.e., Z/Z_☉ = 0.4), although it is less likely that the metallicity in the SN environment is quite this low (Section 4.3). The 8 and 8.5 M_☉ tracks terminate with T_eff = 3615 and 3622 K, log (L_bol/L_☉) = 4.60 and 4.63, and R_⋆ = 508 and 527 R_☉ (respectively), which again agree, to within the uncertainties, with the star's locus in the HRD (the exception being the 7.5 M_☉ track, which terminates at a stage too cool and too luminous than what is observed, and again, we can discount it). Much better agreement exists between the star's properties and the subsolar metallicity tracks, which, all told, imply that the star's initial mass was ∼8–8.5 M_☉. These stellar evolutionary models all have lost ∼0.3 M_☉ of mass prior to reaching their termini.

We can make a direct comparison of our results for the SN 2008bk progenitor with those of Mattila et al. (2008). One can see from Figure 10 that all of our magnitude measurements for the star are ≳ 1σ brighter than those measured by Mattila et al. (2008), particularly their measurement at I and their upper limit at V (which is substantially fainter than our actual detection in this band). We cannot provide an explanation for this difference. However, we feel confident in the veracity and self-consistency of our photometry, based on comparison with pre-existing photometry of stars in the SN field (Section 2.1), and on the relatively low dispersions in the transformation of g'r'i' photometry to VRI from the Gemini images and of the near-IR instrumental photometry to 2MASS magnitudes from the VLT images (Section 3). Additionally, the Elias et al. (1985) RSG intrinsic colors, specifically (V − K)₀, are systematically bluer, for a given T_eff and spectral type, than those found by Levesque et al. (2006). The net effect, as seen in Figure 10, is that higher extinction and reddening are required to allow for a comparison (and not a particularly good one) of the model SED for an M4I supergiant from Elias et al. (1985) with the photometry from Mattila et al. (2008). Simply for the sake of argument, we also show in the figure the SED for an RSG from the MARCS stellar atmosphere models with T_eff = 3500 K (which Mattila et al. assume to be the equivalent of an M4I star at LMC metallicity), adopting our extinction to the SN. This model actually provides a better comparison with the Mattila et al. (2008) photometry than do the Elias et al. (1985) intrinsic colors, and this not only would imply that the effective temperature is cooler than what we have found but does so in agreement with a far lower value for the extinction than what Mattila et al. (2008) had assumed. The implied cooler temperature is driven primarily by the significantly fainter I-band magnitude and upper limit to the V brightness found by Mattila et al. (2008).

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The fainter K-band measurement by Mattila et al. (2008), combined with the implied cooler effective temperature, which corresponds to a larger (positive) BC_K (Levesque et al. 2005, 2006), as well as the lower value for extinction, all lead to a much lower luminosity for the SN progenitor than what we have found to be the case. A comparison of the luminosity and effective temperature with massive-star evolutionary models in an HRD shown in Figure 11 implies that the SN progenitor would have an initial mass well below the threshold mass necessary for core collapse. It is only by virtue of their assumption that A_V ≈ 1.0 mag, which, based on their photometry, results in the star being more luminous than what we find here, that Mattila et al. arrive at its initial mass being M_ini ≈ 8.5 M_☉. As we presented in Section 4.1, we have found no evidence for such a large extinction to the SN.

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Estimating the reddening to the progenitor through comparison with assumed intrinsic properties for RSGs is almost certainly fraught with uncertainties. Mattila et al. (2008) also attempted to estimate the extinction based on the Balmer decrement for an H ii region (W13; McCall et al. 1985), which is 15 from the SN 2008bk site. In general, it is far more accurate to estimate the reddening from the SN light curves and colors, particularly during the plateau phase, where the colors of SNe II-P are remarkably similar (e.g., Bersten & Hamuy 2009). Although our light curves for SN 2008bk are very limited in coverage, we therefore believe that the comparison with the more extensive SN 1999br curves provides a reliable estimate of the extinction to SN 2008bk.

We note that Mattila et al. (2008) assumed the distance modulus from Karachentsev et al. (2003); however, this contributes relatively little to the overall difference between our two studies. Furthermore, our assessments of the metallicity in the SN 2008bk environment differ as well. Mattila et al. (2008) estimated the metallicity, assuming the Pilyugin et al. (2004) metallicity–radial-distance relation for NGC 7793, and concluded that the O abundance was 12 + log(O/H) =8.2 ± 0.1. Bibby & Crowther (2010) also have determined the metallicity gradient in NGC 7793. If we assume the deprojected radial distance, r, of SN 2008bk given by Mattila et al. (2008; 347) and the radial distance at B = 25 mag arcsec⁻², R₂₅ = 465 (Bibby & Crowther 2010, and references therein), then for r/R₂₅ = 0.75, the abundance is a slightly higher 12 + log(O/H) =8.34 ± 0.05. We have shown in Section 4.3 from direct estimation of the O abundance in neighboring H ii regions that 12 + log(O/H) ≈8.4–8.5.