Host Galaxies of Type Ic and Broad-lined Type Ic Supernovae from the Palomar Transient Factory: Implications for Jet Production

Optical spectra were obtained with a variety of telescopes: the 10 m Keck I and Keck II telescopes, the 200-inch (5 m) Hale telescope of Palomar Observatory (P200), and the 8.1 m Gemini-North and Gemini-South telescopes. The spectrographs employed were the Low Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) at Keck I and DEIMOS (Faber et al. 2003) at Keck II, the Double Spectrograph (DBSP; Oke & Gunn 1982) on the P200, and the GMOS-North and GMOS-South (Hook et al. 2003) at Gemini.

The majority of our host galaxy spectra were obtained long after the SNe themselves had faded, including the Keck and P200 runs after 2013 and Gemini runs during 2011. We expect such host spectra to have minimum contamination from the SN emission. Exposure times were chosen to yield S/N > 15 in the Hα line, in order to robustly determine the line flux ratios for metallicity diagnostics. We reobserved if the desired S/N was not reached in an earlier run, but only the spectrum of the best quality for a given host is presented in this paper.

During our major observing runs with Keck I, the spectra of nine hosts were obtained on 2014 November 21 (UT dates are used throughout this paper) and of four hosts on 2015 June 15. We used a 600/4000 grism on the blue side and a 400/8500 grating on the red side, yielding an FWHM resolution of ∼4 Å and ∼7 Å on the blue and red sides (respectively) with a slit width of 1''. The spectrograph and dichroic setup allows continuous wavelength coverage of at least 3500–8000 Å. Given the redshifts of our targets, all of the major nebular emission lines required to derive oxygen abundances, including [O ii] λλ3726, 3729, are within this wavelength range. We used Hg–Ne–Ar comparison lamps for the wavelength calibration. Standard bias frames and lamp flats were obtained for each night. Several standard stars were taken during the nights for the flux calibration.

We placed the slit center at the SN site to catch the immediate environment of the explosion, which can be significantly different from the galaxy nucleus owing to metallicity gradients. LRIS is equipped with an atmospheric dispersion corrector, which allowed us to orient the slit at an angle different from parallactic angle (Filippenko 1982) without any loss from atmospheric dispersion. We chose a position angle (P.A.) that covered both the SN position and the nucleus of the host galaxy along the radial direction. If the SN site is far away from the nucleus with little local host galaxy emission, we can still characterize host properties via the brighter regions closer to the nucleus that fall within our slit. In fact, this only happens for a few cases among the full sample, and they are distinguished by different symbols on the plots in our analysis. A slit width of either 10 or 15 was used, depending on the seeing conditions.

In addition, nine host spectra presented here were acquired at Keck in 2015–2017 (one with DEIMOS and all others with LRIS), with similar instrumental setups to our major Keck runs in 2014 and 2015, so as to deliver a homogeneous data set. Note that the wavelength coverage of the DEIMOS observation starts at 4500 Å; thus, the [O ii] λλ3726, 3729 doublet is outside our coverage for the host galaxy of PTF12hni.

The P200 runs were conducted on 2014 September 30 (for six hosts) and 2015 June 12 and 13 (for 10 hosts), following similar conventions to the Keck runs (e.g., the SN sites were placed at the slit center). We took Fe–Ar comparison-lamp exposures on the blue side and He–Ne–Ar on the red side. The brighter hosts were preferentially observed during the P200 runs.

One host spectrum presented here (of PTF10bip) was obtained with Gemini-South, and the [O ii] λλ3726, 3729 doublet lies outside of the wavelength coverage.

In addition, we gathered data for hosts of five PTF SNe Ic and two PTF SNe Ic-bl that were observed in the year 2012 or earlier when the SN was still present (one of them with P200 and the rest with Keck I; the SN Ic spectra have been published by Fremling et al. 2018). Thus, we can easily locate the SN sites by the bright continuum of SN light in the two-dimensional frames. While the SN spectra were superimposed on the spectra of their host galaxies, we were able to remove them during the analysis since SN spectra have much broader lines than the H ii regions (see Section 3.1.3).

Details about our spectroscopic observations for 46 host galaxies of the PTF SNe in our sample (not including two, PTF12gzk and PTF12hvv, for which we downloaded SDSS spectra; see Section 3.1.4) are shown in Table 1, including both the ones from our recent runs and earlier ones based on data with SN spectra superimposed. Column (1) lists the name of the PTF SN, with the first two digits being the year of SN detection. Column (2) indicates the most up-to-date SN classification performed by us. Column (3) lists the UT date of the observations. The ones based on data with SN spectra superimposed have a UT date in the year 2012 or earlier. Columns (4) and (5) list the telescope and instrument used: Keck I (LRIS), Keck II (DEIMOS), Gemini-S (GMOS-S), or P200 (DBSP). Column (6) lists the spectral resolution on the red and blue sides, respectively. They were measured from the width of night-sky lines, or of comparison-lamp lines if only a few night-sky lines exist on the blue-side spectra. Column (7) lists the position angle of the slit in degrees east of north, Column (8) the airmass, Column (9) the seeing, and Column (10) the slit width. In Column (11) we give the exposure time, with the red and blue sides separated by a slash in case they differ. All but 2 spectra have a minimum wavelength range of 3,300 Å to 8,200 Å. The two spectra that do not, have a range of 4500-9600 Å (DEIMOS) and of 4000-7200 Å (GMOS-S).

We followed standard procedures in IRAF to prepare the Keck/LRIS data obtained from our major runs in 2014 and 2015 for further reduction, including bias subtraction, trimming, and flat-fielding. For the LRIS data obtained before 2013, as well as in 2015–2017 following our major runs, the preprocessing was performed by the automated reduction pipeline in IDL, LPipe (Perley 2019), which delivers similar results to the standard procedures in IRAF. For the P200/DBSP data, we preprocessed with a PyRAF-based reduction pipeline, pyraf-dbsp (Bellm & Sesar 2016).

Subsequent cosmic-ray removal, spectrum extraction, and wavelength calibration were performed in the same manner for all data sets. If at least three exposures were taken on the same target, the imcombine task was performed in IRAF using median-image combine to remove cosmic rays. Otherwise, we ran the IDL routine P-Zap²¹ for cosmic-ray removal, which has been improved for better treatment around bright emission-line regions and absorption features in standard-star spectra. We adopted optimal spectrum extraction from the IRAF task, apall, which by nature applies higher weights to brighter regions in the aperture. The metallicity measurement as a result can be considered as a luminosity-weighted average over the aperture. The final steps of flux calibration, atmospheric band removal, and refinement of wavelength calibration against night-sky lines were performed by our customized IDL routines (Matheson et al. 2001).

In particular, we carefully select apertures for spectrum extraction to best probe the immediate environments of SNe. The spectra should also provide sufficient S/N in major nebular emission lines for metallicity calculation. As a result, we center the aperture at the peak of Hα emission from the nearest star-forming region to the SN site in the slit. However, we caution that we use the term star-forming region here to infer a cluster of regions with significant Hα emission. We cannot spatially resolve individual star-forming regions given the distances of our sources. Given that the progenitors of SNe Ic/Ic-bl are likely to be massive stars with a short lifetime, they generally have not traveled far away from the star-forming regions since birth until explosion. We confirmed by our data that star-forming regions with plenty of Hα emission are usually found very close to the SN site, with an offset usually comparable to the seeing.

Observed long after explosion, most SNe themselves were no longer visible in our data. During our observations, we located the SN site by offsetting from a nearby bright star in the finder chart that was obtained when the SN was still present. In order to locate the SN site along the slit during spectrum extraction, we placed the SN site at the slit center, as well as took standard-star exposures at the slit center. The positional accuracy of the SN site in the slit is comparable to the seeing as determined in this way by matching to the position of standard stars. We therefore chose an aperture size for spectrum extraction to be twice the seeing. Together with the fact that the aperture is centered at the nearest star-forming region, which is usually very nearby, this ensures that the SN site falls within the aperture for most of our targets. We denote such apertures as the SN sites in the subsequent analysis. In the remaining small number of cases (7 out of all 46 host spectra that we extracted), the SN sites have large offsets from the host nucleus or simply are in regions with little Hα emission; for them, the above strategy of aperture placement leaves the SN site outside the aperture. We denote such apertures as "Hii" instead, or "nuc" if that peak of Hα emission also happens to be at the galaxy nucleus. In order to extract spectra with emission lines detected, we compromised by using a region farther away from the SN site in such cases. They are less representative of the immediate environments of the SN explosions and are plotted with different symbols in the figures. However, they constitute only a small fraction (7/48) of all the host spectra that we extracted.

It is also important to appropriately select sky background regions during spectrum extraction. For most projects aimed at the study of SNe themselves as point sources, background regions closely bracketing the SN sites in the slit are chosen. However, the emission from the host galaxy is extended, so that such close backgrounds may still contain star-forming regions from other parts within the same galaxy. Considering that the nebular emission-line ratios vary throughout the galaxy, choosing close background regions would effectively alter the line flux ratios arising from the star-forming region near the SN site from their intrinsic values. We instead chose to place the background regions sufficiently far out to avoid the extended emission from host galaxies, such that they only contain night sky, not galaxy light. Because the background regions are far away from the SN site in extended galaxies, the host spectra extracted at the SN site can be very noisy at the wavelengths of night-sky lines. Such artifacts are masked out during line flux measurements but lead to high uncertainty in the line flux value if that nebular emission line coincides with a night-sky line.

Our final host spectra are released both on the github page of our SNYU group²² and on WISEREP²³ (Yaron & Gal-Yam 2012). Figures 1 and 2 show examples of our spectra for SNe Ic-bl and SNe Ic hosts, respectively, that represent both high-S/N and low-S/N cases, with our spectral fits (which we describe in the next section) superimposed.

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In this paper we focus on the analysis of the nebular emission lines of the host galaxy, since they encode physically important properties of the star-forming regions at the SN sites. However, the presence of stellar absorption features can contaminate the emission components, especially the Balmer lines (e.g., Tremonti et al. 2004). For both the Keck/LRIS and P200/DBSP data, in order to subtract stellar spectra and measure line fluxes from pure nebular emission spectra, we employed the SDSS standard spectral fitting pipeline, platefit (Brinchmann et al. 2004; Tremonti et al. 2004), which can be applied to non-SDSS data. Stellar absorption is usually non-negligible, especially in Hβ and Hγ, even for the spectra extracted at the SN sites that are offset from the galaxy nuclei, as shown in the example host spectra (Figures 1 and 2).

The platefit pipeline models the observed spectrum as a combination of three components: stellar continuum, nebular emission lines, and residual, as also shown in the example plots. The continuum, including all stellar absorption features, is fit to the observed spectrum with the emission-line features masked, using stellar population synthesis templates from Bruzual & Charlot (2003). This approach ensures better constraints on the amounts of stellar absorption than on those derived by only fitting to the wings of absorption features for one Balmer line at a time. The redshift of emission lines is not tied to that of the continuum; it is determined by the fit of a sum of Gaussian functions to the emission-line-only spectrum, assuming that the emission lines have the same velocity offset. Visual inspection confirms that the final fit can very well reproduce the observed spectra, including the wings of the Balmer lines and the global slope of the continuum, with the residuals only being significant at the edges of spectra with unphysical trends, or if there are SN features superimposed on the host spectra (see below).

The full spectra were separated into blue and red sides for both the Keck/LRIS and P200/DBSP data. We stitched the two spectra by applying a scaling factor on the blue side to match the continuum level over the overlapping wavelength regions on both sides. Since the transmission drops off rapidly at the edges of both spectra, small deviations in the wavelength calibration convert to large ones in the flux calibration. Unrealistic rising or falling trends at the edges make it hard to stitch by matching the observed continuum, whereas platefit's residual component characterizes such nonphysical trends. To stitch the blue-side and red-side spectra together, we match the continuum fit as an output component from platefit, free of the artificial rising or falling trends (included in the residual component). We therefore ran platefit twice: the first time to obtain the continuum fits for the two sides in order to then stitch them, and the second time on the stitched spectrum in order to obtain the spectrum with pure nebular emission lines that we use for line flux measurements. The line flux measurements that we present in Appendix A are based on standard single-Gaussian fits to the pure nebular emission-line spectrum and are corrected for Galactic reddening.

To ensure that the automated pipeline, platefit, is working properly on our spectra, we compare the line flux measurements given by platefit with the values we measured by hand via the splot task in IRAF. The platefit method derives uncertainties in line fluxes by the Levenberg–Marquardt least-squares fitting, and we follow Pérez-Montero & Díaz (2003) to derive statistical errors on the splot line fluxes. The uncertainty in the scaling factor applied on the blue-side spectrum for stitching purposes is estimated by the standard deviation of ratios between the continuum from both sides over the whole overlapping wavelength range, being typically ∼10% of the continuum level. We folded this into the variance spectrum to calculate flux uncertainties in both methods. We confirmed that the splot line fluxes generally agree with the platefit ones within the uncertainties, except for the Balmer lines for which only platefit properly corrects stellar absorption.

For the P200 and Keck I data taken in the year 2012 or earlier, the imprints of SN spectra are superimposed on the spectra of host galaxies. We followed a similar approach to analyze these data: we run platefit to measure line fluxes, and it eliminates the SN contribution at the same time. Being much broader than the nebular emission lines, the SN features are treated as residuals by platefit. Various observational setups have been employed to produce these data, but the majority result in spectra with continuous wavelength coverage and spectral resolution comparable to our more recent data, being sufficient to resolve all the nebular emission lines of interest to us for metallicity derivation.

As an exception, very different grating and grism setups were used to observe the host galaxy of PTF12dcp, so a ∼100 Å gap is present between the blue-side and red-side spectra. Instead of matching the continuum level within the overlapping wavelength range, we stitch these spectra based on the Balmer decrement. We predict the Hα flux on the red side from the Hγ and Hβ line fluxes on the blue side. To account for dust extinction, we assume case B recombination (Osterbrock 1989) and the standard Galactic reddening law with R_V = 3.1 (Cardelli et al. 1989). The scaling factor applied to the blue spectrum is thus determined by the ratio between the observed Hα flux and this predicted Hα flux.

For the two spectra obtained at Gemini-South (PTF10bip) and Keck II (PTF12hni), we report the line fluxes measured by the splot task in IRAF. Both of them are star-forming galaxies with little stellar absorption.

We present line-flux measurements for the full sample of 48 hosts of PTF SNe Ic/Ic-bl in Appendix A (including 46 from new observations presented in this work and two from SDSS; see Section 3.1.4). Column (1) lists the name of the PTF SN. Column (2) indicates the type of aperture used for spectrum extraction; values other than "SNsite" indicate that the SN site is outside of the aperture (see above). Column (3) lists the emission-line redshift measured within the aperture. Because the host redshifts reported by the PTF survey are sometimes extracted from the host nucleus, they can be slightly different from the redshifts presented here owing to galaxy rotation. Columns (4)–(11) list flux measurements for all eight of the nebular emission lines needed to derive oxygen abundances, including [O ii] λλ3726, 3729, Hβ λ4861, [O iii] λ4959, [O iii] λ5007, Hα λ6563, [N ii] λ6584, [S ii] λ6717, and [S ii] λ6731 (in units of 10⁻¹⁵ erg s⁻¹ cm⁻², corrected for Galactic reddening and stellar absorption, but not for internal extinction).

To supplement our data set, we searched in the SDSS spectral database for the PTF SN Ic/Ic-bl host galaxies that were not observed by us (or that had bad data quality) and found two of them—the hosts of PTF12gzk (Ic-peculiar) and PTF12hvv (Ic).

For these two hosts, we make use of the emission-line measurements from the MPA-JHU spectroscopic reanalysis of the SDSS DR8, which were also generated by platefit. We include these two hosts in addition to the other hosts observed by us in Appendix A. The [O ii] λλ3726, 3729 doublet is outside the wavelength coverage for PTF12gzk. However, PTF12hvv has a redshift above 0.021, and thus its SDSS spectra cover all of the major emission lines that we need for metallicity derivation, including the [O ii] λλ3726, 3729 lines on the blue end. Note that we queried SDSS for the combined [O ii] λλ3726, 3729 line fluxes from a free fit, because the doublet is similarly unresolved in most of our observations. For PTF12hvv, the SN site is outside of the SDSS fiber area (3'' in diameter), so we list its region type as "nuc" rather than "SNsite" in the table.

All but four of the PTF SN host galaxies are covered by the SDSS imaging survey. We adopt their photometry in the u, g, r, i, z bands from either the NASA-Sloan Atlas (NS-Atlas²⁴ ), if available, or the SDSS catalog otherwise. We ensure that these magnitudes are of good quality in both circumstances.

Although about half of the PTF SN host galaxies are too faint to be included in the SDSS main spectroscopic galaxy sample, all of them are bright enough to be detected by the SDSS imaging survey. We retrieve model magnitudes from the SDSS catalog (DR8), except for the four outside of the SDSS footprint. The DR8 is chosen to be consistent with the other data products that we use, including those from the NS-Atlas and the MPA-JHU spectroscopic reanalysis. We note, however, that the four host galaxies outside of the SDSS DR8 footprint are still outside of the footprint in SDSS DR13. Robust colors are essential for constraining the shapes of the global SEDs. The model magnitudes are chosen because they usually provide the best available colors for extended sources like our low-redshift galaxies, relative to the other magnitudes in the SDSS catalog, such as the Petrosian magnitudes. We correct for Galactic extinction using the far-infrared map from Schlegel et al. (1998) and a standard Galactic reddening law with R_V = 3.1 (Cardelli et al. 1989). We note that the conclusions are unchanged even if we use the new reddening map (Schlafly & Finkbeiner 2011).

While the SDSS photometry pipeline is optimized for small and high surface brightness objects, it suffers from shredding for low-redshift galaxies that are of large angular extent. The shredding happens during deblending, when the light from each "parent" object as an island of contiguous detected pixels is deblended into several different "child" objects. Deblending is necessary to eliminate light contamination from foreground stars and background galaxies, and thus the magnitudes for "parent" objects as intermediate products are usually useless. However, when the deblending process is too aggressive, multiple star-forming sites that are resolved in the disks may be treated as separate child objects by the pipeline. In such cases, the magnitudes for the central child objects usually characterize the redder light from bulges, whereas they miss the bluer light emitted by the star-forming regions at larger radii. If we use the SDSS catalog magnitudes from the central child objects to derive galaxy stellar properties, especially the sSFR that is sensitive to color, we will systematically underestimate sSFR when shredding happens. In the worst-case scenario, the shredding causes inconsistent deblending of light into child objects across bands; for example, the fraction of light deblended into a certain child in the u band may be very different from that deblended into the same child in the r band. This sometimes gives rise to unrealistic colors for each child and thus completely fails the SED fitting.

Visual inspection shows that the SDSS photometry pipeline shredding is significant for eight PTF SN hosts. To alleviate the shredding problem, we utilize the NS-Atlas in a reanalysis of all the galaxies bright enough to be included in the SDSS main galaxy sample (DR8) and with z < 0.05. It creates image mosaics from SDSS and performs photometry in the u, g, r, i, z bands with improved background subtraction. In particular, the NS-Atlas uses a better deblending technique (Blanton et al. 2011) compared to that of the standard SDSS pipeline, with the primary differences being that (a) the NS-Atlas uses constant templates across bands such that the subsequent colors are more robust, and (b) the NS-Atlas requires a much higher significance to deblend a child as a galaxy. These improvements make the NS-Atlas implementation more stable for the large galaxies. When available, the NS-Atlas reanalysis alleviates the shredding problem and avoids the failure in SED fitting that is caused by bad colors.

For the eight hosts that are shredded by the SDSS pipeline, we search in the NS-Atlas and find seven of them (only PTF10aavz is outside of NS-Atlas; see below). For these seven galaxies, we adopt their NS-Atlas Sérsic fluxes, which are more robust compared to the NS-Atlas Petrosian fluxes. In addition, there are 12 PTF SN hosts that are not shredded by the SDSS pipeline but are within the NS-Atlas. We also adopt their NS-Atlas Sérsic fluxes, even though their SDSS pipeline magnitudes are acceptable. For the ones outside of NS-Atlas, we use their model magnitudes from the SDSS pipeline. In fact, the ones outside of NS-Atlas are either faint or distant (z > 0.05), usually with small angular extent, and thus are less likely to be shredded. The host galaxy of PTF10aavz is the only one outside of the NS-Atlas that is shredded by the SDSS pipeline, even though it is a faint, distant, and small galaxy. Usually, the parent objects of nearby bright galaxies with large angular extent include light contamination from foreground stars or background galaxies, so that the magnitudes for such parent objects are useless. Here, however, the parent object of PTF10aavz is deblended into only two children, both of which belong to the host galaxy itself. We know by inspection that the parent object does not include contamination, so that we easily recover its photometry by adopting the model magnitudes for the parent object of the host of PTF10aavz derived by the SDSS standard pipeline.

We also check that the NS-Atlas fluxes are generally consistent with the SDSS pipeline magnitudes that do not suffer from shredding. When compared to the SDSS colors derived from correct pipeline model magnitudes for a big sample of MPA-JHU galaxies, we confirm that the Sérsic fluxes from NS-Atlas result in consistent colors. Therefore, we expect to obtain self-consistent SEDs for the two subsets: 25 of the PTF SN host galaxies with SDSS photometry from the pipeline model magnitudes, and 19 from the NS-Atlas Sérsic fluxes.

For the four PTF SN host galaxies outside of the SDSS footprint, we perform aperture photometry on Pan-STARRS images in the g, r, i, z, y bands, using the Python photometry package photutils. The elliptical aperture is chosen by varying the semimajor axis value with a constant eccentricity so that a sufficient amount of the total galaxy flux is contained. For each fitting, we mask all the pixels of nearby sources that would contaminate the galaxy aperture. We calibrate the galaxy photometry using a star within each field and apply individual zero-points to each aperture to correct the instrumental magnitude of the galaxy. Uncertainties in the measurements are derived by taking a standard deviation of the background measurements.

The far-UV (FUV) luminosity is the most robust SFR indicator for individual galaxies with low total SFRs and low dust attenuation (Lee et al. 2010), such as the PTF SN host galaxies. Thus, we downloaded images of the host galaxies in our sample from GALEX, whose imaging mode surveyed the sky simultaneously in the FUV (effective wavelength of 1516 Å) and the near-UV (NUV; 2267 Å), with a field of view of ∼12 in diameter for each tile (Morrissey et al. 2007). We draw the FUV and NUV magnitudes of the PTF SN host galaxies from the GALEX GR6/7 data release.

The PTF SN host galaxies are usually covered by several tiles generated from multiple satellite visits to the same area of sky, but not combined. Owing to the failure of the FUV detector in 2009, many of these tiles have no FUV coverage. We consider only the tiles with FUV coverage, because the UV continuum at λ < 2000 Å is used as an SFR indicator (e.g., Kennicutt 1998). The GALEX mission includes several survey modes that differ in their exposure time per tile: the All-sky Imaging Survey (AIS; ∼100 s to ∼20.5 mag), the Medium Imaging Survey (MIS; ∼1500 s to ∼23.5 mag), and the Deep Imaging Survey (∼30,000 s to ∼25.0 mag). When adopting the GALEX magnitudes, we give preference to sources extracted from the tile with the longest exposure time. In a few cases, the FUV and NUV objects for the same host are not merged owing to an astrometry error, but we match them by hand. For eight of the PTF SN host galaxies there were no GALEX images since the galaxies were outside of GALEX coverage.

Visual inspection shows that the GALEX pipeline magnitudes of only two PTF SN hosts (PTF12dcp and PTF11jgj) suffer from shredding, because of the poorer imaging resolution (∼45) compared to that of the SDSS, as well as the lower UV source density. We exclude those from our analysis. We further exclude GALEX magnitudes for two other PTF SN hosts from our analysis: PTF10hie (contaminated by a UV-bright star nearby) and PTF11img (not detected in the FUV from an MIS tile).

In summary, GALEX magnitudes with good quality in both the FUV and NUV bands are available for 36 out of all 48 PTF SN host galaxies (23 from AIS and the rest from deeper surveys). We note that the lack of GALEX magnitudes only results in a poorer constraint on the SFR by SED fitting, not a lower limit on the SFR estimate (see Section 5.2).

We select the SDSS galaxies from DR8, which is provided by the MPA-JHU catalog of galaxies, including all the main physical parameters of interest to us: M_* values, SFRs, and emission-line fluxes for the metallicity calculation.

In order to self-consistently compare with our PTF SN Ic/Ic-bl hosts, we retrieve redshifts from the "galSpecInfo" table and line fluxes from the "galSpecLine" table; from the "galSpecExtra" table we get M_* values, SFRs, and metallicities (calculated by Tremonti et al. 2004). The three tables contain the MPA-JHU reanalysis of all the SDSS spectra that are classified as galaxies. Note that for the PTF SN Ic/Ic-bl host galaxies we follow the approach adopted by the MPA-JHU group to obtain line flux measurements (Section 3.1.3) and M_* estimates (Section 5.2). Most importantly, we derive metallicities in four calibrations from the line fluxes for the SDSS galaxies, following what we do for the PTF SN Ic/Ic-bl host galaxies (Section 5.1). Some of the calibrations are very recent and thus are not considered by the previous works that compare the SN Ic-bl and GRB hosts with the SDSS galaxies. For the SFR estimates, the MPA-JHU values that we adopt have been improved from their original values as presented by Brinchmann et al. (2004), so that the out-of-fiber SFRs are derived from SED fitting to u, g, r, i, z photometry. For the population of star-forming galaxies in particular, these MPA-JHU SFRs are consistent with the SFRs that are derived from the SED fitting involving the UV bands (Salim et al. 2016), similar to what we do for the PTF SN Ic/Ic-bl hosts (Section 5.2). Therefore, these M_* values, metallicities, and SFRs for the SDSS galaxies are consistent with those for the PTF SN hosts.

In particular, the SDSS sample serves the purpose of assessing whether the PTF SN Ic/Ic-bl and SN–GRB hosts follow the same mass–metallicity (M–Z) relation as defined by the local galaxies (Section 6.3). Therefore, to select a parent sample of the SDSS galaxies, we adopt the following criteria, which are similar to those of Kewley & Ellison (2008), who derived the M–Z relation for the overall SDSS galaxies.

• 1.  
  For reliable metallicity estimates, S/N > 8 in the strong emission lines ([O ii] λλ3726, 3729, Hβ, [O iii] λ5007, Hα, [N ii] λ6584, [S ii] λ6717, and [S ii] λ6731), following Kewley & Ellison (2008), and S/N > 3 in [O iii] λ4959.
• 2.  
  A lower redshift limit z > 0.04, which corresponds to a flux covering fractions of >20% on average for normal star-forming galaxies observed through the 3'' SDSS fibers (Kewley & Ellison 2008). Such a covering fraction is required for metallicities to begin to approximate global values (Kewley et al. 2005). Plus, the [O ii] λλ3726, 3729 lines are not measured at z < 0.03.
• 3.  
  The M_* value derived from inside the fiber being >20% of that derived from the global photometry, to eliminate the large luminous galaxies that require a higher redshift to satisfy the covering fraction requirement.
• 4.  
  An upper redshift limit z < 0.1, above which the SDSS star-forming sample becomes highly incomplete (Kewley et al. 2006).
• 5.  
  A Baldwin, Phillips, & Terlevich (BPT; Baldwin et al. 1981) class of star-forming galaxy from the "galSpecExtra" table, so that the non-star-forming galaxies and the galaxies containing active galactic nuclei (AGNs) are removed.
• 6.  
  The M_* and metallicity estimates (calculated by Tremonti et al. 2004) are both available from the MPA-JHU catalog.

These selection criteria result in a parent sample of 40,879 SDSS galaxies, with a median redshift z ≈ 0.067. To select a subset that is reasonable for metallicity calculation by our code, pyMCZ (Section 5.1), we randomly sample 500 galaxies from the parent sample. We ensure that the differences are not statistically significant between the distributions of metallicities (calculated by Tremonti et al. 2004), M_* values, and SFRs for this subset of 500 galaxies and those for the parent sample—that is, the subset is representative of the general SDSS population. In support of this, we can reproduce the Kewley & Ellison (2008) M–Z relation with this subset, based on the Tremonti et al. (2004) metallicities. For a comparison to galaxies hosting SNe, however, one can argue that the SDSS galaxies should not be randomly drawn, but be weighted by their SFR (Graham & Fruchter 2013), or by their sSFR. The fact that we do not do this here may explain the small offset between the SN Ic hosts and that of the unweighted SDSS galaxies to an undetermined degree. The goal here is to try to repeat what other works have done regarding the M–Z question; the community is not yet in a position to try to test fundamentally how GRBs select galaxies out of the M–Z–sSFR phase diagram. A comparison sample of SN II hosts from an untargeted transient survey is needed, since those would be tracers of hosts of massive-star explosions (e.g., K. Taggart et al. 2019, in preparation).

The SDSS legacy galaxy redshift survey is highly incomplete below M_* ≈ 10^8.5 M_⊙. While one could correct for incompleteness by applying a volume weight (e.g., Huang et al. 2012b), it is not sufficient for our purpose here because we have applied further selection criteria on emission-line fluxes, etc. The volume weight only corrects for the fact that the faint galaxies below the flux limit are missed, not for the fact that the additional galaxies are missed owing to further selection criteria.

We also note that more recent integral field unit (IFU) based M–Z calibrations have been published, including those based on the CALIFA survey (Sánchez et al. 2017) that mitigate the fiber bias of SDSS. However, since they do not extend to the low galaxy masses in which our PTF SNe Ic-bl and the SN–GRBs are found and are not calculated in the majority of the metallicity scales used in our work, we do not include them here but mention them for completeness.

In contrast to the SDSS, the LVL survey provides a sample of galaxies that is complete in volume within 11 Mpc (Dale et al. 2009), dominated by dwarfs. Thus, the LVL galaxies form a better control sample than the SDSS galaxies (Perley et al. 2016b), for the comparison with the PTF SN host galaxies, especially with the hosts of SNe Ic-bl that have overall low M_* values. Furthermore, the LVL catalog includes photometry from the UV to the near-infrared, yielding M_* estimates from SED fitting. We adopt UV-based SFRs for the LVL sample because they are known to be more reliable than the Hα-based ones owing to stochastic star formation in the regime of low-mass galaxies (Lee et al. 2009).

However, the LVL survey is limited to only the local volume and thus suffers from cosmic variance. Moreover, the most massive galaxies that are rare in the universe are underrepresented in the local volume. Most importantly, the LVL is a photometric survey without spectroscopy; thus, there are no metallicity measurements as part of the initial survey. Metallicity measurements exist in the literature for about 2/3 of the galaxies in that sample, and we use the compilation of Perley et al. (2016b) (see also other references therein). We caution that these metallicities for the LVL galaxies are literature values in a variety of calibrations (typically electron temperature T_e based at low metallicities and various strong-line diagnostics at higher metallicities), whereas for the hosts of PTF SNe and SN–GRBs, we recalculated the metallicities in various calibrations (see Section 5.1). The line fluxes for the LVL galaxies were not published, and thus we cannot run them through pyMCZ, as we do for the SN–GRB hosts. Also, these literature values were derived from spectroscopic observations that covered various fractions of the entire galaxies. Consequently, the average trends as defined by the LVL sample involving metallicities serve the purpose of only a qualitative comparison.

One of the main purposes of this work is to understand the metallicity dependence in the production of different subtypes of the large family of SNe Ic: SNe Ic, SNe Ic-bl, and SN–GRBs. The nebular oxygen abundance is the canonical choice of metallicity indicator for the studies of interstellar medium (ISM), and we use these two terms (metallicity and oxygen abundance) interchangeably in this work. We recalculate the metallicities of the SN–GRB host galaxies and the subset of 500 SDSS galaxies from literature emission-line fluxes by following the same approach we applied to the PTF SN hosts in order to make a self-consistent comparison.

Two main methods of metallicity estimates can be applied to extragalactic studies: the T_e-based method and the strong-line method (see a summary in Bianco et al. 2016, and the references therein). The T_e-based method requires auroral lines such as [O iii] λ4363. However, the auroral lines are generally very weak, and they saturate above solar metallicity (Stasińska 2002). The strong-line methods estimate metallicities from ratios of strong nebular emission lines emitted from H ii regions.

Commonly used line ratios include the following:

$$\begin{eqnarray*}\begin{array}{rcl}{\rm{N}}2{\rm{O}}2 & = & \displaystyle \frac{[{\rm{N}}\,{\rm{II}}]\lambda 6584}{[{\rm{O}}\,{\rm{II}}]\lambda \lambda 3726,3729},\\ {R}_{23} & = & \displaystyle \frac{[{\rm{O}}\,{\rm{II}}]\lambda \lambda 3726,3729+[{\rm{O}}\,{\rm{III}}]\lambda 4959+[{\rm{O}}\,{\rm{III}}]\lambda 5007}{{\rm{H}}\beta },\\ {\rm{O}}3{\rm{N}}2 & = & \displaystyle \frac{[{\rm{O}}\,{\rm{III}}]\lambda 4959+[{\rm{O}}\,{\rm{III}}]\lambda 5007}{{\rm{H}}\beta }\times \displaystyle \frac{{\rm{H}}\alpha }{[{\rm{N}}\,{\rm{II}}]\lambda 6584},\\ {\rm{N}}2 & = & \displaystyle \frac{[{\rm{N}}\,{\rm{II}}]\lambda 6584}{{\rm{H}}\alpha }.\end{array}\end{eqnarray*}$$

Depending on the calibration of the observed emission-line ratios, the strong-line methods can be further categorized into three types: empirical methods that are calibrated on observed T_e-based metallicities, theoretical methods that are calibrated on theoretically simulated line ratios using stellar population and photoionization models, and hybrid methods that are calibrated on a mixture of the above two.

The auroral line that is needed in the T_e-based method is too weak to be detected in the host galaxies of PTF SNe. Thus, we derive the metallicities from strong emission lines using an open-source Python package developed by our group, pyMCZ (Bianco et al. 2016). It is based on the original IDL code of Kewley & Dopita (2002), with updates from Kewley & Ellison (2008), and expanded to include more recent calibrations. Specifically, pyMCZ requires the emission-line fluxes and their uncertainties as inputs for Monte Carlo sampling and calculates the probability distributions (and their median and confidence intervals) of the metallicity in various calibrations. The code also calculates from the Balmer decrement the probability distribution of host galaxy extinction values, E(B − V)_host, and applies internal extinction correction to the emission-line fluxes in the calculation of metallicities. In order to derive the Balmer decrement, Hα and Hβ fluxes are available for all of the host galaxies of PTF SNe and SN–GRBs.

The pyMCZ code samples the synthetic line flux measurements from a Gaussian distribution with standard deviation equal to the measurement uncertainty and centered on the measured flux value. Therefore, Bianco et al. (2016) suggest that the input lines should have an S/N of at least 3, assuring that fewer than ∼1% of the sampled fluxes fall below zero (and are thus invalid). The lines with S/N < 3 may be eliminated by setting their values to NaN in the input files to pyMCZ. The metallicity will be calculated only for the calibrations that use valid, non-NaN line fluxes. By observational design, all of our spectra have S/N > 15 in Hα and S/N > 3 in Hβ, with the only exception being PTF10aavz, which has S/N = 13.5 in Hα at the SN site. However, this does not ensure that the S/N is above 3 for all the other strong lines that we need; the N2 or R₂₃ ratios are exceptionally low in some host spectra.

We may choose not to input the line fluxes with S/N < 3, following the suggestion of Bianco et al. (2016). However, only in a few cases is the low S/N due to noise in the spectra (e.g., the [O iii] λ5007 line of PTF10ciw falls on a night-sky line). For the rest, the low S/N is caused by that line being particularly weak relative to the Balmer lines. For example, the N2 ratio is sensitive to ionization parameter, but to first order, a low N2 ratio indicates a low metallicity. As a result, eliminating the [N ii] line with S/N < 3 generally causes a bias against the most metal-poor systems in the calibrations that require [N ii] flux for calculation. Four of the PTF SN hosts have S/N < 3 in [N ii] λ6584—two of SNe Ic-bl (PTF10qts, PTF10tqv) and the other two of SNe Ic (PTF10hie, PTF11rka)—and all are computed to be metal-poor. Similarly, in the metal-rich regime of log (O/H) + 12 ≳ 8.7, the lower the R₂₃ ratio, the higher the metallicity (e.g., Kewley et al. 2004). Eliminating the [O ii] or [O iii] lines with S/N < 3 generally causes a bias against the most metal-rich systems.

Therefore, we choose to input NaN to pyMCZ only if the lines are outside of the wavelength coverage (including the [O ii] lines for PTF10bip, PTF12gzk, and PTF12hni) or are not detected at all (including both [O iii] lines for PTF10qqd and PTF10yow). They appear as missing values in Appendix A. For the lines detected with S/N < 3, we keep their flux measurements as derived by platefit in the input files to pyMCZ. The pyMCZ code has been modified to properly deal with input lines that have S/N < 3 since it sets invalid negative synthetic line fluxes to zero during sampling, and we check whether a sufficient sample size is retained from 2000 Monte Carlo trials to build the final distribution of the metallicity.

Different metallicity calibrations give systematically different metallicity values, even based on the same line fluxes (e.g., Kewley & Ellison 2008), and there is no consensus on which calibration to use. In order to make sure our results are independent of the chosen metallicity calibration, we present our analysis with four different calibrations that are relatively independent. To decide which calibrations we should present, we examine the intercomparisons between the metallicity values based on our data for all the calibrations implemented by pyMCZ (over 23 of them; for a full definition of the calibrations see Bianco et al. 2016, and references therein).

Although available through pyMCZ, some older calibrations, such as M91 (McGaugh 1991) and Z94 (Zaritsky et al. 1994), are obsolete. We evaluate the performance of the remaining metallicity calibrations in a data-driven fashion, and we do not report metallicities for the calibrations that generally produce measurements with large scatter compared to the results in most of the other calibrations for our 48 PTF SN hosts: that includes M08_O3O2 (Maiolino et al. 2008) and P10_ON and P10_ONS (Pilyugin et al. 2010). In addition, we chose a single calibration for each metallicity diagnostic (set of line ratios). For example, several calibrations are based on N2: D02 (Denicoló et al. 2002), PP04_N2Hα (Pettini & Pagel 2004), KK04_N2Hα (Kobulnicky & Kewley 2004), and M08_N2Hα (Maiolino et al. 2008). We only present the result for one of them, M08_N2Hα. Similarly, where there is more than one calibration based on the same theoretical model, which thus should deliver self-consistent metallicities, we present only one. For example, eight calibrations from Dopita et al. (2013) can be calculated with pyMCZ and our line inputs, but we only present the result for one of them, D13_N2S2_O3S2.

In summary, we choose to present the median values, 16th percentiles, and 84th percentiles of our metallicities, together with E(B − V)_host estimates, in the four calibrations KD02comb, D13_N2S2_O3S2, PP04_O3N2, and M08_N2Hα. Table 3 contains these values for the hosts of PTF SNe Ic/Ic-bl (including the six weird/uncertain SN subtype transients). Table 2 contains the same values for the hosts of SN–GRBs. We calculate them using pyMCZ in the same manner for both data sets to make a fair comparison. Among these four calibrations, KD02comb and D13_N2S2_O3S2 are theoretical, while PP04_O3N2 and M08_N2Hα are hybrid. We note that none of them are empirical, calibrated purely on the T_e-based metallicities. Historically, there have been large systematic offsets between the T_e-based and theoretical calibrations.

Table 2.  SN–GRB Hosts: M_* and SFR from Literature and Our PYMCZ Computations for Reddening and Metallicities

SN–GRB Name	log M*a	SFRa	E(B − V)host	log (O/H) + 12	log (O/H) + 12	log (O/H) + 12	log (O/H) + 12
	(M⊙)	(M⊙ yr−1)	(mag)	D13_N2S2_O3S2	KD02_COMB	PP04_O3N2	M08_N2Hα
GRB 980425/SN 1998bw	8.79 ± 0.30	0.338 ± 0.08	${0.743}_{-0.15}^{+0.143}$	${8.32}_{-0.072}^{+0.066}$	${8.485}_{-0.049}^{+0.068}$	${8.329}_{-0.025}^{+0.024}$	${8.55}_{-0.049}^{+0.046}$
XRF 020903	8.98 ± 0.07	3.445	${0.059}_{-0.035}^{+0.035}$	${8.007}_{-0.111}^{+0.083}$	${8.183}_{-0.045}^{+0.252}$	${8.016}_{-0.019}^{+0.018}$	${8.068}_{-0.058}^{+0.049}$
GRB 030329/SN 2003dh	7.85 ± 0.06	0.143	${0.1}_{-0.019}^{+0.018}$	${7.485}_{-0.051}^{+0.081}$	${8.073}_{-0.018}^{+0.019}$	${7.927}_{-0.091}^{+0.057}$	${7.584}_{-0.21}^{+0.183}$
GRB 031203/SN 2003lw	8.93 ± 0.43	16.484	${0.347}_{-0.098}^{+0.097}$	⋯	${8.647}_{-0.082}^{+0.069}$	${8.066}_{-0.016}^{+0.017}$	${8.282}_{-0.037}^{+0.038}$
GRB/XRF 060218/SN 2006aj	7.89 ± 0.08	0.065	${0.0}_{0.0}^{+0.007}$	${8.357}_{-0.02}^{+0.021}$	${8.125}_{-0.006}^{+0.007}$	${8.125}_{-0.004}^{+0.004}$	${8.194}_{-0.011}^{+0.011}$
GRB 100316D/SN 2010bh	9.04	0.182	${0.199}_{-0.023}^{+0.022}$	${8.393}_{-0.032}^{+0.027}$	${8.46}_{-0.001}^{+0.001}$	${8.259}_{-0.007}^{+0.007}$	${8.491}_{-0.017}^{+0.016}$
GRB120422A/SN 2012bz	9.06 ± 0.04	0.52 ± 0.10	${0.385}_{-0.033}^{+0.035}$	${8.573}_{-0.025}^{+0.026}$	${8.545}_{-0.118}^{+0.057}$	${8.387}_{-0.009}^{+0.008}$	${8.652}_{-0.018}^{+0.018}$
GRB 130427A/SN 2013cq	9.43 ± 0.15	1.17 ± 0.10	${0.195}_{-0.076}^{+0.087}$	${8.343}_{-0.164}^{+0.139}$	${8.63}_{-0.101}^{+0.081}$	${8.407}_{-0.03}^{+0.029}$	${8.694}_{-0.071}^{+0.062}$
GRB 130702A/SN 2013dx	8.01 ± 0.70	0.065	${0.0}_{0.0}^{+0.021}$	⋯	<8.20	⋯	<8.37
GRB 161219B/SN 2016jcab	8.88 ± 1.03	0.25 ± 0.30	${0.0}_{0.0}^{+0.0}$	⋯	${8.115}_{-0.086}^{+0.289}$	${8.305}_{-0.053}^{+0.043}$	${8.402}_{-0.126}^{+0.09}$

Notes.

^aTaken from the GHosts database (consult it for original data references), unless otherwise indicated for GRB 161219B/SN 2016jca, and converted to be consistent with our adopted Chabrier IMF (by adding 0.11 dex to log M_* and by multiplying the SFR by a factor of 1.3; see Section 5.2). ^bFor GRB 161219B/SN 2016jca, the M_* and SFR were taken from Cano et al. (2017a).

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Table 3.  pyMCZ Measurements

PTF Name	SN Type	E(B − V)host	log (O/H) + 12	log (O/H) + 12	log (O/H) + 12	log (O/H) + 12
		(mag)	D13_N2S2_O3S2	KD02_COMB	PP04_O3N2	M08_N2Hα
SN Ic-bl
09sk	Ic-bl	${0.111}_{-0.007}^{+0.007}$	${8.368}_{-0.007}^{+0.006}$	${8.486}_{-0.008}^{+0.009}$	${8.335}_{-0.002}^{+0.002}$	${8.522}_{-0.004}^{+0.004}$
10aavz	Ic-bl	${0.000}_{-0.000}^{+0.000}$	${8.516}_{-0.193}^{+0.151}$	${8.631}_{-0.133}^{+0.078}$	${8.481}_{-0.051}^{+0.044}$	${8.728}_{-0.127}^{+0.095}$
10bzf/SN10ah	Ic-bl	${0.000}_{-0.000}^{+0.000}$	${8.152}_{-0.270}^{+0.188}$	${8.625}_{-0.218}^{+0.146}$	${8.333}_{-0.064}^{+0.052}$	${8.451}_{-0.161}^{+0.117}$
10ciw	Ic-bl	${0.282}_{-0.083}^{+0.092}$	${8.545}_{-0.070}^{+0.073}$	${8.572}_{-0.084}^{+0.074}$	${8.400}_{-0.060}^{+0.096}$	${8.708}_{-0.041}^{+0.037}$
10qts	Ic-bl	${0.000}_{-0.000}^{+0.000}$	${8.108}_{-0.354}^{+0.294}$	${8.033}_{-0.041}^{+0.046}$	${8.081}_{-0.143}^{+0.081}$	${8.089}_{-0.411}^{+0.601}$
10tqv	Ic-bl	${0.007}_{-0.007}^{+0.093}$	${8.118}_{-0.294}^{+0.226}$	${8.168}_{-0.090}^{+0.245}$	${8.268}_{-0.089}^{+0.056}$	${8.312}_{-0.244}^{+0.138}$
10vgv	Ic-bl	${0.070}_{-0.064}^{+0.067}$	${8.852}_{-0.107}^{+0.104}$	${8.811}_{-0.055}^{+0.051}$	${8.399}_{-0.024}^{+0.021}$	${8.677}_{-0.058}^{+0.048}$
10xem	Ic-bl	${0.471}_{-0.006}^{+0.006}$	⋯	${8.075}_{-0.007}^{+0.007}$	${8.082}_{-0.001}^{+0.001}$	${8.118}_{-0.002}^{+0.002}$
11cmh	Ic-bl	${0.000}_{-0.000}^{+0.298}$	${8.654}_{-0.278}^{+0.178}$	${8.524}_{-0.107}^{+0.118}$	${8.550}_{-0.103}^{+0.084}$	${8.737}_{-0.206}^{+0.139}$
11gcj	Ic-bl	${0.000}_{-0.000}^{+0.000}$	${8.257}_{-0.077}^{+0.072}$	${8.229}_{-0.041}^{+0.179}$	${8.273}_{-0.017}^{+0.016}$	${8.444}_{-0.039}^{+0.034}$
11img	Ic-bl	${0.657}_{-0.232}^{+0.267}$	${8.363}_{-0.226}^{+0.176}$	${8.475}_{-0.069}^{+0.073}$	${8.265}_{-0.066}^{+0.051}$	${8.455}_{-0.143}^{+0.102}$
11lbm	Ic-bl	${0.333}_{-0.014}^{+0.015}$	${8.035}_{-0.050}^{+0.049}$	${8.280}_{-0.020}^{+0.019}$	${8.260}_{-0.011}^{+0.010}$	${8.323}_{-0.028}^{+0.026}$
11qcj	Ic-bl	${0.000}_{-0.000}^{+0.000}$	${8.327}_{-0.014}^{+0.014}$	${8.425}_{-0.074}^{+0.043}$	${8.284}_{-0.004}^{+0.003}$	${8.518}_{-0.008}^{+0.008}$
12as	Ic-bl	${0.462}_{-0.017}^{+0.017}$	${8.552}_{-0.020}^{+0.018}$	${8.562}_{-0.013}^{+0.014}$	${8.438}_{-0.005}^{+0.005}$	${8.645}_{-0.012}^{+0.012}$
SN Ic
09iqd	Ic	${0.468}_{-0.049}^{+0.045}$	${8.996}_{-0.047}^{+0.044}$	${8.802}_{-0.054}^{+0.057}$	${8.594}_{-0.013}^{+0.012}$	${8.941}_{-0.038}^{+0.035}$
10bhu	Ic	${0.173}_{-0.083}^{+0.090}$	${8.657}_{-0.037}^{+0.036}$	${8.751}_{-0.068}^{+0.062}$	${8.579}_{-0.020}^{+0.021}$	${8.814}_{-0.026}^{+0.024}$
10fmx	Ic	${0.104}_{-0.104}^{+0.206}$	${8.938}_{-0.114}^{+0.102}$	${8.812}_{-0.137}^{+0.081}$	${8.662}_{-0.060}^{+0.065}$	${8.916}_{-0.083}^{+0.084}$
10hfe	Ic	${0.000}_{-0.000}^{+0.000}$	${8.782}_{-0.011}^{+0.011}$	${8.787}_{-0.020}^{+0.021}$	${8.602}_{-0.005}^{+0.005}$	${8.893}_{-0.009}^{+0.009}$
10hie	Ic	${0.000}_{-0.000}^{+0.045}$	${7.762}_{-0.260}^{+0.227}$	${8.108}_{-0.098}^{+0.125}$	${8.094}_{-0.147}^{+0.088}$	${8.099}_{-0.431}^{+0.591}$
10lbo	Ic	${0.000}_{-0.000}^{+0.058}$	${8.808}_{-0.075}^{+0.072}$	${8.853}_{-0.045}^{+0.036}$	${8.613}_{-0.031}^{+0.031}$	${8.873}_{-0.055}^{+0.056}$
10ood	Ic	${0.210}_{-0.025}^{+0.027}$	${8.510}_{-0.031}^{+0.031}$	${8.541}_{-0.051}^{+0.048}$	${8.304}_{-0.009}^{+0.008}$	${8.528}_{-0.020}^{+0.019}$
10osn	Ic	${0.681}_{-0.071}^{+0.074}$	${9.106}_{-0.027}^{+0.029}$	${8.828}_{-0.162}^{+0.201}$	${8.719}_{-0.025}^{+0.028}$	${9.022}_{-0.027}^{+0.029}$
10qqd	Ic	${1.469}_{-0.146}^{+0.168}$	⋯	${8.818}_{-0.169}^{+0.195}$	⋯	${8.779}_{-0.031}^{+0.027}$
10tqi	Ic	${0.140}_{-0.010}^{+0.010}$	${8.758}_{-0.010}^{+0.010}$	${8.827}_{-0.007}^{+0.008}$	${8.569}_{-0.003}^{+0.003}$	${8.806}_{-0.007}^{+0.007}$
10wal	Ic	${0.120}_{-0.044}^{+0.043}$	${8.772}_{-0.044}^{+0.040}$	${8.884}_{-0.031}^{+0.032}$	${8.656}_{-0.015}^{+0.016}$	${8.849}_{-0.027}^{+0.029}$
10xik	Ic	${0.000}_{-0.000}^{+0.000}$	${8.282}_{-0.154}^{+0.117}$	${8.479}_{-0.359}^{+0.079}$	${8.288}_{-0.034}^{+0.027}$	${8.458}_{-0.082}^{+0.065}$
10yow	Ic	${0.631}_{-0.087}^{+0.097}$	⋯	${9.181}_{-0.061}^{+0.078}$	⋯	${8.909}_{-0.017}^{+0.018}$
10ysd	Ic	${0.222}_{-0.027}^{+0.027}$	${9.209}_{-0.013}^{+0.014}$	${9.136}_{-0.033}^{+0.039}$	${8.875}_{-0.021}^{+0.024}$	${9.378}_{-0.012}^{+0.010}$
10zcn	Ic	${0.411}_{-0.042}^{+0.048}$	${9.115}_{-0.028}^{+0.031}$	${8.986}_{-0.077}^{+0.104}$	${8.851}_{-0.030}^{+0.038}$	${8.950}_{-0.019}^{+0.019}$
11bov/SN11bm	Ic	${0.000}_{-0.000}^{+0.000}$	${8.204}_{-0.031}^{+0.029}$	${8.402}_{-0.140}^{+0.033}$	${8.286}_{-0.008}^{+0.008}$	${8.511}_{-0.016}^{+0.016}$
11hyg/SN11ee	Ic	${0.693}_{-0.040}^{+0.042}$	${9.185}_{-0.018}^{+0.017}$	${9.046}_{-0.039}^{+0.047}$	${8.820}_{-0.018}^{+0.020}$	${9.066}_{-0.016}^{+0.017}$
11ixk	Ic	${0.030}_{-0.030}^{+0.115}$	${8.926}_{-0.043}^{+0.041}$	${8.922}_{-0.087}^{+0.111}$	${8.679}_{-0.027}^{+0.031}$	${9.013}_{-0.038}^{+0.042}$
11jgj	Ic	${0.717}_{-0.086}^{+0.088}$	${9.094}_{-0.030}^{+0.036}$	${8.835}_{-0.095}^{+0.102}$	${8.792}_{-0.039}^{+0.051}$	${8.966}_{-0.016}^{+0.015}$
11klg	Ic	${0.235}_{-0.024}^{+0.022}$	${9.126}_{-0.015}^{+0.015}$	${9.087}_{-0.013}^{+0.013}$	${8.856}_{-0.015}^{+0.014}$	${9.066}_{-0.015}^{+0.017}$
11rka	Ic	${0.090}_{-0.013}^{+0.013}$	${7.726}_{-0.175}^{+0.117}$	${7.977}_{-0.012}^{+0.011}$	${8.018}_{-0.026}^{+0.022}$	${7.856}_{-0.084}^{+0.069}$
12cjy	Ic	${0.124}_{-0.031}^{+0.033}$	${9.145}_{-0.024}^{+0.030}$	${9.055}_{-0.017}^{+0.017}$	${8.919}_{-0.035}^{+0.050}$	${8.984}_{-0.011}^{+0.011}$
12dcp	Ic	${0.300}_{-0.020}^{+0.021}$	${8.807}_{-0.006}^{+0.006}$	${8.669}_{-0.015}^{+0.015}$	${8.497}_{-0.004}^{+0.004}$	${8.782}_{-0.004}^{+0.004}$
12dtf	Ic	${0.485}_{-0.025}^{+0.028}$	${8.481}_{-0.026}^{+0.024}$	${8.384}_{-0.063}^{+0.057}$	${8.281}_{-0.008}^{+0.007}$	${8.501}_{-0.016}^{+0.014}$
12fgw	Ic	${0.604}_{-0.012}^{+0.012}$	${9.031}_{-0.003}^{+0.003}$	${8.861}_{-0.009}^{+0.009}$	${8.688}_{-0.004}^{+0.004}$	${8.903}_{-0.002}^{+0.003}$
12hvv	Ic	${0.017}_{-0.017}^{+0.122}$	${8.735}_{-0.053}^{+0.054}$	${8.759}_{-0.131}^{+0.148}$	${8.627}_{-0.032}^{+0.035}$	${8.870}_{-0.040}^{+0.039}$
12jxd	Ic	${0.495}_{-0.009}^{+0.009}$	${8.985}_{-0.005}^{+0.004}$	${8.912}_{-0.007}^{+0.006}$	${8.701}_{-0.002}^{+0.002}$	${8.971}_{-0.004}^{+0.004}$
12ktu	Ic	${0.354}_{-0.026}^{+0.027}$	${9.201}_{-0.016}^{+0.017}$	${9.099}_{-0.052}^{+0.067}$	${8.874}_{-0.019}^{+0.022}$	${8.974}_{-0.010}^{+0.011}$
Weird/Uncertain SN Subtype
09ps	Ic/Ic-bl	${0.292}_{-0.078}^{+0.083}$	${8.309}_{-0.088}^{+0.073}$	${8.347}_{-0.131}^{+0.116}$	${8.362}_{-0.025}^{+0.026}$	${8.472}_{-0.050}^{+0.042}$
10bip	Ic/Ic-bl	${0.504}_{-0.061}^{+0.065}$	${8.378}_{-0.050}^{+0.042}$	⋯	${8.302}_{-0.013}^{+0.013}$	${8.580}_{-0.027}^{+0.027}$
10gvb	SLSN/Ic-bl	${0.329}_{-0.058}^{+0.061}$	${7.945}_{-0.231}^{+0.191}$	${8.280}_{-0.135}^{+0.129}$	${8.102}_{-0.062}^{+0.045}$	${8.161}_{-0.185}^{+0.118}$
10svt	Ib/c	${0.032}_{-0.020}^{+0.021}$	${8.296}_{-0.079}^{+0.070}$	${8.479}_{-0.061}^{+0.049}$	${8.218}_{-0.016}^{+0.015}$	${8.331}_{-0.042}^{+0.037}$
12gzk	Ic-peculiar	${0.081}_{-0.022}^{+0.022}$	${8.048}_{-0.091}^{+0.072}$	${7.943}_{-0.053}^{+0.046}$	${8.071}_{-0.017}^{+0.015}$	${7.941}_{-0.052}^{+0.046}$
12hni	SLSN/Ic-bl	${0.091}_{-0.024}^{+0.025}$	${8.373}_{-0.024}^{+0.025}$	${8.457}_{-0.007}^{+0.004}$	${8.211}_{-0.006}^{+0.006}$	${8.451}_{-0.013}^{+0.013}$

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In Appendix C, we briefly describe pertinent details of each of the four calibrations we adopt.

There is a long-standing debate about which metallicity calibration should be used, and there are known systematic offsets between the various calibrations (see Kewley & Ellison 2008). Having chosen four calibrations that best fit our needs, we are not generally advocating for the use of these over others. Moreover, it should be noted that the pyMCZ code does not include systematic errors between the calibrations, so the reader should refrain from absolute comparisons of calibrations and especially from comparing galaxies across different calibrations. The metallicity uncertainties presented here are statistical ones and account for the flux uncertainties and calibration uncertainties if provided. The four calibrations are chosen to represent a variety, so as to test whether any trends that we see are calibration dependent. Although the absolute metallicity values vary depending on the calibration used, the relative metallicity trends can be robust and thus should be seen across different calibrations if the analysis is performed self-consistently for the same calibration (Kewley & Ellison 2008).

The BPT diagram was first proposed by Baldwin et al. (1981) to separate the main excitation mechanism of emission-line objects via the line ratios of [O iii] λ5007/Hβ versus [N ii] λ6584/Hα. The bottomleft panel in Figure 4 shows a BPT diagram for the hosts of PTF SNe Ic/Ic-bl and SN–GRBs. The lower solid line in the BPT diagram is an empirical division derived from SDSS galaxies in Kauffmann et al. (2003), and the upper dashed line is a theoretical upper limit for pure starburst models from Kewley et al. (2001). They are usually invoked to distinguish between classical star-forming objects (below the solid line), AGN-powered sources (above the dashed line), and composite objects (in between the two lines).

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The ionization source for all the host galaxies in our PTF SN and SN–GRB samples is star formation rather than AGN activity, except potentially for the host of GRB 031203/SN 2003lw. Thus, the strong-line methods that we adopt for metallicity calculations are valid for almost all of the hosts in our sample; so are the Hα-based SFRs for SN–GRB hosts in particular. However, the AGN contamination may render the metallicity and SFR measurements incorrect for the host of GRB 031203/SN 2003lw. We present our analysis results with and without this object and plot it with a different symbol, in order to assess its impact. See Appendix E for more details on the classification of all host galaxies, especially why we cannot rule out AGN contamination for the host of GRB 031203/SN 2003lw.

The analysis of line flux ratios is a model-independent diagnostic; thus, line-ratio plots are an important diagnostic tool. Before we study what the line ratios imply in terms of the metallicity, ionization, and age conditions, which are all model-dependent quantities, we can make a direct comparison of the line-ratio distribution between our samples to assess statistical differences.

In the bottom left panel of Figure 4, the hosts of PTF SNe Ic are represented by black squares, SNe Ic-bl by blue circles, and SN–GRBs by red diamonds. For the hosts of SNe Ic and SNe Ic-bl, open (not filled) symbols indicate that the SN sites are outside of the apertures for spectral extraction. Among both samples, the open symbols do not systematically deviate from the closed ones; the metallicities of the regions that are less representative of the SN local environments are not significantly different from those that are representative. The hosts of SNe Ic occupy the full range of the sequence, whereas the hosts of SNe Ic-bl and SN–GRBs belong exclusively to the upper left half of the sequence. The difference between the hosts of SNe Ic-bl and SN–GRBs is more subtle. We therefore perform a quantitative comparison between the samples by investigating the two line ratios separately.

In the top and right panels of Figure 4, we respectively compare the empirical cumulative distribution functions (CDFs) of the three samples for these two line ratios. The colored bands denote 1σ flux measurement uncertainties. For each sample, the CDF includes both open and closed symbols from the plot in the bottom left panel. Note that the two SN Ic hosts with no detections in [O iii] λ5007 show up only in the top panel for [N ii] λ6584/Hα. The host of GRB 130702A/SN 2013dx, which has no detection in [O iii] λ5007 and an upper limit in [N ii] λ6584, also shows up only in the top panel: it appears as a value associated with an arrow pointing to the left.

Considering these upper limits, we should describe the CDF of [N ii] λ6584/Hα for SN–GRBs by the Kaplan–Meier estimator, which uniformly distributes the weight of each upper limit among the detections with lower values. In the absence of censored data (lower or upper limits), the Kaplan–Meier estimator reduces to the usual CDF. We use the ASURV package for survival analysis (Lavalley et al. 1992) to calculate the Kaplan–Meier estimator. However, new methods are still needed that combine the virtues of survival analysis and measurement errors (Lavalley et al. 1992). In order to demonstrate how the differences in distributions compare with the typical measurement errors, we choose to plot the usual CDF rather than Kaplan–Meier estimator for SN–GRBs in the top panel by treating the upper limit as uncensored data but indicating it by an arrow.

In the top panel, the overall [N ii] λ6584/Hα ratios for the three samples follow the order of SN–GRB < SN Ic-bl < SN Ic, though this trend has not yet been statistically tested for actual significance. In the right panel, the overall [O iii] λ5007/Hβ ratios for the three samples follow the order of SN Ic < SN Ic-bl < SN–GRB, though the significance of this trend has also not yet been statistically tested. For both line ratios, the differences between the CDFs of SN Ic and SN Ic-bl hosts are much higher than the 1σ measurement errors (colored bands), but those between the CDFs of SN Ic-bl and SN–GRB hosts are less so. For the [N ii] λ6584/Hα ratio in particular, the CDF offset between the hosts of SNe Ic-bl and SN–GRBs can be largely explained by measurement errors.

Thus, in order to assess whether the differences in line-ratio distributions are significant, we perform statistical tests. The tests account for the fact that the CDFs are based on our data, which do not sample the full underlying populations, but the tests do not account for the measurement errors. For each pair of the samples that are adjacent in the sequence of SN Ic, SN Ic-bl, and SN–GRB, we test the null hypothesis that their line ratios are drawn from the same underlying distribution. The ASURV package applies the Logrank test and various generalized Wilcoxon tests on censored data, but the Logrank test can only be used when observations are censored. To be consistent, we report results of the Peto & Peto generalized Wilcoxon test for censored data and apply the Wilcoxon rank sum test with scipy in the absence of censored data. Our conclusion is based on computing the p-value, which is the probability of obtaining an effect at least as extreme as the one observed assuming the truth of the null hypothesis. Throughout this work, we choose a significance level α = 0.05, which indicates a 5% risk of concluding that a difference exists when there is no actual difference (i.e., Type I error). If the p-value we obtain is less than or equal to this significance level, we reject the null hypothesis—that is, we conclude that the difference is statistically significant at the 2σ level.

Between the samples of SN Ic and SN Ic-bl hosts, the p-value of the Wilcoxon rank sum test on the distributions of [N ii] λ6584/Hα ratios is very close to zero and that on the distributions of [O iii] λ5007/Hβ ratios is 0.002 (<0.05).

Now we turn to the important case of comparison between the SN Ic-bl and SN–GRB hosts. If GRB 031203/SN 2003lw with a potential AGN contribution is included in the SN–GRB sample, the p-value of the Peto & Peto generalized Wilcoxon test on the distributions of the [N ii] λ6584/Hα ratio is 0.210 (>0.05), but that of the Wilcoxon rank sum test on the distributions of the [O iii] λ5007/Hβ ratio is 0.022 (<0.05). However, if GRB 031203/SN 2003lw is excluded, the same p-values are 0.26 and 0.08 (both >0.05), respectively, for the [N ii] λ6584/Hα and [O iii] λ5007/Hβ ratios. Owing to the fact that the GRB 031203/SN 2003lw host has a high [O iii] λ5007/Hβ ratio and that the Wilcoxon rank sum test is sensitive to the difference in the tails of the distributions, the null result is reliable for the comparison between the [O iii] λ5007/Hβ ratios of the SN Ic-bl and SN–GRB hosts excluding potential AGNs.

To conclude, we infer from our data that the differences in line-ratio distributions between the populations of SN Ic and SN Ic-bl hosts are statistically significant, but not those between the SN Ic-bl and SN–GRB hosts, especially if the host that may harbor potential AGNs is excluded. We have applied several other hypothesis tests, including the Logrank test and various Generalized Wilcoxon tests on censored data, as well as the K-S test and the A–D test on uncensored data. All of them reach the same conclusion, except for the tests on the [O iii] λ5007/Hβ ratios between the SN Ic-bl and SN–GRB hosts, if potential AGNs are included. However, we note that the small sample sizes of both the SN Ic-bl and SN–GRB hosts may affect the power of these tests, leading to a higher Type II error rate in the presence of inherently different populations.

Even if additional correction for stellar absorption is applied to the SN–GRB hosts, it has little impact on the CDF of [N ii] λ6584/Hα, since the correction is low for Hα. Given a sample of 46 GRB hosts (only five of them are SN–GRB hosts), Savaglio et al. (2009) derive the mean correction for Hα to be 4%, which, if applied to all of our SN–GRB hosts, would suggest a shift in CDF for SN–GRBs by only 0.02 dex to the left in the top panel of Figure 4. However, as the overall correction for Hβ is higher, the CDF of [O iii] λ5007/Hβ for SN–GRB hosts would shift more in the right panel (downward by 0.08 dex, assuming a 20% correction for Hβ from Savaglio et al. 2009, derived from the full sample of GRB hosts), and therefore it would appear even closer to that of SN Ic-bl hosts. This consideration strengthens our result that we find no significant difference in the line-ratio distributions between SN Ic-bl and SN–GRB hosts.

In order to interpret observed line ratios, various theoretical works have combined stellar population synthesis with photoionization models to predict line ratios, given variations in the metallicity, ionization parameter, electron density, and SFH (e.g., Dopita et al. 2000; Kewley et al. 2001). In particular, expected grids of constant metallicities and ionization parameters have been overlaid on a BPT diagram, with all the other parameters fixed—for example, grids calculated based on instantaneous zero-age starburst models or on continuous starburst models. In these works, a well-known degeneracy exists such that a given location in the BPT diagram can be explained by different combinations of metallicity and ionization parameters, especially for continuous starburst models (e.g., Kewley et al. 2001). Therefore, it appears that only when fixing one of the two parameters involved in the grid (metallicity or ionization parameter) is it possible to derive a trend with the other parameter across the BPT diagram.

On the other hand, observations show that the more metal-poor H ii regions are generally located in the upper left corner of the diagram and the more metal-rich ones are located toward the lower right corner (e.g., Sánchez et al. 2015), which cannot be explained purely by the theoretical grids. In fact, the metallicity is observed to anticorrelate with ionization parameter (e.g., Dopita & Evans 1986; Perez-Montero 2014, with metallicities derived from T_e), so that not any arbitrary combination of the two is allowed by nature. For example, given the model grids calculated by Kewley et al. (2001) that assume continuous starbursts, the upper left corner (−1, 0.5) can be explained either by a model with a supersolar metallicity but extremely high ionization parameter or by a model with a subsolar metallicity and moderate ionization parameter. The former model is unrealistic owing to the anticorrelation between the metallicity and ionization parameter, and thus the upper left corner is generally associated with metal-poor H ii regions. In a BPT diagram, the parameter space populated by real H ii regions is therefore much more restricted than that predicted by model grids (see the narrow sequence in Figure 4, though the exact location depends on redshift; e.g., Erb et al. 2006; Shapley et al. 2015). More importantly, after the models with unrealistic combinations of the two parameters are excluded, the rest define a cleaner trend of the increasing metallicity from the upper left to the lower right corner along the sequence. Such a trend sets the foundation of some strong-line methods, which derive metallicities from the line ratios like O3N2 and N2 in certain ranges monotonically. Similarly, an overall trend of decreasing ionization parameter from the upper left to the lower right along the sequence is observed (e.g., Sánchez et al. 2015).

Based on this understanding, we can infer the average trends of gas-phase metallicities and ionization parameters for the hosts of PTF SNe Ic, PTF SNe Ic-bl, and SN–GRBs as populations by comparing their distributions on a BPT diagram in Figure 4, regardless of the apparent degeneracy in model grids. Furthermore, Sánchez et al. (2015) link a location on the BPT diagram to the average age and metallicity of the underlying stellar populations derived from the CALIFA observations. They find that [N ii] λ6584/Hα increases with increasing stellar age and stellar metallicity, whereas [O iii] λ5007/Hβ decreases with increasing stellar age and stellar metallicity. We can therefore infer the properties of underlying stellar populations of the hosts as well by comparing their distributions of line ratios.

We find that the hosts of SNe Ic occupy the full range of the sequence, whereas the hosts of SNe Ic-bl and SN–GRBs belong exclusively to the upper left half of the sequence. In our samples, there seems to be an upper limit in the metallicity of host environment for the formation of SNe Ic-bl and SN–GRBs. In the side panels, the CDFs indicate that the overall metallicities for the three samples appear to follow the order of Z_GRB < Z_Ic-bl < Z_Ic and that the overall ionization parameters appear to follow the opposite order of q_Ic < q_Ic-bl < q_GRB. Regarding the underlying stellar populations, the overall metallicities and ages follow the order of SN–GRB < SN Ic-bl < SN Ic. However, these trends have not yet been statistically tested for actual significance, which we perform below. We note that such qualitative trends are implied by the overall physical conditions of H ii regions observed along the sequence, even without having computed model-dependent values for the quantities of interest, such as metallicity and ionization parameter. We will present direct comparisons of the derived quantities like metallicities in the following sections, as well as test for the significance of the differences between the populations.

The statistics of the metallicity distributions are summarized in Table 4 for each sample and in the four calibrations (D13_N2S2_O3S2, KD02_COMB, PP04_O3N2, and M08_N2Hα), which were chosen for reasons given in Section 5.1. Owing to possible AGN contamination to the hosts of GRB 031203/SN 2003lw and GRB 091127/SN 2009nz, we consider both the cases with and without them in the SN–GRB sample. For the KD02comb, PP04_O3N2 (if potential AGNs are included), and M08_N2Hα calibrations, the SN–GRB sample contains one upper limit (because of GRB 130702A/SN 2013dx), so these statistics are calculated using the ASURV package Kaplan–Meier estimators.

The sample sizes (Column (2) in Table 4) are calibration dependent. Among these four calibrations, KD02comb and M08_N2Hα are the ones computable for all of the hosts in our samples: 28 SNe Ic, 14 SNe Ic-bl, and 10 SN–GRBs (including potential AGNs). Assuming a solar metallicity of log(O/H) + 12 = 8.69 (Asplund et al. 2009), the mean metallicities for the hosts of SNe Ic, SNe Ic-bl, and SN–GRBs excluding potential AGNs are in the ranges of 0.80–1.32 Z_⊙, 0.42–0.62 Z_⊙, and 0.33–0.41 Z_⊙, respectively, across the four scales. Alternatively, assuming a solar metallicity of log(O/H) + 12 = 8.76 ± 0.07 (Caffau et al. 2011), the same values are in the ranges of 0.68–1.12 Z_⊙, 0.36–0.52 Z_⊙, and 0.28–0.35 Z_⊙, respectively. Both the mean and median values show that the metallicities of the three samples follow the sequence of Z_GRB < Z_Ic-bl < Z_Ic, which agrees with the implication from line ratios, though these trends have not yet been statistically tested for actual significance. The mean and median metallicities for the SN Ic hosts are about solar, but those for the SN Ic-bl and SN–GRB hosts are well below solar. The average differences between the SN Ic and SN Ic-bl hosts range from 0.28 dex (PP04_O3N2) to 0.41 dex (D13_N2S2_O3S2).

The average differences between the SN Ic-bl and SN–GRB hosts (excluding potential AGNs) range from only 0.10 dex (in PP04_O3N2) to 0.19 dex (in M08_N2Hα), which are comparable to the standard errors of sample means (SEMs), as listed in Table 4. With the smallest size, the sample of SN–GRB hosts always has the highest SEM among the three (from 0.06 dex for PP04_O3N2 to 0.14 dex for D13_N2S2_O3S2). Columns (5) and (7) list the 25th and 75th percentiles, respectively, and their difference characterizes the standard deviation of the distribution. For the only calibration without upper limits (D13_N2S2_O3S2), the SN Ic sample has the highest standard deviation—that is, SNe Ic occur in galaxies with a large range of metallicities, whereas SNe Ic-bl and SN–GRBs from our samples occur exclusively in galaxies with low metallicities.

In this section, we apply hypothesis tests on the metallicity distributions to determine whether the observed differences between the hosts of SNe Ic, SNe Ic-bl, and SN–GRBs are statistically significant.

For each pair of the samples that are adjacent in the sequence of SN Ic, SN Ic-bl, and SN–GRB, we perform the same tests as in Section 6.1.2 on the line-ratio distributions and adopt the same criteria—we perform the Wilcoxon rank sum test for the null hypothesis that the metallicities are drawn from the same underlying distributions. If an upper limit is involved, we perform the Peto & Peto generalized Wilcoxon test instead. The p-values from these tests are listed in Table 5.

In all calibrations, the differences in metallicities between the samples of SN Ic and SN Ic-bl hosts are statistically significant. We deliberately chose a 2σ statistical significance threshold, as we would not want to hide a small effect by requiring higher statistical significance. However, we note that the difference between SNe Ic and SNe Ic-bl is significant not only at 2σ (p < 0.05) but also at 3σ (p < 0.007) for all but the D13, N2S2, and O3S2 scales, whereas the difference between the samples of SN Ic-bl and SN–GRB hosts is never significant at the 2σ level (p > 0.05; the lowest value we measure is p = 0.081 in the PP04-O3N2 calibration when potential AGNs are included in the sample; Table 5).

These results are consistent with the test results on the line-ratio distributions. We have applied several other hypothesis tests, including the K-S and A–D tests, all of which suggest the same null results.²⁶

Our results agree with the previous findings from K-S tests on host galaxies of untargeted SNe Ic and SNe Ic-bl. For example, Sanders et al. (2012) and Galbany et al. (2016) both find statistically significant differences in metallicity distributions between the samples of SN Ic and SN Ic-bl hosts, in the PP04_N2 and M13_O3N2 calibrations, respectively. However, the PP04_N2 calibration suffers from saturation above solar metallicity. The M13_O3N2 calibration gives systematically lower metallicities for more metal-rich systems compared to all the other calibrations that we consider here, so that the M13_O3N2 calibration results in the smallest variance in metallicities, given the same galaxies. Together with the fact that our sample sizes are larger than theirs by a factor of 3 (for Sanders et al. 2012), we find a difference between the SN Ic and SN Ic-bl hosts that is more significant (i.e., a lower p-value from the K-S test) than those found by Sanders et al. (2012) or Galbany et al. (2016). We note that those two works are not independent, since the untargeted hosts in Galbany et al. (2016) are from the literature, including those presented by Sanders et al. (2012).

However, our results are somewhat at odds with previous works that compare SN Ic-bl hosts with SN–GRB hosts. Based on the metallicities in the KD02 calibration (updated by Kobulnicky & Kewley 2004), Modjaz et al. (2008a) derived a K-S test p value of 0.03 (<0.05) from samples of six SN Ic-bl hosts found in an untargeted fashion and five SN–GRB hosts. Modjaz et al. (2008a), for the first time, pointed out that the targeted surveys are biased toward galaxies that are massive and thus more metal-rich, and they tried to include as many SNe Ic-bl from untargeted surveys as possible. However, owing to the very limited data from untargeted surveys at that time, only half of the SNe Ic-bl in the sample of Modjaz et al. (2008a) were found in an untargeted fashion, whereas the SN–GRBs are always found in an untargeted fashion. Moreover, their SN–GRB sample at that time was small and contained GRB 031203/SN 2003lw with potential AGN contamination. Levesque et al. (2010a) expanded the sample size of GRB hosts to 10, including higher-redshift GRBs without observed SN associations, and compared them with a sample of eight SN Ic-bl hosts selected from Modjaz et al. (2008a) (six of the SNe Ic-bl detected by untargeted surveys). They derived a K-S test p value of 0.03 (<0.05), but a value of 0.06 if GRB 031203/SN 2003lw is excluded (>0.05), which in turn agrees with our null results. The conclusion of Levesque et al. (2010a) was based on the metallicities in the KK04_R₂₃ calibration (see its caveat below). Given that our test results are based on twice larger samples of untargeted SN Ic-bl and SN–GRB hosts, which are all detected in the same untargeted fashion, together with the fact that the metallicity calibrations used by us are more appropriate for such a study (see below), we think that our null results are more reliable.

Indeed, Japelj et al. (2018) also obtain a null result (see their first line in the A–D test results in their Table 5, which gives a p value of 0.43 and 0.23 (both ≫0.05) for two metallicity calibrations), even though they claim the opposite in their conclusions since they do not consider their own statistical evidence. Their SN Ic-bl metallicity sample consists mostly of the untargeted SNe Ic-bl from Modjaz et al. (2008a) and Modjaz et al. (2011), with the remaining few from Sanders et al. (2012), and they compare them to a smaller subset of six SN–GRBs, also included in our sample.

Specifically, the KK04_R₂₃ calibration used by Levesque et al. (2010a) results in a gap in the metallicity distribution among all the SDSS galaxies, which is unphysical. According to Figure 1 from Kewley & Ellison (2008), the gap resides at ∼8.4–8.6 for KK04_R₂₃. It is caused by the relation between R₂₃ and metallicity, which is double valued and has a turnaround point at log(O/H) + 12 ≈ 8.4. While this artificial metallicity gap does not affect rank-order statistics, it does negatively affect the results of computing mass–metallicity relations, as was done by Levesque et al. (2010a), since it obscures the true metallicity distribution. Indeed, the samples of SN Ic-bl hosts and SN–GRB hosts are revealed to be roughly separated by a gap at ∼8.4–8.6 from Levesque et al. (2010a). The difference between the two samples (GRBs vs. SNe Ic-bl) therefore may be exaggerated by this gap, which is artificially introduced by the KK04_R₂₃ calibration.

Other calibrations that rely on R₂₃ are also affected, such as M91 (McGaugh 1991) and KD02 (Kewley & Dopita 2002). However, the KD02 calibration was updated to KD02comb by Kewley & Ellison (2008) (the latter one is used by this work), with modifications that include alleviating the artificial lack of objects with metallicities ∼8.4.

Thus, as we stressed by Modjaz et al. (2008a, 2011) and Modjaz (2012), it is always advisable to present metallicity trends in many different, independent calibrations so as to ensure that any observed trends are not due to artifacts in a particular calibration.

The statistical tests in the previous section account for the fact that the data do not sample the full underlying populations, but they do not include the metallicity uncertainties. In this section, we show the plots of metallicity distributions with confidence bands that are derived from the metallicity uncertainties. In addition, we compare the combined sample across different metallicity calibrations, in order to understand the characteristics intrinsic to these calibrations and the possible impact on our conclusions.

The plots of metallicity distributions are presented in Figure 5. These distributions include objects with host spectra extracted from both the apertures that cover the SN sites (filled markers in Figure 4) and those that do not (unfilled markers in Figure 4). Plotting both together is valid given the fact that the open symbols do not systematically deviate from the closed ones in Figure 4 (except for the open diamond that denotes GRB 031203/SN 2003lw, which may have AGN contamination).

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In Figure 5, the top panels show stacked histograms for the metallicity distributions in four calibrations. We compare the combined distributions from all samples across the calibrations, in order to understand the characteristic of each calibration. The well-known systematic offsets between the calibrations (e.g., Kewley & Ellison 2008) are evident in the plots. For the most metal-rich galaxies in the SN Ic host sample, the metallicities in the KD02comb calibration are on average ∼0.2 dex higher than those in the PP04_O3N2 calibration, which reinforced our statement that the comparison between samples should be performed with metallicities calculated in the same calibration.

Among these four calibrations, the distribution in PP04_O3N2 is the narrowest; it has the lowest standard deviation (0.26 dex for the combined sample of 50 hosts), even though the host galaxies are over a large range of masses and thus should have a large range of metallicities. While Marino et al. (2013) claimed that the M13_O3N2 calibration (not shown) is superior to PP04_O3N2, we think that the M13 calibration is not appropriate for the study of metal-poor galaxies such as those in our sample. Together with the fact that the line ratios of several low-metallicity SN–GRB hosts are outside of the range for the M13_O3N2 calibration, the M13_O3N2 calibration results in an even lower standard deviation than PP04_O3N2 does (0.14 dex for the combined sample of 44 hosts), which is unrealistic considering that the host galaxies are over a large range of masses. The small difference in metallicity distributions between the SN Ic-bl and SN–GRB samples becomes completely indistinguishable if the M13_O3N2 calibration is used.

The bottom panels in Figure 5 show CDFs of metallicities in the four calibrations. The upper limits of GRB 130702A/SN 2013dx in the KD02comb and M08_N2Hα calibrations are denoted by arrows. The statistical tests account for the fact that the data do not sample the full underlying populations, but they do not include the metallicity uncertainties. We hereby derive the confidence bands for the CDFs from metallicity uncertainties via Monte Carlo simulations, which are shown by colored bands around the associated CDFs (central lines).

For each CDF we compute two confidence intervals: one induced by the uncertainty in the line measurements as they propagate into the metallicity calculation, and the other as induced by the limited sample size. The former is an output of the pyMCZ code calculated via Monte Carlo as the 16th and 84th percentiles of the metallicity distribution. The latter is computed by the standard jackknife resampling technique over the SNe, with the upper and lower intervals representing the standard deviation of the bootstrapped sample.

With these confidence intervals the differences between the SN Ic-bl and SN–GRB samples are not statistically significant for all metallicity calibrations, but those between the SN Ic and SN Ic-bl samples are.

Plotting the uncertainty intervals gives us a visual confirmation of our statistical conclusions (Section 6.2.2). The SNe Ic-bl and SN–GRB samples are not statistically significantly different in all metallicity calibrations: the cumulative plots overlap at the 1σ level even when the two uncertainty bands are shown separately, rather than combined. In the literature, cumulative distributions of metallicity are often plotted without uncertainties, and at times these plots have led to statements at odds with the statistical conclusions derived from the same data. For example, Japelj et al. (2018) obtained a positive K-S test at 2σ, p < 0.05 (actual p = 0.03), but, like we do, they obtain a null result at the 2σ level (p = 0.06 > 0.05) if GRB 031203/SN 2003lw is excluded.

In Section 6.2.2 we did not find statistically significant differences between the SN Ic-bl and GRB host populations (p > 0.05) even without consideration of the observational uncertainties, while the tests (e.g., K-S and A–D) naturally account for the limited sample size. Adding the observational uncertainties to these tests is not trivial (doing it with a Monte Carlo approach would indeed expose us to data dredging). But even when simply considering the 2σ upper metallicity limit for the hosts of SNe Ic-bl and the lower limit for the hosts of SNe Ic, which would favor a null result, we find the differences between hosts of SNe Ic-bl and those of SNe Ic to be 2σ significant for all but the KD02 scales.

Finally, we now show that stellar absorption corrections will not change our results significantly, though we do not consider the second-order effect on extinction corrections. While the stellar absorption correction is applied to all the SN Ic and SN Ic-bl hosts, this is the case for only four out of 10 SN–GRB hosts. Assuming typical corrections of 4% for Hα and 20% for Hβ, which are the mean values derived from a sample of GRB hosts by Savaglio et al. (2009), only the calibrations that directly depend on Hβ are highly affected by stellar absorption. Among the four calibrations that we choose, those are KD02comb (it depends on R₂₃ for log (O/H) + 12 < 8.4) and PP04_O3N2. Given the line ratios and the lower-branch relation between the metallicity and log R₂₃ from Kobulnicky & Kewley (2004), applying stellar absorption correction would result in a decrease of ≲0.08 dex in log (O/H) + 12 for only one object, GRB 161219B/SN 2016jca. Considering the small difference between the CDFs of SN Ic-bl and SN–GRB hosts in the KD02comb calibration from Figure 5, a tiny shift of ≲0.08 dex to the left for only one object is unlikely to change our result. Likewise, if Hα increases by 4% and Hβ increases by 20%, the log O3N2 value decreases by 0.06 dex, which corresponds to an increase of only 0.02 dex in log (O/H) + 12 (Pettini & Pagel 2004). A tiny shift of 0.02 dex to the right for five SN–GRB hosts only slightly strengthens our result that the difference between the SN Ic-bl and SN–GRB hosts is not statistically significant. However, this probably explains the fact that the difference between the CDFs of SN Ic-bl and SN–GRB hosts is the most evident in the PP04_O3N2 calibration among the four, although the PP04_O3N2 calibration results in the smallest standard deviation in the metallicity distribution for each sample.

To conclude, the PTF SN Ic-bl host metallicity distribution is statistically consistent with that of the SN–GRB hosts, but inconsistent with the PTF SN Ic hosts, which are generally found at higher metallicities. While no GRBs were observed in conjunction with the PTF SNe Ic-bl, we will discuss in Section 7.1 whether our null result could be due to the fact that the PTF SNe Ic-bl actually hosted off-axis GRBs or on-axis low-luminosity GRBs like GRB 060218.

In Figure 6, we plot the metallicities in the four calibrations versus M_* for the SN host galaxies. To quantify the average M–Z relations, we fit a linear model to each SN host sample and show the results as lines in Figure 6, which share the same color codes as the symbols.

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We are fully aware that the M–Z relation is not perfectly linear. As a result, Kewley & Ellison (2008) fit the M–Z relation by a third-order polynomial, and Tremonti et al. (2004) fit it by a second-order polynomial. Specifically, a gradual flattening occurs above M_* ≈ 10^10.5 M_⊙ (Tremonti et al. 2004). Below M_* ≈ 10^8.5 M_⊙, the M–Z relation is not constrained by the SDSS main spectroscopic galaxy sample, which becomes highly incomplete at the low-mass end. However, the correlation is roughly linear from 10^8.5 to 10¹⁰ M_⊙ (Tremonti et al. 2004). All of the PTF SN Ic-bl and SN–GRB hosts have M_* < 10^9.5 M_⊙ and thus are not affected by the obvious flattening observed over the range for massive galaxies. Together with the fact that the hosts from these two samples (PTF SN Ic-bl and SN–GRB hosts) span a similar M_* range (from 10^7.5 to 10^9.5 M_⊙), we expect the linear fits to provide a fair comparison of the average M–Z trends between the two samples. We note that the linear fit to the PTF SN Ic hosts is less representative of the average M–Z trend, because 11 out of all 28 PTF SN Ic hosts have M_* > 10^10.5 M_⊙. However, we still fit linear models to all three SN host samples to make fair comparisons. Plus, fitting higher-order polynomials may fail to catch the intrinsic trends, given the small sample sizes of SN hosts.

In all the calibrations, the linear fit to the M–Z relation for the SN–GRB hosts falls slightly below that for the PTF SN Ic-bl hosts (red solid lines fall below blue dashed lines in Figure 6). However, the relative position between the M–Z relation for the PTF SN Ic hosts and those for the other two samples depends on the calibration (black dotted lines vs. the others). Not only does the y-intercept of the M–Z relation vary with the metallicity calibration, but so does its slope and even its shape (Kewley & Ellison 2008). Owing to the caveat of nonlinearity in the intrinsic M–Z relation over a large M_* range, a linear fit to the M–Z relation of PTF SN Ic hosts is not robust and varies with the calibration.

To assess whether these differences are significant between the M–Z relations as obeyed by different SN host samples (with the emphasis on the difference between the SN Ic-bl and SN–GRB hosts, owing to the caveat of a linear fit to the SN Ic M–Z relation as discussed above), we fit a linear model for galaxies from each pair of the samples adjacent in the sequence of SN Ic, SN Ic-bl, and SN–GRB:

$$\begin{eqnarray}&&\mathrm{log}({\rm{O}}/{\rm{H}})+12={\beta }_{0}+{\beta }_{1}\mathrm{log}{M}_{* }+{\beta }_{2}R+{\beta }_{3}R\mathrm{log}{M}_{* },\end{eqnarray} \tag{ 1 }$$

where β_i (i = 0, ..., 3) are coefficients to be fit and R is a variable that denotes the SN Ic-bl sample as the reference level:

$$\begin{eqnarray}R=\left\{\begin{array}{ll}0, & \mathrm{if}\ {\rm{a}}\ \mathrm{galaxy}\ \mathrm{belongs}\ \mathrm{to}\ \mathrm{the}\ \mathrm{SN}\ \mathrm{Ic} \mbox{-} \mathrm{bl}\ \mathrm{sample}\\ 1, & \mathrm{otherwise}.\end{array}\right.\end{eqnarray} \tag{ 2 }$$

This multivariant model allows for different y-intercepts and slopes of the average trends as defined by different samples. For example, in the comparison between the SN Ic-bl and SN–GRB hosts, Equation (1) reduces to

$$\begin{eqnarray}&&\mathrm{log}({\rm{O}}/{\rm{H}})+12={\beta }_{0}+{\beta }_{1}\mathrm{log}{M}_{* }\end{eqnarray} \tag{ 3 }$$

for the SN Ic-bl hosts (blue dashed lines in Figure 6), and it reduces to

$$\begin{eqnarray}&&\mathrm{log}({\rm{O}}/{\rm{H}})+12=({\beta }_{0}+{\beta }_{2})+({\beta }_{1}+{\beta }_{3})\mathrm{log}{M}_{* }\end{eqnarray} \tag{ 4 }$$

for the SN–GRB hosts (red solid lines in Figure 6). We exclude GRB 031203/SN 2003lw (with potential AGN contamination) and GRB 130702A/SN 2013dx (the metallicity value is an upper limit) from the fit.

The estimates of the coefficients in Equation (1) follow the Student's t-distribution, and thus we apply Student's t-tests on the hypothesis that β₂ = 0 or β₃ = 0, which is equivalent to testing whether the two average trends are the same as defined by different host samples. Between the SN Ic-bl and SN–GRB hosts, we find that the p-values of the t-tests on the hypothesis that β₂ = 0 or β₃ = 0 are much higher than 0.05 for all four calibrations—that is, the difference between the average M–Z relations as defined by the SN Ic-bl and SN–GRB hosts is not statistically significant. The tests on coefficients from the linear fits to the SN Ic-bl versus SN Ic hosts show similar results. Note that the statistical tests account for the fact that our data do not sample the full underlying populations, but they do not include our data's measurement uncertainties. Considering the uncertainties, the average trends between the samples become even more indistinguishable.

To conclude, in all the calibrations, although the average M–Z relation for the SN–GRB hosts lies slightly below that for the SN Ic-bl hosts, we find this difference to be not statistically significant. Similarly, the difference between the average M–Z relations for the SN Ic-bl and SN Ic hosts is not statistically significant. Nevertheless, the range of SN Ic hosts extends to higher metallicities and higher masses than the other two SN host samples, with the caveat that the M–Z relation becomes nonlinear at this high masses.

Modjaz et al. (2008a), Levesque et al. (2010b), Han et al. (2010), and Graham & Fruchter (2013) argue that the hosts of SN–GRBs lie significantly below the standard luminosity–metallicity (L–Z) relations of local galaxies. In contrast, Leloudas et al. (2015) conclude only that the GRB hosts do not occupy the same region as the SDSS galaxies, which are more massive and more metal-rich. Leloudas et al. (2015) suggest that the GRB hosts form a possible extension toward lower masses, as there are only a small number of low-mass galaxies (M_* < 10^8.5 M_⊙) in the SDSS. However, Graham & Fruchter (2013) accounted for the SDSS mass/luminosity cutoff by both limiting the GRB sample to those with luminosities above a cutoff and extrapolating the SDSS population to lower luminosities, and they showed that in all cases the GRB hosts preferred lower metallicities than expected from the SDSS sample.

Savaglio et al. (2009) argued that GRB hosts lie on the same M–Z relation as regular galaxies. Now with a larger sample size, we examine here whether SN–GRBs occur in host galaxies below the standard M–Z relation. Owing to a positive correlation between the galaxy M_*/L and optical color, the M–Z relation is intrinsically tighter than the L–Z relation, so the former is more appropriate for this investigation.

We first compare the SN host galaxies with 500 galaxies that are representative of the overall SDSS population (Section 4.2.1), in terms of the average M–Z relations. We keep in mind that the SDSS main spectroscopic galaxy sample becomes highly incomplete at the low-mass end. The average SDSS M–Z relations are overlaid in Figure 6 by yellow dashed–dotted lines extending between 10^8.5 < M_* < 10¹¹ M_⊙, as a third-order polynomial fit to the SDSS galaxies. Indeed, the majority of the SN–GRB hosts with M_* > 10^8.5 M_⊙ appear to fall below these average SDSS relations. Likewise, all three average M–Z relations for the SN hosts (SN Ic in black dotted line, SN Ic-bl in blue dashed line, and SN–GRB in red solid line) fall below this SDSS curve above 10^8.5 M_⊙ in all four calibrations, with the caveat in mind of the nonlinearity for SN Ic M–Z relations. The confidence intervals plotted as shaded regions around the line fit represent the uncertainty on the line fit calculated as a two-sided 68% confidence interval—i.e., for α = 0.32, ±t_{1–α/2,n–2} × s , where t is the value of the t-distribution, with n–2 degrees of freedom for the α confidence threshold, and s is the estimated standard deviation of the fit.

However, we argue that the difference between the average SDSS and the average SN–GRB M–Z relations, in particular, is not statistically significant, except for perhaps the metallicities in the KD02comb calibration. In Figure 6, we overlay the 68% confidence intervals of the linear fits to the SN–GRB M–Z relations as red shaded bands. Owing to small sample sizes of the SN–GRB hosts, as well as large scatter of data points around the average relations, the confidence intervals associated with the linear fits are generally wide at a fixed M_*. The yellow dashed–dotted curves for the SDSS M–Z relations therefore always fall within the confidence intervals of the SN–GRB M–Z relations (i.e., the differences are not statistically significant at the 2σ level), except for the KD02comb calibration (the yellow dashed–dotted curve falls outside of the red region). We note that the KD02comb calibration is mildly affected by the discontinuity in the metallicity distribution around log (O/H) + 12 ≈ 8.4. Furthermore, we do not consider the confidence intervals for the SDSS relations here, and the confidence intervals should become even wider if measurement uncertainties are included. Meanwhile, the average SDSS relation is derived from the metallicities measured within the fibers, which preferentially target the nuclear regions, but these have overall higher metallicities compared to the rest of the galaxy owing to negative metallicity gradients, from metal-rich centers to metal-poor outskirts. Thus, the average SDSS relation should shift downward if the metallicities were to be measured at similar galactocentric radii to those for the SN hosts; they would be even closer to the SN–GRB M–Z relation. If we take into account all of these factors, our conclusion is strengthened that the difference between the average SDSS and the average SN–GRB M–Z relation is not significant.

The above analysis, however, is a one-dimensional test that answers the question, "Given a mass value, is the Z value of an SN–GRB host consistent with that of an SDSS galaxy at the same mass on average?" One could conversely ask whether the SDSS galaxies and the SN–GRB hosts occupy the M–Z space in a similar way—this would be a two-dimensional (2D) test.

To answer this question, we performed a cross-match test (Rosenbaum 2005), which compares two multivariate distributions by measuring distances between observations. This is a nonparametric test. The distance between points in the 2D space is measured, and observations are paired according to optimal non-bipartite matching. Optimal non-bipartite matching algorithms find the set of matches that minimize the sum of distances based on a given distance matrix (for a review on optimal non-bipartite matching, see Lu et al. 2011). In the presence of observations from two samples, the test measures the cross-match statistics, which is the number of pairs containing one observation for the first sample and one from the second (in this case, the SDSS galaxies and SN–GRB hosts are the two samples). The fraction of cross-matches has a well-defined probability distribution if the two samples are identically distributed in that space. Thus, a given cross-match fraction is associated with a p-value for the null hypothesis that the two samples are identically distributed. Since our SN–GRB hosts have lower masses (with a maximum mass of 10^9.5 M_⊙) than SDSS galaxies, we restrict the comparison to the same mass range of SN–GRB host and SDSS hosts—that is, we impose a mass cutoff at 10^9.5 M_⊙ for the SDSS galaxies.

The cross-matching algorithm uses the Mahalanobis distance, which takes into account the variance of each variable and the covariance between samples by measuring the Euclidean distance of the decorrelated standardized samples, as a distance metric to assign pairs. This is necessary since the samples are obviously covariant with positive Z versus M relations (Mahalanobis 1936).

Since we have more SDSS galaxies than SN–GRB hosts, to minimize the computational burden of the matching algorithm,²⁷ we randomly select N SDSS galaxies at M < 10^9.5 M_⊙ for each Z diagnostic, where N is the number of SN–GRB hosts (which varies between 7 and 10 for different metallicity calibrations), and then measure the cross-match statistics for this subset of SDSS galaxies and the SN–GRB hosts, repeating this procedure 500 times. We take the mean over the 500 tests to be the value for the cross-match statistics for each Z diagnostic.

The p-value associated with the null hypothesis is 0.028 for KD02comb, 0.23 for D13_N2S2_O3S2, 0.16 for PP04_O3N2, and 0.07 for M08_N2Hα (as listed in Table 6). Three out of the four values are above the 0.05 threshold, and thus the two samples (SN–GRB hosts and the SDSS galaxies) are consistent with each other at the 2σ level based on this second test.

Unfortunately, the power of the test is limited by the small number of objects in the SN–GRB sample, which varies between 7 and 10 depending on the metallicity diagnostic. The power of the test would be much increased with a larger SN–GRB sample, since with such a small number of objects the p-value is high for the smallest possible number of cross-matches. For example, D13_N2S2_O3S2 only has seven SN–GRB hosts with measured Z, and for samples of N = 7 the minimum number of cross-matches (one cross-match) already has a probability of 0.08, which is above the 2σ threshold.

We are aware that the average SN–GRB M–Z relations are not well constrained. The small sample size of SN–GRB hosts may weaken the power of our test to distinguish the small difference between the SDSS and SN–GRB M–Z relations.

We also compare the SN hosts with the LVL galaxies, which are represented by light-gray circles in Figure 6 with symbol sizes proportional to SFRs, following Perley et al. (2016b). The LVL survey is expected to provide a volume-complete sample in the local universe. However, it suffers from cosmic variance, and the metallicities for LVL galaxies are compiled from the literature in heterogeneous calibrations, which are typically based on T_e at low metallicities and on various strong-line diagnostics at higher metallicities (Perley et al. 2016b). Consequently, the M–Z relation as defined by the LVL galaxies serves the purpose of only a qualitative comparison. Qualitatively, the data points for the LVL galaxies, whose metallicity values stay constant across panels, occupy a parameter space similar to that of the overall SN hosts. In the low-mass regime, the LVL galaxies provide a nice supplement to the SDSS galaxies. The SN Ic-bl or SN–GRB hosts give no strong indication of an offset relative to the LVL galaxies. At the high-mass end, the offset between the LVL galaxies and the SN Ic hosts is also inconclusive, given that the LVL survey is biased against the most massive galaxies and that the metallicity values are in heterogeneous calibrations. Only in the PP04_O3N2 calibration do LVL galaxies have systematically higher metallicities at a fixed M_* than the SN Ic hosts.

In conclusion, the average M–Z relations as defined by the SN Ic, SN Ic-bl, and SN–GRB hosts fall slightly below the same relations as defined by the SDSS galaxies above M_* = 10^8.5 M_⊙. However, the differences between these relations are not statistically significant at the 2σ level. In contrast to Levesque et al. (2010b), we do not find a significant offset between SN–GRB host galaxies and those in SDSS, having used a larger data set (by a factor of two larger for SN–GRBs) and a more thorough statistical analysis. When comparing in detail the five SN–GRB hosts we have in common, we find not only that our metallicities are different (though we are using different scales) but also that our host masses are different, which we took from Savaglio et al. (2009). Indeed, Levesque et al. (2010b) use a different code to compute host masses than Savaglio et al. (2009), and their error bars for the host masses are larger than in Savaglio et al. (2009), such that for most SN–GRBs in common (four out of the five) the host masses are formally consistent with each other between the two works within one standard deviation.