CHARACTERIZING THE V-BAND LIGHT-CURVES OF HYDROGEN-RICH TYPE II SUPERNOVAE^*

A detailed description of the data reduction, host galaxy subtraction and photometric processing for all SNe discussed, awaits the full data release. Here we briefly summarize the general techniques used to obtain host galaxy-subtracted, photometrically calibrated V-band light-curves for 116 SNe II.

Data processing techniques for CSP photometry were first outlined in Hamuy et al. (2006) then fully described in Contreras et al. (2010) and Stritzinger et al. (2011). The reader is referred to those articles for additional information. Note, that those details are also relevant to the data obtained in follow-up campaigns prior to CSP (listed above), which were processed in a very similar fashion. One important difference between CSP and prior data is that the CSP magnitudes are in the natural system of the Swope telescope (located at Las Campanas Observatory), whereas previous data are calibrated to the Landolt standard system. Briefly, V-band data were reduced through a sequence of: bias subtractions, flat-field corrections, application of a linearity correction and an exposure time correction for a shutter time delay. Since SN measurements can be potentially affected by the underlying light of their host galaxies, we exercised great care in subtracting late-time galaxy images from SN frames (see, e.g., Hamuy et al. 1993). This was achieved through obtaining host galaxy template images more than a year after the last follow-up image, where templates were checked for SN residual flux (in the case of detected SN emission, additional templates were obtained at a later date). In the case of the CSP sample the majority of these images was obtained with the du-Pont telescope (the Swope telescope was used to obtain the majority of follow-up photometry), and templates which were used for final subtractions were always taken under seeing conditions either matching or exceeding those of science frames. To proceed with host galaxy subtractions, the template images were geometrically transformed to each individual science frame, then convolved to match the point-spread functions, and finally scaled in flux. The template images were then subtracted from a circular region around the SN position on each science frame. This process was outlined in detail in Section 4.1 of Contreras et al. (2010) as applied to the CSP SN Ia sample, where further discussion can be found on the extent of possible systematic errors incurred from the procedure (which were found to be less than 0.01 mag, and are not included in the photometric errors, also see Folatelli et al. 2010). A very similar procedure to the above was employed for the data obtained prior to CSP.

SN magnitudes were then obtained differentially with respect to a set of local sequence stars, where absolute photometry of local sequences was obtained using our own photometric standard observations. V-band photometry for three example SNe is shown in Table 3, and the complete sample of V-band photometry can be downloaded from http://www.sc.eso.org/~janderso/SNII_A14.tar.gz also available at http://csp.obs.carnegiescience.edu/data/), or requested from the author. The.tar file also contains a list of all epochs and magnitudes of upper limits for non-detections prior to SN discovery, together with a results file with all parameters from Table 6, plus other additional values/measurements made in the process of our analysis. Full multi-color optical and near-IR photometry, together with that of local sequences, will be published for all SNe included in this sample in the near future.

While the use of t_PT allows one to measure parameters at consistent epochs with respect to the transition from "plateau" to tail phases, much physical understanding of SNe II rests on having constraints on the epoch of explosion. The most accurate method for determining this epoch for any given SN is when sufficiently deep pre-explosion images are available close to the time of discovery. However, in many cases in the current sample, such strong constraints are not available. Therefore, to further constrain this epoch, matching of spectra to those of a library of spectral templates was used through employing the Supernova Identification (SNID) code (Blondin & Tonry 2007). The earliest spectrum of each SN within our sample was run through SNID and top spectral matches inspected. The best fit was then determined, which gives an epoch of the spectrum with respect to maximum light of the comparison SN. Hence, using the published explosion epochs for those comparison spectra with respect to maximum light, one can determine an explosion epoch for each SN in the sample. Errors were estimated using the deviation in time between the epoch of best fit to those of other good fits listed, and combining this error with that of the epoch of explosion of the comparison SN taken from the literature for each object.

In the case of SNe with non-detections between 1–20 days before discovery, we use explosion epochs as the mid point between those two epochs, with the error being the explosion date minus the non-detection date. For cases with poorer constraints from non-detections, explosion epochs from the spectral matching outlined above are employed. The validity of this spectral matching technique is confirmed by comparison of estimated epochs with SNe non-detections (where strong constraints exist). Where the error on the non-detection explosion epoch estimation is less than 20 days, the mean absolute difference between the explosion epoch calculated using the non-detection and that estimated using the spectral matching is 4.2 days (for the 61 SNe where this comparison is possible). The mean offset between the two methods is 1.5 days, in the sense that the explosion epochs estimated through spectral matching are on average 1.5 days later than those estimated from non-detections. In the Appendix these issues are discussed further, and we show that the inclusion of parameters which are dependent on spectral matching explosion epochs make no difference to our results and conclusions. Finally, we note that a similar analysis was also achieved by Harutyunyan et al. (2008b).

A key SN II light-curve parameter often discussed in the literature is the length of the "plateau." This has been claimed to be linked to the mass of the hydrogen envelope, and to a lesser extent the mass of ⁵⁶Ni synthesized in the explosion (Litvinova & Nadezhin 1985; Popov 1993; Young 2004; Kasen & Woosley 2009; Bersten et al. 2011). Hence, we also attempt to measure this parameter. Before doing so it is important to note how one defines the "plateau" length in terms of current nomenclature in the literature. It is common that one reads that a SN IIP is defined as having "plateau of almost constant brightness for a period of several months." Firstly, it is unclear how many of these types of objects actually exist in nature, as we will show later. Secondly, this phase of constant brightness (or at least constant change in brightness for SNe where significant s₂ values are measured), should be measured starting after initial decline from maximum, a phase which is observed in a significant fraction of hydrogen rich SNe II (at least in the V- and bluer bands).

To proceed with adding clarity to this issue, the start of the "plateau" phase is defined to be t_tran (the V-band transition between s₁ and s₂ outlined in Section 3). The end of the "plateau" is defined as when the extrapolation of the straight line s₂ becomes 0.1 mag more luminous than the light-curve, t_end.¹⁹ This 0.1 mag criterion is somewhat arbitrary, however it ensures that both the light-curve has definitively started to transition from "plateau" to later phases, and that we do not follow the light-curve too far into the transitional phase. Using these time epochs we define two time durations:

• 1.  
  the "plateau" duration: Pd = t_end − t_tran
• 2.  
  the optically thick phase duration: OPTd = t_end − t₀

These parameters are labeled in the light-curve parameter schematic presented in Figure 1. In addition, all derived light-curve parameters: decline rates, magnitudes, time durations, are depicted on their respective photometry in the Appendix.

All measurements of photometric magnitudes are first corrected for extinction due to our own Galaxy, using the re-calibration of dust maps provided by Schlafly & Finkbeiner (2011), and assuming an R_V of 3.1 (Cardelli et al. 1989). We then correct for host galaxy extinction using measurements of the equivalent width (EW) of sodium absorption (NaD) in low resolution spectra of each object. For each spectrum within the sequence (of each SN), the presence of NaD, shifted to the velocity of the host galaxy is investigated. If detectable line absorption is observed a mean EW from all spectra within the sequence is calculated, and we take the EW standard deviation to be the 1σ uncertainty of these values. Where no evidence of NaD is found we assume zero extinction. In these cases, the error is taken to be that calculated for a 2σ EW upper limit on the non-detection of NaD. Host galaxy A_V values are then estimated using the relation taken from Poznanski et al. (2012), assuming an R_V of 3.1 (Cardelli et al. 1989).

The validity of using NaD EW line measurements in low resolution spectra, as an indicator of dust extinction within the host galaxies of SNe Ia has been recently questioned (Poznanski et al. 2011; Phillips et al. 2013). Even in the Milky Way where a clear correlation between NaD EW measurements and A_V is observed, the rms scatter is large. At the same time, absence of NaD is generally a first order approximation of low level or zero extinction, while high EW of NaD possibly implies some degree of host galaxy reddening (Phillips et al. 2013). The use of the Poznanski et al. (2012) relation for the current sample is complicated as it has been shown (e.g., Munari & Zwitter 1997) to saturate for NaD EWs approaching and surpassing 1 Å. Indeed, 10 SNe within the current sample have NaD EWs of more than 2 Å.²⁰ The Poznanski et al. (2012) relation gives an A_V (assuming R_V = 3.1) of 9.6 for an EW of 2 Å, i.e., implausibly high. Therefore, we choose to eliminate magnitude measurements of SNe II in our sample with EW measurements higher than 1 Å, due to the uncertainty in any A_V corrections. In addition, when measuring 2σ upper limits for NaD non-detections, we also eliminate SNe from magnitude analysis if the limits are higher than 1 Å (i.e., spectra are too noisy to detect significant NaD absorption). Finally, those SNe which do not have spectral information are also cut from magnitude analysis.

The above situation is far from satisfying, however for SNe II there is currently no accepted method which accurately corrects for host galaxy extinction. Olivares E. et al. (2010) used the (V − I) color excess at the end of the plateau to correct for reddening, with the assumption that all SNe IIP evolve to similar temperatures at that epoch (see also Nugent et al. 2006; Poznanski et al. 2009; Krisciunas et al. 2009; D'Andrea et al. 2010). Those authors found that using such a reddening correction helped to significantly reduce the scatter in Hubble diagrams populated with SNe IIP. However, there are definite outliers from this trend; e.g., sub-luminous SNe II tend to have red intrinsic colors at the end of the plateau (see, e.g., Pastorello et al. 2004; Spiro et al. 2014), which, if one assumed were due to extinction would lead to corrections for unreasonable amounts of reddening (e.g., in the case of SN 2008bk; G. Pignata 2013, private communication). With these issues in mind we proceed, listing our adopted A_V values measured from NaD EWs in Table 6.²¹

We note that while the current extinction estimates are uncertain, all of the light-curve relations that will be presented below hold even if we assume zero extinction corrections.

Distances are calculated using cosmic-microwave- background-corrected recession velocities if this value is higher than 2000 km s⁻¹, together with an H₀ of 73 km s⁻¹ Mpc⁻¹ (and Ω_m = 0.27, $\Omega _\Lambda$ = 0.73; Spergel et al. 2007), assuming a 300 km s⁻¹ velocity error due to galaxy peculiar velocities. For host galaxies with recession velocities less than 2000 km s⁻¹ peculiar velocities make these estimates unreliable. For these cases "redshift independent" distances taken from NED are employed, where the majority are Tully–Fisher estimates, but Cepheid values are used where available. Errors are taken to be the standard deviation of the mean value of distances in cases with multiple, e.g., Tully–Fisher values, or in cases with single values the literature error on that value. Distance moduli, together with their associated errors are listed in Table 6.

Errors on absolute magnitudes are a combination of uncertainties in: (1) photometric data; (2) extinction estimations and; (3) distances. In (1) when the magnitude is taken from a single photometric point we take the error to be that of the individual magnitude. When this magnitude is obtained through interpolation we combine the errors in quadrature of the two magnitudes used. Published photometric errors are the sum in quadrature of two error components: (1) the uncertainty in instrumental magnitudes estimated from the Poisson noise model of the flux of the SN and background regions, and (2) the errors on the zero point of each image (see Contreras et al. 2010, as applied to the CSP SN Ia sample). In the case of (2) errors in A_V are taken as the standard deviation of the mean measurement of the NaD EWs, together with the error on the relation used (Poznanski et al. 2012). However, it is believed that the error on the relation provided by those authors is significantly underestimated. Using the dispersion of individual measurements on the NaD EW-A_V relation as seen in Phillips et al. (2013), we obtain an additional error of 47% of A_V estimations, which is added to the error budget. In the case of (3) errors for SNe within host galaxies with recession velocities above 2000 km s⁻¹ are derived from assuming peculiar velocity errors of 300 km s⁻¹, while for recession velocities below that limit errors are those published along with the distances used (as outlined above). These three errors are combined in quadrature and are listed for each of the three estimated absolute magnitudes in Table 6.

Decline rate uncertainties come from the linear fits to s₁, s₂ and s₃. The uncertainty in Pd is the error on the epoch of the transition between s₁ and s₂, as estimated in Section 3, while the error on OPTd is that estimated for the explosion epoch, as outlined in Section 3.1. We also combine with the uncertainty in Pd/OPTd, an additional 4.25 days to the error budgets to account for the uncertainty in the definition of t_end. This error is estimated in the following way. For each SN we calculate the average cadence of photometry at epochs in close proximity to t_end. The mean of these cadences for all SNe is 8.5 days. Given that t_end is measured as an interpolation between photometric points (following s₂ together with the morphology of the changing light-curve), we assume the error in defining any epoch at this phase to be half the cadence, i.e., 4.25 days.

An additional magnitude error inherent in all SNe measurements is that due to K-terms (the wavelength shift of the spectral energy distribution with respect to the observer's band-pass, Oke & Sandage 1968). For the current analysis we do not make such corrections owing to the low-redshift of our sample. To test this assumption we follow the technique employed in Olivares E. et al. (2010), and described in Olivares (2008). This involved synthesizing K-terms from a library of synthetic SN spectra, resulting in a range of corrections as a function of (B − V) SN color. At the mean redshift of our sample of 0.018, the average K-correction during the plateau is estimated to be 0.02 mag. At the redshift limit of our sample: 0.077, this mean correction is 0.07 mag. Hence, our neglection of this term is justified. While we also choose to ignore S-corrections (magnitude corrections between different photometric systems), we note again that the CSP data are tied to the natural system of the Swope telescope (see Contreras et al. 2010 for details), while all previous data are calibrated to the Landolt standard system. This may bring differences to the photometry of each sub-sample. For a typical SN, the difference in V-band magnitudes between photometry in the CSP and standard system is less than 0.1 mag at all epochs (with mean corrections of around 0.03 mag). The differences between S-corrections at M_max and M_end are around ∼0.03 mag. Therefore the influence of this difference on decline rate estimations will be negligible (they will be less than this difference). In conclusion, uncertainties in our measurements are dominated by those from distances and extinction estimates, and our neglection of these corrections is very unlikely to affect our overall results and conclusions.

After correcting V-band photometry for both MW and host extinction we produce absolute V-band light-curves by subtracting the distance modulus from SNe extinction corrected apparent magnitudes.

In Figure 2 results of Legendre polynomial fits to the absolute light-curves of all those with explosion epochs defined, and A_V corrections possible are presented. This shows the large range in both absolute magnitudes and light-curve morphologies, the analysis of which will be the main focus of the paper as presented below. In addition, in the Appendix light-curves are presented in more detail for all SNe to show the quality of our data, its cadence, and derived SN parameters. Note that these Legendre polynomial fits are merely used to show the data in a more presentable fashion. They are not used for any analysis undertaken.

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In Figure 3 histograms of the three absolute V-band magnitude distributions: M_max, M_end and M_tail are presented. These distributions evolve from being brighter at maximum, to lower luminosities at the end of the plateau, and further lower values on the tail. Our SN II sample is characterized, after correction for extinction, by the following mean values: M_max = −16.74 mag (σ = 1.01, 68 SNe); M_end = −16.03 mag (σ = 0.81, 69 SNe); M_tail = −13.68 mag (σ = 0.83, 30 SNe).

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The SN II family spans a large range of ∼4.5 mag at peak, ranging from −18.29 mag (SN 1993K) through −13.77 mag (SN 1999br). At the end of their "plateau" phases the sample ranges from −17.61 to −13.56 mag. SN II maximum light absolute magnitude distributions have previously been presented by Tammann & Schroeder (1990) and Richardson et al. (2002). Both of these were B-band distributions. Tammann & Schroeder presented a distribution for 23 SNe II of all types of M_B = −17.2 mag (σ = 1.2), while Richardson et al. found M_B = −17.0 mag (σ = 1.1) for 29 type IIP SNe and M_B = −18.0 mag (σ = 0.9) for 19 type IIL events. Given that our distributions are derived from the V band, a direct comparison to these works is not possible without knowing the intrinsic colors of each SN within both samples. However, our derived M_max distribution is reasonably consistent with those previously published (although slightly lower), with very similar standard deviations.

At all epochs our sample shows a continuum of absolute magnitudes, and the M_max distribution shows a low-luminosity tail as seen by previous authors (e.g., Pastorello et al. 2004; Li et al. 2011). All three epoch magnitudes correlate strongly with each other: when a SN II is bright at maximum light it is also bright at the end of the plateau and on the radioactive tail.

Figure 4 presents histograms of the distributions of the three V-band decline rates, s₁, s₂ and s₃, together with their means and standard deviations. SNe decline from maximum (s₁) at an average rate of 2.65 mag per 100 days, before declining more slowly on the "plateau" (s₂) at a rate of 1.27 mag per 100 days. Finally, once a SN completes its transition to the radioactive tail (s₃) it declines with a mean value of 1.47 mag per 100 days. This last decline rate is higher than that expected if one assumes full trapping of gamma-ray photons from the decay of ⁵⁶Co (0.98 mag per 100 days, Woosley et al. 1989). This gives interesting constraints on the mass extent and density of SNe ejecta, as will be discussed below. We observe more variation in decline rates at earlier times (s₁) than during the "plateau" phase (s₂).

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As with the absolute magnitude distributions discussed above, the V-band decline rates appear to show a continuum in their distributions. The possible exceptions are those SNe declining extremely quickly through s₁: the fastest decliner SN 2006Y with an unprecedented rate of 8.15 mag per 100 days. In the case of s₂ the fastest decliner is SN 2002ew with a decline rate of 3.58 mag per 100 days, while SN 2006bc shows a rise during this phase, at a rate of −0.58 mag per 100 days. The s₂ decline rate distribution has a tail out to higher values, while a sharp edge on the left hand side is seen, with only six SNe having negative decline rates during this epoch.

In Figure 5 we show how the decline rates correlate. A correlation between s₁ and s₂ is observed despite a handful of outliers. s₂ and s₃ also appear to show the same trend: a fast decliner at one epoch is usually a fast decliner at other epochs. This suggestion that more steeply declining SNe II (during s₂) also have faster declining radioactive tails was previously suggested by Doggett & Branch (1985). In both of these plots there is at least one obvious outlier: SN 2006Y. We mark the position of this event here and also on subsequent figures where it also often appears as an outlier to any trend observed. Further analysis of this highly unusual event will be the focus of future work.

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In summary of the overall distributions of decline rates: SNe II which decline more quickly at early epochs also generally decline more quickly both during the plateau and on the radioactive tail.

Having presented parameter distributions and correlations in the previous section, here we turn our attention to investigating whether SN brightness and rate of decline of their light-curves are connected. In some of the plots presented in this section photometric measurements of the prototypical type IIL SN 1979C are also included for comparison (de Vaucouleurs et al. 1981). The positions within the correlations of the prototypical type IIP SN 1999em, plus the sub-luminous type IIP SN 2008bk (both from our own sample) are also indicated.

Given that peak epochs of SNe II are often hard to define, literature measurements of SN II brightness have generally concentrated on some epoch during the "plateau" (e.g., Hamuy 2003a; Nugent et al. 2006). Therefore, we start by presenting the correlation of M_end (brightness at the end of the "plateau") with s₂ in Figure 6. No correlation is apparent which is confirmed by a Pearson's test. Given that M_end does not seem to correlate with decline rates (Figure 30 shows correlations against s₁ and s₃), we move to investigate M_max-decline rate correlations.

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In Figure 7 M_max against s₂ is plotted. It is found that these parameters show a trend with lower luminosity SNe declining more slowly (or even rising in a few cases), and more luminous events declining more rapidly during the "plateau." One possible bias in this correlation is that SNe are included if only one slope is measured (just s₂) together with those events with two. However, making further cuts to the sample (only including those with s₁ and s₂ measurements) does not significantly affect the results and conclusions presented here. Later in Section 5.6 we discuss this issue further and show how using a sub-sample of events with both slopes measured enables us to further refine the predictive power of s₂.

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The above finding is consistent with previous results showing that SNe IIL are generally more luminous than SNe IIP (Young & Branch 1989; Patat et al. 1994; Richardson et al. 2002). It is also interesting to note the positions of the example SNe displayed in Figure 7: the sub-luminous type IIP SN 2008bk has a low luminosity and a very slowly declining light-curve; the prototype type IIL SN 1979C is brighter than all events in our sample, and also has one of the highest s₂ values. The prototype type IIP SN 1999em has, as expected, a small s₂ value, and most (78%) of the remaining SNe II decline more quickly. In terms of M_max, on the other hand, SN 1999em does not stand out as a particularly bright or faint object. We note one major outlier to the trend presented in Figure 7: SN 2008bp with a high s₂ value (3.17 mag per 100 days) but a very low M_max value (−14.54 mag). It is possible that the extinction has been significantly underestimated for this event based on its weak interstellar absorption NaD, and indeed the SN has a red color during the "plateau" (possibly implying significant reddening). Further analysis will be left for future work.

In Figure 8 we plot M_max against s₁. While the significance of correlation is not as strong as seen with respect to s₂, it still appears that more luminous SNe at maximum light decline more quickly also at early times.

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Finally, in Figure 9 M_max against s₃ is presented, and the expected decline rate (dashed horizontal line) if one assumes full trapping of gamma-ray photons from the decay of ⁵⁶Co to ⁵⁶Fe is displayed. There appears to be some correlation in that more luminous SNe II at maximum have higher s₃ values. However, more relevant than a strict one to one correlation, it is remarkable that none of the fainter SNe deviate significantly from the slope expected from full trapping, while at brighter magnitudes significant deviation is observed. The physical implications of this will be discussed below. Finally, we note that while the striking result from Figures 4 and 9 is the number of SNe with s₃ values higher than 0.98 mag per 100 days, and the fact that nearly all of these are overluminous (compared to the mean) SNe II, it is also observed that there are a number of SNe which have s₃ values lower than the expected value. These SNe also generally have lower peak luminosities. Indeed this has been noted before, especially for sub-luminous SNe IIP by Pastorello et al. (2009) and Fraser et al. (2011). In the case of SN 1999em, Utrobin (2007) argued that the discrepancy (from the rate expected due to radioactivity) was due to radiation from the inner ejecta propagating through the external layers and providing additional energy (to that of radioactivity) to the light-curve, naming this period the "plateau tail phase."

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In Figure 10 both the V-band "plateau" duration (Pd) distribution, together with its correlation with M_max are displayed. A large range of Pd values is observed, from the shortest of ∼27 days (again the outlier SN 2006Y discussed above) to the longest of ∼72 days (SN 2003bl), with no signs of distribution bimodality. The mean Pd for the 19 events where a measurement is possible is 48.4 days, with a standard deviation of 12.6. While statistically there is only small evidence for a trend, it is interesting to note that the two SNe with the longest Pd durations are also of low-luminosity, while that with the shortest Pd is one of the most luminous events.

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In Figure 11 both the V-band optically thick phase duration (OPTd) distribution, together with its correlation with M_max are displayed. Again, a large range in values is observed with a mean OPTd of 83.7 days, and σ = 16.7. The mean error on estimated OPTd values is 7.8 ± 3.0 days. Hence, the standard deviation of OPTd values is almost twice as large as the typical error on any given individual SN. This argues that the large range in observed OPTd values is a true intrinsic property of the analyzed sample. The shortest duration of this phase is SN 2004dy with OPTd = 25 days, while the largest OPTd is for SN 2004er, of 120 days. SN 2004dy is a large outlier within the OPTd distribution, marking it out as a very peculiar SN. Further comment on this will be left for future analysis, however we do note that Folatelli et al. (2004) observed strong He i emission in the spectrum of this event, also marking out the SN as spectroscopically peculiar. Again, within the OPTd distribution there appears to be a continuum of events. Although there is no statistical evidence for a correlation between the OPTd and M_max, the most sub-luminous events have some of the longest OPTd, while those SNe with the shortest OPTd durations are more luminous SNe II. These large continuous ranges in Pd and OPTd are in contrast to the claims of Arcavi et al. (2012) who suggested that all SNe IIP have "plateau" durations of ∼100 days (however we note that the Arcavi et al. study investigated R-band photometry, rather than the V-band data presented in the current work). Further comparison of the current results to those of Arcavi et al. will be presented below.

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In Figure 12 correlations between both Pd and OPTd with s₂ are presented. While there is much scatter in the relations, these results are consistent with the picture of faster declining SNe II having shorter duration "plateau" phases (see, e.g., Blinnikov & Bartunov 1993). Indeed, such a trend was first observed by Pskovskii (1967). A similar, but stronger trend is observed when Pd and OPTd are correlated against s₁, as presented in Figure 13.

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Finally, in Figure 14 we present correlations between Pd and OPTd with s₃. As will be discussed in detail below, both OPTd and s₃ provide independent evidence for significant variations in the mass of the hydrogen envelope/ejecta mass at the epoch of explosion. The trend shown in Figure 14 in that SNe with longer OPTd values have smaller s₃ slopes, is consistent with the claim that such variations can be attributed to envelope mass.

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In summary, generally SNe which have shorter duration Pd and OPTd tend to decline more quickly at all epochs.

Given that the exponential tail (phase s₃) of the SN II light-curves are presumed to be powered by the radioactive decay of ⁵⁶Co (see, e.g., Woosley 1988), one can use the brightness at these epochs to determine the mass of ⁵⁶Ni synthesized in the explosion. However, as we have shown above, there is a significant spread in the distribution of s₃ values, implying that not all gamma-rays released during to the decay of ⁵⁶Co to ⁵⁶Fe are fully trapped by the ejecta during the exponential tail, rendering the determination of the ⁵⁶Ni mass quite uncertain. Therefore, we estimate ⁵⁶Ni masses only in cases where we have evidence that s₃ is consistent with the value expected for full trapping (0.98 mag per 100 days). For all other SNe with magnitude measurements during the tail, but either s₃ values significantly higher (0.3 mag per 100 days higher) than 0.98 (mag per 100 days), or SNe with less than three photometric points (and therefore no s₃ value can be estimated), lower limits to ⁵⁶Ni masses are calculated. In addition, for those SNe without robust host galaxy extinction estimates (see Section 3.3) we also calculate lower limits.

To estimate ⁵⁶Ni masses and limits, the procedure presented in Hamuy (2003a) is followed. M_tail V-band magnitudes are converted into bolometric luminosities using the bolometric correction derived by Hamuy et al. (2001), together with the distance moduli and extinction values reported in Table 6.²³ Given our estimated explosion epochs, mass estimates are then calculated and are listed in Table 6.

In Figure 15 we compare OPTd and ⁵⁶Ni masses. Young (2004) and Kasen & Woosley (2009) claimed that heating from the radioactive decay of ⁵⁶Ni should further extend the plateau duration. We do not find evidence for that trend in the current sample (consistent with the finding of Bersten 2013). In fact, if any trend is indeed observed it is the opposite direction to that predicted.

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The range of ⁵⁶Ni masses is from 0.007 M_☉ (SN 2008bk) to 0.079 M_☉ (SN 1992af), and the distribution (shown in Figure 15) has a mean value of 0.033 (σ = 0.024) M_☉. Given the earlier trends observed between s₃ and other parameters it is probable that there is a systematic effect, and those SNe II where only lower limits are possible are probably not simply randomly distributed within the rest of the population. Therefore, we caution that this ⁵⁶Ni synthesized mass distribution is probably biased compared to the true intrinsic range.

Elmhamdi et al. (2003) reported a correlation between the steepness of V-band light-curves during the transition from plateau to tail phases (named the inflection time in their work), and estimated ⁵⁶Ni masses. With the high quality data presented in the current work, we are in an excellent position to test this correlation. The Elmhamdi et al. method entailed weighted least squares minimization fitting of a defined function (their Equation (1)), to the V-band light-curve in the transition from plateau to radioactive phases in the period of ±50 days around the inflection point of this transition. The steepness parameter is then defined as the point at which the derivative of magnitude with time is maximal. We attempt this same procedure for all SNe in the current sample. We find that it is possible to define a reliable steepness (S) term in only 21 cases. This is because one needs extremely well sampled light curves at epochs just before, during and after the transition. Even for well observed SNe this type of cadence is uncommon, and we note that in cases where one can define an S-value, additional data points at key epochs could significantly change the results. We do not find any evidence for a correlation as seen by Elmhamdi et al., and there does not appear to be any trend that could be used for cosmological purposes to standardize SNe II light-curves (see the Appendix for further details).

M_max shows the highest degree of correlation with decline rates of all defined SN magnitudes. From an observational point of view this is maybe somewhat surprising, given the difficultly in defining this parameter: a true maximum is often not observed in our data, and hence in the majority of cases we are forced to simply use the first photometric point available for our estimation. This uncertainty in M_max indeed implies that the intrinsic correlation between M_max and the two initial decline rates, s₁ and s₂, is probably even stronger. Paying close attention to Figure 7 together with Figure 27, it is easy to see why this could be the case. In general a low-luminosity SN has a slow decline rate at both initial and "plateau" epochs. Therefore, if one were to extrapolate back to the "true" M_max magnitude, its measured value would change very little. However, this is not the case for the most luminous SNe. In general these have much faster declining light-curves. Hence, if we extrapolate these back to their "true" peak values, these SNe will have even brighter M_max values, and hence the strength of the correlation could be even higher than that presently measured.

The statement that faster declining SNe (type IIL) are brighter than slower declining ones (type IIP) is not a new result. This has been seen previously in the samples of, e.g., Pskovskii (1967); Young & Branch (1989); Patat et al. (1994) and Richardson et al. (2002). However, (to our knowledge) this is the first time that a wide-ranging correlation as shown in Figure 7 has been presented with the supporting statistical analysis.

Arcavi et al. (2012) recently claimed that SNe IIP and SNe IIL appear to be separated into two distinct populations in terms of their R-band light-curve behavior, possibly suggesting distinct progenitor scenarios in place of a continuum of events. In the current paper we have made no attempt at definitive classifications of events into SNe IIP and SNe IIL (ignoring whether such an objective classification actually exists). However, in the above presented distributions and figures we see no evidence for a separation of events into distinct categories, or a suggestion of bimodality. While it is important to note that these separate analyses were undertaken using different optical filters, these results are intriguing.

In Figure 16 Legendre polynomial fits to all light-curves of SNe with explosion epoch constraints are presented, the same as in Figure 2, but now with all SNe normalized to M_max, and also including SNe where host extinction corrections were not possible. While this figure shows the wide range in decline rates and light-curve morphologies discussed above, there does not appear to be any suggestion of a break in morphologies. Given all of the distributions we present, together with the qualitative arguments of Figure 16, it is concluded that this work implies a continuum of hydrogen-rich SNe II events, with no clear separation between SNe IIP and SNe IIL (at least in the V band).

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To further test this suggestion of an observational continuum, in Figure 17 we present the same light-curves as in Figure 16, but now presented as a density plot. This is achieved in the following way. Photometry for each SN was interpolated linearly to the time interval of each bin (which separates the overall time axis into 20 bins). This estimation starts with the first bin where the first photometric point lies for each SN, and ends at the bin containing the last photometric point used to make Figure 16. This interpolation is done in order to compensate for data gaps and to homogenize the observed light-curve to the given time intervals. In Figure 16 it is hard to see whether there are certain parts of the light-curve parameter space that are more densely populated than others, given that light-curves are simply plotted on top of one another. If the historically defined SNe types IIP and IIL showed distinct morphologies, then one may expect such differences to be more easily observed in a density plot such as that presented in Figure 17. However, we do not observe any such well defined distinct morphologies in Figure 17 (although we note that even the large sample of more than 100 SN light-curves is probably insufficient to elucidate these differences through such a plot). In conclusion, Figure 17 gives further weight to the argument that in the currently analyzed sample there is no evidence for multiple distinct V-band light-curve morphologies, which clearly separate SNe IIP from SNe IIL.

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The suggestion of a large scale continuum derived from our analysis is insightful for the physical understanding of hydrogen-rich explosions. A continuum could imply that the SN II population is formed by a continuum of progenitor properties, such as ZAMS mass, with the possible conclusion that more massive progenitors lose more of their envelopes prior to explosion, hence exploding with lower mass envelopes, producing faster evolving light-curves than their lower progenitor mass companions. We note that the claim of a continuum of properties for explaining differences in hydrogen-rich SNe II light-curves is also supported by previous modeling from, e.g., Blinnikov & Bartunov (1993). These authors suggest that the diversity of events could be explained through differing pre-SNe radii, the power of the pre-SN wind, and the amount of hydrogen left in the envelope at the epoch of explosion.

In the process of this work it has been noted that there is no clear objective classification system for defining a SN IIP from a SN IIL. The original classification was made by Barbon et al. (1979) who from B-band light curves, stated that (1) SNe IIP are characterized by a rapid decline, a plateau, a second rapid decline, and a final linear phase, which in our terminology correspond to s₁, s₂, transition between "plateau" and tail phases (the mid point being t_PT), and s₃ respectively; (2) SNe IIL are characterized by an almost linear decline up to around 100 days post maximum light (also see Doggett & Branch 1985). This qualitative classification then appears to have been used for the last 3 decades without much discussion of its meaning or indeed validity. A "plateau" in the truest sense of the word would imply something that does not change, in this case the light-curve luminosity remaining constant for a period of at least a few months. However, if we apply this meaning to the current sample, claiming that anything which changes at a rate of less than 0.5 mag per 100 days during s₂ is of SN IIP class, then this includes only ∼25% of SNe II in the current sample, much less than the percentages of 75% and 95% estimated by Li et al. (2011) and Smartt et al. (2009) respectively (or the 65% in the original publication of Barbon et al. 1979). Even if we relax this criterion to 1 mag per 100 days, then still only 41% of the current sample would be classified as SNe IIP.

Meanwhile, as outlined above, the generally accepted terminology for SNe IIL appears to be that these events have fast linear decline phases post maximum until they evolve to the radioactive tail. However, it is unclear how many SNe actually exist either in the literature or within our own sample which fulfill this criterion. Two literature prototype type IIL events are SN 1979C and SN 1980K. However, while both of these SNe have relatively fast declining light-curves, they both show evidence for an end to their "plateau" phases, or "breaks" in their light-curves (i.e., an end to s₂ or the optically thick phase, before transition to s₃). This is shown in Figure 18, where the V-band photometry for both objects (data from de Vaucouleurs et al. 1981 and Buta 1982; Barbon et al. 1982 respectively) are plotted, together with the data for the three SNe within our sample which have the highest s₂ values. In the case of four of the five SNe plotted in Figure 18 there is evidence for a "break" in the light-curves, i.e., an end to an s₂ phase, while in the remaining case the data are insufficient to make an argument either way. (We note that in the case of SN 1979C one observes a smooth transition between phases, more than a sharp change in light-curve shape, while in the case of SN 2003ej the evidence for a "break" is supported by only one data point after the s₂ decline).

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It could be that SNe IIL are not solely those that evolve the quickest, but those where there is no evidence for a "plateau" or "break" in their light-curves. Therefore, we visually search through our sample attempting to identify those SNe which are most likely to be classified as SNe IIL in the historically defined terminology. Only six cases are identified, together with SN 2002ew already presented in Figure 18, and their V-band light-curves are displayed in Figure 19. This figure shows some interesting features. At least half of the SNe displayed show signs of a maximum around 10–20 days post explosion, a characteristic that is rare in the full SN II sample. After early epochs it would appear that these events could be defined as having "linear" morphologies. However, there are two important caveats before one can label these as SNe IIL in the historical sense: (1) none of the seven SNe presented in Figure 19 has photometry after day 100 post explosion (with only two SNe having data past 80 days), hence it could be that a "break" before the radioactive tail is merely unobserved due to the lack of late time data, and (2) for about half of the events the cadence at intermediate epochs is such that one may have simply missed any "break" phase during these epochs. Putting these caveats aside, even if we assume that these seven events should be classified as SNe IIL, this would amount to a relative fraction of SNe IIL events in the current sample of ∼6% (of hydrogen rich SNe II), i.e., at lowest limit of previously estimated percentages (Barbon et al. 1979; Smartt et al. 2009; Li et al. 2011). Hence, we conclude that if one uses the literal meaning of the historically defined SNe IIL class, then these events are intrinsically extremely rare.

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Given the arguments presented in the previous two sub-sections: a continuum of events; no clear separation between the historically defined SNe IIP and SNe IIL; a possible lack of any true steeply declining "linear" SNe II; many SNe having much faster declining light-curves than the prototypical type IIP SN 1999em, we believe that it is time for a reappraisal of the SN II light-curve classification scheme. Indeed, the current terminology in the literature, and its use by different researchers prohibits consistent statistical analyses and gives virtually no quantitative information on light-curve morphology. It is therefore proposed that given the easiest parameter to measure for any given SN II is the decline rate during the "plateau" phase, its s₂ value, that this parameter should be used to define any given SN II. This would follow the similar procedure of SN Ia classifications, where individual events are further classified by referring to their ▵m₁₅ value (decline in brightness during the first 15 days post maximum light, Phillips 1993b) or "stretch" parameter (Perlmutter et al. 1997). Hence, we propose that to standardize terminology, future SNe II are referred to as, e.g., "SN1999em, a SN II with s₂ = 0.31." This will enable investigators to define SN samples in a consistent manner which is not currently possible. This is particularly pertinent for future surveys (such as that of the Large Synoptic Survey Telescope; Ivezic et al. 2008) which will produce thousands of SNe II light-curves and where simply referring to a SN as type IIP or type IIL gives little quantitative information. Using a standardized terminology will allow one to define, e.g., a range of SNe II which are good standard candles, i.e., possibly only those traditionally classified as SNe IIP. However, now one could quantify this by giving a sample range of, e.g., −0.5 < s₂ < 1.

5.5.1. The Prevalence of s₁: Extended Cooling in SNe II?

5.5.2. Probing Ejecta/Envelope Properties with s3 and OPTd

5.5.3. Mass Extent and Density Profile of SNe II as the Dominant Physical Parameter

SNe II (or specifically SNe IIP) have long been discussed as complementary (to SNe Ia) distance indicators, with a number of techniques being employed to standardize their luminosities (e.g., the expanding photosphere method: Kirshner & Kwan 1974; Eastman et al. 1996; Dessart & Hillier 2005; Dessart et al. 2008; Jones et al. 2009; Bose & Kumar 2014; the spectral fitting expanding photosphere method: Mitchell et al. 2002; Baron et al. 2004; and the standard candle method: Hamuy & Pinto 2002; Nugent et al. 2006; Poznanski et al. 2009; D'Andrea et al. 2010; Olivares E. et al. 2010). However, a key issue that currently precludes their use for higher redshift cosmology is the need for spectral measurements in these techniques. Any photometric relation between SN II luminosities and other parameters, if found could enable SNe II to be used as accurate high-redshift distance indicators. This would be particularly pertinent when one keeps pushing to higher redshift where the SN Ia rate is expected to drop due to their relative long progenitor lifetimes, while the SNe II rate should remain high as it follows the star formation rate of the Universe.

In Figure 7 a correlation between M_max and s₂ was presented, where more luminous events show steeper declining light-curves. In Figure 20 we now invert the axis of the earlier figure in order to evaluate the predictive power of s₂. The best fit line is estimated by running 10,000 Monte Carlo bootstrap simulations and calculating the mean of the slopes and y-intercept values obtained. This then leads to a relation between s₂ and M_max for the full sample, as presented in the left panel of Figure 20, which has a dispersion of 0.83 mag. However, it was earlier noted in Section 4.2 that in this full sample we are including SNe where only a measurement of s₂ was possible (i.e., no distinction between s₁ and s₂). This may bias the sample, as if an s₁ is not detected but intrinsically is present, then it will merge with s₂, and probably artificially increase the value of s₂ we present in Table 6. Following this we make a cut to our sample to only include SNe where both the measurement of s₁ and s₂ are favored (see Section 3). We then obtain a sample of 22 events. The correlation between s₂ and M_max for this curtailed sample is stronger: running our Monte Carlo simulated Pearson's test gives, r = −0.82 ± 0.05 and P ⩽ 3 × 10⁻⁵. In the right panel of Figure 20 this correlation is presented, and the following relation is derived:

$$\begin{equation*} M_{\rm max}= -1.12(s_2) -15.99 \end{equation*}$$

This relation has a dispersion of only 0.56 mag. While this is still higher than that published for SN II spectroscopic distance methods (and considerably higher than SN Ia), the predictive power of s₂ is becoming very promising. If the accuracy of parameters such as host galaxy extinction can be improved, and SN color information included, then it may be possible to bring this dispersion down to levels where SNe II are indeed viable photometric distance indicators, independent of spectroscopic measurements.²⁴

A model correlation between the SN luminosity at day 50 post explosion (closest to our M_end value) and the duration of the plateau was predicted by Kasen & Woosley (2009) (see also Bersten 2013; Poznanski 2013), which they claimed could (if corroborated by observation) be used to standardize SNe IIP luminosities. We only observe marginal evidence for any such trends.

While statistical studies of SNe II as that presented here are to date rare or even non-existent, they promise to become much more prevalent in the near future, with larger field of view and deeper transient searches planned or underway. During the course of this investigation it has become obvious that a number of key attributes are needed to efficiently further our understanding of hydrogen-rich SNe II through well planned observations. Firstly, strong constraints on the explosion epoch is key, as this allows measurements to be derived with respect to a well defined epoch (in the case of SNe Ia one can use the maximum of the light-curve, however for SNe II such a method contains higher levels of uncertainty). Secondly, high cadence photometry is warranted to be able to differentiate between different slopes such as s₁ and s₂. Indeed, it appears that it is often assumed that SNe IIP light-curves are reasonably well behaved and therefore one can obtained photometry in a more relaxed fashion. However, it is clear from the current work that photometry obtained every few days is needed to further our understanding of the diversity of SNe II: in general one does not know at what stage a SN II will transition from one phase to the other, and data at those points are vital for the phases to be well constrained. Thirdly, detailed observations of the radioactive tails are needed to confirm and further investigate deviations from s₃ values expected from full trapping. Such observations contain direct information on the ejecta profiles of each SN and are key to understanding the progenitor and pre-SN properties of SNe II. While the current study has opened many avenues for further investigation and intriguing insights to the underlying physics of SNe II explosions, continued high quality data are needed to deepen our understanding of hydrogen-rich SNe II. As we have hinted throughout this paper, the CSP has obtained multi-color optical and near-IR light-curves, together with high quality spectral sequences of a large sample of SNe II. The near-IR data could prove key to the understanding of SNe II, and their use as distance indicators, since they are essentially unaffected by dust extinction. The full analysis of those samples will present a large increase in our understanding of the observational diversity of SNe II events.

As noted in Section 1, the currently analyzed sample is an eclectic mix of SNe II, discovered by many different SN search campaigns, of both professional and amateur nature. In this section, we further characterize the SN and host galaxy samples, and briefly discuss some possible consequences of their properties.

Figure 21 presents a pie chart which shows the contributions of various SN programs and individuals to the discovery of SNe presented in this analysis. The largest number of events included, discovered by any one survey/individual are those reported by the Lick Observatory Supernova Search (LOSS/LOTOSS; Leaman et al. 2011), who contribute 41 SNe (∼40%). Surprisingly, the next highest contributor to our sample is Berto Monard, an amateur astronomer from South Africa, with an impressive 12 entries (∼10%). Next is the Chilean Automatic Supernova Search (Pignata et al. 2009) with 11, followed by "Maza" (SNe discovered by investigators at Universidad de Chile during the 1990s, led by Jose Maza), Robert Evans (another amateur astronomer, from Australia), and the Near-Earth Asteroid Tracking (NEAT) survey. All other discoveries are grouped into "Other." The vast majority of SNe were discovered by galaxy targeted surveys (88%, counting SDSS, CSS, and NEAT as non-targeted surveys). As most targeted surveys are biased toward bright nearby galaxies, this may lead to a bias against SNe in low-luminosity host galaxies. These and similar issues are discussed for the LOSS SN sample in Li et al. (2011).

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In Figure 22 we present the host galaxy recession velocity and absolute B-band magnitude distributions respectively. Our sample has a mean recession velocity of 5505 km s⁻¹, equating to a mean redshift of 0.018, and a mean distance of 75 Mpc, with the vast majority of galaxies having velocities lower than 10,000 km s⁻¹. The host galaxy population is characterized as having a well defined absolute magnitude B-band peak at ∼−21 mag, together with a low-luminosity tail down to around −17 mag.²⁵ Host galaxy absolute magnitudes are listed in Table 1. It is interesting to compare this heterogeneous sample with that published by Arcavi et al. (2010) (CC SNe discovered by the Palomar Transient Factory, PTF). While those authors published host galaxy r-band magnitudes (compared to the B-band magnitudes analyzed here), overall the distributions appear qualitatively similar, with the exception that the PTF sample has a much more pronounced lower-luminosity tail. If the intrinsic rate of specific SNe II events changes with host galaxy luminosity (due to, e.g., a dependence on progenitor metallicity), then this could affect the overall conclusions draw from our sample, where we are possibly missing SNe in low-luminosity hosts. A full analysis of these host galaxy properties is beyond the scope of this paper, and a detailed host galaxy study of the CSP sample is underway.

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Table 4 shows a comparison between explosion epochs obtained through both the non-detection and spectral matching methods, for the 61 SNe where this is possible. In Figure 23 we present on the left panel a comparison of these two methods. On the right panel is a histogram showing the offset between the two estimations. One can see that in general very good agreement is found between the two methods, with a mean absolute error of 4.2 days between the different techniques. This gives us confidence in our measurements which are dependent on spectral matching analysis. A feature of the two plots is that where there are differences between the two methods then it is more often that the estimate from the non-detection is earlier than that from spectral matching: there is a 1.5 day mean offset in that direction between the two methods. It is noted that those SNe in Table 4 with the largest offsets between the methods are also the SNe which have the highest errors on the estimations from non-detections, i.e., if SNe have low non-detection errors, then the epochs from the two methods are even more consistent.

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We now re-analyze our sample, but only include those SNe where epochs are derived from non-detections, which one may assume are more accurate, and less dependent on systematics. The results of this re-analysis are as follows. The Pd sub-sample has a mean value of 48.9 ± 14 days, for eight events. This compares to: mean Pd = 48.4 ± 13 for the 19 events of the full sample. The OPTd sub-sample has a mean value of 83.7 ± 21 for 32 SNe, compared to 83.7 ± 17 for the full sample of 72. In addition, the Monte Carlo bootstrap Pearson's tests are also re-run for all sub-sample correlations which are affected by explosion epoch estimates. In Table 5 correlations are compared between the full sample and the sub-set of SNe with non-detection constraints. The results are fully consistent within the errors: despite the low number statistics the strengths of the correlations are very similar in the majority of cases.

The above comparison shows that the inclusion of time durations dependent on spectral matching explosion epochs does not systematically change our distributions, or the strength of presented correlations, and hence gives us further confidence in the results of our full sample.

In Figures 24, 25 and 26 present V-band absolute magnitude light-curves for the full sample of 116 SNe II included in this study, where the measured parameters listed in Table 6 and used in the analysis throughout this work, are also provided in figure form. In Figure 27 an example of the automated s₁–s₂ fitting process is displayed, showing examples of where a simple one slope fit (i.e., s₂ for SN 2008ag), and a two slope fit (s₁, s₂ for SN 2004er) are good representations of the photometry.

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Table 6. SN II V-band Light-curve Parameters

SN	DM	Explosion	tPT	AV(Host)	Mmax	Mend	Mtail	s1	s2	s3	OPTd	Pd	56Ni Mass
	(mag)	Epoch (MJD)	(MJD)	(mag)	(mag)	(mag)	(mag)	(mag 100 day−1)	(mag 100 day−1)	(mag 100 day−1)	(days)	(days)	( M☉)
1986L	31.721(0.20)	46708.0n(6)	46818.4(0.6)	0.00(0.07)	−18.19(0.21)	−16.88(0.22)	−14.37(0.22)	3.32(0.16)	1.28(0.03)	...	93.7(5)	59.2(4)	>0.061
1991al	33.94(0.15)	48443.5s(9)	48518.8(0.6)	0.11(0.07)	−17.62(0.17)	−17.14(0.17)	−14.82(0.17)	...	1.55(0.06)	1.26(0.26)	...	...	0.067$^{+0.016}_{-0.021}$
1992ad	31.13(0.80)	...	...	...	−16.98*(0.80)	−16.13*(0.80)	...	...	2.23(0.04)	...	...	...	...
1992af	34.33(0.12)	48791.5s(6)	48861.1(0.4)	0.00(0.27)	−17.33(0.30)	−17.20(0.30)	−15.06(0.30)	...	0.37(0.09)	1.07(0.08)	54.0(7)	...	0.079$^{+0.018}_{-0.029}$
1992am	36.42(0.05)	...	48947.2(0.6)	...	−18.06*(0.07)	−17.17*(0.08)	...	...	1.17(0.02)	...	...	...	...
1992ba	30.41(0.80)	48888.5s(8)	49014.0(1.2)	0.05(0.03)	−15.39(0.80)	−14.80(0.80)	−12.39(0.80)	...	0.73(0.02)	0.86(0.07)	104.0(9)	...	0.011$^{+0.006}_{-0.015}$
1993A	35.44(0.07)	48995.5n(9)	...	...	−16.44*(0.07)	−15.91*(0.07)	...	...	0.72(0.03)	...	...	...	...
1993K	32.95(0.23)	49065.5n(9)	...	0.37(0.19)	−18.29(0.30)	−17.61(0.30)	...	...	2.46(0.08)	...	...	...	...
1993S	35.60(0.07)	49130.5s(4)	...	0.00(0.24)	−17.52(0.25)	−16.29(0.26)	...	...	2.52(0.05)	...	...	...	...
1999br	31.19(0.40)	51276.5n(4)	...	0.00(0.04)	−13.77(0.40)	−13.56(0.40)	...	...	0.14(0.02)	...	...	...	>0.002
1999ca	33.15(0.21)	51277.5s(7)	51373.2(0.8)	0.26(0.15)	−17.74(0.26)	−16.86(0.26)	−14.04(0.26)	3.41(0.15)	1.73(0.04)	1.74(0.33)	80.5(8)	39.3(4)	>0.047
1999cr	34.70(0.10)	51247.5s(7)	51350.2(3.1)	0.30(0.15)	−17.20(0.19)	−16.53(0.19)	...	1.80(0.06)	0.58(0.06)	...	78.1(8)	41.4(4)	...
1999eg	34.75(0.10)	51440.5s(7)	...	...	−16.86*(0.10)	−16.12*(0.10)	...	...	1.70(0.08)	...	...	...	...
1999em	30.372(0.07)	51476.5n(5)	51590.1(0.9)	0.18a(0.06)	−16.94(0.10)	−16.55(0.10)	−14.11(0.10)	...	0.31(0.02)	0.88(0.05)	96.0(7)	...	0.050$^{+0.008}_{-0.009}$
0210	36.58(0.04)	52489.5(9)s	52591.9(0.3)	...	−16.21*(0.04)	−15.90*(0.04)	...	...	2.21(0.08)	...	90.6(10)	...	...
2002ew	35.38(0.08)	52500.5n(10)	...	0.00(0.07)	−17.42(0.11)	−14.95(0.12)	...	...	3.58(0.06)	...	...	...	...
2002fa	36.92(0.04)	52503.5s(7)	...	...	−16.95*(0.04)	−16.65*(0.04)	...	...	1.58(0.10)	...	67.3(8)	...	>0.066
2002gd	32.50(0.28)	52552.5s(4)	...	0.00(0.06)	−15.43(0.29)	−14.85(0.29)	...	2.87(0.25)	0.11(0.05)	...	...	...	...
2002gw	32.98(0.23)	52559.5s(5)	52661.2(0.8)	0.00(0.05)	−15.76(0.24)	−15.48(0.24)	−13.07(0.24)	...	0.30(0.03)	0.75(0.09)	82.3(6)	...	0.012$^{+0.003}_{-0.004}$
2002hj	34.87(0.10)	52562.5n(7)	52661.8(0.8)	0.00(0.11)	−16.91(0.16)	−16.03(0.16)	−13.59(0.16)	...	1.92(0.03)	1.41(0.01)	90.2(8)	...	>0.026
2002hx	35.59(0.07)	52582.5n(9)	52658.9(0.8)	0.00(0.23)	−17.00(0.25)	−16.36(0.25)	−14.60(0.25)	...	1.54(0.04)	1.24(0.04)	68.0(10)	...	0.053$^{+0.016}_{-0.023}$
2002ig	37.47(0.03)	52572.5s(4)	...	...	−17.66*(0.03)	−16.76*(0.03)	...	...	2.73(0.11)	...	...	...	...
2003B	31.11(0.28)	52616.5s(11)	52713.8(0.9)	0.18(0.09)	−15.54(0.30)	−15.29(0.30)	−12.95(0.30)	...	0.65(0.03)	1.07(0.03)	83.2(12)	...	0.017$^{+0.006}_{-0.009}$
2003E	33.92(0.15)	52634.5s(7)	52765.7(0.8)	...	−15.70*(0.15)	−15.48*(0.15)	...	...	−0.07(0.03)	...	97.4(8)	...	...
2003T	35.37(0.08)	52654.5n(10)	52758.7(0.6)	...	−16.54*(0.08)	−16.03*(0.08)	−13.67*(0.08)	...	0.82(0.02)	2.02(0.14)	90.6(11)	...	>0.030
2003bl	34.02(0.14)	52699.5s(3)	52804.5(0.2)	0.00(0.27)	−15.35(0.31)	−15.01(0.31)	...	1.05(0.35)	0.24(0.04)	...	92.8(5)	71.7(9)	...
2003bn	33.79(0.16)	52694.5n(3)	52813.7(0.7)	0.00(0.07)	−16.80(0.18)	−16.34(0.18)	−13.72(0.18)	0.93(0.06)	0.28(0.04)	...	93.0(5)	53.9(5)	>0.038
2003ci	35.56(0.07)	52711.5n(8)	52817.7(1.0)	...	−16.83*(0.07)	−15.70*(0.07)	...	...	1.79(0.04)	...	92.5(9)	...	...
2003cn	34.48(0.11)	52719.5s(4)	52804.2(0.3)	0.00(0.12)	−16.26(0.17)	−15.61(0.17)	...	...	1.43(0.04)	...	67.8(6)	...	...
2003cx	35.96(0.06)	52728.5s(5)	52828.5(0.8)	0.00(0.17)	−16.79(0.18)	−16.38(0.19)	−14.32(0.19)	...	0.76(0.03)	...	87.8(7)	...	>0.051
2003dq	36.44(0.06)	52731.5n(8)	...	...	−16.69*(0.06)	−15.69*(0.36)	...	...	2.50(0.19)	...	...	...	...
2003ef	34.08(0.14)	52759.5s(9)	52869.9(0.6)	...	−16.72*(0.14)	−16.15*(0.14)	...	...	0.81(0.02)	...	90.9(10)	...	...
2003eg	34.23(0.13)	52773.5s(5)	...	...	−17.81*(0.13)	−14.57*(0.13)	...	...	2.93(0.04)	...	...	...	...
2003ej	34.36(0.12)	52775.5n(5)	...	0.00(0.09)	−17.66(0.16)	−15.66(0.16)	...	...	3.46(0.05)	...	69.0(7)	...	...
2003fb	34.43(0.12)	52776.5s(6)	52874.4(0.6)	...	−15.56*(0.13)	−15.25*(0.13)	−13.10*(0.14)	...	0.48(0.06)	1.61(0.39)	84.3(7)	...	>0.017
2003gd	29.93(0.40)	52767.5s(15)	52840.9(0.2)	0.43b(0.19)	...	−16.40(0.44)	−13.01(0.45)	...	...	1.03(0.04)	...	...	0.012$^{+0.006}_{-0.012}$
2003hd	36.00(0.06)	52857.5s(5)	52952.9(1.2)	0.00(0.19)	−17.29(0.20)	−16.72(0.21)	−13.85(0.21)	...	1.11(0.04)	0.72(0.68)	82.4(6)	...	0.029$^{+0.007}_{-0.009}$
2003hg	33.65(0.16)	52865.5n(5)	52998.6(1.1)	...	−16.38*(0.16)	−15.50*(0.16)	...	1.60(0.06)	0.59(0.03)	...	108.5(7)	67.1(4)	...
2003hk	34.77(0.10)	52867.5s(4)	52961.2(1.6)	...	−17.02*(0.10)	−16.36*(0.10)	−13.14*(0.10)	...	1.85(0.06)	0.40(0.66)	86.0(6)	...	>0.017
2003hl	32.39(0.30)	52868.5n(5)	53005.4(0.1)	...	−15.91*(0.30)	−15.23*(0.30)	...	...	0.74(0.01)	...	108.9(7)	...	...
2003hn	31.15(0.10)	52866.5n(10)	52963.7(0.1)	0.37c(0.10)	−17.11(0.15)	−16.33(0.15)	−13.64(0.15)	...	1.46(0.02)	1.08(0.05)	90.1(10)	...	0.035$^{+0.008}_{-0.011}$
2003ho	33.77(0.16)	52847.5s(7)	52920.9(0.1)	...	...	−14.75*(0.16)	−12.00*(0.16)	...	...	1.69(0.10)	...	...	>0.005
2003ib	34.97(0.09)	52891.5n(8)	...	0.00(0.28)	−17.10(0.30)	−16.09(0.30)	...	...	1.66(0.05)	...	...	...	...
2003ip	34.20(0.13)	52896.5s(4)	52997.6(0.1)	0.13(0.08)	−17.88(0.15)	−16.78(0.16)	...	...	2.01(0.03)	...	80.7(6)	...	...
2003iq	32.39(0.30)	52919.5n(2)	53019.6(0.1)	...	−16.69*(0.30)	−16.18*(0.30)	...	...	0.75(0.03)	...	84.9(4)	...	...
2004dy	35.46(0.07)	53241.0n(3)	53289.0(0.5)	...	−16.03*(0.07)	−16.02*(0.07)	...	...	0.09(0.14)	...	...	25.0(5)	...
2004ej	33.10(0.21)	53224.9s(8)	53338.7(0.6)	0.14(0.07)	−16.76(0.22)	−16.27(0.23)	−13.06(0.23)	...	1.07(0.04)	0.89(0.13)	96.1(9)	...	0.019$^{+0.005}_{-0.007}$
2004er	33.79(0.16)	53271.8n(2)	53429.6(2.5)	0.34(0.17)	−17.08(0.24)	−16.01(0.24)	...	1.28(0.03)	0.40(0.03)	...	120.2(6)	59.2(4)	...
2004fb	34.54(0.11)	53242.6s(4)	...	...	−16.19*(0.11)	−15.46*(0.11)	...	...	1.24(0.07)	...	...	...	...
2004fc	31.68(0.31)	53293.5n(1)	53425.9(1.0)	...	−16.21*(0.31)	−15.41*(0.31)	...	...	0.82(0.02)	...	106.06(4)	...	...
2004fx	32.82(0.24)	53303.5n(4)	53407.3(0.5)	0.00(0.10)	−15.58(0.26)	−15.33(0.26)	−12.87(0.27)	...	0.09(0.03)	0.93(0.08)	68.4(6)	...	0.014$^{+0.004}_{-0.006}$
2005J	33.96(0.14)	53382.8s(7)	53496.6(0.7)	0.22(0.30)	−17.50(0.33)	−16.57(0.33)	...	2.11(0.07)	0.96(0.02)	...	94.0(8)	56.7(4)	...
2005K	35.33(0.08)	53369.8s(7)	53446.6(4.3)	...	−16.57*(0.08)	−16.08*(0.08)	−13.22*(0.08)	...	1.67(0.13)	2.15(0.71)	...	...	>0.016
2005Z	34.61(0.11)	53396.7n(6)	53491.3(1.3)	...	−17.17*(0.11)	−16.17*(0.11)	...	...	1.83(0.01)	...	78.8(7)	...	...
2005af	27.75(0.36)	53323.8s(15)	53434.7(0.2)	0.00(0.12)	...	−14.99(0.38)	−13.41(0.38)	...	...	1.25(0.03)	104.0(16)	...	0.026$^{+0.012}_{-0.021}$
2005an	33.43(0.18)	53428.8s(4)	...	...	−17.07*(0.18)	−15.89*(0.18)	...	3.34(0.06)	1.89(0.05)	...	77.7(6)	36.3(4)	...
2005dk	34.01(0.14)	53599.5s(6)	53702.8(0.4)	...	−17.52*(0.14)	−16.74*(0.14)	...	2.26(0.09)	1.18(0.07)	...	84.2(7)	37.5(5)	...
2005dn	32.83(0.24)	53601.6s(6)	53695.7(0.7)	0.00(0.16)	−17.01(0.29)	−16.38(0.29)	...	...	1.53(0.02)	...	79.8(7)	...	...
2005dt	35.02(0.09)	53605.6n(9)	53736.1(0.7)	0.00(0.14)	−16.39(0.17)	−15.84(0.17)	...	...	0.71(0.04)	...	112.9(10)	...	...
2005dw	34.17(0.13)	53603.6n(9)	53717.0(0.9)	...	−16.49*(0.13)	−15.61*(0.13)	−13.21*(0.13)	...	1.27(0.04)	...	92.6(10)	...	>0.021
2005dx	35.18(0.08)	53615.9s(7)	53719.7(0.8)	0.00(0.28)	−16.05(0.29)	−15.24(0.29)	−12.12(0.29)	...	1.30(0.05)	...	85.6(8)	...	>0.007
2005dz	34.32(0.12)	53619.5n(4)	53730.0(0.6)	0.00(0.12)	−16.57(0.17)	−15.97(0.17)	−13.42(0.18)	1.31(0.08)	0.43(0.04)	...	81.9(6)	37.6(5)	>0.021
2005es	35.87(0.06)	53638.7n(5)	...	...	−16.98*(0.06)	−16.32*(0.06)	...	...	1.31(0.05)	...	...	...	...
2005gk	35.36(0.08)	...	53728.5(0.7)	...	−16.44*(0.08)	−15.89*(0.08)	−13.56*(0.08)	...	1.25(0.07)	...	...	...	...
2005hd	35.38(0.08)	...	53700.9(0.4)	...	...	−17.07*(0.08)	−15.02*(0.08)	...	1.23(0.13)	1.17(0.06)	...	...	...
2005lw	35.22(0.08)	53716.8s(10)	53840.7(1.4)	...	−17.07*(0.08)	−15.47*(0.08)	...	...	2.05(0.04)	...	107.2(11)	...	...
2005me	34.76(0.10)	53721.6s(6)	...	...	−16.83*(0.10)	−15.51*(0.10)	...	3.06(0.12)	1.70(0.06)	...	76.9(7)	43.6(5)	...
2006Y	35.73(0.06)	53766.5n(4)	54824.6(0.5)	0.00(0.11)	−17.97(0.13)	−16.98(0.13)	−14.26(0.13)	8.15(0.76)	1.99(0.12)	4.75(0.34)	47.5(6)	26.9(4)	>0.034
2006ai	34.01(0.14)	53781.8s(5)	53854.0(0.5)	0.00(0.09)	−18.06(0.17)	−17.03(0.17)	−14.53(0.17)	4.97(0.17)	2.07(0.04)	1.78(0.24)	63.3(7)	38.1(4)	>0.050
2006bc	31.97(0.26)	53815.5n(4)	...	...	−15.18*(0.26)	−15.07*(0.26)	...	1.47(0.18)	−0.58(0.04)	...	...	...	...
2006be	32.44(0.29)	53805.8s(6)	53901.4(0.1)	0.00(0.16)	−16.47(0.33)	−16.08(0.33)	...	1.26(0.08)	0.67(0.02)	...	72.9(7)	43.5(4)	...
2006bl	35.65(0.07)	53823.8s(6)	...	...	−18.23*(0.07)	−16.52*(0.07)	...	...	2.61(0.02)	...	...	...	...
2006ee	33.87(0.15)	53961.9n(4)	54072.1(0.6)	0.00(0.09)	−16.28(0.18)	−16.04(0.18)	...	...	0.27(0.02)	...	85.2(6)	...	...
2006it	33.88(0.15)	54006.5n(3)	...	0.00(0.10)	−16.20(0.18)	−15.97(0.19)	...	...	1.19(0.13)	...	...	...	...
2006iw	35.42(0.07)	54010.7n(1)	...	0.00(0.11)	−16.89(0.13)	−16.18(0.14)	...	...	1.05(0.03)	...	...	...	...
2006ms	33.90(0.15)	54034.0n(13)	...	0.00(0.19)	−16.18(0.24)	−15.93(0.24)	...	2.07(0.30)	0.11(0.48)	...	...	...	>0.056
2006qr	34.02(0.14)	54062.8n(7)	54194.1(1.2)	...	−15.99*(0.14)	−14.24*(0.14)	...	...	1.46(0.02)	...	96.9(8)	...	...
2007P	36.18(0.05)	54118.7n(5)	54214.7(1.2)	...	−17.96*(0.05)	−16.75*(0.05)	...	...	2.36(0.04)	...	88.3(7)	...	...
2007U	35.14(0.08)	54134.6s(6)	...	0.00(0.36)	−17.87(0.37)	−16.78(0.37)	...	2.94(0.02)	1.18(0.01)	...	...	...	...
2007W	33.22(0.20)	54136.8s(7)	54270.8(0.7)	0.00(0.08)	−15.80(0.22)	−15.34(0.22)	...	...	0.12(0.04)	...	77.3(8)	...	...
2007X	33.11(0.21)	54143.9s(5)	54256.5(0.6)	0.38(0.19)	−18.22(0.29)	−17.08(0.29)	...	2.43(0.06)	1.37(0.03)	...	97.7(7)	52.6(4)	...
2007aa	31.95(0.27)	54135.8s(5)	54227.4(0.3)	0.00(0.07)	−16.32(0.28)	−16.32(0.28)	...	...	−0.05(0.02)	...	...	...	...
2007ab	34.94(0.09)	54123.9s(10)	54204.0(0.9)	...	−16.98*(0.09)	−16.55*(0.09)	−14.22*(0.09)	...	3.30(0.08)	2.31(0.22)	71.3(11)	...	>0.040
2007av	32.56(0.22)	54175.8s(5)	...	...	−16.27*(0.22)	−15.60*(0.22)	...	...	0.97(0.02)	...	...	...	>0.015
2007hm	34.98(0.09)	54335.6s(6)	54414.4(1.3)	0.00(0.15)	−16.47(0.18)	−16.00(0.18)	...	...	1.45(0.04)	...	...	...	>0.045
2007il	34.63(0.11)	54349.8n(4)	...	0.00(0.11)	−16.78(0.16)	−16.59(0.16)	...	...	0.31(0.02)	...	103.4(5)	...	...
2007it	30.34(0.50)	54348.5n(1)	...	0.06(0.04)	−17.61(0.50)	−14.89(0.50)	...	4.21(0.34)	1.35(0.05)	1.00(0.01)	...	...	0.072$^{+0.031}_{-0.054}$
2007ld	35.00(0.09)	54377.5s(8)	...	0.00(0.14)	−17.30(0.17)	−16.53(0.17)	...	2.93(0.15)	1.12(0.16)	...	...	...	...
2007oc	31.29(0.15)	54388.5n(3)	54470.2(0.2)	0.00(0.06)	−16.68(0.17)	−16.02(0.17)	...	...	1.83(0.01)	...	71.6(7)	...	...
2007od	31.91(0.80)	54402.6s(5)	...	0.00(0.06)	−17.87(0.80)	−16.81(0.80)	...	2.37(0.05)	1.55(0.01)	...	...	...	...
2007sq	34.12(0.13)	54421.8s(4)	54532.4(1.4)	...	−15.33*(0.13)	−14.52*(0.13)	...	...	1.51(0.05)	...	88.3(6)	...	...
2008F	34.31(0.12)	54470.6s(6)	...	...	−15.67*(0.14)	−15.56*(0.12)	...	...	0.45(0.10)	...	...	...	...
2008K	35.29(0.08)	54477.7s(4)	54570.3(0.8)	0.00(0.05)	−17.45(0.10)	−16.04(0.10)	−13.40(0.11)	...	2.72(0.02)	2.07(0.26)	87.1(6)	...	>0.013
2008M	32.55(0.28)	54471.7n(9)	54555.2(0.4)	0.00(0.07)	−16.75(0.29)	−16.17(0.29)	−13.41(0.29)	...	1.14(0.02)	1.18(0.26)	75.3(10)	...	0.020$^{+0.007}_{-0.010}$
2008W	34.59(0.11)	54485.8s(6)	54586.4(0.8)	...	−16.60*(0.11)	−16.05*(0.11)	...	...	1.11(0.04)	...	83.8(7)	...	...
2008ag	33.91(0.15)	54479.9s(6)	54616.8(0.5)	0.00(0.11)	−16.96(0.19)	−16.66(0.19)	...	...	0.16(0.01)	...	103.0(7)	...	...
2008aw	33.36(0.19)	54517.8n(10)	54605.6(0.5)	0.32(0.16)	−18.03(0.25)	−16.92(0.25)	−14.36(0.25)	3.27(0.06)	2.25(0.03)	1.97(0.09)	75.8(11)	37.4(4)	>0.050
2008bh	34.02(0.14)	54543.5n(5)	...	...	−16.06*(0.14)	−15.11*(0.14)	...	3.00(0.27)	1.20(0.04)	...	...	...	...
2008bk	27.682(0.05)	54542.9s(6)	54673.6(1.1)	0.00(0.05)	−14.86(0.08)	−14.59(0.08)	−11.98(0.07)	...	0.11(0.02)	1.18(0.02)	104.8(7)	...	0.007$^{+0.001}_{-0.001}$
2008bm	35.66(0.07)	54522.5n(26)	54620.3(0.4)	0.00(0.07)	−18.12(0.11)	−16.32(0.11)	−12.67(0.10)	...	2.74(0.03)	...	87.0(26)	...	>0.014
2008bp	33.10(0.21)	54551.7n(6)	...	0.54(0.27)	−14.54(0.34)	−13.67(0.35)	...	...	3.17(0.18)	...	58.6(10)	...	...
2008br	33.30(0.20)	54555.7n(9)	...	0.00(0.15)	−15.30(0.25)	−14.94(0.25)	...	...	0.45(0.02)	...	...	...	>0.026
2008bu	34.81(0.10)	54566.8s(7)	54620.5(1.0)	0.00(0.12)	−17.14(0.16)	−16.74(0.16)	−13.71(0.16)	...	2.77(0.14)	2.69(0.52)	44.8(7)	...	>0.020
2008ga	33.99(0.14)	54711.9s(4)	54799.9(0.8)	...	−16.45*(0.14)	−16.20*(0.14)	...	...	1.17(0.08)	...	72.8(6)	...	...
2008gi	34.94(0.09)	54742.7n(9)	...	...	−17.31*(0.09)	−15.86*(0.09)	...	...	3.13(0.08)	...	...	...	...
2008gr	34.76(0.10)	54766.6s(4)	...	0.00(0.05)	−17.95(0.12)	−16.97(0.12)	...	...	2.01(0.01)	...	...	...	...
2008hg	34.36(0.12)	54779.8n(5)	...	0.00(0.28)	−15.43(0.31)	−15.59(0.31)	...	...	−0.44(0.05)	...	...	...	...
2008ho	32.98(0.23)	54792.7n(5)	...	0.16(0.08)	−15.27(0.25)	−15.19(0.25)	...	...	0.30(0.06)	...	...	...	...
2008if	33.56(0.17)	54807.8n(5)	54891.5(0.4)	0.21(0.11)	−18.15(0.20)	−17.00(0.21)	−14.67(0.21)	4.03(0.07)	2.10(0.02)	...	75.9(7)	49.8(4)	>0.063
2008il	34.61(0.11)	54825.6n(3)	...	0.00(0.15)	−16.61(0.19)	−16.22(0.19)	...	...	0.93(0.05)	...	...	...	...
2008in	30.38(0.47)	54822.8s(6)	54930.2(0.1)	0.08(0.05)	−15.48(0.47)	−14.87(0.47)	...	1.82(0.20)	0.83(0.02)	...	92.2(7)	67.2(5)	...
2009N	31.49(0.40)	54846.8s(5)	54963.1(0.2)	0.10(0.06)	−15.35(0.41)	−15.00(0.41)	...	...	0.34(0.01)	...	89.5(7)	...	...
2009ao	33.33(0.20)	54890.7n(4)	...	...	−15.79*(0.20)	−15.78*(0.20)	...	...	−0.01(0.12)	...	41.7(6)	...	...
2009au	33.16(0.21)	54897.5n(4)	...	...	−16.34*(0.21)	−14.69*(0.21)	...	...	3.04(0.02)	...	...	...	...
2009bu	33.32(0.19)	54907.9s(5)	...	0.00(0.10)	−16.05(0.22)	−15.87(0.22)	...	0.98(0.16)	0.18(0.04)	...	...	...	...
2009bz	33.34(0.19)	54915.8n(4)	...	0.00(0.06)	−16.46(0.20)	−16.26(0.20)	...	...	0.50(0.02)	...	...	...	...

Notes. Measurements made of our sample of SNe, as defined in Section 3 and outlined in Figure 1. In the first column we list the SN name. In Column 2 the distance modulus employed for each object is presented, followed by explosion epochs in Column 3, and V-band host-galaxy extinction values in Column 4. If an A_V estimate has not been possible (see Section 3.3) then subsequent magnitudes are presented as lower limits. In Columns 5, 6 and 7 we list the absolute magnitudes of M_max, M_end and M_tail respectively. These are followed by the decline rates: s₁, s₂ and s₃, in Columns 8, 9 and 10 respectively. In Column 11 we present the duration OPTd and in Column 12 the Pd values are listed. Finally, in Column 13 derived ⁵⁶Ni masses (or lower limits) are presented. 1σ errors on all parameters are indicated in parenthesis, and are estimated as outlined in the main text. The values within this table are also archived in a file as part of the photometry package available from http://www.sc.eso.org/~janderso/SNII_A14.tar.gz, where we also include further values/measurements used in the process of our analysis. * Absolute magnitudes are lower limits as no host galaxy extinction correction has been applied. ^aTaken from Hamuy et al. (2001). ^bTaken from Hendry et al. (2005). ^cTaken from Sollerman et al. (2005). ¹ Estimated using a SN Ia distance. ² Estimated using a Cepheid distance. ^sExplosion epoch estimation through spectral matching. ⁿExplosion epoch estimation from SN non-detection.

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In Figure 28 the correlation between s₁ and s₃ is shown. In Figure 29 we present correlations between the 3 brightness measurements: M_max, M_end, and M_tail. A large degree of correlation between all three is observed. M_end is plotted against s₁ and s₃ in Figure 30. M_tail is plotted against s₁, s₂ and s₃ in Figure 31. In Figure 32 we present correlations of Pd and OPTd against M_end.

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In Figure 33 M_end, M_max, and s₂ are plotted against estimated ⁵⁶Ni masses: there appears to be a trend that more luminous SNe synthesize larger amounts of radioactive material, as previously observed by Hamuy (2003a), Bersten (2013) and Spiro et al. (2014), while there is no correlation between ⁵⁶Ni mass and decline rate. Finally, in Figure 34 M_end and ⁵⁶Ni mass are plotted against the steepness parameter S (see Elmhamdi et al. 2003 for more discussion on this topic), where we do not observe trends seen by previous authors.

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