TOWARD CHARACTERIZATION OF THE TYPE IIP SUPERNOVA PROGENITOR POPULATION: A STATISTICAL SAMPLE OF LIGHT CURVES FROM Pan-STARRS1

We select an SN II light-curve sample from the transients discovered and monitored by PS1 since the initiation of the survey in 2010, consisting of 18,953 relevant photometric data points, 5,096 of which are robust transient detections. PS1 is a high-etendue wide-field imaging system, designed for dedicated survey observations and located on the peak of Haleakala on the island of Maui in the Hawaiian island chain. Routine observations are conducted remotely, from the University of Hawaii—Institute for Astronomy Advanced Technology Research Center (ATRC) in Pukalani. A summary of details of PS1 operations relevant to SN studies is given in Rest et al. (2014), and we discuss its key features here.

A complete description of the PS1 system, both hardware and software, is provided by Kaiser et al. (2002). The 1.8 m diameter primary mirror, 33 field of view, and other PS1 optical design elements are described in Hodapp et al. (2004); the array of 60 4800 × 4800, 0258 pixel detectors, and other attributes of the PS1 imager is described in Tonry & Onaka (2009); and the survey design and execution strategy are described in K. C. Chambers (in preparation). The PS1 Medium Deep Survey (MDS) consists of 10 pencil-beam fields observed with a typical cadence of 3 days in each filter, to a 5σ depth of ∼23.3 mag in griz filters and ∼21.7 mag in the y-filter (with observations taken near full Moon).

The PS1 observations are obtained through a set of five broadband filters, which we refer to interchangeably as g_P1, r_P1, i_P1, z_P1, and y_P1 or simply grizy (Stubbs et al. 2010). Although the filter system for PS1 has much in common with that used in previous surveys, such as the Sloan Digital Sky Survey (SDSS; York et al. 2000; Aihara et al. 2011), there are important differences. The g_P1 filter extends 200 Å redward of g_SDSS, and the z_P1 filter is cut off at 9200 Å. SDSS has no corresponding y_P1 filter. Further information on the passband shapes is described in Stubbs et al. (2010). Photometry is in the "natural" PS1 system, m = 2.5log (flux) + m', with a single zero-point adjustment m' made in each band to conform to the AB magnitude scale (Tonry et al. 2012).¹³ We assume a systematic uncertainty of 1% for our PS1 observations owing to the asymmetric PS1 point-spread function and uncertainty in the photometric zero-point calibration (Tonry et al. 2012). See Figure 1 for an illustration of the PS1 photometric sampling and the range in data quality.

Zoom In Zoom Out Reset image size

The standard reduction, astrometric solution, and stacking of the nightly images are done by the Pan-STARRS1 IPP system (Magnier 2006; Magnier et al. 2008). The nightly MDS stacks are transferred to the Harvard Faculty of Arts and Sciences "Odyssey" Research Computing cluster, where they are processed through a frame subtraction analysis using the photpipe image differencing pipeline developed for the SuperMACHO and ESSENCE surveys (Rest et al. 2005; Miknaitis et al. 2007; Rest et al. 2014).

We begin with a selection of PS1-discovered SNe that were classified as Type II through our spectroscopic follow-up campaign: 112 objects in total. One object in our sample, PS1-10ae (SN 2010aq), has previously been reported on in Gezari et al. (2010). We note that the PS1 spectroscopic follow-up is not complete; brighter objects, those with longer plateau durations, and those with the highest ratio of SN to underlying galaxy light are most likely to be overrepresented in our sample, owing to their availability for spectroscopy.

Spectra were obtained using the Blue Channel and Hectospec spectrographs of the 6.5 m MMT telescope (Schmidt et al. 1989; Fabricant et al. 2005), the Low Dispersion Survey Spectrograph (LDSS3) and Inamori-Magellan Areal Camera and Spectrograph (IMACS; Dressler et al. 2006) of the 6.5 m Magellan telescopes, the Gemini Multi-Object Spectrograph of the 8 m Gemini telescopes (GMOS; Hook et al. 2004), and the Andalucia Faint Object Spectrograph and Camera (ALFOSC) at the 2.6 m Nordic Optical Telescope. Objects were classified as Type II by identification of Hα emission not associated with the host galaxy. This selection could possibly include the Type IIP, IIL, IIb, and Type IIn subclasses of the SNe II; we discuss subclassification in Section 3.4.

Additionally, we obtain host galaxy redshift measurements for each object from these spectra, which we use for K-correction (see Section 2.3) and to estimate distance.¹⁴ Figure 2 shows the host galaxy redshift distribution of the PS1 SN II sample, which has [16,50,84]th percentile values of [0.07, 0.11, 0.21]. The subsample classified as SNe IIP (see Section 3.4) has distribution percentile values of [0.07,0.10,0.16]. This difference reflects a population of luminous, distant SNe IIn excluded from the subsample.

Zoom In Zoom Out Reset image size

Details of our final SN IIP sample, as described in Section 3.4, are listed in Table 1.

We use K-corrections to account for the difference between the observed and rest-frame wavelengths of the light collected through the PS1 filters, as a function of the redshift of each object in our sample. We define this correction as K = m_R − M_Q − DM, where m_R is the observed-frame magnitude, M_Q is the emitted-frame absolute magnitude, and DM is the distance modulus (Hogg et al. 2002). We estimate K-corrections using the SN IIP spectral templates provided by P. Nugent (based on observations of SN 1999em; Gilliland et al. 1999; Baron et al. 2004).¹⁵ We interpolate linearly between the spectral templates to obtain K-corrections for arbitrary epochs. We note that we do not warp the spectral templates to match the observed color of the SN, owing to the computational cost involved in doing so dynamically within our probabilistic light-curve fitting methodology (see Appendix A). By testing the effects of warping the spectral templates on the K-correction calculation, we estimate that neglecting this effect will introduce an uncertainty of ∼0.02 mag in the K-correction per 0.1 mag of (V − I) color offset, which is much smaller than typical uncertainties in our color estimates.

Figure 3 illustrates the resulting K-corrections for an illustrative set of epochs. The t = 0 K-correction is linear with z because the postshock breakout cooling phase spectral model is a blackbody; thereafter the K-correction evolution becomes more complex, with spectral features evolving and shifting between bandpasses. The bluer bands have K-corrections more highly dependent on time, as the onset of line blanketing in the spectral model depresses the flux blueward of ∼5000 Å.

Zoom In Zoom Out Reset image size

Deviation of the SN spectral energy distribution from the template spectra will introduce error into our derived K-correction. In particular, we consider here the effect of differences in the SN IIP continuum shape and line-of-sight extinction and estimate the magnitude of these effects by simulation on the template spectra. First, we consider the effect of variation in continuum shape, to first order. We vary the intrinsic (V − I) color of the SN spectrum by ±0.5 mag from the stock template, at fixed redshift (z = 0.1), at fixed epoch (t = 50 days), and with no extinction. The effect of this variance in spectral shape on the K-correction over the full 1 mag color range induces a variation in the K-correction ranging from 0.1 mag in g band to 0.3 mag in y band. Second, we consider the effect of variation in extinction. We vary the extinction from A_V = 0 to 2 mag, at fixed redshift (z = 0.1), at fixed epoch (t = 50 days), and with the color of the stock template. The effect of this variance in spectral shape on the K-correction over the full 2 mag extinction range induces a variation in the K-correction ranging from 0.1 mag in y band to 0.2 mag in i band. These effects are therefore modest and similar in size, depending on the exact parameters of the photometric observation.

We estimate the typical effect of the joint variation in both continuum shape and extinction by means of Monte Carlo simulation. We generate 10, 000 random SN observations with the following conditionally independent distributions of properties meant to approximately mimic the PS1 data set: redshift drawn from z ∼ logN(-2, 0.4), color deviation drawn from Δ(V − I) ∼ N(0, 0.5) mag,¹⁶ extinction drawn from A_V ∼ logN(0, 1) mag, and epoch drawn from t ∼ logN(4, 0.8) days, where N is the normal and logN is the lognormal distribution. We then consider the distribution of residuals of the derived K-corrections from the K-correction expected for a zero-extinction and template-standard color object. In the r band, this distribution has [5, 16, 50, 84, 95] percentile values of [ − 0.10, −0.01, 0.13, 0.40, 0.75] mag. The distribution is similar in other filters. This suggests that these effects exert a small (∼0.1 mag) typical bias and introduces a modest additional uncertainty (∼0.2 mag) in the measured SN photometry. We therefore neglect these effects in the following work but note their importance for studies requiring precision photometry. In the most extreme cases, particularly for the most highly reddened SNe, the simulations suggest that these effects will cause the brightness to be significantly underestimated (by ≳ 0.7 mag). Moreover, the simulated K-correction residuals seem to have little correlation between filters, suggesting that the effects do not significantly bias color inference.

To model the light curve, we use a simple, physically motivated parameterization that captures the essential components of the rise, plateau, and decline phases of the Type IIP light curve. Our model is constructed so that the most salient features of the SN IIP light curve (the plateau duration, peak magnitude, and luminosity evolution of the radioactive decay phase) are represented by directly interpretable parameters.

The light-curve model for the luminosity measured from our PS1 forced photometry, l, in a given optical filter, F, consists of five piecewise components (see Figure 4): a power-law fast-rise phase, a plateau phase divided into exponential rising and declining components, a transitional phase representing the end of the plateau, and a postplateau exponential decay phase:

$$\begin{eqnarray} &&l[t,\ldots ]=\left\lbrace \begin{array}{@{}l@{\quad }l@{}}0,\\ & {\rm if }\; t<t_0 \\ M_1 (t/t_1)^{\alpha },\\ &{\rm if }\; t_0<t<t_0+t_1 \\ M_1 \exp (\beta _1 (t-t_1)),\\ &{\rm if }\; t_0+t_1<t<t_0+t_1+t_p \\ M_p \exp (-\beta _2 (t-(t_p+t_1))),\\ &{\rm if }\; t_0+t_1+t_p<t<t_0+t_1+t_p+t_2 \\ M_2 \exp (-\beta _{dN} (t-(t_2+t_p+t_1))),\\ &{\rm if }\; t_0+t_1+t_p+t_2<t\\ &<t_0+t_1+t_p+t_2+t_d \\ M_d \exp (-\beta _{dC} (t-(t_d+t_2+t_p+t_1))),\\ &{\rm if }\; t_0+t_1+t_p+t_2+t_d<t. \\ \end{array}\right. \end{eqnarray} \tag{ 1 }$$

Zoom In Zoom Out Reset image size

These parameters have the following definitions and interpretations. The time parameters are defined where t is the Modified Julian Date (MJD) epoch of an observation, t₀ is the epoch of explosion, t₁ is the rest-frame duration of the power-law rise phase, t_p is the duration of the exponential rise phase (ending at peak flux), t₂ is the duration of the falling component of the plateau phase, and t_d is the duration of the transitional phase. The flux parameters are defined such that M₁ is the flux at the transition from the power law to the exponential rise phases, M_p is the peak flux, M₂ is the flux at the end of the plateau phase, and M_d is the flux at the transition to the Co decay-dominated phase. The rate parameters are defined such that α is the power-law rise slope, β₁ is the exponential rate constant during the rising phase of the plateau, β₂ is the rate constant during the declining phase of the plateau, β_dN is the exponential decline rate of the transition phase following the plateau, and β_dC is the exponential decay constant corresponding to ⁵⁶Co to ⁵⁶Fe decay. Each parameter is defined independently for each photometric filter, with the exception of t₀. For numerical convenience, we define l in arbitrary scaled units relative to the absolute magnitude M, such that M = −2.5log₁₀(10⁷ × l).

Note that, in order for the light-curve model to be continuous, not all of the parameters may be independent. In particular, for each filter,

$$\begin{eqnarray} M_1 &= M_p / {\exp} (\beta _1 t_p) \end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray} M_2 &= M_p / {\exp} (-\beta _2 t_2) \end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray} M_d &= M_2 / {\exp} (-\beta _{dN} t_d). \end{eqnarray} \tag{ 4 }$$

Furthermore, we note that the postpeak decay rate β₂ is directly related to the quantity Δm₁₅, the decline in magnitudes of the light curve in the 15 days following peak:

$$\begin{eqnarray} \Delta m_{15} &= \frac{15\times 2.5}{\log _e{10}} \beta _2 \sim 16.3 \beta _2. \end{eqnarray} \tag{ 5 }$$

Our model is similar to the linear segmented light-curve fitting approach of, e.g., Patat et al. (1993), but (as we discuss in Section 3.2) our fitting methodology for the knot properties is fully probabilistic rather than manual. We prefer this piecewise analytic formulation to the additive component model used by, e.g., Olivares (2008). The piecewise parameters will in principal have weaker covariance, therefore reducing the posterior curvature and increasing the efficiency of Markov Chain Monte Carlo (MCMC) methods for sampling from the posterior. While this parameterization is designed to capture the phenomenology of SNe IIP, it is in practice quite flexible, as we obtain reasonably descriptive fits to the light curves of other SNe II (e.g., SNe IIn and IIb).

We estimate the posterior distributions of these model parameters using an MCMC method. We employ the C++ library Stan (Stan Development Team 2014a), which implements the adaptive Hamiltonian Monte Carlo (HMC) No-U-Turn Sampler of Hoffman & Gelman (2014). For each multiband SN light curve, we use Stan to return 1000 samples (250 samples each from four independent MCMC chains) from the posterior distribution of the model.¹⁷

In addition to the light-curve parameterization outlined in Section 3, our Stan model includes certain features representing the data acquisition process. To account for uncertainty in the PS1 background template subtractions, we fit for the background level in each filter using an independent set of luminosity parameters, Y_b[F], and an intrinsic model variance, V[F]. We precompute K-correction curves for the redshift of each object in our sample (see Section 2.3) and apply them to the model during the likelihood calculation using the phases corresponding to the sampled explosion date at each step in the MCMC chain.

We employ weakly informative priors (see, e.g., Gelman et al. 2008) to regularize the fitted models to the characteristic SN IIP light-curve shape. These prior distributions are constructed to more than encompass the observed variance in parameter values from well-identified light curves in the data set. The Stan model in Appendix A fully defines the fixed prior distributions we employ, and we discuss their most salient properties here. Figure 5 illustrates the procedure for constructing the prior distributions that we have defined individually per filter in the model. For t₂, we apply a (lognormal) log N(log (100), 0.3) day prior. Together with our prior on t_p (Figure 5), this effectively provides a prior on the plateau duration that has [5, 50, 95]th percentile values of [70, 110, 180] days in i band (and similar values in other bands). This prior is constructed to be weakly informative, having significantly more variance than previously reported SN IIP plateau duration distributions (Arcavi et al. 2012) and covering a range of values similar to that predicted from theoretical modeling (Kasen & Woosley 2009). Perhaps the most informative prior we apply is that on the peak-magnitude distribution, which is observationally motivated. A strong prior is desirable for this parameter because it has the effect of regularizing the light-curve shape in cases where photometric observations before peak are not available. We set this prior to N(− 17.5 mag, 0.8 mag) to approximately match the SN II luminosity function predicted for an R-band magnitude-limited survey by Li et al. (2011) based on observations from the Lick Observatory Supernova Search (LOSS; Figure 6).¹⁸

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In total, including the independent parameters for each light-curve segment and filter, the fitted model for each SN has 61 independent parameters (12 per filter and t₀). We reproduce the fitted light-curve parameters for each object in our sample in Table 2.

Table 2. Pan-STARRS1 Type IIP SN Light-curve Parameters

SN	t0	log α	log β1	log β2	log βdN	log βdC	t1	tp	t2	td	Mp	V
g-band
PS1–10a	$55200.9^{+0.8}_{-0.8}$	$-1.0^{+0.3}_{-0.3}$	$-2.4^{+0.5}_{-0.5}$	$-3.1^{+0.3}_{-0.4}$	$-2.9^{+0.5}_{-0.5}$	$-5.0^{+1.2}_{-1.1}$	$1.0^{+0.3}_{-0.2}$	$5^{+1}_{-1}$	$106^{+33}_{-25}$	$10^{+7}_{-4}$	$2.10^{+0.45}_{-0.25}$	$0.005^{+0.006}_{-0.003}$
PS1–10b	$55204.0^{+0.4}_{-0.5}$	$-1.0^{+0.3}_{-0.3}$	$-2.8^{+0.3}_{-0.3}$	$-2.7^{+0.2}_{-0.2}$	$-3.0^{+0.5}_{-0.5}$	$-4.9^{+1.0}_{-1.1}$	$1.0^{+0.4}_{-0.3}$	$7^{+1}_{-1}$	$102^{+38}_{-28}$	$10^{+6}_{-4}$	$1.93^{+0.11}_{-0.10}$	$0.008^{+0.017}_{-0.006}$
PS1–10q	$55200.4^{+0.7}_{-0.7}$	$-1.0^{+0.3}_{-0.3}$	$-2.4^{+0.5}_{-0.5}$	$-3.1^{+0.0}_{-0.0}$	$-2.9^{+0.5}_{-0.6}$	$-4.9^{+1.0}_{-1.0}$	$1.0^{+0.4}_{-0.3}$	$4^{+1}_{-1}$	$109^{+31}_{-24}$	$10^{+8}_{-4}$	$0.77^{+0.03}_{-0.03}$	$0.016^{+0.004}_{-0.003}$
PS1–10t	$55205.2^{+0.9}_{-0.8}$	$-1.0^{+0.3}_{-0.3}$	$-2.2^{+0.6}_{-0.5}$	$-3.5^{+0.1}_{-0.1}$	$-3.1^{+0.5}_{-0.4}$	$-5.1^{+1.1}_{-0.9}$	$1.0^{+0.3}_{-0.3}$	$5^{+1}_{-1}$	$97^{+32}_{-24}$	$10^{+7}_{-4}$	$0.37^{+0.02}_{-0.02}$	$0.011^{+0.007}_{-0.007}$
PS1–10ae	$55239.3^{+0.1}_{-0.1}$	$-1.1^{+0.3}_{-0.3}$	$-2.7^{+0.5}_{-0.5}$	$-3.3^{+0.1}_{-0.1}$	$-3.0^{+0.5}_{-0.5}$	$-5.6^{+0.7}_{-0.7}$	$0.9^{+0.2}_{-0.2}$	$3^{+1}_{-0}$	$76^{+24}_{-22}$	$10^{+5}_{-4}$	$0.84^{+0.02}_{-0.02}$	$0.005^{+0.006}_{-0.003}$

Notes. Light-curve parameters are listed separately for each photometric band, in sequence. The parameters are defined in Section 3.1. This table includes only SNe classified as SNe IIP by the criteria of Section 3.4.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

Following execution of Stan and posterior sampling, we reconstruct a posterior predictive distribution for each light curve from the model parameter samples (Gelman et al. 2013). This distribution represents the probability for the physical SN light curve to have the luminosity l_m on a grid of times t_m.

Figure 7 illustrates a posterior predictive check for the model fit to the object PS1-11apd, whose well-sampled observations illustrate both the strengths and weaknesses of the five-component model. The rising phase in each band is wellconstrained by the tightest pre-explosion limit, in the y band. The two-component (rising then falling) plateau phase provides an accurate description of the data in the i band, but not in the g band, where the evolution of iron line blanketing (see, e.g., Kasen & Woosley 2009) causes a behavior not captured by the model (falling then rising/plateauing). As is characteristic of the PS1 data, the y-band light curve is more poorly sampled and higher in variance than the other bands. In general, the model parameter inferences are therefore more reliable and directly interpretable in the r, i, and z bands.

Zoom In Zoom Out Reset image size

Figure 8 illustrates fitting behavior for a well-sampled and a poorly sampled PS1 light curve. The top panel shows PS1-12bku, an SN with observations from the rise phase through the end of the plateau. Note that the nonlinear behavior of the light curve during the rise, due to shock breakout and postshock breakout cooling envelope effects (see, e.g., Nakar & Sari 2010; Rabinak & Waxman 2011), is not captured by the power-law rise model, but the explosion epoch itself is fit accurately in the fitted model. PS1-10zu is shown in the bottom panel, an object that apparently exploded during the gap between observing seasons. With observations only available starting a few weeks before the end of the plateau phase and no direct constraints on the explosion epoch, the model fit includes a range of possible explosion dates reflecting the prior distributions for the plateau duration and peak magnitude.

Zoom In Zoom Out Reset image size

We apply a supervised machine learning methodology (see, e.g., Faraway et al. 2014) to classify the SNe II in this sample into their appropriate subclasses and, in particular, to identify SNe IIP for further analysis. Our approach is to first apply "expert knowledge" to manually label a subset of clearly classifiable objects from our sample of 112 SNe II, then uniformly measure light-curve features using the methodology described in Section 3.1, then train a Support Vector Machine (SVM) classifier to a deliberately selected subset of these features, and finally apply that classifier to assign labels to the remaining objects in the sample. In general, spectral classification of distant (z ≳ 0.1) transients is complicated by spectral evolution (see, e.g., Milisavljevic et al. 2013 for a discussion of SNe IIb), exacerbated by the observational cost of obtaining a well-sampled spectral series, and the difficulty in robustly identifying spectral features, exacerbated by the low signal-to-noise ratio of the spectroscopy relative to nearby objects. The methodology discussed below is intended to capitalize on photometric information to help overcome these limitations.

Our procedure is as follows. We begin by manually assigning SN IIP, IIb, IIn, and "II?" (undetermined) classifications to each object in the sample by inspection of their light curves and optical spectra. See, e.g., Li et al. (2011) for a discussion of the photometric and spectroscopic properties of SN II subclasses. We do not establish a label for SNe IIL separate from SNe IIP, but we discuss that subclass later in Section 4.2. We assign SN IIn classifications to 23objects based on the detection of intermediate-width H emission features and/or exceptional luminosity (≲ − 20 mag); SN IIb classifications to 5objects based on the detection of He features (in addition to broad H features) in the optical spectrum and/or an SN I-like light curve, with slow rise and fast decline rate; and SN IIP to 67 objects based on the presence of a broad Hα spectral feature and/or a clearly exhibited plateau-like light curve. Finally, we liberally apply the SN II? classification to 17 objects for which we do not have sufficient data to assign a classification and/or that do not neatly fit the preceding criteria.

We apply our Bayesian light-curve model (Section 3.1) to uniformly measure features of the light curves of every SN II in our PS1 sample. To mirror our expert knowledge, we focus on the peak absolute magnitude (M), the rise time to peak magnitude (t_p), and the postpeak decay rate (β₂) as features capable of distinguishing objects in these subclasses. We identify the i band as the filter in which these features are most discriminating. For self-consistency, we apply the SN IIP theoretical K-corrections (Section 2.3) to every object in the sample.

We then fit a linear SVM classifier (Pedregosa et al. 2011) to the features of the training set. The SVM consists of a series of hyperplanes that optimally divide the feature space to discriminate the training set based on their class labels. The results of this fit are displayed in Figure 9. In summary, the classifier identifies SNe IIn as luminous (primarily M_i < −18 mag) and slowly evolving (log β₂ ≲ −3), SNe IIb as intermediate-luminosity and quickly evolving, and SNe IIP as slowly evolving and spanning a range from subluminous (M_i > −17 mag) to luminous (M_i ∼ −20 mag), accurately reflecting our expert knowledge applied in construction of the training set. Disagreement between object location and shaded labeling in Figure 9 is partially due to variance in the observational data, which limits the efficiency of the classifier, and partially due to the coarse binning of the display slices. We have configured the classifier with the penalty parameter C = 1 and class weights calculated from their representation in the training set.

Zoom In Zoom Out Reset image size

Finally, we apply the classifier to the unclassified (SNII?) objects to infer their subclasses. While "SN IIb" and "IIn" classifications can only be assigned by spectroscopy, by definition, here we are using photometric information to supplement available spectroscopy for the purpose of predicting the most likely spectroscopic subclassification. The classifier identifies 9 of these objects as SNe IIP, which we hereafter incorporate in our SN IIP sample; 6 as SNe IIb; and 3 as SNe IIn.

When applied to the training set, the classifier achieves 83% accuracy across all subtypes, and 89% accuracy for SNe IIP. It mistakenly classifies SNe IIb and IIn as SNe IIP only 22% of the time (the false identification rate) and mistakenly classifies SNe IIP as other classes only 11% of the time (the false negative rate). These statistics imply that, of our sample of 17SNe II?, ∼3 may be incorrectly classified as SNe IIP and ∼3 legitimate SNe IIP may be inadvertently excluded. In combination with our sample of 67 securely identified SNe IIP, this level of false identification would imply a ∼4% contamination rate within the sample. Given the relatively low signal-to-noise ratio of the SN II? objects, the classifier may perform more poorly than on the training data set, but for the same reason, the influence of these objects on our light-curve parameter inferences will be correspondingly suppressed.

We construct grizy SN IIP template light curves based on scaled stacks of our PS1 photometric sample. Figure 10 (left) shows these stacked SN light curves. In each band, we only include objects with a 1σ uncertainty in the peak magnitude of <0.5 mag and with an uncertainty in the plateau epoch of <10 days, as estimated from the marginal posterior of the fitted light-curve model. In total, we include [63, 66, 64, 63, 32] objects in the [g, r, i, z, y]-band templates.

Zoom In Zoom Out Reset image size

Figure 10 (right) shows the template light curves constructed from these data. The template magnitudes are calculated based on the range of observed photometry within a moving window of 6 rest-frame days in width, between ∼ − 10 and 110 days from peak magnitude. Template values are only reported if at least four photometric observations fall in the window. In total, we include [434, 586, 760, 757, 267] observations in constructing the [g, r, i, z, y]-band templates. The templates are reproduced in Table 3.

Table 3. SN IIP grizy Template Light Curves

Epoch	g	r	i	z	y
−15	...	...	...	...	...
−12	...	...	...	$1.32^{+0.29}_{-0.33}$	...
−9	$0.32^{+0.14}_{-0.14}$	$0.61^{+0.38}_{-0.26}$	$0.50^{+1.28}_{-0.19}$	$0.88^{+0.59}_{-0.34}$	$0.26^{+0.43}_{-0.38}$
−6	$0.21^{+0.22}_{-0.14}$	$0.43^{+0.33}_{-0.29}$	$0.34^{+1.00}_{-0.16}$	$0.65^{+0.55}_{-0.35}$	$0.31^{+0.23}_{-0.45}$
−3	$0.09^{+0.22}_{-0.09}$	$0.15^{+0.46}_{-0.15}$	$0.25^{+0.60}_{-0.22}$	$0.51^{+0.38}_{-0.40}$	$0.18^{+0.20}_{-0.29}$

Notes. The reported epoch is in rest-frame days since peak. The grizy photometry is reported in terms of magnitude below peak; the ranges reflect the 16th–84th percentile variation in observed light-curve behavior.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

Past studies have varied widely in their interpretation of a putative, fast-declining subclass of SNe II commonly labeled "SNe IIL." The SN IIL classification was coined by Barbon et al. (1979), in recognition of a set of six SNe II with an unusually fast decline rate of ${\sim }0.05 \ \rm {mag}\ \rm {day}^{-1}$ in the B band, constituting ∼26% of their SN II sample. From a theoretical perspective, a fast-declining SN II suggests a less massive H envelope and consequently less sustained power contribution from H recombination. Likely explanations for diversity in H envelope mass among SN II progenitors include variation in progenitor initial mass, with SNe IIL likely to arise from either progenitors with intrinsically less massive envelopes (e.g., initial masses of ∼7–10 M_☉; Swartz et al. 1991) or more massive stars that have been stripped by strong radiation-driven winds (≳ 18 M_☉; Smith et al. 2011), and/or stars that have been partially stripped by interaction with binary companions (Nomoto et al. 1995).

Observationally, no widely adopted criteria for SN IIL classification have emerged. Patat et al. (1994) divided their SN II light curve set into "linear" and "plateau" classes based on the Barbon et al. (1979) criterion, but they describe the decline rate distribution of these objects as continuous and find no statistical evidence for two modes in the distribution. In their population study of the LOSS SNe, Li et al. (2011) define SNe IIL as having SN IIP-like spectroscopic features, but exhibiting an R-band decline of >0.5 mag after explosion. By their selected criterion, they identify seven unambiguous SNe IIL among 81 SNe II, and they determine SNe IIL to represent 10% of the volume-limited SN II population. They find that the SNe IIL are on average overluminous compared to SNe IIP and therefore would represent ∼25% of a magnitude-limited SN II survey sample. By inspection of a set of 22 SN II light curves from the Caltech Core-Collapse Project and the literature, Arcavi et al. (2012) identify a set of five objects that they describe as SNe IIL. Their selection corresponds to a decline rate criterion of ≳ 0.3 mag within 50 days of explosion. They suggest that these objects form a class "distinct" from SNe IIP and that the two classes together do not form a continuum of decline rates. Most recently, Anderson et al. (2014) have characterized the decline rate distribution of hydrogen-rich SNe as continuous.

We take an empirical approach to searching for evidence of a fast-declining mode in the sample of PS1 objects classified nominally as SNe IIP (see Section 3.4). Figure 11 shows the distribution of mean posterior values for the β₂ plateau decline rate parameter in our fitted light-curve models, among objects with significant constraints on the plateau phase decay behavior. We employ Gaussian kernel density estimation (KDE) to estimate the underlying form of the decline rate distribution from the observed data. We select a KDE bandwidth factor of 0.43 in r band (and similar in other bands) based on the number of objects in the well-constrained sample, following Scott (1992). Inspection of the KDE models in Figure 11 does not indicate the presence of any fast-declining modes, e.g., within the shaded regions corresponding to the Barbon et al. (1979) and Li et al. (2011) criteria. Given the limited sample size, this test would not be sensitive to the existence of a small SN IIL subpopulation if they are subsumed within the fast-declining tail of a more numerous SN IIP population. However, a significant subpopulation (∼20%), as proposed by previous authors, should emerge if present.

Zoom In Zoom Out Reset image size

We therefore conclude that empirical evidence for a distinct SN IIL subpopulation is not present within the PS1 SN II data set, and hereafter we do not distinguish between SNe IIL and IIP. Discounting the existence of an SN IIL subclass differs from the interpretation applied in many past studies but does not disagree quantitatively with past results. Li et al. (2011) adopted an SN IIL classification scheme defined arbitrarily by previous authors (Barbon et al. 1979) for the purpose of estimating volumetric rates. Patat et al. (1994) applied a similar criterion and then tested for a discontinuity between the properties of this subpopulation and the "normal" SN IIP population. They reported a negative result. Arcavi et al. (2012) identified a slow-declining subset of objects in their sample but did not quantitatively test for a discontinuity. Moreover, we note that our sample, consisting of 112 SNe II in total, is ∼40% larger than the Li et al. (2011) SN II sample and ∼5 times larger than the Arcavi et al. (2012) sample. Using a similarly sized sample, Anderson et al. (2014) have reported independent results in agreement with the continuum of decline rates we report here.

Figure 10 further illustrates this result, showing our SN IIP r-band photometry in comparison with the averaged unfiltered SN IIP and SN IIL light curves of Li et al. (2011). Both their templates fall within the photometric range of our observed sample, with their SN IIP template falling near the +1σ range of our light curves and their SN IIL template falling near the median of our light curves. Note that their photometry was collected with an unfiltered photometric system, which Li et al. (2011) compare to R band. This would suggest that their response function includes redder wavelengths than our r-band photometry. This may partially explain the slower decline rates in their sample, as redder filters (e.g., izy-bands) exhibit more gradual SN IIP decline rates in the plateau phase. Regardless, this comparison illustrates that the long-recognized range of decline rates among SNe with broad Hα features falls within the observed, continuous range of decline behavior exhibited by objects classified as SNe IIP in our sample, with no evidence for a second, fast-declining mode in the population.

Recent observational studies have suggested that the plateau durations of SNe IIP are tightly distributed around ∼100 days (Poznanski et al. 2009; Arcavi et al. 2012), in stark contrast to theoretical predictions that they should vary from ∼80 to 200 days given the expected range of progenitor properties, including mass, energy, and radius (see, e.g., Kasen & Woosley 2009). Poznanski (2013) has interpreted this as evidence that the joint parameter space of progenitor properties must be tightly constrained, with the explosion energy scaling precisely with the cube of the mass to produce a roughly constant plateau duration.

We quantitatively assess the plateau duration distribution of our SN IIP sample. In agreement with Arcavi et al. (2012), Poznanski (2013), and Faran et al. (2014), the r-band plateau duration distribution of our sample (Figure 12) is peaked around ∼90–100 days, with median value of 92 days and 1σ variation of 14days. However, the full observed range of plateau durations is significantly larger, 42–126 days. Note that we do not include in this distribution poorly constrained light curves, where the marginalized posterior uncertainty is >80% of the prior variance (24 days at 1σ). For those poorly constrained objects, as Figure 12 illustrates, the posterior is typically peaked around the mean of the prior distribution.

Zoom In Zoom Out Reset image size

Our PS1 sample therefore suggests that the observed variation in SN IIP plateau durations is not as highly constrained as suggested by Poznanski et al. (2009) and Arcavi et al. (2012). However, we do not detect objects with plateaus as long-lived as the least energetic objects produced in the model grid of Kasen & Woosley (2009) (e.g., ∼200 days for kinetic explosion energy of 0.3B at infinity). However, all wide-field surveys will be insensitive to identifying the longest-duration objects for two primary reasons. First, such low-energy explosions will have correspondingly low luminosities (L₅₀ ∼ 41.8, similar to the least luminous objects in our sample; see Table 5) and therefore be subject to Malmquist bias. Second, because the lengths of the observing seasons of each PS1 MD field (typically ≲ 160 days) are similar to the SN IIP plateau duration, there will be an observational bias toward measuring well-constrained plateau durations only for short-duration objects. We therefore interpret the results presented here as a lower limit on the true variation in the SN IIP plateau duration distribution. In a companion paper, Sanders et al. (2014), we use a hierarchical Bayesian light-curve fitting methodology to assess the influence of these biases on our inferred plateau duration distribution and to estimate the underlying plateau duration distribution.

We correct for total extinction (Galactic and host environment) using the (V − I) color excess method of Nugent et al. (2006) as revised by Kasen & Woosley (2009)—see Figure 13. We calculate E(V − I) by comparing with the theoretical baseline (V − I) color¹⁹ for the given V-band luminosity (Equation (15) of Kasen & Woosley 2009) and convert to extinction in each griz band using the extinction curve of Cardelli et al. (1989) and assuming R_V = 3.1. We apply a physically motivated uniform prior enforcing E(V − I) ⩾ 0 mag. The median uncertainty for the extinction estimate of an individual SN is 0.4 mag.

Zoom In Zoom Out Reset image size

We find extinctions varying from 0.0 to 4.8 mag, with a median value of 〈A_V〉 = 1.3 mag. In this distribution we have excluded objects with extinction uncertainties ⩾2 mag, affecting 8 objects. This median is somewhat higher than the mean extinction reported by Smartt et al. (2009) for their sample of SNe IIP with progenitor imaging, 〈A_V〉 = 0.7 ± 1.1 mag. The discrepancy may result from a combination of differences in methodology (the estimates from Smartt et al. 2009 are derived from a heterogeneous set of sources and techniques) and sample selection (given that our PS1 transient search operates in red bands, particularly i and z, it may be relatively insensitive to selection against high-extinction objects). Both observations and theory show that there is significant scatter around the fiducial (V − I) color, indicating intrinsic color variation not accounted for in our color-excess-based extinction estimate. Moreover, the color excess method may be particularly vulnerable to underestimates for low-metallicity progenitors where decreased iron line blanketing would reduce suppression of blue flux. We note that Faran et al. (2014) have recently shown that both photometric and spectroscopic SN IIP extinction correction prescriptions have limited effectiveness (as measured by their ability to reduce the scatter in observed colors) and exhibit systematic offsets relative to each other.

We show the peak absolute magnitude distribution for our PS1 SN IIP sample in each photometric filter in Figure 14. We correct for extinction using the (V − I) color excess method, as described in Section 4.4. Statistics of these distributions are given in Table 4. In this table and hereafter, we include only objects with well-constrained posterior distributions: δM_peak < 0.1 mag at 1σ without extinction correction, and δM_peak < 0.2 mag with correction. The median uncertainty for the absolute magnitude measurement (1σ posterior width) is δM_peak of 0.07 mag in r band without extinction correction, and 0.35 mag after correction.

Zoom In Zoom Out Reset image size

The observed peak magnitude distribution agrees well with the R-band luminosity function of Li et al. (2011), reflected in the prior distribution shown in Figure 14 (see also Section 3.2 and Figure 6). The comparison is somewhat limited, as Li et al. (2011) examined a different filter (R) and did not correct for extinction (although the objects in their sample should have low extinction). Note that this similarity suggests agreement of the observed distribution of peak magnitudes between our surveys. If the prior were simply dominating our inferred peak magnitudes, the posterior medians would all be centered at the prior mean (M_peak = −17.5). This effect can be seen in the y-band peak magnitude distribution shown in Figure 14, where prior information does dominate for a substantial fraction of objects. Extinction correction shifts the median of the distribution by ∼0.6 mag in g band and only by ∼0.1 mag in z band. We regard the y-band distribution as least reliable owing to the small number of objects (N = 15) that pass our posterior width cut, and therefore we do not include them in Table 4.

The extinction-corrected peak magnitude distribution spans a 1σ range of −17.47–−19.28 mag in r band, indicating a factor of ∼3 spread in the luminosity distribution of these SNe. This wide range in SN properties has important implications for the mass distribution of their progenitor stars, which we model and discuss in Section 5.4. Richardson et al. (2014) found a B-band volume-limited peak magnitude distribution with mean and standard deviation of M_B ∼ −17 ± 1 among 74 SNe IIP from the literature, ∼1.5 mag dimmer than the g-band mean peak magnitude we report. The discrepancy in the mean of the absolute magnitude distributions between our study and theirs is likely due to a combination of sample selection effects and extinction correction methodology. Richardson et al. (2014) have considered SNe IIL separately from SNe IIP, which systematically lowers their SN IIP peak magnitude distribution relative to ours (see Section 4.2). Moreover, Richardson et al. (2014) have applied a statistical correction for extinction, assuming a mean value of A_B ∼ 0.3 mag for each CCSN, which is typically ∼1 mag lower than the extinction correction we measure among our SNe IIP with the (V − I) color excess method (Section 4.4).

Upon investigation of the joint posterior parameter distributions among our fitted SN IIP light curves, we identified a highly significant relation between the plateau phase decline rate (β₂) and the extinction-corrected peak magnitude (M_peak) of the SNe. Figure 15 illustrates that these parameters are highly correlated in r band, with Pearson correlation coefficient of −0.50 (p-value of 5 × 10⁻⁰⁶). We have evaluated the strength of the correlation between these parameters in all combinations of photometric filters available from the PS1 data set (Figure 16) and identified this relation to be significant in every band (except y, where the PS1 photometry is limited), though it is strongest in the r and i bands.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In the r band, the relation between these parameters is best fit with the relation

$$\begin{eqnarray} \log \beta _2[r] & = (-13.1\pm 1.2) + M_{{\rm peak}}[r] (-0.47\pm 0.07). \quad \end{eqnarray} \tag{ 6 }$$

This linear fit was obtained using a Bayesian methodology accounting for the two-dimensional covariance of the M_peak and β₂ posterior distributions for each SN and modeling the relationship between these values with an intrinsic scatter V orthogonal to the axis of the fit line (Hogg et al. 2010).

The [16, 50, 84]th percentile values of the intrinsic scatter parameter, projected to the peak magnitude axis, are [0.14, 0.16, 0.19] mag. No samples among the 20, 000 returned from our MCMC fit of this model have positive slopes for the linear fit, supporting the low p-value reported from the Pearson correlation coefficient test above. When we perform the same analysis on the observed absolute peak magnitudes, not corrected for extinction, we find a similar trend, but with somewhat decreased significance (p-value of 1 × 10⁻⁰⁵ and projected intrinsic scatter median V = 0.26 mag). This result suggests that application of the color-excess-based extinction estimates provides measurable success in recovering the intrinsic distribution of light-curve properties, despite the shortcomings described in Section 4.4. Considering the V-band data of Anderson et al. (2014)²⁰ and applying the same Bayesian linear fitting methodology yields a median intrinsic scatter of V = 0.3 mag. The larger intrinsic scatter indicated by the Anderson et al. (2014) data results in part from the much smaller uncertainties in the light-curve parameters of the nearby SNe they study. This discrepancy may imply that the uncertainties in our light-curve parameters are somewhat overestimated, or that theirs are somewhat underestimated.

In past studies, divisions of SN IIP samples into "normal" SN IIP and SN IIL (see Section 4.2) subclasses may have obscured this relation by reducing the dynamic range available for correlations against the decline rate. Anderson et al. (2014) have recently reported an independent discovery of this relation using a similarly sized sample of V-band light curves from a variety of past SN searches. This independent discovery, as well as the multiband manifestation of the relation that we explore here, underscores its physical significance. This result echoes past conclusions that "SNe IIL" are on average more luminous than more slowly declining SNe IIP (e.g., Patat et al. 1994; Li et al. 2011).

The existence of a decline rate–peak magnitude relation for SNe IIP is reminiscent of the well-known width–luminosity relation for SNe Ia (e.g., Phillips et al. 1999). However, while brighter SNe Ia have more slowly declining light curves, brighter SNe IIP instead have faster-declining light curves (Figure 15). Moreover, the SN IIP relation has significant intrinsic scatter: V ∼ 0.2 mag. That the SN IIP decline rate–peak magnitude relation is recoverable at all is testament to the wide range of variation in their plateau phase decline rates, which ranges a factor of ∼20.

The SN Ia decline rate–peak magnitude relation is interpreted as evidence for a fundamental plane or single-parameter family among SN Ia light curves, and a similarly sparse dimensionality may apply to SNe IIP. Several authors have argued for a single parameter source of variation among SN IIP light curves (Hamuy 2003; Poznanski 2013), particularly with respect to the luminosity–velocity relation applied in the standardizable candle method (Hamuy & Pinto 2002; Olivares 2008; D'Andrea et al. 2010). Interpreted together with the results of Section 4.2, this would seem to point to the explosion energy, likely determined by the progenitor initial mass through its influence on the mass of the hydrogen envelope at the time of explosion, as the predominant single parameter continuously determining the fundamental observational properties of the explosions of hydrogen-rich red supergiants, as Anderson et al. (2014) also concluded. However, the presence of significant scatter around the SN IIP decline rate–peak magnitude relation presented here suggests additional correlations with secondary factors, as have emerged among SNe Ia (Wang et al. 2009; Foley et al. 2011). Relevant secondary characteristics of the progenitor stars are likely to include metallicity and rotation velocity.

In general, more massive H-rich envelopes should have longer radiative diffusion times (t_diff∝M/R), suggesting slower light-curve evolution and lower peak magnitudes. However, Poznanski (2013) have found an empirical linear relation between the progenitor initial mass of SNe IIP and their expansion velocities in the plateau phase. With these two factors in opposition, this would suggest that the diffusion time, and perhaps the β₂ parameter, should be nearly constant among SNe IIP. This discrepancy could result from nonlinearity in the relationship between progenitor initial mass and the mass of the hydrogen envelope at the time of explosion or variation in the velocity evolution between SNe IIP. Alternatively, it may challenge the robustness of the linear mass–velocity relation constructed by Poznanski (2013).

For the purpose of comparing with the full-wavelength spectrophotometric models of Kasen & Woosley (2009), we estimate the pseudobolometric (optical–IR) luminosity of each SN by integrating over the multiband (grizy) light-curve model described in Section 3.2. We apply a correction to the pseudobolometric light curves to, primarily, account for unobserved IR flux and some UV emission. We calculate this correction (pBC) by integrating an SN IIP spectral template from a similar epoch (t = +61 days; Gilliland et al. 1999; Baron et al. 2004) over the 'griz' bands, obtaining pBC = 0.38 mag. By using a fixed spectral template, we neglect any intrinsic variation in the SN IIP spectral properties. The modeling in Kasen & Woosley (2009) suggests that any intrinsic color variation among SNe IIP is small, with the bolometric correction estimated to vary by ∼0.1 mag based on differences in progenitor metallicity and initial mass (their Figure 14).

We estimate the ejected mass of radioactive ⁵⁶Ni (M_Ni) by comparison to the late-time light curve of SN 1987A (see Figure 17), following the method of Pastorello et al. (2004). We compare our pseudobolometric light curves (Section 5.1) with the SN 1987A light curve using the late-time (>125 days) rest-frame epoch where the model is most tightly constrained and assuming complete gamma-ray trapping, as in Pastorello et al. (2004); but see also the discussion of gamma-ray trapping in Anderson et al. (2014).

Zoom In Zoom Out Reset image size

The distribution of M_Ni among our PS1 SNe IIP has [16, 50, 84]th percentile values of [0.04, 0.12, 0.20] M_☉ (see Figure 18). We include in this distribution only objects with photometry to directly constrain their light-curve evolution in the radioactive-decay-dominated phase. We identify such objects by looking at the posterior variance in the β_dN parameter, which is δβ_dN = 1 dex at 1σ in cases where the prior alone sets the parameter value. We therefore adopt a cut at δβ_dN < 0.9 dex to exclude poorly constrained Ni masses. We note that, among the entire sample, the typical uncertainty in M_Ni is fairly large (median of 0.4 dex) owing to the relatively poor photometric coverage of the late phases of SNe in the sample. Among the excluded objects, some have unphysically large median estimates for the ejected ⁵⁶Ni mass (M_Ni > 1 M_☉); the high uncertainty in these estimates is appropriately reflected in the confidence intervals quoted in Table 5.

Zoom In Zoom Out Reset image size

Table 5. Light Curve and Modeled Progenitor Parameters for PS1 SNe IIP

PS1 SN	Mp, r	tplateau, r	log10(L50)	Δm15, r	MNi	Min	R0	E51
	(mag)	(days)	(erg s−1)	(mag)	(mag)	(M☉)	(R☉)	(1051 erg)
PS1–10a	$-18.11^{+0.17}_{-0.20}$	$114^{+32}_{-30}$	$42.63^{+0.55}_{-0.41}$	$-0.52^{+0.28}_{-0.38}$	$0.15^{+0.32}_{-0.11}$	...	...	...
PS1–10q	$-17.06^{+0.04}_{-0.05}$	$96^{+4}_{-2}$	$42.42^{+0.15}_{-0.12}$	$-0.26^{+0.02}_{-0.02}$	$0.11^{+0.19}_{-0.07}$	...	...	...
PS1–10ae	$-17.17^{+0.04}_{-0.04}$	$112^{+28}_{-26}$	$41.93^{+0.20}_{-0.13}$	$-0.30^{+0.03}_{-0.04}$	$0.06^{+0.07}_{-0.04}$	...	...	...
PS1–10lv	$-18.43^{+0.04}_{-0.03}$	$109^{+21}_{-7}$	$43.12^{+0.04}_{-0.06}$	$-0.27^{+0.01}_{-0.01}$	$0.20^{+0.14}_{-0.14}$	...	...	...
PS1–10mb	$-15.46^{+0.15}_{-0.17}$	$103^{+27}_{-20}$	$41.80^{+0.20}_{-0.15}$	$-0.08^{+0.04}_{-0.05}$	$0.06^{+0.06}_{-0.04}$	...	...	...

Notes. The r-band peak magnitude (M_{p, r}) is derived directly from the model fits (Section 3.2), including K-corrections, but not corrected for extinction. The r-band plateau duration (t_{plateau, r}) is in rest-frame days, not corrected for contamination by ⁵⁶Ni. The pseudobolometric (optical–IR) luminosity at 50 days (L₅₀) is measured from the fits to the PS1 photometry; the value quoted does not include the bolometric correction described in Section 3.2. The decline rate in r band (Δm_{15, r}; rest-frame days) is measured from the same model fits. The ejected nickel mass is estimated from comparison of the late-time bolometric light curve with that of SN 1987A (but see Section 5.2 for a discussion of reliability). The progenitor initial mass (M_in), radius (R₀), and explosion energy (E₅₁) estimates come from the comparisons (see Section 5.3) with the models of Kasen & Woosley (2009); but see Section 5.4 for a discussion of reliability. These theoretical estimates are reported only if the central mass estimate falls within the model grid (12–25 M_☉), but the full posterior distribution for the reported values includes extrapolations to values beyond the model grid, as reflected in the reported uncertainties. All reported values represent [16,50,84]th percentiles of the posterior distribution.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

Our results suggest a factor of ∼2 smaller M_Ni for most SNe IIP in comparison with typical SNe Ib and Ic, which have 〈M_Ni〉 ≈ 0.20 ± 0.16 M_☉ (Drout et al. 2011). This is consistent with the expectation that SNe Ib and Ic are produced by more massive stellar progenitors than SNe IIP. Our measured M_Ni distribution is similar to that reported by Nadyozhin (2003), who derive M_Ni ranging from 0.03 to 0.4 M_☉ for a set of 11 SNe IIP from the literature, with a mean value of 0.10 M_☉.

We derive physical parameters (including progenitor initial mass, radius, and explosion energy) for the progenitor stars of our SN IIP sample by comparison with the modeling of Kasen & Woosley (2009). In general, more massive progenitor stars produce plateaus that are brighter and of longer duration. There is a secondary contribution from M_Ni that has the effect of increasing the plateau duration. Kasen & Woosley (2009) provide scaling relations for the observable parameters L₅₀ (bolometric luminosity at 50 days after explosion) and t_{p, 0} (plateau phase duration, corrected for extension by ejected ⁵⁶Ni) as a function of E₅₁ (total explosion energy in units of 10⁵¹ erg) and M_in (initial mass of progenitor star). We note that there is a well-known discrepancy between masses derived from hydrodynamic light-curve modeling and direct progenitor searches, with progenitor searches yielding lower mass estimates (Utrobin & Chugai 2008; Maguire et al. 2010).

We derive t_{p, 0} using their Equation (13), which requires an estimate for M_Ni (see Section 5.2), R₀ (the progenitor radius at the time of explosion), and M_ej (the total ejected mass). Following the recommendations of Kasen & Woosley (2009), we calculate values for R₀ and M_ej strictly as a function of M_in by interpolating over the progenitor star model grid used in their study. Solving this system of equations for every sample in the posterior distribution of the light-curve model, we obtain estimates for M_in, M_ej, and E₅₁ for each SN IIP in our sample.

In Figure 19 we compare the observed plateau duration and L₅₀ with model curves from Kasen & Woosley (2009). This comparison illustrates that the observed variation in SN IIP light-curve phenomenology is significantly larger than the range explored by the Kasen & Woosley (2009) model grid, preventing us from performing progenitor parameter estimation for a substantial number of the objects in our sample. Given the observed M_Ni values measured for each individual light curve, 67 of our SNe IIP have light-curve properties outside the region covered by the Kasen & Woosley (2009) models, and we can produce mathematically valid comparisons with model light curves from the Kasen & Woosley (2009) grid for only 8 SNe IIP (see Table 5). Even these comparisons typically yield explosion energies at or above the most energetic models in their grid (E₅₁ > 5). A large number of objects in our sample have luminosities lower than the range of theoretical values for a given plateau duration (falling in the blue shaded region of Figure 19), accounting for 61 of the 67 objects for which we do not report progenitor inferences.

Zoom In Zoom Out Reset image size

We therefore advocate for further theoretical exploration of the SN IIP light-curve parameter phase space through additional hydrodynamic modeling, in order to provide more robust model grids and scaling relations for comparison with observational surveys. In particular, certain modeling systematics should be addressed to enable inference on objects occupying the low-luminosity and short plateau duration parameter space. Dessart & Hillier (2011) have previously recognized a systematic discrepancy between SN IIP model and observed light curves and identified oversized radii in model progenitor stars as the likely cause. Hydrodynamic explosion simulations based on more advanced progenitor star models, taking into account important effects such as rotation on the stellar radius (e.g., Georgy et al. 2013), are needed to overcome this bias. Moreover, synthetic light curves for SNe with progenitor initial masses <12 M_☉, down to the limit for core collapse (e.g., 8 M_☉; see Smartt et al. 2009, and references therein), and higher explosion energies should be produced. Such low-mass progenitors have already been explored in the context of extremely low luminosity SNe IIP like SN 1997D (Chugai & Utrobin 2000), and model light curves of this kind calculated with full self-consistency across the mass and energy spectrum are needed.

Additionally, other progenitor physical parameters will play important secondary roles in determining SN light-curve properties and should be included in future simulations. In particular, lower metallicity can serve to lower the plateau luminosity by decreasing the opacity of the H envelope, therefore lowering plateau luminosities, and by decreasing mass loss, causing longer-lived H recombination and plateau durations (Kasen & Woosley 2009; Dessart et al. 2013). Dessart et al. (2013) have recently performed a theoretical survey of SN IIP radiative properties using a grid of synthetic progenitor stars expanded in parameter scope with respect to the grid of Kasen & Woosley (2009), including core overshoot, rotation, mixing, and metallicity. However, the Dessart et al. (2013) grid was limited to a single initial progenitor mass of 15 M_☉. An expanded survey of the kind performed by Dessart et al. (2013), to provide updated observationally applicable scaling relations of the kind provided by Kasen & Woosley (2009), would be an invaluable tool for inference on the progenitor population of massive star explosions in the nascent untargeted survey era. Photometric galaxy metallicity diagnostics like that presented in Sanders et al. (2013) can be used to observationally estimate metallicities for the progenitor stars of observed SNe to facilitate model comparison.

While theoretical stellar evolution modeling has historically predicted that stars undergoing core collapse up to ∼25 M_☉ should produce SNe IIP (see, e.g., Eldridge 2008; Smartt 2009, and references therein), a variety of observational techniques have failed to identify SN IIP progenitors with masses greater than ∼16 M_☉. The shape of the stellar initial mass function (IMF) can at least help to explain this absence, with ∼8 M_☉ progenitors being a factor of 10–15 times more common than ∼25 M_☉ progenitors. However, even accounting for IMF prescriptions of varying steepness, Smartt (2009) reported an upper limit for the SN IIP progenitor mass of 16.5 M_☉ based on their direct progenitor detection search. Similarly, in an X-ray analysis of SN IIP progenitor mass-loss rates, Dwarkadas (2014) estimated a maximum mass-loss rate of ∼19 M_☉. Black hole fallback formation (Fryer 1999; Heger et al. 2003) and/or progenitor rotation (Georgy et al. 2013; Groh et al. 2013b) may provide a theoretical solution to this "red supergiant problem."

Our results have only indirect implications for the red supergiant problem. While our progenitor mass estimates (e.g., Figure 19) show no evidence for an absence of SN IIP progenitor stars at the high-mass end of the Kasen & Woosley (2009) progenitor grid, our mass estimates are only as reliable as the calibration of the hydrodynamic modeling underpinning them. As we have discussed, there are known systematic offsets between the masses inferred from hydrodynamic modeling and progenitor star photometry, and additional theoretical investigation of this discrepancy is needed to conclusively resolve the red supergiant problem.

However, our observations and modeling suggest that there is no discontinuous distinction between SNe IIP and IIL (Section 4.2). Given the correlation between plateau phase decline rate and luminosity (Section 4.6) and the theoretical connection between luminosity and progenitor mass, the exclusion of luminous "SNe IIL" could obscure the high-mass end of the SN IIP progenitor population. Emphasizing the role of small number statistics in this regime, we note that Smartt (2009) report a progenitor mass upper limit that is already consistent with 20 M_☉ at 2σ, and consistent with >25 M_☉ at 2σ if only events with robust progenitor detections are included in the analysis. Walmswell & Eldridge (2012) have recently considered the extinction due to the dust produced by red supergiant winds and revised the SN IIP upper mass limit to $20^{+6}_{-3}\ M_\odot$ (with 2σ uncertainty). As the direct progenitor search technique has so far only been applied to a handful of objects, we look to future detections of the progenitors of luminous SNe IIP to address the red supergiant problem (see, e.g., Fraser et al. 2010; Elias-Rosa et al. 2011).