MULTICOLOR LIGHT CURVE SIMULATIONS OF POPULATION III CORE-COLLAPSE SUPERNOVAE: FROM SHOCK BREAKOUT TO ⁵⁶CO DECAY

We calculate the light curves of zero-metallicity progenitors using main-sequence masses of ${M}_{{\rm{MS}}}=25,40,100\;$ ${M}_{\odot }$ and explosion energies corresponding to SNe (${E}_{{\rm{51}}}\equiv E/{10}^{51}$ erg = 1) and hypernovae (HNe; ${E}_{{\rm{51}}}\ \geqslant$ 10; see Table 1 for details). The presupernova models include detailed postprocess nucleosynthesis calculations (Tominaga et al. 2007a). Mass loss is considered to be a function of metallicity and is supposed to be zero for Pop III models. The composition of the models after explosive nucleosynthesis and the density structures of presupernova stars are shown in Figure 1. Presupernova stars with ${M}_{{\rm{MS}}}=25,40$ ${M}_{\odot }$ are blue supergiants (BSGs), and these progenitor models have been used by Ishigaki et al. (2014) to provide mixing-fallback best-fit models. The transition between red supergiant (RSG) and BSG zero-metallicity stars is still under investigation, and so we add an RSG progenitor model with ${M}_{{\rm{MS}}}=100$ ${M}_{\odot }$ to provide a more complete picture. The fits of the initial mass distribution to the ensemble of inferred Population III star gives ${87}_{-33}^{+13}$ ${M}_{\odot }$ for the maximum progenitor mass (Fraser et al. 2015), which is close to our choice of 100 ${M}_{\odot }$. For the 100 ${M}_{\odot }$ model, we did not find good mixing-fallback parameters to fit the observed metal-poor stars; nevertheless, the best models have a small mass of ⁵⁶Ni: M(⁵⁶Ni) $\sim {10}^{-7}$ ${M}_{\odot }$.

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Table 1.  Zero Metallicity Explosion Models

Model	Z	M	${T}_{{\rm{c}}}$	Luminosity	Radius	M(H)	Energy	${M}_{{\rm{cut}}}$(ini)	${M}_{{\rm{mix}}}$(out)	M(56Ni)	[C/Fe]a
		(M${}_{\odot }$)	(103 K)	(106L${}_{\odot }$)	(R${}_{\odot }$)	(M${}_{\odot }$)	(${E}_{{\rm{51}}}$)	(M${}_{\odot }$)	(M${}_{\odot }$)	(M${}_{\odot }$)
25z0E1	0	25	40	0.32	30	11.1	1	⋯	1.7	0.2	0.9
25z0E1m								1.7	5.7	0 ... 10−2	1.9
25z0E10							10	⋯	1.6	0.7	0.3
25z0E10m								1.7	6.4	0 ... 10−1	0.5
40z0E1.3m	0	40	27	0.88	85	15.0	1.3	2.0	12.7	0 ... 10−1	0.6
40z0E30							30	⋯	2.0	0.8	0.4
40z0E30m								2.0	5.5	0 ... 10−1	1.3
40z0E30m2								2.5	14.3	0 ... 10−1	0.1
100z0E2m	0	100	3.5	2.2	2200	27.1	2.0	2.0	40	0 ... 100	0.6
100z0E60							60	⋯	2.3	5.2	0.03
100z0E60m								2.3	40	0 ... 100	−0.3

Notes. The numbers shown are the metallicity, main-sequence mass, color temperature, luminosity, radius, hydrogen mass, explosion energy, mixing-fallback inner and outer masses, ⁵⁶Ni mass, and carbon-to-iron ratio.

^aFor mixing-fallback models, the value for the models with the highest amount of ⁵⁶Ni is shown.

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Aspherical effects are taken into account in the mixing-fallback model, which uses three parameters: the initial mass cut ${M}_{{\rm{cut}}}$(ini), the outer boundary ${M}_{{\rm{mix}}}$(out), and the ejection factor f (Tominaga et al. 2007b). The parameters of the mixing-fallback model are chosen around the values which provide the best fit to the observed elemental abundances (Ishigaki et al. 2014). However, in order to investigate the dependence of the light curves on the ejected mass of ⁵⁶Ni, we vary the ejection factor f from ordinary supernova values 0.07–0.2 ${M}_{\odot }$ down to the EMP case of M(⁵⁶Ni) = 10⁻⁷ ${M}_{\odot }$.

For the 40 and 100 ${M}_{\odot }$ SN models, we have to slightly increase the explosion energy from E₅₁ = 1 to 1.3 and to 2, respectively (see Table 1), in order to avoid the numerical oscillation of the internal zones due to fallback in the spherically symmetric approximation. Thus, the luminosities of these models are higher than those for the originally predicted explosion energy E₅₁ = 1. Estimates for the plateau phase (distinctive flat stretch during the decline) provide an increase of 0.3 mag for the 25 ${M}_{\odot }$ model and of 0.7 mag for the 100 ${M}_{\odot }$ model. As the nucleosynthetic products are not influenced much by the small change in the explosion energy, these changes do not lead to any inconsistency. This fallback issue should be investigated in the future with the use of multi-dimensional calculations.

In addition to zero-metallicity progenitors, we adopt progenitors with various metallicities up to solar (see Figure 2 and Table 2). The solar metallicity models are RSGs, so that the density and temperature inside the H-rich envelope are approximately several orders of magnitude lower than those of zero-metallicity models.

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Table 2.  Non-zero Metallicity Explosion Models

Model	Z	M	${T}_{{\rm{c}}}$	Luminosity	Radius	M(H)	Energy	${M}_{{\rm{cut}}}$	M(56Ni)
		(M${}_{\odot }$)	(103 K)	(106L${}_{\odot }$)	(R${}_{\odot }$)	(M${}_{\odot }$)	(${E}_{{\rm{51}}}$)	(M${}_{\odot }$)	(M${}_{\odot }$)
20z-3E1	0.001	20 (20)	2.6	0.12	760	8.7	1	1.5	0; 0.4
20z002E1	0.02	20 (18)	2.4	0.08	800	8.2	1	1.5	0; 0.1
25z002E1	0.02	25 (22)	2.4	0.17	1200	8.7	1	1.5	0; 0.24
25z002E1m	0.02	25 (18)	2.4	0.17	1200	8.7	1	1.7–5.7${}^{*}$	0; 10−3; 0.1
40z002E1	0.02	40 (22)	2.5	0.55	1700	3.7	1	10.0	0
40z002E2	0.02	40 (22)	2.5	0.55	1700	3.7	2	1.5	0.7

Note. The numbers shown are the metallicity, main-sequence mass (presupernova mass), color temperature, luminosity, radius, hydrogen mass, explosion energy, mass cut, mixing-fallback inner and outer masses, and ⁵⁶Ni mass. By ${}^{*}$ mixing-fallback parameters are indicated: ${M}_{{\rm{cut}}}$(ini), ${M}_{{\rm{mix}}}$(out).

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The solar metallicity models undergo mass loss (Figure 2), which is most significant for the 40 ${M}_{\odot }$ model. We do not apply the mixing-fallback scenario for these models, as we use them only for qualitative comparison with zero-metallicity models. The mass of the mixing zone usually does not produce a significant changes in the light curves. However, in order to investigate the mixing effects, we apply the mixing-fallback model to both the 25 ${M}_{\odot }$ zero and solar metallicity progenitors.

Similar to zero-metallicity models, in order to avoid numerical oscillations, we have to slightly change the explosion parameters. We adopt an explosion energy larger than ${E}_{{\rm{51}}}$ = 1 for the 40 ${M}_{\odot }$ solar metallicity supernova model 40z002E2 with a low mass cut.

For calculations of the light curves, we use the multigroup radiation hydrodynamics numerical code stella (Blinnikov et al. 1998, 2000, 2006), and for hypernova simulations we include special relativistic corrections in the hydro code in the manner of Misner & Sharp (1969). stella implicitly solves time-dependent equations for the angular moments of intensity averaged over fixed frequency bands and computes variable Eddington factors that fully take into account the scattering and redshifts for each frequency group in each mass zone. Here, we set 200 frequency groups in the range from 10⁻³ Å to 5 × 10⁴ Å. The explosion is initialized as a thermal bomb just above the mass cut, producing a shock wave that propagates outward. The effect of line opacity is treated as an expansion opacity according to the prescription of Eastman & Pinto (1993; see also Blinnikov et al. 1998). The opacity table includes $1.5\times {10}^{5}$ spectral lines from Kurucz & Bell (1995) and Verner et al. (1996).

In this subsection, we mostly describe the properties of zero-metallicity models at the epoch of shock breakout and the difference between the zero and solar metallicity models. A more detailed investigation of Type II plateau supernova (SN II-P) shock breakout for non-zero-metallicity progenitors has been conducted by Tominaga et al. (2011).

The light curves and spectra at the epoch of shock breakout for zero-metallicity models are presented in Figure 3. The duration of the shock breakout is mostly defined by the radius of the progenitors and varies from ∼100 s for BSGs up to ∼1000 s for RSGs. The peak frequency of BSG models (25,40 ${M}_{\odot }$) is in X-rays and their shock breakout can be detected, for example, by SWIFT/XRT up to $z\sim 0.1$ for SN models and $z\sim 1$ for HN models.

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The shape of the spectrum for the 100 ${M}_{\odot }$ hypernova model is different from the others because of several density peaks in the outer layers of the ejecta. These peaks are formed due to inefficient gas acceleration (Tolstov et al. 2013), and for such cases more reliable calculations can be performed only in multi-dimensional consideration of fragmentation in the outer layer.

The shock breakout phase of solar metallicity supernovae has a larger luminosity, but the effective temperature is much lower for the same mass compared to that for zero-metallicity supernovae (see Table 4). The main properties of the shock breakouts depend on the radius, the ejecta mass, the explosion energy, the opacity, and the density structure of the external layers (see, e.g., the analityc estimates of Imshennik & Nadezhin 1988; Matzner & McKee 1999). The dependence of the duration of the shock breakout ${\rm{\Delta }}{t}_{\mathrm{SBO}}$ and the peak luminosity L_SBO on the presupernova parameters can be estimated as follows (Matzner & McKee 1999):

$$\begin{eqnarray}&&{\rm{\Delta }}{t}_{\mathrm{SBO}}=790{\left(\displaystyle \frac{\kappa }{0.34{{\rm{cm}}}^{2}{{\rm{g}}}^{-1}}\right)}^{-0.58}{\left(\displaystyle \frac{E}{{10}^{51}{\rm{erg}}}\right)}^{-0.79}\\ &&\quad \times {\left(\displaystyle \frac{{\rho }_{1}}{{\rho }_{*}}\right)}^{-0.28}{\left(\displaystyle \frac{M}{10{M}_{\odot }}\right)}^{0.21}{\left(\displaystyle \frac{R}{500{R}_{\odot }}\right)}^{2.16}\;{\rm{s}}\;{\rm{(RSG)}},\\ &&\quad {\rm{\Delta }}{t}_{\mathrm{SBO}}=40{\left(\displaystyle \frac{\kappa }{0.34{{\rm{cm}}}^{2}{{\rm{g}}}^{-1}}\right)}^{-0.45}{\left(\displaystyle \frac{E}{{10}^{51}{\rm{erg}}}\right)}^{-0.72}\\ &&\quad \times {\left(\displaystyle \frac{{\rho }_{1}}{{\rho }_{*}}\right)}^{-0.18}{\left(\displaystyle \frac{M}{10{M}_{\odot }}\right)}^{0.27}{\left(\displaystyle \frac{R}{50{R}_{\odot }}\right)}^{1.90}\;{\rm{s}}\;{\rm{(BSG)}},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{L}_{\mathrm{SBO}}=2.2\cdot {10}^{45}{\left(\displaystyle \frac{\kappa }{0.34{{\rm{cm}}}^{2}{{\rm{g}}}^{-1}}\right)}^{-0.29}{\left(\displaystyle \frac{E}{{10}^{51}{\rm{erg}}}\right)}^{1.35}\\ &&\quad \times {\left(\displaystyle \frac{{\rho }_{1}}{{\rho }_{*}}\right)}^{-0.37}{\left(\displaystyle \frac{M}{10{M}_{\odot }}\right)}^{-0.65}{\left(\displaystyle \frac{R}{500{R}_{\odot }}\right)}^{-0.42}\;\mathrm{erg}\;{{\rm{s}}}^{-1}\;{\rm{(RSG)}},\\ &&\quad {L}_{\mathrm{SBO}}=1.9\cdot {10}^{45}{\left(\displaystyle \frac{\kappa }{0.34{{\rm{cm}}}^{2}{{\rm{g}}}^{-1}}\right)}^{-0.39}\\ &&\quad \quad \times {\left(\displaystyle \frac{E}{{10}^{51}{\rm{erg}}}\right)}^{1.30}{\left(\displaystyle \frac{{\rho }_{1}}{{\rho }_{*}}\right)}^{-0.23}\\ &&\quad \quad \times {\left(\displaystyle \frac{M}{10{M}_{\odot }}\right)}^{-0.69}{\left(\displaystyle \frac{R}{50{R}_{\odot }}\right)}^{-0.22}\;\mathrm{erg}\;{{\rm{s}}}^{-1}\;{\rm{(BSG)}},\end{eqnarray} \tag{ 2 }$$

where $\kappa ,E,M$, and R are the opacity, the explosion energy, the mass of the ejecta, and the radius of the presupernova, respectively. The density factor is ${\rho }_{1}/{\rho }_{*}\approx 1$ for RSG models. For BSGs, ${\rho }_{1}/{\rho }_{*}$ depends on the density structure, composition, and luminosity of the outer layers of the star and varies from ${\rho }_{1}/{\rho }_{*}\approx 50$ for the 25 ${M}_{\odot }$ model to ${\rho }_{1}/{\rho }_{*}\approx 2$ for the 40 ${M}_{\odot }$ model.

The difference between the RSG and BSG models can clearly be seen from the duration of the peak: the larger presupernova radius leads to a longer duration of the shock breakout epoch. Compared with zero-metallicity BSGs, the larger luminosity of the solar metallicity SNe is due to the lower (by several orders of magnitude) opacity of the external layers of RSGs. The photosphere's temperature in RSG models is only 3000–4000 K (in contrast to ∼20,000 K in BSG models), and the opacity of neutral atoms of hydrogen is dominated by bound-bound and bound-free transitions. In agreement with theoretical estimates, this low opacity of the exteral layers increases the luminosity of the shock breakout.

The shock breakout is followed by the "cooling envelope phase," which marks the decline of the luminosity (see Figure 4). The duration of this phase strongly depends on the presupernova radius. For compact BSG progenitors, the duration is much shorter in the optical U and V bands (∼100 s) than for RSGs (∼1 day). After reaching the luminosity minimum, the light curve starts to rise as the heated expanding stellar envelope diffuses outward. For RSG progenitors, the rise time (∼10 days) an order of magnitude longer than for BSG progenitors. This behavior is consistent with the previous investigation of the SN light curves for the early phases (see, e.g., González-Gaitán et al. 2015).

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The presence of the massive hydrogen envelope in zero metalicity presupernova models should produce light curves similar to those of SNe II-P. The duration of the plateau is determined primarily by the mass of the envelope ${M}_{{\rm{ej}}}$ and the other main outburst properties, i.e., the explosion energy E and the initial radius R (Litvinova & Nadezhin 1985; Popov 1993). The SN II-P light curve tails are believed to be powered by ⁵⁶Co decay and the temporal behavior is determined by the ejected mass of ⁵⁶Ni (see, e.g., Nadyozhin 1994). The variation of the ejected mass of ⁵⁶Ni allows us to cover the uncertainty of matter mixing and fallback in aspherical, jet-like explosions. We start with M(⁵⁶Ni) ∼ 0.1 ${M}_{\odot }$ and logarithmically decrease down to ${10}^{-6}$ ${M}_{\odot }$ by a factor of 10 ${M}_{\odot }$. Lower values of M(⁵⁶Ni) lead to extremely small changes in the light curve (${M}_{{\rm{abs}}}\lt -5$), and for practical purposes the light curve with M(⁵⁶Ni) = ${10}^{-6}{M}_{\odot }$ can be used. The light curves for zero-metallicity models are compared with several RSG models with no ⁵⁶Ni.

3.3.1. Plateau Luminosity

During the plateau, the light curve is powered by the recombination of hydrogen previously ionized in the supernova shock. The peak luminosity increases with higher explosion energy and radius, but decreases with higher ejecta mass. The absolute V magnitude can be estimated from Litvinova & Nadezhin (1985):

$$\begin{eqnarray}&&V=-2.34\;\mathrm{lg}\;E-1.80\;\mathrm{lg}\;R+1.22\;\mathrm{lg}\;M-11.307,\end{eqnarray} \tag{ 3 }$$

where E, R, and M are the explosion energy (in ${10}^{50}$ erg), the presupernova radius, and the ejecta mass in solar units, respectively.

The calculations of the zero-metallicity models presented in Figure 5 are consistent with the analytic estimates. The plateau of the 25 ${M}_{\odot }$ and 40 ${M}_{\odot }$ supernovae that have a compact progenitor is rather faint, ${M}_{{\rm{bol}}}\quad \sim$ −15, while the much larger radius of the 100 ${M}_{\odot }$ progenitor leads to an increase in luminosity. In contrast to the zero-metallicity 25–40 ${M}_{\odot }$ models, solar metallicity SNe are about an order of magnitude more luminous (Figure 6) due to the larger radius of their progenitors.

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All of the above are valid for models with a low amount of ⁵⁶Ni. If the ⁵⁶Ni mass in the ejecta is rather high ($M{(}^{56}\mathrm{Ni})$ > $0.01...1\;{M}_{\odot }$), then the ⁵⁶Ni decay can form a more luminous peak. From Figure 5, we see that the ⁵⁶Ni peak is a possible indicator of C-normal EMP stars.

The optical multicolor light curves (Figures 7–8) during the plateau phase demonstrate that the flat shape of the U- and B-band light curves is similar to the shape of the bolometric light curve. The shape of the light curves in the more luminous R and I bands is not as flat and has a peak in the middle of the plateau.

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3.3.2. Plateau Duration

The duration ${\rm{\Delta }}t$ of the light-curve plateau is estimated by Litvinova & Nadezhin (1985) as

$$\begin{eqnarray}&&{\rm{\Delta }}t=-0.191\;\mathrm{lg}\;E+0.186\;\mathrm{lg}\;R+0.566\;\mathrm{lg}\;M+1.047.\end{eqnarray} \tag{ 4 }$$

In agreement with this equation, the larger radius and mass provide a longer duration for the plateau phase, but a larger explosion energy reduces the plateau duration. This behavior is well reproduced in our numerical calculations: in bolometric light curves of zero-metallicity (Figure 5), solar metallicity (Figure 6) models, and in multicolor light curves of zero-metallicity supernova and hypernova models (Figures 7–8).

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The width of the plateau also depends on the depth of the mixed hydrogen-rich layer (see, e.g., Shigeyama & Nomoto 1990). To estimate the influence of mixing, we constructed the models with a uniform abundances distribution and performed a comparison with non-mixed models (Figure 9). The mixing does not greatly change the form of the light curve because the minimum velocity of the hydrogen layer is low for the models.

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The solar metallicity RSG progenitor has a larger radius which leads to a higher luminosity and a longer duration of the SN plateau compared with BSG progenitors. The 20 ${M}_{\odot }$ and 25 ${M}_{\odot }$ RSG models have quite a large amount of ⁵⁶Ni to make the plateau duration longer compared with the low-⁵⁶Ni models (Figure 6).

3.3.3. Photospheric Velocities

In Figure 10, we compare the photosperic velocities for 25 ${M}_{\odot }$ zero and solar metallicity models during the plateau phase. Due to compact presupernova, the zero-metallicity models have a higher velocity and a much faster drop in photospheric velocity. For hypernova models (explosion energy ${E}_{51}$ = 10), the velocity of the outer layers of the ejecta reaches ∼50,000 km s ${}^{-1}$. The maximum photospheric velocity is realized at the beginning of the plateau phase just after shock breakout epoch.

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3.3.4. Color Evolution Curves

Figure 11 presents $B-V$ color evolution curves of 25 ${M}_{\odot }$ progenitors for various values of explosion energy and metallicity. The color evolution curves reveal a common feature: for zero and low-metallicity BSG progenitors, the $B-V$ value during the plateau phase is almost constant, while for solar metallicity RSG progenitors we can see a gradual reddening.

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For a more general investigation, in Figure 11, we compare the color evolution curves calculated by stella with a set of SN II-P and SN 1987A observational data. The modeling of the color evolution curves during the plateau phase demonstrates a cooling rate consistent with that observed for SNe: the decrease in metallicity leads to flattening of the color evolution curve. The flattening of the color curve can also be seen in observations of low-metallicity supernovae (see, e.g., Polshaw et al. 2015).

It is difficult to use the luminosity and the duration of the plateau phase to distinguish between solar and low-metallicity SNe (Figure 12). Zero metallicity normal energy SNe are as luminous as solar metallicity low-energy SNe. Moreover, the light curve of the massive 100 ${M}_{\odot }$ zero-metallicity SNe is quite similar (in the plateau duration and luminosity) to the light curve of less massive (25 ${M}_{\odot }$) solar metallicity stars for the same explosion energy ${E}_{51}$ = 1. The decline of the luminosity after the plateau phase is also quite similar between the zero and solar metallicity progenitors (Figure 12). In this situation, the SN color evolution curve can help to distinguish the metallicity of the progenitor.

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In Figure 13, we compare the color evolution curves for zero and solar metallicity RSG models and find that they also differ in their cooling rates and, consequently, can be distinguished by metallicity. For the massive zero-metallicity BSG presupernova model (40z0E1.3), in contrast to RSGs, the plateau is shorter, but again low metallicity leads to the flattening of the color evolution curve.

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In addition, we confirm the above metallicity dependence for 100 ${M}_{\odot }$ models in which the metallicity of the hydrogen envelope changes gradually from zero to the solar value. The result of this numerical experiment is the same as above: for the zero-metallicity model, the $B-V\;\mathrm{and}\;U-B$ color evolution curves are flat, but the increase in metallicity to the solar value leads to the linear behavior. The color evolution is mostly due to the opacity difference between the zero and solar metallicity models, while the hydrodynamical evolution for both models is similar. In distinguishing between the zero and solar metallicity models, the evolution of the red and infrared color indexes is less informative compared to the $B-V$ color index.

The different behaviors of the low-metallicity and solar metallicity color evolution curves can be used to distinguish between low-metallicity and normal metallicity SNe.

After the plateau phase for low ⁵⁶Ni models, the luminosity starts to decline. The decline rate is defined by the explosion energy (Arnett 1980), opacity, and ⁵⁶Ni and H mixing (see, e.g., Kasen & Woosley 2009; Bersten et al. 2011; Nakar et al. 2015).

The UBVRI light curves for low ⁵⁶Ni models are summarized in Figures 7–8. The radii of BSGs are smaller compared to those of RSGs and the temperature drops faster (Grasberg et al. 1971; Arnett 1980). This leads to the steeper luminosity decline in optical bands for BSG models.

The presence of ⁵⁶Ni finally leads to the tail of the light curve powered by the ⁵⁶Co decay and its temporal behavior is given by (see, e.g., Nadyozhin 1994)

$$\begin{eqnarray}&&{M}_{{\rm{bol}}}=-19.19-2.5\;\mathrm{lg}\left(\tfrac{{M}_{{\rm{Ni0}}}}{{M}_{\odot }}\right)-1.09\tfrac{t}{{\tau }_{{\rm{Co}}}},\end{eqnarray} \tag{ 5 }$$

where $t$ is measured from the moment of explosion ($t=0$), ${M}_{{\rm{Ni0}}}$ is the total mass of ⁵⁶Ni at $t=0$, which decays with a half-life of 6.1 days into ⁵⁶Co, and ${\tau }_{{\rm{Co}}}$ = 111.3 days.

The smooth radioactive tail is reproduced in all of our numerical calculations with good accuracy.

If we increase the ⁵⁶Ni mass from zero in the model, then the radioactive tail becomes more luminous and at some M(⁵⁶Ni) mass value its luminosity at the end of the plateau phase can be comparable to the plateau luminosity. This value can be roughly estimated using Equations (3)–(5), and for our models varies from ∼0.1–0.01 ${M}_{\odot }$ for SNe to ∼0.1–0.5 ${M}_{\odot }$ for HNe. For these values, the nickel peak can be clearly seen in the light curve.

Compared with zero-metallicity SNe models, for solar metallicity models the brightness of the plateau phase is larger and the mass of ⁵⁶Ni for forming the nickel peak is larger: $\gtrsim$0.1 ${M}_{\odot }$.

In Figure 8, we find that the luminosity of the most luminous model, 100z0E60m, without ⁵⁶Ni is higher than for the model with ${\boldsymbol{M}}{(}^{56}\mathrm{Ni}$) = ${10}^{-3}{M}_{\odot }$ in the transition from the plateau to the ⁵⁶Ni tail up to ∼150 days. This behavior is explained by the trapping of thermal photons in the model with ⁵⁶Ni where the transparency is lower (due to a larger amount of ${}^{56}$ Fe produced by ⁵⁶Ni and ⁵⁶Co decay). It takes place until the epoch when radioactive decay overwhelms the emission of thermal photons from the entropy reservoir of the shock heated ejecta of zero ⁵⁶Ni model at t $\gt$ 150 days. Although further, more detailed study may clarify more fully the nature of this effect, it is not important for the goals of our investigation. The behavior of the light curves in those epochs does not change our conclusions.

3.4.1. Mixing

The above estimates for the transition phase do not take mixing into consideration, but accounting for mixing can significantly change the light curve.

To investigate the mixing effect more accurately, we compare a number of 25 ${M}_{\odot }$ models with zero and solar metallicity, varying M(⁵⁶Ni) and calculating the light curves for all of these models with uniform mixing throughout the ejecta (Figure 14). If M(⁵⁶Ni) is rather large ($\gtrsim$0.1 ${M}_{\odot }$), then the mixing reduces the rise time to the ⁵⁶Ni peak (model 25z0E1m). For more plateau luminous models, the mixing slightly reduces the plateau duration for the same reason: the ⁵⁶Ni peak is shifted to earlier times (model 25z002E1m).

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We compare the simulation of the multiband light curves of the 25 ${M}_{\odot }$ hypernova model (${E}_{{\rm{51}}}$ = 10) with light curves calculated by Smidt et al. (2014) for similar models. The luminosity of the plateau and its duration are in good agreement with their calculations. The decline of the light curves after the plateau phase is more sloping in stella calculations, which is due to different procedures used for the opacity calculations. The luminosity at the tail phase must be specified in the future with more detailed opacity calculations that include millions of lines, similar to the existing procedures for type Ia SNe (private communication with E. Sorokina). Detailed opacity calculations and analysis of the transition phase (from the plateau to ⁵⁶Co decay) in models with M(⁵⁶Ni) can help to reveal the physical properties of the presupernova: explosion energy, mixing, and opacity.

In Figure 15, the calculated low-⁵⁶Ni light curves are qualitatively compared with several observed massive Type II SNe (SN 1999em, Elmhamdi et al. 2003; SN 1999br, Pastorello et al. 2004; SN 1997D, Benetti et al. 2001; SN 2004fx, Hamuy et al. 2006; SN 1992ba, SN 2006Y Anderson et al. 2014).

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The luminosity of the plateau for the observed faint supernova SN 1997D is close to the modeled light curves of SNe that have BSG progenitors. Adjusted for the uncertainty of the observed plateau duration and possible asymmetry features, our BSG models with low metallicity could be good candidates for simulations of these objects, in addition to those simulations which already exist (Turatto et al. 1998; Chugai & Utrobin 2000).

The $B-V$ color evolution curves of SN 1999em and SN 1999br are included in the set of SN II-P data (Hamuy 2001) presented in Figure 11. Their color curves are typical of solar metallicity progenitors and the presupernovae of SN 1999em and SN 1999br are supposed to have RSG progenitors. The $B-V$ color evolution curve for SN 1992ba and SN 2004fx are also typical of solar metallicity SNe (Hamuy et al. 2006; Jones et al. 2009).

Since we do not know the moment of explosion in observed SN II-P, it is difficult to distinguish between the low-energy explosion of RSGs (${E}_{51}\quad \sim$ 0.1) and the ordinary BSG SN in the analysis of bolometric light curves (see Figure 12). Analysis of the photosperic velocities and color curve evolution during the plateau phase can provide more information about the progenitor.

While Pop III SNe typically have fainter and shorter plateaus than SNe with solar metallicity, the most important characteristic is the color evolution curve. The color evolution during the plateau phase and the first $10$ days distinguish Pop III SNe from RSG SNe with solar metallicity and SN 1987A-like BSG SNe, respectively (Figure 13). In order to obtain the color evolution, the multicolor observations should be performed every $\sim 2$ days for the first $10$ days and every $\sim 10$ days for the plateau.

Although follow-up observations of nearby SNe realize such multicolor observations with cadences of $\lt 10$ days, SNe with flat color evolution have not yet been discovered (Section 4.1). This might be because most previous SN surveys targeted large nearby galaxies with metal enrichment. Untargeted multicolor SN surveys were performed by SDSS (Sako et al. 2014) and SNLS (Astier et al. 2006; Guy et al. 2010). Their cadences are high enough to draw the color evolution curves at the plateau. We have checked the multicolor light curves of the SDSS sample.⁷ Although the signal-to-noise ratio is poor, a spectroscopically identified SN II (ID 12991) shows blue color and flat color evolution curves during the plateau phase (Figure 16). Although the metallicity of the host galaxy is not metal-poor according to the ${R}_{23}$ method (12$+\mathrm{log}({\rm{O/H}})$ = 8.58, Tremonti et al. 2004; Alam et al. 2015), we propose that the SN took place in the low-metallicity environment. We do not consider red and infrared color evolution curves because it is not informative to distinguish between zero and solar metallicity (see Section 3.3.4).

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There are two ways to detect Pop III SNe in low-metallicity environments that produce C-normal EMP, CEMP, and HMP stars. In order to identify low-⁵⁶Ni SNe, we must follow the light curve until ⁵⁶Co decay. As the tail of the faint SNe for HMP stars is as faint as ${M}_{{\rm{abs}}}\gt -7$, the tail can be detected only if it took place at $\lt 50$ Mpc even with 8 m class telescopes. In contrast, their plateaus are as bright as ${m}_{{\rm{bol}}}\sim 20$, and thus the detection can be made with an untargeted survey with such 1 m class telescopes as PTF (Rau et al. 2009), KISS (Morokuma et al. 2014), and the all-sky survey as Gaia with the broadband G-band limiting magnitude of $G\sim 19$ (Altavilla et al. 2012). In Figure 17, we plot light curves for low-⁵⁶Ni models and designate the detection limits for the Gaia mission. For these surveys, EMP star forming galaxies can also be good targets for finding and identifying supernovae of metal-poor progenitor stars (Thuan 2008; Pilyugin et al. 2014; Guseva et al. 2015).

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The other targets for detecting Pop III SNe are the metal-free pockets at $z\sim 2$. Figure 18 shows the g-band light curves of Pop III SNe at $z=2$. Since Pop III SNe are fainter than SNe with solar metallicity, only SNe with $100\quad {\text{}}{M}_{\odot }$ can be observed with 8 m class telescopes such as Subaru/HSC and LSST. Explosions with ${E}_{51}=1\;\mathrm{and}\;60$ can be detected during the shock breakout phase and the phase lasting from the shock breakout to the plateau, respectively. The UV colors of Pop III SNe also display flat color evolution, in contrast to the increasing UV color evolution of solar metallicity SNe (Figure 19). Therefore, the multicolor optical observation can inform the metallicity of the SN, although spectroscopic follow-up observation is difficult.

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Sources of UV radiation capable of reionizing the universe are still under discussion. According to cosmological models (Barkana & Loeb 2001) and observations (Fan et al. 2006), the reionization of the universe appears to have been well completed at redshift z $\sim$ 6. The first generation of stars could be imporant contributors to the ionization. According to our calculations, the SNe of RSG progenitors provide larger amounts of UV photons at the shock breakout epoch, but still less than BSGs do during their lifetimes.

To estimate the contribution of Pop III SNe to cosmic reionization, we calculate the number of ionizing photons with energy ${E}_{{\rm{ion}}}=h{\nu }_{{\rm{HI}}}\gt 13.6$ eV for all of the models:

$$\begin{eqnarray}&&{N}_{{\rm{UV}}}={\displaystyle \int }_{{\nu }_{{\rm{HI}}}}^{\infty }\tfrac{{F}_{\nu }}{h\nu }d\nu .\end{eqnarray} \tag{ 6 }$$

The results are summarized in the last column of Table 3. The UV photons are mostly produced by shock breakout when the effective temperature is high enough (T ∼ 5 × 10⁵ K), similar to previous estimates from the SN 1987A model (Lundqvist & Fransson 1996). Supernovae with larger explosion energies or larger progenitor radii emit larger numbers of UV photons. However, for BSG progenitors, the number of UV photons during explosions corresponds to only 10–100 years of the main-sequence lifetime (Tumlinson & Shull 2000). RSG progenitors provide a larger amount of UV photons at shock breakout, but still less than those from BSGs during their lifetimes.