Detection and Classification of Supernovae Beyond z ∼ 2 Redshift with the James Webb Space Telescope

SLSNe are the brightest SNe known to date; they can reach or outshine −21 mag in any wavelength bands in the optical or near-ultraviolet (Quimby et al. 2011; Gal-Yam 2012). Observationally they can be classified into two, maybe three, subclasses: members of the SLSN-I class do not show hydrogen in their spectra, unlike the hydrogen-rich SLSN-II events (note that in recent literature the hydrogen-poor SLSN-I events are often referred to simply as SLSNe, which might be a source of potential confusion, because the statistical properties of the two subclasses are systematically different, see below). There might be a third, very rare class, named SLSN-R, that also contains hydrogen-poor objects whose slowly evolving light curves are thought to be powered by an extreme amount (∼5 M_⊙) of radioactive ⁵⁶Ni (Gal-Yam 2012). Such an extreme amount of ⁵⁶Ni could be produced in a very massive core-collapse event induced by pair instability (e.g., SN 2007bi, Gal-Yam et al. 2009). The powering mechanism of the first two subtypes is still debated: several models including magnetar spin-down (e.g., Kasen & Bildsten 2010; Nicholl et al. 2017), or interaction with hydrogen-poor circumstellar shell (Chatzopoulos et al. 2012, 2013) have been proposed, but none of them are able to fully explain all observational aspects of SLSNe.

SLSN-I events are usually found in low-mass, metal-poor host galaxies that most often show extremely strong emission features (Neill et al. 2011; Lunnan et al. 2014, 2015; Leloudas et al. 2015; Perley et al. 2016). In this respect SLSNe-I are similar to LGRBs that also tend to preferlow-metallicity hosts (e.g., Langer & Norman 2006; Woosley & Bloom 2006; Perley et al. 2016). SLSNe-II, however, do not seem to show this trend: they can appear in galaxies that have broader ranges of mass and metallicity (Perley et al. 2016).

Figure 2 shows the blackbody-fitted SEDs of SLSNe at peak brightness shifted to various redshifts. These SEDs were constructed by combining observed, flux-calibrated spectra of various SLSNe (see Wang et al. 2017 for details). It is seen that both SLSN-I and SLSN-II events, in principle, are expected to be brighter than the NIRCam detection limit in the FLARE survey (∼27.3 AB-mag) up to z ∼ 10, in good agreement with the results by Tanaka et al. (2013). Based on this prediction, in Section 5 we estimate the expected number of SLSNe during the FLARE survey time.

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The left panel in Figure 3 shows the observable peak AB-magnitudes of SNe Ia with the four JWST NIRCam filters as above plus two broadband NIRCam W2 filters centered at ∼1.5 and ∼3.2 μm. These curves were calculated from synthetic photometry using the abovementioned JWST filter bandpasses on the Hsiao-templates for SNe Ia (Hsiao et al. 2007). It is seen that SNe Ia are expected to reach the FLARE detection limit in several NIRCam bands up to z ∼ 4. The right panel of Figure 3 illustrates the same conclusion by showing the blackbody-fitted SEDs of SNe Ia (Wang et al. 2017) at various redshifts. Thus, detections of SNe Ia with JWST NIRCam are feasible in the redshift range of 1 < z < 4.

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Since SLSNe are thought to originate from very massive stars, there is practically no delay time between the formation of their progenitors and the explosion. However, the local (low-z) observed rates for SLSNe-I are probably biased by the fact that they tend to occur only in low-metallicity hosts, similar to LGRBs (Section 4.1). Because at high redshifts low-metallicity host galaxies are more abundant, the SLSN-I rates at z > 2 are expected to be boosted up with respect to a rate that is estimated simply by extrapolating the local observed rate with the SFR(z) function. Thus, the observed SLSN rate per redshift bin dz can be expressed as

$$\begin{eqnarray}&&{\dot{N}}_{\mathrm{SLSN}}(z)=\displaystyle \frac{{\dot{n}}_{\mathrm{SLSN}}(z)}{1+z}\,\displaystyle \frac{{dV}}{{dz}},\end{eqnarray} \tag{ 6 }$$

where dV/dz is the comoving volume,

$$\begin{eqnarray}&&{\dot{n}}_{\mathrm{SLSN}}(z)={\epsilon }_{Z}(z)\mathrm{SFR}(z)\end{eqnarray} \tag{ 7 }$$

is the comoving rate of SLSNe, SFR(z) is the cosmic SFR, and _Z(z) is the redshift-dependent efficiency factor that corrects for the metallicity dependence. For SNe with negligible metallicity dependence (e.g., SLSN-II), _Z(z) ≈ 1.

The effect of metallicity on the rates of high-redshift GRBs has been extensively studied in the literature. For example, using model grids of single star progenitors of LGRBs, Yoon et al. (2006) computed the redshift-dependent GRB rate by using metallicity-dependent SFR and adding binaries to the collapsar model of the LGRB progenitors. From the metallicity-dependent star formation history, the observed mass function, and the mass—metallicity relation, they computed the expected GRB rate as function of metallicity and redshift. More recently, many studies found that the metallicity dependence can be parameterized simply by multiplying the SFR(z) function with the efficiency factor (z) = (1 + z)^β, where β ≈ 1.2 (Kistler et al. 2009; Virgili et al. 2011; Robertson & Ellis 2012; Trenti et al. 2013).

Based on the rate modeling of GRBs by Trenti et al. (2013), Wang et al. (2017) applied the DRAGONS semi-analytic galaxy formation model (Mutch et al. 2016) to estimate the expected number of SLSNe at high redshifts. As the progenitor models are poorly constrained, they considered simple empirically motivated models using the mean stellar metallicity of every galaxy at each simulated redshift to calculate the SLSN production efficiency factor, using stellar evolution simulations similar to Yoon et al. (2006) for each galaxy and averaging over all galaxies at that redshift. Assuming strong metallicity dependence they obtained a metallicity correction for the SLSN rate that is similar to that of the GRBs found previously (see above). In particular, they found that the peak of the SLSN rate shifts significantly toward z ∼ 5 if strong metallicity dependence is assumed with respect to the peak at z ≲ 3 when no metal dependence is used.

Recently Prajs et al. (2017) calculated the volumetric rate of SLSNe at z ∼ 1. They also estimated the rate of ultra-long GRBs based on the events discovered by the Neil Gehrels Swift satellite, and showed that it is comparable to the SLSN rate, providing further evidence of a possible connection between these two classes of events.

As the studies mentioned above explain the observed redshift evolution of the ratio of GRB rates and SFR as ∼(1 + z)^1.2 (with some increment from the power law at high redshift), we use this redshift dependence for _Z(z) in Equation (7), i.e., _Z(z) = (1 + z)^1.2. As the metallicities average out through the mass function at a given redshift, this factor provides a reasonable correction for the redshift-dependence of the frequency in low- and high-metallicity host galaxies.

For SLSNe-I we use the observed local volumetric rates published by Cooke et al. (2012), Quimby et al. (2013), and Prajs et al. (2017). For SLSNe-II we adopt the observational rate as given in Quimby et al. (2013), which recently turned out to be consistent with the rates estimated from three SLSNe discovered at z ∼ 2 (Moriya et al. 2019). Since the metallicity dependence of SLSN-II events is less pronounced as for SLSNe-I, their rates at high redshifts might be closer to the one that can be obtained by simply extrapolating their local rates toward higher redshifts along with the SFR(z) function. Nevertheless, we also apply the same redshift-dependent metallicity correction as above for SLSNe-II as well in order to get an upper limit for their high-z rates.

The expected number of SLSNe between redshifts z and z + Δz can be calculated by integrating Equation (7) to get

$$\begin{eqnarray}&&{N}_{\mathrm{SLSN}}={\rm{\Omega }}T{\int }_{z}^{z+{\rm{\Delta }}z}\displaystyle \frac{{\dot{n}}_{\mathrm{SLSN}}(z)}{1+z}\,\displaystyle \frac{{dV}}{{dz}}\,{dz},\end{eqnarray} \tag{ 8 }$$

where Ω is the survey area and T is the survey time. The results (the number of SNe per unit redshift interval within the survey area during the total survey time) are shown in Table 1, where the columns list the predicted number of SLSN-I and -II events with and without the metallicity correction.

The left panel of Figure 4 displays the adopted SLSNe volumetric rates as a function of redshift. The right panel shows the predicted numbers of SLSNe in the survey field at different redshifts with and without the assumed redshift-dependent metallicity correction. It is seen that even if we continue the survey up to 3 yr in the observer's frame, we can expect only very few SLSNe-I at relatively low (z ∼ 2–3) redshifts. SLSNe-II look to be more abundant than SLSNe-I, thus, it is more probable that the newly discovered high-z SLSNe will be SLSN-II events, especially if their rate also (at least slightly) depends on the host metallicity. On the other hand, even though SLSNe can be potentially detectable with JWST up to z ∼ 10, their very low volumetric rate makes them less suitable for constraining the cosmic SFR at z ≳ 5, at least with the relatively small-area survey considered in this paper.

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Note that the uncertainties in the cosmic SFR as well as in the observed SLSN rates make all the predictions on the expected SLSN numbers uncertain by at least a factor of ∼2.

The volumetric rate for SNe Ia is different from that of core-collapse events. Since the progenitors of SNe Ia are binaries containing at least one WD (i.e., evolved) star, a significant delay time between their formation and the SN explosion is expected. Therefore, their rate can be expressed as

$$\begin{eqnarray}&&\begin{array}{l}{R}_{\mathrm{Ia}}(t)=\nu {\displaystyle \int }_{{t}_{F}({z}_{F})}^{t}\mathrm{SFR}(t^{\prime} ){{\rm{\Psi }}}_{\mathrm{DTD}}(t-t^{\prime} ){dt}^{\prime} \\ \quad \ ({z}_{F}=10)\end{array}\end{eqnarray} \tag{ 9 }$$

where the efficiency ν is the number of SNe formed per unit stellar mass (${M}_{\odot }^{-1}$), which is the fraction of WDs in the 3–8 ${M}_{\odot }$ range, z_F is the formation redshift, and Ψ_DTD is their delay time distribution.

For the delay time distribution, various models are proposed in the theoretical and observational literature.

In the SD scenario (corresponding to short delay times), from simple analytic modeling of main-sequence lifetime as a function of mass (e.g., Barbary 2011) one can get

$$\begin{eqnarray}&&{\rm{\Psi }}(t)\propto {t}^{-0.46},\end{eqnarray} \tag{ 10 }$$

On the other hand, double degenerates (long delay) result in

$$\begin{eqnarray}&&{\rm{\Psi }}(t)\propto {t}^{-1}.\end{eqnarray} \tag{ 11 }$$

Population synthesis models predict universal DTD shapes for SNe Ia, independent of the details of common envelope prescription, mass transfer rate, hydrogen retention efficiency, or metallicities (Moe & Di Stefano 2013; Nelemans et al. 2013). For example, Strolger et al. (2004) considered two general forms for the DTD to explain the redshift distribution of SNe Ia discovered in the Hubble Higher-z Supernova Search program between 0.2 < z < 1.6. They applied exponential distributions like

$$\begin{eqnarray}&&{\rm{\Psi }}(t)={e}^{-t/\tau }/\tau \end{eqnarray} \tag{ 12 }$$

or Gaussian distributions

$$\begin{eqnarray}&&{\rm{\Psi }}(t)={e}^{-{\left(t-\tau \right)}^{2}/2{\sigma }^{2}}/\sqrt{2\pi }\sigma \end{eqnarray} \tag{ 13 }$$

assuming either wide (σ = 0.5τ) or narrow (σ = 0.2τ) full width at half maximum (FWHM) for the latter. Also, the peak of the Gaussian distributions was set in between 0.2 < τ < 10 Gyr. Strolger et al. (2004) found τ ∼ 4 Gyr as their best-fit value.

Although at present most of the observational evidence point toward the Ψ(t) ∼ t⁻¹ DTD (e.g., Maoz et al. 2014), in this paper we consider all the DTD forms mentioned above to predict the expected redshift distribution of SNe Ia at z > 1 redshifts. For the delay time parameter we assume τ = 0.5, 1.0, 2.0, 3.0, and 4.0 Gyr.

In Figure 5 the top left panel shows the observed SN Ia rates collected from the literature: the gray symbols are from mostly ground-based observations (Graur et al. 2011, and references therein), while the black filled circles are the final binned rates from the CLASH and CANDELS surveys (Rodney et al. 2014, hereafter R14). The continuous lines represent various theoretical rates corresponding to different DTD forms listed above. The thick red line shows the best-fit SN Ia rate given by R14, which is basically a t⁻¹ DTD scenario with a fraction of "prompt" Ia population, f_p, mixed in:

$$\begin{eqnarray}{\rm{\Psi }}(t)\,=\,\left\{\begin{array}{cc}0 & (t\lt 0.04\,\mathrm{Gyr})\\ 7.132\cdot \eta \cdot {f}_{p}{\left(1-{f}_{p}\right)}^{-1} & (0.04\lt t\lt 0.5\,\mathrm{Gyr})\\ \eta \cdot {t}^{-1} & (t\gt 0.5\,\mathrm{Gyr}),\end{array}\right.\end{eqnarray} \tag{ 14 }$$

where η = 2.25 and f_p = 0.21 were adopted as the best-fit parameters from R14. The thick blue line denotes the parameterized SN Ia rate applied by Hounsell et al. (2018; H18) for estimating the number of SNe Ia in the WFIRST Supernova Survey:

$$\begin{eqnarray}{R}_{\mathrm{Ia}}(z)\,=\,\left\{\begin{array}{lc}2.5\times {10}^{-5}{\left(1+z\right)}^{1.5} & (z\lt 1)\\ 9.7\times {10}^{-5}{\left(1+z\right)}^{-0.5} & (1\lt z\lt 3)\end{array}\right.\end{eqnarray} \tag{ 15 }$$

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It is seen that the ground-based rates are not constraining beyond z > 1, while the R14 and H18 models are in good agreement with the binned HST rates. However, the predicted rates at z > 1 redshifts are uncertain. The new SN Ia discoveries beyond z > 2 would provide critical and unprecedented information on the real nature of the DTD, for example, a better estimate for the fraction of the "prompt" Ia population.

The other panels in Figure 5 plot the expected numbers of SNe Ia in the ∼300 arcmin² survey field during the total survey time (3 yr) assuming the various DTD functions detailed above. All numbers are normalized to the same value in the first redshift bin centered at z = 0.5. Black circles show the R14 rates with a "prompt" fraction of f_p = 0.21, which we use as the best-fit reference rates at z > 1. It is seen that the various DTDs predict roughly similar redshift dependence at z > 1, although the predicted number of SNe Ia may differ by a factor of ≳2 around z ∼ 2. Table 2 lists these numbers for three cases: the SD, DD, and R14 scenarios, as shown above.

The uncertainties of the predicted numbers of SNe Ia are difficult to estimate because of the high uncertainty of the ground-based data and the low number of observational constraints above z ∼ 1 (Figure 5). If we adopt the predictions from the SD and DD scenarios "as is," then their difference may be used as a proxy for the uncertainty of the predicted rate at various redshift: ${\sigma }_{N}\approx 0.5\times | {N}_{\mathrm{SD}}-{N}_{\mathrm{DD}}|$. These numbers are given in the last column of Table 2.

In the left panel of Figure 6 the histogram of the V-band absolute peak brightnesses for the simulated SNe is plotted, while the right panel shows the distribution of the same SN sample in redshift space. The distribution of peak brightnesses introduces a large scatter in the observed peak magnitudes on the Hubble-diagram. This scatter can be reduced by applying the stretch—or decline rate—correction, which is commonly applied for SNe Ia when light curves in the rest-frame optical bands are available. However, in the proposed FLARE survey, as shown below, well-sampled light curves cannot be expected. Thus, alternative methods for taking into account and correcting for the peak brightness distribution are needed.

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We define two types of detection in our simulation. "Strong detection" means that a particular SN is detected (i.e., brighter than 27.3 AB-magnitude, see Section 2) in all four NIRCam filters simultaneously at a given epoch. "Weak detection" is defined as a detection only in at least one NIRCam bandpass at a given epoch. In the full sample containing 320 simulated SNe, 48 pass the "strong detection" criterion on at least 1 epoch during the survey, but only nine of them are detected on two epochs. Since low number statistics may influence the properties of the "strong" sample, we computed 10 different simulations with the same number of SNe whose parameters are randomly distributed within the allowed parameter range. The maximum redshift of these SNe turned out to be z_max ∼ 3.64 ± 0.33, while the average redshift of the "strong detection" subsample is $\langle z\rangle =1.822\pm 0.028$. The number of SNe in the "weak detection" group is 314, 151 of which are detected on two epochs. The maximum redshift in the "weakly detected" sample was 4.98, while the mean redshift of this subsample is $\langle z\rangle =1.921\pm 0.041$.

These numbers suggest that even though a significant number (≲50) of SN Ia detections in all four JWST NIRCam filter bands is expected during the proposed 3 yr long survey, only ≲10% of them would be detected on two consecutive epochs. Such a sparsely sampled "light curve" is clearly not capable of providing the necessary correction for the peak brightness distribution via the usual stretch/decline rate measurement. Moreover, because conventional spectroscopic observations are not feasible for SNe at z ≳ 2, the determination of the redshifts of the detected SNe must rely solely on photometry.

In the following sections we explore the possibilities and the feasibility of estimating the redshift and the true peak brightness of SNe from JWST NIRCam photometry.

In many previous studies the photometric classification of SNe Ia discovered at z > 1 were performed via light-curve fitting (e.g., Jones et al. 2013; Graur et al. 2014; Rodney et al. 2014, 2015; Rubin et al. 2018). For such light-curve simulations usually the SALT2 code (Guy et al. 2007, 2010) is applied. This kind of classification, although being robust, requires not only detections in various wavelength bands, but also multi-epoch (≳4) observations. Also, the reliability of this method is significantly improved if the redshift of the transient can be estimated independently, e.g., by ground-based deep spectroscopy of its host galaxy.

As shown in the previous section, the redshifts of SNe detected with JWST in the FLARE survey must be determined from photometric/SED data. Having accurate and precise photometric redshifts may enable the use of SNe Ia, measured only with photometry, to probe cosmology. This can dramatically increase the science return of future supernova surveys.

For example, the Large Synoptic Survey Telescope will use improved versions of the analytic photo-z estimator of Wang (2007) and Wang et al. (2007). That method uses colors as well as peak magnitudes, or colors only, to estimate the redshift of SNe Ia. It is an empirical, model independent method (no templates used).

Photometric redshifts derived from multi-band photometry are also proposed for thousands of SNe Ia expected from the Dark Energy Survey (Bernstein et al. 2012), although they preferred the photo-z estimates for the host galaxies rather than the SNe, because the coadded frames of galaxies can be ∼2 mag deeper than individual SN frames. Sánchez et al. (2014) presented an in-depth comparison of various photo-z methods and codes available for galaxies, and estimated an ∼0.08 uncertainty in photo-z for a sample of ∼15,000 galaxies.

We propose the photo-z determination for SNe Ia detected with JWST NIRCam by fitting the four-band SEDs with the extended SALT2 templates. The fitting parameters were the epoch of maximum light (t_max), the rest-frame peak V-band absolute magnitude (M_V), the redshift (z) and the SALT2 color parameter (c), while the SALT2 stretch parameter (x₁) was kept fixed at x₁ = 0.938 (see Section 6). This method works for SNe Ia between 1 < z < 4 redshifts, and some examples for the fits to the simulated SN sample are shown in Figure 7. Here the flux uncertainties are derived from the wavelength-dependent flux sensitivity limits for JWST NIRCam as shown on the JWST website.⁴ The best-fit SALT2 templates are found by simple χ² minimization, which seems to be an adequate solution as long as the SALT2 templates can indeed model the evolution of rest-frame SEDs of high-redshift SNe Ia in a similar way as their low-redshift counterparts. Note that because the observed NIR fluxes of SNe Ia above z ∼ 2 are increasingly dominated by their rest-frame optical SEDs, the uncertainties in the rest-frame NIR SEDs do not bias strongly the photo-z determination, especially for z > 3 events when the peak of the SED shifts into the NIRCam bands (see the lower panels in Figure 7).

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Figure 8 (left panel) compares the photo-z estimates with the "true" redshifts for the simulated SN sample. It is seen that the photo-z estimates are the best between the 2 < z < 3.5 redshift interval, as explained above. For z < 2 most of the photo-z values are in reasonable agreement with the true redshifts, although there are some deviating SNe with Δz > 1 residuals. The overall uncertainty, estimated as the standard deviation of the Δz < 0.5 residuals (after removing the outliers that represent ∼20% of the sample), is σ_z ∼ 0.25.

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It is emphasized that this accuracy can be reached only when the SN is successfully detected in all four NIRCam bands. Nondetection in any of these bands can degrade the quality of the fitting, thus, the accuracy of the photo-z estimate.

The right panel of Figure 8 plots the residuals between the simulated and recovered rest-frame phases (i.e., rest-frame days from epoch of maximum light) against redshift. The phases of all the simulated observations could be recovered within ±10 days. Again, the phase determination seems to work better for z > 2 SNe. The uncertainty of the phase determination, estimated as above, is found to be ±4.9 days.

In reality, core-collapse SNe are expected to contaminate the low-redshift (z < 1) sample. Wang et al. (2017) discussed the detection possibility of both SNe II-P and SNe Ib/c based on the Nugent-templates (Nugent et al. 2002). They found that at low redshifts SNe Ib/c are too faint to be detected in the reddest NIRCam filter (F444W) in the FLARE survey (see Figure 7 and Table 2 in Wang et al. 2017). Also, SNe Ib/c have lower rates than Type II SNe, which also reduces the probability of their detection during the survey time. Thus, SNe Ib/c are not likely to pass our "strong" detection criterion. Type II-P SNe, on the other hand, may appear in the survey FoV with a factor of ∼3 lower number in the F444W filter than SNe Ia (Wang et al. 2017), but their NIRCam colors and color evolution looks different from those of SNe Ia (see Section 6.3).

It is concluded that in the 1 < z < 3.5 redshift interval accurate flux measurements of SNe Ia with four JWST NIRCam filter bands allow redshift and phase estimates with ∼0.25 and ±4.9 day uncertainties, respectively. Note, however, that several other disturbing circumstances are ignored in this study, like, e.g., the host galaxy contamination in the SN fluxes, or nonstandard extinction in the host galaxy that cannot be captured by the SALT2 color parameter. Thus, our results are somewhat optimistic, but may serve as a guideline for the real observational studies with JWST.

Tanaka et al. (2013) showed that a near-IR color–color diagram can be a useful tool to identify SLSNe and separate them from fainter foreground transients, like Type II-P SNe that have similar light variation timescales. They proposed the usage of F200W, F227W, and F356W filters in the following combinations: F200W−F277W versus F277W−F356W ([2.0]–[2.8] and [2.8]–[3.6] in their notation). They concluded that faint objects that have positive colors (>0 mag) in both of these combinations are likely to be high-redshift SLSNe.

In the FLARE project Wang et al. (2017) proposed the application of the F200W versus F200W−F444W color–magnitude diagram for classifying various types of transients to be discovered with JWST NIRCam. They confirmed that SLSNe indeed occupy a different region than SNe Type Ia or Type II, although they noted that "ambiguities are inevitable and more data are needed."

In this paper we concentrate on identifying z > 1 SNe Ia using the NIRCam filters. After examining various combinations of the four NIRCam filters considered in this paper (F150W, F200W, F356W, and F444W, see Section 2), we suggest the following combination: F150W−F356W and F200W−F444W. A color–color plot with these indices is shown in the left panel of Figure 9. Red open circles represent those SNe Ia that passed the strong detection limit in our simulation. The subsample of z > 2 SNe is highlighted by blue filled circles. The uncertainty for each color index is computed as during the photo-z estimates (Section 6.2). Also plotted (with squares) are the positions of low-redshift (z < 1) Type II-P SNe around maximum light. Such low-redshift Type II-P SNe are expected to contaminate the sample of z > 1 SNe Ia (Wang et al. 2017). The colors of these Type II-P events are derived using the Nugent-templates (Nugent et al. 2002) after extending the templates up to 5 μm using a Rayleigh–Jeans blackbody tail. Similarly, triangles show the expected colors of SLSNe, whose SEDs are also approximated with blackbodies (see Section 4.1) cooling from T ∼ 15,000 K to T ∼ 6000 K as the SLSN evolves from maximum light to +40 days post-maximum in rest frame (Angus et al. 2018). Low-redshift SNe Ib/c are also shown as asterisks, even though they are not expected to reach our JWST detection limit in the F444W filter for z > 0.5 redshifts (see Figure 7 in Wang et al. 2017). Note that the rest-frame midinfrared SED of SNe Ib/c are uncertain, thus, their colors shown here are based on the same Rayleigh–Jeans approximation as used above for the Type II-P SNe.

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In the right panel of Figure 9 the redshift dependence of the NIRCam color indices are plotted. Although using blackbodies is only a rough approximation, the location of z > 2 SNe Ia in the NIRCam color–color plot seems to be separated from that of core-collapse SNe. This suggests that the classification of SNe based on their NIRCam colors might be feasible.

The left panel in Figure 10 contains the "observed" Hubble-diagram, i.e., the AB-magnitudes of the simulated SNe that passed the detection criterion as functions of redshift, in the 4 NIRCam bands. Dashed horizontal line indicates the assumed detection limit (27.3 AB mag) with NIRCam in the FLARE survey.

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As expected, the scatter on this uncorrected Hubble-diagram exceeds 1 mag in all bands above z ∼ 2 due to (i) the random sampling of the light curve in the observer's frame, (ii) the intrinsic dispersion in the peak magnitudes of SNe Ia (see Figure 6) and (iii) K-corrections due to nonnegligible redshifts.

The current state of the art for correcting for all these effects in order to get a "clean" Hubble-diagram from SN observations is the application of one of the light-curve fitting methods (usually SALT2, see, e.g., Scolnic et al. 2018). In the present case, however, such an approach does not work, as none of the SNe are detected more than twice due to the relatively long adopted cadence (90 days). Thus, alternatives are needed.

Since the only source of information is the flux in different bands (i.e., the SED of the SN), the peak absolute magnitude of the detected SNe must be determined somehow from their measured SED. This is actually done when measuring the photo-z of the SNe (Section 6.2): an output parameter of that fitting is the K-corrected V-band peak absolute magnitude of the best-fit SALT2-template to a particular SN. In the right panel of Figure 10 this quantity is plotted against redshift for all simulated SNe (taken from the input database of the simulation; black circles) as well as their recovered values after template fitting (green squares). The red dots show the case when the correction for the intrinsic distribution of the peak magnitudes (assumed to be Gaussian, Section 6) are also computed via fitting the observed four-band SEDs with the SALT2 templates as described in Section 6.2. This last step would require the knowledge of not only the fiducial peak magnitude of SNe Ia, but also the underlying distribution of the peak magnitudes as a function of redshift, which may not be Gaussian for high-z SNe. Thus, the impressively low scatter of the red dots in the right panel may not be reached from real data without obtaining short-cadence light curves. Since such multi-epoch follow-up observations were quite expensive with JWST, intense follow-up campaigns with other ground- or space-based instruments (Gemini, Keck, and/or HST) would be necessary. Designing and optimizing the details of such follow-up campaigns is beyond the scope of the present paper, but it would be an interesting extension to the FLARE survey (Wang et al. 2017).

Even if light curves were not available, the reduced scatter of the green squares compared to the ≳1 mag scatter in the left panel of Figure 10 is encouraging. Thus, the SED reconstruction using the extended SALT2 templates seems to be a useful approach in extending the observed Hubble-digram of SNe Ia up to z ∼ 3.5.

The green data in the right panel in this figure reveals another effect that may bias the distribution of the measurements on this kind of Hubble-diagram: at z > 2 only the SNe that are intrinsically brighter than the mean of their peak brightness distribution are detected. As the red dots suggest, this Malmquist-bias was clearly not present if the correction for the underlying distribution could be made. Nevertheless, this effect must be taken into account when the Hubble-diagram from such high-z SN observations are to be tested with cosmological models.

Overall, the results above suggests that using such low-cadence JWST data of SNe Ia for cosmology is not trivial, and more thorough studies, which are beyond the scope of the present paper, are necessary to reach this ambitious goal. One of the possibilities is the follow-up of the detected JWST transients with either ground- or space-based telescopes, such as Subaru, VLT, or HST, as discussed in Wang et al. (2017). Details on such a program will be given elsewhere.