Cosmic Core-Collapse Supernovae from Upcoming Sky Surveys

The total cosmic supernova rate (hereafter CSNR)

is the number of events per comoving volume per unit time $t_{\rm em}$ in the emission frame (i.e., cosmic time dilation effects in the observer’s $z=0$ frame are not included). The total rate, and the various differential rates below, can of course be specialized to distinguish different groups of supernovae classified by intrinsic type and/or dependence on local environment.

The present data on high-redshift core-collapse supernovae are too poor to construct an accurate CSNR. But the CSNR is intimately related to cosmic star-formation rate $\dot{\rho}_{\star}=dM_{\star}/dV_{\rm com}dt$ (Madau et al., 1998). The connection is

where $X_{\rm SN}$ is the fraction, by mass, of stars which become supernovae, and $\langle m_{\rm SN}\rangle$ is the average supernova progenitor mass (see Appendix A). A key point is that due to the short core-collapse progenitor lifetimes the two rates scale linearly, ${\cal R}_{\rm SN}\propto\dot{\rho}_{\star}$. The constant of proportionality depends on the initial mass function (IMF). If the IMF changes with time (or environment) this complicates the picture. In producing quantitative estimates we will follow most studies in assuming time-independent IMF. Thus the supernova/star-formation rate proportionality is a constant fixed for all time, namely ${\cal R}_{\rm SN}/\dot{\rho}_{\star}=0.00915\,M_{\odot}^{-1}$ (Appendix A).

Uncertainties in the cosmic rates for both supernovae and star-formation remain considerable. As illustrated in detail by (Strigari et al., 2005), the cosmic star-formation rate is known to rise sharply towards redshift $z\sim 1$. In this low-to-moderate redshift regime, the shape of the rate versus redshift is fairly well known, but as emphasized by Hopkins & Beacom (2006) the normalization remains uncertain to within a factor $\sim 2$. At higher redshifts, the rate becomes even more uncertain, largely due to the paucity of data and also to uncertainties in our knowledge of the degree of dust obscuration. It is also worth noting that most studies to date directly or indirectly use massive stars as proxies for star formation. Consequently, the rate for cosmic massive star formation–and for cosmic supernovae–is less uncertain and IMF-dependent than the total rate.

To illustrate the effects of these uncertainties on the synoptic survey supernova harvest, we have adopted two possible CSNR forms. These appear in Figure 1, which shows the expected supernovae rate assuming a perfect environment (i.e. no dust extinction, etc). The solid curve in Figure 1(a) is the CSNR derived from the cosmic star-formation rate of Cole et al. (2001) with parameters fitted by Hopkins & Beacom (2006) (hereafter the “benchmark” CSNR). This rate sharply rises to a peak at $z\sim 2.5$, followed a strong but less rapid declines out to high redshift. To investigate the impact of the falloff from the peak, we also show in the broken curve an alternate CSNR due to current observational data fitted by Botticella et al. (2008) (hereafter the “alternative” CSNR). This rate also rise to redshift $z\sim 0.5$, though with a different slope; we somewhat arbitrarily set the alternative rate to a constant at $z>0.5$ where the data are unclear; in any case we will find that few events from this high-redshift regime will be accessible to the all-sky surveys which are our focus.

Synoptic surveys will measure several observables associated with cosmic supernovae: their numbers and location, and some portion of their light curves in different bands. Spectroscopic redshifts of host galaxies can also be determined (when visible; see §6.5). Using the number counts and redshift indicators, one can deduce an observed core-collapse rate, per unit redshift and per unit time and solid angle. This observed rate distribution directly encodes the CSNR via

where $V_{com}$ is the comoving volume and $r_{com}(z)$ is the comoving distance out to redshift $z$. The $1+z$ factor corrects for time dilation via $dt_{\rm obs}=(1+z)dt_{\rm em}$.

Figure 1(b) shows the all-sky cumulative frequency of cosmic supernovae for an observer at $z=0$, i.e.,

These curves give the total rate of observed cosmic supernova explosions out to redshift $z$ for an idealized observer monitoring the entire sky out to unlimited depth and without any dust obscuration anywhere along the line of sight.

All of these idealizations will fail, some of them drastically, for real observational programs. Nevertheless, one cannot help but be tantalized by the enormous explosion frequencies indicated in Figure 1(b). With our benchmark CSNR, out to redshift $z=1$, something like $\sim 1$ supernova explodes per second somewhere in the sky. Out to redshift $z=2$, this rate increases to $\sim 6$ events/sec. Clearly, even with a small detection efficiency, synoptic surveys are poised to discover core-collapse supernovae in numbers far exceeding all supernovae in recorded history to date.

For numerical results in Figure 1 and throughout this paper, we adopt a flat cosmology with $\Omega_{\rm m}=0.3$ and $\Omega_{\Lambda}=0.7$. For the Hubble constant we adopt the value $H_{0}=71\ \rm km\,s^{-1}\,Mpc^{-1}$, i.e., $h=0.71$ where $H_{0}=100\ h\ \rm km\,s^{-1}\,Mpc^{-1}$. These values are consistent with recent determinations using WMAP and large-scale structure (Spergel et al., 2007).

The enormous inventory of cosmic supernovae is not, unfortunately, fully observable even for arbitrarily deep surveys. In a realistic environment there are several factors which will hide the supernovae from us; dust extinction is one of the most important, and probably the most uncertain. Core-collapse supernovae mostly explode within regions of vigorous star formation which are thus likely to be dusty environments. Consequently, we expect that some core-collapse supernovae will be obscured to the point where they are not detected in synoptic surveys. The fraction of supernovae lost to dust obscuration, and particularly the possible redshift dependence of this extinction, represents a crucial systematic error which must be addressed before one can use survey data to infer information about supernova populations and their cosmic rates.

For the purposes of our present estimates of survey supernova yields, we follow the approach of Mannucci et al. (2007). These authors characterize losses due to dust extinction and/or reddening in the host galaxies via a fraction $\alpha_{\rm dust}(z)$ of undetected events at each redshift. This fraction could in principle differ for the various core-collapse types; for the present treatment we will assume it is the same for all such events. As core-collapse statistics become available from surveys, this issue can and should be revisited; more on this below. and in §5. The resulting fraction of detected supernovae is thus the complement $f_{\rm dust}(z)=1-\alpha_{\rm dust}(z)$, which measures the reduced supernova detection efficiency in the presence of dust. Expressed as an effective extinction $A$ for the supernova population at $z$, we have $A_{\rm eff}(z)=-1.086\ln f_{\rm dust}$.

Mannucci et al. (2007) estimate the fraction of missing supernovae by comparing the observed detections in the optical with those in radio and near-IR. They conclude that dust evolution is very strong; this becomes a dominant limitation to the discovery of core-collapse events at high redshift. In the local universe, Mannucci et al. (2007) find that the vast majority of the events occurring in massive starbursts (luminous infrared galaxies) are missed. Because these galaxies harbor only a small fraction of the local supernova population, the overall optically missing fraction at $z=0$ is estimated to be rather modest: $\alpha_{\rm dust}=5-10\%$ . If, however, high-redshift star formation occurs in starburst environments (i.e., luminous and ultra-luminous galaxies, which are highly extincted; see e.g. Smail et al., 1997; Hughes et al., 1998; Pérez-González et al., 2003; Le Floc’h et al., 2005; Choi et al., 2006) then the fraction of missing events rises sharply with redshift. Multiwavelength observations of light from pre-supernova massive stars also supports the idea of increasing dust obscuration at high redshift. Adelberger & Steidel (2000) find that ultraviolet light from massive stars in $z\sim 3$ galaxies is mostly reprocessed by dust into thermal submillimeter emission, so that the observable galaxy luminosities have $L_{\rm sub-mm}/L_{\rm UV}\sim 1-100$.

Mannucci et al. (2007) estimate the portion of supernovae which will be “catastrophic losses” to severe extinction, and propose that the missing fraction can be described by a linear relation $\alpha_{\rm dust}(z)=0.05+0.28z$ for the core-collapse supernovae for redshift z$<$2. Thus, the fraction of the supernovae which remain optically detectable is $f_{\rm dust}(z)=1-\alpha_{\rm dust}(z)=0.95-0.28z$ for $z<2$. At higher redshift, Chen et al. (2007) and Gnedin et al. (2008) argue that $f_{\rm dust}$ is small; they find limits consistent with $f_{\rm dust}=0.02$ for these redshifts.

We will smoothly match these two estimates, and adopt a fraction of the supernovae which can be detected after dust extinction of

For these values of $f_{\rm dust}$, the effective extinction varies from $A_{\rm eff}=0.056^{\rm mag}$ at $z=0$ to $A_{\rm eff}=4.25^{\rm mag}$ at $z\geq 3.3$. In practice, we will find that cosmological dimming of supernovae beyond $z\sim 1$ is itself so large that surveys up to and including LSST will see relatively few events, so that the details of the adopted dust model in this regime will not affect our conclusions.

The strong redshift evolution of dust obscuration in the empirical Mannucci et al. (2007) model deserves comment. From a physical point of view, the rise in dust losses $\alpha(z)$ towards high redshift implies that at earlier times, the birth environments of supernovae are significantly more enshrouded than those now. This interesting result itself deserves a deeper elucidation, one which will likely be easier to formulate and test in the presence of survey supernova data. From more practical point of view, our adoption of a model wherein dust losses grow rapidly with $z$ should yield conservative (or at least not optimistic) predictions for the supernova harvest at large redshifts. That is, if it turns out that host galaxy effects do not change rapidly with cosmic time so that the efficiency of supernova detection remains close to the high local value, then our rate predictions at $z\sim 1$ would be boosted by a factor of $\sim 1.5$.

Note also that $f_{\rm dust}$ as Mannucci et al. (2007) and we have defined it characterizes the observable portion of the ensemble of supernovae at a particular redshift. Implicitly, individual supernovae are treated as either detectable or not, i.e., dust effects are considered negligible or total; our calculation treats total, catastrophic losses of supernovae using this $f_{\rm dust}$ formalism. We separately include the effect of partial extinction due to dust, where the apparent magnitude of supernova is reduced but still visible, as discussed in the next section. Of course in reality, all supernovae will experience some level of extinction in their host galaxies, with the distribution of host-galaxy extinctions changing with redshift. A more detailed study of dust effects on supernovae (and uses of supernovae to quantify and calibrate these effects) would be of interest for further investigation; see discussion in §5.

Surveys will discover supernovae monitor lightcurves in one or more passbands Here we will adopt the SDSS $ugriz$ photometric system, which uses AB magnitudes (Fukugita et al., 1996).

The light curve of any supernova will suffer redshifting and time dilation effects. For passband $x$ we put

with $d_{L}$ the luminosity distance and $\mu(z)$ is the usual distance modulus with $d_{0}=10$ pc. The dust extinction $A$ is included via the factor $f_{\rm dust}$ (eq. 5). The $K$-correction accounts for redshifting of the supernova spectrum, and is discussed in Appendix C.

As noted above, at each redshift the effect of dust will be to obscure some fraction of supernovae. The remaining unobscured events will have apparent $x$-filter magnitudes of $m_{x}=M_{x}+\mu(z)+K_{x}(z)$. The expected $m_{x}$ distribution thus reflects the underlying distribution of absolute magnitudes $M_{x}$. Since the Richardson et al. (2002) supernova luminosity function we use is in the $B$-band, we need to find the corresponding $B$-band magnitude in order to find the right corresponding number of supernovae; this transformation to $m_{B}$ is straightforward and is given by $m_{x}=m_{B}+\eta_{xB}$, where

is a color index which translates between the $x$ and $B$ magnitudes in the rest frame, and zeropoint correction is the correction for different zeropoint of the SDSS magnitude system and the Johnson magnitude system. For the spectral shapes $F(\lambda)$ we use the prescriptions of Dahlén & Fransson (1999) as described in Appendix C.

The absolute $x$-band magnitude distribution of unobscured supernovae at redshift $z$ is $\phi_{\rm snlf,x}[M_{x}-\eta_{xB}]$, where $\phi_{\rm snlf,x}$ is the luminosity function in $B$-band as tabulated by Richardson et al. (2002). Therefore the distribution of a certain type of supernova apparent magnitudes $m_{x}$ in $x$-filter is $\phi_{\rm snlf,x}[m_{x}-\mu(z)-K_{x}(z)-\eta_{xB}]$, Thus the fraction of all (unobscured) supernovae at $z$ which fall within the survey $x$-band magnitude limit $m_{\rm lim}^{\rm sn}$ is a sum over the luminosity functions for all core-collapse types:

which is the cumulative fraction of supernovae whose absolute magnitude is brighter than

To develop some intuition, suppose the supernova peak brightnesses lie in a range $M_{\rm peak}\in(M_{\rm bright},M_{\rm dim})$, and ignore for now the effects of dust. Then for low redshifts such that the absolute magnitude limit $M_{\rm lim}$ from eq. (9) is fainter than $M_{\rm dim}$, we can expect to see all supernovae, and $f_{\rm maglim}=1$. For these redshifts, we can study the entire supernova luminosity function and test whether it varies with redshift. On the opposite extreme, for high redshifts such that $M_{\rm lim}$ is dimmer than $M_{\rm bright}$ we can see no supernovae, so $f_{\rm maglim}=0$; this then defines the survey redshift cutoff (for fixed $m_{\rm lim}^{\rm sn}$). Finally, for intermediate $z$ such that $m_{\rm lim}^{\rm sn}-M_{\rm dim}<\mu(z)+K_{x}(z)+\eta_{xB}<m_{\rm lim}^{\rm sn}-M_{\rm bright}$, we have $0<f_{\rm maglim}<1$; over these redshifts the survey samples the bright end of the supernova luminosity function.

Both magnitude limit and dust extinction reduce the expected supernova detection, and do so independently of each other. Consequently, we can find the net supernova detection probability by simply taking the product of the individual factors:

Figure 2 shows the resulting detectable fraction of supernovae. The left panel shows the shape of $f_{\rm maglim}$ for the $g$ and $r$ bands. At redshifts close to zero, $f_{\rm maglim}\approx 1$ which means that almost all supernovae are detected in the local universe. And it approaching to zero at high redshift, which reflects the fact that no supernovae can be detected at high redshift because of the survey deepness. Note that $g$ and $r$ bands are competitive for $m_{\rm lim}^{\rm sn}\leq 24$, but for higher $m_{\rm lim}^{\rm sn}$, $f_{\rm maglim}$ in $g$-band drops a lot faster than those in $r$-band especially around z $\sim$ 0.4, which is cause by the effect of $K$-correction. The figure also shows that for higher $m_{\rm lim}^{\rm sn}$, $f_{\rm maglim}$ decays less rapidly. The right panel shows $f_{\rm detect}$ for different $m_{\rm lim}^{\rm sn}$, using our adopted dust model (eq. 5). We see $f_{\rm detect}$ shows the same trend as $f_{\rm maglim}$ except the detectable fraction is reduced due to dust and we can no longer observe all supernovae even in the local universe. It is also clear to see that going to fainter $m_{\rm lim}^{\rm sn}$ significantly boosts the detectable fraction at high redshift. For $m_{\rm lim}^{\rm sn}=23^{\rm mag}$, $f_{\rm detectable}$ is almost zero at redshift $z\sim 1$ for both $g$ and $r$ bands. But going to $m_{\rm lim}^{\rm sn}=26^{\rm mag}$, $\sim 55\%$ of the supernovae at redshift $z\sim 1$ remain visible both the $g$ and $r$ bands.

This means that deeper surveys (and/or scanning modes in which smaller areas are scanned more deeply) will probe supernovae out to much higher redshifts. Deep survey modes will also probe a much wider regime of the supernova luminosity function and light curves over a broad range of cosmic epochs, thus testing for redshift evolution in supernova properties. The clear lesson is that the scan $m_{\rm lim}^{\rm sn}$ is critical in determining the quality and reach of the supernova science. In particular, we urge that scans strategies include modes which push $>1^{\rm mag}$ deeper than the all-sky depth.

For a given survey with a fixed scanning sky coverage $\Delta\Omega_{\rm scan}$, we can determine the total number of supernovae expected in each redshift bin. We can also forecast the accuracy of the resulting survey determination of the CSNR. Namely, we can turn our sky coverage–monitoring time result (Figure 6) into a specific prediction for the needed time to determine the CSNR to a given precision. In practice, this amounts to a determination of the redshift range over which different surveys can measure the CSNR. Our detailed predictions appear in Appendix B; here we summarize the results.

Several main lessons emerge from considerations of specific surveys. When Pan-STARRS and LSST are online, these surveys will collect a core-collapse supernova harvest far larger than the current set of events ever reported. This alone will make synoptic surveys a transformational point in the study of supernovae.

Moreover, synoptic surveys will detect core-collapse events over a wide redshift ranges. Table 2 summarizes the supernova redshift ranges correspond to the most likely $m_{\rm lim}^{\rm sn}$ of the surveys. The total supernova harvest depends sensitively on the survey depth, and in Appendix B the sensitivity to $m_{\rm lim}^{\rm sn}$ is shown. To determine the redshift ranges shown in Table 2, we set an (arbitrary) lower limit on the number of total supernova counts at $N_{\rm min}=10$. We choose a lower redshift limit $z_{\rm min}$ such the cumulative survey supernova count in one year is $N_{\rm survey}(<z_{\rm min})=N_{\rm min}$. Similarly, the upper limit $z_{\rm max}$ is set by $N(>z_{\rm max})=N_{\rm min}$ is the number of supernovae detected within redshift $z=z_{min}$ within a year.

As seen in Tables 2 and 3, the future surveys will find abundant supernovae over a wide redshift range. At low redshifts, the surveys will detect nearly all of the supernovae within the nearby cosmic volume accessible in their sky coverage. So surveys with a large $\Delta\Omega_{\rm scan}$, such as LSST and Pan-STARRS, have $z_{\rm min}$ which does not depends on $m_{\rm lim}^{\rm sn}$. For DES, $\Delta\Omega_{\rm scan}$ is not as large, so that the number of supernovae brighter than $m_{\rm lim}^{\rm sn}=21^{\rm mag}$ does not accumulate to $N(<z_{\rm min})$=10 until $z_{\rm min}$=0.081. But for depths fainter than $m_{\rm lim}^{\rm sn}=24^{\rm mag}$, the survey does become volume-limited and the supernova counts accumulate to 10 at the same redshift. The upper limit of the redshift $z_{\rm max}$ depends not only on sky coverage but also survey depth. For planned survey depths, DES will gather core-collapse supernovae to about $z\simeq 1.20$; LSST will extend to $z\sim 0.89$, and could go further in modes with smaller sky coverage but deeper exposure.

The large supernova counts and wide redshift ranges together mean that surveys will, by direct counting, map out the CSNR to high precision out to high redshifts. Future surveys should easily achieve 10$\%$ statistical precision for the CSNR for redshifts around which the survey’s counts peak. We see that, with $m_{\rm lim}^{\rm sn}=23^{\rm mag}$, LSST will reach out to $z\sim 0.89$, presuming that the relative fraction of the brightest, farthest-reaching events (of Type IIn and Ic) do not evolve with redshift. If so, then by direct counting future survey should witness the sharp CSNR rise. With deeper exposures and corresponding increases in redshift reach, surveys could begin to test for the behavior of the CSNR above $z=1$, a regime that is currently poorly understood.

Both the survey yields of supernova discoveries, as well as their redshift ranges, are strong functions of survey depth. As shown in Table 3 of Appendix B, each magnitude increase in survey depth yields a large enhancement (a factor $\sim 3$) in total supernova counts. This in turn leads to large enhancements in redshift range, and thus in the range over which the CSNR is measured. As shown in Appendix B, increased monitoring time needed to achieve higher $m_{\rm lim}^{\rm sn}$ will come at some cost, though this will be partially offset by the higher supernova yield in a deeper exposure. Finally, for the large population of low-redshift supernovae, deeper surveys will lead to better lightcurve determination, allow for a more accurate photometry over a larger brightness range and thus longer timescales.

As noted in §3.3.1, our fiducial results are for supernova peak magnitudes whose luminosity functions (each of which is one or two gaussians for each core-collapse type) are nonzero only within $|M-M_{\rm mean}|<2.5\sigma$ away from the mean. This arbitrary cutoff is meant as a compromise which shows the effect of nonzero width of the luminosity functions, without extrapolating too far into the tails in which there is as yet no data. To give a feel for the sensitivity of our results to the assumed luminosity function width we repeated our analysis for luminosity functions with larger and narrower $|M-M_{\rm mean}|$ ranges, (but with fixed observed intrinsic $\sigma$). We find that the total supernova counts vary less than 0.88% when $|M-M_{\rm mean}|$ ranges from $2\sigma$ to $3\sigma$; this insensitivity reflects the fact that the bulk of supernova counts are from events near the means of the distribution. One the other hand, we found that the maximum observed supernova redshift (and thus the depth to which one can probe the CSNR) is very sensitive to the choice of $|M-M_{\rm mean}|$. For example, the LSST maximum supernova redshift in 1 year is $z_{\rm sn,max}=0.89$ for our fiducial choice of $|M-M_{\rm mean}|=2.5\sigma$, as seen in Table 2. On the other hand for $|M-M_{\rm mean}|=2\sigma$ and $3\sigma$, we find $z_{\rm sn,max}=0.73$ and 1.06, respectively. Here rare, intrinsically bright events determine the redshift reach, and the deeper the luminosity function reaches into the bright-end tail, the larger the resulting $z_{\rm sn,max}$. Thus we would expect the intrinsically brightest events, of Type Ibc and Type IIn, to give the greatest redshift reach. Indeed, Cooke (2008) has recently illustrated how Type IIn events can be mapped out to $z>2$ by ground-based 8 meter-class telescopes.

Of course, all of our forecasts assume that the luminosity functions of each supernova type, and the relative frequencies among the supernova types, all remain unchanged at earlier epochs. However, it is entirely plausible and even likely that these properties could evolve, e.g., with metallicity and/or environment. These effects are likely to be crucial in determining the true redshift reach of future sky surveys, and thus predictions such as ours will improve only as real supernova data becomes available with good statistics at ever-increasing redshifts, and one can directly constrain and/or measure evolutionary effects. Moreover, the relatively small sample sizes available to Richardson et al. (2002) could well lead to underestimates of the true range of luminosities of each type. For example, (Gezari et al., 2008) very recently report of an unusually bright Type II-L event, SN 2008es, with peak magnitude $M_{B}\simeq-22.2$, far outside of the absolute magnitude range we have adopted for this subtype.

Indeed, the enormous statistics gathered by future surveys will allow for cross-checks and empirical determination of other evolutionary and systematic effects. A major such effect is dust obscuration, to which we now turn.

As we have indicated in the previous section, synoptic surveys will determine cosmic core-collapse supernova rate with high precision out to high redshifts. Moreover, with the large number of supernova counts, and with light curves and host environments known, the total cosmic core-collapse redshift history can be subdivided according to environment and/or supernova type. For example, with photometric data alone one can determine to high accuracy correlations between supernova rate and host galaxy luminosity and Hubble type. One can compare supernova rates in field galaxies versus those in galaxy groups and clusters. Using galaxy morphology one can investigate correlations between supernovae and galaxy mergers. With the addition of spectroscopic information one can also search for correlations with host galaxy metallicity.

The CSNR is also tightly related to the cosmic star-formation rate. Therefore with the high precision CSNR, and assuming an unchanging initial mass function, one can make a similarly precise measure of the cosmic star-formation rate. On the other hand, one can test for environmental and/or redshift variations in the initial mass function, by comparing the supernova rates based on direct survey counts with the star-formation rates determined via UV and other proxies.

In addition to core-collapse explosions, synoptic surveys will of course by design also discover a similarly huge number of Type Ia supernovae. Thus the Type Ia supernova rates can be compared to those for core collapse events. As has been widely noted (e.g., Gal-Yam & Maoz, 2004; Watanabe et al., 1999; Oda & Totani, 2005; Scannapieco & Bildsten, 2005, and references therein) this will yield information about the distribution of time delays between the core-collapse and thermonuclear events. Moreover, one can explore differences in the environmental correlations for the two supernova types (and subtypes).

Type Ia supernovae have become the premier tool for distance determinations at cosmological scales, thanks to their regular light curves, high peak brightnesses, and relatively less dusty environments. Nevertheless, given the importance of the cosmic distance scale, and the ongoing need for systematic crosschecks and calibration, it is worthwhile to consider other methods. Core-collapse events offer just such a method, via the expanding photosphere/expanding atmosphere method.

This method was originally conceived by Baade (1926) and Wesselink (1946) for study of Cephieds; Kirshner & Kwan (1974) applied the Baade-Wesselink method to supernovae. The key to the technique is to exploit the simple kinematics of a newborn supernova remnant: the freely-expanding photosphere grows in size as $R=vt$. Thus, for purely blackbody emission, the luminosity grows with size (i.e., time) as $L=4\pi R^{2}\sigma T^{4}$. With good sampling to measurements time $t$ since explosion, and spectroscopic inference of $v$ and $T$, one can recover the luminosity. In principle, therefore, one can use the explosion as a standard candle.

In practice, this method has been slow to mature. Until recently, the agreement with independent distance measures has been only good to within a factor $\sim 2$ (e.g., Vinko & Takats, 2007). The complex (out of local thermodynamic equilibrium) spectra of supernovae has proved difficult to adequately model. However, recently important advances have been made in the radiation transfer modeling of young supernova remnants and its fitting to spectra of local supernovae (Baron et al., 2004; Dessart & Hillier, 2005, 2008). Because of this, the expanding photosphere (or more properly, expanding atmosphere) method now appears to be reaching consistency with other distance measures; this method now shows agreement approaching the $\sim 10\%$ level. Similar pecision now seems possiblue using a separate, empirical method (Hamuy & Pinto, 2002) which exploits the observed correlation between luminosity and expansion velocity of Type II-P events. This opens up core-collapse supernovae as alternative distance indicators. Indeed, several group (Nugent et al., 2006; Poznanski et al., 2007; Olivares, 2008) have already applied this method to various collections of Type II-P observations, yielding tight Hubble diagrams out to $z\sim 0.3$.

To use this method as it is currently envisioned, follow-up spectroscopy is mandatory for each event (see §6.5), with photometric surveys identifying the candidates. Obviously, for the largest surveys, in practice only a tiny fraction of core-collapse events could be studied in a (separate) spectroscopic campaign, particularly given that the most common core-collapse types are intrinsically dimmer than Type Ia events and thus require longer exposures to obtain spectra. Followup requirements thus are the limiting factor for the use of core-collapse events as distance indicators.

The situation for Type Ia supernovae is better-studied and also potentially more hopeful. Recent work (Poznanski et al., 2007; Kim & Miquel, 2007; Kunz et al., 2006; Blondin & Tonry, 2007; Wang, 2007; Kuznetsova et al., 2008; Sako et al., 2008) suggests that photometric redshifts of Type Ia events near maximum light could be obtained with sufficient precision (give a low-redshift training set) to provide useful dark energy constraints without spectroscopy. Whether photometric-based distances can be derived for core-collapse events with sufficient accuracy remains to be seen. It nevertheless seems to us a worthy object of further study. In this context it is worth noting that DES plans to do followup spectroscopy on $\sim 25\%$ of Type Ia events (The Dark Energy Survey Collaboration, 2005). We suggest that at least some modest fraction of this follow-up time be dedicated to core-collapse monitoring.

The physics, astrophysics, and cosmology of cosmic core-collapse supernovae is a fertile topic; with our detectability study in hand, a wide variety of problems present themselves. Here we sketch these out; we intend to return to these in future publications.

The huge harvest of core-collapse events will open new windows onto other aspects of supernova physics. For example, the physics of black hole formation in supernovae, and the neutron-star/black hole divide, remain important open questions. Balberg & Shapiro (2001) have estimated the rates of events with observable signatures of black hole formation; LSST should provide a fertile testing ground for these predictions.

The elaboration of the cosmic history and specific sites of high-redshift supernovae will also offer unique new information about supernova “ecology” – i.e., feedback and cycling of energy, mass, and metals into the surrounding environment. For example, large surveys will offer the opportunity to study supernova rates as a function of host galaxy and galaxy clustering, shedding new light onto large-scale star formation and its connection with galaxy evolution. Moreover, DES and other surveys will discover an enormous number of rich galaxy clusters; the occurrence of both Type Ia and core-collapse events in clusters will offer important new insight into the origin of the very high metallicity of intracluster gas (Maoz & Gal-Yam, 2004; Maoz et al., 2005).

Core-collapse supernovae also are the sources, directly or indirectly, of high-energy radiation of various kinds. For example, supernovae act as accelerators of cosmic rays. These in turn interact with interstellar matter to produce high-energy $\gamma$-rays. Pavlidou & Fields (2002) used then-available estimates of the cosmic star-formation rate to show that this $\gamma$-ray signal has a characteristic feature, and makes a significant part of the extragalactic $\gamma$-ray background around $\sim 1$ GeV. With the successful launch of the high-energy $\gamma$-ray observatory GLAST, this component of the $\gamma$-ray background may for the first time be clearly identified. Regardlessly, a sharper knowledge of the cosmic supernova rate (and thus cosmic-ray injection rate) will work in concert with GLAST observations to probe the history of cosmic rays throughout the universe.

The characteristic of Type Ia supernovae are in general very similar to the core-collapse supernovae. Hence the observational requirements for their identification in synoptic surveys are also very similar. The rest-frame, full-width at half-maximum timescale for Type Ia supernovae is $\sim 20$ days. Therefore surveys will need a scan cadence of a few days in order to get a well-sampled light curve. For example, the Pan-STARRS strategy for Type Ia discovery is to sample the light curve every 4 days (Tonry et al., 2003; Tonry, 2003). As we have discussed, this sampling frequency is also suitable for the core-collapse supernovae which the time scale of the light curve also last a few weeks.

Survey supernovae become scientifically useful only when one can establish, at the very least, their redshift and whether they are core collapse or Type Ia. Since followup spectroscopy will not be possible for the large numbers of future events, photometric redshifts will be needed. For events in which a host galaxy is clearly visible, one can use photometric redshifts of the hosts. Here one is helped by the ability of surveys to stack all of the many (non-supernova) exposures to obtain a much deeper image than those with the supernovae. Once the host redshift is know, the supernova type must be determined. Baysean analysis techniques and software (Dahlén & Goobar, 2002; Poznanski et al., 2007) have been developed to distinguish both Type Ia and core-collapse events. These authors find that type discrimination depends crucially on the accuracy with which the redshift is known. For spectroscopic redshifts, their methods is extremely accurate, and for photometric redshifts the method is still quite good, though in this case misclassifications can reach $15-25\%$ depending on $\sigma_{{\rm photo}-z}$.

Followup spectroscopy on a subset of events will be essential to calibrate the accuracy of the photometric typing (and host redshifts). In particular, spectroscopy will be invaluable in identifying and quantifying catastrophic failures in the typing algorithms; on the basis of these it may be possible to refine the routines. As noted in the previous section, followup is also required for any events one hopes to use in distance determinations.

For events without clear host galaxies and without followup, one must resort to photometric redshifts and typing based on the supernova light curve itself, in whatever bands are available. It is not clear that this can be done with any reliability on an event-by-event basis As Poznanski et al. (2007) emphasize, one might make statistical statements about the types and redshifts of the entire class of “hostless” events. Here spectroscopic followup will be essential, not only for determining the supernova redshift but also the nature of the underlying host.