## 3. ResultsUsing the model above we can now estimate the observed number of SNe per square arcmin down to some limiting magnitude, including corrections from extinction and the shift of the spectrum with redshift. As an illustration, we show in Fig. 2 the peak magnitudes (i.e. at
10-15 days after explosion) for Types
IIP, IIL, IIn and Ia as a function of redshift. We also show the
magnitude of a Type IIP at the plateau phase (age
40 days). The magnitude for Type
Ib/c's at peak follows the Type Ia's, except for an off-set of
m
1.5 mag towards fainter magnitudes. The magnitude of SN1987A-like SNe
at the peak resembles the Type IIP at the plateau, but with an off-set
m
2.0 towards fainter magnitudes. Besides the standard flat
= 1 cosmology (hereafter SCDM), we
also show the apparent magnitudes for an open cosmology (OCDM) with
= 0.3 and
= 0, and a flat,
-dominated cosmology
(CDM) w ith
= 0.3 and
= 0.7. Note that the curves have a
dispersion in magnitude according to values given in Table 1. The
dispersion is largest for the Type IIP's; the peak magnitude of these
may vary by more than one magnitude. Fig. 2 shows that the Type Ia's
and the Type IIP's at the plateau drop out of the I and K´-band
at 1 and
4.5, respectively, as a result of
their UV-cutoffs. In contrast, the UV-bright Type IIL's and IIn's stay
relatively bright in the I band even at high
## 3.1. Core collapse ratesThe solid lines in Fig. 3 show the number of predicted core collapse SNe per square arcmin in the R, I, K´ and M´ filters for different limiting AB-magnitudes. Because of the drop in the UV flux, bands bluer than R are of less interest for high redshifts.
According to the specifications, NGST should have a detection limit
of 1 nJy in the J and K´ bands
and 3 nJy in the M´ band for a
10 In Fig. 4 we show the redshift distribution in all bands for
m
For SNe with redshifts 5 we
estimate 1 SN per NGST field in the
M´ filter. The actual numbers of the high- The R and I bands sample light with rest wavelengths short-ward of the peak in the blackbody curves at lower redshifts than the J, K´ and M´ bands do. Besides the drop in luminosity due to the spectral shape (an effect especially pronounced for SNe with strong UV blanketing), these wavelengths are affected by larger extinction. The large K-correction decreases the rates in the R and I bands, and few SNe with 1 are detected in I and R, even for limiting magnitudes 29. Increases in these bands are instead caused by sampling SNe with fainter absolute magnitudes at 1. In Fig. 5 we show the redshift distribution of core collapse and
Type Ia SNe down to I
Table 2 gives some examples of our estimates for the number of
SNe for NGST, VLT/FORS and HST/WFPC2, all for an exposure of
10
So far we have discussed the number of SNe that are simultaneously
observable during one search. To actually detect the SNe, additional
observations are obviously required. Preferentially, a series of
observations of each field should be undertaken in order to obtain a
good sampling of the light curves. This also leads to the detection of
new SNe in the additional frames. The number of new SNe depends on the
total length of the search, and the spacing in time between each
observation. As an illustration, in an idealized situation where a
field is covered continuously during one year, the detected number of
SNe per square degree, with limit I With NGST, using limits as above, we estimate 45 SNe in each frame. The total number of different SNe in a field that is covered continuously during one year is 68. This means that in addition to the 45 SNe observed in the first field, only 23 new SNe have exploded during the year. With three observations and 180 days between the observations, 63 different SNe are detected. Compared to earlier estimates, our use of complete light curves during the whole evolution, as well as distribution of the SNe over time, results in a larger number of SNe, as well as a realistic distribution over redshift for a given magnitude. For example, with the same SFR and extinction, Madau et al. (1998a) predict 7 SNe per NGST field per year in the range 2 4. Our calculations result in 22. The difference is due to the fact that we use light curves covering the whole evolution, which allow us to include SNe at all epochs, instead of only those at peak, which is the case in Madau et al. ## 3.1.1. Shock breakout supernovaeChugai et al. (1999) have noticed that the short peak in the light curve connected with the shock breakout may give rise to a transient event with a duration of a few hours. The possibility to observe this was pointed out already by Klein et al. (1979), although they concentrated mainly on the soft X-ray range. Based on a radiation-hydrodynamics code, similar to that of Eastman et al. (1994), Chugai et al. have calculated monochromatic light curves for a Type IIP SN (or rather a scaled SN 1987A model) and a Type IIb (specifically SN1993J). With a short time interval between observations these SNe will be easily distinguishable from the Type Ia and Ib/c SNe, which have a rise time of t 20 days (at 1), and therefore only show a modest change in luminosity. A major problem in comparing their results to ours is that it is not discussed how they obtain their adopted intrinsic SNR's, although they approximately agree with those used in this paper, as well as Madau (1998). They also neglect dust extinction in their calculations. Using this model, Chugai et al. find that two deep exposures,
separated by 10 days, result in 1.3
Type II SNe in the 6.86.8 square
arcmin field of the VLT/FORS camera, using limit I Using our hierarchical model, which gives approximately the same
SNR up to 2, and the same
observational set-up, as Chugai et al., our calculations result in
0.27 SNe. The reason for our lower
estimate is that Chugai et al. assume all Type II SNe to have the same
steep initial rise as the Type IIP and IIb. In our model we do not
include any shock breakout for Types IIL and IIn, since the early time
behavior of these SN types is not well known. ## 3.2. Type Ia SNeFig. 3 shows that in the R and I bands the number of core collapse
SNe is comparable or larger than the number of Type Ia SNe for
magnitudes fainter than . The exact
crossing point depends on the life time of the SN Ia progenitors, as
well as the Type Ia normalization at low To illustrate the dependence on the progenitor life time, Fig. 3 gives the number of Type Ia SNe for = 0.3, 1 and 3 Gyr in the different filters. Fig. 3 shows that a change in the progenitor life time, , introduces a non-negligible variation in the predicted number of observable SNe. For example, with an NGST detection limit, = 31.4, we predict 8 SNe for the two low values of , and 5 for = 3 Gyr. Observations in the I band with limits and field as for the VLT/FORS (see Table 2) results in 0.8, 1.1, and 1.8 SNe for increasing values of . Counts may therefore seem like a useful probe to distinguish between different progenitor models (Ruiz-Lapuente & Canal 1998). However, the uncertainty in the modeling, especially in the normalization of the Type Ia rates to the local value, makes the counts highly model dependent. In next section we show that this is further hampered by the additional dispersion introduced when considering alternative star formation and extinction models. If both SN type and redshift information are available for the
observed SNe, it may be possible to use the redshift distribution of
the SNe to distinguish between progenitor scenarios. Figs. 1 and 5
show that the peak in the SNR moves to lower The only observational estimate of a Type Ia SNR at moderate
redshift is by Pain et al. (1996). From a careful analysis, using
realistic light curves and spectra, they find a Type Ia rate at
0.4 of
SNe yr ## 3.2.1. Number of pre-maximum Type Ia SNeThe number of simultaneously detectable SNe discussed above is a
result of events over the whole light curve. Using Type Ia's as
standard candles for determination of
requires observations at the peak
of the light curve, i.e that a first detection is made at the rising
part of the light curve. We estimate the number of such SNe by
assuming that the comoving rise time is 15 days. Fig. 6 shows the
number of Type Ia SNe down to different limiting magnitudes before the
peak of the light curve in the I filter for the three values of
. Also shown is the number of such
SNe with 1 (the lower sets of
curves). An I band survey covering a one square degree field with
limiting magnitude I
© European Southern Observatory (ESO) 1999 Online publication: October 4, 1999 |