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Astron. Astrophys. 359, 876-886 (2000)

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6. Discussion

6.1. Peak bolometric flux

The bolometric light curves presented in Fig. 5 were constructed from UBVRI light curves where available (SN 1989B, SN 1991T and SN 1994D). All others are based on BVRI light curves with a correction for the missing U band applied as described in Sect. 5.1.1. The luminosities depend directly on the assumed distance moduli to the individual supernovae. We have used the current best estimates from the literature (Table 1), but some of the distance estimates may change when more accurate distances become available. We also corrected the magnitudes for extinction, which, for some objects, can be fairly substantial (SN 1989B, SN 1991T, and SN 1994ae). From Table 2 it is clear that our sample displays a rather large range in luminosities, both in B and the bolometric maximum. SN 1991bg is 11 times less luminous in B than the brightest SN Ia in the sample, SN 1991T. For the bolometric maximum we find a factor of 12.3. Excluding this peculiar object we still find a range in luminosity of a factor 4.7 in the filter passband and a factor of 3.3 in the bolometric peak flux.


Table 2. Absolute B magnitudes and bolometric luminosities. The bolometric luminosities have been corrected for the missing U band where appropriate. The nickel mass is derived from the luminosity for a rise time of 17 days to the bolometric peak.

6.2. Light curve shape

The shapes of the bolometric light curves are unaffected by the distance modulus and are only marginally influenced by reddening (see Sect. 5). The most striking feature in these light curves is the inflection near 25 days past maximum (Suntzeff 1996). It is observed in all SNe Ia, with the notable exception of SN 1991bg (Fig. 5). The strength of this shoulder varies from a rather weak flattening in the bolometric light curve of SN 1991T to a very strong bump in SN 1994D. This bump arises from the strong secondary maximum in the R and I light curves. The secondary maximum is also observed in the near-IR JHK light curves (Elias et al. 1985, Meikle 2000, Meikle & Hernandez 2000) which have not been used for the calculation of bolometric light curves presented here.

Inspection of Fig. 5 clearly shows the brighter SNe having wider primary peaks than the fainter SNe.

In order to quantify this statement we have measured the width of the bolometric light curve at half the peak luminosity (with [FORMULA] denoting the time it takes to rise and [FORMULA] to decline, see Table 2). There are sufficient pre-maximum observations available for six supernovae (SN 1991T, SN 1992A, SN 1992bc, SN 1992bo, SN 1994D, and SN 1994ae) from which the full width of the peaks can be reliably determined. In three cases the first observations were obtained well below the half-maximum flux level; in the case of SN 1991T we extrapolated our bolometric light curve by about 1.5 days and for SN 1992A and SN 1992bc by 2.5 days. The bright SN 1991T and SN 1992bc show a peak width of 26 and 23 days, respectively, the intermediate SN 1994ae one of 22 days, while the fainter SN 1994D, SN 1992A, and SN 1992bo remained brighter than half their maximum luminosity for about 18 to 19 days.

The pre-maximum rise [FORMULA] in the bolometric light curve is, in all cases, substantially faster than the decline [FORMULA] by between 20 to 30% or a time difference of between 2 to almost 4 days (Table 2).

The decline to half the supernova's peak luminosity [FORMULA] varies from 9 days to 14 days. A weak correlation between maximum brightness and decline rate can be seen (Fig. 9). The sample of SNe was extended to the one used in Sect. 4. In Fig. 9 only those SNe with sufficient time coverage are shown.

[FIGURE] Fig. 9. Rise to and decline from maximum in bolometric light curves. The time between maximum luminosity and half its value is plotted. The sample of SNe was extended to the one used in Sect. 4, the SNe from Table 1 are shown as filled symbols. Only SNe with sufficient coverage (rise: first observation not later than 3 days after [FORMULA], decline: first observation before [FORMULA](Bol)) have been included.

Significant coverage of the rise to maximum is available for only two supernovae. There are too few SNe to make a definitive statement here about the rise times of SNe Ia in general. Nevertheless, our formal fits to SN 1994D and SN 1994ae give rise times of 16.4 and 18.2 days, respectively, for their bolometric light curves. The formal errors in this parameter, derived with the Monte Carlo algorithm described in Sect. 3.2, is 2 days for SN 1994D and 1 day for SN 1994ae. If the bolometric luminosities are calculated by fitting the bolometric light curve from the individual observations, the derived rise times are slightly different (18 and 19 days, respectively). A previous analysis of SN 1994D derived a rise time for the bolometric light curve of 18 days (Vacca & Leibundgut 1996) in fair agreement with our current analysis.

These rise times are significantly larger than those of most explosion models (Höflich et al. 1996, Pinto & Eastman 2000a). These theoretical calculations typically yield rise times of 15 days.

The secondary bump clearly indicates a change in the emission mechanism of SNe Ia. Its varying strength might be related to the release of photons "stored" in the ejecta (the "old" photons described in Pinto & Eastman 2000b and Eastman 1997). In such a scenario the bump arises from the fact that the ejecta become optically thin during this phase, due to subtle differences in the ejecta structure and ejecta velocity.

The exponential decline of the bolometric light curves between 50 and 80 days past bolometric maximum is remarkably similar for all supernovae. The decline at this phase is still dominated by the [FORMULA] decay and the [FORMULA]ray escape fraction (Milne et al. 1999). We find a decline rate of 2.6[FORMULA]0.2 mag per 100 days. The sample is still very small but SN 1991bg stands out with a decline rate of 3.0 mag/(100 days). The uniformity of the late declines indicates that the differences observed at earlier phases are due to photospheric effects when the optical depth for optical radiation is large and not because of the explosion mechanism. In particular the fraction of energy converted to optical radiation at late phases appears to change in an identical fashion for the majority of the objects, although SN 1991bg proves to be the exception to the rule once again. The change in the column density in the different supernovae must be very similar, despite the different luminosities at these epochs. This indicates that the kinetic energy is somehow coupled to the pre-supernova mass.

The decline rate during the same period in the V filter is identical with 2.6[FORMULA]0.2 mag/(100 days) as is also confirmed by the constant fraction of the V to the bolometric flux (cf. Fig. 6). These decline rates have been shown to correlate very well with measurements derived by others (Vacca & Leibundgut 1997). The comparison with other determinations of the decline rate is difficult as the slope of the decline continues to vary even at late epochs (e.g. Suntzeff 1996, Turatto et al. 1996). This dependence on the epochs observed has to be considered when a comparison is attempted. In most cases the decline was estimated out to phases of 200 days (Turatto et al. 1990), which leads to smaller decline rates than we find here. In the case of SN 1991bg the decline rate was measured at early phases, which led to a significantly steeper decline estimate (Filippenko et al. 1992).

Note that the phase range of bolometric light curves presented in this paper is well before any effects of positron escape could be measured (Milne et al. 1999) or the IR catastrophe takes place (Fransson et al. 1996).

6.3. Nickel mass

Given the peak luminosity it is straight forward to derive the nickel mass which powers the supernova emission. Near maximum light the photon escape equals the instantaneous energy input and is directly related to the total amount of [FORMULA] synthesized in the explosion (Arnett 1982, Arnett et al. 1985, Pinto & Eastman 2000a). We have used our bolometric peak luminosities to derive the nickel masses (Table 2). Since we are not sampling all the emerging energy from the SNe Ia, but are restricted to the optical fluxes, we are underestimating the total luminosity. Suntzeff (1996) estimated that about 10% are not accounted by the optical filters near maximum light. All masses thus have to be increased by a factor 1.1. Another uncertainty is the exact rise time, which is an important parameter in the calculation. We have assumed a rise time of 17 days to the bolometric maximum for all supernovae. It is likely that there are significant differences in the rise times and this would alter the estimates for the Ni mass. A longer rise time would imply a larger nickel mass for a given measured luminosity. Decreasing the rise time to 12 days yields only 70% [FORMULA] of the values given in Table 2. Such a short rise time is excluded for most of the SNe Ia, where observations as early as 14 days have been recorded (SN 1990N: Leibundgut et al. 1991a, Lira et al. 1998, SN 1994D: Vacca & Leibundgut 1996), but could still be feasible for SN 1991bg. For a more realistic range of 16 to 20 days between explosion and bolometric maximum the nickel mass would change by only [FORMULA]10% from the values provided here. Clearly, the dominant uncertainty in the determination of the nickel mass stems from the uncertainties in the distances and the extinction corrections.

For a few of the supernovae, nickel masses have been measured by other methods. SN 1991T has an upper limit for the radioactive nickel produced in the explosion of about 1 [FORMULA] based on the 1.644 µm Fe lines (Spyromilio et al. 1992). This value depends on the exact ionization structure of the supernova one year after explosion and a conservative range of 0.4 to 1 [FORMULA] had been derived. This is fully consistent with our estimate. Bowers et al. (1997) have derived nickel masses for several SNe Ia in a similar way. Their best estimates for SN 1991T, SN 1994ae, and SN 1995D are all about half the value found here, when converted to their distances and extinctions. However, they point out that their values should be increased by a factor of 1.2 to 1.7 to account for ionization states not included in their analysis. With this correction we find a good agreement. Cappellaro et al. (1997) derived masses from the late V light curves. There are four objects in common with our study: SN 1991bg, SN 1991T, SN 1992A, and SN 1994D. Adjusting the determinations to the same distances and re-normalizing to our SN 1991T Ni mass, we find a general agreement, although there are differences at the 0.1 [FORMULA] level.

Nickel masses were also derived from the line profiles of [Fe II] and [Fe III] lines in the optical by Mazzali et al. (1998). These measurements depend critically on the ionization structure in the ejecta and had been normalized to a nickel mass of SN 1991T of 1 [FORMULA]. When we scale their masses to our measurement we find a reasonable agreement.

The nickel masses derived in our analysis are well within the bounds of the current models for SN Ia explosions (Höflich et al. 1996, Woosley & Weaver 1994). There seems to be no real difference in [FORMULA] produced by the various explosion models and hence a distinction by the bolometric light curve alone is not possible.

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Online publication: July 13, 2000