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

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5. Bolometric light curves of SNe Ia

The flux emitted by a SN Ia in the UV, optical, and IR wavelengths, the so-called "uvoir bolometric flux", traces the radiation converted from the radioactive decays of newly synthesized isotopes. As nearly 80% of the bolometric luminosity of a typical SN Ia is emitted in the range from 3000 to 10000 Å (Suntzeff 1996), the integrated flux in the UBVRI passbands provides a reliable measure of the bolometric luminosity and therefore represents a physically meaningful quantity. This luminosity depends directly on the amount of nickel produced in the explosion, the energy deposition, and the [FORMULA]-ray escape, but not on the exact wavelengths of the emitted photons.

We used the fits of the filter light curves in the UBVRI passbands to construct an optical bolometric light curve for the SNe in our sample. All objects with well-sampled (U )BVRI light curves and sufficient coverage from pre-maximum to late decline phases have been included. The objects are listed in Table 1. To calculate the absolute bolometric luminosities, one has to account for reddening and distance moduli; the values we adopted were taken from the literature as listed in Table 1. A galactic extinction law has been employed, as justified by Riess et al. (1996b).

The bolometric light curves of our sample of SNe Ia are shown in Fig. 5. Only the time range with all available filter photometry is plotted. The peak luminosities are clearly different for the objects in the sample, and these differences are larger than the uncertainties in the derivation. The most striking feature, however, is the varying strength of the secondary shoulder, which stems from the R and I light curves (see also Suntzeff 1996).

[FIGURE] Fig. 5. Bolometric luminosities for 9 well observed SNe. Only the time range with the maximum number of filters for each supernova is displayed. The reddening and distance moduli have been taken from the literature as listed in Table 1 and corrections for missing U band are applied as described in Sect. 5.1.1.

The distribution of the epochs of the bolometric peak luminosity relative to the B maximum is shown at the bottom of Fig. 4. The time of bolometric maximum suffers from the additional uncertainty that the contributions from the different wavelength regimes change rapidly before and during the peak phase. Since we are not including any UV flux in our calculations and SNe Ia become optically thin in the UV around this phase, the epoch of the maximum could actually shift to earlier times than what we measure. This might explain the discrepancy with the earlier determination of the bolometric maximum for SN 1990N and SN 1992A by Leibundgut (1996) and Suntzeff (1996), respectively, who included IUE and HST measurements.

5.1. Uncertainties introduced by the data

5.1.1. Missing passbands

Flux outsideUBVRI:

In our analysis we have neglected any flux outside the optical wavelength range. In particular, contributions to the bolometric flux from the ultraviolet (below 3200 Å) and the infrared above 1 µm (JHK ) regimes should be considered in the calculations of the bolometric flux. Using HST and IUE spectrophotometry for SN 1990N and SN 1992A, Suntzeff (1996) estimated the fraction of bolometric luminosity emitted in the UV. He found that the bolometric light curve is dominated by the optical flux; the flux in the UV below the optical window drops well below 10% before maximum. The JHK evolution was assumed to be similar to that presented by Elias et al. (1985); these passbands add at most 10% at early times and no more than about 15% 80 days after maximum. For example, examination of the data of SNe 1980N and 1981D (infrared data from Elias et al. (1981) and optical from Hamuy et al. (1991)) shows that not more than 6% of the total flux is emitted beyond I until 50 days past maximum, when the IR data stop.

Corrections for passbands missing in the optical range: For missing passbands between U and I one can infer corrections derived from those SNe Ia which have observations in all filters. Fig. 6 shows the correction factors obtained from SN 1994D. A cautionary note is appropriate here: SN 1994D displayed some unusual features, in particular a very blue color at maximum.

[FIGURE] Fig. 6. Correction factors for missing passbands. The correction factors are obtained by comparing the flux in the passbands with the total UBVRI -flux.

To estimate the flux corrections we divided the flux in each passband by the bolometric flux. Since the filter transmission curves do not continuously cover the spectrum (i. e., there are gaps between U and B as well as between B and V and overlaps between V and R , and R and I ) the coaddition suffers from the interpolation between these passbands.

An interesting result from Fig. 6 is the nearly constant bolometric correction for the V filter. This filter has been used in the past as a surrogate for bolometric light curves (e.g. Cappellaro et al. 1997). We confirm the validity of this assumption for phases between 30 and 110 days after B maximum where the overall variation is less than 3%.

In order to test our procedure, we calculated bolometric light curves for the three SNe Ia which have the full wavelength coverage after purposely omitting one or more passbands and applying the correction factors we derived from SN 1994D. As Fig. 7 demonstrates, the error is less than 10% at all times even if more than one filter is missing, although the errors vary considerably during the peak and the secondary shoulder phases. The results of this exercise gave us confidence that we could correct the bolometric light curves of the remaining six SNe for the missing U band without incurring large errors.

[FIGURE] Fig. 7. Residuals for substituting individual passband observations of SN 1989B by the corrections derived from SN 1994D. The errors never exceed 10% even when more than one filter is missing.

5.1.2. Effects of systematic differences in photometry sets on bolometric light curves

Filter light curves from different observatories often show systematic differences of a few hundredths of a magnitude. We examined the effect such systematic errors might have on our bolometric light curves by artificially shifting individual filter light curves by 0.1 magnitudes and recomputing the bolometric light curves. In all cases the effect on the bolometric light curve is far less than the uncertainties in the distances and the extinction of the supernovae. Shifting the R or I light curve by 0.1 magnitude we found that the bolometric luminosity changed by 2% at maximum and 5% 25 days later (approximately at second maximum). For typical systematic uncertainties of 0.03 magnitudes in all filters, a maximal error of 2 to 3% is incurred.

We also constructed the bolometric light curve of SN 1994D for the individual data sets available (see references to Table 1). The difference never exceeds 4% out to 70 days after maximum even though the photometry in the individual filters differs up to 0.2 magnitudes in U , 0.1 mag in BRI and 0.05 mag in V .

5.2. Uncertainties introduced by external parameters

While uncertainties in the distance moduli will affect the absolute luminosities in each passband (as well as the bolometric luminosity), the shape of the light curve is unaffected. As all distances used here are scaled to a Hubble constant of [FORMULA], the luminosity differences are affected only by errors in the determination of the relative distance modulus.

Reddening, however, affects both the absolute luminosity and the light curve shape. The influence of extinction changes as a function of phase with the changing color of the supernova. A color excess of E(B-V) [FORMULA] decreases the observed bolometric luminosity at [FORMULA] by 15%, while near the time of the second maximum in the R and I light curves ([FORMULA]) the observed bolometric luminosity is reduced by 12%. A stronger extinction of E(B-V) [FORMULA] reduces the observed bolometric luminosity by 67% (56%) at [FORMULA] ([FORMULA]).

The uncertainty in the reddening estimate introduces subtle additional effects. If [FORMULA]E(B-V) [FORMULA] mag at low reddenings (E(B-V) [FORMULA]), an additional uncertainty of 5% in the bolometric luminosity is introduced. At higher reddening values (E(B-V) [FORMULA]), uncertainties of [FORMULA]E(B-V) =0.05 and 0.10 produce changes of 15% and 31% in the bolometric luminosity, respectively.

The decline rate of the bolometric light curve decreases with increasing reddening due to the color evolution of the supernova and the selective absorption. For SN 1994D [FORMULA](bol) would evolve linearly from 1.13 at hypothetical E(B-V) [FORMULA] to 0.99 at E(B-V) [FORMULA]. The linearity breaks down at about E(B-V) [FORMULA].

As described by Leibundgut (1988) the reddening depends on the intrinsic color of the observed object (Schmidt-Kaler 1982). This implies that the color evolution influences the shape of the filter light curves. A color difference of B-V [FORMULA] for SNe Ia in the first 15 days results in an increase of [FORMULA](B ) by [FORMULA] simply due to the color dependence of the reddening. The increase of [FORMULA] for blue filters is larger than for the redder passbands.

5.3. Uncertainties introduced by the method

The effect of fitting the light curves before constructing the bolometric light curves can be seen in Fig. 8. The bolometric flux for SN 1992bc determined in this way is compared against the straight integration over the wavelengths of the filter observations. The agreement between the two approaches is excellent and no differences can be observed. This also applies to the correction for the missing U filter observations. Deviations can be found only for those parameters derived from the light curve, which extrapolate far from the observed epochs, e.g. the rise time.

[FIGURE] Fig. 8. Constructing the bolometric light curves before and after fitting the filter light curves of SN 1992bc. The stars indicate the bolometric luminosity as calculated directly from the observations. The correction for missing U band is applied as described in Sect. 5.1.1, only the epochs with the maximum number of filters are shown. The dotted line is the bolometric luminosity calculated from the fits to the individual passbands.

The integration over wavelengths to calculate the bolometric light curve can be performed in different ways. A straight integration of the broad-band fluxes has to take into account the transmission of and any overlaps and gaps between filters. We experimented with several integration techniques, but found that for all interpolation methods, we reproduced the bolometric flux to within 2% at any epoch we considered. This has already been shown for SN 1987A by Suntzeff & Bouchet (1990). We chose to calculate the bolometric flux by summing the flux at the effective filter wavelength multiplied with the filter bandwidth.

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Online publication: July 13, 2000