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Bolometric Light Curves of Type Ia Supernovae
G. Contardo 1;2 , B. Leibundgut 1
1 European Southern Observatory, Karl­Schwarzschild­Straúe 2, D­85748 Garching,
Germany
2 Max­Planck­Institut f¨ur Astrophysik, Karl­Schwarzschild­Straúe 1, D­85748 Garch­
ing, Germany
1.1 Light Curves of Type Ia Supernovae
Substantial information about the processes in supernovae is contained in their light curves.
They track the temporal evolution of the energy release. The energy is generated in the
explosion by burning matter to nuclear statistical equilibrium, goes into unbinding the white
dwarf and is stored in radioactive material. The light curve itself is defined by the conversion
of the fl­rays from the radioactive decays into lower energy photons and by the escape of the
latter from the ejecta.
Because of their apparent uniformity SNe Ia were used as standard candles for distance
determination and to measure cosmological parameters [1]. The standard candle approach is
the simplest method. But the light curves of SNe Ia show significant differences in their shapes
and maximum luminosities. Phillips [2] showed a relation between maximum brightness and
\Deltam 15 (B), the difference in brightness in the B­band at its maximum and 15 days after.
Hamuy et al. [3] confirmed this relation. Another one parameter model is the Multicolor
Light Curve Shape (MLCS) method of Riess et al. [4], which uses a training set of well
observed SNe to span a range of light curves, described by one parameter.
1.2 Fitting Method
A different approach is fitting the filter light curves independently to avoid intrinsic assump­
tions made in template­fitting techniques. Therefore it is ideally suited for investigating the
non­uniformity of SN Ia explosions. For each supernova the light curve shape parameters
(like rise time, shape around maximum, late decline etc.) are derived individually and can
be searched for correlations. A descriptive model has been fitted to light curves of super­
novae from the Cal'an/Tololo survey [5], a set of supernovae from Riess et al. [6] and other
well observed, high quality data. The time evolution of the observed magnitudes is modeled
as a Gaussian (for the peak phase) atop a linear decay (for the late­time decline), a second
Gaussian in the V, R, and I­band (for the secondary maximum found in that curves) and an
exponential rise function (for the pre­maximum segment), as applied to SN 1994D by Vacca
and Leibundgut [7].
1.3 Epoches of Maxima
With these fits, parameters derived from the light curve shape can be compared more easily.
For example the distribution of the times of maximum light in the different filter light curves
can be examined, as shown in Figure 1. While the U­band light curve peaks before the B
maximum and V and R follow the B, the I light curve reaches maximum even earlier than
the U light curve. This trend is also confirmed by the IR light curves [8]. This is a very clear

2
0
4
8
0
t U ­ t B
0
4
8
0
t V ­ t B
0
4
8
0
t R ­ t B
0
4
8
0
­4 ­2 0 2 4 6 8
t I ­ t B
Figure 1: Relative times of maximum light
in different filters. The vertical lines show
an expanding, adiabatic cooling sphere [9].
­20 0 20 40 60 80 100
day
41.0
41.5
42.0
42.5
43.0
43.5
log
L
in
[erg/s]
91T
95D
94D
94ae
89B
92A
91bg
Figure 2: Bolometric luminosities.
sign of the non­thermal nature of the radiation emitted by SNe Ia. A simple model of an
expanding, adiabatic cooling sphere according to Arnett [9] gives the vertical lines in Figure
1. The maxima at longer wavelengths are reached at later epoches in this model. This is
clearly not seen for most SNe Ia.
1.4 Bolometric Light Curves of Type Ia Supernovae
As nearly 80 % of the bolometric luminosity is emitted in the range from 3000 to 10000 š A
[10], the UBVRI integrated flux is a physically meaningful quantity. It depends on the nickel
production, the energy deposition and the fl­ray escape, but not on the wavelengths of the
emitted photons. The theoretical calculation of the bolometric light curve is much simpler
than the calculation of the filter light curves, as complicated multi­group calculations of the
complete spectrum can be avoided.
But not all SNe are observed in all five bands. In a first approximation it is assumed that
the flux distribution is the same for all SNe. A well observed supernova (SN 1994D) is used
to calculate correction factors for missing pass bands.
If this correction is applied to other SNe, and the distance moduli and reddening are taken
into account [3, 4], one obtains the UBVRI bolometric light curves displayed in Figure 2. The
absolute peak luminosities differ by a factor of 10. The second bump, which can be seen in
the R and I light curves of several SNe, is still visible in the bolometric light curves. These
results show, that there are fundamental differences in the energy release among individual
SNe Ia.
How reliable are these bolometric luminosities and by which quantities are they affected?
In a forthcoming paper [11] a more extended discussion of the errors will be given. The
distance modulus only changes the absolute luminosity. As all distances used here are scaled
to a Hubble constant of H 0 = 65 km s \Gamma1 Mpc \Gamma1 , the luminosity differences are only affected
by errors in the determination of the distance modulus and not by offsets due to the different
methods. If the distance modulus changes by 0.1 mag, the bolometric luminosity changes
by 9 %. Reddening changes the absolute luminosity as well as the shape of the light curve.

3
Reddening of E(B \Gamma V ) = 0:05 still gives 85 % (88 %) of the unreddened bolometric luminosity
at t = t max (t = 20 days ú time of second maximum in R and I), whereas at reddening
of E(B \Gamma V ) = 0:35 only 33 % (44 %) of the unreddened bolometric luminosity remains
at t = t max (t = 20 days). Differences among independent data sets introduce additional
uncertainties. For typical values of ! 0:05 mag [6], however, we find changes of less than
3 %. We have tested also the influence of applying the fitting routine on the individual filter
light curves before constructing the bolometric luminosities by comparing it to bolometric
luminosities calculated directly from the observational data. The integration method and
normalization influence the bolometric luminosities up to 2 %. Finally, the error introduced
by the correction factors for missing U­band is ! 10 %, as has been tested by constructing
artificially data with missing pass bands for SNe which are observed in U, B, V, R, and I.
1.5 Conclusions and Future Work
A sample of supernovae has been used to construct bolometric light curves from observations.
These bolometric light curves can be compared to theoretical models more easily than filter
light curves. Therefore, bolometric light curves are one step from observations to theoretical
models.
In the future, a comparison of the bolometric light curves from observations with those
from theoretical models can supply us with information about the physical processes in SNe
Ia. We will derive the light curve corrections with bolometric light curves instead of filter
light curves to move from an empirical classification to physically meaningful relations.
References
[1] D. Branch and G. A. Tammann, Ann. Rev. Astron. Astrophys. 30 (1992) 359
[2] M.M. Phillips, Astrophys. J. Lett. 413 (1993) 105
[3] M. Hamuy, M.M. Phillips, R.A. Schommer, N.B. Suntzeff, J. Maza and R. Avil'es, Astron.
J. 112 (1996) 2391
[4] A.G. Riess, W.H. Press and R.P. Kirshner, Astrophys. J. 473 (1996) 88
[5] M. Hamuy et al. Astron. J. 112 (1996) 2408
[6] A.G. Riess, PhD thesis, Cambridge: Harvard University (1996)
[7] W.D. Vacca and B. Leibundgut, Astrophys. J. Lett. 471 (1996) 37
[8] J.H. Elias, K. Matthews, G. Neugebauer and S.E. Persson, Astrophys. J. 296 (1985) 379
[9] W.D. Arnett, Astophys. J. 253 (1982) 785
[10] N.B. Suntzeff, in IAU Colloquium, Vol. 145, Supernovae and Supernova Remnants, ed.
R. McCray & Z. Wang, Cambridge: Cambridge University Press (1996) 41
[11] G. Contardo, B. Leibundgut and W.D. Vacca, in preparation