Adjustment

The parameters which we want to estimate are: the flux to the maximum (or in an equivalent way magnitude) and the factor of stretching in each band of observation and the date of the maximum of luminosity (defined by the owner of spectrum of supernova). This last is estimated in a simultaneous way in each band.

The adjustment is carried out in flux to avoid the problems of divergences of the system logarithmic curve magnitudes. That makes it possible in particular to handle negative fluxes.

$\chi^2$ Is thus written:

$$\chi^2 = \sum_{b = bande} \sum_{o = obs}\left( \frac{f_{b,o}-modele(t_{b,o}))}{\sigma_{b,o}} \right)^2$$ (9.6)

with $t_{b, o}$.

The model is written by using 2.34 :

$$modele(t_{b,o}) = \Delta_{b} ~ f((t_{b,o}~-~t_{max})/s)$$ (9.7)

where $f(t)$ the flux simulated in the filter. To pass from the effective filter to the standard filter one simulates the flux of the supernova in the standard filter and one multiplies by $\Delta$ :

$$f_{b,standard}^{obs}(t) = \Delta_{b} f_{b,standard}^{sim} (t)$$ (9.8)

One expresses fluxes in photons a second and per square centimetre.

To pass in magnitude, one uses the definite zero point by 9.2 which one applies to the standard filters:

$$Mag_{b,standard}^{obs}(t_{max}) = -2.5\log_{10}(\Delta_{b} f_{b,standard}^{sim} (t_{max})) + zero_b$$ (9.9)

Figure 9.6: Curve fitting of light of 1992bo discovered within the framework of Calàn-Tololo supernova survey. This supernova has a redshift of 0.018. The result is presented in flux corrected for the Galactique extinction. The two executives of bottom represent the residuals of the adjustment.

Figures 9.7 represent the results of the curve fitting of light of SN1992bo corrected for the Galactique absorption and expressed in the filters B and V standard in flux and magnitude.

Figure 9.7: Curve fitting of light of 1992bo discovered within the framework of Calàn-Tololo supernova survey. This supernova has a redshift of 0.018. The result is presented in magnitude corrected for the Galactique extinction. The two executives of bottom represent the residuals of the adjustment.