the Milky Way extinction, $K_{Y'Y,\gamma}$ is the $K$-correction between rest-frame and observer-frame filters, and $\mu$ is the distance modulus. The coefficients $M_{Y',\gamma}$, $p_{Y',\gamma}$, and $q_{Y',\gamma}$ are model vectors that have been evaluated using nearly 100 well observed low-redshift SNe Ia as a training set. $\gamma=0$ labels quantities at the $B$ band peak magnitude epoch.

    Fitting the model to each SN Ia magnitudes, usually fixing $R_V$ gives $\mu$, $\Delta$, $A_V$ and $t_0$, the $B$-band peak magnitude epoch.

-   The SALT2 fitter [@Guy2007] makes use of a two-dimensional surface in time and wavelength that describes the temporal evolution of the de-redshifted (rest-frame) spectral energy distribution (SED) or specific flux (flux per unit wavelength) for SNe Ia. The original model was trained on a set of combined light-curves and 303 spectra, not only from (very) nearby but also medium and high redshift SN Ia.

    In SALT2, the de-redshifted (rest-frame) specific flux at wavelength $\lambda$ and phase (time) $p$ ($p = 0$ at $B$-band maximum) is modeled by $$\phi(p,\lambda; x_0,x_1,c)=x_0[M_0(t,\lambda)+x_1M_1(t,\lambda)]
    \exp [cC(\lambda)].
    \label{salt2restflux}$$ and does depend, through the parameters $x_0, x_1$, and $c$ on the particular type Ia supernova. $M_0(t, \lambda)$, $M_1(t, \lambda)$, and $C(\lambda)$ are determined from the training process described in [@Guy2007]. 