The Rising Light Curves of Type Ia Supernovae
  We present an analysis of the early, rising light curves of 18 Type Ia
supernovae (SNe Ia) discovered by the Palomar Transient Factory (PTF) and the
La Silla-QUEST variability survey (LSQ). We fit these early data flux using a
simple power-law $(f(t) = {\alpha\times t^n})$ to determine the time of first
light $({t_0})$, and hence the rise-time $({t_{rise}})$ from first light to
peak luminosity, and the exponent of the power-law rise ($n$). We find a mean
uncorrected rise time of $18.98 {\pm} 0.54$ days, with individual SN rise-times
ranging from $15.98$ to $24.7$ days. The exponent n shows significant
departures from the simple 'fireball model' of $n = 2$ (or ${f(t) \propto
t^2}$) usually assumed in the literature. With a mean value of $n = 2.44 {\pm}
0.13$, our data also show significant diversity from event to event. This
deviation has implications for the distribution of 56Ni throughout the SN
ejecta, with a higher index suggesting a lesser degree of 56Ni mixing. The
range of n found also confirms that the 56Ni distribution is not standard
throughout the population of SNe Ia, in agreement with earlier work measuring
such abundances through spectral modelling. We also show that the duration of
the very early light curve, before the luminosity has reached half of its
maximal value, does not correlate with the light curve shape or stretch used to
standardise SNe Ia in cosmological applications. This has implications for the
cosmological fitting of SN Ia light curves.
