Finding the SN explosion time by t-square fitting

In a couple of papers I've read that it's usual practice to fit early rise of supernova luminosity curve by $$t^2$$. Let me describe how I see it:

I take the early fast rising part of luminosity curve and then fit them to a curve:

$$L = a\cdot\left( t - t_0 \right) ^ 2 + L_0,$$

Where $$t_0$$ is the moment of explosion.

Is this approach right?

$$(y-k) = a (x-h)^2$$ is a parabola with its apex at $$(h,k)$$. Therefore, the formula you mentioned above has $$t_0$$ as the time at peak, not at the explosion.
• Okay, but what point should we take as the explosion time if not $h$? Left-side zero of the parabola? Nov 14 '18 at 1:43