## Wednesday, June 5, 2013

### supernovae at high redshift

if you observe a supernova at redshift $z=2$, does the lightcurve get time-dilated due to the Hubble expansion? if yes, by how much? at what redshift would you need to place a supernova if you want to stretch the lightcurve to last a year?

math bonus: just using a compass and a ruler, it is easily possible to construct $\sin(\alpha)$ and $\cos(\alpha)$ of an angle $\alpha$ (how?). can you construct $\sinh(\alpha)$ and $\cosh(\alpha)$ as well for arbitrary angles $\alpha$?

1. all time intervals $\Delta t$ are stretched by the factor $z$,
so that the light curve takes 3 times longer to develop. because supernova light curves typically last 4 weeks, one needs a stretching by 12 for the supernova to last a year, which implies $z=11$.
2. math bonus question: it's straightforward to draw $\cos(\alpha)$ and $\sin(\alpha)$ into a unit circle. what I find amazing is that you can in the same way construct the hyperbolic functions, once a hyperbola is constructed, and this can be done with the Greek geometry rules.