I'm trying to understand the Schechter function, I read on Wikipedia that the L star term in the function is the 'characteristic galaxy luminosity where the power-law form of the function cuts off'. What does this mean exactly?
It's just an empirical fitting function to the brightness distributions. It's found empirically that the number of galaxies in a certain brightness range increases as a power law at the faint end, but drops off more quickly (exponentially) at the bright end. The L* luminosity is where the function transitions from one behavior to the other. These slides have a nice description.
Thanks for the explanation [emoji846]
L* is the luminosity of a giant galaxy like the Milky Way or Andromeda. Such galaxies are rare, and galaxies much brighter are even rarer.