Luminosity
 Functions
 •Solid line is the best
 fit SCHECHTER (1976) function:
 
  
  
  
  
  
   
   
   
   
   
   
   
   
   
   
   
   
  
  
  
   
  
  
 
  
  
  
 
 Where x = L/L*, and L* characterizes
 the “break” luminosity. 
 This
 function is just a power-law (a is the slope) with an exponential cutoff at the
 high-luminosity end.  Simple.   But astronomers use magnitudes and things
 get Ugly: 
 
  
  
  
  
  
   
   
   
   
   
   
   
   
   
   
   
   
  
  
  
  