6. The method of mass moments
For the moments of the -distribution for several events, one obtains following RJM
yields for the case , , and for the average mass (in units of ) as
One sees that the moments of the mass spectrum can be extracted from the moments of the time-scale distribution if the spatial distribution of the mass density and the velocity distribution is given (RJM).
For the moments of the mass spectrum one gets
This gives for
For , one obtains
since , which is the same value as obtained for the expectation value of the lens mass for as derived above, if one considers a single observed event.
© European Southern Observatory (ESO) 1998
Online publication: January 27, 1998