Protostellar half-life: new methodology and estimates
  (Abridged) Protostellar systems evolve from prestellar cores, through the
deeply embedded stage and then disk-dominated stage, before they end up on the
main sequence. Knowing how much time a system spends in each stage is crucial
for understanding how stars and associated planetary systems form, because a
key constraint is the time available to form such systems. Equally important is
understanding what the spread in these time scales is. The most commonly used
method for inferring protostellar ages is to assume the lifetime of one
evolutionary stage, and then scale this to the relative number of protostars in
the other stages, i.e., assuming steady state. This method does not account for
the underlying age distribution and apparent stochasticity of star formation,
nor that relative populations are not in steady state. To overcome this, we
propose a new scheme where the lifetime of each protostellar stage follows a
distribution based on the formalism of sequential nuclear decay. The main
assumptions are: Class 0 sources follow a straight path to Class III sources,
the age distribution follows a binomial distribution, and the star-formation
rate is constant. The results are that the half-life of Class 0, Class I, and
Flat sources are (2.4+/-0.2)%, (4.4+/-0.3)%, and (4.3+/-0.4)% of the Class II
half-life, respectively, which translates to 47+/-4, 88+/-7, and 87+/-8 kyr,
respectively, for a Class II half-life of 2 Myr for protostars in the Gould
Belt clouds with more than 100 protostars. The mean age of these clouds is
1.2+/-0.1 Myr, and the star formation rate is (8.3+/-0.5)x10^-4 Msun/yr. The
critical parameters in arriving at these numbers are the assumed half-life of
the Class II stage, and the assumption that the star-formation rate and
half-lives are constant. This method presents a first step in moving from
steady-state to non-steady-state solutions of protostellar populations.
