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 protostellar systems spend 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 or uncertainty in these inferred 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 lifetime to the relative number of protostars in the other stages , i.e. , the method assumes populations are in steady state .
The number-counting method does not take into account the underlying age distribution and apparent stochasticity of star formation , nor that star formation is sequential , i.e. , 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 .
In this formalism , 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 throughout .
The results are that the half-life of Class 0 , Class I , and Flat sources are ( 2.4 \pm 0.2 ) % , ( 4.4 \pm 0.3 ) % , and ( 4.3 \pm 0.4 ) % of the Class II half-life , respectively , which translates to 47 \pm 4 , 88 \pm 7 , and 87 \pm 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 \pm 0.1 Myr , and the total inferred star formation rate is ( 8.3 \pm 0.5 ) \times 10 ^ { -4 } M _ { \odot } yr ^ { -1 } for a mean protostellar mass of 0.5 M _ { \odot } .
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 .