Protostellar half-life: new methodology and estimates

¹ Centre for Star and Planet Formation, Niels Bohr Institute and Natural History Museum of Denmark, University of Copenhagen, Øster Voldgade 5-7, 1350 Copenhagen K, Denmark
e-mail: lars.kristensen@nbi.ku.dk
² Department of Physics, State University of New York at Fredonia, 280 Central Ave, Fredonia, NY, 14063 USA
³ Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA, 02138 USA

Received: 17 July 2017
Accepted: 30 July 2018

Abstract

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 ± 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 total inferred star formation rate is (8.3 ± 0.5) × 10⁻⁴ M_⊙ yr⁻¹ for a mean protostellar mass of 0.5 M_⊙. 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.