# Variable protostellar mass accretion rates in cloud cores

## TL;DR

This study revisits spherical hydrodynamic models with a polytropic EoS to address the luminosity conundrum in protostar formation, showing that decreasing mass accretion rates over time can explain observed luminosities.

## Contribution

It demonstrates that polytropic models with gamma > 1 naturally produce decreasing accretion rates, offering a solution to the luminosity problem in star formation models.

## Key findings

- Mass accretion rate decreases over time in polytropic models with gamma > 1.
- Protostellar luminosity declines as accretion rate decreases.
- Radial density profiles support the use of polytropic spheres in modeling star formation.

## Abstract

Spherical hydrodynamic models with a polytropic equation of state (EoS) for forming protostars are revisited in order to investigate the so-called luminosity conundrum highlighted by observations. For a molecular cloud (MC) core with such an EoS with polytropic index $\gamma$ >1, the central mass accretion rate (MAR) decreases with increasing time as a protostar emerges, offering a sensible solution to this luminosity problem. As the MAR decreases, the protostellar luminosity also decreases, meaning that it is invalid to infer the star formation time from the currently observed luminosity using an isothermal model. Furthermore, observations of radial density profiles and the radio continua of numerous MC cores evolving towards protostars also suggest that polytropic dynamic spheres of $\gamma$ > 1 should be used in physical models.