Turn up the light: Radiative efficiency of protostars at birth

TL;DR

This work tackles how the radiative efficiency of protostellar accretion shocks, quantified by $f_{\mathrm{acc}}$, and the non-steady accretion rate influence protostellar luminosities and subsequent evolution. The authors perform fully self-consistent radiation hydrodynamic simulations using PLUTO (1D/2D) and RAMSES (3D) to measure $f_{\mathrm{acc}}$ and $\dot{M}_{\mathrm{sc}}$ just outside the second core across different core masses and rotation. They find that protostellar birth begins with a strongly subcritical shock, but $f_{\mathrm{acc}}$ rapidly increases to unity within $\lesssim 100$ years in 1D models, with even earlier transitions in 3D due to polar radiation leakage. This supports a rapid switch to cold accretion and provides time-dependent radiative-feedback inputs for PMS theory, PLF interpretation, sink modeling, and IMF constraints. The study highlights the importance of multi-dimensional effects in protostellar radiative transfer and offers quantitative benchmarks for future simulations and observational comparisons.

Abstract

Early stages of stellar birth comprise of a two-step process involving the formation of two hydrostatic cores. The second step of gravitational collapse sets the radiative efficiency and accretion rate of the young protostar. These two parameters, of prime importance for protostellar evolution, dictate the luminosities and thus play a key role in deciphering the current discrepancy between observational surveys and theoretical models. In this letter, we provide quantitative estimates on the evolution of the radiative efficiency and accretion rate obtained from self-consistent, high-resolution, radiative hydrodynamic simulations performed using the codes PLUTO and RAMSES. The main highlight of our result is that the radiative efficiency reaches unity, that is, supercriticality, relatively quickly after protostellar birth. Supercriticality at the accretion shock is a necessary condition for cold accretion. Our results thus support a rapid transition to the cold accretion scenario, which is one of the assumptions used in Pre-Main Sequence (PMS) models working towards solutions to explain observational data. We briefly discuss the implications of the time evolution of the radiative efficiency factor in the context of the luminosity problem, the Protostellar Luminosity Function (PLF), PMS evolution, accurate sink properties, and the stellar Initial Mass Function (IMF).

Figures (5)

• Figure 1: Radiative efficiency $f_\mathrm{acc}~$ versus mass accretion rate $\dot{M}_\mathrm{sc}$ at the protostellar surface (top) and time since protostellar birth (bottom). Both panels show outcomes from a 1D spherical set-up with different initial molecular cloud core masses using the PLUTO code. Also shown as black circles in both panels is data from a 1 $M_{\odot}$ 3D RAMSES simulation with an initial turbulent Mach number of 0.2. Each plot includes a top subplot with a linear $f_\mathrm{acc}~$ axis ranging from 0 to 1. Typical constant values of $f_\mathrm{acc}~$ used in the literature lie within the grey hatched region.
• Figure 2: Top: Logarithmically scaled (size in au) time snapshot showing the gas density in colour within an infalling envelope, the first core at its final stage, and the onset of the protostar (second core) formation. Bottom: Thermal evolution of a 1 $M_{\odot}$ molecular cloud core highlighting the two-step collapse process. Bottom panel is reproduced from Bhandare2020.
• Figure 3: Radiative efficiency $f_\mathrm{acc}~$ versus mass accretion rate $\dot{M}_\mathrm{sc}$ at the protostellar surface (top) and time since protostellar birth (bottom). Both panels show PLUTO outputs from a 2D spherical set-up with different initial molecular cloud core masses and from a 1 $M_{\odot}$ 2D simulation that includes an initial angular momentum (dashed blue line). Each plot includes a top subplot with a linear $f_\mathrm{acc}~$ axis ranging from 0 to 1. Typical constant values of $f_\mathrm{acc}~$ used in the literature lie within the grey hatched region.
• Figure 4: Time evolution of the radiative flux $F_{\mathrm{rad}}$ (top) and accretion energy flux $F_{\mathrm{acc}}$ (bottom) since protostellar birth. Both panels show outcomes from a 1D spherical set-up with different initial molecular cloud core masses using the PLUTO code. Also shown as black circles in both panels is data from a 3D RAMSES simulation with an initial turbulent Mach number of 0.2.
• Figure 5: Global measurement of the radiative efficiency of the 3D RAMSES run as a function of time (where $t=0$ corresponds to the epoch of protostellar birth), performed at $R_{\mathrm{s}}=1.2$ au (see Eq. \ref{['eq:faccglobal']}). Top panel displays the outgoing radiative luminosity (solid line) and accretion luminosity (dash-dotted line). Bottom panel presents the time integrated luminosities, yielding the radiative energy (solid line) and the accretion energy (dash-dotted line). Bottom panel also shows the global $\mathrm{^{global}}f_\mathrm{acc}(t)~$ (red line) and local (red circles) radiative efficiency.