Radiative Feedback in Population III Protostellar Growth: The Impact of HI Shielding

Abstract

We present a suite of radiation-magnetohydrodynamics simulations from the POPSICLE project that follow the long-term growth (~50 kyr) of primordial protostars while self-consistently coupling radiation, turbulence, and magnetic fields. The simulation suite is designed to quantify the relative impacts of the pathways of radiative feedback in Pop III stars - the extreme-ultraviolet (EUV) ionization and Lyman-Werner (LW) dissociation - by considering simulations with and without their inclusion. We find that without HI shielding, LW feedback alone can suppress and ultimately terminate accretion. With HI shielding, the large column densities near the protostar significantly weaken LW feedback. In the polar direction, atomic hydrogen fully shields LW radiation where $H_2$ self-shielding alone is insufficient. This leads to lower gas temperatures near the protostar and higher accretion rates, yielding larger final stellar masses than in models without shielding. The HII regions remain compact and confined to less than about 100 AU measured outward from the sink accretion radius (75 AU) due to high gas densities and continuous gas replenishment that inhibit the thermal pressure-driven breakout of the ionization front even for high ionizing luminosities. These results demonstrate that the interplay of gas dynamics, shielding, and radiative feedback can significantly alter the growth of Pop III stars. We discuss the implications for the initial mass function of primordial stars and the influence of feedback from early stellar populations.

Figures (10)

• Figure 1: Top panel: Total stellar mass (left axis) and star formation efficiency, $\epsilon_\star$ (right axis), as a function of time since the formation of the first protostar for all four runs. In the run without atomic hydrogen shielding (No-Hshield; yellow curve), the stellar mass is suppressed relative to the Fiducial run (blue curve), which includes H i shielding. In the LW-Only run (pink curve), stellar mass grows slows markedly after formation, and the disk fragments at $\sim 11$ kyr, ultimately producing a total of 11 sink particles by the end of the simulation. The dashed pink curve shows the mass of the most massive sink. Dashed black lines indicate power-law scalings for reference. Grey-shaded bands denote the stellar mass regime in which Pop III stars are expected to explode as core-collapse supernovae (CCSNe) or pair-instability supernovae (PISNe). The stellar mass evolution in the EUV-Only run and the Fiducial run is similar, reflecting the effective shielding of LW radiation in the latter. Bottom panel: Total stellar accretion rate as a function of time for all four runs, averaged over $\Delta t = 500$ yr. The dashed pink curve indicates accretion onto all stars in the LW-Only run after fragmentation.
• Figure 2: Slice plots of gas number density at four evolutionary stages in the Fiducial run. Each row shows a pair of orthogonal slices through the simulation volume, with the left panel taken perpendicular to the $\hat{x}$ direction and the right panel taken perpendicular to the $\hat{z}$ direction. The top row shows the dense, oblate structure that forms at the center of the collapsing gas cloud immediately prior to protostar formation. The second row shows the emergence of a flattened, rotationally supported disk a few thousand years after collapse. The third and fourth rows show the subsequent growth of the disk and surrounding envelope as the system accretes mass over time. The white markers in the lower three rows indicate the locations of sink particles. The spatial scale increases by a factor of five between the upper and lower rows, as indicated by the scale bars
• Figure 3: Column densities of atomic hydrogen, $N_{\text{H\,i}}$ (top panel), and molecular hydrogen, $N_{\mathrm{H_2}}$ (bottom panel), measured from the protostar along the positive $x$ (blue), $y$ (green), and $z$ (red) directions for the Fiducial run (solid lines) and No-Hshield (dashed lines) at t $\simeq$ 6 kyr and M $\simeq 100\ \mathrm{M_\odot}$, corresponding to the same snapshot as the third row of Figure \ref{['fig:density_slices']}. The $z$-axis corresponds to the polar direction, while $x$ and $y$ are radial directions in the disk plane. Insets show the corresponding shielding functions, $f_{\mathrm{shield}}$, from Equation \ref{['eq:fHIfit']} and \ref{['eq:fH2fit']} for each species.
• Figure 4: Spherically averaged radial profiles for the Fiducial (blue lines) and No-Hshield (yellow lines) runs, centered on the protostar at $t \simeq 6$ kyr and $M_\star \simeq 100\,\mathrm{M_\odot}$, corresponding to the same snapshot as the third row of Figure \ref{['fig:density_slices']}. The top panel shows the mass weighted H$_2$ mass fraction, which is higher in the Fiducial run near the sink due to shielding of LW radiation by atomic hydrogen. The middle panel shows the corresponding mass-weighted gas temperature, which is lower in the Fiducial run as a result of more efficient H$_2$ cooling. The bottom panel shows the radial mass flow rate, which is reduced in the No-Hshield run due to enhanced thermal pressure support from the hotter gas.
• Figure 5: Evolution of the H ii region in the Fiducial run. Left panel: The size of the H ii region, $R_{\text{H\,ii}}$ (right axis), shown together with the ionizing photon emission rate, $Q_{\rm{EUV}}$ (left axis), as a function of time. Right panel: The H ii region size, $R_{\text{H\,ii}}$ (left axis), shown together with the median gas number density, $n_{\mathrm{H}}$ (right axis), measured within a cylindrical region centered on the sink particle, with a base radius of 125 AU and extending 100 AU above and below the sink. The H ii region initially grows in tandem with the increasing EUV photon emission rate, and subsequently fluctuates in size in response to variations in both the local gas density and the ionizing luminosity.