FORGE'd in the Early Universe: The Effect of Protostellar Outflows on Pop III Accretion

TL;DR

This work delivers the first cosmological RMHD simulation of a single Pop III protostar using the FORGE'd in FIRE framework, resolving a circumstellar disk and protostellar jets down to au scales. The protostar grows to about $27\,M_{\odot}$ over $\sim 3.1\times 10^{4}$ yr, with jets and radiation feedback regulating accretion and driving large-scale outflows that influence the surrounding gas. The disk remains gravitationally stable ($Q \gg 1$) and is supported by both thermal pressure and turbulence, while magnetic fields are amplified to enable jet launching; these findings imply a self-regulated, moderate-mass Pop III outcome and provide insights into the early IMF and feedback in the first star-forming regions. The study also demonstrates the viability of combining FIRE's cosmological environment with STARFORGE-like protostellar physics to bridge scales from cosmology to circumstellar disks, setting the stage for future investigations of multi-star Pop III populations and their supernovae.

Abstract

We present a cosmological zoom-in radiation magneto-hydrodynamic (RMHD) simulation, using FORGE'd in FIRE, that follows the formation, growth, and evolution of a single metal-free Pop. III (proto)star at redshift $z \sim 14$. The simulation captures a rotationally supported circumstellar disk and protostellar jets, both resolved down to $<100$ au scales. We find the star grows to $\sim 27$ M$_{\odot}$ over $31,000$ years, with its final mass regulated by accretion and protostellar jets. Protostellar jets form because the magnetic mass-to-flux ratio lies within the regime that allows jet launching, and they are further enabled by a rotating circumstellar disk with sufficient gas-magnetic-field coupling, both present in this simulation. These jets regulate accretion onto the (proto)star and drive outflows that collide with infalling gas, slowing inflow at large radii due to the substantial momentum they carry. A circumstellar disk forms, extending out to $\sim 0.01$ pc, which remains gravitationally stable (Q $\gg 1$). The stability of the disk is maintained through both thermal support and turbulence. In this paper we focus on how jets play a critical role not only in shaping the final masses of Pop. III stars but also in directly influencing their surroundings by regulating accretion. These results will provide important insights into the initial mass function and feedback processes in the earliest star-forming regions of the Universe.

Figures (8)

• Figure 1: Visualizations of the gas mass and gas kinetic energy surface densities in our cosmological simulation at redshift $z \sim 14$. We highlight the dynamic range resolved in our simulation by zooming in from galaxy-wide scales on the left to the scales of the circumstellar disk on the right. In both density plots, the color increases from black to white (different properties use different color schemes) on a logarithmic scale, where each panel uses its own dynamic range. For the mass density plots (differentiated with a black through white color scheme) the median gas surface density ($\Sigma_{\mathrm{median}}$) in the top left, top middle, and top right panels are $1.5\times10^{-1}\, M_{\odot}\,\mathrm{pc}^{-2}$, $1.7\times10^{3} \, M_{\odot}\,\mathrm{pc}^{-2}$, and $2.3\times10^{4}\, M_{\odot}\,\mathrm{pc}^{-2}$ respectively. For the bottom middle and bottom right panels, we see the bipolar outflows from protostellar jets (in bright red) extend out to $\sim 1 \,\mathrm{pc}$. The top right panel highlights a circumstellar disk extending out to $\sim 0.01 \, \mathrm{pc}.$
• Figure 2: Effective resolution of the simulation as a function of radial distance from the sink (r). We show the median and $90\%$ inclusion interval (shaded) of the mass resolution and spatial resolution of the gas at various times after sink formation. The top panel plots the mass resolution ($\Delta m$), defined as the gas cell mass. We also include a reference line showing the total enclosed gas mass within a sphere of radius $r$ centered on the sink (M$_{\mathrm{gas}}(r)$). We define the spatial resolution (bottom panel) as $\Delta x \equiv (\Delta m /\rho)^{1/3}$. The resolution rapidly refines as the distance from the sink decreases. The regions near the (proto)star and its disk reach a mass resolution of $\Delta m < 3 \times 10^{-3} \; M_{\odot}$.
• Figure 3: Evolution of the sink particle's physical properties over time. Top Left: The plot shows the evolution of the sink mass, the reservoir mass, the stellar mass, and the circumstellar disk mass. Here, the sink particle represents a subgrid object that accretes gas from its surroundings, with the sink mass defined as the sum of the stellar mass and the reservoir mass. The reservoir is the mass of gas accreted onto the sink that is either incorporated into the star or diverted to a "jet reservoir" used to launch jets. The stellar mass corresponds to the mass accreted onto the star from the reservoir at a rate of $(1 - f_W)\dot{M}_{\mathrm{acc}}$, where $f_W = 0.3$ and $\dot{M}_{\mathrm{acc}}$ is the accretion rate grudic_starforge_2021. The disk mass represents the sum of gas particles traveling on approximately circular orbits around the sink. The total stellar mass grows steadily, reaching a final mass of $\sim 27\,M_{\odot}$. Bottom Left: We plot the total stellar luminosity L$_{\star}$, the accretion luminosity L$_{\mathrm{accretion}} = GM_{\star} \dot{M}/R_{\star}$, and the burning luminosity L$_{\mathrm{burning}} = \mathrm{L}_{\star} - \mathrm{L}_{\mathrm{accretion}}$. The total luminosity increases to $\sim$1.3 $\times 10^{5}$ L$_{\odot}$ by the end of the simulation. The accretion luminosity dominates during the first $9000$ years after sink formation, after which the burning luminosity becomes the primary contribution. Top Right: The stellar radius expands rapidly for the first $9000 \; \mathrm{years}$ due to accretion from the surrounding envelope, and then begins to contract. Bottom Right: Stellar effective (photospheric) temperature (defined such that $\mathrm{L}_{\star} = 4\pi R_{\star}^2 \sigma_{B} T_{eff}^{4}$).
• Figure 4: We compute all profiles in concentric cylindrical annuli centered on the sink particle. For all panels, we average the values over the $15$ preceding snapshots at each plotted time ($\Delta t \sim 650$ years), which suppresses snapshot-to-snapshot fluctuations and avoids features that may be unique to a single snapshot. Top Left: (Median) Gas surface density ($\Sigma_{gas}$) profile versus cylindrical distance from the sink. The protostellar disk extends out to $\sim 0.01 \; \mathrm{pc}$ (where the $v_\phi > v_r$ fraction drops), and we see that the surface density begins to taper out toward the outskirts of the disk. Between $\sim 10^{-3}-10^{1} \; \mathrm{pc}$, we find that $\Sigma_{gas} \propto R^{-1}$. Middle Left: We measure the dimensionless scale-height $H/R$ of the gas (mass-weighted) in each annulus as the median $|z|$ after rotating to the angular momentum axis of that annulus. Bottom Left: We compute the magnetic mass-to-flux ratio $\mu$, in each annulus as $\mu = \frac{(M/\Phi)}{(M/\Phi)_{\rm crit}}$, where $M$ is the gas mass in the annulus, $\Phi$ is the magnetic flux through the annulus, and $(M/\Phi)_{\rm crit} = 1/(2\pi \sqrt{G})$ is the critical value for collapse. Values of $\mu$ below the horizontal reference line satisfy the conditions for jet launching, whereas higher $\mu$ (above the line) suppresses jets given the mass-to-flux constraints from machida_formation_2013 (see Section \ref{['subsec:Circumstellar Disk']} for an explanation). Top Right: Temperature radial profile showing the median temperature in each annulus. T$_{\mathrm{eqm}}$ is the equilibrium temperature set by the balance between accretion heating and optically thin radiative cooling. Middle Right: We compute the Toomre Q of the gas in each annulus as $Q=\frac{c_s\,\kappa}{\pi G\,\Sigma_{\rm gas}}$; values $Q\lesssim 1$ indicate gravitational instability. Bottom Right: Cooling-to-dynamical time ratio $t_{\rm cool}/t_{\rm dyn}$ for each annulus. Values $<1$ indicate the gas cools within a dynamical time, while $>1$ implies dynamical evolution outpaces cooling.
• Figure 5: Chemical structure of the gas surrounding the (proto)star, focusing specifically on the abundances of key species: free electrons ($x_{\rm e}$), ionized hydrogen ($x_{\rm HII}$), molecular hydrogen ($f_{\rm H_{2}}$), and atomic hydrogen ($x_{\rm HI}$). The median species fractions are shown with thick lines, while the mean values are shown with thin lines. We use the same time-averaging scheme described in the caption of Figure \ref{['fig:disk']}.