FORGE'd in FIRE III: The IMF in Quasar Accretion Disks from STARFORGE

Abstract

Recently, we demonstrated self-consistent formation of strongly-magnetized quasar accretion disks (QADs) from cosmological radiation-magnetohydrodynamic-thermochemical galaxy-star formation simulations, including the full STARFORGE physics shown previously to produce a reasonable IMF under typical ISM conditions. Here we study star formation and the stellar IMF in QADs, on scales from 100 au to 10 pc from the SMBH. We show it is critical to include physics often previously neglected, including magnetic fields, radiation, and (proto)stellar feedback. Closer to the SMBH, star formation is suppressed, but the (rare) stars that do form exhibit top-heavy IMFs. Stars can form only in special locations (e.g. magnetic field switches) in the outer QAD. Protostars accrete their natal cores rapidly but then dynamically decouple from the gas and wander, ceasing accretion on timescales ~100 yr. Their jets control initial core accretion, but the ejecta are swept up into the larger-scale QAD flow without much dynamical effect. The strong tidal environment strongly suppresses common-core multiplicity. The IMF shape depends sensitively on un-resolved dynamics of protostellar disks (PSDs), as the global dynamical times can become incredibly short ($\ll$ yr) and tidal fields are incredibly strong, so whether PSDs can efficiently transport angular momentum or fragment catastrophically at $\lesssim 10$ au scales requires novel PSD simulations to properly address. Most analytic IMF models and analogies with planet formation in PSDs fail qualitatively to explain the simulation IMFs, though we discuss a couple of viable models.

Figures (23)

• Figure 1: Projected simulation gas density (§ \ref{['sec:methods']}) at one moment in time (redshift $z\approx 4.4$) when we "zoom in" around the QSO accretion disk (QAD) and circum-quasar medium (CQM). Top: Face-on, color encodes surface density increasing dark-to-light on a log scale (median pixels in the largest-scale panel have $N_{H} \sim 10^{19}\,{\rm cm^{-2}}$ or density $n_{H} \sim 10^{-5}\,{\rm cm^{-3}}$, while in the smallest-scale panel $N_{H} \sim 10^{27}\,{\rm cm^{-2}}$, $n_{H} \sim 10^{12}\,{\rm cm^{-3}}$). Adapted from Fig. 1 in Paper I (re-labeled with the names of characteristic scales used here), to illustrate the "parent" galaxy (a merging, clumpy, gas-rich starburst with galactic SFR $>200\,{\rm M_{\odot}\,yr^{-1}}$) which provides the initial/boundary conditions for our study of SF here (where a star-forming complex of mass $\gtrsim 10^{8}\,M_{\odot}$ passes by a $\sim 10^{7}\,M_{\odot}$ SMBH and is partially tidally disrupted around the BHROI). Gas falls in as a tidally compressed stream in the CQM, which circularizes at $\sim 0.1\,$pc to form the QAD, which we follow down to $r=80\,$au from the SMBH. Bottom: Edge-on, showing distance from SMBH ($r$) along the QAD midplane in a wedge of azimuthal angle ($|\sin{\phi}|<0.3$) versus vertical distance ($z$), both stretched logarithmically. Colors encode gas temperature: $T<10^{3}\,$K ( green), $10^{3}<T<10^{4}$ K ( yellow), $10^{4}<T<10^{5}\,$K ( magenta), $10^{5}<T<10^{6}\,$K ( purple), $T>10^{6}\,$K ( cyan). Adapted from Fig. 9 in Paper I, but labeling radii corresponding to the QAD and CQM, and denoting where the resolution is sufficiently high for our STARFORGE resolved-star-formation model. At larger radii, individual stars are un-resolved and the simulation uses the FIRE model for un-resolved fragmentation, so this part of the simulation informs our boundary conditions but cannot be used to predict the IMF. Subsequently, we focus exclusively on star formation interior to the BHROI, in the STARFORGE regime.
• Figure 2: Properties of the QAD/CQM versus radius $r$ from SMBH (§ \ref{['sec:ism.diff']}). We focus exclusively on radii where STARFORGE physics applies inside our maximum-refinement region (Fig. \ref{['fig:images.faceon.stylized']}). In salient panels, we compare the simulations to the analytic prediction for a standard shakurasunyaev73$\alpha$-disk QAD ($\alpha=0.1$) extrapolated to the same radii. (1) Circular velocity $V_{\rm c} \equiv \sqrt{G M_{\rm enc}(<r)/r}$, with contributions from different mass components (dark matter is present but negligible). The SMBH excision radius truncates the gas at $\lesssim 0.001\,$pc. We label the BHROI. (2) Inflow $\dot{M}_{\rm in}$ and outflow $\dot{M}_{\rm out}$ rates through each annulus, and cumulative SFR (averaged over the previous $t_{\rm dyn}$, summed in radii $<r$). Inflow and outflow co-exist, but a stable $\dot{M}_{\rm in} \sim 10-100\,{\rm M_{\odot}\,yr^{-1}}$ persists. SF is suppressed relatively to inflow on small scales. (3) Gas and stellar surface density $\Sigma$ in cylindrical shells. Surface densities are uniformly $\gtrsim 10^{4}\,{\rm M_{\odot}\,pc^{-2}}$, much higher than LISM GMCs. (4) Gas density $\rho$, showing volume and mass-weighted means ( lines) and $90\%$ inclusion intervals ( shaded; mean can exceed this if the distribution has large "tails"). (5) Temperatures: we plot means and $90\%$ inclusion radii for gas, radiation, and dust temperatures (all explicitly evolved). Temperatures in the QAD approach blackbody equilibrium (different opacities and $\Sigma$ explain differences with SS73). Dust sublimates in-code at $T_{\rm dust} \gtrsim 1500\,$K. (6) Magnetic field strengths: energy-weighted field strength and radial/toroidal/poloidal components. In and outside the CQM fields are crudely isotropic with a mild radial bias, but the mean toroidal component comes to dominate in the QAD. (7) Toomre $Q$ accounting for thermal ($Q_{\rm therm}$), magnetic ($Q_{\rm mag}$), turbulent ($Q_{\rm turb}$), or combined support. The outer CQM has turbulent $Q\sim 1$ with thermal $Q<1$, but even the thermal-only $Q\gg1$ in the QAD. (8) Sonic ($\mathcal{M}_{s} \equiv \delta v_{\rm turb}/c_{s}$) and Alfvénic ($\mathcal{M}_{A} \equiv \delta v_{\rm turb}/v_{A}$) Mach numbers (mass-weighted), for each component of the random motions in the midplane. Dispersions are highly supersonic, trending from super-Alfvénic to sub-Alfvénic at decreasing $r$. While $\Sigma$, $\rho$, and $|{\bf B}|$ are vastly larger than in the LISM, the QAD is vastly lower-density compared to the SS73 model, owing to strong magnetic support (Paper III; note even though $|{\bf B}|$ is lower than in SS73, $v_{A}$ and $v_{A}/c_{s}$ are orders-of-magnitude larger, owing to the different densities). This means $Q$ is larger here by a factor $\gtrsim 10^{5}$ and $\mathcal{M}_{s}$ larger by a factor $\gtrsim 100$.
• Figure 3: Image illustrating the locations of star formation in the CQM/QAD (§ \ref{['sec:where']}). We plot the projected density of gas (face-on to the inner QAD) akin to Fig. \ref{['fig:images.faceon.stylized']}, and superimpose locations of individual (proto)stars ( points). Stars are colored by "dynamical age": time since formation $t_{\ast} < t_{\rm dyn}$ at their current radius ( dark blue), or $<10\,t_{\rm dyn}$ ( light blue) or older ( white). Inset images highly two sub-regions. SF primarily occurs in two regions here: (1) the free-falling, tidally compressed filament fueling the QAD (tidally stripped from larger-scale massive cloud-complexes) in the CQM, and (2) in the outer QAD. The filamentary regions are analogous to LISM-like dense filamentary star-forming regions, though they exhibit structure on much smaller absolute physical owing to the extreme densities and tidal fields (individual "cores" and shock sub-structures have scales $<0.001$ pc, as compared to $\sim 0.1$ pc).
• Figure 4: As Fig. \ref{['fig:wheresf.global']}, but focusing on the QAD (projected face-on and edge-on). SF occurs around where gas circularizes and is stabilized by magnetic fields but is still appreciably gravito-turbulent with a modest thermal-only Toomre $Q_{\rm thermal} \sim 1-10$ (Fig. \ref{['fig:profile.dynamics']}). In the inner QAD at $\ll 0.01\,$pc, where even the thermal-only $Q_{\rm thermal}$ rises to $\gg 10^{2}-10^{3}$, star formation becomes nearly impossible: all stars at these radii are dynamically "old," and formed at larger radii on highly-eccentric orbits.
• Figure 5: Images highlighting the multi-phase structure of the gas over the same range of scales as Figs. \ref{['fig:wheresf.global']}-\ref{['fig:wheresf.qad']}. We plot projected density edge-on, colored by gas temperature: $\ll 10^{4}\,$K ( magenta), $\sim 10^{4}\,$K ( green), and $\gg 10^{4}$ K ( red). Warm/hot, low density gas is present in the CQM from shocks and supernovae explosions, and vents from the inner QAD in a jet-like structure. The outer CQM also exhibits colder "clouds" embedded in warm gas, but the tidally-disrupted GMC-like complex is much more visible as the extended cold "stream," with some material free-falling onto the QAD, until it is heated via accretion and inefficient radiative cooling to temperatures $\gtrsim 1000\,$K.