How supernova feedback turns dark matter cusps into cores

TL;DR

The paper addresses how bursty supernova feedback reshapes dark matter cusps into cores by introducing an analytic impulsive framework that models energy transfer from rapidly changing central potentials to collisionless particles. It shows that rapid, localized gas outflows drive potential fluctuations on timescales shorter than orbital periods, irreversibly heating orbits and generating ~kiloparsec-scale cores, a result validated against high-resolution cosmological simulations with metal cooling. The findings demonstrate that adiabatic approximations fail to capture this mechanism and that core formation can occur even when only a few percent of baryons form stars, provided the bursts are sufficiently frequent and energetic. The work has broad implications for understanding dwarf galaxy structure and suggests similar processes could operate across a wide mass range when central feedback is sufficiently impulsive and recurrent.

Abstract

We propose and successfully test against new cosmological simulations a novel analytical description of the physical processes associated with the origin of cored dark matter density profiles. In the simulations, the potential in the central kiloparsec changes on sub-dynamical timescales over the redshift interval 4 > z > 2 as repeated, energetic feedback generates large underdense bubbles of expanding gas from centrally-concentrated bursts of star formation. The model demonstrates how fluctuations in the central potential irreversibly transfer energy into collisionless particles, thus generating a dark matter core. A supply of gas undergoing collapse and rapid expansion is therefore the essential ingredient. The framework, based on a novel impulsive approximation, breaks with the reliance on adiabatic approximations which are inappropriate in the rapidly-changing limit. It shows that both outflows and galactic fountains can give rise to cusp-flattening, even when only a few per cent of the baryons form stars. Dwarf galaxies maintain their core to the present time. The model suggests that constant density dark matter cores will be generated in systems of a wide mass range if central starbursts or AGN phases are sufficiently frequent and energetic.

Figures (6)

• Figure 1: Spherically averaged halo density profiles for high star-formation threshold (HT, thick red lines) and low threshold (LT, thin blue lines) simulations at $z=4$, shortly before the dark matter profile starts to flatten in the high-threshold model. Solid, dashed and dotted lines show respectively dark matter, gas and stellar content. In the low threshold case, dark matter dominates by orders of magnitude at every radius. In the high threshold case, the gas reaches a comparable density to the collisionless matter in the central regions. Gaseous processes can therefore cause heating of collisionless components (dark matter and stars) in HT but not LT runs.
• Figure 2: (Upper panel) The baryonic mass interior to, from top line to bottom, $1\, \mathrm{kpc}$, $500\, \mathrm{pc}$ and $200\, \mathrm{pc}$ (HT simulation). Bursty central star formation coupled to strong supernova feedback causes coherent, rapid oscillations in the potential interior to $1\, \mathrm{kpc}$. The orbital time of typical dark matter particles interior to $1\, \mathrm{kpc}$ is $\mathrel{\hbox{$\sim$} \hbox{$>$}} 25\, \mathrm{Myr}$. By contrast the simulated supernova bubbles can encompass the inner kiloparsec in around $3\,\mathrm{Myr}$, far too rapidly for the adiabatic approximation to be valid. The lower panel shows the disk-plane density during the starburst event at $t=2.56\,\mathrm{Gyr}$, $z=2.67$. A large underdense bubble has formed at the centre of the disk through thermal expansion of gas heated by multiple supernova explosions. The cross marks the halo centre.
• Figure 3: The mechanism for injecting energy into the dark matter orbits, illustrated by the exact solution for a time-varying harmonic oscillator potential. The lower panel shows (solid line) a solution to the equations of motion where $\omega^2=1$ (blue) at early and late times, while at intermediate times $\omega^2 = 0.1$ (red) mimicking baryonic blowout and recondensation. The changes in potential occur instantaneously; in this case the final amplitude of the oscillation is approximately twice that of the initial orbit. The dashed line shows the solution when the potential changes smoothly over several orbital periods; this gives adiabatic behaviour, so that the final orbit regains the initial amplitude, demonstrating the necessity for relatively sudden potential jumps. The inset figures (top) illustrate how the post-blowout orbit expansion implies that the late-time energy gain dominates over the initial energy loss.
• Figure 4: Using the spherically averaged potential from the simulations, we model the expansion of orbits of test particles at different initial radii (solid lines). Orbits starting significantly within the inner kiloparsec migrate outwards over several gigayears, whereas those starting outside a kiloparsec do not feel the rapid potential variations and so remain near their initial radius. Our model thus explains the flattening of central density cusps into kiloparsec-scale cores in small galaxies through radial outwards migration. As expected the reversible, adiabatic model (illustrated for the innermost orbit by the dashed line) does not correctly model the heating effect of very rapid potential variations in the inner parts of the halo.
• Figure 5: The spherically averaged dark matter density as a function of radius, measured at $z=2$ when the core has formed in the HT simulations (thick dotted line). The solid line shows the density profile at this time according to our model (see text for details); this is seen to be in excellent agreement with the HT simulation. The adiabatic model (dashed line) fails to correctly model the cusp flattening, demonstrating the need for the improved modelling presented here. The LT comparison simulation (dash-dotted line) also remains cusped as explained in Section \ref{['sec:first-sims']}.