How Many Bursts Does it Take to Form a Core at the Center of a Galaxy?

TL;DR

This paper tackles the core-cusp problem in dwarf galaxy halos by introducing a controlled, cosmological, dark-matter-only framework augmented with a central-mass tracer that emulates bursty baryonic outflows. By prescribing the number, timing, and magnitude of central potential fluctuations, the authors systematically explore when and how cores form in classical dwarfs versus ultra-faint dwarfs, including the limiting case of a single early burst. They find that multiple bursts or large total expelled mass promote core formation in classical dwarfs, while single early bursts rarely produce sizable cores in UFD-like halos; timing matters critically for UFDs, with late outflows (z<5) being capable of generating cores under favorable mass conditions. The results offer guidance for sub-grid feedback models in cosmological simulations and help interpret observed dwarf galaxies, suggesting that single bursts are unlikely to explain cored densities in Local Group UFDs under realistic gas fractions and star-formation histories.

Abstract

We present a novel method for systematically assessing the impact of central potential fluctuations associated with bursty outflows on the structure of dark matter halos for classical and ultra-faint dwarf galaxies. Specifically, we use dark-matter-only simulations augmented with a manually-added massive particle that modifies the central potential and approximately accounts for a centrally-concentrated baryonic component. This approach enables precise control over the magnitude, frequency, and timing of rapid outflow events. We demonstrate that this method can reproduce the established result of core formation for systems that undergo multiple episodes of bursty outflows. In contrast, we also find that equivalent models that involve only a single (or small number of) burst episodes do not form cores with the same efficacy. This is important because many UFDs in the Local Universe are observed to have tightly constrained star formation histories that are best described by a single, early burst of star formation. Using a suite of cosmological, zoom-in simulations, we identify the regimes in which single bursts can and cannot form a cored density profile. Our results suggest that it may be difficult to form cores in UFD-mass systems with a single, early burst regardless of its magnitude.

Figures (6)

• Figure 1: Comparison of DM density for the smooth (top panels) and bursty (bottom panels) models implemented using the modified-DMO approach for a halo with mass $9.2 \times 10^{9} M_{\odot}$. Left: Dark matter mass projection made from a $30 \times 30 \times 30$ kpc box surrounding the central halo. The halos look similar, save for their central regions. The smooth model produces a clear peak in density at the very center, while the bursty model reaches a constant density (forms a core) $2.05$ kpc from the center. Right: Tracer mass versus time as well as density profile for the smooth and bursty model. In both cases, the final stellar mass is $3.9 \times 10^{6} M_{\odot}$. The tracer mass in the upper panel represents a galaxy with a smooth history, which follows the SHMR shown in black. The tracer mass evolution in the lower panel represents a galaxy that undergoes five bursts of star formation, expelling $3.6 \times 10^{7} M_{\odot}$ of gas in each burst. The $z=0$ DM density profiles produced from each of these models are also shown. The grey dashed line marks $2.8\times$ the DM particle softening, the point below which numerical effects begin to be important. The smooth model has an inner log-slope $\alpha = -1.40$ when averaged over 1--2% of the virial radius, consistent with an NFW profile. By contrast, when there are episodic bursts, we find a log-slope $\alpha = -0.63$.
• Figure 2: Summary of the inner log-slopes ($\alpha = \frac{\rm {dlog}\rho}{\rm dlogr}$) best-fit core radii $r_{\rm{c}}$ for a classical dwarf galaxy as a function of number of bursts and burst mass.
• Figure 3: Comparison of the relationship between number of bursts and both the core size (right) and inner log-slope (left) for variable (blue) versus fixed (red) total energy transferred to the DM particles via bursty feedback for the classical dwarf galaxy. When the amount of mass expelled in each burst is constant, we find that the profile simply becomes more cored as we increase the number of bursts (increasing the total energy transferred). If instead the mass expelled in each burst is varied such that the total mass expelled is constant, we find a more complex relationship. As the number of bursts is decreased, initially this leads to an increase in the core size. However, if there are fewer than five bursts, this trend reverses. The point marked with an "x" indicates that for this model, the core-Einasto fit is poor.
• Figure 4: Present-day density profiles for a fixed amount of total mass expelled ($1.8 \times 10^{8}M_{\odot}$) over time and a varied number of bursts. The black line depicts the smooth model. As the number of bursts decreases (and therefore, the amount of mass expelled per burst increases) larger cores form. However, cores stop forming altogether when the number of bursts becomes very small (i.e., $\sim 1$--2) despite the large amount of mass being expelled. The gray dashed line indicates the radius at which numerical softening effects begin to impact the results. Note that the results are shown for 1, 2, 3, and 5 bursts (not 4).
• Figure 5: Comparison of the present-day DM density profile for an UFD galaxy if it has a smooth growth history (black) or forms in a single burst at $z=7$ (red) resulting in the ejection of $1.4 \times 10^{4} M_{\odot}$. The density profiles are both cusped with $r_{\rm c} = 0.07, 0.05 ~{\rm and }~ \alpha = -1.25,-1.35$ for the smooth-growth and single-burst models, respectively.