The formation of CDM haloes II: collapse time and tides

We use two cosmological simulations of structure formation in the LambdaCDM scenario to study the evolutionary histories of dark-matter haloes and to characterize the Lagrangian regions from which they form. We focus on haloes identified at redshift z_id=0 and show that the classic ellipsoidal collapse model systematically overestimates their collapse times. If one imposes that halo collapse takes place at z_id, this model requires starting from a significantly lower linear density contrast than what is measured in the simulations at the locations of halo formation. We attempt to explain this discrepancy by testing two key assumptions of the model. First, we show that the tides felt by collapsing haloes due to the surrounding large-scale structure evolve non-linearly. Although this effect becomes increasingly important for low-mass haloes, accounting for it in the ellipsoidal collapse model only marginally improves the agreement with N-body simulations. Second, we track the time evolution of the physical volume occupied by forming haloes and show that, after turnaround, it generally stabilizes at a well-defined redshift, z_c>z_id, contrary to the basic assumption of extended Press-Schechter theory based on excursion sets. We discuss the implications of this result for understanding the origin of the mass-dependence and scatter in the linear threshold for halo formation. Finally, we show that, when tuned for collapse at z_c, a modified version of the ellipsoidal collapse model that also accounts for the triaxial nature of protohaloes predicts their linear density contrast in an unbiased way.Comment: 15 pages, 11 figures, MNRAS in pres

Energy equipartition between stellar and dark matter particles in cosmological simulations results in spurious growth of galaxy sizes

The impact of 2-body scattering on the innermost density profiles of dark matter haloes is well established. We use a suite of cosmological simulations and idealized numerical experiments to show that 2-body scattering is exacerbated in situations where there are two species of unequal mass. This is a consequence of mass segregation and reflects a flow of kinetic energy from the more to less massive particles. This has important implications for the interpretation of galaxy sizes in cosmological hydrodynamic simulations, which nearly always model stars with less massive particles than are used for the dark matter. We compare idealized models as well as simulations from the eagle project that differ only in the mass resolution of the dark matter component, but keep subgrid physics, baryonic mass resolution, and gravitational force softening fixed. If the dark matter particle mass exceeds the mass of stellar particles, then galaxy sizes – quantified by their projected half-mass radii, R50 – increase systematically with time until R50 exceeds a small fraction of the redshift-dependent mean interparticle separation, l (⁠ R 50 ≳0.05×l R50≳0.05×l ⁠). Our conclusions should also apply to simulations that adopt different hydrodynamic solvers, subgrid physics, or adaptive softening, but in that case may need quantitative revision. Any simulation employing a stellar-to-dark matter particle mass ratio greater than unity will escalate spurious energy transfer from dark matter to baryons on small scales

Earth-mass haloes and the emergence of NFW density profiles

We simulate neutralino dark matter (χDM) haloes from their initial collapse, at ∼ earth mass, up to a few percent solar. Our results confirm that the density profiles of the first haloes are described by a ∼r−1.5 power law. As haloes grow in mass, their density profiles evolve significantly. In the central regions, they become shallower and reach on average ∼r−1, the asymptotic form of an NFW profile. Using non-cosmological controlled simulations, we observe that temporal variations in the gravitational potential caused by major mergers lead to a shallowing of the inner profile. This transformation is more significant for shallower initial profiles and for a higher number of merging systems. Depending on the merger details, the resulting profiles can be shallower or steeper than NFW in their inner regions. Interestingly, mergers have a much weaker effect when the profile is given by a broken power law with an inner slope of −1 (such as NFW or Hernquist profiles). This offers an explanation for the emergence of NFW-like profiles: after their initial collapse, r−1.5 χDM haloes suffer copious major mergers, which progressively shallows the profile. Once an NFW-like profile is established, subsequent merging does not change the profile anymore. This suggests that halo profiles are not universal but rather a combination of (1) the physics of the formation of the microhaloes and (2) their early merger history – both set by the properties of the dark matter particle – as well as (3) the resilience of NFW-like profiles to perturbations

Wide binaries in ultrafaint galaxies: a window on to dark matter on the smallest scales

We carry out controlled $N$-body simulations that follow the dynamical evolution of binary stars in the dark matter (DM) haloes of ultra-faint dwarf spheroidals (dSphs). We find that wide binaries with semi-major axes $a\gtrsim a_t$ tend to be quickly disrupted by the tidal field of the halo. In smooth potentials the truncation scale, $a_t$, is mainly governed by (i) the mass enclosed within the dwarf half-light radius ($R_h$) and (ii) the slope of the DM halo profile at $R\approx R_h$, and is largely independent of the initial eccentricity distribution of the binary systems and the anisotropy of the stellar orbits about the galactic potential. For the reported velocity dispersion and half-light radius of Segue I, the closest ultra-faint, our models predict $a_t$ values that are a factor 2--3 smaller in cuspy haloes than in any of the cored models considered here. Using mock observations of Segue I we show that measuring the projected two-point correlation function of stellar pairs with sub-arcsecond resolution may provide a useful tool to constrain the amount and distribution of DM in the smallest and most DM-dominated galaxies.Comment: Accepted to MNRAS Letter

Identifying the disc, bulge, and intra-halo light of simulated galaxies through structural decomposition

We perform a structural decomposition of galaxies identified in three cosmological hydrodynamical simulations by applying Gaussian Mixture Models (GMMs) to the kinematics of their stellar particles. We study the resulting disc, bulge, and intra-halo light (IHL) components of galaxies whose host dark matter haloes have virial masses in the range $M_{200}=10^{11}$-- $10^{15}\,{\rm M_\odot}$. Our decomposition technique isolates galactic discs whose mass fractions, $f_{\rm disc}$, correlate strongly with common alternative morphology indicators; for example, $f_{\rm disc}$ is approximately equal to $\kappa_{{\rm co}}$, the fraction of stellar kinetic energy in co-rotation. The primary aim of our study, however, is to characterise the IHL of galaxies in a consistent manner and over a broad mass range, and to analyse its properties from the scale of galactic stellar haloes up to the intra-cluster light. Our results imply that the IHL fraction, $f_{\rm IHL}$, has appreciable scatter and is strongly correlated with galaxy morphology: at fixed stellar mass, the IHL of disc galaxies is typically older and less massive than that of spheroids. Above $M_{200}\approx 10^{13}\,{\rm M_\odot}$, we find, on average, $f_{\rm IHL}\approx 0.45$, albeit with considerable scatter. The transition radius beyond which the IHL dominates the stellar mass of a galaxy is roughly $30\,{\rm kpc}$ for $M_{200}\lesssim 10^{12.8}\,{\rm M_\odot}$, but increases strongly towards higher masses. However, we find that no alternative IHL definitions -- whether based on the ex-situ stellar fraction, or the stellar mass outside a spherical aperture -- reproduce our dynamically-defined IHL fractions.Comment: 17 pages, 12 figures, submitted to MNRA