The inner structure of ΛCDM haloes – I. A numerical convergence study

By C. Power, J. Navarro, Adrian Jenkins, Carlos S. Frenk, Simon D. M. White, Volker Springel, Joachim Stadel, Thomas R. Quinn. 2002

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We present a comprehensive set of convergence tests which explore the role of various numerical parameters on the equilibrium structure of a simulated dark matter halo. We report results obtained with two independent, state-of-the-art, multi-stepping, parallel N–body codes: PKDGRAV and GADGET. We find that convergent mass profiles can be obtained for suitable choices of the gravitational softening, timestep, force accuracy, initial redshift, and particle number. For softenings chosen so that particle discreteness effects are negligible, convergence in the circular velocity is obtained at radii where the following conditions are satisfied: (i) the timestep is much shorter than the local orbital timescale; (ii) accelerations do not exceed a characteristic acceleration imprinted by the gravitational softening; and (iii) enough particles are enclosed so that the collisional relaxation timescale is longer than the age of the universe. Convergence also requires sufficiently high initial redshift and accurate force computations. Poor spatial, time, or force resolution leads generally to systems with artificially low central density, but may also result in the formation of artificially dense central cusps. We have explored several adaptive time-stepping choices and obtained best results when individual timesteps are chosen according to the local acceleration and the gravitational softening (�ti / (ǫ/ai) 1/2 ), although further experimentation may yield better and more efficient criteria. The most stringent requirement for c is typically that imposed on the particle number by the collisional relaxation criterion, which implies that in order to estimate accurate circular velocities at radii where the density contrast may reach � 10 6 , the region must enclose of order 3000 particles (or more than a few

Subfields: Astronomy and Astrophysics, Instrumentation

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Citations in the corpus

Linking early‐ and late‐type galaxies to their dark matter haloes (2002, background): “This halo model has become more and more accurate due to the fact that detailed analytical descriptions for the structure and clustering of dark matter haloes have become available (e.g., Navarro, Frenk & White 1997; Moore et al. 1998; Bullock et al. 2001; Mo & White 1996, 2002; Power et al. 2002).”
Forged in FIRE: cusps, cores and baryons in low-mass dwarf galaxies (2015, background): “According to well-documented convergence test studies (Power et al. 2003), many previous simulations that have reported core formation on this scale were quite poorly resolved, some at only ∼ 2 − 3 softening lengths.”
The statistics of lambda CDM Halo Concentrations (2007, methodology): “We have therefore compared the potential centre with the result of the “shrinking sphere” algorithm (Power et al. 2003), which is intended to converge towards the density maximum of the most massive substructure, independent of the SUBFIND algorithm.”
Galaxy-induced transformation of dark matter haloes (2009, methodology): “This re-simulation technique follows standard practice, as described, for example, by Power et al. (2003).”
Cold dark matter haloes in the Planck era: evolution of structural parameters for Einasto and NFW profiles (2014, background): “Power et al. (2003) give a number of convergence criteria for N-body simulations.”
Dark matter annihilation in the halo of the Milky Way (2003, methodology): “This subject is still controversial, although the most detailed convergence study to date agrees quite well with our results for the centre of the main halo (Power et al. 2003).”
The unexpected diversity of dwarf galaxy rotation curves (2015, methodology): “Our simulations thus show 4 We adopt in all cases the ‘convergence radius’ introduced by Power et al. (2003), as computed from the DMO simulations.”
The upper bound on the lowest mass halo (2016, methodology): “The softening lengths were selected using the criteria in Power et al. (2003).”
The Formation of a Realistic Disk Galaxy in Λ-dominated Cosmologies (2002, methodology): “Integration parameter values were chosen as suggested in Moore et al. (1998) and then confirmed in Power et al. (2002).”
The formation of disc galaxies in high-resolution moving-mesh cosmological simulations (2013, background): “We note that these softening values follow the optimum choices derived by Power et al. (2003).”