Models of distorted and evolving dark matter haloes

Abstract

We investigate the ability of basis function expansions to reproduce the evolution of a Milky Way-like dark matter halo, extracted from a cosmological zoom-in simulation. For each snapshot, the density of the halo is reduced to a basis function expansion, with interpolation used to recreate the evolution between snapshots. The angular variation of the halo density is described by spherical harmonics, and the radial variation either by biorthonormal basis functions adapted to handle truncated haloes or by splines. High fidelity orbit reconstructions are attainable using either method with similar computational expense. We quantify how the error in the reconstructed orbits varies with expansion order and snapshot spacing. Despite the many possible biorthonormal expansions, it is hard to beat a conventional Hernquist-Ostriker expansion with a moderate number of terms (≳ 15 radial and ≳ 6 angular). As two applications of the developed machinery, we assess the impact of the time-dependence of the potential on (i) the orbits of Milky Way satellites, and (ii) planes of satellites as observed in the Milky Way and other nearby galaxies. Time evolution over the last 5 Gyr introduces an uncertainty in the Milky Way satellites’ orbital parameters of ∼15 per cent, comparable to that induced by the observational errors or the uncertainty in the present-day Milky Way potential. On average, planes of satellites grow at similar rates in evolving and time-independent potentials. There can be more, or less, growth in the plane’s thickness, if the plane becomes less, or more, aligned with the major or minor axis of the evolving halo.

Uncertainties associated with the backward integration of dwarf satellites using simple parametric potentials

“…On the other hand, they neglect any clumpiness, triaxility, twistedness and possible rotation of the halo. It has been recently demonstrated that high fidelity orbit reconstruction can be obtained by modelling the changing complex potential of a simulated isolated MW-mass galaxy using a multipole expansion at ∼100 Myr temporal resolution (Sanders et al 2020). The recent passage of a massive accreted satellite complicates the situation further due to the resonances induced in the central DM halo: large transient density and kinematic perturbations (Choi et al 2009) are produced, creating the classical 'conic' wake trailing the satellite (Chandrasekhar 1943) as well as a collective response to the system as a whole (Garavito-Camargo et al 2019) and leading to a temporary change in the concentration of the halo (Wang et al 2020).…”

“…This ensures that the centre of the MW-mass host is never more than 60 kpc away from the centre of the reference frame, allowing for great accuracy in our backward integrations in the adopted cylindrical coordinate system. We account for the fictious forces arising from our choice of the non-inertial reference frame (Sanders et al 2020). That is the total force on a test particle is…”

“…Recently a few attempts have been made to move beyond simple parametric models and characterise through basis function expansions the evolution of a simulated isolated MW-mass halo (Sanders et al 2020) or a MW-mass halo which suffered a recent massive accretion (Cunningham et al 2020;Garavito-Camargo et al 2020). Sanders et al (2020) have demonstrated that they can achieve high fidelity orbit reconstruction of the orbits of subhaloes in the case of an isolated MW-mass halo using at least 15 radial and 6 angular terms in the basis expansion and a ∼ 100Myr temporal resolution. Since constraining the coefficients of the basis functions of a real life situation like that of the MW and the LMC is an ardous task, most works resort to simple parameteric models of the potential for their convenience.…”

Constraining the Milky Way halo kinematics via its Linear Response to the Large Magellanic Cloud

“…To proceed forward, we follow Kalnajs (1977) who undertook a projection of all perturbed quantities onto a bi-orthogonal basis of potentials and densities. This practice gained a renewed interest in recent years (see, e.g., Garavito-Camargo et al 2021a;Sanders et al 2020) for its ability to solve the Poisson equation by construction, allowing for more natural reconstructions of the gravitational potential in simulations. In the context of linear response theory, this technique can also be used to solve the Poisson equation, while the CBE is transformed into an integral equation in a linear space.…”

Study of the Influence of an Evolving Galactic Potential on the Orbital Properties of 152 Globular clusters with Data from the Gaia EDR3 Catalogue

“…There exist a multitude of scenarios to explain the physical processes of the evolution of galaxies that reproduce well their observed properties. There are a number of papers (Gómez et al 2010;Correa et al 2015;Haghi et al 2015;Sanders et al 2020;Armstrong et al 2021) where various time-dependent model gravitational potentials based on cosmological models of the Universe were used to study the orbital history of Galactic objects. Only a change in the masses of the Galactic potential components are considered in some papers (see, e.g., Armstrong et al 2021); both a change in the masses and a change in the sizes of the components are considered in other papers (Gómez et al 2010;Haghi et al 2015).…”