The mass distribution in and around the Local Group

Abstract

Our Galaxy, Andromeda and their companion dwarf galaxies form the Local Group. Most of the mass in and around it is believed to be dark matter rather than gas or stars, so its distribution must be inferred from the effect of gravity on the motion of visible objects. Modelling efforts have long struggled to reproduce the quiet Hubble flow around the Local Group, as they require unrealistically little mass beyond the haloes of the two main galaxies. Here we revisit this using $Λ$CDM simulations of Local Group analogues with initial conditions constrained to match the observed dynamics of the two main haloes and the surrounding flow. The observations are reconcilable within $Λ$CDM, but only if mass is strongly concentrated in a plane out to 10 Mpc, with the surface density rising away from the Local Group and with deep voids above and below. This configuration, dynamically inferred, mirrors known structures in the nearby galaxy distribution. The resulting Hubble flow is quiet yet strongly anisotropic, a fact obscured by the paucity of tracers at high supergalactic latitude. This flattened geometry reconciles the dynamical mass estimates of the Local Group with the surrounding velocity field, thus demonstrating full consistency within the standard cosmological model.

Figures (7)

• Figure 1: Hubble diagram for the isolated galaxy sample used to trace the velocity field beyond the Local Group. Error bars indicate $1\sigma$ measurement uncertainties on the observed distances and velocities. These velocities, together with the masses, relative positions and motions of the M31 and MW haloes, were used to constrain the initial conditions of a representative ensemble of 169 simulations of the Local Group (ref. wempeConstrainedCosmologicalSimulations2024; labelled W24 in the legend) within the $\Lambda$CDM paradigm. The orange line shows the mean velocity--distance relation for this ensemble. The green line shows the relation obtained from a spherical infall model based on the mean mass profile $M(r)$ of this same ensemble. Shaded regions represent the 16th to 84th percentiles of the simulation-to-simulation scatter (the posterior scatter). Clearly, the two curves are not consistent.
• Figure 1: Anisotropic local Hubble flow and effects of tracer positions. Expanded Hubble diagram showing line-of-sight recession velocity relative to the Local Group barycentre as a function of distance. As in \ref{['fig:hubblediagram']}, blue points are the 31 isolated galaxies used to constrain the local flow and the orange curve shows the mass-weighted mean radial velocity of all matter in the constrained simulation ensemble, with the bands showing the rms scatter between realizations. The red curve shows the mass-weighted velocity-distance relation for material lying in the sheet (defined as $\abs{z}<1Mpc$). It lies close to (but slightly above) the orange curve which gives the same quantity for all matter. The purple curve gives the corresponding relation for high-latitude material ($\abs{b}>45$ deg) and is very different, particularly at larger distances where the differences in recession velocity reach ∼100km.s^-1. This substantial anisotropy of the infall velocity field is also evident in the flow field shown in \ref{['fig:velocityfield']} where infall is directed primarily towards the Local Sheet, rather than towards the Local Group. To validate our results in light of the anisotropic sky distribution of our tracer population, we performed a mock inference in which tracer galaxy velocities were replaced by predictions from a spherical model using the mean mass profile $M(r)$ (the green line, identical to \ref{['fig:hubblediagram']}'s spherical model). The resulting mock ensemble's velocity profile is the brown line, which matches the original ensemble (the orange line) at small radii but approaches the spherical model beyond 1Mpc. The grey line shows a spherical model using the $M(r)$ of the mock inference, which matches that of the original inference. Thus, despite the highly anisotropic distribution of tracers, our inference scheme correctly reproduces $M(r)$ when the underlying mass distribution is, in fact, spherical.
• Figure 2: Various projections of the posterior mean density of the constrained simulation ensemble, normalized by the cosmic mean density, $\overline{\rho}$. The coordinate system is centred on the MW, such that $x$ is along the MW--M31 axis, $y$ is towards increasing declination and $z$ is towards increasing right ascension at the position of M31. Upper left: the density in cylindrical coordinates azimuthally averaged around the $z$ axis with a few representative contours (these were drawn after smoothing with a 40kpc Gaussian filter). Lower left: a projection along the $z$ axis of a slice of depth 8Mpc ($\abs{z} < 4Mpc$). The right panels show the remaining two orthogonal projections, each corresponding to a central slice of depth 8Mpc. White dots indicate the locations of the isolated galaxies used as flow tracers. The white cross indicates the location of the Virgo cluster. No clear overdensity is seen in this direction, and we explicitly checked for any signal with respect to azimuthal angle $\phi - \phi_\text{Virgo}$, finding nothing. This is consistent with the fact that the mean infall to Virgo is removed in the velocity frame of our simulations and that tidal effects due to Virgo should be relatively small over the $<4Mpc$ region where we have included constraints. The density visualizations use a Lagrangian sheet interpolation scheme (Methods).
• Figure 2: Posterior mean density field in a spherical mock inference. Posterior mean matter density field (like \ref{['fig:sheet']}) for the mock ensemble of simulations where all constraints were the same except that the flow tracer velocities were replaced by predictions from a spherical model with the same $M(r)$. This posterior mean field is estimated from 117 simulations homogeneously sampled from the HMC chains. Unlike the results in \ref{['fig:sheet']}, this mock posterior mean field exhibits no clear preferred plane or sheet-like mass concentration, confirming that the sheet-like structure inferred from the real data is driven by the observed kinematics. Interestingly, the posterior density fields obtained from this mock dataset are not fully isotropic; despite tracer velocities being assigned spherically, a significant asymmetry remains between the $+z$ and $-z$ directions. We suspect this is due to the only constraint that breaks the $\pm z$ symmetry: M31's tangential velocity. This requires an appropriate torque from external matter. A quadrupolar matter distribution with the right orientation is visible about $8Mpc$ from the centre (e.g., top right panel), suggesting it accommodates the tangential constraint when the Local Sheet is absent. The isotropic expansion of observed tracers in both sets of chains is presumably inconsistent with the in-plane quadrupole needed to generate M31's observed $y$-component proper motion, which is not fully reproduced in either case.
• Figure 3: Azimuthally averaged density as a function of height $z$ within thick cylindrical shells centred at the MW--M31 barycentre. Here $R = \sqrt{x^2 + y^2}$ and the $z$-axis is the simulation axis most nearly perpendicular to the Local Sheet.