Mapping the Distorted Dark Matter Distribution of the LMC-SMC System Prior to Milky Way Infall with Basis Function Expansions

Abstract

The SMC orbits within the LMC's dark matter (DM) halo in a $\sim$1:10 mass-ratio encounter. The LMC:Milky Way (MW) interaction is also $\sim$1:10, and is expected to perturb the MW's DM distribution. However, no framework exists to quantify the severity of these perturbations over multiple pericenters and longer periods of time, such as the LMC-SMC interaction history. We construct basis function expansions of a high-resolution \textit{N}-body simulation of the Clouds interacting in isolation and analyze their DM distributions at an epoch approximating the time of their infall to the MW. Our goal is to quantify how the Clouds distort each other's DM distributions \textit{without} the MW. The LMC halo's response to the SMC includes a $\sim 20$ kpc long dynamical friction wake and the displacement of the LMC's density center during each SMC pericenter, which produces two overdensities in the LMC halo (at $\sim$60 and $\sim$100 kpc) at MW infall. The SMC's tidal radius at infall is just $\sim4$ kpc, at which point the SMC has lost two-thirds of its initial DM mass to the LMC. The distortions to the Clouds' halos produce a highly asymmetric acceleration field. Accurate orbit integration in the LMC-SMC system must account for the time-dependent shapes of both halos. The SMC-induced perturbations in the LMC DM halo resemble the MW-LMC system, and persist over multiple SMC pericenters. We conclude that 1:10 satellite-host encounters induce characteristic deformations in both DM halos across host-mass scales, with implications for merger rates and tests of DM models.

Figures (21)

• Figure 1: Comparison of the SMC's orbit about the LMC in the simulation by besla_role_2012 (dashed line) vs. the simulation used in this work (H. Rathore et al. in prep; solid line). Orbits are plotted as the distance between the LMC and SMC centers ($d_{SMC-LMC}$) as a function of simulation time. The latest time considered in this work is $t=5.77$ Gyr (dotted vertical line), which corresponds to the time the LMC and SMC are introduced into the MW in Model 2 of besla_role_2012. At this time, the SMC is approaching its third pericenter passage with the LMC.
• Figure 2: Error in each expansion (LMC, SMC, Bound SMC) with respect to the particle density as a function of the truncation order, $n_{max}$ and $l_{max}$, calculated at the MW infall snapshot. A red x shows the value of $n_{max}$ and $l_{max}$ where the error is minimized (see Table \ref{['tab:expansions']}). Left Panel: The LMC Expansion is truncated according to MIRSE (Equation \ref{['eqn:MIRSE']}) at $(n_{max}, l_{max}) = (17, 10)$. Center Panel: The SMC Expansion is truncated at $(n_{max}, l_{max}) = (17, 10)$ according to an MIRSE minimization. Right Panel: The Bound SMC Expansion is constructed to minimize MISE (Equation \ref{['eqn:MISE']}) to prioritize the reconstruction of the high-density inner halo, resulting in a truncation order of $(n_{max}, l_{max}) = (12, 5)$.
• Figure 3: BFE-reconstructed density fields of the isolated LMC-SMC system (no MW) at MW infall. Density fields are plotted in the SMC's orbital plane about the LMC. The locations of the LMC and SMC centers are marked with an x and dot, respectively. The SMC's past orbit is marked with a solid line. Panels (a)-(e) share the same contour scale. (a) The density field of the entire system (c + d). The DM distribution of the LMC-SMC system is distorted at MW infall, exhibiting nonspherical isodensity contours. (b) The sum of the LMC Expansion and Bound SMC Expansion (c + e). The asymmetry in the combined DM distribution at negative x is due to the SMC's extended debris field (see panel (d)). (c) The LMC Expansion. The LMC halo deviates from sphericity due to perturbations from the SMC (see panel (f)). (d) The SMC Expansion. The SMC's debris extends to $\sim100$ kpc from the LMC's center. (e) The Bound SMC Expansion. The SMC's halo is tidally elongated by the LMC over multiple pericenters. (f) The density contrast of the LMC Expansion (panel (c)) computed with respect to the $n=0$, $l=0$ term (see equation \ref{['eqn:odens']}). Perturbations to the LMC's halo induced by the SMC include a dynamical friction wake and two overdensities (at $\sim$60 and $\sim$100 kpc). The overdensities result from the LMC's density center displacement after the SMC's second and third pericenter passages. This figure is comparable to Figure 1 of garavito-camargo_quantifying_2021) for the LMC-MW system. The SMC's wake at MW infall is roughly twice as strong (peak contrast of $\sim 0.4$) as the LMC's wake in an isotropic MW at present-day ($\sim$0.2; garavito-camargo_hunting_2019).
• Figure 4: Density contrast (see Equation \ref{['eqn:odens']}) of the LMC Expansion (no SMC expansion is included) at MW infall for different choices of the maximum expansion order in radial ($n_{max}$; varies between rows) and harmonic ($l_{max}$; varies between columns) terms. The LMC's center is marked with an 'x.' Increasing the radial (harmonic) order of the expansion captures more radial (azimuthal) variations in the density field. The density center displacement from the SMC's third pericenter passage (Inner Overdensity) is captured by the $l=1$ terms. Higher harmonics ($l\geq2$) capture the Outer Overdensity from the density center displacement during the second SMC pericenter and the SMC's wake. Truncating the expansion at $n_{max}=17$ and $l_{max}=10$ accurately recovers the peak amplitudes of the perturbations (see Figure \ref{['fig:MIRSE']}); this is the fiducial expansion order for the LMC in this study.
• Figure 5: Gravitational power ($P_l$; equation \ref{['eqn:power']}) in the first five harmonic orders of the LMC Expansion (no SMC) as a function of time. Top panel: the log power in each harmonic. Center panel: the power in each harmonic normalized by the power in the monopole terms ($l=0$). Bottom panel: the distance between the LMC and SMC centers ($d_{SMC-LMC}$) as a function of time, with pericenter times (at $t=0.44$ and $4.15$ Gyr) marked by dotted lines. MW infall is at the right edge of the plot. The SMC induces a spike in the LMC's dipole ($l=1$) power after each pericenter (marked by dot-dashed lines), which is a characteristic signature of the motion of the inner LMC halo owing to the displacement of the LMC density center. Following the first (second) peak, the dipole power decays exponentially with a decay timescale of 920 (300) Myr, before being reexcited by the SMC during a subsequent pericenter passage. In contrast, quadrupole and higher terms ($l\geq2$), which build up the SMC's wake (see Figure \ref{['fig:odens_orders']}), peak at each SMC pericenter. These $l\geq2$ terms remain elevated compared to the start of the simulation, indicating that the wake persists throughout, despite its variations in strength tied to the SMC's orbit.