Phase_Space_Evolution_of_a_Substellar_Thick_Disk__Dark_Matter_Constraints__the_Collisional_Paradox__and_Observational_Forecasts.pdf

A recent hypothesis proposes that macroscopic interstellar objects (ISOs) could account for up to45% of the locally inferred dark matter budget. Here, a heuristic collisional constraint is introduced toevaluate the physical viability of this scenario. The required ISO number density is found to generatean integrated optical depth that introduces a severe physical tension when cross-referenced with thecontinuous telemetry maintained by deep-space heliopause probes, specifically Voyager 1, Voyager 2,and New Horizons, rendering the high-density ISO scenario inconsistent with empirical observations ata > 3σ confidence level. To resolve this collisional paradox, the galactic-scale spatial distribution andobservational signatures of an orbitally diffused, baryonic substellar population comprising free-floatingplanets (FFPs) and brown dwarfs (BDs) are modeled. Utilizing GPU-accelerated forward orbit integrationsof 2×108 particles over an 11 Gyr baseline within a realistic Galactic potential, it is demonstratedthat the vertical phase mixing of this population, initialized with system-ejection velocity dispersions,naturally establishes a thick-disk configuration. This evolved state is characterized by a vertical scaleheight of z0 ≈ 0.439 kpc and a vertical velocity dispersion of σz = 39.55 km/s at the solar radius. Subsequently,a 30,000-step Markov Chain Monte Carlo (MCMC) optimization framework is applied to fitthe Gaia DR3 Milky Way rotation curve under a physically anchored Gaussian prior on the substellarcentral normalization (σprior = 0.1 dex). Rather than measuring a direct alteration to the dark matterhalo, the inclusion of this kinematically relaxed substellar component quantifies a physically-allowedlocal baryonic reallocation fraction of Y = 1.21%+0.08%−0.07% within the local Galactic potential, whichtranslates to a complementary local baryonic mass density allocation of ∼ 8 × 10−4M⊙ pc−3. Thisstructural mass reallocation is highly decoupled from halo modeling uncertainties, remaining stableacross NFW, Einasto, and Burkert configurations (Y ∈ [1.15%, 1.32%]), and varies by only a factor of1.6 across a factor of 3.6 range in thick-disk vertical scale heights. Furthermore, the integrated thermalemission from this ancient, cold population (Teff ∼ 700 K) peaks at a monochromatic wavelength ofλpeak = 4.14 μm, contributing a monochromatic surface brightness of 0.143nWm−2 sr−1, or 1.43% ofthe absolute COBE/DIRBE 12 μm sky brightness limit. While this diffuse signature operates belowcurrent foreground confusion floors, spatial anisotropy mapping and angular power spectrum analysesvia upcoming wide-field space surveys present testable expectations and qualitative predictions toestablish independent empirical upper limits on the local substellar mass budget.