Astrophysical Dark Matter Populations

• Astrophysical DM populations are hierarchically structured, gravitationally bound systems that include halos, subhalos, and solitonic cores with diverse density profiles.
• They exhibit measurable kinematic and morphological features influenced by baryonic feedback and non-standard DM models, offering critical constraints on dark matter physics.
• Advanced simulations and machine learning emulators integrate observational probes to enhance our understanding of DM across scales from dwarf galaxies to high-redshift minihalos.

Astrophysical dark matter (DM) populations encompass the hierarchically organized, gravitationally bound systems and diffuse backgrounds where non-baryonic DM structures manifest, interact with baryons, and inform both indirect detection strategies and cosmological inference. These populations include halos from subgalactic to cluster scales, substructure systems such as subhalos and tidal debris, cored and cusped density distributions, as well as DM in exceptional environments (e.g., early Universe minihalos, solitonic cores in alternative DM theories, or high-redshift intergalactic medium traced by Ly-α absorption). Their spatial distributions, internal kinematics, and density morphologies encode both primordial physics and astrophysical processes (e.g., baryonic feedback), providing critical constraints for particle DM scenarios, structure-formation paradigms, and indirect or stellar-based detection efforts.

1. Dark Matter Halo Populations and Internal Structure

Astrophysical DM populations are dominated by halos spanning $\sim10^8$–$10^{15}\,M_\odot$, encompassing dwarf spheroidal galaxies (dSphs), Milky Way–scale systems, and galaxy clusters (Anbajagane et al., 2021). The canonical Cold Dark Matter (CDM) paradigm predicts a continuous halo mass function, resulting from hierarchical assembly. Key properties of these halos include:

• Density profile ($\rho(r)$): For dSphs and the Galactic Center (GC), generalized Navarro–Frenk–White (gNFW) and Einasto forms describe $\rho(r)$; the gNFW form

$$\rho(r) = \rho_s \left(\frac{r}{r_s}\right)^{-\gamma} \left(1 + \frac{r}{r_s}\right)^{\gamma-3},$$

where $r_s$ is the scale radius and $\gamma$ the inner slope, interpolates between cored and cusped behaviors (Zitzer, 2015). Clusters similarly obey NFW/Einasto scaling, with baryonic feedback introducing non-monotonic features ("wiggles") in mass-dependent profiles (Anbajagane et al., 2021).

• Subhalo and satellite populations: The subhalo mass function in MW-mass systems follows power-law scaling with an exponential cutoff,

$$N(>M_{\mathrm{sub}}) \approx N_0\left(\frac{M_{\mathrm{sub}}}{M_{\rm cut}}\right)^{-\alpha}e^{-M_{\mathrm{sub}}/M_{\rm cut}},$$

with $\alpha\approx0.9$ (CDM) and normalization $N_0=30$–$50$ at $M_h=1.6\times10^{12}\,M_\odot$ (Nguyen et al., 4 Sep 2024). Warm DM (WDM) and baryonic feedback modulate the abundance and inner concentration of subhalos, with WDM steepening the slope and reducing normalization (Nguyen et al., 4 Sep 2024, Valluri et al., 2022).

• Solitonic cores and granular halos: In fuzzy/wave DM ($\psi$DM) scenarios, halos exhibit a universal soliton core (density scaling $\rho_{sol}\propto r_c^{-4}$, mass–radius relation $M_c\propto r_c^{-1}$) surrounded by a granular, interference-dominated halo. Stars further reshape soliton prominence and halo granularity (Chan et al., 2017).

2. Population Morphologies and Kinematic Diagnostics

Halo morphologies and internal kinematics are critical to distinguishing DM models and feedback impacts:

• Shape and triaxiality: Simulations report density-space minor-to-major axis $s_\rho$ distributed around 0.6 in CDM. Inclusion of baryonic processes mildly rounds halos ($s_\rho$ increases by $\sim$5% near $10^{12}\,M_\odot$), and self-interactions in SIDM or soliton–star coupling in $\psi$DM can further enforce sphericity (Anbajagane et al., 2021, Valluri et al., 2022, Chan et al., 2017).
• Velocity structure: The 3D dispersion ($\sigma_v$), projected LOS/PM dispersions, and $\beta(r)$ anisotropy encode internal dynamics. For dSphs such as Sculptor, $\beta$ transitions from isotropic (core) to radially biased (outskirts) orbits, harmonizing with collisionless DM plus feedback mixing (Polonio et al., 13 Jun 2025). In $\psi$DM, soliton-induced potentials generate central LOS dispersions exceeding standard CDM+stars predictions (Chan et al., 2017).
• Composite density and phase-space segregation: In $\psi$DM with baryons, the composite density around the half-light radius approximates $\rho_{\rm tot}\propto r^{-2}$. Compact baryonic distributions can trigger phase-segregated stellar populations— a dynamically cold cluster in the soliton core and a hot halo component (Chan et al., 2017).

3. Methods for Population Characterization and J-Factor Calculations

Astrophysical DM populations are probed via both semi-analytical fits and direct simulation-driven estimators:

• Semi-analytical approaches: Profiles are fit (e.g., NFW, Einasto) to simulation or stellar-kinematic data, with J-factors computed as

$$J(\Delta\Omega) = \int_{\Delta\Omega} d\Omega \int_{\rm l.o.s.} dl \; \rho^2(r(l,\Omega)),$$

where $\Delta\Omega$ is the observed aperture (Zitzer, 2015, Polonio et al., 13 Jun 2025). For annihilation, $d\Phi_\gamma/dE\propto \langle\sigma v\rangle J$.

• Direct numerical mapping (NAJADS): The NAJADS framework reconstructs $\rho(\vec{x})$ from raw N-body particle data using a nearest-neighbor volume estimator and numerically integrates $J(\psi)$ along the line of sight, natively handling asphericity, triaxiality, and resolved substructure. Deviations from fitted, spherically averaged J-factors can reach $\mathcal{O}(300\%)$ in realistic triaxial halos, highlighting the limitations of analytical models in the presence of lopsidedness and tidal debris (Balaudo et al., 2021).
• Emulation and machine learning: Recent diffusion-model frameworks (e.g., NeHOD) generate full populations of halos and subhalos—including spatial, mass, and concentration distributions—by learning from large suites of hydrodynamic simulations, capturing parameter dependencies on DM physics and feedback (Nguyen et al., 4 Sep 2024).

4. Population Variations Across Environments and Models

Astrophysical DM populations exhibit pronounced, model-dependent variations:

• Dwarf spheroidals: Exemplified by Sculptor, two chemically distinct stellar populations map onto a DM density with inner slope $\gamma=0.39^{+0.23}_{-0.26}$, $r_s=0.79^{+0.38}_{-0.17}$ kpc, and DM-to-stellar mass ratio $\sim$13 at $r_h$. This inner slope is $\sim0.6$ shallower than the pure NFW $\gamma=1$, at $\gtrsim3\sigma$ significance, signaling baryonic core-formation (Polonio et al., 13 Jun 2025).
• MW-galaxy and cluster scales: At $M\sim10^{12}\,M_\odot$, inclusion of baryons increases the NFW concentration normalization $A_c$ by $\sim$25%, and velocity-dispersion normalization $A_\sigma$ by $8\%$; these “wiggles” arise from varied feedback (SN, SMBH) energetics at different mass thresholds (Anbajagane et al., 2021). Warm and self-interacting DM variants suppress low-mass substructures and soften central cusps (WDM/FDM: exponential decline in SHMF below $M_{hm}\sim10^7$–$10^{10}\,M_\odot$) (Valluri et al., 2022, Nguyen et al., 4 Sep 2024).
• High-z minihalos and first stars: Pop III stars form at $z\sim15$ in $10^6\,M_\odot$ minihalos with dense contracted DM; their observed mass can constrain DM-baryon cross sections to limits beyond the “neutrino floor,” with adiabatic contraction predicting core DM densities $\rho_X\sim10^{13}$–$10^{16}$ GeV/cm$^3$ (Ilie et al., 2020).

5. Observational Implications and Detection Strategies

Astrophysical DM populations intersect indirect particle searches and structural tests:

• Indirect detection: J-factor accuracy (mapping $\int \rho^2 ds$ for annihilation, $\int \rho ds$ for decay) is essential for gamma-ray experiments. dSphs provide “clean” targets (e.g., $J_{\rm Segue\;1}\sim10^{19.4}$ GeV$^2$ cm$^{-5}$, $J_{\rm Sculptor}=10^{18.15}$ GeV$^2$ cm$^{-5}$ at $0.5^\circ$), with constraints sensitive to both density profile systematics and modeling uncertainties (Zitzer, 2015, Polonio et al., 13 Jun 2025). J-factor uncertainties from asphericity, boost, or substructure can be substantial, requiring full 3D simulation-based approaches (Balaudo et al., 2021).
• Kinematic and lensing probes: Stacked LOS velocity dispersions, weak lensing (c(M), mass–concentration relation), and strong lensing (central density, subhalo perturbations) map the mass-dependent effects of feedback on DM population properties (Anbajagane et al., 2021, Valluri et al., 2022).
• Stellar streams and phase-space mapping: Tidal streams (e.g., Pal 5, GD-1) constrain dark subhalos via gap statistics; 6D phase-space data (DESI, Gaia) quantifies halo triaxiality ($c/a$), velocity anisotropy $\beta(r)$, and outer halo properties down to $\sim10^7\,M_\odot$ subhalo mass scales (Valluri et al., 2022).
• Exotic populations and dynamical signatures: Soliton cores in $\psi$DM and low-velocity dispersion clusters can produce central dynamical effects (e.g., $\sigma_{\rm LoS}$ rises by a factor of $\gtrsim2$ inside $r_{1/2}$), potentially distinguishable from CDM or baryon-driven cusps via high-resolution spectroscopy (Chan et al., 2017).

6. Feedback, Core Formation, and Outlier Environments

Baryonic feedback modulates population statistics and central density structure:

• Core–cusp transitions: Explosive feedback (e.g., supernovae) in galaxies at specific $M_\star/M_{\rm halo}$ ratios ($\sim5\times10^{-3}$ in Sculptor) can transform NFW cusps into $\sim r_h$-sized cores, softening the inner profile and affecting indirect-detection J-factors (Polonio et al., 13 Jun 2025).
• Mass-dependent "wiggles": At dwarf ($\lesssim10^{11}\,M_\odot$), MW ($\sim10^{12}\,M_\odot$), and group/cluster scales ($\gtrsim10^{13}\,M_\odot$), transitions in cooling vs. feedback dominance imprint systematic deviations in concentration, $\sigma_v$, and formation time distributions—observable as non-monotonic features in stacked populations and scaling relations (Anbajagane et al., 2021).
• High-$z$, high-density systems: In Pop III–hosting minihalos, the dark sector directly limits stellar mass via DM annihilation energy deposition and the Eddington limit, enabling cross-calibration of direct and astroparticle detection regimes (Ilie et al., 2020).

7. Simulation, Emulation, and Future Prospects

Robust characterization of DM populations depends on advances in simulation and data integration:

• Large-scale cosmological and zoom-in suites: Projects such as IllustrisTNG provide $>10^6$ halos across $z=0\textrm{--}12$ with public halo property catalogs and allow extraction of population statistics (KLLR methodology, variance-covariance matrices) for model comparison and machine learning applications (Anbajagane et al., 2021, Nguyen et al., 4 Sep 2024).
• Full-physics and alternative DM models: Simulation suites now explore parameter spaces in SIDM, WDM, and FDM, although comparably deep public datasets for these scenarios remain limited (Valluri et al., 2022).
• Emulator frameworks: NeHOD and related diffusion-model-based emulators enable rapid, differentiable population synthesis for survey forecasting, capturing the feedback and DM-model–dependent modulations in subhalo distributions, concentrations, and clustering (Nguyen et al., 4 Sep 2024).
• Multi-modal observational synergy: Next-generation spectroscopic (DESI), astrometric (Gaia, Roman HLS), and imaging (LSST) surveys, combined with synthetic mock catalogs and 6D phase-space mapping, will test the concordance of DM population statistics with theoretical predictions, including the breakdown scale of $\Lambda$CDM, the role of feedback in shaping DM structure, and the parameter space of viable non-CDM models (Valluri et al., 2022).

Astrophysical DM populations, through their multi-scale, multi-morphology structure, remain central to the ongoing effort to unravel the microphysical nature, gravitational dynamics, and cosmological role of dark matter.