Constraining the Inner Dark-Matter Slope of Sculptor: A Comparative Analysis of Dynamical Methods
Abstract
The core-cusp problem is a discrepancy between simulations and observations of the slopes of inner dark matter density profiles. Splitting dwarf spheroidals by metallicity is a standard method to break the mass-anisotropy degeneracy. Four dynamical methods are applied to the 1339-star Tolstoy et al. (2023) VLT/FLAMES Sculptor catalog: spherical Jeans, GravSphere, the Walker and Peñarrubia (2011) two-population estimator, and a continuous f(J,[Fe/H]) action-based distribution function. This work finds Γ=2.49+0.23−0.20, with 99.6\% of the posterior lying above Γ=2 (84.4\% after λ calibration), robust to membership cuts and metal-poor contamination; GravSphere gives γ=0.46+0.40−0.28. Controlled mocks that hold tracer geometry fixed while breaking the metallicity-kinematics link attribute ∼77--83% of the recovered bias to geometry rather than decomposition itself. The continuous distribution function encodes a metallicity--action coupling kJ inaccessible to any split-based method; a direct action-space computation on 575 stars with Gaia proper motions finds [Fe/H] declining by ∼0.3 dex across three decades in radial action. On the central-density diagnostic of Read et al. (2019), the same posteriors give ρDM(150 pc)=1.77×108 M⊙ kpc−3, agreeing with their independent Sculptor measurement at 0.74σ and placing Sculptor in their cusp-like class. The shallow γ of this work is an asymptotic quantity; the local slope at 150 pc is consistent with the Navarro--Frenk--White profile under the spherical models used here, though a recent axisymmetric analysis using resolved 3D velocities finds a shallow slope over that range and identifies an inclination degeneracy to which spherical models are blind.
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BibTeX
@misc{sanjeev2026constraining,
title = {{Constraining the Inner Dark-Matter Slope of Sculptor: A Comparative Analysis of Dynamical Methods}},
author = {Rishi Sanjeev},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.23618},
eprint = {2608.23618},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.23618},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constraining the Inner Dark-Matter Slope of Sculptor: A Comparative Analysis of Dynamical Methods
AU - Rishi Sanjeev
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2608.23618
UR - https://arxiv.org/abs/2608.23618
AB - The core-cusp problem is a discrepancy between simulations and observations of the slopes of inner dark matter density profiles. Splitting dwarf spheroidals by metallicity is a standard method to break the mass-anisotropy degeneracy. Four dynamical methods are applied to the 1339-star Tolstoy et al. (2023) VLT/FLAMES Sculptor catalog: spherical Jeans, GravSphere, the Walker and Peñarrubia (2011) two-population estimator, and a continuous f(J,[Fe/H]) action-based distribution function. This work finds Γ=2.49^+0.23_−0.20, with 99.6\% of the posterior lying above Γ=2 (84.4\% after λ calibration), robust to membership cuts and metal-poor contamination; GravSphere gives γ=0.46^+0.40_−0.28. Controlled mocks that hold tracer geometry fixed while breaking the metallicity-kinematics link attribute ∼77--83% of the recovered bias to geometry rather than decomposition itself. The continuous distribution function encodes a metallicity--action coupling k_J inaccessible to any split-based method; a direct action-space computation on 575 stars with Gaia proper motions finds [Fe/H] declining by ∼0.3 dex across three decades in radial action. On the central-density diagnostic of Read et al. (2019), the same posteriors give ρ_DM(150 pc)=1.77×10^8 M_⊙ kpc^−3, agreeing with their independent Sculptor measurement at 0.74σ and placing Sculptor in their cusp-like class. The shallow γ of this work is an asymptotic quantity; the local slope at 150 pc is consistent with the Navarro--Frenk--White profile under the spherical models used here, though a recent axisymmetric analysis using resolved 3D velocities finds a shallow slope over that range and identifies an inclination degeneracy to which spherical models are blind.
ER -