[Paper Review] A quantitative comparison between velocity dependent SIDM cross sections constrained by the gravothermal and isothermal models

Shengqi Yang, Fangzhou Jiang+7 more|arXiv (Cornell University)|May 8, 2023

Galaxies: Formation, Evolution, Phenomena4 citations

TL;DR

This study constrains velocity-dependent self-interacting dark matter (SIDM) cross sections using rotation curves and stellar kinematics in 9 isolated galaxies and brightest cluster galaxies (BCGs), applying both gravothermal fluid and isothermal models. It finds consistent but distinct constraints, with the isothermal model favoring cross sections ~4× higher than the gravothermal approach at 2σ confidence.

ABSTRACT

One necessary step for probing the nature of self-interacting dark matter (SIDM) particles with astrophysical observations is to pin down any possible velocity dependence in the SIDM cross section. Major challenges for achieving this goal include eliminating, or mitigating, the impact of the baryonic components and tidal effects within the dark matter halos of interest -- the effects of these processes can be highly degenerate with those of dark matter self-interactions at small scales. In this work we select 9 isolated galaxies and brightest cluster galaxies (BCGs) with baryonic components small enough such that the baryonic gravitational potentials do not significantly influence the halo gravothermal evolution processes. We then constrain the parameters of Rutherford and Moller scattering cross section models with the measured rotation curves and stellar kinematics through the gravothermal fluid formalism and isothermal method. Cross sections constrained by the two methods are consistent at $1σ$ confidence level, but the isothermal method prefers cross sections greater than the gravothermal approach constraints by a factor of $\sim3$.

Motivation & Objective

• To probe the velocity dependence of self-interacting dark matter (SIDM) cross sections using astrophysical observations.
• To mitigate degeneracies from baryonic potentials and tidal effects by selecting isolated systems with minimal baryonic influence.
• To compare the performance and results of the gravothermal fluid formalism and isothermal method in constraining SIDM parameters.
• To derive quantitative constraints on the cross section model σ(v) = σ₀/(1 + v²/ω²)² using rotation curves and line-of-sight velocity dispersions.
• To assess the consistency and differences between two halo modeling approaches in the context of SIDM phenomenology.

Proposed method

• Selects 9 isolated galaxies and BCGs with low baryonic mass fractions to minimize gravitational potential contamination.
• Applies the gravothermal fluid formalism to model halo structure and predict radial velocity dispersion profiles under self-interaction.
• Uses the isothermal approximation as an alternative method to model velocity dispersion and constrain SIDM parameters.
• Employs a double power-law cross section model: σ(v) = σ₀ / (1 + v²/ω²)², with σ₀ and ω as free parameters.
• Models observational effects such as seeing and slit width by convolving 2D velocity dispersion maps with a Gaussian kernel and masking along the slit.
• Derives the line-of-sight velocity dispersion σ_los by combining surface brightness profiles, projected velocity dispersions, and observational blurring effects.

Experimental results

Research questions

• RQ1 How do the gravothermal fluid formalism and isothermal model compare in constraining velocity-dependent SIDM cross sections?
• RQ2 What is the impact of baryonic potentials and tidal effects on the inference of SIDM parameters in galaxy and cluster halos?
• RQ3 What are the best-fit constraints on the parameters σ₀ and ω in the cross section model σ(v) = σ₀ / (1 + v²/ω²)²?
• RQ4 To what extent are the constraints from the two modeling approaches consistent, and what is the implied systematic difference?
• RQ5 How does the inclusion of observational effects (seeing, finite slit width) affect the inferred velocity dispersion profiles and parameter constraints?

Key findings

• The gravothermal fluid formalism yields a best-fit cross section model: log(σ₀/[cm²/g]) = 2.6 / [(log(ω/[km/s])/1.9)^0.85 + (log(ω/[km/s])/1.9)^5.5] - 1.1, valid for log(ω/[km/s]) ≤ 3.7 with a 0.5 dex scatter at 68% confidence level.
• The isothermal model yields a best-fit cross section model: log(σ₀/[cm²/g]) = 3.9 / [(log(ω/[km/s])/1.6)^0.29 + (log(ω/[km/s])/1.6)^5.1] - 0.34, valid for 1.4 ≤ log(ω/[km/s]) ≤ 3.5 with a 0.34 dex scatter at 68% confidence level.
• The two models produce consistent cross section constraints at the 2σ confidence level, though the isothermal model prefers values ~4 times higher than the gravothermal model.
• The baryonic components in the selected systems are well-fit by Hernquist profiles, with minimal impact on halo gravothermal evolution.
• Observational effects such as seeing and slit width are effectively modeled through 2D convolution and masking, improving agreement with measured line-of-sight velocity dispersions.
• The joint analysis of galaxies and clusters provides tighter constraints on velocity-dependent SIDM cross sections than either system alone.