[Paper Review] Dark Matter Strikes Back

P. Salucci|arXiv (Cornell University)|Dec 28, 2016

Astronomy and Astrophysical Research3 citations

TL;DR

This paper demonstrates that the tight correlation between total radial acceleration and baryonic acceleration in spiral galaxies—previously interpreted as evidence against dark matter halos—naturally emerges in the standard ΛCDM framework. By modeling dark matter halos with universal rotation curve (URC) and RTF methods across 153 spirals, the authors show the relationship arises from the less concentrated, more dominant dark matter in low-luminosity systems, not new physics.

ABSTRACT

Mc Gaugh et al. (2016) have found, by investigating a large sample of Spirals, a tight non linear relationship between the total radial acceleration, connected with the Dark Matter phenomenon, and its component which comes from the distribution of baryonic matter, as the stellar and HI disks. The strong link between these two quantities is considered by them and by other researchers, as challenging the scenario featuring the presence of DM halos in galaxies. Or, at least, to indicate the peculiar nature of the underlying dark matter particles. We have explored this issue by investigating a larger number of galaxies by means of several techniques of analysis. Our results support and even increase, both qualitatively and quantitatively, the validity of McGaugh et al. (2016) 's relationship. However, we prove that such relationship exists also in the scenario featuring dark matter halos + ordinary baryonic matter and that it arises by the fact the DM is less concentrated than the luminous matter and it is progressively more abundant in lower luminosity objects. These properties are due to well known astrophysical effects: the implications of this relationship for the properties of dark matter halos are nothing of new or of unexpected. The relationship, definitively, is not a portal to go beyond the standard picture of $Λ$CDM galaxy formation.

Motivation & Objective

• To test whether the McGaugh et al. (2016) observed acceleration relation can be reproduced within the standard ΛCDM framework of dark matter halos.
• To investigate whether the observed tight correlation between total and baryonic accelerations implies a fundamental challenge to the existence of collisionless dark matter particles.
• To determine whether the relationship is a generic consequence of the structural properties of dark and baryonic matter in spiral galaxies, rather than a sign of new physics.
• To assess the robustness of the relation across different modeling techniques and galaxy samples, including both URC and RTF methods.
• To clarify whether the observed correlation implies non-collisionless dark matter or merely reflects astrophysical scaling relations in galaxy formation.

Proposed method

• Modeling the total radial acceleration $ g(r) = V^2(r)/r $ using rotation curve data from 153 spiral galaxies.
• Decomposing the gravitational potential into contributions from dark matter halos ($ g_h $) and baryonic components (stellar disk, bulge, HI disk) via Poisson's equation $ \nabla^2\Phi_i = 4\pi G\rho_i $.
• Applying the Universal Rotation Curve (URC) model to derive halo velocity profiles $ V_{URCH}(x,M_D) $ based on disk mass $ M_D $ and size $ R_{\text{opt}} $, with parameters derived from empirical scaling relations.
• Using the RTF (Rotation Curve Template Function) method to model rotation curves with three components: disk, bulge, and halo, with halo profile $ V_{RTFH} \propto x^2/(x^2 + \alpha^2) $, allowing for both cored (URC) and cusped (NFW) profiles.
• Fitting the RTF model to observed rotation curves by adjusting parameters $ c_h $, $ k_h $, $ c_b $, and $ \alpha $, with $ \alpha \simeq 1^{+1}_{0.5} $ in units of $ R_{\text{opt}} $, to reproduce the $ a_n = a(R_n) $ relationship.
• Comparing predictions from URC and RTF models to the McGaugh relation, confirming consistency within 20% uncertainty in accelerations and <30% in luminous components.

Experimental results

Research questions

• RQ1 Does the McGaugh et al. (2016) observed acceleration relation persist in a standard ΛCDM dark matter halo framework?
• RQ2 Can the tight correlation between total and baryonic accelerations be explained by astrophysical scaling relations rather than new physics?
• RQ3 Is the observed relationship sensitive to the dark matter halo profile (e.g., cored vs. cusped), or does it hold across different halo models?
• RQ4 What role do the structural parameters of the stellar disk (e.g., $ R_D $, $ M_D $, $ R_{\text{opt}} $) play in generating the acceleration relation?
• RQ5 Does the acceleration relation imply that dark matter particles must be non-collisionless, or is it consistent with standard ΛCDM?

Key findings

• The McGaugh et al. (2016) acceleration relation is robustly reproduced in the ΛCDM framework using both URC and RTF modeling techniques.
• The relationship arises naturally from the fact that dark matter halos are less concentrated than baryonic matter and become more dominant in low-luminosity galaxies.
• The URC model yields a halo central density $ \rho_0 \simeq 10^{-23.5} \, \text{g cm}^{-3} $ and core radius $ r_0 \simeq 0.66 + 0.58 \log(M_{\text{vir}}/10^{11} M_\odot) $, consistent with observations.
• The RTF method yields best-fit parameters $ k_h = 0.79 \pm 0.04 $, $ c_h = 0.13 \pm 0.06 $, $ c_b = 0.13 \pm 0.03 $, and $ \alpha = 1^{+1}_{0.5} $, showing the relation holds across different halo profiles.
• The halo contribution to acceleration $ g_h $ remains similar between URC-cored and NFW-cusped models for the same rotation curve, indicating the relation is insensitive to halo cuspiness.
• The observed correlation is not a portal to new physics but a low-resolution manifestation of well-known astrophysical scaling relations in galaxy formation.