The paper "Dark energy and the structure of the Coma cluster of galaxies" by Chernin et al.

The paper "Dark energy and the structure of the Coma cluster of galaxies" by Chernin et al. explores the influence of dark energy on the structure and mass of the Coma cluster of galaxies. The authors approach the Coma cluster as a gravitationally bound system embedded in the dark energy background described by the ΛCDM cosmology. They aim to determine whether the dark energy density is significant enough to affect the structure of such a large cluster.

Key Concepts and Methods:

1. Three Characteristic Masses:

• Matter Mass (Mᴍ): The total mass of matter (dark matter and baryons) within a given radius.

• Dark Energy Effective Mass (Mᴅᴇ or mᵉᶠᶠ): The mass equivalent of the dark energy's gravitational effect within the same radius. It is negative due to dark energy's repulsive nature. It is negative due to dark energy's repulsive nature and is defined as the difference between the gravitating mass and the matter mass, calculated as:

Mᴅᴇ (or mᵉᶠᶠ) = Mɢ - Mᴍ

• Gravitating Mass (Mɢ): The total mass that includes the effect of dark energy, defined as

Mɢ = Mᴍ + Mᴅᴇ (or mᵉᶠᶠ).

2. Zero-Gravity Radius (Rᴢɢ):

• The radius where the gravitational pull due to matter is exactly balanced by the repulsive effect of dark energy.

• Calculated as 

Rᴢɢ = [Mᴍ/(8π/3)ρᴅᴇ]^1/3, 

where Mᴍ is the matter mass, and ρᴅᴇ is the density of dark energy.

3. Matter Density Profile:

• The authors propose a new density profile that accounts for dark energy effects, improving the fit to observational data from 1.4 Mpc to 14 Mpc.

Findings:

1. Impact of Dark Energy:

• At small radii (R ≤ 14 Mpc), dark energy has a negligible effect on the mass distribution, so

Mɢ ≃ Mᴍ. 

• In this context: Mɢ is the gravitational mass. Mᴍ is the matter mass.

• At larger radii (R ≥ 14 Mpc), dark energy significantly affects the structure, and its repulsive effect becomes comparable to or greater than the gravitational attraction of matter.

2. Mass Estimates:

• The upper limit for the total size of the Coma cluster is approximately 20 Mpc, beyond which the cluster cannot remain gravitationally bound due to the repulsive force of dark energy.

• The total matter mass within this radius is estimated to be Mᴍ ≲ 6.2 × 10¹⁵ M⊙.

3. Comparison with Traditional Profiles:

• The NFW (Navarro-Frenk-White) and Hernquist profiles are traditional models used to describe the matter density of clusters but do not adequately account for dark energy.

• The new profile proposed by the authors provides a better fit to observational data, especially at larger radii where dark energy effects are significant.

Conclusion:

The study concludes that dark energy significantly affects the structure of the Coma cluster at large distances from the centre. The proposed matter density profile, which incorporates the effects of dark energy, provides a more accurate representation of the cluster's mass distribution. The findings suggest that the Coma cluster's total matter mass is capped at around 6.2 × 10¹⁵ M⊙, and its size is limited to about 20 Mpc due to the influence of dark energy.

Implications:

• Large-Scale Structure: The results highlight the importance of considering dark energy when studying the structure and mass of galaxy clusters.

• Observational Verification: Future observations can test these predictions, particularly the proposed upper limits on the Coma cluster's size and mass.

• Cosmological Models: The findings reinforce the ΛCDM model and its implications for the role of dark energy in the Universe.

• By integrating dark energy into the analysis, this paper provides a more comprehensive understanding of the Coma cluster's structure, offering insights into the broader effects of dark energy on cosmic structures.

Reference: 

Chernin, A. D., Bisnovatyi-Kogan, G. S.,Teerikorpi, P., Valtonen, M. J., Byrd, G.G., & Merafina, M. (2013). Dark energyand the structure of the Coma cluster ofgalaxies. Astronomy & Astrophysics, 553,A101. https://doi.org/10.1051/0004-6361/201220781