This paper explores the effects of dark energy on the structure of the Coma cluster, one of the most massive gravitationally bound aggregations of matter in the observable universe. Here's a summary of the key points discussed in the paper:
Background: The paper starts by providing background information on the Coma cluster, highlighting its significance as a massive system dominated by dark matter, as inferred from various observations over the years.
Theory: The authors adopt the ΛCDM cosmology, where dark energy is represented by Einstein's cosmological constant Λ. They consider dark energy as a perfectly uniform background with a constant density, producing an antigravity effect that becomes significant on scales of 1-10 Mpc.
Local effects of dark energy: The paper discusses the local weak-field dynamical effects of dark energy, which can be described using Newtonian mechanics. They introduce the concept of the zero-gravity radius (RZG), which defines the boundary within which gravity dominates over dark energy.
Three masses of a regular cluster: The authors define three characteristic masses for a regular cluster like Coma: the matter mass (MM), the effective dark-energy mass (MDE), and the total gravitating mass (MG). These masses are related to each other and depend on the radius from the cluster centre.
Matter mass profile: The paper suggests a new matter density profile that takes into account the effects of dark energy. They compare this new profile with traditional density profiles like the NFW and Hernquist profiles, finding differences in the estimated mass within the cluster.
Discussion: The authors discuss the implications of their findings, including upper limits on the size and mass of the Coma cluster, as well as the potential role of dark energy in shaping the structure of large-scale cosmic objects. They also discuss the estimation of local dark energy density and its implications.
Conclusion: The paper concludes by summarizing their findings, emphasizing the importance of considering dark energy effects when studying the structure and mass of massive cosmic objects like the Coma cluster.
Overall, the paper provides insights into the interplay between dark energy and the large-scale structure of the universe, particularly in the context of massive galaxy clusters like Coma.
Moreover, according to the paper, the "zero-gravity sphere" refers to a hypothetical spherical volume surrounding a gravitationally bound system, such as the Coma cluster of galaxies, where the effects of gravity and dark energy balance each other out. Within this sphere, the gravitational attraction from the mass of the system dominates over the antigravity effect of dark energy.
Specifically, the radius of this zero-gravity sphere (denoted as RZG) marks the boundary beyond which dark energy's antigravity effect becomes stronger than gravity. Inside this sphere, gravity dominates, allowing the system to remain gravitationally bound. However, beyond this radius, dark energy's repulsive effect starts to overcome gravity, leading to a net antigravity force.
In the context of the paper, understanding the radius of the zero-gravity sphere is crucial for estimating the total size and mass of the Coma cluster, as it delineates the boundary within which the cluster can exist as a gravitationally bound system.
In addition to the above, according to the interpretation provided in the paper, gravity and antigravity, caused by dark energy, can coexist within certain regions, but their dominance depends on the distance from the centre of the system.
Coexistence within certain regions: In regions closer to the centre of the system (i.e., within the "zero-gravity sphere"), gravity dominates over the antigravity effect caused by dark energy. Within this sphere, the gravitational attraction from the mass of the system is stronger than the repulsive effect of dark energy, allowing the system to remain gravitationally bound.
Transition at the boundary: However, as one moves beyond the radius of the zero-gravity sphere, the antigravity effect of dark energy starts to become stronger than gravity. In these outer regions, dark energy's repulsive force dominates, leading to a net antigravity effect. This transition marks the boundary where dark energy begins to dominate over gravity.
No effect of gravity in the dominance of dark energy and vice versa: The paper does not suggest that gravity and dark energy completely cancel each other out or that one completely negates the other. Instead, it acknowledges that both forces can exist simultaneously but with varying degrees of dominance depending on the distance from the centre of the system. Within the zero-gravity sphere, gravity is the dominant force, while outside this sphere, dark energy becomes dominant.
In summary, the paper describes a scenario where gravity and dark energy coexist within a system like the Coma cluster, with gravity dominating closer to the centre and dark energy dominating at larger distances from the centre.
Matter Mass and Effective Mass of Dark Energy:
The paper discusses the concept of matter mass and the effective mass of dark energy within the context of analysing the structure of the Coma cluster of galaxies.
Matter mass (MM): The paper defines the matter mass as the total mass of both dark matter and baryonic matter within a given radius of the cluster. It characterizes the distribution of matter within the cluster and is directly related to the gravitational attraction exerted by the mass distribution.
Effective mass of dark energy (MDE): The paper introduces the concept of the effective mass of dark energy, which represents the contribution of dark energy to the total mass within the cluster. This effective mass is negative, indicating that dark energy exerts a repulsive force or "antigravity" within the cluster. The paper suggests that this antigravity effect becomes significant at larger radii from the centre of the cluster.
By considering both the matter mass and the effective mass of dark energy, the paper aims to provide a comprehensive understanding of the gravitational dynamics within the Coma cluster, taking into account the influence of both matter and dark energy on its structure.
Cosmic Tug-of-War:
The concept of a "cosmic tug-of-war" between gravity and dark energy is implicitly described in the paper. The paper discusses how within certain regions, such as the "zero-gravity sphere," gravity dominates over the antigravity effect of dark energy, allowing the system to remain gravitationally bound. However, as one moves beyond this sphere, the balance shifts, and the antigravity effect of dark energy becomes stronger, eventually overcoming gravity's pull. This dynamic interplay between gravity and dark energy can be likened to a tug-of-war, where the dominance of one force over the other depends on the distance from the centre of the system.
Zero-Gravity Sphere:
The paper introduces the concept of the "zero-gravity sphere" as a region within the cluster where the gravitational attraction from the mass of the system exactly balances the repulsive effect of dark energy. Here's a description of the zero-gravity sphere as per the paper:
Definition: The zero-gravity sphere is defined as the region within the cluster where the net gravitational force experienced by a test particle is zero. In other words, it's the boundary beyond which the repulsive force of dark energy becomes stronger than the gravitational attraction from the mass of the cluster.
Characteristics:
Balanced Forces: Within the zero-gravity sphere, the gravitational force pulling objects towards the centre of the cluster is perfectly balanced by the antigravity effect of dark energy pushing objects away.
Critical Radius: The zero-gravity sphere has a critical radius, denoted as RZG, which marks the boundary between regions where gravity dominates and where dark energy dominates.
Implications:
Existence of Bound Systems: Gravitationally bound systems such as the Coma cluster can only exist within their zero-gravity spheres. Beyond this boundary, the repulsive effect of dark energy becomes too strong for gravitational attraction to maintain cohesion.
Limit on Size: The presence of the zero-gravity sphere imposes an upper limit on the size of the cluster. Systems that exceed this size are no longer gravitationally bound and may experience the expansion of the universe due to the dominance of dark energy.
Overall, the zero-gravity sphere concept introduced in the paper provides a framework for understanding the interplay between gravity and dark energy within large-scale structures like galaxy clusters, highlighting the critical role of dark energy in shaping the boundaries and dynamics of such systems.
Reference:
Chernin, A. D., Бисноватый-коган, Г. С., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics, 553, A101. https://doi.org/10.1051/0004-6361/201220781
