Machian Gravity: Confronting Galaxy Cluster Mass Profiles

Abstract

The general theory of relativity (GR) has excelled in explaining gravitational phenomena at the scale of the solar system with remarkable precision. However, when extended to the galactic or cosmological scale, it requires dark matter and dark energy to explain observations. In our previous article (arXiv:2308.04503), we've formulated a gravity theory based in Mach's principle, known as Machian gravity. We demonstrated that the theory successfully explains galactic velocity profiles without requiring additional dark matter components. In previous studies, for a selected set of galaxy clusters, we also showed its ability to explain the velocity dispersion in the clusters without extra unseen matter components. This paper primarily explores the mass profiles of galaxy clusters. We test the Machian Gravity acceleration law on two distinct sets comprising galaxy clusters sourced from various studies. We fitted the dynamic mass profiles using the Machian gravity model. The outcomes of our study show good agreement between the theory and observational results.

Figures (16)

• Figure 1: The plot presents the distributions of several physical properties for the sample of 106 galaxy clusters. The distribution of $\beta$ is comparatively smooth, exhibiting a pronounced peak at approximately $\beta \approx 0.56$. In the upper-right panel, the distribution of the isothermal temperature appears relatively broad, with a maximum around $T \approx 4\,\mathrm{keV}$. Although the central gas density of the clusters spans a wide range, it remains below $0.1 \times 10^{-25}\,\mathrm{g\,cm^{-3}}$ for more than $60\%$ of the systems. Finally, the core radius $r_c$ also shows substantial cluster-to-cluster variation, indicating significant diversity in the spatial extent of the intracluster medium.
• Figure 2: The plot illustrates various characteristics of the clusters. On the left, the graph depicts the relationship between $T$ and $M_{b250}$. The black curve represents the best-fit regression line derived from the data points, indicating an approximately quadratic dependence, with $M_{b250} \propto T^2$. On the right, the plot demonstrates $M_{d250}/M_{b250}$ as a function of $M_{b250}$. It is exhibiting a slight negative correlation, the ratio remains relatively constant (about 10) across the range of $M_{b250}$ values. However, the number of data points is small and their dispersion is too large to support any definitive conclusions.
• Figure 3: The figure presents $M_c$ and $\lambda^{-1}$ as functions of $M_{b250}$ and $r_c$. The results indicate that there is nearly no correlation between $\lambda^{-1}$ and $M_{b250}$. However, all other depicted relationships exhibit a robust positive correlation.
• Figure 4: We analyze all data points from the HIFLUGCS galaxy cluster sample, comprising 419 measurements drawn from 45 clusters. When examining the ratio $M_d/M_b$ as a function of $M_b$, we find a substantial degree of scatter, although a clear negative trend is apparent. The scatter becomes even more pronounced when $M_d/M_b$ is plotted against $r$ or against $M_b / r^2$. Despite this, all of these relations exhibit an overall negative correlation. In contrast, a markedly stronger correlation emerges when $M_d/M_b$ is plotted against $M_b / r$. Since there is no a priori reason to assume that any of these relations should be linear, we employ the Spearman rank correlation coefficient to quantify the strength and monotonicity of the associations. The rank correlation between $M_d/M_b$ and $M_b$ is $-0.798$, indicating a strong negative correlation. The corresponding coefficient for $M_d/M_b$ versus $r$ is $-0.604$. For $M_d/M_b$ versus $M_b / r$, the rank correlation reaches $-0.874$, which is very strong. The rank correlation between $M_d/M_b$ and $M_b / r^2$ is $-0.526$. If we seek the best-fitting monotonic relation of the form $M_b / r^\alpha$, we find that the correlation between $M_d/M_b$ and $M_b / r^{0.9}$ is maximized at $-0.874$, which is effectively identical to the correlation obtained with $M_b / r$. The histogram of $M_d/M_b$ values shows that, for the majority of data points, the ratio lies in the range $\sim 5$–$15$.
• Figure 5: This figure shows 12 cluster pairs whose dynamic mass profiles coincide. We also observe that the baryonic mass distributions of each pair agree with one another. In a framework where dark matter is treated as a fully independent component, there is no obvious theoretical reason why agreement in one type of mass profile should imply agreement in the other. Thus, in these examples, Machian Gravity appears to offer a more satisfactory explanation than the standard dark matter paradigm, since in this theory both $M_c$ and $\lambda^{-1}$ depend on the underlying mass distribution.