Comparison of MOND and Verlinde's emergent gravity in dwarf spheroidals

TL;DR

The paper investigates whether MOND or Verlinde's emergent gravity better explains the radial accelerations observed in 23 dwarf spheroidal galaxies. By computing predicted accelerations $$g_{ m Ver}$$ and $$g_{ m MOND}$$ from baryonic mass profiles and comparing to the observed $$g_{ m obs}$$ through error-weighted fits across galaxies, the authors find Verlinde's predictions align more closely with the data, achieving a combined significance of $$5.2\sigma$$ (Stouffer) and $$4.5\sigma$$ (Fisher). The robustness of the result is tested against the quasi-de Sitter choice for $$a_0$$, and the key improvement is attributed to the Verlinde term involving $$4\pi G \rho_{ m bar} r$$, which cannot be reproduced by MOND. Overall, the study provides strong evidence that Verlinde's emergent gravity more accurately captures the dynamical accelerations in dwarf spheroidal systems without invoking dark matter, with implications for alternative gravity theories in low-acceleration regimes.

Abstract

We apply Modified Newtonian Dynamics (MOND) and Verlinde's emergent gravity separately to calculate the radial accelerations in 23 dwarf spheroidals. Then, we compare them with the observed radial accelerations. In our earlier work, we determined that, when the data set is considered in its entirety without isolating individual dwarf spheroidal, Verlinde's emergent gravity is in close agreement with the observed values. In the present work, we additionally confirm that, for 21 of the 23 samples examined, Verlinde's emergent gravity follows the trend of the observed values within each dwarf spheroidal more closely than MOND. Combining the statistical significance of all the 23 samples, ranging from $-0.25σ$ to 3.41$σ$, we conclude that Verlinde's emergent gravity is favored over MOND at 5.2$σ$.

Figures (4)

• Figure 1: Comparison of the theoretical gravitational accelerations with the observed accelerations for eight classical satellites of the Milky Way. The colored dotted line represents the error-weighted best fit for each data set. For seven of the eight samples, the red dots (Verlinde gravity) fit better than the blue dots (MOND), as the slopes of the red lines (Verlinde gravity) are closer to 45$^\circ$ line than those of the blue lines (MOND).
• Figure 2: Same as Fig. \ref{['eightfigures']}, but for 8 other galaxies
• Figure 3: Same as Fig. \ref{['eightfigures']}, but for 7 other galaxies
• Figure 4: Same as Fig. \ref{['eightfigures']}, except that the Verlinde prediction is replaced by the MOND prediction calculated with Milgrom's constant corresponding to the quasi-de-Sitter value of $a_0$. Changing Milgrom's constant does not significantly alter the trend, indicating that the behavior preferred by Verlinde’s emergent gravity is not simply a consequence of adopting a smaller value of $a_0$. In addition, $g_{\rm Ver}$ is generally larger than $g_{\rm MOND}$, whereas $g_{\rm MOND(quasi)}$ is smaller than $g_{\rm MOND}$. Thus, the trend characteristic of Verlinde's emergent gravity clearly arises from the specific functional form of its formula.