Modified Newtonian Dynamics (MOND), postulating a breakdown of Newtonian
mechanics at low accelerations, has considerable success at explaining galaxy
kinematics. However, the quadrupole of the gravitational field of the Solar
System (SS) provides a strong constraint on the way in which Newtonian gravity
can be modified. In this paper we assess the extent to which modified gravity
formulations of MOND are capable of accounting simultaneously for the Radial
Acceleration Relation (RAR) — encapsulating late-type galaxy dynamics — the
Cassini measurement of the SS quadrupole and the kinematics of wide binaries in
the Solar neighbourhood. We achieve this by extending the method of Desmond
(2023) to infer the location and sharpness of the MOND transition from the
SPARC RAR under broad assumptions for the behaviour of the interpolating
function and external field effect. We constrain the same quantities from the
SS quadrupole, finding that it requires a significantly sharper transition
between the deep-MOND and Newtonian regimes than is allowed by the RAR (an
8.7$sigma$ tension under fiducial model assumptions). This may be relieved by
allowing additional freedom in galaxies’ mass-to-light ratios — which also
provides a better RAR fit — and more significantly by removing galaxies with
bulges. We show that the SS quadrupole constraint implies, to high precision,
no deviation from Newtonian gravity in wide binaries in the Solar
neighbourhood, and speculate on possible resolutions of this incompatibility
between SS and galaxy data within the MOND paradigm.
Examine the conclusions of the following text and outline a future roadmap for readers, indicating potential challenges and opportunities on the horizon.
The Road Ahead: Challenges and Opportunities
The conclusions of the study suggest that modified gravity formulations of Modified Newtonian Dynamics (MOND) may face challenges in simultaneously accounting for the Radial Acceleration Relation (RAR), the Cassini measurement of the Solar System (SS) quadrupole, and the kinematics of wide binaries in the Solar neighbourhood. However, there are also potential opportunities for further investigation within the MOND paradigm. Here is a future roadmap for readers:
1. Exploring MOND’s Ability to Account for RAR
One challenge highlighted by the study is the tension between the MOND formulation and the RAR. Readers can delve deeper into understanding the specific constraints placed on the transition between deep-MOND and Newtonian gravity regimes by the RAR. Further research could focus on refining assumptions about the interpolating function and external field effect to achieve a better fit with the RAR data.
2. Investigating Impact of Mass-to-Light Ratios
The study suggests that allowing additional freedom in galaxies’ mass-to-light ratios could potentially alleviate the tension between the SS quadrupole constraint and the RAR. Readers can explore the implications of varying mass-to-light ratios and how it affects the overall fit with both the RAR and SS quadrupole data. This avenue of research could shed light on the connection between galaxy dynamics and modified gravity formulations.
3. Reconsidering Galaxies with Bulges
An opportunity arises from the finding that removing galaxies with bulges could significantly improve compatibility between the SS quadrupole constraint and the RAR. Readers can engage in further investigation to understand the role of bulges in the context of MOND and its impact on the overall dynamics of galaxies. This exploration may lead to insights into the underlying mechanisms of modified gravity in galaxy kinematics.
4. Addressing Incompatibility in Solar Neighbourhood Binaries
The study highlights that the SS quadrupole constraint implies no deviation from Newtonian gravity in wide binaries in the Solar neighbourhood. Readers can explore potential resolutions for this incompatibility within the MOND paradigm. By investigating alternative explanations or extending MOND’s framework, researchers may uncover new insights into the behavior of gravity at small scales.
Conclusion
While the study presents challenges for modified gravity formulations of MOND, it also offers opportunities for further research and exploration. By delving deeper into the tensions identified and investigating potential solutions, future work can advance our understanding of galaxy dynamics and the role of modified gravity in explaining the universe’s behavior.