Machian MOND: a variable a0 in galaxy clusters
Abstract
Modified Newtonian Dynamics (MOND) generally resolves the need for dark matter in galaxy rotation curves introducing a single new constant of acceleration a0. It is well known that increasing a0 by a factor of a few can alleviate the residual mass discrepancies that MOND leaves in galaxy clusters. Within a parameter-free Machian interpretation of MOND motivated by a0∼ GMu/Ru2 arising from the scalar sum of inverse-square distance gravitational mass contributions in the universe, we promote a0 to a variable in spherically symmetric mass distributions, which is sensitive to mass external to the locally enclosed spherical region. Instead of a boost of a0 in terms of gravitational potentials as in EMOND, we show that a boost in terms of this directionless inverse-square field roughly amounts to the boost needed to accommodate the mass discrepancies of MOND in galaxy clusters, while retaining MOND predictions in galaxies. We begin to generalize this approach by defining a new a'0=G∑imi/|r−ri|2−aN, where aN is the magnitude of the usual Newtonian acceleration.
Versions
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BibTeX
@misc{palomo2026machian,
title = {{Machian MOND: a variable $a_0$ in galaxy clusters}},
author = {Manuel Uruena Palomo and Juan David Santander},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.04894},
eprint = {2608.04894},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.04894},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Machian MOND: a variable a_0 in galaxy clusters
AU - Manuel Uruena Palomo
AU - Juan David Santander
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2608.04894
UR - https://arxiv.org/abs/2608.04894
AB - Modified Newtonian Dynamics (MOND) generally resolves the need for dark matter in galaxy rotation curves introducing a single new constant of acceleration a_0. It is well known that increasing a_0 by a factor of a few can alleviate the residual mass discrepancies that MOND leaves in galaxy clusters. Within a parameter-free Machian interpretation of MOND motivated by a_0∼ GM_u/R_u^2 arising from the scalar sum of inverse-square distance gravitational mass contributions in the universe, we promote a_0 to a variable in spherically symmetric mass distributions, which is sensitive to mass external to the locally enclosed spherical region. Instead of a boost of a_0 in terms of gravitational potentials as in EMOND, we show that a boost in terms of this directionless inverse-square field roughly amounts to the boost needed to accommodate the mass discrepancies of MOND in galaxy clusters, while retaining MOND predictions in galaxies. We begin to generalize this approach by defining a new a'_0=G∑_im_i/|r−r_i|^2−a_N, where a_N is the magnitude of the usual Newtonian acceleration.
ER -