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A first attempt to differentiate between modified gravity and modified inertia with galaxy rotation curves

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 Added by Jonas Petersen
 Publication date 2020
  fields Physics
and research's language is English




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The phenomenology of modified Newtonian dynamics (MOND) on galaxy scales may point to more fundamental theories of either modified gravity (MG) or modified inertia (MI). In this paper, we test the applicability of the global deep-MOND parameter $Q$ which is predicted to vary at the $10%$ level between MG and MI theories. Using mock-observed analytical models of disk galaxies, we investigate several observational uncertainties, establish a set of quality requirements for actual galaxies, and derive systematic corrections in the determination of $Q$. Implementing our quality requirements to the SPARC database yields $15$ galaxies, which are close enough to the deep-MOND regime as well as having rotation curves that are sufficiently extended and sampled. For these galaxies, the average and median values of $Q$ seem to favor MG theories, albeit both MG and MI predictions are in agreement with the data within $1.5sigma$. Improved precision in the determination of $Q$ can be obtained by measuring extended and finely-sampled rotation curves for a significant sample of extremely low-surface-brightness galaxies.



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Dark Matter (DM) and Modified Newtonian Dynamics (MOND) models of rotationally supported galaxies lead to curves with different geometries in $(g_{N},g_{tot})$-space ($g2$-space). Here $g_{tot}$ is the total acceleration and $g_{N}$ is the acceleration as obtained from the baryonic matter via Newtonian dynamics. In MOND modified inertia (MI) models the curves in $g2$-space are closed with zero area and so curve segments at radii $rgeq r_{N}$ (large radii) and $r< r_{N}$ (small radii) coincide, where $r_{N}$ is the radius where $g_N$ is greatest. In DM models with cored density profiles where $g_{tot}$ is also zero at the galactic centre, the curves are again closed, but the area of the closed curves are in general non-zero because the curve segments at radii $rgeq r_{N}$ and $r<r_{N}$ do not coincide. Finally in DM models with cuspy density profiles such as the NFW profile where $g_{tot}$ is formally non-zero at the galactic origin the curves are open, and again the curve segments at radii $rgeq r_{N}$ and $r< r_{N}$ do not coincide. We develop a test of whether data at small and large radii coincide and investigate rotation curves from the SPARC database in order to discriminate between the above geometries. Due to loosely quantified systematic uncertainties we do not underline the result of the test, but instead conclude that the test illustrates the relevance of this type of analysis and demonstrate the ability to discriminate between the considered DM and MI models in this way.
Using a perturbative approach we solve stellar structure equations for low-density (solar-type) stars whose interior is described with a polytropic equation of state in scenarios involving a subset of modified gravity theories. Rather than focusing on particular theories, we consider a model-independent approach in which deviations from General Relativity are effectively described by a single parameter $xi$. We find that for length scales below those set by stellar General Relativistic radii the modifications introduced by modified gravity can affect the computed values of masses and radii. As a consequence, the stellar luminosity is also affected. We discuss possible further implications for higher density stars and observability of the effects before described.
83 - R.H. Sanders 2018
I consider the observed rotation curves of 12 gas-dominated low-surface-brightness galaxies -- objects in which the mass of gas ranges between 2.2 and 27 times the mass of the stellar disk (mean=9.4). This means that, in the usual decomposition of rotation curves into those resulting from various mass components, the mass-to-light ratio of the luminous stellar disk effectively vanishes as an additional adjustable parameter. It is seen that the observed rotation curves reflect the observed structure in gas surface density distribution often in detail. This fact is difficult to comprehend in the context of the dark matter paradigm where the dark halo completely dominates the gravitational potential in the low surface density systems; however it is expected result in the context of modified Newtonian dynamics (MOND) in which the baryonic matter is the only component. With MOND the calculated rotation curves are effectively parameter-free predictions.
156 - F.R. Klinkhamer , M. Kopp 2011
Verlindes heuristic argument for the interpretation of the standard Newtonian gravitational force as an entropic force is generalized by the introduction of a minimum temperature (or maximum wave length) for the microscopic degrees of freedom on the holographic screen. With the simplest possible setup, the resulting gravitational acceleration felt by a test mass m from a point mass M at a distance R is found to be of the form of the modified Newtonian dynamics (MOND) as suggested by Milgrom. The corresponding MOND-type acceleration constant is proportional to the minimum temperature, which can be interpreted as the Unruh temperature of an emerging de-Sitter space. This provides a possible explanation of the connection between local MOND-type two-body systems and cosmology.
We propose helioseismology as a new, precision probe of fifth forces at astrophysical scales, and apply it on the most general scalar-tensor theories for dark energy, known as Degenerate Higher-Order Scalar-Tensor theories (DHOST). We explain how the effect of the fifth force on the solar interior leaves an observable imprint on the acoustic oscillations, and under certain assumptions we numerically compute the non-radial pulsation eigenfrequencies within modified gravity. We illustrate its constraining power by showing that helioseismic observations have the potential to improve constraints on the strength of the fifth force by more than $2$ orders of magnitude, as $-1.8 cdot 10^{-3} leq Y leq 1.2 cdot 10^{-3}$ (at $2sigma$). This in turn would suggest constraints of similar order for the theorys free functions around a cosmological background ($alpha_{text{H}}, beta_{1}$).
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