A heuristic solution for the Pioneer anomaly employing an ELA metric with dark matter in the outskirts of the Solar system

TL;DR

This paper proposes a heuristic ELA metric model with dark matter to explain the Pioneer anomaly, accounting for observed spacecraft acceleration without disrupting planetary orbits, and suggests a dark matter distribution in the outer Solar system.

Contribution

It introduces a novel ELA metric with a specific ansatz for alpha to explain the Pioneer anomaly and models a dark matter distribution in the Solar system's outskirts.

Findings

The model fully accounts for the Pioneer anomaly as a space-time blue-shift effect.

Orbital corrections for Neptune and Pluto are minimized with the branch ansatz.

The effective dark matter distribution has an equation of state between -1 and -0.726.

Abstract

Considering an expanding locally anisotropic (ELA) metric with the Sun as central mass and the heuristic ansatz for the dimensionless functional exponent parameter 'alpha=3+alpha_2(r_1)(1-U_Sun)^2' with a linear ansatz 'alpha_2(r_1)=alpha_2^(2.0)+alpha_2^(2.1) r_1' above 20 AU the pioneer anomaly is fully accounted for as due to the blue-shift of the background space-time. For compatibility with orbital motion within the Solar system it is further considered a branch ansatz for which \alpha_2(r_1)=0 below 20 AU. This construction reduces the physical acceleration correction above 20 AU down to ~10^(-14) m/s^2 outwards from the Sun such that orbital corrections to Neptune and Pluto are less notorious than when the full Pioneer acceleration is considered to be a gravitational acceleration. It is also discussed the effective mass-energy density distribution above 20 AU due to the background corrections, the respective equation of state ('-1 < w < -0.726') and the finite non-null total mass is computed by considering an upper cut-off for the functional parameter 'alpha'. Such effective extended configuration is tentatively interpreted as a cold dark matter distribution.