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General Relativity and Quantum Cosmology

arXiv:2204.07242 (gr-qc)
[Submitted on 14 Apr 2022 (v1), last revised 18 Apr 2022 (this
version, v2)]

Title:Prospects for a local detection of dark matter with future
missions to Uranus and Neptune

Authors:Lorenz Zwick, Deniz Soyuer, Jozef Bucko
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    Abstract: We investigate the possibility of detecting the
    gravitational influence of dark matter (DM) on the trajectory of
    prospective Doppler ranging missions to Uranus and Neptune. In
    addition, we estimate the constraints such a mission can provide
    on modified and massive gravity theories via extra-precession
    measurements using orbiters around the ice giants. We employ
    Monte Carlo-Markov Chain methods to reconstruct fictitious
    spacecraft trajectories in a simplified solar system model with
    varying amounts of DM. We characterise the noise on the Doppler
    link by the Allan deviation $\sigma_{\rm A}$, scaled on the
    Cassini-era value of $\sigma^{\rm{Cass}}_{\rm A}= 3 \times 10^
    {-15}$. Additionally, we compare the precision of prospective
    extra-precession measurements of Uranus and Neptune with the
    expected rates from simulations, in the context of modifications
    to the inverse square law. We estimate that the prospective
    mission will be sensitive to DM densities of the order of $\rho_
    {\rm{DM}} \sim 9 \times 10^{-20} \, (\sigma_{\rm A}/\sigma_{\rm
    A}^{\rm{Cass}}) $ kg/m$^3$, while the $1\sigma$ bound on the
    expected galactic density of $\rho_{\rm{DM}} \sim 5 \times 10^
    {-22}$ kg/m$^3$ decreases as $1.0 \times 10^{-20} \, (\sigma_{\rm
    A}/\sigma^{\rm{Cass}}_{\rm A})^{0.8}$ kg/m$^3$. An improvement of
    two to three orders of magnitude from the baseline Allan
    deviation would guarantee a local detection of DM. Only a
    moderate reduction in ranging noise is required to rule out
    Milgrom's interpolating function with solar system based
    observations, and improve constraints the graviton mass beyond
    current local- or gravitational wave-based measurements. Our
    analysis also highlights the potential of future ranging missions
    to improve measurements of the standard gravitational parameters
    in the solar system.

Comments: Accepted for publication by A&A
          General Relativity and Quantum Cosmology (gr-qc); Cosmology
Subjects: and Nongalactic Astrophysics (astro-ph.CO); Earth and
          Planetary Astrophysics (astro-ph.EP); Instrumentation and
          Methods for Astrophysics (astro-ph.IM)
Cite as:  arXiv:2204.07242 [gr-qc]
          (or arXiv:2204.07242v2 [gr-qc] for this version)
          https://doi.org/10.48550/arXiv.2204.07242
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Lorenz Zwick [view email]
[v1] Thu, 14 Apr 2022 21:43:06 UTC (1,349 KB)
[v2] Mon, 18 Apr 2022 17:59:49 UTC (1,349 KB)
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