Primordial Black Holes in the Solar System (2409.04518v3)

Abstract: If primordial black holes (PBHs) of asteroidal mass make up the entire dark matter, they could be detectable through their gravitational influence in the solar system. In this work, we study the perturbations that PBHs induce on the orbits of planets. Detailed numerical simulations of the solar system, embedded in a halo of PBHs, are performed. We find that the gravitational effect of the PBHs is dominated by the closest encounter. Using the Earth-Mars distance as an observational probe, we show that the perturbations are smaller than the current measurement uncertainties and thus PBHs are not directly constrained by solar system ephemerides. We estimate that an improvement in the ranging accuracy by an order of magnitude or the extraction of signals well below the noise level is required to detect the gravitational influence of PBHs in the solar system in the foreseeable future.

• The paper demonstrates that gravitational perturbations by PBHs on planetary orbits are far below current detection limits.
• It employs N-body simulations with a second-order Leapfrog integrator and DE441 initial conditions over one- and twenty-year spans.
• The analysis finds that the perturbation effects remain largely mass-independent, highlighting the need for enhanced measurement precision.

Primordial Black Holes in the Solar System

Valentin Thoss and Andreas Burkert present a paper on the perturbations induced by primordial black holes (PBHs) on the orbits of planets within the Solar System. The principal goal of the paper is to ascertain whether PBHs, in the mass range typically discussed to potentially constitute dark matter, can be detected through their gravitational effects on planetary bodies.

Summary of Methods and Simulations

The authors implement N-body simulations within a PBH-modified solar system to explore the gravitational perturbations on planetary orbits, focusing particularly on the Earth-Mars distance as an observable metric. In these simulations, a second-order Leapfrog integrator is employed to simulate the motions of the planets under the influence of a halo of PBHs. The simulation data sources initial conditions from the Horizons System's DE441 model. The PBHs themselves are assigned a Maxwellian velocity distribution to reflect solar and galactic constraints.

The paper examines the potential impact of PBHs across a specific and scientifically constrained mass range: from $10^{18}$ g to $10^{21}$ g. The simulations account for a one-year and a twenty-year span to extrapolate the cumulative effect of the PBHs on solar system dynamics. The gravitational effects are thereby integrated, with a special emphasis on their ability to perturb the Earth-Mars distance—a key probe due to its measurement precision.

Findings and Implications

The results indicate that the gravitational perturbations induced by PBHs are significantly below current detection abilities when considering the Earth-Mars distance, which has observational precision up to an order of magnitude of $10^{-11}$. Intriguingly, the intensity of perturbations appears largely independent of PBH mass within this paper's constrained range, due primarily to the compensating effects of scattering rate reductions with increased mass.

The impulse model developed gives a robust theoretical framework that aligns well with simulation outcomes, portraying the perturbations as primarily dependent on the closest PBH encounters to solar system bodies. This model not only rationalizes the current findings but suggests that existing techniques based on Poissonian fluctuations of PBHs might not effectively constrain them as components of dark matter.

Crucially, the authors extrapolate from these results that to detect PBHs using existing solar system data, measurement precision has to be enhanced significantly beyond present capabilities. They further posit that substantial improvement in spacecraft trajectories and planetary ephemerides will be essential if PBHs are to be detected by means of gravitational perturbations on solar system scales.

Discussion on Previous Work and Future Directions

The paper challenges aforementioned conclusive claims, most prominently those that suggest that PBHs are excluded from making up the entirety of the dark matter based on their effects within our solar system. It also evaluates other proposed detection mechanisms, such as the search for impact craters or gravitational microlensing by PBHs, as indirect lines of evidence, albeit presently unconvincing.

Future research paths, as suggested, could include extending the mass range considered, implementing detection mechanisms with improved precision, or considering the effects of clustered PBHs. Such directions underscore not only the constraints of current methodologies but also the potential vastness and complexity of parameter spaces relevant to the dark matter constitution problem.

In conclusion, Thoss and Burkert's analysis offers a detailed numerical and theoretical investigation into the potential solar system-wide implications of primordial black holes. While current detection feasibility remains constrained, the methodological rigor of their simulations provides vital insights into possible future advancements in astronomical measurement capabilities.