Title: And if Vulcan was a primordial black hole of planetary-mass?

Author: Souren P. Pogossian

First author’s institution: Université de Bretagne Occidentale, Brest, France

Status: Accepted to the Journal of Astrophysics and Astronomy [closed access]

General relativity, having hitherto stood up to every observational test, fully explains Mercury’s precession, the gradual change in the orientation of its elliptical orbit, shown in Figure 1. That being said, there is intellectual value in considering exotic explanations to supposedly settled phenomena. Today’s paper does exactly that, considering whether Vulcan does in fact exist in the form of a primordial black hole (PBH). The idea of a PBH hanging out in our Solar System is not new, as it has been suggested that hypothetical “Planet 9” in the outer Solar System could be a PBH.

The discovery of Neptune is one of the great triumphs of Newtonian mechanics. Uranus was discovered to be a planet in 1781 by William Herschel. In the following decades, observers tracked the orbit of Uranus and began to notice unusual deviations. In the 1840s, astronomers John Couch Adams and Urbain Le Verrier realized that the presence of a previously unknown planet could explain the orbit of Uranus. At the urging of Le Verrier, astronomer Johann Gottfried Galle observed a specific patch of the sky where the previously unknown planet, Neptune, was predicted to be and did indeed find it.

Le Verrier was also deeply interested in tracking the orbit of Mercury. With Kepler’s laws, it is straightforward to estimate Mercury’s orbit only accounting for the Sun as a point mass. It is much more complicated to include other effects, such as perturbations from the other planets. In 1859, Le Verrier realized that the orbit could not be explained by Newtonian mechanics alone. Specifically, the orbit was precessing 43 arcseconds/century faster than expected.

To explain this discrepancy, Le Verrier hypothesized additional mass might exist within the orbit of Mercury, in the form of an asteroid belt or a new planet named Vulcan. Fast-forwarding to 1915, Einstein published his general theory of relativity, which explains gravity through the curvature of spacetime and accounts for the 43”/century discrepancy, removing the need for any additional planet. Or does it?

Primordial black holes are hypothesized to have formed in the early Universe from the collapse of extremely overdense regions. Since PBHs are non-luminous, creative methods such as microlensing would be needed to infer their existence. The mass of the hypothetical Vulcan PBH would be ~1.6 times the mass of Mercury, with a Schwarzschild radius of ~0.7 mm. However, there is theoretical uncertainty about how and whether the Solar System could capture a PBH, let alone whether they exist at all.

Today’s paper uses a Newtonian model of an 8-planet Solar System to track the orbits of the planets over a 900-year baseline. The author then uses a 9-planet model, including Vulcan, to track the effect of the additional body on the precession of the inner planets. The measurable quantity is the perihelion advance (PA), which tracks the precession. As shown in Figure 2, an individual planet’s PA is influenced by all the other bodies in the system and has periodic components set by its relative alignment with those other bodies.

By tuning the mass and orbit of Vulcan, it is possible to replicate the observed precession of Mercury’s orbit, as shown in Figure 3. However, the Vulcan model diverges from the general relativistic expectation in predicting the precessions of the other inner planets. The disagreement is on the order of a few arcseconds and thus difficult to measure, but Vulcan’s impact on the inner planets’ orbits extends to other orbital properties as well. Vulcan would bring Earth’s aphelion modestly closer to the Sun (a distance of approximately the radius of Mercury) after 100 years of orbital evolution.

So, it is extraordinarily unlikely that Vulcan exists as a PBH in the inner Solar System. The author of today’s paper does not definitively rule the Vulcan hypothesis out, and more precise long-term observations of the orbits of inner planets would be helpful. If Vulcan did exist, it would entirely upend what we think we know about the history and evolution of the Solar System. I would not bet on it, but PBHs hanging out somewhere in the Solar System might be more likely than we think.

Astrobite edited by Katherine Lee

Featured image credit: Colby, Hall, and Jones & Newman, Library of Congress