Could displaced black holes give cosmic rays an extra boost?

What happens to a galaxy’s central engine when gravitational interactions knock it away from the center? If the displaced black hole can keep collecting gas, it might continue driving powerful outflows. A theoretical preprint by Yury Eroshenko asks whether those outflows could accelerate cosmic rays more effectively in their new surroundings.

The proposed advantage is not a stronger black hole. It is a less restrictive environment: thinner gas lets an outflow’s shock wave move faster, carrying the acceleration region away from intense radiation that would otherwise drain the particles’ energy. Under the paper’s assumptions, protons could reach around 10^19 electronvolts—about ten times the characteristic limit reported in earlier, more detailed calculations for ordinary galactic nuclei. This is a model prediction, not an observed cosmic-ray source identification.

A central engine, displaced

An active galactic nucleus is powered by gas falling toward a supermassive black hole through an accretion disk. When galaxies merge, their black holes can approach one another. The paper considers two ways a black hole could then be displaced.

First, an unequal emission of gravitational waves during a black-hole merger can give the remnant a recoil. The cases emphasized here involve speeds of a few hundred kilometers per second: enough to move the black hole away from its original surroundings, without necessarily escaping the galaxy. Its disk may be destroyed during the merger and later rebuilt from surrounding gas.

Second, an encounter involving three black holes can eject one through a gravitational slingshot. In this scenario, the departing black hole may retain its disk and some closely bound stars, while leaving the more extended dusty torus behind.

Continued activity is conditional. The black hole needs enough gas along its path, and moving too quickly makes collecting that gas harder. Eroshenko also estimates whether surviving stars could supply fuel. In the simplified cluster model, stars are redirected toward the black hole too slowly to provide substantial replenishment; surrounding gas is the more plausible supply.

Comparing two shock waves

The calculation follows a fast gas outflow from an active nucleus and the shock wave it drives into surrounding material. Although the outflow can be extremely fast, the expanding shock considered in the model is generally much slower than light.

Eroshenko uses a spherical shock solution with continuous, constant energy injection. Protons gain energy through first-order Fermi acceleration: repeated interactions across a shock increase their energy, with magnetic fields governing their motion. The calculation assumes Bohm diffusion, a particular prescription for how particles scatter.

The comparison uses surrounding gas densities of one million particles per cubic centimeter for an ordinary central nucleus and 100 for a displaced one. It examines black holes with ten million, 100 million and one billion solar masses. Other assumptions set the nucleus’s luminosity, the fraction powering the outflow and the fraction of outflow energy associated with magnetic fields.

The calculation then compares acceleration with competing limits. Particles must remain confined within the accelerator. They also lose energy when they interact with radiation, producing electron–positron pairs or, at higher energies, pions. The disk’s radiation is calculated by adding contributions from rings at different temperatures; radiation from the dusty torus is considered separately.

Why thinner gas helps

In the lower-density setting, the shock expands faster. That reduces the time spent near the disk’s strongest radiation field. The disk still imposes an energy limit, but a less restrictive one. Moving sufficiently far from the original torus also makes its radiation less important; in this calculation, disk radiation is the stronger restriction anyway.

For the example with a 100-million-solar-mass black hole, the displaced-nucleus calculation reaches roughly 10^19 electronvolts when the shock is about two to three parsecs from the black hole. That distance describes the shock’s size, not how far the black hole has traveled through its galaxy.

A possibility, not a population estimate

The result depends on the assumed gas density, outflow power, magnetic field and particle scattering. A spherical, steadily powered shock simplifies an outflow described as emerging in broad cones; real activity may also be intermittent as the black hole encounters different gas clouds. Only protons are calculated, not heavier nuclei.

The paper discusses observations relevant to displaced or multiple black holes, but does not establish a connection between any particular object and detected ultrahigh-energy cosmic rays. Their abundance and active lifetimes remain insufficiently known to calculate their overall contribution reliably.

The preprint therefore offers a conditional mechanism: displacement could ease an accelerator’s radiation losses. It does not establish that these objects explain the cosmic rays we observe.