Researchers clarify dynamics of black hole rotational energy

Fig. 1. A supermassive black hole surrounded by an
accretion disk, shown in red, emits jets — the vertical
beams. Credit: MIPT

Astrophysicists at MIPT have developed a model for testing a
hypothesis about supermassive black holes at the centers of
galaxies. The new model enables scientists to predict how
much rotational energy a black hole loses when it emits beams
of ionized matter known as astrophysical jets. The energy
loss is estimated based on measurements of a jet’s magnetic
field. The paper was published in the journal Frontiers in
Astronomy and Space Sciences

Astrophysicists have observed hundreds of relativistic —enormous outflows of matter emitted by
active galactic nuclei harboring supermassive . The matter in a jet is accelerated
nearly to the speed of light, hence the term “relativistic.”
Jets are colossal, even by astronomical standards—their length
can be up to several percent of the radius of the host galaxy,
or about 300,000 times larger than the associated black hole.

That said, there is still a lot researchers do not know about
jets. Astrophysicists are not even sure what they are made of
because jet observations yield no spectral lines. Current
consensus holds that jets are likely made of electrons and
positrons or protons, but they remain quite a mystery. As
researchers obtain new data, a more comprehensive and
self-consistent model of this phenomenon is gradually emerging.

The matter orbiting and falling onto a black hole is referred
to as the . It plays a crucial
role in jet formation. A black hole, together with its
accretion disk and jets (fig. 1), are thought to be the most
effective “machine” for converting . If we define the efficiency of such a
system as the ratio of the energy carried away by the jets to
the energy of the accreted matter, it may even exceed 100

Nevertheless, a closer look at the system reveals that the
second law of thermodynamics still holds. This is no perpetual
motion machine. It turns out that part of the energy of the jet
comes from the of the black hole. That is,
by powering a jet, a black hole spins progressively slower.

In a way, this seeming perpetual motion is more like an
electric bike. There is an apparent mismatch between the input
energy of the accreting matter—muscle work, in the case of the
biker—and the output energy of the jet, or the motion of the
bicycle. In both cases, though, there is an additional hidden
energy source—namely, the battery powering the bike’s electric
motor and the rotation of the black hole.

Via accretion, a black hole gains angular momentum—that is, it
starts spinning faster. Jets carry away some of this excess
angular momentum in what is known as rotational energy
extraction. Similar effects are observed in young stars. During
the formation of a star, it captures the matter of the
accretion disk, which has enormous angular momentum. However,
observations show such stars actually rotate rather slowly. All
of the missing angular momenta is used up to power the narrow
jets emitted by these stars.

Fig. 2. Transverse structure of the magnetic field of a jet.
Credit: MIPT

Scientists have recently developed a new method for measuring
the magnetic fields in the jets emitted by the active galactic
nuclei. In her paper, astrophysicist Elena Nokhrina showed that
this method can be used to estimate the contribution of black
hole rotation to jet power. Up until now, the formula for the
channeling of rotational energy into the energy of the jet has
not been tested empirically. Unfortunately, no reliable
observations so far have captured black hole , which is important for estimating
the loss of rotational energy.

A black hole does not have a magnetic field of its own.
However, a vertical magnetic field is generated around it by
the ionized matter in the accretion disk. To estimate the loss
of rotational energy by a black hole, scientists need to find
the through the boundary around a
black hole known as the event horizon.

“Because the magnetic flux is conserved, by measuring its
magnitude in the jet, we also learn the magnetic flux near the
black hole. Knowing the black hole’s mass, we can calculate the
distance from its rotation axis to the event horizon—its
notional boundary. This allows us to estimate the electric
potential difference between the axis of rotation and the
boundary of the black hole. By accounting for the electric
field screening in plasma, it is possible to find the electric
current near the black hole. Knowing both the current and the
difference of potentials, we can estimate the amount of energy
lost by the black hole due to the slowing down of its
rotation,” says Elena Nokhrina, the author of the paper and
deputy head of the relativistic astrophysics laboratory at

The calculations point toward a correlation between the total
power of a jet emitted by a black hole and the loss of
rotational energy by the black hole. Notably, this study makes
use of a recent model of jet structure (fig. 2). Before this
model was advanced, researchers assumed jets to have
homogeneous transverse structure, which is a simplification. In
the new model, the magnetic field of a jet is not homogeneous,
enabling more accurate predictions.

Most of the galaxies hosting jets are too remote for the
transverse structure of their magnetic fields to be discerned.
So the experimentally measured magnetic field is compared with
its model transverse structure to estimate the magnitude of the
field’s components. Only by taking transverse structure into
account is it possible to test the mechanism of black hole
rotation powering jets. Otherwise, it would be necessary to
know the rotation rate.

The hypothesis that was put to the test in the study states
that jet power depends on the magnetic flux and the rotation
rate of the black hole. This makes it possible to gauge to what
extent a jet is powered by rotational energy. Notably, this
theoretical work enables us to estimate how much is lost by a black hole without
knowing its rotation rate—using only the measurements of the jet.

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More information: Elena E. Nokhrina, The Correlation
between the Total Magnetic Flux and the Total Jet Power,
Frontiers in Astronomy and Space Sciences (2017).
DOI: 10.3389/fspas.2017.00063