Centrifugal acceleration of
astroparticle
Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our own ...
s to relativistic energies might take place in rotating astrophysical objects (see also
Fermi acceleration). It is strongly believed that
active galactic nuclei
An active galactic nucleus (AGN) is a compact region at the center of a galaxy that has a much-higher-than-normal luminosity over at least some portion of the electromagnetic spectrum with characteristics indicating that the luminosity is not prod ...
and
pulsars have rotating
magnetospheres, therefore, they potentially can drive charged particles to high and ultra-high energies. It is a proposed explanation for
ultra-high-energy cosmic rays (UHECRs) and extreme-energy cosmic rays (EECRs) exceeding the
Greisen–Zatsepin–Kuzmin limit
The Greisen–Zatsepin–Kuzmin limit (GZK limit or GZK cutoff) is a theoretical upper limit on the energy of cosmic ray protons traveling from other galaxies through the intergalactic medium to our galaxy. The limit is (50 EeV), or about 8 j ...
.
Acceleration to high energies
It is well known that the magnetospheres of
AGNs and
pulsars are characterized by strong magnetic fields that force charged particles to follow the field lines. If the magnetic field is rotating (which is the case for such astrophysical objects), the particles will inevitably undergo
centrifugal acceleration. The pioneering work by Machabeli & Rogava was a
thought experiment in which a bead moves inside a straight rotating pipe. Dynamics of the particle were analyzed both analytically and numerically and it was shown that if the rigid rotation is maintained for a sufficiently long time energy of the bead will asymptotically increase. In particular, Rieger & Mannheim, building on the theory of Machabeli & Rogava, showed that the
Lorentz factor
The Lorentz factor or Lorentz term is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while that object is moving. The expression appears in several equations in special relativit ...
of the bead behaves as
where
is the initial Lorentz factor, Ω is the angular velocity of rotation,
is the radial coordinate of the particle, and
is the speed of light. From this behavior it is evident that radial motion will exhibit a nontrivial character. In due course of motion the particle will reach the light cylinder surface (a hypothetical area where the linear velocity of rotation exactly equals the speed of light), leading to the increase of the
poloidal component of velocity. On the other hand, the total velocity cannot exceed the speed of light, therefore, the radial component must decrease. This means that the
centrifugal force changes its sign.
As is seen from (), the Lorentz factor of the particle tends to infinity if the rigid rotation is maintained. This means that in reality the energy has to be limited by certain processes. Generally speaking, there are two major mechanisms: The inverse
Compton scattering
Compton scattering, discovered by Arthur Holly Compton, is the scattering of a high frequency photon after an interaction with a charged particle, usually an electron. If it results in a decrease in energy (increase in wavelength) of the photon ...
(ICS) and the so-called breakdown of the bead on the wire (BBW) mechanism. For jet-like structures in an
AGN it has been shown that, for a wide range of inclination angles of field lines with respect to the rotation axis, ICS is the dominant mechanism efficiently limiting the maximum attainable Lorentz factors of electrons
. On the other hand, it was shown that the BBW becomes dominant for relatively low luminosity
AGN , leading to
.
The centrifugal effects are more efficient in millisecond
pulsars as the rotation rate is quite high. Osmanov & Rieger considered the centrifugal acceleration of charged particles in the light cylinder area of the Crab-like
pulsars. It has been shown that electrons might achieve the Lorentz factors
via
inverse Compton Klein–Nishina up-scattering.
Acceleration to very high and ultra-high energies
Although the direct centrifugal acceleration has limitations, as analysis shows the effects of rotation still might play an important role in the processes of acceleration of charged particles. Generally speaking, it is believed that the centrifugal relativistic effects may induce plasma waves, which under certain conditions might be unstable efficiently pumping energy from the background flow. On the second stage energy of wave-modes can be transformed into energy of plasma particles, leading to consequent acceleration.
In rotating magnetospheres the
centrifugal force acts differently in different locations, leading to generation of Langmuir waves, or
plasma oscillations via the parametric instability. One can show that this mechanism efficiently works in the magnetospheres of
AGN and
pulsars.
Considering
Crab-like
pulsars it has been shown that by means of the
Landau damping In physics, Landau damping, named after its discoverer,Landau, L. "On the vibration of the electronic plasma". ''JETP'' 16 (1946), 574. English translation in ''J. Phys. (USSR)'' 10 (1946), 25. Reproduced in Collected papers of L.D. Landau, edited a ...
the centrifugally induced electrostatic waves efficiently lose energy transferring it to electrons. It is found that energy gain by electrons is given by
where
,
is the increment of the instability (for details see the cited article),
,
,
is the plasma number density,
is the electron's mass and
is the Goldreich-Julian density. One can show that for typical parameters of the
Crab-like
pulsars, the particles might gain energies of the order of
of
or even
. In case of millisecond newly born pulsars, the electrons might be accelerated to even higher energies of
By examining the magnetospheres of
AGNs, the acceleration of protons takes place through the
Langmuir collapse. As it is shown this mechanism is strong enough to guarantee efficient acceleration of particles to ultra-high energies via the Langmuir damping
:
,
where
is the normalized luminosity of
AGN,
is its normalized mass and
is the Solar mass. As it is evident, for a convenient set of parameters one can achieve enormous energies of the order of
, so
AGNs become cosmic Zevatrons.
References
Further references
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*{{Cite journal , title = Centrifugally Driven Relativistic Dynamics on Curved Trajectories
, last1 = Rogava , first1 = Andria
, last2 = Dalakishvili , first2 = George
, last3 = Osmanov , first3 = Zaza
, journal = General Relativity and Gravitation
, year = 2003 , volume = 35 , issue = 7 , pages = 1133–1152
, arxiv = astro-ph/0303602 , bibcode = 2003GReGr..35.1133R , doi = 10.1023/A:1024450105374 , s2cid = 119440652
Astroparticle physics
Thought experiments in physics