Messengers of the Universe-Cosmic Rays Exploring Supermassive Black Holes

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Review Messengers of the Universe-Cosmic Rays Exploring Supermassive Black Holes

Anna Uryson

Lebedev Physical Institute of Russian Academy of Sciences, Moscow 119991, Russia; [email protected]

Abstract: Cosmic rays were discovered over one hundred years ago but there are still unsolved problems. One of the hot problems is the origin of cosmic rays of the highest energies. Sources are still unclear and it is neither clear how particles gain ultra-high energies. Possible sources of cosmic rays at the highest energies are supermassive black holes. From this perspective we discuss in a popular form some recent developments in cosmic ray studies along with author’s recent results. The paper also offers materials for further reading.

Keywords: cosmic rays; ultra-high energies; active galactic nuclei; supermassive black holes

1. Introduction 1.1. What Are Cosmic Rays? Cosmic rays were discovered by the Austrian physicist Victor Hess in 1912. For his study he used simple portable devices—electroscopes in balloons. For this discovery, Hess received the Nobel Prize in Physics in 1936. Later it was demonstrated that cosmic radiation consisted mainly of charged elementary particles (protons and electrons) and fragments of atomic nuclei (then a very small admixture of gamma quanta and neutrinos was found in cosmic rays). Cosmic particles arrive to Earth from space. In 1930–1940s cosmic ray interactions with matter were studied intensively. These Citation: Uryson, A. Messengers of studies led to the discovery of new elementary particles. the Universe-Cosmic Rays Exploring We now turn from physics history to cosmic ray astrophysics. Supermassive Black Holes. Galaxies Physicists use different types of instruments to detect cosmic rays. These detectors 2021, 9, 2. https://doi.org/10.3390/ can be ground-based or installed on space satellites or at high altitude balloons. galaxies9010002 Particles at energies up to 48 Joule (J) have been detected in cosmic rays. These energies are so high that no particle accelerator built on Earth is able to provide such Received: 30 November 2020 energy, including the most powerful Large Hadron Collider. Accepted: 23 December 2020 It is worth mentioning that in particle physics and astrophysics the energy unit Published: 29 December 2020 electron-volt (eV) is commonly used rather than Joule. So, the maximal energy of particles detected in cosmic rays is about 3 × 1020 eV. Publisher’s Note: MDPI stays neu- The energy range of cosmic rays is extremely large: from 106 up to 3 × 1020 eV. tral with regard to jurisdictional claims Cosmic rays travel with gigantic velocities close to the speed of light. At lower energies in published maps and institutional particles also travel at the same speed. afﬁliations. 1.2. What Is the Origin of Cosmic Rays? Particles at energies lower than 2 × 1010 eV come from the sun, and they are called Copyright: © 2020 by the author. Li- solar cosmic rays. At higher energies, up to 1017–1018 eV, they originate from outside the censee MDPI, Basel, Switzerland. This solar system in our Galaxy in supernova explosions, and are called galactic cosmic rays. article is an open access article distributed Cosmic particles at higher energies, more than 1019 eV, are called ultra-high energy under the terms and conditions of the cosmic rays (UHECRs). This scientiﬁc term contains no information related to the origin of Creative Commons Attribution (CC BY) cosmic particle. It indicates only the particle energy range. Years of research revealed that license (https://creativecommons.org/ cosmic ray accelerators are astrophysical objects located outside our galaxy. licenses/by/4.0/).

Galaxies 2021, 9, 2. https://doi.org/10.3390/galaxies9010002 https://www.mdpi.com/journal/galaxies Galaxies 2021, 9, 2 2 of 16

What are these objects and processes accelerating cosmic rays to ultra-high energies? In the paper we consider, in a popular form, supermassive black holes as possible sources of cosmic rays at the highest energies and discuss the results and problems related to the subject. The structure of the paper is as follows. Methods of cosmic ray detection are given briefly in Section2. Supermassive black holes inside active galactic nuclei are discussed in Sections3–7 as we believe that they are involved in particle acceleration. Theoretical results on cosmic ray acceleration in supermassive black holes are shown in Section8. Section9 describes cosmic ray propagation in the universe. In Section 10 we show how to study processes in supermassive black holes using data on cosmic rays. In Section 11 general outlook on the study of cosmic rays is presented. Processes of cosmic ray acceleration are discussed in Section 12. The conclusion is given in Section 13. Finally, in Section 14 a short list of scientific articles, results of which are used in the paper, is presented. Section14 also briefly describes problems discussed in these articles. It is for those readers who are interested in more details of cosmic ray astrophysics. All references are given in this section.

2. Methods of Cosmic Ray Detection The number of cosmic particles decreases strongly with increasing energy. Due to this, cosmic rays at various energies are detected by different methods. Cosmic rays at energies of E = 106–5 × 108 eV are detected with detectors on board satellites. Cosmic rays at energies of E = 109–1012 eV are detected mainly with detectors on balloons. Particles at higher energies are detected using Earth’s atmosphere. How is that possible? Cosmic rays—primaries—bombard the atmosphere and interact with its molecules. As a result new particles—secondary particles or secondaries are generated, which also interact with atmospheric elements. This process develops as an avalanche producing a huge amount of secondaries that diverge to tens and hundreds of meters. It looks like a thin disk of particles moving through the atmosphere with almost the speed of light and spreading with the atmosphere depth. The shower of particles is called extensive air shower. The axis of the disk is the shower axis and it coincides with the direction of primary’s movement. Figure1 shows the cosmic ray observatory in Tian-Shan mountains, Kazakhstan, with a schematic view of two detectors and their location. Cosmic rays at the energies E ≥ 1014 eV give rise to extensive air showers where particles spread around the area of hundreds square meters. Thus particles can be registered using many small detectors located at the large area. Cosmic rays at ultra-high energies, higher than 1019 eV are rare: 1 particle per km2 per year. Thus very large arrays are required to study ultra-high energy cosmic rays. Those are the Pierre Auger Observatory (PAO) in Argentina called after French physicist Pierre Auger, one of the pioneers in study atmospheric showers, and the telescope array (TA) in Utah, USA. The PAO consists of a 3000 km2 array of 1660 particle detectors, and the TA consists of more than 500 detectors sampling events over 780 km2. Figures2 and3 give a look on the landscape and detectors of the PAO and the TA. Scientists from different countries team up to maintain activity of the arrays and analyze the data. Galaxies 2021, 9, 2 3 of 16 Galaxies 2021, 9, x FOR PEER REVIEW 3 of 17

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Figure 1. Cosmic ray observatory of Lebedev Physical Institute of Russian Academy of Scie Sciences,nces, Tian-Shan mountains. Location and designation of two of the detectors are shown schematically. Source: https://sites.lebedev.ru/ru/lgase/. FigureLocation 1. andCosmic designation ray observatory of two of of the Lebedev detectors Physical are shown Institute schematically. of Russian Source: Academy https://sites.lebedev.ru/ru/lgase/ of Sciences, Tian-Shan mountains.. Location and designation of two of the detectors are shown schematically. Source: https://sites.lebedev.ru/ru/lgase/.

Figure 2. Several detector components of the Pierre Auger Observatory in Argentina. Photo Credit: Tobias Winchen-Own work, CC BY-SA 3.0, Source: https://commons.wikimedia.org/w/index.php?curid=18816298. Figure 2. Several detector components of the Pierre Auger Observatory in Argentina. Photo Credit: Tobias Winchen-Own Figure 2. Several detector components of the Pierre Auger Observatory in Argentina. Photo Credit: Tobias Winchen-Own work, CC BY-SA 3.0, Source: https://commons.wikimedia.org/w/index.php?curid=18816298. work, CC BY-SA 3.0, Source: https://commons.wikimedia.org/w/index.php?curid=18816298.

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Figure 3. One of the detectors of the telescope array cosmic ray observatory in Utah, USA. Photo Credit: John Matthews, University of Utah, Source: archive.unews.utah.edu. FigureFigure 3. 3.One One of of the the detectors detectors ofof thethe telescopetelescope arrayarray cosmic ray observatory in in Utah, Utah, USA. USA. Photo Photo Credit: John Matthews, University of Utah, Source: archive.unews.utah.edu. 2.1.Credit: What John Data Matthews, Are Obtained University with These of Utah,Arrays? Source: archive.unews.utah.edu. 2.1.2.1. What ThoseWhat DataData are Are Areparticle Obtained Obtained energies, with with These Thesearrival Arrays? Arrays? directions and cosmic ray composition (protons or atomicThoseThose nuclei are are particle fragments),particle energies, energies, which arrival arrival are de directions termineddirections and using and cosmic cosmicspecial ray raycomputer composition composition codes. (protons (protons or atomicor atomic nuclei nuclei fragments), fragments), which which are determinedare determined using using special special computer computer codes. codes. 2.2. How Are These Data Used to Reveal Cosmic Ray Origin? 2.2.2.2. How CosmicHow Are Are ray These These arrival Data Data Useddirections Used to to Reveal Reveal on CosmicEarth Cosmic are Ray Ray unusable Origin? Origin? as pointers on sources because chargeCosmicCosmic particles ray ray are arrival arrival deflected directions directions by extragalactic on on Earth Earth are are magnetic unusable unusable fields. as as pointers pointers Particle on onenergies sources sources are because because used tochargecharge investigate particles particles some are are deﬂectedparameters deflected by byof extragalactic sources.extragalactic This magnetic ismagnetic discussed ﬁelds. fields. in Particle Sections Particle energies 9 energiesand 10. are usedare used to investigateto investigateThe cosmic some some ray parameters energyparameters distribution of sources. of sources. This (ene This isrgy discussed isspectrum) discussed in Sectionsof in the Sections PAO9 and 9and 10and. the 10. TA are shownTheThe in cosmicFigure cosmic 4. ray ray energy energy distribution distribution (energy (energy spectrum) spectrum) of of the the PAO PAO and and the the TA TA are are shownshown in in Figure Figure4. 4.

Figure 4. Cosmic ray energyenergy distributiondistribution (energy (energy spectrum) spectrum) obtained obtained at at the the Pierre Pierre Auger Auger Observatory Observatory (PAO) (blue points) and the telescope array (TA) (red points) scaled by E3. In each (PAO)Figure (blue 4. Cosmic points) ray and energy the telescope distribution array (TA)(energy (red spectrum) points) scaled obtained by E3 at. In the each Pierre experiment Auger data of experiment data of different techniques are combined to obtain the spectrum over wide3 energy differentObservatory techniques (PAO) are (blue combined points) to and obtain the tele thescope spectrum array over (TA) wide (red energy points) range. scaled The by ﬁgure E . In iseach taken range.experiment The figure data is of taken different from te thechniques joint report are combined of the PAO to obtainand TA the collaborations spectrum over presented wide energy at the from the joint report of the PAO and TA collaborations presented at the International Cosmic Ray Internationalrange. The figure Cosmic is takenRay Conference from the joint (ICRC) report in 2019.of the The PAO discrepancy and TA collaborations between the presentedPAO and theat the Conference (ICRC) in 2019. The discrepancy between the PAO and the TA results is also discussed in TAInternational results is also Cosmic discussed Ray Conferencein the report. (ICRC) The reference in 2019. Theis in discrepancy Section 14. between the PAO and the theTA report. results The is also reference discussed is in in Section the report. 14. The reference is in Section 14.

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SatellitesSatellites are are also also used used to to obtain obtain some some some in information informationformation onon on ultra-highultra-high ultra-high energy energy energy cosmic cosmic cosmic rays, rays, rays, ininin addition addition to to to ground ground based based arrays. arrays. The TheThe flux ﬂuxflux of of these these particles particles is is extremely extremely low low and and the the indirectindirectindirect method method is is used. used. Ultra-high Ultra-highUltra-high energy energyenergy particles particles propagating propagating in in space space interact interact with with photonsphotons andand and contributecontribute contribute to to theto the the gamma-radiation gamma-radiation gamma-radiation that that isthat registered is is registered registered with apparatuswithwith apparatus apparatus on board. on on board.Knowingboard. Knowing Knowing the value the the of value thevalue gamma-radiation of of the the gamma-radiation gamma-radiation and using and theoreticaland using using theoretical resultstheoretical some results results parameters some some parametersofparameters particle sourcesof of particle particle can sources sources be derived. can can be be Figure derive derive5 d.showsd. Figure Figure the 5 5 shows cosmic shows the raythe cosmic cosmic observatory ray ray observatory observatory Fermi to FermiobtainFermi to datato obtain obtain for ultra-highdata data for for ultra- ultra- energyhighhigh cosmic energy energy ray cosmic cosmic studies. ray ray studies. studies.

FigureFigure 5. 5. The The Fermi Fermi gamma-ray gamma-ray space space telescope. telescope. Photo Photo Credit: Credit: NASA NASA E/PO. E/PO. Sonoma Sonoma State State Figure 5. The Fermi gamma-ray space telescope. Photo Credit: NASA E/PO. Sonoma State University, University,University, Aurore Aurore Simonnet, Simonnet, Source: Source: Aurore Simonnet, Source: https://astro.desy.de/gamma_astronomy/fermi/index_eng.html. https://astro.desy.de/gamma_astrhttps://astro.desy.de/gamma_astronomy/fermi/index_eng.html.onomy/fermi/index_eng.html. Neutrinos are also produced in cosmic ray interactions with photons. Neutrino ﬂux NeutrinosNeutrinos are are also also produced produced in in cosmic cosmic ray ray interactions interactions with with photons. photons. Neutrino Neutrino flux flux isis used to deﬁnedefine sourcesource parametersparameters asas well.well. It It is measured at ground-basedground-based neutrinoneutrino observatories.is used to define One source of them, parameters the IceCube as neutrinowell. It is observatory measured at is locatedground-based near the neutrino South observatories.observatories. One One of of them, them, the the IceCube IceCube neut neutrinorino observatory observatory is is located located near near the the South South Pole. Thousands Thousands of of sensors sensors deep deep within within the the Antarctic Antarctic ice ice are distributed over a cubic kilometer.Pole. Thousands The IceCube of sensors observatory deep within is shown the in Antarctic Figure6. ice are distributed over a cubic kilometer.kilometer. The The IceCube IceCube observatory observatory is is shown shown in in Figure Figure 6. 6.

Figure 6. The IceCube Lab at the South Pole in Antarctica. Image: S. Lidstrom/NSF, Source: icecube.wisc.edu. FigureFigure 6. 6. The The IceCube IceCube Lab Lab at at the the South South Pole Pole in in Antarctica. Antarctica. Image: Image: S. S. Lidstrom/NSF, Lidstrom/NSF, Source: Source: icecube.wisc.edu. icecube.wisc.edu. StudyStudy of of particle particle origin origin using using data data of of ground-based ground-based arrays arrays and and satellites satellites is is discussed discussed ininin Sections Sections Sections 99–11. –9–11.11. 3. Outside the Milky Way; Active Galactic Nuclei 3.3. Outside Outside the the Milky Milky Way; Way; Active Active Galactic Galactic Nuclei Nuclei Our galaxy the Milky Way that contains the solar system is one of many galaxies in OurOur galaxy galaxy the the Milky Milky Way Way that that contains contains the the solar solar system system is is one one of of many many galaxies galaxies in in the universe. thethe universe. universe. A galaxy is a gravitationally bound system consisting of stars (sometimes with planet AA galaxy galaxy is is a a gravitationally gravitationally bound bound system system co consistingnsisting of of stars stars (sometimes (sometimes with with planet planet systems), star remnants, interstellar gas and dust and dark matter. systems),systems), star star remnants, remnants, interstellar interstellar gas gas and and dust dust and and dark dark matter. matter. The central central part part of of many many galaxies galaxies contains contains a acompact, compact, massive massive cluster cluster of ofmatter. matter. It is It is calledThe galacticcentral part nucleus. of many Higher galaxies density contains of matter a compact, in the massive central cluster region of is matter. caused It by is calledcalled galacticgalactic nucleus.nucleus. HigherHigher densitydensity ofof mattermatter inin thethe centralcentral regionregion isis causedcaused byby gravitation. It It pulls pulls the the stars stars and and interste interstellarllar matter matter towards towards the the center and form the nucleus.gravitation. Galaxies It pulls with the small stars mass and have interste no nucleusllar matter as its towards gravity isthe insufﬁcient center and to form pull thethe nucleus. Galaxies with small mass have no nucleus as its gravity is insufficient to pull the matternucleus. towards Galaxies the with center. small mass have no nucleus as its gravity is insufficient to pull the mattermatter towards towards the the center. center.

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Galaxies 2021, 9, 2 6 of 16 Galaxies vary in many features: in appearance, dimension, intensity of star formation, relation between old and young stars. Galaxies are classified according to these features. In additionGalaxies galaxies vary in many differ features: in characteristics in appearance, of the dimension,nucleus. intensity of star formation, In relationmost galaxies, between the old main and part young of stars.energy Galaxies is emitted are classifiedby stars, and according stars also to these provide features. In the nucleusaddition emission. galaxies These differ galact in characteristicsic nuclei are called of the inactive. nucleus. However,In mostthere galaxies,is a small the amount main partof gala of energyxies where is emitted nucleus by emission stars, and is starsextremely also provide powerfulthe compared nucleus emission. to the rest These of the galactic galaxy: nuclei A huge are energy called inactive.stream breaks away from a nucleus, as ifHowever, one hundred there mill is aion small sun-like amount stars of shine galaxies in the where galactic nucleus center. emission The nucleus is extremely emissionpowerful is highly compared variable, sharply to the rest diminishing of the galaxy: and increasing A huge energy during stream a very breaksshort period away from a of time nucleus,(on the scale as if of one hours, hundred days, millionmonths sun-likeand years). stars A shinenucleus in emits the galactic energy center. in different The nucleus bands: radio,emission X-rays, is highly ultraviolet, variable, infrared sharply and diminishing gamma ranges. and increasing Plasma portions during a are very spread short period outwardsof timea nucleus; (on the gas scale clouds of hours, move days, rapidl monthsy in its and vicinity. years). AThese nucleus processes emits energy cannot in be different caused bands:by high radio, volume X-rays, density ultraviolet, of stars infrared or interstellar and gamma matter. ranges. Such Plasma galactic portions nuclei are spread called active.outwards There a nucleus;is only 1% gas of cloudsgalaxies move of this rapidly type in in the its universe. vicinity. These processes cannot be Activecaused galactic by high nuclei volume are densityclassified of in stars types or interstellardepending matter. on the Suchform galacticof their nucleiactivity. are called For instance,active. the There most is powerful only 1% ofgalactic galaxies nuclei of this are type called in thequasars, universe. galaxies with powerful radio emissionActive in galacticnuclei nucleiare called are classified radio galaxies. in types dependingAnother example: on the form galaxies of their with activity. For extremelyinstance, variable the emission most powerful but no galacticso bright nuclei as quasars are called are called quasars, Seyfert galaxies galaxies with (named powerful radio after astronomeremission inSeyfert). nuclei are called radio galaxies. Another example: galaxies with extremely Detailedvariable description emission butof the no soactive bright nucleus as quasars classification are called is Seyfertnot important galaxies for (named our after study. Itsastronomer main goal Seyfert). is given in the next section. Detailed description of the active nucleus classification is not important for our study. 4. ActiveIts Galactic main goal Nuclei is given and in Cosmic the next Rays section. Each active galactic nucleus emits gigantic amount of energy. Possibly cosmic rays 4. Active Galactic Nuclei and Cosmic Rays gain ultra-high energies in energetic processes ongoing in nuclei. Then accelerated particles fly Eachout of active the region galactic where nucleus they emitsgain the gigantic energy, amount escape of from energy. the Possiblygalaxy, travel cosmic rays huge distancesgain ultra-high in space energies and finally in energetic reach Earth. processes Is it possible ongoing to in study nuclei. active Then galactic accelerated nuclei particles by detectingfly out cosmic of the rays region on Earth, where despite they gain particles’ the energy, long flight escape in the from cosmos? the galaxy, travel huge In distancesthis study in it spaceis important and finally to answer reach Earth.the questions: Is it possible what tois studythe source active of galacticenergy nucleiin by active galacticdetecting nuclei, cosmic how rays particles on Earth, are despite accelerated, particles’ and long what flight happens in the cosmos?to the particles during theirIn flight this through study it the is important extragalactic to answerspace. Before the questions: discussing what these is points the source a short of energy descriptionin active of possible galactic cosmic nuclei, ray how sources particles is given are accelerated, in next sections. and what happens to the particles during their flight through the extragalactic space. Before discussing these points a short 5. The Sourcedescription of Energy of possible in Active cosmic Galactic ray sources Nuclei is and given Supermassive in next sections. Black Holes It is5. of The the Source current of opinion Energy innow Active that Galacticnucleus Nucleiactivity and is caused Supermassive by a supermassive Black Holes black hole inIt the is of galactic the current center. opinion What now are thatblack nucleus holes? activity A black is hole caused is bya celestial a supermassive object black with a veryhole strong in the galacticgravitational center. field. What It is are so black strong holes? that nothing, A black even hole islight, a celestial can escape object with from there.a very How strong can gravitationalthat be? To overcome field. It is th soe strongattractive that force nothing, of any even celestial light, canobject, escape a from body shouldthere. move How with can thatthe escape be? To velocity. overcome However, the attractive in black force holes of anyit is celestialhigher than object, the a body speed ofshould light. moveNothing with travels the escape faster velocity.than the However,speed of light in black in the holes universe, it is higher and because than the speed of this itof is light. impossible Nothing to travelsescape fasterfrom thanblack the holes. speed As oflight light is innot the able universe, to leave and black because holes, of this it they areis dark impossible and invisible to escape for fromobserver. black holes. As light is not able to leave black holes, they are At darklarge and distances invisible black for observer.hole gravitation weakens to the level of an “ordinary” star. The radius ofAt the large black distances hole vicinity black holefrom gravitation which nothing weakens including to the levelsignals of come an “ordinary” out is star. called theThe event radius horizon. of the black hole vicinity from which nothing including signals come out is

Whencalled the the black event hole horizon. mass is higher than 105 solar mass (Mʘ) the black hole is called supermassive.When Evidence the black of black hole mass holes is with higher masses than 10M5 solar≈ (105 mass–1011) ( Mʘ )are the observed black hole in is called active galacticsupermassive. nuclei. Evidence of black holes with masses M ≈ (105–1011) are observed in Blackactive holes galactic are so nuclei. extraordinary that people (not physicists) believe that they are mysterious. Black holes are so extraordinary that people (not physicists) believe that they are Blackmysterious. holes are quite unusual celestial objects that were first considered by a brilliant English scientistBlack and holes parson are quite Michell unusual in celestial1783 and objects by a that great were French ﬁrst considered mathematician, by a brilliant physicistEnglish and scientistastronomer and parsonLaplace Michell in 1796 in 1783. In and 1916 by athey great Frenchwere mathematician,rediscovered by physicist and astronomer Laplace in 1796. In 1916 they were rediscovered by Schwarzschild based

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on Einstein ﬁeld equations in general theory of relativity. (The 2020 Nobel prize in Physics was awarded for the theory and astronomical observations of black holes). Interestingly, our galaxy the Milky Way evidently contains the central supermassive black hole with the mass of 106 solar masses. At present its activity is weak. However black hole activity varies in time, and there are evidences that “our” black hole was apparently active, e.g., ~300–400 years ago and ~25,000 years ago. Evidence of the supermassive black hole in the center of our galaxy along with evidence of its activity is the result of astronomical observations during last 20 years.

6. The Accretion Disk around a Supermassive Black Hole Due to the attractive force matter in the vicinity of a black hole falls into it. This matter consists of nearby stars and interstellar gas and dust. Stellar gas from surfaces of nearby stars is also “swallowed” by black holes (dust and interstellar gas contribute much less than the stellar one). Stellar matter falls not vertically but whirling (as stars move on orbits) and thus forming disk around a black hole. The accretion disk is dense. Its thickness depends on black hole characteristics. Matter falling in the black hole gravitational ﬁeld, its potential energy transforms into kinetic energy. As a result the matter accelerates to tremendous velocity, close to the speed of light. Acceleration of the falling matter occurs in exactly the same way as acceleration of a stone falling to the ground. In the disc gas layers move around the center, however with different velocities: the closer to the center, the higher is the speed. The friction between the layers transforms the layer kinetic energy into thermal energy of atoms in the gas. As a result the gas is heated to very high temperature and the disc shines in radio, infrared and optical bands, in X-rays and gamma rays.

7. Magnetic Field of Accretion Discs; Jets Magnetic field threads through interstellar gas and stars: Almost all matter in interstellar medium and stars is ionized, consisting of charged particles. These factors lead to magnetic field line freezing-in: charged particles are as if “fastened” to the line, and it has to move along with moving particles. As magnetic field moves with the falling gas the disc is magnetized. Gas density increasing, the magnetic lines get closer and the field increases. As the result the magnetic field in discs can be much stronger than the field threading through interstellar gas and stars. In the accretion disc, gas not only rotates but also slowly moves in a radial direction (the speed of moving depends on mass and temperature of the disc). In some disks moving and rotating magnetic fields frozen in plasma collimate plasma in columns (protuberances) rising up near the poles. The columns eject plasma blobs that form narrow jets along the disc axis, perpendicularly to the disc plane. In a simplified manner jets can be explained in the following way. Rotating gas moves in the radial direction, the radial velocity depending on the disk mass and temperature. There are discs where gas radial motion is so fast that too much gas arrive to the disc center. The black hole is not able to “eat” the gas completely, and its excess is ejected outward forming jets. A supermassive black hole with the accretion disc and jets is shown in Figure7. Galaxies 2021, 9, 2 8 of 16 Galaxies 2021, 9, x FOR PEER REVIEW 8 of 17

FigureFigure 7. 7.A A supermassive supermassive black black hole hole with thewith accretion the accretion disc and disc jets paintedand jets by painted an artist. by The an author:artist. VictorThe author: Habbic Visions.Victor Habbic Source: Visions.newshub.co.nz Source:. newshub.co.nz.

DiskDisk magneticmagnetic ﬁeld field encircles encircles the the black black hole hole forming forming its its magnetosphere. magnetosphere.

8.8. ParticleParticle AccelerationAcceleration inin thethe VicinityVicinity of of Supermassive Supermassive Black Black Holes Holes SupermassiveSupermassive blackblack holesholes havehave threethree areasareas where where particles particles can can be be accelerated. accelerated. They They areare magnetosphere magnetosphere of of a a black black hole, hole, its its accretion accretion disc disc and and jets. jets. The The accelerating accelerating mechanism mechanism inin each each area area is is different different and and accelerated accelerated particles particles have have different differentenergy energy spectra spectra. . WhatWhat isis anan energyenergy spectrum? spectrum? LetLet usus definedefine the the number number of of particles particles at at equal equal energies energies andand plotplot thethe numbernumber againstagainst thethe particleparticle energy.energy. ThisThis dependencedependence isis calledcalled thetheparticle particle energyenergy spectrumspectrum.. TheThe energyenergy spectrumspectrum cancan bebe obtained obtained alsoalso analytically, analytically, represented represented as as a a formula.formula. The The strict strict definition definition of energyof energy spectrum spectrum is the is number the number dN of particlesdN of particles at the energy at the E in the unit energy interval dE. Energy spectra produced in sources are called injection energy E in the unit energy interval dE. Energy spectra produced in sources are called spectra. It was found theoretically that particles accelerated by the varied mechanisms have injection spectra. It was found theoretically that particles accelerated by the varied different injection spectra (or, in some cases, possibly different spectra). The accelerating mechanisms have different injection spectra (or, in some cases, possibly different spectra). mechanisms and some models are discussed in Section 12. The accelerating mechanisms and some models are discussed in Section 12. Two different ways of particle acceleration are by shock fronts and by electric fields (a Two different ways of particle acceleration are by shock fronts and by electric fields description of mechanisms is given in Section 12.) (a description of mechanisms is given in Section 12.) Based on the theoretical results, in the former case the cosmic ray energy spectrum is Based on the theoretical results, in the former case the cosmic ray energy spectrum is described as dN/dE ∝ E−α, with spectral index α equal to α ≈ (2–2.5). This type of spectra ∝ –α isdescribed called exponential. as dN/dE The E higher, with thespectral energy, index the α faster equal the to numberα ≈ (2–2.5). of particlesThis type decreases of spectra (oris called the higher exponential. is the rate The of particlehigher the number energy, reduction). the faster This the number mechanism of particles works in decreases jets. (or theWhen higher particles is the are rate accelerated of particle by number electric reduction). fields in the This black mechanism hole vicinity, works two in different jets. injectionWhen spectra particles can be are produced. accelerated by electric fields in the black hole vicinity, two differentFirst, injection particles spectra can gain can approximately be produced. equal amounts of energy. In this case the injectionFirst, spectrum particles is can called gain monoenergetic. approximately It isequal shown amounts theoretically of energy. that thisIn this spectrum case the is realizedinjection in spectrum black hole is magnetospheres.called monoenergetic. It is shown theoretically that this spectrum is realizedNext, in the black spectrum hole magnetospheres. can be exponential with spectral indices α ≈ (0–2.1). It means that theNext, number the spectrum of particles can decreases be exponential not so with fast withspectral energy, indices as when α ≈ (0–2.1).α > 2.1. It means The index that valuethe number 0 is realized of particles in processes decreases where not so the fast number with energy, of accelerated as when particles α > 2.1. The is the index same value at any0 is energy.realized We in supposeprocesses that where this energythe number spectrum of accelerated possibly is producedparticles is in the accretion same at discs any andenergy. jets. We suppose that this energy spectrum possibly is produced in accretion discs and jets. At present it is unknown what mechanisms are realized in the vicinity of supermassive blackAt holes. present Can weit determineis unknown in what what processes mechanisms particles are have realized been accelerated?in the vicinity At this of pointsupermassive it seems likeblack we holes. have foundCan we a verydetermine simple in way what to answerprocesses the particles question. have First, been we obtainaccelerated? cosmic At rays this energy point spectrumit seems like on Earth. we have Next, found we compare a very simple the data way with to theoreticalanswer the injectionquestion. spectra, First, we find obtain the best cosmic fitting rays and ener correspondinggy spectrum values on Earth. of α Next,. Thus we we compare reveal how the anddata where with theoretical cosmic rays injection have been spectra, accelerated. find the best fitting and corresponding values of α. ThusHowever, we reveal this how simple and where idea does cosmic not rays work have for thebeen following accelerated. reasons. However, this simple idea does not work for the following reasons. 9. What Happens with Cosmic Rays Flying through the Universe

Leaving their accelerator, cosmic rays then ﬂy away from the galaxy and propagate in extragalactic space. Particles reaching the Earth cover distances of tens of millions and

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hundreds of millions of light years. Those are massive distances. Even photons moving with the fastest speed in the universe cover them in tens of millions and hundreds of millions of years. What happens with cosmic rays propagating through the universe? Galaxies are rare in space and very small on the universe scale. Thus almost all the way cosmic rays fly in the extragalactic space that with a traditional optical telescope seems to be completely empty and dark. However it is not true. There are photons, gas molecules, dust and there are magnetic fields as well. Photons are emitted by stars or left over from the birth of the universe (Big Bang). The photons originated during Big Bang are relic photons. All photons constitute extragalactic background radiation. Gas molecules and dust have no influence on cosmic ray propagation. Extragalactic magnetic fields deflect a charge particle (making particle arrival directions on Earth unusable as pointers on sources). Backgrounds photons influence cosmic rays. Cosmic rays interact with photons and that leads to two effects: modification of the cosmic ray spectrum on Earth and production of extragalactic electromagnetic cascades. The first reveals itself as the lack of particles with energies about 1020 eV (and higher) in the spectrum observed on Earth. On the way through the universe ultra-high energy cosmic rays interact with relic photons producing elementary particles (an interaction with other photons is minor). Thus cosmic rays lose energy. As a result ultra-high energy particles convert to cosmic rays at lower energies and the count of ultra-high energy particles decreases. So, cosmic ray energy spectrum becomes modified. This is called the GZK-effect, and a theoretical upper limit on the energy of cosmic ray protons traveling through the universe to our galaxy is called the GZK-limit (the abbreviation of names Greisen, Zatsepin and Kuzmin, who have predicted in 1966 the spectrum modification). The lower-energy cosmic rays travel practically without interactions as they have insufficient energy for particle production. The second effect—extragalactic electromagnetic cascades, arises in the following way. Interacting with relic photons cosmic rays produce elementary particles. They are short-lived and decay giving rise to electrons, positrons, neutrinos and gamma-quanta. These new particles (except neutrino that travels almost without interaction) in turn interact with background emission generating other electrons, positrons, neutrinos and quanta. This avalanche-like process leads to formation of a gigantic cascade, the particles of which interact with extragalactic emission. Cascade particles diverge at distances that exceed the solar system size. Extragalactic cascades were described independently by Hayakawa and Prilutsky with Rozental in 1966–1970s (in the paper we use “photons” for background particles and “quanta” for the cascade ones).

10. Information Obtained Studying the Cosmic Ray Spectrum and Extragalactic Cascades For the GZK-effect to arise, cosmic rays should interact with relic photons. The probability of interaction is proportional to the distance of particle ﬂight. Thus the cosmic ray spectrum has no GZK-effect, if cosmic ray sources are not far in the scale of the universe (at distances less than ~50 Mpc = 1.5 × 1021 km). It was found experimentally that the spectrum has the GZK-limit and therefore distances from possible sources are more than ~50 Mpc. Now the analysis of the cosmic ray spectrum includes two items. One is the particle injection spectrum (we talk about injection spectra in Section8). In extragalactic space cosmic ray interactions disturb it. Nevertheless the spectrum of cosmic rays on Earth contains information about injection spectra. Another item is cosmological evolution of sources. Cosmic rays arriving on Earth are emitted by sources distributed in the universe. With the distance to a source increasing, particles travel longer times to arrive on Earth, and therefore we observe particles that were emitted at different times: remote sources emitted particles prior to near ones. Therefore at the time of emission they were younger than the latter. So, with distances increasing, the sources are younger. Galaxies 2021, 9, 2 10 of 16

Additionally, when sources were younger their power and the spatial density were higher. Cosmological evolution of sources accounts for time dependence of power and spatial density of sources. The spectrum of cosmic rays on Earth contains this information about sources. How to extract this information? Models of cosmic ray propagation in extragalactic space are considered taking into account injection spectra and varying parameters of cosmological evolution of sources as well. We calculate cosmic ray spectra and compare it with that measured, and the injection spectra along with parameters of cosmological evolution are selected that provide the best ﬁt to the measured spectrum.

Extragalactic Background Radiation The further step toward the revealing of cosmic ray sources involves extragalactic electromagnetic cascades. Quanta produced in cascades are the component of extragalactic background radiation (to distinguish particles constituting background radiation from cascade particles we use “photons” for background particles and “quanta” for the cascade ones). Its main part is emission of discrete extragalactic sources, sources being so faint or far that they cannot be detected using instruments. We believe that there also can be some other processes and particles that contribute to the background emission. For example, dark matter particles (that are hypothetical at the moment) decaying also produce quanta. Extragalactic background emission is measured with scientific apparatus on board satellites. Its studying makes it possible to identify background components and to determine how much cascade quanta contributes to the background emission. Why is it important? The portion of cascade quanta in the extragalactic background radiation depends on cosmic ray injection spectra. They are different depending on the area of particle acceleration, so the portion of cascade quanta reveals the area and mechanism of acceleration (it will be remembered that each area has the own way to accelerate cosmic rays). At present the flux of neutrinos produced in electromagnetic cascades is also used in cosmic ray studies. The method is as follows. Neutrinos arriving from the universe are detected on based-ground arrays. The flux of cascade neutrinos is calculated in models of cosmic ray sources. Models having no contradiction with the measured neutrino flux are selected to determine parameters of possible sources.

11. Study of Ultra-High Energy Cosmic Rays Today Today astrophysicists study ultra-high energy cosmic rays using both ground arrays and satellites. On Earth they measure the cosmic ray spectrum and neutrino flux, while in space it is extragalactic background radiation, the part of which is radiation produced in extragalactic cascades. Data and theoretical results are interpreted as follows. Astrophysicists look for the models of possible sources that provide the best fit to the experimentally obtained energy spectrum. Next, using these models they compute the intensity of cascade quanta and neutrinos. Flux of cascade quanta is a minor part of extragalactic background radiation, and calculated flux should be a minor part of that measured. Similarly flux of cascade neutrinos is analyzed: as it is a minor part of the measured neutrino flux the calculated flux should be a minor part of that measured. Parameters of sources satisfying these criteria are refined in a further study. This is the general outline of how astrophysicists study processes in the black hole vicinity using ultra-high energy cosmic rays. In the next section we describe how particles can be accelerated to ultra-high energies near black holes. Galaxies 2021, 9, 2 11 of 16

12. Particle Acceleration in the Vicinity of Supermassive Black Holes Supermassive black holes have three areas where particles can be accelerated. They are the magnetosphere of a black hole, its accretion disc and jets. The accelerating mechanism in these areas can be different. We consider two possible mechanisms: Fermi acceleration and particle acceleration in electric ﬁelds. The ﬁrst mechanism was described by E. Fermi in 1949 (Fermi acceleration). Before the description of how Fermi acceleration is applied in jets we discuss shocks on the jet surface.

12.1. Shocks in Jets Plasma blobs composing a jet are ejected from the disc through a funnel-shaped channel along the axis of disc rotation. Blobs ﬂy across the disc during months and years (the time depends on disc thickness). All this time a blob interacts with channel sides, i.e., the disc matter, along with the disc emission, as the disc is ﬁlled with photons of various types. On the blob surface interactions disturb some area giving the plasma a push. As a result the plasma layers moves along the blob and puts in motion layers in front. Propa- gating disturbance moving faster than the speed of sound, the shock front arises. What is a shock front? A disturbance in plasma that moves faster than the speed of sound in the medium is called a shock wave. The boundary between the moving plasma and that which is motionless is sharp. It is called the shock front. The plasma density, pressure, temperature and velocity undergo an abrupt change over it.

12.2. Fermi Acceleration Applied to Jets A shock wave makes plasma in a blob move as a stream. A part of energetic particles in the stream cross the shock gaining energy. What happens next? The plasma stream carries the accelerated particle downstream, away from the shock. If the particle returns to the shock front, its energy increases. Can the particle return? Yes, it can and more than once. It occurs as follows. Magnetic field is frozen in a plasma blob. There are areas in the blob that acts as scattering centers: their field is oriented in such a way that it deflects the flying particle towards the shock front. Thus the particle returns on it. The higher is the magnetic field the stronger it makes the particle to deflect. Addi- tionally, the higher is the particle energy, the less is its deviation in the field. Therefore the particle returns at the shock front until its energy increases so high, that the magnetic field in the blob is unable to deflect it back toward the shock front.

Galaxies 2021, 9, x FOR PEER REVIEW Particle motion in an inhomogeneous magnetic ﬁeld near a shock front12 of 17 is shown schematically in Figure8.

Figure 8. A particle motion in an inhomogeneous magnetic ﬁeld near a shock front. The parti- Figure 8. A particle motion in an inhomogeneous magnetic field near a shock front. The particle is showncle is shownby a black by circle, a black the circle,shock front the shockis shown front by dotted is shown line, arrows by dotted indicate line, moving arrows particle indicate moving direction.particle direction.

12.3. Particle Acceleration in Electric Fields The simple case of particle acceleration by electric field is well known from textbooks: a particle with a charge q traveling a distance L in a uniform electrostatic field with a magnitude E gets energy W, equal to W = qEL. In a black hole accretion disc and magnetosphere electric field is induced by the inhomogeneous magnetic field of the rotating accretion disc (the magnetic field is inhomogeneous since gas density is nonuniform). In the accretion disc, particles can be accelerated as follows (see the reference in section 14). In different places of the disc the plasma (with the frozen-in magnetic field) rotates at different speed (this is called differential rotation). As a result in some regions electromagnetic field grows explosively (faster than exponentially in time). These fields are capable of rapidly accelerating charge particles from the disc. For example, in a disc around a black hole with the mass of 108 Mʘ, particles can be accelerated to 1021 eV. In the magnetosphere, particles can be accelerated in the following way. In a rotating black hole an induced electric field is parallel to the magnetic one on the symmetry axis. The electric field direction depends on the directions of both the magnetic field and the hole’s rotation velocity. Thus in the regions near the rotation axis the electric field accelerates particles moving along magnetic lines. The maximal energy of protons is of 1021 eV. Finally, in jets, protons can be accelerated in the following process. Initially they are preaccelerated to relativistic energies by induced electric field in the magnetosphere. A rotating black hole creates the potential difference that is transmitted along magnetic field lines into the jet. Thus in the jet the voltage between the jet axis and the periphery exists. In the jet, preaccelerated protons can gain ultra-high energy passing the total potential difference between the jet axis and the periphery. This mechanism accelerates protons to 1021 eV, the maximal energy depending on the parameters that characterize the structure of the jet. The voltage drop in many situations may be shorted out by plasma. For example, the electric field inside the main part of the disc is fully compensated by the volume charge of the plasma. Nevertheless, there can be regions in the disc where the density of the plasma is usually small. Most likely it takes place during a quiet phase of the supermassive black hole, in contrast to active stages in the black hole evolution. The strong electric field exists possibly without compensation in an area of spinning axis and magnetic poles. There is no compensation of electric field in the black hole magnetosphere: the rotating magnetic field induces the electric field, due to which electromotive force arises (electric currents flow) and the voltage drop is maintained as if by an electrical battery.

Galaxies 2021, 9, x FOR PEER REVIEW 6 of 17

Galaxies vary in many features: in appearance, dimension, intensity of star formation, relation between old and young stars. Galaxies are classified according to these features. In addition galaxies differ in characteristics of the nucleus. In most galaxies, the main part of energy is emitted by stars, and stars also provide the nucleus emission. These galactic nuclei are called inactive. However, there is a small amount of galaxies where nucleus emission is extremely powerful compared to the rest of the galaxy: A huge energy stream breaks away from a nucleus, as if one hundred million sun-like stars shine in the galactic center. The nucleus emission is highly variable, sharply diminishing and increasing during a very short period of time (on the scale of hours, days, months and years). A nucleus emits energy in different bands: radio, X-rays, ultraviolet, infrared and gamma ranges. Plasma portions are spread outwards a nucleus; gas clouds move rapidly in its vicinity. These processes cannot be caused by high volume density of stars or interstellar matter. Such galactic nuclei are called active. There is only 1% of galaxies of this type in the universe. Active galactic nuclei are classified in types depending on the form of their activity. For instance, the most powerful galactic nuclei are called quasars, galaxies with powerful radio emission in nuclei are called radio galaxies. Another example: galaxies with extremely variable emission but no so bright as quasars are called Seyfert galaxies (named after astronomer Seyfert). Detailed description of the active nucleus classification is not important for our study. Its main goal is given in the next section.

4. Active Galactic Nuclei and Cosmic Rays Each active galactic nucleus emits gigantic amount of energy. Possibly cosmic rays gain ultra-high energies in energetic processes ongoing in nuclei. Then accelerated particles fly out of the region where they gain the energy, escape from the galaxy, travel huge distances in space and finally reach Earth. Is it possible to study active galactic nuclei by detecting cosmic rays on Earth, despite particles’ long flight in the cosmos? In this study it is important to answer the questions: what is the source of energy in active galactic nuclei, how particles are accelerated, and what happens to the particles during their flight through the extragalactic space. Before discussing these points a short Galaxiesdescription2021, 9, 2 of possible cosmic ray sources is given in next sections. 12 of 16

5. The Source of Energy in Active Galactic Nuclei and Supermassive Black Holes It is of the current opinion12.3. Particlenow that Acceleration nucleus activity in Electric is Fieldscaused by a supermassive black hole in the galactic center.The What simple are black case of holes? particle A accelerationblack hole is by a electriccelestial field object is well known from textbooks: with a very strong gravitationala particle field. withIt is so acharge strong qthattraveling nothing, a distanceeven light,L incan a escape uniform electrostatic field with a from there. How can that be?magnitude To overcomeE gets th energye attractiveW, equal force to ofW any= qEL celestial. object, a body should move with the escapeIn avelocity. black hole However, accretion in black disc andholes magnetosphere it is higher than electric the field is induced by the speed of light. Nothing travelsinhomogeneous faster than th magnetice speed of field light of in the the rotating universe, accretion and because disc (the magnetic field is inhomo- of this it is impossible to escapegeneous from since black gas holes. density As light is nonuniform). is not able to leave black holes, they are dark and invisible for observer.In the accretion disc, particles can be accelerated as follows (see the reference in At large distances blackSection hole gravitation 14). In different weakens places to the of thelevel disc of thean “ordinary” plasma (with star. the frozen-in magnetic field) The radius of the black holerotates vicinity at differentfrom which speed nothing (this isincluding called differential signals come rotation out). is As a result in some regions called the event horizon. electromagnetic field grows explosively (faster than exponentially in time). These fields

When the black hole massare capableis higher of than rapidly 105 solar accelerating mass (M chargeʘ) the black particles hole from is called the disc. For example, in a disc supermassive. Evidence of aroundblack holes a black with hole masses with theM mass≈ (105 of–10 10118) Mʘ ,are particles observed can bein accelerated to 1021 eV. active galactic nuclei. In the magnetosphere, particles can be accelerated in the following way. In a rotating Black holes are so extraordinaryblack hole an that induced people electric (not physicists) field is parallel believe to the that magnetic they are one on the symmetry axis. The mysterious. electric field direction depends on the directions of both the magnetic field and the hole’s Black holes are quite unusualrotation celestial velocity. objects Thus that in the were regions first considered near the rotation by a brilliant axis the electric field accelerates English scientist and parsonparticles Michell moving in 1783 along and magnetic by a great lines. French The maximal mathematician, energy of protons is of 1021 eV. physicist and astronomer LaplaceFinally, in in 1796 jets,. protons In 1916 can they be accelerated were rediscovered in the following by process. Initially they are preaccelerated to relativistic energies by induced electric field in the magnetosphere. A rotating black hole creates the potential difference that is transmitted along magnetic field lines into the jet. Thus in the jet the voltage between the jet axis and the periphery exists. In the jet, preaccelerated protons can gain ultra-high energy passing the total potential difference between the jet axis and the periphery. This mechanism accelerates protons to 1021 eV, the maximal energy depending on the parameters that characterize the structure of the jet. The voltage drop in many situations may be shorted out by plasma. For example, the electric field inside the main part of the disc is fully compensated by the volume charge of the plasma. Nevertheless, there can be regions in the disc where the density of the plasma is usually small. Most likely it takes place during a quiet phase of the supermassive black hole, in contrast to active stages in the black hole evolution. The strong electric field exists possibly without compensation in an area of spinning axis and magnetic poles. There is no compensation of electric field in the black hole magnetosphere: the rotating magnetic field induces the electric field, due to which electromotive force arises (electric currents flow) and the voltage drop is maintained as if by an electrical battery.

12.4. The Hillas Criterion A particle is accelerated as long as it is confined in the accelerating region. Thus the size L of the essential part of the region containing the field B should be greater than the Larmor radius rL of a relativistic particle of charge Ze: L > rL. Considering gradual modes of acceleration with characteristic velocity of scattering centers β = v/c, B-L relation limiting a particle energy E is: BL > 2E/Zβ. From this relation the energy limit is: E ≤ 0.5 BLZβ (here B is in µG, L is in pc and E is in units of 1015 eV). This limitation has been drawn by the English physicist Hillas and is called the Hillas criterion. The plot showing the magnetic field B versus size L is called the Hillas plot. It is shown in Figure9. Many possible sites of particle acceleration were analyzed, from interplanetary space to clusters of galaxies, i.e., with sizes ranging from kilometers to megaparsecs, and the magnetic field ranging from 1 µG to 1012 G. Very few of them remain as possibilities. Supermassive black hole sites—jets, accretion discs, and magnetospheres—satisfy the Hillas criterion. Accretion disc size is L~1–10 pc, jets are of 1–10’s pc in length (can be longer) and the magnetic field is in the range B~10–103 G or higher. Galaxies 2021, 9, x FOR PEER REVIEW 13 of 17

12.4. The Hillas Criterion A particle is accelerated as long as it is confined in the accelerating region. Thus the size L of the essential part of the region containing the field B should be greater than the Larmor radius rL of a relativistic particle of charge Ze: L > rL. Considering gradual modes of acceleration with characteristic velocity of scattering centers β = v/c, B-L relation limiting a particle energy E is: BL > 2E/Zβ. From this relation the energy limit is: E ≤ 0.5 BLZβ (here B is in μG, L is in pc and E is in units of 1015 eV). This limitation has been drawn by the English physicist Hillas and is called the Hillas Galaxies 2021, 9, 2 criterion. The plot showing the magnetic field B versus size L is called the Hillas plot.13 It of is 16 shown in Figure 9.

FigureFigure 9. 9. SizeSize and and magnetic magnetic field ﬁeld strength strength of of possible sites of particle acceleration. ObjectsObjects belowbelow the thediagonal diagonal line line cannot cannot accelerate accelerate protons protons to 10 to20 10eV.20 eV. This This is the is the plot plot from from the the classical classical article article byHillas, by Hillas,published published in 1984 in (see 1984 Section (see Section 14 for the14 for reference) the reference) and no and supermassive no supermassive black holeblack sites hole are sites shown are shownin it. in it.

12.5.Many Particle possible Energy sites Losses of inparticle Accelerating acceleration Regions were analyzed, from interplanetary space to clustersIn both of accelerationgalaxies, i.e., mechanisms with sizes rang cosmicing from rays notkilometers only gain to energymegaparsecs, but also and lose the it. magneticWhy? field ranging from 1 μG to 1012 G. Very few of them remain as possibilities. SupermassiveMagnetic black field hole in space sites deflects– jets, accret particlesion discs, (due toand Lorentz magnetospheres force) and - thesatisfy particle the Hillastrajectory criterion. bends. Accretion A particle disc moving size is along L~1–10 a curvedpc, jets pathare of emits 1–10’s energy, pc in which length results (can be in longer)particle and energy the magnetic decreasing. field In thisis in casethe range the particle B~10–10 emission3 G or higher. is called synchrotron radiation. A particle moves without deviation only along straight lines of force. When the 12.5.particle Particle reaches Energy a region Losses wherein Accelerating lines of forceRegions bend, the particle deviates emitting energy. TheIn emission both acceleration caused by themechanisms curvature cosmic of magnetic rays forcenot only lines gain is called energycurvature but also radiation lose it.. Why?Nevertheless particles gain ultra-high energy in the black hole vicinity. That is the result of theoretical studies of cosmic ray acceleration in possible sources. In jets particles move in the flow of gas where the magnetic field is directed along the flow. Thus synchrotron losses in jets are insignificant. As field lines curve with distance curvature radiation restricts particle energy. Nevertheless some particles escape the acceleration region without significant curvature losses. The fraction of these particles is one in 300 (for the estimate see the reference in Section 14). In the magnetosphere particles are accelerated by electric fields near the black hole poles, where magnetic and electric fields are uniform or radial. Thus neither curvature emission nor synchrotron one restricts particle energy. In the accretion disc, particles accelerated by electric fields have unimportant synchrotron losses when the velocity of the particle and the magnetic field are coaligned. In addition, synchrotron losses are unimportant in cases where the so-called “surfatron condition” takes place. Galaxies 2021, 9, 2 14 of 16

We described two mechanisms of particle acceleration in the universe: the acceleration through induced electric ﬁeld and Fermi acceleration. Study of cosmic rays will show the role of each process in the black hole vicinity.

13. Conclusions Cosmic rays were discovered in the 1910s, more than 100 years ago. Over these years we learned that they originate in space and bombard the Earth atmosphere producing cascades of elementary particles-extensive air showers. Numerous studies revealed that cosmic rays come from different areas in the universe. Cosmic rays at energies lower than 2 × 1010 eV are ejected from the sun while more energetic particles, at energies up to 1017–1019 eV are produced in our Galaxy in supernova explosions. What is the origin of cosmic rays at higher energies? Latest studies indicate that ultra-high energy cosmic ray sources are located outside our galaxy, inside active galactic nuclei. Supermassive black holes are the objects that supply energy for the nuclei activity, and particles can obtain huge energies in the black hole vicinity. Leaving the area of acceleration cosmic rays travel through the universe interacting with the photons of extragalactic background radiation. These interaction leads to modification of cosmic ray spectrum (the GZK-effect) and generation of extragalactic electromagnetic cascades. Quanta produced in cascades are the component of extragalactic background radiation. The problem from which we began was how particles gained ultra-high energy in active galactic nuclei. Solving this problem we faced the challenge of supermassive black holes: what are processes of particle acceleration in the black hole vicinity? Analyzing these processes we formulated the inverse problem: is it possible to study these processes using cosmic ray data along with theoretical results? The answer is “Yes”, despite cosmic ray interactions in extragalactic space. Here is how it is done: We register cosmic rays, extragalactic background radiation and neutrino flux. Data derived from these experiments are compared with energy spectra of computer models. The models that provide the best fit are used to compute the intensity of cascade quanta and neutrinos. Calculated fluxes of cascade quanta and neutrinos should be a minor part of the measured extragalactic background radiation and neutrino flux. Models satisfying this condition are selected and in these models parameters of source can be used to constrain characteristics of processes of particle acceleration in the black hole vicinity. Certainly, we never can travel or send instruments close to any supermassive black hole, but we have a natural probe for our research—cosmic rays of ultra-high energies.

14. Scientific Articles for Supplementary Reading In this section we present the articles, results of which were used in our paper. Addi- tionally, a short description of analyzed problems is given in the section. The list of articles reflects the author’s interests and is not complete. The ground based arrays registering cosmic rays at ultra-high energies that are the Pierre Auger Observatory and the Telescope Array are described in [1,2]. The results obtained (including spectra and discrepancies between them) are analyzed in, e.g., [3,4]. The particle of the highest energy 3 × 1020 eV was registered in October of 1991 by the High Resolution Fly’s Eye [5], which was previous to the TA. The GZK-effect is presented in papers [6,7] and features of cosmic ray energy spectrum at ultra-high energies are analyzed in [8,9]. Pioneering papers describing extragalactic cascades are [10,11]. The scientific devices for the measurement of background emission (galactic+extragalactic) are Fermi LAT (active) [12], GAMMA-400 (ready for launch) [13] and one of the projects is MAST [14]. Fermi LAT is placed on board the cosmic observatory (satellite) Fermi, and the results obtained with Fermi LAT are given in [12]. Mechanisms of jet formation in black holes are described in [15] (the Blanford-Znajek process) and [16] (the Blanford-Payne process). The simple explanation of jet formation is taken from the Galaxies 2021, 9, 2 15 of 16

popular lecture (in Russian) [17]. We now turn to mechanisms of particle acceleration in the black hole vicinity. Particle acceleration in shock fronts in space was deduced in pioneer articles [18–20]. The mechanism produces exponential particle spectra with the spectral indices of 2–2.5. This mechanism applied to jets is analyzed in, e.g., ([21] and references therein), and application of particle acceleration to ultra-high energies is given in [22]. Cosmic ray acceleration by electric field in magnetospheres of supermassive black holes was described first in [23]. The observational data illustrating validity of the model [23] are given in [24]. The model [23] did not predict the particle injection spectrum. Based on the mechanism [23], in [25] the monoenergetic injection spectrum was suggested and the resulting particle spectra on Earth were compared with cosmic ray data. Injection spectra (very) close to monoenergetic are obtained in the model [26], which is analyzed in [27]. A mechanism of particle acceleration by electric fields in accretion discs is proposed in [28]. It is shown that in some cases particles escape without synchrotron energy losses. The model presented in this paper does not predict the injection spectrum. Based on the described accelerating process the exponential injection spectra with indices of 0–2.2 are suggested in [29], where this mechanism is applied for cosmic ray data analyses. Particle acceleration by electric field in jets is described in [30,31]. Observational data on active galactic nuclei confirming the model are also given in the papers. No results on particle injection spectra are presented. Based on the described accelerating process the spectrum can be assumed as monoenergetic or exponential with indices of 0–2.2. Possible sites of particle acceleration are analyzed in [32], in which Hillas plot is presented. Transport of accelerated particles without energy losses is discussed in [22,30,31] (when particles are accelerated in jets), [23,27] (when particles are accelerated in black hole magnetospheres) and in [28] (when particles are accelerated in accretion discs). There are a number of codes for computer simulation of particle flying in extragalactic space. Public available codes are, for example, ELMAG [33] and TransportCR [34]. Joint analyzes of data on cosmic rays and extragalactic emission as a tool to solve cosmic ray problems is given in, e.g., [29,35,36]. Theoretical description of black holes in the universe is given in ([37] and references therein). Astronomical observations that prove the existence of the supermassive black hole in the center of our galaxy the Milky Way are given in ([38,39] and references therein).

Funding: This research received no external funding. Acknowledgments: The author thanks reviewers for their comments. The author thanks M. Zelnikov for the discussion of conditions under which particles can be accelerated in the black hole magnetosphere. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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