Source of Extragalactic Cosmic Rays

Sources of Extra Galactic Cosmic Rays

As we shaw, CR in supernova remmants or blast waves can only accelerate CR up to 100 Z TeV. In order to explain cosmic rays beyond this energy, one has to invoke other processes such as Non-Linear Diffusion Acceleration, or extremely high magnetic fields (as suggested in Hillas' plot). But relativistic acceleration phenomena need to be considered to expain cosmic rays up to the ankle region.

Binary systems in which a compact object (black hole or neutron star) is permanentely dragging material from a companion object (normally a star for a X-ray binary or a galaxy for Active Galactic Nuclei (AGNs) whirled around an accreation disk can generate enourmous plasma motions with very strong electromagnetic fields.

An artistic representation of 4U 0614+091, a X-ray binary also called a microquasar. Source: ESA

The accretion process

Black holes or neutrino stars have matter acreeting around them which forms due to the gravitational force. The energy gain of a free-falling proton . from infiity to a star of mass M and radius R corresponds to the variation in the gravitational potential:

$\frac{1}{2}m_p v^2 = \Delta E = - \int_\infty^R G\frac{m_p M}{r^2} = G\frac{m_p M}{R^2} \Rightarrow v = \sqrt{\frac{2GM}{R}}$ ,

where the gravitational constant is $G = 6.67408 × 10^{-11} \rm m^3 kg^{-1} s^{-2}$ . When the proton reaches the surface of the star (r = R), all the matter is rapidly decelerated and accumulates on the surface of the star, and the kinetic energy of free-fall matter is radiated away as heat corresponding to the luminosity: $L = \frac{1}{2} \dot{m} v_{eff}^2 = \frac{G M \odot{m}}{R} = \frac{1}{2} \dot{m} c^2 \left(\frac{R_s}{R}\right)$, where the rate at which mass is accreted onto the star is $\dot{m} =\frac{dm}{dt}$ and so the rate at which kinetic energy is dissipated at the surface of the star is the luminosity above. We have used the Schwartzschild radius: $R_S = \frac{2G M}{c^2}$, which is typically the distance of the horizon from a BH. We can define the efficiency of the process of transformationof mass energyinto heat by: $\xi = \frac{R_S}{2R}$, which depends on how compact the star is and on the mass:

• For a white dwarf star: $M \sim M_\odot = 2 \sim 10^{30} \rm kg, \, R \sim 5 \times 10^6 \rm m, \, \xi = 3 \times 10^{-4};$

• For a neutron star: $M \sim M_\odot = 2 \sim 10^{30} \rm kg, \, R \sim 10^4 \rm m , \, \xi = 0.15$;

• For Schwarzschild black holes, typically ξ = 0.06, whilst for maximally rotating Kerr black holes ξ = 0.426. Thus, black holes, and, in particular, maximally rotating black holes, are the most powerful energy sources we know of in the Universe and accretion is the process by which the energy can be released. As a matter of fact, having understood that the process of accretion of mass seems more efficient for black holes than other celestial objects, we need to consider what is accreted, namely a disc. There is no solid surface of the BH onto which matter can fall (unlike for a NS) and if matter fell radially into a BH, no heat could be released.

  The element of in-falling mass, due to some fluctuations of the gravitational potential close to the BH, acquires some angular momentum$\tau = I\Omega = mv_{\perp} r$ with $I = mr^2$. Due to conservation of angular momentum ( $\tau = const$ ), the rotational energy of the matter $E_{rot} =\frac{1}{2} I\Omega^2 = \frac{1}{2} \tau^2/I \propto r^{-2}$ increases more rapidly than its gravitational potential energy ( $\propto r^{-1}$ ) when approaching the BH, and this prevents collapse to $r = 0$ . Thus, matter is prevented from falling directly into the black hole in directions perpendicular to the rotation axis by centrifugal forces. However, matter can collapse along the rotation axis of the infalling material, so that a disc of matter forms about the black hole. The matter in this accretion disc can also fall into the black hole if it loses its angular momentum and this is achieved by viscous forces acting in the disc.

The Eddington luminosity

From the described process of accretion it might seem as though we could generate arbitrarily large luminosities by allowing matter to fall at a sufficiently great rate onto a BH but there is a limit to the luminosity. Eddington luminosity: If the luminosity were too great, radiation pressure would blow away the in-falling matter. This luminosty can be obtained by imposing that the outward directed radiation pressure force ≤ gravitational inward force for matter to be able to fall onto black hole.

Inward force between electron - proton pair: $F_{g} = \frac{G M_{BH}}{r^2}(m_p + m_e)\sim \frac{G M_{BH}m_p}{r^2}$

Outward energy flux at distance r: $F =\frac{L}{4\pi r^2}$ , where L is the luminosity of the source in erg/s. From this we calculate the outward momentum flux or pressure carried by photon=energy/c: $P_{rad}= F/c = \frac{L}{4\pi r^2 c}$ and the the outward force on a single electron (Thompson scattering of radiation on single electrons has a constant cross section $\sigma_{Th} = \frac{8\pi}{3} r_e^2 = 66.5 \rm fm^2,$ where $r_e =$ classical electron radius) is: $F_{rad} = P_{rad} A_{rad} = \frac{\sigma_{Th}L}{4\pi r^2 c}$ . Then the above inequality becomes:

$$F_{rad} \le F_g \Rightarrow \frac{\sigma_{Th}L}{4\pi r^2 c} \le \frac{G M_{BH} m_p}{r^2} \\\Rightarrow L_{Edd} \le \frac{4\pi G c m_p}{\sigma_{Th} M_{BH}} \sim 1.26 \times 10^{46} \left( \frac{M_{BH}}{10^8 M_{\odot}} \right)$$

The dynamo effect

• $\frac{\Delta E}{m_p} = \frac{G Mc^2}{2 GM} = \frac{c^2}{2} \sim 4.5 \cdot 10^{20} \rm erg/g$.

The variable magnetic field of the neutron stars or black holes are perpendicular to the direction of the accreation disk generating a Lorentz force:

So the energy obtained is

where is the distance over which the force acts. Under plausible assumptions (, T, m) energies of eV are possible.

Candidates of Extra Galactic Cosmic Rays Sources

The two main candidates for ExtraGalactic Cosmic Rays are:

• Active Galactic Nuclei (AGN)

• Gamma Ray Bursts

Active Galactic Nuclei (AGNs)

The history of an extraordinary discovery

In 1929 Karl Jansky of the Bell Telephone Labs designed and built of a 14.6 m rotatable, directional antenna system. He discovers that the static interference on transatlantic phone lines was coming from the centre of the Milky way. The noise was too loud to be due to thermal black body radiation. In 1951, Cygnus A at about 220 Mpc, along with Cassiopeia A, and Puppis A were the first "radio stars" identified with an optical source. Cygnus A is the first radio galaxy, having emission lines in its spectrum unliike normal galaxies with a continuum with absorption lines, while the other two are nebulae inside the Galaxy. Below you see the composite image of Cyg A: optical data from the Hubble Space Telescope are represented by gold, while X-ray (Chandra) and radio (VLA) data are shown in blue and red. respectively. The bottom three panels show the individual images of the composite. In 1953 Shklovski suggested the synchrotron nature of the emission from the Crab, due highly relativistic electrons, from the radio to optical, which he extended in 1954 to the ejecta from the nucleus of Virgo A, namely from M87. This was confirmed by Ginzburg ad Gordon with the discovery of the optical polarization from the Crab and by Baade from M87 light. In that year Baade and Minkowskii put forward the hypothesis of the catastrophic nature of radio galaxies. In 1963 Hoyle and Fowler speculated that the tremendous emitted energy is due to the gravitational collapse of a very massive object.

Cyg A Image Credit: X-ray: NASA/CXC/SAO; Optical: NASA/STScI; Radio: NSF/NRAO/AUI/VLA

At the beginning of the '60ies some compact radio sources were collected in the 3C catalogue and A.Sandage proved he identification of 3C 48 identifying strong lines in its spectrum which normally are not present in stars' spectra. Other 3 'quasi stellar objects' (QSO) or quasars were identified, between which 3C 273. The 3C273 radio source position was found with precision of 1 arcsec, which allowed to find the optical counterpart at z = 0.158 (not 1 star but a galaxy). In 1965 Sandage established the existence of other radio-quiet 'small star-like objects' that he understood to be galaxies.

K. Jansky from https://www.bell-labs.com/radio-astronomy-celebration/

When in the beginning of the 60'ies Giacconi and Bruno Rossi found othe first X-ray source Scorpius X-1, it was then found out that also quasars are X-ray emitters.

AGN Classification and the unification model

Active Galactic Nuclei (AGNs) are glaxies with violent energy released from a nucleus with the size of about our solar system and luminosity many thousands larger than the Milky Way. The host galaxy in most cases is not visible because they are outshined by the bright emission from the core. Blocking this last for 3C 273, HST has detected its star light from the host galaxy.

3C 273, Credit Hubble space Telescope

The basic structure of an AGN is:

• A supermassive BH in the core, $10^6 M_\odot < M < 10^{10} M_\odot$, probably spinning.

• An accretion disk: matter with small amount of angularmomentum, attracted by the black hole, forming a disk. This is a major source of power (see section on accretion above). An X-ray emitting corona is around the accretion disk, which is an ensemble of hot and active clumps.

• An obscuring torus located at several pc from the BH, intercepting some fraction of the radiation produced by the disk and re-emitting it in the IR.

• The Broad Line Region (BLR) with small clouds at <1pc moving rapidly (∼ 3000 km s−1), intercepting ∼10% of the ionizing radiation of the disk, and re-emitting it in the form of lines. Doppler shifts broaden the observed lines (from this the name). Narrow Line Region (NLR) at ∼100 pc with less dense clouds moving, less rapidly.

• About 10% of AGNs, besides accreting matter, expel it in 2 opposite jets likely in the rotational axis of the spinning BH. The material inside these jets is moving at relativistic speeds, hence emission is highly beamed, and their appearance depends on the viewing angle. AGNs whose jets point at us are called blazars, other AGNs are called radio–galaxies.

The original unified model of ANGs (Antonucci 1993, Urry & Padovani 1995, Urry 2003) combines large number of sub-groups into a general picture with 2 parameters: the torus inclination to the line of sight and the source luminosity (“unification by inclination”). In this scheme, the nuclear continuum and emission line radiation of AGNs can suffer wavelength dependent scattering, absorption and reflection on the way out t in the torus, in the disk of the host galaxy, in stellar and nuclear outflows, and inside the BLR itself. More recently it was suggested that AGNs can be separated in the two major groups indicated above “radiative mode” and “jet mode” AGNs (Heckman & Best 2014). A extensive review is in this article. Most of the energy output in radiative-mode AGNs results from matter accretion through a central optically thick accretion disk and is in the form of electromagnetic radiation (Seyfert galaxies or QSOs). About 10% of the sources in this group are radio-loud, showing a highly collimated, relativistic radio jet and, occasionally, a gamma-ray jet. As shown above in the section on accretion, radiative mode AGNs are very efficient accretors with $\frac{L_{AGN}}{L_{Edd}} > 0.01$.

Gamma-Ray Burts

• GRBs are short bursts lasting a few seconds of -ray photons from 0.1 - 1 MeV.

• They were discovered in the 60s by the U.S. Vela satellites, which were built to detect gamma radiation pulses emitted by nuclear weapons tested in space as the US suspected the URSS might carry on secret nuclear tests despite the Nuclear Test Ban Treaty.

• They have been hypothesed (given their occurence) to have caused mass extintions events (thousand times since life begun), in particular they are associated with the Ordovician–Silurian extinction.

• There is some observational evidence suggesting that progenitor of a GRB are stars undergoing a catastrophic energy release by the end of their lifes Hypernovas

Sources of UHECR

The accepted phenomenological picuted of GRBs is of a expanding relativistic wind fireball dissipating kinetic energy. The observed afterglow on some GRBs result from the collision of the expanding fireball and the surroundings.

In the fireball, the observed radition is produced by synchrotron emission of shock accelerated electrons, similar to SNRs. Hence, it is likely that protons will be also shock accelerated.

The two conditition for GRBs sources of UHECR are:

1. The proton acceleration time must be smaller that the wind expansion time (burst duration).

2. The proton synchrotron loss time must exceed the acceleration time.

These two conditions lead to a constrain in the Lorentz boost factor for GRBs:

which matches what we see from GRBs. However IceCube has not seen any neutrino associated with GRBs which puts in tension the idea that GRBs can be the only sources of UHECR.