1 / 79

Acceleration of Cosmic Rays

Acceleration of Cosmic Rays. Pankaj Jain IIT Kanpur. spectrum. Flux: number ------------------- m 2 sr s GeV. Knee at 10 15 eV The spectrum steepens after the knee, Ankle at 10 18.5 eV ,

haej
Download Presentation

Acceleration of Cosmic Rays

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Acceleration of Cosmic Rays Pankaj Jain IIT Kanpur

  2. spectrum Flux: number ------------------- m2 sr s GeV Knee at 1015 eV The spectrum steepens after the knee, Ankle at 1018.5 eV, perhaps an indication of a change over from galactic to extragalactic origin

  3. Spectrum KNEE ANKLE

  4. Spectral Index  • Flux 1/E • = 2.7 1015 eV<E<109 eV • = 3.1 1018.5 eV>E >1015 eV •  2.7 E>1018.5 eV At higher energies spectrum again becomes steeper ( > 4)

  5. Origin • The high energy cosmic rays probably arise due to acceleration of charged particles at some astrophysical sites • supernova shock waves • Active galactic nuclei • gamma ray bursts • pulsars • galaxy mergers Bottom up model

  6. Origin Alternatively very massive objects might decay in our galaxy and produce the entire spectrum of high energy cosmic rays The massive objects would be a relic from early universe with mass M > 1015 mass of proton Top Down Model

  7. Origin These massive objects could be: Topological defects Super heavy particles Primordial black holes

  8. Origin Here we shall focus on the Bottom Up Model where the particles are accelerated at some astrophysical sites

  9. Our astrophysical neighbourhood Distance to nearest star  1.3 pc (4 light years) Milky way disk diameter  30 Kpc Galaxies also arrange themselves in Groups or clusters These further organize in super clusters, size about 100 Mpc Beyond this universe is isotropic and homogeneous

  10. The Milky Way

  11. Distribution of galaxies in our neighbourhood CFA Survey 1986

  12. 2dF Galaxy Redshift Survey 3D location of 230 000 galaxies

  13. As we go to distances larger than 100 Mpc we enter the regime of cosmology z = v/c = H0 d (Hubble Law) z  1 at distances of order 1 Gpc As we go to large z (or distance), the Universe looks very different. It has much higher population of exotic objects like Active Galactic Nuclei Gamma Ray Bursts

  14. Acceleration Mechanisms Fermi acceleration Betatron acceleration: acceleration due to time varying electromagnetic fields

  15. Fermi Acceleration: Basic Idea Charged particles are accelerated by repeatedly scattering from some astrophysical structures Ex: Supernova shock waves, magnetic field irregularities At each scattering particles gain a small amount of energy Particles are confined to the acceleration site by magnetic field Shock wave

  16. Supernova Explosion Stars more massive than 3 solar masses end their life in a supernova explosion. This happens when either C or O is ignited in the core. The ignition is explosive and blows up the entire star. For more massive stars the core becomes dominated by iron. Explosion occurs due to collapse of the iron core. The core becomes a neutron star or a black hole

  17. Supernova Explosion Supernova explosions also happen in binary star systems In this case one of the stars accretes or captures matter from its binary partner, becomes unstable and explodes For example, the star may be a white dwarf MWD < 1.44 Solar Mass Chandrasekhar limit If its mass exceeds this limit, it collapses and explodes into a supernova

  18. Supernova Explosion 0.1 sec 0.5 sec 2 hours Brightens by 100 million times months

  19. Supernova Explosion, Aftermath The explosion sends out matter into interstellar space at very high speed, exceeding the sound speed in the medium, leading to a strong shock wave For sufficiently massive star the core becomes a pulsar (neutron star) or a black hole

  20. Brightest supernova observed SN1006 visible in day time 3 times size of Venus Intensity comparable to Moon

  21. Remnant of the Supernova explosion seen in China in AD1054 (Crab Nebula) also observable in day time Expansion: angular size increasing at rate 1.6’’ per 10 years

  22. Magnetic Fields in Astrophysics Magnetic fields are associated with almost all astrophysical sites Our galaxy has a magnetic field of mean strength 3 G The field is turbulent

  23. Magnetic Fields in Astrophysics Cosmic rays are confined at the astrophysical sites by magnetic field They may also scatter on the magnetic field irregularities and gain or loose energy

  24. particles may gain energy by scattering on astrophysical structures U Magnetic cloud

  25. y S: observer x Fermi Acceleration: simple example Mass   U

  26. y’ S’ x’ y S: observer x Fermi Acceleration: simple example In S’: vi’ = v vf’ = -v v Elastic scattering -v U In S: vi = v – U vf = - v – U= - vi - 2U  net gain in speed

  27. simple example cont’ Gain in energy per scattering: E = Ef – Ei = (1/2) m (v+U)2 – (1/2) m (v-U)2 = 2mvU = 2mvi U + 2m U2

  28. This principle used in Voyager

  29. particles move at speed close to the speed of light. Hence we need to make a relativistic calculation at oblique angles v  c (velocity of light) U << c

  30. y S: observer x Relativistic calculation Frame S: angle of incidence =  Ei = E Pi = P  U

  31. y’ S’ x’ Relativistic calculation Frame S’: pix’ = (Px + E U/c2) Ei’ = (E + UPx) Pfx’ = - Pix’ Ef’ = Ei’ Pix’ “Mirror” -Pix’ U Frame S: Ef = (Ef’ – UPfx’)

  32. Relativistic calculation cont’ Gain in energy per scattering: Particles will gain or loose energy depending on the angle of incidence

  33. Fermi Acceleration Lets assume that initially N0 charged particles with mean energy E0 per particle are confined in the accelerating region by magnetic field. they undergo repeated interactions with the magnetic clouds

  34. Fermi Acceleration Charged particles are accelerated by repeatedly scattering from some astrophysical structures per collision U = speed of structure v = speed of particle We need average E/E over many collisions

  35. Fermi Acceleration Prob of collision  v + U cos v Head on collisions are more probable  U

  36. Lets assume that initially N0 charged particles with mean energy E0 per particle are confined in the accelerating region by magnetic field After one collision E = E0 =1+(8/3) (U/c)2 Let P = probability the particle remains in the site after one collision, depends on the time of escape from the site After k collisions we have N = N0Pk particles with energy E  E0 k N( E) = const Eln P/ln  dN = N(E) dE = const Eln P/ln  1

  37. N(E) dE = const Eln P/ln  1  E We have obtained a power law, as desired However it depends on details of the accelerating site such as P, . We see the same  in all directions Also the mean energy gain per collision  U2 Second order Fermi acceleration The process is very slow The particle might escape before achieving required energy or energy losses might become very significant

  38. It would be nice to have a process where the particles gain energy in each encounter. In this case Achieved by Fermi First order mechanism

  39. Reference: High Energy Astrophysics by Malcolm S. Longair

  40. First order Fermi acceleration Particles accelerated by strong shocks generated By supernova explosion strong shock: shock speed >> upstream sound speed (104 Km/s) (10 Km/s) upstream downstream shock US assume that a flux of high energy particles exist both upstream and downstream

  41. First order Fermi acceleration Shock front downstream V2, 2 upstream V1, 1 In shock frame US V2=|US|/4 V1=|US| 1V1 = 2V2 2/1=(+1)/( 1) = 4 for strong shocks  = 5/3 monoatomic or fully ionized gas V2 = V1/4

  42. 3|US|/4 3|US|/4 isotropic isotropic First order Fermi acceleration upstream frame downstream frame The particle velocities are isotropic both upstream and downstream in their local frames. High energy particles are repeatedly brought to the shock front where they undergo acceleration at each crossing

  43. 3|US|/4 isotropic First order Fermi acceleration Consider high energy particles crossing the shock from upstream to downstream The particles hardly notice the shock Downstream medium approaches the particles at speed U = 3US/4

  44. First order Fermi acceleration The particles undergo repeated scattering on magnetic irregularities and become isotropic in downstream medium Let’s determine the energy of the particle in the frame in which the downstream particles are isotropic

  45. U =3US/4 upstream frame E, Px vc downstream upstream In downstream frame: E’ = (E + PxU) U<< c,   1 Velocity of particle v  c E = Pc Px = (E/c) cos E’ = E + (E/c) U cos

  46. We next average this over  from 0 to /2 Rate at which particles approach the shock  cos Number of particles at angle   sin d =d cos Prob. of particle to arrive at shock at angle  P() d = 2 cos dcos

  47. Now the important point is that the situation is exactly identical for a particle crossing the shock from downstream to upstream 3|US|/4 downstream upstream

  48. First order Fermi acceleration For each crossing: U = 3US/4 For each round trip  = E/E0 = 1+ 4U/3c

More Related