COSMIC RAY ANISOTROPIES Pasquale Blasi INAFArcetri Astrophysical Observatory
COSMIC RAY ANISOTROPIES Pasquale Blasi INAF/Arcetri Astrophysical Observatory IN COLLABORATION WITH ELENA AMATO Anisotropy Meeting, Madison, WI, October 2011
SOME STARTING POINTS PARTICLE ACCELERATION AT SHOCKS USUALLY LEADS TO E -2 , TOO FLAT WITH RESPECT TO GAMMA RAY DATA (E-2. 3) NON LINEAR THEORY LEADS TO EVEN HARDER SPECTRA, UNLESS ONE APPEALS TO POORLY KNOWN EFFECTS (VELOCITY AND HELICITY OF THE SCATTERING CENTERS) – Caprioli et al. 2010, Ptuskin and Zirakashvili 2011 STEEPER INJECTION D(E)~Ed with d~1/3 B/C UNFORTUNATELY STILL INCONCLUSIVE IN DETERMINING d. IF TO BELIEVE LOW ENERGY DATA ONE WOULD SAY d=0. 6 -0. 7 AGREEMENT WITH ALL-PARTICLE SPECTRUM + BASIC ACCELERATION THEORY D(E)~Ed with d=0. 6 -0. 7 IMPLICATIONS OF ALL THIS FOR ANISOTROPY ARE QUITE IMPORTANT
SPECTRA AND CHEMICALS REGION WHERE ICECUBE+MILAGRO ANISOTROPY PB + Amato 2011
Basic Concepts on Anisotropy Simple case of uniform disc with discrete sources 0 FOR A HOMOGENEOUS DISC THE PROBABILITY FUNCTION FOR THE SOURCES IS:
DIFFUSIVE CURRENT IN THE CASE OF A HOMOGENEOUS RADIALLY INFINITE DISC THE MEAN VALUE OF THE GRADIENT VANISHES, THEREFORE ONE HAS TO MOVE TO NEXT ORDER (BUT CAREFUL, THIS IS NOT TRUE FOR A GENERIC SOURCE DISTRIBUTION)
THIS IS NOT THE ANISOTROPY BUT RATHER THE FLUCTUATIONS AROUND THE MEAN DUE TO THE OCCASIONAL LOCATION OF NEARBY SOURCES ! THIS IS WHAT SCALES AS D(E) CONCLUSION FOR THE HOMOGENOUS DISC: THE ANISOTROPY IS ZERO ON AVERAGE, WITH REALIZATION DEPENDENT FLUCTUATIONS AROUND THE MEAN THAT SCALE LIKE THE DIFFUSION COEFFICIENT BY CONSTRUCTION THE ANISOTROPY IS ONLY DIPOLAR, AND THIS IS TRUE EVEN IF DIFFUSION IS ANISOTROPIC… PROVIDED THE STATIONARY SOLUTION IS TAKEN FOR CR (NOT NECESSARILY TRUE FOR NEARBY RECENT SOURCES)
INHOMOGEOUS SOURCES WITH H=2
INHOMOGEOUS SOURCES WITH H=4 case d=1/3
INHOMOGEOUS SOURCES WITH H=4 case d=0. 6
INHOMOGENEOUS SOURCES WITH FINITE DURATION
LARGE SCALE vs LOCAL SOURCES
EFFECT OF SPIRAL ARMS
EFFECT OF SPIRAL ARMS The Phase of Anisotropy
HOW BIG A HALO?
HOW BIG A HALO? Phase of Anisotropy
SOME THOUGHTS ON SMALL SCALE ANISOTROPY 1. ISOTROPIC TURBULENCE DOES NOT MEAN ISOTROPIC DIFFUSION 2. DIFFUSION (ISOTROPIC AND ANISOTROPIC) ALWAYS LEAD TO DIPOLEONLY ANISOTROPY ! 3. BUT TIME LIMITED EFFECTS MAY BE TAYLORED TO REPRODUCE THE SMALL SCALE ANISOTROPIES IN CASE OF ANISOTROPIC DIFFUSION (Malkov et al. 2011) 4. IT IS POSSIBLE THAT DELTAB/B~1 AND YET PARALLEL DIFFUSION MUCH FASTER THAN PERPENDICULAR DIFFUSION 5. SMALL SCALES ARE NOT THE ONLY SURPRISING ANISOTROPIES (NO QUADRUPOLE OR OCTUPOLE IS EXPECTED EITHER)
Limits of Diffusion L~10 pc Gyration radius < L for E<1016 e. V THE PATHLENGTH FOR DIFFUSION IS: NO SMALL SCALE ANISOTROPY POSSIBLE IN THE AVERAGE SENSE, BUT ON SCALES SMALLER THAN THE PATHLENGTH STANDARD PREDICTION OF DIPOLAR ANISOTROPY DUE TO DIFFUSIVE CURRENT BREAKS… (TALK BY GIACINTI)
LEPTONS
Which electron spectrum? PRIMARY ELECTRONS + SECONDARY PAIRS (NO SPIRAL ARMS) PB & Amato 2010, 2011
NUMBER OF ELECTRON SOURCES CONTRIBUTING AT GIVEN ENERGIES 10 Ge. V PB & Amato 2010 100 Ge. V 1 Te. V
The effect of spiral arms TIGHT SPIRAL PRIMARY ELECTRONS + SECONDARY PAIRS (SPIRAL ARMS 2. 8 kpc) BROAD SPIRAL PRIMARY ELECTRONS + SECONDARY PAIRS (SPIRAL ARMS 5 kpc) PB & Amato 2011
THE POSITRON FRACTION FOR THE CASE OF TIGHT SPIRAL ARMS THIS SITUATION IS REMINISCENT OF THE PROPAGATION EFFECTS SUGGESTED BY Shaviv et al. 2009, but somewhat at odds with recent Fermi-LAT electron data
A SCHEMATIC VIEW OF A PWN BLAST WAVE SHOCKED ISM CONTACT DISCONTINUI REVERSE SHOCK PULSAR WIND TERMINATION SHOCK (Acceleration site) UNSHOCKED COLD WIND
NS KICKS: ESCAPE THE REMNANT A SIMPLE ESTIMATE: THE NS LEAVES THE REMNANT AT FOR TYPICAL VALUES OF PARAME THE NS LEAVES THE SNR ABOUT ARZOUMANIAN, CHERNOFF, & CORDES, 2002 40, 000 years AFTER EXPLOSION
ENERGETICS OF RUNAWAY NS The energy available after a time T* when the NS is outside the SNR is FOR T*~40, 000 years, one has: We will see later how this compares with energetic requirements imposed by PAMELA results
Positrons from PWNe PB & Amato 2011 PWN No spiral arms
PB & Amato 2010 -2011 SNR Second. PWN
THE POSITRON FRACTION PB & Amato 2011
Anisotropy NO SPIRAL ARMS PB & Amato 2011
Anisotropy SPIRAL ARMS 2. 8 kpc PB & Amato 2011
CONCLUSIONS 1. DIFFUSIVE PROPAGATION OF CR LEADS TO ANISOTROPY 2. THE ANISOTROPY IS DIPOLAR, WITH A COMPONENT DOMINATED BY THE GRADIENT OF SOURCE DENSITY AND ONE DUE TO RANDOM NEARBY RECENT SOURCES (TRUE EVEN FOR SPIRAL ARMS) 3. THE PHASE DUE TO THE STOCHASTIC TERM IS SUBJECT TO SUDDEN CHANGES AS A FUNCTION OF ENERGY 4. THE MAGNITUDE DOES NOT GROW AS D(E) 5. THE FLUCTUATIONS ARE REDUCED FOR LARGE HALO SIZES (HARD TO DESCRIBE OBSERVATIONS) 6. SMALL SCALE ANISOTROPIES LIKELY TO BE A CONSEQUENCE OF THE NON-PERFECTLY-DIFFUSIVE PROPAGATION ON SMALL SCALES AROUND THE EARTH 7. FOR LEPTONS, OBSERVED SPECTRA and ANISOTROPY ARE VERY STRONG FUNCTIONS OF THE LOCATION OF NEARBY SOURCES
- Slides: 31