acceleration of cosmic rays pankaj jain iit kanpur
DESCRIPTION
Spectrum KNEE ANKLETRANSCRIPT
Acceleration of Cosmic Rays
Pankaj JainIIT Kanpur
spectrumspectrum
3/1 E
7.2/1 E
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
Flux: number ------------------- m2 sr s GeV
SpectrumSpectrum
KNEE ANKLE
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)
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
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
Origin
These massive objects could be:
Topological defectsSuper heavy particlesPrimordial black holes
Origin
Here we shall focus on the Bottom Up Model where the particles are accelerated at some astrophysical sites
Our astrophysical neighbourhoodDistance 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
The Milky WayThe Milky Way
CFA Survey 1986
Distribution of galaxies in our neighbourhood
2dF Galaxy Redshift Survey
3D location of230 000 galaxies
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 NucleiGamma Ray Bursts
Acceleration Mechanisms
Fermi acceleration
Betatron acceleration: acceleration due to time varying electromagnetic fields
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 w
ave
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
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 limitIf its mass exceeds this limit, it collapses and explodes into a supernova
0.1 sec
0.5 sec
2 hours
months
Supernova Explosion
Brightens by 100 million times
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
Brightest supernova observed SN1006
visible in day time
3 times size of Venus
Intensity comparable to Moon
Remnant of the Supernova explosion seen in China in AD1054 (Crab Nebula)
Expansion:angular size increasing at rate 1.6’’ per 10 years
also observable in day time
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
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
Magnetic cloud
U
particles may gain energy by scattering on astrophysical structures
Fermi Acceleration: simple example
U
x
y
S: observer
Mass
Fermi Acceleration: simple example
U
v
-v
x
y
S: observer
S’
x’
y’In S’: vi’ = v vf’ = -v
Elastic scattering
In S: vi = v – U vf = - v – U= - vi - 2U net gain in speed
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
This principle used in Voyager
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
Frame S: angle of incidence = Ei = EPi = P
Relativistic calculation
U
x
y
S: observer
Relativistic calculation
U
Pix’
S’
x’
y’
“Mirror”
Frame S’: pix’ = (Px + E U/c2) Ei’ = (E + UPx)
Pfx’ = - Pix
’
Ef’ = Ei
’
Frame S: Ef = (Ef
’ – UPfx’)
22 /1
1
cU
-Pix’
Relativistic calculation cont’
Gain in energy per scattering:
2
2
2 2cos2cU
cUv
EEE
i
if
Particles will gain or loose energy depending on the angle of incidence
Fermi AccelerationLets 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
Fermi Acceleration
2
2 2cos2
cU
cUv
EE
Charged particles are accelerated by repeatedly scattering from some astrophysical structures
U = speed of structure v = speed of particle
per collision
We need average E/E over many collisions
Fermi AccelerationProb of collision v + U cos
2
38
cU
EE
U
Head on collisions are more probable
v
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 = N0 Pk particleswith energy E E0 k
N( E) = const Eln P/ln
dN = N(E) dE = const Eln P/ln 1
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
It would be nice to have a process where the particles gain energy in each encounter.
In this case
cU
EE
Achieved by Fermi First order mechanism
Reference:
High Energy Astrophysics
by
Malcolm S. Longair
First order Fermi acceleration
Particles accelerated by strong shocks generatedBy supernova explosion
strong shock:shock speed >> upstream sound speed (104 Km/s) (10 Km/s)
US
upstreamdownstream
assume that a flux of high energy particles exist both upstream and downstream
shoc
k
First order Fermi acceleration
downstreamV2, 2
upstreamV1, 1
Shock
front
US V1=|US|V2=|US|/4
1V1 = 2V2
2/1=(+1)/( 1) = 4 for strong shocks
= 5/3 monoatomic or fully ionized gas
V2 = V1/4
In shock 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
3|US|/4 3|US|/4isotropic isotropic
First order Fermi acceleration
downstream frame
upstream frame
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
3|US|/4 isotropic
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
First order Fermi acceleration
In downstream frame:
E’ = (E + PxU)U<< c, 1Velocity of particle v cE = Pc Px = (E/c) cosE’ = E + (E/c) U cos
U = 3US/4vc
upstreamdownstream
upstream frame E, Px
coscU
EE
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
1)(2/
0
dP
cU
cUPd
EE
32cos)(
2/
0
Now the important point is that the situation is exactly identical for a particle crossing the shock from downstream to upstream
3|US|/4 upstreamdownstream
For each crossing:
U = 3US/4
First order Fermi acceleration
cU
EE
32
cU
EE
34
For each round trip
= E/E0 = 1+ 4U/3c
Prob. for particle to remain at site
P = 1 Pesc
Let N = number density of particlesflux of particles crossing the shock from either direction = Nc/4
in downstream particles are removed at rate Nv2 = NUs/4Fraction of particles lost per cycle = Us/c = Pesc
P = 1 Us/c
ln P = ln (1Us/c) = Us/c
ln = ln (1+4U/3c) = 4U/3c = Us/c
ln P/ln = 1 N(E) dE E2 dE
We get a power law with exponent 2
We get a universal exponent. However we get 2 instead of 2.7
The spectral index might become steeper if we take into account:
Loss of energy
leakage from our galaxy
Leakage from galaxy
Leaky box modell
Steady state
Source spectrumTime of escape from galaxy
N(E) = observed flux
Acceleration up to KNEE (1015 eV)
N(E) = Q(E) x tesc (E)
Observed fluxSource spectrum
tesc(E) E Q(E) 1/E2
0.6 – 0.7 Spectral index = 2.6 – 2.7
Time of escape from galaxy
Numbers
Typical increase in energy in each crossing of the shock wave = 1 %
Acceleration phase lasts about 105 years
Typical energies that can be achieved are
105 GeV/nucleon
Hence heavier nuclei can achieve higher energies
30
P
Fe
Acceleration beyond KNEE
Furthermore beyond the KNEE milky way magnetic fields may not be able to confine protons
However they can confine heavier nuclei, which may also be accelerated by supernova shock waves
Hence the composition becomes heavier beyond the KNEE
Evidence for supernova acceleration
If high energy particles originate at supernova remnants, then we should also observe gamma rays from these sites
Gamma rays are produced by interaction with other particles.
These gamma rays have been seen and partially confirm the model
Do supernovae produce enough energy to account for cosmic ray energy?
K.E. per supernova 1051 ergs
about 3 supernovae per century
release energy at rate 1042 ergs per sec in the milky way
This is enough to power cosmic rays if 15% goes into these particles
• At E < 1018.5 eV (ankle), the cosmic rays are believed to originate inside the milky way
• At E > 1018.5 eV, their origin is probably extragalactic, beyond the milky way
SpectrumSpectrum
KNEE ANKLE
• At E > 1020 eV, it is very difficulty to find an astrophysical site which can accelerate particles to such high energies
Acceleration beyond 1020 eVWe need to find source which is able to
confine particles at such high energies
Let B = magnetic field, L = size of the region Z = charge on particle
Emax = ZBL
M.BoratavThe basic limitation comes from the magnitude of the magnetic field required to confine high energy particles in a given region.
The likely sites includeGamma Ray BurstsActive Galactic Nuclei
Neutron Star
GRB Protons (100 EeV)
Protons (1 ZeV)Active Galaxies
Colliding Galaxies
Active Galactic Nuclei
Active Galactic Nuclei
The core (quasar) contains a massive black hole which may accelerate particles to very high energies The jets may be beaming towards us (Blazar)
A possible acceleration site associated with shocks formed by colliding galaxies
Time varying magnetic fields
• Some objects such as pulsars have very strong magnetic fields
• As the object rotates the magnetic field changes with time
• This can create very large electric field which can accelerate particles very quickly
• However normally these magnetic fields occur in dense regions, where the particles may also loose considerable energy
Pulsar emits electromagnetic radiation in a cone surrounding the magnetic field dipole axis
Pulsar
Chandra Associates Pulsar and Historic Supernova (386 AD) witnessed by Chinese Astronomers
X-ray image
Constellation: Sagittarius
Beyond 10Beyond 102020 eV eV
It is expected that ultra high energy cosmic rays are either protons, nuclei or photons.
However all of these particles loose significant energy while propagating over cosmological distances at E > 1020 eV.
Protons loose energy by collisions with CMBR
p + 2.7K + p + 0
n + +
Beyond 10Beyond 102020 eV eV
Photons (pair production on background photons), Nuclei (photo-disintegration) are also attenuated. Hence either the source of these particles is within 100 Mpc or
spectrum should strongly decay at E>1020 eV
(GZK cutoff, Greisen-Zatsepin-Kuzmin, 1966)
Spectrum (AUGER)
Yamamoto et al 2007
Conclusions
Supernova shocks in our galaxy are the most likely sites for acceleration upto 1018 eV
The acceleration probably occurs through first order Fermi mechanism
Beyond 1018 eV, the cosmic rays probably originate outside our galaxy
Beyond 1020 eV, there are very few sites which can accelerate particles to such high energies
The KNEE
Furthermore we should observe an anisotropy in the arrival directions of cosmic rays.
This is because we have more supernovas in the center of the galaxy
We are located far from the galactic center
The KNEE
The knee, however, cannot be explained easily
If the protons cannot be accelerated beyond the KNEE and/or
cannot be confined by the galactic magnetic fields, then we might expect an exponential decay.
This would later meet a harder spectrum (=2.7) due to heavier nucleus, such a Helium …
The KNEE
Hence we should see more cosmic rays from the galactic center in comparison to the opposite direction.
Such an anisotropy has not been seen
Hence the cause of KNEE is not understood