ASTROPHYSICAL
POSITRON EXCESSES
PASQUALE BLASI
INAF/OSSERVATORIO ASTROFISICO DI
ARCETRI
WHAT IS THE PROBLEM:
PRIMARY PROTONS:
nCR (E)  N CR (E) R  esc (E)  E - E 
PRIMARY ELECTRONS: (b= d
[or 1-(1/2)(d-1)] for losses)
for diffusion, b=1
ne (E)  Ne (E) R Min  esc (E),  loss(E)  E  e E 
SECONDARY POSITRONS INJECTION:
q (E' )dE'  nCR (E)dE n H  pp c E - -
SECONDARY POSITRONS EQUILIBRIUM:
n (E)  q (E) Min  esc (E),  loss(E)  E
n
(  e )
E
ne
   
CANNOT GROW!
SOME COMMENTS ON
PROPAGATION
0.6
 
H
2
1 E
 esc (E) 
 7.7Myr H kpcD28 
4D(E)
E 0 
2
1
 
E
-1 E
 loss(E) 
 322Myr A16 
2
AE
E 0 
ESCAPE DOMINATES OVER LOSSES IF
2.5
16
E  10 A
4
5
kpc
2.5
28
H D GeV
And using 10Be which gives escape of 20Myr at 10 GeV/n:
2
kpc
1
28
H D ~ 10

2.5
16
E  30 A
GeV
ELECTRON SOURCE
SPECTRUM
n e (E) ~ E
 e 1
LEAKY BOX
A slope
3.3 would imply
  / ~ E
0.6


n e (E) ~ E
DISC
1
 1
2

 e 1

A slope 3.3 would imply
 e  2.3
 p  2.1
 ratio  0.6
 e  2.5 d=0.6
 p  2.1
 ratio  0.2
 e  2.65

A slope 3.3 would imply   2.4 d=0.3
p

 ratio  0.15

SOME MODELS
1. PULSARS
2. REACCELERATION OF SECONDARIES IN SNR
3. NEARBY SOURCES (PSRs, SNRs, …)
ENERGETIC
REQUIREMENTS (1)

 E 
(  2)CR R
COSMIC RAYS
nCR (E) 

(E)


esc
E 02
V
E 0 

(  2)CR R  E 
ne (E)  K ep
  Min[ esc (E),  loss(E)]
2
E0
V E 0 
ELECTRONS
(  )
 
(  2)CR R
  1 E
n (E) 
 0n H c pp
 
2
E0
V
E 0 
Min[ esc (E),  loss(E)]
POSITRONS

n 


1
E
  1

 0 n H c pp
 
 
K ep E 0 
ne normal
ENERGETIC REQUIREMENTS
(2)

(  2) Rp  E 
n (E) 
  Min[ esc (E),  loss(E)]
2
EM
V E M 
(s)

EM is the max energy at the source, e+ is the energy
released in the form of positrons.
2
n (E) 2     E 0 

 
n (E)   2 CR E M 
(s)

  
 E 
R 1 
1

 
R
 0 n H c pp E 0 
RATIO OF SOURCE TO STANDARD POSITRONS

n 
1  E 
  1

 0 n H c pp
 
 
K ep E 0 
ne normal

  1
 0n H c pp  0.013
n (E)
  E 0  R  E 
 385
 
 
n (E)
CR E M  R E 0 
1/ 2
(s)

1.2
Serpico 2009
Requiring Ratio>1
CR   E M 
E  0.048  

   100GeV 
0.83
 R 
  GeV
R 
0.416
0.83
SUMMARY ON PULSARS
The sources are required to have a spectrum with slope
1.4-1.6
A high energy cutoff of >100 GeV is clearly needed
The energy in positrons per source must be such that
eCR /e+~100-1000
Compare with the total energy of
a pulsar
Flux of positrons from pulsars
Hooper, PB, Serpico 2009
ISOLATED PULSARS
Hooper, PB, Serpico 2009
GEMINGA
B0656+14
Anisotropy
Hooper, PB, Serpico 2009
CONCLUSIONS ON
PULSARS
1. On purely energetic grounds they work (relatively large
efficiency)
2. On the basis of the spectrum, it is not clear
1. The spectra of PWN show relatively flat spectra of pairs at
Low energies but we do not understand what it is
2. The general spectra (acceleration at the termination shock)
are too steep
1. The biggest problem is that of escape of particles from the pulsar
1. Even if acceleration works, pairs have to survive losses
2. And in order to escape they have to cross other two shocks
CHARGED SECONDARY
PARTICLES IN THE OLD
SNR
PB 2009
+--++-+--+++++--+-++--++
Advection
+ Diffusion
~D(p)/u
CHARGED SECONDARY
PARTICLES
THE EQUATION DESCRIBING ANY CHARGED PARTICLE IN T
SHOCK REGION IS:
AT THE SHOCK

f ,0
D1 ( p) 1
2
p
  f ,0   2   r 
p
u1 

  0.05
SOLUTION AT THE
SHOCK

1
 p dp'p'  D1 ( p')
2
f ,0 ( p)     r 
Q1 ( p')


2

 0 p'  p  u1
1. In terms of momentum dependence this scales as
D(p)Q(p)~p-g+1
2. The coefficient in front expresses the re-energization
of the secondary particles by the shock (CONSERVES
PARTICLE NUMBER BUT INCREASES THE En/Part)
3. Of course the final f is cut off at the same momentum
as that of the parent protons
SOLUTION AT x
AT A GENERIC LOCATION X DOWNSTREAM OF THE
SHOCK, THE SOLUTION CAN ONLY BE:
0  x  u2 SN
ACCELERATION
TERM
STANDARD TERM, THE

SAME AS FOR GAMMAS
THE POSITRON
“EXCESS”
PB 2009
THE PARAMETERS
TYPICAL VALUES REQUIRED ARE
K B 10  20
B 1
u1  500 1000km/s
n 1- 3 cm-3
THESE MAY BE SUITABLE FOR AN OLD SN-I OR A SN-II
OUTSIDE THE BUBBLE CREATED BY THE WIND OF
THE PRE-SN STAR
THE BULK OF CR ARE ACCELERATED DURING THIS
WHICH IS THE ONE THAT LASTS THE MOST…
THE ELECTRON
SPECTRUM
PB 2009
THE ELECTRON
SPECTRUM
Kep~5 10-3
ANTIPROTONS
PB & Serpico (2009)
SIMPLER CALCULATIONS BECAUSE NO ENERGY LOSSES
SUMMARY ON ACCELERATION IN
SNR
1. THE MECHANISM IS STRONGLY CONSTRAINED BY PBAR
2. THE PARAMETERS NEEDED MAY BE FOUND IN OLD SNR B
NOT IN YOUNG BRIGHT ONES (BUT OLD ONES ARE ALSO
ONES THAT CONTRIBUTE THE BULK OF CRs)
3. A FRACTION OF SNR CLOSE TO MOLECULAR CLOUDS WO
HELP
4. AT HIGH ENERGY, STRONG CONTAMINATION OF THE TOTA
ELECTRON SPECTRUM WITH POSITRONS
MODELS WITH LOCAL
SOURCES
THE GENERAL IDEA IS COMMON TO ALL THESE MODELS: WE
AN EXCESS BECAUSE OF SOME LOCAL SOURCE WHICH DOE
FOLLOW THE AVERAGE
THE MAIN ISSUE THAT NEEDS TO BE INVESTIGATED IS THE
NATURALNESS (or “stability”) OF SUCH MODELS (NAMELY HOW
PROBABLE IT IS TO GET THE NECESSARY CONDITIONS)
THEY CAN BE SNR RELATED (SHAVIV ET AL. 2009) OR PULSAR
RELATED, OR …
THE DIFFUSION-LOSS
HORIZON
~30
~6
~few
REMEMBER THAT FLUX~1/D(E)r and NOT 1/r2 (without losses)
NEARBY SNRs (no additional
e+)
Shaviv et al 2009
JUST AN EXERCISE
CONCLUSIONS:
HOW CAN WE DISCRIMINATE?
1. ANTIPROTONS CAN DISTINGUISH BETWEEN PULSARS
SECONDARY ORIGIN
1. BY THE SAME TOKEN, SECONDARY NUCLEI CAN DO IT
2. IN PULSARS FLUX OF e+ ~ FLUX OF e3. IN REACCELERATION e+ HIGHER THAN e- BY ~50%
4. IN THE SCENARIO OF LOCAL SNR THE TOTAL FLUX OF
ELECTRONS AT HIGH ENERGY IS PURELY e-
5. IN THE OTHER MODELS STRONG CONTAMINATION OF
(is the spectrum of positrons showing a new component