1. Gamma-ray bursts from magnetized collisionally heated jets
Indrek Vurm
(Hebrew University of Jerusalem)
in collaboration with
Andrei Beloborodov (Columbia University)
Juri Poutanen (University of Oulu)
Raleigh 2011

2. Dissipation in compound flows
(Beloborodov 2010) Rn Rs R0
τT=1
τn=1
τγγ=1
Γp~500
DISSIPATION
Γn< Γp
RADIATION DOMINATION
MATTER DOMINATION
ACCELERATION
COASTING
R*~1012 cm
= MeV
Protons and neutron flows decouple at Rn
Proton flow accelerates until Rs at the expense of radiation
Γn< Γp  n-p collisions  dissipation of bulk kinetic energy
Two branches
Elastic: heats the proton component
Inelastic: pion production  muons  electron-positron pairs
= GeV

3. Numerical method: kinetic equations
Mihalas (1980), Beloborodov (2011)
Radiative transfer equation in the flow frame:
- specific intensity
- photon frequency
- emissivity
- angle relative to radial direction
- opacity
- bulk Lorenz factor
Kinetic equation for pairs:
Processes: Compton, synchrotron, pair-production/annihilation, Coulomb collisions
- pair density
- proper time
- electron Lorentz factor
- heating/cooling rate

4. Simulation setup τγγ=1 τT=1 Rs
Simulations run in the comoving frame, starting at Rn
RTE and pair kinetic equations evolved in comoving time
Initial conditions at Rn from relativistic fluid-dynamics
Evolution of particle and photon distributions followed self-consistently until τT«1, τγγ « 1.
Model parameters:
Lp, Ln – kinetic luminosities of the proton and neutron flows
Γp, Γn – corresponding Lorentz factors
εB – magnetization (fraction of flow kinetic energy in B-field)
R0 – radius at the base of the flow Rn R0
DISSIPATION
τn=1
Γn< Γp

5. Spectra: non-magnetized flows
red
- Monte Carlo (Beloborodov 2010)
blue
- kinetic
pairs
MeV
GeV
Heating-cooling balance
cooling,
pair cascades
injection
Lp=1052 erg/s
Ln=2x1051 erg/s
Γp=600, Γn=100
r0=107 erg/s
Thermal
Thermal
Compton
Annihilation line
Non-thermal Compton
γγ - absorption

6. Magnetized flows εB ≠ 0 ⇒ synchrotron emission from non-thermal pairs
Magnetization:
Synchrotron peak:

7. Magnetized flows εB ≠ 0 ⇒ synchrotron emission from non-thermal pairs
softer low-energy slopes
soft excess below ~50 keV
Magnetization:
Synchrotron peak:

8. Magnetized flows εB ≠ 0 ⇒ synchrotron emission from non-thermal pairs
softer low-energy slopes
soft excess below ~50 keV
Magnetization:
Synchrotron peak:

9. Magnetized flows εB ≠ 0 ⇒ synchrotron emission from non-thermal pairs
softer low-energy slopes
soft excess below ~50 keV
εB ≈ 1
suppression of pair cascades
steep high-energy slopes
distinct GeV component
Magnetization:
Synchrotron peak:

10. Magnetized flows εB ≠ 0 ⇒ synchrotron emission from non-thermal pairs
softer low-energy slopes
soft excess below ~50 keV
εB ≈ 1
suppression of pair cascades
steep high-energy slopes
distinct GeV component
Magnetization:
Synchrotron peak:

11. Magnetized flows εB ≠ 0: synchrotron emission from non-thermal pairs
softer low-energy slopes
soft excess below ~50 keV
εB ≈ 1
suppression of pair cascades
steep high-energy slopes
distinct GeV component
- GRB B
red
- simulation
black
GRB B
Magnetization:
Synchrotron peak:
Abdo et al. (2009)

12. Low-energy slope
Photon index vs magnetization
Low-energy photon indices in the commonly observed range for wide range of magnetizations
Nava et al. 2011

13. Soft excess
Significant excess below ~15 keV in 14% of bright BATSE bursts
86 bright bursts (BATSE)
Excesses relative to PL
50/(1+z) keV
15 keV
Preece et al. 1996

14. Low-energy emission
Partially self-absorbed synchrotron emission predicts a universal power-law α = -1
Can extend to the optical band, typical delay ~1 sec
- SSA energy
- emissivity near Es

15. Radiative efficiency ϵ = Lγ/L ~ 0.5
Collisional dissipation retains its efficiency in magnetized flows
Heated flows
ϵ = Lγ/L ~ 0.5
Lγ – radiative luminosity
L – kinetic luminosity
flow

16. Summary Collisional dissipation in magnetized flows:
Band shape preserved
Low-energy photon indices in the commonly observed range over several orders in magnetization
Soft excess, distinct high-energy emission component
Robust prediction of low-energy emission with α = -1
High radiative efficiency maintained