Nonlinear diffusive shock accelerationin GRB afterglows
Curran et al. (2010) (2010ApJ...716L.135C)
Ryan et al. (2015) (2015ApJ...806...15Z)

Don Warren
RIKEN – ABBL
CTA meeting 201514 Jan 2016

The punchline• For typical afterglow parameters,
high-energy part of spectrum
may be observable for ≈104 s
after GRB
• Detection or non-detection
could serve as probe of microphysics at shock frontOutline• Background• Nonlinear diffusive shock acceleration (DSA) in relativisticshocks• Nonlinear shock acceleration of electrons• Afterglow observations by CTA?Background
Afterglow is long-lived (hours, days, months) multiwavelength
relic of GRB

Centralengine

High-Eγ-raysAfterglow

Background
Observations of GRB afterglows cover orders of magnitude intime and energy
Perley et al. (2014)(2014ApJ...781...37P)

Background
Current afterglow studies assume extremely simple model for CR
electrons accelerated by shock
Early times

Late times

N(E)

N(E)

Emin

Emax

EnergyEmin

Emax

Energy(mostly) Fine if shocks are test-particle and unaffected by B- fieldNonlinear diffusive shock accelerationin GRB afterglows
Curran et al. (2010) (2010ApJ...716L.135C)
Ryan et al. (2015) (2015ApJ...806...15Z)

Don Warren
RIKEN – ABBL
CTA meeting 201514 Jan 2016

Background
Current afterglow studies assume extremely simple model for CR
electrons accelerated by shock
Early times

Late times

N(E)

N(E)

Emin

Emax

EnergyEmin

Emax

Energy(mostly) Fine if shocks are test-particle and unaffected by B-fieldBackground(Particle-in-cell)

Per PIC simulations, magnetic field may not be negligible, andaccelerated particles may influence shock structure
εB

Sironi et al. (2013) (2013ApJ...771...54S)

BackgroundSpitkovsky (2008) (2008ApJ...682L...5S)

Strong B-field turbulence in vicinity of shock can scatterparticles back into upstream region ( diffusive shock
acceleration, or DSA)

Pressure from UpS particles affects
inflow of plasma, which affects shock,which affects acceleration, whichaffects pressure from UpS particles…

flow speed
shockX
flow speed
subshock

XBackground
Interaction between shock, B-field
turbulence, and accelerated
particles important!
Leads to more complicated CR
spectrum than simply E-p
PIC simulations impractical if
extended to necessary scales tomodel GRB afterglows
Monte Carlo approach presented
here balances self-consistency &computation time

Sironi et al. (2013) (2013ApJ...771...54S)

Nonlinear DSA in relativistic shocks
Ellison et al. (2013) (2013ApJ...776...46E)

Interaction between shock, B-field
turbulence, and accelerated
particles important!
Efficient DSA by unmodified shocks
does not conserve energy or
momentum flux

Ellison et al. (2013) (2013ApJ...776...46E)

Nonlinear DSA in relativistic shocks
Ellison et al. (2013) (2013ApJ...776...46E)

Interaction between shock, B-field
turbulence, and accelerated
particles important!
Efficient DSA by unmodified shocks
does not conserve energy or
momentum flux
Even in relativistic shocks, musthave precursor & modified
velocity profile

Nonlinear DSA in relativistic shocks
Ellison et al. (2013) (2013ApJ...776...46E)

Effects of NLDSA on spectrum of CR
protons:• Fewer CRs at any particular energy• Region of steep decay before
spectrum flattens to ≈p-4.23• Approx. 30% of energy in CRs, so
acceleration still very efficientNonlinear DSA in relativistic shocks
Ellison et al. (2013) (2013ApJ...776...46E)

As shock slows, CR spectrum
changes too
Single-index approach to CR
energy distribution may nothold at any given instant
Very unlikely to hold acrossextended observations of
GRB afterglows

But what about electrons?

Electron DSA in relativistic shocks
Warren et al. (2015) (2015MNRAS.452..431W)

Electron acceleration much lessefficient than proton acceleration
Without energy transfer from ions,
GRB afterglow would be extremely
faintElectron DSA in relativistic shocks

Sironi et al. (2013) (2013ApJ...771...54S)Electron acceleration much lessefficient than proton acceleration
Without energy transfer from ions,
GRB afterglow would be extremely
faintPIC simulations (Sironi+ 2013,Ardaneh+ 2015) show that thistransfer does occur
As much as 40% of bulk kinetic
energy deposited into electronsElectron DSA in relativistic shocks
Warren et al. (2015) (2015MNRAS.452..431W)

Electron acceleration much lessefficient than proton acceleration
Without energy transfer from ions,
GRB afterglow would be extremely
faintEven 15% transfer causes 1000x
increase in electron presence, but
minimal change to protons

Electron DSA in relativistic shocks
Ellison et al. (2013) (2013ApJ...776...46E)

For protons, not much difference
between unmodified DSA andnonlinear DSA

Electron DSA in relativistic shocks
Warren et al. (2015) (2015MNRAS.452..431W)

For protons, not much difference
between unmodified DSA andnonlinear DSA
For electrons, difference is stark• >100x fewer electron CRs at
highest energies• No clear power law in
NL electron spectrum

10% energy
transferredElectron DSA in relativistic shocks
Warren et al. (2015) (2015MNRAS.452..431W)

Curran et al. (2010) (2010ApJ...716L.135C)

Ryan et al. (2015) (2015ApJ...806...15Z)

Electron DSA in relativistic shocks
Warren et al. (2015) (2015MNRAS.452..431W)

Difference in electron spectrum
visible in broadband photon spectrum
as well
Thermal peak in synchrotron (fromnon-CR electrons) strongly enhanced
in nonlinear model
However: Weibel instability shuts offaround γ0 ≈ 10, so less/no energy
transfer?

Modeling a GRB afterglow
Use Blandford—McKee solution forhydrodynamical baseAt select times, model nonlinear DSA
process using Monte Carlo code
Calculate photon spectra
Two models discussed here:• Far upstream B field of 3 μG
• Far upstream B field of 3 mG

Modeling a GRB afterglow
Stronger magnetic field increases p+ max energy, decreases e—max energy
Shutoff of Weibel
instability is clear
from late-timee— spectra

PRELIMINARYModeling a GRB afterglow• For typical afterglow parameters,
high-energy part of spectrum
may be observable for ≈104 s
after GRB
• Detection or non-detection
could serve as probe of microphysics at shock front (e.g.
strength of turbulent field,decay scale of turbulence)

PRELIMINARY

Conclusions
If CR acceleration by relativistic shocks efficient, must consider
nonlinear interaction between shock & CRs
Shape of electron spectrum strongly affected by energy
transfer & shock speed
Single-value models of GRB afterglows highly likely to bedeficient. Combining entire afterglow into one p, εB, εe, etc.
misses a great deal of structureWith CTA, can (hopefully) observe early phase of afterglow ingreat detail to test theories of relativistic shocks and diffusive
shock acceleration

Bonus slidesLow-B0 model fails toreproduce observed
X-ray fluxes; high-B0
model overproduces at
early times
Spectral break at ≈104 sdue to shutoff of Weibel
instability when γ0 < 10;
it is not a jet break, butdoes occur at same time

PRELIMINARY