Talk by Petar Mimica at the Conference on Computational Physics 2012 in Kobe on October 15th, 2010

7/31/2019 Talk by Petar Mimica at the Conference on Computational Physics 2012 in Kobe on October 15th, 2010

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Numerical simulations of dynamics andemission from relativistic astrophysical jets

Petar Mimicawww.uv.es/[email protected]@mimichaninDepartment of Astronomy and AstrophysicsUniversity of Valencia
http://www.twitter.com/mimichaninhttp://www.twitter.com/mimichaninmailto:[email protected]:[email protected]://www.uv.es/mimicahttp://www.uv.es/mimica


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Outline

1. Introduction: relativistic jets

2. Special relativistic (magneto)hydrodynamics3. Non-thermal particles in relativistic jets

4. Non-thermal emission processes

5. Overview of applications

6. Conclusions


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Relativistic jetsactive galactic nuclei

gamma-ray

burststidal disruption

events

microquasars

appear in a wide variety of astrophysicalscenarios (AGN, TDE, GRB, QSO)

common properties: powered by an accreting compact object collimated relativistic outflows non-thermal emission (synchrotron, IC)

B-fields present, not well constrained


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Simulating relativistic jets

1. relativistic hydrodynamics simulationfinite-volumesmethod of linesshock-capturingRiemann solversoptional: coupling to non-thermal particles

2. non-thermal particle evolutionphenomenological shock accelerationradiative and adiabatic losessemi-analytic electron-kinetic eq. solver

spatial advection

3. radiative transfertime-dependent emission and absorptionrelativistic effects (beaming, Doppler)

light-travel timessynchrotron, inverse-Compton scattering


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Relativistic hydrodynamics@D

@t+r (Dv) = 0

@S

@t+r (S v + pI) = 0

@

@t+r (SDv) = 0

mass conservation momentum conservation energy conservation

h =5

2

P

c2+

s9

4 P

c22

+ 1 TM approximation to Synge equation of stateMignone et al. Astrophys. J. Supplement 160 (2005) 199de Berredo-Peixoto et al. Modern Phys. Lett. A20 (2005) 2723

W :=1

p1 v2/c2

h := 1 +"

c2+

p

c2

Lorentz factor

specific enthalpy

:= W S := hW2v := hW2c2 p Wc2

relativistic rest-mass density relativistic momentum density relativistic energy density

v

rest-mass density pressure flow velocity

primitive variables must be obtained (recovered) from the conserved ones no analytic solution in general, numerical procedure must be used (and it can fail!)


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MRGENESIS

MRGENESIS(Aloyet al. 99 ApJS , Leismann et al.05, A&A, Mimica et al. 07, 09 A&A)

finite volume approach

method of lines: separate semi-discretizationof space and time

time advance: TVD Runge-Kutta methods of2nd and 3rd order

high-resolution shock-capturing scheme

inter-cell reconstruction: up to 3rd order using

PPM algorithm numerical fluxes: Riemann solvers

RMHD: constraint transport to conserve B

orthogonal coordinate systems: Cartesian,cylindrical, spherical

MPI + OpenMP: scales up to 10K cores

HDF5 library for parallel I/O


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Non-thermal particles model: relativistic shocks accelerate

electrons to high energies

phenomenological source term:

electron-kinetic equation

Q() = Q0s; min max

:=1 v2/c2

1/2

@n

(, t

)@t + @@ ( n(, t)) = Q()

= ka ks2

adiabaticcompression orexpansion

synchrotronlosses

ka =1

3

D ln

Dtks =

4TB2

3m2ec2

particle energy losses/gains:

special case: pure synchrotron losses (ka = 0): (t) =(0)

1 + ks(0)t

c(t) =1

kstcooling break: maximum for a given time:


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Solving electron-kinetic equation

test problem: n(, 0) = K

min

q

@n , t

@t+

@

@( n(, t)) = Q()

coolingbreak

= ka ks2

n(i, t) = n(i(0), t)e2kat 1 + i(0)

ks

kaekat 1

2

i(t) = i(0)ekat

1 + i(0)

ks

ka

ekat 1

1

= e3katN(i(0), i+1(0), t)

moving bins solver

coolingbreak

N(i, i+1, t) :=

Zi+1

i

d n(, t)

Mimica+Mon. Not. R. Astron. Soc. 407 (2010) 2501


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Synchrotron radiation

synchrotron emissivity: j() =

p3e3

4mec2B Zd n() R

0

20 =

3e

4mecB

R(x) =1

2

Z

0

d sin2 F

x

sin

F(x) = x

Z1

x

dK5/3()

n() = n(min)

min

q

; min max

j() =

p3e3B

8mec2n(min)

qmin

0

(1q)/2H

02min

, q,max

min

H(x,q, ) =

Zxx/2

d (q3)/2 R()interpolate the function:

advantage: synchrotron computation cost reduced by a factor 50-100 tradeoff: large interpolation table (> 2GB) needs to reside in memory

interpolation table computation: a week on a 16-core machine


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Inverse Compton scattering

0: incoming frequency

1: outgoing frequency1: lower electron Lorentz factor cutoff

IC emissivity for monochromatic

incoming emission is analytic problem 1: compute theemissivity for non-monochromaticincoming radiation

problem 2: compute theincoming radiation spectrum

solution: large interpolationtables

Mimica & Aloy,Mon. Not. R. Astron. Soc.421 (2012) 2635


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Radiative transfer

dI

ds= j + I

radiative transfer equation:

emitting volume

t1

t2

t3

virtual detector

(observer)

motion (v~c)

towards observer

T1T2T3

s

s0

for a fixed T, equation gives an isochrone (s, t) alongeach line of sights = c(t

T) + s0

j

s

T t

: intensity: emission, absorption

: observer time : jet evolution time

: path towards the detector

synchrotron,inverse-Compton

synchrotronself-absorption


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SPectral EVolution code

S. Tabik et al. Computer Physics Communications 183 (2012) 1937

SPEV(Mimica et al., Astrophysical J. 696 (2009) 1142) : non-thermal electron transport and evolution equations time- and frequency-dependent radiative transfer in a dynamically changing background parallelization: MPI (over detector pixels), OpenMP (over particles)

Mimica et al.,Astrophysical J.696 (2009) 1142


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SPectral EVolution code

S. Tabik et al. Computer Physics Communications 183 (2012) 1937

SPEV(Mimica et al., Astrophysical J. 696 (2009) 1142) : non-thermal electron transport and evolution equations time- and frequency-dependent radiative transfer in a dynamically changing background parallelization: MPI (over detector pixels), OpenMP (over particles)



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Simulation building blocksDepending on the application, select one from each row:


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Parsec-scale jets

trailing components

trailing components

main component

main component


jet perturbation seen as asuperluminal (main) component

radio observations do not directlysee the jet

SPEV, 128 frames, 270 x 18 pixels, 3 frequencies

per run: 100 Kh, 0.5 Tb hydro data, 2x105 Lagrangianparticles, 2x106 line-of-sight segments


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syn. peak

Compton peak

Mimicaetal.,Astron.Astrophys.418(

2004)947

Mimica&Aloy,Mon.Not.R.Astron

.Soc.421(2012)2635

Mimic

a&Aloy,Mon.Not.R.Astron

.Soc.401(2010)525

nonmagnetized

weakly magn.

strongly magn.

Blazar flares

blazar light curves: resol. (200x200) ( x T)

900 different shell collisions, 200 Khours


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1D simulations: 106 zones, 108 iterations50 - 100 Kh / run 104 snapshots / run

GRB afterglows


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Mimica, Giannios & Aloy 2009 , Mizuno et al. 2009

Ejecta-medium interaction

1 1

B

:=B

2

4c2

Sari & Piran 1995


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Gamma-ray burst afterglows

references:

Giannios+Astron. Astrophys.478 (2008) 747Mimica+Astron. Astrophys.494 (2009) 879Mimica+Mon. Not. R. Astron. Soc. 407 (2010) 2501

optical flash almost neverobserved: are almost all GRB jets

magnetized?

1

1

optical flash


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Required numerical resolutionNeed to resolve o in at least 104 zones for o ~ 10.total computing domaing: Rtot / o ~ 100 - 1000Ntot ~ 106 - 107 Niter ~ 107 - 108(CFL~0.1)

~ 500 - 1000 CPUs/job usedeach job needs ~ 200 (wall clock) hours to finish.

since xo , we would need ~ 2000 h in 500 -1000 CPUs to run realistic modelswitho ~100.

realistic GRB parameters:Rtot / oAG ~ 3x105 Ntot ~ 3x109 Niter ~ 3x1010

6x105 h on 500 CPU 3x104 h on 10000 CPUs

3x105 (wall clock) on 10000 CPUs (o ~100).

0

1

log

-5 -4 -3

log x

27

28

Niter

x10

3

Fig. A.1.Time (upper panel) and the number of iterationsNiter(lower panel) needed to resolve the Riemann problem in planar

coordinates as a function of the spatial discretization x..

10 20 30

0

0

0.5

1

Fig. A.2. Time needed to resolve the Riemann problem in pla-

nar coordinates as a function of the initial Lorentz factor 0 for

x = 1.5625 105.

Mimica+Astron. Astrophys.494 (2009) 879


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Conclusions MRGENESIS + SPEV is:

a simulation framework that has been successfully applied toAGN, GRB and TDE jets

modular and adaptable to computing at various scales:

small scale computing is used when fast feedback is morevaluable than high spatial and temporal resolution

supercomputing is used when computing time-dependentimages or when performing parameter studies

computation of emission from numerical hydrodynamicsimulations enables direct comparisons with observations

future (MRGENESIS): resistive RMHD, scaling >104 cores

future (SPEV): improved inverse-Compton, polarization,radiative transport in GR

Talk by Petar Mimica at the Conference on Computational Physics 2012 in Kobe on October 15th, 2010

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