Bringing Light from Virtual Jetsto Virtual Detectors

Petar Mimica www.uv.es/mimica Petar.Mimica@uv.es @mimichanin

Department of Astronomy and AstrophysicsUniversity of Valencia

Outline1. Introduction and motivation: relativistic jets

2. Numerical simulations of jet dynamics and emission

• Relativistic (magneto)hydrodynamics

• Non-thermal transport & emission

3. Examples

• Components in parsec-scale jets

• Gamma-ray burst afterglows

4. Conclusions

Numerical simulations

non-thermaltransport & evolution

hydrodynamic simulation of a rel. jet

emission &radiation transfer

1. specify the astrophysical scenario (initial & boundary conditions)

2.evolve the relativistic plasma (conservation laws)

3.periodically store grid snapshots

4.inject Lagrangian particles (non-thermal electrons)

5.transport (spatial) and evolve (temporal) non-thermal electrons

6.store spacetime trajectories and energy distribution

7.compute non-thermal emission8.apply relativistic effects9.solve radiation transfer equation

MRGENESIS (Aloy+ 99, Leismann+ 05, Mimica+ 07, 09)

SPEV (Mimica+ 09)

“experiment”

postprocessing

synthetic observations

Relativistic hydrodynamics@D

@t+r · (Dv) = 0

@S

@t+r · (S⌦ v + pI) = 0

@⌧

@t+r · (S�Dv) = 0

mass conservation momentum conservation energy conservation

equations of RHD

h =5

2

P

⇢c2+

s9

4

✓P

⇢c2

◆2

+ 1 TM approximation to Synge equation of stateMignone et al. Astrophys. J. Supplement 160 (2005) 199de Berredo-Peixoto et al. Modern Phys. Lett. A 20 (2005) 2723

W :=1p

1� v2/c2

h := 1 +"

c2+

p

⇢c2primitive variables

Lorentz factor

specific enthalpy

D := ⇢W S := ⇢hW 2v ⌧ := ⇢hW 2c2 � p� ⇢Wc2

relativistic rest-mass density relativistic momentum density relativistic energy density

conserved variables

⇢ P 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!)

MRGENESIS:a common framework for R(M)HDMRGENESIS is a multidimensional (1D, 2D or 3D) code which allows one to compute problems where RHD or RMHD are relevant.

Employs:• Finite volume approach.

•Method of lines: separate semi-discretization of space and time.

• Time advance: TVD Runge Kutta methods of 2nd and 3rd order.

•High-resolution Shock Capturing scheme.

• Inter-cell reconstruction: up to 3rd order using PPM algorithm.

• In RMHD: constraint transport to conserve ∇B.

•Several orthogonal coordinate systems (Cartesian, Cylindrical, Spherical).

•MPI + OpenMP: scales up to 10K cores

•HDF5 library for parallel I/O

0,00#

20,00#

40,00#

60,00#

80,00#

100,00#

120,00#

64# 128# 256# 512# 1024# 1920# 3600# 7200#

SPEED%UP%

CORES%

SPEED%UP%MPI%vs%MPI.OPENMP%NO%HDF%

MPI#

MPI0OMP#

C. Aloy

Radiative processes in rel. jetssynchrotron emission:• relativistic particles gyrate in the presence of a B-field• local process•computation: double integral @ each point

inverse-Compton scattering:• in general non-local process• requires: incoming radiation for each point•external Compton: double integral @ each point• synchrotron self-Compton: quadruple integral @ each

point

relativistic beaming

– 8 –

coordinate basis. The comoving tetrad e(a) (a = 0, 1, 2, 3), is formed by four vectors, one ofwhich (e(0)) is the four velocity of the matter and the following orthonormality relation is

fulfilled

e(a) · e(b) = !ab, (2)

where !ab is the Minkowski metric (!00 = !1). We explicitly point out that the componentsof tensor quantities with respect to the coordinate and tetrad basis are annotated with Greek

and Latin indices, respectively. The transformation between the basis e(!) and e(a) is given

by the matrix e!a and its inverse matrix e!a! ,

e(a) = e!ae(!), e(!) = e!a! e(a) (3)

In terms of the comoving basis, the Boltzmann equation is

pb

!

e"b

"f

"x"! !a

bcpc "f

"pa

"

=

!

#f

#$

"

coll

. (4)

The symbols !abc are the connection coe"cients in the tetrad frame, for which the following

relations hold

!abc = e"

b e!a! e!c;" = e"

b e!a!#

e!c," + !!

"#e#c

$

, (5)

where the comma stands for partial di#erentiation and the semicolon for covariant di#eren-

tiation.

We introduce the two first moments of the distribution function by the equations

na =

%

d$p2

p0paf, (6)

tab =

%

d$p2

p0papbf, (7)

where p2 = (p0)2!m20c

2 is the square of the NTP three-momentum measured by the comov-

ing observer. The solid-angle ($) integrations are performed over all particle momentumdirections. We note that n0(p)dp gives the number of NTPs per unit volume with modulus

of their three-momentum between p and p+dp measured by an observer comoving with the

matter. Further integration of the above moments na and tab over p,&

"

0 dp, will give us thehydrodynamical moments.

In order to obtain the continuity equation for NTPs, we multiply the Boltzmann equa-tion (4) by (p2/p0), and integrate over $ to yield, after some algebra (for the details see the

appendix A of Webb 1985),

evolution of

non-thermal particles

Radiation transfer• for a fixed observer time T, need to process

the whole spacetime evolution to compute a single virtual image

• tightly coupled, highly non-local problem• 5D problem:• virtual detector image (x, y)• observation time T• observation frequency ν• contributions along the line of sight s

dI⌫ds

= j⌫ + ↵⌫I⌫

radiation transfer equation:

emitting volume

t1t2

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

I⌫ j⌫ ↵⌫

sT t

: intensity : emission, absorption

: observer time : jet evolution time: path towards the detector

synchrotron, inverse-Compton

synchrotron self-absorption

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)

Parsec scale jet

Hydrodynamic model:• initially over-pressured jet•atmosphere with a decreasing

density profile

SPEV

adiabatic

radio map at 10o viewing angle

(in collaboration with: M. A. Aloy, J. M. Martí, I. Agudo, J. L. Gómez, J. A. Miralles)

Injection of a component

•component: velocity perturbation at jet nozzle•component interacts with recollimation shocks•simulation: MRGENESIS, 2D cylindrical, 1600 x 80 zones, 5 x 104 snapshots

Injection of a component

•component: velocity perturbation at jet nozzle•component interacts with recollimation shocks•simulation: MRGENESIS, 2D cylindrical, 1600 x 80 zones, 5 x 104 snapshots

Time-dependent radio emission

simulation: SPEV, 128 frames, 270 x 18 pixels, 3 frequencies, 100 Kh / model0.5 Tb hydro data, 2x105 Lagrangian particles, 2x106 line-of-sight segments

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

Time-dependent radio emission

simulation: SPEV, 128 frames, 270 x 18 pixels, 3 frequencies, 100 Kh / model0.5 Tb hydro data, 2x105 Lagrangian particles, 2x106 line-of-sight segments

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

Components in pc-scale jetsJet of radio galaxy 3C120

Gomez+ Astrophys. J. 561 (2001) L161

Simulated components

main component

trailing components

trailing components

main component

Simulated components

unconvolved data

Simulated components

convolved data

Gamma-ray burst afterglows

•afterglow: a long lasting emission starting at the end of the GRB•early afterglow emission (seconds - minutes): probes the jet

•question: are GRB jets magnetized at the onset of the afterglow?•late afterglow emission (hours - days): probes the environment

•question: can we tell if GRB occured in a massive stellar cluster?•method:

•perform high-resolution RMHD simulations (MRGENESIS)•compute optical and X-ray light curves (SPEV)

(in collaboration with: D. Giannios, M. A. Aloy)

•1D simulations: 106 zones, 108 iterations•50 - 100 Kh / run•≈ 104 snapshots / run

Effect of the magnetic field� :=

B2

4���c2

optical flash dissapears for magnetized jets

Application to observations990123 090102

�0

= 640�

0

= 0.01n

ext

= 10 cm�3

�0

= 940�

0

= 0.1n

ext

= 1 cm�3

✏e = 0.02✏B = 4⇥ 10�7

990123

GRBs with no RS peak observed

090102

optical flash (RS peak) almost never observed: almost all GRB jets magnetized?

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

99.99987% c 99.99994% c

blast wave “probes” ext. medium

RHD simulations

WR O

density profile encountered by the

blast wave

Mimica & Giannios Mon. Not. R. Astron. Soc. 418 (2011) 583

•physical set-up: O star located at 0.7 pc from the progenitor•progenitor wind profile: 5x1011 g cm-1 R-2

•1D RHD simulations of ejecta decelerating in a complex density profile•blast wave: EISO = 1054 erg, Γ0 = 27 at the start of the simulation•synchrotron + IC emission (O star emits 1039.5 erg s-1, hν0 = 10eV)

O star

WR (progenitor)

blast wavepropagation

High energy emission

Giannios Astron. Astrophys. 418 (2008) L55

4 MeV - 4 TeV light curve

• flares at tens of GeV• observable up to redshift 0.5• flares possible at TeV (from dust mid-to-NIR

photons scattering)?• what is the optimal observational strategy?

GRB 94021718 GeV @ 4500 s

Mimica & Giannios Mon. Not. R. Astron. Soc. 418 (2011) 583

Conclusions• current issues in relativistic jet research and the greater

availability of observational data require computationally intensive simulations and the calculation of emission in broad spectral bands

• use of supercomputers is unavoidable and the collaboration with computer scientists is valuable

• numerical R(M)HD simulations are an essential tool for understanding the nature of the relativistic jet dynamics

• computation of emission from numerical simulations enables direct comparisons with observations

• MRGENESIS + SPEV is a versatile framework and has been successfully applied to AGN, GRB and TDE jets

• future: resistive relativistic MHD, improved inverse-Compton, polarization