numerical 3d-hydrodynamic modellingicc.ub.edu/congress/grbinbcn/documents/reitberger.pdf · 2013....

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Workshop on Variable Galactic Gamma-Ray Sources

NUMERICAL 3D-HYDRODYNAMIC MODELLING OF

COLLIDING WINDS IN MASSIVE STAR BINARIES:

particle acceleration & 𝛾-ray emission

NUMERICAL 3D-HYDRODYNAMIC MODELLING OF

COLLIDING WINDS IN MASSIVE STAR BINARIES:

particle acceleration & 𝛾-ray emission

K. Reitberger(1), R. Kissmann(1), A. Reimer(1), G. Dubus(2), and O. Reimer(1)

Barcelona, 04/18/2013

1 Institut für Astro- und Teilchenphysik and Institut für Theoretische Physik, Innsbruck 2 Institut de Planétologie et d’Astrophysique de Grenoble

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* numerical hydrodynamic models simulating the dynamics of wind

acceleration and collision in

course of orbital cycle.

(e.g., Pittard 2009)

* analytical models solving a transport eq. for accelerating

particles and subsequently com-

puting 𝛾-ray fluxes.

(e.g., Reimer et al. 2006)


The current project combines both approaches in a numerical framework.


• Stellar parameters (R,T,m)i , i=1,2

• Wind parameters (M , v∞) i , i=1,2

• Orbital parameters:

• semi-major axis

• Eccentricity

• inclination

• etc.

physics

For any 3D grid-point:

• Wind: ρ, v, T

• Particle spectra (electrons and nucleons)

• Components of 𝛾-ray emission along line of sight

• any other interesting

quantity (energy losses etc.)

Input Output

Workshop on Variable Galactic Gamma-Ray Sources Barcelona, 04/18/2013

I compute stellar wind evolution: • hydrodynamic description (similar to Pittard 2009)

• radiative line-acceleration, gravity and orbital motion

• radiative cooling in wind collision region (WCR)

• isothermal plasma outside WCR

II accelerate particles: • solving transport equation for each grid cell and particle species

• diffuse shock acceleration (DSA), losses by Inverse Compton (IC)

cooling, synchrotron emission, bremsstrahlung, collisions etc.

• particle advection with stellar wind plasma

III 𝜸-ray emission • Use 4D particle distribution in energy and space to compute

• IC-emission (anisotropic - depending on scattering angle)

• Relativistic bremsstrahlung

• 𝜋0-decay and ensuing 𝛾-ray emission

C R O N O S

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*CRONOS (see Kissmann et al. 2008)

• finite-volume hydro/MHD code developed by Ralf Kissmann

• second-order accurate in space

• Using approximate Riemann solvers (hll, hllc for hydro)

• Cartesian, cylindrical and spherical grid layouts possible

• C++ basis

• all modules MPI-parallel

• modular setup allows for easy expansion

• highly portable

Applied to hydrodynamic variables 𝜌, 𝒗, 𝑇

plus 𝑠 ⋅ 𝑛𝐸 advected scalar fields representing 𝑛𝐸 energy bins of 𝑠 different particle species

e.g., electrons and protons with 50 -100 logarithmic bins in interval [1MeV,10 TeV]


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𝜕𝜌

𝜕𝑡+ 𝛻 ∙ 𝜌𝒖 = 0

𝜕𝜌𝒖

𝜕𝑡+ 𝛻 ∙ 𝜌𝒖𝑢 + 𝑃 = 𝜌𝒇

𝜕𝑒

𝜕𝑡+ 𝛻 ∙ 𝑒 + 𝑃 𝒖 =

𝜌

𝑚𝐻

2

Λ 𝑇 + 𝜌𝒇 ∙ 𝒖

governed by

radiative cooling term Λ 𝑇 (following Schure et al. 2009)

force term 𝒇 = (−𝐺𝑀∗,𝑖 𝒓𝑖

𝑟𝑖3

2𝑖=1 + 𝒈𝐿,𝑖)

with line acceleration computed

according to Kudritzki et al. 1989

(modified CAK approximation)


O+O system, a= 400 R⊙

res. 256x256x64

*governed by transport equation

with 𝐸 = 𝐸 𝐷𝑆𝐴 + 𝐸 𝑙𝑜𝑠𝑠 + 𝐸 𝑎𝑑𝑖𝑎𝑏 and 𝑄 =𝜂𝑖𝑛𝑐𝜌

𝜇𝑚𝑝

1

𝑑𝑡

solution via semi-Lagrangian scheme following Crouseilles et al. 2010


𝜕𝑁(𝐸)

𝜕𝑡+ 𝛻 ⋅ 𝒗𝑁 𝐸 +

𝜕

𝜕𝐸𝐸 𝑁 𝐸 = 𝑄𝛿(E − E0)

• compression ratio determined by hydrodynamics 𝑐𝑟 =𝜌𝑝𝑜𝑠𝑡𝑠ℎ𝑜𝑐𝑘

𝜌𝑝𝑟𝑒𝑠ℎ𝑜𝑐𝑘

• shock velocity approximated by 𝑉𝑠 = 𝒗 ⋅ 𝛁𝝆

|𝛁𝝆|

• diffusion coefficient set to multiple of Bohm diffusion

• B-field approximated following Usov & Melrose 1992

• electrons: 𝐸 𝑙𝑜𝑠𝑠 contains IC-cooling (full Klein-Nishina cross-section), synchrotron emission, bremsstrahlung & Coulomb losses

• protons: 𝐸 𝑙𝑜𝑠𝑠 contains losses by nucleon-nucleon interaction & Coulomb losses

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remaining free parameters: surface magnetic field 𝐵𝑠,

diffusion efficiency 𝜁, injection fractions 𝜂𝑖𝑛𝑗𝑒 , 𝜂𝑖𝑛𝑗

𝑝


Determine position of shock by

condition 𝛻 ⋅ 𝒗 < 0

diffusive shock acceleration only

active in shock

wind parameters 𝜌, 𝒗, 𝑇 relevant for loss terms in 𝐸

left:

e- at ~1 MeV log(E2N [MeV cm-3])

left:

p at ~1 MeV log(E2N [MeV cm-3])

right:

p at ~100 MeV log(E2N [MeV cm-3])

right:

e- at ~100 MeV log(E2N [MeV cm-3])


green: N [MeV-1 cm-3] ~102 red: N [MeV-1 cm-3] ~105

electrons at 10 MeV

3D- iso-surface plots

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independent of previous steps. Load simulation results from file for further

calculation.

inverse Compton scattering (anisotropic) • Parameters: inclination and angle between projected line of sight

and apastron

• Simplifications: radiation field monochromatic, stars as point sources

• integration over electron spectrum

• Summation over all contributing grid cells

relativistic Bremsstrahlung • integration over electron spectrum

• following Blumenthal & Gould (1970)

• assume ISM metallicity

𝜋0-decay • integration over proton spectrum to get pion spectrum (formalism by

Pfrommer & Enslin 2004)

• integration over pion spectrum to get 𝛾-ray emission


*IC-flux as determined by our procedure for a single grid-

cell close to the WCR of an average B+WR binary

Comparison to the

analytical result of a

similar system in

Reimer et al. 2006


• radiation field of both stars considered

• monochromatic approximation of photons

• isotropic electron distribution

• declining scattering rate with decreasing

scattering angle

• variations with orbital phase

*• extensive testing and parameter studies

• add pion decay induced γ-ray emission

• publishing detailed description and documentation

• consider additional physics (γ-γ absorption etc.)

• application to specific binary systems like WR 140, η Carinae, etc.

Thank you for your attention!

Questions? Advice? Concerns?

Barcelona, 04/18/2013 Workshop on Variable Galactic Gamma-Ray Sources

numerical 3d-hydrodynamic modellingicc.ub.edu/congress/grbinbcn/documents/reitberger.pdf · 2013....

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