MCRT L13: Time dependence

•  Time dependent MCRT •  Radiation pressure and radiation (magneto) hydrodynamics

Time dependent MCRT •  Homework problem – bin photons according to travel time (total path) •  For time dependent MCRT, emit photons and track them for a set time

interval, Δt, corresponding to a path c Δt, or until they exit the simulation (by escape, absorption, etc)

•  Store the locations, directions, optical depth still to travel, of any photons that have not escaped the system in Δt

•  For time Δt, compute mean intensities, absorbed energy, momentum deposition, number of ionizations, etc

•  Emit more source photons and also re-start the trajectories of any photons in the bank, following all photons for another time step, Δt

•  For each time step, simulation will comprise following source photons and also banked photons that have not escaped the system

•  Follow time dependent heating, cooling, ionization, time variable sources

•  Time dependent radiation-matter interactions: radiation hydrodynamics

Follow source photons for c Δt Bank positions, trajectories of photons still in the system Update quantities: absorbed energy, momentum transfer, etc

Re-start random walks of banked photons and follow for c Δt

Re-start random walks of banked photons and follow for c Δt

Start source photons and follow for c Δt Bank positions, trajectories of photons still in the system Update quantities: absorbed energy, momentum transfer, etc

Re-start random walks of banked photons and follow for c Δt

Re-start random walks of banked photons and follow for c Δt

Re-start random walks of banked photons and follow for c Δt Start source photons and follow for c Δt Bank positions, trajectories of photons still in the system Update quantities: absorbed energy, momentum transfer, etc

Get time dependent grids of heating, ionization, momentum transfer…

Radiation Pressure

Stellar winds accelerated to speeds of 3000km/s by radiation pressure

Teller-Ulam H-bomb design Secondary compressed by

radiation pressure from x-rays… Or is it…?

Optical tweazers: cell trapping & sorting

Radiation Pressure

•  Photons moving in direction n have momentum vector p = ε/c n = hν/c n •  Total momentum per second from a star is L/c •  Conservation of momentum: when photons are scattered or absorbed,

transfer momentum to other particles •  Rate of momentum transfer is vector force: F = dp/dt •  Radiation pressure = force per area

Radiation Hydrodynamics

€

dρdt

+ ρ∇.v = 0 Continuity equation

ρdvdt

= −∇P −∇φ + Frad Momentum equation

P = f (ρ,T) Equation of stateFrad = Radiation pressure

Mechanical momentum from stellar winds, explosions, etc Compute gas temperature to determine gas pressure Can use MCRT photoionization and/or radiative equilibrium codes to determine gas and dust temperatures Compute momentum transfer from photons to matter: radiation pressure

Radiation Pressure •  Momentum per photon packet: ppacket = n ε/c •  Difference in momentum between packets entering and

leaving a cell gives net momentum change of a cell

•  m packets entering cell; n packets leaving cell

€

Δpcell = ppacket, inm∑ − ppacket, out

n∑

€

Fcell, radiation =Δpcell

Δ t

Momentum transferred to particle along direction of photon flight

θ = 0 θ = π

Δp = 0 Δp = 2 ε/c

θ

Δp = (1 - cos θ) ε/c

After many scatterings, albedo = a, the average momentum transfer for isotropic scattering is Δps = aε/c In general, non isotropic scattering: Δps = a (1 - g) ε/c Photon absorbed and re-emitted isotropically, average Δpa = (1 – a) ε/c For absorption and scattering: Δpa+s = (1 - a g) ε/c

g = cosθ = cosθΦ(θ,φ)dΩΩ

∫

Radiation Pressure •  Use pathlength estimators to get radiative force on a cell:

•  Absorbed photons transfer ε/c to cell since re-emission is usually isotropic

•  Scattered photons transfer (1-g) ε/c to cell, where g is average value of cosine of scattering angle €

Frad =LcV

nσ (1− ag) l ˆ n ∑

MCRT on MHD snapshots

HII Region: Hα Radiation pressure timescales MHD: stellar wind bubble

Snapshot density from MHD code, use MCRT: - compute photoionization & gas temperature - compute radiation pressure

Compare radiation pressures and timescales with momentum input from stellar winds Combine MCRT + MHD codes…

η CarinaBarnes, Goncalves, Wood (2014)

Star in a uniform density medium Monte Carlo photoionization Combined MCRT + MHD THE MATTER MOVES!!!!

Lund, Barnes, Vandenbroucke, Goncalves, Wood (2017)

Star in a uniform density medium Monte Carlo photoionization Combined MCRT + MHD THE MATTER MOVES… AS IT SHOULD!!!!

Lund, Barnes, Vandenbroucke, Goncalves, Wood (2017)

Massive star formation

Tim Harries, Exeter (2014)