Ray-Tracing and Flux-Limited-Diffusion for simulating Stellar Radiation Feedback

Transcription

1 Ray-Tracing and Flux-Limited-Diffusion for simulating Stellar Radiation Feedback Rolf Kuiper 1,2 H. Klahr 1, H. Beuther 1, Th. Henning 1, C. Dullemond 3, W. Kley 2, R. Klessen Max Planck Institute for Astronomy Heidelberg, Germany 2 - Computational Physics, Tübingen University, Germany 3 - Institute for Theoretical Astrophysics, Heidelberg University, Germany Fire Down Below - The Impact of Feedback on Star and Galaxy Formation Kavli Institute for Theoretical Physics, Santa Barbara, CA, USA April 17, 2014

2 Radiative Rayleigh-Taylor Instability in ULIRGs E = 0.5 Shane Davis (on Tuesday): Flux-Limited-Diffusion vs. Variable Eddington Tensor for Thermal Radiation Feedback (T ~ 80 K). This talk: Flux-Limited-Diffusion vs. Ray-Tracing for Stellar Radiation Feedback Davis et al. (2014, submitted)

3 Radiation Transport Equation: Ray-Tracing (RT) ~ ~ ri ext I = c 4 ( absb scate) Radiative Flux and Radiation Energy Density: ~F = Z E = 1 c 4 Z 4 Flux-Energy Relation: ~F = R d ~ I(r,,t) d I(r,,t) 4 d ~ I(r,,t) R4 ce d I(r,,t)

4 Radiation Transport Equation: Flux-Limited-Diffusion (FLD) ~ ~ ri ext I = c 4 ( absb scate) Approximations: Locally Isotropic, mean angular values (integral over full r ~ F ~ = c abs (B E) FLD approximation: ~F = D ~r(d re) ~ =c abs (B E) Gray approximation: Opacity is computed from local conditions: Conservation equation Flux-Energy Relation Diffusion equation apple(~x) =apple P/R (T rad (~x))

5 The Hybrid Scheme (RTFLD) Split Radiation Fields: Stellar Irradiation Thermal dust (re-)emission Different Solvers: Ray-Tracing (RT) Flux-Limited-Diffusion (FLD) not to scale Kuiper et al. (2010), A&A 511

6 Outline A. Radiation Transport Problem: Circumstellar Disk Temperatures Setup from Pascucci et al. (2004) benchmark test Setup from Pinte et al. (2009) benchmark test B. Radiation-Hydrodynamics: (1) Stellar Radiative Feedback (2) Radiative Rayleigh-Taylor Instability (3) The Science case: A Solution to the Radiation Pressure Problem in the Formation of the Most Massive Stars

7 Circumstellar Disk Temperatures Setup: Star Disk (flared) Pascucci et al. (2004) Tstar = 5800 K Rstar = 1 R Tau = at 550 nm Pinte et al. (2009) Tstar = 4000 K Rstar = 2 R Tau = at 810 nm Methods/Codes: Monte-Carlo code RADMC as reference (scattering is neglected) MC : Hybrid : FLD : ν-dependent RT for Stellar Gray FLD for Thermal Radiation Gray FLD approximation for both - Stellar and Thermal - Radiation Kuiper & Klessen (2013), A&A 555

8 Results Optically thin (Tau550nm = 0.1): Hybrid accurate up to 3% FLD yields wrong Temperature slope Hybrid/RT/ MC: apple(~x) =apple apple P (T ) o t 550 nm = 0.1 o o o o Hybrid o o = MC x = analytical: Spitzer (1978) o = analytical: gray & isotropic R-R o FLD 10 t 550 nm = 0.1 FLD: apple(~x) =apple P (T rad (~x)) R-R Hybrid FLD Kuiper & Klessen (2013), A&A 555 Fig. 3. Temperature profiles (upper panel) in the midplane of the circumstellar disk for the case of low optical depth 550nm = 0.1. F

9 Results Optically thick (Tau810nm = 10 4 ): Hybrid accurate up to 46% FLD misses Shadowing effects FLD t 810 nm = Hybrid/RT/MC: optically thin medium 10 1 = MC Hybrid R-R optically thick radiative barrier FLD t 810 nm = FLD: optically thin medium Hybrid 0 optically thick radiative barrier R-R Kuiper & Klessen (2013), A&A 555 Fig. 6. Same as Fig. 3 for simulation runs with 810nm = In this highly optical thick case, the results for gray RT gray FLD are identical to the frequency-dependent RT gray

10 Results Optically thick (Tau810nm = 10 4 ): Hybrid accurate up to 46% FLD misses Shadowing effects FLD t 810 nm = Hybrid/RT/MC: optically thin medium ~ optically thick radiative barrier R-R 4 d ~ I(r,,t) 300 ~F = directional history Hybrid = MC R R4 FLD d I(r,,t) ce t 810 nm = FLD: optically thin medium optically thick radiative barrier optically thin medium = free-streaming limit 100 Hybrid 50 ~F = D ~ re ~ re! 0 re ~ ce R-R Kuiper & Klessen (2013), A&A 555 Fig. 6. Same as Fig. 3 for simulation runs with 810nm = In this highly optical thick case, the results for gray RT gray FLD are identical to the frequency-dependent RT gray

11 Conclusion Irradiation! Long-range effect Frequency-dependence! FLD Shadowing! HDTL Fig gray Hybrid = ΔMC t 810 nm freq. Hybrid Kuiper & Klessen (2013), A&A 555

12 Radiation-Hydrodynamics: Stellar Feedback Eddington limit: L M F grav = Proto-Star G M r 2 F rad = apple L 4 r 2 c apple Interstellar medium Dust grains / Molecules / Ionized gas Radiative Force overcomes Gravity: F rad >F grav L M 4 Gc apple Scale-free! RT: apple(~x) =apple apple P (T ) Scale-free! FLD: apple(~x) =apple P (T rad (~x)) Eddington ratio decreases with distance to Star!

13 Radiation-Hydrodynamics: Stellar Feedback RT Kuiper et al. (2012), A&A 537

14 Radiation-Hydrodynamics: Stellar Feedback gray FLD Kuiper et al. (2012), A&A 537

15 Radiative Rayleigh-Taylor Instability E = 0.5: Fgrav ~ Frad E = 0.02: Fgrav >> Frad Davis et al. (2014, submitted) E = 2.0: Frad = 2*Fgrav In this case, the shell is accelerated efficiently and reaches the upper boundary of the domain before the RTI has time to grow appreciable. Jiang, Davis, & Stone (2013)

16 Analytically: Radiative Rayleigh-Taylor Instability Opacity / Radiative force is actually 1-2 orders of magnitude higher than computed within the gray FLD approximation Radiation-pressure-dominated cavities remain stable Massive Stars do not form via Radiative Rayleigh-Taylor Instability a cm s R cavity 2000 AU FLD 1 FLD 2 Ray Tracing Gravity M M a cm s R cavity AU FLD 1 FLD 2 Ray Tracing Gravity M M Kuiper et al. (2012), A&A 537

17 Scientific Application: Radiation Pressure Problem Kuiper et al. (2011), ApJ 732

18 Solving the Radiation Pressure Problem! 10-2 M core = 480 M Ṁ ü yr -1 D M core = 120 M M core = 240 M 10-6 M core = 60 M M ü D First simulations... Kuiper et al. (2010), ApJ 722 Including Radiation Pressure Feedback Forming stars far beyond the Radiation Pressure Barrier! mostly up to the observed upper mass limit M! 140 M

19 Radiation Transport Benchmark: HDTL Fig. 8. Irradiation! Long-range effect 50 gray Hybrid = ΔMC Radiative Stellar Feedback: Hybrid / RT Frequency Dependence! t 810 nm Shadowing! FLD freq. Hybrid gray FLD Summary Radiation Pressure Problem: Solved via Disk Accretion! Ṁ ü yr -1 D M ü D Thanks for your attention!

20 Stability of radiation-pressure-dominated cavities Shell morphology: Frequency-dependent RT: pre-acceleration of layers on top of the cavity shell FLD (E ~ 1.0) RT (E ~ ) 2000 AU Kuiper et al. (2012), A&A 537

21 Double-Check Kuiper et al. (2012): In the RT cases, the radiation pressure exceeds gravity by 1 2 orders of magnitude. Owen, Ercolano, & Clarke (2012): FLD, Hybrid, and MC Radiation Transport [...] we find the FLD method significantly underestimates the radiation pressure by a factor of ~100. Harries, Haworth, & Acreman (2012): MC-Radiation-Hydrodynamics The development and speed of the cavities is similar to that found by Kuiper et al.