Fluid/Kinetic Hybrid Modeling of the Thermosphere of Pluto

Transcription

1 Fluid/Kinetic Hybrid Modeling of the Thermosphere of Pluto Bob Johnson OJ Tucker Alexey N Volkov UVa, Department of Materials Science and Engineering Feb 28, 2012

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3 Motivation Fluid models of the thermosphere and exosphere predict high escape rates (hydrodynamic outflow). Assumes upper boundary of zero pressure and temperature. DSMC models (Tucker, 2009; Volkov, 2011) show that escape for moderate Jean parameters is kinetic, not hydrodynamic. Our paper (Tucker, 2012) presents our hybrid model of Pluto and results.

4 Preliminaries The fluid equations for single component 1D atmosphere ( u c )2 << 1, ν = 0, Kn 1 r 2 nu = φ p GMm = p r rk b T, p = nk bt ( 1 r 2 r 2 κ(t ) T ( r r φ C p T GMm )) r 2 Q(r) is net radiative heating/cooling rate = Q(r)

5 Preliminaries Lower boundary conditions T (r 0 ) = T 0, p(r 0 ) = p 0 u is given entirely by r 2 nu = φ Upper boundary condition: r 2 κ(t ) dt ( dr = φ C p T GMm ) φ E rtop r r top

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7 Model N 2 atmosphere, with VHS model of collisions, κ(t ) = κ 0 T, and Larson-Bornake model of rotational internal energy, C p = 7 2 k b. Obtain fluid solution up to exobase, Kn = 1. Begin DSMC solution at Kn 0.1, using values of T and n from fluid solution. DSMC gives φ and φ E used to update fluid solution. Iterate until φ and T (r) is consistent.

8 No Heating Result Fluid-Jeans, φ = Fluid-DSMC, φ = Radius (km) sonic point rx SHE, φ = rx Kn=.1 rx SHE solution from Strobel (2008) Fluid/DSMC solution does not go sonic Different estimates of φ Temperature (K)

9 Solar Minimum Heating Result T fluid T T kin T rot Fluid/DSMC solution does not go sonic Separation in temperature below exobase

10 Solar Minimum Heating Result Fluid-Jeans, φ = Fluid-DSMC, φ = Radius (km) sonic point rx SHE, φ = rx SHE solution from Strobel (2008) Fluid/DSMC solution does not go sonic rx Kn=.1 Small change in φ large change in T (r) Temperature (K)

11 Solar Medium Heating Result T fluid T T kin T rot Fluid/DSMC solution does not go sonic Separation in temperature below exobase Temperature decrease to far above exobase

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13 DMSC takes too long DSMC suggests φ φ J for λ > 5 (Volkov, 2011) φ J = 1 2 π nv t(1 + λ) exp( λ) r 2 ( ) Cp φ E J = φ J k b T k b λ Used time dependent solver for energy equation.

14 Special Cases Temperature profile up to exobase no heating solar min solar med solar max Radius (km) Top of solution is exobase solution does not go sonic Temp (K)

15 Escape rate dependance on heating 300 φ/ φ J(r0) x s from Strobel (2008) black o from Fluid/DSMC energy limited escape above solar min modified escapes rates little change Qdr/( φ J(r0) kbt0)

16 Escape rate dependance on heating φ/ φ J(r0), φe/( φ J(r0) kbt0) black o from Fluid/DSMC modified escapes rates little change Qdr/( φ J(r0) kbt0)

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18 Sensitivity of HDM solutions to escape rate solutions which have an exobase Gruzinov (2011) defined three regions As λ decreases, models must produce similar escape rates

19 model shows extended atmosphere compare to pure hydro solutions

20 model shows extended atmosphere compare to pure hydro solutions Using Jeans from the upper boundary provide similar solutions to DSMC. Escape rate φ consistent with hydro. Small change in energy flow large change in T (r).

21 model shows extended atmosphere compare to pure hydro solutions Using Jeans from the upper boundary provide similar solutions to DSMC. Escape rate φ consistent with hydro. Small change in energy flow large change in T (r). Significant heating decrease in λ narrow range of φ.

22 Other escape formulations φ (10 27 s 1 ) E esc(mev ) r exo (km) T exo (K) u exo/u t λ exo fluid/jeans Jeans w/ u φ = 2 φ J φ = φ DMSC