Expected dust flux on OSIRIS J. Knollenberg

Model 2D axisymmetric dusty gasdynamic model Gas production rate from simplified thermal model (neglecting heat conduction into the interior) Dust size distribution modelled by 20 discrete sizes in the range 10-8-0.1 m Each size treated as separate dust “fluid” Dust column densities computed by integration along LOS Synthetic images computed by application of Divine (1981) phase function Dust production scaled to fit measured AfRho Assumes negligible influence of dust on gas flow (ok for optically thin comae) Dust fluxes computed inside the inner coma

Model cases 3 heliocentric distances = 1.25,1.97,3.07 AU Gas production according to Mike A’Hearns “OSIRIS” model (Coma-WG) Qg=5.7 1027 s-1 @ 1.25, 1.14 1027 s-1 @ 1.97, 1.58 1026 s-1 @ 3.07 AU Afrho from Fulle et al. (2010) 4m @ 1.25, 0.8 m @ 1.97, 0.35 m @ 3.07 AU Size distribution exponent 3.0-3.5 3 different types of cometary activity M1: homogenous comet covered by thin dust crust “thin” = production distribution on day side driven by direct illumination variable CO2 production with solar input @ Hartley-2 (A’Hearn 2011) small nightside production = 5% of total (arbitrary, “nightside jets”) M2: active icy area on subsolar point + background activity through crust icy area contributes 75% of total production rate M3: active icy area around subsolar point only (single jet case)

Boundary conditions 1: Gas production and temperature

Boundary conditions 2: sublimation coefficient Decrease of sublimation coefficient with temperature (Gundlach, 2011) leads to: Increase of surface temperature by ~ 10 K Sublimation rate hardly influenced !

Boundary conditions 3: Return flux Fsol = Frad + Fsubl + Fcond + (FRTN) Return flux of ~ 25% increases the temperature of an icy active region by about 2 K Gas production rate still very close to free sublimation ZHK Returned particles freezes on surface adding the correponding latent heat FRTN neglected by Crifo (violating energy principle) Heat conduction to interior affects this only minor

Drag force Drag force mainly dependent on cross section / mass ratio A/M Drag coefficent CD only slightly higher for fluffy (fractal) grains Linear relationship between A/M and fractal dimension for D > 2.2 Compact spherical grain model still useful !

Fluid codes at large Rh ? (strict) applicability depends on Rh and gas production model For Rh > 2 AU large parts of coma in transition regime But drag force on dust grains not too different Fluid models still useful (at least for engineering purposes) !

Gas flow field M1 M2 M3

Integration along LOS -> fill factor M1 M2 M3 90° 45°

Dust terminal velocity (Rh=1.25 AU)

Dust (area) fluxes @ 1.25 AU M1 M2 M3 Size distribution exponent = 3.5

Results summary (Area flux) Model Rh AfRho [m] alpha Qd [kg s-1] D/G Coma D/G N Fp (2RN) Fav(2RN) Fp (5 RN Fav (5 RN) Fp (10 RN) Fav (10 RN) M1 1.25 3.95 3.0 313.62 1.64 4.00 2.02E-05 5.05E-06 3.04E-06 8.03E-07 7.42E-07 2.01E-07 3.5 122.57 0.64 1.39 1.11E-04 2.82E-05 1.67E-05 4.49E-06 4.07E-06 1.12E-06 1.97 0.82 20.61 0.54 2.42 2.67E-06 5.84E-07 4.00E-07 9.28E-08 9.74E-08 2.31E-08 0.80 7.72 0.20 0.69 1.23E-05 2.79E-06 1.84E-06 4.45E-07 4.48E-07 1.11E-07 3.07 0.40 2.30 0.35 5.73 1.24E-06 2.02E-07 1.81E-07 3.19E-08 4.36E-08 7.92E-09 0.78 0.12 0.85 3.33E-06 5.85E-07 4.90E-07 9.31E-08 1.19E-07 2.33E-08 M2 646.93 3.36 6.03 3.50E-04 7.52E-06 3.51E-05 1.20E-06 7.70E-06 3.00E-07 221.26 1.15 1.93 1.53E-03 3.86E-05 1.43E-04 6.17E-06 3.11E-05 1.54E-06 106.86 2.77 4.10 6.34E-05 9.84E-07 1.53E-07 1.36E-06 3.68E-08 34.03 0.88 1.27 2.85E-04 5.07E-06 2.71E-05 7.92E-07 5.95E-06 1.88E-07 28.51 4.31 5.98 2.28E-05 2.37E-07 2.20E-06 3.65E-08 4.86E-07 8.90E-09 8.58 1.30 1.78 1.03E-04 9.95E-06 1.83E-07 4.41E-08 M3 1116.20 5.49 7.06 4.76E-04 9.63E-06 4.96E-05 1.09E-05 3.84E-07 400.28 2.47 2.31E-03 5.31E-05 2.21E-04 8.47E-06 4.81E-05 2.12E-06 0.81 135.17 3.87 4.21 7.37E-05 7.24E-06 1.57E-07 1.59E-06 3.93E-08 48.64 1.52 3.85E-04 5.60E-06 3.67E-05 8.94E-07 8.03E-06 2.24E-07 31.53 4.33 4.86 2.21E-05 2.35E-07 2.13E-06 3.74E-08 4.68E-07 9.34E-09 10.75 1.48 1.65 1.14E-04 1.27E-06 2.03E-07 2.41E-06 5.07E-08

Conclusions Dust production rises from a few kg s-1 at 3 AU to several 100 kg s-1 around perihelion Dust/gas ratio (in coma) about 0.3 – 2 (size distribution of Fulle et al, 2010) Area fluxes at 3 AU appear generally low (?) Except for Lander delivery in case of strong jet production model In jet center peak values up to 10-4 s-1 (for alpha=3.5) 2w global mapping => 1% (for „nominal“ alpha=3.0 !) For Rh < 2 AU close flyby‘s might be a problem Largest uncertainty due to uncertainties in size distribution and structure of grains ! To do: integration along model orbits !