J.F. Crifo V.V. Zakharov A.V. Rodionov Adjustment of the gas coma model for assessment of the aerodynamic force on the Rosetta lander. J.F. Crifo V.V. Zakharov A.V. Rodionov

Purposes of the model: Prediction of time dependent spatial structure of the coma for 67P/C-G suitable for analysis of the lander descent on the surface. This excludes: The immediate vicinity of the surface; The outer coma; Minority molecules; Low total gas production rates Q (more exactly low average surface fluxes Q/A where A is the nucleus “total active area”). Computational methods: BE-NSE method: Navier–Stokes equations and molecular mixture laws combined with a locally plane-parallel solution of the collisional Boltzmann equation for the nonequilibrium near-surface Knudsen layer. The Godunov method is used for numerical integration. Efficiency increase with decrease of rarefaction. Direct Simulation Monte Carlo (DSMC): VHS model of elastic collisions, Larsen-Borgnakke model of translational-rotational exchange, Distribution function as boundary condition on the surface. Efficiency increase with increase of rarefaction.

Physical specification of one model solution Nucleus shape model; Spherical harmonic filtering degree, yielding the “initial surface” shape (the initial surface is not the nucleus surface); Sun position in the nucleus frame as a function of time; Parametric gas production model: Distribution of the fluxes of H2O, CO and “third species” on the “initial surface”; Distribution of temperature on the “initial surface” 5. Test particle solution (spherical grains with ad and ρd) for adjustment to the gradients of coma brightness and dust structures (to characterize the gas coma not the dust).

Distribution of surface flux (H2O, CO, …): The nuclei are ice-dust mixtures characterized by the icy area fraction : =const - “homogeneous” nuclei,  ≠ const - “inhomogeneous” nuclei; Qi - total flux; fsun - step function: 0 in shadow, 1 if sunlit; a0 - is a diurnal asymmetry parameter; The upward flux of H2O at each point is computed from a sublimation energy budget equation; κ - internal heat transfer parameter; M0 is taken from solution of the gasdynamic equations of the coma gas outflow.

List of the model free parameters to adjust m=1,2 or 3 sets of molecular initial flux parameters; Each set is assumed due to N “areas”, each area are defined by 6 parameters: The surface sublimation capacity fs; The surface diffusion capacity fd; Parameter defining solar zenith angle dependence a0; Parameter defining source area width; The longitude and colatitude of the area center; In total 6×m×N parameters.

Dust environment Computational methods: Multi-Fluid; Dust Monte Carlo. General comments for the dust model: The dust grains are assumed spherical, isothermal; Only three applied forces are taken into account: the nucleus gravitational force, the gas coma aerodynamic force, and the solar radiation pressure; The aerodynamic force is computed on the base of a gas model of the coma; The mutual grain collisions are neglected; Independent simulation of grain families; At each point and each size, the dust mass flux is proportional to the gas mass flux.

3D+t Gas distribution in the coma (QCO=1027, a0=0.1) Density of H2O Velocity Density of CO overall density

3D+t dust distribution (QCO=1027s-1, ρd=ρN=370 kg/m3) ad=10-3 m Dust density ad=10-7 m Dust velocity

P/Halley Near-Nucleus Dust Coma Azimuthal brightness gradient map derived by Keller et al. 1995 Dust column density of spherical grains of 0.91-μm radius, computed with a singlefluid model. (Crifo et al. 2002) Spherical harmonic representation of P/Halley nucleus (Crifo et al. 2002)

Expected (prospected) INPUTS Nucleus shape. Successive improved versions of the nucleus shape as derived by OSIRIS. LATMOS will construct successive improved versions of the smoothed surface to be used by the gas code as “initial gas flow surface”. Initial gas temperature. It is expected that MIRO will derive nucleus surface temperatures (day and night) and VIRTIS will derive day-side nucleus temperatures. If these data are found compatible with the model needs, LATMOS will use these temperatures to derive "initial gas temperatures " applicable on the “initial gas outflow surface”. Nucleus surface bolometric albedo. For optimizing the LATMOS-computed nucleus surface temperatures, LATMOS needs the OSIRIS-derived surface bolometric albedos. Total molecular production rate. All total gas production rates derived from large distances by MIRO, VIRTIS and ALICE (critical input parameters ). In-situ measured gas density, composition and velocity. The LATMOS model will be optimized for the region scanned by the ROSETTA orbiter, owing to systematic fits to the ROSINA data. Uninterrupted operation of this instrument is nearly a necessary condition for the reliability of the LATMOS model. Near-nucleus white-light coma images. To test the validity of the LATMOS code outside of the region scanned by the orbiter, remote-sensing data must be used. LATMOS will test the quality of the model using the OSIRIS broad-band dust coma images. In-situ measured dust grain velocities. The grain can be considered as a lander with reverse velocity direction: if their velocities are correctly reproduced by the LATMOS model, this maximizes the chances that the model predicts correct aerodynamic pressure from the surface up to the orbiter position. Nucleus surface gravity field. To optimize the use of the GIADA dust velocities to constrain the LATMOS gas model, SONC will provide LATMOS with the GRGS-derived position-dependent gravity vector. Line integrated flux maps of gas coma. SONC will provide LATMOS with the distributions of isophots (e.g. in the form of images) with known level spacing and observational conditions derived by MIRO, VIRTIS, ALICE. The spatial coverage should be 5 km around the nucleus with resolution better than 0.1 of the nucleus size.

Uncertainty associated with observational program (ROSINA, GIADA, VIRTIS, MIRO)  ROSINA For Qco=1027, a0=0.1 Nude gauge png/pbg >1 from R<1400 km (day) and R<400 km (night) i.e from Jul-15! Ram gauge prg/pmin>1 from R<300 km (day) and R<70 km (night) i.e. Jul-15-24.  For Qco=1026, a0=0.1 Nude gauge png/pbg >1 from R<850 km (day) and R<130 km (night) Ram gauge prg/pmin>1 from R<175 km (day) and R<20 km (night) VIRTIS The detailed schedule is not completed at the time (30.10.2013) MIRO Global gas production rates (QH2O, QCO): May-June (Opportunity window 5000 km<R<106 km). Night side temperature: mid-August (refinement in late August-September)  The detailed schedule is not completed at the time (23.10.2013) GIADA Direct measurements: Speed 1÷100 [m/s], Momentum 6.5·10-10÷4·10-4 [kg·m/s], Fluence of dust Particles 1.9·10-9÷2.9·10-4[g/cm2]. Derived measurements: mass, flux, size (min limit for statistics is ~10 grains) For pre-landing orbit: for Q~1027, 91 micron, ~6 grains per hour. In the absence of observational data: Backup model only!

(what the model needs form OSIRIS) Conclusions (what the model needs form OSIRIS) Shape; Bond albedo; Images of full coma with FOV not too large; Image enhancement; Column density (only for several sizes); As much images as possible and as soon as possible :)

EN D

OSIRIS ephemeris distance (km) NAC IFoV (m/px) NAC FoV (km) CG (NAC px) WAC IFoV (m/px) WAC FoV (km) CG (WAC px) 1000000 18599.96 38092.71 0.24 100999.77 206847.53 0.04 100000 1859.96 3809.19 2.42 10099.77 20684.33 0.45 10000 185.96 380.84 24.19 1009.77 2068.01 4.46 1000 18.56 38.01 241.93 100.77 206.38 44.55 100 1.82 3.72 2417.72 9.87 20.22 445.24 70 1.26 2.58 3451.47 6.84 14.01 635.62 50 0.89 4825.71 4.82 9.88 888.69 10 0.14 0.30 22734.08 0.78 1.60 4186.67 5 0.05 0.10 39398.66 0.28 0.57 7255.60 ephemeris Date r (AU) delta (AU) phase angle (°) PsAng (°) PsAmv (°) dist Rosetta-cometa 2014-Mar-01 4.38341888 4.898942886 10.4743 259.268 265.835 5485762.976 2014-Apr-01 4.247314102 4.32176321 13.3559 259.408 263.26 3393904.861 2014-May-01 4.107802901 3.721016688 113.669 260.93 262.109 1395710.467 2014-Jun-01 3.955294666 3.163820366 110.2853 266.831 262.986 225471.6338 2014-Jul-01 3.799335864 2.801915079 1 3.4632 298.56 10507.82038 2014-Jul-15 3.723653624 2.718831917 2.7539 29.21 1894.514892 2014-Jul-24 3.674005494 2.69633868 5.019 57.828 104.483835 2014-Aug-01 3.629212152 2.695929176 7.3078 67.839 92.345717 2014-Aug-15 3.549307815 2.734686827 111.08 76.413 272.984 30.633936 2014-Sep-01 3.44965029 2.834972883 114.7028 81.71 274.121 20.073092 2014-Sep-18 3.347060065 2.971098209 116.9922 84.558 273.941 9.886212 2014-Oct-01 3.266601694 3.085035447 17.8425 85.735 272.958 9.911732 2014-Nov-01 3.067621383 3.336458968 17.1774 86.446 268.484 39.1601 2014-Dec-01 2.865445213 3.49111227 13.8436 86.08 262.723 80 2014-Dec-31 2.653963694 3.517092421 8.8461 87.848 256.73 110.020003

Kitamura 1990

Spherical nucleus with one active ring: gas and dust distribution when the Sun is on-axis. (a) Gas density and velocity field (Knollenberg, 1994); (b) 1.5-μm-radius grain density (Knollenberg, 1994)

2D Test Models Crifo, Loukianov, Rodionov, Zakharov (2003) Zakharov et al. (2008) Zakharov et al. (2009)

2D Test Models rh =1 AU, Q = 3∙1028 s-1, ad = 4.2∙10-2 [m]