1. ISSI Team on modeling cometary environments in the context of the heritage of the Giotto mission to comet Halley and of forthcoming new observations at Comet 67P/Churyumov-Gerasimenko Second Workshop, Bern, 20-24 January 2014 On some aspects of the coupling of the inner neutral and ionized coma Svetoslav Nakov, Monio Kartalev

2. Outline Part 1:  Reminder a fiew results about inner ionized coma, obtained using single fluid gasdynamic model of the interaction with the solar wind  These are results that are very sensitive to the boundary conditions for the flow of cometary ions Part 2:  A simple model (Marconi and Mendis, 1982) of the inner collisional coma (the region, producing the ionized coma ) is adopted.  Several modifications /small improvements of the model are elaborated in order to check the effect on the results - in particular for the production of the particles of the ionized coma and their parameters  The obtained results are very preliminary. This study is a kind of methodological exercises at this stage.

3. Interaction of the ionized coma with the solar wind  Singe fluid gasdynamic model in all regions (shock fitting scheme)  Source and loss terms included in the RHS of all equations:  Region A: (mass-loaded, solar wind) photoionisation  Region B (shocked solar wind): photoionisation charge exchange  Region C (shocked cometary plasma): photoionisation charge transfer `dissociative recombination frictional force  Region D (supersonic radial flow of cometary ions): constant radial velocity w, constant Mach number M, radial density distribution ~ 1/r This model is a replica of the gasdynamic model of Baranov and Lebedev, utilizing different numerical approach

4. Physical specificities in the comet and nonmagnetic planets’ cases Source and sink processes in the mass-loaded solar wind and cometary/ planetary plasmas ( in the most general problem statement )

5. Some model results, demonstrating the sensitivity of the inner ionized coma on:  some details of the model’s parameters  boundary conditions, specifying input (to ionized coma) parameters, coming from collision-dependent inner coma It is worth to emphasize that in our single fluid model All parameters, participating in the reaction coefficients are determined self- consistently The electron temperature, needed for the impact ionization and dissociative recombination is accepted to be equal to the temperature of the considered single fluid gas

6. One of the challenging experimental findings in the inner Halley Coma: Ion pileup boundary, found by Giotto at approximately 8000 km from the nucleus From Gombosi et al. 1996: Comparison of modeled (their model) plasma density with measured ion mass density along the Giotto inbound pass as a function of cometocentric distance. HIS data (Altwegg et al.,1993), HERS data (Neugebauer et al., 1991). Dashed line: model by Schmidt et al, 1988 A coincidence in the frame of the MHD model was reached by these authors, but “paying” for this by introduction of some “ prescribed” outside to the model conditions Somewhere In the region B In this interpretation

7. Outside prescribed conditions, needed to explain the Ion pileup boundary in the frame of the ideal MHD approach From Gombosi et al. 1996: The radial electron temperature profile used in their calculation From Gombosi et al. 1996: The radial recombination rate profile used in their calculation Taken independently “from the experimental data”

8. When the dissociative recombination is included in the Region C, the obtained by the model temperature distribution along a Giotto trajectory also corresponds to the really measured one  The solid line is the single-fluid temperature distribution along Giotto trajectory, obtained by our model in the region inside the contact surface (between the INNER SHOCK and the contact surface)  The dashed line is the real, measured by Giotto electron temperature.

9. Projection of the cometary ion bulk flow vectors into the Halley–Sun– Ecliptic (HSE) plane Giotto IMS-HIS (blue) Rubin et al., 2009 Model velocity component, perpendicular to the radial direction (Region C) along the radius at 108 o from Comet-Sun line. Solid line – with all reaction included Onlny the inclusion of all reactions ensures the coincidence with the observation

10. Dependence of the density distribution along the computational grid radiuses (108 o computational radius is a proxy of the Giotto trajectory) Case 1: All reactions included Only this model case predicts correctly the observed density variation along the trajectory Closest to the Giotto orbit Case 8: Only photoionization included

11. Very strong influence of the Mach number of the outflowing ionized cometary gas Only the Mach number on the inner computational boundary is the difference between these cases M in =1.8 M in > 4

12. Modeling of the near comet atmosphere  The model of Marconi and Mendis, 1982 (hereafter – M&M) is adopted, utilizing up-to-date numerical techniques  H 2 O dominated, multispecies cometary atmosphere (no dust) conservation  Self-consistent set of equations, representing conservation of  number density (for each specie)  momentum (one-fluid approach)  energy (one-fluid approach)  the flux of solar UV radiation  Major photolytic processes  27 most important chemical reactions are taken into account

13.  For mathematical convenience the system of equations is splitted into two subsystems:  System of fluid equations with source and loss RHS  System of equations describing spatial attenuation of each of the considered (by M&M) three bandwidths (“streams”) of the solar UV flux  Additional information about parameters of the considered reactions is needed for closing the system  One dimensional, quasi-steady model, restricted to the Comet-Sun line

14.  Fluid model segment a system of 3 ODEs, representing the conservation laws for number density, momentum and energy. Ideal gas approach Number density Momentum Energy Ideal gas

15.  The source term in the number density equation is:

16.  The second segment the attenuated solar fluxes and photo rate coefficients for the photo reactions  Consideration of fluxes for 1 AU in 3 bandwidths, which are: and correspond to the thresholds of the following 3 most important photolytic processes associated with the absorption of solar UV radiation in the cometary atmosphere:  For a heliocentric distance d( AU ), the 3 fluxes are scaled by

17.  M&M use an average (photo)cross sections over the 3 bandwidths only for the 3 photolytic processes, mentioned above and they are:  For the 1-st process :  For the 2-nd process  For the 3-th process

18.  Having these cross sections, M&M evaluate the attenuated fluxes using the Beer Lambert Law with the simplification that only H 2 O absorbs and only with the first 3 photoreaction channels:  can be attenuated by the 3 processes, so  can be attenuated by the 1-st and the 2-nd processes, so  can be attenuated only by the 1-st process, so

19.  The attenuated photo rates for these 3 main reactions are in : 

20.  For the rest of the photo reactions that they consider, they don’t have any cross sections, so for the evaluation of the rate coefficients for the j-th photo reaction they scale the unattenuated rates as follows:  If the threshold for the photo reaction under consideration is and,then

21.  Thus two independent steps of an interactive solution are formulated:  Knowing the photo rates, we can solve the the fluid ODE system) and vice-versa.

22.  There isn’t a full set of boundary conditions at the comet surface or at a boundary far away from the nucleus (where the solar fluxes are unattenuated and known): o At the comet surface we have the number density of, the velocity, and the temperature. The rest of the number densities are assumed zero. ( Houpis Mendis, 1981) o There are no values for the attenuated solar fluxes at the comet surface, hence we do not have photorate coefficients at the surface too. o The situation at the remote boundary is similar.  Consequently we can’t solve the two components simultaneously.  M&M suggest the following iterative process. The Iterative Procedure

23. solve the 1-st component (ODE system) with constant photo rates, equal to the unattenuated ones Solve the 1- st component with the new photorates Solve the 2-nd component with the new number densities for H2O The Iterative Procedure

24. Reactions used by M&M  27 photo and chemical reactions are considered They are presented in the blue table bellow, with references in the last column : o H=Huebner 1992, o M=M&M 1982, o V&G=E.Vigren & M. Galand 2013. o Values without a reference are used by us. Where 2 values in a row, they are for quiet and for active sun, given by Huebner 1992.  The rates in the table are for 1 AU and unattenuated solar radiation.

25. o In reaction (5) M&M give as products, but the correct products are as listed in the table above (Huebner 1992) o For reaction (2) M&M give much higher rate coefficient of, than the ones used by Huebner and us. Most probably it is because of the use of a higher value for the cross section Chemical reactions, considered by M&M

26.  In reaction (13) we do not account separately for the 3 channels, for producing 3 states of oxygen, but rather consider the concentration of oxygen as a whole, following M&M. It will not affect the temperature or velocity profiles. Also it has a negligible influence on the number densities. In future work we will adjust that simplification. Reactions used by M&M

27.  Reaction (20) we treat as reaction (13) by combining the 4 reaction channels in one.

28.  The source term in the number density equation is:

29.  With pure H2O nucleus we take into consideration the following species : Neutrals: H2O, OH, H, O, H2, O2 Ions: H3O+, H2O+, OH+, O+, H+, H2+, O2+ and electrons e- additional species to the onesused by M&M Modifications Modification of the model by including additional species

30.  The including of O2+ is motivated by the fact that there are only 2 loss reactions for O2 considered by M&M and no loss for O2+  It would be better justified if there are other initial neutrals than H2O, and another production mechanisms of O2+, respectively.  As it is seen, the resulting number density of O2+ for higher heliocentric distances is negligible and at this point with pure H2O nucleus it can be neglected.  However, for low heliocentric distances it becomes as abundant as O+ and H+ Modification of the model by including additional species

31.  The inclusion of H2+ is in a relevance to the included by us additional reactions, among which are photoionization, photodissociation and photodissociative ionization of H2(the 3 main loss mechanisms for H2 with pure H2O nucleus) production of H2+  ionization:  photo dissociation  photodissociative ionization Modification of the model by including additional species

32.  Besides these 3 reactions we include 2 more loss reactions for H2+ of charge exchange with H2O.  The result for 1 AU is again a negligible number density of H2+,because of its destruction in the charge exchange reactions with H2O, which are more efficient, especially near the nucleus, where the temperature is very low.  But at the same time the maximum number density of H2 drops ~4 times, and at the end of the integration interval it is ~2 times smaller. Modification of the model by including additional species

33.  All the additional reactions are listed in the yellow table bellow:  With exception of reaction (34) all the additional reactions have relatively high rate coefficients and mean excess energies. This influences mainly the energy equation (the source term Q) and the concentration of H2, as we saw above. In more details the effect will be discussed in stages bellow. Modification of the model by including additional reactions

34.  Following Vigren&Galand 2013 we adopt the temperature dependence of in the following reactions: M&M additional reactions  The rates, used by M&M, are equal to the coefficients in front of the term Modification of the model by refining some rate coefficients

35.  For 1AU with only that modification, the result is plotted on the right.  As it is expected this refinement in the rates of reactions 8,9,10,11,12 influences the number densities of the ions H2O+, OH+, H+, O+ which take part in the charge exchange reactions with H2O molecule  The region with much lower number densities (up to 10 times) in the case with T dep. exactly match the region, where the temperature drops under 10 K. It is seen that at that temperature the refined rates are ~5.5 times higher. And at the minimum T=5.4K ~ 7.5 times higher Modification of the model by refining some rate coefficients

36.  As we noted, M&M divide the solar radiation into 3 main photon fluxes, corresponding to bandwidths, (1450,1860), (984, 1450) and (0,984) respectively.  Nowadays the computational power is much larger so it is worth to take into account the detailed distribution of the solar radiation with respect to the wavelength.  The solar fluxes for quiet sun we take from Huebner (1992) given for 324 wavelength bins in the interval (0 A, 140 000 A). We are interested only in the UV part. Modification of the model by detailed consideration of the solar radiation and the cross sections as functions of the wavelength

37.  Now we have the unattenuated flux divided into 324 bandwidths for 1 AU :  The photo cross sections for all the photo reactions as functions of, that are listed in the blue and the yellow table, we take from the database on the web page http://phidrates.space.swri.edu/ http://phidrates.space.swri.edu/  Having these data sets, we calculate the rate coefficients and the mean energy release in terms of the cometocentric distance and the wavelength. Modification of the model by detailed consideration of the solar radiation and the cross sections as functions of the wavelength

38.  The discrete formulas:  For each wavelength bin k (k=1,2,..,324) and a heliocentric distance d ( AU ):  Then the rate for the j-th photo reaction is Modification of the model by detailed evaluation of the photo rates

39.  Now in the iterative procedure the evaluation of the attenuated photo rates becomes a little more complicated, because now all the neutral species take role in the absorption of the solar radiation: Modification of the model by detailed evaluation of the photo rates solve the 1-st component with constant photo rates, equal to the unattenuated ones Solve the 1-st component with the new photorates Solve the 2-nd component with the new number densities for H2O, OH, H, H2,O, O2 (all that absorb)

40.  The modification of the mean excess energy (reduced with approaching the nucleus, because of the attenuated solar radiation) decreases the temperature, and the more exothermic reactions, that are included increase it. The combined effect of these is  As a result the temperature far from the nucleus is higher.  Of course there is another aspect that this model shouldn’t be used in this remote region, not being able to treat all the surfaces of discontinuities alone. The effect on the Temperature, because of modification of photo rates

41.  We make simulations for heliocentric distances from 0.5 to 3 AU. The boundary conditions for the number density of, the temperature of the gas, and the one-fluid velocity at the comet surface for different are calculated by making use of a paper by Houpis & Mendis (1981).  It is solved the simplified quasi-steady energy balance equation for the nuclear surface (fast rotating nucleus) together with the integrated Clapeyron-Clausius equation for the vaporization of H2O. It is and not, because the attenuation is mainly in the UV, which is less than 10% of the total radiation. Studying the effect of the heliocentric distance

42. Results  For a comet with a radius equal to that of 67P /CG (~1.7km) the outgassing rate increases from H2O molecules at 3AU to at 0.5AU.  The maximum electron number density increases from at d=3AU to at d=0.5AU and at the same time the maximum location is moved from the nucleus surface towards the sun.  The concentrations of H2O+, OH+, O+, H+ change from being monotonically decreasing at 3AU to monotonically increasing at 0.5AU with moving away from the nucleus. Studying the effect of the heliocentric distance

43.  As approaching the sun, the vaporization becomes stronger, the attenuation of the radiation also, so the maximum in the Ion number density is moved towards the sun.  The effect on the Temperature The effect on the neutral number densities: Studying the effect of the heliocentric distance

44.  The effect on the Mach Number:  For every heliocentric distance, with the boundary conditions that we use,we have slightly supersonic speed at the nucleus surface with a Mach number~1.09  For every d ( AU ) the Mach umber increases and forms a maximum at the same cometocentric distance, for which we have a minimum in the temperature.  The maximum rises up to ~16 at d=2.4 AU and then decreases steadily until reaching ~12 at d=0.5 AU Studying the effect of the heliocentric distance

45.  The effect on velocity:  As noted above, for every heliocentric distance from 0.5 to 3 AU with the used boundary conditions at the surface, the expansion speed is supersonic with Mach ~ 1.09.  The velocity on the surface is rising from 0.35 km/s at 3 AU to 0.39 km/s at 0.5 AU. At the same time the velocity at r=50 km changes from 0.73 to 0.79 km/s. The velocity and Mach number are shown on the animation: Studying the effect of the heliocentric distance

46. Possible activity of our group in Sofia till the final team meeting, supposed to contribute to the project:  Modification and development of our single fluid model of solar wind-comet interaction to 3D approach  Accomplishing papers about re-interpretations of Giotto observations in the inner ionized coma  Accomplishing the started investigations on modeling the collisional comet atmosphere  Hopefully- collaboration with other participant in some interpretations of Halley missions data  Rosetta ?

47. Thank You !