German Aerospace Center Institute of Planetary Research, Berlin Hydrodynamical influence on the formation of HCN and DCN in protostellar clouds C. Tornow, E. Kührt, U. Motschmann Abstract HCN emission or absorption lines observed in the collapsing cloud around low and high mass protostars indicate abundances relative to H which range from 10 -9 to 10 -7 . These large variations are caused by the physical conditions of the molecular cloud. In addition to these properties, the cosmic ray ionisation rate influence the formation efficiency of the HCN molecules. In order to study the impact of a temporally changing gas density, velocity, and temperature a reduced chemical network derived from the UMIST data base is combined with a self similar hydrodynamical model of a collapsing gas sphere. Using a very general initial element distribution of a young molecular cloud the question is discussed whether a gas phase chemistry coupled to the ice phase is able to reproduce the HCN abundance and the DCN/HCN ratio observed in the vicinity of protostars. The differences between the calculated abundances of a hydrodynamical and a hydrostatic model are discussed as well. Introduction Since some of the N-bearing molecules are important prebiotic compounds, especially HCN, the icy part of comets and interplanetary dust particles may have supported the formation of life. The ISO measurements, the Halley missions and ground based observations of bright comets have already provided knowledge on the composition of interstellar and cometary ice. In Table 1 the derived abundances of a number of molecules relative to water are given. Despite the similarities concerning C, H, and O-bearing molecules one realises that the abundances of HCN and NH 3 are very different for the two targets. These differences need to be explained. The study of the chemical composition of pre-cometary ice in the environment of young protostars helps to find an explanation. Volatile N-bearing molecules contained in icy dust grains sublimate in the inner protostellar cloud and clearly change its gas phase chemistry, especially the abundance of HCN and DCN. Thereby, one obtains information on the molecular composition of the pre-cometary ice. Our previous studies show that both, the chemical and hydrodynamical evolution of a collapsing protostellar cloud have to be considered. Table 2 Parameters of equation 3. Table 1 C, H, O, N molecule amount x 0 # (i) in the ice derived for comet Hale-Bopp and for dust grains near protostar NGC 7538 IRS9. (*) The D/H ratio from HCN is ~ 2.8× 10 -3 . where d/dt denotes the total time derivation in a moving reference frame. The curves in Fig. 2 show the hydrodynamic conditions for a moving gas pocket that starts its journey to the centre of the collapsing cloud at different positions in the envelope.         −                 ⋅         −         +         ⋅ − = − + = ∑ ∑ T k ) i ( E exp ) i ( ads x dt (i) dx ) 3 ( T k ) i ( E exp ) i ( ads x x x dt (i) dx B ads B ads k , j ijk j ij 2 / 1 2 / 1 2 / 1 2 / 1 ) i ( m E n 2 ) i ( ) i ( x ) i ( m kT 8 S n a ) i ( m E n 2 ) i ( ) i ( x ) i ( m kT 8 S n a ) k ( x ) j ( ) j ( 2 s * g * 2 s * g 2 2 π π π π π π β α Results One realizes that the considered hydrodynamic model is appropriate for a protostellar cloud core with ~20 M O (Fig. 1). Our results in Fig. 3 show that the main amount of gas phase HCN and DCN is produced in the inner part of the collapsing cloud during the medium and late collapse phase. Comparing the results for the inner gas pocket presented in Fig. 3 and 4 one realizes that the HCN abundances increases clearly if the ice phase contains NH 3 or HCN. Corresponding HCN abundances derived from line intensity measurements for these type of protostars give x(HCN) ≅ 1.8⋅10 -8 (Wright et al., 1996) and 7⋅10 -8 (Comito et al., 2005). Consequently, N- bearing molecules must be contained in the ice phase. Since NH 3 was already detected the amount of HCN in precometary ice must be much lower than in the cometary one (< 1%). In addition one realises from Fig. 4 that the HCN and therefore the DCN abundance are strongly influenced by the cosmic ray ionization rate ζ CR . The gas phase ratio DCN/HCN reaches 10 -3 (see Fig. 4, left) at ~ 10 3 years but decreases shortly afterwards. Finally, it is interesting to note, that the HCN abundances which are calculated for hydrostatic conditions decrease for high ζ CR values or for a collapse proceeding for about 10 3 years (Fig. 5). Fig. 1 Temporal evolution of the physical parameters in Euler coordinates. The solid, dotted, dashed, and dashed-dotted line corresponds to a radial position of about 20, 200, 2000 and 20,000 AU. The last value of nearly 0.2 pc is related to the typical outer boundary of a protostellar cloud with a mass of ~ 20 M O . Fig. 2 Number density, radial velocity and temperature along the path of a gas pocket moving to the collapse centre (Lagrange coordinates). HC position gives the distance from the collapsing centre at which the gas pocket starts and the different curves refer to this position. Within the gas pocket the time derivation results from eq. (2). Fig. 3 Time dependency of HCN and DCN abundance calculated for gas pockets moving to the collapse centre from the following starting positions: 24 AU, 56 AU, 135 AU (upper left), 240 AU, 750 AU (upper right), 2400 AU, 5650 AU (lower left) and 10,050 AU, 18,00 AU (lower right). No initial HCN, DCN is contained in the ice. Hydrodynamical Model The gas flow results from the conservation laws of mass M and momentum ρu where ρ, u, and P denote density, velocity and pressure. For spherical symmetry one gets ρ π ρ ρ π ρ ρ 2 r ) 1 ( 2 2 r u 4 r M 0 r GM r P 1 r u u t u u 4 t M or 0 ) r ( r r t 2 2 = ∂ ∂ = + ∂ ∂ + ∂ ∂ + ∂ ∂ − = ∂ ∂ = ∂ ∂ + ∂ ∂ − The third relation is the Poisson equation, G symbolizes the gravitational constant. Our approach to solve these equations corresponds to the methods of Shu, 1977, and Suto & Silk, 1988. The number density n H = ρ/µm H with m H = 1.67× 10 -27 kg and µ = 2.33 is slightly modified to consider a propagating collapse and the gas temperature (or pressure) can be calculated since an isentropic evolution is assumed. Introducing the adiabatic exponent γ and using the related gas equation one has T = q(n H ) γ -1 with γ = 1.25. Since q is independent of the time it is calculated for the initial conditions at the outer collapse boundary r b . As boundary conditions we have used a stationary profile n H ~ r -2 , n H (r b ) = 10 4 cm -3 , and isothermal conditions T ~ 8.4 K. Fig. 1 shows the resulting temporal evolution of n H , T, the radial velocity u, and the accreted mass M. Introducing the fractional abundance of the gas phase x(i) = n(i) / n H where the index i labels the chemical species the continuity equation in (1) gives ) 2 ( i dt ) i ( dx r ) i ( x u t ) i ( x Γ = = ∂ ∂ + ∂ ∂ Chemical Model The source term Γ i in equation (2) is given by Aikawa et al., 1996. Due to accretion and sublimation processes the gas and ice phase interact with each other. One gets where x*(i) is the fractional abundances for the ice phase, k denotes the Boltzmann constant and the chemical coefficients α ij and β ijk can be calculated from the UMIST data base (Le Teuff et al., 2000). Table 2 explains the meaning of the parameters in the accretion and sublimation terms of equation 3. The adsorption energy for nitrogen E ads (i)/k ~760 K excludes ice phase N 2 in the initial cloud state. If HCN (DCN) is contained in the ice its abundance correspond to 5% of the cometary value in Table 1. The other values x* 0 (i) agree with the related data of the second row in the same table . Using the relevant part of the UMIST data base for HCN and including deuterium chemistry a chemical network with 3209 reactions and 380 species needs to be considered. Based on this knowledge HCN and DCN abundances are calculated from equation 3. Fig. 3 presents the results for a standard cosmic ray ionization rate ζ CR = 1.3 ⋅10 -17 s -1 without initial HCN or DCN in the ice phase. The influence of the ζ CR variation and the type of nitrogen containing ice (NH 3 or HCN) is shown in Fig. 4. All calculations of Fig. 4 are performed for the inner gas pocket. In Fig. 5 the variation of ζ CR = 1.3 ⋅10 -17 s -1 is modelled for a stationary situation. Comparable to Fig. 3 the ice phase does not contain NH 3 or HCN molecules. Table 3 Initial gas and ice phase abundances, where x* 0 (i) = (f M x 0 # (i)/100)⋅ 4π a 2 n s n g /n H. Gas phase species x 0 (i) Ice phase species x* 0 (i) Ice phase species x* 0 (i) E ads (i)/ k in K He 0.15 H 2 O 2.9 10 -4 HDO 9.0 10 -8 4820 H 3 + , H 2 + , H + , He + 1- 2.5 10 -9 CO 8.4 10 -5 - - 960 HD 4.6 10 -5 CO 2 4.8 10 -5 - - 2690 CO 1.9 10 -4 CH 3 OH 9.3 10 -6 CH 2 DOH CH 3 OD ? 4240 N 2 5.6 10 -5 NH 3 2.7 10 -5 NH 2 D ? 3080 H 2 S 2.1 10 -5 HCN 3.6 10 -8 DCN 10 -10 4170 Fig. 4 HCN and DCN abundance evolution calculated for various conditions. Upper and lower left plots show the influence of ζ CR and an NH 3 containing ice phase (ζ CR = 1.3 ⋅10 -18 s -1 solid, ζ CR = 1.3 ⋅10 -17 s -1 dotted, ζ CR = 1.3 ⋅10 -16 s -1 dashed). Upper and lower right plots show the same for HCN containing ice. Aikawa et al., 1997, have published adsorption energies E ads (i) for many species. The initial values x 0 (i) are adapted to a young molecular cloud (Table 3). Since oxygen was not observed as O or O 2 in dense clouds we assume a large amount of ice phase H 2 O. E ads (i) m(i) n g n s a S f M adsorption energy for species i mass of species i dust grain density 2.33 ⋅10 -11 n H dust surface density 3 ⋅10 15 cm -2 grain radius 3.2 ⋅10 -5 cm sticking coeffici ent ~ 0.3 grain mantle fraction ~ 0.325 H 2 O CO CO 2 CH 3 OH H 2 CO CH 4 NH 3 HCN DCN NGC 7538 IRS9 100 29 16.5 3.2 2 1.3 9.3 ? (*) Comet Hale-Bopp 100 23 6 2.4 1.1 0.6 0.7 0.25 Fig. 5 HCN abundance for hydrostatic conditions. Left (right) plot corresponds to temperature and density conditions reached during the collapse after 10 3 (10 5 ) years. ζ CR varies in the same way as in Fig. 4. Contact: carmen.tornow@dlr.de References Aikawa, Y.; Miyama, S. M.; Nakano, T.; Umebayashi, T. 1996. Astrophys. J., 467, 684. Aikawa, Y.; Umebayashi, T.; Nakano, T.; Miyama, S. M. 1997. Astrophys. J. Lett., 486, L51. 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