Radiative Transfer in Protoplanetary Disks

Abstract Protoplanetary disks are the precursors of planetary systems. All building materials needed to assembly the planetary systems are supplied by these reservoirs, including many organic molecules [1,2]. Thus, the physical and chemical properties in Protoplanetary disks set the boundary conditions for the formation and evolution of planets and other solar system bodies. In standard radiative scenario structure and chemistry of protoplanetary disks depend strongly on the nature of central star around which they formed. The dust temperature is manly set by the stellar luminosity, while the chemistry of the whole disk depends on the UV and X ray fluxes [3,4,6,8]. Therefore, a knowledge as accurate as possible of the radiative transfer (RT) inside disks is a prerequisite for their modelling. Actually, real disks are complex, stratified and inhomogeneous environments requiring a detailed dust mixture modelling and the ability to follow the radiation transfer across radial and vertical gradients. Different energetic processes as the mass accretion processes onto the star surface, the viscous dissipative heating dominating the midplane region, and the flared atmospheres radiation reprocessing, have a significant role in the disk structuring [4,5,8]. During the last 10 years many authors suggested various numerical and analytical techniques to resolve the disk temperature structure providing vertical temperature profiles and disk SED databases [4,6]. In this work we present the results of our semi analytical and numerical model solving the radiative transfer problem in two separate interesting disk regions: 1) Disk atmospheres at large radius, r > 10 AU. 2) Vertical disk structure over 1 < r < 10 AU and 10 < r < 100 AU. A simplified analytical approach based on P-N approximation [7] for a rectified disk surface (suitable for limited range of r) is compared and contrasted with a more accurate Monte Carlo integration [5]. Our code can handle arbitrary dust inhomogeneities, vertical and radial, in terms of mineralogical and density changes. Different dust mixture models from Pollack [9], Gail [10] and Henning [11] are implemented and tested. The code solves the RT in the 4 Stokes radiation field formalism providing an accurate radiation flux description and the polarization configuration for UV and X-Ray stellar fluxes in various disk regions (disk surface, disk midplane etc..). The complete model is developed within the context of a classical TTauri protostar and for different dust compositions and different ranges of star luminosity in UV and X -Ray are. The effects on some prebiotic molecules are estimated. References [1]Ehrenfreund, P. & Charnley, S.B. (2000), Ann.Rev.Astr.Astrophys, 38, 427-483. [2]Markwick, A.J. & Charnley, S.B. (2004). in P. Eherenfreund et alt. (eds) "Astrobiology: Future Perspectives", Kluwer, 33-66. [3] Chiang, E. I. & Goldreich, P. (1997), ApJ, 490, 368 [4] D'Alessio, P., Canto, J., Calvet, N., & Lizano, S. (1998), ApJ, 500, 411. [5] Bjorkman, J. E. & Wood, K. 2001, ApJ, 554, 615. [6] Dullemond C. P. & A.Natta 2003, A&A 405, 597-605. [7] B. Davison & J. B. Sykes: Neutron Transport theory, Oxford Press 1958. [8] D'Alessio P. et al (2007), Chondrites and the Protoplanetary Disk, ASPConference Series,Vol.341. [9] J.B.Pollack et al. (1994), ApJ,421:615-639. [10] H.P.Gail, (2001), A&A, v.378 [11] T.Henning & R.Stognienko.(1996), ApJ, 311.