SELF-SIMILARITY AND SCALING BEHAVIOR OF INFRARED-EMISSION FROM RADIATIVELY HEATED DUST .1. THEORY

Dust infrared emission possesses scaling properties that yield powerfu l results with far-reaching observational consequences. Scaling was fi rst noticed by Rowan-Robinson for spherical shells and is shown here t o be a general property of dust emission in arbitrary geometries. Over all luminosity is never an input parameter of the radiative transfer p roblem; spectral shape is the only relevant property of the heating ra diation when the inner boundary of the dusty region is controlled by d ust sublimation. Similarly, the absolute scales of densities and dista nces are irrelevant; the geometry enters only through angles, relative thicknesses and aspect ratios, and the actual magnitudes of densities and distances enter only through one independent parameter, the overa ll optical depth. That is, as long as the overall optical depth stays the same, the system dimensions can be scaled up or down by an arbitra ry factor without any effect on the radiative transfer problem. Dust p roperties enter only through dimensionless, normalized distributions t hat describe the spatial variation of density and the wavelength depen dence of scattering and absorption efficiencies. Scaling enables a sys tematic approach to modelling and classification of IR spectra. We dev elop a new, fully scale-free method for solving radiative transfer, pr esent exact numerical results, and derive approximate analytical solut ions for spherical geometry, covering the entire range of parameter sp ace relevant to observations. For a given type of grains, the spectral energy distribution (SED) is primarily controlled by the profile of t he spatial dust distribution and the optical depth - each density prof ile produces a family of solutions, with position within the family de termined by optical depth. From the model SEDs presented here, the den sity distribution and optical depth can be observationally determined for various sources. Scaling implies tight correlations among the SEDs of various members of the same class of sources such as young stellar objects, late-type stars, etc. In particular, all members of the same class occupy common, well-defined regions in colour-colour diagrams. The observational data corroborate the existence of these correlations .