Sources of Radiation in the Early Universe: The Equation of Radiative Transfer and Optical Distances

We have derived the radiative-transfer equation for a point source with a specified intensity and spectrum, originating in the early Universe between the epochs of annihilation and recombination, at redshifts z_\s =10^8\div 10^4. The direct radiation of the source is separated from the diffuse radiation it produces. Optical distances from the source for Thomson scattering and bremsstrahlung absorption at the maximum of the thermal background radiation are calculated as a function of the redshift z.The distances grow sharply with decreasing z, approaching asymptotic values, the absorption distance increasing more slowly and reaching their limiting values at lower z. For the adopted z values, the optical parameters of the Universe can be described in a flat model with dusty material and radiation, and radiative transfer can be treated in a grey approximation.Comment: 14 pages, 2 figure

Methanol in W3(H2O) and Surrounding Regions

We present the results of an interferometric study of 38 millimeter-wave lines of CH3OH in the region around the water maser source W3(H2O) and a region extending about 30" to the south and west of the hydroxyl maser source W3(OH). The methanol emitting region around W3(H2O) has an extent of 2.0" x 1.2" (4400 x 2600 AU). The density is of order 1.e7 cm-3, sufficient to thermalize most of the methanol lines. The kinetic temperature is approximately 140 K and the methanol fractional abundance greater than 1.e-6, indicative of a high degree of grain mantle evaporation. The W3(H2O) source contains sub-structure, with peaks corresponding to the TW source and Wyrowski's B/C, separated by 2500 AU in projection. The kinematics are consistent with these being distinct protostellar cores in a wide binary orbit and a dynamical mass for the region of a few tens of Mo. The extended methanol emission to the southwest of W3(OH) is seen strongly only from the lowest excitation lines and from lines known elsewhere to be class I methanol masers, namely the 84.5 GHz 5(-1)-4(0)E and 95.2 GHz 8(0)-7(1)A+ lines. Within this region there are two compact clumps, which we denote as swA and swB, each about 15" (0.16 pc projected distance) away from W3(OH). Excitation analysis of these clumps indicates the presence of lines with inverted populations but only weak amplification. The sources swA and swB appear to have kinetic temperatures of order 50-100 K and densities of order 1.e5 - 1.e6 cm-3. The methanol fractional abundance for the warmer clump is of order 1.e-7, suggestive of partial grain mantle evaporation. The clumping occurs on mass scales of order 1 Mo.Comment: 28 pages including 6 figures and 4 tables, accepted by Ap