[tel-00726959, v1] Caractériser le milieu interstellaire ... - HAL - INRIA

V. Guzmán et al.: H 2 CO in the Horsehead PDR: photo-desorption of dust grain ice mantlestel-00726959, version 1 - 31 Aug 2012Fig. 4. H 132 CO and deuterated H 2CO lines detected toward the densecore.Gaussian fits are shown with red lines. For HDCO and D 2 CO theline width was fixed to the width of the HDCO (2 11 −1 10 ) line, becauseit has the best signal-to-noise ratio.are populated following Boltzmann’s law. We built rotational diagramscorrected for line-opacity effects throughln Nthin u+ ln C τ = ln N g u Z − E u, (3)kT rotwhere N is the total column density of the molecule, g u is thelevel degeneracy, E u /k is the energy of the upper level in K,Z is the partition function at the rotational temperature T rot ,τC τ =1−e≤ 1 is a line-opacity correction factor, where τ is−τthe opacity of the line, and Nuthin is the column density of the upperlevel for an optically thin line when the source fills the beam.This last parameter is given byN thinu= 8πkν2 Whc 3 A ul, (4)where k is the Boltzmann constant, ν is the line frequency, Wis the integrated line intensity, h is the Planck constant, c is thespeed of light and A ul is the Einstein coefficient for spontaneousemission.Ortho- and para forms of H 2 CO are treated as differentspecies because radiative transitions between them are forbidden.Resulting rotational diagrams are shown in Fig. 5 forthree different o-H 2 CO (2 12 −1 11 ) and p-H 2 CO (2 02 −1 01 ) lineopacities(τ = 0, 1 and 5). We find column densities of N ∼10 12 −10 13 cm −2 , depending on the opacity. We infer very differentrotational temperatures for o-H 2 CO (T rot ∼ 4−8 K)andp-H 2 CO (T rot ∼ 10−30 K), which are also lower than the wellknownconditions in the PDR (T kin ∼ 60 K) and in the densecore(T kin ∼ 20 K). This suggests that the gas is far from thermalization,and therefore we used these column densities androtational temperatures as an input for a more complex analysisto derive the H 2 CO column densities.Fig. 5. H 2 CO rotational diagrams corrected for line-opacity effects atthe PDR and dense-core position. Rotational temperatures are shownfor each considered opacity.Table 4. H 2 CO critical densities (cm −3 )forthreedifferent collidingpartners computed for T kin = 60 K.J KaK cp-H 2 o-H 2 He2 02 7.2 × 10 5 3.6 × 10 5 1.3 × 10 63 03 1.6 × 10 6 9.9 × 10 5 4.2 × 10 63 22 5.8 × 10 5 4.7 × 10 5 2.5 × 10 62 12 3.7 × 10 5 2.5 × 10 5 8.1 × 10 52 11 4.3 × 10 5 2.2 × 10 5 8.7 × 10 53 13 9.7 × 10 5 7.0 × 10 5 2.3 × 10 63 12 1.3 × 10 6 7.9 × 10 5 3.2 × 10 63.2.3. Radiative transfer modelsThe critical density of a given collisional partner correspondsto the density at which the sum of spontaneous radiative deexcitationrates is equal to the sum of collisional de-excitationrates (γ) ofagivenleveln cr (J Ka K c, T kin ) =∑J ′ A(JK a ′ Ka K c→ J K′ K ′ ′ caK )c ′∑J ′ γ(JK a ′ Ka K c→ J ′ K′ K ′ caK , T kin)· (5)c ′Formaldehyde lines have high critical densities (∼10 6 cm −3 ,see Table 4) compared to the H 2 density in the Horsehead(∼10 4 −10 5 cm −3 ). Because we expect subthermal emission(T ex ≪ T kin ) for transitions with high critical densities comparedto the H 2 density, we used a nonlocal non-LTE radiativetransfer code adapted to the Horsehead geometry to model theobserved H 2 CO line intensities (Goicoechea et al. 2006). Weused a nonlocal code to take into account the radiative couplingbetween different cloud positions that might affect the populationof the energy levels. The code is able to predict the lineA49, page 5 of 9