The Abundance of C₂H₄ in the Circumstellar Envelope of IRC+10216

High spectral resolution mid-IR observations of ethylene (C₂H₄) towards the AGB star IRC+10216 were obtained using the Texas Echelon Cross Echelle Spectrograph (TEXES) at the NASA Infrared Telescope Facility (IRTF). Eighty ro-vibrational lines from the 10.5 µm vibrational mode ν₇ with J ≲ 30 were detected in absorption. The observed lines are divided into two groups with rotational temperatures of 105 and 400 K (warm and hot lines). The warm lines peak at ≃ -14 km s^-1 with respect to the systemic velocity, suggesting that they are mostly formed outwards from ≃ 20R_⋆. The hot lines are centered at -10 km s^-1 indicating that they come from a shell between 10 and 20R_⋆. 35% of the observed lines are unblended and can be fitted with a code developed to model the emission of a spherically symmetric circumstellar envelope. The analysis of several scenarios reveal that the C₂H₄ abundance relative to H₂ in the range 5 - 20R_⋆ is 6.9 × 10^-8 in average and it could be as high as 1.1 × 10^-7. Beyond 20R_⋆, it is 8.2 × 10^-8. The total column density is (6.5 ± 3.0) × 10¹⁵ cm^-2. C₂H₄ is found to be rotationally under local thermodynamical equilibrium (LTE) and vibrationally out of LTE. One of the scenarios that best reproduce the observations suggests that up to 25% of the C₂H₄ molecules at 20R_⋆ could condense onto dust grains. This possible depletion would not influence significantly the gas acceleration although it could play a role in the surface chemistry on the dust grains.