The abundance distribution of C₄H in IRC + 10216

We have observed the N = 9-8 spin doublet emission line of C₄H at 85.6 GHz in the carbon star IRC + 10216 with the BIMA millimeter interferometer. The aperture synthesis images have an angular resolution of ∼10″ and a velocity resolution of ∼1.3 km s^-1. The data clearly show that C₄H is distributed in a shell surrounding the central star, with little emission from the inner envelope. The peak of the average radial brightness profile in a map centered at the systemic velocity and with a width of 10 km s^-1 is ∼0.88 K at a projected radius of 15″. From the brightness temperature profile we infer that the thickness of the shell at half-peak intensity is ∼15″. We derive the abundance of the molecule as a function of distance from the star using an LTE model. The peak abundance is calculated to be 1.8 ×10^-6 (with respect to the H₂ number density) at a radius of 16″.7 or 2.5 × 10¹⁶ cm assuming a distance of 100 pc, a mass-loss rate of 2 × 10^-5 M_⊙ yr^-1, and an outflow velocity of 13.8 km s^-1. We compare our derived C₄H distribution with the predictions of a photochemical model and find that the model underestimates the observed abundance of C₄H by a factor of 5.