[C I] and [C II] emission in the circumstellar envelope of IRC +10216 I. Observational data and NLTE modeling of the [C I] emission

Aims: The study at hand aims to describe the distribution of atomic carbon, C0, throughout the envelope, in support of an improved understanding of its photo-chemistry. Additionally, we also briefly discuss the observation of [CII] emission towards the star. Methods: We obtain spectra of the [CI] $\mathrm{^3P_1} \rightarrow \mathrm{^3P_0}$ fine structure line at projected distances of up to 78" from the star. The line profiles are characterized by both direct fitting of Gaussian components, and by modeling the observed line of the [CI] triplet. We also report the detection of the $\mathrm{^2P_{3/2}} \rightarrow \mathrm{^2P_{1/2}}$ line from the C+ fine structure singlet at the central position and at 32" from the star. Results: The overall picture of the [CI] emission from IRC +10216 agrees with more limited previous studies. The satisfying agreement between the observed and modeled line profiles, with emission at the systemic velocity appearing beyond one beam from the star, rules out that the C0 is located in a thin shell. Given that the bond energy of CO falls only 0.1 eV below the ionization threshold of C0, the absence of observable [CII] emission from sightlines beyond a projected distance of $\sim 10^{17}$ cm from the star (adopting a distance of 130 pc) does not contradict a scenario where the bulk of C0 is located between that of CO and C+, as expected for an external FUV radiation field. This conjecture is also corroborated by a model in which the C0 shell is located farther outside, failing to reproduce the [CI] line profiles at intermediate sky-plane distances from the star. Comparing a photo-chemical model adopted from literature with the simplifying assumption of a constant C0 abundance with respect to the $\mathrm{H}_2$ density, we constrain the inner boundary of the [CI] emitting shell, located at $\sim 10^{16}$ cm from the star.