Context : The carbon-rich asymptotic giant branch star IRC +10216 undergoes strong mass loss , and quasi-periodic enhancements of the density of the circumstellar matter have previously been reported .
The star ’ s circumstellar environment is a well-studied , and complex astrochemical laboratory , with many molecular species proved to be present .
CO is ubiquitous in the circumstellar envelope , while emission from the ethynyl ( C _ { 2 } H ) radical is detected in a spatially confined shell around IRC +10216 .
As reported in this article , we recently detected unexpectedly strong emission from the N = 4 - 3 , 6 - 5 , 7 - 6 , 8 - 7 , and 9 - 8 transitions of C _ { 2 } H with the IRAM 30 m telescope and with Herschel /HIFI , challenging the available chemical and physical models .

Aims : We aim to constrain the physical properties of the circumstellar envelope of IRC +10216 , including the effect of episodic mass loss on the observed emission lines .
In particular , we aim to determine the excitation region and conditions of C _ { 2 } H , in order to explain the recent detections , and to reconcile these with interferometric maps of the N = 1 - 0 transition of C _ { 2 } H .

Methods : Using radiative-transfer modelling , we provide a physical description of the circumstellar envelope of IRC +10216 , constrained by the spectral-energy distribution and a sample of 20 high-resolution and 29 low-resolution CO lines — to date , the largest modelled range of CO lines towards an evolved star .
We further present the most detailed radiative-transfer analysis of C _ { 2 } H that has been done so far .

Results : Assuming a distance of 150 pc to IRC +10216 , the spectral-energy distribution is modelled with a stellar luminosity of 11300 L _ { \sun } and a dust-mass-loss rate of 4.0 \times 10 ^ { -8 } M _ { \sun } yr ^ { -1 } .
Based on the analysis of the 20 high-frequency-resolution CO observations , an average gas-mass-loss rate for the last 1000 years of 1.5 \times 10 ^ { -5 } M _ { \sun } yr ^ { -1 } is derived .
This results in a gas-to-dust-mass ratio of 375 , typical for this type of star .
The kinetic temperature throughout the circumstellar envelope is characterised by three powerlaws : T _ { \mathrm { kin } } ( r ) \propto r ^ { -0.58 } for radii r \leq 9 stellar radii , T _ { \mathrm { kin } } ( r ) \propto r ^ { -0.40 } for radii 9 \leq r \leq 65 stellar radii , and T _ { \mathrm { kin } } ( r ) \propto r ^ { -1.20 } for radii r \geq 65 stellar radii .
This model successfully describes all 49 observed CO lines .
We also show the effect of density enhancements in the wind of IRC +10216 on the C _ { 2 } H-abundance profile , and the close agreement we find of the model predictions with interferometric maps of the C _ { 2 } H N = 1 - 0 transition and with the rotational lines observed with the IRAM 30 m telescope and Herschel /HIFI .
We report on the importance of radiative pumping to the vibrationally excited levels of C _ { 2 } H and the significant effect this pumping mechanism has on the excitation of all levels of the C _ { 2 } H-molecule .

Conclusions :