tokens: rate coefficients. Notes. TW18 and MP17 refer to models with nominal values of the oxygen-bearing influx (see Sect. 4 ). ( a ) CO 2 best-fit mixing ratio at 0.15 mbar from photochemical modelling in Orton et al. (2014b ) is 8.0 × 10 −11 . ( b ) Ice grain ablation influx giving rise to 1.2 × 10 5 and 4.5 × 10 3 cm −2 s −1 for H 2 O and CO 2 , respectively. The outcome of this sensitivity test indicates that a CO relative abundance of 7.0 × 10 −9 at 0.4 mbar allows an optimal match of the line core and wings. Table 4 lists different cases where ( D , t impact ) have been tuned to obtain q CO = (7.0 ± 0.1) × 10 −9 at the ~0.4 mbar region, the delivered CO mass (in g), and the CO mixing ratio obtained in 200–100 mbar. The resulting profiles in the 200–100 mbar region reflect that larger impactors give rise to larger CO abundances although below the upper limits in Teanby Irwin (2013) . Table 4 shows that the solution is degenerate; in other words, the same stratospheric CO mixing ratio abundance can be obtanied with pairs of ( D , t impact ) that represent larger impacts having taken place longer ago, or smaller impactors occurred more recently. For instance, the temporal evolution of the material delivered by a cometary impact indicates that the CO currently observed in the Uranus stratosphere could be due to a comet nucleus of 3.5 km diameter that hit the planet 822 yr ago. Figure 4 shows the comparison of the measured spectra and the modelled radiative transfer as a function of the different CO vertical distribution resulting from steady ice grain ablation and cases 3 and 4 for cometary impact. Any other of the cases in Table 4 will give rise to a CO mixing ratio of ~ 7.0 × 10 −9 at the 0.4 mbar pressure level that will give good match to the Herschel data. Stratospheric CO mixing ratio profiles with an abundance larger than the value in the pressure range probed by Herschel (i.e. between 3 and 0.4 mbar) can in principle be discarded as they will overestimate the observations. Similarly, the tropospheric CO mixing ratio profile has to be lower than the upper limit 2.1 × 10 −9 established by Teanby Irwin (2013) . Equations (14) and (15) in Zahnle et al. (2003) , adapted to Uranus where the impact frequency is ~ 4 times smaller than on Jupiter, allow us to plot the frequency of impact versus the impactor size. Figure 5 displays two different scenarios depending on the origin of the impactors: the size-number distribution of impactors is like that inferred at Jupiter (ecliptic comets), and those impactors more representative of nearly isotropic comets (as long-period or Halley-type comets). Zahnle et al. (2003) conclude that known craters on the Saturnian and Uranian satellites are consistent with either case; that is, both kinds of impactors are in the Uranian system and they could have entered the Uranus atmosphere. Also, Zahnle et al. (2003) assume that the impact rate on Uranus is ~ 0.00125 comets per year (i.e. one impact every ~800 yr)
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