The high-resolution (R = 25,000) infrared M-band spectrum of the massive protostar NGC 7538 IRS 9 shows a narrow absorption feature at 4.779 μm (2092.3 cm^(-1)) that we attribute to the vibrational stretching mode of the ^(13)CO isotope in pure CO icy grain mantles. This is the first detection of ^(13)CO in icy grain mantles in the interstellar medium. The ^(13)CO band is a factor of 2.3 narrower than the apolar component of the ^(12)CO band. With this in mind, we discuss the mechanisms that broaden solid-state absorption bands. It is shown that ellipsoidally shaped pure CO grains fit the bands of both isotopes at the same time. Slightly worse but still reasonable fits are also obtained by CO embedded in N_2-rich ices and thermally processed O_2-rich ices. In addition, we report new insights into the nature and evolution of interstellar CO ices by comparing the very high resolution multicomponent solid ^(12)CO spectrum of NGC 7538 IRS 9 with that of the previously studied low-mass source L1489 IRS. The narrow absorption of apolar CO ices is present in both spectra but much stronger in NGC 7538 IRS 9. It is superposed on a smooth broad absorption feature well fitted by a combination of CO_2 and H_2O-rich laboratory CO ices. The abundances of the latter two ices, scaled to the total H_2O ice column, are the same in both sources. We thus suggest that thermal processing manifests itself as evaporation of apolar ices only and not the formation of CO_2 or polar ices. Finally, the decomposition of the ^(12)CO band is used to derive the ^(12)CO/^(13)CO abundance ratio in apolar ices. A ratio of ^(12)CO/^(13)CO = 71 ± 15 (3 σ) is deduced, in good agreement with gas-phase CO studies (~77) and the solid ^(12)CO_2/^(13)CO_2 ratio of 80 ± 11 found in the same line of sight. The implications for the chemical path along which CO_2 is formed are discussed
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