Limits to Interstellar C₄ and C₅ Towards zeta Ophiuchi

We have made a sensitive search for the origin bands in the known electronic transitions of the linear carbon chains C_4 and C_5 at 3789 and 5109 A towards zeta Oph (A_V <= 1). The incentive was a recent detection of C_3 in this interstellar cloud with a column density of 1.6 x 10^12 cm^-2 plus the availability of laboratory gas phase spectra of C_4 and C_5. Further, some models of diffuse interstellar clouds predict that the abundance of these latter species should be within an order of magnitude of C_3. Despite achieving S/N of 2300 to 2600 per pixel at a resolution of ~110,000, the searches were negative, leading to 3 sigma upper limits to the column density of N(C_5) = 2 x 10^11 cm^-2 and N(C_4) = 4 x 10^12-13 cm^-2 where these values rely on theoretically calculated oscillator strengths. The implication of these limits are discussed on the choice of molecules for study in future attempts to identify the carriers of the stronger diffuse interstellar bands.