Why do these astronomers say that "Carbon chains with more than nine atoms are unstable"?
Unlike the saturated hydrocarbons in kerosene, carbynes are unsaturated carbon chains with alternating single and triple bonds.
Molecules containing such chains are called polyynes, e.g. the short cyanopolyyne HC5N:

H&minus;C&equiv;C&minus;C&equiv;C&minus;C&equiv;N

Those carbon atoms readily interact, and long chains (if they form; see comments) are more likely to crosslink or form cycles than to remain linear.
Tarakeshwar et al. suggest that iron clusters in "pseudocarbynes" inhibit this by bonding to some of the carbons.

Loomis et al. 2016 looked for cyanopolyynes in radio spectra of Taurus molecular cloud 1.
They got a good HC9N signal but did not detect the HC11N lines Travers et al. 1996 observed in the lab.