Why do these astronomers say that "Carbon chains with more than nine atoms are unstable"? The Phys.org article Interstellar iron isn't missing, it's just hiding in plain sight links to the paywalled article On the Structure, Magnetic Properties, and Infrared Spectra of Iron Pseudocarbynes in the Interstellar Medium (Tarakeshwar, Buseck and Timmes, Arizona State University), and says:

The new work may also solve another longstanding puzzle. Carbon chains with more than nine atoms are unstable, the team explains. Yet observations have detected more complex carbon molecules in interstellar space. How nature builds these complex carbon molecules from simpler carbon molecules has been a mystery for many years.
Buseck explained, &quot;Longer carbon chains are stablized by the addition of iron clusters.&quot; This opens a new pathway for building more complex molecules in space, such as polyaromatic hydrocarbons, of which naphthalene is a familiar example, being the main ingredient in mothballs.
Said Timmes, &quot;Our work provides new insights into bridging the yawning gap between molecules containing nine or fewer carbon atoms and complex molecules such as C60 buckminsterfullerene, better known as 'buckyballs.'&quot;

Question: On Earth we don't see a big difference between hydrocarbon chains with lengths below and above 9 (think kerosene, wax...), why is there such a cutoff in stability in interstellar space? What is it about hydrocarbon chains longer than 9 atoms that makes them unstable there but not here?
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.