Information entropy of interstellar and circumstellar carbon-containing molecules: Molecular size against structural complexity

Abstract

Currently, more than 100 carbon-containing molecules have been detected in interstellar medium and circumstellar envelopes. Most of these substances consist of ⩽13 atoms but the questions about the limits of molecular complexity and detection of life-building blocks directly in interstellar conditions remain open. To study how molecular complexity depends on molecular size, we have analyzed the set of the clearly detected space molecules in terms of the information entropy approach. Based on information entropy, we have shown that the points of several natural compounds (urea, pyrimidine, dihydroxyacetone, uracil, cytosine, glycine, and alanine) fall into the range of the values typical for the known interstellar molecules that indicates high probability of their detection in interstellar environment. We have used structural information content (SIC), an index derived from information entropy, for numerical discrimination of the molecules with maximal information entropy. Such molecules have h=hmax and SIC=1 and make up approximately a half of the interstellar set and their percentage is decreased with the size. This trend may be associated with the different stabilities of the molecules with uniform (usually more stable) and diversified (usually less stable) chemical structures, so the detectable molecules with a large size must possess symmetric structure more probably than non-symmetric. The remarkable detection of low-entropy (highly symmetric) fullerene molecules strongly supports this assumption. Additionally, structural information content reflects the depth of hydrogenation of interstellar entities: the molecules with SIC=1 are hydrogen-poor whereas the others are hydrogen-rich. A comparison of our findings with relevant experimental and theoretical works and predictive potential of the model are provided.