The inner wind of IRC+10216 revisited: New exotic chemistry and diagnostic for dust condensation in carbon stars

Aims. We model the chemistry of the inner wind of the carbon star IRC+10216 and consider the effect of periodic shocks induced by the stellar pulsation on the gas to follow the non-equilibrium chemistry in the shocked gas layers. We consider a very complete set of chemical families, including hydrocarbons and aromatics, hydrides, halogens and phosphorous-bearing species. Derived abundances are compared to the latest observational data from large surveys and Herschel. Results. The shocks induce a non-equilibrium chemistry in the dust formation zone of IRC+10216 where the collision destruction of CO in the post-shock gas triggers the formation of O-bearing species (H2O, SiO). Most of the modelled abundances agree very well with the latest values derived from Herschel data on IRC+10216. Hydrides form a family of abundant species that are expelled into the intermediate envelope. In particular, HF traps all the atomic fluorine in the dust formation zone. Halogens are also abundant and their chemistry is independent of the C/O ratio of the star. Therefore, HCl and other Cl-bearing species should also be present in the inner wind of O-rich AGB or supergiant stars. We identify a specific region ranging from 2.5 R* to 4 R*, where polycyclic aromatic hydrocarbons form and grow. The estimated carbon dust-to-gas mass ratio derived from the mass of aromatics ranges from 1.2 x 10^(-3) to 5.8 x 10^{-3} and agrees well with existing observational values. The aromatic formation region is located outside hot layers where SiC2 is produced as a bi-product of silicon carbide dust synthesis. Finally, we predict that some molecular lines will show flux variation with pulsation phase and time (e.g., H2O) while other species will not (e.g., CO). These variations merely reflect the non-equilibrium chemistry that destroys and reforms molecules over a pulsation period in the shocked gas of the dust formation zone.Comment: 15 pages, 10 figures. Accepted for publication in Astronomy & Astrophysic

Generic Feasibility of Perfect Reconstruction with Short FIR Filters in Multi-channel Systems

We study the feasibility of short finite impulse response (FIR) synthesis for perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis banks, we focus on the one with the minimum filter length. For filter banks with oversampling factors of at least two, we provide prescriptions for the shortest filter length of the synthesis bank that would guarantee PR almost surely. The prescribed length is as short or shorter than the analysis filters and has an approximate inverse relationship with the oversampling factor. Our results are in form of necessary and sufficient statements that hold generically, hence only fail for elaborately-designed nongeneric examples. We provide extensive numerical verification of the theoretical results and demonstrate that the gap between the derived filter length prescriptions and the true minimum is small. The results have potential applications in synthesis FB design problems, where the analysis bank is given, and for analysis of fundamental limitations in blind signals reconstruction from data collected by unknown subsampled multi-channel systems.Comment: Manuscript submitted to IEEE Transactions on Signal Processin

A simple model for the evolution of molecular codes driven by the interplay of accuracy, diversity and cost

Molecular codes translate information written in one type of molecules into another molecular language. We introduce a simple model that treats molecular codes as noisy information channels. An optimal code is a channel that conveys information accurately and efficiently while keeping down the impact of errors. The equipoise of the three conflicting needs, for minimal error-load, minimal cost of resources and maximal diversity of vocabulary, defines the fitness of the code. The model suggests a mechanism for the emergence of a code when evolution varies the parameters that control this equipoise and the mapping between the two molecular languages becomes non-random. This mechanism is demonstrated by a simple toy model that is formally equivalent to a mean-field Ising magnet.Comment: Keywords: molecular codes, rate-distortion theory, biological information channels, stochastic maps, genetic code, genetic network