Cosmic-ray ionisation in circumstellar discs

Galactic cosmic rays are a ubiquitous source of ionisation of the interstellar gas, competing with UV and X-ray photons as well as natural radioactivity in determining the fractional abundance of electrons, ions and charged dust grains in molecular clouds and circumstellar discs. We model the propagation of different components of Galactic cosmic rays versus the column density of the gas. Our study is focussed on the propagation at high densities, above a few g cm$^{-2}$, especially relevant for the inner regions of collapsing clouds and circumstellar discs. The propagation of primary and secondary CR particles (protons and heavier nuclei, electrons, positrons, and photons) is computed in the continuous slowing down approximation, diffusion approximation, or catastrophic approximation, by adopting a matching procedure for the different transport regimes. A choice of the proper regime depends on the nature of the dominant loss process, modelled as continuous or catastrophic. The CR ionisation rate is determined by CR protons and their secondary electrons below $\approx 130$ g cm$^{-2}$ and by electron/positron pairs created by photon decay above $\approx600$ g cm$^{-2}$. We show that a proper description of the particle transport is essential to compute the ionisation rate in the latter case, since the electron/positron differential fluxes depend sensitively on the fluxes of both protons and photons. Our results show that the CR ionisation rate in high-density environments, like, e.g., the inner parts of collapsing molecular clouds or the mid-plane of circumstellar discs, is larger than previously assumed. It does not decline exponentially with increasing column density, but follows a more complex behaviour due to the interplay of different processes governing the generation and propagation of secondary particles.Comment: 19 pages, 11 figures, accepted by A&

Proof Systems for Retracts in Simply Typed Lambda Calculus

Abstract. This paper concerns retracts in simply typed lambda calculus assuming βη-equality. We provide a simple tableau proof system which characterises when a type is a retract of another type and which leads to an exponential decision procedure.

Production of atomic hydrogen by cosmic rays in dark clouds

The presence of small amounts of atomic hydrogen, detected as absorption dips in the 21 cm line spectrum, is a well-known characteristic of dark clouds. The abundance of hydrogen atoms measured in the densest regions of molecular clouds can be only explained by the dissociation of H$_2$ due to cosmic rays. We want to assess the role of Galactic cosmic rays in the formation of atomic hydrogen, by using recent developments in the characterisation of the low-energy spectra of cosmic rays and advances in the modelling of their propagation in molecular clouds. We model the attenuation of the interstellar cosmic rays entering a cloud and compute the dissociation rate of molecular hydrogen due to collisions with cosmic-ray protons and electrons as well as fast hydrogen atoms. We compare our results with the available observations. The cosmic-ray dissociation rate is entirely determined by secondary electrons produced in primary ionisation collisions. These secondary particles constitute the only source of atomic hydrogen at column densities above $\sim10^{21}$ cm$^{-2}$. We also find that the dissociation rate decreases with column density, while the ratio between the dissociation and ionisation rates varies between about 0.6 and 0.7. From comparison with observations we conclude that a relatively flat spectrum of interstellar cosmic-ray protons, as the one suggested by the most recent Voyager 1 data, can only provide a lower bound for the observed atomic hydrogen fraction. An enhanced spectrum of low-energy protons is needed to explain most of the observations. Our findings show that a careful description of molecular hydrogen dissociation by cosmic rays can explain the abundance of atomic hydrogen in dark clouds. An accurate characterisation of this process at high densities is crucial for understanding the chemical evolution of star-forming regions.Comment: 7 pages, 7 figures, accepted by Astronomy and Astrophysic

The VLA Survey of the Chandra Deep Field South. IV. Source Population

We present a detailed analysis of 256 radio sources from our deep (flux density limit of 42 microJy at the field centre at 1.4 GHz) Chandra Deep Field South 1.4 and 5 GHz VLA survey. The radio population is studied by using a wealth of multi-wavelength information in the radio, optical, and X-ray bands. The availability of redshifts for ~ 80% of the sources in our complete sample allows us to derive reliable luminosity estimates for the majority of the objects. X-ray data, including upper limits, for all our sources turn out to be a key factor in establishing the nature of faint radio sources. Due to the faint optical levels probed by this study, we have uncovered a population of distant Active Galactic Nuclei (AGN) systematically missing from many previous studies of sub-millijansky radio source identifications. We find that, while the well-known flattening of the radio number counts below 1 mJy is mostly due to star forming galaxies, these sources and AGN make up an approximately equal fraction of the sub-millijansky sky, contrary to some previous results. The AGN include radio galaxies, mostly of the low-power, Fanaroff-Riley I type, and a significant radio-quiet component, which amounts to approximately one fifth of the total sample. The ratio of radio to optical luminosity depends more on radio luminosity, rather than being due to optical absorption.Comment: 13 pages, 8 figures, accepted for publication in the Astrophysical Journa

Unresolved Unidentified Source Contribution to the Gamma-ray Background

The large majority of EGRET point sources remain without an identified low-energy counterpart, and a large fraction of these sources are most likely extragalactic. Whatever the nature of the extragalactic EGRET unidentified sources, faint unresolved objects of the same class must have a contribution to the diffuse extragalactic gamma-ray background (EGRB). Understanding this component of the EGRB, along with other guaranteed contributions from known sources, is essential if we are to use this emission to constrain exotic high-energy physics. Here, we follow an empirical approach to estimate whether a potential contribution of unidentified sources to the EGRB is likely to be important, and we find that it is. Additionally, we show how upcoming GLAST observations of EGRET unidentified sources, as well as of their fainter counterparts, can be combined with GLAST observations of the Galactic and extragalactic diffuse backgrounds to shed light on the nature of the EGRET unidentified sources even without any positional association of such sources with low-energy counterparts.Comment: 11 pages, 5 figures, submitted to Ap

Protonated CO2 in massive star-forming clumps

Interstellar CO2 is an important reservoir of carbon and oxygen, and one of the major constituents of the icy mantles of dust grains, but it is not observable directly in the cold gas because has no permanent dipole moment. Its protonated form, HOCO+, is believed to be a good proxy for gaseous CO2. However, it has been detected in only a few star-forming regions so far, so that its interstellar chemistry is not well understood. We present new detections of HOCO+ lines in 11 high-mass star-forming clumps. Our observations increase by more than three times the number of detections in star-forming regions so far. We have derived beam-averaged abundances relative to H2 in between 0.3 and 3.8 x 10^{-11}. We have compared these values with the abundances of H13CO+, a possible gas-phase precursor of HOCO+, and CH3OH, a product of surface chemistry. We have found a positive correlation with H13CO+, while with CH3OH there is no correlation. We suggest that the gas-phase formation route starting from HCO+ plays an important role in the formation of HOCO+, perhaps more relevant than protonation of CO2 (upon evaporation of this latter from icy dust mantles).Comment: 5 pages, 4 figures, 1 table, accepted for publication in MNRA

Radio faint AGN: a tale of two populations

We study the Extended Chandra Deep Field South (E-CDFS) Very Large Array sample, which reaches a flux density limit at 1.4 GHz of 32.5 microJy at the field centre and redshift ~ 4, and covers ~ 0.3 deg^2. Number counts are presented for the whole sample while the evolutionary properties and luminosity functions are derived for active galactic nuclei (AGN). The faint radio sky contains two totally distinct AGN populations, characterised by very different evolutions, luminosity functions, and Eddington ratios: radio-quiet (RQ)/radiative-mode, and radio-loud/jet-mode AGN. The radio power of RQ AGN evolves ~ (1+z)^2.5, similarly to star-forming galaxies, while the number density of radio-loud ones has a peak at ~ 0.5 and then declines at higher redshifts. The number density of radio-selected RQ AGN is consistent with that of X-ray selected AGN, which shows that we are sampling the same population. The unbiased fraction of radiative-mode RL AGN, derived from our own and previously published data, is a strong function of radio power, decreasing from ~ 0.5 at P_1.4GHz ~ 10^24 W/Hz to ~ 0.04$ at P_1.4GHz ~ 10^22 W/Hz. Thanks to our enlarged sample, which now includes ~ 700 radio sources, we also confirm and strengthen our previous results on the source population of the faint radio sky: star-forming galaxies start to dominate the radio sky only below ~ 0.1 mJy, which is also where radio-quiet AGN overtake radio-loud ones.Comment: 19 pages, 13 figures, accepted for publication in MNRA