Sulphur-bearing molecules in AGB stars I: The occurrence of hydrogen sulfide

Through a survey of (sub-)millimetre emission lines of various sulphur-bearing molecules, we aim to determine which molecules are the primary carriers of sulphur in different types of AGB stars. In this paper, the first in a series, we investigate the occurrence of H$_2$S in AGB circumstellar envelopes and determine its abundance, where possible. We have surveyed 20 AGB stars with a range of mass-loss rates and of different chemical types using the APEX telescope to search for rotational transition lines of five key sulphur-bearing molecules: CS, SiS, SO, SO$_2$ and H$_2$S. Here we present our results for H$_2$S, including detections, non-detections and detailed radiative transfer modelling of the detected lines. We compare results based on different descriptions of the molecular excitation of H$_2$S and different abundance distributions, including those derived from chemical modelling results. We detected H$_2$S towards five AGB stars, all of which have high mass-loss rates of $\dot{M}\geq 5\times 10^{-6}M_\odot$ yr$^{-1}$ and are oxygen-rich. H$_2$S was not detected towards the carbon or S-type stars that fall in a similar mass-loss range. For the stars in our sample with detections, we find peak o-H$_2$S abundances relative to H$_2$ between $4\times 10^{-7}$ and $2.5\times 10^{-5}$. Overall, we conclude that H$_2$S can play a significant role in oxygen-rich AGB stars with higher mass-loss rates, but is unlikely to play a key role in stars of other chemical types or the lower mass-loss rate oxygen-rich stars. For two sources, V1300 Aql and GX Mon, H$_2$S is most likely the dominant sulphur-bearing molecule in the circumstellar envelope.Comment: 14 pages, 7 figures, accepted in A&

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Search for aluminium monoxide in the winds of oxygen-rich AGB stars

Aluminium monoxide, AlO, is likely efficiently depleted from the gas around oxygen-rich evolved stars to form alumina clusters and dust seeds. Its presence in the extended atmospheres of evolved stars has been derived from optical spectroscopy. More recently, AlO gas was also detected at long wavelengths around the supergiant VY CMa and the oxygen-rich asymptotic giant branch (AGB) star o Cet (Mira A). In search of AlO, we mined data obtained with APEX, the IRAM 30m telescope, Herschel/HIFI, SMA, and ALMA, which were primarily aimed at studying other molecular species. We report here on observations of AlO towards a sample of eight oxygen-rich AGB stars in different rotational transitions, up to seven for some stars. We present definite detections of one rotational transition of AlO for o Cet and R Aqr, and tentative detections of one transition for R Dor and o Cet, and two for IK Tau and W Hya. The presented spectra of WX Psc, R Cas, and TX Cam show no signature of AlO. For o Cet, R Aqr, and IK Tau, we find that the AlO(N=9-8) emission likely traces the inner parts of the wind, out to only a few tens of AU, where the gas has not yet reached its terminal velocity. The conclusive detections of AlO emission in the case of o Cet and R Aqr confirm the presence of AlO gas in outflows of AGB stars. The tentative detections further support this. Since most of the observations presented in this study were obtained with stronger emission from other species than AlO in mind, observations with higher sensitivity in combination with high angular resolution will improve our understanding of the presence and behaviour of AlO. From the current data sets we cannot firmly conclude whether there is a direct correlation between the wind properties and the detection rate of AlO emission. We hope that this study can serve as a stimulus to perform sample studies in search of AlO in oxygen-rich outflows.Comment: 9 pages, 9 figures, Accepted for publication in Astronomy & Astrophysic

PO and PN in the wind of the oxygen-rich AGB star IK Tau

Phosphorus-bearing compounds have only been studied in the circumstellar environments (CSEs) of the asymptotic giant branch (AGB) star IRC +10216 and the protoplanetary nebula CRL 2688, both C-rich objects, and the O-rich red supergiant VY CMa. The current chemical models cannot reproduce the high abundances of PO and PN derived from observations of VY CMa. No observations have been reported of phosphorus in the CSEs of O-rich AGB stars. We aim to set observational constraints on the phosphorous chemistry in the CSEs of O-rich AGB stars, by focussing on the Mira-type variable star IK Tau. Using the IRAM 30m telescope and the Submillimeter Array (SMA), we observed four rotational transitions of PN (J=2-1,3-2,6-5,7-6) and four of PO (J=5/2-3/2,7/2-5/2,13/2-11/2,15/2-13/2). The IRAM 30m observations were dedicated line observations, while the SMA data come from an unbiased spectral survey in the frequency range 279-355 GHz. We present the first detections of PN and PO in an O-rich AGB star and estimate abundances X(PN/H2) of about 3x10^-7 and X(PO/H2) in the range 0.5-6.0x10^-7. This is several orders of magnitude higher than what is found for the C-rich AGB star IRC +10216. The diameter (<=0.7") of the PN and PO emission distributions measured in the interferometric data corresponds to a maximum radial extent of about 40 stellar radii. The abundances and the spatial occurrence of the molecules are in very good agreement with the results reported for VY CMa. We did not detect PS or PH3 in the survey. We suggest that PN and PO are the main carriers of phosphorus in the gas phase, with abundances possibly up to several 10^-7. The current chemical models cannot account for this, underlining the strong need for updated chemical models that include phosphorous compounds.Comment: Accepted for publication in Astronomy & Astrophysics, 10 pages, 8 figure

The circumstellar envelope around the S-type AGB star W Aql Effects of an eccentric binary orbit

The CO(J=3-2) emission from the CSE of the binary S-type AGB star W Aql has been observed at subarcsecond resolution using ALMA. The aim of this paper is to investigate the wind properties of the AGB star and to analyse how the known companion has shaped the CSE. The average mass-loss rate during the creation of the detected CSE is estimated through modelling, using the ALMA brightness distribution and previously published single-dish measurements as observational constraints. The ALMA observations are presented and compared to the results from a 3D smoothed particle hydrodynamics (SPH) binary interaction model with the same properties as the W Aql system and with two different orbital eccentricities. Three-dimensional radiative transfer modelling is performed and the response of the interferometer is modelled and discussed. The estimated average mass-loss rate of W~Aql agrees with previous results. The size of the emitting region is consistent with photodissociation models. The CO(J=3-2) emission is dominated by a smooth component overlayed with two weak arc patterns with different separations. The larger pattern is predicted by the binary interaction model with separations of 10" and therefore likely due to the known companion. It is consistent with a binary orbit with low eccentricity. The smaller separation pattern is asymmetric and coincides with the dust distribution, but the separation timescale (200 yrs) is not consistent with any known process of the system. The separation of the known companions of the system is large enough to not have a very strong effect on the circumstellar morphology. The density contrast across the envelope of a binary with an even larger separation will not be easily detectable, even with ALMA, unless the orbit is strongly asymmetric or the AGB star has a much larger mass-loss rate.Comment: 10 pages, 8 figure

Quantum Invariants, Modular Forms, and Lattice Points II

We study the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert fibered homology spheres with M-exceptional fibers. We show that the WRT invariant can be written in terms of (differential of) the Eichler integrals of modular forms with weight 1/2 and 3/2. By use of nearly modular property of the Eichler integrals we shall obtain asymptotic expansions of the WRT invariant in the large-N limit. We further reveal that the number of the gauge equivalent classes of flat connections, which dominate the asymptotics of the WRT invariant in N ->\infinity, is related to the number of integral lattice points inside the M-dimensional tetrahedron

Superstatistics, thermodynamics, and fluctuations

A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary thermodynamics is recovered as a special case of the present theory, and corrections to it can be systematically evaluated. A generalization of Einstein's relation for fluctuations is presented using a maximum entropy condition.Comment: 16 pages, no figures. The title changed, some explanations and references added. Accepted for publication in Phys. Rev.