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B. Larsson

Publications and source records attributed to B. Larsson.

At least 37 records · Page 2Linked to original sources

HERSCHEL-HIFI spectroscopy of the intermediate mass protostar NGC7129 FIRS 2

HERSCHEL-HIFI observations of water from the intermediate mass protostar NGC7129 FIRS 2 provide a powerful diagnostic of the physical conditions in this star formation environment. Six spectral settings, covering four H216O and two H218O lines, were observed and all but one H218O line were detected. The four H2 16 O lines discussed here share a similar morphology: a narrower, \approx 6 km/s, component centered slightly redward of the systemic velocity of NGC7129 FIRS 2 and a much broader, \approx 25 km/s component centered blueward and likely associated with powerful outflows. The narrower components are consistent with emission from water arising in the envelope around the intermediate mass protostar, and the abundance of H2O is constrained to \approx 10-7 for the outer envelope. Additionally, the presence of a narrow self-absorption component for the lowest energy lines is likely due to self-absorption from colder water in the outer envelope. The broader component, where the H2O/CO relative abundance is found to be \approx 0.2, appears to be tracing the same energetic region that produces strong CO emission at high J.

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Herschel observations of deuterated water towards Sgr B2(M)

Observations of HDO are an important complement for studies of water, because they give strong constraints on the formation processes -- grain surfaces versus energetic process in the gas phase, e.g. in shocks. The HIFI observations of multiple transitions of HDO in Sgr~B2(M) presented here allow the determination of the HDO abundance throughout the envelope, which has not been possible before with ground-based observations only. The abundance structure has been modeled with the spherical Monte Carlo radiative transfer code RATRAN, which also takes radiative pumping by continuum emission from dust into account. The modeling reveals that the abundance of HDO rises steeply with temperature from a low abundance ($2.5\times 10^{-11}$) in the outer envelope at temperatures below 100~K through a medium abundance ($1.5\times 10^{-9}$) in the inner envelope/outer core, at temperatures between 100 and 200~K, and finally a high abundance ($3.5\times 10^{-9}$) at temperatures above 200~K in the hot core.

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Variations in H2O+/H2O ratios toward massive star-forming regions

Early results from the Herschel Space Observatory revealed the water cation H2O+ to be an abundant ingredient of the interstellar medium. Here we present new observations of the H2O and H2O+ lines at 1113.3 and 1115.2 GHz using the Herschel Space Observatory toward a sample of high-mass star-forming regions to observationally study the relation between H2O and H2O+ . Nine out of ten sources show absorption from H2O+ in a range of environments: the molecular clumps surrounding the forming and newly formed massive stars, bright high-velocity outflows associated with the massive protostars, and unrelated low-density clouds along the line of sight. Column densities per velocity component of H2 O+ are found in the range of 10^12 to a few 10^13 cm-2 . The highest N(H2O+) column densities are found in the outflows of the sources. The ratios of H2O+/H2O are determined in a range from 0.01 to a few and are found to differ strongly between the observed environments with much lower ratios in the massive (proto)cluster envelopes (0.01-0.1) than in outflows and diffuse clouds. Remarkably, even for source components detected in H2O in emission, H2O+ is still seen in absorption.

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Herschel-HIFI detections of hydrides towards AFGL 2591 (Envelope emission versus tenuous cloud absorption)

The Heterodyne Instrument for the Far Infrared (HIFI) onboard the Herschel Space Observatory allows the first observations of light diatomic molecules at high spectral resolution and in multiple transitions. Here, we report deep integrations using HIFI in different lines of hydrides towards the high-mass star forming region AFGL 2591. Detected are CH, CH+, NH, OH+, H2O+, while NH+ and SH+ have not been detected. All molecules except for CH and CH+ are seen in absorption with low excitation temperatures and at velocities different from the systemic velocity of the protostellar envelope. Surprisingly, the CH(JF,P = 3/2_2,- - 1/2_1,+) and CH+(J = 1 - 0, J = 2 - 1) lines are detected in emission at the systemic velocity. We can assign the absorption features to a foreground cloud and an outflow lobe, while the CH and CH+ emission stems from the envelope. The observed abundance and excitation of CH and CH+ can be explained in the scenario of FUV irradiated outflow walls, where a cavity etched out by the outflow allows protostellar FUV photons to irradiate and heat the envelope at larger distances driving the chemical reactions that produce these molecules.

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Water in low-mass star-forming regions with Herschel: HIFI spectroscopy of NGC1333

'Water In Star-forming regions with Herschel' (WISH) is a key programme dedicated to studying the role of water and related species during the star-formation process and constraining the physical and chemical properties of young stellar objects. The Heterodyne Instrument for the Far-Infrared (HIFI) on the Herschel Space Observatory observed three deeply embedded protostars in the low-mass star-forming region NGC1333 in several H2-16O, H2-18O, and CO transitions. Line profiles are resolved for five H16O transitions in each source, revealing them to be surprisingly complex. The line profiles are decomposed into broad (>20 km/s), medium-broad (~5-10 km/s), and narrow (<5 km/s) components. The H2-18O emission is only detected in broad 1_10-1_01 lines (>20 km/s), indicating that its physical origin is the same as for the broad H2-16O component. In one of the sources, IRAS4A, an inverse P Cygni profile is observed, a clear sign of infall in the envelope. From the line profiles alone, it is clear that the bulk of emission arises from shocks, both on small (<1000 AU) and large scales along the outflow cavity walls (~10 000 AU). The H2O line profiles are compared to CO line profiles to constrain the H2O abundance as a function of velocity within these shocked regions. The H2O/CO abundance ratios are measured to be in the range of ~0.1-1, corresponding to H2O abundances of ~10-5-10-4 with respect to H2. Approximately 5-10% of the gas is hot enough for all oxygen to be driven into water in warm post-shock gas, mostly at high velocities.

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Sensitive limits on the abundance of cold water vapor in the DM Tau protoplanetary disk

We performed a sensitive search for the ground-state emission lines of ortho- and para-water vapor in the DM Tau protoplanetary disk using the Herschel/HIFI instrument. No strong lines are detected down to 3sigma levels in 0.5 km/s channels of 4.2 mK for the 1_{10}--1_{01} line and 12.6 mK for the 1_{11}--0_{00} line. We report a very tentative detection, however, of the 1_{10}--1_{01} line in the Wide Band Spectrometer, with a strength of T_{mb}=2.7 mK, a width of 5.6 km/s and an integrated intensity of 16.0 mK km/s. The latter constitutes a 6sigma detection. Regardless of the reality of this tentative detection, model calculations indicate that our sensitive limits on the line strengths preclude efficient desorption of water in the UV illuminated regions of the disk. We hypothesize that more than 95-99% of the water ice is locked up in coagulated grains that have settled to the midplane.

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Herschel observations of the hydroxyl radical (OH) in young stellar objects

Water in Star-forming regions with Herschel (WISH) is a Herschel Key Program investigating the water chemistry in young stellar objects (YSOs) during protostellar evolution. Hydroxyl (OH) is one of the reactants in the chemical network most closely linked to the formation and destruction of H2O. High-temperature chemistry connects OH and H2O through the OH + H2 <-> H2O + H reactions. Formation of H2O from OH is efficient in the high-temperature regime found in shocks and the innermost part of protostellar envelopes. Moreover, in the presence of UV photons, OH can be produced from the photo-dissociation of H2O. High-resolution spectroscopy of the OH 163.12 micron triplet towards HH 46 and NGC 1333 IRAS 2A was carried out with the Heterodyne Instrument for the Far Infrared (HIFI) on board Herschel. The low- and intermediate-mass YSOs HH 46, TMR 1, IRAS 15398-3359, DK Cha, NGC 7129 FIRS 2, and NGC 1333 IRAS 2A were observed with the Photodetector Array Camera and Spectrometer (PACS) in four transitions of OH and two [OI] lines. The OH transitions at 79, 84, 119, and 163 micron and [OI] emission at 63 and 145 micron were detected with PACS towards the class I low-mass YSOs as well as the intermediate-mass and class I Herbig Ae sources. No OH emission was detected from the class 0 YSO NGC 1333 IRAS 2A, though the 119 micron was detected in absorption. With HIFI, the 163.12 micron was not detected from HH 46 and only tentatively detected from NGC 1333 IRAS 2A. The combination of the PACS and HIFI results for HH 46 constrains the line width (FWHM > 11 km/s) and indicates that the OH emission likely originates from shocked gas. This scenario is supported by trends of the OH flux increasing with the [OI] flux and the bolometric luminosity. Similar OH line ratios for most sources suggest that OH has comparable excitation temperatures despite the different physical properties of the sources.

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Herschel/HIFI discovery of interstellar chloronium (H$_2$Cl$^+$)

We report the first detection of chloronium, H$_2$Cl$^+$, in the interstellar medium, using the HIFI instrument aboard the \emph{Herschel} Space Observatory. The $2_{12}-1_{01}$ lines of ortho-H$_2^{35}$Cl$^+$ and ortho-H$_2^{37}$Cl$^+$ are detected in absorption towards NGC~6334I, and the $1_{11}-0_{00}$ transition of para-H$_2^{35}$Cl$^+$ is detected in absorption towards NGC~6334I and Sgr~B2(S). The H$_2$Cl$^+$ column densities are compared to those of the chemically-related species HCl. The derived HCl/H$_2$Cl$^+$ column density ratios, $\sim$1--10, are within the range predicted by models of diffuse and dense Photon Dominated Regions (PDRs). However, the observed H$_2$Cl$^+$ column densities, in excess of $10^{13}$~cm$^{-2}$, are significantly higher than the model predictions. Our observations demonstrate the outstanding spectroscopic capabilities of HIFI for detecting new interstellar molecules and providing key constraints for astrochemical models.

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Water vapor toward starless cores: the Herschel view

SWAS and Odin provided stringent upper limits on the gas phase water abundance of dark clouds (x(H2O) < 7x10^-9). We investigate the chemistry of water vapor in starless cores beyond the previous upper limits using the highly improved angular resolution and sensitivity of Herschel and measure the abundance of water vapor during evolutionary stages just preceding star formation. High spectral resolution observations of the fundamental ortho water (o-H2O) transition (557 GHz) were carried out with Herschel HIFI toward two starless cores: B68, a Bok globule, and L1544, a prestellar core embedded in the Taurus molecular cloud complex. The rms in the brightness temperature measured for the B68 and L1544 spectra is 2.0 and 2.2 mK, respectively, in a velocity bin of 0.59 km s^-1. The continuum level is 3.5+/-0.2 mK in B68 and 11.4+/-0.4 mK in L1544. No significant feature is detected in B68 and the 3 sigma upper limit is consistent with a column density of o-H2O N(o-H2O) < 2.5x10^13 cm^-2, or a fractional abundance x(o-H2O) < 1.3x10^-9, more than an order of magnitude lower than the SWAS upper limit on this source. The L1544 spectrum shows an absorption feature at a 5 sigma level from which we obtain the first value of the o-H2O column density ever measured in dark clouds: N(o-H2O) = (8+/-4)x10^12 cm^-2. The corresponding fractional abundance is x(o-H2O) ~ 5x10^-9 at radii > 7000 AU and ~2x10^-10 toward the center. The radiative transfer analysis shows that this is consistent with a x(o-H2O) profile peaking at ~10^-8, 0.1 pc away from the core center, where both freeze-out and photodissociation are negligible. Herschel has provided the first measurement of water vapor in dark regions. Prestellar cores such as L1544 (with their high central densities, strong continuum, and large envelopes) are very promising tools to finally shed light on the solid/vapor balance of water in molecular clouds.

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CHESS, Chemical Herschel surveys of star forming regions:Peering into the protostellar shock L1157-B1

The outflow driven by the low-mass class 0 protostar L1157 is the prototype of the so-called chemically active outflows. The bright bowshock B1 in the southern outflow lobe is a privileged testbed of magneto-hydrodynamical (MHD) shock models, for which dynamical and chemical processes are strongly interdependent. We present the first results of the unbiased spectral survey of the L1157-B1 bowshock, obtained in the framework of the key program "Chemical Herschel Surveys of Star Forming Regions" (CHESS). The main aim is to trace the warm and chemically enriched gas and to infer the excitation conditions in the shock region. The CO 5-4 and H2O lines have been detected at high-spectral resolution in the unbiased spectral survey of the HIFI-Band 1b spectral window (555-636 GHz), presented by Codella et al. in this volume. Complementary ground-based observations in the submm window help establish the origin of the emission detected in the main-beam of HIFI, and the physical conditions in the shock.}{Both lines exhibit broad wings, which extend to velocities much higher than reported up to now. We find that the molecular emission arises from two regions with distinct physical conditions: an extended, warm (100K), dense (3e5 cm-3) component at low-velocity, which dominates the water line flux in Band~1; a secondary component in a small region of B1 (a few arcsec) associated with high-velocity, hot (> 400 K) gas of moderate density ((1.0-3.0)e4 cm-3), which appears to dominate the flux of the water line at 179mu observed with PACS. The water abundance is enhanced by two orders of magnitude between the low- and the high-velocity component, from 8e-7 up to 8e-5. The properties of the high-velocity component agree well with the predictions of steady-state C-shock models.

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Herschel-PACS spectroscopy of the intermediate mass protostar NGC7129 FIRS 2

Aims: We present preliminary results of the first Herschel spectroscopic observations of NGC7129 FIRS2, an intermediate mass star-forming region. We attempt to interpret the observations in the framework of an in-falling spherical envelope. Methods: The PACS instrument was used in line spectroscopy mode (R=1000-5000) with 15 spectral bands between 63 and 185 microns. This provided good detections of 26 spectral lines seen in emission, including lines of H2O, CO, OH, O I, and C II. Results: Most of the detected lines, particularly those of H2O and CO, are substantially stronger than predicted by the spherical envelope models, typically by several orders of magnitude. In this paper we focus on what can be learned from the detected CO emission lines. Conclusions: It is unlikely that the much stronger than expected line emission arises in the (spherical) envelope of the YSO. The region hot enough to produce such high excitation lines within such an envelope is too small to produce the amount of emission observed. Virtually all of this high excitation emission must arise in structures such as as along the walls of the outflow cavity with the emission produced by a combination of UV photon heating and/or non-dissociative shocks.

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Water cooling of shocks in protostellar outflows: Herschel-PACS map of L1157

In the framework of the Water in Star-forming regions with Herschel (WISH) key program, maps in water lines of several outflows from young stars are being obtained, to study the water production in shocks and its role in the outflow cooling. This paper reports the first results of this program, presenting a PACS map of the o-H2O 179 um transition obtained toward the young outflow L1157. The 179 um map is compared with those of other important shock tracers, and with previous single-pointing ISO, SWAS, and Odin water observations of the same source that allow us to constrain the water abundance and total cooling. Strong H2O peaks are localized on both shocked emission knots and the central source position. The H2O 179 um emission is spatially correlated with emission from H2 rotational lines, excited in shocks leading to a significant enhancement of the water abundance. Water emission peaks along the outflow also correlate with peaks of other shock-produced molecular species, such as SiO and NH3. A strong H2O peak is also observed at the location of the proto-star, where none of the other molecules have significant emission. The absolute 179 um intensity and its intensity ratio to the H2O 557 GHz line previously observed with Odin/SWAS indicate that the water emission originates in warm compact clumps, spatially unresolved by PACS, having a H2O abundance of the order of 10^-4. This testifies that the clumps have been heated for a time long enough to allow the conversion of almost all the available gas-phase oxygen into water. The total water cooling is ~10^-1 Lo, about 40% of the cooling due to H2 and 23% of the total energy released in shocks along the L1157 outflow.

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Origin of the hot gas in low-mass protostars: Herschel-PACS spectroscopy of HH 46

'Water in Star-forming regions with Herschel' (WISH) is a Herschel Key Programme aimed at understanding the physical and chemical structure of young stellar objects (YSOs) with a focus on water and related species. The low-mass protostar HH 46 was observed with the Photodetector Array Camera and Spectrometer (PACS) on the Herschel Space Observatory to measure emission in H2O, CO, OH, [OI], and [CII] lines located between 63 and 186 um. The excitation and spatial distribution of emission can disentangle the different heating mechanisms of YSOs, with better spatial resolution and sensitivity than previously possible. Far-IR line emission is detected at the position of the protostar and along the outflow axis. The OH emission is concentrated at the central position, CO emission is bright at the central position and along the outflow, and H2O emission is concentrated in the outflow. In addition, [OI] emission is seen in low-velocity gas, assumed to be related to the envelope, and is also seen shifted up to 170 km/s in both the red- and blue-shifted jets. Envelope models are constructed based on previous observational constraints. They indicate that passive heating of a spherical envelope by the protostellar luminosity cannot explain the high-excitation molecular gas detected with PACS, including CO lines with upper levels at >2500 K above the ground state. Instead, warm CO and H2O emission is probably produced in the walls of an outflow-carved cavity in the envelope, which are heated by UV photons and non-dissociative C-type shocks. The bright OH and [OI] emission is attributed to J-type shocks in dense gas close to the protostar. In the scenario described here, the combined cooling by far-IR lines within the central spatial pixel is estimated to be 2 \times 10-2 L_sun, with 60-80% attributed to J- and C-type shocks produced by interactions between the jet and the envelope.

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O18O and C18O observations of rho Oph A

Observations of the (N_J=1_1-1_0) ground state transition of O_2 with the Odin satellite resulted in a about 5 sigma detection toward the dense core rho Oph A. At the frequency of the line, 119 GHz, the Odin telescope has a beam width of 10', larger than the size of the dense core, so that the precise nature of the emitting source and its exact location and extent are unknown. The current investigation is intended to remedy this. Telluric absorption makes ground based O_2 observations essentially impossible and observations had to be done from space. mm-wave telescopes on space platforms were necessarily small, which resulted in large, several arcminutes wide, beam patterns. Although the Earth's atmosphere is entirely opaque to low-lying O_2 transitions, it allows ground based observations of the much rarer O18O in favourable conditions and at much higher angular resolution with larger telescopes. In addition, rho Oph A exhibits both multiple radial velocity systems and considerable velocity gradients. Extensive mapping of the region in the proxy C18O (J=3-2) line can be expected to help identify the O_2 source on the basis of its line shape and Doppler velocity. Line opacities were determined from observations of optically thin 13C18O (J=3-2) at selected positions. During several observing periods, two C18O intensity maxima in rho Oph A were searched for in the 16O18O (2_1-0_1) line at 234 GHz with the 12m APEX telescope. Our observations resulted in an upper limit on the integrated O18O intensity of < 0.01 K km/s (3 sigma) into the 26.5" beam. We conclude that the source of observed O_2 emission is most likely confined to the central regions of the rho Oph A cloud. In this limited area, implied O_2 abundances could thus be higher than previously reported, by up to two orders of magnitude.

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A spectral line survey of Orion KL in the bands 486-492 and 541-577 GHz with the Odin satellite II. Data analysis

We investigate the physical and chemical conditions in a typical star forming region, including an unbiased search for new molecules in a spectral region previously unobserved. Due to its proximity, the Orion KL region offers a unique laboratory of molecular astrophysics in a chemically rich, massive star forming region. Several ground-based spectral line surveys have been made, but due to the absorption by water and oxygen, the terrestrial atmosphere is completely opaque at frequencies around 487 and 557 GHz. To cover these frequencies we used the Odin satellite to perform a spectral line survey in the frequency ranges 486-492 GHz and 541-577 GHz, filling the gaps between previous spectral scans. Odin's high main beam efficiency and observations performed outside the atmosphere make our intensity scale very well determined. We observed 280 spectral lines from 38 molecules including isotopologues, and, in addition, 64 unidentified lines. The beam-averaged emission is dominated by CO, H2O, SO2, SO, 13CO and CH3OH. Species with the largest number of lines are CH3OH, (CH33)2O, SO2, 13CH3OH, CH3CN and NO. Six water lines are detected including the ground state rotational transition o-H2O, its isotopologues o-H218O and o-H217O, the Hot Core tracing p-H2O transition 6(2,4)-7(1,7), and the 2(0, 2)-1(1,1) transition of HDO. Other lines of special interest are the 1_0-0_0 transition of NH3 and its isotopologue 15NH3. Isotopologue abundance ratios of D/H, 12C/13C, 32S/34S, 34S/33S, and 18O/17O are estimated. The temperatures, column densities and abundances in the various subregions are estimated, and we find very high gas-phase abundances of H2O, NH3, SO2, SO, NO, and CH3OH. A comparison with the ice inventory of ISO sheds new light on the origin of the abundant gas-phase molecules.

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A spectral line survey of Orion KL in the bands 486-492 and 541-577 GHz with the Odin satellite I. The observational data

Spectral line surveys are useful since they allow identification of new molecules and new lines in uniformly calibrated data sets. Nonetheless, large portions of the sub-millimetre spectral regime remain unexplored due to severe absorptions by H2O and O2 in the terrestrial atmosphere. The purpose of the measurements presented here is to cover wavelength regions at and around 0.55 mm -- regions largely unobservable from the ground. Using the Odin astronomy/aeronomy satellite, we performed the first spectral survey of the Orion KL molecular cloud core in the bands 486--492 and 541--576 GHz with rather uniform sensitivity (22--25 mK baseline noise). Odin's 1.1 m size telescope, equipped with four cryo-cooled tuneable mixers connected to broad band spectrometers, was used in a satellite position-switching mode. Two mixers simultaneously observed different 1.1 GHz bands using frequency steps of 0.5 GHz (25 hours each). An on-source integration time of 20 hours was achieved for most bands. The entire campaign consumed ~1100 orbits, each containing one hour of serviceable astro-observation. We identified 280 spectral lines from 38 known interstellar molecules (including isotopologues) having intensities in the range 80 to 0.05 K. An additional 64 weak lines remain unidentified. Apart from the ground state rotational 1(1,0)--1(0,1) transitions of ortho-H2O, H218O and H217O, the high energy 6(2,4)--7(1,7) line of para-H2O and the HDO(2,0,2--1,1,1) line have been observed, as well as the 1,0--0,1 lines from NH3 and its rare isotopologue 15NH3. We suggest assignments for some unidentified features, notably the new interstellar molecules ND and SH-. Severe blends have been detected in the line wings of the H218O, H217O and 13CO lines changing the true linewidths of the outflow emission.

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Odin observations of water in molecular outflows and shocks

Aims. We investigate the ortho-water abundance in outflows and shocks in order to improve our knowledge of shock chemistry and of the physics behind molecular outflows. Methods. We have used the Odin space observatory to observe the H2O(110-101) line. We obtain strip maps and single pointings of 13 outflows and two supernova remnants where we report detections for eight sources. We have used RADEX to compute the beam averaged abundances of o-H2O relative to H2. In the case of non-detection, we derive upper limits on the abundance. Results. Observations of CO emission from the literature show that the volume density of H2 can vary to a large extent, a parameter that puts severe uncertainties on the derived abundances. Our analysis shows a wide range of abundances reflecting the degree to which shock chemistry is affecting the formation and destruction of water. We also compare our results with recent results from the SWAS team. Conclusions. Elevated abundances of ortho-water are found in several sources. The abundance reaches values as high as what would be expected from a theoretical C-type shock where all oxygen, not in the form of CO, is converted to water. However, the high abundances we derive could also be due to the low densities (derived from CO observations) that we assume. The water emission may in reality stem from high density regions much smaller than the Odin beam. We do not find any relationship between the abundance and the mass loss rate. On the other hand, there is a relation between the derived water abundance and the observed maximum outflow velocity.

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Circumstellar water vapour in M-type AGB stars: Constraints from H2O(1_10 - 1_01) lines obtained with Odin

Aims: Spectrally resolved circumstellar H2O(1_10 - 1_01) lines have been obtained towards three M-type AGB stars using the Odin satellite. This provides additional strong constrains on the properties of circumstellar H2O and the circumstellar envelope. Methods: ISO and Odin satellite H2O line data are used as constraints for radiative transfer models. Special consideration is taken to the spectrally resolved Odin line profiles, and the effect of excitation to the first excited vibrational states of the stretching modes (nu1=1 and nu3=1) on the derived abundances is estimated. A non-local, radiative transfer code based on the ALI formalism is used. Results: The H2O abundance estimates are in agreement with previous estimates. The inclusion of the Odin data sets stronger constraints on the size of the H2O envelope. The H2O(1_10 - 1_01) line profiles require a significant reduction in expansion velocity compared to the terminal gas expansion velocity determined in models of CO radio line emission, indicating that the H2O emission lines probe a region where the wind is still being accelerated. Including the nu3=1 state significantly lowers the estimated abundances for the low-mass-loss-rate objects. This shows the importance of detailed modelling, in particular the details of the infrared spectrum in the range 3 to 6 micron, to estimate accurate circumstellar H2O abundances. Conclusions: Spectrally resolved circumstellar H2O emission lines are important probes of the physics and chemistry in the inner regions of circumstellar envelopes around asymptotic giant branch stars. Predictions for H2O emission lines in the spectral range of the upcoming Herschel/HIFI mission indicate that these observations will be very important in this context.

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