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G. J. Herczeg

Publications and source records attributed to G. J. Herczeg.

At least 19 recordsLinked to original sources

The distribution of accretion rates as a diagnostic of protoplanetary disc evolution

We show that the distribution of observed accretion rates is a powerful diagnostic of protoplanetary disc physics. Accretion due to turbulent ("viscous") transport of angular momentum results in a fundamentally different distribution of accretion rates than accretion driven by magnetised disc winds. We find that a homogeneous sample of $\gtrsim$300 observed accretion rates would be sufficient to distinguish between these two mechanisms of disc accretion at high confidence, even for pessimistic assumptions. Current samples of T Tauri star accretion rates are not this large, and also suffer from significant inhomogeneity, so both viscous and wind-driven models are broadly consistent with the existing observations. If accretion is viscous, the observed accretion rates require low rates of disc photoevaporation ($\lesssim$$10^{-9}$M$_{\odot}$yr$^{-1}$). Uniform, homogeneous surveys of stellar accretion rates can therefore provide a clear answer to the long-standing question of how protoplanetary discs accrete.

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PENELLOPE IV. A comparison between optical forbidden lines and $\rm H_2$ UV lines in the Orion OB1b and $σ$-Ori associations

Observing the spatial distribution and excitation processes of atomic and molecular gas in the inner regions (< 20 au) of young (< 10 Myr) protoplanetary disks helps us to understand the conditions for the formation and evolution of planetary systems. In the framework of the PENELLOPE and ULLYSES projects, we aim to characterize the atomic and molecular component of protoplanetary disks in a sample of 11 Classical T Tauri Stars (CTTs) of the Orion OB1 and $σ$-Orionis associations. We analyzed the flux-calibrated optical-forbidden lines and the fluorescent ultraviolet $\rm H_2$ progressions using spectra acquired with ESPRESSO at VLT, UVES at VLT and HST-COS. Line morphologies were characterized through Gaussian decomposition. We then focused on the properties of the narrow low-velocity (FWHM < 40 $km$ $s^{-1}$ and |$v_p$| < 30 $km$ $s^{-1}$) component (NLVC) of the [OI] 630 nm line, compared with the properties of the UV-$\rm H_2$ lines. We found that the [OI]630 NLVC and the UV-$\rm H_2$ lines are strongly correlated in terms of peak velocities, full width at half maximum, and luminosity. The luminosities of the [OI]630 NLVC and UV-$\rm H_2$ correlate with the accretion luminosity with a similar slope, as well as with the luminosity of the CIV 154.8, 155 nm doublet. We discuss such correlations in the framework of the currently suggested excitation processes for the [OI]630 NLVC. Our results can be interpreted in a scenario in which the [OI]630 NLVC and UV-$\rm H_2$ have a common disk origin with a partially overlapped radial extension. We also suggest that the excitation of the [OI] NLVC is mainly induced by stellar FUV continuum photons more than being of thermal origin. This study demonstrates the potential of contemporaneous wide-band high-resolution spectroscopy in linking different tracers of protoplanetary disks.

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PENELLOPE III. The peculiar accretion variability of XX Cha and its impact on the observed spread of accretion rates

The processes regulating protoplanetary disk evolution are constrained by studying how mass accretion rates scale with stellar and disk properties. The spread in these relations can be used as a constraint to the models of disk evolution, but only if the impact of accretion variability is correctly accounted for. While the effect of variability might be substantial in the embedded phases of star formation, it is often considered limited at later stages. Here we report on the observed large variation in the accretion rate for one target, XX Cha, and we discuss the impact on population studies of classical T Tauri stars. The mass accretion rate determined by fitting the UV-to-near-infrared spectrum in recent X-Shooter observations is compared with the one measured with the same instrument 11 years before. XX Cha displays an accretion variability of almost 2 dex between 2010 and 2021. Although the timescales on which this variability happens are uncertain, XX Cha displays an extreme accretion variability for a classical T Tauri star. If such behavior is common among classical T Tauri stars, possibly on longer timescales than previously probed, it could be relevant for discussing the disk evolution models constrained by the observed spread in accretion rates. Finally, we remark that previous studies of accretion variability based on spectral lines may have underestimated the variability of some targets.

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Hydrogen Emission from Accretion and Outflow in T Tauri Stars

Radiative transfer modelling offers a powerful tool for understanding the enigmatic hydrogen emission lines from T Tauri stars. This work compares optical and near-IR spectroscopy of 29 T Tauri stars with our grid of synthetic line profiles. The archival spectra, obtained with VLT's X-Shooter, provide simultaneous coverage of many optical and infrared hydrogen lines. The observations exhibit similar morphologies of line profiles seen in other studies. We used the radiative transfer code TORUS to create synthetic H$α$, Pa$β$, Pa$γ$, and Br$γ$ emission lines for a fiducial T Tauri model that included axisymmetric magnetospheric accretion and a polar stellar wind. The distribution of Reipurth types and line widths for the synthetic H$α$ lines is similar to the observed results. However, the modelled infrared lines are narrower than the observations by $\approx 80{~\rm kms}^{-1}$, and our models predict a significantly higher proportion ($\approx 90$ per cent) of inverse P-Cygni profiles. Furthermore, our radiative transfer models suggest that the frequency of P-Cygni profiles depends on the ratio of the mass loss to mass accretion rates and blue-shifted sub-continuum absorption was predicted for mass loss rates as low as $10^{-12}~M_{\odot}{\rm~ yr}^{-1}$. We explore the effect of rotation, turbulence, and the contributions from red-shifted absorption in an attempt to explain the discrepancy in widths. Our findings show that, singularly, none of these effects is sufficient to explain the observed disparity. However, a combination of rotation, turbulence, and non-axisymmetric accretion may improve the fit of the models to the observed data.

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The ODYSSEUS Survey. Motivation and First Results: Accretion, Ejection, and Disk Irradiation of CVSO 109

The Hubble UV Legacy Library of Young Stars as Essential Standards (ULLYSES) Director's Discretionary Program of low-mass pre-main-sequence stars, coupled with forthcoming data from ALMA and JWST, will provide the foundation to revolutionize our understanding of the relationship between young stars and their protoplanetary disks. A comprehensive evaluation of the physics of disk evolution and planet formation requires understanding the intricate relationships between mass accretion, mass outflow, and disk structure. Here we describe the Outflows and Disks around Young Stars: Synergies for the Exploration of ULLYSES Spectra (ODYSSEUS) Survey and present initial results of the classical T Tauri Star CVSO 109 in Orion OB1b as a demonstration of the science that will result from the survey. ODYSSEUS will analyze the ULLYSES spectral database, ensuring a uniform and systematic approach in order to (1) measure how the accretion flow depends on the accretion rate and magnetic structures, (2) determine where winds and jets are launched and how mass-loss rates compare with accretion, and (3) establish the influence of FUV radiation on the chemistry of the warm inner regions of planet-forming disks. ODYSSEUS will also acquire and provide contemporaneous observations at X-ray, optical, NIR, and millimeter wavelengths to enhance the impact of the ULLYSES data. Our goal is to provide a consistent framework to accurately measure the level and evolution of mass accretion in protoplanetary disks, the properties and magnitudes of inner-disk mass loss, and the influence of UV radiation fields that determine ionization levels and drive disk chemistry.

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PENELLOPE II. CVSO 104: a pre-main sequence close binary with an optical companion in Ori OB1

We present results of our study of the close pre-main sequence spectroscopic binary CVSO 104 in Ori OB1, based on data obtained within the PENELLOPE legacy program. We derive, for the first time, the orbital elements of the system and the stellar parameters of the two components. The system is composed of two early M-type stars and has an orbital period of about 5 days and a mass ratio of 0.92, but contrarily to expectations does not appear to have a tertiary companion. Both components have been (quasi-)synchronized, but the orbit is still very eccentric. The spectral energy distribution clearly displays a significant infrared excess compatible with a circumbinary disk. The analysis of HeI and Balmer line profiles, after the removal of the composite photospheric spectrum, reveals that both components are accreting at a similar level. We also observe excess emission in H$α$ and H$β$, which appears redshifted or blueshifted by more than 100 km/s with respect to the mass center of the system depending on the orbital phase. This additional emission could be connected with accretion structures, such as funnels of matter from the circumbinary disk. We also analyze the optical companion located at about 2".4 from the spectroscopic binary. This companion, that we named CVSO 104B, turns out to be a background Sun-like star not physically associated with the PMS system and not belonging to Ori OB1.

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PENELLOPE: the ESO data legacy program to complement the Hubble UV Legacy Library of Young Stars (ULLYSES) I. Survey presentation and accretion properties of Orion OB1 and $σ$-Orionis

The evolution of young stars and disks is driven by the interplay of several processes, notably accretion and ejection of material. Critical to correctly describe the conditions of planet formation, these processes are best probed spectroscopically. About five-hundred orbits of the Hubble Space Telescope (HST) are being devoted in 2020-2022 to the ULLYSES public survey of about 70 low-mass (M<2Msun) young (age<10 Myr) stars at UV wavelengths. Here we present the PENELLOPE Large Program that is being carried out at the ESO Very Large Telescope (VLT) to acquire, contemporaneous to HST, optical ESPRESSO/UVES high-resolution spectra to investigate the kinematics of the emitting gas, and UV-to-NIR X-Shooter medium-resolution flux-calibrated spectra to provide the fundamental parameters that HST data alone cannot provide, such as extinction and stellar properties. The data obtained by PENELLOPE have no proprietary time, and the fully reduced spectra are made available to the whole community. Here, we describe the data and the first scientific analysis of the accretion properties for the sample of thirteen targets located in the Orion OB1 association and in the sigma-Orionis cluster, observed in Nov-Dec 2020. We find that the accretion rates are in line with those observed previously in similarly young star-forming regions, with a variability on a timescale of days of <3. The comparison of the fits to the continuum excess emission obtained with a slab model on the X-Shooter spectra and the HST/STIS spectra shows a shortcoming in the X-Shooter estimates of <10%, well within the assumed uncertainty. Its origin can be either a wrong UV extinction curve or due to the simplicity of this modelling, and will be investigated in the course of the PENELLOPE program. The combined ULLYSES and PENELLOPE data will be key for a better understanding of the accretion/ejection mechanisms in young stars.

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A Differential Measurement of Circumstellar Extinction for AA Tau's 2011 Dimming Event

AA Tau is a classical T Tauri star with a highly inclined, warped circumstellar disk. For decades, AA Tau exhibited photometric and spectroscopic variability that were successfully modelled as occultations of the primary star by circumstellar material. In 2011, AA Tau entered an extended faint state, presumably due to enhanced levels of circumstellar dust. We use two sets of contemporaneous optical-NIR spectra of AA Tau, obtained in December of 2008 and 2014, to directly measure the wavelength-dependent extinction associated with the dust enhancement driving AA Tau's 2011 optical fade. Taken alone, AA Tau's apparent optical-NIR increased extinction curve cannot be fit well with standard extinction laws. At optical wavelengths, AA Tau's dimming event is consistent with predictions of common extinction models for an increase of $A_V=2$, but no such model reproduces AA Tau's color-color excess at NIR wavelengths. We show that veiling emission accounts for the apparent anomalous NIR extinction: after including this veiling flux, AA Tau's dimming event is consistent with a standard $A_V=2$ extinction law across the full optical-NIR range. We also report an increase in AA Tau's mid-IR flux since its 2011 fade, and suggest that an increase in the height of AA Tau's inner disk is the most likely explanation for both the IR brightening and the additional extinction along the line of sight. In addition to informing our understanding of AA Tau, this analysis demonstrates that caution should be exercised when inferring extinction (and stellar parameters) from the NIR color-color excess of young stars with measurable NIR veiling fluxes.

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Observational constraints on dust disk sizes in tidally truncated protoplanetary disks in multiple systems in the Taurus region

The impact of stellar multiplicity on the evolution of planet-forming disks is still the subject of debate. Here we present and analyze disk structures around ten multiple stellar systems that were included in an unbiased, high spatial resolution survey performed with ALMA of 32 protoplanetary disks in the Taurus star-forming region. At the unprecedented spatial resolution of ~0.12" we detect and spatially resolve the disks around all primary stars, and those around eight secondary and one tertiary star. The dust radii of disks around multiple stellar systems are smaller than those around single stars in the same stellar mass range and in the same region. The disks in multiple stellar systems also show a steeper decay of the millimeter continuum emission at the outer radius than disks around single stars, suggestive of the impact of tidal truncation on the shape of the disks in multiple systems. However, the observed ratio between the dust disk radii and the observed separation of the stars in the multiple systems is consistent with analytic predictions of the effect of tidal truncation only if the eccentricities of the binaries are rather high (typically >0.5), or if the observed dust radii are a factor of two smaller than the gas radii, as is typical for isolated systems. Similar high-resolution studies targeting the gaseous emission from disks in multiple stellar systems are required to resolve this question.

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Variability of young stellar objects in the star-forming region Pelican Nebula

We observed a field of $16'\times 16'$ in the star-forming region Pelican Nebula (IC 5070) at $BVRI$ wavelengths for 90 nights spread over one year in 2012-2013. More than 250 epochs in $VRI$-bands are used to identify and classify variables up to $V\sim 21$~mag. We present a catalogue of optical time-series photometry with periods, mean-magnitudes and classifications for 95 variable stars including 67 pre-main-sequence variables towards star-forming region IC 5070. The pre-main-sequence variables are further classified as candidate classical T Tauri and weak-line T Tauri stars based on their light curve variations and the locations on the color-color and color-magnitude diagrams using optical and infrared data together with Gaia DR2 astrometry. Classical T Tauri stars display variability amplitudes up to three times the maximum fluctuation in disk-free weak-line T Tauri stars, which show strong periodic variations. Short-term variability is missed in our photometry within single nights. Several classical T Tauri stars display long-lasting ($\geq 10$ days) single or multiple fading and brightening events up to a couple of magnitudes at optical wavelengths. The typical mass and age of the pre-main-sequence variables from the isochrone-fitting and spectral energy distributions are estimated to be $\le 1~M_\odot$ and $\sim 2$ Myr, respectively. We do not find any correlation between the optical amplitudes or periods with the physical parameters (mass and age) of pre-main-sequence stars.

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The newborn planet population emerging from ring-like structures in discs

ALMA has observed a plethora of ring-like structures in planet forming discs at distances of 10-100 au from their host star. Although several mechanisms have been invoked to explain the origin of such rings, a common explanation is that they trace new-born planets. Under the planetary hypothesis, a natural question is how to reconcile the apparently high frequency of gap-carving planets at 10-100 au with the paucity of Jupiter mass planets observed around main sequence stars at those separations. Here, we provide an analysis of the new-born planet population emerging from observations of gaps in discs, under the assumption that the observed gaps are due to planets. We use a simple estimate of the planet mass based on the gap morphology, and apply it to a sample of gaps recently obtained by us in a survey of Taurus with ALMA. We also include additional data from recent published surveys, thus analysing the largest gap sample to date, for a total of 48 gaps. The properties of the purported planets occupy a distinctively different region of parameter space with respect to the known exo-planet population, currently not accessible through planet finding methods. Thus, no discrepancy in the mass and radius distribution of the two populations can be claimed at this stage. We show that the mass of the inferred planets conforms to the theoretically expected trend for the minimum planet mass needed to carve a dust gap. Finally, we estimate the separation and mass of the putative planets after accounting for migration and accretion, for a range of evolutionary times, finding a good match with the distribution of cold Jupiters.

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Magnetic topologies of young suns: The weak-line T Tauri stars TWA 6 and TWA 8A

We present a spectropolarimetric study of two weak-line T Tauri stars (wTTSs), TWA 6 and TWA 8A, as part of the MaTYSSE (Magnetic Topologies of Young Stars and the Survival of close-in giant Exoplanets) program. Both stars display significant Zeeman signatures that we have modelled using Zeeman Doppler Imaging (ZDI). The magnetic field of TWA 6 is split equally between poloidal and toroidal components, with the largest fraction of energy in higher-order modes, with a total unsigned flux of 840 G, and a poloidal component tilted $35^{\circ}$ from the rotation axis. TWA 8A has a 70 per cent poloidal field, with most of the energy in higher-order modes, with an unsigned flux of 1.4 kG (with a magnetic filling factor of 0.2), and a poloidal field tilted $20^{\circ}$ from the rotation axis. Spectral fitting of the very strong field in \tb (in individual lines, simultaneously for Stokes $I$ and $V$) yielded a mean magnetic field strength of $6.0\pm0.5$ kG. The higher field strengths recovered from spectral fitting suggests that a significant proportion of magnetic energy lies in small-scale fields that are unresolved by ZDI. So far, wTTSs in MaTYSSE appear to show that the poloidal-field axisymmetry correlates with the magnetic field strength. Moreover, it appears that classical T Tauri stars (cTTSs) and wTTSs are mostly poloidal and axisymmetric when mostly convective and cooler than $\sim4300$ K, with hotter stars being less axisymmetric and poloidal, regardless of internal structure.

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Multi-epoch monitoring of the AA Tau like star V354 Mon - Indications for a low gas-to-dust ratio in the inner disk warp

Disk warps around classical T Tauri stars (CTTS) can periodically obscure the central star for some viewing geometries. For these so-called AA Tau-like variables, the obscuring material is located in the inner disk and absorption spectroscopy allows one to characterize its dust and gas content. Since the observed emission from CTTS consists of several components (photospheric, accretion, jet, and disk emission), which can all vary with time, it is generally challenging to disentangling disk features from emission variability. Multi-epoch, flux-calibrated, broadband spectra provide us with the necessary information to cleanly separate absorption from emission variability. We applied this method to three epochs of VLT/X-Shooter spectra of the CTTS V354 Mon (CSI Mon-660) located in NGC 2264 and find that: (a) the accretion emission remains virtually unchanged between the three epochs; (b) the broadband flux evolution is best described by disk material obscuring part of the star, and (c) the Na and K gas absorption lines show only a minor increase in equivalent width during phases of high dust extinction. The limits on the absorbing gas column densities indicate a low gas-to-dust ratio in the inner disk, less than a tenth of the ISM value. We speculate that the evolutionary state of V354 Mon, rather old with a low accretion rate, is responsible for the dust excess through an evolution toward a dust dominated disk or through the fragmentation of larger bodies that drifted inward from larger radii in a still gas dominated disk.

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Magnetic fields of intermediate mass T Tauri stars

Aims. In this paper, we aim to measure the strength of the surface magnetic fields for a sample of five intermediate mass T Tauri stars and one low mass T Tauri star from late-F to mid-K spectral types. While magnetic fields of T Tauri stars at the low mass range have been extensively characterized, our work complements previous studies towards the intermediate mass range; this complementary study is key to evaluate how magnetic fields evolve during the transition from a convective to a radiative core. Methods. We studied the Zeeman broadening of magnetically sensitive spectral lines in the H-band spectra obtained with the CRIRES high-resolution near-infrared spectrometer. These data are modelled using magnetic spectral synthesis and model atmospheres. Additional constraints on non-magnetic line broadening mechanisms are obtained from modelling molecular lines in the K band or atomic lines in the optical wavelength region. Results. We detect and measure mean surface magnetic fields for five of the six stars in our sample: CHXR 28, COUP 107, V2062 Oph, V1149 Sco, and Par 2441. Magnetic field strengths inferred from the most magnetically sensitive diagnostic line range from 0.8 to 1.8 kG. We also estimate a magnetic field strength of 1.9 kG for COUP 107 from an alternative diagnostic. The magnetic field on YLW 19 is the weakest in our sample and is marginally detected, with a strength of 0.8 kG. Conclusions. We populate an uncharted area of the pre-main-sequence HR diagram with mean magnetic field measurements from high-resolution near-infrared spectra. Our sample of intermediate mass T Tauri stars in general exhibits weaker magnetic fields than their lower mass counterparts. Our measurements will be used in combination with other spectropolarimetric studies of intermediate mass and lower mass T Tauri stars to provide input into pre-main-sequence stellar evolutionary models.

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X-Shooter study of accretion in Chamaeleon I: II. A steeper increase of accretion with stellar mass for very low mass stars?

The dependence of the mass accretion rate on the stellar properties is a key constraint for star formation and disk evolution studies. Here we present a study of a sample of stars in the Chamaeleon I star forming region carried out using the VLT/X-Shooter spectrograph. The sample is nearly complete down to M~0.1Msun for the young stars still harboring a disk in this region. We derive the stellar and accretion parameters using a self-consistent method to fit the broad-band flux-calibrated medium resolution spectrum. The correlation between the accretion luminosity to the stellar luminosity, and of the mass accretion rate to the stellar mass in the logarithmic plane yields slopes of 1.9 and 2.3, respectively. These slopes and the accretion rates are consistent with previous results in various star forming regions and with different theoretical frameworks. However, we find that a broken power-law fit, with a steeper slope for stellar luminosity smaller than ~0.45 Lsun and for stellar masses smaller than ~ 0.3 Msun, is slightly preferred according to different statistical tests, but the single power-law model is not excluded. The steeper relation for lower mass stars can be interpreted as a faster evolution in the past for accretion in disks around these objects, or as different accretion regimes in different stellar mass ranges. Finally, we find two regions on the mass accretion versus stellar mass plane empty of objects. One at high mass accretion rates and low stellar masses, which is related to the steeper dependence of the two parameters we derived. The second one is just above the observational limits imposed by chromospheric emission. This empty region is located at M~0.3-0.4Msun, typical masses where photoevaporation is known to be effective, and at mass accretion rates ~10^-10 Msun/yr, a value compatible with the one expected for photoevaporation to rapidly dissipate the inner disk.

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Origin of warm and hot gas emission from low-mass protostars: Herschel-HIFI observations of CO J=16-15. I. Line profiles, physical conditions, and H2O abundance

(Abridged) Through spectrally unresolved observations of high-J CO transitions, Herschel-PACS has revealed large reservoirs of warm (300 K) and hot (700 K) molecular gas around low-mass protostars. We aim to shed light on the excitation and origin of the CO ladder observed toward protostars, and on the water abundance in different physical components using spectrally resolved Herschel-HIFI data. Observations are presented of the highly excited CO line J=16-15 with Herschel-HIFI toward 24 low-mass protostellar objects. The spectrally resolved profiles show two distinct velocity components: a broad component with an average FWHM of 20 km/s, and a narrower component with a FWHM of 5 km/s that is often offset from the source velocity. The average rotational temperature over the entire profile, as measured from comparison between CO J=16-15 and 10-9 emission, is ~300 K. A radiative-transfer analysis shows that the average H2O/CO column-density ratio is ~0.02, suggesting a total H2O abundance of ~2x10^-6. Two distinct velocity profiles observed in the HIFI line profiles suggest that the CO ladder observed with PACS consists of two excitation components. The warm component (300 K) is associated with the broad HIFI component, and the hot component (700 K) is associated with the offset HIFI component. The former originates in either outflow cavity shocks or the disk wind, and the latter in irradiated shocks. The ubiquity of the warm and hot CO components suggests that fundamental mechanisms govern the excitation of these components; we hypothesize that the warm component arises when H2 stops being the dominant coolant. In this scenario, the hot component arises in cooling molecular H2-poor gas just prior to the onset of H2 formation. High spectral resolution observations of highly excited CO transitions uniquely shed light on the origin of warm and hot gas in low-mass protostellar objects.

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Distribution of water in the G327.3-0.6 massive star-forming region

We aim at characterizing the large-scale distribution of H2O in G327.3-0.6, a massive star-forming region made of individual objects in different evolutionary phases. We investigate variations of H2O abundance as function of evolution. We present Herschel continuum maps at 89 and 179 $μ$m of the whole region and an APEX map at 350 μm of the IRDC. New spectral HIFI maps toward the IRDC region covering low-energy H2O lines at 987 and 1113 GHz are also presented and combined with HIFI pointed observations of the G327 hot core. We infer the physical properties of the gas through optical depth analysis and radiative transfer modeling. The continuum emission at 89 and 179 μm follows the thermal continuum emission at longer wavelengths, with a peak at the position of the hot core, a secondary peak in the Hii region, and an arch-like layer of hot gas west of the Hii region. The same morphology is observed in the 1113 GHz line, in absorption toward all dust condensations. Optical depths of ~80 and 15 are estimated and correspond to column densities of 10^15 and 2 10^14 cm-2, for the hot core and IRDC position. These values indicate an H2O to H2 ratio of 3 10^-8 toward the hot core; the abundance of H2O does not change along the IRDC with values of some 10^-8. Infall (over ~ 20") is detected toward the hot core position with a rate of 1-1.3 10^-2 M_sun /yr, high enough to overcome the radiation pressure due to the stellar luminosity. The source structure of the hot core region is complex, with a cold outer gas envelope in expansion, situated between the outflow and the observer, extending over 0.32 pc. The outflow is seen face-on and centered away from the hot core. The distribution of H2O along the IRDC is roughly constant with an abundance peak in the more evolved object. These water abundances are in agreement with previous studies in other massive objects and chemical models.

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Outflows, infall and evolution of a sample of embedded low-mass protostars. The William Herschel Line Legacy (WILL) survey

[Abridged] We present spectroscopic observations in H$_{2}$O, CO and related species with \textit{Herschel} HIFI and PACS, as well as ground-based follow-up with the JCMT and APEX in CO, HCO$^{+}$ and isotopologues, of a sample of 49 nearby ($d<$500\,pc) candidate protostars. These data are used to study the outflow and envelope properties of these sources. We also compile their continuum SEDs in order to constrain their physical properties. Water emission is dominated by shocks associated with the outflow, rather than the cooler, slower entrained outflowing gas probed by ground-based CO observations. These shocks become less energetic as sources evolve from Class 0 to Class I. The fraction of mass in the outflow relative to the total envelope (i.e. $M_{\mathrm{out}}/M_{\mathrm{env}}$) remains broadly constant between Class 0 and I. The median value ($\sim$1$\%$) is consistent with a core to star formation efficiency on the order of 50$\%$ and an outflow duty cycle on the order of 5$\%$. Entrainment efficiency, as probed by $F_{\mathrm{CO}}/\dot{M}_{\mathrm{acc}}$, is also invariant with source properties and evolutionary stage. The median value (6.3\kms{}) suggests an entrainment efficiency of between 30 and 60$\%$ if the wind is launched at $\sim$1AU. $L$[O\,{\sc i}] is strongly correlated with $L_{\mathrm{bol}}$ but not with $M_{\mathrm{env}}$, while low-$J$ CO is more closely correlated with the latter than the former. This suggests that [O\,{\sc i}] traces the present-day accretion activity while CO traces time-averaged accretion over the dynamical timescale of the outflow. $L$[O\,{\sc i}] does not vary from Class 0 to Class I, unlike CO and H$_{2}$O. This is likely due to the ratio of atomic to molecular gas in the wind increasing as the source evolves, balancing out the decrease in mass accretion rate. Infall signatures are detected in HCO$^{+}$ and H$_{2}$O in a few sources.

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