arXiv subjects

Dan M. Watson

Publications and source records attributed to Dan M. Watson.

At least 37 records · Page 2Linked to original sources

arXiv2022

The Rate, Amplitude and Duration of Outbursts from Class 0 Protostars in Orion

At least half of a protostar's mass is accreted in the Class 0 phase, when the central protostar is deeply embedded in a dense, infalling envelope. We present the first systematic search for outbursts from Class 0 protostars in the Orion clouds. Using photometry from Spitzer/IRAC spanning 2004 to 2017, we detect three outbursts from Class 0 protostars with $\ge 2$ mag changes at 3.6 or 4.5 $μ$m. This is comparable to the magnitude change of a known protostellar FU Ori outburst. Two are newly detected bursts from the protostars HOPS 12 and 124. The number of detections implies that Class 0 protostars burst every 438 yr, with a 95% confidence interval of 161 to 1884 yr. Combining Spitzer and WISE/NEOWISE data spanning 2004-2019, we show that the bursts persist for more than nine years with significant variability during each burst. Finally, we use $19-100$ $μ$m photometry from SOFIA, Spitzer and Herschel to measure the amplitudes of the bursts. Based on the burst interval, a duration of 15 yr, and the range of observed amplitudes, 3-100% of the mass accretion during the Class 0 phase occurs during bursts. In total, we show that bursts from Class 0 protostars are as frequent, or even more frequent, than those from more evolved protostars. This is consistent with bursts being driven by instabilities in disks triggered by rapid mass infall. Furthermore, we find that bursts may be a significant, if not dominant, mode of mass accretion during the Class 0 phase.

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arXiv2020

The Herschel Orion Protostar Survey: Far-Infrared Photometry and Colors of Protostars and Their Variations across Orion A and B

The degree to which the properties of protostars are affected by environment remains an open question. To investigate this, we look at the Orion A and B molecular clouds, home to most of the protostars within 500 pc. At ~400 pc, Orion is close enough to distinguish individual protostars across a range of environments in terms of both the stellar and gas projected densities. As part of the Herschel Orion Protostar Survey (HOPS), we used the Photodetector Array Camera and Spectrometer (PACS) to map 108 partially overlapping square fields with edge lengths of 5 arcmin or 8 arcmin and measure the 70 micron and 160 micron flux densities of 338 protostars within them. In this paper we examine how these flux densities and their ratio depend on evolutionary state and environment within the Orion complex. We show that Class 0 protostars occupy a region of the 70 micron flux density versus 160 micron to 70 micron flux density ratio diagram that is distinct from their more evolved counterparts. We then present evidence that the Integral-Shaped Filament (ISF) and Orion B contain protostars with more massive envelopes than those in the more sparsely populated LDN 1641 region. This can be interpreted as evidence for increasing star formation rates in the ISF and Orion B or as a tendency for more massive envelopes to be inherited from denser birth environments. We also provide technical details about the map-making and photometric procedures used in the HOPS program.

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arXiv2020

The VLA/ALMA Nascent Disk and Multiplicity (VANDAM) Survey of Orion Protostars. A Statistical Characterization of Class 0 and I Protostellar Disks

We have conducted a survey of 328 protostars in the Orion molecular clouds with ALMA at 0.87 mm at a resolution of $\sim$0.1" (40 au), including observations with the VLA at 9 mm toward 148 protostars at a resolution of $\sim$0.08" (32 au). This is the largest multi-wavelength survey of protostars at this resolution by an order of magnitude. We use the dust continuum emission at 0.87 mm and 9 mm to measure the dust disk radii and masses toward the Class 0, Class I, and Flat Spectrum protostars, characterizing the evolution of these disk properties in the protostellar phase. The mean dust disk radii for the Class 0, Class I, and Flat Spectrum protostars are 44.9$^{+5.8}_{-3.4}$, 37.0$^{+4.9}_{-3.0}$, and 28.5$^{+3.7}_{-2.3}$ au, respectively, and the mean protostellar dust disk masses are 25.9$^{+7.7}_{-4.0}$, 14.9$^{+3.8}_{-2.2}$, 11.6$^{+3.5}_{-1.9}$ Earth masses, respectively. The decrease in dust disk masses is expected from disk evolution and accretion, but the decrease in disk radii may point to the initial conditions of star formation not leading to the systematic growth of disk radii or that radial drift is keeping the dust disk sizes small. At least 146 protostellar disks (35% out of 379 detected 0.87 mm continuum sources plus 42 non-detections) have disk radii greater than 50 au in our sample. These properties are not found to vary significantly between different regions within Orion. The protostellar dust disk mass distributions are systematically larger than that of Class II disks by a factor of $>$4, providing evidence that the cores of giant planets may need to at least begin their formation during the protostellar phase.

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arXiv2019

The VLA/ALMA Nascent Disk and Multiplicity (VANDAM) Survey of Orion Protostars I. Identifying and Characterizing the Protostellar Content of the OMC2-FIR4 and OMC2-FIR3 Regions

We present ALMA (0.87~mm) and VLA (9~mm) observations toward OMC2-FIR4 and OMC2-FIR3 within the Orion integral-shaped filament that are thought to be the nearest regions of intermediate mass star formation. We characterize the continuum sources within these regions on $\sim$40~AU (0\farcs1) scales and associated molecular line emission at a factor of $\sim$30 better resolution than previous observations at similar wavelengths. We identify six compact continuum sources within OMC2-FIR4, four in OMC2-FIR3, and one additional source just outside OMC2-FIR4. This continuum emission is tracing the inner envelope and/or disk emission on less than 100~AU scales. HOPS-108 is the only protostar in OMC2-FIR4 that exhibits emission from high-excitation transitions of complex organic molecules (e.g., methanol and other lines) coincident with the continuum emission. HOPS-370 in OMC2-FIR3 with L~$\sim$~360~\lsun, also exhibits emission from high-excitation methanol and other lines. The methanol emission toward these two protostars is indicative of temperatures high enough to thermally evaporate methanol from icy dust grains; overall these protostars have characteristics similar to hot corinos. We do not identify a clear outflow from HOPS-108 in \twco, but find evidence of interaction between the outflow/jet from HOPS-370 and the OMC2-FIR4 region. The multitude of observational constraints indicate that HOPS-108 is likely a low to intermediate-mass protostar in its main mass accretion phase and it is the most luminous protostar in OMC2-FIR4. The high resolution data presented here are essential for disentangling the embedded protostars from their surrounding dusty environments and characterizing them.

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arXiv2019

Variability in the Assembly of Protostellar Systems

Understanding the collapse of clouds and the formation of protoplanetary disks is essential to understanding the formation of stars and planets. Infall and accretion, the mass-aggregation processes that occur at envelope and disk scales, drive the dynamical evolution of protostars. While the observations of protostars at different stages constrain their evolutionary tracks, the impact of variability due to accretion bursts on dynamical and chemical evolution of the source is largely unknown. The lasting effects on protostellar envelopes and disks are tracked through multi-wavelength and time domain observational campaigns, requiring deep X-ray, infrared, and radio imaging and spectroscopy, at a sufficient level of spatial detail to distinguish contributions from the various substructures (i.e., envelope from disk from star from outflow). Protostellar models derived from these campaigns will illuminate the initial chemical state of protoplanetary disks during the epoch of giant planet formation. Insight from individual star formation in the Milky Way is also necessary to understand star formation rates in extragalactic sources. This cannot be achieved with ground-based observatories and is not covered by currently approved instrumentation. Requirements: High (v < 10 km/s for survey; v < 1 km/s for followup) spectral resolution capabilities with relatively rapid response times in the IR (3-500 um), X-ray (0.1-10 keV), and radio (cm) are critical to follow the course of accretion and outflow during an outburst. Complementary, AU-scale radio observations are needed to probe the disk accretion zone, and 10 AU-scale to probe chemical and kinematic structures of the disk-forming regions, and track changes in the dust, ice, and gas within protostellar envelopes.

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arXiv2017

The Herschel Orion Protostar Survey: Luminosity and Envelope Evolution

The Herschel Orion Protostar Survey obtained well-sampled 1.2 - 870 micron spectral energy distributions (SEDs) of over 300 protostars in the Orion molecular clouds, home to most of the young stellar objects (YSOs) in the nearest 500 pc. We plot the bolometric luminosities and temperatures for 330 Orion YSOs, 315 of which have bolometric temperatures characteristic of protostars. The histogram of bolometric temperature is roughly flat; 29% of the protostars are in Class 0. The median luminosity decreases by a factor of four with increasing bolometric temperature; consequently, the Class 0 protostars are systematically brighter than the Class I protostars, with a median luminosity of 2.3 L_sun as opposed to 0.87 L_sun. At a given bolometric temperature, the scatter in luminosities is three orders of magnitude. Using fits to the SEDs, we analyze how the luminosities corrected for inclination and foreground reddening relate to the mass in the inner 2500 AU of the best-fit model envelopes. The histogram of envelope mass is roughly flat, while the median corrected luminosity peaks at 15 L_sun for young envelopes and falls to 1.7 L_sun for late-stage protostars with remnant envelopes. The spread in luminosity at each envelope mass is three orders of magnitude. Envelope masses that decline exponentially with time explain the flat mass histogram and the decrease in luminosity, while the formation of a range of stellar masses explains the dispersion in luminosity.

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arXiv2017

Star Formation Under the Outflow: The Discovery of a Non-Thermal Jet from OMC-2 FIR 3 and its Relationship to the Deeply Embedded FIR 4 Protostar

We carried out multiwavelength (0.7-5 cm), multiepoch (1994-2015) Very Large Array (VLA) observations toward the region enclosing the bright far-IR sources FIR 3 (HOPS 370) and FIR 4 (HOPS 108) in OMC-2. We report the detection of 10 radio sources, seven of them identified as young stellar objects. We image a well-collimated radio jet with a thermal free-free core (VLA 11) associated with the Class I intermediate-mass protostar HOPS 370. The jet presents several knots (VLA 12N, 12C, 12S) of non-thermal radio emission (likely synchrotron from shock-accelerated relativistic electrons) at distances of ~7,500-12,500 au from the protostar, in a region where other shock tracers have been previously identified. These knots are moving away from the HOPS 370 protostar at ~ 100 km/s. The Class 0 protostar HOPS 108, which itself is detected as an independent, kinematically decoupled radio source, falls in the path of these non-thermal radio knots. These results favor the previously proposed scenario where the formation of HOPS 108 has been triggered by the impact of the HOPS 370 outflow with a dense clump. However, HOPS 108 presents a large proper motion velocity of ~ 30 km/s, similar to that of other runaway stars in Orion, whose origin would be puzzling within this scenario. Alternatively, an apparent proper motion could result because of changes in the position of the centroid of the source due to blending with nearby extended emission, variations in the source shape, and /or opacity effects.

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arXiv2016

Silicate Composition of the Interstellar Medium

The composition of silicate dust in the diffuse interstellar medium and in protoplanetary disks around young stars informs our understanding of the processing and evolution of the dust grains leading up to planet formation. Analysis of the well-known 9.7μm feature indicates that small amorphous silicate grains represent a significant fraction of interstellar dust and are also major components of protoplanetary disks. However, this feature is typically modelled assuming amorphous silicate dust of olivine and pyroxene stoichiometries. Here, we analyze interstellar dust with models of silicate dust that include non-stoichiometric amorphous silicate grains. Modelling the optical depth along lines of sight toward the extinguished objects Cyg OB2 No. 12 and ζ Ophiuchi, we find evidence for interstellar amorphous silicate dust with stoichiometry intermediate between olivine and pyroxene, which we simply refer to as "polivene." Finally, we compare these results to models of silicate emission from the Trapezium and protoplanetary disks in Taurus.

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arXiv2016

Characterizing the Youngest Herschel-detected Protostars II. Molecular Outflows from the Millimeter and the Far-infrared

We present CARMA CO (J=1-0) observations and Herschel PACS spectroscopy, characterizing the outflow properties toward extremely young and deeply embedded protostars in the Orion molecular clouds. The sample comprises a subset of the Orion protostars known as the PACS Bright Red Sources (PBRS) (Stutz et al. 2013). We observed 14 PBRS with CARMA and 8 of these 14 with Herschel, acquiring full spectral scans from 55 micron to 200 micron. Outflows are detected in CO (J=1-0) from 8 of 14 PBRS, with two additional tentative detections; outflows are also detected from the outbursting protostar HOPS 223 (V2775 Ori) and the Class I protostar HOPS 68. The outflows have a range of morphologies, some are spatially compact, <10000 AU in extent, while others extend beyond the primary beam. The outflow velocities and morphologies are consistent with being dominated by intermediate inclination angles (80 deg > i > 20 deg). This confirms the interpretation of the very red 24 micron to 70 micron colors of the PBRS as a signpost of high envelope densities, with only one (possibly two) cases of the red colors resulting from edge-on inclinations. We detect high-J (J_up > 13) CO lines and/or H_2O lines from 5 of 8 PBRS and only for those with detected CO outflows. The far-infrared CO rotation temperatures of the detected PBRS are marginally colder (~230 K) than those observed for most protostars (~300 K), and only one of these 5 PBRS has detected [OI] 63 micron emission. The high envelope densities could be obscuring some [OI] emission and cause a ~20 K reduction to the CO rotation temperatures.

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arXiv2016

The $Spitzer$ infrared spectrograph survey of protoplanetary disks in Orion A: I. disk properties

We present our investigation of 319 Class II objects in Orion A observed by $Spitzer$/IRS. We also present the follow-up observation of 120 of these Class II objects in Orion A from IRTF/SpeX. We measure continuum spectral indices, equivalent widths, and integrated fluxes that pertain to disk structure and dust composition from IRS spectra of Class II objects in Orion A. We estimate mass accretion rates using hydrogen recombination lines in the SpeX spectra of our targets. Utilizing these properties, we compare the distributions of the disk and dust properties of Orion A disks to those of Taurus disks with respect to position within Orion A (ONC and L1641) and to the sub-groups by the inferred radial structures, such as transitional disks vs. radially continuous full disks. Our main findings are as follows. (1) Inner disks evolve faster than the outer disks. (2) Mass accretion rate of transitional disks and that of radially continuous full disks are statistically significantly displaced from each other. The median mass accretion rate of radially continuous disks in ONC and L1641 is not very different from that in Taurus. (3) Less grain processing has occurred in the disks in ONC compared to those in Taurus, based on analysis of the shape index of the 10 $μ$m silicate feature ($F_{11.3}/F_{9.8}$). (4) The 20-31 $μ$m continuum spectral index tracks the projected distance from the most luminous Trapezium star, $θ^{1}$ Ori C. A possible explanation is the effect of UV ablation of the outer part of the disks.

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arXiv2015

Evolution of Mass Outflow in Protostars

We have surveyed 84 Class 0, Class I, and flat-spectrum protostars in mid-infrared [Si II], [Fe II] and [S I] line emission, and 11 of these in far-infrared [O I] emission. We use the results to derive their mass outflow rates. Thereby we observe a strong correlation of mass outflow rates with bolometric luminosity, and with the inferred mass accretion rates of the central objects, which continues through the Class 0 range the trend observed in Class II young stellar objects. Along this trend from large to small mass-flow rates, the different classes of young stellar objects lie in the sequence Class 0 -- Class I/flat-spectrum -- Class II, indicating that the trend is an evolutionary sequence in which mass outflow and accretion rates decrease together with increasing age, while maintaining rough proportionality. The survey results include two which are key tests of magnetocentrifugal outflow-acceleration mechanisms: the distribution of the outflow/accretion branching ratio b, and limits on the distribution of outflow speeds. Neither rule out any of the three leading outflow-acceleration, angular-momentum-ejection mechanisms, but they provide some evidence that disk winds and accretion-powered stellar winds (APSWs) operate in many protostars. An upper edge observed in the branching-ratio distribution is consistent with the upper bound of b = 0.6 found in models of APSWs, and a large fraction (0.31) of the sample have branching ratio sufficiently small that only disk winds, launched on scales as large as several AU, have been demonstrated to account for them.

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arXiv2015

HOPS 383: An Outbursting Class 0 Protostar in Orion

We report the dramatic mid-infrared brightening between 2004 and 2006 of HOPS 383, a deeply embedded protostar adjacent to NGC 1977 in Orion. By 2008, the source became a factor of 35 brighter at 24 microns with a brightness increase also apparent at 4.5 microns. The outburst is also detected in the submillimeter by comparing APEX/SABOCA to SCUBA data, and a scattered-light nebula appeared in NEWFIRM K_s imaging. The post-outburst spectral energy distribution indicates a Class 0 source with a dense envelope and a luminosity between 6 and 14 L_sun. Post-outburst time-series mid- and far-infrared photometry shows no long-term fading and variability at the 18% level between 2009 and 2012. HOPS 383 is the first outbursting Class 0 object discovered, pointing to the importance of episodic accretion at early stages in the star formation process. Its dramatic rise and lack of fading over a six-year period hint that it may be similar to FU Ori outbursts, although the luminosity appears to be significantly smaller than the canonical luminosities of such objects.

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arXiv2014

Emission from Water Vapor and Absorption from Other Gases at 5-7.5 Microns in Spitzer-IRS Spectra of Protoplanetary Disks

We present spectra of 13 T Tauri stars in the Taurus-Auriga star-forming region showing emission in Spitzer Space Telescope Infrared Spectrograph (IRS) 5-7.5 micron spectra from water vapor and absorption from other gases in these stars' protoplanetary disks. Seven stars' spectra show an emission feature at 6.6 microns due to the nu_2 = 1-0 bending mode of water vapor, with the shape of the spectrum suggesting water vapor temperatures > 500 K, though some of these spectra also show indications of an absorption band, likely from another molecule. This water vapor emission contrasts with the absorption from warm water vapor seen in the spectrum of the FU Orionis star V1057 Cyg. The other six of the thirteen stars have spectra showing a strong absorption band, peaking in strength at 5.6-5.7 microns, which for some is consistent with gaseous formaldehyde (H2CO) and for others is consistent with gaseous formic acid (HCOOH). There are indications that some of these six stars may also have weak water vapor emission. Modeling of these stars' spectra suggests these gases are present in the inner few AU of their host disks, consistent with recent studies of infrared spectra showing gas in protoplanetary disks.

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arXiv2013

HOPS 136: An Edge-On Orion Protostar Near the End of Envelope Infall

Edge-on protostars are valuable for understanding the disk and envelope properties of embedded young stellar objects, since the disk, envelope, and envelope cavities are all distinctly visible in resolved images and well constrained in modeling. Comparing 2MASS, WISE, Spitzer, Herschel, APEX, and IRAM photometry and limits from 1.25 to 1200 microns, Spitzer spectroscopy from 5 to 40 microns, and high-resolution Hubble imaging at 1.60 and 2.05 microns to radiative transfer modeling, we determine envelope and disk properties for the Class I protostar HOPS 136, an edge-on source in Orion's Lynds 1641 region. The source has a bolometric luminosity of 0.8 L_sun, a bolometric temperature of 170 K, and a ratio of submillimeter to bolometric luminosity of 0.8%. Via modeling, we find a total luminosity of 4.7 L_sun (larger than the observed luminosity due to extinction by the disk), an envelope mass of 0.06 M_sun, and a disk radius and mass of 450 AU and 0.002 M_sun. The stellar mass is highly uncertain but is estimated to fall between 0.4 and 0.5 M_sun. To reproduce the flux and wavelength of the near-infrared scattered-light peak in the spectral energy distribution, we require 5.4 x 10^-5 M_sun of gas and dust in each cavity. The disk has a large radius and a mass typical of more evolved T Tauri stars in spite of the significant remaining envelope. HOPS 136 appears to be a key link between the protostellar and optically revealed stages of star formation.

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arXiv2013

Transitional disks and their origins: an infrared spectroscopic survey of Orion A

Transitional disks are protoplanetary disks around young stars, with inner holes or gaps which are surrounded by optically thick outer, and often inner, disks. Here we present observations of 62 new transitional disks in the Orion A star-forming region. These were identified using the \textit{Spitzer Space Telescope}'s Infrared Spectrograph and followed up with determinations of stellar and accretion parameters using the Infrared Telescope Facility's SpeX. We combine these new observations with our previous results on transitional disks in Taurus, Chamaeleon I, Ophiuchus and Perseus, and with archival X-ray observations. This produces a sample of 105 transitional disks of "cluster" age 3 Myr or less, by far the largest hitherto assembled. We use this sample to search for trends between the radial structure in the disks and many other system properties, in order to place constraints on the possible origins of transitional disks. We see a clear progression of host star accretion rate and the different disk morphologies. We confirm that transitional disks with complete central clearings have median accretion rates an order of magnitude smaller than radially continuous disks of the same population. Pre-transitional disks --- those objects with gaps that separate inner and outer disks --- have median accretion rates intermediate between the two. Our results from the search for statistically significant trends, especially related to $\dot{M}$, strongly support that in both cases the gaps are far more likely to be due to the gravitational influence of Jovian planets or brown dwarfs orbiting within the gaps, than to any of the photoevaporative, turbulent or grain-growth processes that can lead to disk dissipation. We also find that the fraction of Class II YSOs which are transitional disks is large, 0.1-0.2, especially in the youngest associations.

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arXiv2013

Anomalous CO2 Ice Toward HOPS-68: A Tracer of Protostellar Feedback

We report the detection of a unique CO2 ice band toward the deeply embedded, low-mass protostar HOPS-68. Our spectrum, obtained with the Infrared Spectrograph onboard the Spitzer Space Telescope, reveals a 15.2 micron CO2 ice bending mode profile that cannot modeled with the same ice structure typically found toward other protostars. We develop a modified CO2 ice profile decomposition, including the addition of new high-quality laboratory spectra of pure, crystalline CO2 ice. Using this model, we find that 87-92% of the CO2 is sequestered as spherical, CO2-rich mantles, while typical interstellar ices show evidence of irregularly-shaped, hydrogen-rich mantles. We propose that (1) the nearly complete absence of unprocessed ices along the line-of-sight is due to the flattened envelope structure of HOPS-68, which lacks cold absorbing material in its outer envelope, and possesses an extreme concentration of material within its inner (10 AU) envelope region and (2) an energetic event led to the evaporation of inner envelope ices, followed by cooling and re-condensation, explaining the sequestration of spherical, CO2 ice mantles in a hydrogen-poor mixture. The mechanism responsible for the sublimation could be either a transient accretion event or shocks in the interaction region between the protostellar outflow and envelope. The proposed scenario is consistent with the rarity of the observed CO2 ice profile, the formation of nearly pure CO2 ice, and the production of spherical ice mantles. HOPS-68 may therefore provide a unique window into the protostellar feedback process, as outflows and heating shape the physical and chemical structure of protostellar envelopes and molecular clouds.

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arXiv2012

A Spitzer IRS Survey of NGC 1333: Insights into disk evolution from a very young cluster

We report on the λ = 5-36μm Spitzer Infrared Spectrograph spectra of 79 young stellar objects in the very young nearby cluster NGC 1333. NGC 1333's youth enables the study of early protoplanetary disk properties, such as the degree of settling as well as the formation of gaps and clearings. We construct spectral energy distributions (SEDs) using our IRS data as well as published photometry and classify our sample into SED classes. Using "extinction-free" spectral indices, we determine whether the disk, envelope, or photosphere dominates the spectrum. We analyze the dereddened spectra of objects which show disk dominated emission using spectral indices and properties of silicate features in order to study the vertical and radial structure of protoplanetary disks in NGC 1333. At least nine objects in our sample of NGC 1333 show signs of large (several AU) radial gaps or clearings in their inner disk. Disks with radial gaps in NGC 1333 show more-nearly pristine silicate dust than their radially continuous counterparts. We compare properties of disks in NGC 1333 to those in three other well studied regions, Taurus-Auriga, Ophiuchus and Chamaeleon I, and find no difference in their degree of sedimentation and dust processing.

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arXiv2011

A Spitzer-IRS Detection of Crystalline Silicates in a Protostellar Envelope

We present the Spitzer Space Telescope Infrared Spectrograph spectrum of the Orion A protostar HOPS-68. The mid-infrared spectrum reveals crystalline substructure at 11.1, 16.1, 18.8, 23.6, 27.9, and 33.6 microns superimposed on the broad 9.7 and 18 micron amorphous silicate features; the substructure is well matched by the presence of the olivine end-member forsterite. Crystalline silicates are often observed as infrared emission features around the circumstellar disks of Herbig Ae/Be stars and T Tauri stars. However, this is the first unambiguous detection of crystalline silicate absorption in a cold, infalling, protostellar envelope. We estimate the crystalline mass fraction along the line-of-sight by first assuming that the crystalline silicates are located in a cold absorbing screen and secondly by utilizing radiative transfer models. The resulting crystalline mass fractions of 0.14 and 0.17, respectively, are significantly greater than the upper limit found in the interstellar medium (< 0.02-0.05). We propose that the amorphous silicates were annealed within the hot inner disk and/or envelope regions and subsequently transported outward into the envelope by entrainment in a protostellar outflow

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