arXiv subjects

U. Gorti

Publications and source records attributed to U. Gorti.

At least 19 recordsLinked to original sources

arXiv2025

Edge-On Disk Study (EODS) II: HCO$^+$ and CO vertical stratification in the disk surrounding SSTTau042021

Context. Edge-on disks offer a unique opportunity to directly examine their vertical structure, providing valuable insights into planet formation processes. We investigate the dust properties, as well as the CO and HCO$^+$ gas properties, in the edge-on disk surrounding the T Tauri star 2MASS J04202144+281349 (SSTTau042021). Aims. We estimate the radial and vertical temperature and density profile for the gas and the dust. Methods. We use ALMA archival data of CO isotopologues and continuum emission at 2, 1.3 and 0.9 mm together with new NOEMA HCO$^+$ 3-2 observations. We retrieve the gas and dust disk properties using the tomographic method and the \textsc{DiskFit} model. Results. The vertical CO emission appears very extended, partly tracing the H$_2$ wind observed by JWST. C$^{18}$O, $^{13}$CO and HCO$^+$ emission characterize the bulk of the molecular layer. The dust and gas have a mid-plane temperatures of $\sim 7-11$ K. The temperature of the molecular layer (derived from $^{13}$CO and HCO$^+$) is on the order of 16 K. HCO$^+$ 3-2 being thermalized, we derive a lower limit for the H$_2$ volume density of $\sim 3 \times 10^6$ cm$^{-3}$ at radius 100-200 au between 1 and 2 scale heights. The atmosphere temperature of the CO gas is of the order $\sim$ 31 K at a radius of 100 au. We directly observe CO and HCO$^+$ gas onto the mid-plane beyond the dust outer radius ($\ge 300$ au). The (gas+dust) disk mass estimated up to a radius of 300 au is on the order of $4.6 \times 10^{-2} \mathrm{M}_\odot$. Conclusions. Thanks to the favorable disk inclination, we present the first quantitative evidence for vertical molecular stratification with direct observation of CO and HCO$^+$ gas along the mid-plane. We estimate the temperature profile with temperature of 7-11 K near the mid-plane, and 15-20 K in the dense part of the molecular layer up to $\sim$ 35 K above.

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arXiv2025

Edge-On Disk Study (EODS) III: Molecular Stratification in the Flying Saucer Disk

Context: Investigating the vertical distribution of molecular content in protoplanetary disks remains difficult in most disks mildly inclined along the line of sight. In contrast, edge-on disks provide a direct (tomographic) view of the 2D molecular brightness. Aims: We study the radial and vertical molecular distribution as well as the gas temperature and density by observing the Keplerian edge-on disk surrounding the Flying Saucer, a Class II object located in Ophiuchus. Methods: We use new and archival ALMA data to perform a tomography of $^{12}$CO, $^{13}$CO, C$^{18}$O, CN, HCN, CS, H$_2$CO, c-C$_3$H$_2$, N$_2$D$^+$, DCN and $^{13}$CS. We analyze molecular tomographies and model data using the radiative transfer code DiskFit. Results: We directly measure the altitude above the mid-plane for each observed species. For the first time, we unambiguously demonstrate the presence of a common molecular layer and measure its thickness: most molecules are located at the same altitude versus radius. Beyond CO, as predicted by chemical models, the CN emission traces the upper boundary of the molecular layer, whereas the deuterated species (DCN and N2D+) resides below one scale-height. Our best fits from DiskFit show that most observed transitions in the molecular layer are thermalized because their excitation temperature is the same, around 17-20 K. Conclusions: These long-integration observations clearly reveal a molecular layer predominantly located around 1-2 scale height, at a temperature above the CO freeze-out temperature. The deuterated molecules are closer to the mid-plane and N2D+ may be a good proxy for the CO snowline. Some molecules, such as CN and H2CO, are likely influenced by the disk environment, at least beyond the mm dust disk radius. The direct observation of the molecular stratification opens the door to detailed chemical modeling in this disk which appears representative of T Tauri disks.

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arXiv2025

Edge-On Disk Study (EODS) II: Thermal Structure of the Flying Saucer Disk

Context. The dust and gas temperature in proto-planetary disks play critical roles in determining their chemical evolution and influencing planet formation processes. Aims. We attempted an accurate measurement of the dust and CO temperature profile in the edge-on disk of the Flying Saucer. Methods. We used the unique properties of the Flying Saucer, its edge-on geometry and its fortunate position in front of CO clouds with different brightness temperatures to provide independent constraints on the dust temperature. We compared it with the dust temperature derived using the radiative transfer code DiskFit and the CO gas temperature. Results. We find clear evidence for a substantial gas temperature vertical gradient, with a cold (10 K) disk mid-plane and a warmer CO layer where T(r) is 27 K at 100 au, dropping with exponent 0.3. Direct evidence for CO depletion in the mid-plane, below about 1 scale height, is also found. At this height, the gas temperature is 15-20 K, consistent with the expected CO freeze out temperature. The dust disk appears optically thin at 345 GHz, and exhibits moderate settling.

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arXiv2024

PRODIGE -- Planet-forming disks in Taurus with NOEMA

We aim to constrain the gas density and temperature distributions as well as gas masses in several T Tauri protoplanetary disks located in Taurus. We use the 12CO, 13CO, and C18O (2-1) isotopologue emission observed at 0.9 with the IRAM NOrthern Extended Millimeter Array (NOEMA) as part of the MPG-IRAM Observatory Program PRODIGE (PROtostars and DIsks: Global Evolution PIs: P. Caselli & Th. Henning). Our sample consists of Class II disks with no evidence of strong radial substructures. We use thesedata to constrain the thermal and chemical structure of these disks through theoretical models for gas emission. To fit the combined optically thick and thin CO line data in Fourier space, we developed the DiskCheF code, which includes the parameterized disk physical structure, machine-learning (ML) accelerated chemistry, and the RADMC-3D line radiative transfer module. A key novelty of DiskCheF is the fast and feasible ML-based chemistry trained on the extended grid of the disk physical-chemical models precomputed with the ANDES2 code. This ML approach allows complex chemical kinetics models to be included in a time-consuming disk fitting without the need to run a chemical code. We present a novel approach to incorporate chemistry into disk modeling without the need to explicitly calculate a chemical network every time. Using this new disk modeling tool, we successfully fit the 12CO, 13CO, and C18O (2-1) data from the CI, CY, DL, DM, DN, and IQ Tau disks. The combination of optically thin and optically thick CO lines allows us to simultaneously constrain the disk temperature and mass distribution, and derive the CO-based gas masses. These values are in reasonable agreement with the disk dust masses rescaled by a factor of 100 as well as with other indirect gas measurements.

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arXiv2021

Evidence for an MHD disk wind via optical forbidden line spectro-astrometry

Spectro-astrometry is used to investigate the low velocity component (LVC) of the optical forbidden emission from the T Tauri stars RU Lupi and AS 205 N. Both stars also have high velocity forbidden emission (HVC) which is tracing a jet. For AS 205 N, analysis reveals a complicated outflow system. For RU Lupi, the [O I] 6300 and [S II] 6716, 6731 LV narrow component (NC) is offset along the same position angle (PA) as the HVC but with a different velocity gradient than the jet, in that displacement from the stellar position along the rotation axis is decreasing with increasing velocity. From the LVC NC PA and velocity gradient, it is inferred that the NC is tracing a wide angled MHD disk wind. A photoevaporative wind is ruled out. This is supported by a comparison with a previous spectro-astrometric study of the CO fundamental line. The decrease in offset with increasing velocity is interpreted as tracing an increase in the height of the wind with increasing disk radius. This is one of the first measurements of the spatial extent of the forbidden emission line LVC NC (~ 40 au, 8 au for RU~Lupi in the [S II] 6731 and [O I] 6300 lines) and the first direct confirmation that the LVC narrow component can trace an MHD disk wind.

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arXiv2020

The Evolution of Disk Winds from a Combined Study of Optical and Infrared Forbidden Lines

We analyze high-resolution (dv=<10km/s) optical and infrared spectra covering the [OI] 6300 angstrom and [NeII] 12.81 micron lines from a sample of 31 disks in different evolutionary stages. Following work at optical wavelengths, we use Gaussian profiles to fit the [NeII] lines and classify them into HVC (LVC) if the line centroid is more (less) blueshifted than 30 km/s with respect to the stellar radial velocity. Unlike for the [OI] where a HVC is often accompanied by a LVC, all 17 sources with a [NeII] detection have either a HVC or a LVC. [NeII] HVCs are preferentially detected toward high accretors (Macc > 10$^{-8}$ Msun/yr) while LVCs are found in sources with low Macc, low [OI] luminosity, and large infrared spectral index (n13-31). Interestingly, the [NeII] and [OI] LVC luminosities display an opposite behaviour with n13-31: as the inner dust disk depletes (higher n13-31) the [NeII] luminosity increases while the [OI] weakens. The [NeII] and [OI] HVC profiles are generally similar with centroids and FWHMs showing the expected behaviour from shocked gas in micro-jets. In contrast, the [NeII] LVC profiles are typically more blueshifted and narrower than the [OI] profiles. The FWHM and centroid vs. disk inclination suggest that the [NeII] LVC predominantly traces unbound gas from a slow, wide-angle wind that has not lost completely the Keplerian signature from its launching region. We sketch an evolutionary scenario that could explain the combined [OI] and [NeII] results and includes screening of hard (~1keV) X-rays in inner, mostly molecular, MHD winds.

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arXiv2018

A Subarcsecond ALMA Molecular Line Imaging Survey of the Circumbinary, Protoplanetary Disk Orbiting V4046 Sgr

We present a suite of ALMA interferometric molecular line and continuum images that elucidate, on linear size scales of $\sim$30--40 AU, the chemical structure of the nearby, evolved, protoplanetary disk orbiting the close binary system V4046 Sgr. The observations were undertaken in the 1.1--1.4 mm wavelength range (ALMA Bands 6 and 7) with antenna configurations involving maximum baselines of several hundred meters, yielding subarcsecond-resolution images in more than a dozen molecular species and isotopologues. Isotopologues of CO and HCN display centrally peaked morphologies of integrated emission line intensity, whereas the line emission from complex nitrile group molecules (HC$_3$N, CH$_3$CN), deuterated molecules (DCN, DCO$^+$), hydrocarbons (as traced by C$_2$H), and potential CO ice line tracers (N$_2$H$^+$, and H$_2$CO) appears as a sequence of sharp and diffuse rings. The dimensions and morphologies of HC$_3$N and CH$_3$CN emission are suggestive of photodesorption of organic ices from the surfaces of dust grains, while the sequence of increasing radius of peak intensity represented by DCN (smallest), DCO$^+$, N$_2$H$^+$, and H$_2$CO (largest) is qualitatively consistent with the expected decline of midplane gas temperature with increasing disk radius. Empirical modeling indicates that the sharp-edged C$_2$H emission ring lies at relatively deep disk layers, leaving open the question of the origin of C$_2$H abundance enhancements in evolved disks. This study of the "molecular anatomy" of V4046 Sgr should serve as motivation for additional subarcsecond ALMA molecular line imaging surveys of nearby, evolved protoplanetary disks aimed at addressing major uncertainties in protoplanetary disk physical and chemical structure and molecular production pathways.

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arXiv2017

The Flying Saucer: Tomography of the thermal and density gas structure of an edge-on protoplanetary disk

Determining the gas density and temperature structures of protoplanetary disks is a fundamental task to constrain planet formation theories. This is a challenging procedure and most determinations are based on model-dependent assumptions. We attempt a direct determination of the radial and vertical temperature structure of the Flying Saucer disk, thanks to its favorable inclination of 90 degrees. We present a method based on the tomographic study of an edge-on disk. Using ALMA, we observe at 0.5$"$ resolution the Flying Saucer in CO J=2-1 and CS J=5-4. This edge-on disk appears in silhouette against the CO J=2-1 emission from background molecular clouds in $ρ$ Oph. The combination of velocity gradients due to the Keplerian rotation of the disk and intensity variations in the CO background as a function of velocity provide a direct measure of the gas temperature as a function of radius and height above the disk mid-plane. The overall thermal structure is consistent with model predictions, with a cold ($< 15-12 $~K), CO-depleted mid-plane, and a warmer disk atmosphere. However, we find evidence for CO gas along the mid-plane beyond a radius of about 200\,au, coincident with a change of grain properties. Such a behavior is expected in case of efficient rise of UV penetration re-heating the disk and thus allowing CO thermal desorption or favoring direct CO photo-desorption. CO is also detected up to 3-4 scale heights while CS is confined around 1 scale height above the mid-plane. The limits of the method due to finite spatial and spectral resolutions are also discussed. This method appears to be very promising to determine the gas structure of planet-forming disks, provided that the molecular data have an angular resolution which is high enough, of the order of $0.3 - 0.1"$ at the distance of the nearest star forming regions.

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arXiv2016

Tracing Slow Winds from T Tauri Stars via Low Velocity Forbidden Line Emission

Using Keck/HIRES spectra Δv ~ 7 km/s, we analyze forbidden lines of [O I] 6300 Å, [O I] 5577 Å and [S II] 6731 Å from 33 T Tauri stars covering a range of disk evolutionary stages. After removing a high velocity component (HVC) associated with microjets, we study the properties of the low velocity component (LVC). The LVC can be attributed to slow disk winds that could be magnetically (MHD) or thermally (photoevaporative) driven. Both of these winds play an important role in the evolution and dispersal of protoplanetary material. LVC emission is seen in all 30 stars with detected [O I] but only in 2 out of eight with detected [S II] , so our analysis is largely based on the properties of the [O I] LVC. The LVC itself is resolved into broad (BC) and narrow (NC) kinematic components. Both components are found over a wide range of accretion rates and their luminosity is correlated with the accretion luminosity, but the NC is proportionately stronger than the BC in transition disks. The FWHM of both the BC and NC correlates with disk inclination, consistent with Keplerian broadening from radii of 0.05 to 0.5 AU and 0.5 to 5 AU, respectively. The velocity centroids of the BC suggest formation in an MHD disk wind, with the largest blueshifts found in sources with closer to face-on orientations. The velocity centroids of the NC however, show no dependence on disk inclination. The origin of this component is less clear and the evidence for photoevaporation is not conclusive.

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arXiv2015

Disk Dispersal: Theoretical Understanding and Observational Constraints

Protoplanetary disks dissipate rapidly after the central star forms, on time-scales comparable to those inferred for planet formation. In order to allow the formation of planets, disks must survive the dispersive effects of UV and X-ray photoevaporation for at least a few Myr. Viscous accretion depletes significant amounts of the mass in gas and solids, while photoevaporative flows driven by internal and external irradiation remove most of the gas. A reasonably large fraction of the mass in solids and some gas get incorporated into planets. Here, we review our current understanding of disk evolution and dispersal, and discuss how these might affect planet formation. We also discuss existing observational constraints on dispersal mechanisms and future directions.

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arXiv2015

Narrow Na and K Absorption Lines Toward T Tauri Stars - Tracing the Atomic Envelope of Molecular Clouds

We present a detailed analysis of narrow of NaI and KI absorption resonance lines toward nearly 40 T Tauri stars in Taurus with the goal of clarifying their origin. The NaI 5889.95 angstrom line is detected toward all but one source, while the weaker KI 7698.96 angstrom line in about two thirds of the sample. The similarity in their peak centroids and the significant positive correlation between their equivalent widths demonstrate that these transitions trace the same atomic gas. The absorption lines are present towards both disk and diskless young stellar objects, which excludes cold gas within the circumstellar disk as the absorbing material. A comparison of NaI and CO detections and peak centroids demonstrates that the atomic and molecular gas are not co-located, the atomic gas is more extended than the molecular gas. The width of the atomic lines corroborates this finding and points to atomic gas about an order of magnitude warmer than the molecular gas. The distribution of NaI radial velocities shows a clear spatial gradient along the length of the Taurus molecular cloud filaments. This suggests that absorption is associated with the Taurus molecular cloud. Assuming the gradient is due to cloud rotation, the rotation of the atomic gas is consistent with differential galactic rotation while the rotation of the molecular gas, although with the same rotation axis, is retrograde. Our analysis shows that narrow NaI and KI absorption resonance lines are useful tracers of the atomic envelope of molecular clouds. In line with recent findings from giant molecular clouds, our results demonstrate that the velocity fields of the atomic and molecular gas are misaligned. The angular momentum of a molecular cloud is not simply inherited from the rotating Galactic disk from which it formed but may be redistributed by cloud-cloud interactions.

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arXiv2015

Rings of C2H in the Molecular Disks Orbiting TW Hya and V4046 Sgr

We have used the Submillimeter Array to image, at ~1" resolution, C2H(3-2) emission from the molecule-rich circumstellar disks orbiting the nearby, classical T Tauri star systems TW Hya and V4046 Sgr. The SMA imaging reveals that the C2H emission exhibits a ring-like morphology within each disk, the inner hole radius of the C2H ring within the V4046 Sgr disk (~70 AU) is somewhat larger than than of its counterpart within the TW Hya disk (~45 AU). We suggest that, in each case, the C2H emission likely traces irradiation of the tenuous surface layers of the outer disks by high-energy photons from the central stars.

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arXiv2015

Probing stellar accretion with mid-infrared hydrogen lines

In this paper we investigate the origin of the mid-infrared (IR) hydrogen recombination lines for a sample of 114 disks in different evolutionary stages (full, transitional and debris disks) collected from the {\it Spitzer} archive. We focus on the two brighter {H~{\sc i}} lines observed in the {\it Spitzer} spectra, the {H~{\sc i}}(7-6) at 12.37$μ$m and the {H~{\sc i}}(9-7) at 11.32$μ$m. We detect the {H~{\sc i}}(7-6) line in 46 objects, and the {H~{\sc i}}(9-7) in 11. We compare these lines with the other most common gas line detected in {\it Spitzer} spectra, the {[Ne~{\sc iii}]} at 12.81$μ$m. We argue that it is unlikely that the {H~{\sc i}} emission originates from the photoevaporating upper surface layers of the disk, as has been found for the {[Ne~{\sc iii}]} lines toward low-accreting stars. Using the {H~{\sc i}}(9-7)/{H~{\sc i}}(7-6) line ratios we find these gas lines are likely probing gas with hydrogen column densities of 10$^{10}$-10$^{11}$~cm$^{-3}$. The subsample of objects surrounded by full and transitional disks show a positive correlation between the accretion luminosity and the {H~{\sc i}} line luminosity. These two results suggest that the observed mid-IR {H~{\sc i}} lines trace gas accreting onto the star in the same way as other hydrogen recombination lines at shorter wavelengths. A pure chromospheric origin of these lines can be excluded for the vast majority of full and transitional disks.We report for the first time the detection of the {H~{\sc i}}(7-6) line in eight young (< 20~Myr) debris disks. A pure chromospheric origin cannot be ruled out in these objects. If the {H~{\sc i}}(7-6) line traces accretion in these older systems, as in the case of full and transitional disks, the strength of the emission implies accretion rates lower than 10$^{-10}$M$_{\odot}$/yr. We discuss some advantages of extending accretion indicators to longer wavelengths.

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arXiv2014

Low EUV Luminosities Impinging on Protoplanetary Disks

The amount of high-energy stellar radiation reaching the surface of protoplanetary disks is essential to determine their chemistry and physical evolution. Here, we use millimetric and centimetric radio data to constrain the EUV luminosity impinging on 14 disks around young (~2-10Myr) sun-like stars. For each object we identify the long-wavelength emission in excess to the dust thermal emission, attribute that to free-free disk emission, and thereby compute an upper limit to the EUV reaching the disk. We find upper limits lower than 10$^{42}$ photons/s for all sources without jets and lower than $5 \times 10^{40}$ photons/s for the three older sources in our sample. These latter values are low for EUV-driven photoevaporation alone to clear out protoplanetary material in the timescale inferred by observations. In addition, our EUV upper limits are too low to reproduce the [NeII] 12.81 micron luminosities from three disks with slow [NeII]-detected winds. This indicates that the [NeII] line in these sources primarily traces a mostly neutral wind where Ne is ionized by 1 keV X-ray photons, implying higher photoevaporative mass loss rates than those predicted by EUV-driven models alone. In summary, our results suggest that high-energy stellar photons other than EUV may dominate the dispersal of protoplanetary disks around sun-like stars.

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arXiv2012

Free-free Emission and Radio Recombination Lines from Photoevaporating Disks

Recent infrared observations have demonstrated that photoevaporation driven by high-energy photons from the central star contributes to the dispersal of protoplanetary disks. Here, we show that photoevaporative winds should produce a detectable free-free continuum emission given the range of stellar ionizing photons and X-ray luminosities inferred for young sun-like stars. We point out that VLA observations of the nearby disk around TWHya might have already detected this emission at centimeter wavelengths and calculate the wind electron density and mass flow rate. We also estimate the intensities of H radio recombination lines tracing the wind and discuss which ones could be detected with current instrumentation. The detection and profiles of these recombination lines would unambiguously prove our inference of free-free emission from photoevaporating disks like TWHya. In addition, radio/millimeter data can help constraining wind parameters such as temperature and electron density that are fundamental in measuring mass flow rates.

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arXiv2011

The Photoevaporative Wind from the Disk of TW Hya

Photoevaporation driven by the central star is expected to be a ubiquitous and important mechanism to disperse the circumstellar dust and gas from which planets form. Here, we present a detailed study of the circumstellar disk surrounding the nearby star TW Hya and provide observational constraints to its photoevaporative wind. Our new high-resolution (R ~ 30,000) mid-infrared spectroscopy in the [Ne II] 12.81 μm line confirms that this gas diagnostic traces the unbound wind component within 10AU from the star. From the blueshift and asymmetry in the line profile, we estimate that most (>80%) of the [Ne II] emission arises from disk radii where the midplane is optically thick to the redshifted outflowing gas, meaning beyond the 1 or 4AU dust rim inferred from other observations. We re-analyze high-resolution (R ~ 48, 000) archival optical spectra searching for additional transitions that may trace the photoevaporative flow. Unlike the [Ne II] line, optical forbidden lines from OI, SII, and MgI are centered at the stellar velocity and have symmetric profiles. The only way these lines could trace the photoevaporative flow is if they arise from a disk region physically distinct from that traced by the [Ne II] line, specifically from within the optically thin dust gap. However, the small (~10 km/s) FWHM of these lines suggest that most of the emitting gas traced at optical wavelengths is bound to the system rather than unbound. We discuss the implications of our results for a planet-induced versus a photoevaporation-induced gap.

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arXiv2007

Detection of [Ne II] Emission from Young Circumstellar Disks

We report the detection of [Ne II] emission at 12.81 micron in four out of the six optically thick dust disks observed as part of the FEPS Spitzer Legacy program. In addition, we detect a H I(7-6) emission line at 12.37 micron from the source RXJ1852.3-3700. Detections of [Ne II] lines are favored by low mid-infrared excess emission. Both stellar X-rays and extreme UV (EUV) photons can sufficiently ionize the disk surface to reproduce the observed line fluxes, suggesting that emission from Ne+ originates in the hot disk atmosphere. On the other hand, the H I(7-6) line is not associated with the gas in the disk surface and magnetospheric accretion flows can account only for at most ~30% of the observed flux. We conclude that accretion shock regions and/or the stellar corona could contribute to most of the H I(7-6)emission. Finally, we discuss the observations necessary to identify whether stellar X-rays or EUV photons are the dominant ionization mechanism for Ne atoms. Because the observed [Ne II] emission probes very small amounts of gas in the disk surface (~10^{-6} Jupiter masses) we suggest using this gas line to determine the presence or absence of gas in more evolved circumstellar disks.

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arXiv2006

Formation and Evolution of Planetary Systems: Upper Limits to the Gas Mass in Disks Around Sun-like Stars

We have carried out a sensitive search for gas emission lines at infrared and millimeter wavelengths for a sample of 15 young sun-like stars selected from our dust disk survey with the Spitzer Space Telescope. We have used mid-infrared lines to trace the warm (300-100 K) gas in the inner disk and millimeter transitions of 12CO to probe the cold (~20 K) outer disk. We report no gas line detections from our sample. Line flux upper limits are first converted to warm and cold gas mass limits using simple approximations allowing a direct comparison with values from the literature. We also present results from more sophisticated models following Gorti and Hollenbach (2004) which confirm and extend our simple analysis. These models show that the SI line at 25.23 micron can set constraining limits on the gas surface density at the disk inner radius and traces disk regions up to a few AU. We find that none of the 15 systems have more than 0.04 MJ of gas within a few AU from the disk inner radius for disk radii from 1 AU up to ~40 AU. These gas mass upper limits even in the 8 systems younger than ~30 Myr suggest that most of the gas is dispersed early. The gas mass upper limits in the 10-40 AU region, that is mainly traced by our CO data, are <2 Mearth. If these systems are analogs of the Solar System, either they have already formed Uranus- and Neptune-like planets or they will not form them beyond 100 Myr. Finally, the gas surface density upper limits at 1 AU are smaller than 0.01% of the minimum mass solar nebula for most of the sources. If terrestrial planets form frequently and their orbits are circularized by gas, then circularization occurs early.

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