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Carlos Carrasco-Gonzalez

Publications and source records attributed to Carlos Carrasco-Gonzalez.

At least 19 recordsLinked to original sources

Modeling (Sub-)millimeter Scattering Properties of Fractal and Consolidated Porous Particles: Applications to Protoplanetary Disks

We perform light-scattering numerical simulations for two dust populations: (i) consolidated porous particles computed with the discrete dipole approximation (ADDA) and (ii) highly porous aggregate models, including fractal and hierarchical aggregates, computed with the multiple-sphere T-matrix method (MSTM). Using DSHARP optical constants, we compute scattering matrices, cross sections, and effective albedo omega_eff for a size distribution n(a) proportional to a^q, with q = -3.5, amin = 0.1 micron, and ten wavelengths from 0.87 to 10 mm. We find that increasing porosity strengthens forward scattering and enhances polarization near theta approximately 90 degrees. For compact spheres, P(90 degrees) times omega_eff peaks near amax approximately lambda divided by 2 pi and then declines, whereas porous particles show a broader peak extending to larger sizes, keeping polarization-based constraints compatible with amax approximately 1 mm. Porosity also lowers kappa_abs at fixed dust mass relative to compact spheres, implying larger inferred dust masses for a given continuum flux.

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Detailed Microwave Continuum Spectra from Bright Protoplanetary Disks in Taurus

We present new observations that densely sample the microwave (4-360 GHz) continuum spectra from eight young systems in the Taurus region. Multi-component, empirical model prescriptions were used to disentangle the contributions from their dust disks and other emission mechanisms. We found partially optically thick, free-free emission in all these systems, with positive spectral indices (median $α_{\rm c} \approx 1$ at 10 GHz) and contributing 5-50% of the 43 GHz fluxes. There is no evidence for synchrotron or spinning dust grain emission contributions for these targets. The inferred dust disk spectra all show substantial curvature: their spectral indices decrease with frequency, from $α_{\rm d} \approx 2.8$-4.0 around 43 GHz to 1.7-2.1 around 340 GHz. This curvature suggests that a substantial fraction of the (sub)millimeter ($\gtrsim$ 200 GHz) dust emission may be optically thick, and therefore the traditional metrics for estimating dust masses are flawed. Assuming the emission at lower frequencies (43 GHz) is optically thin, the local spectral indices and fluxes were used to constrain the disk-averaged dust properties and estimate corresponding dust masses. These masses are roughly an order of magnitude higher ($\approx 1000 \, M_\oplus$) than those found from the traditional approach based on (sub)millimeter fluxes. These findings emphasize the value of broad spectral coverage - particularly extending to lower frequencies ($\sim$cm-band) - for accurately interpreting dust disk emission; such observations may help reshape our perspective on the available mass budgets for planet formation.

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The centimeter emission from planet-forming disks in Taurus

The last decade has witnessed remarkable advances in the characterization of the (sub-)millimeter emission from planet-forming disks. Instead, the study of the (sub-)centimeter emission has made more limited progress, to the point that only a few exceptional disk-bearing objects have been characterized in the centimeter regime. This work takes a broad view of the centimeter emission from a large sample with VLA observations that is selected from previous ALMA surveys of more representative disks in brightness and extent. We report on the detection and characterization of flux at centimeter wavelengths from 21 sources in the Taurus star-forming region. Complemented by literature and archival data, the entire photometry from 0.85 mm to 6 cm is fitted by a two-component model that determines the ubiquitous presence of free-free emission entangled with the dust emission. The flux density of the free-free emission is found to scale with the accretion rate but is independent of the outer disk morphology depicted by ALMA. The dust emission at 2 cm is still appreciable, and offers the possibility to extract an unprecedented large set of dust spectral indices in the centimeter regime. A pronounced change between the median millimeter indices (2.3) and centimeter indices (2.8) suggests that a large portion of the disk emission is optically thick up to 3 mm. The comparison of both indices and fluxes with the ALMA disk extent indicates that this portion can be as large as 40 au, and suggests that the grain population within this disk region that emits the observed centimeter emission is similar in disks with different size and morphology. All these results await confirmation and dedicated dust modeling once facilities like ngVLA or SKA-mid are able to resolve the centimeter emission from planet-forming disks and disentangle the various components.

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Key Science Goals for the Next Generation Very Large Array (ngVLA): Update from the ngVLA Science Advisory Council (2024)

In 2017, the next generation Very Large Array (ngVLA) Science Advisory Council, together with the international astronomy community, developed a set of five Key Science Goals (KSGs) to inform, prioritize and refine the technical capabilities of a future radio telescope array for high angular resolution operation from 1.2 - 116 GHz with 10 times the sensitivity of the Jansky VLA and ALMA. The resulting KSGs, which require observations at centimeter and millimeter wavelengths that cannot be achieved by any other facility, represent a small subset of the broad range of astrophysical problems that the ngVLA will be able address. This document presents an update to the original ngVLA KSGs, taking account of new results and progress in the 7+ years since their initial presentation, again drawing on the expertise of the ngVLA Science Advisory Council and the broader community in the ngVLA Science Working Groups. As the design of the ngVLA has also matured substantially in this period, this document also briefly addresses initial expectations for ngVLA data products and processing that will be needed to achieve the KSGs. The original ngVLA KSGs endure as outstanding problems of high priority. In brief, they are: (1) Unveiling the Formation of Solar System Analogues; (2) Probing the Initial Conditions for Planetary Systems and Life with Astrochemistry; (3) Charting the Assembly, Structure, and Evolution of Galaxies from the First Billion Years to the Present; (4) Science at the Extremes: Pulsars as Laboratories for Fundamental Physics; (5) Understanding the Formation and Evolution of Stellar and Supermassive Black Holes in the Era of Multi-Messenger Astronomy.

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Aligned Grains and Scattered Light Found in Gaps of Planet-Forming Disk

Polarized (sub)millimeter emission from dust grains in circumstellar disks was initially thought to be due to grains aligned with the magnetic field. However, higher resolution multi-wavelength observations along with improved models found that this polarization is dominated by self-scattering at shorter wavelengths (e.g., 870 $μ$m) and by grains aligned with something other than magnetic fields at longer wavelengths (e.g., 3 mm). Nevertheless, the polarization signal is expected to depend on the underlying substructure, and observations hitherto have been unable to resolve polarization in multiple rings and gaps. HL Tau, a protoplanetary disk located 147.3 $\pm$ 0.5 pc away, is the brightest Class I or Class II disk at millimeter/submillimeter wavelengths. Here we show deep, high-resolution 870 $μ$m polarization observations of HL Tau, resolving polarization in both the rings and gaps. We find that the gaps have polarization angles with a significant azimuthal component and a higher polarization fraction than the rings. Our models show that the disk polarization is due to both scattering and emission from aligned effectively prolate grains. The intrinsic polarization of aligned dust grains is likely over 10%, which is much higher than what was expected in low resolution observations (~1%). Asymmetries and dust features are revealed in the polarization observations that are not seen in non-polarimetric observations.

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An SiO Toroid and Wide-angle Outflow associated with the Massive Protostar W75N(B)-VLA2

We have carried out ALMA observations of the massive star-forming region W75N(B), which contains the massive protostars VLA1, VLA2, and VLA3. Particularly, VLA2 is an enigmatic protostar associated with a wind-driven H$_2$O maser shell, which has evolved from an almost isotropic outflow to a collimated one in just 20 years. The shell expansion seemed to be halted by an obstacle located to the northeast of VLA2. Here we present our findings from observing the 1.3 mm continuum and H$_2$CO and SiO emission lines. Within a region of $\sim 30"$ ($\sim 39,000$ au) diameter, we have detected 40 compact mm-continuum sources, three of them coinciding with VLA1, VLA2, and VLA3. While the H$_2$CO emission is mainly distributed in a fragmented structure around the three massive protostars, but without any of the main H$_2$CO clumps spatially coinciding with them, the SiO is highly concentrated on VLA2, indicating the presence of very strong shocks generated near this protostar. The SiO emission is clearly resolved into an elongated structure ($\sim 0.6"\times0.3"$; $\sim 780$ au$\times$390 au) perpendicular to the major axis of the wind-driven maser shell. The structure and kinematics of the SiO emission are consistent with a toroid and a wide-angle outflow surrounding a central mass of $\sim 10$ M$_{\odot}$, thus supporting previous theoretical predictions regarding the evolution of the outflow. Additionally, we have identified the expected location and estimated the gas density of the obstacle that is hindering the expansion of the maser shell.

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Forbidden emission lines in protostellar outflows and jets with MUSE

Forbidden emission lines in protoplanetary disks are a key diagnostic in studies of the evolution of the disk and the host star. We report spatially resolved emission lines, [OI] 6300, 6363, [NII] 6548, 6583, H$α$, and [SII] 6716, 6730 Angstrom that are believed to be associated with jets and magnetically driven winds in the inner disks. Observations were carried out with the optical integral field spectrograph of the Multi Unit Spectroscopic Explorer (MUSE), at the Very Large Telescope (VLT). With a resolution of 0.025 X 0.025 arcsec$^{2}$, we aim to derive the position angle of the outflow/jet (PA$_{outflow/jet}$) that is connected with the inner disk. The forbidden emission lines analyzed here have their origin at the inner parts of the protoplanetary disk. From the maximum intensity emission along the outflow/jet in DL Tau, CI Tau, DS Tau, IP Tau, and IM Lup, we were able to reliably measure the PA$_{outflow/jet}$ for most of the identified lines. We found that our estimates agree with PA$_{dust}$ for most of the disks. These estimates depend on the signal-to-noise level and the collimation of the outflow (jet). The outflows/jets in CIDA 9, GO Tau, and GW Lup are too compact for a PA$_{outflow/jet}$ to be estimated. Based on our kinematics analysis, we confirm that DL Tau and CI Tau host a strong outflow/jet with line-of-sight velocities much greater than 100 km s$^{-1}$, whereas DS Tau, IP Tau, and IM Lup velocities are lower and their structures encompass low-velocity components to be more associated with winds. Our estimates for the mass-loss rate, $\dot{M}_{loss}$, range between (1.1-6.5)X10$^{-7}$-10$^{-8}$ $M_{\odot}$ yr$^{-1}$ for the disk-outflow/jet systems analyzed here. The outflow/jet systems analyzed here are aligned within around 1 degree between the inner and outer disk. Further observations are needed to confirm a potential misalignment in IM Lup.

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Reading M87's DNA: A Double Helix revealing a large scale Helical Magnetic Field

We present unprecedented high fidelity radio images of the M87 jet. We analyzed Jansky Very Large Array (VLA) broadband, full polarization, radio data from 4 to 18 GHz. The observations were taken with the most extended configuration (A configuration), which allow the study of the emission of the jet up to kpc scales with a linear resolution $\sim$10 pc. The high sensitivity and resolution of our data allow to resolve the jet width. We confirm a double-helix morphology of the jet material between $\sim$300 pc and $\sim$1 kpc. We found a gradient of the polarization degree with a minimum at the projected axis and maxima at the jet edges, and a gradient in the Faraday depth with opposite signs at the jet edges. We also found that the behavior of the polarization properties along the wide range of frequencies is consistent with internal Faraday depolarization. All these characteristics strongly support the presence of a helical magnetic field in the M87 jet up to 1 kpc from the central black hole although the jet is most likely particle dominated at these large scales. Therefore, we propose a plausible scenario in which the helical configuration of the magnetic field has been maintained to large scales thanks to the presence of Kelvin-Helmholtz instabilities.

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Characterizing the dust content of disk substructures in TW Hya

We present Atacama Large Millimeter Array (ALMA) observations of TW Hya at 3.1 mm with $\sim50$ milliarcsecond resolution. These new data were combined with archival high angular resolution ALMA observations at 0.87 mm, 1.3 mm, and 2.1 mm. We analyze these multi-wavelength data to infer a disk radial profile of the dust surface density, maximum particle size, and slope of the particle size distribution. Most previously known annular substructures in the disk of TW Hya are resolved at the four wavelengths. Inside the inner 3 au cavity, the 2.1 mm and 3.1 mm images show a compact source of free-free emission, likely associated with an ionized jet. Our multi-wavelength analysis of the dust emission shows that the maximum particle size in the disk of TW Hya is $>1$ mm. The inner 20 au are completely optically thick at all four bands, which results in the data tracing different disk heights at different wavelengths. Coupled with the effects of dust settling, this prevents the derivation of accurate density and grain size estimates in these regions. At $r>20$ au, we find evidence of the accumulation of large dust particle at the position of the bright rings, indicating that these are working as dust traps. The total dust mass in the disk is between 250 and 330 $M_{\oplus}$, which represents a gas-to-dust mass ratio between 50 and 70. Our mass measurement is a factor of 4.5-5.9 higher than the mass that one would estimate using the typical assumptions of large demographic surveys. Our results indicate that the ring substructures in TW Hya are ideal locations to trigger the streaming instability and form new generations of planetesimals.

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Characterization of Ring Substructures in the Protoplanetary Disk of HD 169142 from Multi-Wavelength ALMA Observations

We present a detailed multi-wavelength characterization of the multi-ring disk of HD 169142. We report new ALMA observations at 3 mm and analyze them together with archival 0.89 and 1.3 mm data. Our observations resolve three out of the four rings in the disk previously seen in high-resolution ALMA data. A simple parametric model is used to estimate the radial profile of the dust optical depth, temperature, density, and particle size distribution. We find that the multiple ring features of the disk are produced by annular accumulations of large particles, probably associated with gas pressure bumps. Our model indicates that the maximum dust grain size in the rings is $\sim1$ cm, with slightly flatter power-law size distributions than the ISM-like size distribution ($p\sim3.5$) found in the gaps. In particular, the inner ring ($\sim26$ au) is associated with a strong and narrow buildup of dust particles that could harbor the necessary conditions to trigger the streaming instability. According to our analysis, the snowlines of the most important volatiles do not coincide with the observed substructures. We explore different ring formation mechanisms and find that planet-disk interactions are the most likely scenario to explain the main features of HD 169142. Overall, our multi-wavelength analysis provides some of the first unambiguous evidence of the presence of radial dust traps in the rings of HD 169142. A similar analysis in a larger sample of disks could provide key insights on the impact that disk substructures have on the dust evolution and planet formation processes.

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Science with an ngVLA: Resolved Substructures in Protoplanetary Disks

Terrestrial planets and the cores of giant planets are thought to be built by the collisional agglomeration of solids spanning over 20 orders of magnitude in size within a few million years. However, there is tension between this basic picture of planet formation and standard theoretical assumptions associated with the migration of "pebbles" ($\sim$mm/cm-sized particles) in gas-rich disks and the presumably much longer timescales necessary to assemble ($\sim$km-scale) "planetesimals". To confront these potential theoretical discrepancies with observational constraints, the ideal tracer of the solids concentrated in protoplanetary disk substructures is the 30-100 GHz continuum, which strikes the best balance in sensitivity (emission still bright), optical depth (low enough to reliably estimate densities), and angular resolution (high enough to resolve fine-scale features at disk radii as small as 1 au). With its combination of sensitivity, frequency coverage, and angular resolution, the next-generation VLA will be the only facility that has the capabilities to open up this new window into the physics of planetesimal formation.

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Multiple rings in the transitional disk of GM Aurigae revealed by VLA and ALMA

Our understanding of protoplanetary disks is rapidly departing from the classical view of a smooth, axisymmetric disk. This is in part thanks to the high angular resolution that (sub)mm observations can provide. Here we present the combined results of ALMA (0.9 mm) and VLA (7 mm) dust continuum observations toward the protoplanetary disk around the solar analogue GM Aur. Both images clearly resolve the $\sim$35 au inner cavity. The ALMA observations also reveal a fainter disk that extends up to $\sim250$ au. We model our observations using two approaches: an analytical fit to the observed deprojected visibilities, and a physical disk model that fits the SED as well as the VLA and ALMA observations. Despite not being evident in the deconvolved images, the VLA and ALMA visibilities can only be fitted with two bright rings of radii $\sim$40 and $\sim$80 au. Our physical model indicates that this morphology is the result of an accumulation or trapping of large dust grains, probably due to the presence of two pressure bumps in the disk. Even though alternative mechanisms cannot be discarded, the multiple rings suggest that forming planets may have cleared at least two gaps in the disk. Finally, our analysis suggests that the inner cavity might display different sizes at 0.9 mm and 7 mm. This discrepancy could be caused by the presence of free-free emission close to the star at 7 mm, or by a more compact accumulation of the large dust grains at the edge of the cavity.

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Radio Jets from Young Stellar Objects

Jets and outflows are ubiquitous in the process of formation of stars since outflow is intimately associated with accretion. Free-free (thermal) radio continuum emission is associated with these jets. This emission is relatively weak and compact, and sensitive radio interferometers are required to study it. Observations in the cm range are most useful to trace the base of the ionized jets, close to the central protostar, where optical or near-IR imaging is made difficult by the high extinction present. Radio recombination lines in jets (in combination with proper motions) should provide their 3D kinematics at very small scale. Future instruments such as the Square Kilometre Array (SKA) and the Next Generation Very Large Array (ngVLA) will be crucial to perform this kind of sensitive observations. Thermal jets are associated with both high and low mass protostars and possibly even with substellar objects. The ionizing mechanism of these radio jets appears to be related to shocks in the associated outflows, as suggested by the observed correlation between the cm luminosity and the outflow momentum rate. Some protostellar jets show indications of non-thermal emission in their lobes. Linearly polarized synchrotron emission has been found in the jet of HH 80-81, allowing one to map the jet magnetic field, a key ingredient to determine the collimation and ejection mechanisms. As only a fraction of the emission is polarized, very sensitive observations such as those that will be feasible with the interferometers previously mentioned are required to perform studies in a large sample of sources. Jets are present in many kinds of astrophysical scenarios. Characterizing radio jets in young stars, where thermal emission allows one to determine their physical conditions, would also be useful in understanding acceleration and collimation mechanisms in all kinds of astrophysical jets.

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Radiation Hydrodynamical Turbulence In Protoplanetary Disks: Numerical Models and Observational Constraints

Planets are born in protostellar disks, which are now observed with enough resolution to address questions about internal gas flows. Candidates for driving the flows include magnetic forces, but ionization state estimates suggest much of the gas mass decouples from magnetic fields. Thus, hydrodynamical instabilities could play a major role. We investigate disk dynamics under conditions typical for a T Tauri system, using global 3D radiation hydrodynamics simulations with embedded particles and a resolution of 70 cells per scale height. Stellar irradiation heating is included with realistic dust opacities. The disk starts in joint radiative balance and hydrostatic equilibrium. The vertical shear instability (VSI) develops into turbulence that persists up to at least 1600 inner orbits (143 outer orbits). Turbulent speeds are a few percent of the local sound speed at the midplane, increasing to 20%, or 100 m/s, in the corona. These are consistent with recent upper limits on turbulent speeds from optically thin and thick molecular line observations of TW Hya and HD 163296. The predominantly vertical motions induced by the VSI efficiently lift particles upwards. Grains 0.1 and 1 mm in size achieve scale heights greater than expected in isotropic turbulence. We conclude that while kinematic constraints from molecular line emission do not directly discriminate between magnetic and nonmagnetic disk models, the small dust scale heights measured in HL Tau and HD 163296 favor turbulent magnetic models, which reach lower ratios of the vertical kinetic energy density to the accretion stress.

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The properties of the inner disk around HL Tau: Multi-wavelength modeling of the dust emission

We conducted a detailed radiative transfer modeling of the dust emission from the circumstellar disk around HL Tau. The goal of our study is to derive the surface density profile of the inner disk and its structure. In addition to the Atacama Large Millimeter/submillimeter Array images at Band 3 (2.9mm), Band 6 (1.3mm), and Band 7 (0.87mm), the most recent Karl G. Jansky Very Large Array (VLA) observations at 7mm were included in the analysis. A simulated annealing algorithm was invoked to search for the optimum model. The radiative transfer analysis demonstrates that most radial components (i.e., >6AU) of the disk become optically thin at a wavelength of 7mm, which allows us to constrain, for the first time, the dust density distribution in the inner region of the disk. We found that a homogeneous grain size distribution is not sufficient to explain the observed images at different wavelengths simultaneously, while models with a shallower grain size distribution in the inner disk work well. We found clear evidence that larger grains are trapped in the first bright ring. Our results imply that dust evolution has already taken place in the disk at a relatively young (i.e., ~1Myr) age. We compared the midplane temperature distribution, optical depth, and properties of various dust rings with those reported previously. Using the Toomre parameter, we briefly discussed the gravitational instability as a potential mechanism for the origin of the dust clump detected in the first bright ring via the VLA observations.

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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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Imaging a Central Ionized Component, a Narrow Ring, and the CO Snowline in the Multi-Gapped Disk of HD 169142

We report Very Large Array observations at 7 mm, 9 mm, and 3 cm toward the pre-transitional disk of the Herbig Ae star HD 169142. These observations have allowed us to study the mm emission of this disk with the highest angular resolution so far ($0\rlap."12\times0\rlap."09$, or 14 au$\times$11 au, at 7 mm). Our 7 and 9 mm images show a narrow ring of emission at a radius of $\sim25$ au tracing the outer edge of the inner gap. This ring presents an asymmetric morphology that could be produced by dynamical interactions between the disk and forming planets. Additionally, the azimuthally averaged radial intensity profiles of the 7 and 9 mm images confirm the presence of the previously reported gap at $\sim45$ au, and reveal a new gap at $\sim85$ au. We analyzed archival DCO$^+$(3-2) and C$^{18}$O(2-1) ALMA observations, showing that the CO snowline is located very close to this third outer gap. This suggests that growth and accumulation of large dust grains close to the CO snowline could be the mechanism responsible for this proposed outer gap. Finally, a compact source of emission is detected at 7 mm, 9 mm, and 3 cm toward the center of the disk. Its flux density and spectral index indicate that it is dominated by free-free emission from ionized gas, which could be associated with either the photoionization of the inner disk, an independent object, or an ionized jet.

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A concordant scenario to explain FU Ori from deep centimeter and millimeter interferometric observations

We resolved FU Ori at 29-37 GHz using the JVLA with $\sim$0$''$.07 resolution, and performed the complementary JVLA 8-10 GHz observations, the SMA 224 GHz and 272 GHz observations, and compared with archival ALMA 346 GHz observations to obtain the SEDs. Our 8-10 GHz observations do not find evidence for the presence of thermal radio jets, and constrain the radio jet/wind flux to at least 90 times lower than the expected value from the previously reported bolometric luminosity-radio luminosity correlation. The emission at $>$29 GHz may be dominated by the two spatially unresolved sources, which are located immediately around FU Ori and its companion FU Ori S, respectively. Their deconvolved radii at 33 GHz are only a few au. The 8-346 GHz SEDs of FU Ori and FU Ori S cannot be fit by constant spectral indices (over frequency). The more sophisticated models for SEDs suggest that the $>$29 GHz emission is contributed by a combination of free-free emission from ionized gas, and thermal emission from optically thick and optically thin dust components. We hypothesize that dust in the innermost parts of the disks ($\lesssim$0.1 au) has been sublimated, and thus the disks are no more well shielded against the ionizing photons. The estimated overall gas and dust mass based on SED modeling, can be as high as a fraction of a solar mass, which is adequate for developing disk gravitational instability. Our present explanation for the observational data is that the massive inflow of gas and dust due to disk gravitational instability or interaction with a companion/intruder, was piled up at the few au scale due to the development of a deadzone with negligible ionization. The piled up material subsequently triggered the thermal and the MRI instabilities when the ionization fraction in the inner sub-au scale region exceeded a threshold value, leading to the high protostellar accretion rate.

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