Protoplanetary disks are dispersed by viscous evolution and photoevaporation in a few million years; in the interim small, sub-micron sized dust grains must grow and form planets. The time-varying abundance of small grains in an evolving disk directl
y affects gas heating by far-ultraviolet photons, while dust evolution affects photoevaporation by changing the disk opacity and resulting penetration of FUV photons in the disk. Photoevaporative flows, in turn, selectively carry small dust grains leaving the larger particles---which decouple from the gas---behind in the disk. We study these effects by investigating the evolution of a disk subject to viscosity, photoevaporation by EUV, FUV and X-rays, dust evolution, and radial drift using a 1-D multi-fluid approach (gas + different dust grain sizes) to solve for the evolving surface density distributions. The 1-D evolution is augmented by 1+1D models constructed at each epoch to obtain the instantaneous disk structure and determine photoevaporation rates. The implementation of a dust coagulation/fragmentation model results in a marginal decrease in disk lifetimes when compared to models with no dust evolution; the disk lifetime is thus found to be relatively insensitive to the evolving dust opacity. We find that photoevaporation can cause significant reductions in the gas/dust mass ratio in the planet-forming regions of the disk as it evolves, and may result in a corresponding increase in heavy element abundances relative to hydrogen. We discuss implications for theories of planetesimal formation and giant planet formation, including the formation of gas-poor giants. After gas disk dispersal, $sim 3times 10^{-4}$ ms of mass in solids typically remain, comparable to the solids inventory of our solar system.
From the masses of planets orbiting our Sun, and relative elemental abundances, it is estimated that at birth our Solar System required a minimum disk mass of ~0.01 solar masses within ~100 AU of the star. The main constituent, gaseous molecular hydr
ogen, does not emit from the disk mass reservoir, so the most common measure of the disk mass is dust thermal emission and lines of gaseous carbon monoxide. Carbon monoxide emission generally probes the disk surface, while the conversion from dust emission to gas mass requires knowledge of the grain properties and gas-to-dust mass ratio, which likely differ from their interstellar values. Thus, mass estimates vary by orders of magnitude, as exemplified by the relatively old (3--10 Myr) star TW Hya, with estimates ranging from 0.0005 to 0.06 solar masses. Here we report the detection the fundamental rotational transition of hydrogen deuteride, HD, toward TW Hya. HD is a good tracer of disk gas because it follows the distribution of molecular hydrogen and its emission is sensitive to the total mass. The HD detection, combined with existing observations and detailed models, implies a disk mass >0.05 solar masses, enough to form a planetary system like our own.
We present Herschel PACS spectroscopy of the [OI] 63 micron gas-line for three circumstellar disk systems showing signs of significant disk evolution and/or planet formation: HR 8799, HD 377 and RX J1852.3-3700. [OI] is undetected toward HR 8799 and
HD 377 with 3 sigma upper limits of 6.8 x 10^-18 W m^-2 and 9.9 x 10^-18 W m^-2 respectively. We find an [OI] detection for RX J1852.3-3700 at 12.3 +- 1.8 x 10^-18 W m^-2. We use thermo-chemical disk models to model the gas emission, using constraints on the [OI] 63 micron, and ancillary data to derive gas mass upper limits and constrain gas-to-dust ratios. For HD 377 and HR 8799, we find 3 sigma upper limits on the gas mass of 0.1-20 Mearth. For RX J1852.3-3700, we find two distinct disk scenarios that could explain the detection of [OI] 63 micron and CO(2-1) upper limits reported from the literature: (i) a large disk with gas co-located with the dust (16-500 AU), resulting in a large tenuous disk with ~16 Mearth of gas, or (ii) an optically thick gas disk, truncated at ~70 AU, with a gas mass of 150 Mearth. We discuss the implications of these results for the formation and evolution of planets in these three systems.
We compare line emission calculated from theoretical disk models with optical to sub-millimeter wavelength observational data of the gas disk surrounding TW Hya and infer the spatial distribution of mass in the gas disk. The model disk that best matc
hes observations has a gas mass ranging from $sim10^{-4}-10^{-5}$ms for $0.06{rm AU} <r<3.5$AU and $sim 0.06$ms for $ 3.5 {rm AU} <r<200$AU. We find that the inner dust hole ($r<3.5$AU) in the disk must be depleted of gas by $sim 1-2$ orders of magnitude compared to the extrapolated surface density distribution of the outer disk. Grain growth alone is therefore not a viable explanation for the dust hole. CO vibrational emission arises within $rsim 0.5$AU from thermal excitation of gas. [OI] 6300AA and 5577AA forbidden lines and OH mid-infrared emission are mainly due to prompt emission following UV photodissociation of OH and water at $rlesssim0.1$AU and at $rsim 4$AU. [NeII] emission is consistent with an origin in X-ray heated neutral gas at $rlesssim 10$AU, and may not require the presence of a significant EUV ($h u>13.6$eV) flux from TW Hya. H$_2$ pure rotational line emission comes primarily from $rsim 1-30$AU. [OI]63$mu$m, HCO$^+$ and CO pure rotational lines all arise from the outer disk at $rsim30-120$AU. We discuss planet formation and photoevaporation as causes for the decrease in surface density of gas and dust inside 4 AU. If a planet is present, our results suggest a planet mass $sim 4-7$M$_J$ situated at $sim 3$AU. Using our photoevaporation models and the best surface density profile match to observations, we estimate a current photoevaporative mass loss rate of $4times10^{-9}$ms yr$^{-1}$ and a remaining disk lifetime of $sim 5$ million years.
We present the time evolution of viscously accreting circumstellar disks as they are irradiated by ultraviolet and X-ray photons from a low-mass central star. Our model is a hybrid of a 1D time-dependent viscous disk model coupled to a 1+1D disk vert
ical structure model used for calculating the disk structure and photoevaporation rates. We find that disks of initial mass 0.1M_o around 1M_o stars survive for 4x10^6 years, assuming a viscosity parameter $alpha=0.01$, a time-dependent FUV luminosity $L_{FUV}~10^{-2}-10^{-3}$ L_o and with X-ray and EUV luminosities $L_X sim L_{EUV} ~ 10^{-3}$L_o. We find that FUV/X-ray-induced photoevaporation and viscous accretion are both important in depleting disk mass. Photoevaporation rates are most significant at ~ 1-10 AU and at >~ 30 AU. Viscosity spreads the disk which causes mass loss by accretion onto the central star and feeds mass loss by photoevaporation in the outer disk. We find that FUV photons can create gaps in the inner, planet-forming regions of the disk (~ 1-10 AU) at relatively early epochs in disk evolution while disk masses are still substantial. EUV and X-ray photons are also capable of driving gaps, but EUV can only do so at late, low accretion-rate epochs after the disk mass has already declined substantially. Disks around stars with predominantly soft X-ray fields experience enhanced photoevaporative mass loss. We follow disk evolution around stars of different masses, and find that disk survival time is relatively independent of mass for stars with M <~ 3M_o; for M >~ 3M_o the disks are short-lived(~10^5 years).
Extreme ultraviolet (EUV, 13.6 eV $< h u lta 100$ eV) and X-rays in the 0.1-2 keV band can heat the surfaces of disks around young, low mass stars to thousands of degrees and ionize species with ionization potentials greater than 13.6 eV. Shocks gene
rated by protostellar winds can also heat and ionize the same species close to the star/disk system. These processes produce diagnostic lines (e.g., [NeII] 12.8 $mu$m and [OI] 6300 AA) that we model as functions of key parameters such as EUV luminosity and spectral shape, X-ray luminosity and spectral shape, and wind mass loss rate and shock speed. Comparing our models with observations, we conclude that either internal shocks in the winds or X-rays incident on the disk surfaces often produce the observed [NeII] line, although there are cases where EUV may dominate. Shocks created by the oblique interaction of winds with disks are unlikely [NeII] sources because these shocks are too weak to ionize Ne. Even if [NeII] is mainly produced by X-rays or internal wind shocks, the neon observations typically place upper limits of $lta 10^{42}$ s$^{-1}$ on the EUV photon luminosity of these young low mass stars. The observed [OI] 6300 AA line has both a low velocity component (LVC) and a high velocity component. The latter likely arises in internal wind shocks. For the former we find that X-rays likely produce more [OI] luminosity than either the EUV layer, the transition layer between the EUV and X-ray layer, or the shear layer where the protostellar wind shocks and entrains disk material in a radial flow across the surface of the disk. Our soft X-ray models produce [OI] LVCs with luminosities up to $10^{-4}$ L$_odot$, but may not be able to explain the most luminous LVCs.
We calculate the rate of photoevaporation of a circumstellar disk by energetic radiation (FUV, 6eV $<h u<$13.6eV; EUV, 13.6eV $<h u<$0.1keV; and Xrays, $h u>0.1$keV) from its central star. We focus on the effects of FUV and X-ray photons since EUV ph
otoevaporation has been treated previously, and consider central star masses in the range $0.3-7 {rm M}_{odot}$. Contrary to the EUV photoevaporation scenario, which creates a gap at about $r_gsim 7 (M_*/1{rm M}_{odot})$ AU and then erodes the outer disk from inside out, we find that FUV photoevaporation predominantly removes less bound gas from the outer disk. Heating by FUV photons can cause significant erosion of the outer disk where most of the mass is typically located. X-rays indirectly increase the mass loss rates (by a factor $sim 2$) by ionizing the gas, thereby reducing the positive charge on grains and PAHs and enhancing FUV-induced grain photoelectric heating. FUV and X-ray photons may create a gap in the disk at $sim 10$ AU under favourable circumstances. Photoevaporation timescales for M$_* sim 1{rm M}_{odot}$ stars are estimated to be $sim 10^6$ years, after the onset of disk irradiation by FUV and X-rays. Disk lifetimes do not vary much for stellar masses in the range $0.3-3$M$_{odot}$. More massive stars ($gtrsim 7 {rm M}_{odot}$) lose their disks rapidly (in $sim 10^5$ years) due to their high EUV and FUV fields. Disk lifetimes are shorter for shallow surface density distributions and when the dust opacity in the disk is reduced by processes such as grain growth or settling. The latter suggests that the photoevaporation process may accelerate as the dust disk evolves.
We present self-consistent models of gas in optically-thick dusty disks and calculate its thermal, density and chemical structure. The models focus on an accurate treatment of the upper layers where line emission originates, and at radii $gtrsim 0.7$
AU. We present results of disks around $sim 1{rm M}_{odot}$ stars where we have varied dust properties, X-ray luminosities and UV luminosities. We separately treat gas and dust thermal balance, and calculate line luminosities at infrared and sub-millimeter wavelengths from all transitions originating in the predominantly neutral gas that lies below the ionized surface of the disk. We find that the [ArII] 7$mu$m, [NeII] 12.8$mu$m, [FeI] 24$mu$m, [SI] 25$mu$m, [FeII] 26$mu$m, [SiII] 35 $mu$m, [OI] 63$mu$m and pure rotational lines of H$_2$, H$_2$O and CO can be quite strong and are good indicators of the presence and distribution of gas in disks. We apply our models to the disk around the nearby young star, TW Hya, and find good agreement between our model calculations and observations. We also predict strong emission lines from the TW Hya disk that are likely to be detected by future facilities. A comparison of CO observations with our models suggests that the gas disk around TW Hya may be truncated to $sim 120 $ AU, compared to its dust disk of 174 AU. We speculate that photoevaporation due to the strong stellar FUV field from TW Hya is responsible for the gas disk truncation.
