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.
We present a model in which the 22 GHz H$_2$O masers observed in star-forming regions occur behind shocks propagating in dense regions (preshock density $n_0 sim 10^6 - 10^8$ cm$^{-3}$). We focus on high-velocity ($v_s > 30$ km s$^{-1}$) dissociative
J shocks in which the heat of H$_2$ re-formation maintains a large column of $sim 300-400$ K gas; at these temperatures the chemistry drives a considerable fraction of the oxygen not in CO to form H$_2$O. The H$_2$O column densities, the hydrogen densities, and the warm temperatures produced by these shocks are sufficiently high to enable powerful maser action. The observed brightness temperatures (generally $sim 10^{11} - 10^{14}$ K) are the result of coherent velocity regions that have dimensions in the shock plane that are 10 to 100 times the shock thickness of $sim 10^{13}$ cm. The masers are therefore beamed towards the observer, who typically views the shock edge-on, or perpendicular to the shock velocity; the brightest masers are then observed with the lowest line of sight velocities with respect to the ambient gas. We present numerical and analytic studies of the dependence of the maser inversion, the resultant brightness temperature, the maser spot size and shape, the isotropic luminosity, and the maser region magnetic field on the shock parameters and the coherence path length; the overall result is that in galactic H$_2$O 22 GHz masers these observed parameters can be produced in J shocks with $n_0sim 10^6 - 10^8$ cm$^{-3}$ and $v_s sim 30 -200$ km s$^{-1}$. A number of key observables such as maser shape, brightness temperature, and global isotropic luminosity depend only on the particle flux into the shock, $j=n_0v_s$, rather than on $n_0$ and $v_s$ separately.
We model the production of OH+, H2O+, and H3O+ in interstellar clouds, using a steady state photodissociation region code that treats the freeze-out of gas species, grain surface chemistry, and desorption of ices from grains. The code includes PAHs,
which have important effects on the chemistry. All three ions generally have two peaks in abundance as a function of depth into the cloud, one at A_V<~1 and one at A_V~3-8, the exact values depending on the ratio of incident ultraviolet flux to gas density. For relatively low values of the incident far ultraviolet flux on the cloud ({chi}<~ 1000; {chi}= 1= local interstellar value), the columns of OH+ and H2O+ scale roughly as the cosmic ray primary ionization rate {zeta}(crp) divided by the hydrogen nucleus density n. The H3O+ column is dominated by the second peak, and we show that if PAHs are present, N(H3O+) ~ 4x10^{13} cm^{-2} independent of {zeta}(crp) or n. If there are no PAHs or very small grains at the second peak, N(H3O+) can attain such columns only if low ionization potential metals are heavily depleted. We also model diffuse and translucent clouds in the interstellar medium, and show how observations of N(OH+)/N(H) and N(OH+)/N(H2O+) can be used to estimate {zeta}(crp)/n, {chi}/n and A_V in them. We compare our models to Herschel observations of these two ions, and estimate {zeta}(crp) ~ 4-6 x 10^-16 (n/100 cm^-3) s^-1 and chi/n = 0.03 cm^3 for diffuse foreground clouds towards W49N.
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.
The mass of molecular gas in an interstellar cloud is often measured using line emission from low rotational levels of CO, which are sensitive to the CO mass, and then scaling to the assumed molecular hydrogen H_2 mass. However, a significant H_2 mas
s may lie outside the CO region, in the outer regions of the molecular cloud where the gas phase carbon resides in C or C+. Here, H_2 self-shields or is shielded by dust from UV photodissociation, where as CO is photodissociated. This H_2 gas is dark in molecular transitions because of the absence of CO and other trace molecules, and because H_2 emits so weakly at temperatures 10 K < T < 100 K typical of this molecular component. This component has been indirectly observed through other tracers of mass such as gamma rays produced in cosmic ray collisions with the gas and far-infrared/submillimeter wavelength dust continuum radiation. In this paper we theoretically model this dark mass and find that the fraction of the molecular mass in this dark component is remarkably constant (~ 0.3 for average visual extinction through the cloud with mean A_V ~ 8) and insensitive to the incident ultraviolet radiation field strength, the internal density distribution, and the mass of the molecular cloud as long as mean A_V, or equivalently, the product of the average hydrogen nucleus column and the metallicity through the cloud, is constant. We also find that the dark mass fraction increases with decreasing mean A_V, since relatively more molecular H_2 material lies outside the CO region in this case.
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.
We use observations of the CI, CII, HI, and H_2 column densities along lines of sight in the Galactic plane to determine the formation rate of H_2 on grains and to determine chemical reaction rates with Polycyclic Aromatic Hydrocarbons. Photodissocia
tion region models are used to find the best fit parameters to the observed columns. We find the H_2 formation rate on grains has a low rate (R ~ 1 x 10^(-17) cm^(3) s^(-1)) along lines of sight with low column density (A_V < 0.25) and low molecular fraction (f_(H_2) < 10^(-4)). At higher column densities (0.25 < A_V <2.13), we find a rate of R ~ 3.5x10^(-17) cm^(3) s^(-1). The lower rate at low column densities could be the result of grain processing by interstellar shocks which may deplete the grain surface area or process the sites of H +H formation, thereby inhibiting H_2 production. Alternatively, the formation rate may be normal, and the low molecular fraction may be the result of lines of sight which graze larger clouds. Such lines of sight would have a reduced H_2 self-shielding compared to the line-of-sight column. We find the reaction C^+ +PAH^- --> C + PAH^0 is best fit with a rate 2.4 x 10^(-7) Phi_PAH T_2^(-0.5) cm^(3) s^(-1) with T_2= T/100 K and the reaction C^+ + PAH^0 --> C + PAH^+ is best fit with a rate 8.8x 10^(-9)Phi_PAH cm^(3) s^(-1). In high column density gas we find Phi_PAH ~ 0.4. In low column density gas, Phi_PAH is less well constrained with Phi_PAH ~ 0.2 - 0.4.
