The future of protoplanetary disk models
Greenwood, Aaron James
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Publication date: 2018
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Greenwood, A. J. (2018). The future of protoplanetary disk models: Brown dwarfs, mid-infrared molecular spectra, and dust evolution. Rijksuniversiteit Groningen.
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4
T H E E F F E C T S O F D U S T E V O L U T I O N O N
P R O T O P L A N E TA R Y D I S K S I N T H E
M I D - I N F R A R E D
abstract
The evolution of dust is one of the fundamental pillars upon which we build our understanding of planet formation and the lifetime of protoplanetary disks. How-ever, this evolution is difficult to observe because it operates on Myr timescales, and the dust-rich disk midplanes are typically very optically thick at mid-infrared and optical wavelengths.
In this paper, we couple together the dust evolution code two-pop-py with the thermochemical disk modelling code ProDiMo. We create a series of ther-mochemical disk models that simulate the evolution of dust over time, which includes the radial drift, growth, and settling of dust grains. We examine the effects of this dust evolution on the mid-infrared gas emission, focussing on the mid-infrared spectral lines that are readily observable with Spitzer and the upcoming E-ELT and JWST. The mid-infrared lines of species such as HCN and CO2provide an important diagnostic of the inner disk. Our models show that each species emits from different vertical and radial regions and at different gas temperatures. Hence, analyzing their spectra can give valuable insight into the two-dimensional structure of the disk. Both the E-ELT and JWST will provide a significant boost in sensitivity, spectral resolution, and spatial resolution. In order to make the most of the resulting data, we need to create models that can capture the radiative transfer and temperature structure, and the complex chemical networks that govern each species’ formation.
4.1 introduction
Throughout the few-million-year lifetime of a protoplanetary disk, its evolution is dominated by the gas and dust which accrete onto the star, coalesce into larger bodies, or are dissipated by photoevaporation and stellar winds. The dust in these disks is a significant factor in their evolution. Although dust particles (assuming typical ISM abundances) make up only a small portion of the total disk mass, small grains composed of dust and ice dominate the radiative transfer of the disk and provide “seeds” for planets to form.
Perhaps even more crucial than calculating the total amount of dust in a disk is to determine the distribution of that dust. In the eras of ALMA, JWST, and E-ELT we have both the sensitivity and the angular resolution to spatially resolve nearby protoplanetary disks, to spectrally resolve the emission lines from molecules, and to detect the broad emission features from silicate grains. The distributions of gas and dust in the disk are not necessarily co-spatial. For example, Lin et al. (2006) find with the SMA that the gas disk of AB Aur is likely larger than the dust disk. More recently, Cleeves et al. (2016) use ALMA detect12CO emission in IM Lup out to 970 AU, but find that the dust continuum emission is significantly truncated at 313 AU. Pinte et al. (2018a) directly map temperature and velocity gradients in the disk of IM Lup, using ALMA observations of CO isotopologues. Techniques such as this allow us a greater understanding of the gas structure of disks. The gas-to-dust ratio is not expected to be constant with height, because dust grains are expected to grow and fall towards the midplane (Blum & Wurm 2008; Dominik & Dullemond 2008) and the scale heights of the dust and gas disks may differ (de Gregorio-Monsalvo et al. 2013; Avenhaus et al. 2018) with T Tauri stars and brown dwarfs having flatter dust disks and relatively thicker gas disks than Herbig stars (Mulders & Dominik 2012). A crucial step that we must take is to understand the physics behind these effects, and how we can incorporate them into a thermochemical disk model.
Typical mid-infrared water line fluxes in T Tauri disks have been observed to range between about 2×10−13 erg cm−2 s−1 and 2×10−15 erg cm−2 s−1 (Pontoppidan et al. 2010). The authors also note that there appears to be a sub-class of disks which have strong 14.98 µm CO2emission, but with no detectable contributions in the 14 to 16 µm range from water, HCN, and C2H2. Previous results by Meijerink et al. (2009) and Bosman et al. (2017) suggest that a high gas-to-dust ratio of 1000:1 in the line-emitting regions might be necessary in order to reproduce the mid-infrared line fluxes that we have observed with Spitzer. This ratio has been adopted by the modelling community (Bruderer et al. 2015; Bosman et al. 2017). However, in order to justify this ratio we need to explain what has happened to the dust: if the disk formed from a molecular cloud with a gas-to-dust ratio of 100:1, this dust cannot disappear without reason. We know that dust settles in disks and that the midplanes are typically more dust-rich than the upper layers, but we need to include this dust settling in our models in
4.1 introduction 109 order better to quantify the gas-to-dust ratio of the line-emitting regions. In this paper, for the first time we couple a dust evolution code with a thermochemical modelling code and analyze the effects of dust evolution on the mid-infrared spectral lines. The radial dust distribution is calculated from the dust evolution model, while the vertical dust distribution is calculated with self-consistent dust settling. By feeding this dust structure to a thermochemical model, the molecular abundances and spectral lines are calculated without making assumptions about the gas and dust temperatures, opacities, or the size of the line-emitting region. We show that the gas-to-dust ratio of the mid-infrared line-emitting regions can increase substantially as the dust component of the disk evolves, showing that the combination of dust settling and grain growth is able to explain why we need to increase the gas-to-dust ratio in order to match observed line fluxes.
Accurately determining the gas and dust masses of protoplanetary disks is a difficult task. Primarily, this is due to the fact that much of the line and continuum emission is optically thick: there is no known way to derive gas and dust masses from line and continuum observations that is free of significant degeneracies. Although observing disks with gaps can help to measure scale heights and thus estimate midplane densities, there can be a lot of optically-thick gas and dust in the midplane that cannot be observed directly.
It is also difficult to accurately observe the dust grain size distribution as a function of radius and height. For example, although there is progress to spatially resolve the dust surface density of disks (Pinilla et al. 2014), the measured spectral index is dependant upon assumptions about the dust temperature. Scattered light imaging using SPHERE has been used to observe the surface of dust disks (Ginski et al. 2016; Stolker et al. 2016; Avenhaus et al. 2018; Muro-Arena et al. 2018). Particularly, the survey of eight T Tauri disks introduced by Avenhaus et al. (2018) is a valuable set of observations. Although a detailed analysis of each source is left for forthcoming papers, this first paper provides insights such as showing that all of the observed T Tauri disks appear to have τ =1 surface flaring indices between∼1.1 and∼1.6, and shows striking geometric structures such as gaps, rings, and even the lower disk surface of three disks. If an inclined disk has rings or gaps in the dust structure, the height of the dust scattering surface can be estimated by geometrically fitting these structures (Ginski et al. 2016; Avenhaus et al. 2018).
In comparison to micron-sized dust grains, decimetre-sized bodies have very little effect on the radiative transfer of the disk in the mid-infrared regions. However, their effect on the disk’s evolution is much more significant. Because they are less affected by processes such as viscosity and turbulence, decimetre-sized bodies are more likely to be found close to the disk’s midplane, and are a crucial step towards the eventual formation of planets. Unfortunately, we cannot yet directly observe such large bodies: we must infer their presence through observations of smaller grains and with models of dust evolution.
The purpose of this paper is to analyze the effect of dust evolution and migra-tion on the mid-infrared spectral lines of a T Tauri protoplanetary disk. We do this by modelling the evolution of dust over time, and creating a thermochemical model of the disk at discrete time steps in the evolution. The result is that we can incorporate a self-consistent description of dust evolution into our thermochemi-cal disk models, where the gas-to-dust ratio and dust size distribution vary not only at each timestep, but also vary radially and vertically through the disk. 4.2 dust growth and migration
The migration and evolution of dust is a significant factor in the evolution of a protoplanetary disk. Protoplanetary disks typically only live for up to 10 Myr, so their evolution is remarkably fast (Williams & Cieza 2011). Radial drift depletes the outer disk (& 10 AU) of dust grains, and grain coagulation allows rapid
grain growth in the inner disk, around 1 AU. Decimeter-sized particles are then expected to rapidly drift inwards to the central star (Nakagawa et al. 1986), which can create a barrier towards the formation of larger objects. Due to dust settling, we do not expect to observe micron-sized dust particles in the surface layers of the disk. However, observations of mid-infrared silicate emission clearly indicate the presence of these dust particles (Aitken et al. 1988; Pollack et al. 1994; Kessler-Silacci et al. 2006). Thus, either settling does not sufficiently deplete this population or there is some mechanism which replenishes these grains.
Indeed, we cannot yet explain why small dust grains exist in the outer disk for as long as they do. The problem is that radial drift (Brauer et al. 2008; Birnstiel et al. 2010b) and grain coagulation (Dominik & Dullemond 2008) should rapidly deplete the population of small dust grains. However, it is clear that not only do these small grains persist, exoplanet observations prove that larger objects also regularly survive long enough to form large terrestrial planets.
In order to explain observations of sub-mm sized grains in the outer disk, there must be processes which counteract radial drift and replenish the small grain population that grain coagulation rapidly depletes (Birnstiel et al. 2010a; Pinilla et al. 2013). In order to counteract this loss of small grains through coagulation and radial drift, fragmentation is introduced, whereby collisions between larger aggregated particles can fragment them into smaller particles (Birnstiel et al. 2010b). In brown dwarf disks, turbulence may play a role in counteracting radial drift and slowing the inwards migration of dust (Pinilla et al. 2013).
4.3 modelling strategy 111 4.3 modelling strategy
A total of four separate codes were used in order to produce the models in this paper, each with a distinct purpose. The underlying disk model is based upon the “DIANA standard” T Tauri disk described in Woitke et al. (2016), with the exception of the dust structure. The model parameters used in each code are described later on: this section serves simply as a technical description of how to interface the four codes together.
First, we use the two-population dust evolution codetwo-pop-py1(Birnstiel et al. 2012, 2015, 2017) to model the evolution of dust. The two-pop-py code produces a one-dimensional description of the dust at each age increment. It is a simplified version of the dust evolution code described in Birnstiel et al. (2010a), calibrated with the use of these more complex models and based upon the use of two dust grain populations: a small monomer population, and a large grain population. The small grain population is coupled to the gas, not affected by drift velocities, and is constant in time and space. The population of large grains can grow in size, and is affected by the limiting mechanisms of radial drift and grain fragmentation. The reconstruction of the grain size distribution from the simple two-population model is described by Birnstiel et al. (2015).
Fromtwo-pop-py, we obtain the gas surface density as a function of radius (thegasdensfile), the dust surface density as a function of radius (thedensfile), and a file which describes the dust mass fraction as a function of radius and grain size (thecompositionfile). In the first column of thecompositionfileis the radial grid, and each subsequent column – one column for every grain size – records the fraction of the total mass at that radius that is accounted for by each grain size. These files are produced for each age increment. Aftertwo-pop-py, each age increment becomes its own separate disk model with its own set of inputs and outputs.
Next, we use the code MCMax (Min et al. 2009) to create a two-dimensional model of the disk structure and calculate the dust continuum radiative transfer for the dust temperature. MCMax is able to read in thegasdensfile,densfile, andcompositionfile, using parameter keywords of the same names. We also specify the size of each dust grain with thergrain#parameter, so that the grain sizes are conserved betweentwo-pop-pyand MCMax.
In principle, there are two methods in MCMax to calculating the scale heights of the gas and dust: to have parameterized scale heights, or to solve for hydrostatic equilibrium. We take a hybrid approach: we force the scale heights of the gas to remain parameterized, while allowing the dust to settle in a self-consistent manner (described by Mulders & Dominik 2012). This required some small modifications to the code. Normally, MCMax solves the structure of both the gas and dust for hydrostatic equilibrium and then applies the self-consistent dust 1 two-pop-pyis available on Github at http://birnstiel.github.io/two-pop-py/.
settling. However, we force MCMax to parameterize the gas structure, then solve the dust for hydrostatic equilibrium and apply self-consistent dust settling.
We do not argue for the physical correctness of this procedure (which is unknown), rather for the simplicity it brings. The first argument is that we want to remain as close to the DIANA standard of models as possible, only deviating from the standard with the dust distribution. The second argument is that it simplifies the results and analysis: although the total gas mass in the disk does decrease with age, the gas scale heights remain constant. This allows us better to analyse the effects that different dust distributions have on the mid-infrared molecular lines, under the assumption that everything else is equal.
MCMax outputs aforProDiMo.fits.gzfile, which is an existing option in the code. This file contains the 2D distributions of gas and dust, and the opacities. The third piece of software in the pipeline is ProDiMo (Woitke et al. 2009; Kamp et al. 2010; Aresu et al. 2011), which takes the forProDiMo.fits.gz file and calculates a full thermochemical disk model. Often, a ProDiMo model begins with calculating the parameterized disk structure and then running the radiative transfer. However, in this paper we take the disk structure directly from MCMax. We then run the disk chemistry, taking the reaction rates for 235 species from the UMIST2012 chemical network (McElroy et al. 2013) to calculate the disk’s thermal and chemical equilibrium state. Because the overall opacity and density structure of the disk is fixed, there is no need for global iterations.
The final element is FLiTs, which is able to calculate a high-resolution spectrum from a disk model (Woitke et al. 2018) across the infrared wavelength range. Once again, there is an existing interface between the two codes. ProDiMo writes a ProDiMoForFLiTs.dat file, which contains the gas and dust temperatures, the stellar spectrum and local radiation field, opacities, molecular number densities, and level populations. FLiTs reads this file and calculates the spectrum of the disk for the desired molecules and wavelength range.
4.3.1 Model parameters
Between the different codes, we ensure that the disk parameters remain consistent. Table 4.1 describes the parameters of the T Tauri disk model, which is based upon the T Tauri model in Chapter 3. The spatial grids are not conserved between codes. This is a practical necessity, because each code has a different gridding system. However, there are no significant differences caused by re-gridding, and essential parameters such as the surface density profile, grain size distribution, and dust and gas masses are conserved between each code. We do not aim to accurately model the dust distribution of an observed disk: instead, we assess how changes in the dust distribution can affect mid-infrared lines. Although MCMax determines the stellar luminosity implicitly from the radius
4.4 dust migration and disk surface densities 113 and effective temperature, the resulting 1.0 L is consistent with the luminosity that we explicitly define for ProDiMo.
4.4 dust migration and disk surface densities
The migration of dust in our models is manifested in changes in both the surface densities and dust grain size distributions over time, as computed bytwo-pop-py. These are one-dimensional results, and we later use MCMax to compute the two-dimensional disk structure. The actual timescales are not relevant for this discussion. First, we do not know how accurate the timescales of evolution are: it is more fruitful to compare a disks with different surface densities than to compare disks of different ages, because these parameters are more readily observable. The problem with using disk ages as a basis for comparison is that the ages are very uncertain, both in the models and any observed disks. For example, disks in Ophiuchus are thought to be less than 1 Myr old (Furlan et al. 2009). However, within this sample of similarly-aged disks, basic properties such as the disk mass may vary by about two orders of magnitude (Testi et al. 2016). It is clear that the disks in Ophiuchus vary to a much greater degree than can be explained by age alone.
Another reason why timescales are not strictly relevant is that in each ProDiMo model we use steady-state chemistry: the ProDiMo chemistry is permitted to run for longer than the “age” of thetwo-pop-pymodel. However, the time scales for disk surface chemistry (on the order of years) are much shorter than the timescale of dust evolution (&104years): it is only when considering longer wavelengths
such as the sub-mm that we might need to calculate time-dependent chemistry. Nevertheless, despite these approximations and our uncertainty over the exact timescales of dust evolution, for brevity we refer to each model by itstwo-pop-py age.
Figures 4.1 to 4.3 show how the gas and dust surface densities change, from t0=0.018 Myr to tmax=10 Myr. The dust evolution is much more pronounced than the gas evolution, resulting in significant changes in the gas-to-dust ratio with location and time. Although the gas mass does slowly decrease over time, the loss of dust due to radial drift is much greater: this is what causes the total gas-to-dust ratio of the disk to increase over time, from 100 at t=0 to over 6000
at 10 Myr. For the column of gas at a radius of 1 AU, the youngest model has a gas-to-dust ratio of about 40, whereas the oldest model reaches about 4×104. The changes in gas-to-dust ratio are due to radial drift: as the dust evolves, more and more matter is accreted onto the central star and the overall dust mass of the disk decreases.2
2 Note that in order to simplify the analysis of comparing different dust structures, there is no provision for the accretion luminosity in our MCMax and ProDiMo models.
Table 4.1:A summary of important model parameters used in each step of the procedure. Some parameters, for example the disk mass, are important fortwo-pop-py, MCMax, and ProDiMo.
However, these parameters are not listed for the subsequent codes because their effects are embedded in the data passed between the codes. The only parameter in this table that is passed through to FLiTs is the disk inclination. Of thetwo-pop-pyparameters in this table, the disk mass and gas-to-dust ratio
are only valid for the initial state of the disk. The other parameters in this table are constant in time. Ngrainsis the number of grains used fortwo-pop-py’s reconstruction of the grain size distribution.
Symbol Quantity two-pop-py MCMax ProDiMo
R∗ Stellar radius 2.086 R 2.086 R
M∗ Stellar mass 0.70 M 0.70 M 0.70 M
Mdisk/M∗ Initial disk mass 0.1
Rtaper Taper radius 100 AU 100 AU
γvisc Viscosity exponent 1
Ngrains Number of dust grains 150 150
amin Minimum dust grain size 10−5cm 10−5cm
amax Maximum dust grain size 1.9×102cm
fvac Dust grain porosity (vacuum fraction) 0.25
fmax Maximum hollow volume ratio 0.8
tmax Final timestep 107years
αturb Turbulence 10−3 10−3
Rin Inner radius 0.06835 AU 0.07 AU
Rout Outer radius 2000 AU 600 AU
g/d Initial gas-to-dust ratio 100
T∗ Stellar surface temperature 4000 K 4000 K 4000 K
Nrad Number of radial grid points 240 500 240
Nθ Number of azimuthal grid points 150
NZ Number of vertical grid points 160
Ninner Number of radial points near inner rim 100
gasevol Gas evolution true
D Distance of the disk 140 AU 140 AU
i Inclination of the disk 45◦ 45◦
χISM Interstellar radiation field (Draine 1978) 1 1
H0 Gas scale height at 1 AU 0.05012 AU
β Flaring exponent 1.15
scset Self-consistent dust settling true
L∗ Stellar luminosity 1.0 L
fPAH PAH abundance (relative to ISM) 10−4
fUV/L∗ UV excess 0.01
pUV UV powerlaw exponent 1.3
ζCR Cosmic ray H2ionization rate 1.7×10−17s−1
LX−ray X-ray luminosity 1030erg s−1
The dust is a distribution of hollow spheres, where the maximum fractional volume filled by the central void is 0.8 (Min et al. 2005, 2016). The dust grain mixture in MCMax is 60% amorphous Mg0.7Fe0.3Si O3silicates (Dorschner et al. 1995), 15% amorphous carbon (Zubko et al. 1996), and 25%
vacuum. The viscosity helps define the surface densityΣg(r), where
Σg(r)∝(r/rc)−γviscexph− (r/rc)2−γvisci with a characteristic radius rc=60 AU (Birnstiel et al.
4.5 size of the dust disk 115 The youngesttwo-pop-pymodel is close to the initial state of the system, and the low gas-to-dust ratio in the initial state of the inner disk is the result of a high level of inwards dust mass flux. As the disk ages, radial drift continues to deplete the total dust mass in the disk. One other notable trend in Fig. 4.3 is the “bump” in gas-to-dust ratio, which becomes significant at around 0.32 Myr old and at around r =40 AU and moves inwards with time. This bump is due to
a localized depletion in the dust, reported by Birnstiel et al. (2012) as a pile-up effect caused by increases in the disk temperature due to viscous heating, similar to the grain pile-up in Youdin & Chiang (2004).
Figure 4.4 describes how the gas mass, dust mass, and gas-to-dust ratio vary over time, integrated over the entire disk. This shows how the gas evolution implemented intwo-pop-pyoccurs over a much slower timescale than the dust evolution. As a result, the gas-to-dust ratio of the disk increases rapidly with age. Not only does the gas-to-dust ratio evolve over time, but the dust grain size distribution also changes with time. Figures 4.5 to 4.8 show the vertical cuts of the grain size distribution at radii of 0.1, 1, 10, and 100 AU. At radii of 10 AU or less, the trends are more or less the same: the grain size distribution shows both an overall decrease in surface densities, and a disporportionate depletion of larger grains. Larger grains are transported inwards due to radial drift. As a consequence, in the inner disk at 0.1 AU there exists a significant surface density in grains up to 10 cm in size at an age of 10 Myr. However, at 1 AU this cut-off is at a grain size of 1 cm, and about 0.05 cm at 10 AU. This happens because a population of large grains can only be maintained so long as there is an inwards flux of grains coming from larger radii: once this supply line is exhausted, the large grains will be depleted. The situation is slightly different at 100 AU: although there is no significant population of cm-sized, grains, the population of mm-sized grains grows until an age of 0.56 Myr.
4.5 size of the dust disk
One significant consequence of the method by which we invoke dust settling in our models is that the dust disk is less vertically-extended than the gas disk. We stress that this is not an artefact of parameterizing the gas structure, but a result of the self-consistent description of dust settling. If we instead allow both the gas and dust to reach hydrostatic equilibrium, the dust does still settle in a similar manner into a thinner disk than the gas, such that the upper layers of the fully hydrostatic disk are almost devoid of dust.
The dust disk calculated using self-consistent settling is thinner than the same disk would be if Dubrulle settling (Dubrulle et al. 1995) were used. The main differences between the self-consistent settling method (Mulders & Dominik 2012) and the Dubrulle setting is that the Dubrulle settling uses only the midplane density and temperature: thus, at the lower densities and higher temperatures of the upper disk their analytical solution becomes less accurate. Although
10−1 100 101 102 10−5 10−3 10−1 101 103 r (au) dust surface densit y (g cm − 2) 0.018 Myr0.032 Myr 0.056 Myr 0.1 Myr 0.18 Myr 0.32 Myr 0.56 Myr 1.0 Myr 1.8 Myr 3.2 Myr 5.6 Myr 10 Myr
Figure 4.1: The dust surface density at each disk age increment.
10−1 100 101 102 10−3 10−1 101 103 105 r (au) gas surface densit y (g cm − 2) 0.018 Myr 0.032 Myr 0.056 Myr 0.1 Myr 0.18 Myr 0.32 Myr 0.56 Myr 1.0 Myr 1.8 Myr 3.2 Myr 5.6 Myr 10 Myr
4.5 size of the dust disk 117 10−1 100 101 102 100 101 102 103 104 105 r (au) gas-to-dust ratio 0.018 Myr 0.032 Myr 0.056 Myr 0.1 Myr 0.18 Myr 0.32 Myr 0.56 Myr 1.0 Myr 1.8 Myr 3.2 Myr 5.6 Myr 10 Myr
Figure 4.3: The ratio of the gas surface density to dust surface density at each disk age increment. 104 105 106 107 10-4 10-3 10-2 10-1 102 103 104
Figure 4.4: The dust and gas masses (left axis) and gas-to-dust ratio (right axis) of the entire disk over time.
10−510−410−310−210−1 100 101 102 103 104 105 10−9 10−6 10−3 100 103 106 Grain size (cm) Dust surface densit y (g cm − 2) r = 0.1 au 0.018 Myr 0.032 Myr 0.056 Myr 0.1 Myr 0.18 Myr 0.32 Myr 0.56 Myr 1 Myr 1.8 Myr 3.2 Myr 5.6 Myr 10 Myr
Figure 4.5: A vertical cut of the grain size distribution at r=0.1 AU.
10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 10−11 10−8 10−5 10−2 101 104 Grain size (cm) Dust surface densit y (g cm − 2) r = 1 au 0.018 Myr 0.032 Myr 0.056 Myr 0.1 Myr 0.18 Myr 0.32 Myr 0.56 Myr 1 Myr 1.8 Myr 3.2 Myr 5.6 Myr 10 Myr
4.5 size of the dust disk 119 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 10−11 10−8 10−5 10−2 101 104 Grain size (cm) Dust surface densit y (g cm − 2) r = 10 au 0.018 Myr 0.032 Myr 0.056 Myr 0.1 Myr 0.18 Myr 0.32 Myr 0.56 Myr 1 Myr 1.8 Myr 3.2 Myr 5.6 Myr 10 Myr
Figure 4.7: A vertical cut of the grain size distribution at r=10 AU.
10−5 10−4 10−3 10−2 10−1 10−11 10−8 10−5 10−2 101 104 Grain size (cm) Dust surface densit y (g cm − 2 ) r = 100 au 0.018 Myr 0.032 Myr 0.056 Myr 0.1 Myr 0.18 Myr 0.32 Myr 0.56 Myr 1 Myr 1.8 Myr 3.2 Myr 5.6 Myr 10 Myr
self-consistent settling agrees well with Dubrulle settling in the midplane, in the self-consistent settling description, smaller and smaller particles can decouple from the gas as the height above the midplane increases (Mulders & Dominik 2012). Contrarily, with Dubrulle settling, dust particles remain coupled to the gas, the distribution of<0.1 µm particles is nearly uniform throughout the disk,
and larger grain sizes are affected less by settling than the self-consistent model (Mulders & Dominik 2012).
It is a known phenomenon for dust disks to appear thinner than the gas disk. For example, de Gregorio-Monsalvo et al. (2013) use ALMA to observe the gas and dust structure in the disk HD 163296. They find a thick gas disk from channel maps of CO emission, while a relative lack of emission in the mid- and far-infrared parts of the SED may require a thinner dust disk, implying that significant settling of dust may have occurred. Furthermore, Muro-Arena et al. (2018) observe the disk with SPHERE and find no scattered light emission beyond the second gap at 100 AU. This lack of emission is consistent with a lack of small dust grains near the surface of the disk.
Although HD 163296 appears to have a rather strongly settled dust structure, we do not yet know how typical this result is. Markedly different disks are observed by Avenhaus et al. (2018), who suggest that the τ=1 scattering surface of the IM Lup disk lies at a height of 18 AU at a radius of 100 AU, while a similar figure is likely for the transition disk HD 97048 (Ginski et al. 2016). For comparison, the τ =1 surface (measured vertically, at 0.55 µm) at a radius of 100 AU in our 1 Myr old model is at a height of 4.33 AU above the midplane. The τ=1 surface height increases to 16.0 AU for our 0.10 Myr old model, while the disk at 3.2 Myr old is too optically thin at 100 AU for this surface to exist. Even our youngest models still have a dust disk that is thinner than the gas disk. Figures 4.9 to 4.12 show vertical cuts of the gas-to-dust ratio through the disks at each age: in every case, in the upper layers of the disk where some tenuous gas still exists, the gas-to-dust ratio can easily be 105or more. In the midplane of the inner disk, particularly at 0.1 AU, the gas-to-dust ratio of models younger than 0.56 Myr can be less than 10. This is in contrast to at 100 AU, where most of the disk at 0.018 Myr has a gas-to-dust ratio of 100. At young ages, there are few large grains in the outer disk: the dust only decouples significantly from the gas in the older models, once mm-sized dust grains have formed. However, at the inner radii, there is already a significant population of large grains at t=0.18 Myr. This gives rise to the low gas-to-dust ratio in the midplane at small radii.
From this perspective, the heights of the dust disks in our models appear to span a reasonable range of values. When comparing the thickness of the gas and dust disks, our youngest models may describe dust disks that are comparable to disks such as IM Lup that appear to be less settled, while the older models may be more comparable to disks such as HD 163296, where the dust disk may be significantly settled in comparison to the gas disk.
4.6 mid-infrared spectra 121 100 101 102 103 104 105 106 107 108 109 1010 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ·10−2 Gas-to-dust ratio Heigh t (A U) 0.018 Myr 0.032 Myr 0.056 Myr 0.1 Myr 0.18 Myr 0.32 Myr 0.56 Myr 1.0 Myr 1.8 Myr 3.2 Myr 5.6 Myr 10 Myr
Figure 4.9: Vertical cuts of the gas-to-dust ratio at r=0.1 AU. Note the multiplier of 10−2 on the y-axis.
The structure of the settled dust means that every disk has regions with a gas-to-dust ratio on the order of 1000 or more, which as we find in Section 4.6 is the minimum gas-to-dust ratio from which all species except C2H2tend to emit. 4.6 mid-infrared spectra
The migration and evolution of dust has a profound effect on the mid-infrared spectra and line-emitting regions of our disk model. In order further to discuss the line-emitting regions of each species, it is necessary to define the exact molecular lines we are using, and how the line-emitting regions themselves are derived.
We define the line-emitting region as the area from which 70% of the flux originates, in both the radial and vertical directions. The lower limit, x15, is defined so that 85% of the total line flux of that spectral line is emitted at radii greater than x15. The upper limit, x85, is the opposite – only 15% of the total line flux of that spectral line is emitted at a radius greater than x85. To define the vertical boundaries, we measure the z15 and z85 points for each radial grid point. Thus z15 becomes a vector, along the radius axis. For each radial point, z15 defines the height in the disk above which only 15% of the line flux is emitted. When we measure the properties of the line-emitting region for a given species (such as Tgas), these properties are averaged based upon the volume density of that species across the line-emitting region.
100 101 102 103 104 105 106 107 108 109 1010 0 5· 10−2 0.1 0.15 0.2 Gas-to-dust ratio Heigh t (A U) 0.018 Myr 0.032 Myr 0.056 Myr 0.1 Myr 0.18 Myr 0.32 Myr 0.56 Myr 1.0 Myr 1.8 Myr 3.2 Myr 5.6 Myr 10 Myr
Figure 4.10: Vertical cuts of the gas-to-dust ratio at r=1 AU.
100 101 102 103 104 105 106 107 108 109 1010 0 0.5 1 1.5 2 2.5 Gas-to-dust ratio Heigh t (A U) 0.018 Myr 0.032 Myr 0.056 Myr 0.1 Myr 0.18 Myr 0.32 Myr 0.56 Myr 1.0 Myr 1.8 Myr 3.2 Myr 5.6 Myr 10 Myr
4.6 mid-infrared spectra 123 100 101 102 103 104 105 106 107 108 109 1010 0 5 10 15 20 25 30 35 Gas-to-dust ratio Heigh t (A U) 0.018 Myr 0.032 Myr 0.056 Myr 0.1 Myr 0.18 Myr 0.32 Myr 0.56 Myr 1.0 Myr 1.8 Myr 3.2 Myr 5.6 Myr 10 Myr
Figure 4.12: Vertical cuts of the gas-to-dust ratio at r=100 AU.
Second, we define a sample of lines that we are investigating. Table 4.2 details exactly the molecular lines chosen for analysis, one for each species. For consistency, where possible, we analyze spectroscopic lines that have previously been analyzed in other literature (see references in Table 4.2). Whenever an individual molecular line is referenced in this paper, it refers to the line in this table.
The flux of a particular molecular line is driven primarily by three factors: the gas-to-dust ratio, the gas temperature in the line-emitting region, and the optical depth of the line. Figures 4.13 to 4.16 show how the gas-to-dust ratio, average gas temperature, and line flux change with age in the disk. Although the gas-to-dust ratio of the entire disk begins at 100:1, the self-consistent dust settling is not informed by the “age” of the dust model: it simply solves for the vertical structure of the dust without considering the timescales on which settling occurs, which may take on the order of a few×105years (Dullemond & Dominik 2004). Where we mention the flux of an individual spectral line, these fluxes are calculated using a vertical escape probability method (Woitke et al. 2009). Strictly speaking, these line fluxes are valid only for a face-on disk, because the effects of radial optical depth are not accounted for. In contrast, where we mention the flux densityof a spectrum calculated by FLiTs, this is a somewhat different diagnostic. These spectra have been calculated for an inclined disk and account for both the radial and vertical optical depth. Additionally, they are the flux densities of a convolved spectrum: we are typically measuring the peak flux of a complex of lines, not the integrated flux of a single line.
Table 4.2 :The emission line of each species chosen for analysis, including upper le vel ener gies E up and the Einstein A coef ficient (giving the rate of spontaneous emission). The description of the ro-vibrational lines of CO 2 ,C 2H 2 ,HCN ,and NH 3 is an abbr eviated for m of that described in Jacquemart et al. (2003 ); Rothman et al. (2005 ), wher e v j ar e the nor mal mode vibrational quantum numbers, l j ar e the angular momentum quantum numbers, and lis the absolute value of the sum of l j .The final entr y, for example R11 e, denotes that it is an R-branch transition, the lo w er -state rotational ener gy le vel is 11, and eor f denotes the symmetr y for l-type doubling. Species λ ( µm ) Transition E up ( K ) A ( s− 1 ) Refer ence CO 2 14.98299 v 1v 2l 2v 3r = 01101 → 00001, Q 6 e 983.85 1.527 Bosman et al. (2017 ) C 2H 2 13.20393 v 1v 2v 3v 4v 5l ± = 000011 → 000000, R11 e 1313.1 K 3.509 W oitke et al. (2018 ) HCN 14.03930 v 1v 2l 2v 3 = 0110 → 0000, Q 6 e 1114.1 2.028 Bruder er et al. (2015 ) o-H 2O 17.75408 J0 = 6 → J00 = 5 1278.5 0.002869 Notsu et al. (2017 ) NH 3 10.33756 v 1v 2v 3v 4 = 0100 → 0000, J0 = 3 → J00 = 3 1515.3 11.57 OH 20.11506 J0 = 13.5 → J 00 = 12.5 5527.2 50.47 W oitke et al. (2018 )
4.6 mid-infrared spectra 125 4.6.1 Line fluxes: C2H2in comparison to other species
Throughout the dust evolution simulation, the line flux of each species except C2H2increases by at least an order of magnitude, whereas C2H2remains more or less constant in line flux. This is because C2H2 simply does not exist in these models in the upper layers of the disk, and appears easily to be destroyed when the dust evolves and the disk becomes more optically thin. As the disk ages the remaining C2H2 is concentrated further towards the midplane, and the line-emitting region is pushed both towards the midplane and out to larger radii (up to∼0.6 AU). In these models, we see the same bifurcated structure of C2H2discussed in Chapter 3 and seen also in Walsh et al. (2015). A significant proportion of the line-emitting population of C2H2is below the AV =10 line, meaning that the dust continuum in this region is very optically thick in the mid-infrared. As the dust evolves and becomes more optically thin, the C2H2 responds and shifts closer towards the midplane: there is no chance for the line flux to increase. We have seen in Chapter 3 that the more dust-rich disk model has the strongest C2H2lines, where for all other species the more dust-rich model has weaker lines.
Our models predict line fluxes that are not observable with any current space-craft, but there are clear Spitzer detections of C2H2in T Tauri disks with similar detection rates to the other species (Pontoppidan et al. 2010). Although it is possible that uncertainties in the chemical network and reaction rates are leading to significant inaccuracies in the distribution of C2H2 calculated by ProDiMo, ProDiMo is not the only code that produces such results (see Walsh et al. 2015). It is possible that this discrepancy is a natural consequence of the dust structure of our models.
For all species except C2H2, their behaviour is in line with the intuitive ex-pectation that their line fluxes increase as the dust evolves. This is because the gas-to-dust ratio in the line-emitting region of these species also increases significantly as the dust evolves. The line fluxes produced by these species can match or exceed the line fluxes from previous Spitzer observations (Pontoppidan et al. 2010; Carr & Najita 2011; Salyk et al. 2011).
4.6.2 Properties of the line-emitting regions
Figures 4.13 to 4.17 show changes in the gas-to-dust ratio, gas temperature, vertical dust optical depth, escape probability line flux, and line-emitting area of each line over time. Although for each species the gas-to-dust ratio increases steadily over time, C2H2 has a consistently lower ratio than the other species because its line-emitting area is closer towards the mid-plane. For each species except C2H2, it is clear that they prefer to emit from regions with gas-to-dust ratios of 1000 or more.
The trends in gas temperature are more complex. For C2H2, at 1.8 Myr the gas temperature of the line-emitting region drops dramatically, from about 900 K to 350 K. The temperature drops even more as the disk ages further. This trend is also reflected in the fact that C2H2is in absorption for the oldest few disk models (see Fig. 4.19). The reasons for this are changes in the line-emitting area: the C2H2 abundances in the oldest disk models drop significantly, and the line-emitting area moves outwards and towards the mid-plane. The gas temperatures of the CO2and NH3line-emitting regions stay relatively stable over time. For HCN and H2O, we see an increase in gas temperature, particularly for the oldest models. This is because the line-emitting regions become larger and move towards slightly warmer, higher layers in the disk.
What Fig. 4.16 shows is that if we compute the spectra of our models using FLiTs, we would expect the fluxes of every species except C2H2 to increase significantly as the dust in the disk evolves. This is illustrated by Figs. 4.18 and 4.19, which show that between the youngest and oldest disks models, the peak flux densities for every species except C2H2 increase by factors ranging from 30 for H2O to 200 for OH.
For comparison to the sensitivities of infrared observatories, the median 1 σ mid-infrared line sensitivity of Spitzer is about 8.5×10−19W m−2, thus many individual spectral lines are far too faint for Spitzer to detect.3 However, the ro-vibrational bandheads of species such as CO2contain many lines that at a low spectral resolution are blended together, which is why we can see these species with Spitzer. In some of the more evolved disks, even individual OH, o-H2O, NH3, and HCN lines are significantly above this sensitivity limit (see Fig. 4.16).
Because Spitzer had a low spectral resolution, we generally observe an entire complex of lines that have been blended together. Following the flux densities of the convolved spectra presented in Figs. 4.18 and 4.19, and assuming a 5 σ Spitzersensitivity of 5 mJy, we expect that only C2H2would be undetectable at every age. OH and NH3may only be detectable in more evolved disks, while H2O, HCN, and particularly CO2should be detectable in every model. However, comparing the R = 2 800 spectra with the R = 600 spectra, the complexes of
water lines can easily become blurred at Spitzer’s low spectral resolutions, making it difficult to determine the continuum flux. The continuum sensitivity of JWST’s MIRI instrument is around 0.1 mJy at 15 µm (Glasse et al. 2015), thus with JWST we expect that in every model, all species except C2H2would be detectable.
The behaviour of C2H2is different to the other species: C2H2even goes into absorption at 5.6 Myr and 10 Myr. The line emission features in disk models up to 1.8 Myr old appear to be dominated by emission from near the inner wall, while in the older disk models the line-emitting region extends out to 0.6 AU and is close to the mid-plane. The absorption lines in the 5.6 Myr and 10 Myr old models are likely attributable to the fact that the C2H2emission comes from 3 From the Spitzer IRS Instrument Handbook:http://irsa.ipac.caltech.edu/data/SPITZER/docs/
4.6 mid-infrared spectra 127 10−2 10−1 100 101 101 102 103 104 105 106 Age (Myr) Gas/dust ratio in line-emitting region C2H2 CO2 HCN NH3 OH o-H2O
Figure 4.13: The gas-to-dust ratio in the line-emitting region of each species, over time. The significant bump seen in the gas-to-dust ratio of OH is misleading: our measurement of the line-emitting area is biased by the fact that there is a small amount of OH emission coming from warm upper layers at relatively large radii. These upper layers have a disproportionately high gas-to-dust ratio.
close to the mid-plane. As described in Section 3.4.3, there exists a turnover in the gas temperature around the AV =1 line, such that there may exist clouds of colder gas above the warmer gas in the disk. Absorption lines may result if these clouds of colder gas exist between our line of sight and the line-emitting region of the species. On the other hand, the fact that CO2is the brightest species by a significant margin suggests that our models may be representative of the sub-class discovered by Pontoppidan et al. (2010), where in six disks only CO2 was unambiguously detected. This sub-class may consist of disks where the dust is significantly settled in comparison to the gas, similar to the structure produced in our models by the self-similar dust settling: in this case, we would expect CO2to be the brightest species in the mid-infrared, and thus other species may remain undetected. The reason that CO2fluxes can be so high is that it is a robust species which is able to survive in relatively optically thin regions: as the dust structure evolves and becomes more optically thin, the line-emitting area of CO2 also grows: Fig. 4.17 shows that CO2 can have a line-emitting area of almost 1000 AU2.
10−2 10−1 100 101 200 400 600 800 1,000 Age (Myr) Gas temp erature in line-emitting region (K) C2H2 CO2 HCN NH3 OH o-H2O
Figure 4.14: The density-averaged gas temperature in the line-emitting region of each species, over time.
10−2 10−1 100 101 10−2 10−1 100 101 Age (Myr) AV line C2H2 CO2 HCN NH3 OH o-H2O
Figure 4.15: The density-averaged vertical optical depth of the dust at 20 µm in the line-emitting region of each species, over time.
4.6 mid-infrared spectra 129 10−2 10−1 100 101 10−21 10−20 10−19 10−18 10−17 10−16 Age (Myr) Line flux (w m -2 ) C2H2 CO2 HCN NH3 OH o-H2O
Figure 4.16: The escape probability line flux of each species, over time.
10−2 10−1 100 101 10−3 10−2 10−1 100 101 102 103 Age (Myr) Line-emitting area (au 2 ) C2H2 CO2 HCN NH3 OH o-H2O
Figure 4.17: The line-emitting area, in square astronomical units, of each species over time. This area is calculated from a face-on perspective, assuming that the line emission is a simple annulus encompassed by the inner and outer radii of the line emission (x15 and x85). Much like the gas-to-dust ratio in Fig. 4.13, for less-evolved models, the line-emitting area calculation of OH is biased by small amounts of emission at larger radii.
Wavelength (micron) Flux (mJy) 14.4 14.5 14.6 0 0.5 1 1.5 14.8 14.9 15 15.1 0 100 200 14.6 14.8 0 0.5 1 17.7 17.8 17.9 0 20 40 13.8 13.9 14 14.1 0 5 10 15 13.5 13.6 13.7 13.8 0 0.1 0.2 0.018 Myr 14.4 14.5 14.6 *5 14.8 14.9 15 15.1 14.6 14.8 17.7 17.8 17.9 13.8 13.9 14 14.1 13.5 13.6 13.7 13.8 0.032 Myr 14.4 14.5 14.6 14.8 14.9 15 15.1 14.6 14.8 17.7 17.8 17.9 13.8 13.9 14 14.1 13.5 13.6 13.7 13.8 0.056 Myr 14.4 14.5 14.6 14.8 14.9 15 15.1 14.6 14.8 17.7 17.8 17.9 13.8 13.9 14 14.1 13.5 13.6 13.7 13.8 0.1 Myr 14.4 14.5 14.6 14.8 14.9 15 15.1 14.6 14.8 17.7 17.8 17.9 13.8 13.9 14 14.1 13.5 13.6 13.7 13.8 0.18 Myr 14.4 14.5 14.6 NH3_H 14.8 14.9 15 15.1 CO2_H 14.6 14.8 OH_H 17.7 17.8 17.9 H2O 13.8 13.9 14 14.1 HCN_H 13.5 13.6 13.7 13.8 C2H2_H 0.32 Myr
Figure 4.18: FLiTs spectra of the disk models up to 0.32 Myr old, convolved to a spectral resolution R=2 800 (black lines) and R=600 (red lines). Where indicated, the spectra have been multiplied by 5, 10, or 50 in order to improve visibility. This disk is at an inclination of 45◦. The reason why the spectral lines become weaker at 0.032 Myr, only to
become stronger again at 0.056 Myr, is likely due to the dust evolution: Fig. 4.3 shows that radii smaller than 1 AU, the gas-to-dust ratio drops between the 0.018 Myr and 0.032 Myr models, before increasing again at the 0.056 Myr mark. Because the onset of radial drift suddenly decreases the gas-to-dust ratio, we see a corresponding drop in line fluxes.
4.6 mid-infrared spectra 131 Wavelength (micron) Flux (mJy) 14.4 14.5 14.6 0 50 100 *10 14.8 14.9 15 15.1 0 2,000 4,000 6,000 8,000 *10 14.6 14.8 0 100 200 *50 17.7 17.8 17.9 0 500 1,000 *10 13.8 13.9 14 14.1 0 200 400 600 800 *10 13.5 13.6 13.7 13.8 −0.2 0 0.2 0.56 Myr 14.4 14.5 14.6 *10 14.8 14.9 15 15.1 *5 14.6 14.8 *50 17.7 17.8 17.9 *5 13.8 13.9 14 14.1 *10 13.5 13.6 13.7 13.8 1.0 Myr 14.4 14.5 14.6 *10 14.8 14.9 15 15.1 14.6 14.8 *10 17.7 17.8 17.9 *5 13.8 13.9 14 14.1 *5 13.5 13.6 13.7 13.8 1.8 Myr 14.4 14.5 14.6 14.8 14.9 15 15.1 14.6 14.8 17.7 17.8 17.9 13.8 13.9 14 14.1 13.5 13.6 13.7 13.8 3.2 Myr *10 14.4 14.5 14.6 14.8 14.9 15 15.1 14.6 14.8 17.7 17.8 17.9 13.8 13.9 14 14.1 13.5 13.6 13.7 13.8 5.6 Myr 14.4 14.5 14.6 NH3_H 14.8 14.9 15 15.1 CO2_H 14.6 14.8 OH_H 17.7 17.8 17.9 H2O 13.8 13.9 14 14.1 HCN_H 13.5 13.6 13.7 13.8 C2H2_H 10 Myr *5
Figure 4.19: FLiTs spectra of the disk models from 0.56 Myr old, convolved to a spectral resolution R=2 800 (black lines) and R=600 (red lines). Where indicated, the spectra have been multiplied by 5, 10, or 50 in order to improve visibility. This disk is at an inclination of 45◦. Note that the y-axis limits are different to those in Fig. 4.18
4.7 discussion
As the dust evolves, grains are depleted from the disk and the molecular line emission grows substantially for every species except C2H2. We find that the reason for this is because C2H2emission comes from closer towards the mid-plane than the other molecules, thus it is more affected by both the optical depth of the dust in the disk, and the negative gas temperature gradients around AV =1. As an approximation, the T Tauri spectra observed by Carr & Najita (2011) have peak C2H2flux densities of up to about 20 mJy, and C2H2/HCN line flux ratios between about 0.08 and 0.8. As the line fluxes and spectrum flux densities in Figs. 4.16, 4.18 and 4.19 show, this ratio is significantly lower for our models. We are unable to explain the detections of C2H2 in T Tauri disks, because none of our models produces C2H2lines that are bright enough. However, the fact that C2H2behaves so differently to other species suggests either that uncertainties in the chemical network of C2H2are creating unreliable results for C2H2, or that the dust structure of our models is not representative of disks with C2H2detections.
Another notable result is that CO2is much brighter than all other species in our models, suggesting that our models may be representative of the disks found by Pontoppidan et al. (2010) where only CO2was detected: that is, these sources may have a strongly settled dust structure. The other sources may have a less-settled dust structure with lower CO2line fluxes and more equal ratios between the line fluxes of different species. In all of our models, the CO2spectrum has a brighter flux density than all other species by at least a factor of ten. However, CO2is not the brightest species in terms of the escape probability flux of an individual Q-branch line: for example, the HCN line is almost an order of magnitude brighter at all ages. Thus, the explanation for the relative brightness of CO2, and relative absence of other molecules, likely lies in the dust and temperature structure of the models. This means that the sub-class of disks suggested by Pontoppidan et al. (2010) may have dust disks that are strongly settled relative to their gas disks.
While Pontoppidan et al. (2010) note a strong correlation between spectral type and line detections, there also appears to be a dichotomy in their results between B, A, and F type objects and G, K, and M spectral types. For spectral types earlier than G, there is a dramatic and as-yet unexplained drop in the detection rates of all species except CO. This may appear to be in conflict with Mulders & Dominik (2012), who suggest that late-type (brown dwarf and T Tauri) disks have flatter dust disks and relatively thicker gas disks than earlier (Herbig) disks do.4 The apparent conflict is that in this paper we suggest that a strongly-settled dust structure may lead to CO2emission being much brighter than other species.
4 One caveat to their analysis is that the best-fit brown dwarf, T Tauri, and Herbig disk models have identical outer radii. Their brown dwarf model has a very low surface density and is strongly flared, while the outer radius of 400 AU is not representative of a typical brown dwarf disk.
4.8 conclusion 133 However, if early-type disks have a less-settled dust structure, then our results suggest that the flux ratios between CO2and other species will be lower.
The work by Mulders & Dominik (2012) is based upon SEDs that are biased towards larger radii, and they also state that “regions with the same temperature have a self-similar vertical structure independent of stellar mass”. It is difficult to distinguish changes in the SEDs of our dust evolution models at wavelengths below 30 µm, thus we are probing different parameter spaces and it is difficult to come to a conclusion. The lack of detections around early-type stars could be because the stronger UV radiation of early-type stars is enough to prevent some other species from forming in sufficient quantities: Walsh et al. (2015) find that weaker UV fields do allow for more molecule-rich disk atmospheres, but some complex molecules can still survive. Thermochemical models by Antonellini et al. (2015) have found that strong UV radiation does not suppress water line fluxes and that likely explanation for the lack of water detections around Herbig stars is noisy spectra combined with high continuum flux levels. Future modelling and observational work is required in order thoroughly to understand the interplay between the disk dust structure, the radiation field, and the mid-infrared molecular lines. What appears most clear is that as the main opacity carrier in the disk, the evolution and settling of dust can have a substantial impact.
4.8 conclusion
We have coupled the dust evolution codetwo-pop-pywith the radiative transfer code MCMax, the thermochemical disk modelling code ProDiMo and the line-tracing code FLiTs. We have produced a series of models that simulate the evolution of dust over time in a 2D thermochemical disk model, and have created infrared spectra of these models including C2H2, CO2, HCN, NH3, OH, and H2O mid-infrared line emission.
The main significant result in this paper is that dust evolution has a very clear and straightforward effect on the mid-infrared line fluxes, and that even in the least evolved disk models, the mid-infrared lines prefer to emit from a gas-to-dust ratio of at least 1000:1. This provides a physical explanation for the need in previous literature to use such ratios in order to produce enough line flux to match models with observations.
These results highlight a clear need to better understand the evolution of dust in the inner few AU of protoplanetary disks, and the effect of dust evolution on mid-infrared lines. The spectral type of the central star also has a strong influence on the detectability of molecular lines, a factor which has not been explored. C2H2is the least common molecule to be detected in G, K, and M-type disks, more or less tied with OH. CO2, HCN, and H2O had higher detection frequencies, while CO was very commonly detected (Salyk et al. 2011).
The results in this paper show that the dust structure can significantly affect mid-infrared spectral line fluxes by an order of magnitude or more. This is a double-edged sword: although the dust structure is a significant degeneracy when fitting models to observations, if we can observe the dust directly (for example, by observing the τ=1 surface with scattered-light imaging), the dust
structure also becomes a powerful diagnostic in understanding the mid-infrared emission of T Tauri disks. Upcoming observatories such as JWST and E-ELT will significantly improve our ability to observe these disks, and combined with more sophisticated models, we can build a two- or three-dimensional understanding of dust structure in the inner disk and the mid-infrared spectral lines.
4.9 acknowledgements
We would like to thank Lucia Klarmann, Gabriela Muro Arena, Paola Pinilla, Til Birnstiel, and Michiel Min for their discussions and comments on the manuscript. We also thank the Center for Information Technology of the University of Gronin-gen for their support and for providing access to the Peregrine high performance computing cluster.
