University of Groningen
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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5
C O N C L U S I O N S A N D O U T L O O K
In this thesis, I have worked towards improving our understanding of how to model protoplanetary disks. Chapter 2 investigates how brown dwarf disks might compare to T Tauri disks and whether or not we can model them simply by scaling down a T Tauri disk in mass and radius. Chapters 3 and 4 focus on how dust evolution and how parameters that change the local radiation field (such as the UV excess) can affect the mid-infrared spectra of T Tauri disks, with a view towards preparing for upcoming observatories such as JWST and E-ELT. chapter 2
Chapter 2 begins with the fact that we have never observed a planet orbiting a non-binary brown dwarf, despite the fact that planets are more common around M dwarfs than higher-mass stars. There are some edge cases, such as systems where the companion is greater than the lower mass limit of a brown dwarf: but this means that the companion is no longer a planet, but a brown dwarf in and of itself. 1 The very high companion-to-star mass ratio of such systems also throws
into doubt their mechanism of formation. While strictly speaking the definition of a planet does not account for its formation mechanism, if the companion did not form in a protoplanetary disk but in a manner similar to a binary star system, then it is somewhat misleading to call it a planet: it cannot subsequently be claimed that planets can indeed form around brown dwarfs. Confounding the issue is that planets have been discovered around very low-mass stars close to the mass threshold for the fusion of hydrogen, such as the TRAPPIST-1 system. Although there certainly is some observational bias – brown dwarfs are faint and difficult to observe – the question remains as to whether and how often planets can form around brown dwarfs, and what sorts of planetary systems may form.
1 Perhaps the very definition of a planet is incomplete, because the current definition does not account for the formation mechanism: if a 0.01 M object is formed in a protoplanetary disk, is it a planet?
What if that same object formed not in a disk, but during the core collapse stage? Unfortunately, it is very difficult to determine the formation history of such objects once the disk has dissipated.
136 conclusions and outlook
This lack of planets is what motivates the science behind Chapter 2. In order better to understand where and what type of planets may form in brown dwarf disks, we must understand the physical and chemical structure of these disks. New observatories such as ALMA are capable of spatially resolving brown dwarf disks and observing simple molecular species: with the help of appropriate disk models, we can understand such observations and determine whether brown dwarf disks are physically and chemically similar to T Tauri disks. In this chapter, we take a prototypical T Tauri disk model and scale it down in mass and radius, comparing it to the larger T Tauri model and checking for any significant differences in the observable parameters such as the SED and the sub-mm molecular lines. One significant factor that is still relatively unknown is how large brown dwarf disks are: a few brown dwarf disks have been observed to have outer radii of 100 AU or more, but most have been constrained both theoretically and observationally to outer radii of 40 AU or less. We cover this parameter space by creating a grid of brown dwarf models of varying outer radii. Without any detailed fitting, our adopted fiducial model fits well the SED and the sub-mm CO line flux of the brown dwarf disk ρ Oph 102. Subsequently, we find no significant differences in structure between the brown dwarf and T Tauri disk models: for example, the flux ratios between HCO+ and HCN mid-infrared lines
appear similar to T Tauri disks, and familiar structures such as the CO ice line are seen. We also suggest that the flux ratios between sub-mm lines may be used to find very small disks: relative to CO, as we decrease the disk radius, we find that the sub-mm HCN and C18O line fluxes increase while the HCO+line flux
decreases and13CO stays relatively constant. Simulations by Bate et al. (2003);
Bate (2009) and Bate (2012) suggest that most brown dwarf disks may have outer radii as small as 10 AU. At a distance of 140 pc, that is an angular diameter of 0.0700: this makes it difficult to resolve such disks with ALMA. However, this
chapter suggests that from a large survey of key molecular lines in dwarf disks, we may be able to identify which disks are likely to be very small based upon these ratios.
chapter 3
Chapter 3 changes our focus back to T Tauri stars, and towards mid-infrared wavelengths: specifically, the production of infrared spectra from our 2D ther-mochemical models. Only recently have we begun to produce infrared spectra from 2D thermochemical disk models: most models fitted to Spitzer spectra have been slab models that are intrinsically unable to capture the complex structures in the disk. In this paper we combine thermochemical ProDiMo models with an infrared line-tracing code (FLiTs) to investigate the connection between the local radiation field and the mid-infrared emission lines. The local radiation field is affected by each of the changes we make to our model parameters. We produce a series of models that vary the UV excess, X-ray flux, flaring angle, the amount
of dust settling, and the dust-to-gas ratio. Each of these parameters affects the amount of high-energy radiation that reaches the upper layers of the inner disk that produce the mid-infrared spectral lines, which in turn affects the abundances of the line-emitting species.
From these models, we calculate the mid-infrared line-emitting regions for C2H2, HCN, NH3, OH, H2O, and CO2and analyze how the line fluxes and the
temperature of the line-emitting regions vary in response to these parameters. We find that the gas is often significantly warmer than the dust, which invalidates a common assumption that Tgas =Tdust. The physical size of the line-emitting
area is also not stable across the parameter space, and is particularly sensitive to the UV flux, the dust-to-gas ratio, and the flaring angle. For example, when decreasing the dust-to-gas ratio, the disk becomes more optically thin and so the line-emitting area grows both in radial and vertical extent.
Most importantly, we find in every line-emitting region that there exists both radial and vertical gradients in the gas temperature. Around the AV =1 line,
there exists a localized dip in the gas temperature due to the efficient cooling effect that the mid-infrared emission has on the gas. What this means is that along the line of sight from an observer to the protoplanetary disk, there can exist clouds of slightly cooler gas in front of warmer gas. This cooler gas can absorb some mid-infrared emission, leading to less-bright infrared spectra or even absorption lines. We speculate that extreme cases of such temperature structures may be responsible for the few T Tauri disks (such as IRS 46) that have been observed to have strong mid-infrared absorption lines. These results highlight that the vertical and radial structure of the mid-infrared regions is complex. Observations of the gas scale heights and dust scattering surface are needed in order to constrain the composition of gas and dust, while imaging and high-resolution near-infrared spectra from E-ELT will help to gather spatial and kinematic information about the inner disk. Such a wealth of new data will allow us better to inform our models, and to gain more concrete insights into the line-emitting regions of individual species.
chapter 4
The final science chapter, Chapter 4, takes a similar form and analyzes the mid-infrared emission of the same species as Chapter 3, but instead concentrates on the evolution of dust over time. In the past, dust settling has been invoked as a mechanism for enabling the gas-to-dust ratio in the line-emitting regions to increase to 1000:1, as is necessary in order to reproduce line fluxes from Spitzer. However, we have seen in Chapter 3 that changing the dust settling parameter does not significantly affect the mid-infrared lines. Thus, why might dust evolution be more significant? To answer this question on the significance of dust evolution, we coupled four codes together: two-pop-pyto simulate the
138 conclusions and outlook
loss through accretion), MCMax to calculate the 2D disk structure and apply self-consistent dust settling, ProDiMo to calculate the chemistry, and FLiTs to calculate the mid-infrared spectra.
There are two significant factors at play here that affect the mid-infrared spectra. The first is dust evolution itself: the population of dust grains both large and small decreases over time. Radial drift ensures that larger grains are cleared from the disk more effectively than smaller grains. The gas structure does not significantly change: over the course of 10 Myr, the total gas mass only decreases by 30% while the total dust mass decreases by a factor of 100. This leads to the disk becoming more dust-poor and more optically thin over time. The second factor is the method of settling: we keep a parameterized gas structure, and allow the dust to settle self-consistently based upon this fixed gas structure. The result is a dust disk that is thinner than the gas disk, giving the upper layers of the disk a high gas-to-dust ratio. The self-consistent settling can reduce the abundance of small opacity-carrying dust grains in the upper disk much more easily than Dubrulle settling can. We find that this method of settling may be a straightforward explanation for the canonical 1000:1 gas-to-dust ratio that is frequently used in order to explain mid-infrared line fluxes, because such high fluxes are easily produced in these disk models. Standard ProDiMo models use Dubrulle settling and without dust evolution: the gas-to-dust ratio of these models does not vary radially, and Dubrulle settling is not effective at settling small, opacity-carrying grains in the inner few AU. Furthermore, we find that the flux densities of every species except C2H2 can increase over time by well
over an order of magnitude as the disk becomes older, as a result of increases in the gas-to-dust ratio and line-emitting areas. The CO2flux increases relatively
more than other species, likely owing to its propensity to survive in optically thin disks (this goes back to the reaction networks: the main formation mechanism of CO2in its mid-infrared line-emitting region is from a neutral-neutral reaction
between OH and CO, both of which are very abundant). The bright CO2lines in
our models may be able to explain the sub-class of disks found by Pontoppidan et al. (2010) where only CO2has been detected in the mid-infrared: perhaps these
disks have dust structures more strongly settled and evolved than the others. We note that the characteristics of the C2H2emission are not consistent with all
of the other species analyzed, because C2H2 is easily destroyed and the bulk
of its column density is found in regions where AV ≥ 10. Given that C2H2 is
readily detected by Spitzer in T Tauri disks, this result suggests that further work is necessary in order better to understand the reaction rates and formation and destruction mechanisms of C2H2in optically-thin environments. This chapter
makes clear the significant effect that the dust disk can have on mid-infrared lines. Combining scattered-light imaging that can measure the height of the dust disk with high-resolution infrared spectra promises to be a powerful diagnostic of the dust structure of T Tauri disks. Such measurements can be combined with measurements of the gas scale heights and mm-sized dust grains from ALMA.
concluding remarks and outlook
In the near future, new observatories will significantly improve our ability to observe protoplanetary disks, notably in the near- and mid-infrared. JWST will soon be launching, and will be able to take spectra with significantly higher signal-to-noise than Spitzer before it, while also increasing the spectral resolution from 600 to 2 800. These improvements will enable individual species to be better isolated from a crowded and noisy spectrum, and lines to be more easily isolated from the dust continuum allowing for better continuum placement and line flux measurements. The very high spectral resolutions of E-ELT (and the candidate mission SPICA) will even allow individual lines to be spectrally resolved. E-ELT is expected to spatially resolve the inner few AU of disks with its IFU instrument, which will allow for unprecedented kinematic information about the inner disk. The ability of SPHERE to image the surface of the dust disk in scattered light is crucial to understanding the spectra from JWST: with these measurements, we can gain insight into the dust structure of the observed disk, helping to break the degeneracies imposed by dust on the mid-infrared spectra (see Fig. 5.1). Combining E-ELT images of CO and continuum emission from the inner few AU, scattered light imaging from SPHERE, mid-infrared spectra from JWST, and sub-mm line and continuum emission observations from ALMA will allow us to probe many different regions of a disk. The models in this thesis can help to decide which data are the most necessary to observe, allowing robust (but efficient) multi-observatory observing strategies that can strongly constrain the dust and gas structure of a disk and help us to create well-informed disk models.
In this thesis we have done many things for the first time, and have laid the necessary groundwork for the advanced modelling techniques that will be needed for future observatories. To this end, in each chapter we further explore the capabilities of ProDiMo. We have for the first time scaled down a thermochemical model of a T Tauri disk in order to produce a brown dwarf disk model that is consistent with all existing multi-wavelength data of a typical brown dwarf disk, and we have found that there appear to be no surprising or discontinuous differences between the brown dwarf and T Tauri models. We have analyzed the infrared spectra and line-emitting regions of T Tauri disks in detail, and find that we need to take great care in considering the physical shape, the temperature structure, and the dust properties of these regions. Perhaps most important are the dust properties: dust evolution and settling can greatly affect the mid-infrared spectra of disks. Just as dust evolution affects the mid-infrared spectra, it also drives the formation of planets. Just as these parameters significantly affect the mid-infrared lines, they promise to be powerful diagnostics with which to inform our models. We hope in the future that we can either regularly observe new exoplanets around brown dwarfs, or develop sensitive enough instruments that can image their dust surfaces and help us to understand why planets might be difficult to form in the lowest-mass disks.
140 conclusions and outlook
Figure 5.1: An image from SPHERE on the VLT, of the protoplanetary disk around the star PDS 70. Within this disk is the young planet PDS 70b, with a mass of a few MJup and at a distance of 22 AU from the star (Müller et al. 2018; Keppler et al. 2018). Image reproduced from an ESO press release (eso.org/public/news/eso1821/).
Following more directly from this work, there are several logical steps to take. Further ALMA surveys of brown dwarf disks are underway: one titled "The chemistry of M dwarf protoplanetary disks"(PI: Karin Öberg) is currently observing, will observe five M dwarf disks in seven molecular lines that are often used to probe T Tauri disk chemistry. Another survey, "Brown dwarf disks demographics" (PI: Leonardo Testi), aims to measure the disk masses of all known brown dwarf disks in the ρ Ophiuchus, Lupus, and Chameleon I star-forming regions. Given this upcoming sub-mm data, one avenue of exploration is to compare the mid-infrared spectra of T Tauri disks to that of brown dwarf disks: JWST will easily observe brown dwarf disk spectra, making possible a multi-wavelength study of many low-mass disks. Combining these data sets into models that use ProDiMo and FLiTs will help us to interpret the JWST spectra, and to gain further insight into what the inner few AU of brown dwarf disks may look like.
Another future step is a multi-wavelength study of a T Tauri disk: although SPHERE is not sensitive enough to observe brown dwarf disks, we already have good scattered light observations for T Tauri disks such as IM Lup. Combined with ALMA data, we could create a ProDiMo model with the same gas and dust structure. How would the FLiTs spectra of this model compare to the Spitzer (or JWST) spectra of IM Lup? Do they agree, or are there still degeneracies that need further observations (for example, E-ELT imaging of the inner disk) to break?
The new era of JWST and E-ELT has almost begun, and our modelling tools are now ready and waiting for the challenge.
