The Gas Temperature in the Surface Layers of Protoplanetary Disks

By I. Kamp, C. Dullemond. 2004

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Models for the structure of protoplanetary disks have thus far been based on the assumption that the gas and dust temperatures are equal. The gas temperature, an essential ingredient in the equations of hydrostatic equilibrium of the disk, is then determined from a continuum radiative transfer calculation, in which the continuum opacity is provided by the dust. It has long been debated whether this assumption still holds in the surface layers of the disk, in which the dust infrared emission features are produced. In this paper we compute the temperature of the gas in the surface layers of the disk in a self-consistent manner. The gas temperature is determined from a heating-cooling balance equation in which processes such as photoelectric heating, dissociative heating, dust-gas thermal heat exchange, and line cooling are included. The abundances of the dominant cooling species such as CO, C, C+, and O are determined from a chemical network based on the atomic species H, He, C, O, S, Mg, Si, and Fe. The underlying disk models to our calculations are the models of Dullemond, van Zadelhoff, & Natta. We find that in general the dust and gas temperatures are equal to within 10% for AV ≳ 0.1, which is above the location of the "superheated surface layer" in which the dust emission features are produced. High above the disk surface the gas temperature exceeds the dust temperature and can become—in the presence of polycyclic aromatic hydrocarbons—as high as 600 K at a radius of 100 AU. This is a region in which CO has fully dissociated, but a significant fraction of hydrogen is still in molecular form. The densities are still high enough for nonnegligible H2 emission to be produced. At radii inward of 50 AU, the temperature of the gas above the photosphere can reach up to ~104 K. In the disk surface layers, the gas temperature exceeds the virial temperature of hydrogen. Some of this material could possibly evaporate, but firm conclusions have to await fully self-consistent disk models, in which the disk structure and gas temperature determination will be solved iteratively.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

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Citations in the corpus

H2O and OH Gas in the Terrestrial Planet-forming Zones of Protoplanetary Disks (2008, background): “Vertically integrated H2O:OH ratios have been predicted to be much higher (> 10 5) near 1 AU (Markwick et al. 2002), but significant OH abundances are expected near the C+/C/CO transition zone at large scale heights (Kamp & Dullemond 2004).”
A SPATIALLY RESOLVED INNER HOLE IN THE DISK AROUND GM AURIGAE (2009, background): “…heating of gas in the upper disk by such processes as xray and UV irradiation, dissociative or mechanical heating (e.g. Glassgold et al. 2004; Kamp & Dullemond 2004; Nomura et al. 2007) Nevertheless, while the flux levels vary between the data and model prediction, the similarity in…”
THE TW Hya DISK AT 870 μm: COMPARISON OF CO AND DUST RADIAL STRUCTURES (2011, background): “…account for the effects that X-ray heating, chemical differentiation, and gas-dust temperature departures have on the vertical structure of the disk (e.g., van Zadelhoff et al. 2001; Jonkheid et al. 2004; Kamp & Dullemond 2004; Kamp et al. 2010; Woitke et al. 2009, 2010; Aresu et al. 2011).”
The warm gas atmosphere of the HD 100546 disk seen by Herschel - Evidence of a gas-rich, carbon-poor atmosphere? (2012, methodology): “For protoplanetary disks, physical-chemical models have been applied by e.g. Kamp & van Zadelhoff (2001), Glassgold et al. (2004), Kamp & Dullemond (2004), Gorti & Hollenbach (2004), Nomura & Millar (2005), Aikawa & Nomura (2006), Jonkheid et al. (2004), Jonkheid et al. (2006), Jonkheid et al.…”
Circumstellar Dust Disks in Taurus-Auriga: The Submillimeter Perspective (2005, background): “Interpretation of these lines and those from trace molecular species require sophisticated models of the disk structure (e.g., Dartois, Dutrey, & Guilloteau 2003; Kamp & Dullemond 2004) and chemistry (e.g., van Zadelhoff et al. 2001, 2003; Aikawa et al. 2002; Qi et al. 2003).”
Gas density drops inside dust cavities of transitional disks around young stars observed with ALMA (2015, background): “Furthermore, the gas temperature is decoupled from the dust temperature in the surface of the disk, particularly at the cavity wall that is directly heated and inside thdustdepleted cavity (e.g. Kamp & Dullemond 2004; Jonkheid et al. 2004; Gorti & Hollenbach 2008).”
A PARAMETRIC MODELING APPROACH TO MEASURING THE GAS MASSES OF CIRCUMSTELLAR DISKS (2013, background): “Detailed models of the heating and cooling processes show the gas temperature smoothly transitions from the midplane value to a hotter atmospheric value at z/r ∼ 0.1 − 0.5 for r = 10 − 100 AU (Kamp & Dullemond 2004; Nomura et al. 2007; Gorti & Hollenbach 2008; Woitke et al. 2009).”
Molecules with ALMA at Planet-forming Scales (MAPS). I. Program Overview and Highlights (2021, background): “Globally, protoplanetary disks are characterized by radial and vertical gradients in temperature, density, ionization, and radiation fields (e.g., van Zadelhoff et al. 2001; Dartois et al. 2003; Kamp & Dullemond 2004; Meijerink et al. 2012; Woitke et al. 2016).”
C2D Spitzer-IRS spectra of disks around T Tauri stars. II. PAH emission features (2006, background): “…are a major heating mechanism Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20064830 for the gas in the upper layers of the disk where the gas and dust temperatures are not well coupled (Jonkheid et al. 2004; Kamp & Dullemond 2004).”
A SPITZER SURVEY OF MID-INFRARED MOLECULAR EMISSION FROM PROTOPLANETARY DISKS. I. DETECTION RATES (2010, background): “…heating have been identified: Heating by the stellar optical/infrared continuum of dust and subsequent collisional coupling to the gas, photo-electric heating by UV photons (Jonkheid et al. 2004; Kamp & Dullemond 2004; Nomura & Millar 2005) and ionization heating by X-rays (Glassgold et al. 2004).”
Resolved gas cavities in transitional disks inferred from CO isotopologs with ALMA (2015, background): “In addition, the gas temperature is decoupled from the dust temperature in the upper layers in the disk and at the directly heated cavity wall (e.g., Kamp & Dullemond 2004; Jonkheid et al. 2004; Gorti & Hollenbach 2008).”
Spitzer IRS Spectroscopy of IRAS-discovered Debris Disks (2006, methodology): “The approximation Tex = Tgr is valid for optically thick, flared disks for AV > 0.1 (Kamp & Dullemond 2004) but invalid for debris disks around A-type stars where the disk gas and dust are too tenuous to heat the gas via gas-grain collisions (Kamp & van Zadelhoff 2004).”
Radiation thermo-chemical models of protoplanetary disks I. Hydrostatic disk structure and inner rim (2009, methodology): “The central midplane of the disk belowAV ≈ 10 is dominated by thermal accommodation which assuresTg ≈ Td (see also Kamp & Dullemond, 2004; Nomura & Millar, 2005; Gorti & Hollenbach, 2008).”