A typical T Tauri ProDiMo model Peter Woitke, Feb. 2013

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1 A typical T Tauri ProDiMo model Peter Woitke, Feb. 3 The following ProDiMo model of a typical T Tauri star is designed to predict continuum and line fluxes that roughly resemble the observations of real classii TTauri stars. The effective stellar temperature is chosen as T eff =K, and the stellar luminosity L =L ; these values correspond to spectral type K7, a stellar mass of M =.7M and an age of about. Myrs. Spectral Energy Distribution -9-9 dist = pc R = star + UV log ν F ν [erg/cm /s] - log ν F ν [erg/cm /s] - -3 dist = pc star + UV model incl = o -3 model incl = o.... λ [µm] λ [µm] Figure : Resulting SED for a typical TTauri disc setup, right hand side includes all calculated spectral lines at high spectral resolution R =. The calculated spectral energy distribution (SED, see Fig. ) is featured by a powerlaw UV stellar input spectrum, to roughly account for the UV-excess of T Tauri stars, which intersects the photospheric input spectrum at about 3 nm and results in a total UV luminosity of L (9. to nm), an X-ray input spectrum (not shown), emitted from the position of the central star, with a total X-ray luminosity of 3 erg/s with an X-ray emission temperature of 7 K, a strong near-ir excess ( to 7µm) of about.l, clearly visible silicate dust emission features around and µm, a descending SED-slope beyond µm, as is typical for continuous (nontransitional) T Tauri discs, a.3mm flux of about mjy at pc, and a mm-slope of β = log(f ν )/ log(λ).

2 7 8 log n <H> [cm -3 ]. N <H> [cm - ] z / r. =,rad = 3 = =,rad =. =..... Figure : Assumed hydrogen nuclei column density structure N H (r) (l.h.s.) and local particle density structure n H (r,z) (l.h.s.). Disk Shape and Dust Settling The density setup is parametric in this model, see Fig., i.e. the disc shape is fixed by powerlaws for the column density and scale height as function of radius. However, we use a modified powerlaw here, with exponential tapering off, for the column density as Σ(r) r ǫ exp ( (r/r tap ) ǫ) () H(r) = H (r/r ) β () which can naturally explain the often somewhat larger spectral appearance of the disc in (sub-)mm molecular lines, because the lines remain optically thick even at large radii where the continuum is already optically thin and vanishes in the background. The quite tall inner disc, and a very modest increase of the height z where the radial reaches and. (as function of radius, see red dashed lines in Fig. ) are key to produce the desired SED features (Fig. ). The tall inner disc is needed to intercept enough star light to re-radiate it as prominent near-ir excess, and the very modest disc flaring produces the desired SED-slope around µm. In contrast, hydrostatic disc models have very thin inner discs, and strongly flaring outer discs. Dust settling is included according to Dubrulle et al.(99), assuming an equilibrium between upward turbulent mixing and downward gravitational settling. This results in a size-dependent reduction of the dust scale-heights H(r, a) with respect to the gas scale-height H(r), dependent on turbulent mixing parameter α, as ) = ( H(r,a) H(r) +γ α Ω f, (3) where Ω is the Keplerian orbital frequency, γ and f =(ρ d a)/(ρc s ) is the frictional timescale, ρ d is the dust material density, ρ is the midplane gas density, and c s is the midplane sound speed.

3 8 log gas/dust -. - log <a 3 > /3 [mic] z / r = = AV = z / r = = AV = AV = AV = Figure 3: Resulting gas/dust mass ratio (l.h.s.) and mean dust particle size (r.h.s.) in a model with turbulent mixing parameter α= 3. The resulting local dust/gas mass ratios and mean dust particle sizes a 3 /3 are shown in Fig. 3. Note that the dust settling according to (Dubrulle et al.99) is density-dependent, and so the effects on local dust/gas and size distribution are much more pronounced in the tenuous outer layers. The regions important for line emission (roughly...)caneasilyhavegas/dustratiosthatarelargerbyseveralordersof magnitude as compared to the overall (volume integrated) gas/dust ratio, here assumed to be. The following table summarizes the parameters of the model quantity symbol value stellar mass M.7M effective temperature T eff K stellar luminosity L.L UV luminosity L UV L X-ray luminosity L X 3 erg/s disc gas mass M gas 3 M disc dust mass M dust 3 M inner disc radius R in 7AU tapering-off radius R tap AU outer disc radius R out AU column density power index ǫ. reference scale height H AU reference radius r AU flaring power index β. minimum dust particle radius a min µm maximum dust particle radius a max mm dust size dist. power index a pow 3. dust settling turbulence parameter α dust composition Mg SiO % (volume fractions) amorph. carbon % vacuum % PAH abundance rel. to ISM f PAH chemical heating efficiency γ chem disk inclination i o distance d pc 3

4 3K K 3 Gas and Dust Temperatures 7K log T dust log T gas K 3K K K K K K K 3K K K z / r. 7K K 3K K K K z / r K. 3K K K.. K.. Figure : Resulting dust and gas temperature structures. The resulting dust and gas temperatures in this model are shown in Fig.. Ignore the red regions on the r.h.s. of Fig., the gas densities are so low here, that these regions are completely irrelevant for both continuum and line emission (the X-rays cause an HII region here). Important are the warm disc surface layers below (down to about = ) where typically T gas > T dust. This is key to produce the emission lines as observed (negative temperature gradients would result in absorption lines!), and it is important that the temperature contrast between dust and gas is modest to fit the observed line flux magnitudes. In contrast, T gas =T dust can safely be assumed in the midplane regions ( >), where the densities are large (inelastic dust-gas collisions are frequent) and where the UV and X-ray radiation fields, which cause the temperature differences, cannot penetrate into. Figure shows the leading heating and cooling processes. Particularly important for the line formation regions are PAH-heating, exothermic chemical reactions, several follow-up heating processes after photo-excitation or photo-dissociation of H, and neutral carbon ionization. The most important cooling processes are thermal accommodation, H O ro-vibrational lines, CO ro-vibrational lines, [OI]3µm and [CII]7µm line emission. It is important to have ro-vibrational lines, not only rotational, actually for both cooling and heating. K Chemical structure Figure shows some results concerning the chemical composition in the disc. The disc is mainly made of H, however the uppermost layers are atomic, or even fully ionized (by X-rays). The free electrons are donated by H + in the uppermost layers, by C + in a transition layer, then by a small fraction of metal atoms not bound in refractory dust materials like Fe +, Mg + and S +. In the deeper layers, the free electron concentration is

5 heating cooling heating by coll. de-excitation of Hexc heating by formation of H on dust heating by thermal accomodation on grains heating by C photo-ionisation cosmic ray heating PAH heating IR background heating by HO rot-vib X-ray Coulomb heating chemical heating background heating by CH rovib (pseudo-nlte) cooling by thermal accomodation on grains Ly-alpha line cooling OI line cooling CO rot & ro-vib cooling HO rot and rovib cooling NH3 rot cooling OIII line cooling HCN rovib cooling (pseudo-nlte) Figure : Most important heating and cooling processes for the gas. very small, like to, creating a dead zone, where the few electrons created by cosmic rays are absorbed by PAH particles, creating PAH. The chemistry shows a typical PDR/XDR like layered structures, with transitions H H, C + C CO COice, and O OH H O H Oice. However, in the close and very dense midplane, conditions are more like in planetary atmospheres, with very abundant CH, CO, H O and NH 3 gas, but not so much CO. The CO-poor midplane may be an artifact of the assumption of chemical equilibrium, because the chemical relaxation timescales here (and only here) can exceed the age of the star. The chemistry in the outer layers can show quite unusual pathways as compared to standard astro-chemical models for interstellar clouds, because the the dust settling can lead to quite dense yet almost dust-free local conditions, where one of the most important reactions dust + H + H dust + H becomes very slow because of the lacking dust surface. The model predicts the snowline (transition between gaseous and frozen water) to besituatedataboutau,butviscousheatinginthemidplane(ignoredinthismodel) might shift it further outward. Anyway, at higher altitudes, the snowline bends and becomes almost a horizontal line, because the water ice is UV photo-desorbed in the directly irradiated layers.

6 H e H - log ε (H) - - log ε (H) - Td=K - AV=. AV=. AV= Td= K - log ε (elec). AV= AV= C.. C - CO - log ε (C+) log ε (C) - log ε (CO) log - = χ/n O.. - H O - log ε (OH) log ε (O) OH Td us t= K log ε (HO) K K CH. - CO ice -. log ε (HO#) H O ice - log ε (CH). = log ε (CO#). log χ/n K K K Figure : Particle concentrations in the disc with respect to hydrogen nuclei. First row: atomic hydrogen (left), H (middle) and electrons (right). Second row: ionized carbon (left), neutral carbon (middle) and CO (right). Third row: atomic oxygen (left), OH (middle) and gaseous water (right). Last row: gaseous CH (left), water ice (middle) and CO ice (right).

7 µm 3µm µm µm 3µm µm µm µm AV= µm AV= AV= - AV= 8 log n<h> [cm-3] -.. Figure 7: Disc regions responsible for 9% of the continuum flux in the vertically upward direction (both thermal emission and scattering) at different wavelengths. λ = 3.8 µm inclination = 3o λ = 3 µm inclination = 3o log Iν [erg/s/cm/hz/sr] " x " log Iν [erg/s/cm/hz/sr].3" x.3" - log I* / log Imax = -.3 /. log I* / log Imax =.9 /.89 Figure 8: Two examples of calculated images, at 3.8 µm (left) and 3 µm (right). Note the different angular scaling, and the logarithmic intensity color coding. Predicted Continuum Observations The model predicts continuum fluxes (SED), images, and visibilities at various wavelengths. Figure 7 indicates the disc regions mainly responsible for the continuum emis7

8 3 CO J = 8 Fline = 3.E- W/m log nco [cm-3] 8. Fline =.8E- W/m cont log nco [cm-3] µm i =.o d = pc Fline = 3.33E- W/m Fcont = 9.9E- Jy FWHM = 3.7 km/s vsep =. km/s µm i =.o d = pc Fline =.3E- W/m Fcont = 9.7E- Jy FWHM = 3. km/s vsep =. km/s - 3." x 3." log Iline [erg/cm/s/sr].8" x.8" 3. µm i =.o d = pc Fline =.9E- W/m Fcont = 9.E- Jy FWHM = 3.9 km/s vsep =.7 km/s log Iline [erg/cm/s/sr] log nco [cm-3]. Fline = 7.7E- W/m. line C8O 3.µm cont cont line 3CO 33µm. C8 O J = CO J = CO 3µm line -.37" x.37" log Iline [erg/cm/s/sr] Figure 9: Line predictions for three CO isotopologues J =. The upper row shows the analysis, with continuum (black) and line (blue) optical depths, and cumulative flux. The black encircled zones identify the line emitting regions responsible for 9% of the line flux. The lower figures show the resulting spectra and line maps. sion at different wavelengths. Figure 8 shows two examples of calculated images, one in the IR and one at mm-wavelengths. The spectral appearance at 3.8 µm is dominated by the inner rim, whereas the disc has an apparent size of about AU at λ =.3 mm. Note that the scattering is treated as isotropic in this ProDiMo model, so the preferred forward scattering by the surface of the close disc half in the l.h.s. image is not properly accounted for by the model. Predicted Line Observations The model makes detailed predictions about various emission line fluxes (actually thousands of them, ranging from the optical to mm-wavelengths), as well as line velocityprofiles, molecular maps and channel maps for selected lines on demand. In Figure 9 we see the results for the J = lines of the three isotopologues CO, 3 CO, C8 O. Since these molecules have different abundances (assumed to be.,, and with respect to CO, respectively), the lines in the series become less optically thick, are formed deeper and closer in, their FWHM and peak separation increases. The less 8

9 o-h O 3.3 µm p-h O µm o-ho 3.3µm 8 Fline = 3.7E-9 W/m 8 log nho [cm-3] - 8 Fline = 8.9E-9 W/m cont cont 8 log nho [cm-3] log nho [cm-3]. Fline =.7E-9 W/m. cont 8. line 8 o-ho 38.9µm line 8 line 8 o-h O 38.9 µm p-ho 89.99µm µm i =.o d = pc Fline =.E-9 W/m Fcont =.E+ Jy FWHM =.8 km/s vsep = 9. km/s µm i =.o d = pc Fline =.3E-9 W/m Fcont =.3E+ Jy FWHM =.8 km/s vsep =. km/s " x " log Iline [erg/cm/s/sr] µm i =.o d = pc Fline =.3E-9 W/m Fcont =.E- Jy FWHM =. km/s vsep =. km/s " x " log Iline [erg/cm/s/sr] - -." x." log Iline [erg/cm/s/sr] Figure : Three water lines probing different disc regions, around AU, AU, and AU. abundant isotopologues form their lines in deeper layers, which makes the line ratio dependent on the vertical temperature gradients. These gradients, in return, depend on the assumption about the dust settling... Figure shows similar results for three selected water lines, which according to the model are emitted by completely different spatial regions of the disc. Trying a nebular analysis on these fluxes (e.g. deriving the rotational excitation temperature by a rotational diagram, assuming that all lines are emitted by the same gas with the same temperature) would obviously be quite misleading. Figure shows calculated channel maps for 3 CO J =. One can see the much larger apparent size of the CO-disc ( 8 AU) as compared to the continuum ( AU, upper left), although the local (column-integrated) gas/dust ratio is constant and equal to by assumption in this model. The simple truth is that the CO molecular lines are still optically thick, even 3 CO at 8 AU, where the dust continuum is optically thin, has vanished, and becomes unobservable. The channel maps show an interesting feature in form of double-arc-like emission structures. These arcs (or loops) originate from the two opposite sides of the disc. The brighter arc comes from the near surface, and the dimmer arc from the surface of the far side. There is less CO emission from in-between, because (i) the temperatures are lower in the midplane, and (ii) because of CO freeze-out. 9

10 continuum v = -.8 km/s v = -3. km/s v = -. km/s v = -. km/s v = -.9 km/s v = -.8 km/s v = -.78 km/s v = -9 km/s v = km/s v = 9 km/s v =.78 km/s v =.8 km/s v =.9 km/s v =. km/s v =. km/s v = 3. km/s v =.8 km/s integrated line intensity µm i =. o d = pc F line =.3E- W/m F cont = 9.7E- Jy 3 3 I ine [K km/s] F ν [Jy] Figure : Channel maps of the TTauri model seen in 3 CO J=. Note the doublearc emission structures which originate from the near and the far sides of the disc.

11 contact: Dr. Peter Woitke Scottish Universities Physics Alliance (SUPA) University of St. Andrews School of Physics & Astronomy North Haugh St Andrews KY 9SS Scotland, UK Tel: 33 8 Fax: 33 3 Peter.Woitke@st-andrews.ac.uk