<table><caption>**Table 16**
(Continued)</caption><thead><tr><th rowspan="2">Species</th><th rowspan="2">λ (μm)</th><th colspan="2">Line Flux (W m<sup>-2</sup>)</th><th colspan="2">FWHM (km s<sup>-1</sup>)</th><th rowspan="2">Size (au)</th></tr><tr><th>Observed</th><th>Model</th><th>Observed</th><th>Model</th></tr></thead><tbody><tr><td><sup>13</sup>CO</td><td>906.846</td><td>4.4 ± 2.7(-20)</td><td>9.5(-20)</td><td>...</td><td>1.0</td><td>119.7</td></tr><tr><td><sup>13</sup>CO</td><td>453.497</td><td>1.8 ± 0.3(-19)</td><td>4.0(-19)</td><td>1.4 ± 0.1</td><td>1.1</td><td>98.2</td></tr><tr><td><sup>13</sup>CO</td><td>272.204</td><td>3.6 ± 0.4(-19)</td><td>1.9(-19)</td><td>...</td><td>1.5</td><td>66.1</td></tr><tr><td>C<sup>18</sup>O</td><td>1365.430</td><td>5.0 ± 1.4(-21)</td><td>6.0(-21)</td><td>...</td><td>1.1</td><td>109.7</td></tr><tr><td>HCO<sup>+</sup></td><td>3361.334</td><td>2.5 ± 0.4(-21)</td><td>1.2(-21)</td><td>...</td><td>0.7</td><td>175.9</td></tr><tr><td>HCO<sup>+</sup></td><td>1120.478</td><td>1.1 ± 0.2(-19)</td><td>6.6(-20)</td><td>...</td><td>0.8</td><td>177.5</td></tr><tr><td>HCO<sup>+</sup></td><td>840.380</td><td>2.7 ± 0.1(-19)</td><td>1.2(-19)</td><td>0.7 ± 0.1</td><td>0.8</td><td>177.8</td></tr><tr><td>HCN</td><td>1127.520</td><td>7.5 ± 1.5(-20)</td><td>8.4(-20)</td><td>...</td><td>0.8</td><td>170.5</td></tr><tr><td>HCN</td><td>845.663</td><td>1.1 ± 0.3(-19)</td><td>1.5(-19)</td><td>...</td><td>0.8</td><td>161.7</td></tr><tr><td>N<sub>2</sub>H<sup>+</sup></td><td>1072.557</td><td>2.0 ± 0.4(-20)</td><td>6.6(-21)</td><td>...</td><td>0.8</td><td>125.0</td></tr><tr><td>N<sub>2</sub>H<sup>+</sup></td><td>804.439</td><td>5.7 ± 0.9(-20)</td><td>1.1(-20)</td><td>...</td><td>0.8</td><td>119.2</td></tr><tr><td>HD</td><td>112.053</td><td>6.3 ± 0.7(-18)</td><td>4.8(-19)</td><td>...</td><td>1.9</td><td>63.9</td></tr><tr><td>HD</td><td>56.223</td><td>&lt;8.1(-18)</td><td>8.2(-20)</td><td>...</td><td>3.3</td><td>75.8</td></tr><tr><td>OH</td><td>55.890</td><td>2.2 ± 0.1(-17)</td><td>5.0(-18)</td><td>...</td><td>8.2</td><td>4.5</td></tr><tr><td>OH</td><td>55.950</td><td>2.7 ± 0.1(-17)</td><td>5.8(-18)</td><td>...</td><td>7.8</td><td>4.6</td></tr><tr><td>CO</td><td>4.609</td><td>6.4 ± 0.2(-18)</td><td>5.6(-18)</td><td>7.2 ± 0.2</td><td>12.3</td><td>4.6</td></tr><tr><td>CO</td><td>4.657</td><td>3.7 ± 0.2(-18)</td><td>2.8(-18)</td><td>7.2 ± 0.3</td><td>4.9</td><td>4.8</td></tr><tr><td>CO</td><td>4.682</td><td>4.1 ± 0.2(-18)</td><td>3.4(-18)</td><td>7.7 ± 0.3</td><td>4.9</td><td>5.0</td></tr><tr><td>CO</td><td>4.754</td><td>6.2 ± 0.1(-18)</td><td>6.5(-18)</td><td>7.1 ± 0.2</td><td>11.7</td><td>4.6</td></tr><tr><td>CO</td><td>4.793</td><td>7.2 ± 0.3(-18)</td><td>6.7(-18)</td><td>7.7 ± 0.3</td><td>12.6</td><td>4.6</td></tr><tr><td>CO</td><td>4.966</td><td>3.9 ± 1.0(-18)</td><td>3.2(-18)</td><td>18.5 ± 1.0</td><td>16.4</td><td>0.5</td></tr><tr><td>CO</td><td>4.990</td><td>2.3 ± 0.7(-18)</td><td>2.8(-18)</td><td>11.8 ± 1.0</td><td>16.5</td><td>0.5</td></tr><tr><td>O I</td><td>0.630</td><td>1.2 ± 0.1(-16)</td><td>2.2(-16)</td><td>10.0 ± 1.0</td><td>12.2</td><td>6.2</td></tr><tr><td>O I</td><td>0.557</td><td>1.7 ± 0.5(-17)</td><td>4.3(-17)</td><td>10.0 ± 1.0</td><td>19.2</td><td>0.8</td></tr><tr><td>S<sup>+</sup></td><td>0.406</td><td>4.4 ± 0.5(-17)</td><td>1.7(-19)</td><td>...</td><td>8.7</td><td>9.3</td></tr><tr><td>Ne<sup>+</sup></td><td>12.814</td><td>7.0 ± 0.2(-17)</td><td>3.4(-17)</td><td>...</td><td>4.5</td><td>45.8</td></tr><tr><td>Ne<sup>++</sup></td><td>15.554</td><td>5.0 ± 2.0(-18)</td><td>1.2(-17)</td><td>...</td><td>4.3</td><td>88.5</td></tr><tr><td>o-H<sub>2</sub></td><td>17.033</td><td>1.2 ± 0.2(-17)</td><td>5.9(-19)</td><td>...</td><td>4.7</td><td>24.9</td></tr><tr><td>p-H<sub>2</sub></td><td>12.277</td><td>7.0 ± 2.0(-18)</td><td>2.4(-19)</td><td>...</td><td>5.6</td><td>40.9</td></tr></tbody></table>
<figure><img src="image_37.png" /><figcaption>**Figure 20.** Left: Fit of radial intensity profile to archival ALMA 850 µm continuum data. Right: CO *J* = 3–2 line from TW Hya disk model in comparison to ALMA data.</figcaption></figure>

(A color version of this figure is available in the online journal.)

to further reduce the UV and X-ray irradiation of the outer disk, which would weaken the [O I] 63 µm line. This issue might be related with the different X-ray luminosities reported in the literature (factor of ten, see Section 4.1 for details). But we have not tested the older lower X-ray luminosity with our model, furthermore a strong variability in X-rays is also a possible scenario.

McClure et al. (2016) derived a disk gas mass in the range of (1.0–4.7) × 10⁻² *M*☉ based on measurements of the HD *J* = 1–0 spectral line and suggests a lower CO gas phase abundance of up to a factor of 5 compared to the canonical abundance of ≈10⁻⁴ (relative to molecular hydrogen), but the case of no CO depletion is also possible. This is consistent with our model with a disk gas mass of 1.6 × 10⁻² *M*☉ and no CO depletion additionally to freeze-out. We note that the HD line was not included in our modeling.

As the disk of DM Tau is large and bright it is a popular target for molecular line observations and disk chemistry studies (e.g., Dutrey et al. 1997; Öberg et al. 2010; Loomis et al. 2015; Teague et al. 2015; Semenov et al. 2018). One interesting example is the detection of C₂H (Henning et al. 2010; Bergin et al. 2016) in DM Tau. The authors suggest that the X-ray/UV radiation and dust evolution play a crucial role for the C₂H abundance. Our model and the collected data provides additional constraints on the disk physical structure (e.g., radiation fields) and is therefore a ideal test-bed for further chemical studies although a more elaborate chemical network is likely required.

### 4.5.13. CY Tau

CY Tau has an SED (see Figure 1) with almost no 10 and 20 µm silicate emission features, that is steeply declining in the mid-IR, and has only a modest far-IR excess. At longer wavelengths this excess drops steadily all the way up to about 850 µm. The mm-fluxes are strong. The model explains this particular SED-shape by a very cold yet massive and strongly settled outer disk which is located in the shadow of a tenuous, tall inner disk (Figure 27).

The gas/dust ratio was fixed at 100 during the model fitting. The total disk mass of 0.12 *M*☉ is exceptionally large for this *M*★ = 0.43 *M*☉ T Tauri star, even larger than the value 0.10 *M*☉ obtained from the pure SED-fit, see Table 4. All observed emission lines are predicted well (Table 20). The CO *J* = 2–1 to ¹³CO *J* = 2–1 line ratio is observed to be quite small, only ~2. The model manages to explain this peculiar line ratio by an almost sharp outer edge with ϵ = 0.11 and γ = −0.34.

Figure 28 shows a FLiTs spectrum for the R-branch of fundamental CO *v* = 1–0, with a very good fit of a number of individual lines including some CO *v* = 2–1 and o-H₂O lines, which was only obtained after lowering the column densities in the inner disk zone while simultaneously increasing the scale heights.

### 4.5.14. RECX 15

RECX 15 is an exceptional case, the only gas-rich protoplanetary disk in an otherwise rather old star formation cluster, which seems to be as small as 5 au in radius (Woitke et al. 2011, 2013). Figure 29 shows the density structure and surface
<figure><img src="image_38.png" /><figcaption>**Figure 21.** Left: SED-fit of GM Aur. Right: CO *J* = 2–1 line in comparison to the GM Aur data. (A color version of this figure is available in the online journal.)</figcaption></figure>

density profiles (gas and dust) for this object. RECX 15 must have lost its outer disk for some reason, possibly due to a close encounter. Only few gas lines have been detected, among them [O I] 63 µm, [O I] 6300 Å and o-H₂ 2.121 µm. Our ALMA cycle-0 data shows a faint, very broad CO *J* = 3–2 line (FWHM ≈ 15 km s⁻¹) which only a tiny Keplerian disk can explain (Figure 30). There is no spatially resolved data, not even with ALMA. The model manages to fit the SED (Figure 1) and the emission lines with a strongly flared, tall disk, strengthening our general conclusion that the inner disks of T Tauri stars are vertically much more extended than previously thought. The o-H₂ 2.121 µm line is underpredicted by a factor 15, though. The gas/dust mass ratio is found to be ~3500, an very unusual value for outer disks, but maybe not so atypical for the inner disks of transitional disks (Table 4). All line fits are summarized in Table 21.

## 4.6. Systematic Line Flux Deviations

We conclude this study by looking out for possible systematic weaknesses in our models, for example lines that are always predicted to be too strong or too weak. This would indicate some principle problem in our modeling assumptions or techniques, for example that certain molecules are always underabundant or overabundant with respect to observations due to an issue in the chemistry. Figures 31 and 32 show the ratios of predicted to observed line fluxes, for a sample of frequently observed emission lines. We note here again that all lines have been simultaneously fitted by one model for each

object, which at the same time fits the continuum observations (SED and some images) as good as possible.

These figures do not reveal any severe weaknesses. The CO 3–2 and CO 2–1 isotopologue lines are typically well-fitted within a factor of two or better. The [O I] 6300 Å line maybe somewhat underpredicted for luminous stars, whereas the fits are fine for the T Tauri stars. The [O I] 63 µm line proves to be quite difficult to fit, we arrive at deviations within a factor 4 or less, with a slight tendency to overpredict. The other lines shown in Figure 32 show no obvious trends either. The frequently observed HCO⁺ 3–2 line usually fits fine, as well as the N₂H⁺ line, whereas the situation is more diverse for the HCN 3–2 and CN lines. An exception is AB Aur where the line data might be confused with foreground cloud absorption. The CO *J* = 18–17 line tends to be somewhat underpredicted by our models for the T Tauri stars.

## 5. Summary and Outlook

The European FP7 project DIANA has performed a coherent analysis of a large set of observational data of protoplanetary disks by means of state-of-the-art thermo-chemical disk models. We used multi-wavelength, multi-instrument, mostly archival data comprising photometry, low-resolution IR to far-IR spectra, continuum images and line observations of different kinds and different quality. Our goal was to fit all collected observational data simultaneously by means of a single disk model, separately for each object in our target list. Our aim was to conclude about the disk shape, the masses of the disks and
<table><caption>**Table 17**
Model Properties and Comparison of Computed Spectral Line Properties with Observations from GMAur.properties</caption><thead><tr><th colspan="2">DIANA Standard Fit Model Properties</th></tr></thead><tbody><tr><td>Minimum dust temperature [K]</td><td>6</td></tr><tr><td>Maximum dust temperature [K]</td><td>886</td></tr><tr><td>Mass-mean dust temperature [K]</td><td>18</td></tr><tr><td>Minimum gas temperature [K]</td><td>7</td></tr><tr><td>Maximum gas temperature [K]</td><td>26157</td></tr><tr><td>Mass-mean gas temperature [K]</td><td>19</td></tr><tr><td>mmopalenesslope (0.85–1.3) mm</td><td>1.3</td></tr><tr><td>cmopalenesslope (5–10) mm</td><td>1.7</td></tr><tr><td>mm-SED-slope (0.85–1.3) mm</td><td>2.4</td></tr><tr><td>cm-SED-slope (5–10) mm</td><td>3.5</td></tr><tr><td>10 µm silicate emission amplitude</td><td>1.8</td></tr><tr><td>Naked star luminosity [L<sub>☉</sub>]</td><td>0.7</td></tr><tr><td>Bolometric luminosity [L<sub>☉</sub>]</td><td>0.9</td></tr><tr><td>Near-IR excess (λ = 2.07–6.84 µm) [L<sub>☉</sub>]</td><td>0.03</td></tr><tr><td>Mid IR excess (λ = 6.84–29.9 µm) [L<sub>☉</sub>]</td><td>0.05</td></tr><tr><td>Far-IR excess (λ = 29.9–998. µm) [L<sub>☉</sub>]</td><td>0.14</td></tr></tbody></table>

<table><thead><tr><th rowspan="2">Species</th><th rowspan="2">λ (μm)</th><th colspan="2">Line Flux (W m<sup>-2</sup>)</th><th colspan="2">FWHM (km s<sup>-1</sup>)</th><th rowspan="2">Size (au)</th></tr><tr><th>Observed</th><th>Model</th><th>Observed</th><th>Model</th></tr></thead><tbody><tr><td>O I</td><td>0.630</td><td>3.9 ± 1.0(−17)</td><td>1.2(−17)</td><td>42.0 ± 0.0</td><td>10.4</td><td>27.5</td></tr><tr><td>CO</td><td>4.649</td><td>1.3 ± 0.9(−18)</td><td>1.2(−16)</td><td>22.8 ± 0.0</td><td>9.0</td><td>19.4</td></tr><tr><td>CO</td><td>4.657</td><td>9.0 ± 8.0(−19)</td><td>8.3(−17)</td><td>15.6 ± 0.0</td><td>9.1</td><td>19.4</td></tr><tr><td>CO</td><td>4.699</td><td>1.0 ± 0.8(−18)</td><td>2.0(−16)</td><td>19.6 ± 0.0</td><td>9.0</td><td>19.4</td></tr><tr><td>CO</td><td>4.708</td><td>1.1 ± 0.8(−18)</td><td>1.9(−16)</td><td>18.0 ± 0.0</td><td>9.1</td><td>19.4</td></tr><tr><td>CO</td><td>4.717</td><td>1.1 ± 0.8(−18)</td><td>1.7(−16)</td><td>18.0 ± 0.0</td><td>9.1</td><td>19.4</td></tr><tr><td>CO</td><td>4.726</td><td>1.5 ± 0.9(−18)</td><td>1.3(−16)</td><td>26.9 ± 0.0</td><td>9.1</td><td>19.5</td></tr><tr><td>CO</td><td>4.735</td><td>1.6 ± 0.9(−18)</td><td>9.7(−17)</td><td>25.4 ± 0.0</td><td>9.1</td><td>19.5</td></tr><tr><td>CO</td><td>4.745</td><td>2.2 ± 1.1(−18)</td><td>6.7(−17)</td><td>37.2 ± 0.0</td><td>9.1</td><td>19.5</td></tr><tr><td>CO</td><td>4.754</td><td>2.7 ± 1.2(−18)</td><td>4.5(−17)</td><td>44.6 ± 0.0</td><td>9.1</td><td>19.5</td></tr><tr><td>CO</td><td>4.763</td><td>2.3 ± 1.1(−18)</td><td>3.0(−17)</td><td>35.6 ± 0.0</td><td>9.1</td><td>19.5</td></tr><tr><td>CO</td><td>4.773</td><td>2.9 ± 1.2(−18)</td><td>2.0(−17)</td><td>42.9 ± 0.0</td><td>9.1</td><td>19.6</td></tr><tr><td>CO</td><td>4.793</td><td>2.8 ± 1.2(−18)</td><td>9.1(−18)</td><td>46.3 ± 0.0</td><td>9.1</td><td>19.7</td></tr><tr><td>Ne<sup>+</sup></td><td>12.814</td><td>1.2 ± 0.3(−17)</td><td>6.8(−18)</td><td>...</td><td>9.5</td><td>53.3</td></tr><tr><td>O I</td><td>63.183</td><td>3.8 ± 0.5(−17)</td><td>7.2(−17)</td><td>...</td><td>5.4</td><td>230.2</td></tr><tr><td>o-H<sub>2</sub>O</td><td>63.323</td><td>&lt;7.3(−18)</td><td>4.3(−18)</td><td>...</td><td>9.1</td><td>20.2</td></tr><tr><td>CO</td><td>1300.404</td><td>1.5 ± 0.3(−19)</td><td>1.0(−19)</td><td>...</td><td>2.7</td><td>402.8</td></tr><tr><td>HCO<sup>+</sup></td><td>1120.478</td><td>3.9 ± 0.1(−20)</td><td>1.2(−20)</td><td>...</td><td>3.5</td><td>346.6</td></tr></tbody></table>
<figure><img src="image_39.png" /><figcaption>**Figure 22.** GM Aur density and surface density plots. For details see Figure 4. (A color version of this figure is available in the online journal.)</figcaption></figure>

<figure><img src="image_40.png" /><figcaption>**Figure 23.** BP Tau density and surface density plots. For details see Figure 4. (A color version of this figure is available in the online journal.)</figcaption></figure>

their physical parameters, the properties of the dust grains, the internal gas and dust temperature structures in the disks, and the chemical composition. The driving question of the project was “does this work?” Can we fit all available observational data with a standardized modeling approach, using 2D thermo-chemical disk models, only by varying the disk mass and shape

parameters, the gas/dust ratio and the dust size and opacity parameters?

The answer is a surprisingly clear yes. In reality, disks are very complicated objects, individual, time-dependent and not strictly axi-symmetric. Yet, by allowing just for two disk zones, an inner and an outer disk, we could find parameter
<figure><img src="image_41.png" /><figcaption>**Figure 24.** Model prediction and observed high-resolution Keck/NIRSPEC spectrum of the R-branch of fundamental CO *v* = 1–0 around 4.6 µm in BP Tau. (A color version of this figure is available in the online journal.)</figcaption></figure>

combinations for our models, which predict observations that
resemble most of the continuum and line data we could find,
simultaneously. In particular, we did not need individual
adjustments of element abundances, but achieved all our fits by
using standard ISM element abundances with strongly depleted
heavy elements.

Our data analysis was performed in three steps, (i) finding
the stellar parameters including detailed UV and X-ray
properties, (ii) using fast Monte-Carlo RT models to fit the
SED in order to roughly determine the disk shape and dust
opacity parameters, and (iii) using self-consistent radiation
thermo-chemical models in application to an enlarged set of
observational data, including all line and image data, to
complete the fit. During the last modeling phase, the various
disk shape, dust settling and opacity parameters were not
frozen, but were continued to be varied for finding the best-
fitting parameter values. This procedure distinguishes our work
from most previous studies.

For most objects, however, we found at least one observation
which we could not fit at all together with the other
observations. This could be caused, for example, by the
variability of an object or simply due to issues with foreground
clouds or secondary sources in the field of view observed with
different instruments. It could also be caused, of course, by
some missing physics or chemistry in our models, but as
Figures 31 and 32 show, we could not find any systematic
problem. In case of such unclear or un-fittable data, the only
practical way forward was to exclude such data or to artificially
increase the respective measurement errors, otherwise the
χ²-minimization desperately tries to improve the fit of exactly
those data which we trust the least. Thus, our data selection and
definition of χ² was not mathematically sound; it was based on
and required human judgment. We therefore do not claim to
have found a unique solution of the disk structure of our targets.

An MCMC analysis might have revealed some interesting
parameter degeneracies and credibility intervals, but was
judged to be computationally unfeasible. A single thermo-
chemical disk model takes about 10 CPU hours, the number of
free parameters is about 20, and so hundreds of thousands of
disk models would have needed to be calculated to determine
those errorbars, which would have taken about 500 CPU-years
for a single object.

Therefore, the intention of this project was not to determine
all disk parameters with errorbars.<fnref n="17" /> Instead, we have found
some re-occurring patterns and trends in the models that helped
us to better fit the data, which offers new ways to understand
and explain disk observations in general, new clues for data
interpretation, and useful starting points for future modeling
purposes. We summarize these findings below.

*Dust properties.* The key to arrive at our simultaneous
continuum and line fits often was to vary the dust size and
opacity parameters that have an important influence on how
deep the stellar UV photons penetrate into the disk, causing gas
heating and line emission. We used the DIANA dust opacities
for disks (Min et al. 2016b), based on a power-law dust size
distribution with an effective mixture of laboratory silicate and
amorphous carbon. Since our size distribution is typically
extended to a few millimeters, our dust is much more
transparent in the UV than standard interstellar dust, but rather
opaque at 850 µm, $\kappa_{850}^{\text{abs}} \approx 6.3_{-2.3}^{+3.5} \text{ cm}^2/\text{g}(\text{dust})$, which is
somewhat larger than the frequently used value of
3.5 $\text{cm}^2/\text{g}(\text{dust})$ originally proposed by Beckwith et al.
(1990) as order-of-magnitude estimate of 10 $\text{cm}^2/\text{g}(\text{dust})$ at
1000 GHz, and later scaled to 850 µm using $\kappa_{\nu}^{\text{abs}} \propto 1/\lambda$.

<footnote n="17">¹⁷ Appendix B contains a rough estimate of parameter uncertainties by probing the curvature in the local χ² minimum.</footnote>
<table><caption>**Table 18**
Model Properties and Comparison of Computed Spectral Line Properties with Observations from BPTau.properties</caption><thead><tr><th colspan="2">DIANA Standard Fit Model Properties</th></tr></thead><tbody><tr><td>Minimum dust temperature [K]</td><td>4</td></tr><tr><td>Maximum dust temperature [K]</td><td>1723</td></tr><tr><td>Mass-mean dust temperature [K]</td><td>15</td></tr><tr><td>Minimum gas temperature [K]</td><td>4</td></tr><tr><td>Maximum gas temperature [K]</td><td>40000</td></tr><tr><td>Mass-mean gas temperature [K]</td><td>18</td></tr><tr><td>mmopalenesslope (0.85–1.3) mm</td><td>1.4</td></tr><tr><td>cmopalenesslope (5–10) mm</td><td>1.6</td></tr><tr><td>mmSEDslope (0.85–1.3) mm</td><td>1.9</td></tr><tr><td>cmSEDslope (5–10) mm</td><td>3.3</td></tr><tr><td>10 µm silicate emission amplitude</td><td>1.7</td></tr><tr><td>Naked star luminosity [L<sub>☉</sub>]</td><td>1.0</td></tr><tr><td>Bolometric luminosity [L<sub>☉</sub>]</td><td>1.3</td></tr><tr><td>Near-IR excess (λ = 2.05–6.90 µm) [L<sub>☉</sub>]</td><td>0.13</td></tr><tr><td>Mid IR excess (λ = 6.90–29.3 µm) [L<sub>☉</sub>]</td><td>0.10</td></tr><tr><td>Far-IR excess (λ = 29.3–970. µm) [L<sub>☉</sub>]</td><td>0.03</td></tr></tbody></table><table><thead><tr><th rowspan="2">Species</th><th rowspan="2">λ (µm)</th><th colspan="2">Line Flux (W m<sup>-2</sup>)</th><th colspan="2">FWHM (km s<sup>-1</sup>)</th><th rowspan="2">Size (au)</th></tr><tr><th>Observed</th><th>Model</th><th>Observed</th><th>Model</th></tr></thead><tbody><tr><td>CO</td><td>1300.403</td><td>8.7 ± 2.0(–21)</td><td>1.1(–20)</td><td>4.2 ± 0.4</td><td>2.9</td><td>125.0</td></tr><tr><td><sup>13</sup>CO</td><td>1360.227</td><td>1.1 ± 0.5(–21)</td><td>1.5(–21)</td><td>...</td><td>3.8</td><td>76.2</td></tr><tr><td>CN</td><td>1321.390</td><td>2.4 ± 0.5(–21)</td><td>2.8(–22)</td><td>...</td><td>2.6</td><td>143.4</td></tr><tr><td>CO</td><td>4.633</td><td>1.7 ± 0.3(–17)</td><td>1.2(–17)</td><td>65.0 ± 4.0</td><td>87.0</td><td>0.6</td></tr><tr><td>CO</td><td>4.477</td><td>1.9 ± 0.2(–17)</td><td>1.3(–17)</td><td>70.0 ± 3.0</td><td>88.4</td><td>0.3</td></tr><tr><td>O I</td><td>63.183</td><td>9.5 ± 2.7(–18)</td><td>2.7(–17)</td><td>...</td><td>2.7</td><td>140.2</td></tr><tr><td>o-H<sub>2</sub>O</td><td>63.323</td><td>&lt;9.3(–18)</td><td>5.9(–19)</td><td>...</td><td>27.4</td><td>1.2</td></tr></tbody></table>
<figure><img src="image_42.png" /><figcaption>**Figure 25.** DM Tau density and surface density plots. For details see Figure 4. (A color version of this figure is available in the online journal.)</figcaption></figure>

<figure><img src="image_43.png" /></figure>

**Dust settling.** Another important degree of freedom for the fitting was the dust settling, which has opposite effects on continuum and line fluxes in the mid and far-IR, and can hence be used to break some degeneracies with disk flaring as known from pure SED-fitting. Our results suggest that dust settling is rather strong in these disks, and hence the turbulence rather weak, $log_{10} \alpha_{set} = -2.9 \pm 0.9$ as compared to the standard value of $10^{-2}$. This is in agreement with the analysis by Pinte et al. (2016) of the HL Tau rings as seen with ALMA.

**PAH properties.** Our simultaneous fits of the PAH properties in protoplanetary disks show an underabundance of PAHs $f_{PAH} \approx 0.005-0.8$ with respect to the standard abundance in the ISM ($10^{-6.52}$ PAH molecules/H-nucleus Tielens 2008), with large individual scatter. The PAH abundance is relevant to the model, in particular, by converting blue and soft UV photon energies into heat, which leads to additional line emission. We have solely considered small PAHs (circumcononene) with 54 carbon atoms, and our fits to a few Herbig Ae stars, where multiple mid-IR PAH emission features have been detected, show that these PAHs are mostly charged (60%-98%). We did not consider PAHs in disk gaps as discussed by Maaskant et al. (2014).

**Two-zone disks.** In 18 out of 27 cases, we decided to switch from a one-zone disk setup to a two-zone setup already during the SED-fitting phase. This was found to be necessary to fit certain properties in the photometric and low-resolution spectroscopic data including the PAH emission features. Some of these objects are well-known transitional disks, but for others this is not so clear, for

example CY Tau, where the SED points to a massive yet very cold outer disk. Such disk properties can be produced by setting up a semi-transparent tall inner disk that casts a shadow onto the outer disk.

**Gas-rich, tall inner disks.** The two-zone scenario was often found to be useful to explain objects with very faint far-IR lines. In fact, 12 out of our 14 completed DIANA standard models used a two-zone setup. These tall inner disks shield the outer disk from the UV irradiation by the star, hence lead to less disk heating and line emission. Such inner disks do not obey the condition of hydrostatic equilibrium, in particular those of the T Tauri stars, so their nature can be disputed. However, we could not find any observation that could rule out such a scenario. On the contrary, having that tenuous, tall inner disk definitely helps to explain some of the strong optical lines (such as [O I] 6300 Å) and strong near-IR lines (such as CO fundamental), which are preferentially emitted by these inner disks. Interestingly, the gas/dust ratio in these inner disk zones was often found to be large, up to 90,000 for HD 163296, but never smaller than the standard value of 100.

**Dust masses and cold disks.** We found that the classical dust mass-determination method according to Equation (13) seems not entirely justified. According to our results, disks can be very cold in the midplane <10 K, and since a large fraction of the disk mass resides in those cold midplane areas, emission at 850 µm is generally far less intense than expected from the
<table><caption>**Table 19**
Model Properties and Comparison of Computed Spectral Line Properties with Observations from DMTau.properties</caption><thead><tr><th colspan="2">DIANA Standard Fit Model Properties</th></tr></thead><tbody><tr><td>Minimum dust temperature [K]</td><td>5</td></tr><tr><td>Maximum dust temperature [K]</td><td>242</td></tr><tr><td>Mass-mean dust temperature [K]</td><td>9</td></tr><tr><td>Minimum gas temperature [K]</td><td>5</td></tr><tr><td>Maximum gas temperature [K]</td><td>15978</td></tr><tr><td>Mass-mean gas temperature [K]</td><td>13</td></tr><tr><td>mm-opacity-slope (0.85–1.3) mm</td><td>1.0</td></tr><tr><td>cm-opacity-slope (5–10) mm</td><td>1.3</td></tr><tr><td>mm-SED-slope (0.85–1.3) mm</td><td>2.1</td></tr><tr><td>cm-SED-slope (5–10) mm</td><td>3.1</td></tr><tr><td>10 µm silicate emission amplitude</td><td>2.0</td></tr><tr><td>Naked star luminosity [L<sub>☉</sub>]</td><td>0.3</td></tr><tr><td>Bolometric luminosity [L<sub>☉</sub>]</td><td>0.4</td></tr><tr><td>Near-IR excess (λ = 2.02–6.72 µm) [L<sub>☉</sub>]</td><td>0.00</td></tr><tr><td>Mid IR excess (λ = 6.72–29.5 µm) [L<sub>☉</sub>]</td><td>0.02</td></tr><tr><td>Far-IR excess (λ = 29.5–991. µm) [L<sub>☉</sub>]</td><td>0.04</td></tr></tbody></table>

<table><thead><tr><th rowspan="2">Species</th><th rowspan="2">λ (μm)</th><th colspan="2">Line Flux (W m<sup>-2</sup>)</th><th colspan="2">FWHM (km s<sup>-1</sup>)</th><th rowspan="2">Size (au)</th></tr><tr><th>Observed</th><th>Model</th><th>Observed</th><th>Model</th></tr></thead><tbody><tr><td>Ne<sup>+</sup></td><td>12.814</td><td>5.5 ± 1.1(-18)</td><td>3.3(-17)</td><td>...</td><td>15.3</td><td>7.4</td></tr><tr><td>O I</td><td>63.183</td><td>7.0 ± 2.0(-18)</td><td>4.6(-17)</td><td>...</td><td>3.0</td><td>331.6</td></tr><tr><td>O I</td><td>145.525</td><td>&lt;3.6(-18)</td><td>1.2(-18)</td><td>...</td><td>8.5</td><td>164.3</td></tr><tr><td>C II</td><td>157.740</td><td>&lt;3.6(-18)</td><td>4.5(-18)</td><td>...</td><td>1.5</td><td>565.0</td></tr><tr><td>o-H<sub>2</sub>O</td><td>63.323</td><td>&lt;5.4(-18)</td><td>8.8(-19)</td><td>...</td><td>9.3</td><td>11.9</td></tr><tr><td>CO</td><td>866.963</td><td>1.9 ± 0.1(-19)</td><td>3.7(-19)</td><td>...</td><td>1.8</td><td>448.9</td></tr><tr><td>CO</td><td>1300.404</td><td>1.1 ± 0.3(-19)</td><td>1.2(-19)</td><td>...</td><td>1.8</td><td>443.9</td></tr><tr><td><sup>13</sup>CO</td><td>1360.227</td><td>4.0 ± 0.5(-20)</td><td>1.8(-20)</td><td>...</td><td>2.2</td><td>324.3</td></tr><tr><td>C<sup>18</sup>O</td><td>1365.421</td><td>5.0 ± 0.5(-21)</td><td>3.8(-21)</td><td>...</td><td>2.4</td><td>289.5</td></tr><tr><td>CN</td><td>881.097</td><td>6.7 ± 0.7(-20)</td><td>1.6(-19)</td><td>...</td><td>1.7</td><td>470.5</td></tr><tr><td>CN</td><td>1321.390</td><td>3.6 ± 0.3(-20)</td><td>6.5(-20)</td><td>...</td><td>1.6</td><td>482.0</td></tr><tr><td>HCN</td><td>845.663</td><td>1.9 ± 0.2(-20)</td><td>1.2(-19)</td><td>...</td><td>1.8</td><td>415.3</td></tr><tr><td>HCN</td><td>1127.520</td><td>2.6 ± 0.5(-20)</td><td>7.6(-20)</td><td>...</td><td>1.7</td><td>440.5</td></tr><tr><td>HCO<sup>+</sup></td><td>840.380</td><td>7.5 ± 0.4(-20)</td><td>7.2(-20)</td><td>...</td><td>1.8</td><td>439.8</td></tr><tr><td>HCO<sup>+</sup></td><td>1120.478</td><td>4.8 ± 0.1(-20)</td><td>4.4(-20)</td><td>...</td><td>1.7</td><td>461.8</td></tr><tr><td>N<sub>2</sub>H<sup>+</sup></td><td>804.439</td><td>&lt;6.7(-21)</td><td>1.2(-20)</td><td>...</td><td>2.0</td><td>273.2</td></tr><tr><td>N<sub>2</sub>H<sup>+</sup></td><td>1072.557</td><td>9.3 ± 0.9(-21)</td><td>7.1(-21)</td><td>...</td><td>2.0</td><td>289.6</td></tr></tbody></table>
<figure><img src="image_44.png" /><figcaption>**Figure 26.** Left: CO 2–1 line flux and velocity profile in comparison to SMA data of DM Tau. Right: Same for HCO$^+$ 3–2 line at 1.12 mm. (A color version of this figure is available in the online journal.)</figcaption></figure>

<figure><img src="image_45.png" /><figcaption>**Figure 27.** CY Tau density and surface density plots. For details see Figure 4. (A color version of this figure is available in the online journal.)</figcaption></figure>

Rayleigh–Jeans limit. This finding is supported by Guilloteau et al. (2016) who found temperatures as low as 5–7 K for the large grains in the Flying Saucer. We find the mean disk temperatures to vary by an order of magnitude among individual disks. Disks can be optically thick even at mm-wavelengths. We therefore found disk masses that are often much larger than

stated elsewhere, see Table 7. The determination of dust sizes from the SED millimeter-slope is equally affected by these physical effects. We found that the dust mm-opacity-slope is only weakly correlated to the resulting SED-slope.

*Dust/gas ratio.* Concerning the gas/dust ratio in the outer disk, our results are inconclusive. Disregarding those DIANA
<table><caption>**Table 20**
Model Properties and Comparison of Computed Spectral Line Properties with Observations from CYTau.properties</caption><thead><tr><th colspan="2">DIANA Standard Fit Model Properties</th></tr></thead><tbody><tr><td>Minimum dust temperature [K]</td><td>5</td></tr><tr><td>Maximum dust temperature [K]</td><td>1683</td></tr><tr><td>Mass-mean dust temperature [K]</td><td>9</td></tr><tr><td>Minimum gas temperature [K]</td><td>5</td></tr><tr><td>Maximum gas temperature [K]</td><td>40000</td></tr><tr><td>Mass-mean gas temperature [K]</td><td>12</td></tr><tr><td>mmopalenesslope (0.85–1.3) mm</td><td>1.3</td></tr><tr><td>cmopalenesslope (5–10) mm</td><td>1.7</td></tr><tr><td>mmSED-slope (0.85–1.3) mm</td><td>1.6</td></tr><tr><td>cmSED-slope (5–10) mm</td><td>3.0</td></tr><tr><td>10 µm silicate emission amplitude</td><td>1.6</td></tr><tr><td>Naked star luminosity [L<sub>☉</sub>]</td><td>0.4</td></tr><tr><td>Bolometric luminosity [L<sub>☉</sub>]</td><td>0.5</td></tr><tr><td>Near-IR excess (λ = 2.07–6.96 µm) [L<sub>☉</sub>]</td><td>0.06</td></tr><tr><td>Mid IR excess (λ = 6.96–29.5 µm) [L<sub>☉</sub>]</td><td>0.03</td></tr><tr><td>Far-IR excess (λ = 29.5–973. µm) [L<sub>☉</sub>]</td><td>0.01</td></tr></tbody></table><table><thead><tr><th rowspan="2">Species</th><th rowspan="2">λ (µm)</th><th colspan="2">Line Flux (W m<sup>-2</sup>)</th><th colspan="2">FWHM (km s<sup>-1</sup>)</th><th rowspan="2">Size (au)</th></tr><tr><th>Observed</th><th>Model</th><th>Observed</th><th>Model</th></tr></thead><tbody><tr><td>CO</td><td>1300.403</td><td>1.6 ± 0.3(–20)</td><td>2.0(–20)</td><td>2.4 ± 0.2</td><td>2.3</td><td>199.7</td></tr><tr><td><sup>13</sup>CO</td><td>1360.227</td><td>7.8 ± 0.9(–21)</td><td>6.0(–21)</td><td>2.5 ± 0.2</td><td>2.6</td><td>199.3</td></tr><tr><td>O I</td><td>63.183</td><td>1.2 ± 0.1(–17)</td><td>5.6(–18)</td><td>...</td><td>3.2</td><td>143.2</td></tr><tr><td>O I</td><td>0.630</td><td>7.8 ± 0.5(–18)</td><td>9.4(–18)</td><td>42.0 ± 3.0</td><td>59.0</td><td>0.4</td></tr><tr><td>o-H<sub>2</sub>O</td><td>63.323</td><td>&lt;1.2(–17)</td><td>1.4(–19)</td><td>...</td><td>29.8</td><td>0.7</td></tr><tr><td>CO</td><td>4.633</td><td>6.0 ± 2.0(–18)</td><td>6.6(–18)</td><td>75.0 ± 11.0</td><td>14.0</td><td>4.1</td></tr><tr><td>CO</td><td>4.920</td><td>5.0 ± 1.0(–18)</td><td>4.2(–18)</td><td>86.0 ± 9.0</td><td>92.1</td><td>0.1</td></tr></tbody></table>
<figure><img src="image_46.png" /><figcaption>**Figure 28.** Comparison of the observed and modeled CO rovibrational spectrum with continuum. (A color version of this figure is available in the online journal.)</figcaption></figure>

<figure><img src="image_47.png" /><figcaption>**Figure 29.** RECX 15 density and surface density plots. For details see Figure 4. (A color version of this figure is available in the online journal.)</figcaption></figure>

standard models where gas/dust = 100 was enforced, the remaining 8 models have gas/dust = 120$^{+170}_{-70}$.

We offer all collected observational data at http://www.univie.ac.at/diana and provide all modeling results at http://www-star.st-and.ac.uk/~pw31/DIANA/DIANAstandard. The 2D physico-chemical structures of our objects can be downloaded from these internet portals for further inspection and analysis. All model parameters are offered in an easy-to-use

format, see Appendix A, and all users of MCFOST, MCMax or ProDiMo can download setup files to re-run our disk models. This ensures the transparency of our modeling work, and their re-use in future applications.

The use of the DIANA disk models beyond the project has already started. Stolker et al. (2017) used the DIANA SED model for the interpretation of multi-epoch VLT/SPHERE scattered light images of HD 135344B. They use our model to
<figure><img src="image_48.png" /><figcaption>**Figure 30.** Model fit to our CO 3–2 ALMA cycle-0 observations of RECX 15. (A color version of this figure is available in the online journal.)</figcaption></figure>

illustrate that a small misalignment between the inner and the outer disk (2.6) can explain the observed broad, quasi-stationary shadowing in north-northwest direction. The effects of inclined inner disks on line fluxes would be worth studying in the future. As a second example, Muro-Arena et al. (2018) used the DIANA SED model of HD 163296 to analyze the combined VLT/SPHERE and ALMA continuum data set for this object. Even though clear ring structures are seen and the model is eventually refined to show a surface density modulation, the average surface density profile stays the same as in the DIANA SED model. This illustrates that in some cases, the detailed disk substructures are minor modulations of the global 2D disk models. These substructures are key for the planet formation processes, but have only little effect on global observables such SEDs and unresolved line observations that arise from an extended radial region of the disk. Lastly, the MWC 480 and Lk Ca 15 disk models can serve as an interesting starting point for the analysis of the full ALMA spectral scan (ALMA community proposal 2015.1.00657.S searching for complex molecules, led by Karin Öberg et al.). These examples illustrate the potential of the 2D disk models presented in this paper for future data analysis and interpretation, even in the realm of observed 3D disk substructures.

The authors acknowledge funding from the EU FP7-2011 under grant agreement No. 284405. J.D.I. gratefully acknowledges support from the DISCSIM project, grant agreement

<figure><img src="image_49.png" /><figcaption>**Figure 31.** Summary of line fitting results from the DIANA-standard models. The y-axis shows the line fluxes as predicted by the models divided by the observed line fluxes $F_{\text{line}}^{\text{mod}}/F_{\text{line}}^{\text{obs}}$ on log-scalings as indicated on the right. If a dot is positioned at 0.5, for example, it means that the model underpredicts the line flux by a factor of 2. An arrow indicates that the observation is an upper limit. An arrow starting at 1 indicates a good match—the model predicts a line flux lower or equal to the observational $3\sigma$ upper limit. If, however, the arrow starts at 2, it means that the model predicts a line flux that is a factor 2 larger than the $3\sigma$ upper limit. Systematic errors in the observations are typically of order (10–30)%.</figcaption></figure>

(A color version of this figure is available in the online journal.)

341137, funded by the European Research Council under ERC-2013-ADG. Astrophysics at Queen's University Belfast is supported by a grant from the STFC (ST/P000312/1). O.D. acknowledges the support of the Austrian Research Promotion Agency (FFG) to the project JetPro, funded within the framework of the Austrian Space Applications Program (ASAP) FFG-854025. This paper makes use of the following ALMA data: RECX 15: ADS/JAO.ALMA#2011.0.00133.S (RECX 15) and ADS/JAO.ALMA#2011.0.00629.S (DM Tau and MWC 480). ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ.
<table><caption>**Table 21**
Model Properties and Comparison of Computed Spectral Line Properties with Observations from RECX15.properties</caption><thead><tr><th colspan="2">DIANA Standard Fit Model Properties</th></tr></thead><tbody><tr><td>Minimum dust temperature [K]</td><td>32</td></tr><tr><td>Maximum dust temperature [K]</td><td>1396</td></tr><tr><td>Mass-mean dust temperature [K]</td><td>86</td></tr><tr><td>Minimum gas temperature [K]</td><td>44</td></tr><tr><td>Maximum gas temperature [K]</td><td>26982</td></tr><tr><td>Mass-mean gas temperature [K]</td><td>116</td></tr><tr><td>mm-opacity-slope (0.85–1.3) mm</td><td>0.8</td></tr><tr><td>cm-opacity-slope (5–10) mm</td><td>1.6</td></tr><tr><td>mm-SED-slope (0.85–1.3) mm</td><td>2.5</td></tr><tr><td>cm-SED-slope (5–10) mm</td><td>3.5</td></tr><tr><td>10 µm silicate emission amplitude</td><td>1.4</td></tr><tr><td>Naked star luminosity [L<sub>☉</sub>]</td><td>0.1</td></tr><tr><td>Bolometric luminosity [L<sub>☉</sub>]</td><td>0.2</td></tr><tr><td>Near-IR excess (λ = 2.02–6.72 µm) [L<sub>☉</sub>]</td><td>0.02</td></tr><tr><td>Mid IR excess (λ = 6.72–29.5 µm) [L<sub>☉</sub>]</td><td>0.02</td></tr><tr><td>Far-IR excess (λ = 29.5–991. µm) [L<sub>☉</sub>]</td><td>0.01</td></tr></tbody></table>

<table><thead><tr><th rowspan="2">Species</th><th rowspan="2">λ (µm)</th><th colspan="2">Line Flux (W m<sup>-2</sup>)</th><th colspan="2">FWHM (km s<sup>-1</sup>)</th><th rowspan="2">Size (au)</th></tr><tr><th>Observed</th><th>Model</th><th>Observed</th><th>Model</th></tr></thead><tbody><tr><td>CO</td><td>866.963</td><td>8.2 ± 0.6(−21)</td><td>6.0(−21)</td><td>14.9 ± 2.3</td><td>12.6</td><td>5.4</td></tr><tr><td>O I</td><td>63.183</td><td>3.0 ± 0.3(−17)</td><td>2.6(−17)</td><td>...</td><td>13.8</td><td>6.0</td></tr><tr><td>O I</td><td>0.630</td><td>6.5 ± 2.5(−17)</td><td>1.3(−16)</td><td>38.0 ± 10.0</td><td>20.8</td><td>3.4</td></tr><tr><td>o-H<sub>2</sub></td><td>2.121</td><td>2.5 ± 0.1(−18)</td><td>1.7(−19)</td><td>18.0 ± 1.2</td><td>66.9</td><td>2.0</td></tr><tr><td>O I</td><td>145.525</td><td>&lt;6.0(−18)</td><td>1.4(−18)</td><td>...</td><td>13.2</td><td>5.5</td></tr><tr><td>C II</td><td>157.740</td><td>&lt;9.0(−18)</td><td>1.8(−19)</td><td>...</td><td>14.0</td><td>6.0</td></tr><tr><td>CO</td><td>90.162</td><td>&lt;9.6(−18)</td><td>7.3(−19)</td><td>...</td><td>19.9</td><td>3.7</td></tr><tr><td>CO</td><td>79.359</td><td>&lt;2.4(−17)</td><td>5.6(−19)</td><td>...</td><td>25.0</td><td>2.3</td></tr><tr><td>CO</td><td>72.842</td><td>&lt;8.1(−18)</td><td>4.7(−19)</td><td>...</td><td>28.7</td><td>2.1</td></tr><tr><td>o-H<sub>2</sub>O</td><td>180.488</td><td>&lt;5.1(−18)</td><td>9.2(−20)</td><td>...</td><td>24.2</td><td>4.3</td></tr><tr><td>o-H<sub>2</sub>O</td><td>179.526</td><td>&lt;5.1(−18)</td><td>1.2(−19)</td><td>...</td><td>20.1</td><td>4.8</td></tr><tr><td>o-H<sub>2</sub>O</td><td>78.742</td><td>&lt;3.0(−17)</td><td>1.2(−18)</td><td>...</td><td>21.3</td><td>4.8</td></tr><tr><td>p-H<sub>2</sub>O</td><td>89.988</td><td>&lt;9.6(−18)</td><td>6.8(−19)</td><td>...</td><td>24.2</td><td>4.4</td></tr></tbody></table>
<figure><img src="image_50.png" /><figcaption>**Figure 32.** Continued from Figure 31. (A color version of this figure is available in the online journal.)</figcaption></figure>

## Appendix A
### Uploaded Model Data

The model data uploaded to the DIANA database<fnref n="18" /> are organized in five sets:

1. `{object-name}.para`,

2. `{object-name}.properties`,

3. `{object-name}_DIANAfit.ps.gz`,

4. `{object-name}_ModelOutput.tgz`, and

5. `{object-name}_ModelSetup.tgz`.

Examples of the `.para` and `.properties` files are shown in Figures 33 and 34, respectively.

The `.para` files contain the complete set of modeling parameters, as well as a few quantities related to the stellar properties. These values are listed in a generic form to make them readable even to end-users not working with ProDiMo, MCFOST or MCMax. The different blocks of the `.para` files (see Figure 33) list the parameter names and units of the stellar parameter, some observational parameters like distance and inclination, two essential switches (one or two-zone model? PAHs included in RT?), the dust material and settling

parameters, the PAH parameters, the gas parameters, as well as the disk shape, mass, and dust size parameters separately for the inner (for two-zone models) and the outer disk zones. The meaning of all physical quantities is explained in Woitke et al. (2016).

The `.properties` files contain a selection of important model output quantities, as well as some predicted observations, see Figure 34. The first block contains minimum, maximum and mean values of the gas and dust temperatures in the disk. The second block lists total masses of chemicals, and mean values thereof, for example,

$$ \langle T_{\text{gas}}^{\text{H}_2} \rangle = \frac{\int T_{\text{gas}} n_{\text{H}_2} dV}{\int n_{\text{H}_2} dV}, \qquad (20) $$

where $n_{\text{H}_2}$ is the particle density of molecular hydrogen, $T_{\text{gas}}$ the gas temperature, and $\int dV$ is the integration in cylindrical coordinates over radius $r$ and height over midplane $z$ in the disk. In the shown example, we find the mean gas temperature of atomic hydrogen to be ≈660 K and the mean gas temperature of molecular hydrogen to be ≈21 K.

The next block summarizes some predictions of directly observable continuum properties, such as the millimeter and centimeter slopes, the amplitude of the 10 µm silicate emission feature, and near-IR, mid-IR and far-IR excesses, followed by two blocks which contain the model SED computed by MCFOST and ProDiMo, the latter comes with an apparent size at all wavelengths, i.e., the radius of a circle in the image plane which contains 95% of the spectral flux. The apparent sizes are derived without convolution with any instrumental PSF, and are computed without direct starlight.

The second block from the bottom shows predictions and properties of a generic sample of 102 spectral emission lines. The name of the atom or molecule, the line center wavelength, the total line flux, the continuum flux, the FWHM of the line velocity-profile, the apparent size of the line emitting region (as above), and averages of density, gas and dust temperature and optical extinction over the line emitting regions. Studying the output for the CO isotopologue lines around 1.3 mm shows that the ¹²CO line comes from less dense but warmer gas, whereas the ¹³CO, C¹⁸O and C¹⁷O lines originate in successively cooler and deeper disk layers. Note that $\langle T_{\text{gas}} \rangle \approx \langle T_{\text{dust}} \rangle$ for all CO isotopologue lines, whereas the [O I] 63 µm line has $\langle T_{\text{gas}} \rangle > \langle T_{\text{dust}} \rangle$. This information is available for all 102 lines for all finished DIANA standard models.

The last block compares observed with predicted line properties including line fluxes, FWHMs and apparent sizes. In the case of TW Hya, 57 line observations have been collected, and accounted for in the fitting of the model parameters.

The DIANAfit.ps.gz files contain graphical output pages of the following model results: 2D-density structure (gas and dust), gas/dust ratio, mean dust sizes, column density structure,

<footnote n="18">¹⁸ http://www.univie.ac.at/diana, see also http://www-star.st-and.ac.uk/~pw31/DIANA/SEDfit/SEDmodels_index.html and http://www-star.st-and.ac.uk/~pw31/DIANA/DIANAstandard for direct access.</footnote>
DIANA standard model parameters

------------------------------------------

object = TWHya

<table><tr><td>Mstar [Msun]</td><td>=</td><td>0.7500</td></tr><tr><td>Teff [K]</td><td>=</td><td>4000.00</td></tr><tr><td>Lstar [Lsun]</td><td>=</td><td>0.2420</td></tr><tr><td>Rstar [Rsun]</td><td>=</td><td>1.0888</td></tr><tr><td>log(g)</td><td>=</td><td>4.2389</td></tr><tr><td>L_UV (91.2-205 nm) [Lsun]</td><td>=</td><td>1.2836E-05</td></tr><tr><td>L_UV (91.2-111 nm) [Lsun]</td><td>=</td><td>3.0319E-06</td></tr><tr><td>L_X (&gt;0.1 keV) [Lsun]</td><td>=</td><td>7.6790E-04</td></tr><tr><td>L_X (1-10 keV) [Lsun]</td><td>=</td><td>7.0413E-05</td></tr><tr><td>Mdot [Msun/yr]</td><td>=</td><td>1.5000E-09</td></tr><tr><td>interstellar A_V</td><td>=</td><td>0.1999</td></tr><tr><td>interstellar R_V</td><td>=</td><td>3.1000</td></tr></table>

------------------------------------------
distance [pc] = 51.0
inclination [deg] = 7.0
disk PA [deg] = n.a.
disk zones = 2
PAHs in RT = .false.

------------------- dust parameters -------------------
Mg0.7Fe0.3SiO3 [Vol%] = 0.5010
amC-Zubko [Vol%] = 0.2490
vacuum [Vol%] = 0.2500
alpha_settle = 5.2351E-03

------------------- PAH parameters -------------------
ratio charged PAHs = n.a.
number of carbon atoms = 54.0000
number of hydrogen atoms = 18.0000

------------------- gas parameters -------------------

<table><tr><td>chemical heating efficiency</td><td>=</td><td>0.0180</td></tr><tr><td>turbulent velocity [km/s]</td><td>=</td><td>0.1000</td></tr><tr><td>type of chemistry</td><td>=</td><td>large DIANA standard with D</td></tr><tr><td colspan="3">inner zone</td></tr><tr><td>gas mass [Msun]</td><td>=</td><td>1.0503E-06</td></tr><tr><td>dust mass [Msun]</td><td>=</td><td>1.3266E-09</td></tr><tr><td>inner radius [AU]</td><td>=</td><td>0.0781</td></tr><tr><td>outer radius [AU]</td><td>=</td><td>4.5784</td></tr><tr><td>col.dens.power-index</td><td>=</td><td>-0.7788</td></tr><tr><td>scale height @ 1AU [AU]</td><td>=</td><td>0.0279</td></tr><tr><td>flaring index</td><td>=</td><td>1.2052</td></tr><tr><td>minimum dust radius [mic]</td><td>=</td><td>0.00114</td></tr><tr><td>maximum dust radius [mic]</td><td>=</td><td>5734.897</td></tr><tr><td>size-dist. power-index</td><td>=</td><td>3.9926</td></tr><tr><td>fPAH</td><td>=</td><td>0.0080</td></tr></table>

------------------- outer zone -------------------
disk gas mass [Msun] = 4.4769E-02
disk dust mass [Msun] = 1.0142E-04
inner radius [AU] = 4.5784
tapering-off radius [AU] = 48.0055
outer radius [AU] = 192.9500
col.dens.power-index = 1.5181
tapering-off power-index = 0.4452
scale height @ 100AU [AU] = 6.2615
flaring index = 1.2121
minimum dust radius [mic] = 0.00114
maximum dust radius [mic] = 5734.9
size-dist. power-index = 3.9926
fPAH = 0.0806

<caption>**Figure 33.** Example file TWHya.para which contains all model parameters of the TW Hya disk model in an easy to understand, simple generic format.</caption>
<table><caption>**Figure 34.** Example file TWHya.properties which contains a collection of important physico-chemical results and predictions of observational quantities from the model, such as continuum and line fluxes, apparent sizes, FWHM of lines, etc. Note the "..." in the figure which means that a number of lines have been omitted here for clarity. Mean value (.) refer to averages over the specific line emission regions. The size [au] is the radius of a circle in the image plane that contains 95% of the flux.</caption><thead><tr><th colspan="5">DIANA standard fit model properties</th></tr><tr><th colspan="5">object = TWHya</th></tr></thead><tbody><tr><td>minimum dust temperature [K]</td><td>=</td><td>7.24</td><td></td><td></td></tr><tr><td>maximum dust temperature [K]</td><td>=</td><td>1112.40</td><td></td><td></td></tr><tr><td>mass-mean dust temperature [K]</td><td>=</td><td>21.05</td><td></td><td></td></tr><tr><td>minimum gas temperature [K]</td><td>=</td><td>7.35</td><td></td><td></td></tr><tr><td>maximum gas temperature [K]</td><td>=</td><td>40000.00</td><td></td><td></td></tr><tr><td>mass-mean gas temperature [K]</td><td>=</td><td>21.29</td><td></td><td></td></tr><tr><td colspan="5">------ species masses and mass-mean temperatures ------</td></tr><tr><td colspan="5">240 species</td></tr><tr><td>species mass [Msun]</td><td>&lt;Tgas&gt;[K]</td><td>&lt;Tdust&gt;[K]</td><td>&lt;AV&gt;</td><td></td></tr><tr><td>e- 4.924E-13</td><td>5659.18</td><td>65.89</td><td>7.630E-01</td><td></td></tr><tr><td>H+ 7.613E-10</td><td>6088.93</td><td>66.04</td><td>8.591E-01</td><td></td></tr><tr><td>H 3.304E-07</td><td>664.48</td><td>58.94</td><td>6.566E-03</td><td></td></tr><tr><td>H2 3.219E-02</td><td>21.29</td><td>21.28</td><td>1.404E+03</td><td></td></tr><tr><td colspan="5">...</td></tr><tr><td colspan="5">------ continuum properties ------</td></tr><tr><td>mm-opacity-slope (0.85-1.3)mm</td><td>=</td><td>1.2244</td><td></td><td></td></tr><tr><td>cm-opacity-slope (5-10)mm</td><td>=</td><td>1.3924</td><td></td><td></td></tr><tr><td>mm-SED-slope (0.85-1.3)mm</td><td>=</td><td>2.1526</td><td></td><td></td></tr><tr><td>cm-SED-slope (5-10)mm</td><td>=</td><td>3.0310</td><td></td><td></td></tr><tr><td>10mic silicate emission amplitude</td><td>=</td><td>2.1760</td><td></td><td></td></tr><tr><td>naked star luminosity [Lsun]</td><td>=</td><td>0.2719</td><td></td><td></td></tr><tr><td>bolometric luminosity [Lsun]</td><td>=</td><td>0.3455</td><td></td><td></td></tr><tr><td>near IR excess [Lsun]</td><td>=</td><td>6.8858E-03</td><td>(lam=2.02-6.99mic)</td><td></td></tr><tr><td>mid IR excess [Lsun]</td><td>=</td><td>2.7334E-02</td><td>(lam=6.99-29.4mic)</td><td></td></tr><tr><td>far IR excess [Lsun]</td><td>=</td><td>3.6517E-02</td><td>(lam=29.4-972.mic)</td><td></td></tr><tr><td colspan="5">...</td></tr><tr><td colspan="5">------ MCFOST SED ------</td></tr><tr><td colspan="5">125 points</td></tr><tr><td>lam[mic]</td><td>Fnu[Jy]</td><td></td><td></td><td></td></tr><tr><td>9.2100E-02</td><td>6.4362E-05</td><td></td><td></td><td></td></tr><tr><td>9.3928E-02</td><td>2.8237E-04</td><td></td><td></td><td></td></tr><tr><td>9.5791E-02</td><td>4.7802E-04</td><td></td><td></td><td></td></tr><tr><td colspan="5">...</td></tr><tr><td colspan="5">------ ProDiMo SED and apparent size ------</td></tr><tr><td colspan="5">300 points</td></tr><tr><td>lam[mic]</td><td>Fnu[Jy]</td><td>size[AU]</td><td></td><td></td></tr><tr><td>1.0012E+00</td><td>7.1632E-01</td><td>3.7740E+01</td><td></td><td></td></tr><tr><td>1.0409E+00</td><td>7.4734E-01</td><td>3.7515E+01</td><td></td><td></td></tr><tr><td>1.0821E+00</td><td>7.7549E-01</td><td>3.7258E+01</td><td></td><td></td></tr><tr><td colspan="5">...</td></tr><tr><td colspan="5">------ line properties ------</td></tr><tr><td colspan="5">102 lines</td></tr><tr><td>lam[mic]</td><td>lflux[W/m2]</td><td>Fcont[Jy]</td><td>FWHM[km/s]</td><td>size[AU]</td></tr><tr><td>CO 1300.403</td><td>1.6578E-19</td><td>0.615366</td><td>0.814</td><td>162.399</td></tr><tr><td>13CO 1360.228</td><td>2.5141E-20</td><td>0.554141</td><td>0.966</td><td>123.788</td></tr><tr><td>C18O 1365.430</td><td>6.0085E-21</td><td>0.549196</td><td>1.061</td><td>109.722</td></tr><tr><td>C17O 1334.098</td><td>1.9415E-21</td><td>0.579859</td><td>1.082</td><td>106.615</td></tr><tr><td>HCO+ 1120.478</td><td>6.5941E-20</td><td>0.861775</td><td>0.793</td><td>177.482</td></tr><tr><td>[OI] 63.183</td><td>1.3759E-16</td><td>4.619789</td><td>1.325</td><td>97.677</td></tr><tr><td colspan="5">...</td></tr><tr><td colspan="5">------ comparison observed/model line properties ------</td></tr><tr><td colspan="5">57 spectral lines</td></tr><tr><td>lam[mic]</td><td>obs lineflux [W/m2]</td><td>model</td><td>obs.FWHM[km/s]</td><td>model size[AU]</td></tr><tr><td>OI 63.18367060</td><td>3.70E-17 +/- 1.00E-18</td><td>1.3761E-16</td><td>0.00 +/- 0.00</td><td>1.3281 9.7579E+01</td></tr><tr><td>o-H2O 20.34147403</td><td>5.20E-18 +/- 2.00E-18</td><td>1.8208E-17</td><td>0.00 +/- 0.00</td><td>11.3296 7.7652E-01</td></tr><tr><td>o-H2O 23.85979742</td><td>1.10E-17 +/- 2.00E-18</td><td>2.5681E-17</td><td>0.00 +/- 0.00</td><td>10.1508 2.1124E+00</td></tr><tr><td>o-H2O 25.36599169</td><td>6.60E-18 +/- 2.00E-18</td><td>2.6824E-17</td><td>0.00 +/- 0.00</td><td>9.8190 3.4773E+00</td></tr><tr><td>o-H2O 30.52542262</td><td>2.40E-17 +/- 2.00E-18</td><td>2.4765E-17</td><td>0.00 +/- 0.00</td><td>8.9982 4.7101E+00</td></tr><tr><td>o-H2O 30.87089842</td><td>1.60E-17 +/- 2.00E-18</td><td>2.0718E-17</td><td>0.00 +/- 0.00</td><td>9.2165 4.5666E+00</td></tr></tbody></table>

scale height as function of radius, UV field-strength $\chi$, radial optical depths for UV photons and X-rays, X-ray ionization rate $\zeta_X$, dust, gas and PAH temperature structures, chemical and cooling relaxation timescales, Rosseland-mean dust opacity, sound speed, the most important heating and cooling processes, mean dust opacity as function of wavelength, SED, magnification of mid-IR region, apparent size and continuum

emission regions as function of wavelength, enlargements of SED in selected spectral windows with emission lines overplotted, continuum images at near-IR to mm wavelengths, comparison of model to observed intensity profiles after PSF-convolution, concentration of selected chemicals as 2D-contour plots, 2D-plots of the line emission regions that produce >50% of the line flux (available for all 102 generic emission lines),
computed velocity profiles for the observed lines in comparison to the data (where available), and line intensity plots (after averaging over $\theta$ in concentric rings) as function of r.

The ModelOutput.tgz files contain all model output data as listed above (and more) in numerical tables where each line corresponds to a (r, z)-point in the model. These data can be used, for example, to make your own plots, for example to look for the various ice-lines.

The ModelSetup.tgz files contain all numerical input and data-files necessary to recompute the model. These files are included in the format required for ProDiMo, MCFOST and MCMAX. The data-files include the observational data in the “model-friendly” input format requested by ProDiMo.

## Appendix B
Uncertainties in Disk Parameter Determination

Our derived values of the model parameter concerning disk shape, gas, dust and PAH parameters are subject to large uncertainties, partly due to measurement errors and calibration uncertainties of the astronomical instruments used, but partly also due to well-known fitting degeneracies, in particular if the disk model is only fitted to SED data.

Absolute measurement errors are typically 10%–30%, for example due to calibration uncertainties, usually larger than the quoted measurement uncertainties. This is particularly relevant for multi-instrument data as we consider in this paper. Another source for uncertainties are numerical errors. For computational grid sizes 100 × 100 as used here, line flux predictions from the models are uncertain by about 10% (Woitke et al. 2016, see Appendix F therein) due to numerical problems to properly resolve the sometimes very small (i.e., very thin) line forming regions.

A proper resolution of all modeling uncertainties and degeneracies would require a Bayesian analysis, which needs about 10⁶ models for each object in a ~20-dimensional parameter space. After careful consideration, the team decided

not to perform such a Bayesian analyses, because it would surpass our already considerable numerical efforts in this project to determine the $\chi^2$ minimums by a large factor.

However, to get a rough impression of our modeling uncertainties, we consider here some deviations $dp_j$ from the best values $p_j^{opt}$ of parameter j in both directions from the local $\chi^2$-minimum as

$$ \chi_{\min}^2 = \chi^2(p_j^{opt}), \qquad (21) $$

$$ \chi_{j+}^2 = \chi^2(p_j^{opt} + \delta_{j,j'} dp_{j'}), \qquad (22) $$

$$ \chi_{j-}^2 = \chi^2(p_j^{opt} - \delta_{j,j'} dp_{j'}), \qquad (23) $$

and then fit a parabola to the three points {$\chi_{j-}^2, \chi_{\min}^2, \chi_{j+}^2$} in each parameter dimension j to (i) check whether the best parameter value $p_j^{opt}$ actually sits in a multi-dimensional minimum as expected, and (ii) to determine the distance $\Delta p_j$ by which parameter j can be varied, until a considerable worsening of the fit is obtained as

$$ \chi^2(p_j^{opt} + \delta_{j,j'} \Delta p_{j'}) = \chi_{\min}^2 + 0.1. \qquad (24) $$

Typically, our best fits have $\chi_{\min} \approx 1...3$. The constant offset of 0.1 is chosen “by eye,” such that a human can effortlessly identify the best fitting model among all three models with parameter values $p_j^{opt} - \Delta p_j, p_j^{opt}$ and $p_j^{opt} + \Delta p_j$ by looking at all the fits to the various continuum and line data.

Table 22 lists these local estimates $\Delta p_j$ of our parameter confidence intervals for three selected DIANA standard models. The first two objects HD 163296 and TW Hya have rich continuum and line data, the last object BP Tau has less data, with emphasis on the CO rovibrational data which probes first and foremost the inner disk.

The formal conclusion from this exercise is that we can fit disk gas masses by roughly a factor of two, and dust masses by about 20%. However, this disregards any degeneracies with e.g., the dust opacity parameters. Some parameters like the
<table><caption>**Table 22**
Error Estimations for Three Example Disks; See the Text for Further Explanations</caption><thead><tr><th></th><th>HD 163296</th><th>TW Hya</th><th>BP Tau</th></tr></thead><tbody><tr><td colspan="4"><strong>Dust parameters</strong></td></tr><tr><td>Minimum dust size a<sub>min</sub> [µm]</td><td>0.020 ± 140%</td><td>0.0011 ± 55%</td><td>0.049 ± 14%</td></tr><tr><td>Maximum dust size a<sub>max</sub> [mm]</td><td>8.2 ± 71%</td><td>5.7 ± 105%</td><td>3.1 ± 60%</td></tr><tr><td>Dust size distribution powerlaw index a<sub>pow</sub></td><td>3.71 ± 0.08</td><td>3.99 ± 0.08</td><td>3.97 ± 0.05</td></tr><tr><td>Volume fraction of amorphous carbon amC [%]</td><td>6.0 ± 1.3</td><td>25 ± 3</td><td>17 ± 4</td></tr><tr><td>Dust settling parameter α<sub>settle</sub></td><td>6.6(-3) ± 87%</td><td>5.2(-3) ± 120%</td><td>6.0(-5) ± 20%</td></tr><tr><td colspan="4"><strong>PAH and gas parameters</strong></td></tr><tr><td>Abundance of PAHs f<sub>PAH</sub></td><td>0.076 ± 0.06</td><td>0.08 ± 0.1</td><td>0.12 ± 0.28</td></tr><tr><td>Efficiency of chemical heating γ<sub>chem</sub></td><td>0.19 ± 0.28</td><td>0.014 ± 0.025</td><td>0.13 ± 0.15</td></tr><tr><td colspan="4"><strong>Inner disk parameters</strong></td></tr><tr><td>Gas mass M<sub>gas</sub> [M<sub>☉</sub>]</td><td>1.3(-4) ± 58%</td><td>1.1(-6) ± 31%</td><td>7.1(-7) ± 17%</td></tr><tr><td>Dust mass M<sub>dust</sub> [M<sub>☉</sub>]</td><td>1.5(-9) ± 45%</td><td>1.3(-9) ± 62%</td><td>6.9(-9) ± 18%</td></tr><tr><td>Inner radius R<sub>in</sub> [au]</td><td>0.41 ± 14%</td><td>0.078 ± 46%</td><td>0.060 ± 33%</td></tr><tr><td>Column density exponent ϵ</td><td>1.11 ± 0.39</td><td>-0.78 ± 0.29</td><td>0.52 ± 0.06</td></tr><tr><td>Scale height at 1 au H [au]</td><td>0.077 ± 5%</td><td>0.028 ± 14%</td><td>0.12 ± 6%</td></tr><tr><td>Flaring exponent β</td><td>1.01 ± 0.11</td><td>1.21 ± 0.13</td><td>1.22 ± 0.02</td></tr><tr><td colspan="4"><strong>Outer disk parameters</strong></td></tr><tr><td>Gas mass M<sub>gas</sub> [M<sub>☉</sub>]</td><td>5.8(-1) ± 60%</td><td>4.5(-2) ± 45%</td><td>6.4(-3) ± 50%</td></tr><tr><td>Dust mass M<sub>dust</sub> [M<sub>☉</sub>]</td><td>1.7(-3) ± 15%</td><td>1.0(-4) ± 14%</td><td>1.4(-4) ± 25%</td></tr><tr><td>Inner radius R<sub>in</sub> [au]</td><td>3.7 ± 18%</td><td>4.6 ± 9%</td><td>1.3 ± 7%</td></tr><tr><td>Tapering-off radius R<sub>taper</sub> [au]</td><td>130 ± 15%</td><td>48 ± 9%</td><td>32 ± 55%</td></tr><tr><td>Column density exponent ϵ</td><td>0.95 ± 0.20</td><td>1.52 ± 0.13</td><td>0.65 ± 0.18</td></tr><tr><td>Tapering-off exponent γ</td><td>0.20 ± 0.30</td><td>0.45 ± 0.23</td><td>0.67 ± 0.23</td></tr><tr><td>Scale height at 100 au H [au]</td><td>6.5 ± 0.2</td><td>6.3 ± 0.3</td><td>7.1 ± 0.3</td></tr><tr><td>Flaring exponent β</td><td>1.11 ± 0.03</td><td>1.21 ± 0.03</td><td>1.12 ± 0.02</td></tr></tbody></table>

PAH abundance (none of the selected objects has clear PAH detections in the mid-IR) and the chemical heating efficiencies can only be determined by order of magnitude, power law indices can roughly be determined by 0.1–0.3, but some disk shape parameters like the scale height and flaring exponent can be determined more precisely, by about 5%–15%.

## Appendix C
Detailed mid-IR Spectra

Figure 35 shows enlargements of our SED-fitting models in the mid-IR region in comparison to the *Spitzer/IRS*, *ISO/SWS* and photometric data for 27 objects. These results are discussed in Section 3.2.
<figure><img src="image_51.png" /><figcaption>**Figure 35.** Enlargements of the SED-fits in the mid-IR region on linear scales, centered around the broad silicate emission feature at 10 µm and the PAH emission features at 3.3, 6.25, 7.85, 8.7, 11.3, and 12.7 µm. All results have been obtained with the DIANA standard dust opacities, see text, where only the powerlaw parameters of the dust size-distribution and the volume fraction of amorphous carbon was varied for the fit. Therefore, detailed fits of the spectral shapes of the features are not expected. Concerning the PAHs, only the abundance of the PAHs and the fraction of charged PAHs was varied for fitting.</figcaption></figure>
<figure><img src="image_52.png" /><figcaption>Figure 35. (Continued.)</figcaption></figure>
<figure><img src="image_53.png" /><figcaption>Figure 35. (Continued.)</figcaption></figure>
<figure><img src="image_54.png" /><figcaption>Figure 35. (Continued.)</figcaption></figure>
<figure><img src="image_55.png" /><figcaption>Figure 35. (Continued.)</figcaption></figure>

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