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Home All issues Volume 582 (October 2015) A&A, 582 (2015) A105 Online Material
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Issue
A&A
Volume 582, October 2015
Article Number A105
Number of page(s) 30
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/201525724
Published online 20 October 2015

Online material

Appendix A: Additional figures

thumbnail Fig. A.1

Mixing coefficient models. For further details see Fig. 4.

thumbnail Fig. A.2

Flaring index exponent models. For further details see Fig. 4.

thumbnail Fig. A.3

Maximum dust size models. For further details see Fig. 4.

thumbnail Fig. A.4

Dust size distribution power law index models. For further details, see Fig. 4.

thumbnail Fig. A.5

ISM radiation field models. For further details see Fig. 4.

thumbnail Fig. A.6

Fraction of PAHs models. a) Emitting region water column density for dust-to-gas mass ratio models; this region comprises 15−85% of the radially and vertically integrated flux. Green vertical dotted lines distinguish the reservoirs. b) Theoretical Spitzer SH/LH modules spectra (R = 600) for a dust-to-gas model series, continuum subtracted, and arbitrarily shifted. c) Average extension of the line emitting region, which comprises 50% of the line flux radially and vertically for 12.407 μm. d) Average extension of the line emitting region, which comprises 50% of the line flux radially and vertically for 538.29 μm.

thumbnail Fig. A.7

Gas mass content models. For further details see Fig. 4.

Appendix B: Computation of properties in the line emitting region

The different water lines are divided in groups based on their spatial origin. The latter is defined as that part of the disk from which a cumulative radially and vertically integrated flux of 15% to 85% of the total flux is produced. For each of these regions, averaged physical conditions ⟨X⟩ are derived, such as the density of water, density of the collisional partners (e−, H, H2), Tgas and Tdust by numerically integrating over the emitting region (Eq. (B.1)), i.e., (B.1)In order to determine the continuum extinction, a vertical integration is performed from the disk surface to the midplane. τν is the continuum optical depth at the frequency of the line. It is related to the dust density ρdust and dust mass extinction coefficient κν. The integration is performed numerically, as follows: (B.2)

Through interpolation, we find the value at which τν = 1. The optical depth is evaluated at the radial midpoint of the emitting region.

Appendix C: Model details

The following appendix shows a number of additional plots. These can be useful for the interpretation of the main results and conclusions reported in the paper.

Here we show the Herschel/HIFI fundamental o-H2O and p-H2O lines fluxes behavior with the different parameters.

thumbnail Fig. C.1

Line fluxes behavior for Herschel/HIFI lines 538.29 μm and 269.27 μm for different model series. First row left: dust-to-gas mass ratio, d/g. First row right: mixing parameter, αset. Second row left: disk flaring, β. Second row right: maximum grain size amax. Third row left: power law index of grain size distribution, apow. Third row right: strength of UV radiation field, χISM. Bottom left: PAH abundance, fPAH. Bottom right: disk gas mass, Mgas.

thumbnail Fig. C.2

Standard model, from top to bottom and from left to right: Tgas with overplotted gas temperature contours (white/black) and AV = 1, 10 (red), Tdust with overplotted temperature contours (black/white) and AV = 1, 10 (red), dust-to-gas mass ratio, average dust grain size, main cooling processes (CII fine structure lines, dust grain-gas thermal exchange, Ly α line, neutral O line cooling, CO rotational and ro-vibrational cooling, water rotational and ro-vibrational cooling, formaldehyde rotational cooling, ammonia rotational cooling, OIII line cooling), main heating processes (collisional excitation of vibrationally excited H2, chemical heating due to H2 formation on dust grains, dust grain-gas thermal exchange, heating from the superthermal photo-electrons produced by C, heating by cosmic rays, heating by the photo-electrons produced by polycyclic aromatic hydrocarbons, IR heating due to the water transitions, heating by mutual electron collisions, Coulomb heating, produced by X-rays photoionization, reaction free energy heating from exothermic reactions).

thumbnail Fig. C.3

Ratios between Herschel/HIFI & Spitzer/IRS lines 538.29 μm/12.407 μm and 269.27 μm/12.453 μm for different model series. First row: dust-to-gas mass ratio, d/g. Second row: mixing parameter, αset. Third row: disk flaring, β. Fourth row: maximum grain size, amax.

thumbnail Fig. C.4

Ratios between Herschel/HIFI & Spitzer/IRS lines 538.29 μm/12.407 μm and 269.27 μm/12.453 μm for different model series. Top: power law index of grain size distribution, apow. Second line: strength of UV radiation field, χISM. Third line: PAH abundance, fPAH. Fourth line: disk gas mass, Mgas.

Here, we also present plots collecting the main properties of the standard model: Tgas, Tdust, the local dust-to-gas mass ratio, local average dust size, and the main heating and cooling processes.

Line ratio plots are used to compare the relative behavior of the mid- and far-IR lines, considering two representative Spitzer water transitions and the Herschel fundamental ortho and para water lines. To show the trend clearly, we add a parabolic regression to the data (magenta lines).

Appendix D: Mid- and far-IR observations

Far-IR line fluxes have been obtained from the literature. Mid-IR blends have been extracted from IRS spectra fitting a Gaussian function plus a linear continuum, computing the error in the flux as noise of the continuum, (D.1)This procedure is formally identical to that used in Pontoppidan et al. (2010b). Table D.1 lists all the observational data shown in Fig. 6 with respective references.

The mid-IR color 13.5/30 continuum flux is defined as pure ratio between the Spitzer/IRS fluxes at 13.5 μm and 30 μm, similarly to what is done in Acke et al. (2009) for the 30/13.5 continuum ratio. The observations overplotted include the errors propagated accordingly to (D.2)

Table D.1

Line and continuum observations of the targets discussed in the main paper.

Appendix A: Additional figures

thumbnail Fig. A.1

Mixing coefficient models. For further details see Fig. 4.
thumbnail Fig. A.2

Flaring index exponent models. For further details see Fig. 4.
thumbnail Fig. A.3

Maximum dust size models. For further details see Fig. 4.
thumbnail Fig. A.4

Dust size distribution power law index models. For further details, see Fig. 4.
thumbnail Fig. A.5

ISM radiation field models. For further details see Fig. 4.
thumbnail Fig. A.6

Fraction of PAHs models. a) Emitting region water column density for dust-to-gas mass ratio models; this region comprises 15−85% of the radially and vertically integrated flux. Green vertical dotted lines distinguish the reservoirs. b) Theoretical Spitzer SH/LH modules spectra (R = 600) for a dust-to-gas model series, continuum subtracted, and arbitrarily shifted. c) Average extension of the line emitting region, which comprises 50% of the line flux radially and vertically for 12.407 μm. d) Average extension of the line emitting region, which comprises 50% of the line flux radially and vertically for 538.29 μm.
thumbnail Fig. A.7

Gas mass content models. For further details see Fig. 4.

Appendix B: Computation of properties in the line emitting region

The different water lines are divided in groups based on their spatial origin. The latter is defined as that part of the disk from which a cumulative radially and vertically integrated flux of 15% to 85% of the total flux is produced. For each of these regions, averaged physical conditions ⟨X⟩ are derived, such as the density of water, density of the collisional partners (e−, H, H2), Tgas and Tdust by numerically integrating over the emitting region (Eq. (B.1)), i.e., (B.1)\appendix \setcounter{section}{2} \begin{equation} \label{(6)} \centering \left<X\right>=\frac{\int\limits_{r_\mathrm{in}}^{r_\mathrm{out}}\int\limits_{z_\mathrm{low}}^{z_\mathrm{high}}Xn_\mathrm{gas}2\pi r{\rm d}r{\rm d}z}{\int\limits_{r_\mathrm{in}}^{r_\mathrm{out}}\int\limits_{z_\mathrm{low}}^{z_\mathrm{high}}n_\mathrm{gas}2\pi r{\rm d}r{\rm d}z} \cdot \end{equation}X=∫rinrout∫zlowzhighXngas2πrdrdz∫rinrout∫zlowzhighngas2πrdrdz·In order to determine the continuum extinction, a vertical integration is performed from the disk surface to the midplane. τν is the continuum optical depth at the frequency of the line. It is related to the dust density ρdust and dust mass extinction coefficient κν. The integration is performed numerically, as follows: (B.2)\appendix \setcounter{section}{2} \begin{equation} \label{(11)} \centering \tau_{\nu}(z)=\int_{z_\mathrm{max}(r)}^{z(r,\tau_{\nu}=1)}\rho(r,z)\kappa_{\nu}{\rm d}z . \end{equation}τν(z)=∫zmax(r)z(r,τν=1)ρ(r,z)κνdz.Through interpolation, we find the value at which τν = 1. The optical depth is evaluated at the radial midpoint of the emitting region.

Appendix C: Model details

The following appendix shows a number of additional plots. These can be useful for the interpretation of the main results and conclusions reported in the paper. Here we show the Herschel/HIFI fundamental o-H2O and p-H2O lines fluxes behavior with the different parameters.
thumbnail Fig. C.1

Line fluxes behavior for Herschel/HIFI lines 538.29 μm and 269.27 μm for different model series. First row left: dust-to-gas mass ratio, d/g. First row right: mixing parameter, αset. Second row left: disk flaring, β. Second row right: maximum grain size amax. Third row left: power law index of grain size distribution, apow. Third row right: strength of UV radiation field, χISM. Bottom left: PAH abundance, fPAH. Bottom right: disk gas mass, Mgas.
thumbnail Fig. C.2

Standard model, from top to bottom and from left to right: Tgas with overplotted gas temperature contours (white/black) and AV = 1, 10 (red), Tdust with overplotted temperature contours (black/white) and AV = 1, 10 (red), dust-to-gas mass ratio, average dust grain size, main cooling processes (CII fine structure lines, dust grain-gas thermal exchange, Ly α line, neutral O line cooling, CO rotational and ro-vibrational cooling, water rotational and ro-vibrational cooling, formaldehyde rotational cooling, ammonia rotational cooling, OIII line cooling), main heating processes (collisional excitation of vibrationally excited H2, chemical heating due to H2 formation on dust grains, dust grain-gas thermal exchange, heating from the superthermal photo-electrons produced by C, heating by cosmic rays, heating by the photo-electrons produced by polycyclic aromatic hydrocarbons, IR heating due to the water transitions, heating by mutual electron collisions, Coulomb heating, produced by X-rays photoionization, reaction free energy heating from exothermic reactions).
thumbnail Fig. C.3

Ratios between Herschel/HIFI & Spitzer/IRS lines 538.29 μm/12.407 μm and 269.27 μm/12.453 μm for different model series. First row: dust-to-gas mass ratio, d/g. Second row: mixing parameter, αset. Third row: disk flaring, β. Fourth row: maximum grain size, amax.
thumbnail Fig. C.4

Ratios between Herschel/HIFI & Spitzer/IRS lines 538.29 μm/12.407 μm and 269.27 μm/12.453 μm for different model series. Top: power law index of grain size distribution, apow. Second line: strength of UV radiation field, χISM. Third line: PAH abundance, fPAH. Fourth line: disk gas mass, Mgas.
Here, we also present plots collecting the main properties of the standard model: Tgas, Tdust, the local dust-to-gas mass ratio, local average dust size, and the main heating and cooling processes. Line ratio plots are used to compare the relative behavior of the mid- and far-IR lines, considering two representative Spitzer water transitions and the Herschel fundamental ortho and para water lines. To show the trend clearly, we add a parabolic regression to the data (magenta lines).

Appendix D: Mid- and far-IR observations

Far-IR line fluxes have been obtained from the literature. Mid-IR blends have been extracted from IRS spectra fitting a Gaussian function plus a linear continuum, computing the error in the flux as noise of the continuum, (D.1)\appendix \setcounter{section}{4} \begin{equation} \label{fit} F(\lambda) = A \times e^{(\lambda-\lambda_0)^2/(2\sigma)^2} + B \times \lambda + C . \end{equation}F(λ)=A×e(λ−λ0)2/(2σ)2+B×λ+C.This procedure is formally identical to that used in Pontoppidan et al. (2010b). Table D.1 lists all the observational data shown in Fig. 6 with respective references. The mid-IR color 13.5/30 continuum flux is defined as pure ratio between the Spitzer/IRS fluxes at 13.5 μm and 30 μm, similarly to what is done in Acke et al. (2009) for the 30/13.5 continuum ratio. The observations overplotted include the errors propagated accordingly to (D.2)\appendix \setcounter{section}{4} \begin{equation} \label{err} \sigma_{\mathrm{ratio}}=\frac{F_{13.5}}{F_{30}}\cdot\sqrt{\left(\frac{\sigma_{13.5}}{F_{13.5}}\right)^2+\left(\frac{\sigma_{30}}{F_{30}}\right)^2}\cdot \end{equation}σratio=F13.5F30·σ13.5F13.52+σ30F302·
Table D.1

Line and continuum observations of the targets discussed in the main paper.


© ESO, 2015

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