Candidate Water Vapor Lines to Locate the H_{2}O Snowline through High-Dispersion Spectroscopic Observations II. The Case of a Herbig Ae Star
Shota Notsu, Hideko Nomura, Daiki Ishimoto, Catherine Walsh, Mitsuhiko Honda, Tomoya Hirota, T. J. Millar
aa r X i v : . [ a s t r o - ph . E P ] J a n Candidate Water Vapor Lines to Locate the H O Snowlinethrough High-Dispersion Spectroscopic Observations II. The Caseof a Herbig Ae Star
Shota Notsu , , Hideko Nomura , Daiki Ishimoto , , Catherine Walsh , , Mitsuhiko Honda ,Tomoya Hirota , and T. J. Millar Department of Astronomy, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwake-cho,Sakyo-ku, Kyoto 606-8502, Japan Department of Earth and Planetary Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku,Tokyo 152-8551, Japan Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK Department of Physics, School of Medicine, Kurume University, 67 Asahi-machi, Kurume, Fukuoka830-0011, Japan National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, UniversityRoad, Belfast, BT7 1NN, UK Research Fellow of Japan Society for the Promotion of Science (DC1) [email protected]
This paper was received by The Astrophysical Journal (ApJ) on October 27th, 2016,and was accepted on January 13th, 2017.
ABSTRACT
Observationally measuring the location of the H O snowline is crucial for understanding theplanetesimal and planet formation processes, and the origin of water on Earth. In disks aroundHerbig Ae stars ( T ∗ ∼ , M ∗ & M J ), the position of the H O snowline is further fromthe central star compared with that around cooler, and less massive T Tauri stars. Thus, theH O emission line fluxes from the region within the H O snowline are expected to be stronger.In this paper, we calculate the chemical composition of a Herbig Ae disk using chemical kinetics.Next, we calculate the H O emission line profiles, and investigate the properties of candidatewater lines across a wide range of wavelengths (from mid-infrared to sub-millimeter) that canlocate the position of the H O snowline. Those line identified have small Einstein A coefficients( ∼ − − − s − ) and relatively high upper state energies ( ∼ O snowline. Since the fluxes of thoseidentified lines from Herbig Ae disks are stronger than those from T Tauri disks, the possibilityof a successful detection is expected to increase for a Herbig Ae disk.
Subject headings: astrochemistry— protoplanetary disks— ISM: molecules— sub-millimeter & infrared:planetary systems— stars: formation . Introduction Observationally locating the position of the H Osnowline (Hayashi 1981; Hayashi et al. 1985) in aprotoplanetary disk is important. It will provideinformation on the physical and chemical con-ditions in disks, such as the temperature struc-ture, the dust-grain size distribution, and the wa-ter vapor distribution in the disk midplane (e.g.,Oka et al. 2011; Piso et al. 2015), and will giveconstraints on the current formation theories ofplanetesimals and planets (e.g., ¨Oberg et al. 2011;Okuzumi et al. 2012; Ros & Johansen 2013). Itwill help clarify the origin of water on rockyplanets including the Earth (e.g., Morbidelli et al.2000, 2012, 2016; Sato et al. 2016). Banzatti et al.(2015) and Cieza et al. (2016) recently showedthat the presence of the H O snowline leads to asharp discontinuity in the radial profile of the dustemission spectral index, due to the replenishmentof small grains through fragmentation because ofthe change in fragmentation velocities across theH O snowline. Through recent space and groundinfrared spectroscopic observations for proto-planetary disks, some infrared H O lines, whichmainly trace the disk surface, have been detected(for more details, see e.g., Pontoppidan et al.2010b; van Dishoeck et al. 2014; Blevins et al.2016; Banzatti et al. 2016; Notsu et al. 2016).The velocity profiles of emission lines from pro-toplanetary disks are usually affected by Dopplershift due to Keplerian rotation and thermal broad-ening. Therefore, the velocity profiles are sensitiveto the radial distribution of the line-emitting re-gions. In our previous paper (paper I, Notsu et al.2016), we calculated the chemical compositionand the H O line profiles in a T Tauri disk ,and identified candidate H O lines especially atsub-millimeter wavelengths, to locate the posi-tion of the H O snowline through future high-dispersion spectroscopic observations. Our calcu-lations showed that the fluxes of H O lines withsmall Einstein A coefficients ( A ul ∼ − − − s − ) and relatively high upper state energies(E up ∼ O snowline. Therefore, their profiles In the remainder of this paper, we define the protoplanetarydisks around T Tauri/Herbig Ae stars as “T Tauri/HerbigAe disks”. could be used to locate the position of the H Osnowline. This is because the water gas columndensity of the region inside the H O snowline ishigh enough that all lines are optically thick aslong as A ul > − s − . On the other hand, theregion outside the H O snowline has lower watergas column densities and lines with larger Einstein A coefficients have a more significant contributionto their fluxes since the lines are optically thin.The wavelengths of those candidate lines we iden-tified to locate the position of the H O snowlineoverlap with the capabilities of ALMA. In ad-dition, we calculated the profiles of lines whichhave been detected by previous spectroscopic ob-servations using
Herschel (e.g., the ortho-H O63.32 µ m and 538.29 µ m lines). These lines are lesssuited to locate the position of the H O snowline,because they are not dominated in flux by theregion inside the snowline.In this work (paper II), we extend our disk chem-ical model and the H O line profile calculationsto the case of a Herbig Ae disk. We discuss thedifferences in disk chemical structures and lineproperties between the cases of a T Tauri disk(paper I) and a Herbig Ae disk (this paper). Weinvestigate the line properties in detail for can-didate water lines to locate the position of theH O snowline over a wide wavelength range frommid-infrared to sub-millimeter, and discuss thepossibility of detecting such lines with future ob-servations. The methods are outlined in Section2. The results and discussions are described inSections 3 and 4, respectively, and the conclusionsare listed in Section 5.
2. Methods
The physical structures of the protoplanetarydisk models used here are calculated using themethods in Nomura & Millar (2005) including X-ray heating (Nomura et al. 2007). A more de-tailed description of the background theory andcomputation of this physical model is describedin the original papers (Nomura & Millar 2005;Nomura et al. 2007) and paper I (Notsu et al.2016). Walsh et al. (2010, 2012, 2014a, 2015),Heinzeller et al. (2011), Furuya et al. (2013), Notsu et al.(2015), and Notsu et al. (2016) used the samephysical models for a T Tauri disk and a Herbig2ig. 1.— The total gas number density in cm − (top left), the gas temperature in Kelvin (top right), thedust temperature in Kelvin (bottom left), and the UV flux in erg cm − s − (bottom right) of a Herbig Aedisk as a function of the disk radius in au and height (scaled by the radius, z/r ) up to maximum radius of r =300 au. 3e disk to study various chemical and physicaleffects, and they also describe the calculation ofthe physical structures in detail.In paper I (Notsu et al. 2016), we adopted thephysical model of a steady, axisymmetric Keple-rian disk surrounding a T Tauri star with mass M ∗ =0.5 M J , radius R ∗ =2.0 R J , and effectivetemperature T ∗ =4000K (Kenyon & Hartmann1995). In this paper, we adopt the physicalmodel of a disk surrounding a Herbig Ae starwith M ∗ =2.5 M J , R ∗ =2.0 R J , and T ∗ =10,000K(see also Walsh et al. 2015). In our disk physicalmodels, we adopt a viscous parameter α =10 − ,a mass accretion rate ˙ M =10 − M J yr − , andgas-to-dust mass ratio g/d = 100. The valuesof total disk mass are M disk ∼ . × − M J for the T Tauri disk (Heinzeller et al. 2011), and M disk ∼ . × − M J for the Herbig Ae disk.We adopt the same compact and spherical dust-grain model of Nomura & Millar (2005). Theyassume that dust and gas are well mixed, andthat the dust grains consist of silicate grains, car-bonaceous grains, and water ices. They adoptthe dust-grain size distribution which is consis-tent with the extinction curve observed in denseclouds (Mathis et al. 1977; Weingartner & Draine2001). The stellar UV radiation field in our HerbigAe disk model has no excess emission components(e.g., optically thin hydrogenic bremsstrahlung ra-diation and Lyman- α line emission), although thatin our T Tauri disk model has such excess emissioncomponents (for more detail, see Nomura & Millar2005, Walsh et al. 2015 and Notsu et al. 2016). InFigure 1, we display the gas number density incm − (top left), the gas temperature in K (topright, T g ), the dust-grain temperature in K (bot-tom left, T d ), and the wavelength-integrated UVflux in erg cm − s − (bottom right) of a Herbig Aedisk as a function of disk radius in au and height(scaled by the radius, z/r ).Here we focus on the differences between the phys-ical structures of the T Tauri disk (see Figure 1of paper I, Notsu et al. 2016) and the Herbig Aedisk. The density in the atmosphere of the HerbigAe disk (e.g., n H = 6 × cm − at r = 5 auand z/r = 0 .
1) is lower than that of the T Tauridisk (e.g., n H = 2 × cm − at r = 5 au and z/r = 0 . H of the Her-big Ae disk (e.g., H/r ∼ . r = 5 au) is smallerthan that for the disks around the T Tauri disk(e.g., H/r ∼ . r = 5 au). The gas density andtemperature distributions of the disks are obtainedself-consistently by iteratively solving the equa-tions for hydrostatic equilibrium in the verticaldirection and local thermal balance between heat-ing and cooling of gas (Nomura & Millar 2005).The gas and dust temperatures throughout mostof the Herbig Ae disk, and the strength of theUV flux in the disk surface of the Herbig Ae diskare higher compared with those of the T Tauridisk, although the stellar UV radiation field inour Herbig Ae disk model has no excess emissioncomponents, apart from that in our T Tauri diskmodel. This is because the photospheric black-body radiative flux from the central Herbig Aestar is larger than that from the central T Tauristar. The strength of the X-ray flux in the disksurface of the Herbig Ae disk is lower comparedwith that of the T Tauri disk, since we adopteda smaller value of X-ray luminosity in the HerbigAe disk ( L X ∼ × erg s − ) compared withthat in the T Tauri disk ( L X ∼ erg s − ).To investigate the chemical structure of theHerbig Ae disk, we use a large chemical net-work which includes gas-phase reactions and gas-grain interactions (freeze-out of gas moleculeson dust grains, and thermal and non-thermaldesorption from dust grains). The initial ele-mental fractional abundances (relative to totalhydrogen nuclei density) we use are the set ofatomic oxygen-rich low-metallicity abundancesfrom Graedel et al. (1982), listed in Table 8 ofWoodall et al. (2007), which is the same set asused in paper I (Notsu et al. 2016). We adopt thesame chemical network as described in paper I(Notsu et al. 2016). Henning & Semenov (2013),Dutrey et al. (2014), and Haworth et al. (2016)reviewed the recent development of calculationsfor chemical structure in protoplanetary disks.Using the H O gas abundance distribution ob-tained from our chemical calculation describedin the previous paragraph, we calculate the H Oemission line profiles ranging from near-infraredto sub-millimeter wavelengths from the Herbig H = c s / Ω ∝ M − . ∗ T . g , where c s and Ω are the soundspeed and Keplerian angular velocity, respectively.
4e disk assuming Keplerian rotation, and iden-tify the lines which are the best candidates forprobing emission from the inner thermally des-orbed water reservoir, i.e., within the H O snow-line. We also study how the line fluxes and pro-file shapes depend on the position of the H Osnowline. In paper I (Notsu et al. 2016), weadopted the same calculation method to deter-mine the H O emission line profiles from a TTauri disk (based on Rybicki & Lightman 1986,Hogerheijde & van der Tak 2000, Nomura & Millar2005, and Sch¨oier et al. 2005), with the detailedmodel explained in Section 2.3 of paper I. The codewhich we have built for calculating emission lineprofiles is a modification of the original 1D codecalled RATRAN (Hogerheijde & van der Tak2000). We adopt the data of line parameters in theLeiden Atomic and Molecular Database LAMDA (Sch¨oier et al. 2005). Here we note that in ourmethod, we adopt the assumption of local thermalequilibrium (LTE) to obtain the level populationsof the water molecule ( n u and n l ). In Section4.2, we discuss the validity of this assumption. Inaddition, we set the ortho to para ratio (OPR) ofwater to its high-temperature value of 3 through-out the disk.
3. Results3.1. The distributions of H O gas and ice Figure 2 shows the fractional abundances (rela-tive to total gas hydrogen nuclei density, n H ) ofH O gas and ice in a Herbig Ae disk as a functionof disk radius r and height scaled by the radius( z/r ). Here we focus on the differences in H Odistributions between the cases of a Herbig Aedisk and a T Tauri disk (see Figure 2 of paper I,Notsu et al. 2016).The H O snowline of the Herbig Ae disk ex-ists at a radius of r ∼
14 au in the midplane( T g ∼ T d ∼ r ∼ http://home.strw.leidenuniv.nl/~michiel/ratran/ http://home.strw.leidenuniv.nl/~moldata/ Fig. 2.— The fractional abundance (relative to to-tal hydrogen nuclei density) distributions of H Ogas (top) and H O ice (bottom) of a Herbig Aedisk as a function of disk radius and height (scaledby the radius, z/r ) up to maximum radius of r =300au.5e disk, are higher than that of our T Tauri disk.Inside the H O snowline, the temperature exceedsthe sublimation temperature under the pressureconditions in the midplane of the Herbig Ae disk( T g ∼ T d ∼ O is re-leased into the gas-phase by thermal desorption.Here we note that the sublimation temperatureunder the pressure conditions in the midplane ofthe Herbig Ae disk ( T g ∼ T d ∼ T g ∼ T d ∼ − − n H ∼ − cm − ) versus ( n H ∼ − cm − ). Accord-ing to Eq. (3)-(5) in Section 2.2.2 of paper I(Notsu et al. 2016), the sublimation temperatureis higher if the gas number density is also higher.The temperature of the region just inside theH O snowline in the Herbig Ae disk (between7 − T g ∼ − O molecules(e.g., O+H → OH+H and OH+H → H O+H) isnot efficient compared with the inner region at ahigher temperature ( T g > r < − O gas ( ∼ − ). A similar distri-bution of gas-phase H O in the midplane of a Her-big Ae disk is reported in Figure 1 of Woitke et al.(2009b). Here we also note that Eistrup et al.(2016) calculated the chemical evolution of a diskmidplane under both molecular and atomic initialconditions as initial chemical abundances. Theyshowed that in the latter atomic conditions, theabundance of H O gas and ice around the H Osnowline ( ∼ − ) is smaller than that for molec-ular initial abundances ( ∼ − ). This is becauseO is formed in the gas-phase via O+OH → O +Hand remains in the gas phase since its sublima-tion temperature is much lower than that of othermolecules like H O. This reaction route competeswith gas-phase H O formation. In the outer disk, the fractional abundance of H Ogas is also relatively high ( ∼ − − − ) in thehot surface layer and at the H O sublimation (pho-todesorption) front compared with the cold mid-plane region of the outer disk ( . − − − ),as also shown in the T Tauri disk model (paper I,Notsu et al. 2016).Here we note that the region with a high H Ogas abundance ( ∼ − ) in the disk midplane ex-tends to a larger radius ( r ∼
10 au) at z/r & z/r ∼ r ∼ − H/r ∼ . r = 5 au) is smaller than that for the T Tauridisk (e.g., H/r ∼ . r = 5 au) and the radi-ation from the central Herbig Ae star is strongerthan that from the central T Tauri star, thus thegas temperature of the Herbig Ae disk around z/r ∼ . z/r ∼ − . O gas and ice for both theT Tauri disk (see Figure 3 of paper I, Notsu et al.2016) and the Herbig Ae disk. In the Herbig Aedisk case, the column density of H O gas and icein the disk midplane flips across the H O snowlineas expected ( r ∼
14 au). The column density ofH O gas is high ( ∼ − cm − ) in the in-ner high-temperature region of the disk midplanewith r < − ∼ − cm − ) in the midplane between 7 − O snow-line ( < cm − ). The column density profile ofH O ice is roughly opposite. In the T Tauri diskcase, the column densities of H O gas and ice inthe disk midplane flips across the H O snowlinemore steeply following the steeper temperaturegradient. The Bottom panel of Figure 3 showsthe radial profiles of the column density in cm − of H O ice and gas in the Herbig Ae disk, whichhave been vertically integrated from z = ∞ to (i) −∞ , (ii) z ( τ . µ m = 1), (iii) z ( τ . µ m = 1),and (iv) z ( τ . µ m = 1). τ λ is the total opticaldepth value at each wavelength, λ , including gas6
1 10 100 C o l u m n D en s i t y [ c m − ] r [AU] H O gas T TauriH O ice T TauriH O gas Herbig AeH O ice Herbig Ae
1 10 100 C o l u m n D en s i t y [ c m − ] r [AU] H O gas TotalH O ice TotalH O gas t (17.75 m m)=1H O gas t (61.32 m m)=1H O gas t (682.66 m m)=1 Fig. 3.— Top panel: The radial profiles of thevertically integrated column density in cm − ofH O gas and ice in the T Tauri disk ( green dottedline and black dashed dotted line ) and the Her-big Ae disk ( red solid line and blue dashed line ).Bottom panel: The radial profiles of the columndensity in cm − of H O ice ( blue dashed line )and gas in the Herbig Ae disk, which are verti-cally integrated from z = ∞ to −∞ ( red solidline ), to z ( τ . µ m = 1) ( black bold solid line ),to z ( τ . µ m = 1) ( green dotted line ), and to z ( τ . µ m = 1) ( orange dashed dotted line ). Since τ . µ m at z = −∞ is lower than unity at r & r .
10 au. and dust components. In Section 4.3, we discussabout this panel in detail.Previous analytical models and numerical simula-tions derived the position of the H O snowline ofan optically thick disk for given parameters, suchas mass ( M ∗ ) and temperature ( T ∗ ) of the cen-tral star, a viscous parameter α , an accretion rate˙ M , a gas-to-dust mass ratio g/d , and the averagedust grain size a and opacity (e.g., Davis 2005;Garaud & Lin 2007; Min et al. 2011; Oka et al.2011; Du & Bergin 2014; Harsono et al. 2015;Mulders et al. 2015; Piso et al. 2015; Sato et al.2016), and suggested that the position of the H Osnowline changes, as these parameters change. Inthe case of Herbig Ae disks with M ∗ ∼ . M J ,˙ M ∼ − M J yr − , g/d = 100, and a ∼ . µ m,the position of the H O snowline is ∼ −
20 au.In our calculations we use similar parameters for M ∗ , ˙ M and a , and the H O snowline appears ata radius of around 14 au in the midplane, withinthe range of previous studies. H O emission lines from a Herbig Aedisk In this Section, we first describe the detailed prop-erties of seven characteristic pure rotational ortho-H O lines (see Table 1 and Section 3.2.1) for theHerbig Ae disk. These seven lines (including theortho-H O 682.66 µ m line) are candidates for trac-ing emission from the hot water reservoir withinthe H O snowline. In Section 3.2.2, we describethe properties of the 63.32 and 538.29 µ m lines,which are examples of lines which are less suitedto trace emission from the water reservoir withinthe H O snowline. We consider these two lines totest the validity of our model calculations, sincethe fluxes of these two lines from protoplanetarydisks have been observed with
Herschel . Theproperties of near-, and mid-infrared H O emis-sion lines which do not trace emission from thehot water vapor within the H O snowline are alsodescribed in this subsection. Since we investi-gated the profiles and properties of three lines( λ =682.66, 63.32, 538.29 µ m) for the T Tauri diskin paper I (Notsu et al. 2016), here we mainly fo-cus on the differences between the line propertiesbetween the T Tauri disk and the Herbig Ae disk.In Section 3.2.3 and Section 4.4, we show and dis-7uss other candidate lines which trace the emissionfrom the hot water vapor within the H O snowlinefrom mid-infrared to sub-millimeter wavelengths,and their properties, especially the variation inline fluxes with wavelength. In Section 3.2.4, weshow and discuss normalized radial cumulativeline fluxes for the lines discussed in Sections 3.2.1-3.2.3.In this paper, we show and discuss only the re-sults concerning ortho-H O lines, since the num-ber densities and the fluxes of ortho-H O lines arelarger than those of para-H O lines, due to theassumption, OPR=3. The line selection processis described in detail in Section 3.2 of paper I(Notsu et al. 2016). H O emission lines which traceemission from the hot water vapor withinthe H O snowline Figure 4 shows the emission profiles of seven rep-resentative characteristic pure rotational ortho-H O lines at λ =17.75 µ m (top left), 24.00 µ m (topcenter), 61.32 µ m (top right), 94.17 µ m (middleleft), 482.99 µ m (middle center), 682.66 µ m (mid-dle right), and 933.28 µ m (bottom), for the HerbigAe disk. These lines have small values of A ul ( ∼ − − − s − ) and relatively large valuesof upper E up ( ∼ − O lines which traceemission from the hot water gas within the H Osnowline. The H O 933.28 µ m, 682.66 µ m, and482.99 µ m lines fall in ALMA band 7, 8, and 9,respectively. The H O 17.75 µ m line and 24.00 µ mline are Q band lines at mid-infrared wavelengths,and the H O 17.75 µ m line falls in the wave-length coverage of SPICA/SMI-HRS (see Section4.4). The detailed parameters, such as transitions( J K a K c ), wavelength λ , frequency, A ul , E up , crit-ical density n cr = A ul /< σv > , and total linefluxes are listed in Table 1. In Table 1, we alsoshow the values of the total fluxes from both theHerbig Ae disk and the T Tauri disk (see also pa-per I, Notsu et al. 2016). In calculating the valuesfrom the T Tauri disk, we use the same method as < σv > is the collisional rates for the excitation of H O byH and electrons for an adopted collisional temperature of200K from Faure & Josselin (2008). in paper I (Notsu et al. 2016). In calculating allline profiles in this paper (see Figures 4, 7, 10, and14), we assume that the distance d to the object is140pc ( ∼ the distance of Taurus molecular cloud),and the inclination angle i of the disk is 30 degs.As shown in all panels in Figure 4, the contri-butions from the optically thin surface layer ofthe outer disk ( r =14-30 au) are very small com-pared with those from the optically thick regionnear the midplane of the inner disk ( r <
14 au),and they show the characteristic double-peakedprofile due to Keplerian rotation. This is becausethese lines, which have small Einstein A coeffi-cients ( A ul ∼ − − − s − ) and relativelylarge upper state energies (E up ∼ O vapor inside the H O snowline.In Section 2.3 and 3.2.1 of paper I (Notsu et al.2016), we explained the reason why these lineshave such properties.In the cases of candidate H O lines except the482.99 µ m and 682.66 µ m lines (see Figure 4), al-most all of the emission fluxes ( > O gas abundance( ∼ − , r < µ m and 682.66 µ m lines (seeFigure 4), most of the emission fluxes ( ∼ − O gasabundance ( ∼ − , r < ∼ − O gas abundance ( ∼ − , r =8-14 au). The position of the two peaks and therapid drop in flux density between the peaks con-tains information on the distribution of hot H Ogas within the H O snowline.Figures 5 and 6 show the line-of-sight emissivity(emissivity times extinction, η ul e − τ ul ; see Equa-tion (14) of Paper I, Notsu et al. 2016) and thetotal optical depth, τ ul (gas emission and dust)distributions of these seven H O lines, respec-tively. We assume that the inclination angle, i , ofthe disk is 0 deg in making these figures (see Fig-ures 5, 6, 8, 9, and 13), and thus the line-of-sightdirection is from z = + ∞ to −∞ at each diskradius. In the left panels of Figure 5, we over-8ig. 4.— The velocity profiles of seven characteristic pure rotational ortho-H O lines at λ =17.75 µ m (topleft), 24.00 µ m (top center), 61.32 µ m (top right), 94.17 µ m (middle left), 482.99 µ m (middle center), 682.66 µ m(middle right), and 933.28 µ m (bottom), which have small A ul and large E up , from the Herbig Ae disk. Theseare candidate H O lines to trace the hot water vapor within the H O snowline. In calculating the line profilesin this paper (see Figures 4, 7, 10, and 14), we assume that the distance to the object d is 140pc ( ∼ thedistance of Taurus molecular cloud), and the inclination angle of the disk, i , is 30 degree. The parametersand total fluxes of these H O lines are listed in Table 1 and B.1.
Red solid lines are the emission line profilesfrom inside 8 au (=the inner high temperature region), blue dashed lines are those from inside 14 au ( ∼ insidethe H O snowline), green dotted lines are those from 14-30 au ( ∼ outside the H O snowline), and black dasheddotted lines are those from the total area inside 30 au.9able 1: Calculated representative ortho-H O line parameters and total line fluxes J K a K c λ Freq. A ul E up n cr HAe flux , TT flux , [ µ m] [GHz] [s − ] [K] [cm − ] [W m − ] [W m − ]6 -5 × − . × . × − . × − -5 × − . × . × − . × − -6 × − . × . × − . × − -7 × − . × . × − . × − -4 × − . × . × − . × − -5 × − . × . × − . × − -9 × − . × . × − . × − -7 . × . × − . × − -1 × − . × . × − . × − -16 . × . × − . × − -12 . × . × − . × − -6 . × . × − . × − -6 × − . × . × − . × − In calculating the value of line wavelength from the value of line frequency, we use the valueof speed of light c =2 . × m s − . The total flux of each emission line from the Herbig Ae disk. In calculating the total fluxes of these H O lines, we use a distance of d = 140pc and aninclination angle of i =30 degree. The total flux of each emission line from the T Tauri disk (see also paper I, Notsu et al.2016). O lines at λ =17.75 µ m (top left and right),24.00 µ m (middle left and right), 61.32 µ m (bottom left and right), which have small A ul and large E up , fromthe Herbig Ae disk. In the left panels, we overplot the total optical depth contours (cid:0) τ ul =0.1 (red crosspoints), 1 (cyan circle points), and 10 (orange square points) (cid:1) on top of these line emissivity panels (see alsoFigure 6). In the right panels, we overplot the gas temperature T g contours (cid:0) T g =120K (red cross points),170K (blue circle points), and 300K (cyan square points), see also Figure 1 (cid:1) . We assume that the inclinationangle, i , of the disk is 0 deg in making these figures in this paper (see Figures 5, and 8), and the emissivityis calculated along the line from z=+ ∞ to - ∞ at each disk radius. The units are W m − Hz − sr − .11ig. 5.— (Continued.) The line-of-sight emissivity distributions of the H O lines at λ =94.17 µ m (top left andright), 482.99 µ m (second line left and right), 682.66 µ m (third line left and right), and 933.28 µ m (bottomleft and right), which have small A ul and large E up , from the Herbig Ae disk.12ig. 6.— The line-of-sight total optical depth τ ul ( s, x, y, ν ) (gas emission and dust) distributions of the H Olines at λ =17.75 µ m (top left), 24.00 µ m (top center), 61.32 µ m (top right), 94.17 µ m (middle left), 482.99 µ m(middle center), 682.66 µ m (middle right), and 933.28 µ m (bottom), which have small A ul and large E up , fromthe Herbig Ae disk. We assume that the inclination angle, i , of the disk is 0 deg in making these figures inthis paper (see Figure 6 and 9), and thus the optical depth is calculated along the line from z=+ ∞ to - ∞ ateach disk radius. In calculating the values of τ ul ( s, x, y, ν ), we consider the contributions of both absorptionby dust grains and the line absorption by the H O gas.13lot the total optical depth contours ( τ ul =0.1, 1,and 10) on top of these line emissivity panels (seealso Figure 6). In the right panels, we overplotthe gas temperature T g contours ( T g =120, 170,and 300K, see also Figure 1). Figure 13 in Ap-pendix A shows the vertical distributions of thenormalized cumulative line emissivity at r =5 au(top two panels), r =10 au (middle two panels),and r =30 au (bottom two panels), and of thegas temperature T g . The left three panels showthe distributions for these seven H O lines. Wenormalize the cumulative emissivity of each lineusing the values at z = −∞ . According to Figures5, 6, and 13, the values of emissivity at r .
14 au(= the position of the H O snowline), T g & z/r ∼ . − .
12 are larger than those of theoptically thin hot surface layer and the photodes-orbed layer of the outer disk, and in particularthose in the region with a higher H O gas abun-dance ( ∼ − , r < − T g & z/r ∼ . − .
12 are much larger. Emission from z ∼ r . Omolecules in the upper disk layer. Nevertheless,we can extract information on the distribution ofhot H O vapor inside the H O snowline. This isbecause within r <
14 au (= the position of theH O snowline), the H O gas fractional abundanceis relatively constant over z/r ∼ r (see also Figure 2). Strictly speak-ing, as we described in Section 3.1, the region witha high H O gas abundance ( ∼ − ) extends to aradius of r ∼
10 au at z/r ∼ z ∼ r ∼ O distribution inthe inner disk within the H O snowline.The differences in the properties of the line profiles(see Figures 4, 5, 6, and 13) come from the differ-ences in A ul , E up , and wavelengths among lines.For the lines with similar wavelengths, the valuesof optical depth tend to be larger as values of A ul of the lines become larger, since the absorption byexcited H O molecules increases. In addition, thevalues of optical depth become larger as values of E up become smaller, since the line absorption be- come stronger even in the colder region of the disk.For the lines at shorter wavelengths, the opac-ity of the dust grains becomes larger (e.g.,Nomura & Millar 2005). In the cases of shorterwavelength (mid- and far-infrared) lines, the ab-sorption by the dust grains mainly determines to-tal optical depth profiles (including gas and dustcomponents) and line emitting regions in the bothinner and outer disk. In contrast, for the lineswith longer wavelengths, the values of the line ab-sorption by excited molecules become larger (seealso Equation (10) of Paper I (Notsu et al. 2016))even if the values of A ul and E up are similar. Inthe case of longer wavelength lines (sub-millimeterlines), the line absorption by excited moleculesmainly determines the total optical depth profilesand line emitting regions in the inner disk mid-plane with a high H O gas abundance ( ∼ − , r < − O 482.99 µ m and 682.66 µ m lines have rel-atively smaller values of E up ( < E up . In addition,they have longer wavelengths ( > µ m) com-pared with other lines, thus the dust opacity issmaller and they can trace the regions closer to themidplane in the outer disk. These are the reasonswhy emission fluxes from the region with a rela-tively high H O gas abundance ( ∼ − , r =8-14au) are not so small ( ∼ −
20% of total emissionfluxes) compared to the region with a high H Ogas abundance ( ∼ − , r < O 933.28 µ m line resides in the sub-millimeterregion, this line has a larger E up (=1861.2K) thanother lines, and thus most of the emission flux isemitted from the region with high temperatureand a high H O gas abundance ( ∼ − , r < O snowline location and theouter edge of the hot H O gas region is not solarge (several au), the influence is not so seriouswhen we want to get information on the overallH O distribution of the inner disk and roughlyestimate the position of the H O snowline. How-ever, if we observe several candidate H O lines14ith small A ul ( ∼ − − − ), various E up (e.g., ∼ − O snowline, butalso the H O gas abundance and the gas temper-ature in the disk midplane. In addition, we couldtrace the water reservoir within the H O snowlinefrom the Keplerian line profiles independently re-gardless of the assumption of the relation betweendisk gas temperature and radius, as adopted inprevious works to get the H O distributions (e.g.,Zhang et al. 2013; Blevins et al. 2016). We notethat the previous observations of H O lines withlarge A ul ( ∼ − − s − ) and very high E up ( > H O lines which are less suited to traceemission from water reservoir within the H O snowline In the top left panel of Figure 7, we show the lineprofile for the H O 63.32 µ m line. The contributionfrom the optically thin surface layer of the outerdisk ( r =14-30 au) is large (three times larger influx density) compared with that of the opticallythick region near the midplane of inner disk ( r < O lines which trace the emission fromthe hot water vapor within the H O snowline.This is because the H O 63.32 µ m line has a large A ul (=1.772 s − ), although E up (=1070.6K) issimilar to that of the candidate ortho-H O lines(e.g., E up =1088.7K for the 682.66 µ m line). Thedetailed parameters, such as transitions ( J K a K c ),wavelength, frequency, A ul , E up , critical density n cr , and total line fluxes of the ortho-H O linesdiscussed in this subsection are listed in Table 1.According to Figures 8, 9 and 13, the values ofemissivity of the H O 63.32 µ m line in the opti-cally thin hot surface layer of outer disk are asstrong as that of the optically thick region insidethe H O snowline. The area of the outer H O line emitting region is larger than that of the innerregion for this line, and thus emission from theouter part dominates. Therefore, we propose thatthis line is not optimal to detect emission fromthe hot water vapor within the H O snowline inHerbig Ae disk case, as we also found for the TTauri disk (Notsu et al. 2016).We note that previous space far-infrared low-dispersion spectroscopic observations with
Herschel /PACS ( R ∼ O emission lines with large A ul ( ∼ − − s − ) and relatively large E up ( ∼ µ m line from the gas-rich Her-big Ae disk around HD163296, although the de-tections of these lines are only slightly above 3 σ (e.g., Fedele et al. 2012, 2013; Meeus et al. 2012;Tilling et al. 2012; Dent et al. 2013). Althoughthe profiles of these lines are spectrally unre-solved, a comparison of line strength with modelsindicates that the emitting region of these ob-servations originates in the hot surface layer ofthe outer disk ( r>
15 au, e.g., Fedele et al. 2012,2013). The total integrated line flux of this H O63.32 µ m line from the disk around HD163296 (ata distance d of ∼
122 pc and inclination i of 44deg) is observed to be (2 . ± . × − W m − ,and the values of the other lines (e.g., ortho-H O56.82 µ m and 71.95 µ m lines) are roughly simi-lar (e.g., Fedele et al. 2012; Meeus et al. 2012).Meeus et al. (2012) and Fedele et al. (2013) de-termined that the upper limits of the total fluxesof such H O emission lines, including the H O63.32 µ m from other Herbig Ae disks ( d ∼ − − and a few 10 − Wm − . These values are roughly several tens oftimes smaller than the value which we calculatein this paper for this particular Herbig Ae diskmodel (see also Table 1, d =140 pc) if we considerthe difference in the distances from the solar sys-tem. We note that our model disk is not intendedto be representative of any particular source. Wediscuss this issue further in Section 4.3.In the top right panel of Figure 7 we show theline profile for the H O line at 538.29 µ m. Thecontribution from the outer disk ( r =14-30 au) islarge compared to that from the optically thick re-gion near the midplane of the inner disk ( r <
14 au)and the width between the double peaks of the line15ig. 7.— (Top two panels): The velocity profiles of two characteristic pure rotational ortho-H O lines at λ =63.32 µ m (top left) and 538.29 µ m (top right) from the Herbig Ae disk. They are examples of lines which areless suited to trace emission from water vapor within the H O snowline. (Middle two panels): The velocityprofiles of mid-infrared ortho-H O lines at λ =12.40 µ m (middle left), 12.45 µ m (middle right) from the HerbigAe disk. Both lines have much larger values of A ul and E up than those of the candidate mid-infared H Olines to trace the emission from the H O vapor within the H O snowline. (Bottom two panels): The velocityprofiles of near-infrared ortho-H O lines at λ =4.96 µ m (bottom left), 4.43 µ m (bottom right) from the HerbigAe disk. Both lines have the same values of E up (=4180.4K), the former line has a larger value of A ul andthe latter line has a smaller value of A ul . Red solid lines are the emission line profiles from inside 8 au (=theinner high temperature region), blue dashed lines are those from inside 14 au ( ∼ inside the H O snowline), green dotted lines are those from 14-30 au ( ∼ outside the H O snowline), and black dashed dotted lines arethose from the total area inside 30au. 16ig. 8.— The line-of-sight emissivity distributions of the two characteristic H O lines at λ =63.32 µ m (topleft and right) and 538.29 µ m (bottom left and right), which have various A ul and E up , from the Herbig Aedisk. In the left panels, we overplot the total optical depth contours (cid:0) τ ul =0.1 (red cross points), 1 (cyancircle points), and 10 (orange square points) (cid:1) on top of these line emissivity panels (see also Figure 9). Inthe right panels, we overplot the gas temperature T g contours (cid:0) T g =120K (red cross points), 170K (bluecircle points), and 300K (cyan square points), see also Figure 1 (cid:1) .17ig. 8.— (Continued.) (Top and second line panels): The line-of-sight emissivity distributions of mid-infrared H O lines at λ =12.40 µ m (top left and right), 12.45 µ m (second line left and right) from the HerbigAe disk. Both lines have much larger values of A ul and E up than those of the candidate mid-infared H O lineswhich trace emission from the hot water vapor within H O snowline. (Third line and bottom panels): Theline-of-sight emissivity distributions of near-infrared H O lines at λ =4.96 µ m (third left and right), 4.43 µ m(bottom left and right) from the Herbig Ae disk. Both lines have the same values of E up (=4180.4K), theformer line has a larger value of A ul and the latter line has a smaller value of A ul .18ig. 9.— (Top two panels): The line-of-sight total optical depth τ ul ( s, x, y, ν ) (gas emission and dust)distributions of two characteristic H O lines at 63.32 µ m (top left) and 538.29 µ m (top right) from the HerbigAe disk. (Middle two panels): The line-of-sight optical depth distributions of mid-infrared ortho-H O linesat λ =12.40 µ m (middle left), 12.45 µ m (middle right) from the Herbig Ae disk. Both lines have much largervalues of A ul and E up than those of the candidate mid-infared H O lines which trace emission from thehot water vapor within H O snowline. (Bottom two panels): The line-of-sight optical depth distributions ofnear-infrared ortho-H O lines at λ =4.96 µ m (bottom left), 4.43 µ m (bottom right) from the Herbig Ae disk.Both lines have the same values of E up (=4180.4K), the former line has a larger value of A ul and the latterline has a smaller value of A ul . 19rofile is around two times narrower than those ofcandidate H O lines which trace the emission fromthe hot water vapor within the H O snowline, al-though the A ul is not so high (=3.497 × − s − ).This is because this H O 538.29 µ m line is theground-state rotational transition and has a low E up (=61.0K) compared with the other lines dis-cussed in this paper. The flux of this line comesmainly from the outer cold water vapor in thephotodesorbed layer.According to Figures 8 and 13, the value of theemissivity of the H O 538.29 µ m at each ( r, z ) inthe photodesorbed layer is comparable inside andoutside the H O snowline. However, because ofthe larger surface area of the outer disk most disk-integrated emission from this line arises from theouter disk. In addition, in the outer disk mid-plane opacity of this line (see Figure 9) is around10 − times higher than those of the ortho-H O 482.99 µ m and 682.66 µ m lines, although thewavelength and thus the dust opacity are similar.This is because this line has a small value of E up and the level population of H O for this line isvery high near the midplane of cold outer disk.On the basis of these properties, we propose thatthis line is not optimal to detect emission fromthe hot water vapor within the H O snowline inthe Herbig Ae disk case, as also concluded for theT Tauri disk (Notsu et al. 2016).We mention that previous space high-dispersionspectroscopic observations with
Herschel /HIFIdetected this line from disks around one Her-big Ae star HD100546 and two T Tauri starsTW Hya and DG Tau (e.g., Hogerheijde et al.2011; Podio et al. 2013; van Dishoeck et al. 2014;Salinas et al. 2016). The number of detec-tions is small because the line flux is low com-pared with the sensitivity of that instrument(Antonellini et al. 2015). The detected line profileand other line modeling work (e.g., Meijerink et al.2008; Woitke et al. 2009b; Antonellini et al. 2015)suggested that the emitting region arises in thecold outer disk, consistent with the results of ourmodel calculations.Here we note that since we define OPR =3 (=thevalue in the high temperature region) throughoutthe disk, we may be overestimating the line flux of the ortho-H O 538.29 µ m line (for more details,see Section 2.3 of paper I, Notsu et al. 2016). Inaddition, since the flux of this line is controlledby the outer cold H O gas which is desorbedfrom the cold dust-grain surfaces, it also may benecessary to include grain-surface reactions (e.g.,Hasegawa et al. 1992) for accurate determinationof the gas phase H O abundance in this region.The middle two panels of Figure 7 show the pro-files for the pure rotational mid-infrared ortho-H O lines at λ =12.40 µ m (middle left), 12.45 µ m(middle right) from the Herbig Ae disk. Figures8, 9, and 13 also show the line-of-sight emissivity,the total optical depth (gas emission and dust),and the vertical normalized cumulative emissiv-ity distributions of these two mid-infrared H Olines from the Herbig Ae disk, respectively. Bothlines have much larger values of A ul ( > − )and E up ( > O lines that trace emission fromthe H O vapor within the H O snowline in thedisk midplane (see Table 1 and B.1), and thusthey mainly trace emission from the hot surface ofthe inner and outer disk. The velocity profiles ofthese two lines were obtained by previous ground-based mid-infrared spectroscopic observations us-ing VLT/VISIR (Pontoppidan et al. 2010b) frombright T Tauri disks (AS 205N and RNO 90).They show the Keplerian double-peaked or flat-topped (for low inclination objects) profiles, andthe line emitting region is the hot disk surface.The bottom two panels of Figure 7 show the pro-files of pure rotational near-infrared ortho-H Olines at λ =4.96 µ m (bottom left), 4.43 µ m (bottomright) from the Herbig Ae disk. Figures 8, 9, and13 also show the line-of-sight emissivity, the totaloptical depth (gas emission and dust), and thevertical normalized cumulative emissivity distri-butions of these near-infrared lines for the HerbigAe disk, respectively. Both lines have the samemuch larger values of E up (=4180.4K), the formerline has a larger value of A ul (=3.260 s − ) and thelatter has a smaller value of A ul (= 2 . × − s − ). For the former case, since it has much largervalues of A ul and E up than those of the candi-date H O lines (see Table 1 and B.1), it mainlytraces the emission from the hot surface of theinner and outer disk. This line has similar values20f A ul and E up with the observed near-infraredrovibrational H O lines in L band (Mandell et al.2012). For the latter smaller A ul line case, sincethe value of E up in this near-infrared line is muchlarger ( > Olines which trace the emission from the hot watervapor within the H O snowline from mid-infraredto sub-millimeter wavelengths, it only traces thevery innermost region ( r < µ mline case). In addition, the widths between thetwo peaks of the Keplerian profiles of these near-and mid-infrared lines with large E up are largerthan those of candidate H O lines which tracethe emission from the hot water within the H Osnowline (see Figures 4, 7, and 14). These arebecause they trace the innermost hot region com-pared with the region around the H O snowline.Here we note that previous near- and mid-infraredspectroscopic observations using VLT/CRIRESand
Spitzer /IRS for Herbig Ae disks (e.g., Pontoppidan et al.2010a; Fedele et al. 2011; Salyk et al. 2011) havenot detected any H O lines regardless of the valueof A ul . We discuss this issue in Section 4.3. More-over, as we described in Section 2.3, the levelpopulations of the water molecule are calculatedunder LTE, as opposed to non-LTE. However, aswe discuss further in Section 4.2, in our LTE cal-culations there is a possibility that we have over-estimated the emission fluxes of strong H O lineswith large A ul which trace the hot surface layer,as found in previous studies (e.g., Meijerink et al.2009; Woitke et al. 2009b; Banzatti et al. 2012;Antonellini et al. 2015). H O emis-sion lines which trace emission from thehot water vapor within H O snowline Figure 10 shows the total fluxes of the variousortho-H O lines which are the candidates for trac-ing emission from hot water vapor within the H Osnowline for a Herbig Ae disk (top panel) and a TTauri disk (bottom panel). We select those linesfrom the LAMDA database (see Section 2.3 of pa-per I, Notsu et al. 2016) which have both smallvalues of A ul (10 − < A ul < − s − ) and rela-tively large values of E up (700 < E up < λ ∼ − µ m, be- cause we do not have candidate lines which traceemission from the hot water vapor within H Osnowline with wavelengths λ < µ m on the basisof our criteria for A ul and E up . The values of E up of lines for wavelengths λ < µ m are too large( & λ < µ m is expected to be too largeto trace the emission from the midplane of thedisk (see Sections 3.2.2 and 4.3). The detailedparameters, such as transitions ( J K a K c ), wave-length, frequency, A ul , E up , and total line fluxesof these candidate ortho-H O lines shown in Fig-ure 10 are listed in Table B.1 of Appendix B. InFigure 10 and Table B.1, we show both values forthe total fluxes from the Herbig Ae disk and the TTauri disk. In addition, Figure 14 in Appendix Cshows the profiles of mid-infrared candidate lines( λ ∼ − µ m) for the Herbig Ae disk. All linesin this Figure are listed in Table B.1.On the basis of Figure 10, Figure 14, Table 1,and Table B.1, the values of fluxes of these linesfrom the Herbig Ae disk are around 10 − larger than those of the T Tauri disk. This isbecause the position of the H O snowline in theHerbig Ae disk exists at a larger radius from thecentral star than that in the T Tauri disk. Inaddition, the peak fluxes of these lines becomelarger as the values of A ul become larger and E up become smaller. Moreover, the values of totalflux tend to be larger as the wavelengths of theseH O lines become shorter. This is because thepeak wavelengths of the Planck function at thegas temperatures around the H O snowline ( T g ∼ O lines which trace emission from the hot wa-ter vapor within H O snowline are ∼ − and ∼ − times larger than those of sub-millimeter H O lines, respectively, and there aredifferences in the line flux ratio of mid-infraredlines to sub-millimeter lines between the HerbigAe and the T Tauri disks. These are becausethe amount of hot H O gas around the region at τ ul . Osnowline are higher in the Herbig Ae disk modelthan that in the T Tauri disk.On the basis of Figure 14, most of the emission21ig. 10.— The total fluxes of the ortho-H O lineswhich are best candidates to trace the emissionfrom the water vapor within the H O snowline, fora Herbig Ae disk (top panel) and a T Tauri disk(bottom panel). We select these lines based ontheir small Einstein A coefficients of 10 − < A ul < − s − and relatively large excitation energiesof 700 < E up < λ ∼ − µ m. flux from these mid-infrared lines comes from theregion with a high H O gas abundance ( ∼ − , r < λ ∼ − µ m) and rela-tively larger values of E up ( ∼ − O 17.75 and 24.00 µ m lines) among allcandidate lines which trace the emission from thehot H O vapor within the H O snowline (see Ta-ble B.1).
Figure 11 shows the normalized radial cumula-tive fluxes for seven H O lines at λ =682.66 µ m,63.32 µ m, 538.29 µ m, 12.40 µ m, 12.45 µ m, 4.96 µ m,and 4.43 µ m. We discussed the properties of theseseven lines in Sections 3.2.1 and 3.2.2. Accordingto these figures, around 90% of the flux of the682.66 µ m line is emitted from the region insidethe H O snowline ( r <
14 au). In contrast, emis-sion from the 63.32 µ m and the 538.29 µ m linesis emitted mostly from the region outside theH O snowline. In addition, although the 63.32 µ mline is mainly emitted from the region between r ∼ −
200 au, the 538.29 µ m line is mainly emit-ted from a region much further out ( r ∼ − µ m, 12.45 µ m, and 4.96 µ m lines aremainly emitted both from the regions within 3au and outside the H O snowline ( r >
14 au). Theemission from the region between 3-14au (= theH O snowline) is much smaller. The 4.43 µ m lineis mainly emitted from the innermost region ofthe disk ( r < E up ( > O lines that trace thehot water vapor within the H O snowline and the63.32 µ m line. Thus, the values of flux densitiesfrom the hot surface layer of the inner disk arelarger. The 4.43 µ m line has a smaller value of A ul (= 2 . × − s − ) and thus the values of fluxdensities from the hot surface layer of the outer22isk are much smaller, but the other three lineshave larger values of A ul ( > − ) and thus thevalues of flux densities from the hot surface layerof the outer disk are larger.Figure 12 shows the normalized radial cumulativefluxes for seven rotational ortho-H O lines thattrace the hot water vapor within the H O snow-line: λ =17.75 µ m, 24.00 µ m, 61.32 µ m, 94.17 µ m,482.99 µ m, 682.66 µ m, and 933.28 µ m. We dis-cussed the properties of these seven lines in Sec-tions 3.2.1 and 3.2.3. In the cases of the H O482.99 µ m and 682.66 µ m lines, most of the fluxis emitted from the region with a high H O gasabundance ( ∼ − , r < O gas abundance ( ∼ − , r =8-14 au). Onthe other hand, for the other H O lines, almostall of the emission flux comes from the regionwith a high H O gas abundance ( ∼ − , r < E up and the dust opacity atdifferent wavelengths. The H O 482.99 µ m and682.66 µ m lines have relatively smaller values of E up ( < > µ m),as discussed in Section 3.2.1. In Figure 12, lineswhich have larger E up and shorter wavelengthstend to be emitted from the innermost regionwithin the H O snowline.
4. Discussion4.1. Influence of model assumptions onthe properties of H O emission lines In Section 3.2.4 of paper I (Notsu et al. 2016), wediscussed the uncertainties in our model predic-tions in detail, and we also discussed the behaviorof the H O lines for some cases in which we ar-tificially changed the distribution of H O vapor,the position of the H O snowline, and the frac-tional abundance of H O gas in the outer disksurface layer (see Figures 8 and 9 of paper I,Notsu et al. 2016). We explored different values ofthe H O snowline radius to simulate the effects of(i) increased and decreased viscous heating (e.g.,Oka et al. 2011; Harsono et al. 2015), (ii) usingdifferent dust opacities due to dust-grain growth(e.g., Aikawa & Nomura 2006; Oka et al. 2011).We varied the abundance of water vapor in the
1 10 N o r m a li z ed C u m u l a t i v e F l u x r [AU]
1 10 100 N o r m a li z ed C u m u l a t i v e F l u x r [AU] Fig. 11.— The radial distributions of the nor-malized cumulative flux for seven pure rotationalortho-H O lines at λ =682.66 µ m ( red solid line ),63.32 µ m ( orange dotted line ), 538.29 µ m ( bluedashed line ), 12.40 µ m ( black long dashed line ),12.45 µ m ( brown dashed two dotted line ), 4.96 µ m( green dashed dotted line ), and 4.43 µ m ( violet longdashed dotted line ). The vertical straight lines dis-play the positions of r =8 au ( orange dotted line )and 14 au ( grey dotted line ), respectively. We nor-malized the cumulative flux of each line using thevalues at r = 30 au (top panel) and at r = 300au (bottom panel). We assume that the inclina-tion angle of the disk i is 0 degree in making thesefigures.23
1 10 N o r m a li z ed C u m u l a t i v e F l u x r [AU]
1 10 100 N o r m a li z ed C u m u l a t i v e F l u x r [AU] Fig. 12.— The radial distributions of the nor-malized cumulative flux for seven pure rotationalortho-H O lines at λ =17.75 µ m ( black long dashedline ), 24.00 µ m ( blue dashed line ), 61.32 µ m ( vi-olet dotted line ), 94.17 µ m ( green dashed dottedline ), 482.99 µ m ( brown dashed two dotted line ),682.66 µ m ( red solid line ), and 933.28 µ m ( orangelong dashed dotted line ). These are candidateortho-H O lines to trace the emission from the hotwater vapor within the H O snowline. The verti-cal straight lines display the positions of r =8 au( orange dotted line ) and 14 au ( grey dotted line ),respectively. We normalized the cumulative fluxof each line using the values at r = 30 au (toppanel) and at r = 300 au (bottom panel). We as-sume that the inclination angle of the disk i is 0degree in making these figures. disk atmosphere to simulate the effects of (iii) in-creasing/decreasing the strength of UV photore-actions. We found that in the cases for whichthe H O snowline is more distant from the centralstar, and the fractional abundance of H O gasin the disk atmosphere is lower than that in theoriginally adopted T Tauri disk, the line fluxesfrom the hot inner disk midplane inside the H Osnowline are more dominant from those from theouter disk (e.g., Walsh et al. 2012).An analysis of spectral energy distributions (SEDs)classified Herbig Ae/Be stars into two groups(group I/II, Meeus et al. 2001). Group I sourcesshow both power-law and blackbody componentsup to far-infrared wavelengths in their SEDs.SEDs of group II sources can be well modeled withonly a single power law from mid- to far-infraredwavelengths. Meeus et al. (2001) suggested thatgroup I sources have a flaring disk while the groupII disks are geometrically flat. Meeus et al. (2001)proposed a possible evolutionary scenario wherea group I flaring disk evolves into a group II flatdisk through grain growth and settling of grainsonto the disk midplane (see also Dominik et al.2003; Dullemond & Dominik 2004).However, recent high-spatial resolution obser-vations at various wavelengths have revealeda more complex structure in disks, with innerholes and/or gaps toward many group I sourcessuch as HD100546 (e.g., Benisty et al. 2010;Pani´c et al. 2014; Walsh et al. 2014b), HD142527(e.g., Fujiwara et al. 2006; Fukagawa et al. 2006,2013), and HD169142 (e.g., Benisty et al. 2010;Honda et al. 2012). On the other hand, there islittle evidence for inner holes and/or gaps reportedtoward group II disks, and they seem to have aradially continuous structure (e.g., Honda et al.2015). Honda et al. (2012) and Maaskant et al.(2013) suggested that most group I sources can beclassified as (pre-)transitional disks. Transitionaland pre-transitional disks are protoplanetary diskswith an inner hole and/or gaps indicated by alack of near-infrared/mid-infrared excess in theirSEDs (e.g., Strom et al. 1989; Espaillat et al.2007). They pointed out that there is no sig-nificant difference in age between groups I andII sources (Meeus et al. 2001; Honda et al. 2015).Therefore, recent studies (e.g., Maaskant et al.24013; Honda et al. 2015) suggested that bothgroup I and II sources had experienced differ-ent evolutionary paths from some common pri-mordial and continuous flaring disks. Here wenote that Menu et al. (2015), Isella et al. (2016),and Zhang et al. (2016) suggested that some ge-ometrically flat disks (group II disk) have gaps.Menu et al. (2015) suggested flat disks with gapsare most likely descendants of flat disks withoutgaps. Banzatti et al. (2016) discovered a correla-tion between water line fluxes at λ =2.9 µ m and10 − µ m and the size of inner disk gaps/holesas probed by 4.7 µ m CO rovibrational emissionlines. They described that the lower detection fre-quency of near- and mid-infrared water vapor linesin disks around intermediate mass stars ( M ∗ =1.5-4 M J ) is linked to inner gaps/holes with depletedmolecular gas content of the disks out to close toor beyond the H O snowline.Our Herbig Ae disk model adopted in this pa-per has a radially continuous structure with noinner hole and/or gap. If we adopt a disk modelwith an inner hole and/or gap, the emission fluxesof H O lines, especially from the hot water va-por inside the H O snowline is expected to de-crease. Recently ALMA observations with highspatial resolution have been conducted towardsprotoplanetary disks with various central starmasses/ages (e.g., ALMA Partnership et al. 2015;Andrews et al. 2016; Isella et al. 2016; Tsukagoshi et al.2016), and will help understand these evolution-ary scenarios.
In this subsection, we discuss the validity of theassumption of LTE. As we discussed in paper I(Notsu et al. 2016), the assumption of LTE is validin calculating the emission flux of the 682.66 µ mline. This is because this line mainly comes fromthe hot region around z/r ∼ . Osnowline where the total gas density ( ∼ − cm − ) is much larger than the critical density forthis line (n cr = 1 . × cm − , see also Table 1).On the other hand, in our LTE calculations itremains possible that we have overestimated theemission flux of strong H O lines with large A ul ( ∼ − − s − ) which trace the hot surface layer of the inner/outer disk (e.g., the 12.40 µ m andthe 63.32 µ m lines) and lines which trace the coldwater vapor in the photodesorbed layer (e.g., the538.29 µ m line). The values of n cr of these lines(e.g., n cr = 1 . × , 1 . × , and 2 . × cm − for the 12.40 µ m, the 63.32 µ m, and the538.29 µ m lines, respectively) are larger than orsimilar to the total gas density in the hot surfacelayer of the inner/outer disk ( ∼ − cm − )and the photodesorbed layer ( ∼ − cm − ).Previous studies which model such H O lines(e.g., Meijerink et al. 2009; Woitke et al. 2009b;Banzatti et al. 2012; Antonellini et al. 2015, 2016)showed that non-LTE calculations are importantfor the latter lines. They suggested that non-LTE effects may, however, alter line fluxes byfactors of only a few for moderate excitation lines( E up < a few thousand K). Moreover, currentnon-LTE calculations are likely to remain inac-curate, due to the incompleteness and uncer-tainty of collisional rates (e.g., Meijerink et al.2009; Banzatti et al. 2012; Kamp et al. 2013;Zhang et al. 2013; Antonellini et al. 2015).We calculated the critical density n cr of the sixother lines discussed in Section 3.2.1 and Figures4, 5, and 6 as probes interior to the H O snow-line (the 17.75, 24.00, 61.32, 94.17, 482.99, and933.28 µ m lines, see Table 1). n cr for the sub-millimeter lines at 482.99, 682.66, and 933.28 µ m(3 . × , 1 . × , and 4 . × cm − , respec-tively) are lower than the values of the total gasdensity in the hot surface layer of the outer disk( ∼ − cm − ) and in the photodesorbed wa-ter layer ( ∼ − cm − ). In contrast, n cr forthe mid- to far-infrared lines (8 . × , 1 . × ,4 . × , and 3 . × cm − for the 17.75, 24.00,61.32, and 94.17 µ m lines, respectively) are simi-lar to and larger than the values of the total gasdensity in those regions. This is because the latterinfrared lines have larger Einstein A coefficientsand shorter wavelengths compared with the afore-mentioned sub-millimeter lines. If the wavelengthof a line is shorter, the energy difference betweenthe upper and lower state is larger and the valueof collisional rates < σv > tends to be smaller(Faure & Josselin 2008). However, emission fromthese lines mainly comes from the hot water vaporwithin the H O snowline where total gas density ismuch larger ( ∼ − cm − ) than the values25f n cr , and thus it is valid to use LTE to calculatetheir fluxes. H O line observations inHerbig Ae disks Since H O line emission from the disk midplaneis likely obscured by dust grains at near- to mid-infrared wavelengths (Walsh et al. 2015), the “vis-ible” H O gas column density at these wave-lengths is smaller than the total H O columndensity integrated over the disk in the verticaldirection (see e.g., Figure 3). For example, inWalsh et al. (2015), the visible column density at14 µ m in the Herbig Ae disk case is ∼ − cm − within the H O snowline. In the bottompanel of Figure 3, the visible H O gas columndensities at 17.75, 61.32, and 682.66 µ m in theHerbig Ae disk are ∼ − cm − withinthe H O snowline, which are lower than thoseof Walsh et al. (2015). This is because the to-tal integrated column density of water vapor inour model ( ∼ − cm − ) is lower thanthat of Walsh et al. (2015) ( ∼ − cm − ),and because absorption by dust grains is dom-inant in the disk midplane and the disk sur-face ( τ ul .
1) compared to that by excited gasmolecules, especially remarkable in the cases ofinfrared lines (see also Section 3.2.1). Previousnear- and mid-infrared spectroscopic observationsusing instruments on ground and space telescopes(e.g., VLT/CRIRES and
Spitzer /IRS) for HerbigAe disks (Pontoppidan et al. 2010a; Fedele et al.2011; Salyk et al. 2011) have not detected the H Olines, and they derive upper limits for H O gas col-umn densities ( . cm − ). However, such near-and mid-infrared H O lines are observed in manyT Tauri disks (e.g., Pontoppidan et al. 2010a,see also Section 1 of paper I, Notsu et al. 2016).H O lines at far-infrared wavelengths have beendetected with
Herschel /PACS only in the diskaround HD163296, although this emission origi-nates in the hot surface layer of the outer disk ( r >
15 au), and it is farther out than that expectedfor emission at shorter wavelengths (Fedele et al.2012, 2013; Meeus et al. 2012). From these ob-servational results, there is an important questionas to why the detection rate for near- and mid-infrared H O lines for T Tauri disks is higher thanthat for Herbig Ae disks. Previous studies (e.g., Woitke et al. 2009b; Pontoppidan et al.2010a; Fedele et al. 2011; Meeus et al. 2012; Walsh et al.2015; Antonellini et al. 2015, 2016) discussed someanswers to the above question. Here we high-light some important ideas (see also Section 3.2.2).First, there may be additional destruction routesfor gas-phase water in the inner disk atmosphere,not yet included in the chemical networks wehave adopted, for example the reaction to pro-duce OH via photodissociation of H O by Lyman- α photons (Walsh et al. 2015). Second, dust-grain settling and dust-grain growth can reducethe total dust-grain surface area and possiblyincrease the UV irradiation rates in the upperdisk (e.g., Vasyunin et al. 2011; Akimkin et al.2013), which can push the molecular layer deeperinto the disk atmosphere. Hence, a higher frac-tion of the gas-phase water may be hidden fromview (e.g., Walsh et al. 2015; Krijt et al. 2016).We note that HD100546, for which far-infraredH O lines have not been detected, has very highUV flux from the central star and even at 30au the UV field is expected to be too strong forgas-phase water to survive (Meeus et al. 2012).Tilling et al. (2012) modeled the disk of HD163296and pointed out that the dust material is settled.Meanwhile, dust-grain growth and the dust-grainshape also affect the UV field through scatteringefficiency in the disk atmosphere. If the dust-grain radius is large enough compared with thewavelength of radiation from the central star,forward scattering by dust grains becomes effi-cient and the UV field decreases in the disk at-mosphere (e.g., Bethell & Bergin 2011). The gastemperature in the disk atmosphere, which af-fects the H O line fluxes, is also controlled bythe UV radiation field. If the UV radiation fieldincreases/decreases, the gas temperature in thedisk atmosphere will become higher/lower. Wehave assumed isotropic dust scattering and thegrain size distribution of the dark cloud modelwith compact and spherical dust grains (For moredetails, see Nomura & Millar 2005 and paper I,Notsu et al. 2016), and these assumptions will af-fect the resulting H O line fluxes. Third, if thedisk is transitional and has a significant gap/holein the inner disk (e.g., HD100546), the line fluxesfrom the inner disk atmosphere will be decreased(e.g., Banzatti et al. 2016, see also Section 4.1).26ourth, in Herbig Ae disks the strong infrared ex-cess of dust emission might veil the faint emissionof molecular lines at infrared wavelengths (e.g.,Lahuis et al. 2007; Pontoppidan et al. 2010a; Fedele et al.2011; Antonellini et al. 2015, 2016). Previousline modeling calculations such as Du & Bergin(2014) and Antonellini et al. (2015, 2016) con-cluded the infrared and sub-millimeter water linefluxes are affected by many parameters relatedto disk physical structure, such as dust-size dis-tribution, dust-to-gas mass ratio, disk gas mass,maximum dust size, and luminosity of the centralstar. Antonellini et al. (2015, 2016) showed thatthe sensitivity and spectral resolution of previ-ous mid-infrared observations (e.g.,
Spitzer /IRS)were not sufficient to detect the detailed profilesof even strong H O lines (with large A ul ) in manydisks, especially disks around high-mass HerbigAe/Be stars. This was because of the presenceof noise in the spectra which can mask the lineemission, combined with the high dust continuumflux (the noise level is proportional to the dustcontinuum flux). H O lines to trace the H O snowline Since the velocity width between the emissionpeaks is ∼
20 km s − , high-dispersion spectro-scopic observations (R= λ / δλ> tens of thousands)of the H O lines in Table B.1 are needed to traceemission from the hot water vapor within theH O snowline. Their profiles contain informa-tion which can be used to locate the position ofthe H O snowline. The area of the emitting re-gions are small ( r< r <
14 au for a Herbig Ae disk) compared withthe total disk size. The spectral resolution (ofmany instruments) and sensitivity used for previ-ous mid-infrared, far-infrared, and sub-millimeterobservations (e.g.,
Spitzer /IRS,
Herschel /PACS,
Herschel /HIFI) were not sufficient to detect andresolve the candidate lines we identified in TableB.1 which trace emission from the hot water vaporwithin H O snowline.Among the various H O lines in ALMA band8, the H O 682.66 µ m line is the most suitable to trace emission from the hot water vapor within theH O snowline. Other candidate sub-millimeterH O lines to trace the H O snowline, having thesame order-of-magnitude fluxes, exist in ALMAbands 7, 9 and 10 ( ∼ − µ m). The H O933.28 µ m and 482.99 µ m lines are the most suit-able lines in ALMA band 7 and 9, respectively.Here we note that although there is no candi-date ortho-H O line in ALMA band 10, somecandidate para-H O lines do fall in this band.With ALMA, we can now conduct high sensi-tivity (cid:0) ∼ − − − W m − (5 σ , 1 hour) (cid:1) ,high-dispersion (R > <
100 mas) spectroscopic observa-tions. Since the total fluxes of the candidate sub-millimeter lines which trace the emission from hotwater vapor within the H O snowline are low in TTauri disks ( ∼ − − − W m − ), they remainchallenging to detect with current ALMA sensitiv-ity unless we have an unrealistically long integra-tion time (see paper I, Notsu et al. 2016). How-ever, in hotter Herbig Ae disks, in younger T Tauridisks (e.g., HL Tau, ALMA Partnership et al.2015; Banzatti et al. 2015; Harsono et al. 2015;Zhang et al. 2015; Okuzumi et al. 2016), and indisks around FU Orionis type stars (e.g., V883Ori, Cieza et al. 2016), the H O snowline existsat a larger radius and the fluxes of these lines willbe stronger compared with those in our fiducial TTauri disk.Our calculations for a Herbig Ae disk predict thefluxes of the 482.99 µ m (band 9), 682.66 µ m (band8), and 933.28 µ m (band 7) lines to be around10 − − − W m − if we assume that the dis-tance to the object d is 140pc ( ∼ the distance ofTaurus molecular cloud), and the inclination an-gle of the disk i is 30 deg. Thus the possibilityof a successful detection is expected to increasein such Herbig Ae disks and could be achievedwith current ALMA capabilities. Here we mentionthat the 933.28 µ m line has been detected withhigh spectral resolution in the disk and outflowaround the massive protostar candidate, Source Iin Orion KL (Hirota et al. 2014), using ALMA,and around the embedded low mass protostar(Class I), HL Tau, using SMA (Kristensen et al.2016). Kristensen et al. (2016) suggested that fu-ture observations at higher sensitivity and angularresolution with ALMA will clarify the origin of this27ater emission from HL Tau and resolve the diskstructures.Candidate H O lines to trace the H O snowlineexist over a wide wavelength range, from mid-infrared to sub-millimeter. As we discuss in Sec-tion 3.2.3, the values of the total fluxes tend toincrease as the wavelengths of the candidate H Olines which trace emission from the hot watervapor within H O snowline become shorter (seeTable 1, B.1, and Figure 10). There are futuremid-infrared instruments covering the part of Qband which will enable high sensitivity and high-dispersion spectroscopic observations: the HRS onSPICA Mid-infrared Instrument (SPICA/SMI)and Mid-Infrared Camera High-disperser & IFUspectrograph on the Thirty Meter Telescope(TMT/MICHI, e.g., Packham et al. 2012). HRSon SPICA/SMI will have a relatively high spec-tral resolution (R ∼ (cid:0) ∼ − W m − (5 σ , 1 hour) (cid:1) com-pared with previous mid-infrared instruments atthe same wavelengths. TMT/MICHI will havea high spectral resolution (R ∼ − (cid:0) ∼ − W m − (5 σ , 1 hour) (cid:1) .The H O 17.75 µ m and 24.00 µ m lines are inthe Q band at mid-infrared wavelengths, andthe former line falls in the wavelength coverageof SPICA/SMI-HRS and TMT/MICHI. Here wenote that since TMT is a ground-based telescope,the effect of atmospheric absorption has to beconsidered carefully in selecting lines from thecandidate line list. Figure 14 in Appendix Cshows the profiles of mid-infrared candidate lines( λ ∼ − µ m) which trace emission from thehot water vapor within H O snowline. All ofthe lines in this Figure are also listed in TableB.1. Our calculations for a Herbig Ae disk sug-gest that the fluxes of the stronger candidate H Olines in Q band (including 17.75 µ m and 24.00 µ mlines) are ∼ − − − W m − . Since HRSon SPICA/SMI has a high sensitivity in Q band,we predict not only successful detections for someHerbig Ae disks, but also suggest the possibilityof a survey of the locations of H O snowlines inHerbig Ae disks in nearby ( .
150 pc) star-formingregions for the first time. Moreover, since HRSon SPICA/SMI has an especially high sensitivity, successful detections are expected even for T Tauridisks in nearby ( . ∼
410 pc), with several hours of observa-tions. Our calculations for a T Tauri disk (see Ta-ble 1 and B.1) show that the fluxes of the strongestcandidate H O lines at Q band (including 17.75 µ mand 24.00 µ m lines) are ∼ − − − W m − .We also expect to detect emission from those can-didate lines (some of which are not accessible fromthe ground) which trace emission from the hotwater vapor within the H O snowline using otherhigh sensitivity mid-infrared and far-infrared in-struments on future space telescopes, such asThe Mid-Infrared Instrument on board the JamesWebb Space Telescope (JWST/MIRI ), SPICAFAR-infrared Instrument (SPICA/SAFARI), andMRS of SPICA/SMI. Since the spectral resolu-tion of these instruments is not so high ( ∼ a fewthousands), we cannot resolve the velocity profilesof these candidate lines at sufficient resolution tolocate the position of the H O snowline. How-ever, it will be possible to detect the total fluxesof these candidate lines with these high sensitiv-ity instruments. Our results suggest that theselines mainly trace emission from the hot watervapor within the H O snowline. Moreover, sincethe sensitivity of these instruments is very high,meaning that the time necessary for a detectionis not very long, we expect to detect emissionfrom the hot H O gas inside the H O snowline forvarious protoplanetary disks, which are suitablecandidates for high-dispersion spectroscopic ob-servations with future instruments (e.g., ALMA,SPICA/SMI-HRS).
5. Conclusion
In this paper, we calculated the disk water vapordistribution and corresponding H O line profilesfor a Herbig Ae disk, and identified candidate wa-ter lines which can locate the position of the H Osnowline across a wide wavelength range from mid-infrared to sub-millimeter.First we calculated the chemical composition us-ing a self-consistent physical model of a Herbig Ae http://ircamera.as.arizona.edu/MIRI/index.htm O gas and ice, and the position of the H Osnowline. We found that the abundance of H O ishigh (up to 10 − ) in the inner region with highertemperature ( & ∼ − ∼ − ) between 7 − O snowline, ∼ ∼ − − − ) in the hot surface layer and thephotodesorbed region of the outer disk, comparedto its value ( ∼ − ) in the regions outside theH O snowline near the equatorial plane. The po-sition of the H O snowline in the Herbig Ae diskis further from the central star compared to thatin the T Tauri disk, in agreement with previousstudies (e.g., Woitke et al. 2009b).Second, we calculated the H O line profiles, andshowed that H O emission lines with small Ein-stein A coefficients ( A ul ∼ − − − s − ) andrelatively high upper state energies (E up ∼ O snowline, and therefore their profiles po-tentially contain information which can be usedto locate the position of the snowline. Since thefluxes of these lines from Herbig Ae disks are largerthan those from T Tauri disks, the possibility ofa successful detection is expected to increase fora Herbig Ae disk. The wavelengths of those lineswhich are the best candidates to locate the posi-tion of the H O snowline range from mid-infraredto sub-millimeter. The values of total fluxes tendto be larger as the wavelengths of the H O linesbecome shorter. This is because the peak wave-length of the Planck function at the gas tempera-ture around the H O snowline ( T g ∼ −
200 K)is in the mid-infrared region.In addition, we investigated the properties ofwater lines which have been detected by pre-vious spectroscopic observations (e.g., 63.32 µ m,538.29 µ m). These lines are less suited to locatethe H O snowline, because they are not dominatedby emission from the region within the H O snow-line. The properties of near-, and mid-infraredH O emission lines which do not trace emissionfrom the hot water vapor within the H O snowlineare also discussed.The wavelengths of such candidate lines which trace emission from the hot water vapor withinH O snowline overlap with the capabilities ofALMA and future mid-infrared high-dispersionspectrographs (e.g., SPICA/SMI-HRS). The suc-cessful detection in a Herbig Ae disk could beachieved with current ALMA capabilities usingseveral lines. Mid-infrared instruments such asHRS on SPICA/SMI would have a high sensi-tivity in the Q band (e.g., ∼ µ m), and wepredict not only successful detections for someHerbig Ae disks, but also suggest the possibilityof a survey of H O snowline locations in manyHerbig Ae disks in nearby ( . . The vertical distributions of normalized cumulative line emissivity Figure 13 shows the vertical distributions of the normalized cumulative line emissivity at r =5 au (top twopanels), r =10 au (middle two panels), and r =30 au (bottom two panels), and of the gas temperature T g .The left three panels show the distributions for seven H O lines at λ =17.75 µ m, 24.00 µ m, 61.32 µ m, 94.17 µ m,482.99 µ m, 682.66 µ m, and 933.28 µ m, for the Herbig Ae disk. The right three panels show the distributionsfor seven H O lines at λ =682.66 µ m, 63.32 µ m, 538.29 µ m, 12.40 µ m, 12.45 µ m, 4.96 µ m, and 4.43 µ m. for theHerbig Ae disk. We normalize the cumulative emissivity of each line using the values at z = −∞ .The differences in the properties of the line profiles (see also Figures 4, 5, 6, 7, 8, and 9) come fromthe differences in A ul , E up , and wavelengths among lines. For the lines with similar wavelengths, the emit-ting regions tend to be in the upper region of the disk as values of A ul of the lines become larger, sincethe absorption by excited H O molecules increases. In addition, in the sub-millimeter lines, the values ofnormalized cumulative line emissivity are smaller than unity at z/r ∼
0. It is because the values of dustopacity at sub-millimeter wavelengths are smaller than those at infrared wavelengths (see also Figures 5, 6,8, and 9). B. H O line parameters and fluxes The detailed parameters, such as transitions ( J K a K c ), wavelength, frequency, A ul , E up , and total line fluxesof the candidate ortho-H O lines which trace emission from the hot water vapor within the H O snowline arelisted in Table B.1. In Table B.1, we show the values of the total fluxes from both disks around the HerbigAe star and the T Tauri star. Some of these lines are also listed in Table 1. The line selection method isdescribed in Section 3.2.3. 30
100 1000 10000 N o r m a li z ed C u m u l a t i v e E m i ss i v i t y G a s T e m pe r a t u r e [ K ] z/r T gas m m24.00 m m61.32 m m94.17 m m482.99 m m682.66 m m933.28 m m
100 1000 10000 N o r m a li z ed C u m u l a t i v e E m i ss i v i t y G a s T e m pe r a t u r e [ K ] z/r T gas m m63.32 m m538.29 m m12.40 m m12.45 m m4.96 m m4.43 m m
100 1000 10000 N o r m a li z ed C u m u l a t i v e E m i ss i v i t y G a s T e m pe r a t u r e [ K ] z/r T gas m m24.00 m m61.32 m m94.17 m m482.99 m m682.66 m m933.28 m m
100 1000 10000 N o r m a li z ed C u m u l a t i v e E m i ss i v i t y G a s T e m pe r a t u r e [ K ] z/r T gas m m63.32 m m538.29 m m12.40 m m12.45 m m4.96 m m4.43 m m
10 100 1000 10000 N o r m a li z ed C u m u l a t i v e E m i ss i v i t y G a s T e m pe r a t u r e [ K ] z/r T gas m m24.00 m m61.32 m m94.17 m m482.99 m m682.66 m m933.28 m m
10 100 1000 10000 N o r m a li z ed C u m u l a t i v e E m i ss i v i t y G a s T e m pe r a t u r e [ K ] z/r T gas m m63.32 m m538.29 m m12.40 m m12.45 m m4.96 m m4.43 m m Fig. 13.— The vertical distributions of the normalized cumulative line emissivity at r =5 au (top two panels), r =10 au (middle two panels), and r =30 au (bottom two panels), and of the gas temperature T g at Kelvin( gray dotted line ). The left three panels show the distributions for seven pure rotational ortho-H O lines at λ =17.75 µ m ( red solid line ), 24.00 µ m ( black long dashed line ), 61.32 µ m ( blue dashed line ), 94.17 µ m ( browndashed two dotted line ), 482.99 µ m ( green dashed dotted line ), 682.66 µ m ( violet long dashed dotted line ), and933.28 µ m ( orange dotted line . The right three panels show the distributions for seven pure rotational ortho-H O lines at λ =682.66 µ m ( violet long dashed dotted line ), 63.32 µ m ( red solid line ), 538.29 µ m ( black longdashed line ), 12.40 µ m ( blue dashed line ), 12.45 µ m ( brown dashed two dotted line ), 4.96 µ m ( green dasheddotted line ), and 4.43 µ m ( orange dotted line ). We normalized the cumulative emissivity of each line usingthe values at z = −∞ . We assume that the inclination angle of the disk i is 0 degree in making these figures.31 able B.1Candidate ortho- H O line parameters and total line fluxes (11 − µ m) J K a K c λ Freq. A ul E up HAe flux , TT flux , [ µ m] [GHz] [s − ] [K] [W m − ] [W m − ]7 -6 × − . × − . × − -6 × − . × − . × − -5 × − . × − . × − -7 × − . × − . × − -6 × − . × − . × − -5 × − . × − . × − -7 × − . × − . × − -8 × − . × − . × − -7 × − . × − . × − -8 × − . × − . × − -7 × − . × − . × − -5 × − . × − . × − -6 × − . × − . × − -7 × − . × − . × − -9 × − . × − . × − -7 × − . × − . × − -5 × − . × − . × − -8 × − . × − . × − -4 × − . × − . × − -10 × − . × − . × − -8 × − . × − . × − -7 × − . × − . × − -6 × − . × − . × − -8 × − . × − . × − -8 × − . × − . × − -6 × − . × − . × − -7 × − . × − . × − -5 × − . × − . × − -10 × − . × − . × − -9 × − . × − . × − -7 × − . × − . × − -7 × − . × − . × − -9 × − . × − . × − -7 × − . × − . × − -5 × − . × − . × − -9 × − . × − . × − -7 × − . × − . × − -6 × − . × − . × − -7 × − . × − . × − -5 × − . × − . × − able B.1— Continued J K a K c λ Freq. A ul E up HAe flux , TT flux , [ µ m] [GHz] [s − ] [K] [W m − ] [W m − ]7 -8 × − . × − . × − -4 × − . × − . × − -6 × − . × − . × − -5 × − . × − . × − -9 × − . × − . × − In calculating the value of line wavelength from the value of line frequency, we usethe value of speed of light c =2 . × m s − . The total flux of each emission line from the Herbig Ae disk. In calculating the total fluxes of these H O lines, we use a distance d = 140pc andan inclination angle of i =30 degree. The total flux of each emission line from the T Tauri disk (see also paper I,Notsu et al. 2016). 33 . The profiles of candidate mid-infrared H O lines to trace the H O snowline Figure 14 shows the profiles of mid-infrared candidate H O lines which trace the hot water vapor within theH O snowline ( λ ∼ − µ m). All of the lines in this Figure are also listed in Table B.1. We discuss theproperties of these lines in Sections 3.2.3 and 4.4. 34ig. 14.— The velocity profiles of mid-infrared ortho-H O lines at λ =11.88 µ m (top left), 13.01 µ m (topright), 15.49 µ m (middle left), 16.33 µ m (middle right), 16.73 µ m (bottom left), and 17.75 µ m (bottom right),from the Herbig Ae disk. These exist between 11-25 µ m and are also the best mid-infrared candidate ortho-H O lines to trace the hot water vapor within the H O snowline. The parameters and total fluxes of theseortho-H O lines are reported in Table B.1.
Red solid lines are the emission line profiles from inside 8 au (=theinner high temperature region), blue dashed lines are those from inside 14 au ( ∼ inside the H O snowline), green dotted lines are those from 14-30 au ( ∼ outside the H O snowline), and black dashed dotted lines arethose from the total area inside 30au. 35ig. 14.— (Continued.) The velocity profiles of mid-infrared ortho-H O lines at λ =19.53 µ m (top left),19.64 µ m (top right), 21.12 µ m (middle left), 21.19 µ m (middle right), 21.57 µ m (bottom left), and 24.00 µ m(bottom right), from the Herbig Ae disk. 36 EFERENCES
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