OH mid-infrared emission as a diagnostic of H_2O UV photodissociation. I. Model and application to the HH 211 shock
Benoît Tabone, Marc C. van Hemert, Ewine F. van Dishoeck, John H. Black
AAstronomy & Astrophysics manuscript no. tabone_MvH_EvD_JB © ESO 2021February 23, 2021
OH mid-infrared emission as a diagnostic of H O UVphotodissociation
I. Model and application to the HH 211 shock
Benoît Tabone , Marc C. van Hemert , Ewine F. van Dishoeck , , John H. Black Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstrasse1, 85748 Garching, Germany Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, 43992, Onsala,SwedenFebruary 23, 2021
ABSTRACT
Context.
Water is an important molecule in interstellar and circumstellar environments. Previous observations of mid-infrared (IR)rotational lines of OH toward star-forming regions suggest that OH emission may be used to probe the photodissociation of water.
Aims.
Our goal is to propose a method to quantify H O photodissociation and measure the local ultraviolet (UV) flux from observa-tions of mid-infrared OH lines.
Methods.
Cross sections for the photodissociation of H O resolving individual electronic, vibrational, and rotational states of the OHfragment are collected. The state distribution of nascent OH following H O photodissociation is computed for various astrophysicallyrelevant UV radiation fields (e.g., a single Ly α line or a broadband spectrum). These distributions are incorporated in a new molecularexcitation code called GROSBETA , which includes radiative pumping, collisional (de)excitation, and prompt emission (i.e., followingthe production of OH in excited states). The influence of the photodissociation rate of H O, the spectral shape of the UV radiationfield, the density, the temperature of the gas, and the strength of the IR background radiation field on the integrated line intensities arestudied in detail. As a test case, our model is compared to
Spitzer -IRS observations at the tip of the HH 211 bow-shock.
Results.
The OH rotational line intensities in the range 9 − µ m, covering rotational transitions with N up =
18 to 45, are proportionalto the column density of H O photodissociated per second by photons in the range 114 −
143 nm (denoted as Φ ˜ B ) and do not dependon other local properties such as the IR radiation field, the density, or the kinetic temperature. Provided an independent measurementof the column density of water is available, the strength of the local UV radiation field can be deduced with good accuracy, regardlessof the exact shape of the UV field. In contrast, OH lines at longer far-IR wavelengths are primarily produced by IR radiative pumpingand collisions, depending on the chemical pumping rate defined as D ˜ B = Φ ˜ B / N (OH) and on the local physical conditions ( n H , T K , IRradiation field). Our model successfully reproduces the OH mid-IR lines in the 10 − µ m range observed toward the tip of the HH211 bow-shock and shows that the jet shock irradiates its surroundings, exposing H O to a UV photon flux that is about 5 × timeslarger than the standard interstellar radiation field. We also find that chemical pumping by the reaction H + O may supplement theexcitation of lines in the range 16 − µ m, suggesting that these lines could also be used to measure the two-body formation rates ofOH. Conclusions.
The mid-IR lines of OH constitute a powerful diagnostic for inferring the photodissociation rate of water and thus theUV field that water is exposed to. Future JWST-MIRI observations will be able to map the photodestruction rate of H O in variousdense ( n H (cid:38) cm − ) and irradiated environments and provide robust estimates of the local UV radiation field. Key words.
Stars: formation – molecular processes – radiative transfer – ISM: astrochemistry – Individual: HH 211
Use \ titlerunning to supply a shorter title and / or \ authorrunning to suply a shorter list of author.
1. Introduction
Oxygen is the third-most abundant element in the interstellarmedium (ISM) after hydrogen and helium. Water is an im-portant oxygen-bearing molecule in the formation of stars andplanets.Water ice promotes the coagulation of dust grains, fromdense clouds to planet-forming disks (Chokshi et al. 1993; Testiet al. 2014; Schoonenberg & Ormel 2017), and water vapor isan important coolant of the gas in warm molecular environments(Neufeld et al. 1995), particularly in embedded protostellar sys-tems (Karska et al. 2013). Ultimately, the delivery of water toyoung planets and small bodies conditions the emergence of lifeas we know it (Chyba & Hand 2005). Following the trail of wa- ter and its associated chemistry from clouds to young formingplanets is a major goal of astrochemistry (van Dishoeck et al.2014).Infrared (IR) observations, supplemented by chemical mod-eling, have demonstrated that abundant ice is built at the sur-face of grains in cold dense clouds, locking in ∼
25% of theoxygen (Cuppen & Herbst 2007; Boogert et al. 2015). En routeto the protostellar disk, condensed H O is released into the gasphase by passive heating from the accreting protostar (Cecca-relli et al. 1996) and jet-driven shocks (e.g., Flower & Pineaudes Forêts 2012). Under these dense ( n H (cid:38) cm − ) and warm( T (cid:38)
200 K) conditions, oxygen chemistry is then driven by fast
Article number, page 1 of 22 a r X i v : . [ a s t r o - ph . GA ] F e b & A proofs: manuscript no. tabone_MvH_EvD_JB neutral-neutral reactions and photodissociation. In this context,the hydroxyl radical (OH) is a key reactive intermediate betweenatomic oxygen and water. The available gas-phase atomic oxy-gen is converted into OH by the reaction O + H → OH + H,followed by the formation of water through OH + H → H O + H. OH is destroyed by the latter reaction, by the former reactionin the backward direction, and by UV photodissociation. Wateris also destroyed either by the backward reaction H O + H → OH + H or by photodissociation leading mostly to OH.The observations of warm H O and OH vapor toward em-bedded protostars culminated with the
Herschel Space Observa-tory (van Dishoeck et al. 2011), which outperformed previousfar-IR and submillimeter observatories (e.g., SWAS, Odin, ISO-LWS). The detection of far-IR OH lines in inner envelopes andoutflows (Wampfler et al. 2010, 2011, 2013; Goicoechea et al.2015), supplemented by similar detections in prototypical pho-todissociation regions (Goicoechea et al. 2011; Parikka et al.2017) and extragalactic sources (Sturm et al. 2011; González-Alfonso et al. 2012) evidenced the presence of an active warmoxygen chemistry in dense interstellar environments. One of themost striking results is the relatively low abundance of gaseouswater found toward most of the protostellar sources, which con-trasts with the abundant water ice supplied by the infalling en-velope. In particular, multiple outflow components, which dom-inate H O emission, exhibit abundances ranging from 10 − to10 − (Kristensen et al. 2012; Nisini et al. 2013; Kristensenet al. 2017). Water vapor from envelopes and perhaps embed-ded disks is typically traced by H O and H
O lines and is bestobserved by
Herschel -HIFI and (sub)millimeter interferometers(NOEMA, SMA, ALMA). While Visser et al. (2013) show thatwater abundance can be as high as 10 − , most of the protostellarsystems exhibit lower water abundances, typically ranging be-tween 10 − and 10 − (Jørgensen & van Dishoeck 2010; Perssonet al. 2012, 2016; Harsono et al. 2020). Following the dissipationof the envelope, near- and mid-IR observations from space (e.g., Spitzer ) and from the ground (e.g., VLT-CRIRES) have unveiledabundant hot water vapor in the planet-forming regions of ClassII disks ( (cid:46)
10 au, Pontoppidan et al. 2014) but surprisingly dryHerbig disks (Pontoppidan et al. 2010; Fedele et al. 2011; Walshet al. 2015).The solution to this conundrum of low water abundance maylie in the impact of the ultraviolet (UV) radiation field producedby the accreting young star or strong jet shocks ( V (cid:38)
40 km s − ).Observations of hydrides provide evidence of the driving role ofUV irradiation in the chemistry of protostars (Benz et al. 2016).It has been proposed that the low abundance of H O in protostel-lar outflows is the result of the UV photodissociation of H O va-por (Nisini et al. 2002, 2013; Karska et al. 2014). The low waterabundance in embedded protostellar disks is generally attributedto the freeze-out of water (Visser et al. 2009). However, recentconstraints on the thermal structures of Class 0 disk-like struc-tures may contradict this interpretation (van ’t Ho ff et al. 2020)and require the e ffi cient destruction of H O or a large opacity ofthe dust in the far-IR.The impact of UV photodissociation is generally explored bymeans of astrochemical models (van Kempen et al. 2010; Visseret al. 2012; Panoglou et al. 2012; Yvart et al. 2016). However,the strength of the local UV radiation field incident on disks,envelopes, and outflows is poorly known, due to the complexsources of UV emission and the unknown level of dust and gasattenuation on the line of sight, severely limiting the diagnosticcapabilities. Assessing the exact role of UV photodissociationof water from astrochemical models based only on molecularabundances remains highly uncertain. Alternatively, the excitation of molecular species providesin some cases a direct access to their formation and destruc-tion routes. In irradiated regions, IR lines of H and CO fromro-vibrationally excited levels trace the UV pumping followedby radiative decay (Krotkov et al. 1980; Black & van Dishoeck1987) and have been used to probe the photodissociation of thesespecies (Röllig et al. 2007; Thi et al. 2013). The excitation ofreactive species for which the collisional time scale is compa-rable to the destruction time scale, carry also key informationon their formation and destruction rates through a process called”chemical pumping” (Black 1998). So far, the incorporation ofa state-to-state chemistry in models (i.e., models considering thestate distribution of the reagents and the products) have been car-ried out only for a handful of molecular ions relevant for di ff useISM and early universe (Godard & Cernicharo 2013; Stäuber &Bruderer 2009; Coppola et al. 2013).Mid-infrared observations with Spitzer -IRS toward proto-stellar outflows and young disks evidenced the presence of a su-perthermal population of rotationally excited OH with energiesup to E up (cid:39) Ophotodissociation. Specifically, seminal works have shown thatH O photodissociation through the ˜ A excited electronic state ofH O ( λ (cid:38)
143 nm) produces OH in vibrationally hot but rota-tionally cold states (e.g., Hwang et al. 1999a; Yang et al. 2000;van Harrevelt & van Hemert 2001), whereas photodissociationthrough the ˜ B state (114 (cid:46) λ (cid:46)
143 nm) produces OH in highrotational states with levels up to N (cid:39)
47 ( E (cid:39) O photodissocia-tion, a process called ”prompt emission”. If consistently mod-eled, rotational lines of OH can thus give a direct access to thephotodissociation of H O. However, a detailed modeling that in-cludes chemical data accumulated over the past decades is lack-ing.Probing H O photodissocation in astrophysical environ-ments may also lead to unique constraints on the local UV irradi-ation field that H O is exposed to. The far-UV radiation field is akey parameter that controls the chemical, physical, and dynam-ical evolution of circumstellar regions. It regulates the overallchemistry of disk upper layers (e.g., van Dishoeck et al. 2006;Walsh et al. 2012) and outflows (Panoglou et al. 2012; Taboneet al. 2020), the thermal structure of disks (Gorti & Hollen-bach 2004; Bruderer et al. 2012; Woitke et al. 2016), and thecoupling between the gas and the magnetic field (e.g., Gammie1996; Wang et al. 2019). The impact of the UV radiation field de-pends not only on attenuation processes, but also on its spectralshape. While the interstellar radiation field exhibits a broadbandemission down to 91 nm (Habing 1968; Draine 1978; Mathiset al. 1983), the UV radiation emitted by accreting nascent stars(Bergin et al. 2003; Herczeg et al. 2004; Yang et al. 2012;Schindhelm et al. 2012) or by strong jet shocks ( (cid:38)
40 km s, − Raymond 1979; Dopita & Sutherland 2017) is often dominatedby Lyman- α emission, leading to the selective photodissociationof species that exhibit large photodissociation cross sections at121 . and CO lines ex-cited by UV pumping probe only UV photons in narrow lines at <
114 nm that are rapidly attenuated and are not indicative ofthe broadband UV spectrum relevant for the other UV photopro-
Article number, page 2 of 22enoît Tabone, Marc C. van Hemert, Ewine F. van Dishoeck, John H. Black: OH mid-infrared emission as a diagnostic of H O UVphotodissociation cesses. Chemical diagnostics have also been proposed but theyrely either on H UV pumping (e.g., CN formed from excitedH , Cazzoletti et al. 2018) or depend on elemental abundanceratios (e.g., hydrocarbons, Bergin et al. 2016).In this work, we explore the potential of the OH mid-IRlines for probing H O photodissociation and the local UV ra-diation field under a broad range of physical conditions repre-sentative of dense irradiated environments, such as molecularshocks, circumstellar media, and prototypical photodissociationregions (PDRs). To reach this goal, results of quantum mechan-ical calculations resolving the electronic, vibrational, and rota-tional states of the OH product following H O dissociation atdi ff erent UV wavelengths are collected. The distribution of theOH fragments following H O photodissociation by UV fields ofvarious spectral shapes are derived. The emerging line intensitiesare then calculated using
GROSBETA , a new molecular excitationcode that includes prompt emission, radiative decay, collisional(de)excitation, and IR radiative pumping in a slab approach. Forsake of conciseness, ro-vibrational lines of OH are not studied inthis work.In Sect. 2, we present the OH model and the basics of
GROSBETA . The competition of the di ff erent excitation processeson the OH line intensities are studied in detail for H O photodis-sociation at Ly α ( λ = . O photodissociated per unit time, the photodis-sociation rate of H O, and the strength of the local UV radiationfield is proposed and applied to
Spitzer -IRS observations of thetip of the HH 211 protostellar bow-shock. Our findings are sum-marized in Sect. 5.
2. Model H O photodissociation can produce OH with high rotational andvibrational quantum numbers in the X Π ground and the A Σ + first excited electronic states. Our OH model includes the en-ergy levels provided by Brooke et al. (2016) and Yousefi et al.(2018) and made available on the EXOMOL database . Figure 1-a shows the electronic, vibrational, and rotational levels includedin the model. Regarding the ground electronic state OH( X Π ),vibrational levels up to (cid:51) =
13 were included. We retained ro-tational levels that are stable against dissociation and in partic-ular included energy levels above the dissociation energy of theOH( X ) that are stabilized by the centrifugal barrier (Chang et al.2019). This corresponds to a quantum number of N =
54 in the (cid:51) = N denotes the rotational quantum number as-sociated with the motion of the nuclei. Each rotational level isfurther split into two spin-orbit manifolds corresponding to pro-jected quantum numbers of the sum of the electronic orbital andspin angular momenta of Ω = / Ω = / J = N + / J = N − /
2, respectively. Lastly, each rota-tional level ( N , Ω ) is further split by the Λ -doubling into two lev-els labeled by their spectroscopic parity index e / f . Our model http: // / , Tennyson et al. (2016) The spectroscopic parity index is related to the parity p = + / − bythe relation (cid:15) = p ( − J − / , where (cid:15) = e states and (cid:15) = − f states. includes the fine structure and Λ -splitting of the OH( X Π )( (cid:51) , N )states. Hyperfine structure is not considered in this work.Regarding the OH( A Σ + ) state, levels with (cid:51) ≥ (cid:51) = N ≥
26 and the (cid:51) = N ≥
17 levels are predissociated(Yarkony 1992). Therefore, we limited the OH( A ) levels to lower N of the (cid:51) = , A Σ + )( (cid:51) ) states were alsotaken into account. In the following, the electronic, vibrational,rotational, fine-structure, and parity states of OH are labeled as Λ , (cid:51) , N , Ω , and (cid:15) , respectively. Our OH model includes 54276 radiative transitions with theircorresponding Einstein- A coe ffi cients from Brooke et al. (2016)and Yousefi et al. (2018). The mid- and far-IR lines of OH origi-nate from radiative transitions occurring within vibrational states( ∆ (cid:51) =
0) of the OH( X ) state (Fig. 1-c). Figure 1-b shows the ra-diative transitions that connect levels within a vibrational level ofthe X Π ground state. The radiative transitions with the highestEinstein- A coe ffi cients are the intra-ladder rotational transitions N → N − J → J −
1) that preserve the e / fparity. These transitions give rise to lines from the mid- to thefar-IR (see Fig. 1-c). The cross-ladder transitions connecting the Ω = / Ω = / J -conserving( ∆ N = −
1) and e / f conserving transitions, and J → J ± ∆ N = , −
2) and e / f parity changing transitions. Einstein- A co-e ffi cients of the latter two kinds are at least an order of magnitudelower than intra-ladder transitions and can be used to measurethe opacity of the intra-ladder lines. Lastly, the Λ -doubling tran-sitions, that lie from centimeter to sub-millimeter wavelengthsare also considered in this work. Rovibrational transitions followthe same selection rules and any rovibrational transition accom-panied by any change of vibrational quantum number (cid:51) (cid:48) → (cid:51) (cid:48)(cid:48) is included in this work. Rovibrational lines (cid:51) (cid:48) = → (cid:51) (cid:48)(cid:48) = µ m. Transitionsconnecting to the OH( A Σ + ) state are electronic dipole allowedat near UV wavelengths. O photodissociation
The OH state-specific formation rate associated with the photo-processH O + h ν → OH( λ, Λ , (cid:51) , N , Ω , (cid:15) ) + H (1)can be expressed as k ( Λ , (cid:51) , N , Ω , (cid:15) ) = (cid:90) λ η ( λ, Λ , (cid:51) , N , Ω , (cid:15) ) ¯ σ ( λ ) I ( λ ) d λ (2)and measured in cgs units in s − . In this equation, η ( λ, Λ , (cid:51) , N , Ω , (cid:15) ) is the probability of forming OH in a givenstate following H O photodissociation by a photon of wave-length λ , ¯ σ is the total photodissociation cross section ([cm ]) ofH O → OH + H at that wavelength, and I ( λ ) is the photon fluxaveraged over all incidence angles ([photon cm − s − cm − ]).We assumed that the fine structure and Λ -doubling states ofOH are equally populated by the photoprocess (1) so that η doesnot depend on Ω and (cid:15) . It is also convenient to define the nascentstate distribution of the OH fragments as f ( Λ , (cid:51) , N ) = k ( Λ , (cid:51) , N )¯ k , (3) Article number, page 3 of 22 & A proofs: manuscript no. tabone_MvH_EvD_JB E n e r g y E / k B ( K ) N-1 J-1N J N J + 1 fefefefe fe
Ω = 3/2Ω = 1/2
N - 2 J -1N-1 JN-2 J-2 fe
10 20 30 50 70 100 ∏ ( µ m) ° ° ° ° N o r m a li z e d i n t e n s i t y Δ J = 0, ΔΩ = − 1Δ J = − 1, Ω = 3/2Δ J = − 1, Ω = 1/2Δ J = ± 1, ΔΩ = − 1 Δ v = 0 X Π A Σ + v = 13 v = 0 a) b) N =54 c)
16 410 24 N up =29 8 v = 0 v = 1 N = 20N =40N =30N = 10
Fig. 1.
OH model adopted in this work. a) X Π and A Σ + electronic levels split into vibrational levels and further split into rotational levelslabeled by N (left ladder corresponding the OH(X Π )( (cid:51) =
0) state). The red line indicates the dissociation energy of OH(X Π ). b) Structure of therotational ladders of OH(X Π ) within a vibrational state that gives rise to mid- and far-IR lines. Each N level is split by the spin-orbit couplingand the Λ -doubling. The two spin-orbit states are labeled by the Ω quantum number and the Λ -doubling states are labeled by their (cid:15) = e / f spectroscopic parity. Radiative transitions included in our model and emerging from the four N -levels are also depicted by arrows. There are threekinds of transitions: intra-ladder rotational transitions (blue and red arrows), cross-ladder transitions (orange, with ∆ N = +
1, and green, with ∆ N = , Λ -doubling transitions (purple). c) Optically thin LTE spectrum of OH at T K =
750 K. The color code is the same as panel b) andis repeated in Fig. 4 and 9. The upper N level is indicated for some transitions. The Λ -doubling lines are too weak and at longer radio wavelengthsto appear in this spectrum. Ro-vibrational lines are at shorter wavelengths than shown here ( λ (cid:46) . µ m). where ¯ k is the total rate for the photdissociation process (1). Fora monochromatic UV radiation field emitting at a wavelength λ , f i = η ( λ, i ).The absorption of a UV photon in the range 143 to 190 nmexcites H O in its first excited singlet state ˜ A (first absorptionband) and leads to a direct dissociation to OH + H. In this work,we adopted the OH state-specific cross sections computed by vanHarrevelt & van Hemert (2001) using a wave packet approach.These data successfully reproduce the total photodissociationcross section of water in the considered energy range as wellas the OH distributions measured by time-of-flight spectroscopytechniques (Yang et al. 2000). Figure 2-a shows the distributionof the OH fragments following photodissociation by a photon ofwavelength λ =
166 nm, where the cross section of the first ab-sorption band peaks. Throughout the first absorption band, OHis produced in a rotationally cold ( N (cid:46)
9) but vibrationally hotstate (see also Appendix A). The proportion of vibrationally ex-cited states increases with photon energy.The absorption of a UV photon in the second absorptionband ( ˜ B state of H O) results in a nonadiabatic transition, lead-ing to OH in its ground electronic state and in a direct dissoci-ation forming electronically excited OH. The second absorptionband produces a broad continuum bump in the photodissocia-tion cross section of H O in the range 114 to 143 nm. However,shortward of 124 . C and ˜ D states arebound states and predissociated by the ˜ B state. We consequentlyassumed that these channels lead to the same state distributionof the OH fragments as that via the ˜ B state at the same photonenergy. This is further supported by the agreement between ex-periments at λ ≤
124 nm (e.g., Ly α , Harich et al. 2000) andtheoretical work considering only the fragmentation dynamicsfrom the ˜ B state (van Harrevelt & van Hemert 2000, 2008). Inthe following, we use the term "photodissociation through the ˜ B state" to refer to photodissociation in the range 114 to 143 nm.In order to obtain the relevant OH distributions, we repeated thequantum wave packet calculations as described in van Harrev-elt & van Hemert (2000), but using the Dobbyn and Knowlespotential (Dobbyn & Knowles 1997) instead of the Leiden po-tential since it was found that it gave better agreement with ex-periments (Fillion et al. 2001). In this wavelength range, H Ophotodissociation also leads to O with a branching ratio com-puted by van Harrevelt & van Hemert (2008). We used the totalphotodissociation cross section measured by Mota et al. (2005)that includes features due to the ˜ C and ˜ D states of H O (see Fig.A.3). The photodissociation cross section of H O → OH + Hwas then derived by taking into account the branching ratio ofthe OH forming channel as described by Heays et al. (2017).
Article number, page 4 of 22enoît Tabone, Marc C. van Hemert, Ewine F. van Dishoeck, John H. Black: OH mid-infrared emission as a diagnostic of H O UVphotodissociation N f i ( % ) TW hya N f i ( % ) N f i ( % ) ISRF N f i ( % )
166 nm N f i ( % ) TW hya N f i ( % ) N f i ( % ) ISRF N f i ( % )
166 nm v=0 v=1 v=2
OH(X)OH(A) α )
166 nm
NEW!!! a)b)
Fig. 2.
State distribution of the OH product following H O photodisso-ciation at two photon wavelengths. a) At λ =
166 nm, H O dissociatingvia its first excited ˜ A electronic state and producing OH in rotationallycold but vibrationally hot states. b) At λ = . O dissociat-ing via its second excited ˜ B electronic state and producing OH in rota-tionally hot but vibrationally cold states. Vibrational quantum numbersare color coded as indicated in the top panel. The distributions withinOH(X Π , (cid:51) ) and OH(A Σ + , (cid:51) ) are plotted in solid and dashed lines, re-spectively, as a function of the rotational quantum number N . Only vi-brational levels that contribute at least 0.1% to the population of nascentOH are shown. As an example, we show in Fig. 2-b the distibution of OHproducts at Ly α wavelength ( λ = . X Π ) with low vibrationalexcitation but high rotational excitation. OH is produced pref-erentially in the ground vibrational and electronic state, and theresulting rotational distribution within this state peaks around N =
45, corresponding to an energy level of (cid:39) N (cid:39)
35 up to N (cid:39)
49. The other vibrational states follow a similar rotationaldistribution as that of the (cid:51) = X )( (cid:51) ≥
1) states at Ly α . A fraction of OH is alsoproduced in the excited electronic state OH( A ) for λ <
137 nm.The rotational distributions of the (cid:51) = , X ) but shifted toward lower N numbers.Shortward of λ =
114 nm, photodissociation proceeds viaeven more excited electronic states of H O and systematic quan-tum calculations are lacking. Time-of-flight spectroscopy indi-cates that at λ =
115 nm OH distributions are vibrationally hot-ter than those computed through the ˜ B but still rotationally hot(Chang et al. 2019). Photodissociation shortward of λ =
114 nmmay also produce preferentially atomic oxygen instead of OH.In this work, we neglected the contribution of OH producedthrough photodissociation at wavelengths shorter than 114 nm.Our adopted chemical dataset pertains only to water in therotational ground state ("cold water"). Experimental data sug-gest that photodissociation of "warm water" could result in a small change in the rotational distribution of OH in the range N (cid:39) −
40 (Hwang et al. 1999b). This change would howevera ff ect only lines coming from N (cid:38)
32 in the 9 − . µ m range(see Sec. 3). Additionally, the adopted dataset does not includethe fine-structure and the Λ -doubling states of the OH products.Recent theoretical investigations suggest that photodissociationthrough the ˜ B state produces OH preferentially in the A (cid:48) symmet-ric states, that corresponds to the ( Ω = / , e ) and ( Ω = / , f )states (Zhou et al. 2015). This asymmetry is also expected todepend on the rotational state of the parent H O, which is notconsidered here. New quantum calculations resolving the fine-structure and the Λ -doubling state and including the rotationalstate of the parent H O are needed to study in detail the A (cid:48) / A (cid:48)(cid:48) asymmetry. Our predictions presented in Sec. 3 remain valid bysumming the line intensities over the fine-structure and Λ dou-blets of each N up line. When radiative processes dominate, the emitted spectrum of OHwill be governed by the state-specific dissociation rates of H O(see Eq. (2)) and by the spontaneous transition probabilities inthe subsequent cascade of vibronic and rotational transitions.This is called the prompt spectrum of OH. In astrophysicallyrelevant conditions, excited states of OH can be populated insteady-state by various other collisional and radiative processes,and these excited molecules also contribute to an observablespectrum. Thus the true population of excited OH di ff ers fromthe nascent population.In this work, the OH level populations and the line intensitieswere computed with a new code named GROSBETA (Black et al.in prep.). This code is based on a single-zone model, followingthe formalism presented in van der Tak et al. (2007) and imple-mented in the
RADEX code. Under the assumption of statisticalequilibrium, the local population densities, denoted n i [cm − ],are given by dn i dt = (cid:88) j (cid:44) i P ji n j − n i (cid:88) j (cid:44) i P i j + (cid:88) k F ki − (cid:88) k (cid:48) n i D k (cid:48) i = , (4)where F ki and n i D k (cid:48) i are the formation and destruction rates([cm − s − ]) for level i = ( Λ , (cid:51) , N , Ω , (cid:15) ) and are associated withthe chemical reactions labeled k and k (cid:48) , respectively. The P i j arethe radiative and collisional transition probabilities i → j givenby P i j = (cid:40) A i j + B i j ¯ J ν ij + C i j ( E i > E j ) B i j ¯ J ν ij + C i j ( E i < E j ) . (5)Here, A i j and B i j are the Einstein coe ffi cients of spontaneousand induced emission, C i j are the collisional rates [s − ], and ¯ J ν ij is the mean specific intensity at the frequency of the radiativetransition i → j averaged over the line profile. As in van derTak et al. (2007), the contribution of the lines to the local radia-tion field was computed following the escape probability methodfor a uniform sphere setting the line width to ∆ V = − .When all other physical parameters (e.g., density and tempera-ture) are fixed, the solution depends only on the value of the ratio N (OH) / ∆ V .The collisional (de)excitation rates in Eq. (5) were computedconsidering collision with H and He for the OH levels withinthe (cid:51) = ffi cients from O ff er et al. (1994) https://home.strw.leidenuniv.nl/~moldata/radex.html Article number, page 5 of 22 & A proofs: manuscript no. tabone_MvH_EvD_JB and Kłos et al. (2007), respectively. The rate coe ffi cients com-puted by O ff er et al. (1994) that include levels up to N = N numbers (see Appendix B).The induced radiative rates in Eq. (5) depend upon mean in-tensities ¯ J ν at the frequencies of all OH transitions. Thus the ex-citation model requires a specified ambient radiation field. Purerotational and vibration-rotation transitions involve infrared ra-diation, which we parametrized as a blackbody intensity (Planckfunction) at a temperature T IR times a geometrical dilution fac-tor W . For illustration, we took W =
1. This gives a sim-ple parametrization of the IR radiation field and a reasonablygood proxy for the local radiation field in the far-IR regime rel-evant for the IR radiative pumping of pure rotational lines of theOH( X Π )( (cid:51) =
0) state. The impact of a more complex and real-istic IR radiation field on the line intensities is briefly discussedin Sec. 3.1.2. Electronic transitions A − X respond to the near-ultraviolet. In this work, we neglected the impact of the near-UVradiative pumping.The impact of formation and destruction of OH on its levelpopulation is described by the last two terms in Eq. (4). Whenactivation barriers can be overcome ( T K (cid:38)
200 K), OH is primar-ily produced by the reaction of O atoms with H and is rapidlyconverted into H O by the reaction with H . In turn, OH can alsobe regenerated from H O by UV photodissociation or by the re-action with atomic hydrogen. Photodissociation of OH, whichis generally slower than H O photodissociation (depending onthe spectral shape of the UV radiation field, see Heays et al.2017), can also limit the abundance of OH. The formation anddestruction routes are described by the state specific rates F ki and D k (cid:48) i , respectively. Their relative importance depends on the exactphysical conditions. A complete model coupling chemistry andexcitation of OH is beyond the scope of the present paper andfor the sake of generality and conciseness, we made a numberof simplifying assumptions to focus on the impact of H O pho-todissociation on OH excitation in various environments with alimited number of free parameters. The possible impact of O + H on the excitation of OH is discussed in Sec. 4.2.1. In this work,we assumed that chemical steady-state holds, so that F ≡ (cid:88) k (cid:88) i F ki = (cid:88) i n i D i , (6)where F is the total formation rate of OH ([cm − s − ]), and D i ≡ (cid:80) k D ki the total destruction rate of level i ([s − ]). We alsoneglected any state selective destruction of OH assuming thatOH is destroyed at the same rate for each state denoted here as D (i.e., D i does not depend on i ) . Finally, we assumed that onlyH O photodissociation leading to OH modifies the level popula-tion of OH, with a state specific rate of F i = n (H O) k ( i ), where n (H O) is the number density of H O and k ( i ) the state specificformation rate defined in Eq. (2).Equation (4) can then be rewritten as an equation on the col-umn density of OH in the levels i denoted as N i , upon which lineintensities depend. Assuming constant concentrations and exci-tation conditions along the line of sight, this yields (cid:88) j (cid:44) i P ji N j − N i (cid:88) j (cid:44) i P i j + Φ × (cid:32) f i − N i N (OH) (cid:33) = , (7) D i is the probability of OH in a given state to be destroyed [in s − ].Consequently, this assumption leads to D = D i and not D i = D / n , with n the number of OH levels included in the model, as stated in Stäuber& Bruderer (2009). with f i the state distribution of the OH fragments as defined inEq. (3) and Φ ≡ N (H O) ¯ k (8)the column density of H O photodissociated per unit time ([cm − s − ]). The state distribution f i depends on the spectral shapeof the UV radiation field. In this work, we explore UV radia-tion fields of various shape that are given in Fig. A.3, includingnarrow-band and broadband UV spectra.Equation (7) shows that Φ is the relevant parameter that ul-timately controls the impact of prompt emission on the OH lineintensities. The relation between the strength of the UV radia-tion field and Φ depends on its spectral shape. For a Ly α UVradiation field
Φ = . × G N (H O)10 cm cm − s − , (9)and for a Draine ISRF, Φ = . × G N (H O)10 cm cm − s − , (10)where G is the intensity integrated between 91 and 200 nm, inunits of the Draine (1978) radiation field (2 . × − W m − ).In this work we adopt Φ = cm − s − as a fiducial value andexplore a broad range of values (see Table 1). Φ can also be written as Φ ≡ D N (OH) , (11)where D ([s − ]) is generally referred to as a destruction rate (seee.g., van der Tak et al. 2007; Stäuber & Bruderer 2009). Sincechemical steady-state is assumed, D is also connected to the for-mation rate of OH. If other chemical reactions participate to theformation and destruction of OH (see Eq. (4)) and if these addi-tional reactions form and destroy OH in proportion to their localpopulation densities, then Eq. (7) still holds but D would not beassociated with a destruction rate. D should rather be associatedwith a chemical pumping rate equal to the formation rate of thespecies by the considered process (in cm − s − ) divided by itsparticle number density.The line intensities were computed taking into account opti-cal depth e ff ects under the large velocity approximation. Whencalculating the line intensities, we assumed that the IR contin-uum background interacting with the gas is not along the sameline of sight as the observations are taken. That is, the IR fieldcontributes to the radiative pumping but not to the line forma-tion. Throughout this work, we present line intensities I in ergs − cm − , which are sometimes called emergent fluxes. That is,our I is related to the specific intensity in a line I ν in erg s − cm − Hz − sr − by I = π (cid:82) I ν d ν . One can recover the observed lineflux by the relation: F = I π ∆Ω , (12)where ∆Ω is the solid angle subtended by the source.In other words, the populations and the line intensities ofOH were computed from statistical equilibrium calculations in-volving prompt emission, IR radiative pumping and collisionalexcitation. Our model is controlled by six parameters summa-rized in Table 1: the spectral shape of the UV radiation field thatdetermines the distribution of nascent OH denoted as f i , the col-umn density of H O photodissociated per unit time denoted as Φ , the column density of OH N (OH), the proton density n H , thekinetic temperature T K , and the temperature of the IR radiationfield T IR . Article number, page 6 of 22enoît Tabone, Marc C. van Hemert, Ewine F. van Dishoeck, John H. Black: OH mid-infrared emission as a diagnostic of H O UVphotodissociation
Table 1.
Parameters of the model and their fiducial values.
Parameter Units Range FiducialShape of the UV field . see text Ly α Φ ≡ N (H O) k cm − s − -10 N (OH) cm − − n H cm − -10 T K K − T IR K 50, 120 120 D (1) s − − -10 − − Notes. (1) the chemical pumping rate is not considered as a free param-eter here since
D ≡ Φ / N (OH). Table 2.
Rotational lines used as a template for the di ff erent excitationregimes. Transition λ i j E i A i j Π Ω (cid:48) ( N (cid:48) , (cid:15) (cid:48) ) → Π Ω (cid:48)(cid:48) ( N (cid:48)(cid:48) , (cid:15) (cid:48)(cid:48) ) ( µ m) (K) (s − ) Π / (30 , f ) → Π / (29 , f ) 10.8 22600 3.5(2) Π / (5 , f ) → Π / (3 , f ) 24.6 875 3.8(-2) Π / (10 , f ) → Π / (9 , f ) 27.4 2905 2.0(1)
3. Results
Figure 3 illustrates the di ff erence between OH spectra follow-ing H O photodissociation through the ˜ A and ˜ B state. Photodis-sociation via the H O ˜ A state leads to an OH spectrum dom-inated by far-IR lines coming from low rotational levels. H Ophotodissociation does not impact the mid- and far-IR spectrumsince only collisions and IR pumping contribute to the excitationof those lines. In contrast, photodissociation through the H O ˜ B state produces additional lines lying in the mid-IR coming fromhigh- N states (15 (cid:46) N (cid:46) Ophotodissociation. In this section, we shall identify the physi-cal quantities that can be retrieved from the intensities of themid- and far-IR lines. To do so, an in-depth study of the exci-tation mechanisms is provided in the case of photodissociationby Ly α photons (121.6 nm). The impact of a broadband UV ra-diation field, for which photodissociation proceeds through boththe H O ˜ A and ˜ B states is then studied. As seen in Sect. 2.2, photodissociation of H O by Ly α photonsproduces OH in high rotational states (Fig. 2-b). Figure 4 illus-trates the influence of the column density of H O photodisso-ciated per unit time denoted as Φ and of the column density ofOH, N (OH). The results of a more systematic exploration of theparameter space are presented in Fig. 5 by focusing on the inten-sities of three representative rotational lines that will be observedby JWST-MIRI (see Table 2). N lines: Prompt emission The mid-IR spectrum ( λ (cid:46) µ m) is dominated by pure intra-ladder rotational lines emerging from levels with high rotationalquantum number ( N ≥ > Φ (top and mid-dle panels) but do not depend on N (OH) (top and bottom pan-els). The relative intensities of the intra-ladder lines depend nei-ther on N (OH) nor on Φ so we focus on the intensity of the
10 20 40 100 ° ° ° ° °
10 20 40 100 ∏ ( µ m) ° ° ° ° ° I ( e r g c m ° s ° )
10 15 20 30 50 100 ° ° °
10 15 20 30 50 100 ∏ ( µ m) ° ° ° I ( e r g c m ° s ° ) α )166 nm NEW!!!
Fig. 3.
Infrared spectra of OH following H O photodissociation at twophoton wavelengths computed with
GROSBETA . Top: At λ =
166 nm,H O dissociating via its first excited ˜ A electronic state and produc-ing rotationally cold OH. The OH infrared spectrum is dominated byfar-IR lines excited by collisions and IR radiative pumping. Bottom: At λ = . O dissociating via its second excited ˜ B elec-tronic state and producing rotationally hot OH. OH lines in the mid-IR with N up = −
45 trace H O photodissociation through this elec-tronic state. The density, temperature of the background radiation andkinetic temperature are fixed to their fiducial values (see Table 1) and
Φ = cm − s − . In this figure, all lines are colored red, even if com-ing from cross-ladder and intra-ladder transitions. Π / (30 , f ) → Π / (29 , f ) line at 10.8 µ m (see Table 2) as aproxy for the intensities of the mid-IR lines. Figure 5 (left pan-els) shows that the absolute line intensity is directly proportionalto Φ and does not depend on other parameters such as N (OH), T IR or n H . This is one of the most fundamental properties ofthe high- N lines that makes them an unambiguous diagnosticof H O photodissociation.This very simple result points toward a simple excitationprocess. Due to the high energy of the upper levels, IR radia-tive pumping does not contribute to the excitation of these lines.De-excitation by stimulated emission by the IR background isalso negligible as long as the photon occupation number is muchsmaller than unity in the mid-IR domain, a condition that is ful-filled over the full parameter space. Due to the very high crit-ical densities of these levels ( n crit (cid:38) cm − ), collisional(de)excitation is also negligible. Instead, the level populations,and the intensity of the lines coming from those levels, are set bythe radiative cascade following the formation of OH in high- N states by H O photodissociation. The line intensities, or equiva-lently the number of radiative transitions per unit time betweentwo excited levels, are then directly proportional to the forma-tion rate of OH in higher excited states, which is proportional tothe photodissociation rate of H O. The proportionality betweenthe mid-IR line intensity and Φ is thus a direct consequence ofthe radiative cascade.In order to analyze the relative intensity of the mid-IR lines,it is then convenient to define the normalized and dimensionless Article number, page 7 of 22 & A proofs: manuscript no. tabone_MvH_EvD_JB
10 20 30 50 100 ° ° ° ° °
10 20 30 50 100 ° ° ° ° ° I ( e r g c m ° s ° )
10 20 30 50 100 ∏ ( µ m) ° ° ° ° ° Φ = 10 cm −2 s −1 cm −2 s −1 cm −2 s −1 cm −2 cm −2 N (OH) = 10 cm −2
30 20 1040 46 6 3 3 1
NEW!
Fig. 4.
Infrared spectra of OH depending on the column density of H O photodissociated per unit time Φ and on N (OH) computed with GROSBETA for a Ly α UV radiation field. The density, temperature of the background radiation and kinetic temperature are fixed to their fiducial values (seeTable 1). Following the color code used in Fig. 1, intra-ladder rotational lines are in red and blue and cross-ladder lines are in orange and green. Λ -doubling lines are too weak to appear here. The weak mid-IR lines lying in the range ∼ µ m are intra-ladder rotational lines within theOH( X )( (cid:51) =
1) state. The N up rotational number of the upper energy level is indicated for selected lines. © (cm ° s ° ) ° ° ° ° I n t e n s i t y ( e r g c m ° s ° ) µ m © (cm ° s ° ) ° ° ° ° ° ° ° µ m n H (cm ° ) ° ° ° ° ° ° ° I n t e n s i t y ( e r g c m ° s ° ) n H (cm ° ) ° ° ° ° ° ° ° Φ = c m − s − n H = c m − cm −2 cm −2
120 K K
1 prompt emission
2 IR pumping
3 IR pumping+collisions
4 collisions (LTE)
Fig. 5.
OH line intensities and the associated excitation processes as a function of Φ and n H for various values of N (OH) and T IR . The colorindicates the value of N (OH) and the line style the value of T IR as defined in the right panels. The black circle indicate the fiducial model.The processes that dominate the excitation of the lines depending on the explored parameters are indicated along each curve. Left:
Intra-ladderrotational line at 10.8 µ m coming from a high- N level ( N = E up = Φ . Right:
Cross-ladder rotational lineat 24.6 µ m coming from a low- N level ( N = E up =
875 K). This line traces the bulk population of OH. As such, it depends on N (OH), T IR and n H but does not depend on Φ .Article number, page 8 of 22enoît Tabone, Marc C. van Hemert, Ewine F. van Dishoeck, John H. Black: OH mid-infrared emission as a diagnostic of H O UVphotodissociation
20 30 40 50 N up . . . . . . N o r m a li z e dph o t o n i n t e n s i t y I N , ≠ , ≤ Ly α Fig. 6.
Normalized photon intensity of the OH( X Π )( (cid:51) =
0) intra-laddermid-IR lines as a function of the quantum number of the upper energylevel N up . The photon intensities are computed for the fiducial valuesof the parameters and divided by Φ (see Eq. (13)). Circle and trianglemarkers correspond to lines belonging to the Ω = / Ω = / Λ -doublets are indiscernible in this plot. In thisregime, rotational levels are only populated by the radiative cascade ofOH photofragments and I N , Ω ,(cid:15) , depends only on the spectral shape ofthe adopted radiation field. The solid line is an analytical model that as-sumes that the intra-ladder lines within the (cid:51) = (cid:51) = line intensity I N , Ω ,(cid:15) = I Ω ,(cid:15) N → N − h ν Φ , (13)where I Ω ,(cid:15) N → N − is the integrated intensity (in erg s − cm − ) of the N → N − Ω and the parity (cid:15) , and ν is thefrequency of the line. As long as the population of the high- N levels is set by the radiative cascade, I N , Ω ,(cid:15) depends only on thedistribution of nascent OH, or equivalently on the spectral shapeof the UV field, and not on Φ or on any other physical parameter.Figure 6 shows that I N , Ω ,(cid:15) depends mostly on N and very littleon Ω and (cid:15) . This is due to the fact that in our model, levels areassumed to be populated by H O photodissociation regardlessof their Ω and (cid:15) states. In the following, we thus omit the refer-ence to Ω and (cid:15) and note the normalized line intensity as I N . I N increases with decreasing N , with a sti ff rise between N = N =
35. This feature is also visible in Fig. 4 where theline intensities increase with wavelength between 9 and 10 µ m.For 22 ≤ N ≤ I N is rather constant, corresponding also toa rather flat mid-IR spectra between 10 and 20 µ m (see Fig. 4).This results in suprathermal excitation temperatures that vary be-tween 2300 K for the lines at λ (cid:39) µ m up to 13000 K for thelines at λ (cid:39) µ m.The normalized intensity I N is directly related to the distri-bution of nascent OH. Interestingly, I N can be interpreted as theprobability that a photodissociation event H O → H + OH even-tually leads to a radiative decay N → N − I N is necessarily smaller than unity. Becausewe assume the spin-orbit and Λ -doubling states to be equallypopulated by H O photodissociation, I N (cid:46) /
4. Owing to the selection rules, the rotational cascade within the (cid:51) = N → N − X Π )with little change of rotational number. Consequently, the forma-tion of an OH fragment in an OH( Λ , (cid:51) = , N (cid:48) ) state eventuallyleads to an intra-ladder transitions N → N −
1, with N ≤ N (cid:48) . Weplot in Fig. 6 (solid line) an analytical prediction of I N assumingthat transitions N → N − (cid:51) = f i . The model reproduces theincrease in I N with deceasing N well, showing that its globalvariation with N is mostly due the fact that more and more OHfragments are added to the N → N − N decreases. The radiative cascade should then rather be seen asa ”radiative river” that grows by it tributaries. In particular, thesteep increase in I N from N =
47 to 35 is due to the fact thatmost of the OH fragments are produced with these N -quantumnumbers (see Fig. 2-b).We also note that for N <
35, our analytical model progres-sively underestimates I N . This is due to the contribution of theOH fragments produced in vibrationally excited states that arenot included in our first analytical model. In Fig. 6 (dashed line)we show the analytical prediction of I N assuming that any OHproduced in an OH( Λ )( (cid:51) , N ) state immediately decays toward theOH( X Π )( (cid:51) = , N −
1) state. The model overestimates I N show-ing that vibrationally excited states tend to undergo rotationaltransitions within (cid:51) ≥ (cid:51) = I N is set by the population of nascent OH following photodis-sociation of H O. Our two simple analytical models, which relyonly on the knowledge of the distribution of the OH fragments f i , allow one to bracket I N . N lines Figure 4 shows that, in contrast to the mid-IR lines, the far-IR lines ( λ > µ m) do not depend on the column densityof H O photodissociated per unit time Φ but on N (OH). Thesame conclusions apply to the cross-ladder transitions apparentfrom 20 µ m to 114 µ m. All these lines arise from N (cid:46) E up (cid:46) N levels. Because ofthe high optical depth of the intra-ladder lines, we focus in thefollowing on the optically thin cross-ladder transition at 24 . µ mthat arises from a N = Φ but on N (OH), T IR , and n H . Promptemission is always negligible and the line intensity is the resultof a competition between collisional (de-)excitation and IR ra-diative pumping.Figure 5 (lower right panel) highlights three distinct excita-tion regimes as a function of density. At low density, the intensitydoes not depend on the density but on T IR . In this regime, labeledby (cid:173) , levels are exclusively populated by IR radiative pumping.Because of our specific choice of the IR radiation field, all low-energy levels are thermalized to the same excitation temperatureequal to T IR and the intensities of the optically thin lines are I i → j (cid:39) A i j g i N (OH) Q ( T IR ) hc λ i j e − E i / k B T IR , (14)where Q ( T IR ) is the partition function of OH. The intensity of theline at 24 . µ m is simply proportional to N (OH) and increases Article number, page 9 of 22 & A proofs: manuscript no. tabone_MvH_EvD_JB with T IR . For an IR radiation field that deviates from a black-body, the excitation of the OH( X Π )( (cid:51) = , N ) levels is morecomplex. In this general case, the radiation brightness temper-ature T rad varies with wavelength across the far-IR spectrum ofOH ( λ (cid:46) µ m ). As a rule of thumb, the line intensity is thenbracketed between our predictions with an undiluted blackbodyat a value of T IR that lies between the minimum and maximumvalues of T rad .At intermediate density, the intensity increases with n H . Forour fiducial values of T IR and T K , it corresponds to densities be-tween 10 and 10 cm − . In this regime, labeled by (cid:174) , collisionscontribute to the excitation of the levels. However, line inten-sities also depend on T IR , showing that IR radiative pumping isalso relevant. Since the density is smaller than the critical densityof the upper energy level ( n H ∼ cm − ), the de-excitation ofthe level is via radiative decay. Interestingly, the critical densityabove which collisions contribute to the excitation of the levelsdepends on T IR and on T K . It is lower for a lower T IR (Fig. 5, bot-tom right) or for a higher T K (not shown here). By comparing therates of collisional excitation with the IR radiative pumping rate,collisions take over from IR radiative pumping in the excitationof a given N -level for n H (cid:38) n γ ( ν N ) n crit e h ν N / k B T K (cid:39) n crit e h ν N / k B (1 / T K − / T IR ) , (15)where ν N denotes the frequency of the N → N − n γ is the photon occupation number, and where weassume h ν N (cid:29) T IR for the second term. With n crit having a weakdependence on T K , the critical density above which collisionstake over from IR radiative pumping depends on the contrastbetween the temperature of the gas and that of the radiation field.Finally, above the critical density of the upper energy level( n crit (cid:39) cm − ), the line intensity converges toward its LTEvalue. In this regime, labeled by (cid:175) , collisions control the exci-tation and the de-excitation of the level and Eq. (14) gives theintensity of the optically thin line by substituting T IR by T K .One has to keep in mind that when IR radiative pumping isrelevant for the excitation of a level, the geometry of the sourceturns out to be of great importance for the formation of the linecoming from this level. We recall that the line intensities pre-sented in this work are computed assuming that the IR back-ground does not contribute to the line formation process. If thebackground IR field does contribute to the observed emission,lines can be weaker or seen in absorption (see OH lines observedby Wampfler et al. 2010, 2013). Collisions can also play a role inthe formation of the line even when negligible in the excitation ofthe levels. Models incorporating specific source geometries arebeyond the scope of this work and have already been exploredto analyze low- N OH lines observed by
Herschel toward pro-tostars and photodissociation regions (Goicoechea et al. 2011;Wampfler et al. 2013). N lines We have shown in Section 3.1.1 that the high- N rotational linesexcited by prompt emission are proportional to Φ and can thus beused to probe the photodissociation of H O. In contrast, low- N lines do not depend on Φ and trace the bulk population of OH. Itis thus of a great importance to determine if a line coming froman intermediate- N level is indeed excited by prompt emission orby other processes such as IR radiative pumping or collisions.Figures 7-a and b show that the intermediate − N line at27.4 µ m, which originates from a N =
10 level, shares featuresof low- N and high- N lines. This complex excitation pattern is the result of the competition between prompt emission, IR ra-diative pumping and collisions. Figure 7-c summarizes the dom-inant excitation processes as a function of the density n H and thechemical pumping rate D = Φ / N (OH) for the fiducial values of T IR and N (OH).For high values of the chemical pumping rate, the line in-tensity normalized by N (OH) is proportional to D (Fig. 7-a).This corresponds to the right part of the parameter space shownin Fig. 7-c. In this regime, the excitation of the upper energylevel is dominated by prompt emission (regime (cid:172) ) and we re-cover the result obtained for the high- N lines that the line in-tensity is proportional to Φ = D N (OH) (Sec. 3.1.1). Figure 7-ashows that below a critical value of the chemical pumping rate,denoted here as D crit , the intensity does not depend on D as IRradiative pumping or collisions take over from prompt emission.This corresponds to the left region of the parameter space (Fig.7-c). The excitation of the line as a function of the density thenfollows a pattern similar to that found for low − N lines (Fig. 7-b). At low density, the excitation is dominated by IR radiativepumping (regime (cid:173) ) whereas at higher density collisions pro-gressively take over (regime (cid:174) ). We find that for the fiducial val-ues of T IR and T K , collisions contribute to the excitation of theline above n H (cid:39) cm − . However, we recall that the e ff ect ofcollisions on levels with N (cid:38) ffi cients for theselevels. In other words, the parameter space is divided into tworegions: a region dominated by prompt emission for which re-sults found in Sec. 3.1.1 apply, and a region dominated by otherexcitation processes for which results found in Sec. 3.1.2 apply.The boundary between the two regions is defined by D crit (green line Fig. 7-c). Its value depends on the parameters thatcontrol the thermal and radiative excitation of OH, namely n H , T K , and T IR . For example, Fig. 7-a shows that D crit increasesfrom ∼ × − to ∼ × − s − by increasing the densityfrom n H = to 10 cm − . Since D crit quantifies the competitionbetween thermal or radiative excitation and prompt emission, italso depends on the upper energy level of the line. We derive inAppendix E simple estimates of D crit as a function of the ex-citation conditions ( n H , T IR , and T K ) for any rotational level.In particular, we show that the schematic view of the parame-ter space proposed in Fig. 7-c remains valid for the low- N linesfor which the boundary is shifted to the right, and for high- N lines, for which the boundary is shifted to the left by orders ofmagnitudes. The integrated intensities of the lines coming from high- N levels( N (cid:38)
20) are proportional to the column density of H O pho-todissociated per unit time and do not depend on other physicalparameters. The shape of the mid-IR spectrum is only set by thedistribution of the nascent OH and we define a normalized inten-sity of the intra-ladder lines, denoted as I N (Fig. 6). The cross-ladder and intra-ladder rotational lines coming from low- N lev-els ( N (cid:46)
6) are populated by IR radiative pumping or collisionsand are thus tracing the bulk population of OH. Intermediate- N lines can be either excited by prompt emission, IR radiativepumping and / or collisions (see Fig. 7-c). Article number, page 10 of 22enoît Tabone, Marc C. van Hemert, Ewine F. van Dishoeck, John H. Black: OH mid-infrared emission as a diagnostic of H O UVphotodissociation ° ° ° D (s ° ) ° ° ° ° ° ° ° I n t e n s i t y / N ( O H )( e r g s ° ) µ m ° ° ° ° ° ° ° ° D (s ° ) ° ° ° ° ° ° ° ° ° I n t e n s i t y / N ( O H )( e r g s ° ) µ m n H (cm ° ) ° ° ° ° ° ° ° ° ° I n t e n s i t y / N ( O H )( e r g s ° ) ° ° ° ° ° ° ° ° D (s ° ) ° ° ° ° ° ° ° ° ° I n t e n s i t y / N ( O H )( e r g s ° ) µ m n H (cm ° ) ° ° ° ° ° ° ° ° ° I n t e n s i t y / N ( O H )( e r g s ° ) D = 10 -9 s -1 n H = c m − n H (cm −3 ) D (s −1 ) Collision (LTE)IR pumping Chemical pumping ≃ Collision+IR pumping n H = 10 cm −3 a) b) c)
32 1 2 3 12 3 4 D c r it = × − Fig. 7.
Transition from prompt emission to thermal or radiative excitation as revealed by the intensity of the intermediate N =
10 rotationalline at 27.4 µ m. The dominant excitation processes are indicated by (cid:172) , (cid:173) , (cid:174) , (cid:175) as defined in Fig. 5. a) Line intensity normalized by N (OH) as afunction of D ≡ Φ / N (OH). The transition between radiative pumping and prompt emission depends on D and on n H . In particular, one can definea critical pumping rate D crit below which thermal or radiative excitation processes take over from prompt emission. b) Line intensity normalizedby N (OH) as a function of n H for D = − s − < D crit . c) Schematic parameter space indicating the dominant excitation process of the N = n H and D . We note that whereas the specific values of D and n H reported in the x- and y-axis are for the N =
10 line, thisschematic view remains valid for any rotational line. The prompt emission region is delimited by D crit (green line). The regime (cid:172) corresponds tothe excitation regime of high- N line whereas the regimes (cid:173) , (cid:174) and (cid:175) correspond to the excitation regime of low- N lines. Panels a) and b) are cutsin the parameter space and are indicated by red, magenta and blue lines. The temperature of the IR background, the kinetic temperature and thecolumn density of OH are fixed to their fiducial values. The other parameters are indicated in each panel. Table 3.
Branching ratio between H O photodissociation leading to OHthrough the ˜ A state ( λ (cid:38)
143 nm) and the ˜ B state (114 (cid:46) λ (cid:46)
143 nm)for UV radiation fields of various spectral shapes.
Radiation field ˜ A ˜ B Ly α
0% 100%T Tauri 13% 87%ISRF 46% 54%Blackbody 1000K 82% 18%
Figure 8 shows the state distribution of the OH fragments fol-lowing H O photodissociation by UV radiation fields of vari-ous spectral shapes. As shown in Section 3.1.1, the OH( A )( (cid:51) , N )states decay toward the ground electronic state with little changeof N . We consequently plot only the sum of the rotational distri-bution of OH( X ) and OH( A ) as defined by˜ f i = f ( X , (cid:51) , N ) + f ( A , (cid:51) , N ) , (16)where the factor stands for the di ff erent degeneracies betweenOH( A )( (cid:51) , N ) and OH( X )( (cid:51) , N ) states. The distribution of nascentOH computed from Eqs. (2) and (3) results from photodissoci-ation at various wavelengths. As shown in Sec. 2.2, the distri-bution of the OH fragment η ( λ, i ) depends markedly on the UVwavelength (see Fig. A.1). One of the most prominent di ff er-ences is between photodissociation longward of λ =
143 nm,that produces OH( X ) in low- N states, and photodissociationshortward of this value that produces OH( X ) in high- N states anda small fraction of electronically excited OH( A ) with N ≤ O photodissociation by abroad UV radiation field reflects the relative contribution of thedi ff erent photodissociation channels. The fraction of photodisso-ciation that proceeds through the two channels is given in Table3. We first study the e ff ect a radiation field representative of theUV spectrum emitted by an accreting T Tauri star that includesa UV continuum plus emission lines (see Fig. A.3). As shownby Bergin et al. (2003) and Schindhelm et al. (2012), Ly α emis-sion dominates over the continuum emission with ∼
90% of H Ophotodissociation done by Ly α photons. It results in a state dis-tribution that is similar to that produced by a pure Ly α radiationfield (Fig. 8-a). Contribution of H O photodissociation throughthe H O ˜ A state ( λ ≥
143 nm), that represents ∼
10% of the totalphotodissociation rate, is however seen at N ≤ Ophotodissociation then proceeds through a broad wavelengthrange and results in a distribution of OH fragments that exhibitsfeatures of both photodissociation through the H O ˜ A and ˜ B state(Fig. 8-b). Photodissociation through the ˜ B state creates a peakin the rotational distribution around N =
41 similar to that pro-duced by photodissociation by Ly α , though somewhat smoother.OH( A ) states are produced with a broad range of rotational quan-tum numbers, which results in a small bump in the rotational dis-tribution that is perceptible in the range N = −
27. We notethat a significant fraction of the OH( A ) products are dissociativeand therefore not visible in Fig. 8-b. Photodissociation throughthe H O ˜ A state, that represents 46% of the total photodissocia-tion rate, yields to a prominent peak at low- N numbers.A UV radiation field with a blackbody shape at T = O photodissociation pro-ceeds through the ˜ A state (82%). The resulting distribution ofnascent OH is then dominated by low- N numbers whereas thebump at N (cid:39)
40 is reduced accordingly (Fig. 8-c).In other words, the state distribution of OH following H Ophotodissociation by a broad UV spectrum exhibits a bump athigh- N number and a peak at low- N number. The amount ofOH produced with high- N numbers is globally proportional tothe fraction of photodissociation occurring through the ˜ B state( λ <
143 nm).
Article number, page 11 of 22 & A proofs: manuscript no. tabone_MvH_EvD_JB N f i ( % ) TW hya N f i ( % ) N f i ( % ) ISRF N f i ( % ) Black body 10000K N f i ( % ) TW hya N f i ( % ) N f i ( % ) ISRF N f i ( % ) Black body 10000K N f i ( % ) TW hya N f i ( % ) N f i ( % ) ISRF N f i ( % ) Black body 10000K v=0 v=1 v=2
T TauriISRF10 000 K
NEW!!!!! a)b)c)
Fig. 8.
Rotational distribution of the OH fragments following H O pho-todissociation by UV radiation fields of di ff erent shapes. The impact ofthree radiation fields is explored: a) a radiation field representative ofan accreting T Tauri star dominated by a Ly α emission line, b) an ISRFradiation field and c) a blackbody radiation field at 10 000 K. Vibra-tional quantum number are color coded as indicated in the top panel.The distribution is summed over the two electronic states. Only vibra-tional levels that contribute to at least 1.5% to the population of nascentOH are shown. As shown in the case of H O photodissociation by a Ly α radia-tion field, mid-IR lines are proportional to Φ . The same conclu-sion applies for any UV radiation field and we show in Fig. 9the mid-IR spectrum emitted by OH for the UV radiation fieldsexplored in this work, for the same value of Φ .The mid-IR line intensities depend markedly on the shape ofthe radiation field. The main di ff erence resides in the absoluteline intensity between 10 and ∼ µ m. For example, line inten-sities are ∼ K than for a TTauri radiation field. As seen in the case of a Ly α radiation field,mid-IR lines are fueled by the radiative decay of OH producedin high- N states. The absolute mid-IR line intensities are thenproportional to the fraction of OH produced in a rotationally ex-cited state, which is also proportional to the column density ofH O photodissociated through ˜ B state ([cm − s − ]) as defined by Φ ˜ B ≡ N (H O) (cid:90) nm nm σ ( λ ) I ( λ ) d λ. (17)
10 12 14 16 18 20 22 24
10 12 14 16 18 20 22 24 I ( e r g c m ° s ° )
10 12 14 16 18 20 22 24 ∏ ( µ m) T TauriISRF10 000 K
Fig. 9.
OH mid-infrared spectrum for various UV spectra computedwith
GROSBETA for
Φ = cm − s − . Other parameters are constantand equal to their fiducial values given in Table 1. In this regime, theintensity of intra-ladder lines (red and blue) are proportional to Φ anddo not depend on other parameters such as T IR or n H . This is further shown in Fig. 10, where the line intensities nor-malized by Φ ˜ B as defined by I ˜ BN , Ω ,(cid:15) ≡ I Ω ,(cid:15) N → N − h ν Φ ˜ B (18)are the about same for the di ff erent UV fields (within 20%).In other words, the absolute intensity of mid-IR lines tracesthe amount of H O photodissociated through the ˜ B state ( λ <
143 nm). It follows that the absolute intensity is, to a first approx-imation, only proportional to Φ ˜ B , regardless of the exact shapeof the UV radiation field.The other di ff erence resides in the relative intensity of thelines, that reveals the precise shape of the rotational distributionof nascent OH fragments. This is best seen in Fig. 10. The in-crease in the line intensities from N up =
46 down to N up ∼ α radiation fields than for the othertwo. These di ff erences are due di ff erences in the exact shape ofthe rotational distributions of the OH( X ) fragments shown in Fig.8. In the case of T Tauri and Ly α radiation fields, the peak athigh- N is more pronounced than for the broadband UV spectra.The di ff erences in the rotational distributions at lower N , that aremostly due to di ff erences in the OH( A ) distributions, result in mi-nor di ff erences in the line intensities in the range N up = − N lines Regarding far-IR lines and cross-ladder mid-IR lines, thatemerge from N (cid:46) Φ . In the case of the photodissociation by a Ly α radiation field studiedin Sec. 3.1, Φ = Φ ˜ B and I N = I ˜ BN Article number, page 12 of 22enoît Tabone, Marc C. van Hemert, Ewine F. van Dishoeck, John H. Black: OH mid-infrared emission as a diagnostic of H O UVphotodissociation
15 20 25 30 35 40 45 50 N up . . . . . . N o r m a li z e dph o t o n i n t e n s i t y I B N , ≠ , ≤ Ly TW Hya ISRF Blackbody at 10 K α Fig. 10.
Normalized photon intensity of the OH( X Π )( (cid:51) =
0) intra-ladder mid-IR lines as a function of the quantum number of the upperenergy level N up . The intensities are computed for the fiducial values ofthe parameters (see Table 1) and normalized by the column density ofwater photodissociated via its ˜ B state (see Eq. (18)). Circle and trianglemarkers correspond to lines belonging to the Ω = / Ω = / Λ -doublets are indiscernible in this plot. In thisregime, rotational levels are only populated by the radiative cascadeof OH photofragments and I ˜ BN , Ω ,(cid:15) , depends only on the shape of theadopted radiation field. This is a surprising result since UV radiation fields with a signif-icant flux longward of 143 nm, produce OH with low rotationalquantum numbers. Our finding indicates that the contribution ofthis rotationally cold population of nascent OH to the excitationof low- N levels within (cid:51) = ff ects the intensity of the rotational lines are the one producedwith a high rotational number, typically N (cid:38)
15. However, wenote that for much lower IR radiation fields and lower densities,these lines might be fueled by prompt emission (see Fig. 7-c,regime (cid:172) ). In that case, we expect to have a competition patternbetween excitation via the H O ˜ A state and the ˜ B state.As studied in the case of photodissociation by a Ly α radia-tion field, intermediate- N lines can be excited either by promptemission or IR radiative pumping and / or collisions. For a givenset of physical parameters { T IR , T K , n H } , the transition betweenprompt emission and the other excitation processes is controlledby the chemical pumping rate D ≡ Φ / N (OH) as summarizedin Fig. 7-c. The analysis proposed in Sec. 3.1.3 can be general-ized to any UV radiation field by simply substituting D by D ˜ B as defined by D ˜ B = Φ ˜ B / N (OH) . (19)We note that for the explored UV radiation fields, this adaptationhas little impact on the transition between prompt emission andthe other excitation processes.
4. Discussion and application to HH 211
In this section, we present a method for observationally inferringthe photodissociation rate of H O and deducing the local UVradiation field. As an illustration, our model is applied to the
Spitzer -IRS observations of the apex of the HH 211 bow-shockpublished by Tappe et al. (2008). O photodissociated per second
Our results show that the absolute intensities of the intra-ladderlines in the mid-IR are proportional to the column density ofH O photodissociated per second via the ˜ B state, denoted as Φ ˜ B (see Fig. 10). To our knowledge, the only alternative process thatcan also excite the rotational levels of energy E up ≥ O (Beenakker et al. 1974;Bodewits et al. 2019). In some situations, such as disks aroundyoung stellar objects where there might be a source of energeticelectrons ( (cid:38)
10 eV), the high- N OH lines would thus trace thedestruction of H O via both e-impact and UV photodissocia-tion. Complementary diagnostics, such as lines emerging fromthe triplet electronic states of H or CO that can be excited e ffi -ciently by electron impact but not by UV absorption, can help todetermine if OH lines might also trace the electron impact dis-sociation of H O. In this context, the predictions presented inthis work remain valid as long as the destruction rate of H O byUV photodissociation dominates over destruction by e-impact, acondition that is generally satisfied in irradiated regions.Consequently, the mid-IR lines of OH( X )( (cid:51) =
0) provide arobust measurement of the column density of H O photodisso-ciated in the range 114 to 143 nm. This key quantity can be ob-servationally derived using the relation Φ ˜ B = I N , Ω ,(cid:15) h ν I ˜ BN , Ω ,(cid:15) , (20)with I ˜ BN , Ω ,(cid:15) provided in Fig. 10 and in Appendix D. As shownabove, I ˜ BN , Ω ,(cid:15) depends little on the spectral shape of the UV radi-ation field, and, in the absence of any other information, Φ ˜ B canstill be derived with a high accuracy ( ∼ Φ ˜ B should be considered as an instanta-neous measurement of the photodissociation activity. If the emit-ting region is unresolved, the derived value of Φ ˜ B depends on theassumed source size as for any determination of a column den-sity. Strictly speaking, the total flux integrated over a region onthe sky gives the total number of H O molecules photodissoci-ated per second in that region.
The small deviations in the relative line intensities could be usedto constrain the spectral shape of the radiation field (see Fig. 9and 10). In particular, our results show that a Ly α dominated ra-diation field produces a steeper increase in the photon line inten-sities with decreasing N up . However, detecting these small dif-ferences in the intensities in the range 9 to 11 µ m requires an ac-curate relative flux calibration. In fact, the 10 µ m silicate featureplays a significant role in the dereddening of the fluxes at visualextinctions A V (cid:38)
10. In that perspective, the relative intensityof the lines between (cid:39) µ m in regions with high ex-tinction should be interpreted with caution since the exact shapeof the extinction curve varies significantly with A v (Chapmanet al. 2009; McClure 2009; Hensley & Draine 2020). We positthat a significant extinction in the mid-IR hampers the diagnos-tic capabilities of the OH lines to securely constrain the shape ofthe local UV radiation field. The impact of the rotational excita-tion of the parent H O may also complicate the interpretation of
Article number, page 13 of 22 & A proofs: manuscript no. tabone_MvH_EvD_JB the relative line intensities and detailed quantum calculations areneeded to propose robust diagnostics based on the exact shapeof the OH mid-IR spectrum. O Our work shows that the detection of mid-IR lines of OH isprime evidence for the presence of H O, in particular in envi-ronments where the H O column density is limited by strongUV fields. If an independent measurement of the local UV radi-ation field can be observationally obtained, the column densityof H O that it exposed to the UV field can be deduced as N (H O) = Φ ˜ B k ˜ B , (21)where k ˜ B is the photodissociation rate in s − associated with H O → OH + H through the H O ˜ B state.Conversely, the OH emission can be used to measure thephotodissociation rate k ˜ B by measuring the column density ofwater N (H O): k ˜ B = Φ ˜ B N (H O) , (22)where Φ ˜ B is measured from the mid-IR lines of OH (see Eq.(20)). This quantity being a ratio between a column density and Φ ˜ B , it does not depend on the assumed source size.The measurement of N (H O) is challenging and may be themajor source of uncertainty in the determination of k ˜ B . Besidesthe uncertainties that plague the determination of the columndensities, the variation of the UV field and of the number densityof H O along the line of sight may be an important bias. Indeed,irradiated environments exhibit a layered structure with physicalconditions that vary steeply with distance, due to the attenuationof the radiation field or shocks. Because the OH mid-IR lines areoptically thin and depend little on the shape of the UV radiationfield, our predictions can be directly extended to any physicalstructure with I N = I ˜ BN (cid:90) z n H O ( z ) k ˜ B ( z ) dz , (23)with n H O ( z ) the local number density of H O and k ˜ B ( z ) the localphotodissociation rate of H O through the ˜ B state. Φ ˜ B being aquantity integrated along the line of sight, a spatial variation ofthe UV radiation field and of n H O ( z ) does not a ff ect its measure-ment. On the contrary, k ˜ B is a local quantity and Eq. (22) shouldbe applied with caution. Considerations on the geometry and onthe viewing angle of the source may also help. Our model shows that the OH mid-IR lines trace the photodis-sociation of H O by photons in the range 114 −
143 nm. Assuch, mid-IR OH lines carry information on the local UV ra-diation field in this range. In the following, we note F ˜ BUV , thephoton flux integrated between 114 and 143 nm, which is F ˜ BUV = × cm − s − for a Draine radiation field. The photodissoci-ation rate k ˜ B is the integral over the wavelength of the local UVradiation field multiplied by the photodissociation cross section: k ˜ B = (cid:90)
143 nm114 nm I ( λ ) σ ( λ ) d λ. (24) Strictly speaking, the conversion between k ˜ B and the local UVflux F ˜ BUV should then rely on the knowledge of the shape of theUV radiation field. However, for the considered radiation fields,the intensity weighted cross section averaged between 114 and143 nm varies only by a factor of ∼ σ (cid:39) × − cm . Thus, Eq. (24) can be approximated by F ˜ BUV (cid:39) k ˜ B × − cm , (25)with a typical uncertainly of about a factor of three. The
Spitzer -IRS observations of the apex of the young proto-stellar jet HH 211 provide one of the best examples of highlyrotationally excited OH. Figure 11 shows the unique sequenceof superthermal OH emission lines unveiled from 10 µ m downto 30 µ m coming from rotational levels between N =
34 to N =
9. The association between OH mid-IR emission and ongo-ing H O photodissociation is further supported by the detectionof a compact H α emission by Walawender et al. (2006), tracinga strong UV emitting shock in the close vicinity of the OH emis-sion. Complementary observations of H rovibrational emission(2.12 µ m, Hirano et al. 2006) and in the sub-millimeter domainunveiled a complex structure of multiple molecular bow-shocksencompassing the strong shock (Tappe et al. 2012). N > lines From the
Spitzer -IRS spectrum published by Tappe et al. (2008),we measure a flux of the OH line at 14.6 µ m of F = . × − erg s − cm − in an aperture of Ω = . × − sr. This lineemerges from the N =
20 level of the OH( X )( (cid:51) =
0) stateand corresponds to an intensity integrated over solid angle of I = . × − erg s − cm − (see Eq. (12)). Figure 10 indicatesthat the conversion factor for each component of the quadrupletis ∼ .
2, regardless the spectral shape of the radiation field. At
Spitzer -IRS spectral resolution ( R (cid:39)
600 for the short–high mod-ule), the Λ -doublet and the fine-structure is however not spec-trally resolved. Equation (20) then yields a column density ofH O photodissociated per unit time of Φ ˜ B = I × . h ν = . × cm − s − , (26)where the factor 4 stands for the sum over the four componentsof quadruplet, and ν is the frequency of the line. This corre-sponds to a total number of H O molecule photodissociated persecond of 4 × molecule s − .Figure 11 (top panel) compares a synthetic spectrum of OHproduced by a Ly α radiation field with the Spitzer -IRS spectrumbetween 10 and 16 µ m. We recall that in this wavelength range,the spectrum depends only on Φ ˜ B and not on n H , T K or T IR . Ourmodel reproduces well the sequence of the lines coming from N =
31 down to N = µ m are over-estimated by the model. The extinction correction ( A v =
10 mag,Walawender et al. 2006) cannot explain this discrepancy sincethe extinction curve used by Tappe et al. (2008) tends to overesti-mate the extinction at 10 µ m. An ISRF UV radiation field, whichproduces relatively weaker line fluxes shortward of 11 µ m doesnot significantly improve the fit. Alternatively, we posit that therotational state of the parent H O could modify the rotationaldistribution above N (cid:39)
30. JWST observations with a higher
Article number, page 14 of 22enoît Tabone, Marc C. van Hemert, Ewine F. van Dishoeck, John H. Black: OH mid-infrared emission as a diagnostic of H O UVphotodissociation
27 28 29 30 31 32 3330 ∏ ( µ m) F l u x ( W m ° µ m ° ) £ °
10 11 12 13 14 15 16 ∏ ( µ m) F l u x ( W m ° µ m ° ) £ ° H O N (OH) = 2 × 10 cm −2 N (H O) = 2.2 × 10 cm −2 T K = 1300 K n H = 5 × 10 cm −3 Φ ˜ B = 2.1 × 10 cm −2 s −1 OH (Ly ) α Cross-ladder
10 10
30 20 very NEW!!!! H S ( ) H S ( )[ C l I] ?
10 11 12 13 14 15 16 ∏ ( µ m) F l u x ( e r g s ° c m ° µ m ° ) £ ° × 10 −13 × 10 −13 × 10 −13 Fig. 11.
Comparison of the
Spitzer -IRS mid-IR spectrum of the tip of HH 211 outflow from Tappe et al. (2008) (black lines) and of a synthetic
GROSBETA spectrum for OH (in red) and H O (in blue). The best fit parameters are indicated in the top right parts of the panels. The
GROSBETA spectra are plotted assuming a source size equal to the extraction aperture ∆Ω = . × − sr. The rotational quantum number N up are indicatedfor some OH lines. The model reproduces well the OH lines at 10-16 µ m, but underproduces them at longer wavelengths. signal-to-noise ratio, combined with modeling including the ro-tational state of the parent H O are required to clarify this. Φ ˜ B can then be used to derive k ˜ B , provided the column den-sity of H O is known. Rotational lines of H O are detected fromthe far-IR with
Herschel -PACS to the mid-IR with
Spitzer -IRS,spanning energy levels from 110 up to 1800 K. The mid-IR lineshave been analyzed using
GROSBETA and we derive a columndensity of 2 . + . − . × cm , a density of n H (cid:39) × cm − ,and a temperature of T K (cid:39) T ex (cid:39)
90 K, Dionatos et al. 2018). This suggests thatboth mid-IR and far-IR lines trace the same warm H O reservoirthat is photodissociated. Assuming a common origin for the OHand H O lines, Eq. (22) yields k ˜ B (cid:39) . ± × − s − . (27)The strong shock revealed by compact H α emission is ex-pected to produce a UV field dominated by Ly α photons. Equa-tion (24) then gives F ˜ BUV (cid:39) . × photon cm − s − , whichcorresponds to a UV photon flux 5 × times larger than that ofthe Draine ISRF in the range 91 . −
200 nm. This value is well inline with models of fast dissociative shocks with V S (cid:39)
50 km s − and n H (cid:39) × cm − (Raymond 1979; Lehmann et al. 2020), as-suming that H O is produced in the warm postshock without fur-ther dilution of the UV radiation field. An origin of OH and H O emission in slower shocks passively illuminated by the strongerdissociative shock is also possible (see models of Melnick &Kaufman 2015; Godard et al. 2019). Spatially resolved obser-vations with JWST-MIRI of both OH mid-IR lines and atomiclines that trace fast dissociative shocks such as [NeII] at 12 . µ m or [Ni II] at 6 . µ m (Hollenbach & McKee 1989) are required todistinguish the two possible scenarios. Figure 11-b shows that the OH lines coming from lower N lev-els are detected with the Spitzer -IRS long-high module. In par-ticular, the cross-ladder transition at 28.9 µ m is well reproducedby our GROSBETA model with a column density of N (OH) = × cm − , assuming a density of n H = × cm − and atemperature of T K = O lines. Thismodel is illustrative since the emission of the OH cross-ladderline might originates from a di ff erent layer of gas but its suggestsa N (OH) / N (H O) ratio of about (cid:39) .
9. This value lies in the up-per part of the range 10 − to 0 . (cid:39) . A V regions of the Orion Bar ( (cid:38)
1, Goicoecheaet al. 2011). This further supports the driving role of UV pho-todissociation in preventing the full conversion of OH into H Oand in maintaining a relatively high N (OH) / N (H O) ratio un-
Article number, page 15 of 22 & A proofs: manuscript no. tabone_MvH_EvD_JB der warm conditions. Interestingly, detailed models of molecu-lar shocks do predict that both, fast dissociative shocks and pas-sively irradiated slow shocks exhibit high N (OH) / N (H O) ratios(Neufeld & Dalgarno 1989; Godard et al. 2019; Lehmann et al.2020).For this set of
GROSBETA parameters, the intra-ladder rota-tional lines longward of λ = µ m are underestimated by our GROSBETA model by up to a factor of eight. As shown in Sec.3.1.3, these intermediate- N lines (9 < N <
15) are excited eitherby prompt emission, or by IR radiative pumping or collisions. InHH 211, the IR background detected by
Spitzer -IRS is too weakto have a significant impact on the excitation of these levels. Infact, for the selected set of parameters, the excitation is domi-nated by prompt emission (right part of the schematic diagram,Fig. 7-c). One could invoke collisional excitation to take overfrom prompt emission and increase the intensities of the intra-ladder transitions. This can be achieved by either decreasing thechemical pumping rate D or by increasing n H and / or T K (i.e.,increasing D crit , see Fig. 7-c). Because Φ = D N (OH) is con-strained by the lines in the range 10 to 16 µ m, the intensityof the chemical pumping rate D can only be decreased by in-creasing N (OH). However, increasing N (OH), n H or T K wouldincrease the intensities of the cross-ladder transitions, which arealready well reproduced by our model. In other words, collisionsor IR radiative pumping cannot reconcile our models with obser-vations.Interestingly, in this wavelength range, Λ doublets are spec-trally resolved and show an asymmetry between A (cid:48) and A (cid:48)(cid:48) Λ -doublet states of about a factor of 1.5-2. As discussed by Carr &Najita (2014), this further supports the minimal impact of colli-sional (de)excitation since collisions might eliminate asymmetryin the population. This suggests that the intermediate- N transi-tions reveal another excitation process that is not included in ourmodel.The reaction H + O can produce OH in rotationally andvibrationally excited states and supplement the excitation ofintermediate- N levels. In particular, experimental data show thatthe reactionH + O( D) → OH + H (28)produces OH with rotational number between N =
10 and 25with a large fraction produced in (cid:51) ≥ A (cid:48) states (Liu et al. 2000). Interestingly, the discrepancy be-tween our predictions and the Spitzer -IRS spectra increases from N ∼
16 down to N ∼
9. The case of chemical excitation byreaction (28) can be treated in a similar way as we describedthe excitation of OH following H O photodissociation (see Sec.3.1.1). In the case of H O photodissociation, the line intensitiesare given by the column density of OH formed by H O photodis-sociation. Similarly, reaction (28) will increase the line intensi-ties in proportion to the number of OH produced per second viathis reaction. The discrepancy between the model and the ob-servations suggests that the formation rate of OH via Eq. (28)is about 6 times larger than that via H O photodissociation. In-terestingly, at the density derived by our non-LTE analysis ofH O lines, O( D) would be converted into OH instead of de-caying via the radiative transition at λ = ffi cient production of O( D), either by OHor H O photodissociation, or by collisional excitation. Still, theestimated column density ratio OH / H O appears to be too lowfor OH photodissociation to take over from H O photodissocia-tion in the excitation of OH mid-IR lines. Moreover, at Ly α , only ∼
10% of the water photodissociation ends in O( D) (Slanger &Black 1982; van Harrevelt & van Hemert 2008), a fraction that . . . . . F l u x ( W m ° µ m ° ) £ ° .
05 13 . ∏ ( µ m) F l u x ( W m ° µ m ° ) £ ° N up = 23 / , f / , e / , e / , f Fig. 12.
Expected OH mid-IR spectrum at JWST-MIRI resolving power( R (cid:39) − Spitzer -IRS observations of HH 211. The weak linesaround 9.8 µ m are pure rotational lines within the OH( X )( (cid:51) =
1) state. is too small for the required e ffi ciency of O( D) production. Al-ternatively, the reaction between O( P) and vibrationally excitedH , known to be present at the tip of the bow-shock, could lead toOH in rotationally (and vibrationally) excited states (Gorti et al.2011; Carr & Najita 2014). These additional chemical pumpingroutes could also impact the excitation of even lower- N lines.Further modeling combining OH excitation and chemistry is re-quired to clarify the excitation of the intermediate- N lines. JWST-MIRI will provide a unique view in the mid-IR regime bycombining spectroscopic and imaging capabilities (Rieke et al.2015; Wright et al. 2015). At the observed wavelength range(5 − µ m), JWST will be able to detect pure rotational linescoming from N ≥
10 and cross-ladder lines coming from N ≥ N ro-tational lines.Up to now, OH mid-IR lines tracing H O photodissociationhave been detected toward three protostellar outflows (Tappeet al. 2012) and a large number of protoplanetary disks (Pontopp-idan et al. 2010; Salyk et al. 2011; Carr & Najita 2011, 2014). We
Article number, page 16 of 22enoît Tabone, Marc C. van Hemert, Ewine F. van Dishoeck, John H. Black: OH mid-infrared emission as a diagnostic of H O UVphotodissociation predict that the jump in sensitivity will extend the detectability ofhigh- N lines to other irradiated environments. Since the line in-tensities depend on the local abundance of H O and on the localradiation field, only astrochemical models designed for specificsources can robustly predict mid-IR line intensities. However,the detectability of the mid-IR lines as a function of the physi-cal conditions can be explored with simple chemical arguments.The line emissivity per hydrogen atom depends on x (H O) G ,where x (H O) is the H O abundance with respect to the totaldensity of H atoms and G the local UV flux (see Eq. (23)). Inwarm and irradiated environments (fast shocks, disk surface lay-ers, low A V depths of prototypical PDRs), one can assume thatH O is destroyed by photodissociation and formed in the gasphase by two-body reactions so that x (H O) ∝ n H / G . For coolerregions, for which H O vapor is produced by photodesorption orby gas-phase ion-neutral routes, the scaling is expected to be dif-ferent. Therefore, at least for warm environments, the emissivityof the OH lines per total hydrogen is expected to scale with thedensity. This may explain why superthermal OH emission hasbeen detected by
Spitzer in dense environments and remains un-detected is classical photodissociation regions (Goicoechea et al.2011). We thus posit that high- N lines could be detected byJWST-MIRI in more di ff use regions. Observation of dense clas-sical PDRs such as the Orion bar or NGC 2023 should be con-sidered as primary targets. In even more di ff use environments,such as translucent clouds, we expect OH mid-IR lines to re-main undetected where we estimate Φ (cid:39) − cm − s − (Flagey et al. 2013), corresponding to line intensities as low as ∼ − − − erg s − cm − sr − .The sensitivity of JWST will also allow us to probe the mid-IR emission in deeply embedded protostars. At high extinction( A V (cid:38) µ m will be par-ticularly suited to minimize the IR extinction. The OH mid-IRemission can then constitute a unique tool to unravel the poorlyknown physical and chemical structure of young protostellardisks. Regarding protostellar jets and outflows, it will allow us totest if the low water abundance derived from Herschel observa-tions is due to UV photodissociation or other physical processes(Karska et al. 2014).The spatial resolution provided by mapping capabilities willalso be crucial to constrain the emitting region of OH and mapthe photodissociation of H O. For dense environments, maps of N (H O) can be built from pure rotational lines of H O lying typ-ically longward of 20 µ m ( E up (cid:46) R ∼ − O photodissocia-tion that will challenge current quantum calculations. Figure 12shows a synthetic spectrum at MIRI-MRS spectral resolution.First, MIRI-MRS will give access to the OH lines in the range9-10 µ m that are directly populated by H O photodissociation(35 < N up <
46, see also Fig. 8). The Λ -doublets up to N up = N up =
29 will be spectrally resolved.This information will help to further constrain the shape of theUV radiation field and understand the impact of the rotationalstate of the parent H O. New quantum calculations, including therotational state of H O, and the fine-structure and the Λ -doublingof the OH product, are warranted.
5. Conclusion
In this work, we explore the potential of the OH( X )( (cid:51) = , N )mid-IR emission to probe H O photodissociation. To reach thisgoal, results from quantum mechanical calculations resolvingthe electronic, vibrational and rotational state of the OH productfollowing H O photodissociation at di ff erent UV wavelengthsare collected. The distribution of the OH photofragments is thencalculated for UV fields of various spectral shapes and includedin a new radiative transfer code called GROSBETA . The impact ofprompt emission (i.e., formation of OH in excited states follow-ing H O photodissociation), collisional excitation and radiativepumping is extensively studied.The main conclusions of this study are:1. The mid-IR emission of OH in the range 9-16 µ m is an unam-biguous tracer of H O photodissociation. The mid-IR emis-sion is the result of the rotational radiative cascade of OHphotofragments within the (cid:51) = O chemistry. In particular, the line intensities aredirectly proportional to the column density of H O photodis-sociated per second by photon in the range 114 −
143 nm,denoted as Φ ˜ B . The conversion factors between the line in-tensities and Φ ˜ B is provided for each rotationally excited lineand for UV radiation fields of various shapes in Fig. 10 andin Appendix D. These conversion factors depend little on theexact spectral shape of the UV radiation field.2. Provided a measurement of the column density of the irradi-ated water is known, the photodissociation rate by photonsin the range 114 −
143 nm can be inferred (see Eq. (22)). TheUV flux can then be deduced with good accuracy, regardlessof the shape of the UV radiation field. Alternatively, providedan estimate of the strength of the local UV radiation field isavailable, the column density of H O can be derived.3. The precise state distribution of the OH fragments dependson the spectral shape of the UV radiation field and resultsin small di ff erences in the shape of mid-IR spectrum of OH.This suggests that the relative line intensities, if accuratelymeasured, can be used to derive constraints on the spectralenergy distribution of the UV radiation field.4. The lower rotational levels, probed either by cross-ladder ro-tational lines shortward of 30 µ m, or by far-IR rotationallines, are excited by IR radiative pumping or collisions. Weprovide criteria to determine if a rotational level of an inter-mediate energy (typically E up = , N (cid:39)
10) is excitedby prompt emission or thermal processes.5. As a test case, our model is applied to an irradiated regionlocated at the tip of the HH 211 protostellar jet. Our simplesingle-zone model reproduces the
Spitzer -IRS spectrum inthe range 11-16 µ m and shows that water is exposed to a UVphoton flux that is about ∼ × times larger than the stan-dard UV interstellar radiation field. Discrepancies betweenour predictions and the observations at longer wavelengthsuggest that additional chemical pumping processes such asthe reaction H + O might contribute to the excitation of therotational levels between N ∼ − N = N (cid:39)
45 corresponding to energy levels from800 K up to 45000 K. We posit that the jump in sensitivitywill unveil OH mid-IR emission in new environments suchas classical photodissociation regions (e.g., Orion bar) andembedded protostars. Moreover, armed with good spectralresolution ( R ∼ − Article number, page 17 of 22 & A proofs: manuscript no. tabone_MvH_EvD_JB − µ m and to the fine-structure and Λ -doubling state dis-tribution of the OH fragments.Our work demonstrates the potential of OH mid-IR lines toprobe H O photodissocation and the strength of the UV field.New quantum calculations and astrochemical models taking intoaccount the quantum state of the species are warranted to lever-age future JWST observations and unveil oxygen chemistrythrough the excitation of OH.
Acknowledgements.
The authors thank the anonymous referee for their construc-tive comments. B.T. would also like to thank B. Godard, A. Bosman and A. Faurefor fruitful discussions. This work is part of the research programme Dutch As-trochemistry Network II with project number 614.001.751, which is (partly) fi-nanced by the Dutch Research Council (NWO).
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OH(X) v=0 v=1 v=2 v=3 v=4
OH(X,v=2)OH(A,v=0) OH(X,v=1)OH(X,v=3)OH(A,v=1) N N λ (nm) N λ (nm) − . − . − . − . − . − . − . − . . N N λ (nm) N λ (nm) − . − . − . − . − . − . − . − . . N N λ (nm) N λ (nm) − . − . − . − . − . − . − . − . . log ( η ) OH(A)
Fig. A.1.
Rotational distributions of nascent OH for various vibrationaland electronic states as a function of the photodissociation wavelength.The OH distributions are summed over fine-structure and Λ -doublingstates. The di ff erence in the rotational distribution between photodisso-ciation through the ˜ A ( λ >
143 nm) and ˜ B ( λ <
143 nm) states of H Ois clearly visible.
Appendix A: Distribution of OH fragments
In this appendix, we present the state distribution of OH follow-ing H O photodissociation as a function of the UV wavelengthimplemented in our model. The data stem from the quantum cal-culations published in van Harrevelt & van Hemert (2000) andvan Harrevelt & van Hemert (2001). For the latter, the calcula-tions have been repeated using an another potential energy sur-face that gives better agreement with experiments (see Sec. 2.2).As discussed in Sec. 2.2, we denote as η ( λ, Λ , (cid:51) , N ) the probabil-ity to form OH in the state OH( Λ )( (cid:51) , N ) following H O photodis-sociation by a photon of wavelength λ . Figure A.1 shows therotational distributions of OH as function of the photon wave-length for di ff erent electronic and vibrational states. Figure A.2gives the vibrational distributions for each electronic state. Thedistributions shown in Fig. A.1 and A.2 do not account for thesubsequent dissociation of the OH products. For example, theOH( A ) rotational levels with (cid:51) ≥ O photodissociation by UV radiation fields of dif-ferent shapes are computed using Eq. (2) and (3). Figure A.3presents the spectral shape of the radiation fields adopted inthis work. The radiation fields representative of an accreting T λ (nm) . . . . . . η ( Λ , v ) λ (nm) . . . . . . . η ( Λ , v ) N N λ (nm) N λ (nm) OH(X,v=0)
OH(X) v=0 v=1 v=2 v=3 v=4
OH(X,v=2)OH(A,v=0) OH(X,v=1)OH(X,v=3)OH(A,v=0) N N λ (nm) N λ (nm) − . − . − . − . − . − . − . − . . N N λ (nm) N λ (nm) − . − . − . − . − . − . − . − . . N N λ (nm) N λ (nm) − . − . − . − . − . − . − . − . . log ( η ) OH(A)
Fig. A.2.
Vibrational distributions of nascent OH for the two electronicstates of OH as a function of the UV wavelength. The distributions η are summed over rotational, fine-structure and Λ -doubling states.The di ff erence in the vibrational distribution between photodissociationthrough the ˜ A ( λ >
143 nm) and ˜ B ( λ <
143 nm) states of H O is clearlyvisible.
Tauri star and of the interstellar radiation field corresponds tothose used by Heays et al. (2017) and are available at https://home.strw.leidenuniv.nl/~ewine/photo/ . The UV ra-diation field named "Ly α " is a single Ly α line ( λ = .
567 nm)with a Doppler broadening parameter of b =
200 km s − . Thetotal photodissociation cross section of H O leading to OH (Fig.A.3) is collected by Heays et al. (2017) from Fillion et al. (2003,2004), Mota et al. (2005), and van Harrevelt & van Hemert(2008).
Appendix B: Collisional rate coefficients
The collisional rate coe ffi cients between OH and H computedby O ff er et al. (1994) that include levels up to N = N numbers assuming that the downwardrates follow k N → N (cid:48) = g N (cid:48) ae − b ∆ E / T K , (B.1)where N and N (cid:48) designate the rotational quantum number of theupper and lower levels, ∆ E the energy di ff erence between theselevels and g N (cid:48) the degeneracy of the lower energy level. The pa-rameters a and b are the best fit coe ffi cients of available data attemperature T K . Collisions with the ortho and para states of H have been considered separately. In this work, T K ≥
500 K andwe adopted the rate coe ffi cient computed at a maximum kinetictemperature of T K =
300 K by O ff er et al. (1994) without anyfurther extrapolation. The relative proportion of ortho and parapopulations of H is set to 3. We estimate that the extrapolatedrate coe ffi cients are accurate within a factor of ten. Collisional(de)excitation involving vibrational and electronic states is notconsidered here. Collisional excitation by electrons and H canalso be relevant in certain irradiated environments. However, toour knowledge, the corresponding rate coe ffi cients have not yetbeen computed: Thus, we neglected the contribution of electronsand H to the excitation of OH. Article number, page 19 of 22 & A proofs: manuscript no. tabone_MvH_EvD_JB
T Tauri ISRF Blackbody at 10 K ˜ A ˜ B ˜ C ˜ D ˜ A ˜ B Fig. A.3.
Radiation fields and H O photodissociation cross section forphotodissociation adopted in this work.
Top:
Spectral shape of the radi-ation fields as a function of wavelength. The radiation fields have beenscaled to agree with the integrated energy-intensity of the Draine 1978radiation field between 91.2 and 200 nm, that is 2 . × − W m − . Bot-tom:
Photodissociation cross section of H O producing OH adopted inthis work (black) and the extension to 911 Å (gray). The features dueto photodissociation through the ˜ A , ˜ B , ˜ C , and ˜ D states of H O are alsoindicated.
Appendix C: Analytical model for mid-IR lines
The link between the state distribution of OH fragments f i (Fig.2 and 8) and the variation of the line intensities with the upper N number (see Fig. 6 and 9), quantified here by I N , can be clarifiedby a simple analytical model of the radiative cascade. Neglectingcollisional (de)exciatation and radiative pumping, and assumingthat the fraction of OH in rotationally excited states constitutesa negligible fraction of the total population of OH, the statisticalequilibrium equation (see Eq. (7)) for high- N states yields (cid:88) i > j M i j N j + Φ × f i = M i j = (cid:40) A i j ( E i > E j ) − A i j ( E i < E j ) , (C.1)where N i is the column density of OH in the state i , and A i j theEinstein-A coe ffi cient of the spontaneous emission i → j . Thisequation being linear in N i and the right hand side term depend-ing linearly on Φ , shows that N i is proportional to Φ and that therelative population N i / N (OH) depends only on the Einstein- A coe ffi cients and on f i but not on Φ . Consequently, the linear re-lation between high- N line integrated intensities and Φ shown inFig. 5 (top right panel), as well as the fact that the global shape of
20 30 40 50 N up . . . . . . N o r m a li z e dph o t o n i n t e n s i t y I N , ≠ , ≤ Ly TW Hya ISRF Blackbody at 10 K α Fig. C.1.
Normalized photon intensity of the OH( X Π )( (cid:51) =
0) intra-ladder mid-IR lines as a function of the rotational number of the upperenergy level. The intensities are computed for the fiducial parametersgiven in Table 1 and for three spectral shapes of the UV field (colorcoded), and divided by Φ according to Eq. 13. Circle and triangle mark-ers correspond to lines belonging to the Ω = / Ω = / Λ -doublets are indiscernible in this plot. In this regime,rotational levels are only populated by the radiative cascade of OHphotofragments. The solid line is the analytical model assuming thatthe intra-ladder lines within the (cid:51) = (cid:51) = the mid-infrared spectrum is independent of Φ , is a characteristicfeature of the radiative cascade.The radiative matrix M i j in Eq. (C.1) can be greatly re-duced by noting that the radiative decays of the N levels withinthe X Π ( (cid:51) =
0) state are dominated by pure rotational N → N − (cid:51) = , N ) and assuming that all OH photofrag-ments produced in the OH(A Σ + ) ( (cid:51) = , N ) state decay imme-diately to the OH( X Π ) ( (cid:51) = , N ) state, Eq. (C.1) applied to theOH( X )( (cid:51) = , N ) levels yields A N + → N N N + − A N → N − N N + Φ × ˜ f ( N , (cid:51) = (cid:39) , (C.2)with˜ f ( N , (cid:51) = = f ( X , N , (cid:51) = + f ( A , N , (cid:51) = , (C.3)where the factor stands for the di ff erent degeneracies betweenthe OH( X )( (cid:51) , N ) and OH( A )( (cid:51) , N ) states. The solution of Eq.(C.2) is then A N → N − N N (cid:39) ˜ I N Φ , (C.4)where˜ I N (cid:39) (cid:88) N (cid:48) ≥ N ˜ I ( N (cid:48) , (cid:51) =
0) (C.5)
Article number, page 20 of 22enoît Tabone, Marc C. van Hemert, Ewine F. van Dishoeck, John H. Black: OH mid-infrared emission as a diagnostic of H O UVphotodissociation is the probability to form OH in the ground vibrational state witha rotational number larger than N . The high- N lines are found tobe optically thin. Their integrated intensities are then given by I ( N → N − = ˜ I N hc λ Φ . (C.6)Thus, according to our analytical model, the normalized inte-grated photon intensity I N corresponds to ˜ I N , the probabilityto form an OH photofragment in a (cid:51) = N (cid:48) larger than N . In particular, the line intensities N → N − A coe ffi cients. Thisequation reflects the fact that any OH produced in an excited ro-tational level N (cid:48) will eventually decay through the N → N − N ≤ N (cid:48) . Because each rotational state of OH issplit into two spin-orbit substates that are further subdivided intotwo Λ -doubling states, ˜ I N ≤ /
4, as seen in Figs. 6 and C.1.As discussed in Sec. 3.1.1 and further shown in Fig. C.1,our model underestimates the line intensities computed with
GROSBETA . This indicates that the radiative decay from vibra-tionaly excited levels contributes to the population of X Π ( N , (cid:51) =
0) levels. In order to take into account the contribution of vi-brationaly excited levels, we assume that any OH producedin a vibrationally excited state immediately decays toward the X Π ( (cid:51) =
0) state with no change of the rotational number. Thisleads to a normalized integrated photon intensity of˜ I N (cid:39) (cid:88) (cid:51) ≥ (cid:88) N (cid:48) ≥ N ˜ I ( N (cid:48) , (cid:51) ) . (C.7)This model always overestimates the line intensities (dashedlines, Figs. 6 and C.1). This is due to the fact that for N (cid:38) A coe ffi cients of rovibrational transitions are smallerthan those of pure rotational transitions. Thus, an OH fragmentproduced in a (cid:51) > (cid:51) = N number than its nascent one. Be-low N (cid:39)
25, the analytical model reproduces well the computedintensities as all levels produced in higher N numbers in (cid:51) > (cid:51) = N <
25 are thus tracing the production of OH in high rotationalstates, even though the decay of electronically excited OH in theground vibrational state also contributes to the variation of I N below N (cid:39) Appendix D: Conversion factors
Table D.1 gives the line intensities of the OH mid-IR lines in thepure radiative cascade regime normalized by Φ ˜ B denoted as I ˜ B (see Eq. (18)). The intensity of the N up → N up − X )( (cid:51) =
0) state are summed over the four components of thequadruplet. I ˜ B can be used to convert any line intensity into acolumn density of H O photodissociated per second through theH O ˜ B state denoted as Φ ˜ B using Eq. (20). Appendix E: Critical pumping rate
Figure 7-c summarizes the dominant excitation processes asa function of the density n H and the chemical pumping rate D = Φ / N (OH) for a given OH line. The parameter space issplit in two regions: For low values of D , the excitation is dom-inated thermal and radiative processes whereas for high valuesof D the excitation is set by the radiative cascade of the OHphotofragments. Table D.1.
Conversion factors between the photon intensity integratedover solid angle (in photon cm − s − ) of the rotational lines N up → N up − Φ ˜ B (moleculecm − s − ). N up Ly α T Tauri ISRF BB 10 K10 0.96 0.94 0.88 0.8811 0.95 0.92 0.86 0.8512 0.93 0.91 0.84 0.8313 0.92 0.89 0.82 0.8114 0.90 0.88 0.80 0.7915 0.88 0.86 0.78 0.7716 0.87 0.84 0.76 0.7517 0.85 0.83 0.74 0.7318 0.83 0.81 0.72 0.7119 0.82 0.80 0.70 0.6920 0.80 0.78 0.69 0.6821 0.78 0.76 0.67 0.6622 0.76 0.74 0.66 0.6523 0.75 0.73 0.65 0.6324 0.74 0.72 0.64 0.6225 0.73 0.71 0.63 0.6126 0.72 0.70 0.61 0.6027 0.72 0.69 0.60 0.5828 0.71 0.69 0.59 0.5729 0.70 0.68 0.58 0.5630 0.69 0.67 0.56 0.5431 0.68 0.66 0.55 0.5232 0.67 0.64 0.53 0.5033 0.65 0.63 0.51 0.4834 0.63 0.61 0.48 0.4535 0.61 0.59 0.45 0.4236 0.58 0.56 0.42 0.3837 0.54 0.52 0.39 0.3538 0.50 0.49 0.35 0.3139 0.46 0.44 0.31 0.2740 0.42 0.40 0.27 0.2341 0.37 0.36 0.23 0.1942 0.33 0.31 0.18 0.1443 0.29 0.27 0.14 0.1144 0.23 0.22 0.11 0.0845 0.16 0.15 0.07 0.0546 0.07 0.07 0.05 0.0347 0.03 0.03 0.03 0.0248 0.01 0.01 0.01 0.0149 0.00 0.00 0.01 0.00The boundary between the two regions is defined by D crit (green line Fig. 7-c). Its value depends on the physical condi-tions of the gas, namely n H , T IR , and T K . For example, Fig. 7-ashows that D crit increases from 2 × − to 2 × − s − by in-creasing the density from n H = to 10 cm − . We propose hereto derive simple estimates of D crit for any rotational level andany T K and T IR . To do so, we compare the intensity predicted bya pure radiative cascade (see Eq. (13) and Fig. 6) to that producedby collisions and / or IR radiative pumping only. In the pure IR ra-diative pumping regime (regime (cid:173) ), the line intensity is given byEq. (14). This yields to a critical chemical pumping rate abovewhich prompt emission sets the population of a level N of D crit ( T ex , N ) = g N A N → N − I N Q ( T ex ) e − E N / k B T ex , (E.1) Article number, page 21 of 22 & A proofs: manuscript no. tabone_MvH_EvD_JB N up ° ° ° ° ° ° ° D c r i t ( s ° ) K K K Fig. E.1.
Critical value of the chemical pumping rate D crit ≡ ( Φ / N (OH)) crit below which populations in the X Π ( (cid:51) = , N , Ω ) statesare populated by collisions or IR radiative pumping processes ratherthan by prompt emission. Collisions or IR radiative pumping are as-sumed to populate the levels according to a Boltzmann distribution of asingle temperature T ex . Because Einstein- A coe ffi cients di ff er betweenthe two rotational ladders, two D crit exist for each N quantum number.For simplicity, we have assumed I N = .
25 for all N (see sec. C). where T ex = T IR . This equation can also be directly transposedto the high density regime for which T ex (cid:39) T K (regime (cid:175) ). Forintermediate densities, for which both collisions and IR radia-tive pumping are relevant (regime (cid:174) ), D crit varies smoothly from D crit ( T IR ) to D crit ( T K ) (see Fig. 7-c).Figure E.1 shows D crit as a function of the upper N num-ber of the level and as a function of the excitation temperature. D crit ( T ex , N ) decreases with N , demonstrating that lines withhigher N are less sensitive to thermal or radiative excitation pro-cesses and more sensitive to prompt emission. This is mostly dueto the fact that these lines are coming from levels that are muchhigher in energy than T K or T IR . For higher temperatures, ther-mal processes are more e ffi cient at populating higher N levelsresulting in an increase in D crit . We also note that the decreasein D crit with N is sti ff , showing that for given chemical pump-ing rate, the transition between lines excited by prompt emissionand lines excited by IR radiative pumping or collisions is welldefined. In particular, we recover the fact that when collision arenegligible and for T IR =
120 K, D crit (cid:39) − s − for the linecoming from N =
10. In contrast, a chemical pumping rate of atleast 10 − s − is required to excite the line coming from N = N levels prompt emission dominates for rates as low as D (cid:39) − s − . This shows that the schematic view of the pa-rameter space proposed in Fig. 7-c remains valid for the low- N lines for which the boundary is shifted to the right, and for high- N lines, for which the boundary is shifted to the left by orders ofmagnitudes.lines, for which the boundary is shifted to the left by orders ofmagnitudes.