HCN emission from translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMC Revisiting its role as a tracer of the dense gas reservoir for star formation

Context. Massive stars form within dense clumps inside giant molecular clouds (GMCs). Finding appropriate chemical tracers of the dense gas ( n (H 2 ) > several 10 4 cm − 3 or A V > 8mag) and linking their line luminosity with the star formation rate is of critical importance. Aims. Our aim is to determine the origin and physical conditions of the HCN-emitting gas and study their relation to those of other molecules. Methods. In the context of the IRAM30m ORION-B large program, we present 5deg 2 ( ∼ 250pc 2 ) HCN, HNC, HCO + , and CO J = 1 − 0 maps of the Orion B GMC, complemented with existing wide-field [C i ]492GHz maps, as well as new pointed observations of rotationally excited HCN, HNC, H 13 CN, and HN 13 C lines. We compare the observed HCN line intensities with radiative transfer models including line overlap e ff ects and electron excitation. Furthermore, we study the HCN / HNC isomeric abundance ratio with updated photochemical models


Introduction
Massive stars dominate the injection of radiative energy into their interstellar environment through ultraviolet (UV) photons.They form within cold clumps of dense gas inside giant molecular clouds (GMCs, e.g., Lada 1992;Lada & Lada 2003).Observations reveal that the star formation rate (SFR) is close to linearly proportional to the cloud mass above a visual extinction threshold of A V ≃ 8 mag (Schmidt 1959(Schmidt , 1963;;Kennicutt 1998a,b;Lada et al. 2010;Evans et al. 2020), which corresponds to an approximate gas density threshold of n(H 2 ) > 10 4 cm −3 (e.g., Bisbas et al. 2019).In galaxies, the far-infrared (FIR) dust luminosity (L FIR , defined between 40 µm and 500 µm, see Sect.2.5 and Sanders & Mirabel 1996) provides a measure of the SFR, especially in starbursts (e.g., Kennicutt 1998a).The L FIR and the HCN J = 1-0 line luminosity (L HCN 1−0 ) are linearly correlated over a broad range of spatial scales and galaxy types, from spatially resolved star-forming clumps (L FIR ≃10 4 L ⊙ ) to ultraluminous infrared galaxies (ULIRGs, with L FIR ≥10 11 L ⊙ ) (Solomon et al. 1992;Gao & Solomon 2004b;Wu et al. 2010).These studies suggest that L HCN 1−0 is a good tracer of the dense star-forming gas mass.However, the L CO 1−0 to L FIR luminosity ratio in ULIRGs is lower than in normal galaxies.This leads to a superlinear relationship L FIR ∝ L N > 1 CO (e.g., Kennicutt 1998b;Gao & Solomon 2004a).The above relations are observational proxies of the so-called Kennicutt-Schmidt (KS) relationship, Σ SFR = a Σ N H 2 , where Σ SFR and Σ H 2 are the SFR and molecular gas surface densities.One obtains N≈1.5 assuming that a roughly constant fraction of the gas present in molecular clouds is subsequently converted into stars each free-fall time (e.g., Madore 1977;Elmegreen 2002).
HCN has a high dipole moment (µ e = 2.99 D), 30 times higher than that of CO.The HCN J = 1-0 line is commonly used as a tracer of dense gas because of its high critical density (n cr ), the density for which the net radiative decay from J=1 equals the rate of collisional (de-)excitations out of the upper level.This results in n cr (HCN J=1-0) ≃ 3×10 5 cm −3 for collisions with H 2 at 20 K (see Table 1 for references on spectroscopy and collisional rate coefficients).However, as lines become optically thick, radiative trapping becomes important, leading to lower effective critical densities (n cr, eff ; e.g., Evans 1999;Shirley 2015).
The end 14 N atom has a large nuclear electric quadrupole moment (O'Konski & Ha 1968) and nuclear spin I=1.The large quadruple moment coupling with the molecular rotation induces a hyperfine splitting of each rotational level (J) of HCN, in three hyperfine levels F (= I + J) that vary between |I − J| and I + J, except for J=0 which only has a single level.The rotational transition J = 1-0 splits into three hyperfine transitions: F=0-1, F=2-1, and F=1-1, separated by -7.1 km s −1 and +4.9 km s −1 from the central component F=2-1, respectively (e.g., Ahrens et al. 2002;Goicoechea et al. 2022).The three hyperfine structure (HFS) lines of the J=1-0 transition are usually well spectrally resolved by observations toward GMCs of the Galactic disk.In principle, this is convenient since the relative HCN J=1-0 HFS line intensity ratios can provide the line opacity and the excitation temperature (T ex ), thus avoiding the need to observe isotopologues or multiple-J lines.However, only in the optically thin limit (τ → 0) are the relative HFS line intensity ratios equal to their relative line strengths (1:5:3), is the linewidth the same for the three HFS lines, and is T ex exactly the same for the three HFS transitions, with T ex = T k if local thermodynamic equilibrium (LTE) prevails.For optically thick lines, the line intensity ratios approach unity.Overall, the expected HCN J=1-0 HFS line intensity ratio ranges are R 02 =W(F=0-1)/W(F=2-1)=[0.2,1] and R 12 =W(F=1-1)/W(F=2-1)=[0.6,1], where we define the integrated line intensity as W = T mb (v) dv (in K km s −1 ).Interestingly, the observed interstellar line ratios are usually outside these ranges.This is called anomalous HCN emission.
Since the first detection of anomalous HCN J=1-0 HFS emission, several theoretical studies have tried to explain its origin.Proposed explanations are as follows: radiative trapping combined with efficient collisional excitation from J=0 to 2 (Kwan & Scoville 1975); HFS line overlap effects (Guilloteau & Baudry 1981;Daniel & Cernicharo 2008;Keto & Rybicki 2010); resonant scattering by low density halos (Gonzalez-Alfonso & Cernicharo 1993); and line overlaps together with electron-assisted weak collisional excitation (Goicoechea et al. 2022).A proper treatment of the HCN excitation in GMCs thus requires (i) the radiative effects induced by high line opacities and HFS line overlaps to be modeled and (ii) the HFS-resolved inelastic collision rate coefficients to be known.Recent developments include collisions of HCN with p-H 2 , o-H 2 , and e − (Faure et al. 2007b;Faure & Lique 2012;Hernández Vera et al. 2017;Magalhães et al. 2018;Goicoechea et al. 2022).
Mapping large areas of nearby molecular clouds (a few hundred pc 2 ) in molecular rotational lines different than CO, and at the high spatial resolution (< 0.1 pc) needed to separate the emission from the different cloud component (cores, filaments, and ambient gas), has always been a difficult challenge.Recent surveys of GMCs, sensitive to the line emission from star-forming clumps and their environment, suggest that a significant fraction of the HCN J = 1-0 emission stems from low visual extinctions (A V , i.e., from low density gas; e.g., Pety et al. 2017;Shimajiri et al. 2017;Kauffmann et al. 2017;Evans et al. 2020;Barnes et al. 2020;Tafalla et al. 2021;Patra et al. 2022;Dame & Lada 2023).Even the most translucent (Turner et al. 1997) and diffuse molecular clouds (A V < 1 mag) show HCN J =1-0 emission and absorption lines (Liszt & Lucas 2001;Godard et al. 2010) compatible with HCN abundances similar to those inferred in dense molecular clouds, 10 −8 -10 −9 (e.g., Blake et al. 1987).
Giant molecular clouds are illuminated by UV photons from nearby massive stars and by the interstellar radiation field.They are also bathed by cosmic ray particles.Ultraviolet radiation favors high electron abundances (the ionization fraction or χ e ) in the first A V ≈ 2-3 mag into the cloud (e.g., Hollenbach et al. 1991).In these cloud surface layers, most electrons arise from the photoionization of carbon atoms.Hence, χ e ≃ χ(C + ) ≃ a few 10 −4 (Sofia et al. 2004).At intermediate cloud depths, from A V ≈ 2-3 to 4-5 mag depending on the gas density, cloud porosity to UV photons (Boisse 1990), and abundance of low ionization potential elements such as sulfur determine the ionization fraction (e.g., χ e ≃ χ(S + ) ≃ a few 10 −5 in Orion A; Goicoechea & Cuadrado 2021).At much larger A V , deeper inside the dense cores shielded from external UV radiation, χ e is much lower, ∼ 10 −7 -10 −8 .These χ e values apply to GMCs in the disk of the galaxy exposed to standard cosmic ray ionization rates, ζ CR = 10 −17 -10 −16 s −1 (Guelin et al. 1982;Caselli et al. 1998;Goicoechea et al. 2009).
More than 45 years ago, Dickinson et al. (1977) suggested that electron collisions contribute to the rotational excitation of very polar neutral molecules (see also Liszt 2012).These molecules have large cross sections for collisions with electrons (Faure et al. 2007b).This implies that the rate coefficients of inelastic collisions with electrons can be at least three orders of magnitude greater than those of collisions with H 2 and H. Hence, electron collisions contribute to, and even dominate, the excitation of these molecules when (i) χ e is higher than the critical fractional abundance of electrons, χ * cr (e − ) = n cr (e − ) / n cr (H 2 ), and (ii) the gas density n(H 2 ) is lower than the critical density for collisions with H 2 , n(H 2 ) < n cr (H 2 ).For HCN J = 1-0, this implies χ e ≳ 10 −5 and n(H 2 ) ≲ 10 5 cm −3 (Dickinson et al. 1977;Liszt 2012;Goldsmith & Kauffmann 2017;Goicoechea et al. 2022).Table 1 lists the frequency, upper level energy, n cr , and critical fractional abundance χ * cr (e − ) of the lines relevant to this work.Galactic and extragalactic studies typically overlook the role of electron excitation (e.g., Yamada et al. 2007;Behrens et al. 2022).However, the ionization fraction in the interstellar medium (ISM) of galaxies can be very high because of enhanced cosmic ray ionization rates and X-ray fluxes driven by accretion processes in their nuclei (Lim et al. 2017).Mapping nearby GMCs in our Galaxy offers a convenient template to spatially resolve and quantify the amount of low surface brightness HCN emission (affected by electron excitation) not directly associated with dense star-forming clumps.This emission component is usually not considered in extragalactic studies (e.g., Papadopoulos et al. 2014;Stephens et al. 2016).
Here we carry out a detailed analysis of the extended HCN J = 1-0 line emission, and that of related molecules, obtained in the framework of the large program Outstanding Radio-Imaging of Orion B (ORION-B) over 5 deg 2 (see Fig. 1 for an overview).These maps cover five times larger areas than those Table 1.Spectroscopic parameters of the lines studied in this work (from Endres et al. 2016, and references therein), critical densities for collisions with p-H 2 and electrons at 20 K (if LTE prevails, 99.82 % of H 2 is in para form), and critical fractional abundance of electrons (see text).Notes.We define the critical density as the H 2 (or e − ) density at which A ul equals the sum of all upward and downward collisional rates from the upper level.That is, n cr = A ul / i u γ ui .For collisions with electrons, we consider only dipole-allowed transitions.We define the critical fractional abundance of electrons as χ * cr,e = n e cr / n originally presented by Pety et al. (2017).We revisit the diagnostic power of the HCN J = 1-0 emission as a tracer of the dense molecular gas reservoir for star formation.This paper is organized as follows.In Sect.2, we introduce the most relevant regions in Orion B as well as the observational dataset.In Sect.3, we present and discuss the spatial distribution of different tracers.In Sect.4, we analyze the extended HCN emission and derive gas physical conditions.In Sect.5, we reassess the chemistry of HCN and HNC in FUV-illuminated gas.In Sect.6, we discuss the relevance and properties of the low-density extended cloud component, we determine the dense gas mass conversion fac-tor α(HCN), and discuss the I FIR -W scalings we find between different emission lines and FIR dust intensities.In Sect.7, we summarize our findings and give our conclusions.

The Orion B GMC
Orion B, in the Orion complex, east of the Orion Belt stars, is one of the nearest GMCs (e.g., Anthony-Twarog 1982).Here we adopt a distance 1 of d = 400 pc.Orion B is a good template to study the star formation processes in the disk of a normal galaxy.This is an active but modest star-forming region (with a low SFR∼1.6×10−4 M ⊙ yr −1 and low star-formation efficiency, SFE ∼ 1%, e.g., Lada et al. 2010;Megeath et al. 2016;Orkisz et al. 2019) that contains thousands of dense molecular cores: starless, prestellar, and protostellar cores (e.g., Könyves et al. 2020).Massive star formation is highly concentrated in four main regions: NGC 2071 and NGC 2068 in the northeast, and NGC 2023 and NGC 2024 in the southwest.Table 2 summarizes the properties of the massive stars that create H ii regions in the field.Figure 2b shows the position and extent of these H ii regions (marked with circles).Orion B hosts a complex network of filaments.The main and longest filaments are the Flame and Hummingbird filaments, Orion B9, and the Cloak (Orkisz et al. 2019;Gaudel et al. 2023).Appendix A outlines the main properties of these regions.Notes.a Distance to the ionizing star (as in Pety et al. 2017).b Radius of the circles draw in Fig. 2b (as in Gaudel et al. 2023).
Table 3. Representative environments of our pointed observations.We sort these positions in decreasing order of T rot (HCN) (see also 1 Interferometric observations of the σ Ori system provides a distance of ∼ 388 pc (Schaefer et al. 2016).Recent determinations using GAIA also estimate ∼ 400 pc (e.g., Zucker et al. 2019;Rezaei Kh. et al. 2020).

ORION-B molecular line maps in the 3 mm band and spatial smoothing
The ORION-B project (PIs: J. Pety and M. Gerin) is a large program that uses the 30m telescope of the Institut de Radioastronomie Millimétrique (IRAM) to map a large fraction of the Orion B molecular cloud (5 square-degrees, 18.1×13.7 pc2 ).Observations were obtained using the EMIR090 receiver at ∼21 ′′ −28 ′′ resolution.The FTS backend provided a channel spacing of 195 kHz (0.5-0.7 km s −1 depending on the line frequency).The typical 1σ line sensitivity in these maps is ∼100 mK per velocity resolution channel.The full field of view was covered in about 850 hours by (on-the-fly) mapping rectangular tiles with a position angle of 14°in the Equatorial J2000 frame that follows the global morphology of the cloud.Data reduction was carried out using GILDAS 2 /CLASS and CUBE.This includes gridding of individual spectra to produce regularly sampled maps, at a common angular resolution of 30 ′′ , with pixels of 9 ′′ size, about one third of the angular resolution of the telescope (half power beam width, HPBW).The projection center of the maps is located on the Horsehead photodissociation region (PDR) at 5h40m54.27s, -02°28 ′ 00.0 ′′ .We rotated the maps counter-clockwise by 14°a round this center.Pety et al. (2017) presents a detailed description of the observing procedure and data reduction.Here we focus on a global analysis of the HCN J = 1-0 emission, and its relation to that of HNC, 12 CO, and HCO + .Orion B shows three main velocity components at the local standard of rest (LSR) velocities ∼2.5, ∼6, and ∼10 km s −1 (Gaudel et al. 2023).Here we obtained the line intensity maps (zero-order moment maps) integrating each line spectrum in the velocity ranges [−5, +25] km s −1 (for 12 CO and HCN J=1−0 lines) and [0, +18] km s −1 (for HNC and HCO + J=1−0).We refer to Gaudel et al. (2023) for a thorough analysis of the 13 CO and C 18 O J = 1-0 maps and gas kinematics.
To match the resolution of the [C i] 492 GHz map (see next Section), and since we are interested in the faint and extended molecular emission, we spatially smoothed the original line maps to an angular resolution of ∼2 ′ (∼0.2 pc).This allows us to recover a significant fraction of low surface brightness line emission at large spatial scales.Spatial smoothing improves the root mean square (rms) to ∼25 mK per velocity channel.Thus, it improves the detection limit and signal-to-noise ratio (S/N) of the faint and extended emission.Figure 2 shows the spatially smoothed maps.

Wide-field [C i] 492 GHz map
We complement our molecular line maps with an existing widefield map of the ground-state fine structure line ( 3 P 1 -3 P 1 ) of neutral atomic carbon, the [C i] 492 GHz line, obtained with the Mount Fuji submillimeter-wave telescope.These observations reached a rms noise of ∼0.45 K per 1.0 km s −1 velocity channel (Ikeda et al. 2002).The angular resolution is ∼2 ′ .Figure 2h shows the [C i] 492 GHz line integrated intensity map in the LSR velocity range [+3, +14] km s −1 .

Pointed observations of rotationally excited lines
In addition to the molecular J=1-0 line maps, we observed several cloud positions (see Table 3 for the exact coordinates and details) in rotationally excited lines (J=2-1, 3-2, and 4-3).We obtained these observations also with the IRAM-30m telescope.We observed 14 positions representative of different cloud environments: cold and dense cores, filaments and their surroundings, (average spectrum) 30" 120" Notes.
(2), (3): Line intensity and line peak temperature of the average spectrum in the mapped area.( 4) and ( 5): Line luminosity in K km s −1 pc 2 and L ⊙ units.(6) Dense gas mass M dg to line luminosity ratio, where M dg =3.1×10 3 M ⊙ (mass at A V >8 mag).( 7) and ( 8): Percentage of the mapped area with 3σ line detections.( 9): Ratio of cloud areas with 3σ line detection after spatial smoothing.
In order to compare line intensities at roughly the same 30 ′′ resolution, we averaged small raster maps centered around each target position and approximately covering the area of a 30 ′′ diameter disk (Fig. F.1 in the Appendix shows our pointing strategy).The total integration time per raster-map was ∼1 h, including on and off integrations.The achieved rms noises of these observations, merging all observed positions of a given raster-map, are ∼22 mK (J=2-1), ∼20 mK (J=3-2), and ∼30 mK (J=4-3), per 0.5 km s −1 velocity channel.Table F.1 in the Appendix summarizes the frequency ranges observed with each backend, the HPBW, and the number of pointings of each raster map.
We analyzed these pointed observations with CLASS.We subtracted baselines fitting line-free channels with first or second order polynomial functions.We converted the intensity scale from antenna temperature, T * A , to main-beam temperature, T mb , as T mb = T * A × F eff /B eff , where F eff and B eff are the forward and beam efficiencies 3 .Figure 3 shows a summary of the spectra.Figures G.1 and G.2 show the complete dataset.
2.5.Herschel T d , A V , and G ′ 0 maps In addition to the molecular and atomic line maps, we also make use of the dust temperature (T d ) and 850 µm dust opacity (τ 850 µm ) maps fitted by Lombardi et al. (2014) on a combination of Planck and Herschel data from the Herschel Gould Belt Survey (HGBS) (André et al. 2010).In Appendix C we provide additional details on these maps.We estimated the (line of sight) visual extinction from the τ 850 µm dust opacity map following Pety et al. (2017): (1) By taking the τ 850 µm error map of Lombardi et al. (2014), we determine that the mean 5σ error of the A V map is about 0.8 mag.This value is slightly above our molecular line detection threshold (A V ≃ 0.3-0.4mag, see Fig. 4).Thus, we caution that one can probably not trust any A V -W trend below A V ≃ 0.8 mag.For each line of sight, we determined the FIR surface brightness, I FIR , from spectral energy distributions (SED) fits, by integrating: from λ = 40 to 500 µm.In this expression, B ν (T d ) is the blackbody function, τ ν =τ ν 850 µm (ν/ν 850 µm ) β is the frequency-dependent dust opacity (we adopt the same emissivity exponent as Lombardi et al. 2014), and T d is an effective dust temperature.
We estimate the strength of the far-UV (FUV) radiation field (6 < E < 13.6 eV), in Habing units (G ′ 0 ), from I FIR using: In this expression we assume that the FIR continuum emission arises from dust grains heated by stellar FUV and visible photons (Hollenbach & Tielens 1999).We use the notation G ′ 0 (meaning approximate G 0 ) because this expression is precise for a face-on PDR (e.g., it is valid for NGC 2024 and NGC 2023).Because of their edge-on geometry, Eq. ( 3) is less accurate for the Horsehead PDR and IC 434 front (although it provides the expected G 0 within factors of a few).In addition, Eq. (3) provides an upper limit to the actual G 0 toward embedded star-forming cores (at high A V ).These cores emit significant non-PDR FIR dust continuum.To directly compare our line emission maps with the A V , G ′ 0 , and I FIR maps, we also spatially smoothed these SED-derived maps to an angular resolution of 120 ′′ (Figs.2a and b).

Results
3.1.Spatial distribution of the HCN J = 1-0 emission, relation to other chemical species, and A V and G ′ 0 maps Figure 1 shows a composite RGB image of the mapped area (∼ 5 deg 2 = 250 pc 2 ).This image shows extended HCN J=1-0 Figure 2 shows the spatial distribution of the 12 CO, HCO + , HCN, and HNC J=1-0 integrated line intensities, W (also dubbed line surface brightness) at a common resolution of ∼2 ′ (∼0.2 pc, thus matching the angular resolution of the [C i] 492 GHz map in Fig. 2g).W(HCN J=1-0) refers the sum of the three HFS components.The emission from all species peaks toward NGC 2024.
The last column in Table 4 shows that spatial smoothing (increasing the line sensitivity at the expense of lower spatial resolution) allows us to detect HCN and HNC J=1-0 emission from a cloud area nearly four times bigger than from maps at ∼30 ′′ resolution.For CO J=1-0 (very extended emission) the recovered area is smaller.CO J=1-0 shows the most widespread emission.It traces the most extended and translucent gas, arising from 90% of the mapped area.HCO + and HCN J=1-0 are the next molecular lines showing the most extended distribution, 73% and 60% of the total observed area, respectively.On the other hand, HNC J=1-0 shows a similar distribution as C 18 O J=1-0 (Gaudel et al. 2023).
Table 4 provides the total line luminosity (L line ) from the mapped area in L ⊙ units.L line is the power emitted through a given line.It also provides L ′ line (in units of K km s −1 pc 2 ), with: where Ω is the solid angle subtended by the source area and W average is the average spectrum over the mapped area A. This last quantity is commonly used to express mass conversion factors (see Sect. 6.3) and it is also frequently used in the extragalactic context (e.g., Gao & Solomon 2004a;Carilli & Walter 2013).The 12 CO J=1-0 luminosity over the mapped area, ∼1.7 L ⊙ , is more than a hundred times higher than L HCO + 1−0 and L HCN 1−0 .Figures 2a and 2b show maps of visual extinction (A V ) and the approximate strength of the FUV radiation field G ′ 0 (see Sect. 2.5).Table 5 summarizes the median, average, and standard deviation values of the SED-derived parameters.The star-forming cores at the center of the NGC 2024 have the highest A V values, with a secondary peak toward NGC 2023 star-forming cores.The highest values of G ′ 0 correspond to cloud areas in the vicinity of the H ii regions NGC 2024 (G ′ 0 ≈ 104 ), with a contribution from the neighbor H ii region created by Alnitak star (G ′ 0 ≈ 10 3 ), NGC 2023 (G ′ 0 ≈ 10 3 ), IC 435 (G ′ 0 ≈ 10 2 ), and the ionization front IC 434 (G ′ 0 ≈ a few 10 2 ) that includes the iconic Horsehead Nebula.On the other hand, the easter part of the cloud shows low surface brightness I FIR emission compatible with G ′ 0 of a few to ≃ 10.The median G ′ 0 in the mapped region is 9. Figure 4 shows 2D histograms of the CO, HCN, HCO + , HNC J=1-0, and [C i] 492 GHz integrated line intensities as function of the visual extinction into the cloud 4 .The running median of the HCN J = 1−0 emission increases with extinction at A V > 3 mag, whereas the running median of the HNC J = 1-0 emission shows a similar change of tendency but at higher extinction depths A V > 5 mag.As HCN, the largest number of We note that the 5σ error of A V is ≃ 0.8 mag.Thus, one cannot trust any trend below this threshold.
HCO + J = 1−0 and [C i] 492 GHz line detections in the map occur at A V ≃ 3 mag.Atomic carbon, however, shows an approximate bimodal behavior with A V (it shows both bright and faint emission at high A V ).Indeed, while A V is the total visual extinction along each line of sight, we expect that in many instances the [C i] 492 GHz emission mostly arises from cloud rims close to the C 0 /CO transition (e.g., Hollenbach et al. 1991).On the other hand, lines of sight of large A V and very bright [C i] 492 GHz emission (such as NGC 2024) probably trace FUV-illuminated surfaces of multiple dense cores and PDRs along the line of sight.
Following Pety et al. (2017), Fig. 5a shows the fraction of total L line within a set of four visual extinction masks.The mask with A V >15 mag (∼1% of the total mapped area) represents the highest density gas associated with dense cores.The mask within the A V range 8 to 15 mag (∼3% of the mapped area) is right above the extinction threshold above which the vast majority of prestellar cores are found in molecular clouds (e.g., Lada 1992;Lada et al. 2010;Wu et al. 2010;Evans et al. 2020).Below this threshold, we create two masks to differentiate the emission associated with A V below 4 mag (translucent and PDR gas; ∼80% of the mapped area) and 4 < A V < 8 mag (intermediate cloud depths representing ∼16% of the mapped area).We find that more than half of the total CO J = 1-0 intensity arises from the lowest extinction mask A V <4 mag.Interestingly, about a 30% of the total HCN J = 1-0 emission arises from gas also at A V <4 mag.Most of the HCN and HNC J = 1-0 emission arises from regions at visual extinctions between 4 and 8 mag, and only 10% of the HCN emission arises from regions at very high visual extinctions, A V > 15 mag.Likewise, the HCN and HNC 2D histograms peak at A V lower than 3 mag (HCN) and 5 mag (HNC).This contrasts with the N 2 H + J=1-0 emission, which arises from cold and dense gas shielded from FUV radiation at A V > 15 mag (see Pety et al. 2017).For each molecular line, Fig. 5b shows the typical (the statistical mode) intensity W toward each of the four extinction masks.The CO J = 1-0 emission is bright (∼1 K km s −1 ) even at A V < 4 mag, and very bright (> 10 K km s −1 ) toward all the other masks (although optically thick).
The typical HCN, HNC, and HCO + J=1-0 line intensities are above 1 K km s −1 for A V > 15 mag (dense gas).For lower A V , the lines are fainter but detectable.Since the translucent gas spans much larger areas than the dense gas (96% of the mapped cloud is A V < 8 mag, 80% at A V < 3 mag), in many instances it is the widespread and faint extended emission that dominates the total luminosity.We stress that ∼70% of the HCN J = 1-0 line luminosity in Orion B arises from gas at A V < 8 mag (and 50% of the FIR dust luminosity).Table 4 summarizes the line intensities and line luminosities over the mapped area.
Figure 5c shows the cumulative fractions of the integrated intensities for CO, HCO + , HCN, HNC J=1-0 as a function of A V .The cumulative distributions are different for each species.We define the visual extinction that contains 50% of the total integrated line intensity as the characteristic A V , such as W(A V < A char V )=50% (e.g., Barnes et al. 2020).We find that the characteristic A char V for CO J=1-0 is 3.8 mag, which implies that 50% of the CO total intensity arises from gas below A V = 3.8 mag.For HCO + , HCN, and HNC J = 1-0 lines, we find A char V of 5.0, 5.8, and 6.7 mag, respectively.These values agree with recent studies of the star-forming regions Orion A and W49 (Kauffmann et al. 2017;Barnes et al. 2020).

HCN/CO, HCN/HNC, HCN/HCO + , and [C i]/CO line intensity ratio maps
The spatial distribution of the HCN J = 1-0 line emission compared to that of other molecules provides information about the origin and the physical conditions of the HCN-emitting gas. Figure 6 shows the HCN / 12 CO J=1-0, HCN / HNC J=1-0, and HCN / HCO + J=1-0 integrated line intensity ratios.We generated these maps by taking only line signals above 3σ for each species (i.e., we show regions where the emission from both species spatially coexist along the line of sight).In addition, Fig. 6d shows a map of the [C i] 492 GHz/CO J=1-0 integrated line intensity ratio5 ).Table 6 summarizes the average and median line intensity ratios in the mapped region.-HCN/CO J = 1-0: The average line intensity ratio is 0.015, with a standard deviation of 0.023.In the inner regions of the cloud, close to the Cloak, Orion B9, Hummingbird, and Flame filaments, the ratio increases with A V (shown in contours).We also find high line intensity ratios (∼ 0.1) in the FUV-illuminated cloud edges (see discussion in Sect.6.2).
-HCN/HNC J = 1-0: The average line intensity ratio is 3.1, with a standard deviation of 1.2.The lowest ratios, ∼0.5-0.9, appear in cold and low I FIR regions such as the Cloak and Orion B9.
-HCN/HCO + J = 1-0: The average line intensity ratio is 0.9, with a standard deviation of 0.4.In general, this line ratio displays small variations across the cloud.The Cloak, the center of NGC 2024, the Flame Filament, and the Horsehead show a line intensity ratio above one (reddish areas in Fig. 6c).All these regions host starless and prestellar cores (Könyves et al. 2020).-[C i] 492 GHz/CO J=1-0: The average line intensity ratio is 0.20, with a standard deviation of 0.26.In PDR gas, this ratio is roughly inversely proportional to the gas density (see e.g., Kaufman et al. 1999).We find the highest ratios, above one, toward the FUV-illuminated edges of the cloud.
We also investigate the possible spatial correlations of the above line intensity ratios with the SED derived parameters G ′ 0 , T d , T peak (CO), and A V .Only the HCN / HNC J = 1-0 line intensity map shows a (weak) monotonic correlation with G ′ 0 (Spearman correlation rank of 0.6; see Table 6).This spatial correlation is not linear (the Pearson correlation rank is 0.5 in log-log scale and 0.008 in linear scale) but suggests a connection between the HCN/HNC abundance ratio and the FUV radiation field.Figures B.1 and B.2 show 2D histograms of the studied line intensity ratios as function a of A V and I FIR , respectively.

HCN excitation, radiative transfer models, and gas physical conditions
In this section we analyze the large scale HCN J = 1-0 emission in detail.We, (i) derive excitation temperatures (T ex ) and HCN column densities, N(HCN), using the LTE-HFS fitting method, (ii) analyze the anomalous HCN J=1-0 HFS emission, (iii) determine the physical conditions of the widespread and extended HCN J = 1-0 emitting gas, and (iv) derive rotational temperatures, T rot , and N(HCN) in a sample of representative positions observed in rotationally excited HCN and H 13 CN lines.In order to determine all these parameters at the highest possible spatial resolution, throughout all this section we make use of maps and pointed observations at an effective 30 ′′ resolution (∼0.06 pc).

HCN column density and T ex using the LTE-HFS method
Firstly, we determine T ex (J = 1-0) and the opacity-corrected column density N τ,corr (HCN) by applying the LTE-HFS fitting method in CLASS 2 (Appendix D.1).This method uses as input the line separations and 1:5:3 intrinsic line strengths of the J = 1-0 HFS components.The LTE-HFS fitting method assumes that: (i) all HFS lines have the same T ex and linewidth ∆v, and (ii) the velocity-dependent line opacities have Gaussian profiles.Thus, one can express the continuum-substracted main beam temperature at a given velocity v of the J = 1-0 line profile as: where τ(v) is the sum of the HFS line opacities: In the above expressions, τ 0 i is the opacity of each HFS component i at (each) line center (v 0 i ), and ϕ(v − v 0 i ) is a Gaussian profile centered at v 0 i .In the LTE-FTS fitting method, one fixes the sum of all HCN J = 1-0 HFS line center opacities, τ 0 , following their intrinsic line strengths: In the Rayleigh-Jeans regime, J(T ex ) → T ex .Thus, the LTE-HFS fitting method returns T ex and τ 0 as outputs.We use these parameters to derive N τ,corr (HCN).In order to obtain satisfactory fits, we applied this method to the brightest regions, those T peak mb (HCN J = 1-0 F=2-1, ≥ 0.5 K = 5σ), associated with the main cloud velocity component at v LSR ≃10 km s −1 .

Large-scale anomalous HCN J = 1-0 HFS emission
To study the HCN J = 1-0 emission in more detail we extracted the intensity and linewidth of each HFS component individually (by fitting Gaussians).Figures 7c and 7d show the spatial distribution of the HFS line intensity ratios, R 02 =W(F=0-1)/W(F=2-1) and R 12 =W(F=1-1)/W(F=2-1), respectively, and Fig. 8a shows their histograms.In addition, Fig. 8b shows the histograms of the HFS linewidth ratios, R ∆v 02 =∆v(F=0-1)/∆v(F=2-1) and R ∆v 12 =∆v(F=1-1)/∆v(F=2-1).The red curve in Fig. 8a shows the expected R 02 and R 12 ratios in LTE as line opacities increase.We note that the majority of observed ratios in the map are far from the LTE curve.Indeed, the histogram of the intensity ratio R 02 peaks at 0.21, with a median value of 0.25 whereas the histogram of the intensity ratio R 12 peaks at 0.52, with a median value of 0.56.Therefore, the intensity ratio R 12 is typically anomalous6 over large cloud scales.
Non-LTE radiative transfer models including line overlap effects show that these anomalous intensity ratios imply that lines are optically thick and that a single T ex does not represent the excitation of these HFS levels (Gonzalez-Alfonso & Cernicharo 1993; Goicoechea et al. 2022).This questions the precision of the parameters obtained from the LTE-HFS fitting method.To illustrate this, Fig. D.1 shows the (poor) best LTE-HFS fit to the HCN J=1-0 HFS lines toward the Horsehead PDR.
The linewidth of the faintest F=0-1 HFS component in the map ranges from ∼1 to ∼2 km s −1 (see also Table G.1).These linewidths are broader than the narrow linewidths, ∼0.5 km s −1 , typically observed in Orion B toward dense and FUV-shielded cold cores in molecules such as H 13 CO + (e.g., Gerin et al. 2009).Thus, HCN J=1-0 traces a different cloud component.Figure 8b shows the histogram of the HFS linewidth ratios R ∆v 02 and R ∆v 12 .They peak at 0.75 and 0.91 respectively, with median values of 0.91 and 1.03.That is, the linewidths of the different HFS components are not the same and line opacity broadening matters.Non-LTE models including line overlap predict these anomalous linewidth ratios, R ∆v 1, when HFS lines become optically thick (e.g., see Fig. 3 of Goicoechea et al. 2022).

Physical conditions of the extended low surface brightness HCN J=1-0 emitting gas
Here we compare the observed line integrated intensities W(HCN J = 1-0) with a grid of non-local and non-LTE radiative transfer models calculated by Goicoechea et al. (2022).These models include HFS line overlaps and use new HFS-resolved collisional rate coefficients for inelastic collisions of HCN with para-H 2 , ortho-H 2 , and electrons in warm gas.
The grid of single-component (T k =60, 30, and 10 K) staticcloud (no velocity field) models encompass the HCN column densities predicted by our chemical models (Sect.5) and typically observed in Orion B (Fig. 7b): N(HCN)=10 13 cm −2 , representative of optically thin or marginally optically thick HCN J=1-0 HFS lines, and N(HCN)=10 14 cm −2 , representative of bright optically thick lines.The range in gas densities n(H 2 ) goes from  and R 12 stands for W(F=1-1)/W(F=2-1).The red curve in panel (a) shows the expected LTE ratios as line opacities increase.The red star marks the non-anomalous ratios in the optically thin limit τ → 0 (1σ is the standard deviation relative to the mean line ratios).
∼107 cm −3 , only relevant to hot cores and protostellar envelopes, to nearly 10 2 cm −3 , relevant to the most extended and FUVilluminated component of GMCs.As we are mostly interested in this component, these models compute the HCN excitation for three different electron abundances: χ e = 10 −4 , 2×10 −5 , and 0. Figure 9 shows model results (continuous curves) in the form of predicted line intensities W(HCN J = 1-0) as a function of n(H 2 ).
The right panels in Fig. 9 show histograms with the distribution of W(HCN J = 1-0) detections (> 3σ) in individual pixels of the map.The mean (median) intensity 7 in these pixels is 1.4 K km s −1 (0.97 K km s −1 ).The pink shaded area in Fig. 9 represents the 1σ dispersion relative to the mean W(HCN J = 1-0) value.However, while about 70% of the observed intensities have a value below the mean, less than 1% of the observed intensi-ties have a value above 10 K km s −1 (very bright HCN emission).In the following we take W(HCN J = 1-0) = 1 K km s −1 as the reference 7 for the extended cloud emission.Models with N(HCN)=10 13 cm −2 (Fig. 9a) encompass this W(HCN J = 1-0) intensity level.The gas temperature in this cloud component is T k ≃ 30 to 60 K (translucent gas and UV-illuminated cloud edges; see specific PDR models in Sect.5).Using N(HCN) = 10 13 cm −2 and neglecting electron collisional excitation (χ e = 0) we determine an upper limit to the gas density of n(H 2 ) ≃ (1-3) × 10 4 cm −3 .
On the other hand, the strongest HCN-emitting regions in Orion B, those with W(HCN J = 1-0) > 6 K km s −1 , only represent ∼15% of the total HCN J = 1-0 luminosity in the map.This bright HCN emission can only be reproduced by models with N(HCN)=10 14 cm −2 and higher gas densities, n(H 2 ) > 10 5 cm −3 .

Rotationally excited HCN and H 13 CN toward representative cloud environments in Orion B
To complement our analysis of the HCN J = 1-0 emission at large spatial scales, and to determine more accurate HCN column densities, here we analyze our multiple-J HCN and H 13 CN line observations toward 14 positions in Orion B (see Table 3 for a brief explanation).Figure 3 shows a selection of the spectra.We detect HCN J = 2-1 and J=3-2 toward all positions, and HCN J = 4-3 toward five of the 14 observed positions (Fig. G.1 in the Appendix shows the spectra of all observed positions).
The HCN J=2-1 transition has six HFS lines that, for the narrow line widths in Orion B, blend into three lines with apparent relative intensity ratios ∼1:9:2 in the LTE and optically thin limit (red vertical lines in Fig. 3).The HCN J=3-2 transition also has six HFS lines.Only the central ones are blended and cannot be Ratio satellite(R)/main spectrally resolved.This gives the impression of three lines with relative intensity ratios 1:25:1 in the LTE and optically thin limit (e.g., Ahrens et al. 2002;Loughnane et al. 2012).We term these three apparent components (blueshifted, central, and redshifted) of the J=2-1 and J=3-2 rotational lines as "satellite (B)," "main," and "satellite (R)," respectively.We recall that these overlapping lines in the HCN J = 2-1 and 3-2 transitions are responsible of the observed anomalous HCN J = 1-0 HFS line intensity ratios (Goicoechea et al. 2022, and references therein).Blue and red curves in Fig. 11 show the expected HCN J = 2-1 and J = 3-2 HFS intensity ratios satellite (R)/main versus satellite (B)/main in LTE as line opacities increase.Only when τ 2−1 → 0 and τ 3−2 → 0, one should detect the ∼1:9:2 and ∼1:25:1 HFS ratios.The filled dots in Fig. 11 show the observed ratios (summarized in Table D.1 of the Appendix) toward the sample of representative positions that could be fitted with three Gaussian lines.This plot shows that several HCN J = 2-1, and specially J = 3-2, HFS line intensity ratios do not lie on the LTE curves even for elevated line opacities.That is, the emission of rotationally excited HCN lines can also be anomalous.

HCN and HNC rotational diagrams
Here we estimate the degree of excitation (by determining rotational temperatures, T rot ) and column densities of HCN and HNC toward the sample of representative positions.We analyze the detected rotationally excited HCN (up to J = 4-3) and HNC (up to J = 3-2) lines by constructing rotational population diagrams in Appendix E (Goldsmith & Langer 1999).We derive N(HCN), and N(HNC) ignoring their HFS structure (i.e., only the total line intensity of each rotational transition matters).This is a valid approximation to obtain T rot from observations of multiple-J lines.We derive the HCN column density and rotational temperature under the assumption of optically thin emission (N thin and T thin rot ).We also determine their opacity-corrected values (N τ,corr and T τ,corr rot ) by using the H 13 CN line intensities (see Fig. G.1) and assuming that the emission from HCN and H 13 CN lines arise from the same gas.Except for the brightest position #1, the derived HCN rotational temperatures range from 4 to 10 K (i.e.subthermal excitation), and N τ,corr (HCN) ranges from 5×10 12 to 3.4×10 13 cm −2 .Table 7 summarizes the derived values and Appendix E shows the resulting rotational diagram plots.We employ the same methodology for HNC and HN 13 C. Rotational temperatures are also low, from 5 to 11 K. HNC column densities range from ∼10 12 to 1.6×10 13 cm −2 (see Table E.1).

Comparison with single-component non-LTE models
Most of the observed representative positions likely have velocity, temperature, and density gradients (specially prestellar cores and protostars).However, carrying out a complete, sourceby-source, radiative transfer analysis is beyond the scope of this study (more focused on the extended cloud component).
Here we just used the outputs of the grid of single-component and static models computed by Goicoechea et al. (2022), and presented in Sect.4.3, to estimate the physical conditions (gas temperature and densities) compatible by the detected rotationally excited HCN line emission.We compared the observed line intensity ratios R J 21 =W(HCN J=2-1)/W(HCN J=1-0) and R J 31 =W(HCN J=3-2)/W(HCN J=1-0) summarized in Table 7 with the models shown in Fig. 10 of Goicoechea et al. (2022).As an example, the observed line ratios toward the Horsehead PDR are R J 21 = 0.5 and R J 31 = 0.13.These ratios can be explained by models with T k = 30-60 K and n(H 2 ) of a few 10 4 cm −3 .Position #14 shows the lowest line ratios of the sample, R J 21 = 0.3 and R J 31 = 0.06, which is consistent with n(H 2 ) of a few 10 4 cm −3 .On the other hand, the observed line intensity ratios toward position #1 (center of NGC 2024) are R J 21 = 0.9 and R J 31 = 1.2.In this position we derive the highest HCN rotational temperature (∼38±10 K).The observed R J 31 > R J 21 intensity ratios are consistent with the presence of dense gas, n(H 2 ) ≥ 10 6 cm −3 .
These results roughly agree with the spatial correlation between the HCN/HNC J = 1-0 integrated line intensity ratio and G ′ 0 in the entire region.Figure 12 shows a 2D histogram of the observed W(HCN)/W(HNC) J = 1-0 intensity ratio as a function of G ′ 0 in the mapped region.The running median HCN/HNC J = 1-0 intensity ratio increases from ≃ 1 at G ′ 0 ≃10 to ≃ 3 at G ′ 0 ≃ 200.For higher values of G ′ 0 , the running median intensity ratio stays roughly constant at ≃ 3-4.We estimate that the higher HCN J = 1-0 line opacity toward these bright positions (at least τ ≃ 5-10, see Table D.1) compared to that of HNC J = 1-0 (on the order of τ ≃ 1-3,Table E.1) contributes to the observed constancy of the line intensity ratio.
In FUV-illuminated environments, the strength of the radiation field influences the gas chemistry and determines much of the gas temperature and electron abundance (see Sect. 5).At a given abundance, HNC responds more weakly to electron excitation than HCN.In particular, the HCN J = 1-0 critical fractional abundance of electrons (χ * cr,e in Table 1) is a factor of ∼ 4 lower than that of HNC J = 1-0.Moreover, HNC is typically less abundant in FUV-illuminated gas (Sect.5).
In addition, as HCN and HNC rotational lines become optically thick, HFS line overlap effects become important for both species.However, their relative effect as a function of J are differ-Table 8. HNC rotational temperatures, HCN/HNC column density, and line intensity ratios toward selected positions in Orion B.

Pos.
T rot (HNC) Notes.† The lower value of the ratio adopts column densities obtained from rotational diagrams in the optically thin limit.The higher value of the ratio implements a line opacity correction (see Tables 7 and E.1) .ent (Daniel & Cernicharo 2008).These aspects ultimately drive their excitation and contribute to the slightly different rotational temperatures we infer for the two species.Still, modeling the HFS resolved excitation of HNC is beyond the scope of our study.Future determinations of HFS-resolved HNC-H 2 inelastic collision rate coefficients will make such detailed studies feasible.

HCN and HNC chemistry in FUV-illuminated gas
To guide our interpretation of the extended HCN J = 1-0 emission, here we reassess the chemistry of HCN, HNC, and related species in FUV-illuminated gas.The presence of FUV photons, C + ions, C atoms, and high electron abundances triggers a distinctive nitrogen chemistry, different to that prevailing in cold and dense cores (e.g., Hily-Blant et al. 2010) shielded from FUV radiation.Sternberg & Dalgarno (1995), Young Owl et al. (2000) and Boger & Sternberg (2005) previously studied the formation and destruction of HCN in FUV-irradiated gas.
Here we used an updated version of the Meudon PDR code (Le Petit et al. 2006) that implements a detailed treatment of the penetration of FUV photons (Goicoechea & Le Bourlot 2007) and includes v-state-dependent reactions of FUV-pumped H 2 (v) (hereafter H * 2 ) with neutral N atoms leading to NH + H (Goicoechea & Roncero 2022), as well as reactions of o-H 2 and p-H 2 with N + ions, leading to NH + + H (Zymak et al. 2013).
We also included the isomerization reaction: ).In our models we initially adopt E b = 1200 K (see Graninger et al. 2014).
We also included the isomerization reaction: which is generally not included in dark cloud chemical models but plays a role in FUV-illuminated gas.We adopt a rate coefficient k(T ) = 1.6×10 −10 cm 3 s −1 and no energy barrier (from calculations by Loison et al. 2014;Loison & Hickson 2015).In order to accurately treat the photochemistry of HCN and HNC, our models explicitly integrate their photodissociation and photoionization cross sections at each cloud depth.We use the wavelength-dependent cross sections tabulated in Heays et al. (2017), which include a theoretical calculation of the HNC photodissociation cross section by Aguado et al. (2017).For the interstellar radiation field, this cross section implies that HNC is photodissociated about two times faster than HCN.
We adopted a H 2 cosmic ray ionization rate ζ CR of 10 −16 s −1 , typical of translucent gas and cloud edges in the disk of the galaxy (e.g., Indriolo et al. 2015).We assumed standard interstellar dust grain properties and extinction laws.We ran photochemical models adapted to the illumination conditions and gas densities at large scales in Orion B. In particular, we adopted a representative FUV field of G 0 = 100, typical of the Horsehead edge, the IC 434 ionization front, and close to the mean G 0 in the mapped area (see Table 5).Nonetheless, we note that adopting lower G 0 values basically shifts the abundance profiles to lower cloud depths but the following chemical discussion remains very similar.Figure 13 shows the predictions of constant density models, with n H = 5×10 3 cm −3 (left panels) and n H = 5×10 4 cm −3 (right panels).Figures 13a and 13b show the predicted column density ratios (upper panels) and abundance 8 profiles (lower panels) as a function of cloud depth, in mag of visual extinction 9 .
We determine molecular column densities at a given cloud depth A V (or cloud path length l) by integrating the predicted depth-dependent abundance profile, x(species), from 0 to A V : where x(l) is the species abundance, with respect to H nuclei 7 , at a cloud path length l.

Chemistry at cloud edges, A V < 4 mag
The red shaded areas in Fig. 13 show model results for A V < 4 mag typical of FUV-illuminated cloud edges.FUV photons drive the chemistry in these translucent layers that host the C + to C transition and have high electron abundances: from x e ≃ x(C + ) ≃ 10 −4 to x e ≃ 10 −6 depending on A V and G 0 /n H .To simplify our chemical discussion, Fig. 14 summarizes the network of dominant chemical reactions at A V < 4 mag.Wherever C + is abundant, reactions of CH 2 with N atoms dominate the formation of HCN and HNC, as shown by the red curves in Fig. 13c and 13d.These two figures show the contribution (in percent) of the main HCN and HNC formation and destruction reactions as a function of cloud depth.The second most important path for HCN and HNC formation at A V < 4 mag is HCNH + dissociative recombination.HCN and HNC destruction is governed by photodissociation and by reactions with C + .Their exact contribution depends on the gas density and G 0 .Our model assumes that the rate coefficient of reactions C + + HCN and C + + HNC, as well as the branching ratios of dissociative recombination HCNH + + e → HCN/HNC + H, are identical for both isomers (e.g., Semaniak et al. 2001).Therefore, the N(HCN)/N(HNC) column density ratio at A V < 4 mag basically depends on the differences between HCN and HNC photodissociation cross sections.Wherever photodissociation dominates (e.g., green curves in Figs.13c and 13d), we predict N(HCN)/N(HNC) ≃ 1.5-2.5.These values are consistent with the ratio inferred toward the rim of the Horsehead, a nearly edge-on PDR (see Table 8).
Neutral atomic carbon reaches its abundance peak at A V ≃ 1-3 mag (depending on n H ), which is relevant to understand the nature of the extended [C i] 492 GHz emission in Orion B (Fig. 2h).The isomerization reaction C + HNC → HCN + C as well as reaction N + HCO → HCN + O provide additional formation paths for HCN at A V < 4 mag (black and gray curves in Figs.13c and 13d).These two reactions enhance the HCN/HNC column density ratio to ∼5-15 at A V ≃ 3 mag.These ratios agree with the high N(HCN)/N(HNC) ratios we infer toward NGC 2024 (e.g., positions #1 and #2 in Table 8).
We end this subsection by giving the HCN and HNC column densities predicted by the n H = 5×10 3 cm −3 (5×10 4 cm −3 ) models at A V = 4 mag: N(HCN) = 4.5 × 10 12 cm −2 (2.4 × 10 12 cm −2 ) 8 Because at low A V the abundance of H atoms can be significant, in this Section we provide the abundance of a given species (x) with respect to H nuclei.That is, x(species) = n(species) / n H , where n H = n(H) + 2n(H 2 ).If the abundance of H atoms is negligible, then x(species) = 0.5 χ(species).
9 In these 1D PDR models, the cloud depth or shielding (A V in mag of visual extinction) refers to the extinction normal to the cloud surface and parallel to the FUV illumination direction.In general, this extinction is different from A V determined from observations and the dust SED along a given line of sight.Only for a face-on cloud (with the illuminating stars in the observed line of sight) both magnitudes are equivalent.and N(HNC) = 1.8 × 10 12 cm −2 (4.5 × 10 11 cm −2 ).These column densities are representative of extended and translucent gas.

Intermediate depths, 4 mag < A V < 8 mag
The yellow shaded areas in Fig. 13 show model results for 4 mag < A V < 8 mag.In these intermediate-depth cloud layers, the FUV flux diminishes and most carbon becomes locked in CO. Figure 15 summarizes the dominant chemical reactions in these molecular cloud layers.As shown in Figs.13c and 13d, HCN and HNC are now predominantly destroyed by reactions with abundant molecular and atomic ions (H + 3 and C + at low densities, H + 3 , HCO + , and H 3 O + at higher densities).The main formation route for HCN and HNC switches to HCNH + dissociative recombination (blue curves in Figs.13c and 13d).For equal branching ratios (Semaniak et al. 2001), the predicted N(HCN)/N(HNC) column density ratio is ≃ 1-2.Indeed, our observations of Orion B reveal N(HCN)/N(HNC) ratios and W(HCN J=1-0)/W(HNC J=1-0) line intensity ratios of ≃ 1-2 toward positions with low G ′ 0 values (see Table 8 and Fig. 6).The abundance of HCNH + , the precursor of HCN and HNC at large A V (Figs. 13c and 13d), depends on the H + 3 abundance, which is sensitive to the penetration of FUV radiation and to the cosmic ray ionization rate.The H + 3 abundance is higher at lower n H because the higher penetration of FUV radiation reduces the abundances of the neutral species (CO, O, N 2 , and S) that destroy H + 3 .In addition, the H + 3 abundance scales with ζ CR .We run a few models with ζ CR rates significantly lower than assumed in Fig. 13 and indeed they produce lower HCNH + abundances than those shown in Figs.13a and 13b.This leads to higher HCN/HNC abundance ratios (see also Behrens et al. 2022)  N + HCO → HCN + O, (11) becomes more important than HCNH + dissociative recombination.Reaction ( 11) is often quoted in chemical networks (Mitchell 1984;Young Owl et al. 2000) but no detailed study seems to exist.We end this subsection by providing HCN and HNC column densities predicted at A V = 8 mag.The PDR model with n H = 5×10 3 cm −3 (5×10 4 cm −3 ) predicts N(HCN) = 6.2 × 10 13 cm −2 (6.4 × 10 12 cm −2 ) and N(HNC) = 5.2 × 10 13 cm −2 (3.2 × 10 12 cm −2 ).These column densities encompass the range of HCN (see Table 7) and HNC (see Table E.1) column densities we infer toward the observed sample of representative positions in Orion B.

On HNC destruction reactions
Previous studies invoked that the isomerization reaction H + HNC → HCN + H determines a temperature dependence of the N(HCN)/N(HNC) ratio in warm molecular gas (Schilke et al. 1992;Herbst et al. 2000;Graninger et al. 2014;Hacar et al. 2020).In our PDR models, the gas temperature is T ≃ 50 K at A V ≃ 1 mag, and T ≃ 15 K at A V ≃ 4 mag (upper panels of Fig. 13a and 13b).We run the same two models adopting E b = 200 K for reaction (8) and found that reducing E b has little effect on the predicted N(HCN)/N(HNC) ratio (blue continuous curves in the upper panels of Figs.13a and 13b).Even at A V < 2 mag, where the abundance of H atoms and T are moderately high, the N(HCN)/N(HNC) ratio increases by less than 30 % (i.e., the effects are very small).We note that in all these models, HCN and HNC photodissociation, as well as C + HNC → HCN + C reactions, are faster than the isomerization reaction H + HNC (see Figs. 13c and 13d).
We run a more extreme model adopting E b = 0 K.That is to say, as if reaction (8) was barrierless.Only in this case, the isomerization reaction H + HNC → HCN + H would dominate HNC destruction (specially at large A V ), increasing the N(HCN)/N(HNC) ratio.However, this choice of E b results in very low HNC column densities, 2×10 12 cm −2 and 3×10 11 cm −2 at A V = 8 mag for n H = 5×10 3 cm −3 and 5×10 4 cm −3 , respectively.These N(HNC) values are much lower than the N(HNC) column densities we infer from observations (Table E.1).In addition, models with E b = 0 K would imply very high N(HCN)/N(HNC) = 30-75 ratios, something not seen in our observations (Table 8).
Some studies also suggest that in cold molecular gas, reaction HNC + O → CO + NH dominates HNC destruction, and thus it controls the HCN/HNC abundance ratio if the energy barrier of this particular reaction is low, E b ≃ 20-50 K (Schilke et al. 1992;Hacar et al. 2020).However, these values are much lower than the expected theoretical barrier (A. Zanchet, priv.comm. and Lin et al. 1992).Overall, our observational results are more consistent, at least for the extended cloud emission, with a greater dependence of the N(HCN)/N(HNC) ratio on the FUV radiation field (as suggested in planetary nebulae, Bublitz et al. 2019Bublitz et al. , 2022)).

Discussion
In this section we discuss the nature of the extended HCN J = 1-0 emission observed in Orion B and its relation to other species.We conclude by comparing the observed line intensity vs. FIR dust continuum intensity scalings with the line luminosity vs. SFR scaling laws typically inferred in extragalactic studies.
6.1.The origin of the extended HCN J=1-0 emission: weak collisional excitation vs. scattering The existence of a widespread HCN J = 1-0 emission component in low density gas, weakly collisionally excited, but enhanced by electron collisions (see Sect. 4.3), may affect the interpretation of the extragalactic relationship HCN luminosity versus SFR.Alternatively, the extended HCN J = 1-0 emission we observe in Orion B might arise from photons emitted in dense star-forming cores that become resonantly scattered by halos of low density gas.This seems to be the case, albeit at much smaller spatial scales, in dense cores inside cold dark clouds shielded from stellar FUV radiation (e.g., Langer et al. 1978;Walmsley et al. 1982;Cernicharo et al. 1984b;Gonzalez-Alfonso & Cernicharo 1993).
The above two scenarios lead to different HCN J = 1-0 HFS line intensity ratios (see predictions by Goicoechea et al. 2022), which can be tested on the basis of HFS resolved observations of the extended gas emission in GMCs.In particular, if the observed HCN J = 1-0 HFS photons arise from dense gas and become resonantly scattered by interacting with a low density halo, then both the R 02 and R 12 HFS line intensity ratios should be very anomalous.That is, R 02 < 0.2 and R 12 < 0.6.On the other hand, if the HCN J = 1-0 emission intrinsically arises from low density gas, far from dense cores, models predict that weak collisional excitation drives the HFS intensity ratios to R 02 ≳ 0.2 and R 12 ≲ 0.6.
Figure 8a shows that the most common HCN J = 1-0 HFS line intensity ratios in Orion B are R 02 ≳ 0.2 and R 12 < 0.6 (Fig. 7).Hence, the very anomalous ratios predicted by the scattering halo scenario are rarely encountered at large scales.Therefore, we conclude that the extended HCN J = 1-0 emission in Orion B is weakly collisionally excited, and it mostly arises from low density gas.In particular, we determined n(H 2 ) of several 10 3 cm −3 to 10 4 cm −3 (see Sect. 4.3).This result contrasts with the prevailing view of HCN J = 1-0 emission as a tracer of dense gas (e.g., Gao & Solomon 2004a,b;Rosolowsky et al. 2011;Jiménez-Donaire et al. 2017, 2019;Sánchez-García et al. 2022;Rybak et al. 2022).Extragalactic studies frequently interpret the HCN/CO J = 1-0 line luminosity ratio as a tracer of the dense gas fraction (e.g., Lada 1992;Gao & Solomon 2004b,a;Usero et al. 2015;Gallagher et al. 2018;Jiménez-Donaire et al. 2019;Neumann et al. 2023).This interpretation assumes that CO J = 1-0 line emission is a tracer of the bulk molecular gas, whereas HCN J = 1-0 traces dense gas in star-forming cores (at high A V ).Normal galaxies have low luminosity ratios L HCN /L CO = 0.02-0.06while luminous and ultraluminous galaxies have L HCN /L CO > 0.06.By contrast, Helfer & Blitz (1997) argue that the HCN/CO intensity ratio could measure the total hydrostatic gas pressure.
Figure 16a shows a 2D histogram of the HCN/CO J =1-0 line intensity ratios in Orion B as a function of A V .The 2D histogram shows a bimodal behavior.There is a first branch at A V > 3 mag where W(HCN)/W(CO) J =1-0 increases with extinction (the assumed behavior in extragalactic studies).The running median W(HCN)/W(CO) J =1-0 ratio increases from ≳ 0.02 (at A V ≃ 8 mag) to ∼ 0.1 (dense cores at larger A V ).In addition, there is a second branch at A V < 3 mag where W(HCN)/W(CO) J =1-0 increases with decreasing extinction.This is somehow unexpected, because the running median intensity ratio reaches high values, ≳ 0.1, in diffuse gas at A V ≃ 1 mag.
Fig. 6a shows the spatial distribution of the HCN/CO J = 1-0 intensity ratios in Orion B. The ratio is indeed high toward the dense gas in filaments and cores.In addition, W(HCN)/W(CO) J =1-0 also increases toward the east rim of the cloud that borders the ionization front IC 434.Owing to the roughly edge-on geometry with respect to the illuminating stars, we can easily spatially resolve these FUV-illuminated cloud edges (high χ e ) from the more shielded cloud interior.This picture agrees with HCN J = 1-0 emission arising from extended and relatively low density gas, n(H 2 ) ≤ 10 4 cm −3 , in GMCs illuminated by FUV radiation, and being boosted by electron excitation.This extended cloud component must be common in GMCs that host young massive stars, or have massive stars in their vicinity.

Cloud porosity to FUV radiation: HCN 1-0 emission from high electron abundance gas traced by [C ii] 158 µm and extended [C i] 492 GHz emission
The ionization fraction in cloud edges and in gas translucent to FUV-radiation is high.It starts at χ e ≃ a few 10 −4 , where the electron abundance is controlled by the photoionization of carbon atoms, thus leading to χ e ≃ χ(C + ) at A V ≲ 2 mag.These cloud layers emit bright FIR [C ii] 158 µm fine-structure line emission.Slightly deeper inside the molecular cloud, at A V ≲ 3 mag, the flux of FUV photons decreases to the point where the gas becomes fully molecular, and neutral atomic carbon (C 0 ) becomes more abundant than C + (see PDR models in Figs.13a and 13b).Our models predict χ e ≳ 10 −5 at the C 0 abundance peak, where the [C i] 492 GHz line emission reaches its intensity peak.
Figure 17a shows a [C ii] 158 µm line emission map of the Horsehead nebula and the ionization front IC 434 observed with SOFIA (Pabst et al. 2017) and convolved to the 30 ′′ resolution of the ORION-B maps.The C + map shows faint [C ii] 158 µm emission from the (nearly edge-on) molecular PDR at the rim of the Horsehead.It also shows bright [C ii] 158 µm emission from the neutral atomic PDR, χ(H) ≫ χ(H 2 ) at A V < 1 mag, that delineates the edge of IC 434 and shows very little CO emission (e.g., Bally et al. 2018).Fig. 17c shows a closer look to the HCN/CO J = 1-0 line intensity ratio.The ratio is particularly high, ≥ 0.12 (green contours), toward the FUV-illuminated cloud edge.This area matches the [C ii] 158 µm emission from the rim of the Horsehead.As n(H 2 ) is a few 10 4 cm −3 (e.g., Pabst et al. 2017) and χ * cr, e (HCN J = 1-0) < χ e ≃ χ(C + ) ≃ 10 −4 , electron excitation boosts the HCN emission (see Fig. 10), and thus the HCN/CO J = 1-0 line intensity ratio.
Figure 17b shows a map of the [C i] 492 GHz line emission around the Horsehead nebula observed with Caltech Submillimeter Observatory (Philipp et al. 2006) and smoothed to 30 ′′ resolution.The HCN J = 1-0 emission nicely follows that of [C i] 492 GHz.This agrees with the widespread nature of neutral atomic carbon, and with the similar spatial distribution of [C i] 492 GHz and HCN J = 1-0 emission seen at much larger scales (cf., the complete Orion B maps in Fig. 2h).This observational result indicates that C 0 coexists with HCN in large areas of the cloud, which implies moderate ionization fractions, χ e ≳ 10 −6 to several 10 −5 , in gas where [C i] 492 GHz and HCN J = 1-0 emissions coexist.
Since the spatial and velocity distribution of the large-scale [C i] 492 GHz and 13 CO J= 1-0 emission are very similar (Ikeda et al. 2002), the presence of C 0 cannot be restricted to cloud edges (A V < 3 mag).Otherwise Fig. 2h would only show bright [C i] 492 GHz emission parallel to the IC 434 front associated with the rims of all nearly edge-on PDRs such as the Horsehead (zoomed in Fig. 17).Instead, the [C i] 492 GHz emission is widespread and extended through the cloud.We find that [C i] 492 GHz also linearly correlates with the HCO + , HCN, and 13 CO J = 1-0 emission (Pearson coefficients of 0.80, 0.79, and 0.73 respectively).These correlations include many positions at A V > 3 mag (60% of [C i] 492 GHz detections, and 70% of total [C i] 492 GHz luminosity, see Fig. 4).Therefore, C 0 must be abundant also toward the cloud interior.The most plausible scenario suggested by these maps is that GMCs are porous to FUV radiation.This is consistent with the detection of very extended 70 µm dust emission from FUV-illuminated grains (see Fig. 1).This implies that GMCs are inhomogeneous, and we are detecting [C i] 492 GHz emission from the cloud edges as well as from FUV-illuminated surfaces of structures located at moderate cloud depths (typically modeled as clumps, filamentary, or fractal structures, e.g., Boisse 1990;Falgarone et al. 1991;Spaans 1996;Stutzki et al. 1998;Barnes et al. 2013).Unfortunately, while ALMA, Keck, and JWST observations show surprisingly rich small-scale substructures in the prototypical PDR the Orion Bar (Goicoechea et al. 2016;Habart et al. 2023a,b), similar sub-arcsecond resolution observations of the [C i] 492 GHz are still missing.Such observations will help to constrain the small-scale origin of C 0 .6.2.2.High HCN/CO J = 1-0 and [C i] 492 GHz/CO J = 1-0 line intensity ratios from gas at A V < 3 mag We close our discussion of the bimodal behavior of the W(HCN)/W(CO) J = 1-0 intensity ratio by providing more evidence that FUV radiation (leading to abundant C 0 and moderate χ e ) is ultimately responsible of the increased ratios observed at A V < 3 mag (Fig. 16a).These regions correspond to translucent gas and FUV-illuminated cloud edges.They coincide with enhanced [C i] 492 GHz/CO J=1-0 line intensity ratios (Fig. 6), which traces low-density PDRs (Hollenbach et al. 1991;Kaufman et al. 1999).Hence, we expect that both ratios are related.
Figure 16 shows the distribution of [C i] 492 GHz/CO J = 1-0 and HCN/CO J = 1-0 intensity ratios in Orion B. The upperright panel shows all detections (at all A V ) in the map.The running median clearly shows that, above a threshold of W(HCN)/W(CO) J = 1-0 ≳ 0.02, the ratio quickly increases with the [C i] 492 GHz/CO J = 1-0 intensity ratio.The lower panels in Fig. 16 separate the HCN/CO and [C i]/CO detections in the lines of sight with A V < 3 mag (Fig. 16c) and A V > 3 mag (Fig. 16d).These plots show that the HCN/CO J = 1-0 line intensity ratio linearly correlates with [C i] 492 GHz/CO J = 1-0 at A V < 3 mag.
Hence, the ratios follow the increasing electron abundance in PDR gas.On the other hand, the ratios are not correlated at higher A V > 3 mag.As a corollary, our observations imply that the detection of high HCN/CO J = 1-0 line intensity ratios do not always imply the presence of dense gas.The existence of a low-A V branch, from extended FUV-illuminated low-density gas, leads to increasing ratios with decreasing A V .This cloud component cannot be overlooked, specially in the context of the very large scale emission from GMCs, otherwise the mass of the dense molecular gas can easily be overestimated.In the next section we specifically quantify the amount of dense molecular gas traced by the HCN J = 1-0 emission.6.3.The dense gas mass conversion factor α (HCN J=1-0) Using the dust SEDs across the observed field 10 , we derive the mass of the dense gas in the mapped area (represented by gas at A V > 8 mag, e.g., Lada et al. 2010).The likely density of this cloud component is n(H 2 ) > 10 4 cm −3 (e.g., Bisbas et al. 2019).We obtain M dg =3.1×10 3 M ⊙ , which accounts for about 20% of the total mass (M H 2 ,tot ∼ 1.7×10 4 M ⊙ ) in the mapped area.These numbers imply a dense gas surface density (Σ dg = M dg / A) and a total gas surface density (Σ H 2 ,tot = M H 2 ,tot / A) of Σ dg = 13 M ⊙ pc −2 and Σ H 2 ,tot = 70 M ⊙ pc −2 , respectively, where in both cases we divide by the total mapped area, A ≃ 250 pc 2 .
High spatial resolution observations of the dust SED are rarely available in extragalactic studies.Hence, it is appropriate to calibrate the mass of the dense molecular gas with the emitted luminosity of a convenient molecular line tracer, with HCN J = 1-0 being the traditional choice.Hence, it is common to define: where L ′ (HCN) is the total HCN J = 1-0 line luminosity in the mapped area (in K km s −1 pc 2 ) as defined in Eq. ( 4).Gao & Solomon (2004a) originally estimated α(HCN) = 10 M ⊙ / K km s −1 pc 2 .Recent dust continuum and line emission surveys determine α(HCN) in a few local GMCs (e.g., Shimajiri et al. 2017;Kauffmann et al. 2017;Barnes et al. 2020).
These studies find quite a diversity of α(HCN) values, from 10 to 500 M ⊙ / K km s −1 pc 2 .However, these surveys typically map starforming clumps and their immediate environment (areas <1 deg 2 ) but do not account for, or do not spatially resolve, the extended HCN J =1-0 emission from low density and more translucent gas.This emission is weakly excited (T CMB ≲ T ex ≪ T k ), but because it covers large spatial scales, its total line luminosity typically exceeds the line luminosity from dense gas in star-forming cores at A V > 8 mag (∼30% in Orion B).
Here we determine α for HCN, HCO + , and HNC J = 1-0 lines in Orion B. We obtain L ′ (HCN)=110 K km s −1 pc 2 for HCN J =1-0, which implies a dense mass conversion factor α(HCN) = 29 M ⊙ / K km s −1 pc 2 .Table 4 summarizes the luminosities and α values derived for other molecules.A recent survey of the Perseus low-mass star-forming region (at 11 arcmin resolution and covering 8.1 deg 2 or ∼215 pc 2 ) finds α(HCN) = 92 M ⊙ / K km s −1 pc 2 , L ′ (HCN) = 55.3K km s −1 , and M dg =5.1×10 3 M ⊙ (Dame & Lada 2023).As FUV radiation favors the formation of HCN and the excitation of the J = 1-0 line at large spatial scales (enhanced by electron collisions; Sect.6.1), our study suggests that the lower α(HCN) value in Orion B is linked to the presence of FUV radiation from massive stars.Indeed, Shimajiri et al. (2017) mapped small areas of Orion B, 10 Appendix C.2 details how we determine the gas mass.
Aquila, and Ophiuchus star-forming cores (<10 pc 2 ).They find that α(HCN) anticorrelates with G 0 .We do find this tendency at the much larger spatial scales of our maps, but not a strong anticorrelation.This can be explained by the nonlinear dependence of the HCN abundance, HCN J = 1-0 line emission, and electron abundance with G 0 .
All in all, we conclude that there is no universal α(HCN J =1-0) value, as environmental conditions and contribution of the low density extended cloud component at different angular scales likely vary from cloud to cloud.In Orion B, the cloud mass at A V > 8 mag is similar to that at A V < 3 mag.This results in a similar value of the mass to total L ′ (HCN) ratio in both cloud components.Thus, it will not be straightforward to distinguish, based on the observation of a single line, which component dominates the emission from spatially unresolved GMCs.

Schmidt-like laws: Spatially resolved relations between molecular and atomic lines with FIR intensities
On more global spatial scales (hundreds of parsec to kiloparsec scales) than those discussed in our study, observations of nearby normal galaxies find a tight, close to linear, correlation between the HCN J = 1-0 line luminosity and the FIR luminosity (a proxy of the SFR when averaged on such global scales; Solomon et al. 1992;Gao & Solomon 2004a;Kennicutt & Evans 2012).However, when considering starburst galaxies and (U)LIRGs, the relation often deviates from linearity (e.g., Gao et al. 2007;García-Burillo et al. 2012;Usero et al. 2015;Sánchez-García et al. 2022).These luminous galaxies lie above the FIR-HCN correlation observed in nearby normal galaxies.They also display high HCN/CO J = 1-0 line luminosity ratios (∼ 0.2) interpreted as galaxies having high fractions of dense molecular gas.Our survey of Orion B provides access to the local properties that contribute to the large averages seen in galaxies.In this section we discuss the spatially resolved relationships between I FIR and CO, HCN, HCO + , HNC J=1-0, and [C i] 492 GHz line intensities (W) mapped in Orion B.
Figure 18 shows 2D histograms of the observed W(CO), W(HCN), W(HCO + ), W(HNC), and W([C i] 492 GHz) line intensities (in K km s −1 ) as a function of I FIR (in erg s −1 cm −2 sr −1 ).We find that the observed line intensities W scale with I FIR as a power law.As we fit these points using an orthogonal regression method 11 in log(y)-log(x) space and we use the appropriate error bars (the standard deviation) in both axes, we can present the scalings as I FIR ∝ W N (as in Fig. 18) or as W ∝ I 1/N FIR (as in Fig. B.3).Perhaps provocatively, and in order to promote the comparison with the extragalactic scalings SFR-L mol (e.g., Gao & Solomon 2004a;Shirley et al. 2008;Shetty et al. 2013Shetty et al. , 2014a,b),b), here we start discussing the power-law indexes N.
As discussed in Sect.2.5, I FIR is a surrogate of the local FUV radiation field, G ′ 0 (upper panel x-axis of Fig. 18).FUV photons are related to the presence of massive O and B stars that have short lifetimes.Thus, the FIR emission from FUV-heated grains is ultimately related to the SFR.However, the statistical connection between SFR and FIR luminosities in galaxies holds when averaging over large cloud samples (e.g., Kennicutt & Evans 2012).Therefore, the extrapolation of the local scalings in Orion B to galaxies (global averages) has to be taken with caution, bearing in mind that I FIR traces the strength of the FUV radiation field, but L FIR over a small region does not trace the true SFR12 .By fitting all points in Fig. 18, we find that W(CO), W(HCO + ) and W(HCN J=1-0) scale with I FIR as a power law with N ∼ 0.9-1.3.However, W(HNC J=1-0) and W([C i] 492 GHz) show a different behavior, with a power-law index N ∼ 1.8-2.2.A closer inspection of the I FIR -W(CO J = 1-0) running median shows two clear tendencies.The median toward the brightest FIR positions (I FIR > 0.4 erg s −1 cm −2 sr −1 or G ′ 0 > 1500, mostly arising from NGC 2024 star-forming clump) shows a powerlaw index of N ∼ 4.8.On the other hand, the faintest I FIR and W(CO J = 1-0) positions show N ∼ 0.4 (sublinear relationship).This faint CO emission is associated with widespread and very extended diffuse gas (low A V and G ′ 0 < 20).The I FIR -W(HCN J = 1-0) and I FIR -W(HCO + J = 1-0) histograms are quite similar.They also reveal two different tendencies.Fitting the brightest I FIR positions alone, most of them associated with dense gas in NGC 2024 (as demonstrated by the detection of bright HCN J = 4-3 line emission, Fig. 3), provides N∼1.6 for HCN and N∼2.4 for HCO + (superlinear relationships).In contrast, the most comextragalactic scalings (e.g., Kennicutt 1998a), these FIR luminosities translate into a SFR of 2.6×10 −5 M ⊙ yr −1 , which is nearly an order of magnitude lower than the SFR estimated by counting young stellar objects (YSOs), 1.6×10 −4 M ⊙ yr −1 (Lada et al. 2010).Pabst et al. (2021) find a similar result in Orion A, namely that SFR(FIR) < SFR(YSOs).mon low surface brightness HCN J = 1-0, HCO + J = 1-0, and I FIR positions (those with G ′ 0 < 20) show N∼0.6 (i.e., not far from the extended and diffuse CO emission index).Interestingly, the I FIR -W(HNC J=1-0) and I FIR -W([C i]492 GHz) histograms show a single superlinear tendency across the map, with N∼1.8 and 2.2, respectively.Hence, HNC and [C i] 492 GHz have a very different behavior compared to the other species.The derived N index for HNC resembles the index we find for HCN at the highest values of I FIR (G ′ 0 > 1500 and dense gas), whereas the single index for [C i] 492 GHz resembles that of HCO + at high G ′ 0 .This similitude must reflect their related chemistry and excitation conditions.
From the point of view of the local gas properties, Figs.18  and B.3 show that W(CO J = 1-0), W(HCO + J = 1-0), and W(HCN J = 1-0) intensities increase with increasing I FIR up to G ′ 0 ≃ 20.Most of these positions refer to the extended cloud component, which hosts low densities and thus, the HCN J = 1-0 line is weakly collisionally excited (see Sect. 4.3), with n(H 2 ) < n cr, eff (HCN 1-0) and thus, T ex < T k .Under these conditions (effectively thin emission), W(HCN J = 1-0) scales with N(HCN) even for large line opacities (see also Liszt & Pety 2016).Furthermore, our chemical analysis shows that models with a higher G 0 /n H ratio produce more HCN (Sect.5 and Fig. 13).In addition, electron excitation contributes to enhance W(HCN J = 1-0) at low densities.These conditions favor the emission of CO, HCO + , and HCN as G ′ 0 increases.On the other hand, Figs.18 and B.3 show that W(CO J = 1-0), W(HCO + J = 1-0), and W(HCN J = 1-0) respond weakly to I FIR once the FUV field becomes too intense (G ′ 0 > 1500).These other regions at large A V host denser gas, so that n(H 2 ) > n cr, eff (HCN 1-0), and J = 1-0 lines turn into very optically thick, thus becoming less sensitive to column densities.Interestingly, W(HNC J = 1-0) and W([C i] 492 GHz) weakly respond to I FIR at all G ′ 0 .We already showed that HNC traces slightly denser gas than HCN (Fig. 5c) and that HNC responds less to electron excitation (Table 1).In addition, the observed W(HCN 1-0)/W(HNC 1-0) intensity ratio increases with the FUV field for G ′ 0 < 200 (Fig. 12).Indeed, our chemical models show that the HNC abundance is lower in the FUV-illuminated gas (Sect.5).This gas is usually at lower density than the FUVshielded cold gas.Thus, we expect that most of the HNC J = 1-0 emission arises from gas in which n(H 2 ) > n cr, eff (HNC 1-0).These facts explain the weaker response of W(HNC J = 1-0) to FUV radiation.Finally, PDR models predict that the C 0 column density is a weak function of gas density and especially of G 0 (e.g., Hollenbach et al. 1991).This is consistent with the weak scaling we find in Orion B.
As a corollary, we conclude that our large-scale and spatially resolved lines maps of a local GMC show a variety of powerlaw indexes, I FIR ∝ W N (or W ∝ I 1/N FIR ).These N indexes resemble the kind of Kennicutt-Schmidt power-law indexes, SFR ∝ L N mol , found in galaxy surveys that average multiple GMCs (e.g., Wu et al. 2005Wu et al. , 2010;;Kennicutt & Evans 2012;García-Burillo et al. 2012;Sánchez-García et al. 2022).We attribute the different scalings in Orion B to the different gas densities, excitation regimes, and chemistry of the star-forming (dense and compact) versus non-star-forming (low density, extended, and FUV-illuminated) environments.However, while it is tempting to extrapolate our results to the extragalactic scalings (as in Krumholz & Thompson 2007;Narayanan et al. 2008), we still need to better understand the spatial scales at which L FIR becomes a reliable tracer of the global SFR, as well as the connection between the extragalactic averages versus our spatially resolved scalings.

Summary and conclusions
In the context of the IRAM 30m ORION-B large program, we presented a detailed analysis of 5 deg 2 (∼250 pc 2 ) HCN, HNC, HCO + , CO J=1-0, and [C i] 492 GHz line emission maps of the Orion B GMC.We complemented this dataset with new pointed observations of rotationally excited HCN, HNC, H 13 CN, and HN 13 C lines.We constructed integrated line intensity (W), visual extinction, and I FIR (a proxy of G 0 ) maps from existing dust SED observations.We summarize our results as follows: -About 70% of the total HCN J=1-0 luminosity, L ′ (HCN J = 1-0) = 110 K km s −1 pc −2 , arises from gas at A V < 8 mag (Sect.3.1), that is, from gas below the common extinction threshold of star-forming cores.About 80% of the total cloud mass and 50% of the total FIR luminosity (mostly arising from FUV-heated dust grains) also steams from A V < 8 mag.
-Most of the widespread and extended HCN J = 1-0 emission arises from weakly collisionally excited gas with n(H 2 ) ≲ 10 4 cm −3 .That is, it is not line radiation emitted by dense cores that is resonantly scattered by low density halos (Sect.6.1).This is demonstrated by the typical HCN J = 1-0 HFS intensity ratios R 02 ≳ 0.2 and R 12 < 0.6 observed at large scales.Even lower densities are possible in FUV-illuminated gas if χ e ≥ 10 −5 and electron collisional excitation dominates (Sect.4.3).
-The HCN/HNC J = 1-0 line intensity ratio is sensitive to the strength of the FUV radiation field.Our chemical models and observations suggest that the HCN/HNC abundance ratio is more sensitive to G 0 than to T k (Sect.5).In particular, HNC is a slightly better tracer of dense gas, defined as n(H 2 ) > 10 4 cm −3 , than HCN, because its abundance is lower in the FUV-illuminated gas (translucent gas and cloud edges).This gas is usually at lower density than the FUV-shielded cold gas.In addition, HNC is less sensitive to electron excitation than HCN (Table 1).
-The HCN/CO J=1-0 line intensity ratio (Sect.3.2), widely used as a tracer of the dense gas fraction, shows a bimodal behavior with respect to A V , with an inflection point at A V ≲ 3 mag (Sect.6.2) typical of translucent gas and FUV-illuminated cloud edges.The extended cloud HCN J = 1-0 emission (Sect.4.3) explains the low A V branch of the observed distribution of the HCN/CO J =1-0 line intensity ratio.The highest HCN/CO J =1-0 line intensity ratios (∼ 0.1) at A V < 3 mag correspond to regions displaying high [C i] 492 GHz/CO J =1-0 intensity ratios too (> 1).These values are characteristic of lowdensity PDRs and χ e ≳ 10 −5 .Therefore, we conclude that the detection of high HCN/CO J = 1-0 intensity ratios does not always imply the presence of dense gas.
-Given the widespread and extended nature of the [C i]492 GHz emission (a typical tracer of PDR gas), and its spatial correlation with W(HCO + J = 1-0), W(HCN J = 1-0), and W( 13 CO J = 1-0) (see Sect. 6.2.1), the extended component of Orion B (and likely in most GMCs), must be porous to FUV radiation from nearby massive stars.Indeed, 70% of the total [C i] 492 GHz luminosity arises from lines of sight with A V > 3 mag (i.e., not exactly from the cloud surface).In addition, the 70 µm continuum emission from FUV-illuminated dust grains is very extended.The enhanced FUV field favors the formation of HCN and the excitation of the J = 1-0 line at large scales, not only in dense star-forming cores.This is exemplified by the relatively low value of the dense gas mass to the HCN J = 1-0 line luminosity ratio, α (HCN) = 29 M ⊙ / K km s −1 pc 2 , in Orion B (Sect.6.3).The existence of a widespread HCN J = 1-0 emission component associated with low density gas affects the interpretation of the extragalactic relationship L HCN versus SFR.
-The low-surface brightness and extended HCN J = 1-0 and HCO + J = 1-0 emissions (≲ 1 K km s −1 ) scale with I FIR with a similar power-law index (Sect.6.4).Together with CO J = 1-0, these lines respond to the increasing I FIR up to G ′ 0 ≃ 20.On the other hand, the bright HCN emission (> 6 K km s −1 ) from dense gas in star-forming clumps weakly responds to I FIR once the FUV radiation field becomes too intense (G ′ 0 > 1500).HNC J = 1-0 and [C i] 492 GHz lines weakly respond to I FIR at all G ′ 0 .-Our large-scale and spatially resolved lines maps of a local GMC show a variety of power-law indexes, I FIR ∝ W N (from sublinear to superlinear), that resemble the kind of Kennicutt-Schmidt power-law indexes, SFR ∝ L N mol , found in surveys of different galaxy types that spatially average multiple GMCs (e.g., Kennicutt & Evans 2012).We attribute the different scalings in Orion B to the different gas densities, excitation regimes, and chemistry of the star-forming (compact) versus nonstar-forming (extended) environments (Sect.6.4).
Our study stresses the major contribution of the extended and low density component of GMCs to the total CO, HCO + , and HCN J = 1-0 line luminosity.It also enables us to remark that there is a need to carry out sensitive wide field surveys of galactic GMCs in multiple molecular lines.This will allow us to determine the properties of the star formation environment and to better understand the origin of the extragalactic Kennicutt-Schmidt scalings on global galaxy averages.In Orion B, the HCN J = 1-0 line intensity at any position of the extended cloud component is obviously much fainter than that arising from dense star-forming clumps such as NGC 2024.However, the much larger area of the extended cloud component at low A V implies that the emission arising from dense cores does not dominate the HCN J=1-0 line luminosity from GMCs (see also Santa-Maria et al. 2021).Finally, better knowledge of the rate coefficient of some critical gas-phase reactions, namely reaction NCO + N → HCN + O and reactions of HNC with H, C, and O atoms, will help us to refine our abundance estimations from chemical models.partition function at a temperature of T ex , g u is the statistical weight of the transition upper level, and E u /k is the upper level energy.The rotational partition function can be approximated with precision as: where B 0 is the rotational constant (McDowell 1988).We took the HCN HFS spectroscopic parameters compiled in CDMS (Endres et al. 2016, and references therein).This fitting method works better on high S/N spectra.Thus, we only applied it to the main cloud velocity component (v LSR ≃10 km s −1 ) where S/N>5σ.  in the LTE and optically thin limit (green lines), the result of the LTE-HFS fit in CLASS (blue curve), and a non-LTE radiative transfer model (red curve, Goicoechea et al. 2022).

D.2. HCN J = 2-1 and 3-2 HFS line ratios
The HCN J=2-1 transition has six HFS lines that blend into three lines with relative intensity ratios ∼1:9:2 in the LTE and optically thin limit.The HCN J=3-2 transition also has six HFS lines.Only the central ones are blended and cannot be spectrally resolved.This gives the impression of three lines with relative intensity ratios 1:25:1 in the LTE and optically thin limit (e.g., Ahrens et al. 2002;Loughnane et al. 2012).Here we term these three apparent components (blueshifted, central, and redshifted) of the J=2-1 and J=3-2 rotational lines as "satellite(L)," "main," and "satellite(R)," respectively.Table D.1 provides the entries used to construct Fig. 11.

Fig. 1 .
Fig. 1.Composite image of the ∼ 5 deg 2 area mapped in Orion B. Red color represents the PACS 70 µm emission tracing FUV-illuminated extended warm dust.Green color represents the cloud depth in magnitudes of visual extinction, A V ∝ N(H 2 ).Blue color represents the HCN J=1−0 line intensity.We note that outside the main filaments most of the HCN J=1−0 emission is at A V < 4 mag.

Fig. 2 .
Fig. 2. Maps of Orion B in different tracers.(a) Visual extinction A V , (b) Approximate FUV field, G ′ 0 (see text), (d) 12 CO J=1-0 peak temperature (in K).(c) and (e) to (h) 12 CO, HCO + , HCN, HNC J=1-0, and [C i] 492 GHz (from Ikeda et al. 2002) integrated line intensity maps (in K km s −1 ) spatially smoothed to an angular resolution of ∼2 ′ .Dashed black boxes mark the Cloak, Orion B9, Hummingbird, and Flame filament.Circles mark the extension of the H ii regions in NGC 2024, NGC 2023, IC 434, IC 435, and around the star Alnitak.The HH dot marks the position of the Horsehead PDR, the projection center of the maps.

Fig. 3 .
Fig. 3. Selection of HCN J = 1-0 to 4-3, and HNC J=3-2 line detections toward representative cloud environments in Orion B. Red lines show the expected relative HFS line intensities in the LTE and optically thin limit.Table 4. Characteristics of the molecular line emission over 5 deg 2 of Orion B.

Fig. 4 .
Fig. 4. Distribution of 12 CO, HCN, HCO + , HNC J=1-0, and [C i] 492 GHz line intensities as a function of A V .The dashed red lines show the running median (median values of the line intensity within equally spaced log A V bins).Error bars show the line intensity dispersion.We note that the 5σ error of A V is ≃ 0.8 mag.Thus, one cannot trust any trend below this threshold.

Fig. 5 .
Fig. 5. Line emission properties as a function of A V .(a) Fractions (in %) of line luminosities emitted in each A V mask.(b) Typical (the mode) line intensity in each A V mask.(c) Cumulative line luminosity.

Table 6 .
Statistics of 5 deg 2 line intensity ratio maps shown in Fig. 6.Notes.† ρ(G ′ 0 ) is the Spearman correlation rank with the G ′ 0 map.See also Fig. B.2 in the Appendix.

Fig. 8 .
Fig.8.Histograms of HCN J=1-0 HFS (a) Line intensity ratios, and (b) Line-width ratios observed in Orion B. R 02 stands for W(F=0-1)/W(F=2-1) and R 12 stands for W(F=1-1)/W(F=2-1).The red curve in panel (a) shows the expected LTE ratios as line opacities increase.The red star marks the non-anomalous ratios in the optically thin limit τ → 0 (1σ is the standard deviation relative to the mean line ratios).

Fig. 11 .
Fig. 11.HCN J = 2-1 and J = 3-2 HFS intensity ratios satellite(R)/main versus satellite(B)/main (see Sect. 4.4 for their definition) in LTE and as line opacities increase.Blue and red dots show the observed HFS line ratios toward the representative positions (see Table D.1).

Fig. 12 .
Fig. 12. 2D histogram of the observed HCN/HNC J=1-0 line intensity ratio as a function of G ′ 0 in the Orion B map.The dashed black curve shows the running median.The error bars show the standard deviation.
with a rate coefficient k(T ) = 10 −10 exp (−E b /T ), where E b is the reaction energy barrier.Theoretical calculations agree on the presence of a barrier, however, different methods provide slightly different barrier heights: ∼2130 K(Talbi et al. 1996), ∼1670 K(Sumathi & Nguyen 1998), and ∼960 K(Petrie 2002

Fig. 13 .
Fig. 13.Constant density gas-phase PDR models with G 0 =100 and n H =5×10 3 cm −3 (left) and 5×10 4 cm −3 (right).These models adopt E b = 1200 K for Reaction (8).Upper panels in (a) and (b): Dashed curves show the depth-dependent column density ratios of selected species (left y-axis).The blue continuous curves in the upper panels of (a) and (b) show the HCN/HNC column density ratio adopting E b = 200 K. Green continuous curves show the temperature structure as a function of A V (right y-axis).Lower panels in (a) and (b): Abundance profiles with respect to H nuclei. (c) and (d): Contribution (in percent) of the main formation and destruction reactions for HCN (continuous curves) and HNC (dashed curves).

Fig. 16 .
Fig. 16.2D histograms.(a) Visual extinction A V as a function of the HCN/CO J=1-0 integrated intensity ratio (from maps at 120 ′′ resolution).Dashed red, yellow, green, and blue horizontal lines are the visual extinction values 1, 4, 8, and 15 mag, respectively.Above each line, we show the percentage of the total HCN J = 1-0 luminosity that comes from the different A V ranges.(b), (c), and (d) 2D histogram of the observed [C i] 492 GHz/CO J=1−0 line intensity ratio (in units of K km s −1 ) as function of the observed HCN/CO J=1-0 line ratio for all A V , for A V < 3 mag, and for A V > 3 mag.The dashed black curve shows the running median.Error bars show the standard deviation in the x-axis.

6. 2 .
Bimodal behavior of the HCN/CO J=1-0 line intensity ratio as a function of A V

Fig. 18 .
Fig. 18. 2D histograms of the 12 CO, HCN, HCO + , HNC, J=1-0, and [C i] 3 P 1 − 3 P 0 line intensities as a function of FIR intensity in Orion B (from maps at 120 ′′ resolution).The dashed red lines show the running median (median values of the integrated intensity within equally spaced log I FIR bins).The error bars show their dispersion.Black lines (and associated text) show a linear fit (orthogonal regression in log(y)-log(x))to all observed positions in each map.Magenta lines and blue lines show a linear fit to a range of I FIR < 6×10 −3 erg s −1 cm −2 sr −1 and (0.4-7.7) erg s −1 cm −2 sr −1 , respectively.We note that in each plot the number of line detections is different.
Figure D.1 shows the anomalous HCN J=1-0 spectrum observed (at by the IRAM 30m telescope toward the Horsehead PDR position δv ≃0.16 km s −1 resolution).This figure compares the expected HFS line strengths

Fig
Fig. D.1.HCN J = 1-0 HFS lines toward the Horsehead PDR.The right axis shows the normalized line intensity to make clear that the observed HFS emission differs from the optically thin LTE line ratios 1:5:3 (green lines).Red curves show the results of a non-LTE radiative transfer model including line overlaps (for details, see Sect.5.1 in Goicoechea et al. 2022).Blue curves show the best LTE-HFS fit using CLASS 2 .

Table 2 .
Properties of the massive stars creating H ii regions.

Table 4 .
Characteristics of the molecular line emission over 5 deg 2 of Orion B.

Table 5 .
SED derived parameters from 5 deg 2 maps of Orion B.