equation

$\BODY$ (1)

11institutetext: Instituto de Física Fundamental (CSIC). Calle Serrano
121-123, 28006, Madrid, Spain, 11email<EMAIL_ADDRESS>22institutetext:
IRAM, 300 rue de la Piscine, 38406 Saint Martin d’Hères, France.
33institutetext: LERMA, Observatoire de Paris, PSL Research University, CNRS,
Sorbonne Universités, 75014 Paris, France. 44institutetext: Chalmers
University of Technology, Department of Space, Earth and Environment, 412 93
Gothenburg, Sweden. 55institutetext: LERMA, Observatoire de Paris, PSL
Research University, CNRS, Sorbonne Universités, 92190 Meudon, France.
66institutetext: Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, GIPSA-Lab,
Grenoble, 38000, France. 77institutetext: Univ. Lille, CNRS, Centrale Lille,
UMR 9189 - CRIStAL, 59651 Villeneuve d’Ascq, France. 88institutetext:
Université de Toulon, Aix Marseille Univ, CNRS, IM2NP, Toulon, France.
99institutetext: Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux,
CNRS, B18N, Allee Geoffroy Saint-Hilaire,33615 Pessac, France.
1010institutetext: Instituto de Astrofísica, Pontificia Universidad Católica
de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile.
1111institutetext: Institut de Recherche en Astrophysique et Planétologie
(IRAP), Université Paul Sabatier, Toulouse cedex 4, France. 1212institutetext:
Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL,
CNRS, Sorbonne Université, Université de Paris, Sorbonne Paris Cité, Paris,
France. 1313institutetext: Jet Propulsion Laboratory, California Institute of
Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA. 1414institutetext:
National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA,
22903, USA. 1515institutetext: Department of Physics, The University of Tokyo,
7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan. 1616institutetext: Research
Center for the Early Universe, The University of Tokyo, 7-3-1, Hongo, Bunkyo-
ku, Tokyo, 113-0033, Japan. 1717institutetext: Harvard-Smithsonian Center for
Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA. 1818institutetext:
School of Physics and Astronomy, Cardiff University, Queen’s buildings,
Cardiff CF24 3AA, UK.

# 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

M. G. Santa-Maria HCN emission from translucent gas and UV-illuminated cloud
edges revealed by wide-field IRAM 30m maps of the Orion B GMCHCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMC J. R. Goicoechea HCN emission from translucent gas and
UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the Orion B
GMCHCN emission from translucent gas and UV-illuminated cloud edges revealed
by wide-field IRAM 30m maps of the Orion B GMC J. Pety HCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMCHCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMCHCN
emission from translucent gas and UV-illuminated cloud edges revealed by wide-
field IRAM 30m maps of the Orion B GMCHCN emission from translucent gas and
UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the Orion B
GMC M. Gerin HCN emission from translucent gas and UV-illuminated cloud edges
revealed by wide-field IRAM 30m maps of the Orion B GMCHCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMC J. H. Orkisz HCN emission from translucent gas and UV-
illuminated cloud edges revealed by wide-field IRAM 30m maps of the Orion B
GMCHCN emission from translucent gas and UV-illuminated cloud edges revealed
by wide-field IRAM 30m maps of the Orion B GMCHCN emission from translucent
gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the
Orion B GMCHCN emission from translucent gas and UV-illuminated cloud edges
revealed by wide-field IRAM 30m maps of the Orion B GMC F. Le Petit HCN
emission from translucent gas and UV-illuminated cloud edges revealed by wide-
field IRAM 30m maps of the Orion B GMCHCN emission from translucent gas and
UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the Orion B
GMC L. Einig HCN emission from translucent gas and UV-illuminated cloud edges
revealed by wide-field IRAM 30m maps of the Orion B GMCHCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMCHCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMCHCN
emission from translucent gas and UV-illuminated cloud edges revealed by wide-
field IRAM 30m maps of the Orion B GMC P. Palud HCN emission from translucent
gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the
Orion B GMCHCN emission from translucent gas and UV-illuminated cloud edges
revealed by wide-field IRAM 30m maps of the Orion B GMCHCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMCHCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMC V. de
Souza Magalhaes HCN emission from translucent gas and UV-illuminated cloud
edges revealed by wide-field IRAM 30m maps of the Orion B GMCHCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMC I. Bešlić HCN emission from translucent gas and UV-
illuminated cloud edges revealed by wide-field IRAM 30m maps of the Orion B
GMCHCN emission from translucent gas and UV-illuminated cloud edges revealed
by wide-field IRAM 30m maps of the Orion B GMC L. Segal HCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMCHCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMCHCN
emission from translucent gas and UV-illuminated cloud edges revealed by wide-
field IRAM 30m maps of the Orion B GMCHCN emission from translucent gas and
UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the Orion B
GMC S. Bardeau HCN emission from translucent gas and UV-illuminated cloud
edges revealed by wide-field IRAM 30m maps of the Orion B GMCHCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMC E. Bron HCN emission from translucent gas and UV-
illuminated cloud edges revealed by wide-field IRAM 30m maps of the Orion B
GMCHCN emission from translucent gas and UV-illuminated cloud edges revealed
by wide-field IRAM 30m maps of the Orion B GMC P. Chainais HCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMCHCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMC J.
Chanussot HCN emission from translucent gas and UV-illuminated cloud edges
revealed by wide-field IRAM 30m maps of the Orion B GMCHCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMC P. Gratier HCN emission from translucent gas and UV-
illuminated cloud edges revealed by wide-field IRAM 30m maps of the Orion B
GMCHCN emission from translucent gas and UV-illuminated cloud edges revealed
by wide-field IRAM 30m maps of the Orion B GMC V. V. Guzmán HCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMCHCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMC A. Hughes
HCN emission from translucent gas and UV-illuminated cloud edges revealed by
wide-field IRAM 30m maps of the Orion B GMCHCN emission from translucent gas
and UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the
Orion B GMC D. Languignon HCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMCHCN
emission from translucent gas and UV-illuminated cloud edges revealed by wide-
field IRAM 30m maps of the Orion B GMC F. Levrier HCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMCHCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMC D. C. Lis
HCN emission from translucent gas and UV-illuminated cloud edges revealed by
wide-field IRAM 30m maps of the Orion B GMCHCN emission from translucent gas
and UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the
Orion B GMC H. S. Liszt HCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMCHCN
emission from translucent gas and UV-illuminated cloud edges revealed by wide-
field IRAM 30m maps of the Orion B GMC J. Le Bourlot HCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMCHCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMC Y. Oya HCN
emission from translucent gas and UV-illuminated cloud edges revealed by wide-
field IRAM 30m maps of the Orion B GMCHCN emission from translucent gas and
UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the Orion B
GMCHCN emission from translucent gas and UV-illuminated cloud edges revealed
by wide-field IRAM 30m maps of the Orion B GMCHCN emission from translucent
gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the
Orion B GMC K. Öberg HCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMCHCN
emission from translucent gas and UV-illuminated cloud edges revealed by wide-
field IRAM 30m maps of the Orion B GMC N. Peretto HCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMCHCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMC E. Roueff
HCN emission from translucent gas and UV-illuminated cloud edges revealed by
wide-field IRAM 30m maps of the Orion B GMCHCN emission from translucent gas
and UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the
Orion B GMC A. Roueff HCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMCHCN
emission from translucent gas and UV-illuminated cloud edges revealed by wide-
field IRAM 30m maps of the Orion B GMC A. Sievers HCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMCHCN emission from translucent gas and UV-illuminated
cloud edges revealed by wide-field IRAM 30m maps of the Orion B GMC P.-A.
Thouvenin HCN emission from translucent gas and UV-illuminated cloud edges
revealed by wide-field IRAM 30m maps of the Orion B GMCHCN emission from
translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m
maps of the Orion B GMC S. Yamamoto HCN emission from translucent gas and UV-
illuminated cloud edges revealed by wide-field IRAM 30m maps of the Orion B
GMCHCN emission from translucent gas and UV-illuminated cloud edges revealed
by wide-field IRAM 30m maps of the Orion B GMCHCN emission from translucent
gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of the
Orion B GMCHCN emission from translucent gas and UV-illuminated cloud edges
revealed by wide-field IRAM 30m maps of the Orion B GMC

(Received 2023; accepted 2023)

###### Abstract

Context. Massive stars form within dense clumps inside giant molecular clouds
(GMCs). Finding appropriate chemical tracers of the dense gas ($n$(H2) $>$
several 104 cm-3 or AV $>$ 8 mag) 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 IRAM 30m ORION-B large program, we present 5
deg2 ($\sim$250 pc2) HCN, HNC, HCO+, and CO $J$=1$-$0 maps of the Orion B GMC,
complemented with existing wide-field [C i] 492 GHz maps, as well as new
pointed observations of rotationally excited HCN, HNC, H13CN, and HN13C lines.
We compare the observed HCN line intensities with radiative transfer models
including line overlap effects and electron excitation. Furthermore, we study
the HCN/HNC isomeric abundance ratio with updated photochemical models.

Results. We spectroscopically resolve the HCN $J$ = 1–0 hyperfine structure
(HFS) components (and partially resolved $J$=2$-$1 and 3$-$2 components). We
detect anomalous HFS line intensity (and line width) ratios almost everywhere
in the cloud. About 70% of the total HCN $J$=1–0 luminosity, $L^{\prime}$(HCN
$J$ $=$ 1$-$0) $=$ 110 K km s-1 pc-2, arises from $A_{\mathrm{V}}$ $<$ 8 mag.
The HCN/CO $J$=1$-$0 line intensity ratio, widely used as a tracer of the
dense gas fraction, shows a bimodal behavior with an inflection point at
$A_{\mathrm{V}}$ $\lesssim$ 3 mag typical of translucent gas and illuminated
cloud edges. We find that most of the HCN $J$ $=$ 1–0 emission arises from
extended gas with $n$(H2) $\lesssim$ 104 cm-3, and even lower density gas if
the ionization fraction is $\chi_{e}$ $\geq$ 10-5 and electron excitation
dominates. This result contrasts with the prevailing view of HCN $J$ $=$ 1–0
emission as a tracer of dense gas and explains the low-$A_{\mathrm{V}}$ branch
of the HCN/CO $J$ $=$1–0 intensity ratio distribution. Indeed, the highest
HCN/CO ratios ($\sim$ 0.1) at $A_{\mathrm{V}}$ $<$ 3 mag correspond to regions
of high [C i] 492 GHz/CO $J$ $=$1$-$0 intensity ratios ($>1$) characteristic
of low-density photodissociation regions. The low surface brightness
($\lesssim$ 1 K km s-1) and extended HCN and HCO+ $J$ $=$ 1–0 emission scale
with $I_{\rm FIR}$ – a proxy of the stellar far-ultraviolet (FUV) radiation
field – in a similar way. Together with CO $J$ $=$ 1–0, these lines respond to
increasing $I_{\rm FIR}$ up to $G_{0}$ $\simeq$ 20\. On the other hand, the
bright HCN $J$ $=$ 1–0 emission ($>$ 6 K km s-1) from dense gas in star-
forming clumps weakly responds to $I_{\rm FIR}$ once the FUV field becomes too
intense ($G_{0}$ $>$ 1500). In contrast, HNC $J$ $=$ 1–0 and [C i] 492 GHz
lines weakly respond to $I_{\rm FIR}$ for all $G_{0}$. The different power law
scalings (produced by different chemistries, densities, and line excitation
regimes) in a single but spatially resolved GMC resemble the variety of
Kennicutt-Schmidt law indexes found in galaxy averages.

Conclusions. Given the widespread and extended nature of the [C i] 492 GHz
emission, as well as its spatial correlation with that of HCO+, HCN, and 13CO
$J$ = 1–0 lines (in this order), we argue that the edges of GMCs are porous to
FUV radiation from nearby massive stars. Enhanced FUV radiation favors the
formation and excitation of HCN on large scales, not only in dense star-
forming clumps, and it leads to a relatively low value of the dense gas mass
to total luminosity ratio, $\alpha$ (HCN) $=$ 29 M⊙ / (K km s-1pc2) in Orion
B. As a corollary for extragalactic studies, we conclude that high HCN/CO
$J$=1–0 line intensity ratios do not always imply the presence of dense gas,
which may be better traced by HNC than by HCN.

###### Key Words.:

ISM: individual (Orion B) — ISM: molecular clouds — photon-dominated region —
low surface brightness

##  1 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 $A_{\mathrm{V}}\\!\simeq$ 8 mag (Schmidt, 1959, 1963;
Kennicutt, 1998a, b; Lada et al., 2010; Evans et al., 2020), which corresponds
to an approximate gas density threshold of $n$(H2) $>$ 104 cm-3 (e.g., Bisbas
et al., 2019). In galaxies, the far-infrared (FIR) dust luminosity ($L_{\rm
FIR}$, defined between 40 $\upmu$m and 500 $\upmu$m, see Sect. 2.5 and Sanders
& Mirabel, 1996) provides a measure of the SFR, especially in starbursts
(e.g., Kennicutt, 1998a). The $L_{\rm FIR}$ and the HCN $J$ $=$ 1–0 line
luminosity ($L_{\rm HCN\,1-0}$) are linearly correlated over a broad range of
spatial scales and galaxy types, from spatially resolved star-forming clumps
($L_{\mathrm{FIR}}\\!\simeq$104 $L_{\odot}$) to ultraluminous infrared
galaxies (ULIRGs, with $L_{\mathrm{FIR}}\\!\geq$1011 $L_{\odot}$) (Solomon et
al., 1992; Gao & Solomon, 2004b; Wu et al., 2010). These studies suggest that
$L_{\rm HCN\,1-0}$ is a good tracer of the dense star-forming gas mass.
However, the $L_{\rm CO\,1-0}$ to $L_{\mathrm{FIR}}$ luminosity ratio in
ULIRGs is lower than in normal galaxies. This leads to a superlinear
relationship $L_{\rm FIR}$ $\propto$ $L_{\rm CO}^{N\,>\,1}$ (e.g., Kennicutt,
1998b; Gao & Solomon, 2004a). The above relations are observational proxies of
the so-called Kennicutt-Schmidt (KS) relationship, $\Sigma_{\rm SFR}$ = $a$
$\Sigma_{\rm H_{2}}^{N}$, where $\Sigma_{\rm SFR}$ and $\Sigma_{\rm H_{2}}$
are the SFR and molecular gas surface densities. One obtains $N$$\approx$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 ($\mu_{e}$ $=$ 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 ($n_{\mathrm{cr}}$), 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 $n_{\mathrm{cr}}$(HCN
$J$=1–0) $\simeq$ 3$\times$105 cm-3 for collisions with H2 at 20 K (see Table
1 for references on spectroscopy and collisional rate coefficients). However,
as lines become optically thick, radiative trapping becomes important, leading
to lower effective critical densities ($n_{\mathrm{cr,\,eff}}$; e.g., Evans,
1999; Shirley, 2015).

The end 14N 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-1and +4.9 km s-1from 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 ($T_{\mathrm{ex}}$), thus avoiding the need to observe
isotopologues or multiple-$J$ lines. However, only in the optically thin limit
($\tau\rightarrow 0$) 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 $T_{\mathrm{ex}}$ exactly the same for the three HFS
transitions, with $T_{\mathrm{ex}}=T_{\mathrm{k}}$ 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 $W$ = $\int T_{\rm mb}(v)\,dv$ (in K km s-1). Interestingly,
the observed interstellar line ratios are usually outside these ranges. This
is called anomalous HCN emission.

Early studies of the HCN $J$=1–0 emission from warm GMCs revealed anomalous
$R_{12}$ ¡ 0.6 and $R_{02}\,\\!\gtrsim$ 0.2 ratios (Wannier et al., 1974;
Clark et al., 1974; Gottlieb et al., 1975). Cold dark clouds show HFS
anomalies toward embedded cores (Walmsley et al., 1982) and around them
(Cernicharo et al., 1984a). More modern observations confirm the ubiquity of
the HCN $J$=1–0 HFS line intensity anomalies toward low- and high-mass star-
forming cores (e.g., Fuller et al., 1991; Sohn et al., 2007; Loughnane et al.,
2012; Magalhães et al., 2018).

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 $p$-H2, $o$-H2, and $e^{-}$ (Faure et al., 2007b; Faure
& Lique, 2012; Hernández Vera et al., 2017; Magalhães et al., 2018; Goicoechea
et al., 2022).

Figure 1: Composite image of the $\sim$ 5 deg2 area mapped in Orion B. Red
color represents the PACS 70 $\upmu$m emission tracing FUV-illuminated
extended warm dust. Green color represents the cloud depth in magnitudes of
visual extinction, $A_{\mathrm{V}}$ $\propto$ $N$(H2). 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 $A_{\mathrm{V}}$ $<$ 4 mag. Table 1:
Spectroscopic parameters of the lines studied in this work (from Endres et
al., 2016, and references therein), critical densities for collisions with
$p$-H2 and electrons at 20 K (if LTE prevails, 99.82 % of H2 is in $para$
form), and critical fractional abundance of electrons (see text).

Species | Transition | Frequency |  $E_{\mathrm{u}}$/$k_{\mathrm{B}}$ | $A_{\mathrm{ul}}$ |  $n^{\mathrm{H_{2}}}_{\mathrm{cr},u}$ ($T_{\mathrm{k}}$=20 K) |  $n^{e}_{\mathrm{cr},u}$ ($T_{\mathrm{k}}$=20 K) | $\chi^{*}_{\mathrm{cr},e}$ | Ref. collisional rates
---|---|---|---|---|---|---|---|---
|  | [GHz] | [K] | [s-1] | [cm-3] | [cm-3] |  |  $para$-H2, e-
HCN |  $J$=1–0 |  088.63185 |  04.25 | 2.41$\times$10-5 | 2.7$\times$105 | 3.2 | 1.2$\times$10-5 | a,b
HCN |  $J$=2–1 | 177.26122 | 12.76 | 2.31$\times$10-4 | 2.3$\times$106 | 38 | 1.7$\times$10-5 |
HCN |  $J$=3–2 | 265.88650 | 25.52 | 8.36$\times$10-4 | 5.8$\times$106 | 168 | 2.9$\times$10-5 |
HCN |  $J$=4–3 | 354.50548 | 42.53 | 2.05$\times$10-3 | 1.6$\times$107 | 485 | 3.0$\times$10-5 |
HNC |  $J$=1–0 |  090.66357 |  04.35 | 2.69$\times$10-5 | 7.0$\times$104 | 3.6 | 5.2$\times$10-5 | a,b
HNC |  $J$=3–2 | 271.98114 | 26.11 | 9.34$\times$10-4 | 2.2$\times$106 | 191 | 8.6$\times$10-5 |
HCO+ |  $J$=1–0 |  089.18852 |  04.28 | 4.19$\times$10-5 | 4.5$\times$104 | 2.0 | 4.4$\times$10-5 | c,d
HCO+ |  $J$=2–1 | 178.37506 | 12.84 | 4.02$\times$10-4 | 4.0$\times$105 | 21 | 5.3$\times$10-5 |
HCO+ |  $J$=3–2 | 267.55763 | 25.68 | 1.45$\times$10-3 | 1.5$\times$106 | 84 | 5.8$\times$10-5 |
HCO+ |  $J$=4–3 | 356.73422 | 42.80 | 3.57$\times$10-3 | 3.1$\times$106 | 223 | 7.1$\times$10-5 |
CO |  $J$=1–0 | 115.27120 |  05.53 | 7.20$\times$10-8 | 5.7$\times$102 | … | … | e
C0 |  ${}^{3}P_{1}$-${}^{3}P_{0}$ | 492.16065 | 23.62 | 7.88$\times$10-8 | 5.5$\times$102 | 410 | 7.0$\times$10-1 | f,g

111We define the critical density as the H2 (or $e^{-}$) density at which
$A_{ul}$ equals the sum of all upward and downward collisional rates from the
upper level. That is, $n_{\mathrm{cr}}=A_{ul}\,/\,\sum_{i\neq u}\gamma_{ui}$.
For collisions with electrons, we consider only dipole-allowed transitions. We
define the critical fractional abundance of electrons as
$\chi^{*}_{\mathrm{cr},e}$ = $n^{e}_{\mathrm{cr}}$ /
$n^{\mathrm{H_{2}}}_{\mathrm{cr}}$. References: (a) Hernández Vera et al.
(2017); (b) Faure et al. (2007b); (c) Denis-Alpizar et al. (2020); (d) Faure
et al. (2007a, 2009); (e) Yang et al. (2010); (f) Schroder et al. (1991); (g)
Johnson et al. (1987).

Mapping large areas of nearby molecular clouds (a few hundred pc2) 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
($A_{\mathrm{V}}$, 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
($A_{\mathrm{V}}$ $<$ 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 $\chi_{e}$) in the first $A_{\mathrm{V}}$ $\approx$ 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,
$\chi_{e}$ $\simeq$ $\chi$(C+) $\simeq$ a few 10-4 (Sofia et al., 2004). At
intermediate cloud depths, from $A_{\mathrm{V}}\\!\approx$ 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., $\chi_{e}$ $\simeq$ $\chi$(S+) $\simeq$ a few 10-5
in Orion A; Goicoechea & Cuadrado, 2021). At much larger $A_{\mathrm{V}}$,
deeper inside the dense cores shielded from external UV radiation, $\chi_{e}$
is much lower, $\sim$ 10-7–10-8. These $\chi_{e}$ values apply to GMCs in the
disk of the galaxy exposed to standard cosmic ray ionization rates,
$\zeta_{\rm CR}$ = 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 H2 and H. Hence,
electron collisions contribute to, and even dominate, the excitation of these
molecules when (i) $\chi_{e}$ is higher than the critical fractional abundance
of electrons, $\chi^{*}_{\mathrm{cr}}$(e-) = $n_{\mathrm{cr}}$(e-) /
$n_{\mathrm{cr}}$(H2), and (ii) the gas density $n$(H2) is lower than the
critical density for collisions with H2, $n$(H2) $<$ $n_{\mathrm{cr}}$(H2).
For HCN $J$ = 1–0, this implies $\chi_{e}$ $\gtrsim$ 10-5 and
$n$(H2)$\;\lesssim$ 105 cm-3 (Dickinson et al., 1977; Liszt, 2012; Goldsmith &
Kauffmann, 2017; Goicoechea et al., 2022). Table 1 lists the frequency, upper
level energy, $n_{\mathrm{cr}}$, and critical fractional abundance
$\chi^{*}_{\mathrm{cr}}$(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 deg2 (see
Fig. 1 for an overview). These maps cover five times larger areas than those
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 factor $\alpha$(HCN), and discuss the $I_{\rm FIR}$–$W$ scalings we
find between different emission lines and FIR dust intensities. In Sect. 7, we
summarize our findings and give our conclusions.

##  2 Observations

###  2.1 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
distance222Interferometric observations of the $\sigma$ Ori system provides a
distance of $\sim$ 388 pc (Schaefer et al., 2016). Recent determinations using
GAIA also estimate $\sim$ 400 pc (e.g., Zucker et al., 2019; Rezaei Kh. et
al., 2020). 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$\sim$1.6$\times$10-4 $M_{\odot}$
yr-1 and low star-formation efficiency, SFE $\sim$ 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.

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

H ii region | Spectral type | Distancea | Radiusb
---|---|---|---
|  | [pc] | [arcmin]
IC 434 | O9.5V B | 388$\pm$1 | 42
NGC 2024 | O9.5V | 415 | 12
Around Alnitak | O9.7Ib+B0III C | 290$\pm$21 | 11
IC 435 | B5V D | 170$\pm$37 | 3
NGC 2023 | B1.5V C | 360$\pm$35 | 2.5

333a 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 $T_{\rm rot}$(HCN) (see also Table 7).

Pos. | (R.A., Dec.) | Environment
---|---|---
| [h:m:s, $\degree$:$\arcmin$:$\arcsec$] |
#1 | 5:41:44.4, -1:54:45.4 |  | Protostellar core
---
NGC 2024(FIR-4)
#2 | 5:41:24.1, -1:50:49.5 |  | Irradiated prestellar core
---
(NGC 2024 bubble)
#3 | 5:42:25.3, -1:59:33.2 | Starless core
#4 | 5:43:55.9, -1:34:21.4 | Orion B9 (south)
HH PDR | 5:40:53.9, -2:28:00.0 |  | Warm PDR
---
#6 | 5:41:36.5, -1:57:38.5 |  | NGC 2024 south:
---
dust ridge
#7 | 5:42:03.2, -2:02:35.8 |  | Prestellar core
---
in the Flame Filament
#8 | 5:42:02.9, -2:07:45.2 | Protostellar core (YSO)
HH Core | 5:40:55.6, -2:27:38.0 |  | DCO+ emission peak
---
#10 | 5:42:06.8, -2:03:33.5 | #7 surroundings
#11 | 5:41:20.2, -2:13:03.6 |  | NGC 2023 north
---
surroundings
#12 | 5:40:58.1, -2:08:41.9 | Prestellar core
#13 | 5:41:40.0, -1:36:13.6 | Filament surroundings
#14 | 5:46:43.7, -0:54:22.6 | Cloak

Figure 2: Maps of Orion B in different tracers. (a) Visual extinction
$A_{\mathrm{V}}$, (b) Approximate FUV field, $G_{0}^{\prime}$ (see text), (d)
12CO J=1–0 peak temperature (in K). (c) and (e) to (h) 12CO, 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 $\sim$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. Figure 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 deg2 of Orion B.

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
---|---|---|---|---|---|---|---|---
Line | Intensity ($W_{\mathrm{{average}}}$) | $T_{\mathrm{mb}}^{\mathrm{peak}}$ |  $L$uminosity ($L^{\prime}$) |  $L$uminosity ($L$) |  $\alpha$ (molecule) | $A_{\mathrm{cov}}$ |  $A_{\mathrm{cov}}^{120^{\prime\prime}}$/$A_{\mathrm{cov}}^{30^{\prime\prime}}$
| [K km/s] | [K] | [K km s-1pc2] | [$L_{\odot}$] | [$M_{\odot}$/(K km s-1pc2)] | [%] |
| (average spectrum) |  |  |  | 30” | 120” |
12CO $J$=1–0 | 30.60 | 5.400 | 7300 | 1.7$\times$10${}^{0\phantom{-}}$ |  000.43 | 78 | 92 | 1.2
HCO+ $J$=1–0 |  00.52 | 0.140 |  0120 | 1.4$\times$10-2 |  025.00 | 21 | 73 | 3.5
HCN $J$=1–0 |  00.46 | 0.060 |  0110 | 1.2$\times$10-2 |  029.00 | 16 | 60 | 3.8
HNC $J$=1–0 |  00.15 | 0.040 |  0040 | 4.1$\times$10-3 |  088.00 | 9 | 33 | 3.8

444(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 pc2 and
$L_{\odot}$ units. (6) Dense gas mass $M_{\mathrm{dg}}$ to line luminosity
ratio, where $M_{\mathrm{dg}}$=3.1$\times$103 $M_{\odot}$ (mass at
$A_{\mathrm{V}}$¿8 mag). (7) and (8): Percentage of the mapped area with
3$\sigma$ line detections. (9): Ratio of cloud areas with 3$\sigma$ line
detection after spatial smoothing.

###  2.2 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$\times$13.7 pc2). Observations were obtained using the EMIR090 receiver
at $\sim$21′′$-$28′′ resolution. The FTS backend provided a channel spacing of
195 kHz (0.5-0.7 km s-1 depending on the line frequency). The typical
1$\sigma$ line sensitivity in these maps is $\sim$100 mK per velocity
resolution channel. The full field of view was covered in about 850 hours by
(on-the-fly) mapping rectangular tiles with a position angle of 14$\degree$ in
the Equatorial J2000 frame that follows the global morphology of the cloud.
Data reduction was carried out using GILDAS555See
https://www.iram.fr/IRAMFR/GILDAS /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 5$\mathrm{h}$40$\mathrm{m}$54.27$\mathrm{s}$, -02$\degree$28′00.0″. We
rotated the maps counter-clockwise by 14$\degree$ around 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, 12CO, and HCO+. Orion B shows three main
velocity components at the local standard of rest (LSR) velocities $\sim$2.5,
$\sim$6, and $\sim$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 12CO 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 13CO and C18O $J$ = 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 $\sim$2′
($\sim$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 $\sim$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.

###  2.3 Wide-field [C i] 492 GHz map

We complement our molecular line maps with an existing wide-field 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
$\sim$0.45 K per 1.0 km s-1 velocity channel (Ikeda et al., 2002). The angular
resolution is $\sim$2′. Figure 2h shows the [C i] 492 GHz line integrated
intensity map in the LSR velocity range $[+3,+14]$ km s-1.

###  2.4 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, PDRs adjacent to H ii regions and cloud environment. Figure 2
shows the location of these positions. We used the EMIR receivers E150 (at 2
mm), E230 (at 1.3 mm), and E330 (at 0.9 mm) in combination with the FTS
backend (195 kHz spectral resolution). The HPBW varies as
$\approx$2460/Freq[GHz]666See https://publicwiki.iram.es/Iram30mEfficiencies.
For the E1, E2, and E3 bands, the HPBW is $\sim$14′′, $\sim$9′′, and
$\sim$7′′, respectively. We carried out dualband observations combining the E1
and E3 bands, during December 2021 and 2022, under excellent winter conditions
($\sim$1–4 mm of precipitable water vapor, pwv). We obtained the E2 band
observations during three different sessions: (i) December 2021: pwv¡4 mm
(positions #1, #2, #4, #10, and #11), (ii) March 2022: pwv¿6 mm (#3 and #7),
(iii) May 2022: pwv$\sim$5 mm ( #6, #8, #12, #13, and #14).

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. 26 in the
Appendix shows our pointing strategy). The total integration time per raster-
map was $\sim$1 h, including on and off integrations. The achieved rms noises
of these observations, merging all observed positions of a given raster-map,
are $\sim$22 mK ($J$=2–1), $\sim$20 mK ($J$=3–2), and $\sim$30 mK ($J$=4–3),
per 0.5 km s-1velocity channel. Table 11 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, $T_{\mathrm{A}}^{*}$,
to main-beam temperature, $T_{\mathrm{mb}}$, as $T_{\mathrm{mb}}$ =
$T_{\mathrm{A}}^{*}\times$ Feff/Beff, where $F_{\mathrm{eff}}$ and Beff are
the forward and beam efficienciesfootnote 6. Figure 3 shows a summary of the
spectra. Figures 27 and 28 show the complete dataset.

###  2.5 Herschel Td, $A_{\mathrm{V}}$, and $G_{0}^{\prime}$ maps

In addition to the molecular and atomic line maps, we also make use of the
dust temperature ($T_{\mathrm{d}}$) and 850 $\upmu$m dust opacity
($\tau_{\mathrm{850\,\upmu m}}$) 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
$\tau_{850\,\upmu\mathrm{m}}$ dust opacity map following Pety et al. (2017):

$A_{\mathrm{V}}=2.7\times
10^{4}\;\tau_{850\,\upmu\mathrm{m}}\;[\mathrm{mag}].$ (2)

By taking the $\tau_{850\,\upmu\mathrm{m}}$ error map of Lombardi et al.
(2014), we determine that the mean 5$\sigma$ error of the $A_{\mathrm{V}}$ map
is about 0.8 mag. This value is slightly above our molecular line detection
threshold ($A_{\mathrm{V}}$ $\simeq$ 0.3-0.4 mag, see Fig. 4). Thus, we
caution that one can probably not trust any $A_{\mathrm{V}}$–$W$ trend below
$A_{\mathrm{V}}$ $\simeq$ 0.8 mag. For each line of sight, we determined the
FIR surface brightness, $I_{\mathrm{FIR}}$, from spectral energy distributions
(SED) fits, by integrating:

$I_{\mathrm{FIR}}=\int I_{\nu}\;d\nu=\int
B_{\nu}(T_{\mathrm{d}})[1-e^{-\tau_{\nu}}]\leavevmode\nobreak\ d\nu,$ (3)

from $\lambda$ = 40 to 500 $\upmu\mathrm{m}$. In this expression,
$B_{\nu}$($T_{\mathrm{d}}$) is the blackbody function,
$\tau_{\nu}$=$\tau_{\nu_{\mathrm{850\,\upmu\mathrm{m}}}}(\nu/\nu_{\mathrm{850\,\upmu\mathrm{m}}})^{\beta}$
is the frequency-dependent dust opacity (we adopt the same emissivity exponent
as Lombardi et al., 2014), and $T_{\rm d}$ is an effective dust temperature.

We estimate the strength of the far-UV (FUV) radiation field (6 $<$ $E$ $<$
13.6 eV), in Habing units ($G_{0}^{\prime}$), from $I_{\mathrm{FIR}}$ using:

$G_{0}^{\prime}=\frac{1}{2}\frac{I_{\mathrm{FIR}}\,[\rm
erg\,s^{-1}\,cm^{-2}\,sr^{-1}]}{1.3\times 10^{-4}}.$ (4)

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 $G_{0}^{\prime}$ (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. (4) 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. (4) provides an upper limit to the
actual $G_{0}$ toward embedded star-forming cores (at high $A_{\mathrm{V}}$).
These cores emit significant non-PDR FIR dust continuum. To directly compare
our line emission maps with the $A_{\mathrm{V}}$, $G_{0}^{\prime}$, and
$I_{\mathrm{FIR}}$ maps, we also spatially smoothed these SED-derived maps to
an angular resolution of 120′′ (Figs. 2a and b).

Table 5: SED derived parameters from 5 deg2 maps of Orion B.

Parameter | Median | Mean value | Std. dev. | Units
---|---|---|---|---
$T_{\mathrm{d}}$ | 18 | 20 | 4 | K
$A_{\mathrm{V}}$ | 2.6 | 3.2 | 3 | mag
$I_{\mathrm{FIR}}$ | 0.002 | 0.02 | 0.3 | erg s-1 cm-2 sr-1
$G_{0}^{\prime}$ | 9 | 70 | 1000 | Habing

##  3 Results

###  3.1 Spatial distribution of the HCN J = 1–0 emission, relation to other
chemical species, and $A_{\mathrm{V}}$ and $G_{0}^{\prime}$ maps

Figure 1 shows a composite RGB image of the mapped area ($\sim$ 5 deg2 = 250
pc2). This image shows extended HCN $J$=1–0 emission far from the main dense
gas filaments (where $A_{\mathrm{V}}$ $>$ 8 mag), as well as very extended 70
$\upmu$m dust emission (e.g., André et al., 2010) from FUV-illuminated warm
grains. Figure 2 shows the spatial distribution of the 12CO, HCO+, HCN, and
HNC $J$=1–0 integrated line intensities, $W$ (also dubbed line surface
brightness) at a common resolution of $\sim$2′ ($\sim$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 $\sim$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 C18O $J$=1–0 (Gaudel et al., 2023).

Table 4 provides the total line luminosity ($L_{\rm line}$) from the mapped
area in $L_{\odot}$ units. $L_{\rm line}$ is the power emitted through a given
line. It also provides $L^{\prime}_{\rm line}$ (in units of K km s-1 pc2),
with:

${L^{\prime}_{\mathrm{line}}=d^{2}\,\int
T_{\mathrm{mb}}(v)\,dv\,d\Omega\,=\,W_{\mathrm{average}}\,\times\,A,}$ (5)

where $\Omega$ is the solid angle subtended by the source area and
$W_{\mathrm{average}}$ 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 12CO $J$=1–0 luminosity over the
mapped area, $\sim$1.7 $L_{\odot}$, is more than a hundred times higher than
$L_{\rm HCO^{+}\,1-0}$ and $L_{\mathrm{HCN\,1-0}}$.

Figures 2a and 2b show maps of visual extinction ($A_{\mathrm{V}}$) and the
approximate strength of the FUV radiation field $G_{0}^{\prime}$ (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 $A_{\mathrm{V}}$ values, with a secondary peak toward
NGC 2023 star-forming cores. The highest values of $G_{0}^{\prime}$ correspond
to cloud areas in the vicinity of the H ii regions NGC 2024 ($G_{0}^{\prime}$
$\approx$ 104), with a contribution from the neighbor H ii region created by
Alnitak star ($G_{0}^{\prime}$ $\approx$ 103), NGC 2023 ($G_{0}^{\prime}$
$\approx$ 103), IC 435 ($G_{0}^{\prime}$ $\approx$ 102), and the ionization
front IC 434 ($G_{0}^{\prime}$ $\approx$ a few 102) that includes the iconic
Horsehead Nebula. On the other hand, the easter part of the cloud shows low
surface brightness $I_{\mathrm{FIR}}$ emission compatible with
$G_{0}^{\prime}$ of a few to $\simeq$ 10\. The median $G_{0}^{\prime}$ in the
mapped region is 9.

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

Figure 5: Line emission properties as a function of $A_{\mathrm{V}}$. (a)
Fractions (in %) of line luminosities emitted in each $A_{\mathrm{V}}$ mask.
(b) Typical (the mode) line intensity in each $A_{\mathrm{V}}$ mask. (c)
Cumulative line luminosity.

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
cloud777Section 6.4 discusses the relation between these lines and
$I_{\mathrm{FIR}}$.. The running median of the HCN $J$ = 1$-$0 emission
increases with extinction at $A_{\mathrm{V}}$ ¿ 3 mag, whereas the running
median of the HNC $J$ = 1–0 emission shows a similar change of tendency but at
higher extinction depths $A_{\mathrm{V}}$ ¿ 5 mag. As HCN, the largest number
of HCO+ $J$ = 1$-$0 and [C i] 492 GHz line detections in the map occur at
$A_{\mathrm{V}}$ $\simeq$ 3 mag. Atomic carbon, however, shows an approximate
bimodal behavior with $A_{\mathrm{V}}$ (it shows both bright and faint
emission at high $A_{\mathrm{V}}$). Indeed, while $A_{\mathrm{V}}$ 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 C0/CO transition (e.g., Hollenbach et al., 1991). On the other hand, lines
of sight of large $A_{\mathrm{V}}$ 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 $L_{\rm
line}$ within a set of four visual extinction masks. The mask with
$A_{\mathrm{V}}$¿15 mag ($\sim$1% of the total mapped area) represents the
highest density gas associated with dense cores. The mask within the
$A_{\mathrm{V}}$ range 8 to 15 mag ($\sim$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 $A_{\mathrm{V}}$ below 4 mag
(translucent and PDR gas; $\sim$80% of the mapped area) and 4 $<$
$A_{\mathrm{V}}$ $<$ 8 mag (intermediate cloud depths representing $\sim$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 $A_{\mathrm{V}}$¡4 mag.
Interestingly, about a 30% of the total HCN $J$ = 1–0 emission arises from gas
also at $A_{\mathrm{V}}$¡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,
$A_{\mathrm{V}}$ $>$ 15 mag. Likewise, the HCN and HNC 2D histograms peak at
$A_{\mathrm{V}}$ lower than 3 mag (HCN) and 5 mag (HNC). This contrasts with
the N2H+ $J$=1–0 emission, which arises from cold and dense gas shielded from
FUV radiation at $A_{\mathrm{V}}$ $>$ 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
($\sim$1 K km s-1) even at $A_{\mathrm{V}}$ $<$ 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 $A_{\mathrm{V}}$ $>$ 15 mag (dense gas). For lower $A_{\mathrm{V}}$, the
lines are fainter but detectable. Since the translucent gas spans much larger
areas than the dense gas (96% of the mapped cloud is $A_{\mathrm{V}}$ ¡ 8 mag,
80% at $A_{\mathrm{V}}$ ¡ 3 mag), in many instances it is the widespread and
faint extended emission that dominates the total luminosity. We stress that
$\sim$70% of the HCN $J$ = 1–0 line luminosity in Orion B arises from gas at
$A_{\mathrm{V}}$ ¡ 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 $A_{\mathrm{V}}$. 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
$A_{\mathrm{V}}$, such as $W(A_{\mathrm{V}}$ $<$
$A_{\mathrm{V}}^{\mathrm{char}})$=50% (e.g., Barnes et al., 2020). We find
that the characteristic $A_{\mathrm{V}}^{\mathrm{char}}$ for CO $J$=1–0 is 3.8
mag, which implies that 50% of the CO total intensity arises from gas below
$A_{\mathrm{V}}$ = 3.8 mag. For HCO+, HCN, and HNC $J$ = 1–0 lines, we find
$A_{\mathrm{V}}^{\mathrm{char}}$ 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).

###  3.2 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 / 12CO $J$=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 3$\sigma$ 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 ratio888To obtain the [C i]
492 GHz/CO $J$=1–0 line ratio with line intensities in erg cm-2 s-1 sr-1 one
has to multiply by (492 GHz/115 GHz)3 $\simeq$ 78.). Table 6 summarizes the
average and median line intensity ratios in the mapped region.

Table 6: Statistics of 5 deg2 line intensity ratio maps shown in Fig. 6.

Line Intensity Ratio | Median | Average | std |  $\rho$ ($G_{0}^{\prime}$)†
---|---|---|---|---
HCN / CO $J$ = 1–0 | 0.011 | 0.015 | 0.023 |  -0.4
HCN / HNC $J$ = 1–0 | 2.7 | 3.1 | 1.2 |  -0.6
HCN / HCO+ $J$ = 1–0 | 0.9 | 0.88 | 0.4 |  -0.2
[C i] / CO $J$ = 1–0 | 0.15 | 0.20 | 0.26 | -0.3

999†$\rho$($G_{0}^{\prime}$) is the Spearman correlation rank with the
$G_{0}^{\prime}$ map. See also Fig. 20 in the Appendix.

Figure 6: Line intensity ratio maps. Contours show $A_{\mathrm{V}}$= 4, 6, 8,
and 15 mag.

— 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
$A_{\mathrm{V}}$ (shown in contours). We also find high line intensity ratios
($\sim$ 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, $\sim$0.5-0.9, appear in cold and low
$I_{\rm FIR}$ 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 $G_{0}^{\prime}$, $T_{\rm
d}$, $T_{\rm peak}$(CO), and $A_{\rm V}$. Only the HCN / HNC $J$ = 1–0 line
intensity map shows a (weak) monotonic correlation with $G_{0}^{\prime}$
(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 19 and 20 show 2D histograms of the
studied line intensity ratios as function a of $A_{\mathrm{V}}$ and $I_{\rm
FIR}$, respectively.

##  4 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 ($T_{\rm ex}$) 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, $T_{\mathrm{rot}}$, and $N$(HCN) in a sample of
representative positions observed in rotationally excited HCN and H13CN 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 ($\sim$0.06 pc).

###  4.1 HCN column density and $T_{\rm ex}$ using the LTE-HFS method

Firstly, we determine $T_{\mathrm{ex}}$ ($J$ = 1–0) and the opacity-corrected
column density $N^{\mathrm{\tau,corr}}$(HCN) by applying the LTE-HFS fitting
method in CLASSfootnote 5 (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 $T_{\mathrm{ex}}$ and linewidth $\Delta v$, 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:

${T_{\mathrm{mb}}(v)=[J(T_{\rm ex})-J(T_{\rm bg})]\,[1\,-\,e^{-\tau(v)}],}$
(6)

where $\tau(v)$ is the sum of the HFS line opacities:

${\tau(v)=\sum_{i}^{\rm
HFS}\tau_{i}\,(v-v_{i}^{0}),\,\,\,\,{\rm{with}}\,\,\,\,\tau_{i}\,(v-v_{i}^{0})=\tau_{i}^{0}\,\phi(v-v_{i}^{0}).}$
(7)

In the above expressions, $\tau_{i}^{0}$ is the opacity of each HFS component
$i$ at (each) line center ($v_{i}^{0}$), and $\phi(v-v_{i}^{0})$ is a Gaussian
profile centered at $v_{i}^{0}$. In the LTE-FTS fitting method, one fixes the
sum of all HCN $J$ = 1–0 HFS line center opacities, $\tau^{0}$, following
their intrinsic line strengths:

${\tau^{0}=\tau_{F=1-0}^{0}+\tau_{F=2-1}^{0}+\tau_{F=1-1}^{0}=\frac{3}{9}\,\tau^{0}+\frac{5}{9}\,\tau^{0}+\frac{1}{9}\,\tau^{0}.}$
(8)

In the Rayleigh-Jeans regime, $J(T_{\rm ex})\rightarrow T_{\rm ex}$. Thus, the
LTE-HFS fitting method returns $T_{\mathrm{ex}}$ and $\tau^{0}$ as outputs. We
use these parameters to derive $N^{\mathrm{\tau,corr}}$ (HCN). In order to
obtain satisfactory fits, we applied this method to the brightest regions,
those $T_{\rm mb}^{\rm peak}$(HCN $J$ = 1–0 $F$=2–1, $\geq$ 0.5 K =
5$\sigma$), associated with the main cloud velocity component at
$v_{\mathrm{LSR}}\simeq$10 km s-1.

Figure 7: Spatial distribution of $T_{\mathrm{ex}}$(HCN $J$=1–0) and $N$(HCN)
estimated from LTE-HFS fits, and maps of HCN $J$=1–0 HFS intensity ratios. (a)
$T_{\mathrm{ex}}$(HCN $J$=1–0). (b) Opacity-corrected column densities
$N$(HCN). (c) and (d) $R_{02}$ and $R_{12}$ (white color corresponds to non-
anomalous ratios).

Figure 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 $\tau\rightarrow 0$ (1$\sigma$ is the standard deviation relative to the
mean line ratios).

Figure 7 shows the resulting HCN column density and $T_{\mathrm{ex}}$ maps in
a smaller but high S/N submap. The average (median) $T_{\mathrm{ex}}$ ($J$ =
1–0) in the region is 5 K (4.5 K), implying subthermal emission, that is,
$T_{\mathrm{ex}}$ $\ll$ $T_{\mathrm{k}}$ and $n$(H2) $<$ $n_{\rm cr,\,eff}$.
NGC 2024 shows the highest values, with $T_{\mathrm{ex}}$ ¿ 15 K.
$N^{\mathrm{\tau,corr}}$(HCN) ranges between 1013 and a few 1014 cm-2. The
average (median) column is 3.4$\cdot$1013 cm-2 (1.3$\cdot$1013 cm-2).

Figure 9: Comparison of observed $W$(HCN $J$=1–0) intensities in Orion B and
predictions from nonlocal and non-LTE radiative transfer models including line
overlap for (a) $N$(HCN)=1013 cm-2 and (b) $N$(HCN)=1014 cm-2. The continuous
curves show model results for $T_{\mathrm{k}}$=60, 30, and 10 K (red, green,
and blue curves, respectively), different ionization fractions:
$\chi_{\mathrm{e}}$ = 0 (continuous curves), $\chi_{\mathrm{e}}$ =
2$\cdot$10-5 (dashed curves), and $\chi_{\mathrm{e}}$ = 10-4 (dotted curves).
The pink and orange horizontal line mark the mean and median values of W(HCN
$J$=1–0). The pink shaded area represents the standard deviation (1$\sigma$)
relative to the mean detected W(HCN $J$=1–0) intensities in Orion B (at 30′′).
Positions in the pink area account for $\sim$70 % of the total $L_{\rm
HCN\,1-0}$ in the map. The right panels show an histogram with the
distribution of W(HCN $J$=1–0) detections in individual map pixels.

###  4.2 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, $R^{\Delta v}_{02}$=$\Delta v$($F$=0–1)/$\Delta v$($F$=2–1) and
$R^{\Delta v}_{12}$=$\Delta v$($F$=1–1)/$\Delta v$($F$=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 anomalous101010We recall
that the range of possible HFS line intensity ratios in LTE are
$R_{02}$=$[$0.2, 1$]$ and $R_{12}$=$[$0.6, 1$]$. Outside these ranges, HFS
ratios are called anomalous (and very anomalous if $R_{02}$ $<$ 0.2 and
$R_{12}$ $<$ 0.6). Only in LTE, HFS lines have the same $T_{\mathrm{ex}}$ and
same linewidths, thus $R^{\Delta v}$=1. 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 $T_{\mathrm{ex}}$ 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. 24 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
$\sim$1 to $\sim$2 km s-1 (see also Table 12). These linewidths are broader
than the narrow linewidths, $\sim$0.5 km s-1, typically observed in Orion B
toward dense and FUV-shielded cold cores in molecules such as H13CO+ (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 $R_{02}^{\Delta v}$
and $R_{12}^{\Delta v}$. 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^{\Delta v}$$\neq$1, when HFS lines become optically thick (e.g., see Fig. 3
of Goicoechea et al., 2022).

###  4.3 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 $para$-H2, $ortho$-H2, and electrons in warm gas.

The grid of single-component ($T_{\mathrm{k}}$=60, 30, and 10 K) static-cloud
(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)=1013 cm-2, representative of optically thin or marginally optically
thick HCN $J$=1–0 HFS lines, and $N$(HCN)=1014 cm-2, representative of bright
optically thick lines. The range in gas densities $n$(H2) goes from $\sim$107
cm-3, only relevant to hot cores and protostellar envelopes, to nearly 102
cm-3, relevant to the most extended and FUV-illuminated component of GMCs. As
we are mostly interested in this component, these models compute the HCN
excitation for three different electron abundances: $\chi_{\mathrm{e}}$ =
10-4, 2$\times$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
$n$(H2).

The right panels in Fig. 9 show histograms with the distribution of $W$(HCN
$J$ = 1–0) detections ($>$ 3$\sigma$) in individual pixels of the map. The
mean (median) intensity111111This value is higher than the line intensity of
the average HCN $J$ = 1–0 spectrum over the full mapped area (see Table 4),
thus including emission free pixels. The mean and median $W$(HCN $J$ = 1–0)
intensity values computed considering pixels with CO $J$ = 1–0 detections
above 3$\sigma$ are 1.0 and 0.7 K km s-1, respectively. 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
1$\sigma$ 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 intensities 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 reference11 for the extended cloud emission. Models with $N$(HCN)=1013
cm-2 (Fig. 9a) encompass this $W$(HCN $J$ = 1–0) intensity level. The gas
temperature in this cloud component is $T_{\mathrm{k}}$ $\simeq$ 30 to 60 K
(translucent gas and UV-illuminated cloud edges; see specific PDR models in
Sect. 5). Using $N$(HCN) = 1013 cm-2 and neglecting electron collisional
excitation ($\chi_{e}$ $=$ 0) we determine an upper limit to the gas density
of $n$(H2) $\simeq$ (1–3) $\times$ 104 cm-3.

Figure 10 shows the effect of electron excitation predicted by radiative
transfer models appropriate to this extended and translucent gas (adopting
$n$(H2) = 5 $\times$103 cm-3). The plot shows how $W$(HCN $J$ = 1–0) (red
curves) and $T_{\mathrm{ex}}$(HCN $J$ = 1–0 $F$ = 2–1) (blue curves) increase
as the electron abundance $\chi_{e}$ increases. The reference intensity value,
$W$(HCN $J$ = 1–0) = 1 K km s-1, intersects the model curves at an electron
abundance of a few 10-5 and $T_{\mathrm{ex}}$ $\simeq$ 3.2–3.5 K. These low
excitation temperatures imply weak collisional excitation, but still
$T_{\mathrm{ex}}$ $>$ $T_{\rm CMB}$.

Interestingly, the extended HCN $J$ = 1–0 emission observationally correlates
well with the [C i] 492 GHz emission (see Fig. 2 and Sect. 6.2.1). In
addition, our photochemical models show that $\chi_{e}$ reaches $\gtrsim$ 10-5
in the [C i] 492 GHz emitting cloud layers (Figs. 13a,b). For such high
$\chi_{e}$ values, electron excitation enhances the HCN $J$ = 1–0 emission at
low gas densities (see Fig. 10 and Goldsmith & Kauffmann, 2017; Goicoechea et
al., 2022). Hence, we estimate that the median gas density in the extended
cloud component is $n$(H2) $\simeq$ (4–7) $\times$ 103 cm-3 if $\chi_{e}$
$\simeq$ 2$\times$10-5 (or $\simeq$ 103 cm-3 if $\chi_{e}$ $\simeq$ 10-4).

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 $\sim$15$\%$ of the total HCN
$J$ = 1–0 luminosity in the map. This bright HCN emission can only be
reproduced by models with $N$(HCN)=1014 cm-2 and higher gas densities, $n$(H2)
$>$ 105 cm-3.

Table 7: HCN $J$ = 1–0 HFS line intensity ratios, $W$(HCN $J$ = 2–1) / $W$(HCN
$J$ = 1–0) and $W$(HCN $J$ = 3–2) / $W$(HCN $J$ = 1–0) line intensity ratios,
and parameters derived from rotational population diagrams, computed in
Appendix E, toward a sample of representative cloud positions.

Pos. | HCN J=1–0 | Excited HCN | Rotational diagrams
---|---|---|---
| $R_{02}$ | $R_{12}$ | $R_{02}^{\Delta v}$ | $R_{12}^{\Delta v}$ | $R\frac{J=2-1}{J=1-0}$ | $R\frac{J=3-2}{J=1-0}$ | $T_{\mathrm{rot}}^{\mathrm{thin}}$ | $N^{\mathrm{thin}}$ | $T_{\mathrm{rot}}^{\mathrm{\tau,corr}}$ | $N^{\mathrm{\tau,\mathrm{corr}}}$
|  |  |  |  |  |  | [K] | 1013 [cm-2] | [K] | 1013 [cm-2]
#1 | 0.3 | 0.4 | 1.1 | 1.1 | 0.9$\pm$0.4 | 1.2$\pm$0.5 | 18$\pm$5 | 5$\pm$3 | 38$\pm$10 | 86$\pm$20
#2 | 0.2 | 0.7 | 1.2 | 1.9 | 1.0$\pm$0.4 | 0.7$\pm$0.3 | 11$\pm$2 | 0.8$\pm$0.3 | 10$\pm$1 | 1.5$\pm$0.3
#3 | 0.3 | 0.4 | 0.9 | 1.1 | 1.0$\pm$0.4 | 0.5$\pm$0.2 | 10$\pm$1 | 0.9$\pm$0.4 | 7$\pm$1 |
#4 | 0.6 | 0.5 | 1.0 | 1.0 | 0.7$\pm$0.3 | 0.2$\pm$0.1 | 9$\pm$2 | 0.2$\pm$0.1 | 7$\pm$1 | 0.5$\pm$0.3
HH PDR | 0.3 | 0.5 | 0.7 | 0.9 | 0.5$\pm$0.2 | 0.13$\pm$0.04 | 8$\pm$1 | 0.5$\pm$0.3 | 5$\pm$1 | 1.6$\pm$1.4
#6 | 0.2 | 0.6 | 0.8 | 0.9 | 0.6$\pm$0.2 | 0.4$\pm$0.2 | 7$\pm$1 | 1.1$\pm$0.7 |  |
#7 | 0.3 | 0.5 | 0.8 | 1.0 | 0.8$\pm$0.3 | 0.3$\pm$0.1 | 6.6$\pm$0.8 | 0.8$\pm$0.3 | 5.2$\pm$0.3 | 2.4$\pm$0.4
#8 | 0.5 | 0.6 | 0.8 | 1.0 | 0.7$\pm$0.3 | 0.3$\pm$0.1 | 6.1$\pm$0.6 | 0.5$\pm$0.1 | 4.2$\pm$0.2 | 3.0$\pm$0.7
HH Core | 0.3 | 0.5 | 0.7 | 1.0 | 0.5$\pm$0.2 | 0.16$\pm$0.08 | 5.3$\pm$0.7 | 0.7$\pm$0.4 | 4.3$\pm$0.5 | 2.2$\pm$1.1
#10 | 0.2 | 0.5 | 0.7 | 1.1 | 0.4$\pm$0.2 | 0.12$\pm$0.04 | 5.0$\pm$0.9 | 0.4$\pm$0.2 |  |
#11 | 0.3 | 0.6 | 0.8 | 1.0 | 0.4$\pm$0.2 | 0.10$\pm$0.04 | 6.8$\pm$0.9 | 0.5$\pm$0.3 |  |
#12 | 0.4 | 0.5 | 0.8 | 0.8 | 0.3$\pm$0.1 | 0.10$\pm$0.04 | 4.7$\pm$0.9 | 0.7$\pm$0.5 |  |
#13 | 0.2 | 0.6 | 1.0 | 1.1 | 0.3$\pm$0.1 | 0.09$\pm$0.04 | 4.7$\pm$0.8 | 0.4$\pm$0.2 |  |
#14 | 0.4 | 0.5 | 1.0 | 1.1 | 0.3$\pm$0.1 | 0.06$\pm$0.02 | 4.4$\pm$0.5 | 0.4$\pm$0.2 |  |

121212 The uncertainty in R02, R12, R${}^{\Delta v}_{02}$, and R${}^{\Delta
v}_{12}$ is between 10 and 20%.

Figure 10: $W$(HCN $J$ = 1–0) (red curves) and $T_{\mathrm{ex}}$ (HCN $J$=1–0
$F$=2–1) (blue curves) predicted by non-LTE radiative transfer models,
appropriate to extended and translucent gas, as a function of electron
abundance. The vertical pink shaded area intersects the typical $W$(HCN $J$ =
1–0) $=$ 1 K km s-1 intensity level ($\pm$ 20%). Figure 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 9).

###  4.4 Rotationally excited HCN and H13CN 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 H13CN 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. 27 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
$\sim$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 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 $\tau_{2-1}$ $\rightarrow$ 0 and
$\tau_{3-2}$ $\rightarrow$ 0, one should detect the $\sim$1:9:2 and
$\sim$1:25:1 HFS ratios. The filled dots in Fig. 11 show the observed ratios
(summarized in Table 9 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.

####  4.4.1 HCN and HNC rotational diagrams

Here we estimate the degree of excitation (by determining rotational
temperatures, $T_{\mathrm{rot}}$) 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 $T_{\mathrm{rot}}$ from observations of multiple-$J$
lines. We derive the HCN column density and rotational temperature under the
assumption of optically thin emission ($N^{\mathrm{thin}}$ and
$T_{\mathrm{rot}}^{\mathrm{thin}}$). We also determine their opacity-corrected
values ($N^{\tau,\mathrm{corr}}$ and $T_{\mathrm{rot}}^{\tau,\mathrm{corr}}$)
by using the H13CN line intensities (see Fig. 27) and assuming that the
emission from HCN and H13CN 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 $N^{\mathrm{\tau,corr}}$(HCN) ranges
from 5$\times$1012 to 3.4$\times$1013 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 HN13C. Rotational temperatures are also low,
from 5 to 11 K. HNC column densities range from $\sim$1012 to 1.6$\times$1013
cm-2 (see Table 10).

####  4.4.2 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, source-by-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 $T_{\mathrm{k}}$ = 30-60 K and $n$(H2) of a few 104 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 $n$(H2) of a few 104 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 ($\sim$38$\pm$10 K). The
observed $R^{J}_{31}$ ¿ $R^{J}_{21}$ intensity ratios are consistent with the
presence of dense gas, $n$(H2) $\geq$ 106 cm-3.

###  4.5 HCN/HNC intensity and column density ratios

Table 8 summarizes the resulting $N$(HCN)/$N$(HNC) column density ratios
obtained from rotational population diagrams (Sect. 4.4.1) as well as
$W$(HCN)/$W$(HNC) $J$ = 1–0 and $J$ = 3–2 line intensity ratios. The positions
that host lower excitation conditions (e.g., low $T_{\rm rot}$(HNC)) tend to
have lower $N$(HCN)/$N$(HNC) column and $W$(HCN)/$W$(HNC) intensity ratios.
Mildly FUV-illuminated environments such as the Horsehead nebula show
$W$(HCN)/$W$(HNC) line intensity ratios of about two, whereas the most FUV-
shielded cold cores and their surroundings (positions #7, #8, #10, #13)
display ratios of about one. On the other hand, the most FUV-irradiated and
densest cloud environments (those with HCN $J$ = 4–3 detections in NGC 2024)
show ratios of at least four (positions #1 and #2).

These results roughly agree with the spatial correlation between the HCN/HNC
$J$ = 1–0 integrated line intensity ratio and $G_{0}^{\prime}$ 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 $G_{0}^{\prime}$ in the mapped region.
The running median HCN/HNC $J$ = 1–0 intensity ratio increases from $\simeq$ 1
at $G_{0}^{\prime}$ $\simeq$10 to $\simeq$ 3 at $G_{0}^{\prime}$ $\simeq$
200\. For higher values of $G_{0}^{\prime}$, the running median intensity
ratio stays roughly constant at $\simeq$ 3-4. We estimate that the higher HCN
$J$ = 1–0 line opacity toward these bright positions (at least $\tau$ $\simeq$
5–10, see Table 9) compared to that of HNC $J$ = 1–0 (on the order of $\tau$
$\simeq$ 1–3,Table 10) contributes to the observed constancy of the line
intensity ratio.

Table 8: HNC rotational temperatures, HCN/HNC column density, and line
intensity ratios toward selected positions in Orion B.

Pos. |  $T_{\mathrm{rot}}$(HNC) | $\frac{N(\mathrm{HCN})}{N(\mathrm{HNC})}^{\dagger}$ | $\frac{W(\mathrm{HCN})}{W(\mathrm{HNC})}$ | $\frac{W(\mathrm{HCN})}{W(\mathrm{HNC})}$
---|---|---|---|---
|  |  |  $J$=1–0 |  $J$=3–2
#1 | 11 $\pm$ 2 | 3 – 54 | 4 | 4
#2 | 9 $\pm$ 2 | 4 – 7.5 | 4 | 3
#3 | 7 $\pm$ 1 | 3 – 14 | 4 | 5
#4 | 6 $\pm$ 1 | 0.7 – 1.7 | 0.8 | 0.6
HH PDR | 5 $\pm$ 1 | 1.7 – 5 | 2 | 2
#6 | 6 $\pm$ 1 | 3 | 3 | 5
#7 | 8 $\pm$ 1 | 1.2 – 4 | 1 | 0.6
#8 | 8 $\pm$ 1 | 0.8 – 5 | 1 | 0.5
HH Core | 6 $\pm$ 1 | 2 – 5 | 2 | 1.6
#10 | 6 $\pm$ 1 | 1.3 | 1 | 0.8
#11 | – | – | 3 | –
#12 | 6 $\pm$ 1 | 1.7 | 2 | 1.2
#13 | 5 $\pm$ 1 | 1.3 | 1 | 0.8
#14 | 5 $\pm$ 1 | 4 | 3 | 2

131313†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 10) .

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 ($\chi_{\rm cr,e}^{*}$ in Table 1)
is a factor of $\sim$ 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 different (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–H2 inelastic collision rate
coefficients will make such detailed studies feasible.

Figure 12: 2D histogram of the observed HCN/HNC $J$=1–0 line intensity ratio
as a function of $G_{0}^{\prime}$ in the Orion B map. The dashed black curve
shows the running median. The error bars show the standard deviation. Figure
13: Constant density gas-phase PDR models with $G_{0}$=100 and
$n_{\mathrm{H}}$=5$\times$103 cm-3 (left) and 5$\times$104 cm-3 (right). These
models adopt $E_{b}$ = 1200 K for Reaction (9). 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
$A_{\mathrm{V}}$ (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).

##  5 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 H2($v$) (hereafter H${}_{2}^{*}$)
with neutral N atoms leading to NH $+$ H (Goicoechea & Roncero, 2022), as well
as reactions of $o$-H2 and $p$-H2 with N+ ions, leading to NH+ $+$ H (Zymak et
al., 2013).

We also included the isomerization reaction:

$\rm{HNC\,+H\,\rightarrow\,HCN\,+\,H},$ (9)

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: $\sim$2130 K (Talbi et al., 1996), $\sim$1670 K (Sumathi & Nguyen,
1998), and $\sim$960 K (Petrie, 2002). In our models we initially adopt
$E_{b}$ = 1200 K (see Graninger et al., 2014). We also included the
isomerization reaction:

$\rm{HNC\,+C\,\rightarrow\,HCN\,+\,C},$ (10)

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$\times$10-10 cm3 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 H2 cosmic ray ionization rate $\zeta_{\rm CR}$ 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 $n_{\rm H}$ = 5$\times$103 cm-3
(left panels) and $n_{\rm H}$ = 5$\times$104 cm-3 (right panels). Figures 13a
and 13b show the predicted column density ratios (upper panels) and
abundance141414Because at low $A_{\mathrm{V}}$ 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) / $n_{\rm H}$,
where $n_{\rm H}$ = $n$(H) + 2$n$(H2). If the abundance of H atoms is
negligible, then $x$(species) = 0.5 $\chi$(species). profiles (lower panels)
as a function of cloud depth, in mag of visual extinction151515In these 1D PDR
models, the cloud depth or shielding ($A_{\mathrm{V}}$ 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 $A_{\mathrm{V}}$ 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..

We determine molecular column densities at a given cloud depth
$A_{\mathrm{V}}$ (or cloud path length $l$) by integrating the predicted
depth-dependent abundance profile, $x$(species), from 0 to $A_{\mathrm{V}}$:

${N(l)=\int_{0}^{{\rm{A_{\mathrm{V}}}}}x(l)\,n_{\rm H}\,dl,}$ (11)

where $x$($l$) is the species abundance, with respect to H nuclei7, at a cloud
path length $l$.

###  5.1 Chemistry at cloud edges, $A_{\mathrm{V}}<4$ mag

The red shaded areas in Fig. 13 show model results for $A_{\mathrm{V}}<4$ 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 $x_{\rm e}$ $\simeq$ $x$(C+) $\simeq$ 10-4 to
$x_{\rm e}$ $\simeq$ 10-6 depending on $A_{\mathrm{V}}$ and $G_{0}$/$n_{\rm
H}$. To simplify our chemical discussion, Fig. 14 summarizes the network of
dominant chemical reactions at $A_{\mathrm{V}}<4$ mag. Wherever C+ is
abundant, reactions of CH2 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 $A_{\mathrm{V}}<4$ 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 $\rightarrow$ HCN/HNC $+$ H, are identical for both isomers (e.g.,
Semaniak et al., 2001). Therefore, the $N$(HCN)/$N$(HNC) column density ratio
at $A_{\mathrm{V}}<4$ 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)
$\simeq$ 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 $A_{\mathrm{V}}$ $\simeq$
1–3 mag (depending on $n_{\rm H}$), 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 $\rightarrow$ HCN + C as well as reaction N + HCO
$\rightarrow$ HCN + O provide additional formation paths for HCN at
$A_{\mathrm{V}}$ $<$ 4 mag (black and gray curves in Figs. 13c and 13d). These
two reactions enhance the HCN/HNC column density ratio to $\sim$5-15 at
$A_{\mathrm{V}}$ $\simeq$ 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 $n_{\rm H}$ $=$ 5$\times$103 cm-3 (5$\times$104 cm-3) models at
$A_{\mathrm{V}}$ $=$ 4 mag: $N$(HCN) = 4.5 $\times$ 1012 cm-2 (2.4 $\times$
1012 cm-2) and $N$(HNC) = 1.8 $\times$ 1012 cm-2 (4.5 $\times$ 1011 cm-2).
These column densities are representative of extended and translucent gas.

Figure 14: Dominant chemical reactions in FUV-illuminated gas.

###  5.2 Intermediate depths, 4 mag $<\\!A_{\mathrm{V}}\\!<$ 8 mag

The yellow shaded areas in Fig. 13 show model results for 4 mag
$<\\!A_{\mathrm{V}}\\!<$ 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 H3O+ 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 $\simeq$
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 $\simeq$ 1–2 toward
positions with low $G_{0}^{\prime}$ values (see Table 8 and Fig. 6).

Figure 15: Dominant chemical reactions in FUV-shielded gas.

The abundance of HCNH+, the precursor of HCN and HNC at large $A_{\mathrm{V}}$
(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 $n_{\rm H}$ because the
higher penetration of FUV radiation reduces the abundances of the neutral
species (CO, O, N2, and S) that destroy H${}_{3}^{+}$. In addition, the
H${}_{3}^{+}$ abundance scales with $\zeta_{\rm CR}$. We run a few models with
$\zeta_{\rm CR}$ 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)
because reaction:

$\rm{N\,+HCO\,\rightarrow\,HCN\,+\,O},$ (12)

becomes more important than HCNH+ dissociative recombination. Reaction (12) 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
$A_{\mathrm{V}}$ $=$ 8 mag. The PDR model with $n_{\rm H}$ $=$ 5$\times$103
cm-3 (5$\times$104 cm-3) predicts $N$(HCN) = 6.2 $\times$ 1013 cm-2 (6.4
$\times$ 1012 cm-2) and $N$(HNC) = 5.2 $\times$ 1013 cm-2 (3.2 $\times$ 1012
cm-2). These column densities encompass the range of HCN (see Table 7) and HNC
(see Table 10) column densities we infer toward the observed sample of
representative positions in Orion B.

###  5.3 On HNC destruction reactions

Previous studies invoked that the isomerization reaction H $+$ HNC
$\rightarrow$ 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 $T$ $\simeq$ 50 K at $A_{\mathrm{V}}$ $\simeq$ 1 mag, and
$T$ $\simeq$ 15 K at $A_{\mathrm{V}}$ $\simeq$ 4 mag (upper panels of Fig. 13a
and 13b). We run the same two models adopting $E_{b}$ = 200 K for reaction (9)
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 $A_{\mathrm{V}}$ $<2$ 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 $\rightarrow$ 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 (9) was barrierless. Only in this case, the isomerization reaction H
$+$ HNC $\rightarrow$ HCN $+$ H would dominate HNC destruction (specially at
large $A_{\mathrm{V}}$), increasing the $N$(HCN)/$N$(HNC) ratio. However, this
choice of $E_{b}$ results in very low HNC column densities, 2$\times$1012 cm-2
and 3$\times$1011 cm-2 at $A_{\mathrm{V}}$ = 8 mag for $n_{\rm H}$ =
5$\times$103 cm-3 and 5$\times$104 cm-3, respectively. These $N$(HNC) values
are much lower than the $N$(HNC) column densities we infer from observations
(Table 10). 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
$\rightarrow$ CO $+$ NH dominates HNC destruction, and thus it controls the
HCN/HNC abundance ratio if the energy barrier of this particular reaction is
low, $E_{b}$ $\simeq$ 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., 2019, 2022).

##  6 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.

Figure 16: 2D histograms. (a) Visual extinction $A_{\mathrm{V}}$ 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 $A_{\mathrm{V}}$ 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
$A_{\mathrm{V}}$, for $A_{\mathrm{V}}$ ¡ 3 mag, and for $A_{\mathrm{V}}$ ¿ 3
mag. The dashed black curve shows the running median. Error bars show the
standard deviation in the x-axis.

###  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 $R_{02}\\!\gtrsim$ 0.2 and $R_{12}$ $\lesssim$ 0.6.

Figure 8a shows that the most common HCN $J$ = 1–0 HFS line intensity ratios
in Orion B are $R_{02}$ $\gtrsim$ 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 $n$(H2) of several
103 cm-3 to 104 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).

###  6.2 Bimodal behavior of the HCN/CO J=1–0 line intensity ratio as a
function of $A_{\mathrm{V}}$

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 $A_{\mathrm{V}}$).
Normal galaxies have low luminosity ratios $L_{\rm HCN}$/$L_{\rm CO}$ =
0.02–0.06 while luminous and ultraluminous galaxies have $L_{\rm HCN}$/$L_{\rm
CO}$ $>$ 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 $A_{\mathrm{V}}$. The 2D histogram shows a bimodal
behavior. There is a first branch at $A_{\mathrm{V}}$ $>$ 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 $\gtrsim$ 0.02 (at $A_{\mathrm{V}}$ $\simeq$ 8 mag) to $\sim$
0.1 (dense cores at larger $A_{\mathrm{V}}$). In addition, there is a second
branch at $A_{\mathrm{V}}$ $<$ 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, $\gtrsim$ 0.1, in diffuse gas at
$A_{\mathrm{V}}$ $\simeq$ 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 $\chi_{e}$) from the
more shielded cloud interior. This picture agrees with HCN $J$ = 1–0 emission
arising from extended and relatively low density gas, $n$(H2) $\leq$ 104 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.

####  6.2.1 Cloud porosity to FUV radiation: HCN 1–0 emission from high
electron abundance gas traced by [C ii] 158 $\upmu$m 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 $\chi_{e}$ $\simeq$ a few 10-4, where the electron
abundance is controlled by the photoionization of carbon atoms, thus leading
to $\chi_{e}$ $\simeq$ $\chi$(C+) at $A_{\mathrm{V}}$ $\lesssim$ 2 mag. These
cloud layers emit bright FIR [C ii] 158 $\upmu$m fine-structure line emission.
Slightly deeper inside the molecular cloud, at $A_{\mathrm{V}}$ $\lesssim$ 3
mag, the flux of FUV photons decreases to the point where the gas becomes
fully molecular, and neutral atomic carbon (C0) becomes more abundant than C+
(see PDR models in Figs. 13a and 13b). Our models predict $\chi_{e}$ $\gtrsim$
10-5 at the C0 abundance peak, where the [C i] 492 GHz line emission reaches
its intensity peak.

Figure 17: 30′′-resolution view of the Horsehead. (a) [C ii] 158 $\upmu$m
(Pabst et al., 2017) and (b) [C i] 492 GHz (Philipp et al., 2006) integrated
line intensity maps (from 7 to 18 km s-1). (c) R=HCN/CO intensity ratio and
(d) HCN $J$=1–0 line intensity maps. Contours on [C ii] 158 $\upmu$m map:
HCN/CO ratio (R=0.06 and 0.12). Contours on [C i] 492 GHz map: HCN $J$=1–0
surface brightness (W=2.7, 4.5, and 6 K km s-1).

Figure 17a shows a [C ii] 158 $\upmu$m 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 $\upmu$m emission from the (nearly edge-on) molecular
PDR at the rim of the Horsehead. It also shows bright [C ii] 158 $\upmu$m
emission from the neutral atomic PDR, $\chi$(H) $\gg$ $\chi$(H2) at
$A_{\mathrm{V}}$ $<$ 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,
$\geq$ 0.12 (green contours), toward the FUV-illuminated cloud edge. This area
matches the [C ii] 158 $\upmu$m emission from the rim of the Horsehead. As
$n$(H2) is a few 104 cm-3 (e.g., Pabst et al., 2017) and
$\chi_{\rm\,cr,\,e}^{*}$(HCN $J$ = 1–0) $<$ $\chi_{e}$ $\simeq$ $\chi$(C+)
$\simeq$ 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 C0 coexists with
HCN in large areas of the cloud, which implies moderate ionization fractions,
$\chi_{e}$ $\gtrsim$ 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 13CO $J$= 1–0 emission are very similar (Ikeda et al., 2002), the presence
of C0 cannot be restricted to cloud edges ($A_{\mathrm{V}}$ $<$ 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 13CO $J$ = 1–0 emission (Pearson
coefficients of 0.80, 0.79, and 0.73 respectively). These correlations include
many positions at $A_{\mathrm{V}}$ $>$ 3 mag (60% of [C i] 492 GHz detections,
and 70% of total [C i] 492 GHz luminosity, see Fig. 4). Therefore, C0 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 $\upmu$m 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 C0.

####  6.2.2 High HCN/CO J = 1–0 and [C i] 492 GHz/CO J = 1–0 line intensity
ratios from gas at $A_{\mathrm{V}}$ ¡ 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 C0 and moderate $\chi_{e}$) is ultimately responsible of the
increased ratios observed at $A_{\mathrm{V}}$ ¡ 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 upper-right panel shows all detections
(at all $A_{\mathrm{V}}$) in the map. The running median clearly shows that,
above a threshold of $W$(HCN)/$W$(CO) $J$ = 1–0 $\gtrsim$ 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 $A_{\mathrm{V}}$ $<$ 3 mag (Fig. 16c) and $A_{\mathrm{V}}$
$>$ 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
$A_{\mathrm{V}}$ $<$ 3 mag. Hence, the ratios follow the increasing electron
abundance in PDR gas. On the other hand, the ratios are not correlated at
higher $A_{\mathrm{V}}$ ¿ 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-$A_{\mathrm{V}}$
branch, from extended FUV-illuminated low-density gas, leads to increasing
ratios with decreasing $A_{\mathrm{V}}$. 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 $\alpha$ (HCN $J$=1–0)

Using the dust SEDs across the observed field161616Appendix C.2 details how we
determine the gas mass., we derive the mass of the dense gas in the mapped
area (represented by gas at $A_{\mathrm{V}}$ $>$ 8 mag, e.g., Lada et al.,
2010). The likely density of this cloud component is $n$(H2) $>$ 104 cm-3
(e.g., Bisbas et al., 2019). We obtain $M_{\mathrm{dg}}$=3.1$\times$103
$M_{\odot}$, which accounts for about 20% of the total mass
($M_{\mathrm{H_{2},tot}}$ $\sim$ 1.7$\times$104 $M_{\odot}$) in the mapped
area. These numbers imply a dense gas surface density ($\Sigma_{\mathrm{dg}}$
= $M_{\mathrm{dg}}$ / $A$) and a total gas surface density
($\Sigma_{\mathrm{H_{2},tot}}$ = $M_{\mathrm{H_{2},tot}}$ / $A$) of
$\Sigma_{\mathrm{dg}}$ = 13 $M_{\odot}$ pc-2 and $\Sigma_{\mathrm{H_{2},tot}}$
= 70 $M_{\odot}$ pc-2, respectively, where in both cases we divide by the
total mapped area, $A$ $\simeq$ 250 pc2.

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:

$M_{\mathrm{dg}}\,=\,\alpha(\mathrm{HCN})\,\cdot\,L^{\prime}(\mathrm{HCN}),$
(13)

where $L^{\prime}$(HCN) is the total HCN $J$ = 1–0 line luminosity in the
mapped area (in K km s-1 pc2) as defined in Eq. (5). Gao & Solomon (2004a)
originally estimated $\alpha$(HCN) = 10 $M_{\odot}$ $/$ K km s-1 pc2. Recent
dust continuum and line emission surveys determine $\alpha$(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 $\alpha$(HCN) values, from
10 to 500 $M_{\odot}$ / K km s-1 pc2. However, these surveys typically map
star-forming clumps and their immediate environment (areas $<$1 deg2) 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 ($T_{\rm CMB}$ $\lesssim$ $T_{\rm ex}$ $\ll$ $T_{\rm k}$), but because
it covers large spatial scales, its total line luminosity typically exceeds
the line luminosity from dense gas in star-forming cores at $A_{\mathrm{V}}$
$>$ 8 mag ($\sim$30$\%$ in Orion B).

Here we determine $\alpha$ for HCN, HCO+, and HNC $J$ = 1–0 lines in Orion B.
We obtain $L^{\prime}$(HCN)=110 K km s-1 pc2 for HCN $J$ =1–0, which implies a
dense mass conversion factor $\alpha$(HCN) = 29 $M_{\odot}$ / K km s-1 pc2.
Table 4 summarizes the luminosities and $\alpha$ values derived for other
molecules. A recent survey of the Perseus low-mass star-forming region (at 11
arcmin resolution and covering 8.1 deg2 or $\sim$215 pc2) finds $\alpha$(HCN)
= 92 $M_{\odot}$ / K km s-1 pc2, $L^{\prime}$(HCN) = 55.3 K km s-1, and
$M_{\mathrm{dg}}$=5.1$\times$103 $M_{\odot}$ (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 $\alpha$(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, Aquila, and Ophiuchus star-forming cores ($<$10
pc2). They find that $\alpha$(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 $\alpha$(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 $A_{\mathrm{V}}$ $>$ 8 mag is similar to
that at $A_{\mathrm{V}}$ $<$ 3 mag. This results in a similar value of the
mass to total $L^{\prime}$(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.

###  6.4 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 ($\sim$ 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 $I_{\rm FIR}$ 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 $I_{\mathrm{FIR}}$ (in erg s-1 cm-2 sr-1). We find that the observed line
intensities $W$ scale with $I_{\mathrm{FIR}}$ as a power law. As we fit these
points using an orthogonal regression method171717Using the Scipy-odr package
(Branham, 1995; Virtanen et al., 2020).
https://docs.scipy.org/doc/scipy/reference/odr.html 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 $I_{\mathrm{FIR}}$ $\propto$ $W^{N}$ (as in
Fig. 18) or as $W$ $\propto$ $I_{\mathrm{FIR}}^{1/N}$ (as in Fig. 21). Perhaps
provocatively, and in order to promote the comparison with the extragalactic
scalings SFR–$L_{\rm mol}$ (e.g., Gao & Solomon, 2004a; Shirley et al., 2008;
Shetty et al., 2013, 2014a, 2014b), here we start discussing the power-law
indexes $N$.

As discussed in Sect. 2.5, $I_{\mathrm{FIR}}$ is a surrogate of the local FUV
radiation field, $G^{\prime}_{0}$ (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 $I_{\mathrm{FIR}}$ traces the strength of the FUV radiation
field, but $L_{\mathrm{FIR}}$ over a small region does not trace the true
SFR181818The total FIR luminosity in the mapped region of Orion B ($\sim$ 250
pc2) is $L_{\rm FIR}$ = 1.5$\times$105 $L_{\odot}$ (or $\Sigma_{\rm FIR}$ =
6$\times$102 $L_{\odot}$ pc-2). Using the extragalactic scalings (e.g.,
Kennicutt, 1998a), these FIR luminosities translate into a SFR of
2.6$\times$10-5 $M_{\odot}$ yr-1, which is nearly an order of magnitude lower
than the SFR estimated by counting young stellar objects (YSOs),
1.6$\times$10-4 $M_{\odot}$ yr-1 (Lada et al., 2010). Pabst et al. (2021) find
a similar result in Orion A, namely that SFR(FIR) $<$ SFR(YSOs). .

Figure 18: 2D histograms of the 12CO, 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
$I_{\mathrm{FIR}}$ 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 $I_{\mathrm{FIR}}$ ¡ 6$\times$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.

By fitting all points in Fig. 18, we find that $W$(CO), $W$(HCO+) and $W$(HCN
$J$=1–0) scale with $I_{\mathrm{FIR}}$ as a power law with $N$ $\sim$ 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 $N$ $\sim$ 1.8–2.2. A closer inspection of the
$I_{\mathrm{FIR}}$–$W$(CO $J$ = 1–0) running median shows two clear
tendencies. The median toward the brightest FIR positions ($I_{\mathrm{FIR}}$
$>$ 0.4 erg s-1 cm-2 sr-1 or $G^{\prime}_{0}$ $>$ 1500, mostly arising from
NGC 2024 star-forming clump) shows a power-law index of $N$ $\sim$ 4.8. On the
other hand, the faintest $I_{\mathrm{FIR}}$ and $W$(CO $J$ = 1–0) positions
show $N$ $\sim$ 0.4 (sublinear relationship). This faint CO emission is
associated with widespread and very extended diffuse gas (low $A_{\mathrm{V}}$
and $G^{\prime}_{0}$ $<$ 20).

The $I_{\mathrm{FIR}}$–$W$(HCN $J$ = 1–0) and $I_{\mathrm{FIR}}$–$W$(HCO+ $J$
= 1–0) histograms are quite similar. They also reveal two different
tendencies. Fitting the brightest $I_{\mathrm{FIR}}$ 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$$\sim$1.6 for HCN
and $N$$\sim$2.4 for HCO+ (superlinear relationships). In contrast, the most
common low surface brightness HCN $J$ = 1–0, HCO+ $J$ = 1–0, and
$I_{\mathrm{FIR}}$ positions (those with $G^{\prime}_{0}<20$) show
$N$$\sim$0.6 (i.e., not far from the extended and diffuse CO emission index).
Interestingly, the $I_{\mathrm{FIR}}$–$W$(HNC $J$=1–0) and
$I_{\mathrm{FIR}}$–$W$([C i]492 GHz) histograms show a single superlinear
tendency across the map, with $N$$\sim$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 $I_{\mathrm{FIR}}$ ($G_{0}^{\prime}>1500$ and dense
gas), whereas the single index for [C i] 492 GHz resembles that of HCO+ at
high $G^{\prime}_{0}$. This similitude must reflect their related chemistry
and excitation conditions.

From the point of view of the local gas properties, Figs. 18 and 21 show that
$W$(CO $J$ = 1–0), $W$(HCO+ $J$ = 1–0), and $W$(HCN $J$ = 1–0) intensities
increase with increasing $I_{\mathrm{FIR}}$ up to $G^{\prime}_{0}$ $\simeq$
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 $n$(H2) $<$ $n_{\rm cr,\,eff}$(HCN 1–0) and
thus, $T_{\rm ex}$ $<$ $T_{\rm k}$. 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 $G_{0}$/$n_{\rm H}$ 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 $G^{\prime}_{0}$ increases.

On the other hand, Figs. 18 and 21 show that $W$(CO $J$ = 1–0), $W$(HCO+ $J$ =
1–0), and $W$(HCN $J$ = 1–0) respond weakly to $I_{\mathrm{FIR}}$ once the FUV
field becomes too intense ($G^{\prime}_{0}$ $>$ 1500). These other regions at
large $A_{\mathrm{V}}$ host denser gas, so that $n$(H2) $>$ $n_{\rm
cr,\,eff}$(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 $I_{\mathrm{FIR}}$ at all
$G^{\prime}_{0}$. 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 $G^{\prime}_{0}$ $<$ 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 FUV-shielded cold
gas. Thus, we expect that most of the HNC $J$ = 1–0 emission arises from gas
in which $n$(H2) $>$ $n_{\rm cr,\,eff}$(HNC 1-0). These facts explain the
weaker response of $W$(HNC $J$ = 1–0) to FUV radiation. Finally, PDR models
predict that the C0 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 power-law indexes, $I_{\mathrm{FIR}}$
$\propto$ $W^{N}$ (or $W$ $\propto$ $I_{\mathrm{FIR}}^{1/N}$). These $N$
indexes resemble the kind of Kennicutt-Schmidt power-law indexes, SFR
$\propto$ $L_{\rm mol}^{N}$, found in galaxy surveys that average multiple
GMCs (e.g., Wu et al., 2005, 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 $L_{\rm FIR}$ becomes a reliable tracer of the
global SFR, as well as the connection between the extragalactic averages
versus our spatially resolved scalings.

##  7 Summary and conclusions

In the context of the IRAM 30m ORION-B large program, we presented a detailed
analysis of 5 deg2 ($\sim$250 pc2) 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, H13CN, and HN13C
lines. We constructed integrated line intensity ($W$), visual extinction, and
$I_{\rm FIR}$ (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, $L^{\prime}$(HCN $J$ $=$ 1–0)
$=$ 110 K km s-1 pc-2, arises from gas at $A_{\mathrm{V}}$ $<$ 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 $A_{\mathrm{V}}$
$<$ 8 mag.

– We detect anomalous HCN $J$ = 1–0 HFS line intensity ratios (also in the HCN
$J$ = 2–1 and 3–2 transitions) almost everywhere in the cloud (Sect. 4.4).
That is, HCN $J$ = 1–0 $R_{02}$ = $W$($F$=0–1)/$W$($F$=2–1) and $R_{12}$ =
$W$($F$=1–1)/$W$($F$=2–1) hyperfine line intensity ratios outside the LTE
range $R_{02}$ = [0.2, 1] and $R_{12}$ = [0.6, 1]. We also detect anomalous
HFS line width ratios. That is, $\Delta v$($F$=0–1) $\neq$ $\Delta v$($F$=2–1)
$\neq$ $\Delta v$($F$=1–1) (Sect. 4.2). Radiative effects induced by moderate
line opacities and HFS line overlaps produce these anomalous ratios, which are
inconsistent with the common assumption of the same $T_{\rm ex}$ and line
width for all HFS lines of a given rotational transition.

– Most of the widespread and extended HCN $J$ $=$ 1–0 emission arises from
weakly collisionally excited gas with $n$(H2) $\lesssim$ 104 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 $R_{02}$ $\gtrsim$ 0.2 and $R_{12}$ ¡ 0.6 observed at
large scales. Even lower densities are possible in FUV-illuminated gas if
$\chi_{e}$ $\geq$ 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 $T_{\rm k}$
(Sect. 5). In particular, HNC is a slightly better tracer of dense gas,
defined as $n$(H2) $>$ 104 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
$A_{\mathrm{V}}$, with an inflection point at $A_{\mathrm{V}}$ $\lesssim$ 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
$A_{\mathrm{V}}$ branch of the observed distribution of the HCN/CO $J$ $=$1–0
line intensity ratio. The highest HCN/CO $J$ $=$1–0 line intensity ratios
($\sim$ 0.1) at $A_{\mathrm{V}}$ $<$ 3 mag correspond to regions displaying
high [C i] 492 GHz/CO $J$ $=$1–0 intensity ratios too ($>$ 1). These values
are characteristic of low-density PDRs and $\chi_{e}$ $\gtrsim$ 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 $W$(13CO $J$ $=$ 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 $A_{\mathrm{V}}$ $>$ 3 mag (i.e.,
not exactly from the cloud surface). In addition, the 70 $\upmu$m 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, $\alpha$ (HCN) $=$ 29 M⊙ / K km s-1 pc2, 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 $L_{\rm HCN}$ versus SFR.

– The low-surface brightness and extended HCN $J$ $=$ 1–0 and HCO+ $J$ $=$ 1–0
emissions ($\lesssim$ 1 K km s-1) scale with $I_{\rm FIR}$ with a similar
power-law index (Sect. 6.4). Together with CO $J$ $=$ 1–0, these lines respond
to the increasing $I_{\rm FIR}$ up to $G^{\prime}_{0}$ $\simeq$ 20\. On the
other hand, the bright HCN emission ($>$ 6 K km s-1) from dense gas in star-
forming clumps weakly responds to $I_{\rm FIR}$ once the FUV radiation field
becomes too intense ($G^{\prime}_{0}$ $>$ 1500). HNC $J$ $=$ 1–0 and [C i] 492
GHz lines weakly respond to $I_{\rm FIR}$ at all $G^{\prime}_{0}$.