11institutetext:  Instituto de Física Fundamental, CSIC, Calle Serrano 123,
E-28006 Madrid, Spain
11email<EMAIL_ADDRESS>22institutetext: Observatorio Astronómico
Nacional, IGN, Calle Alfonso XII 3, E-28014 Madrid, Spain 33institutetext:
Observatorio de Yebes, IGN, Cerro de la Palera s/n, E-19141 Yebes,
Guadalajara, Spain 44institutetext: Centro de Astrobiología (CSIC/INTA), Ctra.
de Torrejón a Ajalvir km 4, 28806, Torrejón de Ardoz, Spain

# The abundance and excitation of molecular anions
in interstellar clouds††thanks: Based on observations carried out with the
Yebes 40m telescope (projects 19A003, 20A014, 20A016, 20B010, 20D023, 21A006,
21A011, 21D005, 22B023, and 23A024) and the IRAM 30m telescope. The 40m radio
telescope at Yebes Observatory is operated by the Spanish Geographic Institute
(IGN; Ministerio de Transportes, Movilidad y Agenda Urbana). IRAM is supported
by INSU/CNRS (France), MPG (Germany), and IGN (Spain).

M. Agúndez 11 N. Marcelino 2233 B. Tercero 2233 I. Jiménez-Serra 44 J.
Cernicharo 11

(Received; accepted)

We report new observations of molecular anions with the Yebes 40m and IRAM 30m
telescopes toward the cold dense clouds TMC-1 CP, Lupus-1A, L1527, L483,
L1495B, and L1544. We detected for the first time C3N- and C5N- in Lupus-1A
and C4H- and C6H- in L483. In addition, we report new lines of C6H- toward the
six targeted sources, of C4H- toward TMC-1 CP, Lupus-1A, and L1527, and of
C8H- and C3N- in TMC-1 CP. Excitation calculations using recently computed
collision rate coefficients indicate that the lines of anions accessible to
radiotelescopes run from subthermally excited to thermalized as the size of
the anion increases, with the degree of departure from thermalization
depending on the H2 volume density and the line frequency. We noticed that the
collision rate coefficients available for the radical C6H cannot explain
various observational facts, which advises for a revisitation of the collision
data for this species. The observations presented here, together with
observational data from the literature, are used to model the excitation of
interstellar anions and to constrain their abundances. In general, the anion-
to-neutral ratios derived here agree within 50 % (a factor of two at most)
with literature values, when available, except for the C4H-/C4H ratio, which
shows higher differences due to a revision of the dipole moment of C4H. From
the set of anion-to-neutral abundance ratios derived two conclusions can be
drawn. First, the C6H-/C6H ratio shows a tentative trend in which it increases
with increasing H2 density, as expected from theoretical grounds. And second,
it is incontestable that the higher the molecular size the higher the anion-
to-neutral ratio, which supports a formation mechanism based on radiative
electron attachment. Nonetheless, calculated rate coefficients for electron
attachment to the medium size species C4H and C3N are probably too high and
too low, respectively, by more than one order of magnitude.

###### Key Words.:

astrochemistry – line: identification – molecular processes – radiative
transfer – ISM: molecules – radio lines: ISM

##  1 Introduction

The discovery of negatively charged molecular ions in space has been a
relatively recent finding (McCarthy et al., 2006). To date the inventory of
molecular anions detected in interstellar and circumstellar clouds consists of
four hydrocarbon anions, C4H- (Cernicharo et al., 2007), C6H- (McCarthy et
al., 2006), C8H- (Brünken et al., 2007a; Remijan et al., 2007), and C10H-
(Remijan et al., 2023), and four nitrile anions, CN- (Agúndez et al., 2010),
C3N- (Thaddeus et al., 2008), C5N- (Cernicharo et al., 2008), and C7N-
(Cernicharo et al., 2023a). The astronomical detection of most of these
species has been possible thanks to the laboratory characterization of their
rotational spectrum (McCarthy et al., 2006; Gupta et al., 2007; Gottlieb et
al., 2007; Thaddeus et al., 2008). However, the astronomical detection of
C5N-, C7N-, and C10H- is based on high level ab initio calculations and
astrochemical arguments (Botschwina & Oswald, 2008; Cernicharo et al., 2008,
2020, 2023a; Remijan et al., 2023). In fact, in the case of C10H- it is not
yet clear whether the identified species is C10H- or C9N- (Pardo et al.,
2023).

The current situation is such that there is only one astronomical source where
the eight molecular anions have been observed, the carbon-rich circumstellar
envelope IRC +10216 (McCarthy et al., 2006; Cernicharo et al., 2007, 2008;
Remijan et al., 2007; Thaddeus et al., 2008; Agúndez et al., 2010; Cernicharo
et al., 2023a; Pardo et al., 2023), while the first negative ion discovered,
C6H- (McCarthy et al., 2006), continues to be the most widely observed in
astronomical sources (Sakai et al., 2007, 2010; Gupta et al., 2009; Cordiner
et al., 2011, 2013).

Observations indicate that along each of the series C2n+2H- and C2n-1N- (with
$n$ = 1, 2, 3, 4) the anion-to-neutral abundance ratio increases with
increasing molecular size (Millar et al., 2017). This is expected according to
the formation mechanism originally proposed by Herbst (1981), which involves
the radiative electron attachment to the neutral counterpart of the anion
(Herbst & Osamura, 2008; Carelli et al., 2013). However, the efficiency of
this mechanism in interstellar space has been disputed (Khamesian et al.,
2016), and alternative formation mechanisms have been proposed (Gianturco et
al., 2016). Currently there is not yet consensus on the formation mechanism of
molecular anions in space (see discussion in Millar et al. 2017). Moreover,
detections of negative ions other than C6H- in interstellar clouds are scarce,
and thus our view of the abundance of the different anions in interstellar
space is statistically very limited.

Apart from the anion-to-anion behavior it is also interesting to know which is
the source-to-source behavior. That is, how does the abundance of anions
behave from one source to another. Based on C6H- detections, the C6H-/C6H
abundance ratio seems to increase with increasing H2 volume density (Sakai et
al., 2007; Agúndez et al., 2008; Cordiner et al., 2013), which is expected
from chemical considerations (e.g., Flower et al. 2007; see also Sect. 6).
However, most anion detections in interstellar clouds have been based on one
or two lines and their abundances have been estimated assuming that their
rotational levels are populated according to local thermodynamic equilibrium
(LTE), which may not be a good assumption given the large dipole moments, and
thus high critical densities, of anions. Recently, rate coefficients for
inelastic collisions with H2 or He have been calculated for C2H- (Dumouchel et
al., 2012; Gianturco et al., 2019; Franz et al., 2020; Toumi et al., 2021;
Dumouchel et al., 2023), C4H- (Senent et al., 2019; Balança et al., 2021),
C6H- (Walker et al., 2016, 2017), CN- (Kłos & Lique, 2011; González-Sánchez et
al., 2020), C3N- (Lara-Moreno et al., 2017, 2019; Tchakoua et al., 2018), and
C5N- (Biswas et al., 2023), which makes it possible to study the excitation of
anions in the interstellar medium.

Here we report new detections of anions in interstellar sources. Concretely,
we detected C3N- and C5N- in Lupus-1A and C6H- and C4H- in L483. We also
present the detection of new lines of C4H-, C6H-, C8H-, C3N-, and C5N- in
interstellar clouds where these anions have been already observed. We use the
large observational dataset from this study, together with that available from
the literature, to review the observational status of anions in interstellar
clouds and to carry out a comprehensive analysis of the abundance and
excitation of anions in the interstellar medium.

##  2 Observations

###  2.1 Yebes 40m and IRAM 30m observations from this study

The observations of cold dark clouds presented in this study were carried out
with the Yebes 40m and IRAM 30m telescopes. We targeted the starless core
TMC-1 at the cyanopolyyne peak position (hereafter TMC-1 CP)111TMC-1 CP:
$\alpha_{J2000}=4^{\rm h}41^{\rm m}41.9^{\rm s}$ and
$\delta_{J2000}=+25^{\circ}41^{\prime}27.0^{\prime\prime}$, the starless core
Lupus-1A222Lupus-1A: $\alpha_{J2000}=15^{\rm h}42^{\rm m}52.4^{\rm s}$ and
$\delta_{J2000}=$-$34^{\circ}07^{\prime}53.5^{\prime\prime}$, the prestellar
cores L1495B333L1495B: $\alpha_{J2000}=4^{\rm h}15^{\rm m}41.8^{\rm s}$ and
$\delta_{J2000}=+28^{\circ}47^{\prime}46.0^{\prime\prime}$ and L1544444L1544:
$\alpha_{J2000}=5^{\rm h}4^{\rm m}18.0^{\rm s}$ and
$\delta_{J2000}=+25^{\circ}11^{\prime}10.0^{\prime\prime}$, and the dense
cores L1527555L1527: $\alpha_{J2000}=4^{\rm h}39^{\rm m}53.9^{\rm s}$ and
$\delta_{J2000}=+26^{\circ}03^{\prime}11.0^{\prime\prime}$ and L483666L483:
$\alpha_{J2000}=18^{\rm h}17^{\rm m}29.8^{\rm s}$ and
$\delta_{J2000}=$-$4^{\circ}39^{\prime}38.3^{\prime\prime}$, which host a
Class 0 protostar. All observations were done using the frequency switching
technique to maximize the on-source telescope time and to improve the
sensitivity of the spectra.

The Yebes 40m observations consisted in a full scan of the $Q$ band (31-50
GHz) acquired in a single spectral setup with a 7 mm receiver, which was
connected to a fast Fourier transform spectrometer that provides a spectral
resolution of 38 kHz (Tercero et al., 2021). The data of TMC-1 CP are part of
the on-going QUIJOTE line survey (Cernicharo et al., 2021). The spectra used
here were obtained between November 2019 and November 2022 and contain a total
of 758 h of on-source telescope time in each polarization (twice this value
after averaging both polarizations). Two frequency throws of 8 and 10 MHz were
used. The sensitivity ranges from 0.13 to 0.4 mK in antenna temperature. The
data of L1544 were taken between October and December 2020 toward the position
of the methanol peak of this core, where complex organic molecules have been
detected (Jiménez-Serra et al., 2016), and are part of a high-sensitivity
Q-band survey (31 h on-source; Jiménez-Serra et al. in prep.). The data for
the other sources were obtained from July 2020 to February 2023 for L483 (the
total on-source telescope time is 103 h), from May to November 2021 for L1527
(40 h on-source), from July 2021 to January 2023 for Lupus-1A (120 h on-
source), and from September to November 2021 for L1495B (45 h on-source).
Different frequency throws were adopted depending on the observing period,
which resulted from tests done at the Yebes 40m telescope to find the optimal
frequency throw. We used frequency throws of 10 MHz and 10.52 MHz for L483, 10
MHz for L1544, 8 MHz for L1527, and 10.52 MHz for Lupus-1A and L1495B. The
antenna temperature noise levels, after averaging horizontal and vertical
polarizations, are in the range 0.4-1.0 mK for L483, 1.3-1.8 mK for L1544,
0.7-2.7 mK for L1527, 0.7-2.8 mK for Lupus-1A, and 0.8-2.6 mK for L1495B.

The observations carried out with the IRAM 30m telescope used the 3 mm EMIR
receiver connected to a fast Fourier transform spectrometer that provides a
spectral resolution of 49 kHz. Different spectral regions within the 3 mm band
(72-116 GHz) were covered depending on the source. The data of TMC-1 CP
consist of a 3 mm line survey (Marcelino et al., 2007; Cernicharo et al.,
2012) and spectra observed in 2021 (Agúndez et al., 2022; Cabezas et al.,
2022). The data of L483 consists of a line survey in the 80-116 GHz region
(see Agúndez et al. 2019), together with data in the 72-80 GHz region, which
are described in Cabezas et al. (2021). Data of Lupus-1A, L1495B, L1521F,
L1251A, L1512, L1172, and L1389 were observed from September to November 2014
during a previous search for molecular anions at mm wavelengths (see Agúndez
et al. 2015). Additional data of Lupus-1A were gathered during 2021 and 2022
during a project aimed to observe H2NC (Agúndez et al., 2023). In the case of
L1527, the IRAM 30m data used were observed in July and August 2007 with the
old ABCD receivers connected to an autocorrelator that provided spectral
resolutions of 40 or 80 kHz (Agúndez et al., 2008).

The half power beam width (HPBW) of the Yebes 40m telescope is in the range
35-57 ′′ in the $Q$ band, while that of the IRAM 30m telescope ranges between
21 ′′ and 34 ′′ in the 3 mm band. The beam size can be fitted as a function of
frequency as HPBW(′′) = 1763/$\nu$(GHz) for the Yebes 40m telescope and as
HPBW(′′) = 2460/$\nu$(GHz) for the IRAM 30m telescope. Therefore, the beam
size of the IRAM 30m telescope at 72 GHz is similar to that of the Yebes 40m
at 50 GHz. The intensity scale in both the Yebes 40m and IRAM 30m telescopes
is antenna temperature, $T_{A}^{*}$, for which we estimate a calibration error
of 10 %. To convert antenna temperature into main beam brightness temperature
see foot of Table LABEL:table:lines_anion. All data were analyzed using the
program CLASS of the GILDAS software777https://www.iram.fr/IRAMFR/GILDAS/.

Figure 1: Lines of C6H- observed in this work toward six cold dense clouds
using the Yebes 40m telescope. See line parameters in Table
LABEL:table:lines_anion. Figure 2: Lines of C4H- observed in this work toward
TMC-1 CP, Lupus-1A, L1527, and L483 using the Yebes 40m and IRAM 30m
telescopes. See line parameters in Table LABEL:table:lines_anion. Figure 3:
Lines of C8H- observed toward TMC-1 CP and lines of the nitrile anions C3N-
and C5N- observed toward TMC-1 CP and Lupus-1A using the Yebes 40m and IRAM
30m telescopes. See line parameters in Table LABEL:table:lines_anion.

###  2.2 Observational dataset of anions in dark clouds

In Table LABEL:table:lines_anion we compile the line parameters of all the
lines of negative molecular ions detected toward cold dark clouds, including
lines from this study and from the literature. The line parameters of C7N-
observed toward TMC-1 CP are given in Cernicharo et al. (2023a) and are not
repeated here. In the case of C10H- in TMC-1 CP we do not include line
parameters here because the detection by Remijan et al. (2023) is not based on
individual lines but on spectral stack of many lines. The lines of molecular
anions presented in this study are shown in Fig. 1 for C6H-, Fig. 2 for C4H-,
and Fig. 3 for the remaining anions, i.e., C8H-, C3N-, and C5N-. Since we are
interested in the determination of anion-to-neutral abundance ratios, we also
need the lines of the corresponding neutral counterpart of each molecular
anion, which are the radicals C4H, C6H, C8H, C3N, and C5N. The velocity-
integrated intensities of the lines of these species are given in Table
LABEL:table:lines_neutral.

According to the literature, the most prevalent molecular anion, C6H-, has
been detected in 11 cold dark clouds: TMC-1 CP (McCarthy et al., 2006), L1527
and Lupus-1A (Sakai et al., 2007, 2010), L1544 and L1521F (Gupta et al.,
2009), and L1495B, L1251A, L1512, L1172, L1389, and TMC-1 C (Cordiner et al.,
2011, 2013). All these detections were based on two individual or stacked
lines lying in the frequency range 11-31 GHz (see Table
LABEL:table:lines_anion). Here we present additional lines of C6H- in the $Q$
band for TMC-1 CP, Lupus-1A, L1527, L1495B, and L1544, together with the
detection of C6H- in a new source, L483, through six lines lying in the $Q$
band (see Fig. 1).

Molecular anions different to C6H- have turned out to be more difficult to
detect as they have been only seen in a few sources. For example, C4H- has
been only detected in three dark clouds, L1527 (Agúndez et al., 2008),
Lupus-1A (Sakai et al., 2010), and TMC-1 CP (Cordiner et al., 2013). These
detections rely on one or two lines (see Table LABEL:table:lines_anion). Here
we report the detection of two additional lines of C4H- in the $Q$ band toward
these three sources, together with the detection of C4H- in one new source,
L483 (see Fig. 2).

The hydrocarbon anion C8H- has been observed in two interstellar sources.
Brünken et al. (2007a) reported the detection of four lines in the 12-19 GHz
frequency range toward TMC-1 CP, while Sakai et al. (2010) reported the
detection of this anion in Lupus-1A through two stacked lines at 18.7 and 21.0
GHz (see Table LABEL:table:lines_anion). Thanks to our Yebes 40m data, we
present new lines of C8H- in the $Q$ band toward TMC-1 CP (see Fig. 3).

Finally, the nitrile anions C3N- and C5N- have resulted to be quite elusive as
they have been only seen in one cold dark cloud, TMC-1 CP (Cernicharo et al.,
2020). Here we present the same lines of C3N- and C5N- reported in Cernicharo
et al. (2020) in the $Q$ band, but with improved signal-to-noise ratios, plus
two additional lines of C3N- in the 3 mm band. We also present the detection
of C3N- and C5N- in one additional source, Lupus-1A (see Fig. 3).

##  3 Physical parameters of the sources

Table 1: Source parameters.

Source |  | Type |  | $\Delta v$ |  | $T_{k}$ |  |  $n$(H2)
---|---|---|---|---|---|---|---|---
|  |  | Ref |  |  (km s-1) |  | (K) | Method | Ref |  |  (cm-3) | Method | Ref
TMC-1 CP |  | starless | (1) |  | 0.60 |  | 9 |  CH3CCH, CH3C4H | (8) |  |  1.0 $\times$ 104 |  HC3N with 13C | (8)
Lupus-1A |  | starless | (2) |  | 0.50 |  | 11 |  CH3CCH | (8) |  |  1.8 $\times$ 104 |  HC3N with 13C | (8)
L1527 |  | protostar | (3) |  | 0.60 |  | 14 |  CH3CCH | (3,8) |  |  $>$ 1 $\times$ 105 |  HC3N with 13C | (8)
L483 |  | protostar | (4) |  | 0.52 |  | 12 |  CH3CCH | (8) |  |  5.6 $\times$ 104 |  HC3N with 13C | (8)
L1495B |  | prestellar | (5) |  | 0.50 |  | 9 |  CH3CCH | (8) |  |  1.6 $\times$ 104 |  HCC13CN | (8)
L1544 |  | prestellar | (5) |  | 0.60 |  | 10 |  NH3, C17O, SO2 | (9,10,11) |  |  2 $\times$ 104 |  SO, SO2 | (11,12)
L1521F |  | prestellar | (5) |  | 0.45 |  | 9 |  CH3CCH, NH3 | (8,13) |  |  1 $\times$ 104 | HCCNC | (8)
L1251A |  | protostar | (6) |  | 0.40 |  | 10 |  HC3N hfs | (6) |  |  2.1 $\times$ 104 |  HC3N | (6)
L1512 |  | starless | (5) |  | 0.30 |  | 10 |  HC3N hfs | (6) |  |  2.6 $\times$ 104 |  HC3N | (6)
L1172 |  | protostar | (7) |  | 0.55 |  | 10 |  HC3N hfs | (6) |  |  7.5 $\times$ 104 |  HC3N | (6)
L1389 |  | protostar | (6) |  | 0.40 |  | 10 |  HC3N hfs | (6) |  |  5.2 $\times$ 104 |  HC3N | (6)
TMC-1 C |  | starless | (5) |  | 0.18 |  | 10 |  HC3N hfs | (6) |  |  1.1 $\times$ 104 |  HC3N | (6)

References: (1) Suzuki et al. (1992). (2) Sakai et al. (2010). (3) Sakai et
al. (2008). (4) Agúndez et al. (2019). (5) Crapsi et al. (2005). (6) Cordiner
et al. (2013). (7) Visser et al. (2002). (8) This work (see text). (9) Tafalla
et al. (2002). (10) Bacmann et al. (2002). (11) Vastel et al. (2018). (12)
Punanova et al. (2018). (13) Codella et al. (1997).

The interstellar clouds where molecular anions have been detected are 12 in
total and comprise cold dense cores in different evolutionary stages, such as
starless, prestellar, and protostellar (see Table 1). The classification as
protostellar cores is evident in the cases of L1527 and L483 as the targeted
positions are those of the infrared sources IRAS 04368+2557 and IRAS
18148$-$0440, respectively (Sakai et al., 2008; Agúndez et al., 2019). We also
classified L1251A, L1172, and L1389 as protostellar sources based on the
proximity of an infrared source (L1251A IRS3, CB17 MMS, and IRAS 21017+6742,
respectively) to the positions targeted by Cordiner et al. (2013). The
differentiation between starless and prestellar core is in some cases more
ambiguous. In those cases we followed the criterion based on the N2D+/N2H+
column density ratio by Crapsi et al. (2005). In any case, for our purposes it
is not very important whether a given core is starless or prestellar.

To study the abundance and excitation of molecular anions in these 12
interstellar sources through non-LTE calculations we need to know which are
the physical parameters of the clouds, mainly the gas kinetic temperature and
the H2 volume density, but also the emission size of anions and the linewidth.
The adopted parameters are summarized in Table 1.

Given that C6H- has not been mapped in any interstellar cloud to date, it is
not known whether the emission of molecular anions in each of the 12 sources
is extended compared to the telescope beam sizes, which are in the range 21-67
′′ for the Yebes 40m, IRAM 30m, and GBT telescopes at the frequencies targeted
for the observations of anions. Therefore one has to rely on maps of related
species. In the case of TMC-1 CP we assume that anions are distributed in the
sky as a circle with a diameter of 80 ′′ based on the emission distribution of
C6H mapped by Fossé et al. (2001). Recent maps carried out with the Yebes 40m
telescope (Cernicharo et al., 2023b) support the previous results of Fossé et
al. (2001). For the remaining 11 sources, the emission distribution of C6H is
not known and thus we assume that the emission of anions is extended with
respect to the telescope beam. This assumption is supported by the extended
nature of HC3N emission in the cases of L1495B, L1251A, L1512, L1172, L1389,
and TMC-1 C, according to the maps presented by Cordiner et al. (2013), and of
multiple molecular species, including C4H, in L1544, according to the maps
reported by Spezzano et al. (2017).

The linewidth adopted for each source (see Table 1) was calculated as the
arithmetic mean of the values derived for the lines of C6H- in the $Q$ band
for TMC-1 CP, Lupus-1A, L1527, L1495B, and L1544. In the case of L483 we
adopted the value derived by Agúndez et al. (2019) from the analysis of all
the lines in the 3 mm band. For L1521F, L1251A, L1512, L1172, and L1389 the
adopted linewidths come from IRAM 30m observations of CH3CCH in the 3 mm band
(see Sect. 2.1). Finally, for TMC-1 C we adopted as linewidth that derived for
HC3N by Cordiner et al. (2013).

The gas kinetic temperature was determined for some of the sources from the
$J$ = 5-4 and $J$ = 6-5 rotational transitions of CH3CCH, which lie around
85.4 and 102.5 GHz, respectively. We have IRAM 30m data of these lines for
TMC-1 CP, Lupus-1A, L483, L1495B, and L1521F, while for L1527 we used the data
obtained with the Nobeyama 45m telescope by Yoshida et al. (2019). Typically,
the $K$ = 0, 1, and 2 components are detected, which allow us to use the line
intensity ratio between the $K$ = 1 and $K$ = 2 components, belonging to the
$E$ symmetry species, to derive the gas kinetic temperature. Since transitions
with $\Delta K$ $\neq$ 0 are radiatively forbidden, the relative populations
of the $K$ = 1 and $K$ = 2 levels are controlled by collisions with H2 and
thus are thermalized at the kinetic temperature of H2. We do not use the $K$ =
0 component because it belongs to a different symmetry species, $A$, and
interconversion between $A$ and $E$ species is expected to be slow in cold
dense clouds and thus their relative populations may not necessarily reflect
the gas kinetic temperature.

Figure 4: $\chi^{2}$ as a function of H2 volume density and column density of
each of the three 13C isotopologues of HC3N in TMC-1 CP. Contours correspond
to 1, 2, and 3 $\sigma$ levels. The three maps have the same scale in the $x$
and $y$ axes to facilitate the comparison. The column density of HCC13CN is
clearly higher than those of H13CCCN and HC13CCN. The volume density of H2 is
constrained to a very narrow range, (0.9-1.1) $\times$ 104 cm-3, by the three
13C isotopologues of HC3N.

For TMC-1 CP we derive kinetic temperatures of 8.8 $\pm$ 0.6 K and 9.0 $\pm$
0.6 K from the $J$ = 5-4 and $J$ = 6-5 lines of CH3CCH, respectively.
Similarly, using the $J$ = 8-7 through $J$ = 12-11 lines of CH3C4H, which lie
in the $Q$ band, we derive temperatures of 9.1 $\pm$ 0.7 K, 8.7 $\pm$ 0.6 K,
9.0 $\pm$ 0.6 K, 8.1 $\pm$ 0.7 K, and 9.1 $\pm$ 0.8 K, respectively. We thus
adopt a gas kinetic temperature of 9 K, which is slightly lower than values
derived in previous studies, 11.0 $\pm$ 1.0 K and 10.1 $\pm$ 0.9 K at two
positions close to the cyanopolyyne peak using NH3 (Fehér et al., 2016) and
9.9 $\pm$ 1.5 K from CH2CCH (Agúndez et al., 2022). In Lupus-1A we derive
temperatures of 11.4 $\pm$ 1.7 K and 10.2 $\pm$ 1.1 K from the $J$ = 5-4 and
$J$ = 6-5 lines of CH3CCH, respectively. We thus adopt a gas kinetic
temperature of 11 K, which is somewhat below the value of 14 $\pm$ 2 K derived
in Agúndez et al. (2015) using the $K$ = 0, 1, and 2 components of the $J$ =
5-4 transition of CH3CCH. In L1527 we derive 13.6 $\pm$ 2.5 K and 15.1 $\pm$
2.4 K from the line parameters of CH3CCH $J$ = 5-4 and $J$ = 6-5 reported by
Yoshida et al. (2019). We thus adopt a kinetic temperature of 14 K, which
agrees perfectly with the value of 13.9 K derived by Sakai et al. (2008) using
CH3CCH as well. The gas kinetic temperature in L483 has been estimated to be
10 K by Anglada et al. (1997) using NH3, while Agúndez et al. (2019) derive
values of 10 K and 15 $\pm$ 2 K using either 13CO or CH3CCH. A new analysis of
the CH3CCH data of Agúndez et al. (2019) in which the weak $K$ = 3 components
are neglected and only the $K$ = 1 and $K$ = 2 components are used results in
kinetic temperatures of 11.5 $\pm$ 1.1 K and 12.6 $\pm$ 1.5 K, depending on
whether the $J$ = 5-4 or $J$ = 6-5 transition is used. We thus adopt a kinetic
temperature of 12 K for L483. For L1495B we derive 9.1 $\pm$ 0.9 K and 9.2
$\pm$ 0.7 K from CH3CCH $J$ = 5-4 and $J$ = 6-5, and we thus adopt a kinetic
temperature of 9 K. In L1521F we also adopt a gas kinetic temperature of 9 K
since the derived temperatures from CH3CCH $J$ = 5-4 and $J$ = 6-5 are 9.0
$\pm$ 0.7 K and 8.9 $\pm$ 0.9 K. The value agrees well with the temperature of
9.1 $\pm$ 1.0 K derived by Codella et al. (1997) using NH3. For the remaining
cores, the gas kinetic temperatures were taken from the literature, as
summarized in Table 1.

To estimate the volume density of H2 we used the 13C isotopologues of HC3N
when these data were available. We have Yebes 40m data of the $J$ = 4-3 and
$J$ = 5-4 lines of H13CCCN, HC13CCN, and HCC13CN for TMC-1 CP, Lupus-1A,
L1527, and L483. Data for one or various lines of these three isotopologues in
the 3 mm band are also available from the IRAM 30m telescope (see Sect. 2.1)
or from the Nobeyama 45 telescope (for L1527; see Yoshida et al. 2019). Using
the 13C isotopologues of HC3N turned out to constrain much better the H2
density that using the main isotopologue because one gets rid of optical depth
effects. We carried out non-LTE calculations under the Large Velocity Gradient
(LVG) formalism adopting the gas kinetic temperature and linewidth given in
Table 1 and varying the column density of the 13C isotopologue of HC3N and the
H2 volume density. As collision rate coefficients we used those calculated by
Faure et al. (2016) for HC3N with ortho and para H2, where we adopted a low
ortho-to-para ratio of H2 of 10-3, which is theoretically expected for cold
dark clouds (e.g., Flower et al. 2006). The exact value of the ortho-to-para
ratio of H2 is not very important as long as the para form is well in excess
of the ortho form, so that collisions with para H2 dominate. The best
estimates for the column density of the 13C isotopologue of HC3N and the
volume density of H2 are found by minimizing $\chi^{2}$, which is defined as

$\chi^{2}=\sum_{i=1}^{N_{l}}\Bigg{[}\frac{(I_{calc}-I_{obs})}{\sigma}\Bigg{]}^{2},$
(1)

where the sum extends over the $N_{l}$ lines available, $I_{calc}$ and
$I_{obs}$ are the calculated and observed velocity-integrated brightness
temperatures, and $\sigma$ are the uncertainties in $I_{obs}$, which include
the error given by the Gaussian fit and the calibration error of 10 %. To
evaluate the goodness of the fit, we use the reduced $\chi^{2}$, which is
defined as $\chi^{2}_{red}$ = $\chi^{2}_{min}$/($N_{l}-p$), where
$\chi^{2}_{min}$ is the minimum value of $\chi^{2}$ and $p$ is the number of
free parameters. Typically, a value of $\chi^{2}_{red}$ $\lesssim$ 1 indicates
a good quality of the fit. In this case we have $p$ = 2 because there are two
free parameters, the column density of the 13C isotopologue of HC3N and the H2
volume density. Errors in these two parameters are given as 1 $\sigma$, where
for $p$ = 2, the 1 $\sigma$ level (68 % confidence) corresponds to
$\chi^{2}$+2.3. The same statistical analysis is adopted in Sect. 5 when
studying molecular anions and their neutral counterparts through the LVG
method. In some cases in which the number of lines is small or the H2 density
is poorly constrained, the H2 volume density is kept fixed. In those cases $p$
= 1 and the 1 $\sigma$ error (68 % confidence) in the column density is given
by $\chi^{2}$+1.0.

In Fig. 4 we show the results for TMC-1 CP. In this starless core the H2
volume density is well constrained by the four available lines of the three
13C isotopologues of HC3N to a narrow range of (0.9-1.1) $\times$ 104 cm-3
with very low values of $\chi^{2}_{red}$. We adopt as H2 density in TMC-1 CP
the arithmetic mean of the values derived for the three isotopologues, i.e.,
1.0 $\times$ 104 cm-3 (see Table 1). Similar calculations allow to derive H2
volume densities of 1.8 $\times$ 104 cm-3 for Lupus-1A, 5.6 $\times$ 104 cm-3
for L483, and a lower limit of 105 cm-3 for L1527 (see Table 1). The value for
L483 is of the same order than those derived in the literature, 3.4 $\times$
104 cm-3 from the model of Jørgensen et al. (2002) and 3 $\times$ 104 cm-3,
from either NH3 (Anglada et al., 1997) or CH3OH (Agúndez et al., 2019). For
L1495B we could only retrieve data for one of the 13C isotopologues of HC3N,
HCC13CN, from which we derive a H2 density of 1.6 $\times$ 104 cm-3 (see Table
1). In the case of L1521F, 13C isotopologues of HC3N were not available and
thus we used lines of HCCNC, adopting the collision rate coefficients
calculated by Bop et al. (2021), to derive a rough estimate of the H2 volume
density of 1 $\times$ 104 cm-3 (see Table 1). Higher H2 densities, in the
range (1-5) $\times$ 105 cm-3, are derived for L1521F from N2H+ and N2D+
(Crapsi et al., 2005), probably because these molecules trace the innermost
dense regions depleted in CO.

Figure 5: Excitation temperature (color-coded map) as a function of quantum
number of upper level (x-axis) and H2 volume density (y-axis) for six negative
molecular anions as obtained from LVG calculations adopting a gas kinetic
temperature of 10 K, a column density of 1011 cm-2, and a linewidth of 0.5 km
s-1. The references for the dipole moments are Brünken et al. (2007b) for
C2H-, Botschwina (2000) for C4H-, Blanksby et al. (2001) for C6H-, Botschwina
et al. (1995) for CN-, Thaddeus et al. (2008) and Kołos et al. (2008) for
C3N-, and Botschwina & Oswald (2008) for C5N-. For reference, the white dotted
vertical line indicates the $J$ level at which the energy is 10 K. The
microwave and mm spectral regions observable with radiotelescopes are
indicated. The small dark blue regions in the bottom-left corner of the C4H-,
C6H-, and C3N- panels correspond to negative excitation temperatures.

For the remaining sources we adopted H2 volume densities from the literature
(see Table 1). For L1544 we adopted a value of 2 $\times$ 104 cm-3 from the
analysis of SO and SO2 lines by Vastel et al. (2018). This H2 density is in
agreement with the range of values, (1.5-4.0) $\times$ 104 cm-3, found by Bop
et al. (2022) in their excitation analysis of HCCNC and HNC3. Note that H2
volume densities toward the dust peak are larger than 106 cm-3. However, as
shown by Spezzano et al. (2017), the emission of C4H probes the outer shells
and thus a density of a few 104 cm-3 is appropriate for our calculations
toward the CH3OH peak. In the cases of L1251A, L1512, L1172, L1389, and TMC-1
C, we adopted the H2 densities from the analysis of HC3N lines by Cordiner et
al. (2013). The reliability of the H2 volume densities derived by these
authors is supported by the fact that the densities they derive for TMC-1 CP
and L1495B, 1.0 $\times$ 104 cm-3 and 1.1 $\times$ 104 cm-3, respectively, are
close to the values determined in this study from 13C isotopologues of HC3N
(see Table 1).

In spite of the different evolutionary status of the 12 anion-containing
clouds, the gas kinetic temperatures and H2 volume densities at the scales
proven by the Yebes 40m, IRAM 30m, and GBT telescopes are not that different.
Gas temperatures are restricted to the very narrow range 9-14 K, while H2
densities are in the range (1.0-7.5) $\times$ 104 cm-3, at the exception of
L1527 which has an estimated density in excess of 105 cm-3 (see Table 1).

##  4 Excitation of anions: general considerations

One may expect that given the large dipole moments of molecular anions, as
high as 10.4 D in the case of C8H- (Blanksby et al., 2001), the rotational
levels should be populated out of thermodynamic equilibrium in cold dark
clouds. This is not always the case as it will be shown here. To get insight
into the excitation of negative molecular ions in interstellar clouds we run
non-LTE calculations under the LVG formalism adopting typical parameters of
cold dark clouds, i.e., a gas kinetic temperature of 10 K, a column density of
1011 cm-2 (of the order of the values typically derived for anions in cold
dark clouds; see references in Sect. 2.2), and a linewidth of 0.5 km s-1 (see
Table 1), and we varied the volume density of H2 between 103 and 106 cm-3. The
sets of rate coefficients for inelastic collisions with H2 adopted are
summarized in Table 2. In those cases in which only collisions with He are
available we scaled the rate coefficients by multiplying them by the square
root of the ratio of the reduced masses of the H2 and He colliding systems.
When inelastic collisions for ortho and para H2 are available, we adopted a
ortho-to-para ratio of H2 of 10-3.

Table 2: Collision rate coefficients used in this study. Species |  Collision data available$?$ | Reference
---|---|---
| Adopted colliding system |
Molecular anions
C2H- | Yes |  C2H- – $p$-H2 | Toumi et al. (2021)
C4H- | Yes |  C4H- – ($o$/$p$)-H2 | Balança et al. (2021)
C6H- | Yes |  C6H- – ($o$/$p$)-H2 | Walker et al. (2017)
C8H- | No |  C6H- – ($o$/$p$)-H2 | Walker et al. (2017)
CN- | Yes |  CN- – ($o$/$p$)-H2 | Kłos & Lique (2011)
C3N- | Yes |  C3N- – ($o$/$p$)-H2 | Lara-Moreno et al. (2019)
C5N- | No |  C6H- – ($o$/$p$)-H2 | Walker et al. (2017)
Radicals
C4H | No |  HC3N – ($o$/$p$)-H2 | Faure et al. (2016)
C6H | Yes |  C6H – He | Walker et al. (2018)
C8H | No |  HC5N – $p$-H2 | Lique (priv. comm.)
|  | \+ IOS | Alexander (1982)
C3N | Yes |  C3N – He | Lara-Moreno et al. (2021)
C5N | No |  HC5N – $p$-H2 | Lique (priv. comm.)
|  | \+ IOS | Alexander et al. (1986)

In Fig. 5 we show the calculated excitation temperatures ($T_{\rm ex}$) of
lines of molecular anions as a function of the quantum number $J$ of the upper
level and the H2 volume density. The different panels correspond to different
anions and show the regimes in which lines are either thermalized ($T_{\rm
ex}$ $\sim$ 10 K) of subthermally excited ($T_{\rm ex}$ $<$ 10 K). To
interpret these results it is useful to think in terms of the critical
density, which for a given rotational level can be evaluated as the ratio of
the de-excitation rates due to spontaneous emission and due to inelastic
collisions (e.g., Lara-Moreno et al. 2019). Collision rate coefficients for
transitions with $\Delta J$ = $-$1 or $-$2, which are usually the most
efficient, are of the order of 10-10 cm3 s-1 at a temperature of 10 K for the
anions for which calculations have been carried out (see Table 2). The
Einstein coefficient for spontaneous emission depends linearly on the square
of the dipole moment and the cube of the frequency. Therefore, the critical
density (and thus the degree of departure from LTE) is very different
depending on the dipole moment of the anion and on the frequency of the
transition. Regarding the dependence of the critical density on the dipole
moment, C2H- and CN- have a similar weight, and thus their low-$J$ lines,
which are the ones observable for cold clouds, have similar frequencies.
However, these two anions have quite different dipole moments, 3.1 and 0.65
Debye, respectively (Brünken et al., 2007b; Botschwina et al., 1995), which
make them to show a different excitation pattern. As seen in Fig. 5, the
low-$J$ lines of CN- are in LTE at densities above 105 cm-3 while those of
C2H- require much higher H2 densities to be in LTE. With respect to the
dependence of the critical density with frequency, as one moves along the
series of increasing weight C2H- $\rightarrow$ C4H- $\rightarrow$ C6H- or CN-
$\rightarrow$ C3N- $\rightarrow$ C5N- (see Fig. 5), the most favorable lines
for detection in cold clouds (those with upper level energies around 10 K)
shift to lower frequencies, which make the Einstein coefficients, and thus the
critical densities, to decrease. That is, the lines of anions targeted by
radiotelescopes are more likely to be thermalized for heavy anions than for
light ones (see the higher degree of thermalization when moving from lighter
to heavier anions in Fig. 5).

Figure 6: Same as Fig. 5 but for the radicals C6H and C3N adopting in this
case a column density of 1012 cm-2. The references for the dipole moments are
Woon (1995) for C6H and McCarthy et al. (1995) for C3N.

The volume densities of H2 in cold dark clouds are typically in the range
104-105 cm-3 (see Table 1). Therefore, if C2H- is detected in a cold dark
cloud at some point in the future, the most favorable line for detection, the
$J$ = 1-0, would be most likely subthermally excited, making necessary to use
the collision rate coefficients to derive a precise abundance. In the case of
a potential future detection of CN- in a cold interstellar cloud, the $J$ =
1-0 line would be in LTE only if the H2 density of the cloud is $\geq$ 105
cm-3 and out of LTE for lower densities (see Fig. 5). The medium-sized anions
C4H- and C3N- are predicted to have their $Q$ band lines more or less close to
LTE depending on whether the H2 density is closer to 105 or to 104 cm-3, while
the lines in the 3 mm band are likely to be subthermally excited unless the H2
density is above 105 cm-3 (see Fig. 5). For the heavier anions C6H- and C5N-,
the lines in the $K$ band are predicted to be thermalized at the gas kinetic
temperature, while those in the $Q$ band may or may not be thermalized
depending on the H2 density (see Fig. 5). Comparatively, the $Q$ band lines of
C5N- are more easily thermalized than those of C6H- because C5N- has a smaller
dipole moment than C6H-. We note that the results concerning C5N- have to be
taken with caution because we used the collision rate coefficients calculated
for C6H- in the absence of specific collision data for C5N- (see Table 2). We
did similar calculations for C8H-, C10H-, and C7N- (not shown) using the
collision rate coefficients of C6H-. We find that the lines in a given
spectral range deviate more from thermalization as the size of the anion
increases. In the $K$ band, the lines of C6H- and C5N- are thermalized, while
those of C10H- become subthermally excited at low densities, around 104 cm-3.
In the $Q$ band the deviation from thermalization is even more marked for
these large anions.

In summary, non-LTE calculations are particularly important to derive accurate
abundances for anions when just one or two lines are detected and these lie in
a regime of subthermal excitation, as indicated in Fig. 5. This becomes
critical, in order of decreasing importance, for C2H-, CN-, C4H-, C3N-, C6H-,
C8H-, and C5N- (for the three latter only if observed at frequencies above 30
GHz). The drawback is that the H2 volume density must be known with a good
precision if one aims at determining the anion column density accurately with
only one or two lines.

Table 3: Results from LVG and rotation diagram analyses.

Source | Species |  $N_{l}$ a |  |  $n$(H2) | $N$ | $\chi^{2}_{\rm red}$ |  | $T_{\rm rot}$ | $N$ |  | $N$ | Ref
---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  (cm-3) |  (cm-2) |  |  | (K) |  (cm-2) |  |  (cm-2) |
|  |  |  | LVG |  | Rotation diagram |  | Literature
TMC-1 CP |  C6H- | 11 |  |  (5.9 $\pm$ 1.6) $\times$ 103 |  (1.5 $\pm$ 0.2) $\times$ 1011 | 0.38 |  |  5.5 $\pm$ 0.3 |  (2.3 $\pm$ 0.4) $\times$ 1011 |  |  1.0 $\times$ 1011 | (1)
TMC-1 CP |  C4H- | 2 |  |  5.9 $\times$ 103 b |  (2.1 $\pm$ 0.2) $\times$ 1010 | – |  |  5.5 b |  2.4 $\times$ 1010 |  |  8.0 $\times$ 109 | (2)
TMC-1 CP |  C8H- | 12 |  |  (1.8 $\times$ 0.8) $\times$ 104 |  (2.0 $\pm$ 0.4) $\times$ 1010 | 0.97 |  |  7.1 $\pm$ 0.5 |  (2.7 $\pm$ 0.7) $\times$ 1010 |  |  2.1 $\times$ 1010 | (3)
TMC-1 CP |  C3N- | 4 |  |  (1.5 $\pm$ 0.6) $\times$ 104 |  (6.4 $\pm$ 0.8) $\times$ 1010 | 0.04 |  |  6.0 $\pm$ 0.5 |  (8.8 $\pm$ 1.8) $\times$ 1010 |  |  1.3 $\times$ 1011 | (4)
TMC-1 CP |  C5N- | 6 |  |  (5.4 $\times$ 2.3) $\times$ 103 |  (8.8 $\times$ 1.4) $\times$ 1010 | 0.44 |  |  6.6 $\pm$ 0.7 |  (1.2 $\pm$ 0.4) $\times$ 1011 |  |  2.6 $\times$ 1011 | (4)
Lupus-1A |  C6H- | 8 |  |  $>$ 1.5 $\times$ 104 |  (8.6 $\pm$ 0.6) $\times$ 1010 | 1.06 |  |  12.0 $\pm$ 1.5 |  (8.8 $\pm$ 1.5) $\times$ 1010 |  |  6.5 $\times$ 1010 | (5)
Lupus-1A |  C4H- | 4 |  |  (3.5 $\pm$ 1.5) $\times$ 104 |  (2.2 $\pm$ 0.4) $\times$ 1010 | 2.23 |  |  6.9 $\pm$ 0.9 |  (3.2 $\pm$ 0.9) $\times$ 1010 |  |  4.4 $\times$ 1010 | (5)
Lupus-1A |  C8H- | 2 |  |  1.8 $\times$ 104 b |  (1.9 $\pm$ 0.3) $\times$ 1010 | – |  |  12.0 b |  2.1 $\times$ 1010 |  |  |
Lupus-1A |  C3N- | 1 |  |  1.8 $\times$ 104 b |  (4.0 $\pm$ 1.2) $\times$ 1010 | – |  |  12.0 b |  5.1 $\times$ 1010 |  |  |
Lupus-1A |  C5N- | 5 |  |  $>$3 $\times$ 103 |  (5.5 $\pm$ 0.8) $\times$ 1010 | 1.52 |  |  12.0 b |  5.8 $\times$ 1010 |  |  |
L1527 |  C6H- | 8 |  |  $>$ 1 $\times$ 104 |  (4.5 $\pm$ 0.5) $\times$ 1010 | 1.23 |  |  10.9 $\pm$ 1.7 |  (5.4 $\pm$ 1.4) $\times$ 1010 |  |  5.8 $\times$ 1010 | (6)
L1527 |  C4H- | 4 |  |  $>$ 7 $\times$ 104 |  (1.5 $\pm$ 0.2) $\times$ 1010 | 0.18 |  |  16.1 $\pm$ 3.3 |  (1.6 $\pm$ 0.5) $\times$ 1010 |  |  1.6 $\times$ 1010 | (7)
L483 |  C6H- | 6 |  |  $>$1 $\times$ 104 |  (2.0 $\pm$ 0.3) $\times$ 1010 | 1.03 |  |  12.0 b |  2.1 $\times$ 1010 |  |  |
L483 |  C4H- | 2 |  |  5.6 $\times$ 104 b |  (6.4 $\pm$ 1.3) $\times$ 109 | – |  |  12.0 b |  8.9 $\times$ 109 |  |  |
L1495B |  C6H- | 7 |  |  (2.3 $\pm$ 1.0) $\times$ 103 |  (4.5 $\pm$ 1.7) $\times$ 1010 | 1.62 |  |  5.0 $\pm$ 0.6 |  (5.9 $\pm$ 2.7) $\times$ 1010 |  |  3.4 $\times$ 1010 | (2)
L1544 |  C6H- | 5 |  |  $>$ 1 $\times$ 103 |  (2.5 $\pm$ 1.0) $\times$ 1010 | 1.01 |  |  6.5 $\pm$ 1.6 |  (3.2 $\pm$ 1.8) $\times$ 1010 |  |  3.1 $\times$ 1010 | (8)
L1521F |  C6H- | 1 |  |  1 $\times$ 104 b |  (3.4 $\pm$ 0.8) $\times$ 1010 | – |  |  9.0 b |  4.2 $\times$ 1010 |  |  3.4 $\times$ 1010 | (8)
L1251A |  C6H- | 2 |  |  2.1 $\times$ 104 b |  (2.2 $\pm$ 0.4) $\times$ 1010 | – |  |  10.0 b |  2.5 $\times$ 1010 |  |  2.3 $\times$ 1010 | (2)
L1512 |  C6H- | 2 |  |  2.6 $\times$ 104 b |  (1.4 $\pm$ 0.2) $\times$ 1010 | – |  |  10.0 b |  1.6 $\times$ 1010 |  |  1.5 $\times$ 1010 | (2)
L1172 |  C6H- | 2 |  |  7.5 $\times$ 104 b |  (2.4 $\pm$ 0.3) $\times$ 1010 | – |  |  10.0 b |  2.5 $\times$ 1010 |  |  2.4 $\times$ 1010 | (2)
L1389 |  C6H- | 2 |  |  5.2 $\times$ 104 b |  (2.0 $\pm$ 0.3) $\times$ 1010 | – |  |  10.0 b |  2.2 $\times$ 1010 |  |  2.1 $\times$ 1010 | (2)
TMC-1 C |  C6H- | 2 |  |  1.1 $\times$ 104 b |  (4.5 $\pm$ 0.5) $\times$ 1010 | – |  |  10.0 b |  5.2 $\times$ 1010 |  |  4.8 $\times$ 1010 | (2)
TMC-1 CP |  C6H | 17 |  |  (7.5 $\pm$ 2.8) $\times$ 105 |  (4.8 $\times$ 0.2) $\times$ 1012 | 3.60 |  |  7.0 $\pm$ 0.3 |  (6.2 $\pm$ 0.7) $\times$ 1012 |  |  3.0 $\times$ 1012 | (6)
TMC-1 CP |  C4H | 13 |  |  (8.6 $\pm$ 0.9) $\times$ 103 |  (8.5 $\pm$ 0.7) $\times$ 1013 | 3.29 |  |  5.5 $\pm$ 0.1 |  (1.05 $\pm$ 0.07) $\times$ 1014 |  |  7.1 $\times$ 1014 | (7)
TMC-1 CP |  C8H | 21 |  |  1.0 $\times$ 104 b |  (3.0 $\pm$ 0.1) $\times$ 1011 | 2.86 |  |  6.8 $\pm$ 0.2 |  (8.0 $\pm$ 1.4) $\times$ 1011 |  |  4.6 $\times$ 1011 | (3)
TMC-1 CP |  C3N | 10 |  |  (1.2 $\pm$ 0.2) $\times$ 104 |  (1.2 $\pm$ 0.1) $\times$ 1013 | 1.50 |  |  4.8 $\pm$ 0.1 |  (1.7 $\pm$ 0.2) $\times$ 1013 |  |  1.8 $\times$ 1013 | (4)
TMC-1 CP |  C5N | 12 |  |  $>$ 1 $\times$ 103 |  (4.7 $\pm$ 0.3) $\times$ 1011 | 0.18 |  |  9.1 $\pm$ 0.9 |  (4.8 $\pm$ 1.0) $\times$ 1011 |  |  6.0 $\times$ 1011 | (4)
Lupus-1A |  C6H | 16 |  |  $>$ 7$\times$ 105 |  (3.7 $\pm$ 0.2) $\times$ 1012 | 1.11 |  |  10.7 $\pm$ 0.7 |  (3.8 $\pm$ 0.4) $\times$ 1012 |  |  3.1 $\times$ 1012 | (5)
Lupus-1A |  C4H | 10 |  |  (1.2 $\pm$ 0.2) $\times$ 104 |  (8.4 $\pm$ 0.9) $\times$ 1013 | 1.56 |  |  7.3 $\pm$ 0.2 |  (8.0 $\pm$ 0.6) $\times$ 1013 |  |  5.0 $\times$ 1014 | (5)
Lupus-1A |  C8H | 2 |  |  1.8 $\times$ 104 b |  (2.7 $\pm$ 0.4) $\times$ 1011 | – |  |  10.7 b |  2.8 $\times$ 1011 |  |  3.5 $\times$ 1011 | (5)
Lupus-1A |  C3N | 8 |  |  (3.5 $\pm$ 0.5) $\times$ 104 |  (6.2 $\pm$ 0.5) $\times$ 1012 | 1.19 |  |  6.8 $\pm$ 0.2 |  (8.1 $\pm$ 0.8) $\times$ 1012 |  |  |
Lupus-1A |  C5N | 10 |  |  1.8 $\times$ 104 b |  (3.1 $\pm$ 0.2) $\times$ 1011 | 1.38 |  |  7.6 $\pm$ 1.7 |  (4.9 $\pm$ 2.7) $\times$ 1011 |  |  |
L1527 |  C6H | 16 |  |  $>$ 1.5 $\times$ 106 |  (8.8 $\pm$ 0.4) $\times$ 1011 | 0.66 |  |  19.6 $\pm$ 3.4 |  (9.7 $\pm$ 1.6) $\times$ 1011 |  |  6.2 $\times$ 1011 | (6)
L1527 |  C4H | 10 |  |  (1.4 $\pm$ 0.6) $\times$ 105 |  (2.9 $\pm$ 0.1) $\times$ 1013 | 0.29 |  |  13.4 $\pm$ 0.5 |  (2.9 $\pm$ 0.2) $\times$ 1013 |  |  1.5 $\times$ 1014 | (7)
L483 |  C6H | 14 |  |  (4.1 $\pm$ 1.6) $\times$ 105 |  (7.5 $\pm$ 0.5) $\times$ 1011 | 0.22 |  |  8.3 $\pm$ 0.6 |  (8.7 $\pm$ 1.5) $\times$ 1011 |  |  |
L483 |  C4H | 14 |  |  (1.3 $\pm$ 0.2) $\times$ 104 |  (2.3 $\pm$ 0.2) $\times$ 1013 | 3.94 |  |  7.0 $\pm$ 0.1 |  (3.0 $\pm$ 0.2) $\times$ 1013 |  |  1.2 $\times$ 1014 | (9)
L1495B |  C6H | 16 |  |  (7.0 $\pm$ 2.8) $\times$ 105 |  (1.5 $\pm$ 0.1) $\times$ 1012 | 1.04 |  |  7.0 $\pm$ 0.3 |  (1.8 $\pm$ 0.2) $\times$ 1012 |  |  2.5 $\times$ 1012 | (2)
L1544 |  C6H | 11 |  |  (1.6 $\pm$ 0.7) $\times$ 105 |  (8.7 $\pm$ 1.5) $\times$ 1011 | 1.19 |  |  5.4 $\pm$ 0.4 |  (1.4 $\pm$ 0.3) $\times$ 1012 |  |  1.2 $\times$ 1012 | (8)
L1521F |  C6H | 2 |  |  1 $\times$ 104 b |  (9.5 $\pm$ 2.0) $\times$ 1011 | – |  |  9.0 b |  1.0 $\times$ 1012 |  |  8 $\times$ 1011 | (8)
L1251A |  C6H | 3 |  |  2.1 $\times$ 104 b |  (1.5 $\pm$ 0.2) $\times$ 1012 | – |  |  10.0 b |  7.8 $\times$ 1011 |  |  7.6 $\times$ 1011 | (2)
L1512 |  C6H | 5 |  |  2.6 $\times$ 104 b |  (7.6 $\pm$ 0.6) $\times$ 1011 | – |  |  10.0 b |  5.5 $\times$ 1011 |  |  4.6 $\times$ 1011 | (2)
L1172 |  C6H | 1 |  |  7.5 $\times$ 104 b |  (8.0 $\pm$ 1.1) $\times$ 1011 | – |  |  10.0 b |  7.6 $\times$ 1011 |  |  7.1 $\times$ 1011 | (2)
L1389 |  C6H | 3 |  |  5.2 $\times$ 104 b |  (4.4 $\pm$ 0.6) $\times$ 1011 | – |  |  10.0 b |  5.0 $\times$ 1011 |  |  4.7 $\times$ 1011 | (2)
TMC-1 C |  C6H | 1 |  |  1.1 $\times$ 104 b |  (5.5 $\pm$ 0.6) $\times$ 1012 | – |  |  10.0 b |  1.6 $\times$ 1012 |  |  1.5 $\times$ 1012 | (2)

a Number of lines included in the analysis.
b Parameter was fixed to the value determined for a similar species, if
possible, or to the value given in Table 1.
References: (1) McCarthy et al. (2006). (2) Cordiner et al. (2013). (3)
Brünken et al. (2007a). (4) Cernicharo et al. (2020). (5) Sakai et al. (2010).
(6) Sakai et al. (2007). (7) Agúndez et al. (2008). (8) Gupta et al. (2009).
(9) Agúndez et al. (2019).

In the case of the neutral counterparts of molecular anions, collision rate
coefficients have been calculated for C6H and C3N with He as collider (Walker
et al., 2018; Lara-Moreno et al., 2021). We thus carried out LVG calculations
similar to those presented before for anions. In this case we adopt a higher
column density of 1012 cm-2, in line with typical values in cold dark clouds
(see references in Sect. 2.2). The results are shown in Fig. 6. It is seen
that in the case of C3N, the excitation pattern is similar to that of the
corresponding anion, C3N-, shown in Fig. 5. The thermalization of C3N occurs
at densities somewhat higher compared to C3N-, mainly because the collision
rate coefficients calculated for C3N with He (Lara-Moreno et al., 2021) are
smaller than those computed for C3N- with para H2 (Lara-Moreno et al., 2019).
We note that this conclusion may change if the collision rate coefficients of
C3N with H2 are significantly larger than the factor of 1.39 due to the change
in the reduced mass when changing He by H2. In the case of C6H however the
excitation behavior is very different to that of C6H- (compare C6H- in Fig. 5
with C6H in Fig. 6). The rotational levels of the radical are much more
subthermally excited than those of the corresponding anion, with a difference
in the critical density of about a factor of 30. This is a consequence of the
much smaller collision rate coefficients calculated for C6H with He (Walker et
al., 2018) compared to those calculated for C6H- with para H2 (Walker et al.,
2017), a difference that is well beyond the factor of 1.40 due to the change
in the reduced mass when changing He by H2.

##  5 Anion abundances

Figure 7: Excitation and abundance analysis for C3N- in TMC-1 CP. The left
panel shows $\chi^{2}$ as a function of the H2 volume density and the column
density of C3N-, where contours correspond to 1, 2, and 3 $\sigma$ levels. The
right panel shows the rotation diagram.

We evaluated the column densities of molecular anions and their corresponding
neutral counterparts in the 12 studied sources by carrying out LVG
calculations similar to those described in Sect. 3 for the 13C isotopologues
of HC3N. We used the collision rate coefficients given in Table 2. Gas kinetic
temperatures and linewidths were fixed to the values given in Table 1, the
ortho-to-para ratio of H2, when needed, was fixed to 10-3, and both the column
density of the species under study and the H2 volume density were varied. The
best estimates for these two parameters were found by minimization of
$\chi^{2}$ (see Sect. 3). In addition, to evaluate the rotational temperature,
and thus the level of departure from LTE, and to have an independent estimate
of the column density, we constructed rotation diagrams.

The LVG method should provide a more accurate determination of the column
density than the rotation diagram, as long as the collision rate coefficients
with para H2 and the gas kinetic temperature are accurately known. If an
independent determination of the H2 volume density is available from some
density tracer (in our case the 13C isotopologues of HC3N are used in several
sources), a good agreement between the values of $n$(H2) obtained from the
species under study and from the density tracer supports the reliability of
the LVG analysis. We note that densities do not need to be similar if the
species studied and the density tracer are distributed over different regions,
although in our case we expect similar distributions for HC3N, molecular
anions, and their neutral counterparts, as long as all them are carbon chains.
A low value of $\chi^{2}_{red}$, typically $\lesssim$ 1, is also indicative of
the goodness of the LVG analysis. If the quality of the LVG analysis is not
satisfactory or the collision rate coefficients are not accurate, a rotation
diagram may still provide a good estimate of the column density if the number
of detected lines is high enough and they span a wide range of upper level
energies. Therefore, a high number of detected lines makes likely to end up
with a correct determination of the column density. On the other hand, if only
one or two lines are detected, the accuracy with which the column density can
be determined relies heavily on whether the H2 volume density, in the case of
an LVG calculation, or the rotational temperature, in the case of the rotation
diagram, are known with some confidence.

Figure 8: Volume density of H2 in various cold dark clouds determined through
LVG calculations using different tracers. Green points correspond to densities
derived from 13C isotopologues of HC3N (see values in Table 1), while blue and
magenta points correspond to densities obtained from the anion C6H- and the
radical C6H, respectively (see values in Table 3). Note that H2 densities
derived through C6H- are close to those derived by 13C isotopologues of HC3N,
while H2 densities derived through C6H are systematically higher by factors of
10-50. Table 4: Recommended column densities and anion-to-neutral abundance
ratios.

|  $N$ (cm-2) |  $N$ (cm-2) |  |  Ratio ($\%$) |  |  Ratio ($\%$) | Ref
---|---|---|---|---|---|---|---
| This work |  | Literature
|  C4H- |  C4H |  |  C4H-/C4H |
TMC-1 CP |  (2.1 $\pm$ 0.6) $\times$ 1010 |  (8.5 $\pm$ 2.6) $\times$ 1013 |  |  0.025 $\pm$ 0.007 |  |  0.0012 $\pm$ 0.0004 | (1)
Lupus-1A |  (2.2 $\pm$ 0.7) $\times$ 1010 |  (8.4 $\pm$ 1.3) $\times$ 1013 |  |  0.026 $\pm$ 0.005 |  |  0.0088 $\pm$ 0.0053 | (2)
L1527 |  (1.5 $\pm$ 0.2) $\times$ 1010 |  (2.9 $\pm$ 0.4) $\times$ 1013 |  |  0.052 $\pm$ 0.004 |  | 0.011 | (3)
L483 |  (6.4 $\pm$ 1.9) $\times$ 109 |  (2.3 $\pm$ 0.3) $\times$ 1013 |  |  0.028 $\pm$ 0.008 |  |  |
|  C6H- |  C6H |  |  C6H-/C6H |
TMC-1 CP |  (1.5 $\pm$ 0.2) $\times$ 1011 |  (4.8 $\pm$ 1.4) $\times$ 1012 |  |  3.1 $\pm$ 0.6 |  | 2.5 | (4)
Lupus-1A |  (8.6 $\pm$ 1.3) $\times$ 1010 |  (3.7 $\pm$ 1.1) $\times$ 1012 |  |  2.3 $\pm$ 0.5 |  |  2.1 $\pm$ 0.6 | (2)
L1527 |  (4.5 $\pm$ 0.7) $\times$ 1010 |  (8.8 $\pm$ 2.6) $\times$ 1011 |  |  5.1 $\pm$ 1.1 |  |  9.3 $\pm$ 2.9 | (5)
L483 |  (2.0 $\pm$ 0.3) $\times$ 1010 |  (7.5 $\pm$ 2.3) $\times$ 1011 |  |  2.7 $\pm$ 0.6 |  |  |
L1495B |  (4.5 $\pm$ 1.4) $\times$ 1010 |  (1.5 $\pm$ 0.5) $\times$ 1012 |  |  3.0 $\pm$ 0.8 |  |  1.4 $\pm$ 0.2 | (1)
L1544 |  (2.5 $\pm$ 0.8) $\times$ 1010 |  (8.7 $\pm$ 2.6) $\times$ 1011 |  |  2.9 $\pm$ 0.8 |  |  2.5 $\pm$ 0.8 | (6)
L1521F |  (3.4 $\pm$ 1.0) $\times$ 1010 |  (1.0 $\pm$ 0.3) $\times$ 1012 |  |  3.4 $\pm$ 1.0 |  |  4 $\pm$ 1 | (6)
L1251A |  (2.2 $\pm$ 0.7) $\times$ 1010 |  (7.8 $\pm$ 2.3) $\times$ 1011 |  |  2.8 $\pm$ 0.8 |  |  3.0 $\pm$ 0.6 | (1)
L1512 |  (1.4 $\pm$ 0.4) $\times$ 1010 |  (5.5 $\pm$ 1.7) $\times$ 1011 |  |  2.5 $\pm$ 0.7 |  |  3.3 $\pm$ 0.4 | (1)
L1172 |  (2.4 $\pm$ 0.7) $\times$ 1010 |  (7.6 $\pm$ 2.3) $\times$ 1011 |  |  3.2 $\pm$ 0.9 |  |  3.3 $\pm$ 0.5 | (1)
L1389 |  (2.0 $\pm$ 0.6) $\times$ 1010 |  (5.0 $\pm$ 1.5) $\times$ 1011 |  |  4.0 $\pm$ 1.1 |  |  4.4 $\pm$ 0.8 | (1)
TMC-1 C |  (4.5 $\pm$ 1.4) $\times$ 1010 |  (1.6 $\pm$ 0.5) $\times$ 1012 |  |  2.8 $\pm$ 0.8 |  |  3.1 $\pm$ 0.3 | (1)
|  C8H- |  C8H |  |  C8H-/C8H |
TMC-1 CP |  (2.0 $\pm$ 0.3) $\times$ 1010 |  (3.0 $\pm$ 0.9) $\times$ 1011 |  |  6.7 $\pm$ 1.4 |  | 5 | (7)
Lupus-1A |  (1.9 $\pm$ 0.6) $\times$ 1010 |  (2.7 $\pm$ 0.8) $\times$ 1011 |  |  7.0 $\pm$ 2.0 |  |  4.7 $\pm$ 1.7 | (2)
|  C3N- |  C3N |  |  C3N-/C3N |
TMC-1 CP |  (6.4 $\pm$ 1.0) $\times$ 1010 |  (1.2 $\pm$ 0.2) $\times$ 1013 |  |  0.53 $\pm$ 0.04 |  | 0.71 | (8)
Lupus-1A |  (4.0 $\pm$ 1.2) $\times$ 1010 |  (6.2 $\pm$ 0.9) $\times$ 1012 |  |  0.65 $\pm$ 0.13 |  |  |
|  C5N- |  C5N |  |  C5N-/C5N |
TMC-1 CP |  (8.8 $\pm$ 1.3) $\times$ 1010 |  (4.7 $\pm$ 0.7) $\times$ 1011 |  |  19 $\pm$ 1 |  | 43 | (8)
Lupus-1A |  (5.5 $\pm$ 0.8) $\times$ 1010 |  (3.1 $\pm$ 0.5) $\times$ 1011 |  |  18 $\pm$ 1 |  |  |

References: (1) Cordiner et al. (2013). (2) Sakai et al. (2010). (3) Agúndez
et al. (2008). (4) McCarthy et al. (2006). (5) Sakai et al. (2007). (6) Gupta
et al. (2009). (7) Brünken et al. (2007a). (8) Cernicharo et al. (2020).

In Table 3 we present the results from the LVG analysis and the rotation
diagram for all molecular anions detected in cold dark clouds and for the
corresponding neutral counterparts, and compare the column densities derived
with values from the literature, when available. In general, the column
densities derived through the rotation diagram agree within 50 %, with those
derived by the LVG analysis. The sole exceptions are C8H in TMC-1 CP and C6H
in TMC-1 C. In the former case, the lack of specific collision rate
coefficients for C8H probably introduces an uncertainty in the determination
of the column density. In the case of C6H in TMC-1 C, the suspected problem in
the collision rate coefficients used for C6H (see below) is probably behind
the too large column density derived by the LVG method.

We first discuss the excitation and abundance analyses carried out for
negative ions. For the anions detected in TMC-1 CP through more than two
lines, i.e., C6H-, C8H-, C3N-, and C5N-, the quality of the LVG analysis is
good (in Fig. 7 we show the case of C3N-). First, the number of lines
available is sufficiently high and they cover a wide range of upper level
energies. Second, the values of $\chi^{2}_{\rm red}$ are $\lesssim$ 1\. And
third, the H2 densities derived are on the same order (within a factor of two)
of that obtained through 13C isotopologues of HC3N. The rotational
temperatures derived by the rotation diagram indicate subthermal excitation,
which is consistent with the H2 densities derived and the excitation analysis
presented in Sect. 4. We note that the column densities derived by the
rotation diagram are systematically higher, by $\sim$ 50 %, compared to those
derived through the LVG analysis. These differences are due to the breakdown
of various assumptions made in the frame of the rotation diagram method,
mainly the assumption of a uniform excitation temperature across all
transitions and the validity of the Rayleigh-Jeans limit. Only the assumption
that $\exp(h\nu/kT_{ex})-1$ = $h\nu/kT_{ex}$, implicitly made by the rotation
diagram method in the Rayleigh-Jeans limit, already implies errors of 10-20 %
in the determination of the column density for these anions. We therefore
adopt as preferred values for the column densities those derived through the
LVG method and assign an uncertainty of 15 %, which is the typical statistical
error in the determination of the column density by the LVG analysis. The
recommended values are given in Table 4. Based on the same arguments, we
conclude that the LVG analysis is satisfactory for C6H- and C5N- in Lupus-1A ,
C6H- and C4H- in L1527, and C6H- in L483, and thus adopt the column densities
derived by the LVG method with the same estimated uncertainty of 15 % (see
Table 4). In other cases the LVG analysis is less reliable due to a variety of
reasons: only one or two lines are available (C4H- in TMC-1 CP, C8H- and C3N-
in Lupus-1A, C4H- in L483, and C6H- in the clouds L1521F, L1251A, L1512,
L1172, L1389, and TMC-1 C), the parameter $\chi^{2}_{\rm red}$ is well above
unity (C4H- in Lupus-1A), or the column density has a sizable error (C6H- in
L1495B and L1544). In those cases we adopt the column densities derived by the
LVG method but assign a higher uncertainty of 30 % (values are given in Table
4).

In order to derive anion-to-neutral abundance ratios, we applied the same
analysis carried out for the anions to the corresponding neutral counterparts.
We first focus on the radical C6H. There is one striking issue in the LVG
analysis carried out for this species: the H2 volume densities derived through
C6H are systematically higher, by 1-2 orders of magnitude, than those derived
through the 13C isotopologues of HC3N (see Fig. 8). This fact, together with
the previous marked difference in the excitation pattern compared to that of
C6H- discussed in Sect. 4, suggests that the collision coefficients adopted
for C6H, which are based on the C6H – He system studied by Walker et al.
(2018), are too small. A further problem when using the collision coefficients
of Walker et al. (2018) is that the line intensities from the
${}^{2}\Pi_{1/2}$ state, which in TMC-1 CP are around 100 times smaller than
those of the ${}^{2}\Pi_{3/2}$ state, are overestimated by a factor of $\sim$
10\. All these issues indicate that it is worth to undertake calculations of
the collision rate coefficients of C6H with H2. The suspected problem in the
collision rate coefficients of C6H make us to adopt a conservative uncertainty
of 30 % in the column densities derived. Moreover, in those sources in which
C6H is observed through just a few lines (L1521F, L1251A, L1512, L1172, L1389,
and TMC-1 C) we need to fix the H2 density to the values derived through other
density tracer (see Table 1), and given the marked difference between the H2
densities derived through C6H and other density tracers, it is likely that the
C6H column densities derived by the LVG method are unreliable. In these cases
we therefore adopted as preferred C6H column densities those obtained from the
rotation diagram (see Table 4). For the other neutral radicals, we adopted the
column densities derived by the LVG method with an estimated uncertainty of 15
% when the LVG analysis was satisfactory (C3N and C5N in TMC-1 CP, C4H, C3N,
and C5N in Lupus-1A, and C4H in L1527) and a higher uncertainty of 30 %
otherwise (C4H and C8H in TMC-1 CP, C8H in Lupus-1A, and C4H in L483).

The recommended column densities for molecular anions and their neutral
counterparts, and the corresponding anion-to-neutral ratios, are given in
Table 4. Since the lines of a given anion and its corresponding neutral
counterpart where in most cases observed simultaneously, we expect the error
due to calibration to cancel when computing anion-to-neutral ratios. We
therefore subtracted the 10 % error due to calibration in the column densities
when computing errors in the anion-to-neutral ratios. In general, the
recommended anion-to-neutral abundance ratios agree within 50 % with the
values reported in the literature, when available. Higher differences, of up
to a factor of two, are found for C6H- in L1527 and L1495B and for C5N- in
TMC-1 CP. The most drastic differences are found for the C4H-/C4H abundance
ratio, for which we derive values much higher than those reported in the
literature. The differences are largely due to the fact that here we adopt a
revised value of the dipole moment of C4H (2.10 D; Oyama et al. 2020), which
is significantly higher than the value of 0.87 D calculated by Woon (1995) and
adopted in previous studies. This fact makes the column densities of C4H to be
revised downward by a factor of $\sim$ 6, and consequently the C4H-/C4H ratios
are also revised upward by the same factor.

##  6 Discussion

Having at hand a quite complete observational picture of negative ions in the
interstellar medium, as summarized in Table 4, it is interesting to examine
which lessons can be learnt from this. There are at least two interesting
aspects to discuss. First, how do the anion-to-neutral abundance ratio behave
from one source to another, and whether the observed variations can be related
to some property of the cloud. And second, within a given source, how do the
anion-to-neutral abundance ratio vary for the different anions, and whether
this can be related to the formation mechanism of anions.

Regarding the first point, since C6H- is the most widely observed anion, it is
very convenient to focus on it to investigate the source-to-source behavior of
negative ions. The detection of C6H- in L1527 and the higher C6H-/C6H ratio
derived in that source compared to that in TMC-1 CP led Sakai et al. (2007) to
suggest that this was a consequence of the higher H2 density in L1527 compared
to TMC-1 CP. This point was later on revisited by Cordiner et al. (2013) with
a larger number of sources detected in C6H-. These authors found a trend in
which the C6H-/C6H ratio increases with increasing H2 density and further
argued that this ratio increases as the cloud evolves from quiescent to star-
forming, with ratios below 3 % in quiescent sources and above that value in
star-forming ones.

There are theoretical grounds that support a relationship between the C6H-/C6H
ratio and the H2 density. Assuming that the formation of anions is dominated
by radiative electron attachment to the neutral counterpart and that they are
mostly destroyed through reaction with H atoms, as expected for the conditions
of cold dense clouds (Flower et al., 2007), it can be easily shown that at
steady state the anion-to-neutral abundance ratio is proportional to the
abundance ratio between electrons and H atoms, which in turn is proportional
to the square root of the H2 volume density (e.g., Flower et al. 2007). That
is,

$\rm\frac{C_{6}H^{-}}{C_{6}H}\propto\frac{e^{-}}{H}\propto{\textit{n}}(H_{2})^{1/2}.$
(2)

Figure 9: Anion-to-neutral ratio C6H-/C6H (see values in Table 4) as a
function of H2 volume density. We do not give errors in the H2 densities
because this parameter is not derived in a coherent way for all sources (see
Table 1). The dotted line represents the trend expected according to theory
(see text). Figure 10: Observed anion-to-neutral abundance ratios (referred to
the left $y$ axis) in cold interstellar clouds where molecular anions have
been detected to date. Values are given in Table 4. Referred to the right $y$
axis and following the same color code we also plot as dotted horizontal lines
the calculated rate coefficients at 300 K for the reaction of radiative
electron attachment to the neutral counterpart. Adopted values are 1.1
$\times$ 10-8 cm3 s-1 for C4H, 6.2 $\times$ 10-8 cm3 s-1 for C6H and C8H
(Herbst & Osamura 2008; they are shown slightly displaced for visualization
purposes), 2.0 $\times$ 10-10 cm3 s-1 for C3N (Petrie & Herbst, 1997; Harada &
Herbst, 2008), and 1.25 $\times$ 10-7 cm3 s-1 for C5N (Walsh et al., 2009).
The scale of the right $y$ axis is chosen to make the rate coefficient of
electron attachment to C6H to coincide with the mean of C6H-/C6H ratios and to
cover the same range in logarithmic scale than the left $y$ axis, which allows
to visualize any potential proportionality between anion-to-neutral ratio and
radiative electron attachment rate.

In Fig. 9 we plot the observed C6H-/C6H ratio as a function of the H2 density
for the 12 clouds where this anion has been detected. This is an extended and
updated version of Figure 5 of Cordiner et al. (2013), where we superimpose
the theoretical trend expected according to Eq. (2). In general terms, the
situation depicted by Fig. 9 is not that different from that found by Cordiner
et al. (2013). The main difference concerns L1495B, for which we derive a
higher C6H-/C6H ratio, 3.0 % instead of 1.4 %. Our value should be more
accurate, given the larger number of lines used here. Apart from that, the
C6H-/C6H ratio tends to be higher in those sources with higher H2 densities,
which tend to be more evolved. This behavior is similar to that found by
Cordiner et al. (2013). The data points in Fig. 9 seem to be consistent with
the theoretical expectation. We however caution that there is substantial
dispersion in the data points. Moreover, the uncertainties in the anion-to-
neutral ratios, together with those affecting the H2 densities (not shown),
make it difficult to end up with a solid conclusion on whether or not
observations follow the theoretical expectations. If we restrict to the five
best characterized sources (TMC-1 CP, Lupus-1A, L1527, L483, and L1495B), all
them observed in C6H- through four or more lines and studied in the H2 density
in a coherent way, then the picture is such that all sources, regardless of
its H2 density, have similar C6H-/C6H ratios, at the exception of L1527, which
remains the only data point supporting the theoretical relation between anion-
to-neutral ratio and H2 density. It is also worth noting that when looking at
C4H-, L1527 shows also an enhanced anion-to-neutral ratio compared to TMC-1
CP, Lupus-1A, and L483. Further detections of C6H- in sources with high H2
densities, preferably above 105 cm-3, should help to shed light on the
suspected relation between anion-to-neutral ratio and H2 density. This however
may not be easy because chemical models predict that, although the C6H-/C6H
ratio increases with increasing H2 density, an increase in the density also
brings a decrease in the column density of both C6H and C6H- (Cordiner &
Charnley, 2012).

The second aspect that is worth to discuss is the variation of the anion-to-
neutral ratio for different anions within a given source. Unlike the former
source-to-source case, where variations were small (a factor of two at most),
here anion-to-neutral ratios vary by orders of magnitude, i.e., well above
uncertainties. Figure 10 summarizes the observational situation of
interstellar anions in terms of abundances relative to their neutral
counterpart. The variation of the anion-to-neutral ratios across different
anions is best appreciated in TMC-1 CP and Lupus-1A, which stand out as the
two most prolific sources of interstellar anions. The lowest anion-to-neutral
ratio is reached by far for C4H-, while the highest values are found for C5N-
and C8H-. We caution that the C5N-/C5N ratio could have been overestimated if
the true dipole moment of C5N is a mixture between those of the ${}^{2}\Sigma$
and ${}^{2}\Pi$ states, as discussed by Cernicharo et al. (2008), in a case
similar to that studied for C4H by Oyama et al. (2020). For the large anion
C7N-, the anion-to-neutral ratio is not known in TMC-1 CP but it is probably
large, as suggested by the detection of the lines of the anion and the non
detection of the lines of the neutral (Cernicharo et al., 2023a). In the case
of the even larger anion C10H-, the anion is found to be even more abundant
than the neutral in TMC-1 CP by a factor of two, although this result has
probably an important uncertainty since the detection is done by line stack
(Remijan et al., 2023). Moreover, it is yet to be confirmed that the species
identified is C10H- and not C9N- (Pardo et al., 2023). In any case, a solid
conclusion from the TMC-1 CP and Lupus-1A data shown in Fig. 10 is that when
looking at either the hydrocarbon series of anions or at the nitrile series,
the anion-to-neutral ratio clearly increases with increasing size. The most
straitforward interpretation of this behavior is related to the formation
mechanism originally proposed by Herbst (1981), which relies on the radiative
electron attachment (REA) to the neutral counterpart and for which the rate
coefficient is predicted to increase markedly with increasing molecular size.

If electron attachment is the dominant formation mechanism of anions and
destruction rates are similar for all anions, we expect the anion-to-neutral
abundance ratio to be proportional to the rate coefficient of radiative
electron attachment. That is,

$\rm\frac{A^{-}}{A}\propto{\textit{k}_{REA}},$ (3)

where A- and A are the anion and its corresponding neutral counterpart,
respectively, and $k_{\rm REA}$ is the rate coefficient for radiative electron
attachment to A.

To get insight into this relation we plot in Fig. 10 the rate coefficients
calculated for the reactions of electron attachment forming the different
anions on a scale designed on purpose to visualize if observed anion-to-
neutral ratios scale with calculated electron attachment rates. We arbitrarily
choose C6H- as the reference for the discussion. If we first focus on the
largest anion C8H-, we see that the C8H-/C8H ratios are systematically higher,
by a factor of 2-3, than the C6H-/C6H ones, while Herbst & Osamura (2008)
calculate identical electron attachment rates for C6H and C8H. Similarly, the
C5N-/C5N ratios are higher, by a factor of 6-8 than the C6H-/C6H ratios, while
the electron attachment rate calculated for C5N is twice of that computed for
C6H in the theoretical scenario of Herbst & Osamura (2008). That is, for the
large anions C8H- and C5N- there is a deviation of a factor of 2-4 from the
theoretical expectation given by Eq. (3). This deviation is small given the
various sources of uncertainties in both the observed anion-to-neutral ratio
(mainly due to uncertainties in the dipole moments) and the calculated
electron attachment rate coefficient. The situation is different for the
medium size anions C4H- and C3N-. In the case of C4H-, anion-to-neutral ratios
are $\sim$ 100 times lower than for C6H-, while the electron attachment rate
calculated for C4H is just $\sim$ 6 times lower than that computed for C6H.
The deviation from Eq. (3) of a factor $\sim$ 20, which is significant, is
most likely due to the electron attachment rate calculated for C4H by Herbst &
Osamura (2008) being too large. In the case of C3N-, the observed anion-to-
neutral ratios are 4-6 times lower than those derived for C6H-, while the
electron attachment rate calculated by Petrie & Herbst (1997) for C3N is 300
times lower than that computed for C6H by Herbst & Osamura (2008). Here the
deviation is as large as two orders of magnitude and it is probably caused by
the too low electron attachment rate calculated for C3N. In summary,
calculated electron attachment rates are consistent with observed anion-to-
neutral ratios for the large species but not for the medium-sized species C4H
and C3N, in which cases calculated rates are too large by a factor of $\sim$
20 and too small by a factor of $\sim$ 100, respectively.

Of course, the above conclusion holds in the scenario of anion formation
dominated by electron attachment and similar destruction rates for all anions,
which may not be strictly valid. For example, it has been argued (Douguet et
al., 2015; Khamesian et al., 2016; Forer et al., 2023) that the process of
radiative electron attachment is much less efficient than calculated by Herbst
& Osamura (2008), with rate coefficients that are too small to sustain the
formation of anions in interstellar space. Millar et al. (2017) discuss this
point making the difference between direct and indirect radiative electron
attachment, where for long carbon chains the direct process would be slow,
corresponding to the rates calculated by Khamesian et al. (2016), while the
indirect process could be fast if a long-lived superexcited anion is formed,
something that has some experimental support. Millar et al. (2017) conclude
that there are enough grounds to support rapid electron attachment to large
carbon chains, as calculated by Herbst & Osamura (2008). The formation
mechanism of anions through electron attachment is very selective for large
species and thus has the advantage of naturally explaining the marked
dependence of anion-to-neutral ratios with molecular size illustrated in Fig.
10, something that would be difficult to explain through other formation
mechanism. Indeed, mechanisms such as dissociative electron attachment to
metastable isomers such as HNC3 and H2C6 (Petrie & Herbst, 1997; Sakai et al.,
2007) or reactions of H- with polyynes and cyanopolyynes (Vuitton et al.,
2009; Martínez et al., 2010; Khamesian et al., 2016; Gianturco et al., 2016;
Murakami et al., 2022) could contribute to some extent but are unlikely to
control the formation of anions since they can hardly explain why large anions
are far more abundant than small ones.

##  7 Conclusions

We reported new detections of molecular anions in cold dense clouds and
considerably expanded the number of lines through which negative ions are
detected in interstellar clouds. The most prevalent anion remains to be C6H-,
which to date has been seen in 12 interstellar clouds, while the rest of
interstellar anions are observed in just 1-4 sources.

We carried out excitation calculations, which indicate that subthermal
excitation is common for the lines of interstellar anions observed with
radiotelescopes, with the low frequency lines of heavy anions being the
easiest to thermalize. Important discrepancies between calculations and
observations are found for the radical C6H, which suggest that the collision
rate coefficients currently available for this species need to be revisited.

We analyzed all the observational data acquired here and in previous studies
through non-LTE LVG calculations and rotation diagrams to constrain the column
density of each anion in each source. Differences in the anion-to-neutral
abundance ratios with respect to literature values are small, less than 50 %
in general and up to a factor of two in a few cases. The highest difference is
found for the C4H-/C4H ratio, which is shifted upward with respect to previous
values due to the adoption of a higher dipole moment for the radical C4H.

The observational picture of interstellar anions brought by this study shows
two interesting results. On the one side, the C6H-/C6H ratio seems to be
higher in clouds with a higher H2 density, which is usually associated to a
later evolutionary status of the cloud, although error bars make it difficult
to clearly distinguish this trend. On the other hand, there is a very marked
dependence of the anion-to-neutral ratio with the size of the anion, which is
in line with the formation scenario involving radiative electron attachment,
the theory of which must still be revised for medium size species such as C4H
and C3N.

###### Acknowledgements.

We acknowledge funding support from Spanish Ministerio de Ciencia e Innovación
through grants PID2019-106110GB-I00, PID2019-107115GB-C21, and
PID2019-106235GB-I00.

## References

  * Agúndez et al. (2008) Agúndez, M., Cernicharo, J., Guélin, M., et al. 2008, A&A, 478, L19
  * Agúndez et al. (2010) Agúndez, M., Cernicharo, J., Guélin, M., et al. 2010, A&A, 517, L2
  * Agúndez et al. (2015) Agúndez, M., Cernicharo, J., & Guélin, M. 2015, A&A, 577, L5
  * Agúndez et al. (2019) Agúndez, M., Marcelino, N., Cernicharo, J., et al. 2019, A&A, 625, A147
  * Agúndez et al. (2022) Agúndez, M., Marcelino, N., Cabezas, C., et al. 2022, A&A, 657, A96
  * Agúndez et al. (2023) Agúndez, M., Roncero, O., Marcelino, N., et al. 2023, A&A, in press
  * Alexander (1982) Alexander, M. H. 1982, J. Chem. Phys., 76, 5974
  * Alexander et al. (1986) Alexander, M. H., Smedley, J. E., & Corey, G. C. 1986, J. Chem. Phys., 84, 3049
  * Anglada et al. (1997) Anglada, G., Sepúlveda, I., & Gómez, J. F. 1997, A&AS, 121, 255
  * Bacmann et al. (2002) Bacmann, A., Lefloch, B., Ceccarelli, C., et al. 2002, A&A, 389, L6
  * Balança et al. (2021) Balança, C., Quintas-Sánchez, E., Dawes, R., et al. 2021, MNRAS, 508, 1148
  * Biswas et al. (2023) Biswas, R., Giri, K., González-Sánchez, L. et al. 2023, MNRAS, 522, 5775
  * Blanksby et al. (2001) Blanksby, S. J., McAnoy, A. M., Dua, S., & Bowie, J. H. 2001, MNRAS, 328, 89
  * Bop et al. (2021) Bop, C. T., Lique, F., Faure, A., et al. 2021, MNRAS, 501, 1911
  * Bop et al. (2022) Bop, C. T., Desrousseaux, B., & Lique, F. 2022, A&A, 662, A102
  * Botschwina et al. (1995) Botschwina, P., Seeger, S., Mladenovic, M., et al. 1995, Int. Rev. Phys. Chem., 14, 169
  * Botschwina (2000) Botschwina, P. 2000, 55th Ohio Symposium on Molecular Spectroscopy, TC06
  * Botschwina & Oswald (2008) Botschwina, P. & Oswald, R. 2008, J. Chem. Phys., 129, 044305
  * Brünken et al. (2007a) Brünken, S., Gupta, H., Gottlieb, C. A., et al. 2007a, ApJ, 664, L43
  * Brünken et al. (2007b) Brünken, S., Gottlieb, C. A., Gupta, H., et al. 2007b, A&A, 464, L33
  * Cabezas et al. (2021) Cabezas, C., Agúndez, M., Marcelino, N., et al. 2021, A&A, 654, A45
  * Cabezas et al. (2022) Cabezas, C., Agúndez, M., Marcelino, N., et al. 2022, A&A, 657, L4
  * Carelli et al. (2013) Carelli, F., Satta, M., Grassi, T., & Gianturco, F. A. 2013, ApJ, 774, 97
  * Cernicharo et al. (2007) Cernicharo, J., Guélin, M., Agúndez, M., et al. 2007, A&A, 467, L37
  * Cernicharo et al. (2008) Cernicharo, J., Guélin, M., Agúndez, M., et al. 2008, ApJ, 688, L83
  * Cernicharo et al. (2012) Cernicharo, J., Marcelino, N., Roueff, E., et al. 2012, ApJ, 759, L43
  * Cernicharo et al. (2020) Cernicharo, J., Marcelino, N., Pardo, J. R., et al. 2020, A&A, 641, L9
  * Cernicharo et al. (2021) Cernicharo, J., Agúndez, M., Kaiser, R. I., et al. 2021, A&A, 652, L9
  * Cernicharo et al. (2023a) Cernicharo, J., Pardo, J. R., Cabezas, C., et al. 2023a, A&A, 670, L19
  * Cernicharo et al. (2023b) Cernicharo, J., Tercero, B., Marcelino, N., et al. 2023b, A&A, submitted
  * Codella et al. (1997) Codella, C., Welser, R., Henkel, C., et al. 1997, A&A, 324, 203
  * Cordiner et al. (2011) Cordiner, M. A., Charnley, S. B., Buckle, J. V., et al. 2011, ApJ, 730, L18
  * Cordiner & Charnley (2012) Cordiner, M. A. & Charnley, S. B. 2012, ApJ, 749, 120
  * Cordiner et al. (2013) Cordiner, M. A., Buckle, J. V., Wirström, E. S., et al. 2013, ApJ, 770, 48
  * Crapsi et al. (2005) Crapsi, A., Caselli, P., Walmsley, C. M., et al. 2005, ApJ, 619, 379
  * Douguet et al. (2015) Douguet, N., Fonseca dos Santos, S., Raoult, M., et al. 2015, J. Chem. Phys., 142, 234309
  * Dumouchel et al. (2012) Dumouchel, F., Spielfiedel, A., Senent, M. L., & Feautrier, N. 2012, Chem. Phys. Lett., 533, 6
  * Dumouchel et al. (2023) Dumouchel, F., Quintas-Sánchez, E., Balança, C., et al. 2023, J. Chem. Phys., 158, 164307
  * Faure et al. (2016) Faure, A., Lique, A., & Wiesenfeld, L. 2016, MNRAS, 460, 2103
  * Fehér et al. (2016) Fehér, O., Tóth, L. V., Ward-Thompson, D., et al. 2016, A&A, 590, A75
  * Flower et al. (2006) Flower, D. R., Pineau des Forêts, G., & Walmsley, C. M. 2006, A&A, 449, 621
  * Flower et al. (2007) Flower, D. R., Pineau des Forêts, G., & Walmsley, C. M. 2007, A&A, 474, 923
  * Forer et al. (2023) Forer, J., Kokoouline, V., & Stoecklin, T. 2023, Phys. Rev. A, 107, 043117
  * Fossé et al. (2001) Fossé, D., Cernicharo, J., Gerin, M., & Cox, P. 2001, ApJ, 552, 168
  * Franz et al. (2020) Franz, J., Mant, B. P., González-Sánchez, L., et al. 2020, J. Chem. Phys., 152, 234303
  * Frayer et al. (2018) Frayer, D. T., Ghigo, F., & Maddalena, R. J. 2018, GBT Memo #301
  * Gianturco et al. (2016) Gianturco, F. A., Satta, M., Mendolicchio, M., et al. 2016, ApJ, 830, 2
  * Gianturco et al. (2019) Gianturco, F. A., González-Sánchez, L., Mant, B. P., & Wester, R. 2019, J. Chem. Phys., 151, 144304
  * González-Sánchez et al. (2020) González-Sánchez, L., Mant, B. P., Wester, R., & Gianturco, F. A. 2020, ApJ, 897, 75
  * Gottlieb et al. (2007) Gottlieb, C. A., Brünken, S., McCarthy, M. C., & Thaddeus, P. 2007, J. Chem. Phys., 126, 191101
  * Gupta et al. (2007) Gupta, H., Brünken, S., Tamassia, F., et al. 2007, ApJ, 655, L57
  * Gupta et al. (2009) Gupta, H., Gottlieb, C. A., McCarthy, M. C., & Thaddeus, P. 2009, ApJ, 691, 1494
  * Harada & Herbst (2008) Harada, N. & Herbst, E. 2008, ApJ, 685, 272
  * Herbst (1981) Herbst, E. 1981, Nature, 289, 656
  * Herbst & Osamura (2008) Herbst, E. & Osamura, Y. 2008, ApJ, 679, 1670
  * Jiménez-Serra et al. (2016) Jiménez-Serra, I., Vasyunin, A. I., Caselli, P., et al. 2016, ApJ, 830, L6
  * Jørgensen et al. (2002) Jørgensen, J. K., Schöier, F. L., & van Dishoeck, E. F. 2002, A&A, 389, 908
  * Khamesian et al. (2016) Khamesian, M., Douguet, N., Fonseca dos Santos, S., et al. 2016, Phys. Rev. Lett., 117, 123001
  * Kłos & Lique (2011) Kłos, J. & Lique, F. 2011, MNRAS, 418, 271
  * Kołos et al. (2008) Kołos, R., Gronowski, M., & Botschwina, P. 2008, J. Chem. Phys., 128, 154305
  * Lara-Moreno et al. (2017) Lara-Moreno, M., Stoecklin, T., & Halvick, P. 2017, MNRAS, 467, 4174
  * Lara-Moreno et al. (2019) Lara-Moreno, M., Stoecklin, T., & Halvick, P. 2019, MNRAS, 486, 414
  * Lara-Moreno et al. (2021) Lara-Moreno, M., Stoecklin, T., & Halvick, P. 2021, MNRAS, 507, 4086
  * McCarthy et al. (1995) McCarthy, M. C., Gottlieb, C. A., Thaddeus, P., et al. 1995, J. Chem. Phys., 103, 7820
  * McCarthy et al. (2006) McCarthy, M. C., Gottlieb, C. A., Gupta, H., & Thaddeus, P. 2006, ApJ, 652, L141
  * Marcelino et al. (2007) Marcelino, N., Cernicharo, J., Agúndez, M., et al. 2007, ApJ, 665, L127
  * Martínez et al. (2010) Martínez Jr., O., Yang, Z., Demarais, N. J., et al. 2010, ApJ, 720, 173
  * Millar et al. (2017) Millar, T. J., Walsh, C., & Field, T. A. 2017, Chem. Rev., 117, 1765
  * Murakami et al. (2022) Murakami, T., Iida, R., Hashimoto, Y., et al. 2022, J. Phys. Chem. A, 126, 9244
  * Oyama et al. (2020) Oyama, T., Ozaki, H., Sumiyoshi, Y., et al. 2020, ApJ, 890, 39
  * Pardo et al. (2023) Pardo, J. R., Cabezas, C., Agúndez, M., et al. 2023, A&A, submitted
  * Petrie & Herbst (1997) Petrie, S. & Herbst, E. 1997, ApJ, 491, 210
  * Punanova et al. (2018) Punanova, A., Caselli, P., Feng, S., et al. 2018, ApJ, 855, 112
  * Remijan et al. (2007) Remijan, A. J., Hollis, J. M., Lovas, F. J., et al. 2007, ApJ, 664, L47
  * Remijan et al. (2023) Remijan, A., Scolati, H. N., Burkhardt, A. M., et al. 2023, ApJ, 944, L45
  * Sakai et al. (2007) Sakai, N., Sakai, T., Osamura, Y., & Yamamoto, S. 2007, ApJ, 667, L65
  * Sakai et al. (2008) Sakai, N., Sakai, T., Hirota, T., & Yamamoto, S. 2008, ApJ, 672, 371
  * Sakai et al. (2010) Sakai, N., Shiino, T., Hirota, T., et al. 2010, ApJ, 718, L49
  * Senent et al. (2019) Senent, M. L., Dayou, F., Dumouchel, F., et al. 2019, MNRAS, 486, 422
  * Spezzano et al. (2017) Spezzano, S., Caselli, P., Bizzocchi, L., et al. 2017, A&A, 606, A82
  * Suzuki et al. (1992) Suzuki, H., Yamamoto, S., Ohishi, M., et al. 1992, ApJ, 392, 551
  * Tafalla et al. (2002) Tafalla, M., Myers, P. C., Caselli, P., et al. 2002, ApJ, 569, 815
  * Tchakoua et al. (2018) Tchakoua, T., Motapon, O., & Nsangou, M. 2018, J. Phys. B: At. Mol. Opt. Phys., 51, 045202
  * Tercero et al. (2021) Tercero, F., López-Pérez, J. A., Gallego, J. D., et al. 2021, A&A, 645, A37
  * Thaddeus et al. (2008) Thaddeus, P., Gottlieb, C. A., Gupta, H., et al. 2008, ApJ, 677, 1132
  * Toumi et al. (2021) Toumi, I., Yazidi, O., & Najar, F. 2021, RSC Adv., 11, 13579
  * Vastel et al. (2018) Vastel, C., Quénard, D., Le Gal, R., et al. 2018, MNRAS, 478, 5514
  * Visser et al. (2002) Visser, A. E., Richer, J. S., & Chandler, C. J. 2002, ApJ, 124, 2756
  * Vuitton et al. (2009) Vuitton, V., Lavvas, P., Yelle, R. V., et al. 2009, Planet. Space Sci., 57, 1558
  * Walker et al. (2016) Walker, K. M., Dumouchel, F., Lique, F., & Dawes, R. 2016, J. Chem. Phys., 145, 024314
  * Walker et al. (2017) Walker, K. M., Lique, F., Dumouchel, F., & Dawes, R. 2017, MNRAS, 466, 831
  * Walker et al. (2018) Walker, K. M., Lique, F., & Dawes, R. 2018, MNRAS, 473, 1407
  * Walsh et al. (2009) Walsh, C., Harada, N., Herbst, E., Millar, T. J. 2009, ApJ, 700, 752
  * Woon (1995) Woon, D. E. 1995, Chem. Phys. Lett., 244, 45
  * Yoshida et al. (2019) Yoshida, K., Sakai, N., Nishimura, Y., et al. 2019, PASJ, 71, S18

##  Appendix A Supplementary table

Table 5:  Observed line parameters of molecular anions in interstellar clouds. Species | Transition | Frequency |  | $V_{\rm LSR}$ | $\Delta v$ |  $T_{A}^{*}$ peak a |  $\int T_{A}^{*}dv$ a |  | Telescope | Reference
---|---|---|---|---|---|---|---|---|---|---
|  | (MHz) |  |  (km s-1) |  (km s-1) | (mK) |  (mK km s-1) |  |  |
TMC-1 CP
C6H- | 4-3 | 11014.896 |  |  $+$5.80(2) | 0.38(4) | 25(3) | 10.1(33) |  | GBT | McCarthy et al. (2006)
| 5-4 | 13768.614 |  |  $+$5.80(11) | 0.44(7) | 24(3) | 11.2(43) |  | GBT | McCarthy et al. (2006)
| 10-9 | 27537.130 | { |  |  |  | 41.6(90) b,c | } | GBT | Cordiner et al. (2013)
| 11-10 | 30290.813 |  |  |
| 12-11 | 33044.488 |  |  $+$5.78(1) | 0.73(1) | 22.3(23) | 17.4(18) |  | Yebes 40m | This work
| 13-12 | 35798.153 |  |  $+$5.78(1) | 0.70(1) | 20.9(22) | 15.5(17) |  | Yebes 40m | This work
| 14-13 | 38551.808 |  |  $+$5.78(1) | 0.64(2) | 18.9(20) | 12.8(14) |  | Yebes 40m | This work
| 15-14 | 41305.453 |  |  $+$5.79(2) | 0.56(3) | 17.2(19) | 10.3(12) |  | Yebes 40m | This work
| 16-15 | 44059.085 |  |  $+$5.79(2) | 0.57(3) | 12.8(15) | 7.7(10) |  | Yebes 40m | This work
| 17-16 | 46812.706 |  |  $+$5.81(2) | 0.59(4) | 9.6(13) | 6.0(8) |  | Yebes 40m | This work
| 18-17 | 49566.313 |  |  $+$5.84(3) | 0.56(5) | 5.4(10) | 3.2(5) |  | Yebes 40m | This work
C4H- | 2-1 | 18619.761 |  |  $+$5.70(5) | 0.43(13) |  |  1.0(3) b,d |  | GBT | Cordiner et al. (2013)
| 4-3 | 37239.410 |  |  $+$5.81(2) | 0.71(2) | 6.0(7) | 4.5(6) |  | Yebes 40m | This work
| 5-4 | 46549.156 |  |  $+$5.81(2) | 0.55(3) | 5.8(8) | 3.4(4) |  | Yebes 40m | This work
C8H- | 11-10 | 12833.460 |  |  $+$5.71(5) | 0.36(4) | 8(1) | 3.1(10) |  | GBT | Brünken et al. (2007a)
| 12-11 | 14000.134 |  |  $+$5.86(5) | 0.37(4) | 7(1) | 2.8(10) |  | GBT | Brünken et al. (2007a)
| 13-12 | 15166.806 |  |  $+$5.84(6) | 0.45(4) | 6(1) | 2.9(10) |  | GBT | Brünken et al. (2007a)
| 16-15 | 18666.814 |  |  $+$5.80(7) | 0.34(5) | 10(2) | 3.6(16) |  | GBT | Brünken et al. (2007a)
| 27-26 | 31500.029 |  |  $+$5.82(4) | 0.63(10) | 1.28(28) | 0.86(20) |  | Yebes 40m | This work
| 28-27 | 32666.670 |  |  $+$5.76(3) | 0.76(6) | 1.08(26) | 0.87(15) |  | Yebes 40m | This work
| 29-28 | 33833.309 |  |  $+$5.90(12) | 0.68(17) | 0.78(19) | 0.56(18) |  | Yebes 40m | This work
| 30-29 | 34999.944 |  |  $+$5.86(6) | 0.60(10) | 0.87(20) | 0.56(14) |  | Yebes 40m | This work
| 31-30 | 36166.576 |  |  $+$5.83(8) | 0.32(20) | 1.01(24) | 0.34(10) |  | Yebes 40m | This work
| 32-31 | 37333.205 |  |  $+$5.73(5) | 0.66(11) | 0.87(23) | 0.61(16) |  | Yebes 40m | This work
| 33-32 | 38499.831 |  |  $+$5.81(9) | 0.82(17) | 0.68(20) | 0.60(18) |  | Yebes 40m | This work
| 34-33 | 39666.453 |  |  $+$5.93(10) | 0.40(12) | 0.44(21) |  0.19(7) e |  | Yebes 40m | This work
C3N- | 4-3 | 38812.797 |  |  $+$5.78(1) | 0.88(2) | 4.2(2) | 3.9(5) |  | Yebes 40m | This work
| 5-4 | 48515.872 |  |  $+$5.86(2) | 0.61(4) | 6.3(9) | 4.1(6) |  | Yebes 40m | This work
| 8-7 | 77624.540 |  |  $+$5.88(3) | 0.52(8) | 7.1(17) | 3.9(9) |  | IRAM 30m | This work
| 10-9 | 97029.687 |  |  $+$5.77(4) | 0.38(6) | 2.7(8) | 1.1(3) |  | IRAM 30m | This work
C5N- | 12-11 | 33332.570 |  |  $+$5.83(1) | 0.71(3) | 6.5(7) | 4.9(6) |  | Yebes 40m | This work
| 13-12 | 36110.238 |  |  $+$5.80(1) | 0.64(2) | 6.1(7) | 4.1(5) |  | Yebes 40m | This work
| 14-13 | 38887.896 |  |  $+$5.81(1) | 0.63(2) | 6.5(8) | 4.4(5) |  | Yebes 40m | This work
| 15-14 | 41665.541 |  |  $+$5.82(2) | 0.58(2) | 5.7(7) | 3.5(5) |  | Yebes 40m | This work
| 16-15 | 44443.173 |  |  $+$5.79(2) | 0.56(2) | 4.7(6) | 2.8(4) |  | Yebes 40m | This work
| 17-16 | 47220.793 |  |  $+$5.81(2) | 0.50(4) | 3.6(6) | 1.9(3) |  | Yebes 40m | This work
Lupus-1A
C6H- | 7-6 | 19276.037 |  |  $+$5.046(8) | 0.16(2) |  85(8) b |  14(2) b |  | GBT | Sakai et al. (2010)
| 8-7 | 22029.741 |  |  $+$5.034(10) | 0.17(2) |  94(11) b |  15(3) b |  | GBT | Sakai et al. (2010)
| 12-11 | 33044.488 |  |  $+$5.06(2) | 0.59(3) | 30.1(37) | 18.9(24) |  | Yebes 40m | This work
| 13-12 | 35798.153 |  |  $+$5.08(2) | 0.51(3) | 32.9(40) | 17.8(25) |  | Yebes 40m | This work
| 14-13 | 38551.808 |  |  $+$5.05(2) | 0.48(4) | 30.4(38) | 15.7(20) |  | Yebes 40m | This work
| 15-14 | 41305.453 |  |  $+$5.09(3) | 0.40(7) | 32.7(42) | 13.8(19) |  | Yebes 40m | This work
| 16-15 | 44059.085 |  |  $+$5.07(3) | 0.55(6) | 24.2(35) | 14.2(22) |  | Yebes 40m | This work
| 17-16 | 46812.706 |  |  $+$5.10(6) | 0.51(8) | 17.1(33) | 9.3(18) |  | Yebes 40m | This work
C4H- | 4-3 | 37239.410 |  |  $+$5.078(13) | 0.34(3) |  59(5) b |  19(5) b |  | GBT | Sakai et al. (2010)
| 4-3 | 37239.410 |  |  $+$5.04(4) | 0.78(7) | 7.4(14) | 6.1(11) |  | Yebes 40m | This work
| 5-4 | 46549.156 |  |  $+$5.05(9) | 0.45(12) | 9.8(27) | 4.7(13) |  | Yebes 40m | This work
| 9-8 | 83787.297 |  |  $+$5.23(6) | 0.47(12) | 10.4(31) | 5.3(13) |  | IRAM 30m | This work
C8H- | 16-15 | 18666.814 | { | $+$5.014(11) | 0.09(3) | 35(9) | 4(1) b,c | } | GBT | Sakai et al. (2010)
| 18-17 | 21000.145
C3N- | 4-3 | 38812.797 |  |  $+$5.16(15) | 0.96(15) | 2.8(10) | 2.8(9) |  | Yebes 40m | This work
C5N- | 12-11 | 33332.570 |  |  $+$5.11(7) | 0.50(9) | 8.4(16) | 4.4(10) |  | Yebes 40m | This work
| 13-12 | 36110.238 |  |  $+$5.11(7) | 0.44(9) | 6.5(13) | 3.1(7) |  | Yebes 40m | This work
| 14-13 | 38887.896 |  |  $+$5.13(7) | 0.64(8) | 8.0(17) | 5.4(11) |  | Yebes 40m | This work
| 15-14 | 41665.541 |  |  $+$5.14(9) | 0.37(10) | 9.2(19) | 3.7(9) |  | Yebes 40m | This work
| 16-15 | 44443.173 |  |  $+$5.09(10) | 0.58(15) | 6.1(18) | 3.8(11) |  | Yebes 40m | This work
L1527
C6H- | 7-6 | 19276.037 |  |  $+$5.93(9) | 0.45(11) |  14(3) b |  7(2) b |  | GBT | Sakai et al. (2007)
| 8-7 | 22029.741 |  |  $+$5.89(3) | 0.49(10) |  26(4) b |  18(4) b |  | GBT | Sakai et al. (2007)
| 12-11 | 33044.488 |  |  $+$5.90(5) | 0.85(10) | 9.6(14) | 8.6(16) |  | Yebes 40m | This work
| 13-12 | 35798.153 |  |  $+$5.85(4) | 0.60(4) | 11.4(20) | 7.3(18) |  | Yebes 40m | This work
| 14-13 | 38551.808 |  |  $+$5.84(3) | 0.61(5) | 12.0(18) | 7.8(12) |  | Yebes 40m | This work
| 15-14 | 41305.453 |  |  $+$5.90(3) | 0.60(4) | 16.4(25) | 10.4(19) |  | Yebes 40m | This work
| 16-15 | 44059.085 |  |  $+$5.90(3) | 0.52(4) | 14.5(23) | 8.0(16) |  | Yebes 40m | This work
| 17-16 | 46812.706 |  |  $+$5.83(5) | 0.58(8) | 11.1(23) | 6.8(14) |  | Yebes 40m | This work
C4H- | 4-3 | 37239.410 |  |  $+$5.92(12) | 0.80(20) | 3.2(10) | 2.7(7) |  | Yebes 40m | This work
| 5-4 | 46549.156 |  |  $+$6.05(15) | 0.73(15) | 4.9(19) | 3.8(13) |  | Yebes 40m | This work
| 9-8 | 83787.297 |  |  $+$5.80(3) | 0.62(9) | 13(2) | 8(1) |  | IRAM 30m | Agúndez et al. (2008)
| 10-9 | 93096.550 |  |  $+$5.90(4) | 0.59(9) | 11(2) | 7(1) |  | IRAM 30m | Agúndez et al. (2008)
L483
C6H- | 12-11 | 33044.488 |  |  $+$5.38(6) | 0.66(8) | 4.9(11) | 3.4(8) |  | Yebes 40m | This work
| 13-12 | 35798.153 |  |  $+$5.33(5) | 0.70(7) | 5.8(10) | 4.3(8) |  | Yebes 40m | This work
| 14-13 | 38551.808 |  |  $+$5.33(5) | 0.78(7) | 5.2(9) | 4.3(9) |  | Yebes 40m | This work
| 15-14 | 41305.453 |  |  $+$5.29(6) | 0.46(9) | 5.3(12) | 2.6(6) |  | Yebes 40m | This work
| 16-15 | 44059.085 |  |  $+$5.24(10) | 0.75(12) | 4.8(12) | 3.8(10) |  | Yebes 40m | This work
| 17-16 | 46812.706 |  |  $+$5.34(7) | 0.63(9) | 5.0(14) | 3.4(9) |  | Yebes 40m | This work
C4H- | 4-3 | 37239.410 |  |  $+$5.39(8) | 0.73(12) | 2.8(7) | 2.2(5) |  | Yebes 40m | This work
| 5-4 | 46549.156 |  |  $+$5.37(10) | 0.44(15) | 2.7(12) |  1.3(5) e |  | Yebes 40m | This work
L1495B
C6H- | 10-9 | 27537.130 | { |  |  |  | 9.6(20) b,c | } | GBT | Cordiner et al. (2013)
| 11-10 | 30290.813 |  |  |
| 12-11 | 33044.488 |  |  $+$7.66(5) | 0.80(7) | 5.9(12) | 5.0(9) |  | Yebes 40m | This work
| 13-12 | 35798.153 |  |  $+$7.65(5) | 0.50(8) | 5.8(12) | 3.1(6) |  | Yebes 40m | This work
| 14-13 | 38551.808 |  |  $+$7.58(7) | 0.39(10) | 4.3(11) | 1.8(4) |  | Yebes 40m | This work
| 15-14 | 41305.453 |  |  $+$7.66(10) | 0.36(14) | 6.6(16) | 2.6(6) |  | Yebes 40m | This work
| 16-15 | 44059.085 |  |  $+$7.61(8) | 0.49(12) | 4.1(11) | 2.1(6) |  | Yebes 40m | This work
L1544
C6H- | 7-6 | 19276.037 e | { |  $+$7.08(3) | 0.16(3) | 16(2) | 6.0(18) | } | GBT | Gupta et al. (2009)
$+$7.30(3) | 0.13(3) | 26(2)
| 12-11 | 33044.488 |  |  $+$7.11(13) | 0.67(28) | 4.5(16) | 3.2(14) |  | Yebes 40m | This work
| 13-12 | 35798.153 |  |  $+$7.04(10) | 0.48(16) | 4.1(12) | 2.1(9) |  | Yebes 40m | This work
| 14-13 | 38551.808 |  |  $+$6.98(8) | 0.50(13) | 6.0(16) | 3.2(12) |  | Yebes 40m | This work
| 15-14 | 41305.453 |  |  $+$7.34(18) | 0.76(36) | 4.6(15) | 3.7(16) |  | Yebes 40m | This work
L1521F
C6H- | 7-6 | 19276.037 e | { |  $+$6.33(5) | 0.18(3) | 17(2) | 7.0(17) | } | GBT | Gupta et al. (2009)
$+$6.64(5) | 0.35(9) | 9(2)
L1251A
C6H- | 10-9 | 27537.130 | { |  |  |  | 6.5(17) b,c | } | GBT | Cordiner et al. (2013)
| 11-10 | 30290.813 |  |  |
L1512
C6H- | 10-9 | 27537.130 | { |  |  |  | 4.3(8) b,c | } | GBT | Cordiner et al. (2013)
| 11-10 | 30290.813 |  |  |
L1172
C6H- | 10-9 | 27537.130 | { |  |  |  | 6.7(15) b,c | } | GBT | Cordiner et al. (2013)
| 11-10 | 30290.813 |  |  |
L1389
C6H- | 10-9 | 27537.130 | { |  |  |  | 5.9(14) b,c | } | GBT | Cordiner et al. (2013)
| 11-10 | 30290.813 |  |  |
TMC-1 C
C6H- | 10-9 | 27537.130 | { |  |  |  | 13.6(25) b,c | } | GBT | Cordiner et al. (2013)
| 11-10 | 30290.813 |  |  |
Table 5: continued.

a Unless otherwise stated, the intensity scale is antenna temperature
($T_{A}^{*}$). It can be converted to main beam brightness temperature
($T_{\rm mb}$) by dividing by $B_{\rm eff}$/$F_{\rm eff}$, where $B_{\rm eff}$
is the main beam efficiency and $F_{\rm eff}$ is the telescope forward
efficiency. For the Yebes 40m telescope in the $Q$ band $B_{\rm eff}$ = 0.797
$\exp$[$-$($\nu$(GHz)/71.1)2] and $F_{\rm eff}$ = 0.97
(https://rt40m.oan.es/rt40m_en.php), for the IRAM 30m telescope $B_{\rm eff}$
= 0.871 $\exp$[$-$($\nu$(GHz)/359)2] and $F_{\rm eff}$ = 0.95
(https://publicwiki.iram.es/Iram30mEfficiencies), and for the GBT telescope we
adopt $F_{\rm eff}$ = 1.0 and $B_{\rm eff}$ = 1.32 $\times$ 0.71
$\exp$[$-$($\nu$(GHz)/103.7)2] (Frayer et al., 2018). The error in $\int
T_{A}^{*}dv$ includes the contributions from the Gaussian fit and from
calibration (assumed to be 10 %). b Intensity scale is $T_{\rm mb}$. c Average
of two lines. d Line neglected in the analysis. Intensity should be $\sim$ 3
times larger to be consistent with the other lines. e Line detected
marginally.

Table 6:  Observed velocity-integrated line intensities of neutral counterparts of molecular anions in interstellar clouds. Species | Transition | Frequency (MHz) |  $\int T_{A}^{*}dv$ (mK km s-1) a | Telescope | Reference
---|---|---|---|---|---
TMC-1 CP
C6H |  ${}^{2}\Pi_{3/2}$ $J=15/2-13/2$ $a$ | 20792.907 |  133(24) b | GBT | Sakai et al. (2007)
|  ${}^{2}\Pi_{3/2}$ $J=15/2-13/2$ $b$ | 20794.475 |  112(22) b | GBT | Sakai et al. (2007)
|  ${}^{2}\Pi_{3/2}$ $J=21/2-19/2$ $a$ | 29109.658 |  332.4(420) b | GBT | Cordiner et al. (2013)
|  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $a$ | 31881.860 | 175.6(176) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $b$ | 31885.541 | 173.5(175) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=25/2-23/2$ $a$ | 34654.037 | 158.9(160) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=25/2-23/2$ $b$ | 34658.383 | 158.5(160) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $a$ | 37426.192 | 141.5(180) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $b$ | 37431.255 | 141.1(175) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=29/2-27/2$ $a$ | 40198.323 | 119.3(149) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=29/2-27/2$ $b$ | 40204.157 | 118.6(147) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $a$ | 42970.432 | 93.4(106) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $b$ | 42977.089 | 93.3(106) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $a$ | 45742.519 | 73.0(98) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $b$ | 45750.052 | 73.4(99) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=35/2-33/2$ $a$ | 48514.584 | 52.6(73) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=35/2-33/2$ $b$ | 48523.044 | 52.2(70) | Yebes 40m | This work
C4H |  $N=2-1$ $J=3/2-1/2$ | 19054.476 |  411.3(418) b | GBT | Cordiner et al. (2013)
|  $N=4-3$ $J=9/2-7/2$ | 38049.654 | 1369(138) | Yebes 40m | This work
|  $N=4-3$ $J=7/2-5/2$ | 38088.461 | 1007(102) | Yebes 40m | This work
|  $N=5-4$ $J=11/2-9/2$ | 47566.792 | 1094(111) | Yebes 40m | This work
|  $N=5-4$ $J=9/2-7/2$ | 47605.496 | 864(87) | Yebes 40m | This work
|  $N=9-8$ $J=19/2-17/2$ | 85634.010 | 417(53) | IRAM 30m | Agúndez et al. (2008)
|  $N=9-8$ $J=17/2-15/2$ | 85672.580 | 386(49) | IRAM 30m | Agúndez et al. (2008)
|  $N=10-9$ $J=21/2-19/2$ | 95150.393 | 251(26) | IRAM 30m | This work
|  $N=10-9$ $J=19/2-17/2$ | 95188.947 | 243(26) | IRAM 30m | This work
|  $N=11-10$ $J=23/2-21/2$ | 104666.568 | 111(12) | IRAM 30m | This work
|  $N=11-10$ $J=21/2-19/2$ | 104705.108 | 105(13) | IRAM 30m | This work
|  $N=12-11$ $J=25/2-23/2$ | 114182.523 | 60(8) | IRAM 30m | This work
|  $N=12-11$ $J=23/2-21/2$ | 114221.023 | 47(6) | IRAM 30m | This work
C8H |  ${}^{2}\Pi_{3/2}$ $J=53/2-51/2$ $a$ | 31093.035 | 6.0(7) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=53/2-51/2$ $b$ | 31093.415 | 4.4(6) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=55/2-53/2$ $a$ | 32266.325 | 4.3(6) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=55/2-53/2$ $b$ | 32266.735 | 4.2(6) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=57/2-55/2$ $a$ | 33439.612 | 3.5(5) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=57/2-55/2$ $b$ | 33440.052 | 3.4(6) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=59/2-57/2$ $b$ | 34613.367 | 2.7(3) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=61/2-59/2$ $a$ | 35786.176 | 3.0(4) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=61/2-59/2$ $b$ | 35786.679 | 2.4(3) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=63/2-61/2$ $a$ | 36959.452 | 2.3(3) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=63/2-61/2$ $b$ | 36959.989 | 2.2(3) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=65/2-63/2$ $a$ | 38132.725 | 1.7(2) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=65/2-63/2$ $b$ | 38133.297 | 1.5(2) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=67/2-65/2$ $a$ | 39305.995 | 1.4(2) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=67/2-65/2$ $b$ | 39306.602 | 1.4(2) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=69/2-67/2$ $a$ | 40479.260 | 1.2(2) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=69/2-67/2$ $b$ | 40479.904 | 1.2(2) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=71/2-69/2$ $a$ | 41652.522 | 0.8(1) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=71/2-69/2$ $b$ | 41653.203 | 0.9(1) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=73/2-71/2$ $a$ | 42825.779 | 0.7(1) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=73/2-71/2$ $b$ | 42826.499 | 0.7(1) | Yebes 40m | This work
C3N |  $N=4-3$ $J=9/2-7/2$ | 39571.347 | 332(34) | Yebes 40m | This work
|  $N=4-3$ $J=7/2-5/2$ | 39590.181 | 240(25) | Yebes 40m | This work
|  $N=5-4$ $J=11/2-9/2$ | 49466.421 | 244(25) | Yebes 40m | This work
|  $N=5-4$ $J=9/2-7/2$ | 49485.224 | 198(20) | Yebes 40m | This work
|  $N=9-8$ $J=19/2-17/2$ | 89045.583 | 64.2(73) | IRAM 30m | This work
|  $N=9-8$ $J=17/2-15/2$ | 89064.347 | 58.6(68) | IRAM 30m | This work
|  $N=10-9$ $J=21/2-19/2$ | 98940.087 | 28.1(36) | IRAM 30m | This work
|  $N=10-9$ $J=19/2-17/2$ | 98958.770 | 22.7(30) | IRAM 30m | This work
|  $N=11-10$ $J=23/2-21/2$ | 108834.254 | 11.6(24) | IRAM 30m | This work
|  $N=11-10$ $J=21/2-19/2$ | 108853.012 | 21.2(35) | IRAM 30m | This work
C5N |  $N=12-11$ $J=25/2-23/2$ | 33668.234 | 5.6(7) | Yebes 40m | This work
|  $N=12-11$ $J=23/2-21/2$ | 33678.966 | 5.9(7) | Yebes 40m | This work
|  $N=13-12$ $J=27/2-25/2$ | 36474.308 | 5.8(7) | Yebes 40m | This work
|  $N=13-12$ $J=25/2-23/2$ | 36485.042 | 5.5(7) | Yebes 40m | This work
|  $N=14-13$ $J=29/2-27/2$ | 39280.369 | 5.1(7) | Yebes 40m | This work
|  $N=14-13$ $J=27/2-25/2$ | 39291.105 | 5.0(7) | Yebes 40m | This work
|  $N=15-14$ $J=31/2-29/2$ | 42086.415 | 4.7(6) | Yebes 40m | This work
|  $N=15-14$ $J=29/2-27/2$ | 42097.151 | 4.4(6) | Yebes 40m | This work
|  $N=16-15$ $J=33/2-31/2$ | 44892.444 | 4.6(6) | Yebes 40m | This work
|  $N=16-15$ $J=31/2-29/2$ | 44903.182 | 4.4(6) | Yebes 40m | This work
|  $N=17-16$ $J=35/2-33/2$ | 47698.457 | 3.7(5) | Yebes 40m | This work
|  $N=17-16$ $J=33/2-31/2$ | 47709.196 | 3.4(5) | Yebes 40m | This work
Lupus-1A
C6H |  ${}^{2}\Pi_{3/2}$ $J=15/2-13/2$ $a$ | 20792.907 |  114(14) b | GBT | Sakai et al. (2010)
|  ${}^{2}\Pi_{3/2}$ $J=15/2-13/2$ $b$ | 20794.475 |  131(16) b | GBT | Sakai et al. (2010)
|  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $a$ | 31881.860 | 150.3(166) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $b$ | 31885.541 | 153.1(163) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=25/2-23/2$ $a$ | 34654.037 | 151.6(161) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=25/2-23/2$ $b$ | 34658.383 | 150.0(159) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $a$ | 37426.192 | 140.3(143) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $b$ | 37431.255 | 141.0(148) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=29/2-27/2$ $a$ | 40198.323 | 126.2(134) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=29/2-27/2$ $b$ | 40204.157 | 124.8(130) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $a$ | 42970.432 | 115.5(123) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $b$ | 42977.089 | 114.9(123) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $a$ | 45742.519 | 90.7(125) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $b$ | 45750.052 | 91.3(128) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=35/2-33/2$ $a$ | 48514.584 | 73.6(109) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=35/2-33/2$ $b$ | 48523.044 | 66.9(103) | Yebes 40m | This work
C4H |  $N=4-3$ $J=9/2-7/2$ | 38049.654 | 1219(123) | Yebes 40m | This work
|  $N=4-3$ $J=7/2-5/2$ | 38088.461 | 921(94) | Yebes 40m | This work
|  $N=5-4$ $J=11/2-9/2$ | 47566.792 | 1123(114) | Yebes 40m | This work
|  $N=5-4$ $J=9/2-7/2$ | 47605.496 | 846(86) | Yebes 40m | This work
|  $N=8-7$ $J=17/2-15/2$ | 76117.439 | 1124(114) | IRAM 30m | This work
|  $N=8-7$ $J=15/2-13/2$ | 76156.028 | 1024(104) | IRAM 30m | This work
|  $N=9-8$ $J=19/2-17/2$ | 85634.010 | 779(83) | IRAM 30m | This work
|  $N=9-8$ $J=17/2-15/2$ | 85672.580 | 730(77) | IRAM 30m | This work
|  $N=11-10$ $J=23/2-21/2$ | 104666.568 | 349(39) | IRAM 30m | This work
|  $N=11-10$ $J=21/2-19/2$ | 104705.108 | 334(38) | IRAM 30m | This work
C8H |  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $a$ | 19359.975 |  10(2) b | GBT | Sakai et al. (2010)
|  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $b$ | 19360.123 |  9(2) b | GBT | Sakai et al. (2010)
C3N |  $N=4-3$ $J=9/2-7/2$ | 39571.347 | 251(30) | Yebes 40m | This work
|  $N=4-3$ $J=7/2-5/2$ | 39590.181 | 175(19) | Yebes 40m | This work
|  $N=5-4$ $J=11/2-9/2$ | 49466.421 | 177(19) | Yebes 40m | This work
|  $N=5-4$ $J=9/2-7/2$ | 49485.224 | 138(15) | Yebes 40m | This work
|  $N=9-8$ $J=19/2-17/2$ | 89045.583 | 141.5(150) | IRAM 30m | This work
|  $N=9-8$ $J=17/2-15/2$ | 89064.347 | 126.7(136) | IRAM 30m | This work
|  $N=10-9$ $J=21/2-19/2$ | 98940.087 | 74.6(83) | IRAM 30m | This work
|  $N=10-9$ $J=19/2-17/2$ | 98958.770 | 66.0(74) | IRAM 30m | This work
C5N |  $N=12-11$ $J=25/2-23/2$ | 33668.234 | 4.5(12) | Yebes 40m | This work
|  $N=12-11$ $J=23/2-21/2$ | 33678.966 | 7.0(14) | Yebes 40m | This work
|  $N=13-12$ $J=27/2-25/2$ | 36474.308 | 4.8(11) | Yebes 40m | This work
|  $N=13-12$ $J=25/2-23/2$ | 36485.042 | 5.7(11) | Yebes 40m | This work
|  $N=14-13$ $J=29/2-27/2$ | 39280.369 | 7.8(24) | Yebes 40m | This work
|  $N=14-13$ $J=27/2-25/2$ | 39291.105 | 5.7(15) | Yebes 40m | This work
|  $N=15-14$ $J=31/2-29/2$ | 42086.415 | 4.1(9) | Yebes 40m | This work
|  $N=15-14$ $J=29/2-27/2$ | 42097.151 | 4.8(11) | Yebes 40m | This work
|  $N=16-15$ $J=33/2-31/2$ | 44892.444 | 3.2(9) | Yebes 40m | This work
|  $N=16-15$ $J=31/2-29/2$ | 44903.182 |  1.8(8) d | Yebes 40m | This work
L1527
C6H |  ${}^{2}\Pi_{3/2}$ $J=15/2-13/2$ $a$ | 20792.907 |  24(5) b | GBT | Sakai et al. (2007)
|  ${}^{2}\Pi_{3/2}$ $J=15/2-13/2$ $b$ | 20794.475 |  21(5) b | GBT | Sakai et al. (2007)
|  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $a$ | 31881.860 | 34.8(75) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $b$ | 31885.541 | 26.0(59) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=25/2-23/2$ $a$ | 34654.037 | 29.3(34) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=25/2-23/2$ $b$ | 34658.383 | 31.8(37) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $a$ | 37426.192 | 31.7(46) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $b$ | 37431.255 | 32.2(51) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=29/2-27/2$ $a$ | 40198.323 | 32.7(50) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=29/2-27/2$ $b$ | 40204.157 | 32.3(48) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $a$ | 42970.432 | 30.2(47) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $b$ | 42977.089 | 31.1(49) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $a$ | 45742.519 | 30.5(48) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $b$ | 45750.052 | 31.3(49) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=35/2-33/2$ $a$ | 48514.584 | 27.3(48) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=35/2-33/2$ $b$ | 48523.044 | 26.9(47) | Yebes 40m | This work
C4H |  $N=4-3$ $J=9/2-7/2$ | 38049.654 | 388(39) | Yebes 40m | This work
|  $N=4-3$ $J=7/2-5/2$ | 38088.461 | 295(30) | Yebes 40m | This work
|  $N=5-4$ $J=11/2-9/2$ | 47566.792 | 434(44) | Yebes 40m | This work
|  $N=5-4$ $J=9/2-7/2$ | 47605.496 | 347(35) | Yebes 40m | This work
|  $N=9-8$ $J=19/2-17/2$ | 85634.010 | 747(86) | IRAM 30m | Agúndez et al. (2008)
|  $N=9-8$ $J=17/2-15/2$ | 85672.580 | 712(82) | IRAM 30m | Agúndez et al. (2008)
|  $N=11-10$ $J=23/2-21/2$ | 104666.568 | 542(64) | IRAM 30m | Agúndez et al. (2008)
|  $N=11-10$ $J=21/2-19/2$ | 104705.108 | 487(59) | IRAM 30m | Agúndez et al. (2008)
|  $N=12-11$ $J=25/2-23/2$ | 114182.523 | 462(59) | IRAM 30m | Agúndez et al. (2008)
|  $N=12-11$ $J=23/2-21/2$ | 114221.023 | 406(53) | IRAM 30m | Agúndez et al. (2008)
L483
C6H |  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $a$ | 31881.860 | 29.4(34) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $b$ | 31885.541 | 31.0(36) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=25/2-23/2$ $a$ | 34654.037 | 28.4(32) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=25/2-23/2$ $b$ | 34658.383 | 27.7(31) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $a$ | 37426.192 | 26.2(29) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $b$ | 37431.255 | 26.2(30) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=29/2-27/2$ $a$ | 40198.323 | 24.4(28) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=29/2-27/2$ $b$ | 40204.157 | 23.2(27) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $a$ | 42970.432 | 19.7(23) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $b$ | 42977.089 | 20.4(24) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $a$ | 45742.519 | 13.6(22) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $b$ | 45750.052 | 14.2(21) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=35/2-33/2$ $a$ | 48514.584 | 13.0(23) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=35/2-33/2$ $b$ | 48523.044 | 13.7(24) | Yebes 40m | This work
C4H |  $N=4-3$ $J=9/2-7/2$ | 38049.654 | 470(48) | Yebes 40m | This work
|  $N=4-3$ $J=7/2-5/2$ | 38088.461 | 356(36) | Yebes 40m | This work
|  $N=5-4$ $J=11/2-9/2$ | 47566.792 | 439(50) | Yebes 40m | This work
|  $N=5-4$ $J=9/2-7/2$ | 47605.496 | 352(36) | Yebes 40m | This work
|  $N=8-7$ $J=17/2-15/2$ | 76117.439 | 375(38) | IRAM 30m | This work
|  $N=8-7$ $J=15/2-13/2$ | 76156.028 | 337(35) | IRAM 30m | This work
|  $N=9-8$ $J=19/2-17/2$ | 85634.010 | 272(27) | IRAM 30m | Agúndez et al. (2019)
|  $N=9-8$ $J=17/2-15/2$ | 85672.580 | 249(24) | IRAM 30m | Agúndez et al. (2019)
|  $N=10-9$ $J=21/2-19/2$ | 95150.393 | 157(15) | IRAM 30m | Agúndez et al. (2019)
|  $N=10-9$ $J=19/2-17/2$ | 95188.947 | 147(14) | IRAM 30m | Agúndez et al. (2019)
|  $N=11-10$ $J=23/2-21/2$ | 104666.568 | 110(10) | IRAM 30m | Agúndez et al. (2019)
|  $N=11-10$ $J=21/2-19/2$ | 104705.108 | 100(9) | IRAM 30m | Agúndez et al. (2019)
|  $N=12-11$ $J=25/2-23/2$ | 114182.523 | 64(6) | IRAM 30m | Agúndez et al. (2019)
|  $N=12-11$ $J=23/2-21/2$ | 114221.023 | 64(6) | IRAM 30m | Agúndez et al. (2019)
L1495B
C6H |  ${}^{2}\Pi_{3/2}$ $J=13/2-11/2$ $a$ | 18020.606 |  55(10) c | GBT | Gupta et al. (2009)
|  ${}^{2}\Pi_{3/2}$ $J=13/2-11/2$ $b$ | 18021.783 |  55(10) c | GBT | Gupta et al. (2009)
|  ${}^{2}\Pi_{3/2}$ $J=21/2-19/2$ $a$ | 29109.658 |  141.6(164) b | GBT | Cordiner et al. (2013)
|  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $a$ | 31881.860 | 51.9(59) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $b$ | 31885.541 | 47.9(53) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=25/2-23/2$ $a$ | 34654.037 | 46.8(52) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $a$ | 37426.192 | 45.4(51) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $b$ | 37431.255 | 42.8(49) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=29/2-27/2$ $a$ | 40198.323 | 36.2(42) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=29/2-27/2$ $b$ | 40204.157 | 37.7(42) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $a$ | 42970.432 | 33.3(40) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $b$ | 42977.089 | 33.6(40) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $a$ | 45742.519 | 24.7(38) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=33/2-31/2$ $b$ | 45750.052 | 24.0(35) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=35/2-33/2$ $a$ | 48514.584 | 19.4(32) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=35/2-33/2$ $b$ | 48523.044 | 18.6(33) | Yebes 40m | This work
L1544
C6H |  ${}^{2}\Pi_{3/2}$ $J=13/2-11/2$ $a$ | 18020.606 | 51(11) | GBT | Gupta et al. (2009)
|  ${}^{2}\Pi_{3/2}$ $J=13/2-11/2$ $b$ | 18021.783 | 50(11) | GBT | Gupta et al. (2009)
|  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $a$ | 31881.860 | 23.8(36) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=23/2-21/2$ $b$ | 31885.541 | 30.0(44) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=25/2-23/2$ $a$ | 34654.037 | 25.7(39) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=25/2-23/2$ $b$ | 34658.383 | 31.6(48) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $a$ | 37426.192 | 23.3(36) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=27/2-25/2$ $b$ | 37431.255 | 19.9(34) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=29/2-27/2$ $b$ | 40204.157 | 18.0(31) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $a$ | 42970.432 | 13.6(26) | Yebes 40m | This work
|  ${}^{2}\Pi_{3/2}$ $J=31/2-29/2$ $b$ | 42977.089 | 12.1(23) | Yebes 40m | This work
L1521F
C6H |  ${}^{2}\Pi_{3/2}$ $J=13/2-11/2$ $a$ | 18020.606 | 36(10) | GBT | Gupta et al. (2009)
|  ${}^{2}\Pi_{3/2}$ $J=13/2-11/2$ $b$ | 18021.783 | 26(9) | GBT | Gupta et al. (2009)
L1251A
C6H |  ${}^{2}\Pi_{3/2}$ $J=21/2-19/2$ $a$ | 29109.658 | 36(8) | GBT | Cordiner et al. (2011)
|  ${}^{2}\Pi_{3/2}$ $J=21/2-19/2$ $b$ | 29112.730 | 35(8) | GBT | Cordiner et al. (2011)
|  ${}^{2}\Pi_{3/2}$ $J=21/2-19/2$ $a$ | 29109.658 |  43.6(65) b | GBT | Cordiner et al. (2013)
L1512
C6H |  ${}^{2}\Pi_{3/2}$ $J=13/2-11/2$ $a$ | 18020.606 |  20(7) c | GBT | Gupta et al. (2009)
|  ${}^{2}\Pi_{3/2}$ $J=13/2-11/2$ $b$ | 18021.783 |  20(7) c | GBT | Gupta et al. (2009)
|  ${}^{2}\Pi_{3/2}$ $J=21/2-19/2$ $a$ | 29109.658 | 27(5) | GBT | Cordiner et al. (2011)
|  ${}^{2}\Pi_{3/2}$ $J=21/2-19/2$ $b$ | 29112.730 | 28(5) | GBT | Cordiner et al. (2011)
|  ${}^{2}\Pi_{3/2}$ $J=21/2-19/2$ $a$ | 29109.658 |  26.3(35) b | GBT | Cordiner et al. (2013)
L1172
C6H |  ${}^{2}\Pi_{3/2}$ $J=21/2-19/2$ $a$ | 29109.658 |  41.1(57) b | GBT | Cordiner et al. (2013)
L1389
C6H |  ${}^{2}\Pi_{3/2}$ $J=13/2-11/2$ $a$ | 18020.606 |  10(6) c | GBT | Gupta et al. (2009)
|  ${}^{2}\Pi_{3/2}$ $J=13/2-11/2$ $b$ | 18021.783 |  10(6) c | GBT | Gupta et al. (2009)
|  ${}^{2}\Pi_{3/2}$ $J=21/2-19/2$ $a$ | 29109.658 |  27.1(40) b | GBT | Cordiner et al. (2013)
TMC-1 C
C6H |  ${}^{2}\Pi_{3/2}$ $J=21/2-19/2$ $a$ | 29109.658 |  88.1(105) b | GBT | Cordiner et al. (2013)
Table 6: continued.

a Unless otherwise stated, the intensity scale is antenna temperature
($T_{A}^{*}$). It can be converted to main beam brightness temperature
($T_{\rm mb}$) by dividing by $B_{\rm eff}$/$F_{\rm eff}$ (see caption of
Table LABEL:table:lines_anion. The error in $\int T_{A}^{*}dv$ includes the
contributions from the Gaussian fit and from calibration (assumed to be 10 %).
b Intensity scale is $T_{\rm mb}$. c Intensity distributed equally among the
two fine components. d Marginal detection.