Interstellar nitrile anions: Detection of C$_3$N$^-$ and C$_5$N$^-$ in TMC-1 [^1]



Introduction
============

The importance of anions in the chemistry of interstellar clouds was analyzed in the early years of astrochemistry by @Dalgarno1973. The presence of carbon chain negative ions in space was predicted on the ground that electron radiative attachment is efficient for molecules with large electron affinities and dense vibrational spectra [@Sarre1980; @Herbst1981].

The first anion detected in space, C$_6$H$^-$, was observed towards TMC-1 [@McCarthy2006]. Lines from this species were already reported as unidentified features in the line survey of IRC+10216 performed with the Nobeyama 45 m telescope by @Kawaguchi1995. Their assignation to C$_6$H$^-$ was not possible until the laboratory observations of @McCarthy2006 became available. Nevertheless, @Aoki2000 suggested that the carrier of these lines was C$_6$H$^-$ from ab initio calculations. The laboratory and space detection of this species prompted attention to the abundance of hydrocarbon anions in interstellar and circumstellar clouds. C$_4$H$^-$ was first discovered in the circumstellar cloud IRC+10216 by @Cernicharo2007 and then in the interstellar clouds L1527 and TMC-1 [@Sakai2008; @Agundez2008a; @Cordiner2013]. C$_6$H$^-$ was also detected towards other interstellar sources [@Sakai2007; @Gupta2009; @Cordiner2011; @Cordiner2013]. Following the observation of C$_8$H$^-$ in the laboratory [@Gupta2007] this anion was found in TMC-1 [@Brunken2007] and IRC+10216 [@Kawaguchi2007; @Remijan2007].

The nitrile anions CN$^-$, C$_3$N$^-$ and C$_5$N$^-$ were first detected in the circumstellar envelope of the carbon-rich star IRC+10216 [@Agundez2010; @Thaddeus2008; @Cernicharo2008]. While accurate laboratory frequencies were available for CN$^-$ and C$_3$N$^-$ [@Gottlieb2007; @Thaddeus2008; @Amano2008], the assignment of C$_5$N$^-$ was based on the coincidence of the observed rotational constants with *ab initio* calculations by @Botschwina2008 and @Aoki2000. Although this species is the best candidate for this identification, the lack of precise laboratory frequencies prevents us from ruling out other species involving metals, which are present in IRC+10216. For example, MgC$_3$N and MgC$_4$H have been recently detected in IRC+10216 based on *ab initio* calculations [@Cernicharo2019] and they have rotational constants $B$ just a few megahertz below that of C$_5$N$^-$. Moreover, there is controversy about the formation of C$_n$N$^-$ anions through radiative electron attachment to C$_n$N radicals, for which calculated rate constants differ by orders of magnitude [@Walsh2009; @Khamesian2016; @Millar2017]. Hence, the detection of these anions in cold dark clouds and the determination of their abundances are an important step forward in understanding their chemistry in different astronomical environments.

In this Letter we present the detection of C$_3$N$^-$ and C$_5$N$^-$ in the cold dark core TMC-1. This is the first time nitrile anions are observed in the interstellar medium. The C$_3$N/C$_3$N$^-$ and C$_5$N/C$_5$N$^-$ abundance ratios derived are discussed within the frame of a chemical model of a cold dense cloud.

![Lines of C$_3$N$^-$ observed towards TMC-1 in the 31.0-50.3 GHz frequency range. The abscissa corresponds to the local standard of rest velocity in km s$^{-1}$. Frequencies and intensities for the observed lines are given in Table \[tab\_c3nm\_tmc1\]. The ordinate axis represents the antenna temperature in mK corrected for atmospheric and telescope losses.<span data-label="fig_c3nm_tmc1"></span>](fig_c3nm_tmc1)

![Same as Fig. \[fig\_c3nm\_tmc1\] but for C$_5$N$^-$. Observed frequencies and intensities are given in Table \[tab\_c5nm\_tmc1\].<span data-label="fig_c5nm_tmc1"></span>](fig_c5nm_tmc1)

Observations
============

The Q-band (31.0-50.3 GHz) observations of TMC-1 ($\alpha_{2000}$=4$^h$ 41$^m$ 42.0$^s$, $\delta_{2000}$=25$^o$ 41$'$ 27.6$''$) were carried out during the winter 2019/2020 with the 40 m radio telescope of the Yebes observatory (IGN, Spain), hereafter Yebes 40 m. Observations of IRC+10216 in the same frequency band were performed in spring 2019 and have been previously described by @Cernicharo2019 and @Pardo2020. New receivers were built within the Nanocosmos project[^2] and installed at the telescope [@Tercero2020]. They were used for the observations presented in this work. The Q-band receiver consists of two HEMT cold amplifiers covering the 31.0-50.3 GHz band with horizontal and vertical polarisations. Receiver temperatures vary from 22 K at 32 GHz to 42 K at 50 GHz. The backends are $16\times2.5$ GHz fast Fourier transform spectrometers (FFTS) with a spectral resolution of 38.1 kHz providing the whole coverage of the Q band in both polarisations. The main beam efficiency varies from 0.6 at 32 GHz to 0.43 at 50 GHz. Pointing corrections obtained by observing strong nearby quasars and were always within 2-3$''$.

For IRC+10216 the observing mode was position switching with an off position at 300$''$ in azimuth. The final spectra were smoothed to a resolution of 0.15 MHz, that is a velocity resolution of $\approx$1.5 and 0.9 km s$^{-1}$ at 31 and 50 GHz, respectively. The sensitivity of the final spectra varies between 0.4 mK and 1 mK per 0.15 MHz channel across the Q band, which is a factor of $\approx$10 better than previous observations in the same frequency range with the Nobeyama 45 m telescope taken with a spectral resolution of 0.5-0.625 MHz [@Kawaguchi1995].

<span><span>cccccc</span></span> Transition& $\nu_{rest}^a$& v$_{LSR}$ & $\Delta$v$^b$ & $\int$T$_A^*$dv $^c$ & T$_A^*$\
& (MHz) & (km s$^{-1}$)& (km s$^{-1}$) & (mK km s$^{-1}$) & (mK)\

<span>*J*=4-3 F=4-3</span>\
<span>*+* F=5-4</span> & 38812.810 & 5.82$\pm$0.05 & 0.51$\pm$0.13& 2.4$\pm$0.3& 4.5\
<span>*J*=4-3 F=3-2</span> & 38812.728 & 5.84$\pm$0.10 & 0.68$\pm$0.16& 2.3$\pm$0.4& 3.3\
<span>*J*=5-4 </span> & 48515.874 & 5.90$\pm$0.03 & 0.50$\pm$0.07& 3.5$\pm$0.3& 6.5\

The TMC-1 Q-band observations were performed using the frequency switching technique with a frequency throw of 10MHz. The nominal spectral resolution of 38.1 kHz was left unchanged for the final spectra because of the low temperature of this source and, therefore, narrowness of its lines. The average noise at this spectral resolution in the Q band ranges from $\sim$0.7 mK at 31 GHz to $\sim$2 gfischer@example.org GHz, which considerably improves previous line surveys in this frequency range for this source [@Kaifu2004].

In order to improve the rotational constants of C$_5$N$^-$ we used all lines of this species observed with the IRAM 30 m telescope since its detection [@Cernicharo2008]. These observations in the $\lambda$ 3 mm band have been described in detail by @Cernicharo2019. They correspond to observations acquired during the last 35 years covering the 70-116 GHz range with very high sensitivity (1-3 mK) over 1 MHz wide channels. Examples of these data can be found in @Cernicharo2004 [@Cernicharo2007; @Cernicharo2008; @Cernicharo2019] and @Agundez2008b [@Agundez2014].

The beam size of the Yebes 40 m in the Q band is in the range 36-56$''$, while that of the IRAM 30 m telescope in the 3 mm domain is 21-30$''$. Pointing corrections were obtained by observing strong nearby quasars or SiO masers for both sources. Pointing errors were always within 2-3$''$. The intensity scale for the observations with both telescopes, antenna temperature (T$_A^*$), was obtained after a calibration procedure that uses two absorbers at different temperatures and the atmospheric transmission model (ATM; @Cernicharo1985 [@Pardo2001]). Calibration uncertainties are $\sim$10 %. Additional uncertainties could arise, in the case of IRC+10216, from the line intensity fluctuation induced by the time variation of the stellar infrared flux [@Cernicharo2014; @Pardo2018]. All data were analyzed via the GILDAS package[^3].

<span><span>ccrccc</span></span> & $\nu_{obs}^a$& $\nu_{o}-\nu_{c}^b$ & $\Delta$v$^c$ & $\int$T$_A^*$dv $^d$ & T$_A^*$\
& (MHz) & (kHz) & (kms$^{-1}$)& (mK kms$^{-1}$) & (mK)\
12& 33332.572 & 1.7& 0.75$\pm$0.08& 5.0$\pm$0.2& 6.2\
13& 36110.244 & 5.5& 0.73$\pm$0.07& 5.5$\pm$0.2& 7.1\
14& 38887.893 & -2.6& 0.54$\pm$0.09& 3.7$\pm$0.3& 6.4\
15& 41665.548 & 7.1& 0.50$\pm$0.16& 2.4$\pm$0.4& 4.6\
16& 44443.178 & 4.5& 0.63$\pm$0.15& 3.3$\pm$0.5& 4.9\
17& 47220.754 &-38.8& 0.76$\pm$0.19& 2.0$\pm$0.5& 2.5\

![Rotational diagram for the observed lines of C$_5$N$^-$ in TMC-1.<span data-label="trot_tmc1"></span>](trot_tmc1)

Results {#sec:results}
=======

One of the most remarkable results from the Q-band observations in TMC-1 and IRC+10216 is the presence of a forest of weak lines. Most of these can be assigned to known species and only a few remain unidentified in IRC+10216 [@Cernicharo2019; @Pardo2020] and TMC-1 (Marcelino et al., in preparation). For both sources the level of sensitivity in this work has been increased, as commented previously, by a factor 5-10 with respect to previous works with other telescopes at the same frequencies [@Kawaguchi1995; @Kaifu2004]. This high sensitivity has also allowed us to detect all known C$_{2n}$H and C$_{2n+1}$N anions in TMC-1. In this paper we focus on C$_3$N$^-$ and C$_5$N$^-$ lines in TMC-1. In addition, we use the observed frequencies of C$_5$N$^-$ transitions towards IRC+10216 for an improved determination of the rotational and distortion constants of this anion.

C$_3$N$^-$
----------

Laboratory work exists for this anion and frequencies are well determined with accuracies of $\simeq$2 kHz [@Thaddeus2008]. This species has two rotational transitions in the 31.0-50.3 GHz frequency range. Figure \[fig\_c3nm\_tmc1\] shows both of these transitions towards TMC-1, while the derived line parameters are given in Table \[tab\_c3nm\_tmc1\]. This species was searched towards TMC-1 by @Thaddeus2008 without success, and to the best of our knowledge, this is the first time this anion has been detected in an interstellar cloud.

C$_5$N$^-$
----------

The detected lines of C$_5$N$^-$ towards TMC-1 are shown in Fig. \[fig\_c5nm\_tmc1\]. Only the <span>*J*</span>=18-17 gfischer@example.org MHz has not been detected. This is, however, justified since the sensitivity of the data at 50 GHz is 3 mK, whereas the expected <span>*J*</span>=18-17 line intensity is below 5 mK (see also Fig. \[fig\_c5nm\_tmc1\]). No C$_5$N$^-$ lines were detected with the Nobeyama 45 m telescope by @Kaifu2004.

In order to derive precise frequencies for C$_5$N$^-$ in TMC-1 we fitted, in our Yebes 40 m data, the central v$_{LSR}$ of the line emission from well-known species for which accurate laboratory rotational frequencies exist. From the seven HC$_5$N rotational transitions in the Q band (<span>*J*</span>$_{up}$=12 to <span>*J*</span>$_{up}$=18), @Cernicharo2020 derive a v$_{LSR}$ of 5.83$\pm$0.01 km s$^{-1}$. From the $^{13}$C and $^{15}$N isotopologues of HC$_5$N, they obtain v$_{LSR}$ = 5.84$\pm$0.01 km s$^{-1}$. Hence, we adopt a v$_{LSR}$ of 5.83 km s$^{-1}$ for further frequency determinations in TMC-1. The value given by @Kaifu2004 is 5.85 km s$^{-1}$, which is practically identical to our result within the uncertainties. Derived line parameters for C$_5$N$^-$ in TMC-1 are given in Table \[tab\_c5nm\_tmc1\].

The characteristic U-shaped line profiles exhibited by molecular lines in IRC+10216 allow an accurate central frequency determination, within $\simeq$50 kHz [@Cernicharo2018], in spite of the broad emission that covers 29 km s$^{-1}$ [@Cernicharo2000]. The v$_{LSR}$ of the source, -26.5 km s$^{-1}$, has been well determined from the observation of hundreds of lines [@Cernicharo2000]. The observed C$_5$N$^-$ lines in IRC+10216 at $\lambda$$\sim$7mm (Q band) are shown in Fig. \[fig\_c5nm\_irc\]. Frequencies and other line parameters are given in Table \[tab\_c5nm\_irc\]. This table also includes lines observed in the 3 mm data obtained after the detection of this species in 2008. All lines at 3 mm re-observed after @Cernicharo2008 have a spectral resolution of 0.198 MHz; these lines are shown in Fig. \[fig\_irc\_3mm\].

New rotational constants for C$_5$N$^-$ {#new_rot_cons}
---------------------------------------

The frequencies of a linear molecular species can be fitted to this standard expression involving the rotational quantum number J, rotational constant $B_0$, and the distortion constant $D_0$:

$\nu(J\rightarrow$$J-1)$=2$B_0$J - 4$D_0$J$^3$.\
Using all observed C$_5$N$^-$ lines in both sources, the fit provides the following results:

$B_0$=1388.86681(19) MHz

$D_0$=34.44(13)$\times$10$^{-6}$ MHz,

where values between parentheses represent the 1$\sigma$ uncertainty for the fitted parameters. The data were weighted in the fit according 1/$\delta v^2$, where $\delta v$ is the estimated uncertainty on the observed frequencies. The correlation coefficient between $B_0$ and $D_0$ is 0.738 and the standard deviation between the predicted and observed frequencies is 66 kHz. These values significantly improve those derived from previous observations by @Cernicharo2008, $B_0$=1388.860(2) and $D_0$=33(1)$\times$10$^{-6}$ MHz. We tried to fit the distortion constant of order six ($H_0$), but the derived value is only marginally significant. Its inclusion reduces the weighted deviation from 1.03 to 0.89 and the standard deviation from 66 to 53.7 kHz. However, it increases the correlation between the fitted parameters. The derived values in this case, are written as

$B_0$=1388.86734(25) MHz

$D_0$=35.68(44)$\times$10$^{-6}$ MHz

$H_0$=5.0(1.7)$\times$10$^{-10}$ MHz.\
The differences between observed and calculated frequencies are given in Tables \[tab\_c5nm\_tmc1\] and \[tab\_c5nm\_irc\] for TMC-1 and IRC+10216, respectively. New rotational parameters were also derived for C$_5$N (see Section \[app\_c5n\_rot\]).

Discussion
==========

Only two rotational C$_3$N$^-$ lines have been detected in TMC-1. We assumed a volume density of H$_2$ of 4$\times$10$^4$ cm$^{-3}$ (see e.g. @Fosse2001), a kinetic temperature of 10 K, a dipole moment for the molecule of 2.27 D [@Pascoli1999], and the collisional rates of C$_3$N$^-$/H$_2$ from @Lara2019. For simulating the source we assumed a circular uniform brightness distribution with a radius of 40$''$ (see e.g. the intensity maps of different carbon chains presented by @Fosse2001). With this assumed size the source completely covers the main beam of the Yebes 40 gfischer@example.org.

Using the large velocity gradient approximation (LVG) implemented in MADEX [@Cernicharo2012], and correcting the intensities of all observed transitions for the beam efficiency and the source beam dilution, we derive a column density of <span>*N*</span>(C$_3$N$^-$)=1.3$\times$10$^{11}$ cm$^{-2}$.

For C$_5$N$^-$ we have enough observed lines to build the rotational diagram shown in Fig \[trot\_tmc1\]. A dipole moment of 5.2 D was adopted for this species [@Botschwina2008]. A source size identical to that of C$_3$N$^-$ was adopted. We derive a rotational temperature of 6.4$\pm$0.6 K and a column density of (2.6$\pm$0.9)$\times$10$^{11}$ cm$^{-2}$. We also performed an LVG calculation with MADEX adopting for C$_5$N$^-$ the collisional rates of C$_6$H$^-$/p-H$_2$ [@Walker2017]. For a kinetic temperature of 10 K, the observed intensities corrected for beam efficiency and source beam dilution can be reproduced with a column density of 9$\times$10$^{11}$ cm$^{-2}$. If the collisional rates of HC$_5$N/p-H$_2$ are adopted (F. Lique, private communication), then the column density is 1.5$\times$10$^{11}$ cm$^{-2}$. Hence, the difference by a factor two of the latter value with respect to that from the rotational diagram is due to the uncertainties on both the collisional rates and the assumed H$_2$ volume density. We adopt for C$_5$N$^-$ the column density derived from the rotational diagram of Fig. \[trot\_tmc1\].

The derived line parameters for C$_3$N and C$_5$N are given in Tables \[tab\_c3n\_tmc1\] and \[tab\_c5n\_tmc1\]. For C$_3$N collisional rates are not available and we assumed a rotational temperature of 7 K (that is similar to that of C$_5$N$^-$) to compute line intensities assuming local thermodynamical equilibrium conditions (LTE). Assuming the same source size as for the anions, we derive <span>*N*</span>(C$_3$N)=1.8$\times$10$^{13}$ cm$^{-2}$. For C$_5$N we can build a rotational diagram based on the data provided in Table \[tab\_c5n\_tmc1\], which yields <span>*T*$_{rot}$</span>=10.1$\pm$1.90 K and <span>*N*</span>(C$_5$N)=(6.0$\pm$2.5)$\times$10$^{11}$ cm$^{-2}$. The adopted dipole moment for this species is 3.385 D [@Botschwina1996]. Hence, the <span>*N*</span>(C$_3$N)/<span>*N*</span>(C$_3$N$^-$) and <span>*N*</span>(C$_5$N)/<span>*N*</span>(C$_5$N$^-$) abundance ratios in TMC-1 are $\sim$140, and $\sim$2.3, respectively.

In IRC+10216 @Thaddeus2008 derived a N(C$_3$N)/N(C$_3$N$^-$) abundance ratio of $\simeq$194, and @Cernicharo2008 obtained a N(C$_5$N)/N(C$_5$N$^-$) abundance ratio around 2. Hence, the observed abundance ratios between neutral radicals C$_n$N and their anions are very similar in interstellar and circumstellar clouds.

One of the problems in obtaining the C$_n$N/C$_n$N$^-$ abundance ratio is the assumed permanent dipole moment for the neutrals. In the case of C$_5$N, the dipole moment for the ground $^2\Sigma$ electronic state was calculated by @Botschwina1996. However, as discussed by @Cernicharo2008, the C$_5$N radical has a low lying $^2\Pi$ electronic state with a dipole moment of $\sim$1 D [@Pauzat1991]. Detailed calculations by @Botschwina1996 indicate that it lies 500 cm$^{-1}$ above the $^2\Sigma$ ground state. Hence, C$_5$N could have a dipole moment between these two values in the case of admixing between the $^2\Sigma$ and the $^2\Pi$ states. A dipole moment averaged over both electronic states (i.e., twice as small as that calculated for the unperturbed $^2\Sigma$ state) would raise the C$_5$N/C$_5$N$^-$ abundance ratio to $\sim8$ in TMC-1 and IRC+10216, which is very similar to the C$_6$H/C$_6$H$^-$ ratio in IRC+10216 [@Cernicharo2007].

The same situation applies to C$_4$H and C$_4$H$^-$. The neutral radical also has a $^2\Sigma^+$ ground electronic state with a first excited $^2\Pi$ electronic state very close in energy. The case has been recently discussed by @Oyama2020 who computed a dipole moment for C$_4$H 2.4 times larger than the value of the $^2\Sigma^+$ state alone. The effect is a decrease by a factor $\sim$6 on the derived C$_4$H column densities and an increase of the C$_4$H/C$_4$H$^-$ abundance ratio by the same factor.

![Neutral-to-anion abundance ratios calculated with the chemical model are shown as a function of time and compared with observed values. The early time (10$^5$-10$^6$ yr) at which calculated abundances agree better with observations (see e.g. @Agundez2013) is indicated. A conservative uncertainty of a factor of 2 is adopted for the observed ratios.<span data-label="fig_ratios_anions"></span>](fig_ratios_anions){width="\columnwidth"}

The chemistry of negative ions in cold interstellar clouds has been discussed by @Walsh2009 and @Millar2017. In the light of the discovery of interstellar C$_3$N$^-$ and C$_5$N$^-$, we revisit the chemistry of these species in this work. We performed a chemical model of a cold dark cloud with typical physical parameters ($T_k$ = 10 K, $n_{\rm H}$ = $2\times10^4$ cm$^{-3}$, $\zeta$ = $1.3\times10^{-17}$ s$^{-1}$, $A_V$ = 30 mag) and "low metal" elemental abundances (see @Agundez2013). We adopted the University of Manchester Institute of Science and Technology <span>RATE12</span> reaction network [@McElroy2013], with a subset of reactions involving HCCN from @Loison2015. According to the model, formation of C$_3$N$^-$ does not occur via radiative electron attachment to C$_3$N, which is slow [@Petrie1997], but through reactions between N atoms and bare carbon-chain anions C$_n^-$ (with $n \geq 6$), which are rapid and produce several nitrile radical and anions [@Eichelberger2007]. In the case of C$_5$N$^-$, the reaction of radiative electron attachment to C$_5$N is rapid [@Walsh2009] and dominates the synthesis of this anion. Formation of C$_3$N$^-$ through dissociative electron attachment to metastable isomers such as HNC$_3$ [@Harada2008] is included and occurs to some extent, although most of C$_3$N$^-$ is formed by N + C$_n$$^-$ reactions. Reactions of H$^-$ with HC$_3$N and HC$_5$N could be a source of C$_3$N$^-$ and C$_5$N$^-$, although they are likely to be too slow at 10 K based on calculations for similar reactions of H$^-$ with C$_2$H$_2$ and C$_4$H$_2$ [@Gianturco2016]. Destruction of C$_3$N$^-$ and C$_5$N$^-$ is dominated by reactions with neutral atoms H, O, and C in cold dark clouds. Nitrile anions have been shown to react rapidly with polar molecules at low temperatures [@Joalland2016]. However, it is unlikely that this is a major loss channel for anions in cold dense clouds because, apart from CO, molecules have much lower abundances than neutral atoms.

The much larger rate constant of radiative electron attachment to C$_5$N compared to C$_3$N is the main reason why C$_5$N$^-$ is calculated to be much more abundant with respect to the neutral than C$_3$N$^-$ (see Fig. \[fig\_ratios\_anions\]). The results of our model are similar to the theoretical predictions of @Walsh2009. Calculated neutral-to-anion abundance ratios during the so-called early time (10$^5$-10$^6$ yr), at which calculated abundances agree better with observations (see e.g. @Agundez2013), agree well with the values retrieved from observations for C$_3$N$^-$, although they are somewhat higher for C$_5$N$^-$ (see Fig. \[fig\_ratios\_anions\]). We note that, as discussed above, the observed C$_5$N/C$_5$N$^-$ ratio could be as high as $\sim8$, in which case model and observations would agree much better. Finally, we point out that the chemical model predicts an abundance of $\sim3\times10^{-11}$ relative to H$_2$ for CN$^-$. Adopting a column density of 10$^{22}$ cm$^{-2}$ for H$_2$ [@Cernicharo1987], the predicted column density of CN$^-$ would be $3\times10^{11}$ cm$^{-2}$, which is below the $3\sigma$ upper limit of $1.4\times10^{12}$ cm$^{-2}$ derived by @Agundez2008a.

This work definitively excludes metal-bearing species, or vibrationally excited states of other known species, as carriers for the series of lines assigned to C$_5$N$^-$ by @Cernicharo2008, and gives strong support to this identification.

We thank Spanish Ministerio de Ciencia e Innovación for funding support through project AYA2016-75066-C2-1-P. We also thank ERC for funding through grant ERC-2013-Syg-610256-NANOCOSMOS. MA and CB thank Ministerio de Ciencia e Innovación for Ramón y Cajal grant RyC-2014-16277 and Juan de la Cierva grant FJCI-2016-27983. We thank support from French National Research Agency through project Anion Cos Chem (ANR-14-CE33-0013). We would like to thank our referee, Prof. S. Yamamoto, for useful comments and suggestions.

Ag<span>ú</span>ndez, M., Cernicharo, J., Guélin, et al., 2008a, , 478, L19 Ag<span>ú</span>ndez, M., Fonfría, J. P., Cernicharo, J., et al., 2008b, , 479, 493 Ag<span>ú</span>ndez, M., Cernicharo, J., Guélin, M., et al., 2010, , 517, L2 Agúndez, M. & Wakelam, V. 2013, <span>Chem. Rev.</span>, 113, 8710 Agúndez, M., Cernicharo, J., & Guélin, M., 2014, , 570, 45 Amano, T., 2008, J. Chem. Phys., 129, 244305 Aoki, K., 2000, Chem. Phys. Lett., 323, 55 Botschwina, P., 1996, Chem. Phys. Lett., 259, 627 Botschwina, P., Oswald, R., 2008, J. Chem. Phys., 129, 044305 Brünken, S., Gupta, H., Gottlieb, C.A., et al., 2007, , 664, L43 Cernicharo, J. 1985, Internal IRAM report (Granada: IRAM) Cernicharo, J. & Guélin, M. 1987, , 176, 299 Cernicharo, J., Guélin, M., & Kahane, C. 2000, , 142, 181 Cernicharo, J., Guélin, M., & Pardo, J. R. 2004, , 615, L145 Cernicharo, J., Guélin, M., Agúndez, M., et al. 2007, , 467, L37 Cernicharo, J., Guélin, M., Agúndez, M. et al., 2008, , 688, L83 Cernicharo, J., 2012, in ECLA 2011: Proc. of the European Conference on Laboratory Astrophysics, EAS Publications Series, 2012, Ed.: C. Stehl, C. Joblin, & L. d'Hendecourt (Cambridge: Cambridge Univ. Press), 251; `https://nanocosmos.iff.csic.es/?page\_id=1619` Cernicharo, J., Teyssier, D., Quintana-Lacaci, G., et al., 2014, , 796, L21 Cernicharo, J., Guélin, M., Agúndez, M., et al., 2018, , 618, A4 Cernicharo, J., Cabezas, C., Pardo, J. R., et al., 2019, , 630, L2 Cernicharo, J., Marcelino, N., Cabezas, C., et al., in preparation Cordiner, M. A., Charnley, S. B., Buckle, J. V., et al., 2011, , 730, L18 Cordiner, M. A., Buckle, J. V., Wirström, E. S., et al. 2013, , 770, 48 Dalgarno, A., McCray, R.A., 1973, , 181, 95 Eichelberger, B., Snow, T. P., Barckholtz, C., & Bierbaum, V. 2007, , 667, 1283 Fossé, D., Cernicharo, J., Gerin, M., Cox, P., 2001, , 552, 168 Gianturco, F.A., Satta, M., Mendolicchio, M., et al., 2016, , 830, 2 Gottlieb, C.A., Brünken, S., McCarthy, M.C., Thaddeus, P., 2007, J. Chem. Phys., 126, 191101 Gupta, H., Brünken, S., Tamassia, F., et al., 2007, , 655, L57 Gupta, H., Gottlieb, C.A., McCarthy, M.C., Thaddeus, P., 2009, , 691, 1494 Harada, N. & Herbst, E. 2008, , 685, 272 Herbst, E. 1981, Nature, 289, 656 Joalland, B., Jamal-Eddine, N., K<span>ł</span>os, J., et al. 2016, J. Phys. Chem. Lett., 7, 2957 Kaifu, N., Ohishi, M., Kawaguchi, K., et al., 2004, PASJ, 56, 69 Kasai, Y., Sumiyoshi, Y, Endo, Y., Kawaguchi, K., 1997, , 477, L65 Kawaguchi, K., Kasai, Y., Ishikawa, S., Kaifu, N. 1995, PASJ, 47, 853 Kawaguchi, K., Fujimori, R., Aimi, S., 2007, PASJ, 59, L47 Khamesian, M., Douguet, N., Fonseca, S., et al., 2016, Phys. Rev. Lett., 117, 123001 Lara-Moreno, M., Stoecklin, T., Halvick, P., 2019, MNRAS, 486, 414 Loison, J. C., Hébrard, E., Dobrijevic, M., et al. 2015, , 247, 218 McCarthy, M.C., Gottlieb, C.A., Gupta, H.C., et al., , 2006, 652, L141 McElroy, D., Walsh, C., Markwick, A. J., et al. 2013, , 550, A36 Millar, T. J., Walsh, C., & Field, T. A. 2017, <span>Chem. Rev.</span>, 117, 1765 Müller, H.S.P., Schlöder, F., Stutzki, J., Winnewisser, G., 2005, <span>J. Mol. Struct.</span>, 742, 215 Pardo, J. R., Cernicharo, J., Serabyn, E. 2001, IEEE Trans. Antennas and Propagation, 49, 12 Pardo, J. R., Cernicharo, J., Velilla-Prieto, L., et al. 2018, , 615, L4 Pardo, J. R., Bermúdez, C., Cabezas, C., et al., 2020, , 640, L13 Pascoli, G., Lavendy, H., 1999, Chem. Phys. Lett., 312, 333 Pauzat, F., Ellinger, Y., McLean, A.D., 1991, , 369, L13 Petrie, S. & Herbst, E. 1997, , 491, 210 Pickett, H. M. 1991, JMoSp, 148, 371 Remijan, A. J., Hollis, J. M., Lovas, F. J., et al. 2007, , 664, L47 Sarre, P. J. 1980, J. Chem. Phys., 77(7-8), 769 Sakai, N., Sakai, T., Osamura, T., Yamamoto, S., 2007, , 667, L65 Sakai, N., Sakai, T., Yamamoto, S., 2008, , 673, L71 Tercero, F., et al., 2020, , submitted Oyama, T., Ozaki, H., Sumiyoshi, Y., et al., 2020, , 890, 39 Thaddeus, P., Gottlieb, C.A., Gupta, H., et al. 2008, ApJ, 677, 1132 Walker, K.M., Ligue, F., Dumouchel, F., Dawes, R., 2017, MNRAS, 466, 831 Walsh, C., Harada, N., Herbst, E., & Millar, T. J. 2009, , 700, 752

Additional tables and figures
=============================

Line parameters for C$_5$N$^-$ towards IRC+10216 are given in Table \[tab\_c5nm\_irc\]. The observed lines are shown in Figures \[fig\_c5nm\_irc\] and \[fig\_irc\_3mm\]. The data in the 3 mm domain (see Fig. \[fig\_irc\_3mm\]) considerably improve the signal to noise ratio of the lines reported by @Cernicharo2008. The new rotational constants derived from these frequencies and those of TMC-1 are discussed in Section \[new\_rot\_cons\].

The observed line parameters for C$_3$N and C$_5$N in TMC-1, which are needed to compute the column density of these species and to compare with that of their anions, are given in Tables \[tab\_c3n\_tmc1\] and \[tab\_c5n\_tmc1\]. For C$_3$N, accurate frequency predictions can be found in the Cologne Database for Molecular Spectroscopy (CDMS; @Muller2005). However, we discuss below the case of C$_5$N, as significant deviations between predicted and measured frequencies in space are observed.

![Rotational transitions of C$_5$N$^-$ observed towards IRC+10216 in the 31-50 GHz range. Derived frequencies and intensities are given in Table \[tab\_c5nm\_irc\]. Figure \[fig\_irc\_3mm\] shows the lines of the same species observed with the IRAM 30 m telescope at $\lambda$=3mm .<span data-label="fig_c5nm_irc"></span>](fig_c5nm_irc)

\[\] ![image](fig_irc_3mm)

<span><span>ccccc</span></span> & $\nu_{obs}^a$ & $\nu_{o}-\nu_{c}^b$ &$\int$Tdv$^c$& Notes\
& (MHz) & (MHz) & (K km s$^{-1}$)&\
12& 33332.508$\pm$0.050&-0.062 & 0.063$\pm$0.003&\
13& 36110.197$\pm$0.050&-0.040 & 0.091$\pm$0.003&\
14& 38887.789$\pm$0.100&-0.105 & 0.154$\pm$0.005& 1\
15& 41665.527$\pm$0.050&-0.013 & 0.115$\pm$0.003&\
16& 44443.116$\pm$0.050&-0.057 & 0.108$\pm$0.003&\
17& 47220.740$\pm$0.050&-0.052 & 0.102$\pm$0.003&\
18& 49998.450$\pm$0.100&+0.052 & 0.100$\pm$0.005& 1\
26& 72218.580$\pm$0.050&-0.049 & 0.303$\pm$0.008&\
27& 74996.039$\pm$0.050&-0.032 & 0.308$\pm$0.005&\
28& 77773.492$\pm$0.050&+0.002 & 0.297$\pm$0.004&\
29& 80550.817$\pm$0.050&-0.070 & 0.264$\pm$0.009&\
30& 83328.258$\pm$0.050&-0.003 & 0.216$\pm$0.007&\
31& & & & 2\
32& 88882.883$\pm$0.050&-0.052 & 0.233$\pm$0.003&\
33& 91660.297$\pm$0.050&+0.063 & 0.232$\pm$0.003&\
34& 94437.518$\pm$0.050&+0.011 & 0.238$\pm$0.003&\
35& 97214.796$\pm$0.050&+0.042 & 0.216$\pm$0.006&\
36& 99991.999$\pm$0.050&+0.026 & 0.207$\pm$0.006&\
37& 102769.266$\pm$0.100&+0.101 & 0.266$\pm$0.007& 3\
38& 105546.319$\pm$0.050&-0.008 & 0.202$\pm$0.006&\
39& 108323.470$\pm$0.050&+0.010 & 0.130$\pm$0.003&\
40& 111100.565$\pm$0.100&+0.002 & 0.111$\pm$0.008&\
41& 113877.556$\pm$0.100&-0.081 & 0.092$\pm$0.015& 1\
48& 133316.175$\pm$0.150&-0.078 & 0.056$\pm$0.010& 4\

<span><span>cccccc</span></span> & $\nu_{rest}^a$ & v$_{LSR}$ & $\int$Tdv$^b$ & $\Delta$v$^c$ & T$_a^*$\
& (MHz) &(km s$^{-1}$)&(mK kms$^{-1}$)& (kms$^{-1}$)& (mK)\
4 4.5 4.5$\rightarrow$3 3.5 4.5& 39571.110$\pm$0.027 &5.78$\pm$0.02& 5.7$\pm$1.0& 0.61$\pm$0.05& 8.8\
4 4.5 3.5$\rightarrow$3 3.5 2.5& 39571.319$\pm$0.003 &5.72$\pm$0.01& 136.7$\pm$1.0& 0.56$\pm$0.01& 230.6\
4 4.5 4.5$\rightarrow$3 3.5 3.5& 39571.326$\pm$0.003$^f$ & & & &\
4 4.5 5.5$\rightarrow$3 3.5 4.5& 39571.397$\pm$0.003 &5.73$\pm$0.01& 160.0$\pm$3.0& 0.51$\pm$0.02& 297.2\
4 4.5 3.5$\rightarrow$3 3.5 3.5& 39574.032$\pm$0.044 &5.61$\pm$0.02& 6.0$\pm$1.0& 0.53$\pm$0.04& 10.7\
4 3.5 3.5$\rightarrow$3 2.5 3.5& 39587.553$\pm$0.048 &5.86$\pm$0.03& 7.8$\pm$1.0& 0.59$\pm$0.04& 12.3\
4 3.5 2.5$\rightarrow$3 2.5 1.5& 39590.129$\pm$0.004 &5.73$\pm$0.01& 45.4$\pm$1.0& 0.36$\pm$0.01& 119.3\
4 3.5 3.5$\rightarrow$3 2.5 2.5& 39590.204$\pm$0.004 &5.70$\pm$0.01& 179.5$\pm$3.0& 0.56$\pm$0.01& 301.2\
4 3.5 4.5$\rightarrow$3 2.5 3.5& 39590.212$\pm$0.004$^f$ & & & &\
4 3.5 2.5$\rightarrow$3 2.5 2.5& 39591.004$\pm$0.028 &5.62$\pm$0.02& 7.6$\pm$1.0& 0.58$\pm$0.05& 12.4\
5 5.5 $\rightarrow$4 4.5$^e$& 49466.424$\pm$0.003 &5.70$\pm$0.02& 201.4$\pm$3.0& 0.66$\pm$0.04& 286.9\
5 4.5 $\rightarrow$4 3.5$^e$& 49485.227$\pm$0.005 &5.67$\pm$0.02& 164.8$\pm$3.0& 0.64$\pm$0.04& 242.1\

<span><span>cccccc</span></span> & $\nu_{obs}^a$ & $\int$Tdv$^b$ & $\Delta$v$^c$ & T$_a^*$\
& (MHz) &(mK kms$^{-1}$)& (kms$^{-1}$)& (mK)\
12 12.5& 33668.248& 7.4$\pm$0.5& 0.80$\pm$0.04& 8.8\
12 11.5& 33678.986& 6.6$\pm$0.5& 0.85$\pm$0.05& 7.4\
13 13.5& 36474.328& 6.3$\pm$0.7& 0.65$\pm$0.31& 9.1\
13 12.5& 36485.068& 4.3$\pm$0.6& 0.52$\pm$0.05& 7.7\
14 14.5& 39280.400& 5.8$\pm$0.6& 0.55$\pm$0.05& 9.9\
14 13.5& 39291.136& 5.1$\pm$0.8& 0.62$\pm$0.07& 7.8\
15 15.5& 42086.452& 3.6$\pm$0.9& 0.44$\pm$0.07& 7.8\
15 14.5& 42097.179& 2.9$\pm$1.0& 0.46$\pm$0.08& 6.0\
16 16.5& 44892.479& 3.7$\pm$1.0& 0.64$\pm$0.14& 5.4\
16 15.5& 44903.223& 3.5$\pm$1.0& 0.39$\pm$0.10& 8.4\
17 17.5& 47698.500& 4.1$\pm$1.1& 0.48$\pm$0.13& 8.2\
17 16.5& 47709.233& 7.5$\pm$1.1& 0.78$\pm$0.12& 9.0\

New rotational parameters for C$_5$N {#app_c5n_rot}
------------------------------------

For C$_5$N the frequencies of rotational lines up to $J$=6 ($\nu_{max}$=16.842 GHz) were measured in the laboratory by @Kasai1997. These authors provide frequency predictions up to 98.2 GHz that are systematically below the observed frequencies of this species towards TMC-1 (data provided in Table \[tab\_c5n\_tmc1\]) and IRC+10216 (data provided in Table \[tab\_c5n\_irc\]). In order to derive more accurate predictions we fitted the observed astronomical frequencies to the same Hamiltonian than @Kasai1997. The fits only consider frequencies measured in astronomical (space) sources that have an unresolved hyperfine structure and a merged set of space and laboratory frequencies. The results are provided in Table \[tab\_c5n\_rot\]. The poorly determined distortion constant from the laboratory data alone is responsible for the observed discrepancies. The new $D$ value derived from space data alone is 44.2$\pm$0.2 Hz, compared with the laboratory value of 50$\pm$10 Hz. In IRC+10216 several additional doublets of C$_5$N are detected between $J_{up}$=40 to $J_{up}$=48. However, their line intensity is weak and the derived frequencies have uncertainties of $\sim$1 MHz. These have not been included in the fit.

In addition we combined in one fit all the rotational transitions measured so far for C$_5$N, including those from laboratory measurements and those observed in TMC-1 and IRC+10216. We used the SPFIT program [@Pickett1991]. The results are shown in Table \[tab\_c5n\_rot\]. In all these fits the data were weighted according 1/$\sigma^2$, where $\sigma$ is the estimated uncertainty on the measured frequencies. We obtained new values for the rotational and centrifugal distortion constants for the three spin-rotation constants and also for the nuclear quadruple coupling constant. In total we analyzed 69 rotational transitions. We tried to determine additional parameters such as the distortion constant $H$ or the spin-rotation constant $\gamma$$_D$, but the attempts resulted to be unfruitful. The uncertainty in the rotational constant, $B$, improves from 0.54 kHz at @Kasai1997 to 0.15 kHz. The most significant change corresponds to the distortion constant, which has an uncertainty of 10 Hz from the laboratory data alone, and 0.3 Hz when the lines from TMC-1 and IRC+10216 are included.

The fit to the TMC-1 and IRC+10216 alone allows us to predict frequencies without hyperfine splitting with an accuracy better than 0.1 MHz up to $N_{up}$=55 ($\nu\sim$154.3 GHz). Observable hyperfine splitting in TMC-1 could occur for transitions with $N\leq$8 ($\nu\sim$22.4 GHz). In this case, the merged fit to the laboratory and space data is recommended to compute the expected frequencies.

<span><span>cccc</span></span> & $\nu_{obs}^a$ & $\int$T$_A^*$dv$^b$ & Notes\
& (MHz) &(mK kms$^{-1}$) &\
26 26.5& 72951.721$\pm$0.050& 18$\pm$6& 1,A\
26 25.5& ......... & ....... & 2\
27 27.5& 75757.571$\pm$0.050& 23$\pm$3& A\
27 26.5& 75768.214$\pm$0.100& 29$\pm$5& 1,B\
28 28.5& 78563.437$\pm$0.100& 18$\pm$3& B\
28 27.5& 78573.910$\pm$0.100& 19$\pm$3& B\
29 29.5& 81368.856$\pm$0.150& 32$\pm$2& C\
29 28.5& 81379.846$\pm$0.150& 28$\pm$2& C\
30 30.5& 84174.795$\pm$0.200& 31$\pm$6& C\
30 29.5& ......... & ....... & 2\
31 31.5& 86980.324$\pm$0.150& 25$\pm$3& C\
31 30.5& ......... & ....... & 2,C\
32 32.5& 89785.932$\pm$0.150& 27$\pm$1& C\
32 31.5& 89796.811$\pm$0.150& 33$\pm$2& C\
33 33.5& 92591.638$\pm$0.150& 24$\pm$1& C\
33 32.5& 92602.409$\pm$0.150& 29$\pm$1& C\
34 34.5& 95397.144$\pm$0.200& 43$\pm$7& 1,C\
34 33.5& ......... & ....... & 2\
35 35.5& 98202.488$\pm$0.150& 24$\pm$3& C\
35 34.5& 98213.325$\pm$0.200& 15$\pm$5& 1,C\
36 36.5& 101008.060$\pm$0.150& 30$\pm$3& C\
36 35.5& 101018.872$\pm$0.150& 26$\pm$3& C\
37 37.5& 103813.438$\pm$0.150& 32$\pm$4& C\
37 36.5& 103824.263$\pm$0.150& 32$\pm$4& 1,C\
38 38.5& 106618.712$\pm$0.200& 46$\pm$4& C\
38 37.5& 106629.939$\pm$0.200& 29$\pm$4& C\
39 39.5& .......... & ....... & 2\
39 38.5& .......... & ....... & 2\
40 40.5& 112229.929$\pm$0.500& 25$\pm$5& C\
40 39.5& 112240.834$\pm$0.500& 28$\pm$6& C\

<span><span>|c|c|c|c|c|c|</span></span> Constant$^a$ & Lab$^b$ & TMC-1$^c$ & TMC-1 & IRC+10216 $^d$ & Space + Lab$^e$\
$B$ & 1403.07981(54)& 1403.07995(19) & 1403.08041(13)& 1403.07974(15)\
$D$ & 0.000050(10) & 0.00004324(41) & 0.00004423(20)& 0.00004354(30)\
$\gamma$ &-10.7472(35) &-10.7363(23) &-10.7360(44) &-10.7478(27)\
$b$ & 1.583(13) & ........ & ........ & 1.5810(94 )\
$c$ & -3.613(25) & ........ & ........ & -3.615(18)\
$eQq$ & -4.341(17) & ........ & ........ & -4.342(13)\
$N_{max}^f$ & 6 & 17 & 40 & 40\
$\sigma$(kHz)$^g$& 10 & 4.1 & 122 & 96\

[^1]: Based on observations carried out with the Yebes 40 m telescope (projects 19A003, 19A010, and 20A014) and the Institut de Radioastronomie Millimétrique (IRAM) 30 m telescope. The 40 m radiotelescope 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).

[^2]: `https://nanocosmos.iff.csic.es/`

[^3]: `http://www.iram.fr/IRAMFR/GILDAS`

{'source': 'arXiv_out/2009'}