Laboratory spectroscopic study of the $^{15}$N isotopomers of cyanamide, H$_2$NCN, and a search for them toward IRAS 16293$-$2422 B

TL;DR

This study provides precise laboratory spectroscopic data for $^{15}$N isotopomers of cyanamide, aiding astronomical searches, but these isotopomers remain undetected in current observations of IRAS 16293-2422 B.

Contribution

The paper reports new and improved spectroscopic parameters for $^{15}$N isotopomers of cyanamide, enabling more accurate predictions for astronomical detection.

Findings

Laboratory spectra obtained between 192 and 507 GHz.

No unambiguous detection of $^{15}$N isotopomers in PILS data.

Tentative lines suggest a low $^{14}$N/$^{15}$N ratio.

Abstract

Cyanamide is one of the few interstellar molecules containing two chemically different N atoms. It was detected recently toward the solar-type protostar IRAS 16293-2422 B together with H$_2$N$^{13}$CN and HDNCN in the course of the Atacama Large Millemeter/submillimeter Array (ALMA) Protostellar Interferometric Line Survey (PILS). The detection of the 15N isotopomers or the determination of upper limits to their column densities was hampered by the lack of accurate laboratory data at the frequencies of the survey. We wanted to determine spectroscopic parameters of the $^{15}$N isotopomers of cyanamide that are accurate enough for predictions well into the submillimeter region and to search for them in the PILS data. We investigated the laboratory rotational spectra of H$_2^{15}$NCN and H$_2$NC$^{15}$N in the selected region between 192 and 507~GHz employing a cyanamide sample in natural isotopic composition. Additionally, we recorded transitions of H$_2$N$^{13}$CN. We obtained new or improved spectroscopic parameters for the three isotopic species. Neither of the $^{15}$N isotopomers of cyanamide were detected unambiguously in the PILS data. Two relatively clean lines can be tentatively assigned to H$_2^{15}$NCN. If confirmed, their column densities would imply a low $^{14}$N/$^{15}$N ratio for cyanamide toward this source. The resulting line lists should be accurate enough for observations up to about 1 THz. More sensitive observations, potentially at different frequencies, may eventually lead to the astronomical detection of these isotopic species.

Tables

Table 1. Table 1: Spectroscopic parameters X a superscript 𝑋 𝑎 X^{a} (MHz) and their differences Δ ​ X b Δ superscript 𝑋 𝑏 \Delta X^{b} (MHz) of cyanamide isotopologs.

Parameter	H${}_{}{}^{15}{}_2{}^{}$NCN		H2NC15N		H2N13CN		H2NCN
$\Delta E$	1460174	. (120)	1486116	. (118)	1486522	. (66)	1486004	.275 (185)
$F_{ac}$	342	.505 (46)	335	.828 (47)	345	.963 (59)	346	.5304 (245)
$F_{ac}^K$	$-$1	.442	$-$1	.415	$-$1	.457	$-$1	.4577 (40)
$F_{ac}^J\times {10}^3$	1	.2756 (113)	1	.1048 (119)	1	.2514 (108)	1	.2009 (89)
$F_{ac}^{JK}\times {10}^6$	$-$48	.69	$-$47	.52	$-$50	.54	$-$50	.57 (155)
$F_{ac}^{JJ}\times {10}^9$	10	.64	10	.32	11	.34	11	.36 (48)
$A$	307819	.7 (241)	308328	.7 (239)	308205	.1 (122)	308298	.054 (66)
$\Delta A/2$	$-$3838	.00	$-$3844	.35	$-$3842	.81	$-$3843	.971 (33)
$B$	9845	.11174 (75)	9794	.54528 (82)	10117	.07868 (93)	10121	.205258 (188)
$\Delta B/2$	$-$8	.74933 (71)	$-$8	.09439 (79)	$-$8	.56394 (93)	$-$8	.551540 (113)
$C$	9604	.18856 (76)	9555	.59774 (79)	9862	.34933 (114)	9866	.291773 (186)
$\Delta C/2$	$-$0	.28904 (77)	$-$0	.26534 (81)	$-$0	.35051 (110)	$-$0	.368180 (109)
$D_K$	36	.036	36	.110	36	.070	36	.0421 (44)
$\Delta D_K/2$	$-$8	.084	$-$8	.101	$-$8	.092	$-$8	.0857 (33)
$D_{JK}\times {10}^3$	368	.428 (80)	357	.939( 80)	377	.325 (101)	377	.705 (40)
$\Delta D_{JK}/2\times {10}^3$	$-$19	.239 (44)	$-$17	.766 (42)	$-$18	.097 (83)	$-$18	.494 (26)
$D_J\times {10}^3$	3	.59457 (39)	3	.50397 (38)	3	.75968 (31)	3	.759689 (180)
$\Delta D_J/2\times {10}^3$	0	.01490 (34)	0	.01741 (32)	0	.01813 (26)	0	.018511 (49)
$d_1\times {10}^6$	$-$126	.84 (48)	$-$117	.29 (49)	$-$129	.70 (36)	$-$130	.2699 (176)
$\Delta d_1/2\times {10}^6$	8	.89 (47)	9	.37 (49)	10	.88 (36)	10	.5633 (225)
$d_2\times {10}^6$	$-$25	.100 (283)	$-$23	.484 (304)	$-$27	.739 (219)	$-$27	.2965 (45)
$\Delta d_2/2\times {10}^6$	4	.931 (150)	4	.062 (206)	5	.516 (165)	5	.2987 (43)
$H_K\times {10}^3$	10	.76	10	.79	10	.77	10	.760 (84)
$\Delta H_K/2\times {10}^3$	$-$6	.45	$-$6	.47	$-$6	.46	$-$6	.453 (78)
$H_{KJ}\times {10}^6$	$-$219	.2 (50)	$-$267	.7 (48)	$-$196	.2 (45)	$-$264	.41 (234)
$\Delta H_{KJ}/2\times {10}^6$	71	.6 (12)	70	.6 (10)	82	.3 (7)	73	.64 (180)
$H_{JK}\times {10}^6$	0	.889 (73)	1	.115 (70)	0	.945 (44)	1	.0798 (167)
$\Delta H_{JK}/2\times {10}^6$	$-$0	.250 (27)	$-$0	.268 (23)	$-$0	.297 (11)	$-$0	.2879 (65)
$H_J\times {10}^9$	$-$0	.761	$-$0	.750	$-$0	.825	$-$0	.826 (77)
$\Delta H_J/2\times {10}^9$	0	.189	0	.186	0	.204	0	.205 (9)
$L_K\times {10}^6$	16	.00	16	.07	16	.04	16	.01
$\Delta L_K/2\times {10}^6$	$-$5	.31	$-$5	.34	$-$5	.32	$-$5	.32
$L_{KKJ}\times {10}^6$	$-$4	.118 (88)	$-$3	.439 (82)	$-$5	.800 (54)	$-$3	.681 (46)
$\Delta L_{KKJ}/2\times {10}^6$	0	.343	0	.343	0	.353	0	.353 (39)
$L_{JK}\times {10}^9$	17	.78 (223)	10	.10 (199)	17	.44 (94)	12	.47 (42)
rms	0	.040	0	.037	0	.043	0	.098
${\sigma }^b$	0	.82	0	.86	0	.98	0	.94

Table 2. Table 2: Assigned transitions for H 15 2 superscript subscript absent 2 15 {}_{2}^{15} NCN, observed transition frequency (MHz), experimental uncertainty Unc. (MHz), residual O − - C between observed frequency and that calculated from the final set of spectroscopic parameters, weight for blended lines, and source of line.

$J^{\prime }$	$K_a^{\prime }$	$K_c^{\prime }$	${\text{varv}}_t^{\prime }$	$J^{\prime \prime }$	$K_a^{\prime \prime }$	$K_c^{\prime \prime }$	${\text{varv}}_t^{\prime \prime }$	Frequency		Unc.	O$-$C	Weight
1	0	1	0	0	0	0	0	19458	.1	0.1	$-$0.15777		Tyler et al. (1972)
2	0	2	0	1	0	1	0	38916	.282	0.100	0.00717		Brown et al. (1985)
7	0	7	0	6	0	6	0	136194	.32870	0.05000	0.00263		Kraśnicki et al. (2011)
8	0	8	0	7	0	7	0	155645	.83281	0.05000	$-$0.01287		Kraśnicki et al. (2011)
9	0	9	0	8	0	8	0	175095	.43308	0.05000	$-$0.00786		Kraśnicki et al. (2011)
21	6	15	1	20	6	14	1	407549	.715	0.050	0.05275	0.5000	Koeln
21	6	16	1	20	6	15	1	407549	.715	0.050	0.05275	0.5000	Koeln
25	6	19	1	24	6	18	1	485115	.812	0.050	0.04584	0.5000	Koeln
25	6	20	1	24	6	19	1	485115	.812	0.050	0.04584	0.5000	Koeln
26	6	20	1	25	6	19	1	504502	.373	0.030	$-$0.03347	0.5000	Koeln
26	6	21	1	25	6	20	1	504502	.373	0.030	$-$0.03347	0.5000	Koeln

Table 3. Table 3: Initial spectroscopic parameters X a superscript 𝑋 𝑎 X^{a} (MHz) and their differences Δ ​ X b Δ superscript 𝑋 𝑏 \Delta X^{b} (MHz) of cyanamide isotopologs derived from the previously published data. Our present data are given for H 2 N 13 CN to allow a direct comparison

Parameter	H${}_{}{}^{15}{}_2{}^{}$NCN		H2NC15N		H2N13CN		H2N13CN, new
$\Delta E$	1462540	. (106)	1486091	. (133)	1486783	. (96)	1486522	. (66)
$F_{ac}$	342	.74 (23)	335	.42 (41)	345	.999 (69)	345	.963 (59)
$F_{ac}^K$	$-$1	.442	$-$1	.415	$-$1	.457	$-$1	.457
$F_{ac}^J\times {10}^3$	1	.156	1	.125	1	.2388 (130)	1	.2514 (108)
$F_{ac}^{JK}\times {10}^6$	$-$48	.69	$-$47	.52	$-$50	.54	$-$50	.54
$F_{ac}^{JJ}\times {10}^9$	10	.64	10	.32	11	.34	11	.34
$A$	308298	.	308298	.	308209	.3 (182)	308205	.1 (122)
$\Delta A/2$	$-$3844	.	$-$3844	.	$-$3842	.81	$-$3842	.81
$B$	9845	.1075 (35)	9794	.5437 (55)	10117	.07913 (141)	10117	.07868 (93)
$\Delta B/2$	$-$8	.7495 (36)	$-$8	.0946 (61)	$-$8	.56355 (140)	$-$8	.56394 (93)
$C$	9604	.1941 (33)	9555	.5997 (44)	9862	.34845 (140)	9862	.34933 (114)
$\Delta C/2$	$-$0	.28904 (77)	0	.2699 (49)	0	.35121 (136)	$-$0	.35051 (110)
$D_K$	36	.042	36	.042	36	.070	36	.070
$\Delta D_K/2$	$-$8	.086	$-$8	.086	$-$8	.092	$-$8	.092
$D_{JK}\times {10}^3$	367	.767 (92)	358	.168( 109)	376	.911 (169)	377	.325 (101)
$\Delta D_{JK}/2\times {10}^3$	$-$19	.186 (139)	$-$17	.628 (168)	$-$17	.972 (102)	$-$18	.097 (83)
$D_J\times {10}^3$	3	.6056 (207)	3	.4887 (218)	3	.76075 (44)	3	.75968 (31)
$\Delta D_J/2\times {10}^3$	0	.0165 (204)	0	.0405 (221)	0	.01861 (34)	0	.01813 (26)
$d_1\times {10}^6$	$-$119	.81	$-$118	.22	$-$130	.23 (44)	$-$129	.70 (36)
$\Delta d_1/2\times {10}^6$	9	.71	9	.59	10	.54 (44)	10	.88 (36)
$d_2\times {10}^6$	$-$24	.383	$-$23	.984	$-$27	.119 (280)	$-$27	.739 (219)
$\Delta d_2/2\times {10}^6$	4	.733	4	.656	5	.484 (167)	5	.516 (165)
$H_K\times {10}^3$	10	.76	10	.76	10	.77	10	.77
$\Delta H_K/2\times {10}^3$	$-$6	.45	$-$6	.45	$-$6	.46	$-$6	.46
$H_{KJ}\times {10}^6$	$-$257	.	$-$256	.	$-$235	.5 (118)	$-$196	.2 (45)
$\Delta H_{KJ}/2\times {10}^6$	72	.	71	.	84	.4 (32)	82	.3 (7)
$H_{JK}\times {10}^6$	1	.020	1	.012	1	.122 (86)	0	.945 (44)
$\Delta H_{JK}/2\times {10}^6$	$-$0	.273	$-$0	.270	$-$0	.267 (26)	$-$0	.297 (11)
$H_J\times {10}^9$	$-$0	.761	$-$0	.750	$-$0	.825	$-$0	.825
$\Delta H_J/2\times {10}^9$	0	.189	0	.186	0	.204	0	.204
$L_K\times {10}^6$	16	.0	16	.0	16	.04	16	.04
$\Delta L_K/2\times {10}^6$	$-$5	.3	$-$5	.3	$-$5	.32	$-$5	.32
$L_{KKJ}\times {10}^6$	$-$3	.58	$-$3	.56	$-$4	.953 (239)	$-$5	.800 (54)
$\Delta L_{KKJ}/2\times {10}^6$	0	.343	0	.343	0	.353	0	.353
$L_{JK}\times {10}^9$	11	.8	11	.7	12	.21 (266)	17	.44 (94)
rms	0	.039	0	.032	0	.042	0	.043
${\sigma }^b$	0	.61	0	.58	0	.87	0	.98

Full text

*Aims. *We wanted to determine spectroscopic parameters of the 15N isotopomers of cyanamide that are accurate enough for predictions well into the submillimeter region and to search for them in the PILS data.

Methods. We investigated the laboratory rotational spectra of H${}_{2}^{15}$NCN and H2NC15N in the selected region between 192 and 507 GHz employing a cyanamide sample in natural isotopic composition. Additionally, we recorded transitions of H2N13CN.

*Results. *We obtained new or improved spectroscopic parameters for the three isotopic species. Neither of the 15N isotopomers of cyanamide were detected unambiguously in the PILS data. Two relatively clean lines can be tentatively assigned to H${}_{2}^{15}$NCN. If confirmed, their column densities would imply a low 14N/15N ratio for cyanamide toward this source.

*Conclusions. *The resulting line lists should be accurate enough for observations up to about 1 THz. More sensitive observations, potentially at different frequencies, may eventually lead to the astronomical detection of these isotopic species.

1 Introduction

Cyanamide, H2NCN, is one of the few interstellar molecules that contain two chemically inequivalent N atoms.111The other are N2H+, N2O, aminoacetonitrile (NH2CH2CN), a heavy homolog of cyanamide, and $E$-cyanomethanimine ($E$-HNCHCN), see e.g., the Molecules in Space page (https://cdms.astro.uni-koeln.de/classic/molecules) of the Cologne Database for Molecular Spectroscopy (Endres et al. 2016), or the list of Interstellar and Circumstellar Molecules of the Astrochymist page (http://www.astrochymist.org/astrochymist_ism.html). It was among the molecules detected early in the interstellar medium (ISM) by radio astronomical means (Turner et al. 1975). The detection was made toward the prolific high-mass star-forming region Sagittarius (Sgr) B2, which is close to the Galactic center. There is also a report on the detection of H2NCN toward the nearby Orion-KL region (White et al. 2003) and the high-mass protostar IRAS 20126+410 (Palau et al. 2017). Cyanamide was also found in two nearby starburst galaxies NGC 253 (Martín et al. 2006) and M82 (Aladro et al. 2011).

Coutens et al. (2018) reported the first detection of H2NCN toward two solar-type protostars; one was IRAS 16293$-$2422 B with the Atacama Large Millimeter/submillimeter Array (ALMA) in the framework of the Protostellar Interferometric Line Survey (PILS), and the other was NGC 1333 IRAS2A in the course of Plateau de Bure Interferometer (PdBI) observations. More recently, a tentative detection was also reported toward the low-mass protostellar source Barnard 1b (Marcelino et al. 2018).

Isotopic fractionation in the N isotopes has attracted considerable interest in recent years. Very different 14N/15N ratios have been determined in star-forming regions which range from less than 100 to around 1000 (e.g., Milam & Charnley 2012; Bizzocchi et al. 2013; Wampfler et al. 2014), compared to the terrestrial ratio of 272 (Berglund & Wieser 2011). However, the reasons for the enrichment or depletion in 15N are not clear at present.

In order to address the possible N-fractionation for cyanamide, reliable transition frequencies of these rarer isotopologs are critical. The laboratory rotational spectrum of the H2NCN main isotopolog has been studied extensively since the fairly early days of microwave spectroscopy (Tyler et al. 1959), especially by Read et al. (1986) and by Birk et al. (1993). Only very limited information was available for minor isotopologs of cyanamide (Tyler et al. 1972; Brown et al. 1985) until fairly recently when Kraśnicki et al. (2011) reported millimeter and in part submillimeter transition frequencies for numerous isotopic species. Kisiel et al. (2013) presented updated accounts on H2NCN, HDNCN, and D2NCN. The line lists of the 15N isotopomers covered 135$-$176 GHz ($J^{\prime\prime}=6$ to 8) besides some older, lower-accuracy data with $J^{\prime\prime}=0$ or 1 (Kraśnicki et al. 2011). Therefore, we decided to record rotational transitions of H${}_{2}^{15}$NCN and H2NC15N between 192 and 507 GHz which should be sufficient to search for these isotopic species throughout the entire presently available frequency range of ALMA up to almost 1 THz. In the course of our measurements, we also recorded some transitions of H2N13CN to improve its spectroscopic parameters somewhat.

2 Spectroscopic properties of cyanamide

Cyanamide is an asymmetric rotor with $\kappa=(2B-A-C)/(A-C)=-0.9983$, very close to the symmetric limit of $-1$. A model of the molecule is shown in Fig 1. It is nonplanar with two equivalent configurations, albeit with a low barrier to planarity (Kisiel et al. 2013). Tunneling between the two minima lifts the degeneracy and creates tunneling substates $0^{+}$ and a $0^{-}$ which are separated by 1486 GHz (or 49.57 cm*-1* or 71.32 K). The symmetry of the planar transition state is $C_{\rm 2v}$ with the $a$-axis being the symmetry axis. The spin-statistics of the two equivalent H nuclei lead to ortho and para states with a spin-statistical weight ratio of 3 : 1. The ortho states are described by $K_{a}$ being even in $0^{+}$ and odd in $0^{-}$. Transitions within the tunneling states obey $a$-type selection rules with $\mu_{a}(0^{+})=(4.25\pm 0.02)$ D and $\mu_{a}(0^{-})=(4.24\pm 0.02)$ D (Brown et al. 1985). Tunneling occurs along the $c$-inertial axis, hence the two tunneling states are connected by $c$-type transitions with $\mu_{c}=(0.91\pm 0.02)$ D (Brown et al. 1985).

Carbon has two stable isotopes with mass numbers 12 and 13; the terrestrial abundances of the latter is 1.11 % (Berglund & Wieser 2011). The corresponding abundance of 15N is 0.36 %, much less than the dominant 14N.

3 Laboratory spectroscopic details and observed lines

The investigations of isotopic cyanamide were carried out in a five-meter long double-path glass cell at room temperature and under slow flow conditions. A commercial sample from Sigma-Aldrich was used without further purification. The sample required slight heating to reach a sufficient vapor pressure which was maintained at about 0.5 Pa inside the cell. We employed three frequency multipliers (Virginia Diodes, Inc.) driven by an Agilent E8257D synthesizer as sources with appropriate Schottky diodes as detectors to cover frequencies between 192 and 507 GHz. Frequency modulation reduces standing waves, and the demodulation at twice the modulation frequency leads to approximately second-derivative line-shapes. Further details on the spectrometer system are available in Martin-Drumel et al. (2015).

We optimized the conditions, measurement time, pressure, and modulation deviation, by recording selected transitions of H2N13CN with $K_{a}$ values of 1 and 2 around 300 GHz which were well predicted by the available data (Kraśnicki et al. 2011). An integration time of 60 ms per measurement point of one scan upward in frequency and one downward was sufficient for these lines and most of the 15N isotopomers. Several scans were coadded for some weaker lines.

The available H${}_{2}^{15}$NCN and H2NC15N transition frequencies obeyed $a$-type selection rules ($\Delta K_{a}=0$ and $\Delta K_{c}=1$). They covered $J=7-6$ to $9-8$ with $K_{a}\leq 5$ and 4 for 0+ and 0-, respectively, from Kraśnicki et al. (2011), and some $J=1-0$ and $2-1$ transitions from Tyler et al. (1972) and Brown et al. (1985). The resulting spectroscopic parameters were good enough to find transitions with low values of $J$, starting with $10-9$ around 195 GHz and low values of $K_{a}$. We determined new spectroscopic parameters and covered several higher $J$ up to $26-25$ near 505 GHz. The $K_{a}$ range extended eventually to 7 and 6 for 0+ and 0-, respectively. The uncertainties ranged from 20 kHz for isolated lines with symmetric line shape and good signal-to-noise ratio to 100 kHz.

Subsequently, we recorded H2N13CN transitions to supplement earlier measurements by Kraśnicki et al. (2011). Their data included $J=6-5$ to $8-7$ and $29-28$ to $32-31$ with $K_{a}\leq 5$ and 6 for 0+ and 0-, respectively, at frequencies of 119 to 161 and 578 to 641 GHz. Our data covered $J=13-12$ to $25-24$ and mostly higher $K_{a}$ values, 6 for 0- and 7 for 0+ and 0-, along with some lower-$K_{a}$ data. We assigned uncertainties of 20 or 30 kHz to our H2N13CN transition frequencies. Figure 2 displays the $0^{-}$, $J_{K_{a},K_{c}}=14_{1,14}-13_{1,13}$ transition of each of the three isotopologs.

4 Determination of spectroscopic parameters

We used Pickett’s SPCAT and SPFIT programs (Pickett 1991) to predict and fit rotational spectra of the minor isotopic species of cyanamide employing the reduced axis system Hamiltonian (Pickett 1972), as was done previously (Read et al. 1986; Birk et al. 1993; Kraśnicki et al. 2011; Kisiel et al. 2013). We used Watson’s $S$ reduction of the rotational Hamiltonian, in contrast to the latest two publications but in agreement with earlier work. Noting that the ground vibrational state $\varv=0$ consists of the substates 0+ and 0-, we fit average spectroscopic parameters $X=(X(0^{+})+X(0^{-}))/2$ and $\Delta X=X(0^{-})-X(0^{+})$, as proposed by Christen & Müller (2003). The model was tested for the rotational spectrum of NH2D and applied successfully in an analysis of the rotational and rovibrational spectra of H2DO+ (Müller et al. 2010). The advantage of being able to add parameters or their differences separately was particularly apparent in the case of ethanethiol (Müller et al. 2016). As the available experimental lines of the minor isotopic species are considerably smaller than those of the main species, we estimated several of the higher-order parameters of the former by scaling parameters of the main isotopolog by the ratios of appropriate powers of $A-(B+C)/2$, $B+C$, and $B-C$, as done recently for H2C16O, H2C17O, and H2C18O (Müller & Lewen 2017). A similar approach was taken for fitting spectra of isotopic species of cyanamide (Kraśnicki et al. 2011).

Our reanalysis of H2NCN data started with the line list from Kisiel et al. (2013). The very extensive line list was not reproduced within experimental uncertainties on average, such that the authors omitted transitions with residuals between observed transition frequencies and those calculated from the final set of spectroscopic parameters exceeding three times the uncertainties. Initially, we weighted down these lines, but omitted most of them in the end because the residuals in our final fit were very similar to those of the previous fit. In fact, our final parameter set differed effectively only slightly from that obtained by Kisiel et al. (2013). We added fixed values of $L_{K}$ and $\Delta L_{K}$ to account better for transitions higher in $K_{a}$, especially $c$-type transitions between the tunneling states. The parameter values were obtained from a fit to the line list deposited in the JPL catalog archive (Pickett et al. 1998) which was based on Read et al. (1986) and Birk et al. (1993) and which extended to transitions considerably higher in $K_{a}$. In addition, we did not use $\Delta L_{JK}$ in the fit. Our parameter values were in good agreement with those of Kisiel et al. (2013), as was expected. The majority of their transition frequencies were obtained by far-infrared spectroscopy. They were reproduced on average to $\sim$0.00023 cm*-1*, slightly above the reported uncertainties of $\sim$0.00020 cm*-1*. Therefore, we increased the uncertainties to $\sim$0.00025 cm*-1*. The parameter values changed little, but now not only the frequencies determined with microwave accuracy were reproduced within uncertainties on average, but also the far-infrared transition frequencies.

The details for determining spectroscopic parameters were the same for the two 15N isotopomers of cyanamide and for H2N13CN. The parameter set of the main isotopic species was taken as a start. Low-order spectroscopic parameters were fit until the transition frequencies were reproduced within around five times the experimental uncertainties. At each step, we searched for the parameter which improved the quality of the fit the most. Subsequently, parameters still kept fixed were scaled with appropriate powers of the ratios of $B+C$ and $B-C$. Since $A$ was correlated with $\Delta E$, scaling with appropriate powers of the ratios of $A-(B+C)/2$ was done subsequently; $\Delta A$ was scaled with the ratio of $A$; the distortion corrections to $F_{ac}$ were scaled in addition with the ratios of the $F_{ac}$. In the next step, parameters of higher order were released until the qualities of the fits no longer significantly improved. In a final step, $\Delta A$ was scaled again with the ratio of $A$. Kraśnicki et al. (2011) assigned uncertainties of 50 kHz to their transition frequencies. These were appropriate in the case of the 15N isotopomers. In the case of H2N13CN, they were slightly pessimistic at lower frequencies (119$-$161 GHz) and slightly optimistic at higher frequencies (578$-$644 GHz). Uncertainties of 30 and 60 kHz, respectively, turned out to be appropriate. Uncertainties of 100 kHz were used for the few older transition frequencies (Tyler et al. 1972; Brown et al. 1985). The transition frequencies of each isotopic species as well as subsets thereof were reproduced mostly within and always close to the experimental uncertainties on average. The resulting spectroscopic parameters are given in Table 1 together with those of the main isotopic species. The experimental line lists have been deposited at the Centre de Données astronomiques de Strasbourg (CDS) as three separate ascii files. A portion is shown for one isotopolog in Table 2 of Appendix A.

The line lists are quite similar in quantum number coverage among the three minor isotopic species and even more so among the two 15N isotopomers. Therefore, it is not so surprising that the parameters determined in the fits are the same and their respective uncertainties are quite similar. Some smaller uncertainties of specific H2N13CN parameters compared to those of the 15N species are a consequence of lines with higher values of $J$ (Kraśnicki et al. 2011). Our initial fits of the old data are summarized in Table 3 of Appendix B together with our new parameters for H2N13CN. The uncertainties of all parameters improved slightly upon addition of our experimental data. The main aspect in case of the two 15N isotopomers is the increase of determined spectroscopic parameters from ten to 22 because of the increase in $J$ from 9 to 26 and in $K_{a}$ from 5 to 7. The spectroscopic parameters included in the fit are equivalent to those of Kraśnicki et al. (2011); similar to that work, values for $A$, $D_{K}$, and so on were taken from the main isotopic species and the remaining parameters were estimated as described above.

It is also not surprising that the NH2 tunneling splitting is not affected within uncertainties by substituting the distant cyano-N atom, only marginally affected by substitution of the closer cyano-C atom, and somewhat more by the substitution of the amino-N atom. Replacing one or both of the H atoms by D affects the tunneling splitting much more (Kisiel et al. 2013). The heavy atoms are all located close to the $a$-axis, see for example Fig. 3 in Kraśnicki et al. (2011), hence heavy atom substitutions do not change the $A$ rotational parameter much. In addition, the C atom is quite close to the center of mass of the molecule such that its substitution changes $B$ and $C$ only slightly whereas replacing one of the N atoms cause larger changes. Changes in higher order spectroscopic parameters often reflect the changes in $B+C$ and $B-C$, but exceptions occur, especially for some of the higher order parameters.

5 Astronomical search

We used the ALMA PILS data to search for the 15N isotopomers of cyanamide. PILS is an unbiased molecular line survey of the Class 0 protostellar binary IRAS 16293$-$2422 carried out in band 7 of ALMA and covering the spectral range 329.15$-$362.90 GHz at 0.244 MHz resolution (project-id: 2013.1.00278.S, PI: Jes K. Jørgensen333http://youngstars.nbi.dk/PILS/). Details of the survey have been presented by Jørgensen et al. (2016). The spectral sensitivity is also very high, 7$-$10 mJy beam*-1* channel*-1* or 4$-$5 mJy beam*-1* km s*-1* such that line confusion is reached in considerable parts of the survey. This high sensitivity is very important for searching for less abundant molecules or for minor isotopic species of somewhat more abundant molecules. Many of our analyses focused on source B because of its smaller lines widths of $\sim$1 km s*-1* compared to around 3 km s*-1* for source A. Among the most exciting results was the detection of methyl chloride toward both sources as the first interstellar organohalogen compound (Fayolle et al. 2017) besides numerous isotopologs containing D or 13C, many of them for the first time in space (Coutens et al. 2016; Jørgensen et al. 2016; Persson et al. 2018; Coutens et al. 2018; Calcutt et al. 2018; Jørgensen et al. 2018).

Coutens et al. (2018) analyzed column densities of cyanamide isotopologs toward a position offset by 0.5$\arcsec$ from the continuum peak of source B ($\alpha_{\rm J2000}=16^{\rm h}32^{\rm m}22\aas@@fstack{s}58$, $\delta_{\rm J2000}=-24\degr 28\arcmin 32.8\arcsec$). This position was chosen to minimize the effects of line self-absorption, which was particularly prominent for the main isotopolog of cyanamide. The emission lines were modeled under the assumption of local thermodynamic equilibrium, which is reasonable at the high densities and high temperatures of source B, with an excitation temperature $T_{\rm ex}=300$ K, a source size of 0.5$\arcsec$, and a full line width at half maximum (FWHM) of 1 km s*-1*. A column density of $7\times 10^{13}$ cm*-2* was obtained for the H2N13CN isotopolog. Assuming a standard 12C/13C ratio, the abundance of the main isotopolog is about $4.8\times 10^{15}$ cm*-2*.

As a result of our spectroscopic investigation, we can now search for the 15N isotopomers of cyanamide with confidence. The molecules have several lines in the range of PILS, but most of them were well below the limit of detection or, in some cases, blended with bright lines of other species. We find two lines that can potentially be assigned to H${}_{2}^{15}$NCN (see Fig. 3) and none for H2NC15N. We carefully checked that the two potential lines of H${}_{2}^{15}$NCN were not due to any other species already identified toward this source and that no line expected to be observed was missing. Using the same position, $T_{\rm ex}$, source size, and $FWHM$ as for H2NCN, we obtain a good model for a column density of $6\times 10^{13}$ cm*-2* (see Fig. 3). As the spectra of IRAS 16293$-$2422 are very line-rich, more transitions need to be detected to claim a secure detection. For now, this column density can only be considered as an upper limit. A 3$\sigma$ upper limit of $3\times 10^{13}$ cm*-2* is derived for H2NC15N. This corresponds to 14N/15N ratios of $\gtrsim$80 for H${}_{2}^{15}$NCN and $\gtrsim$160 for H2NC15N. For comparison in the same source, the 14N/15N ratio of CH3CN is about 250 (Calcutt et al. 2018), while a similar lower limit of 100 was derived for NH2CHO (Coutens et al. 2016). Single-dish observations of two and one transitions of HCN and HNC isotopologs led to ratios of $163\pm 20$, $190\pm 38$, and $242\pm 32$, respectively (Wampfler et al. 2014).

More sensitive observations are required to confirm the detection of H${}_{2}^{15}$NCN and possibly identify H2NC15N in IRAS 16293$-$2422. Such observations may be more promising at lower frequencies because line blending and issues due to absorption are likely smaller. In addition, observations are, for the most part, easier at lower frequencies. On the other hand, the intensities of cyanamide emission drop fast at lower frequencies. Therefore, we inspected a synthetic spectrum of the 200$-$320 GHz region for bright lines of the 15N isotopomers of cyanamide that are not blended with lines of species in a synthetic spectrum which includes most of the species identified in the PILS data with certainty. About 20 lines of H${}_{2}^{15}$NCN and less than 10 lines of H2NC15N are currently predicted to be free of blending. Since most of the blends in the PILS Band 7 data are caused by known species, it may well be that a fair fraction of the about 30 lines of cyanamide containing 15N will eventually turn out to be unblended.

6 Conclusion and outlook

Our studies of isotopic cyanamide yielded greatly extended experimental line lists of H${}_{2}^{15}$NCN and H2NC15N up to 507 GHz. The resulting spectroscopic parameters should permit sufficiently accurate extrapolation in $J$ up to $\sim$1 THz, that is, throughout all presently available ALMA bands. Extrapolation in $K_{a}$ may be questionable because of vibration-rotation interaction, but the covered range should be sufficient for all minor isotopic species. Transitions between the tunneling states, which obey $c$-type selection rules, cannot be predicted with meaningful accuracy. These transitions are quite weak and have, to the best of our knowledge, not been identified in space even for the main isotopic species. The line list of H2N13CN has been extended somewhat in the course of the present investigation, and the spectroscopic parameters have been improved.

Calculated line lists of these three isotopic species, including information on their intensities and their calculated uncertainties, will be provided or updated in the catalog section444https://cdms.astro.uni-koeln.de/classic/entries/ of the Cologne Database for Molecular Spectroscopy, CDMS (Endres et al. 2016). Files containing the experimental lines or parameters along with auxiliary files are available in the data section of the CDMS555https://cdms.astro.uni-koeln.de/classic/predictions/daten/Cyanamide/.

A first attempt to search for the 15N isotopologs of cyanamide in the PILS data turned out to be negative. The two lines assignable to H${}_{2}^{15}$NCN would imply a low 14N/15N ratio if their identity were to be confirmed. Future, more sensitive observations of IRAS 16293$-$2422 are required to improve the upper limits or even lead to an unambiguous detection of at least one of the isotopic species.

Acknowledgements.

The measurements in Köln were supported by the Deutsche Forschungsgemeinschaft (DFG) in the framework of the collaborative research grant SFB 956, project B3. A.C.’s postdoctoral grant is funded by the ERC Starting Grant 3DICE (grant agreement 336474) under the European Union’s Horizon 2020 research and innovation program. A.C. is grateful to COST (European Cooperation in Science and Technology) for a STSM grant from the COST Action CM1401 “Our Astro-Chemical History”. O.Z. is funded by the DFG via the Gerätezentrum “Cologne Center for Terahertz Spectroscopy”. The research of J.K.J. is supported by the European Research Council through the ERC Consolidator Grant “S4F” (grant agreement No 646908) and Centre for Star and Planet Formation funded by the Danish National Research Foundation. This paper makes use of the following ALMA data: ADS/JAO.ALMA$\#$2013.1.00278.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. Our research benefited from NASA’s Astrophysics Data System (ADS).

Appendix A. Supplementary material

Appendix B. Fits of previous data