11institutetext: Max-Planck-Institut für Extraterrestrische Physik,
Giessenbachstrasse 1, 85748 Garching, Germany 22institutetext: University of
Bologna, Dipartimento di Chimica “Giacomo Ciamician”, Bologna, Italy

# Nitrogen fractionation towards a pre-stellar core traces isotope-selective
photodissociation

S. Spezzano 11 P. Caselli 11 O. Sipilä 11 L. Bizzocchi 22

###### Abstract

Context. Isotopologue abundance ratios are important to understand the
evolution of astrophysical objects and ultimately the origins of a planetary
system like our own. Being nitrogen a fundamental ingredient of pre-biotic
material, understanding its chemistry and inheritance is of fundamental
importance to understand the formation of the building blocks of life.

Aims. We aim at studying the 14N/15N ratio in HCN, HNC and CN across the
prototypical pre-stellar core L1544. This study allows us to test the proposed
fractionation mechanisms for nitrogen.

Methods. We present here single-dish observations of the ground state
rotational transitions of the 13C and 15N isotopologues of HCN, HNC and CN
with the IRAM 30m telescope. We analyse their column densities and compute the
14N/15N ratio map across the core for HCN. The 15N-fractionation of CN and HNC
is computed towards different offsets across L1544.

Results. The 15N-fractionation map of HCN towards a pre-stellar core is
presented here for the first time. Our map shows a very clear decrease of the
14N/15N ratio towards the southern edge of L1544, where carbon chain molecules
present a peak, strongly suggesting that isotope-selective photodissociation
has a strong effect on the fractionation of nitrogen across pre-stellar cores.
The 14N/15N ratio in CN measured towards four positions across the core also
shows a decrease towards the South-East of the core, while HNC shows opposite
behaviour. We also measured the 12CN/13CN ratio towards four positions across
the core.

Conclusions. The uneven illumination of the pre-stellar core L1544 provides
clear evidence that 15N-fractionation of HCN and CN is enhanced toward the
region more exposed to the interstellar radiation field. Isotope-selective
photodissociation of N2 is then a crucial process to understand 15N
fractionation, as already found in protoplanetary disks. Therefore, the
15N-fractionation in pre-stellar material is expected to change depending on
the environment within which pre-stellar cores are embedded. The 12CN/13CN
ratio also varies across the core, but its variation does not affect our
conclusions on the effect of the environment on the fractionation of nitrogen.
Nevertheless, the interplay between the carbon and nitrogen fractionation
across the core warrants follow-up studies.

###### Key Words.:

ISM: clouds - ISM: molecules - radio lines: ISM

##  1 Introduction

Isotopologue abundance ratios are pivotal for tracing the origin and evolution
of the molecular material in the process of star and planetary system
formation. Stable isotope ratios can in fact be measured in star-forming
regions as well as in the Solar System. Nitrogen has two stable isotopes, 14N
and 15N. The 14N/15N ratio varies greatly across the Solar System, depending
on material and molecular tracer. This ratio is $\sim$440 in the solar wind
and Jupiter (reflecting the composition of the protosolar nebula), $\sim$270
on Earth (for molecular nitrogen), $\sim$150 in comets (for CN, HCN and NH2),
and $\sim$200 in protoplanetary disks (for HCN) (Füri & Marty, 2015; Guzmán et
al., 2015). The origins of the different 14N/15N ratios among Solar System
bodies are not yet fully understood. However, given that nitrogen is generally
enriched in 15N in more pristine material like comets, the different 14N/15N
ratios that we observe are potentially inherited from the early phase in the
formation of the Solar System. Furthermore, recent observations of different
14N/15N ratios in HCN and CN towards a protoplanetary disk point to the
existence of multiple isotopic reservoirs of nitrogen for forming planets
(Hily-Blant et al., 2019). In the dense interstellar medium, the 14N/15N ratio
is inferred from N-bearing species and it is 300-500 for CN, HCN and HNC
(Hily-Blant et al., 2013a, b). The 14N/15N ratio in N2H+ instead varies from
180 to 1000 (Fontani et al., 2015; Bizzocchi et al., 2013; Redaelli et al.,
2018; Colzi et al., 2019). State-of-the-art reaction networks fail to
reproduce the 14N/15N variation in N2H+ (Roueff et al., 2015; Wirström &
Charnley, 2018), although a faster recombination with electrons of the 15N
isotopologues in L1544 with respect to the normal species might explain the
depletion of N2H+ in 15N (Loison et al., 2019; Hily-Blant et al., 2020;
Redaelli et al., 2020). The use of 13C isotopologues to derive the column
densities of CN, HCN and HNC is suggested to be done with caution by Roueff et
al. (2015) because of the possible depletion of 13C with respect to the
interstellar medium (ISM) 12C/13C ratio, and of the interdependence of the 13C
and 15N chemistry (Colzi et al., 2020).

Aside from local nuclear synthesis that cause an increasing excess of 15N
towards the Galactic centre (Adande & Ziurys, 2012), two main mechanisms are
responsible for the nitrogen fractionation in the ISM: isotope exchange at
low-temperatures and isotope-selective photodissociation. Isotope exchange is
the main chemical path to enrich molecules in deuterium towards the center of
pre-stellar cores (e.g. Caselli et al. 2003). In the case of HCN, as an
example for nitrogen bearing species, the isotope exchange reaction is

$\rm HC^{14}NH^{+}+^{15}N\rightleftarrows HC^{15}NH^{+}+^{14}N+35K,$ (1)

followed by the dissociative recombination of the cation with electrons. The
isotope exchange reactions enrich molecules in the heavier isotope at low
temperature because of the lower zero-point energy of the heavier molecular
species and the exothermicity of the reaction (Terzieva & Herbst, 2000). The
isotope exchange reactions involving nitrogen were later found to have
barriers (Roueff et al., 2015), and hence are not favourable to reproduce its
fractionation (Wirström & Charnley, 2018). Isotope-selective photodissociation
favours the photodissociation of the 15N-bearing isotopologues of N2. Being
14N2 more abundant, it can self-shield better than 14N15N and is consequently
less affected by photodissociation (Heays et al., 2014; Visser et al., 2018).
With 14N15N more photodissociated than 14N2, the 15N available to form
molecules increases. The effect of selective isotope-photodissociation on
nitrogen fractionation has already been clearly observed in protoplanetary
disks (Hily-Blant et al., 2019). The effect of the local physical conditions
on the fractionation of nitrogen in star-forming regions has been recently
explored by Colzi et al. (2018) who found large scatter in the 14N/15N ratio
in HCN towards high-mass star forming cores. However, the spatial variation of
the 14N/15N ratio towards pre-stellar cores has not been mapped yet.
Isotope-selective photodissociation is expected to be effective only at very
low extinction (AV = 1-3 mag, Heays et al. 2014), and it is not considered in
chemical models for the fractionation of nitrogen in dense cores. Its effects
are only considered as inherited from the parent cloud (Furuya & Aikawa, 2018;
Furuya et al., 2018), and they still cannot reproduce the ”anti-fractionation”
of nitrogen measured in N2H+ (Redaelli et al., 2020).

In this paper we present the first 14N/15N ratio map towards the prototypical
pre-stellar core L1544, showing clear evidence that isotope-selective
photodissociation is affecting the 15N fractionation in HCN. The same result
is found for CN towards four offsets across the core, and qualitatively for
HNC. In Section 2 we describe the observations and in Section 3 the analysis
of the data. Our results are reported in Section 4, and finally we discuss our
conclusions and outlook in Section 5.

Figure 1: Integrated intensity maps of the 1-0 transitions of H13CN and HC15N
towards the inner 2′ $\times$2′ of L1544. The 30′′ beam of the 30m telescope
is shown at the bottom left of each map. The solid white contours are the 30%,
60% and 90% of the peak intensity of the N(H2) map of L1544 computed from
$Herschel$/SPIRE data (Spezzano et al., 2016). The dashed black contours
indicate the 10$\sigma$ integrated emission with steps of 10$\sigma$ for
H13CN, and 5$\sigma$ with steps of 5$\sigma$ for HC15N ($rms_{H^{13}CN}$= 6 mK
km s-1, $rms_{HC^{15}N}$=7 mK km s-1). Table 1: Spectroscopic parameters of
the observed lines

Molecule | Transition | Rest frequency | $E_{\text{up}}$ | TMB | vLSR | FWHM | W | Ntotaa$a$Column densities computed towards the dust peak assuming Tex =3.5 K for HCN isotopologues, Tex =4.5 K for HNC isotopologues, and Tex =4.2 K for CN isotopologues (Padovani et al., 2011; Hily-Blant et al., 2013a, b).
---|---|---|---|---|---|---|---|---
|  | (MHz) | (K) | K | km/s | km/s | K km/s | 1012cm-2
H13CN |  $J$= 1-0 $F$ = 2-1 | 86340.1666(1) | 4.1 | 0.53(6) | 7.14(2) | 0.51(4) | 0.28(2) | 3.19(2)
HC15N |  $N$= 1-0 | 86054.9664(1) | 4.1 | 0.235(6) | 7.18(1) | 0.49(1) | 0.120(2) | 0.56(3)
HN13C |  $N$= 1-0 $F^{\prime}_{1}$-$F_{1}$ = 1-0 | 87090.675(4)bb$b$One of the four ”effective” hyperfine components following the description of van der Tak et al. (2009) | 4.2 | 0.41(1) | 7.143(3) | 0.25(2) | 0.10(1) | 2.5(2)
H15NC |  $N$= 1-0 | 88865.676(5)cc$c$The rest frequency reported in the JPL catalogue for the 1-0 transition of H15NC is 88865.71(4). For this work we used the rest frequency derived from our observations, which is consistent with the JPL value within its error bar.  | 4.3 | 0.67(2) | 7.257(4) | 0.425(8) | 0.302(7) | 1.0(2)
CN |  $N$= 1-0 $J$ = 1/2-1/2 $F$= 1-1 | 113123.370(5) | 5.4 | 0.87(2) | 7.109(4) | 0.465(8) | 0.427(6) | 517(7)
13CN |  $N$= 1-0 $J$ = 3/2-1/2 $F_{1}$= 2-1 $F$= 3-2 | 108780.20(5) | 5.2 | 0.13(8) | 7.18(1) | 0.39(3) | 0.057(3) | 2.7(1)
C15N |  $N$ = 1-0 $J$ = 3/2-1/2 $F$= 2-1 | 110024.6(1) | 5.3 | 0.056(1) | 7.09(2) | 0.38(6) | 0.023(4) | 0.48(6)

111Numbers in parentheses denote $1\sigma$ uncertainties in unit of the last
quoted digit. The frequencies in the Table are reported in the CDMS and JPL
catalogues (Müller et al., 2005; Pickett et al., 1998) and are derived from
the laboratory work in Fuchs et al. 2004; Creswell et al. 1976; van der Tak et
al. 2009; Bogey et al. 1984; Klisch et al. 1995 and the interstellar detection
reported in Saleck et al. 1994.

##  2 Observations

The emission maps of the 1-0 transition of the 13C and 15N isotopologues of
CN, HCN an HNC towards L1544 were obtained using the IRAM 30m telescope (Pico
Veleta, Spain) in 2 different observing runs in 2013 and 2015. We performed a
2.5′ $\times$2.5′ on-the-fly (OTF) map centred on the source dust emission
peak ($\alpha_{2000}$ = 05h04m17s.21, $\delta_{2000}$ = +25∘10′42′′.8). We
used position switching with the reference position set at (-180′′,180′′)
offset with respect to the map centre. The observed transitions are summarised
in Table 1. The EMIR E090 receiver was used with the Fourier transform
spectrometer backend (FTS) with a spectral resolution of 50 kHz. For the HN13C
1-0 transition we used the VESPA backend with a spectral resolution of 6 kHz.
The mapping was carried out in good weather conditions ($\tau_{225GHz}$ $\sim$
0.3) and a typical system temperature of Tsys $\sim$ 90-150 K. The data
processing was done using the GILDAS software (Pety, 2005). The emission maps
have a beam size of 30.1′′, and were gridded to a pixel size of 6′′ with the
CLASS software in the GILDAS package, which corresponds to $\sim$1/5 of the
beam size, chosen to ensure Nyquist sampling. The integrated intensity maps of
H13CN and HC15N shown in Figure 1 have been computed in the 6.8-7.8 km s-1
velocity range, where the vLSR of the source is 7.2 km s-1. The integrated
emission maps of H13CN and HC15N are shown in Figure 1. Given the weakness of
the lines, we could not produce maps for 13CN and C15N. We were nevertheless
able to extract their spectra towards different regions across L1544, and they
are shown in Section 3.

Figure 2: 14N/15N ratio map of HCN towards L1544. The map was computed only in
the pixels where the integrated emission of both H13CN and HC15N was detected
with a signal-to-noise ratio larger than 5. The IRAM 30m beam of 30′′
($\sim$5000 au) are shown in the bottom right of the map. The solid white
contours are the 30%, 60% and 90% of the peak intensity of the N(H2) map of
L1544 computed from $Herschel$/SPIRE data (Spezzano et al., 2016). The column
density of HCN was computed from the column density of H13CN assuming the
12C/13C ratio of 68 (Milam et al., 2005). The corresponding error is shown in
Figure 6.  Figure 3: Left panel: H2 column density map of L1544 computed from
$Herschel$/SPIRE observations (Spezzano et al., 2016). The black crosses show
the centre of the areas where the spectra shown in the right panel have been
extracted. The black circles show the regions where the spectra shown in the
right panel have been averaged. Right panel: Spectra of 13CN ($N,J,F_{1},F$ =1
3/2 2 3 - 0 1/2 1 2) in black and C15N ($N,J,F$= 1 3/2 2 - 0 1/2 1) in red,
extracted towards the offsets marked in the left panel. The values in boldface
in blue report the 14N/15N ratio in CN for each set of spectra derived using
the 12CN column density directly from the spectra shown in Figure 7. The
values in boldface in green report the 14N/15N ratio computed from the column
density of 13CN using the 12C/13C ratio of 68 (Milam et al., 2005).

##  3 Analysis

The spectrum of the 1-0 transition of H13CN observed toward the dust peak of
L1544 was extracted from the centre of the map shown in Figure 1 and fit with
the Hyperfine Structure (HFS) tool in class using frequencies measured in the
laboratory (Fuchs et al., 2004) with the assumption of the same excitation
temperature of the hyperfine components. We derived Tex= 3.5 K and an optical
depth of 0.4, 2 and 1.2 for the $J$ = 1-0 $F$ = 1-1, 2-1, and 0-1 components,
respectively. We repeated the same exercise towards a sample of 4 other
positions in the mapped area, to test whether we could assume a constant 3.5 K
Tex across L1544, which was the case. The integrated intensity maps shown in
Figure 1 have been used to compute the column density maps of H13CN and HC15N
assuming Tex = 3.5 K, and subsequently the 14N/15N ratio map shown in Figure
2. In order to retrieve the column density of the main isotopologue, we have
multiplied the map of H13CN with the isotopic ratio for the local interstellar
medium, 12C/13C = 68 (Milam et al., 2005). The column density maps have been
computed using the formula reported in Mangum & Shirley (2015) for the
optically thick emission, assuming that the source fills the beam, and with a
constant Tex = 3.5 K:

$N_{tot}=\frac{8\pi\nu^{3}Q_{rot}(T_{ex})W}{c^{3}A_{ul}g_{u}}\frac{e^{\frac{E_{u}}{kT}}}{J(T_{ex})-J(T_{bg})}\frac{\tau}{1-e^{-\tau}},$
(2)

with

$\tau=\ln\left(\frac{J(T_{ex})-J(T_{bg})}{J(T_{ex})-J(T_{bg})-T_{mb}}\right).\\\
$ (3)

where $\frac{\tau}{1-e^{-\tau}}$ is the optical depth correction factor,
$\tau$ is the line opacity,
$J(T)={\frac{h\nu}{k}}(e^{\frac{h\nu}{kT}}-1)^{-1}$ is the equivalent
Reyleigh-Jeans temperature, $k$ is the Boltzmann constant, $\nu$ is the
frequency of the line, $h$ is the Planck constant, $c$ is the speed of light,
$A_{ul}$ is the Einstein coefficient of the transition, $g_{u}$ is the
degeneracy of the upper state, $E_{u}$ is the energy of the upper state, and
$Q_{rot}$ is the partition function of the molecule at the given temperature
$T_{ex}$. $T_{bg}$, $T_{mb}$ are the background (2.7 K) and the main beam
temperatures respectively. The maps shown in Figure 2 have been computed only
in the pixels where the integrated emission of both molecules was detected
with a signal-to-noise ratio larger than 5.

The emission maps of 13CN and C15N do not have a signal-to-noise ratio that
allows for the computation of the 14N/15N ratio map. To check whether the same
trend observed in HCN is also found in CN, we averaged the C15N 1-0 transition
and one of the hyperfine components of the 13CN 1-0 transition towards several
positions across the core. In the left panel of Figure 3 the regions where the
spectra of C15N and 13CN have been averaged are marked as black circles on the
H2 column density map of L1544. The size of the areas has been optimised to
have a signal-to-noise ratio of at least 3. The black crosses mark the center
of each region, and their offsets with respect to the center of the map (i.e.
the dust peak of L1544) are reported in the respective spectra shown in the
right panel. The right panel of Figure 3 shows the averaged spectra from each
region.

The hyperfine structure of the 1-0 transition of HN13C could not be resolved
with the 6 kHz resolution of the VESPA spectra. The line shape that we observe
deviates from previous observations towards other starless cores, e.g. van der
Tak et al. (2009); Padovani et al. (2011), suggesting that some of the
hyperfine transitions might be self-absorbed. We used the four effective
hyperfine transitions described in van der Tak et al. (2009) and derived the
optical depth of each component using the HFS tool in class. The resulting
$\tau$ are 1.7, 3.1, 1.9 and 0.1, for the four lines ordered by increasing
velocity. Given that the weakest hfs component, at 87090.67 MHz, is optically
thin towards the dust peak, we performed a gaussian fit with 4 components for
all pixels in our map with pyspeckit (Ginsburg & Mirocha, 2011), with the aim
of isolating the thin component and using it to compute the column density
map. Unfortunately, the resulting integrated intensity map is observed at a
3$\sigma$ only in the central 30′′ of the map. We extracted the spectra of
HN13C and H15NC towards the same positions used for the CN isotopologues in
Figure 3, see Figure 4. To make a direct comparison also with HCN, we have
extracted the spectra of the 13C and 15N isotopologues of HCN towards the same
regions, see Figure 5.

##  4 Results and discussion

The 14N/15N ratio map of HCN in the left panel of Figure 2 shows a clear
decrease towards the South-East of L1544. The HC14N/HC15N in the North-West of
the core is 367$\pm$54, while in the South-East it is 187$\pm$34\. Towards the
dust peak the HC14N/HC15N 437$\pm$63, similar to the 14N/15N ratio reported
for HC3N in Hily-Blant et al. 2018. The pre-stellar core L1544 is located at
the end of a filament in the eastern edge of the Taurus Molecular Cloud.
Because of its location and its structure, the southern part of L1544 is more
efficiently illuminated by the interstellar radiation field (ISRF) than the
northern part, and this has already been shown to have an impact on the
chemical differentiation within the core (Spezzano et al., 2016). The 14N/15N
ratio map of HCN towards L1544 in this work suggests that the uneven
illumination from the ISRF on L1544 has an impact on the 15N fractionation. As
the largest 15N fractionation is observed toward the Southern part of L1544,
the most illuminated by the ISRF, we conclude that the dominant fractionation
process is the isotope-selective photodissociation of N2 (Heays et al., 2014).
Guzmán et al. (2017) tentatively observed the effect of isotope-selective
photodissociation towards the protoplanetary disk V4046 Sgr. This result was
later confirmed by Hily-Blant et al. (2019) towards the disk orbiting the T
Tauri star TW Hya. The 14N/15N ratio in HCN increases towards the dust peak of
L1544 because we are looking through the densest regions of L1544, where the
high density reduces the efficiency of the photodissociation, and consequently
the enrichment of 15N in molecular species.

While we cannot compute the 14N/15N ratio maps for CN, the spectra extracted
towards four positions across the core in Figure 3 strongly suggest that also
for CN the nitrogen fractionation is affected by the ISRF. In boldface in each
spectrum is reported the 14N/15N ratio for CN derived in the corresponding
region. In green we report the C14N/C15N derived using the 12C/13C ratio of
68, as we did for HCN, and the resulting 14N/15N ratio is similar for both
molecules. In blue instead we report the C14N/C15N derived using directly 12CN
towards those positions, see Appendix B for more information. The 12C/13C
ratio observed for CN ranges from 120 to 190 and the correspondent C14N/C15N
ratios are as high as 1100, similar to what observed for N2H+ in L1544 and
other starless cores (Bizzocchi et al., 2013; Redaelli et al., 2018). The
large 12C/13C and 14N/15N ratios that we present here for CN warrant a
dedicated in-depth study of the fractionation of carbon and nitrogen in L1544.
It is however important to note that 12CN/13CN ratios larger than 68 have
already been observed towards L1544 in Hily-Blant et al. (2010), and are
predicted by the chemical models in Roueff et al. (2015) and Colzi et al.
(2020), although for either early time steps or low volume densities. For the
purpose of this Letter we highlight that our conclusions on the effect of the
illumination on the C14N/C15N are not affected by the choice of 12C/13C ratio.
We do not use the 12C/13C ratio derived from CN for HCN, because the two
molecules do not necessarily share all fractionation pathways, as shown in
Figures 6 and 7 of Colzi et al. (2020).

Figure 4 shows the spectra of the 1-0 transitions of HN13C and H15NC extracted
in the same position used for CN in Figure 3 and for HCN in Figure 5. We
computed the HN13C column density using the thin hyperfine component of the
1-0 transition following the description of the four effective components
described in van der Tak et al. (2009), the 12C/13C ratio of 68, and Tex = 4.5
K derived from the class HFS fit towards the dust peak. In boldface in each
spectrum is reported the 14N/15N ratio for HNC derived in the corresponding
region using the 12C/13C ratio of 68. The resulting 14N/15N ratios are
significantly different with respect to HCN and CN, and the trend across the
core shows an increase of the 14N/15N ratio towards the South-East, contrary
to what we observe for HCN and CN. While spatial variations of the
fractionation of HCN, CN and HNC across a core have not been explored by
chemical models yet, Figure 8 in Roueff et al. (2015) show that their 14N/15N
abundance ratio profiles can differ, especially between 105 and 106 yr.
Nevertheless, the 14N/15N ratios in HCN, CN and HNC shown in Figure 8 of
Roueff et al. (2015) only range between 390 and 450, while we observe ratios
that vary from 150 to 450. Non-LTE modelling is necessary to confirm our
results, in particular for the HN13C line where an isolated hyperfine
component is not present.

##  5 Conclusions

Our 14N/15N ratio map of HCN towards L1544 shows for the first time that the
fractionation of nitrogen presents significant variations across a pre-stellar
core. The 14N/15N ratio in HCN decreases towards the South-East of the core,
the region of L1544 that corresponds to a steeper drop in H2 column density
and is consequently more efficiently illuminated by the ISRF. This was already
shown in previous observations of carbon-chain molecules which in fact peak
toward the region L1544 more exposed to the ISRF, where a significant fraction
of carbon is maintained in atomic form (Spezzano et al., 2016). The same trend
is observed also for CN and the opposite trend is observed for HNC. Our
results indicate that isotope-selective photodissociation plays an important
role in the fractionation of nitrogen in L1544. 14N15N photodissociates more
efficiently than 14N2 because it is not abundant enough to self-shield. The
photodissociation of 14N15N is expected to be more efficient towards the more
illuminated southern part of the core, where more atomic 15N will be available
to form cyanides like HCN and CN. HNC shows opposite behaviour with respect to
HCN and CN. Further studies are necessary to understand the underlying cause.

The effect of isotope-selective photodissociation in nitrogen fractionation
has already been observed towards a protoplanetary disk where the irradiation
from UV photons in the inner part of the disk translates into a lower 14N/15N
ratio in HCN (Hily-Blant et al., 2019). With our work we show that the uneven
illumination from the ISRF onto a pre-stellar core has an effect on the
14N/15N ratio through the isotope-selective photodissociation. With the
14N/15N ratio in atomic nitrogen decreasing towards the southern part of
L1544, the 14N2/14N15N ratio will have the opposite behaviour and increase
towards the South of L1544, because the 14N2 is expected to be less affected
by photodissociation. As a consequence, we expect the 14N/15N ratio in
molecules that are formed from molecular nitrogen, like N2H+, to show the
opposite behaviour with respect to HCN and CN. This trend has already been
observed towards the high-mass star forming region IRAS 05358+3543 in Colzi et
al. (2019). Future maps of 14N2H+/14N15NH+ or 14N2H+/15N14NH+ towards L1544
are needed to confirm this point for low-mass star-forming regions.

We also present here the direct measurement of the 12CN/13CN ratio across
L1544, showing that it ranges between 130 and 190 in the inner 2$\times$2
arcmin2 of the core. Furthermore, we show that column density ratios between
the 13C and 15N isotopologues is $\sim$6 for HCN and CN and $\sim$2 for HNC
towards the dust peak. A dedicated work on the chemical modelling of carbon
and nitrogen fractionation towards L1544 in currently ongoing. Nevertheless,
our results on CN indicate that the effect of the illumination on the nitrogen
fractionation of HCN and CN across the core is not affected by the
fractionation of carbon.

Pre-stellar cores provide the budget of material that will finally be
inherited by forming planets. In order to assess what is the 14N/15N budget
that can be inherited from pre-stellar cores, it is important to consider the
illumination-induced variations across the core, which could account for
different 15N reservoirs of future stellar systems, together with the 15N
fractionation variation within a protoplanetary disk (Hily-Blant et al., 2017,
2019).

###### Acknowledgements.

The authors wish to thank Laura Colzi for useful discussion, and the anonymous
referee for insightful suggestions. We gratefully acknowledge the support of
the Max Planck Society.

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##  Appendix A Observed spectra

Figures 4 and 5 show the spectra of the 13C and 15N isotopologues of HCN and
HNC towards the positions shown in the left panel of Figure 3 (where the
spectra of 13CN and C15N were extracted). A sharp decrease can be seen towards
the South in the lines of the 13C isotopologues, while the intensities of the
lines of the 15N isotopologues are almost constant across the core.

The spectra shown in Figures 4 and 5, as well as in Figure 3 show a small
shift in velocity across the core. Such shift is predicted by the model from
Ciolek & Basu (2000) shown in Fig. 6 in Caselli et al. (2002), and has already
been observed in L1544, see for example Figure B.1 in Spezzano et al. (2016).

Figure 6 shows the error map on the HC14N/HC15N column density ratio map, and
is calculated by propagating the errors on the column density maps of H13CN
and HC15N, which include the rms of the spectra as well as a 10% calibration
error.

Figure 4: Spectra of HN13C ($N$ = 1-0) in black and H15NC ($N$= 1-0) in red
extracted in the regions shown as black circles in the left panel in Figure 3.
The values in boldface report the 14N/15N ratio in HNC for each set of spectra
derived using the 12C/13C ratio of 68 (Milam et al., 2005). Figure 5: Spectra
of H13CN ($J,F$ = 1 2 - 0 1) in black and HC15N ($N$= 1-0) in red extracted in
the regions shown as black circles in the left panel in Figure 3. The values
in boldface report the 14N/15N ratio in HCN for each set of spectra derived
using the 12C/13C ratio of 68 (Milam et al., 2005). Note the sharp decrease of
the H13CN line toward the South, when compared to the almost constant HC15N.
Figure 6: Error map of 14N/15N ratio of HCN towards L1544. The map was
computed only in the pixels where the integrated emission of both H13CN and
HC15N was detected with a signal-to-noise ratio larger than 5. The IRAM 30m
beam of 30′′ ($\sim$5000 au) are shown in the bottom right of the map. The
solid white contours are the 30%, 60% and 90% of the peak intensity of the
N(H2) map of L1544 computed from $Herschel$/SPIRE data (Spezzano et al.,
2016).

##  Appendix B Effect of the 12C/13C fractionation

We extracted the spectra of the $N$ =1-0 $J$ = 3/2-1/2 $F_{1}$ = 2-1 $F$ = 3-2
transition of 13CN and the $N$ =1-0 $J$ = 1/2-1/2 $F$ = 1-1 of CN towards the
four position marked in the left panel in Figure 3 and derived the 12CN/13CN,
see Figure 7. We used the map of the weakest hyperfine component of the 1-0
transition of the main isotopologue, which is only slightly optically thick,
with $\tau$ ranging from 1.1 to 1.4 across the map, and does not show signs of
self-absorption in our spectra with 50 kHz resolution. In contrast to the
spectra shown in Figures 5 and 4, where the lines of the 13C and 15N
isotopologues do not decrease at the same pace towards the south of L1544, the
intensity variations of the lines of 12CN and 13CN do not show a substantial
difference. We computed the column density for 12CN and 13CN from the spectra
shown in Figure 7, assuming optically thick emission, and Tex=4.2K. The
excitation temperature and optical depth were derived by modelling the
observed line of 12CN with RADEX assuming a kinetic temperature of 8 K and a
volume density of 1$\times$105 cm-3, and is consistent with the excitation
temperature previously derived for 13CN and C15N in Hily-Blant et al. (2013a).
Please note that the choice of volume density has an impact on the resulting
excitation temperature, and consequently on the optical depth of the 12CN line
and the resulting column density. For example, if we assume a volume density
of 5$\times$105 cm-3, the corresponding excitation temperature is 5 K, which
reduces the optical depth of the 12CN line by almost a factor of two, and in
turn decreases the 12CN/13CN ratios in the central and northern offset, where
the 12CN line is brighter. The 12CN/13CN ratio derived in this work
(193$\pm$10 towards the dust peak) is larger than the values derived in B1b,
where 12CN/13CN = 50${}^{19}_{11}$ (Daniel et al., 2013). However, the
chemical models presented in Colzi et al. (2020) can reproduce values of
12CN/13CN larger than 68 (the isotopic ratio for the local interstellar
medium, Milam et al. 2005), as seen in Figure 7 of Colzi et al. (2020). The
variation of the 12CN/13CN ratio with density and time in the models are
mainly connected to the competition between the enrichment of carbon monoxide
in 13C and the availability of 13C+. Our results on CN indicate that the
effect of the illumination on the nitrogen fractionation across the core is
not affected by the fractionation of carbon. Consequently, we can assume that
the 14N/15N ratio map of HCN in the left panel of Figure 2 might need to be
corrected by an offset (i.e. a different 12C/13C ratio), but it will not
change its trend substantially because of the carbon fractionation. Chemical
modeling for the combined fractionation of carbon and nitrogen are currently
undergoing and go beyond the scope of this Letter. It is however important to
note that the ratio between the 13C and 15N isotopologues for CN and HCN is
the same towards the dust peak of L1544, $\sim$6, and drops for both molecules
to $\sim$3 towards the South-West of the core, strongly suggesting that both
molecules undergo the same chemical paths for the fractionation of Nitrogen.
While the normal isotopologues trace the core and the cloud where the core is
embedded, it is safe to assume that the 13C and 15N isotopologues trace only
the core. Therefore, it might be more appropriate to compare the 13C and 15N
isotopologue ratios instead of the ratios involving the main isotopologue,
even when it is possible to derive a direct measurement.

Figure 7: Spectra of 13CN ($N$ =1-0 $J$ = 3/2-1/2 $F_{1}$ = 2-1 $F$ = 3-2) in
black and CN ( $N$ =1-0 $J$ = 1/2-1/2 $F$ = 1-1) in red extracted in the
regions shown as black circles in the left panel in Figure 3. The 12CN/13CN
column density ratio derived towards the four offsets is written in boldface
in each spectrum.