# Ultra-faint [C II] emission in a redshift = 2 gravitationally-lensed metal-
poor dwarf galaxy

M. Rybak Leiden Observatory, Niels Bohrweg 2, 2333CA Leiden, The Netherlands
E. da Cunha International Centre for Radio Astronomy Research (ICRAR),
University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D)
B. Groves International Centre for Radio Astronomy Research (ICRAR),
University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
Research School of Astronomy and Astrophysics, Australian National University,
Canberra, ACT 2611, Australia  J. A. Hodge Leiden Observatory, Niels Bohrweg
2, 2333CA Leiden, The Netherlands  M. Aravena Núcleo de Astronomía, Facultad
de Ingeniería y Ciencias, Universidad Diego Portales, Av. Ejército 441,
Santiago, Chile  M. Maseda Leiden Observatory, Niels Bohrweg 2, 2333CA Leiden,
The Netherlands  L. Boogaard Leiden Observatory, Niels Bohrweg 2, 2333CA
Leiden, The Netherlands  D. Berg Department of Astronomy, The University of
Texas at Austin, 2515 Speedway Blvd Stop C1400, Austin, TX 78712, USA  S.
Charlot Sorbonne Université, UPMC-CNRS, UMR7095, Institut d’Astrophysique de
Paris, F-75014, Paris, France  R. Decarli INAF — Osservatorio di Astrofisica e
Scienza dello Spazio, via Gobetti 93/3, I-40129, Bologna, Italy  D. K. Erb The
Leonard E. Parker Center for Gravitation, Cosmology and Astrophysics,
Department of Physics, University of Wisconsin-Milwaukee, 3135 N Maryland
Avenue, Milwaukee, WI 53211, USA  E. Nelson Department of Astrophysical and
Planetary Sciences, University of Colorado, Boulder, CO 80309, USA  C.
Pacifici  Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,
MD 21218, USA  K. B. Schmidt Leibniz-Institut für Astrophysik Potsdam (AIP),
An der Sternwarte 16, 14482 Potsdam, Germany  F. Walter Max-Planck Institut
für Astronomie, Königstuhl 17, D-69117, Heidelberg, Germany  National Radio
Astronomy Observatory, Pete V. Domenici Array Science Center, P.O. Box O,
Socorro 87801, USA  A. van der Wel Sterrenkundig Observatorium, Department of
Physics and Astronomy, Ghent University, Belgium  Max-Planck Institut für
Astronomie, Königstuhl 17, D-69117, Heidelberg, Germany

(Received 13th September 2020; Revised 4th January 2020; Accepted 5th January
2020)

###### Abstract

Extreme emission-line galaxies (EELGs) at redshift $z=1-2$ provide a unique
view of metal-poor, starburst sources that are the likely drivers of the
cosmic reionization at $z\geq 6$. However, the molecular gas reservoirs of
EELGs - the fuel for their intense star-formation - remain beyond the reach of
current facilities. We present ALMA [C II] and PdBI CO(2–1) observations of a
$z=1.8$, strongly lensed EELG SL2S 0217, a bright Lyman-$\alpha$ emitter with
a metallicity 0.05 $Z_{\odot}$. We obtain a tentative ($\sim$3-4$\sigma$)
detection of the [C II] line and set an upper limit on the [C II]/SFR ratio of
$\leq 1\times 10^{6}~{}L_{\odot}$/($M_{\odot}$ yr-1), based on the synthesized
images and visibility-plane analysis. The CO(2–1) emission is not detected.
Photoionization modelling indicates that up to 80% of the [C II] emission
originates from neutral or molecular gas, although we can not rule out that
the gas is fully ionized. The very faint [C II] emission is in line with both
nearby metal-poor dwarfs and high-redshift Lyman $\alpha$ emitters, and
predictions from hydrodynamical simulations. However, the [C II] line is
30$\times$ fainter than predicted by the De Looze et al. [C II]-SFR relation
for local dwarfs, illustrating the danger of extrapolating locally-calibrated
relations to high-redshift, metal-poor galaxies.

Dwarf galaxies (416) – Lyman-alpha galaxies (978) – High-redshift galaxies
(734) – Submillimeter astronomy (1647)

††journal: ApJ††facilities: ALMA, IRAM:Interferometer

##  1 Introduction

The Epoch of Reionization (EoR) is one of the main frontiers of present-day
astrophysics. Recent results suggest that the reionization is likely driven by
low-metallicity, dwarf ($M_{\star}\lesssim 10^{9}$ $M_{\odot}$) galaxies with
intense star formation rates; due to their low gas and dust content, a large
fraction of UV photons will be able to escape and reionize the neutral
intergalactic medium (e.g., Robertson et al., 2010, 2015; Atek et al., 2015;
Stark, 2016). These metal-poor, dwarf galaxies contribute significantly to the
cosmic star-forming rate (SFR) at $z\geq 3$ (e.g., Bouwens et al., 2009).
Consequently, characterizing the star-forming processes in $z\geq 6$ dwarf
galaxies presents a crucial step towards understanding the evolution of
galaxies at early cosmic times. However, these faint, high-redshift dwarf
galaxies remain elusive due to the limitations of current facilities (mainly
the Hubble Space Telescope and the Spitzer Space Telescope), along with the
fact that for the most distant targets the diagnostic-rich optical emission is
shifted to the near-IR regime and thus currently unobservable - a situation
that will be soon remedied by the James Webb Space Telescope. Consequently,
large uncertainties remain on the physical mechanisms of galaxy-led
reionization, such as the actual fraction of ionizing photons that escape
their interstellar medium (ISM), their star formation efficiency, and feedback
processes at play.

An alternative to studying directly the $z\geq 6$ dwarf galaxies is to target
the intermediate-redshift ($z\sim 2$) extreme emission line galaxies (EELGs;
van der Wel et al., 2011; Atek et al., 2011; Maseda et al., 2013, 2014; Amorín
et al., 2015), which are likely analogues of primordial galaxies at the EoR
and can be studied much more efficiently, particularly in emission and
absorption lines. EELGs have been identified through extremely high equivalent
widths (EWs) of optical emission lines such as [O III] 5007 Å (with rest-frame
EW exceeding 500Å), via excess emission in HST/WFC3 broad-band filters (van
der Wel et al., 2011), and through HST/WFC3 grism spectroscopy (Maseda et al.,
2018). Spectroscopic and photometric follow-up confirm that these are low-mass
($M_{\star}\sim 10^{8}-10^{9}\,M_{\odot}$), low-metallicity
($Z<0.30\,Z_{\odot}$) dwarf galaxies with high SFRs ($\sim
10-100\,M_{\odot}\rm{yr}^{-1}$), likely undergoing an intense but short-lived
burst of star formation (e.g., Maseda et al., 2013, 2014; Masters et al.,
2014; Tang et al., 2019).

While rest-frame UV and optical studies of high-redshift star-forming dwarfs
have primarily targeted the ionized ISM, their intense star formation must be
fueled by cold neutral gas. In particular, measuring the cold gas reservoirs
of high-redshift dwarfs is crucial for understanding the timescales on which
their high-mass star formation can be maintained. However, direct observations
of the cold ISM phase in these faint, metal-poor sources are extremely
challenging, even at $z\sim 1-2$.

Our best bet for probing the molecular gas content of this metal-poor galaxies
is the [C II] 158-$\mu$m line, thanks to its low critical density and large
intrinsic brightness. At $z\sim 2$, Herschel and ALMA Band 9 [C II]
observations have been instrumental in probing the gas content of
$M_{\star}=10^{9}-10^{11}$ $M_{\odot}$ galaxies (e.g., Stacey et al. 2010;
Brisbin et al. 2015; Schaerer et al. 2015; Zanella et al. 2018). Crucially,
for the EoR sources, the [C II] line is easily observable with ALMA and has
become the chief probe of cool gas in early galaxies (e.g., Maiolino et al.
2005, 2015; Knudsen et al. 2016; Bradač et al. 2017; Matthee et al. 2019; see
Hodge & da Cunha 2020 for a recent review). At the same time, the [C II]
emission in high-redshift galaxies has been explored by a number of
cosmological (e.g., Olsen et al. 2017; Lagache et al. 2018) and zoom-in
simulations (e.g., Vallini et al. 2015; Katz et al. 2017; Pallottini et al.
2019; Lupi & Bovino 2020).

In this paper, we attempt to study the neutral ISM in a strongly
gravitationally lensed $z\sim 2$ SL2S 0217, targeting the [C II] line with
Atacama Large Millimetre/sub-millimetre Array (ALMA), and CO(2–1) with the
Plateau de Bure Interferometer (PdBI). Thanks to its large magnification, SL2S
0217 provides a unique opportunity to detect the neutral ISM in a high-
redshift EELG with a stellar mass of just $10^{8}$ $M_{\odot}$ \- 1 dex lower
than any previous $z\sim 2$ study.

This paper is structured as follows: § 2 presents our ALMA and PdBI
observations, data combination and imaging procedures; § 3 presents the
derivation of the source-plane upper limits on the [C II] and CO(2–1)
luminosities. In § 4, we compare our [C II] non-detection to the expectations
photoionization modelling (§ 4.1), various empirical and theoretical [C
II]-SFR relationships (§ 4.2) as well as local and high-redshift observations
(§ 4.3). Finally, we discuss the fate of the molecular gas in SL2S 0217 (§
4.4) and the prospects of detecting the [C II] emission from SL2S 0217-like
dwarfs in the Epoch of Reionization (§ 4.5).

##  2 Observations and imaging

###  2.1 Target description

SL2S 021737–051329 (henceforth SL2S 0217, J2000 02h 17m 37.237s -05d13m29.7s)
is a redshift $z=1.844$ EELG, strongly gravitationally lensed by a $z=0.6459$
elliptical galaxy. SL2S 0217 was serendipitously discovered by Geach et al.
(2007, source ID SXDF-iS-170569). Thanks to its position under the cusp of the
lensing caustic, SL2S 0217 is lensed into a brilliant, 2.5-arcsec long
Einstein arc, with a fainter counter-image. The lens system includes a second,
doubly-imaged background source SL2S 0217.X at $z=2.29$ (Brammer et al.,
2012).

The stellar content of SL2S 0217 was studied by Brammer et al. (2012, B12)
using HST GRISM spectroscopy and Berg et al. (2018, B18) using Keck/LRIS
optical spectroscopy. Pixellated lens modelling of SL2S 0217 based on the HST
data111see also Tu et al. (2009) and B12 for parametric lens models. was
performed by Cooray et al. (2011), B18 and Erb et al. (2019); in the B18
model, the HST F606W continuum is magnified by a factor of $\sim 17$, with a
source-plane UV half-light radius of $\sim 0.35$ kpc. We adopt the source-
plane properties listed in Table 1, based on the B18 lens model. The
$Z=0.05~{}Z_{\odot}$ metallicity of SL2S 0217 is typical of $z\sim 6$ galaxies
with the same stellar mass (c.f. FirstLight simulations, Langan et al. 2020),
underlining its suitability as a EoR analogue.

The spatial distribution of the Ly$\alpha$ emission in SL2S 0217 was studied
by Erb et al. (2019, E19) using narrow-band HST imaging. This revealed a
0.6-kpc offset between Ly$\alpha$ and the UV continuum, indicating a varying
column density of neutral hydrogen across the source, with the bulk of the
Ly$\alpha$ photons escaping along a low column density channel. The long-
wavelength spectral energy distribution of SL2S 0217 is only poorly sampled,
with a single detection in the Spitzer/MIPS 24-$\mu$m imaging (B12; 7.3–9.1
$\mu$m rest-frame, including the 7.7 and 8.6 $\mu$m PAH bands) which indicates
a significant hot-dust and/or PAH emission. In this paper, we extend this
comprehensive dataset to the far-infrared and mm-wave regime, targeting the [C
II] 158 $\mu$m line.

We assume a flat $\Lambda$CDM cosmology, with $\Omega_{m}=0.315$ and
$H_{0}=67.4$ km s-1 Mpc-1 (Planck Collaboration et al., 2020). At $z=1.844$,
this translates to a luminosity distance $D_{L}=14460$ Mpc; 1 arcsec
corresponds to a physical distance of 8.65 kpc (Wright, 2006).

Table 1: SL2S 0217: intrinsic (de-lensed) properties adapted from Berg et al. (2018, B18) and Erb et al. (2019, E19), with the [C II] and CO(2–1) upper limits derived assuming the $R\leq 3$ kpc aperture from the 1-arcsec taper images (Fig. 1) and a magnification factor $\mu=16$. For the solar metallicity, we adopt the Asplund et al. (2009) value of 12+log(O/H)=8.69. Molecular gas mass $M_{\mathrm{H_{2}}}$ is derived from the [C II] luminosity using the Madden et al. (2020) conversion factor.  |  |  | Reference
---|---|---|---
$z_{\mathrm{spec}}$ |  | 1.844 | B18
M⋆ | [$M_{\odot}$] | $(1.8\pm 0.4)\times 10^{8}$ | B18
SFR | [$M_{\odot}$ yr-1] | 23$\pm$2 | B18
$\mu_{\mathrm{UV}}$ |  | 17.3$\pm$1.2 | B18
12+log(O/H) |  | 7.5 | B18
$R_{\mathrm{1/2}}^{\mathrm{UV}}$ | [kpc2] | 1.0$\times$0.5 | E19
$L_{\mathrm{[CII]}}$ | [$L_{\odot}$] |  $\leq 2.1\times 10^{7}$ (3.2$\sigma$)a | § 3.1
$L^{\prime}_{\mathrm{[CII]}}$ | [K km s-1 pc2] |  $\leq 1\times 10^{8}$ (3.2$\sigma$) | § 3.1
$S_{\mathrm{160\mu m}}$ | mJy |  $\leq 0.23$ (3$\sigma$) | § 3.1
$L_{\mathrm{CO(2-1)}}$ | [$L_{\odot}$] |  $\leq 1.3\times 10^{5}$ (3$\sigma$) | § 3.1
$L^{\prime}_{\mathrm{CO(2-1)}}$ | [K km s-1 pc2] |  $\leq 4\times 10^{8}$ (3$\sigma$) | § 3.1
$M_{\mathrm{H_{2}}}^{\mathrm{[CII]}}$ | [$M_{\odot}$] |  $\leq 2.1\times 10^{9}$ (3.2$\sigma$) | § 4.4
a Based on our tentative image-plane detection, see Fig. 2.

###  2.2 ALMA Band 9 observations and imaging

We combine deep ALMA Band 9 observations of the [C II] line ($f_{0}$=1900.539
GHz) and the underlying rest-frame 160-$\mu$m continuum from the ALMA projects
#2016.1.00142.S and #2016.1.00776.S.

The ALMA programme #2016.1.00142.S (PI: da Cunha) observations were carried
out in two array configurations: C43-1 (2018 July 6) and C43-2 (2018 August
16). The baseline length ranged between 15 and 314 m (C43-1) and 15 to 479 m
(C43-2). Forty 12-m antennas were used on both dates. The primary beam FWHM
was 9.0 arcsec at 680 GHz. The precipitable water vapour (pwv) ranged between
0.4 and 0.5 mm. The total observing time was 2.7 hours, with a total on-source
time of 67 minutes.

The spectral setup consisted of four spectral windows (SPWs) with 480 channels
of 3.906 MHz each, giving a total bandwidth of 2.0 GHz per SPW. The individual
SPWs were centered at 667.61, 669.53, 649.91 and 648.03 GHz.

As the ALMA pipeline products suffered from calibration issues, we calibrated
the data manually by completely flagging antennas with high system
temperature: C43-1 configuration: DA62, DA44, DA50, DV09, DV24; C43-2: DA62.
We used DV07 as the reference antenna due to its low system temperature, good
bandpass stability, and central position in the array.

We supplemented these data by observations from the ALMA programme
#2016.1.00776.S (PI: Cooray). These were taken in two array configurations:
C43-2 with forty-seven 12-m antennas (2018 October 19) and C43-6 with fifty-
one 12-m antennas (2016 October 1 and 14). The baseline length ranged between
15 and 3145 m (C43-6) and baselines 15 and 484 m (C43-2), pwv ranged between
0.55 and 0.80 mm. The on-source time was 47.0 min for each configuration. The
spectral setup consisted of four SPWs configured with 128 15.625-MHz-wide
channels (2.0 GHZ bandwidth per SPW), with central frequencies of 664.95,
666.64, 668.34 and 670.03 GHz. For the C43-6 configuration, we manually
flagged antennas DA43, DV14, DV17. This reduced the total number of antennas
to 48.

For the imaging, we concatenate the visibilities from both ALMA programmes to
maximize the S/N; the total on-source time is 160 min. For the C43-6
configuration, we discard all baselines longer than 1000 k$\lambda$, as adding
the long baselines significantly reduces the surface brightness sensitivity of
the combined dataset. The resulting (u,v)-plane coverage provides sensitivity
to spatial scales between 0.21 and 6.2 arcsecs; given the arc length of 2.5
arcsec, we do not expect any structure to be resolved out.

We produce dirty images of the concatenated dataset using natural weighting,
at the full angular resolution and using a 0.5 and 1.0-arcsec Gaussian taper.
For the [C II] line, we create several dirty-image cubes using different
(u,v)-plane tapers (no taper, 0.5 and 1.0-arcsec taper) and channel width
($\Delta f=$ 50-500 MHz, equivalent to 25-225 km s-1). The
$\sigma_{\mathrm{rms}}$ levels in the resulting images match the expected ALMA
sensitivity within 10%.

For the continuum image, we combine all the SPWs, flagging the channels
affected by atmospheric lines. The resulting beam sizes and rms sensitivity
for the [C II] and Band 9 continuum imaging are listed in Table 2. With a
sensitivity of $\sigma_{\mathrm{rms}}=1.3$ mJy/beam over 250 MHz bandwidth
(3.7 mJy/beam over 10 km s-1), the combined dataset ranks among the deepest
ALMA Band 9 observations to-date.

Figures 1 presents the resulting synthesised images. We do not find any
significant ($\geq 5\sigma$) [C II] or rest-frame 160-$\mu$m continuum
emission. However, the [C II] images show a suggestive 2-3$\sigma$ emission
along the main Einstein arc (see discussion below). In addition, we obtain a
tentative (2-4$\sigma$) detection of the rest-frame 140-$\mu$m continuum from
the secondary lensed source SL2S 0217.X ($z=2.29$, B12).

The ALMA data were reduced and imaged using the Common Astronomy Software
Applications package (Casa, McMullin et al. 2007), versions 5.1 and 5.4.

Figure 1: ALMA Band 9 imaging: dirty naturally-weighted images of the [C II] line (upper) and continuum (lower) at full resolution and 0.5 and 1.0 arcsec taper, overlayed with the HST F606W imaging (Brammer et al. 2012, white contours). The [C II] emission is integrated over 250 MHz (110 km s-1) bandwidth centered at 667.97 GHz; this part of the spectrum shows the tentative 2-3$\sigma$ extended emission. The black contours start at $\pm 2\sigma$ and increase in steps of 1$\sigma$. The HST contours are drawn at 5, 10, 20, 40, 60 and 80% of the surface brightness maximum. The dashed line (left) indicates the $R=3$ kpc aperture used to extract the upper limits (see § 3.1). No continuum emission from the main source is detected; the second lensed source (SL2S 0217.X, $z=2.29$) is tentatively detected at 2-4$\sigma$ significance in each image.  Table 2: ALMA Band 9 synthesized beam size, position angle and rms sensitivity for the [C II] line (measured at 668 GHz over 250 MHz bandwidth) and the rest-frame 160-$\mu$m continuum as a function of (u,v)-taper.  taper | beam FWHM (PA) |  $\sigma$ ([CII]) |  $\sigma$ (cont.)
---|---|---|---
| [arcsec, deg] | [mJy beam-1] | [mJy beam-1]
full-res | 0.26$\times$0.23 (57) | 1.28 | 0.23
0.5 arcsec | 0.65$\times$0.57 (-9) | 1.44 | 0.29
1.0 arcsec | 1.01$\times$0.92 (-9) | 1.91 | 0.44

Figure 2: ALMA Band 9 spectrum of SL2S 0217 at 100 MHz (45 km s-1) resolution,
extracted for the full-resolution and 1.0 arcsec taper images, and the three
source-plane apertures. The shaded regions indicate $\sigma_{\mathrm{rms}}$
for each channel. We obtain a tentative (3-4$\sigma$) [C II] 158-$\mu$m
detection at 667.97 GHz (offset from the systemic velocity by $\sim$50 km s-1)
.

###  2.3 PdBI Band 1 observations and imaging

In addition to the ALMA observations of the [C II] 158-$\mu$m line, we target
the CO(2–1) line using the Plateau de Bure Interferometer (PdBI) with the
WideX correlator (programme X037, PI: Aravena). The PdBI data were taken
between 2013 June 15 and 2013 September 14 in a total of 16 successful tracks.
The total on-source time was 29.6 hours (5-antennas equivalent); the total
observing time was 40 h. All observations were carried our in the most compact
D-configuration, with five 15-meter antennas. The baseline length ranged
between 15 and 97 m, resulting in a synthesized beam FWHM = 7 arcsec; the
source is thus completely unresolved. The observations covered a frequency
range of 79.6 - 83.2 GHz with a spectral resolution of 2 MHz. The resulting
rms sensitivity at the expected frequency of the CO(2–1) line is 0.28 mJy
beam-1 over 100 km s-1 bandwidth. The data were reduced using the Gildas/Clic
package (http://www.iram.fr/IRAMFR/GILDAS).

##  3 Results

###  3.1 [CII] line and 160-$\mu$m continuum

####  3.1.1 Searching for signal in the image plane

To convert the image-plane [C II] flux to source-plane (intrinsic) flux, we
need to account for the gravitational lensing. The magnification of the
extended source depends on its surface brightness distribution and the lensing
geometry. Although we could simply assume that the [C II] emission is co-
spatial with the HST continuum, resolved observations of high-redshift
galaxies have revealed kpc-scale offsets between the rest-frame UV and [C II]
emission (e.g., Maiolino et al. 2015; Carniani et al. 2017) and very extended
[C II] reservoirs (e.g., Carniani et al. 2018; Matthee et al. 2019; Carniani
et al. 2020). If [C II] is significantly offset from the UV continuum, the [C
II] might be less magnified the UV, increasing the source-plane
$L_{\mathrm{[CII]}}$ upper limit.

We consider three circular source-plane apertures centered on the UV-continuum
peak, with a radius $R=$1.0, 2.0 and 3.0 kpc; the latter is comparable to the
largest [C II] reservoirs observed in (much more massive) $z\sim 6$ galaxies
(Carniani et al., 2020). We project these into the sky-plane using the Cooray
et al. (2011) lens model for the lensing galaxy. To maximize the S/N, we
consider only the part of the sky-plane aperture corresponding to the main arc
(Figure 1); as the arc accounts for 95% of the total flux. The magnification
factor is $\mu$ = 43, 25 and 16 for the $R=$1, 2 and 3-kpc apertures,
respectively.

We note that in the synthesis imaging, the area under a dirty beam integrates
to zero for large aperture sizes, unlike for a classical point-spread
function. Consequently, flux measurements extracted from _dirty_ images over
extended areas might be biased, particularly in presence of strong positive or
negative sidelobes. However, the dirty beams corresponding to the Fig. 1
images are well-described by a central Gaussian with only very small sidelobes
($\leq$5%) within the apertures considered here. Our flux limits should
therefore be robust.

Figure 2 shows the spectra extracted from within these apertures, at 100 MHz
resolution, which reveal an excess flux at 667.9 GHz. The excess signal is
unlikely to be caused by e.g. continuum contamination or phase errors. At 250
MHz binning (110 km s-1), the excess is detected at $3.2-4.3\sigma$
significance, depending on the taper and aperture used.

No continuum signal is detected at $\geq 3\sigma$ significance; we therefore
put a conservative 3$\sigma$ upper limit on the rest-frame 160-$\mu$m flux
$S_{\mathrm{160\mu m}}\leq 0.23$ mJy, based on the 1.0-arcsec taper images and
the $R\leq 3$ kpc aperture.

####  3.1.2 Searching for signal in the (u,v) plane

As the spatial filtering by the incomplete (u,v)-plane coverage might decrease
the sensitivity to extended emission in the synthesized images, we try to
confirm our tentative detection of the [C II] line in the (u,v)-plane. How
bright can the [C II] emission be to be still consistent with the observed
visibilities?

We use the following approach by adapting the (u,v)-plane lens-modelling
technique from Rybak et al. (2015); Rybak (2017). First, we extract the
visibility data (real and imaginary parts) at 669.970$\pm$0.125 GHz (same
bandwidth as used for the image-plane analysis). The noise on the
real/imaginary visibilities is estimated by taking the rms of visibilities for
a given baseline for each individual scan. As the noise per polarization might
differ, we do not combine the XX and YY polarizations into the Stokes $I$. We
then calculate the expected signal $V(u,v)^{\mathrm{model}}$ for each
visibility as

$V(u,v)^{\mathrm{model}}=\sum_{l,m}B(l,m)I(l,m)e^{2\pi i(ul+vm)},$ (1)

where $B$ is the primary beam response (approximated by a Gaussian), $I$ the
input sky brightness distribution, and $m,l$ the sky-plane coordinates. We
consider the following sky-plane [C II] surface brightness distributions: HST
F606W arc (see Fig. 1) and the $R\leq 1$, 2 and 3 kpc apertures; the total
flux varies between 0 and 50 mJy. We calculate the log-likelihood value $\log
L\propto-\sum_{i}(V(u_{i},v_{i})^{\mathrm{model}}-V(u_{i},v_{i})^{\mathrm{data}})^{2}/\sigma(u_{i},v_{i})^{2}$.
As a control test, we perform the same analysis for a “line-free” part of the
spectrum (680.000$\pm$0.125 GHz).

Figure 3 shows the derived probability distribution function (PDF) for
$S_{\mathrm{[CII]}}$. For the $R\leq 2$ kpc and $R\leq 3$ kpc apertures, the
PDF peaks around $S_{\mathrm{[CII]}}=15$ mJy, whereas for the HST-based
aperture, the PDF peaks at 0 mJy. Reassuringly, the PDF for the “line-free”
part of the spectrum peaks near $S_{\mathrm{[CII]}}=0$ mJy (dashed lines) for
all apertures. Tweaking the noise calculation (e.g., by combining the
polarizations, calculating the rms over several scans) does not substantially
change the PDFs. This might be indicative of an extended [C II] emission in
SL2S 0217. However, the $S_{\mathrm{[CII]}}=15$ mJy solution is not strongly
preferred over the $S_{\mathrm{[CII]}}=0$ mJy, our null hypothesis.

Consequently, we adopt a [C II] upper limit of $S_{\mathrm{[CII]}}\leq 21$ mJy
over 250 MHz (110 km s-1) bandwidth, measured for the 1.0-arcsec uv-taper and
$R\leq 3$ kpc source-plane aperture (3.2$\sigma$ significance). The 1.0-arcsec
taper maximizes the surface-brightness sensitivity, while large aperture size
accounts for a potentially very extended [C II] emission. This line flux
corresponds to a sky-plane luminosity of $L_{\mathrm{[CII]}}\leq 3.4\times
10^{8}$ $L_{\odot}$; after de-lensing ($\mu=16$), we set a source-plane upper
limit of $L_{\mathrm{[CII]}}\leq 2.1\times 10^{7}$ $L_{\odot}$. The line width
adopted here is comparable to the typical line FWHM of $\sim 120$ km-1 of
$z\sim 2$ EELGs (Maseda et al., 2014).

Figure 3: (u,v)-plane analysis of the ALMA [C II] 158-$\mu$m observations:
Probability distribution function (PDF) of the sky-plane [C II] flux for a 250
MHz bandwidth (see Fig 1), assuming different surface brightness distributions
and compared to the sky-plane limit (21 mJy). Colored dashed lines indicate
sky-flux PDFs for a “line-free” part of the data (i.e., where no signal is
expected). Although the [C II] PDF peaks around 15 mJy for $R\leq 2$, 3 kpc
apertures, this solution is not strongly preferred over the null hypothesis
($S_{\mathrm{[CII]}}=0$ mJy) and is below the sky-plane limit. This result
does not depend on the noise model used. We therefore adopt an upper limit on
$S_{\mathrm{[CII]}}$=21 mJy based on image-plane analysis.

###  3.2 CO(2–1) line

As shown in Figure 4, we do not detect any significant CO(2–1) line emission
towards SL2S 0217; the PdBI spectrum is consistent with pure noise. Assuming
the same aperture and 110 km s-1 linewidth as for the [C II] line (see Figure
1), we set a 3$\sigma$ upper limit on $L_{\mathrm{CO(2-1)}}\leq 1.3\times
10^{5}~{}L_{\odot}$, $L^{\prime}_{\mathrm{CO(2-1)}}\leq 4\times 10^{8}$ K km
s-1 pc2 (source-plane).

Figure 4: PdBI spectrum of SL2S 0217 with 100 km s-1 frequency bins. The
shaded region indicates the $\sigma_{\mathrm{rms}}$ for each channel. We do
not detect any significant CO(2–1) emission from SL2S 0217.

##  4 Discussion

###  4.1 Photoionization modelling

With an ionization energy of 11.3 eV, the [C II] 158-$\mu$m emission222In this
section, we explicitly state the wavelengths of individual emission lines for
clarity. can arise from all ISM phases: molecular (H2), neutral (H), and
ionized (H+). Although studies of nearby galaxies have shown that at $Z\leq
0.25~{}Z_{\odot}$ almost all [C II] emission arises from the neutral ISM
(Croxall et al., 2017; Sutter et al., 2019), the large ionizing flux and
limited self-shielding due to low metallicity in SL2S 0217 might cause the
ionized component to dominate its $L_{\mathrm{[CII]}}$ (Ferrara et al., 2019).
In SL2S 0217, the semi-forbidden C II]2325Å emission line and the C II
absorption line detected in the Keck spectra (B18) confirm the presence of at
least some C+ in the ionized ISM. But _can_ the ionized gas account for the
entire [C II] 158-$\mu$m emission?

We address this question by using photoionization modelling to predict the [C
II] 158-$\mu$m emission from the ionized ISM using the Mappings V
photoionization code (Allen et al., 2008; Groves & Allen, 2010). We focus on
the [C II] 158$\mu$m far-IR line and the rest-frame UV C II] 2325Å line and
the C III] 1909Å doublet333Here, we treat the ISM as uniform. However, as
shown by E19, the UV spectral slope varies considerably across the source; the
C II], [C II] and C III] lines are thus likely not co-spatial on sub-
kiloparsec scales., which are all predicted by Mappings V. The photoionization
modelling provides a lower limit on $L_{\mathrm{[CII]}}$, as the contribution
of [C II] 158 $\mu$m from photon-dominated regions (PDRs) (e.g., Hollenbach &
Tielens, 1997) is not included in the Mappings models. Due to the lack of
constraints on the PDR phase (just our [C II] 158-$\mu$m and a very weak
CO(2–1) upper limits, we refrain from modelling the neutral/molecular ISM.

The semi-forbidden C III] 1909Å doublet originates in the H II regions (e.g.,
Jaskot & Ravindranath 2016; Kewley et al. 2019; Vallini et al. 2020), and -
thanks to its brightness - is a convenient tracer of ionized gas in the EoR
(Stark et al., 2015, 2017; Zitrin et al., 2015); the C II] 2325Å line traces
the outer layers of H II regions, which also emit the [C II] 158 $\mu$m line.
Based on our upper limits and B18 spectroscopy, the observed ratios are [C II]
158 $\mu$m / C II] 2325Å$\leq$ 4.7, [C II] 158 $\mu$m / C III] 1909Å $\leq$
0.8 and C III] 1909Å / C II] 2325Å = 6.2$\pm$0.5 (in W m-2 units). Using C II]
instead of any of the other UV lines detected in the Keck spectrum by B18
avoids systematic uncertainties related to the carbon abundance and ionization
state.

To set the ionizing radiation field, we use the Starburst99 stellar population
models444For the case considered here, the predicted line intensities differ
only marginally ($\leq 0.1$ dex) between the different stellar model
libraries. See D’Agostino et al. 2019 for a detailed comparison. (Leitherer et
al., 1999, 2010), including also the effects of stellar rotation on the
emitted spectra of massive stars, as described in Levesque et al. (2012).

Following the B18 modelling of the UV spectrum, we set the model metallicity
to $0.05\,Z_{\odot}$ and assume an instantaneous starburst. We explore models
with electron densities between $n_{e}$=10 and 100 cm-3, since the C II]
2325Å/ [C II] 158$\mu$m flux ratio is very sensitive to density due to the low
critical density of the [CII] 158$\mu$m line in ionised gas ($n_{e}$=50 cm3).
We vary the ionization parameter $U$ (defined as the ratio of the $\geq 13.6$
eV photon number density and the gas density $n$) and the age of the ionizing
star cluster (in steps of 0.5 Myr). We adopt a one-dimensional plane-parallel
geometry as appropriate for the expected geometry in SL2S 0217: a screen of
ionized ISM on front of an ionizing cluster. Figure 5 shows the predicted [C
II] 158 $\mu$m / C II] 2325Å and C III] 1909Å / C II] 2325Å ratios for each
realization.

The C III] 1909Å/C II] 2325 Å ratio depends both on the ionisation parameter
(impacting both the gas temperature and ionization state) and the age of the
starburst (affecting the relative number of C+ ionizing photons, $>$24.4 eV,
to C0 ionizing photons, $>$11.3 eV). See Jaskot & Ravindranath (2016); Kewley
et al. (2019) for other examples, and the color axes in Fig. 5.

As the [C II] 158 $\mu$m and C II] 2325 Å lines arise only from a single
species and ionisation state, their ratio is purely dependent upon the
electron density and temperature, which drive the relative collisional rates.
Because of the low critical density for [C II] 158 $\mu$m ($n_{e}\simeq 50$
cm-3) and high excitation energy of the C II] 2325 Å line, the [C II] 158
$\mu$m / C II] 2325 Å ratio depends strongly on both electron density and
temperature.

We find that, for $n_{e}=100$ cm-3 (the value assumed by B18), Mappings
predicts $\log(L_{\mathrm{[CII]158\mu
m}}^{\mathrm{ion}}/L_{\mathrm{CII]2325\AA}})\sim-0.5\pm 0.5$ (Figure 5). For
$n_{e}=10$ cm-3, the ratio is typically 0.5 dex higher, as the critical
density for [C II] 158$\mu$m is lower than for C II]2325Å. Therefore, we
conservatively assume that $\log(L_{\mathrm{[CII]158\mu
m}}^{\mathrm{ion}}/L_{\mathrm{CII]2325\AA}})$ = 0$\pm$1\. Given the C II]2325Å
flux of $1.11\times 10^{-17}$ erg s-1 cm-2 (flux of the brightest line in the
C II] triplet, measured by B18; this is the line predicted by Mappings), we
estimate an on-sky [C II] 158$\mu$m line luminosity $L_{\mathrm{[CII]158\mu
m}}^{\mathrm{ion}}\sim 7.3\times 10^{7}\,L_{\sun}$.

This estimate is approximately 5$\times$ lower than our [C II] 158 $\mu$m
upper limit ($L_{\mathrm{[CII]158\mu m}}^{\mathrm{sky}}\leq 3.4\times
10^{8}\,L_{\sun}$) although the lack of $n_{e}$ constraints implies a $\sim$1
dex uncertainty in the predicted flux ratio.

For most of the $n_{e}$, $U$ models considered here, our [C II] 158 $\mu$m
upper limit is higher than the contribution from the ionized ISM; the
neutral/molecular ISM can account for up to 80% of the [C II] 158 $\mu$m line
flux, similar to the $z=0$ low-metallicity galaxies (Croxall et al., 2017;
Cormier et al., 2019). However, in the low-density, high-ionization regime
($n_{e}=10$ cm-3, log $U\geq-3.5$), the predicted [C II] 158-$\mu$m luminosity
exceeds our upper limits. In such case, the ISM in SL2S 0217 will be fully
ionized.

Figure 5: Mappings modelling of C+/C2+ emission lines from the ionized ISM as
a function of the starburst age (upper) and the ionization parameter $U$
(lower). We show the ratios of [C II] 158$\mu$m, C II] 2325Å and C III] 1909Å
luminosities for an instantaneous star-formation burst, $Z=0.05~{}Z_{\odot}$,
$n_{e}=$10 and 100 cm-3. The grey lines connect models with constant $U$ and
increasing age. The shaded area is excluded by the [C II] 158 $\mu$m / C III]
1909Å ratio. The upper limit on $L_{\mathrm{[CII]}}$ is consistent with a
young ($<$5 Myr) starburst over a wide range $U$ and allows for a substantial
[C II] emission from the neutral ISM.

###  4.2 Comparison with empirical models and simulations

We now compare SL2S 0217 to predictions for [C II] luminosity from various
empirical models and hydrodynamical simulations. Thanks to the stream of high-
redshift [C II] detections from ALMA (Hodge & da Cunha, 2020), the [C II]
emission from high-redshift galaxies has been extensively studied by a number
of high-resolution hydrodynamical simulations. Our tentative [C II] detection
in a $Z=0.05~{}Z_{\odot}$ dwarf allows us to validate these models in the
poorly explored high-SFR, low-metallicity regime.

Namely, we consider the following [C II]-SFR relations: the empirical De Looze
et al. (2014) relation for nearby low-metallicity dwarf galaxies, the Herrera-
Camus et al. (2015) calibration for nearby star-forming galaxies, as well as
predictions from simulations of Vallini et al. (2015); Olsen et al. (2017) and
Lagache et al. (2018). Table 3 lists the respective [C II]-SFR relations and
the predicted source-plane [C II]/SFR ratio for SL2S 0217. Figures 6 and 7
compare the $L_{\mathrm{[CII]}}$ and $L_{\mathrm{[CII]}}$/SFR in SL2S 0217
with relations from Table 3, and low- and high-redshift observations (see
below) as a function of SFR and metallicity.

Our upper limit is in agreement with the metallicity-dependent relations of
Vallini et al. (2015) and Olsen et al. (2017). On the other hand, the [C II]
emission in SL2S 0217 is at least 30$\times$ fainter than expected from the
locally-calibrated De Looze et al. (2014), a $\geq$4$\sigma$ tension. The
Herrera-Camus et al. (2015) relation predicts even higher
$L_{\mathrm{[CII]}}$/SFR with a smaller scatter ($\sim 0.2$ dex); this is
likely a consequence of a relatively high metallicity of their sample (12 +
log(O/H)=7.7-8.8).

Finally, Lagache et al. (2018) underpredict the SL2S 0217 [C II] luminosity by
a factor of 20; however, given the 0.5 dex 1$\sigma$ scatter of the Lagache et
al. (2018) trend, our upper limit is still consistent with it at 2.5$\sigma$
level. We note that the Lagache et al. (2018) simulations contain a
significant number of galaxies with SFR, metallicity and $L_{\mathrm{[CII]}}$
consistent with SL2S 0217.

The strong dependence of the $L_{\mathrm{[CII]}}$/SFR ratio on average gas
metallicity is supported by the high-resolution simulations of high-$z$ dwarf
galaxies by Lupi & Bovino (2020): for $Z\leq 0.1~{}Z_{\odot}$, they find
$L_{\mathrm{[CII]}}$/SFR$\leq 10^{6}$ $L_{\odot}$/($M_{\odot}$ yr-1),
consistent with our upper limit.

Finally, we consider the analytical model of Ferrara et al. (2019), who
investigated low [C II] luminosities of some of the high-$z$ UV-selected
sources. In the low-metallicity, high-$\Sigma_{\mathrm{SFR}}$ regime of SL2S
0217, the [C II] surface density $\Sigma_{\mathrm{[CII]}}$ is given by:

$\Sigma_{\mathrm{[CII]}}=1.8\times
10^{7}\left(\frac{n_{\mathrm{gas}}}{n_{500}}\right)\ln\left(\frac{U}{0.001}\right),$
(2)

where $n_{500}=500$ cm-3. For SL2S 0217, with an ionization parameter $\log
U=-1.5$ (B18) and assuming that [C II] is co-spatial with the UV continuum,
Eq. (2) matches our $\Sigma_{\mathrm{[CII]}}$ upper limit for
$n_{\mathrm{gas}}\simeq 150$ cm-3 ($n_{\mathrm{gas}}$ decreases further if [C
II] is more extended than the UV continuum). As the Ferrara et al. model
directly sets $U\propto\Sigma_{\mathrm{SFR}}/\Sigma_{\mathrm{gas}}^{2}$, to
reconcile the high $U$ and $\langle\Sigma_{\mathrm{SFR}}\rangle$, SL2S 0217
has to be an extreme starburst, with a gas surface density
$\Sigma_{\mathrm{gas}}\simeq 3.5\times 10^{8}$ $M_{\odot}$ kpc-2. This roughly
agrees with the expectation from the E19 gas column density estimate
$N_{\mathrm{HI}}\simeq 10^{21.7}$ cm-3, which predicts
$\Sigma_{\mathrm{gas}}=N_{\mathrm{HI}}\times m_{\mathrm{proton}}\simeq 8\times
10^{7}$ $M_{\odot}$ kpc-2.

Table 3: [C II]-SFR relations referenced in this work, with the expected [C II]/SFR ratio for SL2S 2017, given the parameters from Table 1. The [C II]/SFR ratio in SL2S 0217 is $\leq 1\times 10^{6}$ $L_{\odot}$/($M_{\odot}$ yr-1).  Reference | [C II]-SFR |  $L_{\mathrm{[CII]}}$/SFR | Note
---|---|---|---
|  | [$L_{\odot}$/($M_{\odot}$ yr-1)] |
De Looze et al. (2014) | $\log L_{\mathrm{[CII]}}=1.25\log(\mathrm{SFR})+7.16$ | $3\times 10^{7}$ | Local dwarf galaxies (Cormier et al., 2015)
Herrera-Camus et al. (2015) | $\log L_{\mathrm{[CII]}}=0.97\log(\mathrm{SFR})+7.66$ | $4\times 10^{7}$ | Local star-forming galaxies
Vallini et al. (2015) | $\log L_{\mathrm{[CII]}}=7.0+1.2\log(\mathrm{SFR})+0.021\log(Z)+$ | $9\times 10^{5}$ | Zoom-in simulations, $z=6.6$
|  $+0.012\log(\mathrm{SFR})\log(Z)-0.74\log^{2}(Z)$ |  |  $Z=0.05-1~{}Z_{\odot}$, SFR = 1-100 $M_{\odot}$ yr-1
Olsen et al. (2017)a | $\log L_{\mathrm{[CII]}}=7.17+0.55\log\mathrm{SFR}+0.23\log Z$ | $1.8\times 10^{6}$ | Zoom-in simulations, $z\sim 6$,
|  |  |  $M_{\star}=(6-80)\times 10^{8}$ $M_{\odot}$,
|  |  | SFR = $3-20~{}M_{\odot}$ yr-1, $Z=0.16-0.45~{}Z_{\odot}$
Lagache et al. (2018)b | $\log L_{\mathrm{[CII]}}=7.1+\left(1.4-0.07z\right)\log(\mathrm{SFR})-$ | $2.2\times 10^{7}$ | Semi-analytic models, $z=4-7$
| $-0.07z$ |  |  $Z=0.004-4.4$ $Z_{\odot}$
a not correcting for the CMB temperature effects which are negligible at
$z\sim 2$ (c.f. Olsen et al. 2018 erratum).
b no metallicity dependence, weak evolution with redshift $z$.

Figure 6: [C II] luminosity (left) and the [C II]/SFR ratio versus SFR (right)
in SL2S 0217, compared to the nearby Dwarf Galaxy Survey (Cormier et al.,
2015, 2019) and Alpine samples (Schaerer et al., 2020), and $z=2-7$
observations of low-mass galaxies (Schaerer et al., 2015; Knudsen et al.,
2016; Bradač et al., 2017), colored by 12 + log (O/H). For the Alpine sources,
we use the publicly-available SED-based SFR estimates from Faisst et al.
(2020). The different lines indicate different models from Table 3: Vallini et
al. (2015) for $Z=0.025$ (thinnest line), 0.05, and 0.1 $Z_{\odot}$
(thickest); De Looze et al. (2014) (with 1$\sigma$ scatter indicated by
shading); Olsen et al. (2017) and Lagache et al. (2018). We do not show the
Herrera-Camus et al. (2015) relation, as it generally predicts higher
$L_{\mathrm{[CII]}}$ than De Looze et al. (2014) over the SFR range studied
here. The [C II]/SFR ratio in SL2S 0217 is at least 30$\times$ lower than
predicted by the De Looze et al. (2014) relation.  Figure 7: [C II]/SFR ratio
as a function of metallicity: comparison of SL2S 0217 to the Cormier et al.
(2015), Knudsen et al. (2016) and Bradač et al. (2017) sources (color-coded by
SFR), and the different relations from § 4.2, all for SL2S 0217-like SFR=23
$M_{\odot}$ yr-1. The [C II]/SFR ratio in SL2S 0217 is consistent with the
metallicity-dependent relations of Vallini et al. (2015) and Olsen et al.
(2017), but much lower than predicted by De Looze et al. (2014) and Lagache et
al. (2018).

###  4.3 Comparison with low-metallicity galaxies near and far

In the present-day Universe, SL2S 0217 can be directly compared to galaxies
from the Dwarf Galaxy Survey (DGS) (Madden et al., 2013), which span $Z$ =
0.02 - 1.0 $Z_{\odot}$ and SFR = 0.0005 - 25 $M_{\odot}$ yr-1; 48 galaxies
from the DGS sample were targeted with Herschel PACS far-IR spectroscopy by
Cormier et al. (2015). Although the DGS sample shows a broad [C II]/SFR
correlation, the [C II]/SFR ratio varies between $10^{5.0}$ and $10^{9.5}$
$L_{\odot}/(M_{\odot}\mathrm{yr}^{-1})$ (Figure 6). Four DGS sources have [C
II]/SFR ratios similar or lower than SL2S 0217. In particular, SBS 0335-052 -
which matches SL2S 0217 in terms of the rest-frame UV line ratios and the
overall SED (E18) - has [C II]/SFR $\simeq 5.5\times 10^{5}$
$L_{\odot}$/($M_{\odot}$ yr-1), directly comparable to our upper limits.

At $z=1-2$, the bulk of [C II] and CO molecular gas studies have focused on
relatively massive galaxies with $M_{\star}\geq 10^{1}0~{}M_{\odot}$ (e.g.,
Stacey et al. 2010; Brisbin et al. 2015; Zanella et al. 2018). The only
exception is the strongly lensed $M_{\star}\simeq 2.5\times 10^{9}M_{\odot}$
galaxy detected in [C II] and CO(3–2) by Schaerer et al. (2015); however, it
is still $\sim 10\times$ more massive and metal-enriched than SL2S 0217. The
[C II]/SFR ratio measured by Schaerer et al. (2015) is $10^{7}~{}L_{\odot}$ /
($M_{\odot}$ yr-1), 1 dex higher than in SL2S 0217.

At $z\geq 6$, two $z=6-7$ EELGs lensed by galaxy clusters have been detected
in the [C II] emission by Knudsen et al. (2016, who also obtained a strong
upper limit on another source) and Bradač et al. (2017). Similar to SL2S 0217,
all three sources have [C II]/SFR $\leq 3\times 10^{6}$, significantly lower
that the locally-calibrated De Looze et al. (2014) relation (Figure 6). While
the Knudsen et al. (2016) [C II]-detected source has a relatively low SFR and
high stellar mass ($M_{\star}\simeq 3\times 10^{9}$ $M_{\odot}$), the Bradač
et al. (2017) source is very similar to SL2S 0217, with SFR$\simeq 9$
$M_{\odot}$ yr-1, $M_{\star}\simeq 10^{8}$ $M_{\odot}$ and $Z=0.2$
$Z_{\odot}$.

At higher stellar masses ($M_{\star}=10^{9}-10^{11}~{}M_{\odot}$), the Alpine
ALMA large programme (Le Fèvre et al., 2020; Faisst et al., 2020; Béthermin et
al., 2020) has recently observed the [C II] line in 189 $z=4-6$ galaxies with
SFR = $1-100$ $M_{\odot}$ yr-1 (Schaerer et al., 2020). The Alpine sources are
generally consistent with the De Looze et al. (2014) relation and have higher
[C II]/SFR than SL2S 0217, likely due to their presumably higher metallicity
(23 out of 118 Alpine sources are detected in the rest-frame 160-$\mu$m
continuum indicating substantial dust masses, Béthermin et al. 2020).

Finally, Figure 8 compares the [C II] luminosity and [C II]/SFR ratio in SL2S
0217 to the compilation of $z=5-7$ Ly$\alpha$ emitters (Harikane et al., 2018;
Matthee et al., 2019), and the Alpine survey (Schaerer et al., 2020). The
Ly$\alpha$ EW correlates closely with the Ly$\alpha$ photons escape fraction
(e.g., Verhamme et al. 2017; Harikane et al. 2018; Matthee et al. 2019); the
sources with high Ly$\alpha$ EW are thus expected to be depleted in neutral
ISM. For SL2S 0217, E19 derived a photometric EW = 218$\pm$12 Å. Compared to
the $z\geq 5$ Ly $\alpha$ emitters, SL2S 0217 has a low [C II]/SFR ratio and
is a factor of $\sim 3$ below the Harikane et al. (2020) empirical Ly$\alpha$
EW - [C II]/SFR relation. The low [C II]/SFR ratio in SL2S 0217 might be
driven by its relatively compact size: its source-plane
$R_{1/2}^{\mathrm{UV}}\sim$0.35kpc, compared to $\sim$1 kpc radii for $z\sim$6
sources (Carniani et al., 2018, 2020; Matthee et al., 2019) which might
increase the ionized ISM fraction, suppressing the [C II] emission.

Figure 8: Upper limits on the [C II]/SFR ratio in SL2S 0217 versus the
Ly$\alpha$ equivalent width (E19), compared to the Harikane et al. (2018) and
Matthee et al. (2019) compilations of $z=5-7$ Ly$\alpha$ emitters and the
$z=4.4-5.9$ Alpine survey Schaerer et al. (2020). SL2S 0217 is a factor of 3
below the empirical relation of Harikane et al. (2020).

###  4.4 The fate of molecular gas in SL2S 0217

Given the upper limits on the [C II] and CO(2–1) luminosity, what can we say
about the state of the molecular gas in SL2S 0217? Does SL2S 0217 still
contain a substantial molecular gas reservoir, or is it at the very end of its
starburst phase, with the ISM depleted and ionized? We briefly discuss three
facets of this problem: i) limits on the molecular gas mass, ii) the
possibility of the ISM being fully ionized and iii) photoevaporation of
molecular gas.

First, adopting the conservative magnification factor $\mu=16$, the CO(2–1)
upper limit translates to a (very weak) 3$\sigma$ upper limit
$M_{\mathrm{H_{2}}}\leq 2\times 10^{9}~{}M_{\odot}$, where we assume
$r_{2/1}=0.6$ (Cormier et al., 2014) and a Galactic
$\alpha_{\mathrm{CO}}=4.4M_{\odot}$/(K km s-1 pc2). However, studies of nearby
low-metallicity dwarfs (e.g., Schruba et al. 2012; Hunt et al. 2015; Shi et
al. 2016) found $\alpha_{\mathrm{CO}}$ up to 3 dex higher than the Galactic
value, significantly weakening our $M_{\mathrm{gas}}$ upper limit.

Alternatively, we can estimate the molecular gas mass $M_{\mathrm{H_{2}}}$
from the [C II] luminosity, as originally proposed by Zanella et al. (2018).
Due to the very low metallicity of SL2S 0217, rather than using the Zanella et
al. (2018) relation (see below), we use the recently-published relation of
Madden et al. (2020) calibrated on the DGS sample:

$M_{\mathrm{H_{2}}}^{\mathrm{[CII]}}\,(\mathrm{M20})=132\times
L_{\mathrm{[CII]}}^{0.97},$ (3)

. which for SL2S 0217 yields $M_{\mathrm{H_{2}}}\leq 2.1\times 10^{9}$
$M_{\odot}$. Alternatively, using the Zanella et al. (2018) relation
calibrated on more massive main-sequence galaxies:

$M_{\mathrm{H_{2}}}^{\mathrm{[CII]}}\,(\mathrm{Z18})=30\times
L_{\mathrm{[CII]}},$ (4)

we obtain $M_{\mathrm{H_{2}}}\leq 0.8\times 10^{9}$ $M_{\odot}$; although the
extrapolation of the Zanella et al. (2018) relation to the low-$Z$ regime
might not be straightforward. Both $M_{\mathrm{gas}}$ estimates imply a high
gas mass fraction
$f_{\mathrm{gas}}=M_{\mathrm{gas}}/(M_{\mathrm{gas}}+M_{\star})\simeq 0.8$.
This is consistent with high gas fractions and dynamical mass estimates for
$z=1-2$ EELGs (Maseda et al., 2014) and simulations of high-redshift dwarf
galaxies (Ceverino et al., 2018).

A gas mass of $\sim 10^{8}$ $M_{\odot}$ is also supported by the expectations
from the Ferrara et al. (2019) model and the column-density estimates from E19
(see § 4.2).

A gas mass of $10^{8}$ $M_{\odot}$ is further supported by the high
$\Sigma_{\mathrm{SFR}}$/$U$ ratio in SL2S 0217 (see § 4.2). With SFR=23
$M_{\odot}$ yr-1, SL2S 0217 will deplete its gas in $\sim$10 Myr (likely much
faster, as some gas might be expelled from the system). This suggests that
SL2S 0217 is in a final stage of an intense starburst.

Second, as indicated in § 4.1, a substantial fraction of the gas reservoir
might be ionized. Namely, the maximum column density proposed by E19
($\Sigma_{\mathrm{HI}}\leq 10^{21.7}$ cm-2) is comparable to the ionized gas
column depth of $\sim 10^{21.3}$ cm-2 predicted by Ferrara et al. (2019) for
SL2S 0217-like ionization parameter and metallicity. The fraction of the
ionized gas might be further increased due to additional ionizing sources. In
particular, the unusually strong He II emission in SL2S 0217 cannot be
reproduced by standard photoionization models (B18) and requires additional
ionization source, such as radiative shocks (Allen et al., 2008; Plat et al.,
2019) or high-mass X-ray binaries as seen in, e.g., a nearby dwarf I Zw 18
(Lebouteiller et al. 2017; Schaerer et al. 2019, but c.f. Plat et al. 2019).
This extra ionization would increase the contribution of the ionized ISM to
the [C II] luminosity compared to our photoionization models; on the other
hand, strong FUV fields might suppress the [C II] emission by ionizing C+ into
C2+ (e.g., Langer & Pineda 2015).

Third, the combination of the strong FUV fields and the lack of ISM self-
shielding at low metallicities can lead to a rapid ionization and
photoevaporation of the molecular clouds on 1-10 Myr timescales, thus further
suppressing the [C II] emission (Vallini et al., 2017).

We note that in the very near future, the warm neutral or molecular gas might
be traced at mid-infrared wavelengths via the PAHs or rotational-vibrational
H2 emission using the James Webb Space Telescope. Alternatively, the gas mass
in SL2S 0217 can be constrained kinematically (e.g., Calistro Rivera et al.
2018), using the integrated-field spectroscopy of the bright C III] 1909Å line
(Maseda et al., in prep.).

###  4.5 Detectability of [CII] emission from metal-poor dwarfs at $z\geq 6$

What are the prospects of detecting the [C II] 158-$\mu$m emission in SL2S
0217 if it was at $z\sim 6$? Assuming $L_{\mathrm{[CII]}}=2.6\times 10^{7}$
$L_{\odot}$, achieving a spatially unresolved 5$\sigma$ detection at $z=6$
would require $\sigma_{\mathrm{rms}}\sim 50$ $\mu$Jy over 100 km s-1
bandwidth, which corresponds to $\sim$10 hours of ALMA on-source time. For
comparison, the deepest ALMA Band 6 observations to-date, delivered by the
Aspecs (Walter et al., 2016; González-López et al., 2020) and Almacal (Oteo et
al., 2016) projects and the Fujimoto et al. (2016) compilation, reach
sensitivities of $\sigma_{\mathrm{rms}}\sim 100$ $\mu$Jy over the same
bandwidth.

Another promising way of studying the population of galaxies at high redshift
is the line-intensity mapping (e.g. Gong et al. 2012; Silva et al. 2015). The
feasibility of the [C II]-intensity mapping measurements depends critically on
the [C II] luminosity function at $z\geq 6$. A recent [C II]-intensity mapping
feasibility study of Yue & Ferrara (2019) considered several [C II] luminosity
function models. The detectability of the [C II] power spectrum is the highest
for the De Looze et al. (2014) dwarf-galaxies relation, and lowest for the
Vallini et al. (2015) relation; the predictions for the expected power-
spectrum and shot-noise signal from the two models differ by a factor of
$\sim$30\. Consequently, if the low [C II]/SFR ratio in SL2S 0217 can be taken
to validate the Vallini et al. (2015) and Olsen et al. (2017) [C II]
luminosity models, the $z\geq 6$ [C II] intensity mapping signal will fall
below the detection threshold of the potential ALMA or single-dish intensity-
mapping experiments (e.g., a 1000-hour programme on the CCAT-p telescope,
Stacey et al. 2018). Our analysis highlights the need to properly account for
the metallicity evolution of galaxies and its impact on the [C II] emission.

##  5 Summary and Conclusions

We have presented deep ALMA and PdBI observations of the [C II] 158-$\mu$m and
CO(2–1) emission in the $z=1.844$ strongly lensed metal-poor dwarf galaxy SL2S
0217. In one of the deepest ALMA Band 9 observations to-date, we obtain a
tentative 3-4$\sigma$ detection of the [C II] line. No CO(2–1) emission is
detected in the PdBI observations.

Our main conclusions are:

  * •

We report a tentative (3-4$\sigma$) detection of the [C II] line based on the
image-plane spectra; the source-plane luminosity is $L_{\mathrm{[CII]}}\leq
2.1\times 10^{7}$ $L_{\odot}$, derived from 1.0-arcsec taper imaging, $R\leq$3
kpc aperture and a 250 MHz bandwidth. We do not find strong evidence for [C
II] emission in the (u,v)-plane. The rest-frame 160-$\mu$m continuum and the
CO(2–1) line are not detected. Our tentative [C II] detection extends the
molecular gas studies at $z\sim 2$ by 1 dex in stellar mass, down to the
$M_{\star}\simeq 10^{8}$ $M_{\odot}$ regime.

  * •

The upper limit on the $L_{\mathrm{[CII]}}$/SFR ratio in SL2S 0217 is $2\times
10^{6}$ $L_{\odot}$/($M_{\odot}$ yr-1), within the range spanned by nearby
dwarf galaxies (Cormier et al., 2015), as well as $z\geq 5$ lensed dwarf EELGs
and Ly$\alpha$ emitters.

  * •

The [C II]/ SFR ratio in SL2S 0217 is consistent with the Vallini et al.
(2015) and Olsen et al. (2017) simulations-based models. However, the [C
II]/SFR ratio in SL2S 0217 is $30\times$ lower than predicted by the locally-
calibrated De Looze et al. (2014) relation.

  * •

We use Mappings photoionization modelling to predict the fraction of [C II]
emission arising in the ionized ISM. We find that our upper limit leaves room
for a significant (up to 80%) contribution from the PDRs; however, we can not
exclude that the ISM is fully ionized, particularly for low electron density.
The contribution from the ionized ISM might be boosted due to extra ionizing
radiation from e.g., shocks or X-ray binaries. Future ALMA and JWST
observations of PDR tracers will allow us to directly probe the
neutral/molecular ISM.

  * •

The tentative [C II] detection and the high $\Sigma_{\mathrm{SFR}}$ and
ionization parameter suggest a gas mass of few $10^{8}$ $M_{\odot}$. In this
scenario, SL2S 0217 will be in a late phase of an extreme starburst and
deplete its gas reservoir in $<$10 Myr. More robust constraints on the gas
mass might be obtained from spatially-resolved spectroscopic observations of
the bright rest-frame FUV lines.

  * •

If SL2S 0217 is representative of the $z\geq 6$ low-mass galaxies, these will
be within reach of deep-field ALMA observations (even without gravitational
lensing). On the other hand, a strong dependence of [C II]/SFR ratio on
metallicity might strongly suppress the [C II] signal in line-intensity
mapping experiments.

The large discrepancy between the [C II]/SFR ratio in SL2S 0217 and the
widely-used De Looze et al. (2014) relation for present-day dwarf galaxies
highlights the limitations of applying locally established relations to high
redshift. At the same time, the good agreement between our tentative [C II]
detection, high-redshift observations, and simulations confirms that - though
challenging to study - SL2S 0217 remains a powerful analogue of the sources
from the Epoch of Reionization.

We thank the anonymous referee for their careful and constructive review of
this manuscript which improved the content and clarity of this paper. This
paper makes use of the following ALMA data: ADS/JAO.ALMA #2016.1.00142.S and
#2016.1.00776.S. ALMA is a partnership of ESO (representing its member
states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST 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.
This work is based on observations carried out under project number X037 with
the IRAM PdBI Interferometer. IRAM is supported by INSU/CNRS (France), MPG
(Germany) and IGN (Spain). We acknowledge assistance from Allegro, the
European ALMA Regional Center node in the Netherlands. MR and JAH acknowledge
support of the VIDI research programme with project number 639.042.611, which
is (partly) financed by the Netherlands Organisation for Scientific Research
(NWO). MR acknowledges support from the Leids Kerkhoven-Bosscha Fonds, subsidy
number 19.2.075. EdC gratefully acknowledges the Australian Research Council
as the recipient of a Future Fellowship (project FT150100079) and the ARC
Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D;
project CE170100013). MA has been supported by the grant “CONICYT + PCI +
INSTITUTO MAX PLANCK DE ASTRONOMIA MPG190030” and “CONICYT+PCI+REDES 190194.”
DKE is supported by the US National Science Foundation through the Faculty
Early Career Development (CAREER) Program, grant AST-1255591. CP is supported
by the Canadian Space Agency under a contract with NRC Herzberg Astronomy and
Astrophysics.

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