# NOEMA observations of GN-z11: Constraining Neutral Interstellar Medium and
Dust Formation in the Heart of Cosmic Reionization at $z=10.6$

Y. Fudamoto,1,2 P. A. Oesch,3,4 F. Walter,5 R. Decarli,6 C. L. Carilli,7 A.
Ferrara,8 L. Barrufet,3R. Bouwens,9 M. Dessauges-Zavadsky,3 E. J. Nelson,10 H.
Dannerbauer,11 G. Illingworth,12 A. K. Inoue,1,13R. Marques-Chaves,3 I. Pérez-
Fournon,11,14 D. A. Riechers,15 D. Schaerer,3 R. Smit,16 Y. Sugahara,1,2P. van
der Werf,17
1Waseda Research Institute for Science and Engineering, Faculty of Science and
Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan
2National Astronomical Observatory of Japan, 2-21-1, Osawa, Mitaka, Tokyo,
Japan
3Department of Astronomy, University of Geneva, Chemin Pegasi 51, 1290
Versoix, Switzerland
4International Associate, Cosmic Dawn Center (DAWN)
5Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
6INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, via
Gobetti 93/3, I-40129, Bologna, Italy
7National Radio Astronomy Observatory, P. O. Box 0,Socorro, NM 87801, USA
8Scuola Normale Superiore, Piazza dei Cavalieri 7, 50126 Pisa, Italy
9Leiden Observatory, Leiden University, NL-2300 RA Leiden, Netherlands
10Department for Astrophysical and Planetary Science, University of Colorado,
Boulder, CO 80309, USA
11Instituto de Astrofísica de Canarias (IAC), E-38205 La Laguna, Tenerife,
Spain
12Department of Astronomy and Astrophysics, University of California, Santa
Cruz, CA 95064, USA
13Department of Physics, School of Advanced Science and Engineering, Faculty
of Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku
, Tokyo 169-8555, Japan
14Universidad de la Laguna, Dpto. Astrofísica, E-38206 La Laguna, Tenerife,
Spain
15I. Physikalisches Institut, Universität zu Köln, Zülpicher Strasse 77,
D50937 Köln, Germany
16Astrophysics Research Institute, Liverpool John Moores University, 146
Brownlow Hill, Liverpool L3 5RF, United Kingdom
17Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The
Netherlands
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present results of dust continuum and [C ii]$\,158\,{\rm\mu m}$ emission
line observations of a remarkably UV-luminous ($M_{\rm UV}=-21.6$) galaxy at
$z=10.603$: GN-z11. Using the Northern Extended Millimeter Array (NOEMA),
observations have been carried out over multiple observing cycles. We achieved
a high sensitivity resulting in a $\lambda_{\rm rest}=160\,{\rm\mu m}$
continuum $1\,\sigma$ sensitivity of $13.0\,\rm{\mu Jy/beam}$ and a [C ii]
emission line $1\,\sigma$ sensitivity of $31\,\rm{mJy/beam\,km/s}$ using
$50\,\rm{km/s}$ binning with a $\sim 2\,{\rm arcsec}$ synthesized beam.
Neither dust continuum nor [C ii]$\,158\,{\rm\mu m}$ line emission are
detected at the expected frequency of $\nu_{\rm[CII]}=163.791\,\rm{GHz}$ and
the sky location of GN-z11. The upper limits show that GN-z11 is neither
luminous in $L_{\rm IR}$ nor $L_{\rm[CII]}$, with a dust mass $3\,\sigma$
limit of ${\rm log}(M_{\rm dust}/{\rm M_{\odot}})<6.5-6.9$ and with a [C ii]
based molecular gas mass $3\,\sigma$ limit of ${\rm log}(M_{\rm
mol,[CII]}/{\rm M_{\odot}})<9.3$. Together with radiative transfer
calculations, we also investigated the possible cause of the dust poor nature
of the GN-z11 showed by the blue color in the UV continuum of GN-z11
($\beta_{\rm UV}=-2.4$), and found that $\gtrsim 3\times$ deeper observations
are crucial to study dust production at very high-redshift. Nevertheless, our
observations show the crucial role of deep mm/submm observations of very high
redshift galaxies to constrain multiple phases in the interstellar medium.

###### keywords:

galaxies: formation – galaxies: ISM – (ISM:) dust, extinction

††pubyear: 2023††pagerange: NOEMA observations of GN-z11: Constraining Neutral
Interstellar Medium and Dust Formation in the Heart of Cosmic Reionization at
$z=10.6$–NOEMA observations of GN-z11: Constraining Neutral Interstellar
Medium and Dust Formation in the Heart of Cosmic Reionization at $z=10.6$

##  1 Introduction

The first few hundred million years after the Big Bang at redshifts of $z>10$
are the last major unexplored epoch in the history of the Universe. Recently,
the arrival of the JWST has opened a completely new window to observe the very
high redshift Universe. JWST/NIRCam’s unprecedented sensitivity at infrared
wavelengths has enabled confident photometric information on $z_{\rm phot}>10$
candidates detected over multiple bands (e.g., Castellano et al., 2022;
Finkelstein et al., 2022; Naidu et al., 2022; Hainline et al., 2023; Harikane
et al., 2023). At the same time, spectroscopy with JWST obtained multiple
emission lines in the rest-frame UV to optical wavelength, providing
unambiguous spectroscopic redshifts (e.g., Roberts-Borsani et al., 2022;
Morishita et al., 2022; Cameron et al., 2023; Bunker et al., 2023b; Boyett et
al., 2023; Matthee et al., 2023; Williams et al., 2023) and unprecedented
diagnostic power of interstellar medium (ISM) properties for the first time
(e.g., Carnall et al., 2023; Nakajima et al., 2023; Tacchella et al., 2022;
Sanders et al., 2023; Laseter et al., 2023). This started to reveal a detailed
picture of galaxy formation at $z>10$, which was extremely challenging to
reach before the JWST era (see Madau & Dickinson, 2014, for a review).

GN-z11 is the highest-redshift galaxy identified using the Hubble Space
Telescope (HST) and the Spitzer Space Telescope (Oesch et al., 2016). GN-z11,
was first identified from HST imaging data from the CANDELS survey (Bouwens et
al., 2010; Grogin et al., 2011; Koekemoer et al., 2011). In particular, it
lies in the CANDELS DEEP area in the GOODS-North field at RA, Dec$=$
12:36:25.46, +62:14:31.4 (J2000). GN-z11 was found to be the brightest galaxy
candidate at $z>10$ (Bouwens et al., 2015; Oesch et al., 2015). From HST
WFC3/IR G141 slitless grism spectroscopy, the galaxy had a redshift of $z_{\rm
grism}=11.09^{+0.08}_{-0.12}$ through the identification of the Ly$\alpha$
continuum break (Oesch et al., 2016).

Due to the extremely high UV-luminosity of $M_{\rm UV}=-21.6$, detailed JWST
observations of GN-z11 have already been performed. The JWST Advanced Deep
Extragalactic Survey (JADES; Eisenstein et al. 2023) obtained deep JWST
NIRSpec slit spectroscopy and confirmed its redshift to be $z=10.6034\pm
0.0013$ based on detections of multiple emission lines (Bunker et al., 2023a).
Together with photometric information obtained with JWST NIRCam imaging,
studies confirmed that GN-z11 is the most UV-luminous galaxy at $z>10$ known
to date (e.g., Harikane et al., 2023; Hainline et al., 2023). In particular,
the extremely compact morphology ($R_{\rm e}=64\pm 20\,{\rm pc}$; Tacchella et
al. 2023) and the large UV luminosity ($M_{\rm UV}=-21.6\pm 0.02$; Tacchella
et al. 2023) suggest that GN-z11 could represent very early onset of AGN
activity (Maiolino et al., 2023a) or that it shows possible signatures of
population-III stars in its surrounding blob (Maiolino et al., 2023b). At the
same time, the significant detection of nitrogen emission lines (NIV] 1486Å
and NIII] 1750Å) and the large over-abundance seen in the N/O ratio could
require a new scenario of nitrogen production and/or oxygen depletion (Cameron
et al., 2023), such as the formation of supermassive stars through stellar
collisions in an extremely dense environment (Charbonnel et al., 2023).

With the newly obtained detailed observations from JWST/NIRCam and
JWST/NIRSpec, GN-z11 remains one of the most important galaxies at $z>10$ to
understand gas fueling mechanism for galaxy growths and dust production in the
early Universe. To fully understand the formation of this remarkably luminous
galaxy and to constrain the formation mechanisms of massive galaxies at
$z>10$, it is essential to investigate multiple components of its interstellar
medium (ISM) as well as dust formation and dust-obscured star formation
activity. In addition to the rest-frame UV images and spectra, information
about the dust and neutral ISM properties from rest-frame far-infrared (FIR)
spectroscopy is thus required to provide a comprehensive picture arising from
observations covering a wide wavelength range (see Carilli & Walter, 2013;
Hodge & da Cunha, 2020, for reviews).

Here, we report millimeter wavelength observations of GN-z11 using the
Northern Extended Millimeter Array (NOEMA), targeting the dust continuum and
the [C ii]$\,158\,{\rm\mu m}$ emission line. Using the highly sensitive data
obtained for GN-z11, we constrain its ISM properties, dust-obscuration, as
well as dust production efficiency by comparing with dust enrichment and
geometry models from Ferrara et al. (2022).

This paper is organized as follows: in §2, we summarize the NOEMA observations
so far performed for GN-z11. In §3, we present our data analysis and
measurements for the [C ii]$\,158\,{\rm\mu m}$ emission line and $\lambda\sim
160\,{\rm\mu m}$ dust continuum. In §4, we present the results. We present
discussions in §5. Finally, we conclude with the summary in §6. Throughout
this paper, we assume a cosmology with
$(\Omega_{m},\Omega_{\Lambda},h)=(0.3,0.7,0.7)$, and the Chabrier (Chabrier,
2003) initial mass function (IMF), where applicable. With these cosmological
parameters, 1 arcsec corresponds to $4.0\,{\rm kpc}$ in proper coordinate and
the luminosity distance is $1.11\times 10^{5}\,{\rm Mpc}$ at $z=10.603$.

##  2 Observations

###  2.1 NOEMA Observations

Over the past years, NOEMA has targeted GN-z11 to search for the [C
ii]$\,158\,{\rm\mu m}$ emission line based on the redshift estimated from its
early photometric and grism data from HST to explore its emission in the FIR.
Deep NOEMA observations were conducted as separate observation projects across
four cycles in the years 2014, 2016, 2018, and 2019. We summarize these
observations in the following:

Observations in 2014: Using the WideX correlator, GN-z11 was observed by
scanning the frequency range between 161.9 and 176.3 GHz (PI: C. Carilli).
With 6 antennae, 4 different frequency settings were used. Each tuning has a
3.6GHz bandwidth. The total on-source time was 46.6 hours, most of the data
were taken in good to excellent conditions, and little flagging was required.
The spectral scan observations aimed to search for [CII] $158\,\mathrm{\mu m}$
emission line covering redshifts of $z\sim 9.78-10.74$, i.e., a photometric
redshift range estimated based on the HST and Spitzer photometry (Bouwens et
al., 2015; Oesch et al., 2015).

Observations in 2016: Using a single tuning with the WideX correlator, GN-z11
was observed with 8 antennae (PI: F. Walter and P. Oesch). The on-source time
was 5.2 hours in good weather conditions. Data calibration was done in a
standard manner at IRAM, and only minor flagging was required. The frequency
between $155.2-158.8\,\rm{GHz}$ was tuned to target [CII] emission line at
redshifts between $10.97-11.25$ based on the updated redshift estimation using
the HST grism spectroscopy (Oesch et al., 2016).

Observations in 2018: Deeper spectral scans were performed for GN-z11 with 9
antennae and with the newly installed Polyfix correlator in 2018 (PI: F.
Walter and P. Oesch). With a total on-source time of 17.4 hours, two Polyfix
tunings were used to cover the frequency range between
$152.9-163.6\,\rm{GHz}$. These observations aimed to observe [C ii] within the
redshift range of $z_{\rm[CII]}=10.62-11.43$. Compared to the 2016
observations, these observations were deeper and covered a wider frequency
range. The weather conditions were good. Data calibration was performed in a
standard manner at IRAM, and minor flagging was required.

Observations in 2019: Follow-up observations of GN-z11 were again performed
with 10 antennae with the Polyfix correlator (PI: F. Walter and P. Oesch).
Total on-source time was 11.4 hours. A single tuning of the Polyfix correlator
covered $156.9-164.6\,\rm{GHz}$, covering [C ii] redshifts between
$z_{\rm[CII]}=10.55-11.11$. Weather conditions were generally good and minor
flagging was required. We note that the observations in 2019 eventually
covered the [C ii] emission line from the actual spectroscopic redshift
($z_{\rm spec}=10.60$; Bunker et al., 2023a) of GN-z11 using the updated NOEMA
interferometer.

All the calibrations of phase, absolute flux, and amplitude were performed
using the GILDAS software111https://www.iram.fr/IRAMFR/GILDAS/ with the
support of IRAM astronomers.

###  2.2 JWST Observations

We obtained near-IR (NIR) images of GN-z11 from a JWST cycle-1 medium program
entitled “First Reionization Epoch Spectroscopic Complete Observation”
(FRESCO; Oesch et al. 2023). We used the F444W image as a sky location prior
for extracting a spectrum and searching for dust continuum emission associated
with GN-z11. A comprehensive description of the survey design, data reduction,
and analysis can be found in Oesch et al. (2023).

Using JWST NIRCam (Rieke et al., 2005), FRESCO performed deep slitless grism
observations in the northern and southern GOODS/CANDELS fields using F444W
filters with a medium spectral resolution of $R=1600$. Simultaneously, broad-
and medium-band images of the fields were acquired using the F444W, F210M, and
F182M bands. The imaging integration times were $0.26\,\rm{hours}$,
$1\,\rm{hours}$, and $1.2\,\rm{hours}$ per pointing for F444W, F210M, and
F182M bands, respectively. The data were reduced using the grizli software
(v1.7.11), which is publicly available (Brammer, 2018; Brammer et al., 2022).
The $5\,\sigma$ depth of the observations for the F444W imaging is $\sim
28.2\,{\rm mag}$ for imaging observations (Oesch et al., 2023).

##  3 Analysis

###  3.1 Dust Continuum, IR Luminosity, and Dust Mass

Using the GILDAS package CLIC, the combined continuum uv-table of GN-z11 was
made using all existing NOEMA data. We then imaged the continuum data using
the GILDAS Mapping package using a pixel size of $0.4^{\prime\prime}$. The
resulting continuum map has a synthesized beam full-width-at-half-maximum
(FWHM) of $2.05^{\prime\prime}\times 1.83^{\prime\prime}$, and an RMS of
$13\,\rm{\mu Jy/beam}$. In the continuum image, we only find a $\sim
2\,\sigma$ signal $\sim 1^{\prime\prime}$ offset from GN-z11, and found no
clear signals co-located with the JWST NIRCam F444W detection of GN-z11 (Fig.
1). Thus, we concluded that the dust continuum of GN-z11 is not detected from
the existing NOEMA observations.

As the dust continuum is not detected, we estimated upper limits for the dust
continuum emission and IR luminosity. Using the RMS of the continuum image, we
obtained a $3\,\sigma$ upper limit of $<39\,\rm{\mu Jy}$. The upper limit of
IR luminosity is then estimated by assuming a FIR SED for the GN-z11 by
integrating a modified blackbody function between the rest-frame wavelength of
$8-1000\,{\rm\mu m}$. In particular, we assumed a dust temperature of
$T_{d}=82\,\rm{\rm K}$ by extrapolating a dust temperature evolution estimated
in Sommovigo et al. (2022)222We assumed transmissivity of the ISM to be
$T=0.9$ as assumed by Fujimoto et al. (2022), and a gas phase metallicity of
$0.04\,{\rm Z_{\odot}}$ obtained in the SED fitting in Tacchella et al. (2023)
. The derived dust temperature of $82\,\rm{\rm K}$ is much higher (by $\gtrsim
30\,\rm{K}$) than those of $z\sim 7$ galaxies (e.g., Algera et al., 2023) but
consistent with that currently estimated from one of the highest redshift dust
detection at $z=8.31$ ($>80\,{\rm K}$; Bakx et al., 2020). We discuss impacts
of assuming a lower dust temperature in §3.1.1. We also assumed a dust
emissivity index of $\beta=2.0$ as is also assumed when estimating $T_{\rm d}$
in Sommovigo et al. (2022), and applied a correction of the cosmic microwave
background (CMB) attenuation based on da Cunha et al. (2013). Due to the high
CMB temperature of $31.7\,\rm{K}$ at $z=10.603$, the CMB attenuation with the
assumed dust temperature is large and we need to multiply the dust continuum
emission by $1/0.88$. Finally, we obtained a $3\,\sigma$ upper limit for the
IR luminosity of $<3.6\times 10^{12}\,{\rm L_{\odot}}$.

Using the $3\,\sigma$ continuum upper limit and the assumed dust temperature
of $T_{\rm d}=82\,{\rm K}$, we estimated a dust mass upper limit in GN-z11. We
used a dust mass absorption coefficient of
$\kappa_{d}(\lambda_{\mathrm{rest}})=30\times(100\,{\rm\mu
m}/\lambda_{\mathrm{rest}})^{\beta}\,\mathrm{cm^{2}\,g^{-1}}$ (Inoue et al.,
2020), which is estimated as a typical value from different dust compositions
and temperatures using laboratory experiments (e.g., Mennella et al., 1998;
Chihara et al., 2001; Boudet et al., 2005). We then applied a correction for
the CMB and obtained a dust mass upper limit of ${\rm log\,}(M_{\rm
d}\,/\,\rm{M_{\odot}})<6.5$ ($3\,\sigma$).

####  3.1.1 Dust Temperature Uncertainty

The typical dust temperature of star-forming galaxies at very high redshift is
unconstrained from observations. Moreover, the assumed dust temperature has a
large impact on the estimated IR luminosity (see discussion e.g., by Ferrara
et al. 2017; Ma et al. 2019; Fudamoto et al. 2020; Faisst et al. 2020; Lower
et al. 2023). Especially, our assumed dust temperature is much higher than
those directly measured in lower redshift galaxies (e.g., $T_{\rm d}\sim
45\,{\rm K}$ at $z\sim 5-7$; Liang et al. 2019; Béthermin et al. 2020; Faisst
et al. 2020; Algera et al. 2023). Thus, to test the assumed dust temperature
and to understand its impact on the IR luminosity upper limit, we employed an
alternative method to estimate a dust temperature limit.

We tested the assumed dust temperature using the FIS22 code presented in
Fudamoto et al. (2022). FIS22 uses simple assumptions about star-to-ISM
geometry and the radiation equilibrium between dust attenuation and re-
emission. Using the measured size of the star-forming region, the code allows
us to obtain estimations of dust temperature from a single FIR continuum
observation. To estimate the limit, we assumed the size of the star-forming
region from the UV emission (i.e., $R_{\rm e}=64\pm 20\,{\rm kpc}$; Tacchella
et al. 2023), and the average ISM clumpiness parameter of ${\rm log\,\xi_{\rm
clp}}=-1.02$ as found in Fudamoto et al. (2022). With a fixed size and an
upper limit on FIR emission, we are able to obtain a lower limit on dust
temperature. With the assumed dust size and UV luminosity of $L_{\rm
UV}=7.40\pm 0.01\times 10^{11}\,\rm{L_{\odot}}$, we obtained $T_{\rm
d}>54\,{\rm K}$. The derived lower limit indeed supports the high dust
temperature of $T_{\rm d}$ assumed in our calculation. We note that the
estimated dust temperature and its limit is still uncertain as the method
assumes that the dust has the same spatial distribution as the UV emission.
Nevertheless, we use the $T_{\rm d}=54\,{\rm K}$ as a lower limit case as it
currently gives the lowest $T_{\rm d}$ estimation.

In this lower limiting dust temperature case of $T_{\rm d}=54\,{\rm K}$, we
find the $3\,\sigma$ upper limit of IR luminosity to be $<7.7\times
10^{11}\,{\rm L_{\odot}}$ (i.e., $\sim\times 5$ smaller than that found by
assuming $T_{\rm d}=82\,{\rm K}$). We further noticed that a dust temperature
assumption lower than $50\,{\rm K}$ does not change the IR luminosity upper
limit as the CMB correction becomes large and mitigates the difference of the
dust temperature assumption. Thus, a systemic uncertainty of a factor $\sim 5$
is very conservative. In the following discussions, we derive several
estimates based on assuming the $82\,{\rm K}$ and $54\,{\rm K}$ dust
temperatures.

Figure 1: $8^{\prime\prime}\times 8^{\prime\prime}$ cutout of the JWST F444W
image obtained by the FRESCO JWST survey (background; Oesch et al. 2023) and
dust continuum (orange contours) of GN-z11: Solid contours show 1, 2$\,\sigma$
and dashed contours show -3, -2, -1$\sigma$ where $1\,\sigma=13.0\,\mathrm{\mu
Jy/beam}$. The white ellipse in the lower left corner shows the synthesized
beam FWHM of the combined dust continuum image ($2.1^{\prime\prime}\times
1.8^{\prime\prime}$).

###  3.2 [C ii]$\,158\,{\rm\mu m}$ Emission Line

Figure 2:  Left Panel:  The NOEMA spectrum of GN-z11 with $50\,\mathrm{km/s}$
binning. The gray solid line shows the RMS of each channel. The NOEMA
observation covers [C ii]$\,158\,\rm{\mu m}$ emission line of GN-z11 at the
observed frequency of $\nu_{\rm obs}=163.84\,{\rm GHz}$ with the $z_{\rm
spec}=10.60$ (Red line). From the data cube and extracted spectrum, we do not
find any signal of the [C ii] emission line. Right panel:
$8^{\prime\prime}\times 8^{\prime\prime}$ cutout of JWST F444W image
(background) and [C ii] emission line moment-0 map (contours) of GN-z11.
Contours show 1, 2, 3$\sigma$ and dashed contours show -3, -2, -1$\sigma$. The
moment-0 map of the data cube is made by integrating over the $150\,\rm{km/s}$
of the [C ii] emission line frequency. RMS of the image is $29\,{\rm
mJy\,km/s}$, providing a $3\,\sigma$ upper limit of [C ii] luminosity
$<1.7\times 10^{8}\,{\rm L_{\odot}}$.

The sky frequency of the [C ii]$\,158\,{\rm\mu m}$ emission line of GN-z11,
$\nu_{\rm[CII]-sky}=163.791\,{\rm GHz}$, is covered by the observations in
2014 and 2019. From these observations, we focus on the observations of 2019
in our analysis which has much higher sensitivity than that of 2014 by using
upgraded receivers with ten antennae. Using the GILDAS Mapping package, we
created a data cube with $50\,{\rm km/s}$ spectral binning with a pixel
angular size of $0.4^{\prime\prime}$. The resulting data cube has a RMS of
$\sim 0.31\,{\rm mJy/beam}$ in the $50\,{\rm km/s}$ binning at
$\nu=163.791\,{\rm GHz}$.

We then extracted a spectrum of GN-z11 using a circular aperture with a radius
of $r=1^{\prime\prime}$ on top of the JWST detection of GN-z11 (left panel of
Fig. 2). The $1^{\prime\prime}$ radius is consistent with the NOEMA beam size.
At the frequency of [C ii] at $z=10.603$, we only find $<1\,\sigma$ signals in
the spectra. To search for any spatially off-set signals, we further created a
[C ii]$\,158\,\rm{\mu m}$ emission moment-0 map. To create the [C ii] moment-0
image, we assumed the line width of [C ii] emission to be $150\,{\rm km/s}$,
which is consistent with recent FIR emission line observations of $z>9$
galaxies (e.g., Hashimoto et al., 2018). In the surrounding area of the
GN-z11, we only find $\sim 1\,\sigma$ signals (Fig. 2) which is much lower
than the typical secure detection thresholds for lines with well-known sky
location and spectroscopic redshift (e.g., $>3.5\,\sigma$; Béthermin et al.
2020). Based on these results, we concluded that the [C ii]$\,158\,\rm{\mu m}$
emission line is not detected in the current NOEMA data.

Based on the non-detection, we measured a $3\,\sigma$ upper limit of the [C
ii] emission line luminosity by measuring three times the pixel-by-pixel RMS
of the moment-0 map. We obtained a $3\,\sigma$ [C ii] flux upper limit of
$0.087\,\rm{Jy\,km/s}$, and $L_{\rm[CII]}$ upper limit of GN-z11 of
$<1.7\times 10^{8}\,{\rm L_{\odot}}$.

NOEMA Measurements
---
$f_{\rm[CII]}$ |  $<29\,{\rm mJy\,km/s}$ ($3\,\sigma$ limit)
${\rm log\,}(L_{\rm[CII]}\,/\,\rm{L_{\odot}})$ |  $<8.2$ ($3\,\sigma$ limit)
$f_{\rm cont,160\,{\mu m}}$ |  $<39\,\rm{\mu Jy}$ ($3\,\sigma$ limit)
${\rm log\,}(L_{\rm IR}\,/\,\rm{L_{\odot}})$ |  $<12.5$ (with $T_{\rm d}=82\,{\rm K}$)
|  $<11.9$ (with $T_{\rm d}=54\,{\rm K}$)
${\rm log\,}(M_{\rm d}\,/\,\rm{M_{\odot}})$ |  $<6.5$ (with $T_{\rm d}=82\,{\rm K}$)
|  $<6.9$ (with $T_{\rm d}=54\,{\rm K}$)
| and $\kappa_{d}(\lambda_{\mathrm{rest}})=30\times(100\,{\rm\mu
m}/\lambda_{\mathrm{rest}})^{\beta}\,\mathrm{cm^{2}\,g^{-1}}$)
Table 1: Measured properties of GN-z11 from NOEMA observations.

##  4 Results

###  4.1 Dust Obscured Star Formation Activity of GN-z11

With the relatively high upper limit of $L_{\rm IR}$, the dust-obscured star
formation rate is only weakly constrained with ${\rm SFR_{IR}}<430\,{\rm
M_{\odot}\,yr^{-1}}$ with $T_{\rm d}=82\,{\rm K}$ and $<92\,{\rm
M_{\odot}\,yr^{-1}}$ with $T_{\rm d}=54\,{\rm K}$ assuming a conversion of
${\rm SFR_{IR}}=1.2\times 10^{-10}\,L_{\rm IR}\,{\rm
M_{\odot}\,yr^{-1}\,L_{\odot}^{-1}}$ (Madau & Dickinson, 2014; Inami et al.,
2022). The weak upper limit on ${\rm SFR_{IR}}$ despite the deep continuum
observations is due to the assumed high dust temperature of $T_{\rm
d}=82\,{\rm K}$ and $54\,{\rm K}$. Using these limits, the infrared excess
(IRX$={\rm log}(L_{\rm UV}/L_{\rm IR})$; Meurer et al. 1999) $3\,\sigma$ limit
of GN-z11 is estimated to be $>-0.9$ to $>-1.5$. To further constrain the dust
obscured star formation activity of GN-z11, accurate constraints on the dust
temperature is essential via deep observations at wavelengths $<1\,{\rm mm}$.

With the estimated stellar mass of $\sim 10^{9}\,{\rm M_{\odot}}$ (Tacchella
et al., 2023), the dust mass upper limit shows a stellar-to-dust mass ratio of
$\xi_{\rm d}\lesssim 0.003$ for $T_{\rm d}=82\,{\rm K}$ and $\xi_{\rm
d}\lesssim 0.008$ for $T_{\rm d}=54\,{\rm K}$. These limits are consistent
with typical values in lower redshift galaxies (e.g., Calura et al., 2017;
Dayal et al., 2022).

###  4.2 [C ii]$\,158\,\rm{\mu m}$ Emission Line

Figure 3: Star formation rate versus [C ii] emission line luminosity of
GN-z11. Previous observations of $z>6$ are also plotted with gray points
(Harikane et al. 2020; Fudamoto et al. 2023; Schouws et al. 2022 and
references therein). Downward triangles show $3\,\sigma$ upper limit in case
of non-detections. Lines show previously obtained relations for low- and high-
redshift galaxies (solid: Schaerer et al. 2020, Dashed: De Looze et al. 2014).
For the SFR of GN-z11, we adopted the SED fitting results of
$21^{+22}_{-10}\,{\rm M_{\odot}\,yr^{-1}}$ from Tacchella et al. (2023).

To compare the star formation activity and $L_{\rm[CII]}$ of GN-z11, we
adopted the total star-formation rate (SFR) of $21^{+22}_{-10}\,{\rm
M_{\odot}\,yr^{-1}}$ obtained in the spectral energy distribution (SED)
fitting in Tacchella et al. (2023). We find that based on the upper limit
$L_{\rm[CII]}$ from our measurement, GN-z11 has $L_{\rm[CII]}$ consistent with
or slightly smaller than that of low redshift similarly star-forming galaxies
(Fig. 3). Although few observational studies of the SFR-$L_{\rm[CII]}$
relation for galaxies at $z>10$, this shows that the [C ii] luminosity of
GN-z11 is not enhanced compared with the relation obtained for star-forming
galaxies at lower redshifts.

The existence of an active galactic nucleus (AGN) was proposed in GN-z11 based
on the significant detection of [Neiv]$\,\lambda 2423$ using deep NIRSpec
observation (Maiolino et al., 2023a). If the rest-frame UV emission of GN-z11
is dominated by AGN activity, the SFR of GN-z11 might be overestimated and
thus our constraints on the SFR-$L_{\rm[CII]}$ relation of GN-z11 should be
lifted.

##  5 Discussion

###  5.1 Molecular gas mass and gas depletion time scale at $z=10.6$

Figure 4: Evolution of the molecular mass fraction ($f_{\rm molgas}=M_{\rm
molgas}/(M_{\rm molgas}+M_{\rm star0})$) across a wide redshift range. Various
indicators are used to estimate molecular gas mass: CO emission lines and dust
continuum at $z<4$ (Dessauges-Zavadsky et al. 2017; Scoville et al. 2017;
Tacconi et al. 2018, 2020, see also Boogaard et al. 2020), [C ii] emission
lines at $4<z<6$ from the ALPINE survey (Dessauges-Zavadsky et al., 2020) and
at $z\sim 7$ from the REBELS survey (Aravena et al. submitted). Data points
for the $z<8$ samples represent mean values and errorbars are 16th to 84th
percentiles within the distribution. Upper limit of GN-z11 is within the range
of $z>4$ galaxy observations.

Recent studies showed that the dominant fraction of [C ii]$\,158\,{\rm\mu m}$
emission lines arise from neutral gas, such as neutral photo-dissociation
regions (PDRs). In particular, luminous galaxies typically have $>80\%$ of the
[C ii] emission originate from the PDRs (Díaz-Santos et al., 2017). For high-
redshift galaxies, this feature is further supported by detailed calculations
and observations of emission lines arising from HII regions (Decarli et al.,
2014; Witstok et al., 2022; Decarli et al., 2022). This makes the [C
ii]$\,158\,{\rm\mu m}$ emission line an excellent tracer of star-forming
neutral gas (e.g., Zanella et al., 2018; Sommovigo et al., 2021).

Using the formalism presented in Zanella et al. (2018), we estimate the upper
limit of the molecular gas mass of GN-z11 to be ${\rm log\,}(M_{\rm
mol}\,/\,\rm{M_{\odot}})<9.7$. With the estimated stellar mass of $\sim
10^{9}\,{\rm M_{\odot}}$ (Tacchella et al., 2023), the molecular gas fraction
($f_{\rm mol}=M_{\rm mol}/(M_{\rm star}+M_{\rm mol})$) of GN-z11 is $f_{\rm
mol}<0.83$ ($3\,\sigma$). The upper limit from the [C ii] observations is
largely consistent with lower redshift galaxies (Fig. 4). With the estimated
star formation rate of $21\,{\rm M_{\odot}\,yr^{-1}}$ (Tacchella et al.,
2023), the molecular gas depletion time of GN-z11 is $t_{\rm depl}<0.2\,{\rm
Gyr}$ ($3\,\sigma$). While the contribution from the AGN to the UV-luminosity
is needed to estimate a more accurate SFR, the result suggests that GN-z11
might deplete all molecular gases before $z\gtrsim 8$, unless molecular gas is
rapidly replenished by accretion.

Recent CO and [CI] emission line observations using $z\sim 6$ AGNs suggest
that [C ii] based molecular gas mass measurements could be systematically
higher by $\sim 0.5\,{\rm dex}$ compared with those estimated from [Ci] and/or
CO observations (Neeleman et al., 2021; Decarli et al., 2022). Thus if the
$\sim 0.5\,{\rm dex}$ over-prediction is the case for our estimations, the
upper limit might need to be systematically lowered, providing stronger
constraints. Deeper observations of the [C ii] emission line and observations
of other molecular gas indicator (e.g., emission lines from [CI] and/or CO)
will be crucial to further constrain these essential parameters of galaxy
growth.

###  5.2 Expected dust opacity and constraints on the dust formation

Here, we compare our dust continuum upper limits with recent theoretical
analysis of $z>10$ UV-luminous galaxies (e.g., Ferrara et al., 2023).

Ferrara et al. (2023) discussed that the JWST based finding of very blue and
compact galaxies was surprising. Indeed, the observed dust optical depth at
the rest-frame $1500\,{\rm\AA}$ deduced for GN-z11 is $\tau_{1500}=0.49$
(corresponding to $A_{V}=0.17$, Bunker et al. 2023b). This low value does not
agree with the expected dust optical depth estimated from the extremely
compact effective radius ($r_{\rm e}=64\,{\rm pc}$; Tacchella et al. 2023) and
the dust mass associated with the estimated massive stellar mass ($\sim
10^{9}\,{\rm M_{\odot}}$). By assuming a standard dust-to-stellar mass ratio
$\xi_{d}\sim 0.002$, appropriate for a Salpeter IMF ($1-100\,{\rm M_{\odot}}$)
and a dust yield of $0.1\,{M_{\odot}}$ per supernova, we estimate a dust mass
of $M_{\rm d}\sim 10^{6}\,{\rm M_{\odot}}$ (e.g., Hirashita et al., 2014). If
UV and dust are co-located in the tiny $\sim 64\,{\rm pc}$ region, using the
calculation performed in Ferrara et al. (2023), we estimated that the
resulting optical depth would be $\tau_{1500}\sim 500$, i.e. far exceeding the
observed value.

The dust envelope can be made less opaque if the dust has a spatial
distribution that is much more extended than the stellar $r_{e}$. In
particular, assuming a spherical dust distribution, the observed value
$\tau_{1500}=0.49$ is recovered if the dust distribution is expanded out to
$r\sim 30\times r_{\rm e}$ to $100\times r_{\rm e}$ (i.e., $\sim 2\,{\rm kpc}$
to $\sim 6.4\,{\rm kpc}$). Physically, this configuration can be achieved, for
example, as a result of an outflow emanating from the galaxy. The presence of
radiation-driven dusty outflows could arise from the super-Eddington nature of
galaxies like GN-z11 (Ferrara et al., 2023; Ziparo et al., 2023; Fiore et al.,
2023).

In our observations, we find a $\lambda_{\rm rest}=160\,{\rm\mu m}$ dust
continuum of $<13\,{\rm\mu Jy}$ at $1\,\sigma$ ($<26\,{\rm\mu Jy}$,
$2\,\sigma$). This value is higher than the predicted one at any stage during
the outflow expansion. In fact, when the outflow has expanded the dust
distribution so as to produce the observed value of $\tau_{1500}$, we predict
that the $160\,{\rm\mu m}$ flux should be $4.5\,{\rm\mu Jy}$, hence about 3
times below our upper limit. Clearly, uncertainties are related to the assumed
value of $\xi_{d}$. The present observations, however, can be used to obtain a
limit on $\xi_{d}<0.014$ at $1\,\sigma$ ($\xi_{d}<0.32$ at $2\,\sigma$), which
translates a predicted upper limit on the dust mass of $<7\times 10^{6}\,{\rm
M_{\odot}}$ $(<1.6\times 10^{8}\,{\rm M_{\odot})}$. Thus, at least $3\times$
deeper continuum observations would be crucial to provide constraints on dust
formation at $z>10$ and to test the proposed scenario to explain the very blue
color of high-redshift massive compact galaxies.

##  6 Conclusion

In this paper, we present results based on NOEMA observations of GN-z11
targeting the [C ii]$\,158\,\rm{\mu m}$ emission line and the underlying dust
continuum from a UV luminous star-forming galaxy GN-z11 at $z=10.60$. We found
the following results:

$\bullet$ Although NOEMA observations were extremely deep and covered the sky
frequency of the [C ii]$\,158\,{\rm\mu m}$ emission line, we did not detect
either [C ii]$\,158\,{\rm\mu m}$ or dust continuum. We reported $3\,\sigma$
upper limits of the [C ii] luminosity ($L_{\rm[CII]]}<1.7\times 10^{8}\,{\rm
L_{\odot}}$) and the IR luminosity ($L_{\rm IR}<3.6\times 10^{12}\,{\rm
L_{\odot}}$).

$\bullet$ Based on the upper limits, we found that GN-z11 is not bright either
in [C ii] emission or dust continuum. The upper limit $L_{\rm[CII]}$ of GN-z11
is consistent or could be slightly smaller than that predicted from the
SFR-$L_{\rm[CII]}$ relation observed from lower redshift galaxies at $z<8$.

$\bullet$ As [C ii] emission mostly traces the neutral ISM, we estimate a
molecular gas mass for GN-z11 using the relation in Zanella et al. (2018). We
find an upper limit of $M_{\rm mol}<5.0\times 10^{9}\,{\rm M_{\odot}}$, and a
depletion time of $<0.2\,{\rm Gyr}$, suggesting that the GN-z11 could deplete
all the star-forming gas by $z\gtrsim 8$.

$\bullet$ The blue color ($\beta=-2.4$) suggests that GN-z11 is dust poor,
which is consistent with the non-detection of dust continuum. The current
upper limit is $>\times 2$ above the expected continuum flux density expected
assuming typical dust production.

Our observations of GN-z11 showcase the crucial constraints that submm/mm
observations can provide for very early galaxies.

## Acknowledgements

This work is based on observations carried out under project number XACE,
XBCE, XCCE, XDCE, S16CQ, W17FD, and W18FD with the IRAM NOEMA Interferometer.
IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). YF,
AKI, YS acknowledge support from NAOJ ALMA Scientific Research Grant number
2020-16B. YF further acknowledges support from support from JSPS KAKENHI Grant
Number JP23K13149. PAO acknowledges support from the Swiss National Science
Foundation through project grant 200020_207349. The Cosmic Dawn Center (DAWN)
is funded by the Danish National Research Foundation under grant No. 140. HD
acknowledges financial support from the Agencia Estatal de Investigación del
Ministerio de Ciencia e Innovación (AEI-MCINN) under grant (La evolución de
los cíumulos de galaxias desde el amanecer hasta el mediodía cósmico) with
reference (PID2019-105776GB-I00/DOI:10.13039/501100011033).

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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