New constraints on the molecular gas content of a z ∼ 8 galaxy from JVLA CO(J=2-1) observations

As the primary fuel for star formation, molecular gas plays a key role in galaxy evolution. A number of techniques have been used for deriving the mass of molecular reservoirs in the early Universe (e.g., [CII]158 𝜇 m, [CI], dust continuum), but the standard approach of CO-based estimates has been limited to a small number of galaxies due to the intrinsic faintness of the line. We present Jansky Very Large Array (JVLA) observations of the 𝑧 ∼ 8 . 31 galaxy MACS0416_Y1, targeting CO(2-1) and rest-frame radio continuum emission, which result in upper limits on both quantities. Adding our continuum limit to the published far-infrared (FIR) spectral energy distribution (SED), we find a small non-thermal contribution to the FIR emission, a low dust mass (log 10 ( M D / M ⊙ ) ∼ 5), and an abnormally high dust temperature (T D ≳ 90 K) that may indicate a recent starburst. Assuming a low metallicity ( 𝑍 / 𝑍 ⊙ ∼ 0 . 25), we find evidence for 𝑀 H 2 , CO ≲ 10 10 M ⊙ , in agreement with previous [CII] investigations ( 𝑀 H 2 , [ CII ] ∼ 10 9 . 6 M ⊙ ). Upcoming JWST observations of this source will result in a precise determination of 𝑍 , enabling better constraints and an unprecedented view of the gaseous reservoir in this primordial starburst galaxy


INTRODUCTION
Molecular gas reservoirs in galaxies act as potential fuel for future star formation.This gas may be accreted from cosmic filaments or through collisions with gas-rich companions (i.e., 'wet' mergers).Recent observations suggest that the cosmic density of molecular gas increased from early times until a peak between  ∼ 3 and  ∼ 1 and decreased to the present day (e.g., Decarli et al. 2019;Aravena et al. 2023;Boogaard et al. 2023).This evolution matches the cosmic density of star formation rate (e.g., Bouwens et al. 2020), suggesting that star formation in early galaxies ( > 4, or ≲ 1.5 Gyr after the Big Bang) was powered by gas accreted from past mergers and inflows.
Using the Jansky Very Large Array (JVLA), we observed this object in CO(2-1) emission and rest-frame radio continuum emission.While this resulted in a non-detection, it enables us to place new constraints on the molecular gas content, non-thermal emission, and dust properties in this high-redshift source.We use a standard concordance cosmology (ℎ  , Ω  , Ω Λ = 0.7, 0.3, 0.7) throughout, where 1 ′′ ∼ 4.7 kpc at  ∼ 8.31.

DATA CALIBRATION AND IMAGING
Our observations were taken with the JVLA in A-configuration over nine 3 hr executions between 24 December 2020 -29 January 2021 under the partially completed project 20B-194.The bandpass and flux calibrator was 3C147, while J0416-1851 was used as a phase calibrator.In order to target CO(2-1) at 24.758 GHz, we used two basebands in , each with eight spectral windows (SPWs) of 64 channels of 2 MHz.
Due to an error in scan intent declarations, the flux and bandpass calibration scans were unusable, so an extra 30 minute scan of the phase calibrator was taken.Since J0416-1851 is a high-quality ('P'grade) calibrator, we were able to use these observations to determine its flux and thus use it as a flux/bandpass calibrator for the previous scans.
The nine executions were calibrated using the Common Astronomy Software Applications package (CASA; CASA Team et al. 2022) using a standard high-frequency calibration pipeline, but with a manual flux calibration (i.e., no CASA fluxscale) due to the observation setup.The resulting visibilites were inspected, and additional flagging of bad antennas and edge flagging was performed before the pipeline was re-run.One execution was excluded because of significant calibration issues.
Continuum images were created using CASA tclean with the linefree SPWs of all acceptable executions in multifrequency synthesis (MFS) mode with natural weighting.This results in a synthesised beam of 0.19 ′′ × 0.09 ′′ at 180.0 • and root mean square (RMS) noise level of 1.9 Jy beam −1 .
The basebands of each execution that contained redshifted CO(2-1) emission were separated (CASA split), combined into a single 1.9 Jy beam −1 ).For reference, we include a three-colour image of HST/WFC3 (F105W/F125W/F140W).The synthesised beam is represented by a filled red ellipse to the lower left, while the assumed aperture of MACS0416_Y1 is given as a hollow white ellipse.measurement set (CASA concat), and imaged (CASA tclean in 'cube' mode, natural weighting, 6 MHz channels), resulting in a cube with a mean synthesised beam of 0.17 ′′ × 0.09 ′′ at 180.1 • and a mean RMS noise level per channel of ∼ 30 Jy beam −1 .Since no continuum emission is detected (see Section 3.1), we do not perform continuum subtraction.

Continuum
No significant emission is detected in our continuum image (  ∼ 25 GHz), as seen in Figure 1.To place a conservative estimate on the continuum emission, we use a large elliptical aperture of double the deconvolved [OIII]88m full width at half maximum (FWHM) of Tamura et al. (2019), resulting in 1.0 ′′ × 0.6 ′′ .This implies a 3 upper limit of  12 < 28 Jy.Here, we combine this upper limit with archival continuum flux density values to examine the constraints on dust properties and SFR that these implies.
Only three FIR continuum observations have been published to date: S 850 m = 137 ± 26  Jy and S 1.5 mm < 18  Jy from Tamura et al. (2019), and S 1.14 mm < 174  Jy from Bakx et al. (2020), where each limit is 3.Several other ALMA programs have targeted the 850 m and 1.14 mm emission, so future works may combine them to place tighter estimates on each flux density.However, only one program has targeted this source at ∼ 3.2 mm (band 3, 2021.1.00075.S; PI Ono).We apply the ALMA staff calibration (i.e., ScriptForPI.py) to the raw data and create a 3.2 mm continuum image using CASA tclean with MFS mode, natural weighting, and a conservative frequency range to exclude possible line emission.This results in a continuum non-detection, and a 3 upper limit of S 3.2 mm < 21  Jy.
We begin by adopting the modified blackbody (MBB) model of Carniani et al. (2019), which includes the cosmic microwave background (CMB) corrections of da Cunha et al. ( 2013) and makes no assumption on optical depth.If we assume the dust is emitted from approximately the same area as the [OIII] emission and adopt a dust absorption coefficient of   = 0.04 m 2 kg −1 at a critical density of 250 GHz (Beelen et al. 2006), then this model is reduced to three free parameters: the dust mass (M D ), dust temperature (T D ), and dust emissivity index (   ).To extend this model to lower frequencies, we include the non-thermal emission (i.e., combined synchrotron and free-free) model of Algera et al. (2021), which also only has three free variables: the synchtrotron slope (   ), a normalisation factor (  ′ ), and the fraction of flux from the free-free component (   ℎ ).
With only one detection and four upper limits, we cannot place constraints on all six free parameters of this model simultaneously.Instead, we may explore the constraints that our radio and FIR points give.First, we assume standard values for    = 0.8 and   ℎ = 0.1 (e.g., Condon 1992;Algera et al. 2021), and normalise the non-thermal emission so that our continuum limits are met (see 'MaxR' results in left panel of Figure 2).This results in a limit of S 1.4 GHz < 120  Jy, or a SFR 1.4GHz limit of ≲ 2.5 × 10 4 M ⊙ year −1 (Condon 1992).This is much greater than the expected SFR of this object (SFR∼ 60 − 100 M ⊙ year −1 ; Bakx et al. 2020), so this limit is not highly constraining.Since the radio continuum point is not informative, we may assume a smaller SFR∼ 10 2 M ⊙ year −1 , which implies a much smaller radio contribution (see 'MinR' results in right panel of Fig. 2).
In both cases of radio emission ('MaxR' and 'MinR'), we examine the FIR portion of the SED by assuming a dust temperature (40 K, 85 K, or 130 K) and explore what M D and    values are required for a given dust temperature to satisfy the  850  detection and  1.5  non-detection.We find that a larger non-thermal contribution requires a smaller dust mass and steeper spectrum (i.e., higher    ).On the other hand, a higher dust temperature requires a larger dust mass and shallower slope, and results in a higher FIR luminosity (area between the dashed vertical lines) and thus SFR    .
Since this SED only contains a single point, these models are for illustration only.But given the SFR of this source and the fact that    values greater than ∼ 2.5 are rarely seen (e.g., Witstok et al. 2023), it is likely that: i.) Non-thermal emission does not significantly contribute to the FIR luminosity, ii.)The dust temperature is high (≳ 90 K), and iii.)The dust mass is quite small (M D ∼ 10 5 M ⊙ ).These last two conclusions are in agreement with the SED analysis of Bakx et al. (2020).
Note that these dust masses are smaller than that of Tamura et al. (2019, M D = 4 × 10 6 M ⊙ ), who assumed    = 1.5, T D = 50 K, and a different dust absorption coefficient.The primary difference is their use of a UV-to-FIR SED model that includes dust attenuation and scaled FIR templates, rather than our use of a single MBB with a flexible    and T D = 50 K.We are unable to recreate a model that uses    = 1.5 and T D = 50 K and obeys S 850 m = 137 ± 26  Jy and S 1.5 mm < 18  Jy, suggesting that a future flexible UV-to-FIR SED model is required.
Briefly, we note that the derived luminosity-weighted dust temperature limit implied by our exploration (T D ≳ 90 K) is much higher than commonly used mass-weighted dust temperatures at low-redshift (T D = 25 K; Scoville et al. 2016), as well as other high-redshift luminosity-weighted values (e.g.; T D ∼ 40 − 70 K at  ∼ 5 − 7, Bakx et al. 2021;Ikarashi et al. 2022;Jarugula et al. 2021;Manning et al. 2022;Vieira et al. 2022).While dust temperature has been found to increase with redshift (e.g., Bouwens et al. 2020;Witstok et al. 2023;Jones & Stanway 2023), most correlations would predict T D ∼ 60 − 70 K at  = 8.31.The fact that we predict a higher temperature could be interpreted in multiple ways: i.) MACS0416_Y1 may contain abnormally warm dust due to its high specific SFR (e.g., Liang et al. 2019;Mitsuhashi et al. 2023), ii.)The correlation between redshift and dust temperature is exponential rather than linear (e.g., Viero et al. 2022), or iii.)The current dataset (a single point and multiple upper limits) and/or model (modified blackbody) are insufficient to describe the dust properties.Since many studies of dust properties at high-redshift use a single FIR continuum detection and assume a dust temperature or template (e.g., Béthermin et al. 2020;Fudamoto et al. 2021;Bowler et al. 2023), more observations are required to resolve this ambiguity.

Molecular gas
A spectrum extracted from our combined data cube using an ellipse centred on the expected location of MACS0416_Y1 is shown in Figure 3.It is clear that the observed spectrum (black line) shows no significant line emission.If there was indeed 10 10 M ⊙ of molecular gas, then we would expect the line profile shown by the red Gaussian (peak amplitude=0.097mJy, FWHM= 200 km s −1 ; assuming   = 0.8 M ⊙ (   −1  2 ) −1 ), which peaks at < 1.That is, we lack the sensitivity to confirm or rule out this amount of molecular gas.
To place an upper limit on the integrated flux density, we first collapse the data cube around the expected CO(2-1) frequency, assuming a width of ∼ 200 km s −1 (based on FWHM [OIII]88m ; Tamura et al. 2019).This map (shown in the right panel of Fig. 3) has an RMS noise level of 4.5 mJy beam −1 km s −1 , corresponding to a 3 upper limit on the integrated flux density of Δv CO(2−1) < 72 mJy km s −1 .
Using the standard equation of Solomon et al. (1992), this results in an upper limit of: where we have assumed a starburst-like   and  21 , as motivated by the high [OIII] 88m/[CII] 158 m ratio detected by Tamura et al. (2019) and Bakx et al. (2020), as well as the discovery of a likely starburst-driven dust bubble in high-resolution [OIII] 88m imaging (Tamura et al. 2023).The effect of observing CO against the CMB is taken into account through the factor f CMB (da Cunha et al. 2013): where S CO is the CO(2-1) flux density and   () is a blackbody function.We assume that the dust and molecular gas are in thermal equilibrium (T ex,CO = T D ∼ 90 K).This dust temperature is the lower limit implied by the SED exploration of Section 3.1, and a higher T D results in a higher     and thus smaller limit on M H 2 (e.g.,     = 0.84 for T D = 130 K, yielding a limit of M H 2 < 2.2 × 10 10 M ⊙ ).These temperatures are quite high, but a derivation of  , requires multiple CO detections and excitation modelling (e.g., Daddi et al. 2015).If we assume T D = 90 K, but Milky Way-like values of   ∼ 4.3 and r 21 ∼ 0.5 (e.g., Carilli & Walter 2013), this results in a much more conservative limit of M H 2 < 2.6 × 10 11 M ⊙ .
Previous [CII] observations yielded a luminosity of L [   ] = (1.40 ± 0.22) × 10 8 L ⊙ (Bakx et al. 2020).This line has proven to be a reliable tracer of SFR in galaxies at low and high redshift (e.g., De Looze et al. 2014;Schaerer et al. 2020), although some studies have found that it acts as a reliable tracer of molecular gas (e.g., Zanella et al. 2018;Madden et al. 2020;Gurman et al. 2023)   where  ′ = / ⊙ .If we assume  ′ ∼ 0.25 (Bakx et al. 2020), this results in   ∼ 10 −3.5 , and a predicted gas mass of   2 ∼ 10 8.5 M ⊙ .Since this relation was derived using a sample of starforming main sequence galaxies at  ∼ 0 − 6 and MACS0416_Y1 is likely a starbursting galaxy at higher redshift, it is conceivable that MACS0416_Y1 may feature an even smaller   value (as seen in other high-redshift sources; e.g., Hashimoto et al. 2023), and consequently a higher   2 .
A [CII] velocity gradient was detected in this source, which was assumed to be rotation, resulting in a dynamical mass estimate of   = (1.2 ± 0.4) × 10 10 M ⊙ (Bakx et al. 2020).Since highresolution [OIII] observations revealed that this source is composed of several clumps with complex kinematics, this value may only be used as an approximate estimate.However, since the stellar mass of this object is approximately  * ∼ 10 9 M ⊙ (Tamura et al. 2019) and we find a small dust mass (M D ∼ 10 5 M ⊙ ), there may be room in the mass budget for a large amount of gas (∼ 10 10 M ⊙ ).

CONCLUSION
Here, we present an updated analysis of the dust and molecular gas properties in the  ∼ 8.31 galaxy MACS0416_Y1, including both archival data and new JVLA observations targeting CO(2-1) and rest-frame radio continuum emission.
Since the continuum emission is not detected at   ∼ 25 GHz, we examine the implications this has on the non-thermal emission.Assuming a standard non-thermal fraction and synchrotron slope, our non-detection implies a 1.4 GHz upper limit of  1.4   < 120  Jy.If the Kennicutt (1998) scaling law is applied, this results in a SFR radio ≲ 2.5 × 10 4 M ⊙ year −1 .This is much larger than the observed SFR, implying an uninformative constraint.Assuming a lower SFR∼ 10 2 M ⊙ year −1 results in  1.4   ∼ 0.5  Jy, and thus a minuscule contribution of nonthermal emission to the luminosity.
The archival FIR SED (which consists of multiple non-detections and one detection) is re-examined and modelled with a modified blackbody.We find that these data suggest a low dust mass (∼ 10 5 M ⊙ ) and high dust temperature (T D ≳ 90 K), in agreement with past results (Bakx et al. 2020).
Our non-detection of CO(2-1) is used to place a constraint on M  2 , which is compared to estimates from [CII] luminosity, dust mass, and [CII] kinematics.While the L [CII] -based estimate of the H 2 mass (∼ 4.2 × 10 9 M ⊙ ) is in agreement with the CO-based limit (< 2.5 × 10 10 M ⊙ ) and a mass decomposition based on M , [   ] (< 1.1 × 10 10 M ⊙ ), the dust-to-gas ratio-based estimate is much lower (∼ 3.1 × 10 8 M ⊙ ).If the [CII]-based estimate is accurate, this suggests a higher gas-to-dust ratio than previously expected .
While the constraints in this work are not yet precise, they will be refined greatly in the near future through synergy with highresolution ALMA [CII], [CI], and CO observations as well as JWST/NIRSpec IFU observations (Witstok et al. in prep).These will result in new estimates of the gas-phase metallicity, nonthermal and FIR continuum emission, SFR, and gas properties in MACS0416_Y1, enabling a detailed view of this primordial galaxy.

Figure 2 .
Figure 2. Radio-FIR SED of MACS0416_Y1.We include our upper limit of the 25 GHz flux density, as well as a detection and limits from Tamura et al. (2019), Bakx et al. (2020), and archival data (band 3, 2021.1.00075.S; PI Ono).The detection is shown as a black circle with 1 error bars, while the upper limits are shown at 3 as downward-facing red triangles.The left panel shows the assumption of maximum non-thermal contribution, while the right panel includes the non-thermal contribution assuming SFR∼ 100 M ⊙ year −1 .In each panel, we show illustrative models that meet the detections and limits.Dashed vertical lines denote the integration range for L FIR (  = 42.5 − 122.5 m).

Table 1 .
Ono et al. 2022;Feruglio et al. 2023.2017)sourceimplies   2 ∼ 4.2×10 9 M ⊙ , which is in agreement with the mass limits imposed by Estimates of M  2 from different tracers.thenon-detection of CO(2-1) and from a dynamical mass decomposition, as well as an approximate dust-based estimate.Cosmological zoom-in simulations of galaxies at  ∼ 6 − 7 suggest smaller gas masses for a comparable galaxy (  2 ∼ 10 8.5 M ⊙ ,Vallini et al. 2012;Pallottini et al. 2017), while observations of more massive galaxies at  ∼ 6 − 7 return larger molecular gas masses (e.g.,Ono et al. 2022;Feruglio et al. 2023).It can be clearly seen from the values listed in Table1that the available data suggest a broad mass range of   2 ∼ 10 8.5−11.3M ⊙ .In order to place a tighter constraint, the gasphase metallicity is required to calibrate   and   . Lckily, upcoming JWST observations of this source with the integral field unit (IFU) of the Near-InfraRed Spectrograph (NIRSpec; PID 1208, PI Willott) will target MACS0416_Y1 in both low-( ∼ 100; Prism) and high-spectral resolution ( ∼ 2700; G395H), which will result in a precise estimate of metallicity through well-tested rest-frame optical line ratios.