在3毫米波长带1（REST帧400μm）中观察到该靶标的NOEMA作为S20DA项目的一部分（主要研究人员：D。A. Riechers，F。Walter）。在2020年7月26日至2020年8月25日之间，在良好的天气条件下观察到三个部分重叠的光谱设置，使用10个天线，最紧凑的D配置，使用7.7 GHz（双极极化）的带宽，每个边带2-MHz光谱分辨率。我们还包括了先前发表的5个观察，2012年2月6日至2012年5月31日在A和D配置中分别调查为110.128和113.819 GHz，以及在2012年6月1日至2017年6月4日之间以及2017年7月10日之间未发表的观察结果，并在D构型中调查了78.544和101.819.819 GHZ的D配置。研究者：D。A. Riechers），所有使用3.6 GHz的带宽（双极化），总共产生了21种观察跑。附近的无线电数量用于复杂的增益，带通和绝对通量校准。在0.87毫米波长4（REST-frame122μM）中还观察到该靶标的NOEMA作为X0CC项目的一部分（主要研究员：D。A. Riechers）。在2013年12月4日至2015年3月12日的良好天气条件下，在三个天线的三个观测跑中进行了观测，在2015年3月12日的情况下进行了观测，频段4接收器调整为335.5 GHz，并使用3.6 GHz的带宽（双极化）。附近的无线电类星机用于复杂的收益， 带通和绝对通量校准。Gildas软件包用于数据校准和成像。成像之前，将所有3毫米数据组合到单个可见性立方体。成像是通过天然基线加权进行的。频段4数据还用BRIGGS稳健加权成像，以增加空间分辨率。通过将可视性数据平均为以2.04 GHz为中心的2.04 GHz的带宽，创建了在H2O线的频率下的连续发射图。选择此范围是为了避免带通道中的其他线路。从可见度平面中的H2O线立方体中减去连续发射。线吸收的矩0图像是通过在100 MHz的带宽上集成信号之前和连续减法后创建的，对应于395 km s -1。由此产生的R.M.S.在扩展数据中提供了噪声水平。

　　通过同时在图1中所示的一维光谱中，通过同时对线和连续发射（包括连续元的线性项）同时提取H2O（110-101）线的通量（包括连续元的线性项），该光谱是从图像库中提取的。源在H2O（110-101）线的频率下无法解决，因此主要的不确定性是由于连续发射的斜率以及附近其他线的适当拟合，尤其是CO（5-4）。这些参数中的不确定性是引用不确定性的一部分。我们发现一条线峰值通量为-818±145μjy，最大宽度最大（FWHM）为507±111 km s -1，中心的频率为75.8948 GHz（±46 km s -1）（±46 km s -1； <10%—that is, minor compared with the measurement uncertainty). Given the rest frequency of the line of 556.9359877 GHz, this corresponds to a redshift of 6.3383, which is consistent with the systemic redshift of HFLS3 (z = 6.3335 and 6.3427 with uncertainties of ±14 and ±54 km s−1 at Gaussian FWHM of 243 ± 39 and 760 ± 152 km s−1, respectively, for the two velocity components detected in the 158-μm [CII] line)5. For comparison, the H2O(202–111) and H2O(211–202) emission lines in HFLS3 have FWHM of 805 ± 129 and 927 ± 330 km s−1, respectively5—that is, only marginally broader than the 110–101 line at the current measurement uncertainties. The continuum flux at the line frequency is 396 ± 15 μJy, corresponding to 48% ± 9% of the absorption-line flux (the relative flux calibration uncertainty between the line and continuum emission is negligible). We also measured the 335.5-GHz continuum flux by two-dimensional fitting to the continuum emission in the visibility plane. We find a flux of 33.9 ± 1.1 mJy, which agrees with previous lower-resolution observations at the same wavelength5. The major (minor) axis FWHM diameter of the source is 0.617 ± 0.074 arcsec (0.37 ± 0.20 arcsec). This yields the physical source size quoted in the main text at the redshift of HFLS3.

　　The H2O(110–101) line leads to a decrement in continuum photons from the starburst and, as such, is observed as a lack of continuum emission at its frequency at the position of the starburst. It therefore appears as negative flux in an image where starburst continuum emission has been subtracted. In addition, (sub)millimetre-wavelength interferometric images reveal structure against a flat sky background defined by the large-scale CMB surface brightness, which the interferometer does not detect itself due to its limited spatial sampling. Therefore the fraction of the signal due to the decrement in CMB photons at the position of the starburst not only appears as negative flux without subtracting any further signal but it also corresponds to a lack of continuum emission at the line frequency in practice. As the mere presence of an absorption-line signal stronger than the measured continuum emission implies absorption against the CMB, this interpretation is not limited by uncertainties in the galaxy continuum flux or uncertainties in the absolute flux calibration.

　　RADEX is a radiative transfer program to analyse interstellar line spectra by calculating the intensities of atomic and molecular lines, assuming statistical equilibrium and considering collisional and radiative processes, as well as radiation from background sources. Optical depth effects are treated with an escape probability method8. Studies of nearby star-forming galaxies show that the observed absorption strengths of the ground-state H2O and H2O+ transitions are due to cooler gas that is located in front of, and irradiated by, a warmer background source that is emitting the infrared continuum light that also excites the higher-level H2O emission lines11,29. We therefore adopt the same geometry for the modelling in this work, which is adequately treated within RADEX (that is, treating the dust continuum plus the CMB as background fields for the absorbing material)8. The dust continuum emission is modelled as a grey body with treating Tdust, βIR and the wavelength where the dust optical depth reaches unity as free-fitting parameters for each dust continuum size and TCMB sampled by the models. The observed spectral energy distribution of HFLS3, including all literature5 photometry and the measurements presented in this work, is then treated as the contrast between the dust continuum and CMB background fields, such that the resulting fit parameters for the dust continuum source change with TCMB in a self-consistent manner. In the RADEX models, we derive the H2O peak absorption depth into the CMB. We then multiply the best matching peak absorption depth found by RADEX with a Gaussian matched to the fitted line centroid and line width obtained from the observed line profile in Fig. 2 to determine the model line profile. In this approach, the shallower absorption in the line wings either corresponds to a lower filling factor of the H2O layer at the corresponding velocities or to lower H2O column densities. Although collisions of H2O molecules with H2 is another mechanism that can modify the level populations especially at very high gas densities (which is an important mechanism for the cooling of low-excitation-temperature transitions of molecules like H2CO to below TCMB)12,30, the RADEX models show that they do not affect our findings (see Fig. 3c). We therefore adopt models with essentially no collisions by assuming a very low gas density of n(H2) = 10 cm−3. We then compare our findings to those obtained when adopting conditions that are similar to those found in local starburst galaxies11 and to those found for high-density environments with n(H2) >105 cm -3。在101级碰撞的横截面总是大于110级别的碰撞，而与碰撞伴侣无关，碰撞的温度发生在31,32,33中。因此，相对于101个基态，碰撞不能负责110水平的过度繁殖，并且与没有碰撞相比，在非常高的气体密度下，通过降低TCMB-Tex温度差异，涉及碰撞的净效应是降低CMB的吸收深度的净效应。作为参考，碰撞对TCMB测定的影响对于局部星爆的典型条件（即N（H2）〜104 cm -3; TKIN = 20-180 K）11的影响可以忽略不计，并且仅开始对非常高的密度n（H2）> 105 cm -3产生影响。对于给定的连续源大小，对于高密度情况而言，TCMB上的约束将更紧（即，与观察值更快与观察值不一致），而没有碰撞的情况，因此后一种方法更保守（见图3B）。因此，碰撞激发的总体影响将是对源规模的更严格的要求，涵盖了部分和水柱，因此它们的包含只会进一步加强我们的结论。我们注意到，这与紫外线研究的情况相反，3,17,19,20,21,22,22,23,24,25,25,26,27,28，其中忽视碰撞激发会导致TCMB的保守性较低。如果我们假设H2O吸收是从红外连续发射区域内出现的，那么由于从Starburst中降低了有效的辐射场强度，因此可能需要更大的源尺寸才能获得相同的吸收线强度。假设此类几何形状无法产生H2O（110-101）的附近星系的先前建模尝试（110-101） 解释HFLS3观察结果所需的量表上的线吸收，这可能表明将需要更复杂的假设11。因此，由此产生的约束将再次变得不那么保守，也许以与高密度情况相似的方式起作用。从模型中不包括这两种效应都会导致对TCMB及其不确定性的最大保守估计。假设平面或类似的几何形状而不是球形几何形状只会对我们的发现产生较小的影响8。图3中所示的模型假定统一的填充因子，这是最保守的可能的假设。对于所有TCMB值，预测的吸收强度超过观察到的值的所有TCMB值仍然可以使用较低的覆盖部分（参见图3B中的阴影区域）。作为参考，对于图3中考虑的不同情况，显示了与观测信号强度的连续大小一致的最小覆盖分数。在图2中所述的不同情况也发现了线的吸收，对于图2B所示的解决方案，τh2O的光学深度为τh2O= 21.1。为了确定效应变得可观察到的红移（图3C），我们将R108μM，TDUST，βIR和MDUST固定在观察到的值和H2O柱密度上的值与对应于模型光谱的值。H2O线吸收到HFLS3的尘埃连续体中的吸收在Z> 2.9处可以看到，但是进入CMB的吸收仅在z> 4.5处观察到（或对于H2密度> 105 cm -3）。这些值解释了由于带红移的TCMB变化，灰尘灰体光谱的形状变化（即538-μm和108-μm光子的相对可用性变化）。为了更好地量化不同建模参数的影响，我们的tdust和βir都超出了先前估计的不确定性 （未考虑文献中TCMB变化的名义参考值是TDUST = K和βIR=）5,6。这是必要的，因为这两个参数都取决于我们模型中不同的TCMB（因此正在更改图3b，c）中的参数，因此需要重新评估它们的真实不确定性。我们在1.6-2.4范围内独立地变化了βIR，并且在±20 K范围内作为TCMB围绕最佳拟合值的函数在±20 K范围内。这表明，与最佳拟合的βir> 2.0和tdust降低了10 k以上，与光谱能量分布数据的拟合非常差，而低于最佳拟合值的Δβir> -0.1比测量的R108μm+1σ需要更大的连续尺寸，因此尺寸限制了。除了这些范围外，整个范围内的极值将分别在R108μM +1σ和R108μM +2σ情况下，预测的TCMB中的不确定性范围仅扩大-1.7和+5.4 K和-0.8和+4.4 K。为了进行比较， +1σ和 +2σ不确定性范围之间的差异为-3.6和+3.8 K）。这表明，尘埃光谱能量分布拟合参数对TCMB中的不确定性的影响对连续大小测量中的那些是亚抑制剂。相反，我们研究了TCMB变化对最佳拟合TDUST和βIR的影响。对于对应于R108μm+1σ和R108μm+2σ范围的值，TDUST通常会通过 <0.5 K and βIR typically changes by <0.1–0.2 when varying the parameters independently. These changes are larger than the actual uncertainties, because the fit to the dust spectral energy distribution becomes increasingly poorer with these single-parameter variations. At the same time, these changes are subdominant to those induced by changes in dust continuum size within the +1σ and +2σ uncertainty ranges, which is consistent with our other findings.

　　Five H2O lines were previously detected towards HFLS3 (202–111, 211–202, 312–221, 312–303 and 321–312) and two additional lines were tentatively detected (413–404 and 422–413)5. The Jup = 3 transitions are due to ortho-H2O and all other transitions are due to para-H2O. All of these transitions appear in emission. Given the high critical densities of these transitions, our RADEX models cannot reproduce the strength of these lines as the same time as the observed ortho-H2O(110–101) absorption strength, which suggests that they emerge from different gas components. For reference, to reproduce the strength of the H2O(211–202) in Fig. 1 alone with collisional excitation, n(H2) = 2 × 107 cm−3 and Tkin = 200 K would be required, but the H2O(110–101) would no longer appear in absorption against the CMB if it were to emerge from the same gas component. This is consistent with the picture that the H2O absorption is due to a cold gas component along the line of sight to the warm gas that gives rise to the emission lines11. Observations of the para-H2O(111–000) ground state do not currently exist for HFLS3, but our models do not show this line in absorption towards the CMB.

　　Our models show that the lower limit on TCMB at a given redshift based on the observed H2O absorption is due to the minimum ‘seed’ level population due to the CMB black-body radiation field. To determine a conservative lower limit, we have calculated models with continuum sizes up to r108μm = 5 kpc (see Fig. 3b), corresponding to a +7.5σ deviation from the observed continuum size, and recorded the temperatures at which such weakly constrained models turn into absorption. We find that this results in a lower limit of TCMB >7–8 K，独立于模型假设。仅此发现并不能解释图3b中上限的存在。对于给定的粉尘连续发射的给定尺寸，TCMB的增加还需要增加MDUST才能仍然重现观察到的灰尘光谱分布，从而导致在给定波长下有效增加灰尘光学深度。光学深度上升的结果是，灰色光谱在538和108μm之间越来越类似于黑体光谱，因此，对CMB的H2O吸收降低。对于给定的粉尘连续大小和吸收强度，这种效果是允许TCMB的上限。

　　图4中文献数据显示的不确定性是从文献来源中采用的，而无需修改，它们通常代表各个测量值或样品平均值中的统计不确定性。Individual cluster measurements of the thermal SZ effect may be affected by dust associated with foreground galaxies or the Milky Way, the galaxy clusters or background galaxies that may be amplified by gravitational lensing, uncertainties in the reconstruction of the Compton-y parameter maps due to flux uncertainties, radio emission due to active galactic nuclei and/or relics, the kinetic and relativistic SZ effects, and通用带通和校准不确定性17。此外，群集几何形状的不确定性以及CMB光子通过群集的视线路线距离以及群集内气体温度限制了单个SZ测量的精度。样本平均值也可能会受到堆叠过程中系统学的影响。各个数据点偏离至少两个标准偏离趋势的偏差，这可能表明超出提供的统计误差栏以外的残留不确定性，因此被低估了图4中所示的误差线。紫外线吸收线的测量值的主要不确定性来源是由于假设没有碰撞激发的假设，这在图4所示的统计不确定性中未考虑。为了扩展较早的估计21，我们计算了典型的TKIN，N（H）和从[CI]测量的典型TKIN的RADEX模型，这表明碰撞激发有助于较低细化结构的预测TEX。尽管我们显示了原始的未修改数据，但 因此，除了统计不确定性外，由于模型依赖性激发校正，基于紫外线的测量值受到不确定性的影响。此外，诸如[CI]线之类的示踪剂的精细结构水平可以通过紫外线激发和随后的级联反应而激发。为了基于这些测量值来限制TCMB，必须知道动力学温度，颗粒密度和局部紫外线辐射场，并且通常根据用于约束TCMB的物种以外的其他示踪剂来确定。同样，某些测量基于光谱未解决的线，这限制了基于热拓宽的动力学温度测量的精度21。由于这些不确定性，基于紫外线的测量值可能与标准λCDM值一致，但它们并不构成TCMB的直接测量，而没有明显的进一步假设。作为参考，基于[CI]测量值（不包括上限）的中位TCMB/（1+Z）估计值为3.07 K，中位绝对偏差为0.09 K，标准偏差为0.31K。因此，当前样品中位数中位数偏离量偏离了λCDM值，该偏差约为λCDM值。基于CO，[CI]和[CII]的（未校正）测量的组合提供的中位数为2.84 K，中值的绝对偏差为0.15 K，标准偏差为0.25K。这突显了上述校正的重要性以及与系统的不确定性相差的校正的重要性。基于H2O的测量值的不确定性的主要来源，超出了线启动模型部分中所述的警告，是对源大小的统计不确定性，缺乏对吸收H2O柱密度的直接测量， 尘埃吸收系数和填充因子的变化。鉴于其他分子线检测提出的高金属性，由于源尺寸的源大小和动态质量测量值对气体质量的限制，高填充因子的限制限制，由于当前数据的空间分辨率有限，不确定性的主要不确定性源于源大小。因此，应通过获得更高（子）KPC解决方案（即，即，即 <0.2”) imaging with the Atacama Large Millimeter/submillimeter Array (ALMA; for other targets) and planned upgrades to NOEMA, and, in the future, with the Next Generation Very Large Array (ngVLA). Statistical uncertainties will also be greatly reduced by observing larger samples of massive star-forming galaxies over the entire redshift range where measurements are possible, closing the gap to SZ-based studies, which are currently limited to z < 1. The resulting improvement in precision will provide the constraints that are necessary to confirm or challenge the evolution of the CMB temperature with redshift predicted by standard cosmological models.

　　The frequency range currently covered by NOEMA is 70.4–119.3, 127.0–182.9 and 196.1–276.0 GHz (with greatly reduced sensitivity above about 115 and 180 GHz in the first two frequency ranges). ALMA covers the 84–500-GHz range with gaps at 116–125 and 373–385 GHz, with a future extension down to 65 GHz (with greatly reduced sensitivity below about 67 GHz). The ngVLA is envisioned to cover the 70–116-GHz range. Excluding regions of poor atmospheric transparency, the H2O(110–101) line is therefore observable in these frequency ranges at redshifts of z = 0.1–0.4, 0.5–2.0, 2.1–3.4 and 3.8–6.9 in principle, but the detectability of the line in absorption against the CMB is probably limited to the z ~ 4.5–6.9 range if the spectral energy distribution shape of HFLS3 is representative. At lower frequencies, the Karl G. Jansky Very Large Array and, in the future, ALMA and the ngVLA also provide access to the <52-GHz range, such that the signal also becomes observable at z >9.7原则上。总之，在大约15亿年的宇宙历史中，可以从地面探索地面H2O过渡到此处确定的CMB的吸收。

　　为了调查预期是否可以检测到不同星系群体的效果，我们已将建模应用于Z = 3.9 Quasar APM 08279+5255，为此，粉尘光谱分布分布由主要的220-K粉尘组成，由弱的65-k粉尘组成，仅贡献了10-15％的远处，远不复存在的差异。亮度35,36,37,38,39,40,41,42,43,44,45,46。这些模型表明，预计该线将在发射中发生，并且在任何红移时都无法检测到该线在具有相似尘埃光谱分布的星系中至少z = 12。其他远红外，高红移，主动银河核心星系通常显示出其低温粉尘成分的相对贡献，因此在不太极端的情况下，这种效果可能仍可检测到。对于比HFLS3较低的灰尘温度的星系，即使在较低的红移处也可能存在效果，但通常预计通常会弱弱，并且在TCMB接近其TDUST的红移时会消失。对于类似于银河系的中心区域但类似特性的尘埃谱分布形状，预计该效果将在其红移峰处降低两个以上的数量级，并且在HFLS3的红移时几乎无法观察到。因此，尘土飞扬的星座星系似乎是检测效果的一些最佳环境。

　　为了确定绝热指数，我们假设标准的Friedmann – Lemaitre-Robertson-Robertson-Walker宇宙学具有零曲率和物质放射流体，该液体遵循主要文本中引用的标准保绝热方程。这将对应于红移缩放tcmb（z）= tcmb（z = 0）*（1+z）3（γ -1），在存在不随红移而缩放的暗能量密度的情况下。深色能量密度被参数化以用功率定律（1+z）M缩放，其中m = 0对应于宇宙常数。使用标准假设，这会产生TCMB的红移缩放（参考文献15）：

　　以及状态pde =weffρde的有效暗能方程，其中状态参数的有效方程weff =（m/3） - 1。此拟合函数在这里使用ωm的规范值，0 = 0.315（参考文献4）。与所有其他不确定性来源相比，ωm的不确定性很小，因此被忽略了。拟合中使用的所有数据均在扩展数据表1中提供（参考文献36,37,38,39,40,41,41,42,42,43,44,45,46）。