使用过滤器 ，F090W
，F115W，F150W ，F200W，F277W
，F277W，F356W ，F410M和F444W观察到JWST/NIRCAM成像的群集字段MAC J1423.8+2404
，使用过滤器进行了成像，并在6.4 ks中触及了6.4 ks ，每个ks insible to Signal-noise-noise bartio copt in coptio coptio coptio coptio coptio 。还使用过滤器F115W
，F150W和F200W观察到JWST/NIRISS成像
。 　　为了减少成像数据，我们使用参考文献中更详细介绍的光度管道。44 。简而言之 ，使用公共grism红移和线分析软件Grizli43减少了原始数据
，该软件掩盖了成像人工制品，可根据Gaia Data Release 3 Catalogue13提供星体校准 ，并使用Astrodrizzle移动图像。如参考文献中所述
，应用了光度零点
。34。使用六个firefly闪光的Nircam观察器创建的RGB图像如图1所示 。我们使用了图像，如参考文献中所述 ，已删除了明亮的群集星系和簇内光
。4：使用GAIA-RVS的银河系中最古老的薄盘。astron 。天体
。688，a167（2024）。（ICL）在第4条中呈现 。href =“ https://www.nature.com/articles/S41586-024-08293-0#REF-CR25”F090W
，F115W，F150W ，F200W
，F277W，F277W ，F356W
，F410M和F444W的NIRCAM深度（0.3'直径孔径）为7.2 、6.6
、5.2、5.2 、4.4、3.0
、3.0、3.0 、3.0
、2.9、5.5和4.3 njy，以及f150 and f150 and f150＆f1155F200WN分别为3.6 、4.3和4.0 NJY ，为41
。 　　我们在10个JWST频段（NIRIS：F115WN
，F150WN和F200WN; NIRCAM：F115W，F150W ，F200W
，F277W，F277W ，F356W，F410M和F444W）中执行光度法
，其中从他们的道德上拟合了Virefly Parkle。在其他JWST和HST过滤器中，没有或几乎没有检测到萤火虫火花 。因此 ，我们为整个来源放置了上限
。由于对象至少分为10个不同的簇和一个弥漫性星系分量
，因此我们使用Galfit10进行形态拟合以提取光度信息。 　　通过在参考文献中描述的方法中，通过堆叠明亮 ，孤立的
，非饱和的恒星的中位数堆叠的中位数来提取点扩散功能 。28.用于将所有数据均质化到F444W分辨率的卷积内核是使用photutils.psf。使用splitcosinebellwindow（）窗口函数匹配以消除高频噪声的匹配，这是由于浮点数不正确 ，在采取傅立叶变换比时浮点不正确
。我们优化了每个窗口函数的形状
，以最大程度地减少每个源滤波器的卷曲恒星之间的中间残差和来自目标F444W滤波器的恒星。 　　对于形态学拟合，我们在BCG提取的图像中所有10个过滤器中创建了10英寸×10英寸的邮票 。我们通过视觉检查确定了10个集群中心的先验
。尽管十个中有九个作为点源出现 ，但FF-4具有细长的形状
，并且似乎无法解决。我们首先通过拟合（1）FF-4的椭圆形高斯（1）拟合椭圆形高斯来确定10个簇的中央坐标；（2）其他九个集群的九点源；（3）另一个具有弯曲模式的椭圆形高斯，以弥漫性弧向F115W图像打开 ，该图像具有最高的分辨率（最小的PSF） 。自由参数是所有组件的中心和总磁通量，FF-4的半径和轴比
，以及弧线的半径，轴比和弯曲模式（B2）
。通过直观检查F115W图像来确定坐标的初始猜测。一旦我们从F115W获得了所有组件的拟合中心坐标 ，我们再次适合F444W中的所有11个组件
，ARC和FF-4的信噪比最高，以确定半径 ，轴比
，轴的比率，椭圆形的位置角度以及ARC的弯曲模式B2 。 　　我们将F115W的最佳拟合中心坐标用作所有过滤器中的中央坐标
。但是 ，我们没有固定中央坐标
，而是允许Galfit适合它们在非常狭窄的±0.5像素（0.02英寸）内的每个过滤器中，以说明PSF中心的不确定性。我们还从F444W拟合中修复了弯曲模式B2（2.14） ，椭圆半径（3.9英寸）
，轴比（0.08）和位置角（0.08）和位置角（-51.8°） 。我们还固定FF4的形态，也有半径= 0.59英寸 ，轴比= 0.1，位置角= -53°
。 　　现在
，我们将所有11个组件都适合所有10个过滤器，以确定它们的通量。所得模型和残差在扩展数据中显示 。拟合中的残差可忽略不计 ，如所有过滤器中的galfit拟合中的χ2/ν〜1所示。这证实了原始的视觉印象
，即十个簇中的九个未解决，并且存在额外的平滑组件
。 　　为了得出我们的通量估算中的不确定性 ，我们在10英寸×10英寸的邮票中（避免边缘）中注入了100个随机位置的完整萤火虫闪光模型
，并以完全相同的Galfit设置进行重新装修。我们发现，在任何过滤器中 ，拟合通量和注入的通量之间均无明显的系统偏移
，这表明我们的光度计技术对所有过滤器的背景变化都是可靠的 。光度法的不确定性是根据100个改装通量的双重量表计算得出的
。所得的光度法和模型的RGB图像和残差在扩展数据中显示。在三个重叠过滤器中Niriss和Nircam通量之间的一致性是对光度法稳健性的另一个确认 。我们已经使用了更新的零点34，并使用参考文献中的颜色过量E（B-V）= 0.0272校正了银河系灭绝
。6并在参考文献中采用灭绝法。35使用灭绝系数和颜色过量RV = 3.1之间的因子 。 　　已经获得了Macs J1423.8+2404的NIRSPEC光谱 ，并获得了萤火虫闪光
，FF-BF和FF-NBF的光谱
。FF-BF的光谱是参考文献中样本的一部分。23，ZSPEC = 8.2953±0.0005 。使用棱镜/透明分散器和滤波器观察到光谱 ，通过每个群集的三个微骨器组件（MSA）掩码，每个MSA配置的总曝光时间为2.9 ks
。 　　使用STSCI JWST Pipeline（软件v.1.8.4和JWST_1030.PMAP）和MSAExp Package31处理NIRSPEC数据。我们将标准JWST管道用于1级处理
，其中我们从原始数据中获得了拟合文件的速率 。我们启用了跳步选项Expand_large_events通过雪球残留物来减轻污染，并使用了自定义持久性校正 ，该校正掩盖了以下1,200 s在任何读取组中接近饱和度的像素。然后
，我们使用MSAEXP进行了2级处理，为此我们进行了标准波长校准 ，扁平场
，路径损耗校正和光度校准，并在背景减法之前获得了2D光谱
。由于中央和上百叶窗包含不同的簇（请参见图2a以找到快门位置） ，我们需要自定义的背景减法以避免自我提取。我们通过堆叠和平滑空像素中的天空光谱并获得背景减去萤火虫火花的2D频谱来构建背景2D频谱来做到这一点 。我们确认这种自定义背景减法方法以及文献4. Astrophys中使用的标准毛毛雨背景减法方法
。J. 928
，106（2022）。我们最终在狭缝1中分别提取1D光谱，并在参考资料中使用反相位加权内核来折叠2D光谱 。 　　图2显示了由群集FF-6主导的裂隙1中萤火虫闪光的1D光谱
。 　　该频谱在λobs〜3.5μm处的Balmer跳跃和λOBS1.4μm的周转率可能是由于两光子发射的。这些特征表明 ，静脉连续体应在其余框架紫外线的恒星连续体上占主导地位
，以在狭缝1中的光谱（如Z = 5.9 Galaxy中，参考文献12中发现） 。因此 ，我们使用光电离心代码Cloudy v.23（参考文献5）对光谱的连续体进行了对光谱的连续体进行建模
。为了确定连续模型拟合中的灰尘衰减值，我们首先通过拟合高斯曲线来测量Hγ/Hβ的比率。该比率与B病例重组非常吻合
，并且没有明显的灰尘衰减 。因此，在连续频谱建模中 ，我们使用的纯氢气通过具有黑色SED的电离源而没有灰尘衰减
。我们改变了黑体（TEFF）的有效温度和（离子化）氢气（）的电子温度
，并通过χ2最小化搜索最合适的模型连续体。在连续拟合中，我们掩盖了排放线区域和所有波长λobs< 1.2 μm at which the Lyman break is seen in the slit 2 spectrum, because this region may be affected by a neutral hydrogen damping wing. The best-fit model has log(Teff/K) = 5.10 and , which is fully consistent with the results in ref. 12. The result of continuum fitting does not change if we consider a slight dust attenuation (AV = 0.1 mag) in the fitting. As discussed in ref. 12, the effective temperature of log(Teff/K) = 5.10 is much hotter than typical massive type O stars and is suggestive of this star-forming cluster having a top-heavy IMF. The IMF of this cluster is further discussed in section ‘SED fitting analysis’. 　　Note that the UV continuum turnover feature could be because of the absorption from dense neutral hydrogen either in the intergalactic medium (IGM) or in the circumgalactic medium (CGM). However, in the case of slit 1 spectrum, we expect the effect of IGM and CGM damping absorption to be negligible or limited at λobs < 1.2 μm based on the blue continuum and sharp drop-out in the slit 2 spectrum (see section ‘Spectral fitting in Firefly Sparkle slit 2’ for details of slit 2 spectrum). Considering the spatial proximity of the slit 1 and slit 2 regions (Fig. 2), we can assume the absorption feature from line-of-sight neutral hydrogen to be the same in the slit 1 and slit 2 spectra. The slit 2 spectrum is rather blue and has a sharp Lyman break starting at λobs = 1.2 μm, whereas the slit 1 spectrum shows the turnover starting at λobs ~ 1.4 μm. Thus, the turnover feature should not be because of the neutral hydrogen absorption, but rather because of the intrinsic continuum shape of the source. Nevertheless, to avoid the possible effect of the neutral hydrogen absorption, we mask out λobs < 1.2 μm in the nebular continuum fitting above (corresponding to 1,290 Å in the rest frame). 　　Having the model continuum, we subtract the underlying model continuum from the observed spectrum and measure the spectroscopic redshift and emission line fluxes by fitting Gaussian profiles. The best-fitting model spectrum with nebular continuum and Gaussian profiles is shown in Fig. 2b (red solid curve). We securely detect emission lines of λλ4959, 5007, Hβ, λ4363, Hγ, Hδ and [Ne]λλ3869, 3889. We do not find significant detection of []λ3727 and obtain an upper limit for the flux of this line. There is a tentative detection of the blended line of [O]λλ1661 + 1666, although the spectral resolution of the prism is low at this wavelength making this doublet difficult to securely detect and separate from Heλ1640. We use these emission line fluxes to estimate the physical parameters in slit 1. We first estimate the dust attenuation based on Balmer decrements. Both the Hγ/Hβ and Hδ/Hβ ratios are consistent with theoretical predictions in case B recombination21 within the uncertainties, suggesting there is no significant dust attenuation (Extended Data Fig. 3, red squares in the left). This result is consistent with the initial measurement before the continuum fitting above and supports the validity of the dust-free assumption in the nebular continuum fitting process. Therefore, we do not correct for dust attenuation in the following measurements of emission line ratios and physical parameters in this section. 　　We next measure the electron temperature using temperature-sensitive emission line ratios: [O]4959+5007/[O]4363 and [O]5007/[O]1661+1666. We assume the electron density to be ne = 103 cm−3, which is consistent with recent JWST observations of similarly high-z galaxies7 and obtain consistent independent temperature measurements within the uncertainties ( and , respectively; Extended Data Fig. 3 (right)). Note that because the [O]λλ1661 + 1666 detection is tentative and potentially blended with Heλ1640, we consider [O]λ4363 to be more reliable. 　　We note that in ref. 16, the authors measured a similar ratio of [O]4959+5007/[O]4363 in the z = 6 galaxy RXCJ2248-ID to that of slit 1. In ref. 16, medium resolution spectroscopy was used to determine the electron density directly. They found that when using lines with higher ionization potential than O+, the electron density was higher (ne ~ 105 cm−3) than is typically found from []λ3727 (ref. 7). This high electron density leads to a lower electron temperature for their galaxy of . Similarly, if we assume the electron density of ne = 105 cm−3 instead for our slit 1 spectrum, the electron temperature from [O]λ4363 becomes , which is in between the two measurements based on [O]λλ1661 + 1666 and [O]λ4363 when assuming ne ~ 103 cm−3 above. To consider the possibility of a somewhat higher electron density in the highly ionized region, we adopt the mean value of our two electron temperature measurements () as our fiducial value and propagate the full range of the two measurement uncertainties into the following metallicity measurement. 　　Based on the electron temperature measurement, we obtained the oxygen abundance from [O]4959+5007/Hβ and [O]3727/Hβ ratios, following the prescription in ref. 8. We assume the electron density to be ne = 103 cm−3. The total oxygen abundance is calculated from O++/H+ and O+/H+, and the higher ionizing state oxygen is ignored30. As the [O]λ3727 emission line is undetected, we can obtain only an upper limit for O+/H+, but the upper limit for the abundance of the singly ionized oxygen is negligibly small as compared with the doubly ionized oxygen. We thus derived the total oxygen abundance from O++/H+, yielding ( assuming the solar abundance to be 8.69; ref. 38). 　　We also derive the ionization parameters using the ionization-sensitive emission line ratios: [O]5007/[O]3727 and [Ne]3869/[O]3727. Following the prescription in refs. 45,46, we obtain the lower limit for the ionization parameters (log  U) from these two ratios. Both ratios provide a similar limit of log U >-2.0 。 　　在扩展数据表1中列出了所有发射线通量测量和萤火虫火花缝隙中的衍生物理参数。我们还比较了图2D中其他星系群中的萤火虫闪光的诊断发射线比
。我们使用电离敏感线比O32（[O] 5007/[O] 3727）和温度敏感的线比RO3（[O] 4959+5007/[O] 4363） ，并将这些线比与以前的[O]λ4363-检测的Galaxies在z = 2-9的comperivations进行比较。观察14 。扩展数据图3（中间）提供了类似的比较
，但使用了另一个电离敏感的线比Ne3O2（[NE] 3869/[O] 3727）而不是O32
。 　　与缝隙1相反，萤火虫闪光缝隙2中提取的1D光谱没有显示螺旋连续性特征 ，并且蓝色连续体相当光滑
，由于lyman折断λobs〜1.2μm。因此，我们通过将高斯轮廓与连续体拟合通过在每个发射线周围的恒定偏移来建模的情况下 ，从狭缝2频谱中得出发射线通量 。我们检测[O]λλ4959,5007
，Hβ，Hγ ，Hδ，[NE]λ3869和[O]λ3727在SLIT 2 Spectrum中的发射线
，但未检测到[O]λ4363
。 　　然后，我们以与Firefly Sparkle Slit 1 Spectrum相同的方式得出物理属性。我们测量了Balmer减少 ，Hγ/Hβ和Hδ/Hβ的尘埃衰减
，并发现两个线比与情况B重组后的预测比率很好（扩展数据中的蓝色正方形图3（左）） 。这表明在狭缝2光谱中，灰尘衰减也可以忽略不计 ，我们不会进行灰尘衰减校正
。 　　由于我们未检测到狭缝2光谱中[O]λ1666或[O]λ4363的温度敏感发射线
，因此我们无法测量电子温度和直接温度方法的金属性。因此，我们仅通过[O]λ4363的非检测来获得电子温度（）的上限 。萤火虫火花缝2中的电子温度显示为（1σ）或 <4.5 × 104 K (3σ). To visualize the difference in physical properties in slit 1 and slit 2, we show the diagnostic emission line ratios of Firefly Sparkle slit 2 in Fig. 2d and Extended Data Fig. 3 (middle) as well. 　　SEDs derived from our photometry were analysed using a slightly modified version of the Dense Basis method18,47 to determine non-parametric SFHs, masses and ages for our sources in Firefly Sparkle. We adopt the Calzetti attenuation law48 and a Kroupa IMF32 with a flat prior for the high-mass slope α  [1., 4.]. We run fits using both the MILES stellar libraries29 and MESA Isochrones and Stellar Tracks (MIST; ref.  17), as well as the Binary Population and Spectral Synthesis (BPASS; refs. 26,36) models to consider for the presence of binary populations. As the latest BPASS version in FSPS (-bin-imf135all 100) assumes a Salpeter IMF with an upper mass cutoff of 100M and does not allow for a varying IMF, we only vary the top-heavy slope of the Kroupa IMF in the MILES + MIST runs with an upper mass cutoff of 120M. This should be considered while comparing the physical properties from the two runs, as allowing for a varying IMF based on the MILES + MIST configuration results in lower stellar masses for those runs because they are preferentially fit with top-heavy SSPs with a greater fraction of light coming from more massive stars. We fix the redshift to that found from the NIRSpec Prism spectroscopy by the [O] λ4959 line at zspec = 8.296 ± 0.001. All other parameters are left free. We run the SED fits in two configurations to account for different possibilities of the nature of the individual clusters: 　　We perform our fitting in two stages—we initially perform a joint spectrophotometric fit to the NIRSpec Prism spectrum along with the HST + NIRISS + NIRCam photometry in the slits in which both exist (Extended Data Fig. 4). We correct for slit loss considering two factors—the amount of light lost due to the changing PSF as a function of wavelength and an overall multiplicative correction to match the spectrum against the photometric measurements. We modify the default Dense Basis method in this stage to additionally fit for the slope at the massive end of the IMF, the gas-phase metallicity and the ionization parameter, using the relevant parameters from FSPS (imf3, gas_logz and gas_logu). Doing so allows us to substantially constrain priors on star formation rate, IMF, dust, ionization parameter and metallicity that we then use to fit the photometry. We find that the fits are consistent with negligible dust attenuation, consistent with our estimates from measuring the Balmer decrement. We also find that our fits rule out the part of parameter space consistent with the canonical Chabrier-like or Kroupa-like IMF (with the high-mass slope ≈ 2.3) in favour of more top-heavy slopes of about for slit 1, which contains portions of clusters 3, 4, 5 and 6. We find weaker constraints from the spectrum for slit 2, which still skews towards top-heaviness but with large uncertainties of about . Finally, we find estimates of both stellar and gas-phase metallicities to be sub-solar, consistent with estimates from the line ratios. 　　Using our photometry (Extended Data Table 4), we now determine the stellar properties of each individual component by running a second set of fits using the same set of parameters that are used to fit the spectrophotometry. Although parameters such as the metallicity and ionization parameter are only loosely constrained by these fits, we obtain parameter estimates for the stellar masses, star formation rates and ages of the individual star clusters with uncertainties that marginalize over the variations in the other parameters. 　　Both photometry and corresponding fits to the SED fit are shown in Extended Data Fig. 5, with variations in the stellar mass, age and reduced χ2 of the fits for each of the four scenarios (SSPs fits with MILES + MIST and BPASS, and Dense Basis fits with MILES + MIST and BPASS) shown in Extended Data Table 2. All 10 components have intrinsic (corrected for magnification) stellar masses of about 105–106M and sSFR of 10−7 yr−1. Although the error bars are large, the distinct colours of the clusters hint at different formation times. Although the smooth component contains a large fraction of the stellar mass, the bulk (about 57%) lies in the clusters. Extended Data Table 3 lists the physical properties of the individual components as well as the full Firefly Sparkle, BF and NBF galaxies. 　　We find that the SSP fits are generally less massive compared with the Dense Basis fits, because the light from the SED is modelled by a single epoch of star formation instead of an extended episode. As light from the massive stars responsible for young star formation are much brighter than older stellar populations, they can describe the observed SED with a lower mass. However, the SSP fits often cannot capture both the UV slopes and the nebular emission in the rest-optical, as seen for clusters 1, 3, 7 and 8 in Extended Data Fig. 5 and often approximate it using a Balmer break, leading to posteriors consistent with much older ages than the median values. 　　Although the tage from SSP and t50 from Dense Basis fits (Extended Data Table 2) may seem inconsistent, it is important to note that the Dense Basis fits for most star clusters indicate a sharp burst of star formation within the past 10 million years (Extended Data Fig. 6). By design, an SSP is biased towards this recent burst, whereas a non-parametric SFH can accommodate extended episodes of star formation. However, with our current data, we cannot distinguish between extended SFH in the star clusters and the contribution of light from the diffused arc. 　　The masses of the clusters also scale with the top-heaviness of the high-mass end of the IMF in the MILES + MIST fits, with lower masses for more top-heavy IMF values as that scale the amount of light from massive stars. In comparison, the BPASS fits in the current setup are done at the canonical Kroupa IMF, leading to higher masses for those fits. At the same IMF slope, the masses are comparable within uncertainties for the different SPS models, and the sSFR and age/t50 values are consistent even marginalizing over the IMF posteriors. Given the observational constraints and the χ2 from the fits in Extended Data Table 2, it is not currently possible to definitively rule out any of the current fitting approaches. 　　We use Lenstool9 to build a strong lensing model of the MACS 1423 cluster, to be fully presented in Desprez et al. (manuscript in preparation). This model is constrained with the three multiple image systems that were leveraged in ref. 3, for which we provide additional information obtained from the CANUCS data. The first two systems are those presented in ref. 27, one at z = 2.84 for which we account for the two clusters visible in the four images of the objects, and the second one with three images at z = 1.779 for which we identify another cluster in the two northernmost images for improved constraints. The last system is composed of five images11 for which we provide a new spectroscopic redshift measurement of z = 1.781 that is in agreement with photometric and geometric redshifts previously measured. 　　The different mass components are parameterised as double Pseudo-Isothermal Elliptical (dPIE) profiles4. The model is composed of a large cluster scale mass halo, an independent galaxy scale centred on the brightest cluster galaxy and small galaxy scale mass components to account for the contribution of all cluster members that follow a mass–luminosity scaling relation22. For all galaxies, their positions, ellipticities and orientations have been fixed to these measured from the images. The final best model manages to reproduce the position of the input multiple images with a distance rms of 0.46″. 　　Magnifications are obtained by generating convergence and shear maps around the Firefly Sparkle with a size of 20″ and a resolution of 10 milli-arcsec per pixel. Uncertainties in the magnifications are computed from 100 randomly selected models from the optimization of Lenstool after its convergence around the minimum χ2. The numbers provided in Extended Data Table 3 are the median and ±1σ limits on the distribution of the 100 values obtained at the position of each cluster. We measured the average magnification of the FF-arc by using the GALFIT model of the arc (in F200W) and selecting all pixels with flux >最大通量的10％
。然后 ，我们计算了所有选定像素的最佳放大值
，并计算了这些像素的平均值和标准偏差值，以找到ARC的放大倍率（μ= 24.4±6.0）。 　　使用最佳的Galfit模型进行源平面重建 ，以计算10星簇的源平面位置和放大倍率 。我们使用Lenstool生成了银河系弥漫光的源平面图像重建
，并使用其光谱的平滑PSF卷入模型。我们使用Galfit将与适当的PSF相连的10个点源添加到具有脱氧通量的星形簇的源平面位置的扩散源平面模型
。重复此过程以在所有过滤器中生成源平面模型。我们还使用相同的处方生成一个质量图，用消灭量的质量代替了灭绝的通量 。所得的源平面RGB图像和质量图如图4C ，d所示
。 　　现在，我们研究了星形簇的空间特性。即使在我们最高的分辨率F115W Nircam图像中
，十星级中的九个也没有解决 。FF-4的视觉形状略微伸长，但拟合的主要轴大小（0.01）比最小的PSF小 ，这使得尺寸估计值不可靠
。因此
，我们使用NIRCAM F115W PSF（0.02）的半宽的半宽度最大，以设置所有10颗星簇的大小上限。为了确定未解决源的大小的上限 ，我们使用放大倍率1/λt的切向特征值
，该值在14到24之间 。这导致大小上限在4 pc和7 pc之间
。中央恒星簇具有最高的放大倍率和最小的上限，而在ARC的两端附近的群体最低。我们使用尺寸的上限和消除恒星质量来计算恒星表面密度的下限 ，如图3B所示 。 　　为了估计MW-MAS和M31-MAS星系在较高红移时的祖细胞的恒星质量范围
，我们采用了一种半经验方法，结合了模拟和观察结果
。根据参考文献中的丰度匹配代码确定 ，我们假设不断发展的共同移动数量密度。20
，对于MW和M31质量类似物，Z = 0分别为Z = 0 。该代码使用峰值光环质量函数计算Z2处的过去的中值星系密度 ，Z1的初始数量密度。由于每单位单位单位的合并速率大约是恒定的，因此任何给定星系的祖细胞累积数密度的演变是幂律
，其更改为（0.16ΔZ）DEX
。 　　在参考20，使用峰值光环质量功能 ，因为所得的中值数密度不受恒星质量和发光度的散射影响。但是
，这种散射确实会影响累积数密度的1σ误差 。1σ或68％的范围随着红移的增加而增长，但对于更大的星系 ，这种生长也更高
。 　　作为参考的代码。20不计算出恒星的质量
，我们使用各种监测的恒星质量函数（SMF）获得了MW和M31类似物的祖细胞的恒星质量范围 。15,19,40
。我们在每个ΔZ处采用中位累积数密度，以找到与相应SMF相关的恒星质量。此外 ，然后使用每个红移的给定数量密度的1σ误差来确定祖细胞恒星质量的1σ误差 。在Z = 8.3时
，MW祖细胞的中位数为中值，M31祖细胞的中位数为中位数
。带有恒星质量的萤火虫闪闪发光肯定在银河系和M31祖细胞的1σ恒星质量范围内。有关祖细胞匹配技术的更多详细信息 ，请参见参考 。37
。