The Evaporating Massive Embedded Stellar Cluster IRS 13 Close to Sgr A*. I. Detection of a Rich Population of Dusty Objects in the IRS 13 Cluster

The Spectrograph for INtegral Field Observations in the Near Infrared (SINFONI, Eisenhauer et al. 2003; Bonnet et al. 2004) and Nasmyth Adaptive Optics System (NAOS) Near-infrared Imager and Spectrograph (CONICA), abbreviated as NACO (Lenzen et al. 2003; Rousset et al. 2003), were mounted at the Very Large Telescope on top of Cerro Paranal, Chile. The near-infrared imager NACO operates in the H, K, L, and M band and provides a set of narrow filters. NACO is equipped with an S13, S27, and S54 camera with a related spatial pixel scale of 13.3 mas, 27.0 mas, and 54.3 mas, respectively.

Furthermore, SINFONI is capable of providing a spectrum along with the produced image because of its integrated field unit (IFU). Hence, every pixel shows a related spectrum, resulting in a 3D data cube (two spatial dimensions and one spectral dimension). The SINFONI data used here were observed in the H + K band (1.4–2.4 μm) with a related pixel scale of 01 and a spectral resolution of 1500. Adaptive optics is enabled for both instruments. We apply common reduction steps, like the LINEARITY/DARK correction resulting in FLAT FIELDING. The prementioned reduction steps are applied to the data of both instruments. Because of the spectroscopic characteristics of SINFONI, we also use a WAVELENGTH and DISTORTION calibration. It should be noted that NACO and SINFONI have been decommissioned since 2019. As a successor, ERIS (Davies et al. 2018) combines the capabilities of NACO and SINFONI.

The Atacama Large Millimeter/submillimeter Array (ALMA) is on the Chajnantor Plateau, in Chile. The radio and submillimeter (submm) observations can be executed between 31 and 1000 GHz. The majority of the ALMA CO data used in this work (Prog. ID: 2015.1.01080.S) have been reduced with Common Astronomy Software Applications (CASA, CASA Team et al. 2022) and analyzed and discussed in Tsuboi et al. (2017b, 2019, 2020a, 2020b). In addition, we use scientific-ready data from the ALMA archive related to the Prog. ID 2012.1.00543.S (Martín et al. 2012; Moser et al. 2017). The ALMA data discussed and analyzed in this work show CO v = 0 (transition 3–2) at 343 GHz.

For the flux analysis based on the presented multiwavelength observations, we use the radiative transfer code HYPERION ⁶ using dust grains as ray-tracing sources (Robitaille 2011, 2017). For the spectrum that serves as an input quantity for HYPERION, we use flux density values estimated from the magnitude of the related source. Consequently, we measure the peak counts of the object of interest and compare it with a reference source with known properties. For this, we use

$$\begin{eqnarray}&&{\mathrm{mag}}_{\mathrm{obj}}={\mathrm{mag}}_{\mathrm{ref}}-2.5\mathrm{log}\left(\displaystyle \frac{{\mathrm{counts}}_{\mathrm{obj}}}{{\mathrm{counts}}_{\mathrm{ref}}}\right)\end{eqnarray} \tag{ 1 }$$

where mag_ref and counts_ref refer to the reference source, and mag_obj and counts_obj to the analyzed object. We estimate the source flux with

$$\begin{eqnarray}&&{f}_{\mathrm{obj}}={f}_{\mathrm{ref}}\,\times \,{10}^{[-0.4({\mathrm{mag}}_{\mathrm{obj}}-{\mathrm{mag}}_{\mathrm{ref}})]}\end{eqnarray} \tag{ 2 }$$

where f_ref donates the flux (called zero flux) of the reference source. The basic settings for the code are listed in Table 1.

The code allows modeling various components of YSOs, such as the gaseous accretion disk or bipolar cavities (see Figure 1 and Sicilia-Aguilar et al. 2016). For the code used in this analysis, we model a flared disk with increasing height. The shape of the flared disk is described with

$$\begin{eqnarray}&&{h}_{(R)}={h}_{0}{\left(\displaystyle \frac{R}{{R}_{0}}\right)}^{\beta }\end{eqnarray} \tag{ 3 }$$

where we set β = 1.25 following the settings used in Robitaille (2011, 2017). Furthermore, a flattened rotational and infalling dust envelope (Ulrich type, see Ulrich 1976) can be modeled depending on the flux density. Because HYPERION uses grains as emitters, the properties of dust are directly related to the outcome of the model. Therefore, in the following section, we will outline the dust model used for the radiative transfer analysis. For the assumed model that is used in HYPERION, we construct a dusty envelope and a gaseous accretion disk that are arranged around a stellar core. Because of the lack of high-resolution (spectral/spatial) IFU data covering the IRS 13 region, we cannot validate or exclude the presence of bipolar cavities (an example of these cavities is displayed in Peißker et al. 2019). In summary, our assumed model resembles the composition of a class I YSO (Figure 1).

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2.3.1. Dust models

The high-pass-filtering technique is a common tool for deblurring imaging data by minimizing the influence of the point-spread function (PSF) wings of a bright star. While the Lucy Richardson (LR) algorithm (Lucy 1974) offers a variety of setup parameters, the smooth-subtract algorithm is a robust approach to analyzing the data. Critically, the LR algorithm tends to transform elongated structures into point sources. While this does not necessarily exclude the usage of the algorithm on regions with extended structures, IRS 13 shows elongated and compact objects with unknown nature. ⁷ The accessible implementation into the process of analyzing the data is done by smoothing the original image I_orig with a Gaussian kernel with a size that should be in the range of the PSF measured in the data. The resulting smoothed image I_smo describes a low-pass-filtered version of I_orig. With

$$\begin{eqnarray}&&{I}_{\mathrm{orig}}\,-\,{I}_{\mathrm{smo}}={I}_{\mathrm{high}}\end{eqnarray} \tag{ 4 }$$

we acquire the high-pass-filtered version I_high of I_orig. To enhance the image quality, one can apply a Gaussian smoothing filter smaller than the PSF to I_high. A comparable description of this process is outlined in Peißker et al. (2022) as well. A rather qualitative comparison is presented in the following, where we investigate the astrometric and photometric imprint of the high-pass filter on the data. In general, we find no significant difference between a stellar position determined in I_orig or I_high. For the flux shown in Figure 2, we find an uncertainty of about 20% between filtered and nonfiltered data. Taking into account the usual flux density uncertainties shown, for example, in Peißker et al. (2023b) and this work, the value distribution shown in Figure 2 is well inside the expected range. We emphasize that we expect a flux difference between high-pass-filtered and nonfiltered data due to the presence of elongated structures, such as the minispiral (see Figure 3). High-pass filtering tends to convert elongated structures into point sources, resulting in a broader flux distribution, as shown in Figure 2. Therefore, the analysis of individual sources with the high-pass filter presented here should be carried out with caution.

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The analysis of about two decades of near-infrared (NIR) and mid-infrared (MIR) NACO data revealed 33 sources that can be observed in various bands in addition to previously known dust-enshrouded objects. In Figure 3, we show the L-band detection of all the investigated sources in this work. In addition, Appendix D and Appendix E reveal the related H- and K-band identification of the dusty sources (DS). The rich data set permits us to produce light curves and individual detections of all new DS objects (Appendix F). Furthermore, Table 2 lists the magnitudes of the newly discovered DS objects. We compare all the known IRS 13 objects with the literature and list the new sources identified in Table 13, Appendix B. Consistent with the literature, we identified all known sources in the L, K, H, and M band. Because every previous analysis of the cluster covered only a fraction of the objects investigated here, our objective was to provide a complete list of all sources with a consistent nomenclature. To avoid confusion with existing studies of the region, we adapt the nomenclature for the brightest sources (E1–E7 and α-ι) of the IRS 13 cluster.

For the analysis of the data, we applied the introduced image sharpener and extracted the positions with a Gaussian fit with dimensions that correspond to the PSF of the data. The FWHM is about 5 to 6 pixels. With a spatial pixel scale for the L-band data of 27 mas, the dimensions of the corresponding PSF are about 13 –16. For the K-band data and a related spatial pixel scale of 13 mas, the dimensions of the PSF transfer to 06 –07. Because the sources studied in this work have dominant MIR emissions suffering from reduced confusion and crowding, we focus on the L band and M band whenever the detection of the objects in the NIR is blended. Because of the prominent and variable background of the crowded and dense cluster, we did not apply a local background subtraction, because we consider confusion the dominant source of uncertainty. Especially DS4 and DS5 suffer from confusion and blending effects that are confronted by the usage of the mean covering almost two decades of observations (Table 2).

Simultaneously with the photometric analysis presented in Section 3.1, we estimate the proper motion of the investigated cluster members. Because of the chance of confusion regarding the detectability of the DS, we use K- and L-band observations whenever possible carried out with NACO between 2002 and 2019. Except for 2014 and 2015, we trace the objects listed in Table 13 in the majority of available observations. We fit a PSF-sized Gaussian to each individual source to extract its position (Table 3). The origin of our reference frame coincides with the position of Sgr A*. For this, we identify the position of the B2V star S2 and use its well-known and observed orbital solution. From the orbital solution and the position of S2 (Do et al. 2019), we derive the location of Sgr A*. We refer to Appendix C, which lists all positions of S2 and the dusty sources investigated in this work. Because the IRS 13 cluster is about 0.12 pc away from the location of the SMBH, we assume an approximately vanishing velocity v_{Sgr A*} of Sgr A*. Even for objects close to Sgr A*, the velocity effect caused by v_{Sgr A*} is in the subpixel regime (Parsa et al. 2017). We list the resulting proper motion of the DS and all other objects investigated in this work in Table 3. Because of the high degree of crowding, the standard-deviation-based uncertainties may not cover the full set of entities. With upcoming JWST observations, we expect decreased astrometric uncertainties from the Mid-Infrared Instrument (MIRI) IFU data due to unique Doppler-shifted emission lines. However, we use the results from the presented astrometric analysis to investigate the cluster and the sources for any anisotropy. We will use the approach of Eckart & Genzel (1997) and Genzel et al. (2000), where the authors used the anisotropy parameter to analyze the stellar content of the S cluster. The anisotropy parameter is defined as

$$\begin{eqnarray}&&{\gamma }_{{TR}}=\displaystyle \frac{{v}_{T}^{2}-{v}_{R}^{2}}{{v}_{T}^{2}+{v}_{R}^{2}}\end{eqnarray} \tag{ 5 }$$

where v_T and v_R refer to the proper motion components perpendicular and parallel to the projected radius vector in the sky, respectively. The anisotropy parameter ${\gamma }_{{TR}}$ provides an accessible numerical approach to investigate IRS 13–related objects for abnormalities. These abnormalities would imply a tendency for a specific stellar type or substructure. A uniform data point distribution indicates a continuous and randomized structure of the cluster. For example, Ali et al. (2020) expected a sine-like distribution for the inclination angle. While this cannot be transferred to the anisotropy parameter, the Gaussian-shaped and uniform cluster discussed in von Fellenberg et al. (2022) can be used for the expected distribution of the dusty sources. Therefore, we will investigate the cluster sample for Gaussian-like structures to investigate the presence of substructures.

Table 3. Proper Motions of the Sources Investigated in This Work Based on L-band Observations Carried Out With NACO Between 2002 and 2018

ID	r0,R.A.(mas)	r0,Decl.(mas)	vR.A.(km s−1)	vDecl.(km s−1)	Δr0,R.A. (mas)	Δr0,Decl.(mas)	ΔvR.A. (km s−1)	ΔvDecl.(km s−1)
α	−2677.0	−1479.1	87.4	51.6	3.2	1.9	18.9	11.5
β	−2890.0	−1246.0	73.4	115.4	3.0	4.1	16.2	21.8
γ	−3088.0	−1003.0	−73.0	170.2	3.4	3.2	18.5	7.8
δ	−2903.6	−854.3	7.9	142.3	1.0	4.3	5.0	26.1
	−2883.0	−1015.0	42.9	158.9	2.3	6.7	12.9	34.5
ζ	−3150.8	−826.5	−128.9	203.5	5.5	7.7	31.0	42.7
η	−3104.0	−654.9	−27.8	68.0	1.2	2.7	6.6	14.8
ϑ	−2700.0	−892.0	90.4	140.8	4.8	5.5	28.7	32.1
ι	−3043.4	−1240.4	−54.2	81.9	3.4	4.3	18.7	23.8
1	−2795.0	−276.4	−74.0	−94.0	2.0	2.6	13.6	17.1
2	−2954.4	−175.8	9.2	248.0	4.6	10.5	26.4	60.9
3	−3070.9	−251.8	43.5	280.6	4.4	10.1	22.8	57.8
4	−2687.0	−480.3	21.2	−18.8	5.1	2.0	24.6	11.5
5	−2935.5	−408.9	−65.0	117.9	4.6	9.0	30.8	60.3
6	−3182.0	−421.7	−151.6	289.2	6.0	12.8	32.1	62.6
7	−3217.6	−531.3	−124.7	329.7	5.2	11.9	20.2	61.5
8	−3430.4	−636.4	−289.6	443.0	11.7	18.6	67.6	104.6
9	−3597.6	−435.1	31.1	−125.5	3.2	5.6	19.3	35.3
10	−3844.4	−387.9	152.5	−445.1	4.4	10.3	32.3	77.1
11	−2323.4	−891.0	12.3	−56.2	0.9	2.1	4.6	11.3
12	−2484.7	−830.9	175.1	−330.6	5.7	11.4	30.8	62.4
13	−3593.2	−723.4	−381.0	317.9	17.1	14.1	78.8	66.4
14	−3629.7	−867.4	−468.4	242.8	14.3	7.9	74.6	37.9
15	−3526.0	−917.0	−427.7	247.2	20.3	10.4	97.6	47.1
16	−3909.4	−767.9	−17.5	−106.5	3.3	5.5	21.9	33.8
17	−4106.0	−930.8	−61.6	62.1	3.9	2.8	19.6	16.2
18	−4267.0	−858.9	−191.4	−34.7	8.7	5.2	48.9	31.1
19	−4178.5	−956.4	−229.2	−100.4	13.4	7.2	67.2	35.4
20	−4017.9	−1125.5	−190.6	1.7	7.5	2.1	36.6	10.6
21	−3781.6	−1318.7	−327.4	69.3	12.9	2.8	64.7	15.6
22	−3383.1	−1021.1	−187.9	207.5	8.5	9.8	44.0	48.6
23	−2543.5	−1155.7	161.4	5.1	6.8	7.3	39.0	42.2
24	−2461.0	−1441.3	172.1	−93.8	7.8	6.4	38.8	34.1
25	−2410.6	−1687.7	152.6	5.2	5.9	2.6	30.5	13.0
26	−2801.4	−1750.3	103.3	28.9	4.7	2.0	29.5	11.5
27	−3404.0	−720.0	−51.6	−231.9	2.8	7.9	14.7	41.1
28	−2551.8	−1318.4	166.4	124.0	7.6	6.0	43.7	34.0
29	−2429.7	−1719.9	66.85	401.1	8.9	6.6	29.9	22.1
30	−2921.1	−2047.5	66.85	133.7	10.6	7.6	35.6	25.4
31	−2948.4	−1474.2	−200.5	200.5	10.7	5.4	35.6	17.5
32	−2730.0	−1064.7	−468.0	133.7	9.6	4.0	32.2	13.3
33	−2921.1	−1283.1	−200.5	−267.4	10.5	4.5	35.2	15.1
E1	−2935.0	−1637.2	−84.3	−280.0	4.9	10.9	25.4	55.9
E2	−3161.5	−1729.6	−145.2	−86.2	3.8	2.4	24.9	17.3
E3	−3171.0	−1521.0	−71.5	−135.2	3.5	5.4	19.4	27.9
E4	−3201.0	−1424.0	−182.2	23.2	8.4	6.8	38.5	36.7
E5.0	−3401.0	−1528.0	−110.6	45.4	5.2	3.9	31.1	22.0
E5.1	−3413.0	−1579.3	−317.4	−69.6	15.2	8.6	75.1	38.2
E7	−3549.0	−1260.0	148.3	−55.4	6.3	2.5	28.9	12.9

Note. The uncertainties represent the standard deviation. The distance of the DS indicates the related position in 2002.

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In Table 3, we list the resulting proper motions of all investigated objects (Table 13) with the related distances to Sgr A*. Using the proper motions listed in Table 3, we derive the velocity–velocity diagram (Figure 4). From the fit and the data points displayed in Figure 4, it is evident that the proper motion of the investigated sources shows an asymmetric distribution around the geometrical center, implying the presence of a trend. Translating this finding to a density as a function of quadrant yields:

• 1:  
  13 sources in a (26.5%)
• 2:  
  19 sources in b (38.8%)
• 3:  
  7 sources in c (14.3%)
• 4:  
  10 sources in d (20.4%)

Based on this analysis, the significance of a trend for the proper motion of the DS lacks a reasonable level of explicitness. From the analysis of the proper motion distribution, it is implied that the dusty sources follow a rather uniform arrangement, which is furthermore reflected in the Gaussian-like density probability displayed in Figure 5. This figure shows the Gaussian distribution of the dusty sources around the geometrical center of the cluster as a function of the distance d, which is estimated with p_(geo) = p_(x,y) − p_aver(x,y). In the given relation, p_{( geo)} is the geometrical center of the cluster, p_aver(x,y) is the averaged distance of all cluster sources to Sgr A*, and p_(x,y) is the averaged distance of a single source between 2002 and 2018. With this, the presentation of the distribution of the DS shown in Figure 5 does not reflect possible existing anomalies of the cluster. Despite the decreased surface density at about 06 indicated in Figure 5, we find a probability density consistent that resembles a Gaussian function as we would expect for a uniform cluster (Genzel et al. 2000). Because p_{( geo)} does not necessarily have to be located at the highest stellar density, the Gaussian fit exhibits an offset from d = 0 mas, as illustrated Figure 5. Therefore, we aim to expand the search for substructures and translate the estimated values in Table 3 into the anisotropy parameter ${\gamma }_{{TR}}$ indicated by Equation (5). In the first three plots displayed in Figure 6, we show ${\gamma }_{{TR}}$ as a function of distance from Sgr A* for the E stars, dusty sources, and all combined sources. The apparent continuous distribution of the data points for all sources illustrated in Figure 4 and Figure 6 is expected because of the shared parameter. However, if we separate the distribution of the anisotropy parameter into four bins with a corresponding size of 0.5 each, we find indications for a slight overdensity close to ±1. In particular, we find:

• 1:  
  14 sources between 1.0 and 0.5
• 2:  
  6 sources between 0.5 and 0.0
• 3:  
  9 sources between 0.0 and −0.5
• 4:  
  19 sources between −0.5 and −1.0

We normalize the distribution to the total number of sources and estimate that about 30% of the sources are in the 0.5 to 1.0 bin, while almost 40% can be found in the −0.5 to −1.0 bin, suggesting an overdensity of sources in bin 1 and bin 4. In particular, this overdensity is reflected in the lower-right plot of Figure 6. There, we show the normalized number of sources as a function of the anisotropy parameter ${\gamma }_{{TR}}$. In the same plot, we incorporate the theoretical probability distribution (PDF) with a constant anisotropy, where we adapt the corresponding normalized function

$$\begin{eqnarray}&&\mathrm{PDF}({\gamma }_{{TR}}){\rm{d}}{\gamma }_{{TR}}=\displaystyle \frac{{\rm{n}}!{\left(\sqrt{1+{\gamma }_{{TR}}}\right)}^{2n-1}}{\pi (2{\rm{n}}-1)!!\sqrt{1-{\gamma }_{{TR}}}}{\rm{d}}{\gamma }_{{TR}}\end{eqnarray} \tag{ 6 }$$

from Genzel et al. (2000). In the above equation, n refers to a power-law distribution index with β = 1/2 − n. We can now assume numerical values representing a constant anisotropy that classifies uniform clusters. For example, the magenta PDF in the lower-right plot of Figure 6 is calculated with Equation (6) and a constant anisotropy of β = − 3/2 resembling the results of Genzel et al. (2000). ⁸ From the data points representing the sources in IRS 13 shown in Figure 6, it becomes directly obvious that the cluster is not uniform and shows anisotropy that peaks at ±1 in strong agreement with Genzel et al. (2000). However, for the results displayed in Figure 6, we picked only one numerical value for β to maintain clarity. To inspect the expected distribution of an anisotropic cluster, we use Monte Carlo simulations, shown in Figure 7. This figure strengthens our results, which show a peak of ${\gamma }_{{TR}}$ at ±1 as well. In Figure 7, we simulate 10,000 stars and find an overdensity at ${\gamma }_{{TR}}\pm 1$ as for IRS 13. Therefore, the investigated cluster that harbors the dusty sources is not uniform. In addition, we estimate a velocity dispersion from the data listed in Table 3 and illustrated in Figure 4 of 128.86 ± 0.14 km s⁻¹ for the cluster. From this we can directly derive the mass that is needed to bind the stars to the cluster. With M_IRS13 = 〈v²〉 · R/G where R = 0.01pc donates the approximate size of the cluster and G the gravitational constant, we get ∼(3.9 ± 0.1) × 10⁴ M_⊙ in agreement with independently calculated literature values (see Schödel et al. 2005; Paumard et al. 2006; Tsuboi et al. 2017b, 2020b). This enclosed mass estimate can be used to calculate the Hill radius r_Hill to inspect the gravitational bounds of the IRS 13 cluster. We use

$$\begin{eqnarray}&&{r}_{\mathrm{Hill}}=D{\left({M}_{\mathrm{IRS}13}/3{M}_{\mathrm{SgrA}* }\right)}^{1/3},\end{eqnarray} \tag{ 7 }$$

where D donates the distance to Sgr A* and M_SgrA* the related mass of the SMBH. We use D = 0.15 pc and M_SgrA* = 4 × 10⁶ M_⊙ (Peißker et al. 2022; Event Horizon Telescope Collaboration et al. 2022) and get r_Hill = 0.022 pc = 22 m pc. Because we investigate the complete IRS 13 region, including the E stars and the dusty objects (Figure 3), r_Hill is in remarkable agreement with the measured diameter of the cluster core region (≈45m pc, see Section 4).

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We use a multiwavelength approach to investigate the nature of the brightest M-band dust objects in the IRS 13 cluster (Figure 8). Starting from Figure 8 in the M band, we analyze the emission of the dust objects in the H, K, and L band (see also Figure 3). Because Viehmann et al. (2006) analyzed an extensive amount of stellar sources in the environment of Sgr A* in various bands (see also Bhat et al. 2022), we use the close-by star IRS 2L as a reference source (Table 4). Because Viehmann et al. used part of the here investigated data set, the choice of the reference star ensures a consistent photometric approach. Because of the dominant contribution of Wolf-Rayet and O stars E1, E2, E3, and E4 (Maillard et al. 2004) in all the bands, we will use a high-pass filter to minimize the PSF wings. This process used is already described in detail in Section 2.4 and Peißker et al. (2022). The photometric robustness of high-pass filters compared with the raw data is further investigated in Ott et al. (1999). To inspect the validity of the proposed photometric robustness discussed in Ott et al., we compare the estimated L-band magnitudes of DS1 (Figure 3) in the raw data with the results of the high-pass filtering. As listed in Table 5, we do not find a significant difference between the filtered and nonfiltered data in agreement with the analysis of Ott et al. (1999). We would like to emphasize that the analysis of the investigated dusty objects focuses on the colors defined as the difference between two magnitudes. The colors are not affected by systematic differences potentially induced by the applied high-pass filter, because variations would be canceled out. However, using Equation (1) with the magnitudes of reference star IRS 2L (Table 4), we estimate the magnitudes for the dusty sources and the main-sequence stars E1–E7 (Figure 8). Consult Table 6 for the related values, including the standard deviation. From the H–K and K–L colors of the investigated sources, we do find a substantial difference between the two groups (dusty sources—E stars) of cluster members (Figure 9). In addition to the sources investigated here, we also include magnitudes from the related publication of various other objects, such as DSO/G2 (Peißker et al. 2021c), X3 (Peißker et al. 2023b), and X7 (Peißker et al. 2021a). A complete list of all used sources analyzed for Figure 9 is listed in Table 6. The findings presented in Figure 9 agree with the studies and classifications presented in Peißker et al. (2020c) and will be discussed in Section 4. Because we derived the magnitudes of the IRS 13 sources, we will estimate the related flux density and the corresponding uncertainties with Equation (2). The flux density is useful to estimate the spectral energy distribution (SED) of the individual sources, which will be presented in the next section. Compared with the literature, we maximize the spectral coverage and include the radio data observed ⁹ with ALMA (Figure 10) and previously analyzed, e.g., in Tsuboi et al. (2017b). Because of the science-ready character of the calibrated data, we list the corresponding flux values of the dusty sources in Table 7.

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Table 6. Dereddened Magnitude and Flux Estimates of the E Stars and the Brightest Dusty Sources of the IRS 13 Cluster (See Figure 3)

ID	H Band		K Band		L Band		M Band		K–L	H–K
	(mag)	(mJy)	(mag)	(mJy)	(mag)	(Jy)	(mag)	(Jy)
α	20.68 ± 0.85	${0.35}_{-0.19}^{+0.41}$	15.75 ± 0.14	4.18 ${}_{-0.50}^{+0.57}$	9.48 ± 0.30	0.17 ${}_{-0.04}^{+0.05}$	7.56 ± 0.17	0.59 ${}_{-0.08}^{+0.10}$	6.27 ± 0.29	4.93 ± 0.29
β	19.74 ± 0.04	${0.83}_{-0.03}^{+0.03}$	15.18 ± 0.21	7.06 ${}_{-1.24}^{+1.50}$	8.79 ± 0.78	0.32 ${}_{-0.16}^{+0.34}$	7.57 ± 0.14	0.59 ${}_{-0.07}^{+0.08}$	6.39 ± 0.29	4.56 ± 0.13
γ	16.28 ± 0.20	20.22${}_{-3.40}^{+4.09}$	14.19 ± 0.30	17.58 ${}_{-4.24}^{+5.59}$	9.26 ± 0.98	0.21 ${}_{-0.12}^{+0.31}$	7.91 ± 0.29	0.43 ${}_{-0.10}^{+0.13}$	4.93 ± 0.34	2.09 ± 0.05
δ	19.56 ± 0.48	${0.98}_{-0.35}^{+0.54}$	15.90 ± 0.28	3.64 ${}_{-0.82}^{+1.07}$	9.16 ± 0.76	0.23 ${}_{-0.11}^{+0.23}$	7.70 ± 0.17	0.52 ${}_{-0.07}^{+0.08}$	6.74 ± 0.09	3.66 ± 0.52
	⋯	⋯	16.27 ± 0.22	2.58 ${}_{-0.47}^{+0.58}$	9.50 ± 1.16	0.17 ${}_{-0.11}^{+0.32}$	8.34 ± 0.52	0.29 ${}_{-0.11}^{+0.17}$	6.77 ± 0.69	⋯
ζ	20.06 ± 0.46	${0.62}_{-0.21}^{+0.32}$	16.01 ± 0.62	3.29 ${}_{-1.43}^{+2.53}$	9.38 ± 0.84	0.19 ${}_{-0.10}^{+0.22}$	8.12 ± 0.29	0.35 ${}_{-0.08}^{+0.10}$	6.63 ± 0.11	4.05 ± 0.09
η	15.29 ± 0.16	50.34${}_{-6.89}^{+7.99}$	12.80 ± 0.19	63.27 ${}_{-10.15}^{+12.10}$	9.25 ± 0.71	0.21 ${}_{-0.10}^{+0.19}$	8.11 ± 0.23	0.35 ${}_{-0.06}^{+0.08}$	3.55 ± 0.26	2.49 ± 0.02
ϑ	21.04 ± 0.25	${0.25}_{-0.05}^{+0.06}$	⋯	⋯	10.29 ± 1.22	0.08 ${}_{-0.05}^{+0.17}$	9.14 ± 0.39	0.13 ${}_{-0.04}^{+0.06}$	⋯	⋯
ι	16.67 ± 0.21	14.12${}_{-2.48}^{+3.01}$	14.23 ± 0.29	16.95 ${}_{-3.97}^{+5.19}$	9.71 ± 1.62	0.14 ${}_{-0.10}^{+0.48}$	8.12 ± 0.45	0.35 ${}_{-0.12}^{+0.18}$	4.52 ± 0.66	2.44 ± 0.25
	(mag)	(Jy)	(mag)	(Jy)	(mag)	(Jy)	(mag)	(Jy)
E1	11.16 ± 0.06	2.25 ${}_{-0.12}^{+0.12}$	9.19 ± 0.17	1.75 ${}_{-0.25}^{+0.29}$	7.69 ± 0.65	0.90 ${}_{-0.40}^{+0.74}$	6.96 ± 0.33	1.03 ${}_{-0.27}^{+0.36}$	1.50 ± 0.23	1.97 ± 0.03
E2	11.31 ± 0.08	1.96 ${}_{-0.13}^{+0.15}$	9.23 ± 0.21	1.69 ${}_{-0.29}^{+0.36}$	7.07 ± 0.64	1.60 ${}_{-0.71}^{+1.29}$	6.17 ± 0.27	2.14 ${}_{-0.47}^{+0.60}$	2.16 ± 0.21	2.08 ± 0.02
E3	14.43 ± 0.59	0.11 ${}_{-0.04}^{+0.08}$	10.79 ± 0.67	2.66 ${}_{-0.18}^{+0.34}$	6.52 ± 0.51	2.66 ${}_{-1.00}^{+1.59}$	5.17 ± 0.01	5.39 ${}_{-0.04}^{+0.04}$	4.27 ± 0.08	3.64 ± 0.26
E4	12.62 ± 0.15	0.58 ${}_{-0.07}^{+0.08}$	10.25 ± 0.33	1.45 ${}_{-0.17}^{+0.23}$	7.18 ± 0.65	1.45 ${}_{-0.65}^{+1.19}$	6.15 ± 0.15	2.18 ${}_{-0.28}^{+0.32}$	2.77 ± 0.31	2.37 ± 0.08
E5.0	⋯	⋯	14.24 ± 0.41	0.65 ${}_{-0.01}^{+0.01}$	8.04 ± 0.99	0.65 ${}_{-0.39}^{+0.97}$	6.68 ± 0.31	1.34 ${}_{-0.33}^{+0.44}$	6.20 ± 0.70	⋯
E5.1	⋯	⋯	14.53 ± 0.09	0.61 ${}_{-0.01}^{+0.01}$	8.11 ± 0.87	0.61 ${}_{-0.34}^{+0.75}$	6.95 ± 0.29	1.04 ${}_{-0.24}^{+0.32}$	6.42 ± 0.48	⋯
E7	13.21 ± 0.11	0.54 ${}_{-0.02}^{+0.02}$	10.61 ± 0.11	0.32 ${}_{-0.04}^{+0.05}$	8.82 ± 0.71	0.32 ${}_{-0.15}^{+0.29}$	8.92 ± 0.85	0.17 ${}_{-0.09}^{+0.20}$	1.79 ± 0.29	2.60 ± 0.05
	(mag)	(Jy)	(mag)	(Jy)	(mag)	(Jy)	(mag)	(Jy)
IRS 3	14.68 ± 0.12	0.08 ${}_{-0.01}^{+0.02}$	9.66 ± 0.62	1.14 ${}_{-0.49}^{+0.88}$	6.03 ± 0.03	4.19 ${}_{-0.12}^{+0.11}$	2.99 ± 0.14	40.16 ${}_{-4.86}^{+5.53}$	3.63 ± 0.32	5.02 ± 0.35
IRS7	9.26 ± 0.04	13.12 ${}_{-0.60}^{+0.36}$	6.50 ± 0.10	20.95 ${}_{-1.85}^{+2.02}$	6.01 ± 0.05	4.26 ${}_{-0.19}^{+0.20}$	3.12 ± 0.49	35.63 ${}_{-11.94}^{+20.33}$	0.49 ± 0.08	2.76 ± 0.07

Note. For comparison, we also list the measured values of IRS 3 and IRS 7. The indicated uncertainties of the magnitudes and fluxes for all objects are based on the standard deviation except for IRS 3 and IRS 7. The uncertainties for the two bright stars are adapted from published studies, namely Blum et al. (1996), Viehmann et al. (2006), and Pott et al. (2008). The used reference magnitudes for IRS 2L are listed in Table 4. For , E5.0, and E5.1, we do not find H-band emission above the detection limit, which might be due to confusion. The uncertainties of the magnitudes and fluxes reflect the standard deviation. As pointed out by Fritz et al. (2010) and implied by the east–west elongation indicated in Eckart et al. (2004), E3 may be a collection of several less luminous stars. Controversially, Tsuboi et al. (2017b) associates E3 with the location of a possible IMBH.

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Table 7. Flux Density Values for the Dusty Objects Derived From CO ALMA Observations

ID	CO (v=0), 343 GHz
	[mJy]
α	1.43 ± 0.5
β	1.05 ± 0.5
γ	1.09 ± 0.5
δ	1.91 ± 0.5
	1.38 ± 0.5
ζ	0.61 ± 0.5
η	(0.19 ± 0.5)*
ϑ	(1.15 ± 0.5)**
ι	1.29 ± 0.5
IRS 3	129.1 ± 55.1
IRS7	34.4 ± 0.4

Note. Please see Figure 10 for the related source identification. For η, we only estimate an upper limit, whereas ϑ seems to be confused with δ. We use IRS 13E3 as a reference source with a corresponding peak flux of 10.5 ± 0.5 mJy and adapt the uncertainty as proposed in Tsuboi et al. (2017a). These submm/radio flux values in combination with the IR values listed in Table 6 are used for the input spectrum of HYPERION.

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The spectral analysis of the O- and W-type stars of the IRS 13 cluster is well covered in the literature (Maillard et al. 2004). Despite bright emission in various bands, the dusty sources analyzed in the literature lack a detailed spectral analysis. We apply the 3D radiative transfer model implemented in the HYPERION code and incorporate the results listed in Table 6 and Table 7. These flux density values are used as input parameters from which HYPERION estimates the best-fit SED. The spectrum is renormalized and ensures a high synergy between the observations and the simulations. The uncertainties of the input flux density values (Table 6) estimated from the standard deviation do account for a variable background, close-by sources, and the stellar density as well as the embedded structure (eminent in the L and M band) of the cluster.

To motivate the usage of HYPERION, which models the emission of YSOs, we refer to the color–color diagram shown in Figure 9, which justifies our approach. Incorporating the derived flux and uncertainty values, we find a best-fit solution for the spectral energy distribution of the dusty sources, as shown in Figure 11. We list related input parameters, such as stellar mass and luminosity, in Table 8. In agreement with the top-heavy mass function derived by Paumard et al. (2006) and Lu et al. (2013), we find several massive and high-mass YSOs in the IRS 13 cluster, in line with its exceptional high core density of ${\rho }_{\mathrm{core}}\geqslant 3\times {10}^{8}{M}_{\odot }\,{\mathrm{pc}}^{-3}$ (Paumard et al. 2006). Except for η, all investigated sources exhibit a stellar mass between 4.0 and 10.0 M_⊙. Taking into account the stellar properties of the dusty sources in combination with the accretion rate (denoted as the infall rate in Table 8), we classify these objects as massive Herbig Ae/Be stars. Because of their nature, these dusty sources have an age of 10⁴–10⁵ yr and show a strong photometric correlation (Figure 9) with the recent discovery of the HMYSO X3 (Peißker et al. 2023b). Regarding η, more data are needed to classify the low-mass source. However, the shape of the related SED implies that η could be associated with a low-mass T Tauri star (Beckwith et al. 1990; Kenyon & Hartmann 1995).

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Table 8. Best-fit Parameters Describing the Flux Density Distribution of the Dusty Sources of IRS 13 Indicating Their Stellar Nature Using the Radiative Transfer Model HYPERION

ID	Mass (M⊙)	Luminosity (103 × L⊙)	Infall rate $({10}^{-6}\times {\dot{M}}_{\odot }$)	Radius (R⊙)	Disk mass (M⊙)	Disk size (AU)	Envelope size (AU)
α	5.0 ± 1.0	9 ± 1	5 ± 1	2 ± 0.5	0.1 ± 0.01	0.06-200	0.09-500
β	8.0 ± 1.0	10 ±	0.3 ± 1	3 ± 0.5	0.01 ± 0.005	0.04-200	0.09-350
γ	6.0 ± 1.0	9 ± 1	0.3 ± 0.1	4 ± 1	0.05 ± 0.01	0.04-200	0.09-500
δ	10.0 ± 2.0	11 ± 1	0.5 ± 0.1	3 ± 1	0.01 ± 0.001	0.04-200	0.09-700
	7.0 ± 2.0	7 ± 2	0.5 ± 0.1	3 ± 2	0.1 ± 0.01	0.04-200	0.09-700
ζ	4.0 ± 1.0	7 ± 1	0.3 ± 0.1	3 ± 1	0.06 ± 0.01	0.04-100	0.09-500
η	0.5 ± 0.2	2 ± 0.5	⋯	0.8 ± 0.2	0.005 ± 0.002	0.13-50	⋯
ϑ	7.0 ± 1.5	8 ± 1	0.5 ± 0.1	3 ± 1	0.01 ± 0.02	0.04-200	0.04-700
ι	10 ± 2.0	12 ± 2	0.05 ± 0.01	7 ± 2	0.5 ± 0.1	0.02-100	0.04-700

Note. We motivate the application of the radiative transfer model describing YSOs by the clear color–color classification shown in Figure 9. Considering the pronounced slope of the NIR/MIR SED and their related position in the color–color diagram, it is suggested that the nature of these sources allows the classification as candidate YSOs (class I) (Lada 1987). For a demonstration of HYPERION's feedback after incorporating the estimated flux density values for IRS 3, please refer to Section 4.2.

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NACO L-band observations of IRS 13 revealed 33 unknown objects in addition to previously investigated dust and stellar sources (Table 13; see Maillard et al. 2004; Eckart et al. 2013). The brightest sources, donates with Greek letters, can be observed in various bands ranging from the infrared to the radio/submm domain. Because the majority of the studied MIR dust sources exhibit K- and H-band NIR counterparts (see Appendix D and Appendix E), a stellar nature is inevitable. Compared with the main-sequence E stars (O/WR-type), the K–L and H – K colors of the dusty sources are represented by two to three times higher numerical values. These high-infrared H – K and K – L colors suggest, together with the survey of Ishii et al. (1998), a YSO classification for the bright dusty objects of IRS 13. Further studies of YSOs were carried out by Lada & Adams (1992), who used J – H and H – K colors for their classification. Although the geometrical composition of the circumstellar components influences the NIR emission of YSOs, our derived H – K colors are in agreement with studies of intermediate and high-mass YSOs (see also Berrilli et al. 1992). A further indicator that underlines the classification of the dusty sources as YSOs is illustrated in Figure 11. The flux density values, covering a spectral range between the IR and the submm/radio, are fitted with a model representing the typical emission of Class I YSOs. While the best-fit models presented in Figure 11 do not necessarily exclude other interpretations of the flux density distribution of the dusty sources, it is still a strong footprint of YSOs. Observations with the JWST and MIRI will potentially reveal typical emission lines that are associated with YSOs (see Section 4.6). We note that there is increased confusion and noise level when investigating J-band NACO observations, which requires a detailed data-processing method such as the Lucy Richardson deconvolution algorithm (Lucy 1974). However, these analysis steps exceed the scope of this work and will be part of a future publication. It should be noted that the classification of the brightest L-band sources in our sample exhibits a flux density distribution that agrees very well with class I YSOs except for η. The SED of this source shows similarities to a low-mass T Tauri star (Chiang & Goldreich 1997; Scoville & Burkert 2013). Hence, we will focus on the rather ambiguous classification of η using the J–H and H – K colors. Despite the challenges with respect to the J-band analysis of the dusty sources of IRS 13, we identify η without confusion about noise (Figure 12), and infer a related magnitude of mag_J = 18.8 ± 0.6 that results in J – H = 3.5 with H – K = 2.5 (Table 6). Taking into account the color–color analysis of Lada & Adams (1992), Ito et al. (2008), and Ojha et al. (2009), η appears to be a low-mass class I YSO that conflicts with the results of the radiative transfer model presented in Section 3.4 because of the missing envelope. We can only speculate on possible explanations for the interplay of the missing envelope with the photometric footprint of a class I YSO candidate. One option could be the intrinsic orientation of the system toward the observer. As implied by the SED results present in Figure 11, the inclination does have a considerably large impact on the shape of the distribution. Another option could be an evolutionary transition to the class II stage or a partial detachment of the envelope, as is already suggested for the class I YSO L1489 IRS (Brinch et al. 2007). Despite the exact classification, the global interpretation as a low-mass YSO is still plausible. Because DSO/G2 (Peißker et al. 2021c) is also classified as a low-mass YSO (see Zajaček et al. 2017), it is implied that both sources share a common nature. In summary, the general trend suggests that sources above the solid line illustrated in Figure 9 can be classified as YSOs, which implies that IRS 13 harbors two generations of stellar objects.

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Here we want to take a critical look at the results regarding the classification of the dusty sources as YSOs. In Eckart et al. (2004), the authors proposed for the first time the idea of associating the dusty sources of IRS 13 using a color–color diagram such as the one displayed in Figure 9. In agreement with Eckart et al. (2004) and the analysis of X3 presented in Peißker et al. (2023b), we found distinguishing colors compared with known main-sequence stars such as IRS 3 (Pott et al. 2008). To expand the color–color analysis of the dusty sources, we decided to apply the radiative transfer code HYPERION (Robitaille 2011, 2017) to the flux density values listed in Table 6. Although we find satisfying solutions to the flux density values in combination with the colors of the dusty sources (Figure 11), the outcome of the radiative transfer model could be biased because we already assumed a YSO classification. Therefore, we want to investigate the validity of this approach by using the class I model used for the SED shown in Figure 11 with the flux density values of the embedded and cool carbon star IRS 3. This star is most probably in the helium-core burning phase with a related stellar temperature of 3000 K based on the interferometric observations carried out with the MID-infrared Interferometric instrument/Very Large Telescope Interferometer (Leinert et al. 2003; Pott et al. 2008). For the stellar analysis of IRS 3 presented in Pott el al., the authors used the 1D radiative transfer code DUSTY (Ivezic et al. 1999), which is developed for AGB stars exhibiting radiatively driven winds. The NIR and MIR flux density values for IRS 3 listed in Table 6 are in reasonable agreement with the results presented in Figure 16 in Pott et al. (2008). Deviations between our estimated flux values and the ones derived by Pott et al. are reflected by the uncertainties given in Table 6 and the error bars shown in Figure 13. Using the estimated stellar properties of Pott et al. (2008) results in the magenta-colored SED displayed in Figure 13. Comparing the magenta-colored result with the measured flux density of IRS 3 reveals that HYPERION is not suitable to reflect the SED of the star. Using the upper limit of Pott el al. for a hot C-rich star with an amorphous carbon grain-dominated circumstellar dust distribution produces the brown-colored SED shown in Figure 13. In summary, the authors of Pott et al. conclude that IRS 3 is a cool carbon AGB star. However, we speculatively implement a stellar temperature of 1.9 × 10⁵ K in our radiative transfer model and find that this setting reflects the NIR and MIR emission. Neither of the presented SED solutions for IRS 3 using HYPERION fits the submm/radio flux. Taking into account the silicate absorption feature of IRS 3 observed in the N band (Pott et al. 2008), we can safely conclude that our speculative solution (black SED, Figure 13) is not valid. It is further well known that the existence of silicates requires a stellar temperature of a few 1000 K (Kozasa & Sogawa 1999; Tsuchikawa et al. 2021), in line with the established results for IRS 3 in the literature. Therefore, we conclude that the SED solution displayed in Figure 11 is a strong indication for the classification of the dusty sources as YSOs. The radiative transfer model HYPERION is not suitable for embedded main-sequence stars, which emphasize the color–color results presented in Figure 9.

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Because of the complexity of possible formation scenarios for the IRS 13 cluster, we refer to Paper II. However, we briefly want to outline the basic idea to explain the findings presented in this work. As proposed by Wang et al. (2020), ¹⁰ the resulting trajectory of the young cluster that spirals in toward the inner parsec could have resulted in the bow-shock formation caused by the supersonic motion of the cluster, cluster stellar wind, NSC winds, and the ISM. The dense region in the bow-shock shell would then be the birthplace of the second generation of IRS 13 stars (see Table 9). We note that the S cluster (Eckart & Genzel 1996) exhibits a similar composition of stellar objects as listed in Table 9 (Habibi et al. 2017; Peißker et al. 2020c; Ciurlo et al. 2020; Peißker et al. 2021c, 2023a). However, one would naturally expect a certain degree of elongation for an extended structure that gravitationally interacts with an SMBH such as Sgr A* (see simulations of Hobbs & Nayakshin 2009; Jalali et al. 2014). While the dimensions and nature of IRS 13 will be the focus of Paper II, we want to note that the [Fe iii] emission of the cluster implies a larger structure than is known from the literature. Considering the forbidden [Fe iii] line distribution presented in Lutz et al. (1993), we find that the peak emission of the iron line clearly envelopes the IRS 13 and the IRS 2 region, suggesting a combined setup of the northern and southern cluster region (see Figure 14). It is already known that IRS 2C is a foreground star, while IRS 2L and IRS 2S are embedded in the dust feature associated with IRS 13 (Buchholz et al. 2013). However, our proposed interpretation of the dimensions of the cluster is in line with the polarization measurements of Buchholz et al. (2013) and Roche et al. (2018). The polarimetric and magnetic field line analysis of Roche et al. reveals that the dust feature, which envelopes IRS 13 and IRS 2L/2C, is a coherent structure. The line distribution of [Fe iii] and the MIR dust emission match the size of the polarization region of IRS 13 in Buchholz et al. (2013) and Roche et al. (2018) underlying the proposed dimensions of the cluster in this work. In Paper II, we will present N-body simulations of an inspiraling cluster toward the inner parsec and investigate the possibility of such an event.

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As we have shown in Figure 6, the investigated cluster member sample shows a nonuniform distribution. In addition, most of the stars in the NSC follow this nonisotropic kinematic pattern, which historically resulted in the finding of a counterclockwise and clockwise disk, abbreviated as CCWS and CWS respectively (Genzel et al. 1996; Paumard et al. 2006). The mentioned velocity pattern is characterized by the normalized angular momentum j, which is defined by Genzel et al. (2003) as

$$\begin{eqnarray}&&j=({{xv}}_{y}\,-\,{{yv}}_{x})/{{pv}}_{p}\end{eqnarray} \tag{ 8 }$$

where x, v_x , y, and v_y refer to RA and decl. coordinates and their related components of proper motion, respectively, while the total distance and proper motion are given by p and v_p . With the above equation and the numerical values given in Table 3, we find the same distribution (Figure 15) for IRS 13 sources as shown in Paumard et al. (2006). In analogy to the anisotropy parameter shown in Figure 6, we divide the data presented in Figure 15 into four bins. We estimate that the bin with j ∈ {0.5, 1.0} contains 22% of the sources; for j ∈ {0.0, 0.5}, we get 8%; for j ∈ {0.0, − 0.5}, there are 10% of the sources; and finally, for j ∈ { − 0.5, − 1.0}, we obtain 60%. Therefore, we find an overdensity in bin 4, which strengthens our result presented in Figure 6. Because a nonuniform cluster is supposed to peak at ${\gamma }_{{TR}}=\pm 1$ as shown in Figure 7, ¹¹ it is expected to find anisotropic structures in the angular momentum plot displayed in Figure 15. For our sample, we clearly identify an overdensity at j = −1 (Figure 15), suggesting a CCW disk membership (Paumard et al. 2006; Ali et al. 2020; von Fellenberg et al. 2022). Based on this finding, we propose three different scenarios:

• [a]  
  The (C)CWS characterization of stars in the inner parsec is valid for all (gravitationally bound) subregions,
• [b]  
  The stellar overdensity of the IRS 13 cluster is the result of the intercepting disks of the CCW and CW systems,
• [c]  
  The IRS 13 cluster shows the imprint of the CCW and CW systems.

Concerning [a], we want to highlight the theoretical work of Hobbs & Nayakshin (2009), who predict two warped stellar disks/distributions for infalling molecular clouds. In addition, Ali et al. (2020) find a similar distribution for the S stars, which suggests that a two-disk or even a multidisk structure is present for other subregions as well, presumably those that are gravitationally bound to the SMBH or an IMBH. It needs to be verified by N-body numerical simulations how long the original disklike stellar structure that bears imprints of the formation mechanism can survive within the NSC. As mentioned before, the results presented in Figure 15 do reveal that the majority of investigated cluster members (>50%) are part of at least one disk, presumably the CCW disk. In addition, Paumard et al. (2006) suggested that the IRS 13 cluster may result from the interaction of the CCW and CW disks, i.e., scenario [b]. Although this scenario cannot be excluded, it implies an underlining rotation pattern that may have been created by infalling clouds in the first place (see [a] and Hobbs & Nayakshin (2009)). Because the E stars seem to be members of both distributions (Figure 6, upper left plot), the scenario seems plausible. However, we will investigate this particular point in more detail in Paper II because it would exceed the scope of this work. For the last scenario, [c], the IRS 13 cluster serves as a tracer for the underlining disk pattern. The infalling cluster IRS 13 may have intercepted the CCW and CW disks, which led to compressed gas densities that triggered star formation. Likewise, for [b], we will focus on this point in Paper II. Independent of the exact relation between IRS 13 and the (C)CW disks, we want to stress that Hansen & Milosavljević (2003) demanded a second black hole of ≈10⁴ M_⊙ in order to explain the unusually young age of the S-cluster stars (Morris 1993; Ghez et al. 2003; Habibi et al. 2017). The mass estimate is in the same order as the estimated enclosed mass for IRS 13 of 3.9 × 10⁴ M_⊙. Because of the age of the S-cluster members, IRS 13 is most certainly not a suitable candidate for process explaining the presence of young stars close to Sgr A*. But it is an interesting scientific question to explore and maybe even link possible large-scale imprints on molecular clouds in the circumnuclear disk (CND) from the enclosed mass of the IRS 13 cluster.

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Considering the young age of the IRS 13 cluster members, we should have detected an increased multiplicity and companion fraction (Portegies Zwart et al. 2010). Surprisingly, only one binary system close to IRS 13 is known (Pfuhl et al. 2014), which might not be related to the cluster in the first place. Taking into account the important role of binaries, especially for the evolution of massive stars (Sana et al. 2012), we expect frequent updates on the detection of binary systems in the IRS 13 cluster, particularly with the upcoming Extremely Large Telescope (ELT).

For example, Gautam et al. (2019) identified more than a dozen possible periodic systems. Because of resolution limitations, observation of visual binaries remains unlikely, damping the number of methods to detect such systems. Therefore, high-cadence observations with the scientific goal of identifying magnitude or line-of-sight (LOS) variations will remain the sufficient approach for multiplicity analysis.

However, given the number of sources investigated in this work, we speculatively expect at least one binary system among the sample. From the analysis, we observed minor position fluctuations of γ and ζ. These uncertainties may result from a confusion problem due to the high source density (Paumard et al. 2006).

Assuming that the above-mentioned uncertainties cannot be explained by source confusion, we will use the definition of Reipurth & Zinnecker (1993) and Duchêne et al. (2001) for the multiplicity fraction (MF) and the related companion fraction (CF). Consequently, MF is defined as

$$\begin{eqnarray}&&\mathrm{MF}=\displaystyle \frac{{\rm{B}}+{\rm{T}}+{\rm{Q}}+\cdot \cdot \cdot }{{\rm{S}}+{\rm{B}}+{\rm{T}}+{\rm{Q}}+\cdot \cdot \cdot }\end{eqnarray} \tag{ 9 }$$

where S defines the number of single stars and B is the number of binary star systems. Triple and quadruple star systems are defined by T and Q letters in the above equation. In addition, CF can be written as

$$\begin{eqnarray}&&\mathrm{CF}=\displaystyle \frac{2{\rm{B}}+3{\rm{T}}+4{\rm{Q}}+\cdot \cdot \cdot }{{\rm{S}}+2{\rm{B}}+3{\rm{T}}+4{\rm{Q}}+\cdot \cdot \cdot }\end{eqnarray} \tag{ 10 }$$

and defines the ratio of stars with a companion. For simplicity, we assume that γ and ζ are two binary systems. In total, we derived seven orbital solutions for the brightest sources of the sample. These boundary conditions are translated to MF ∼ 28% and CF ∼ 44% using Equation (9) and Equation (10), respectively. If we assume a rough cluster age of 4 ± 1 Myr based on the most evolved E stars (Maillard et al. 2004; Paumard et al. 2006; Zhu et al. 2020), we find similar MF and CF values in other clusters with a comparable age, such as RCW 108 (Comerón et al. 2005; Comerón & Schneider 2007) and the SMC cluster NGC 330 (Bodensteiner et al. 2021). If these numbers hold, it would demonstrate comparable star formation channels between different (Galactic) clusters. We want to note that we assumed for the above discussion the presence of two unconfirmed binaries. However, we anticipate multiple opportunities for upcoming instruments and observation campaigns covering the IRS 13 cluster.

Despite strong indications for the nature of the dusty objects, the data lack detailed spectroscopic analysis. For YSOs of type I, we would typically use tracers such as H₂ (Glassgold et al. 2004), H₂O (Gibb et al. 2000), and HCN (Lahuis et al. 2006) to confirm the classification. Considering the recent start of the scientific operations of the James Webb Space Telescope, the upcoming guaranteed time observations (GTO) ¹² of the GC will minimize the uncertainties of the YSO classification for the dusty sources. We note that there are publicly available archive ¹³ data observed with NIRSPEC in 2023. Consequently, we used this data set to inspect the spectral NIR emission and parts of the L band (MIR) for the presence of individual line tracers. Due to the absence of telluric emission/absorption lines, we find an unaffected Paα line but also strong water absorption features (Moultaka et al. 2015). With a nominal resolution power of ∼2700 with the G235H/F170LP setting, we identify several single emission and absorption lines (e.g., Brδ, HeI, Brγ, and CO band heads) in the H and K band that are well known from SINFONI observations of the same region (Peißker et al. 2020b, 2021a, 2023b). Considering the recent identification of snowlines in the spectrum of HH 48 NE, we expect similar findings in the GC with NIRSPEC in addition to YSO tracers that could potentially be identified with MIRI. Although the spatial L-band resolution of NACO and MIRI (JWST) is sufficiently comparable, a stable PSF and longer on-source integration times could result in new insights into the IRS 13 cluster. With the demonstrated capabilities of the JWST (Figure 16), we will search for tracers associated with YSOs (Peißker et al. 2023b). Because some dusty sources are close to the E stars, we aim to increase the number of cluster samples to verify our findings on the warped disk structure of IRS 13. In addition to the continuum detections presented in this work, we expect an increase in the number of line-emitting sources, such as G2/DSO (Peißker et al. 2021c), observed with the MIRI and NIRSPEC IFU data.

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The source DS1 is one of the brightest H- and K-band objects of the here presented sample. In Figure Set 19, we show a confusion-free detection of DS1 in 2004.

We do not detect a K- and H-band counterpart above the noise level for both sources, which is due to the high level of crowding. However, NACO K-band data of 2018 reveal some promising candidates that might be associated with DS2 and DS3.

Despite the close distance to DS1, the object DS4 can be observed without confusion. This object is a prime example of magnitude-confusion susceptibility; if the investigated object is bright enough, the close distance to a brighter object does not affect the observability. An example of a toxic magnitude-confusion susceptibility is displayed in the DS2 & DS3 detection in Figure Set 19.

The L-band detection of DS5 close to DS1. As for DS2 and DS3, the magnitude-confusion susceptibility is high, which might be the reason for the nondetection of DS5 in the H and K band. The classification of a coreless dust blob is rather unlikely because of evaporation timescales in a radiative-dominated environment. For example, Stewart et al. (2016) and Höfner & Freytag (2019) report variations of dust clouds close to stars on timescales of a few years.

We identified DS6 in the H, K, and L band and DS7 in the L band. Close to DS6, a bright star is observable in the H and K band with no L-band counterpart, demonstrating the challenges of the multiwavelength analysis.

Like other fainter sources, the observation of DS8 is challenging because of the surrounding stars. While the L-band emission exhibits a low level of confusion, the detection of DS8 in the NIR bands is hindered by the presence of close-by stars.

Because of their colors presented in Figure 9, DS9 and DS10 are most likely embedded stars, such as IRS 3. For cosmetic reasons, we use the K-band observation of 2009, which translates into a minor offset compared with the H- and L-band data from 2004. This apparent misalignment is not in conflict with the overall identification of the two stars.

As for DS9 and DS10, we use K-band data of 2009 to complement the observations in the H and L band of 2004. Both sources, DS11 and DS12, can be most likely classified as stellar sources encircled by a dusty envelope.

For DS13, we note an increased magnitude-confusion susceptibility throughout the accessible IR bands. The observation of fainter DS sources is even more challenging because of the high stellar density.

Both sources, DS14 and DS15, are detected in the H, K, and L band but suffer from increased confusion. In Figure Set 19, we show data observed in 2004 (H and L band) and 2009 (K band). The K-band detection of DS15 is especially exposed to the dominant emission of close-by stars, including their respective PSF wings. Despite these challenges, we managed to estimate the K-band magnitude of DS15 for several epochs as indicated in the light curve.

While we identified a confusion-free detection of DS17, the close-by and fainter object DS16 experiences the dominant imprint surrounding stars. As for DS14 and DS15, we use data from 2004 (H and L band) and 2009 (K band) for cosmetic reasons. The detection of DS16 especially demonstrates the challenges of this analysis. While the observation of DS16 is confusion-free in the L band, the detection in the NIR bands requires the astrometric identification in the MIR band to avoid a false association.

Because of the close distance to the bright star DS17, the detection of DS18 and DS19 is hindered. Hence, the magnitude-confusion susceptibility is increased.

For DS20, we do not find increased confusion due to crowding. The magnitude-confusion susceptibility is lowered.

The source DS21 is close to the E star E7. Because of the bright emission of the E stars, the source suffers from blending and dominant PSF wings, although DS21 seems isolated. Despite the challenges of the identification related to DS21, we identify the source in several epochs.

The detection of DS22 in the H and K band is challenging because of the close distance of several surrounding stars. As demonstrated for DS20, the close distance of bright stars does not have to result in lowered detectability. However, because of the low K- and H-band magnitude of DS22, the detection of the source is limited to a few epochs.

Like DS22, the source DS23 suffers from close-by stars and increased confusion.

The bright source is at the eastern edge of the IRS 13 cluster and, therefore, is not affected by the dominant crowding of the inner core region. We detect DS24 without confusion in various epochs.

Like DS24, the source DS25 is at the edge of the cluster. The chance for confusion is lowered, which is why we detect the source in all analyzed bands.

The source DS26 is affected by the dominant PSF wings of E1, the O supergiant in the core of IRS 13. Therefore, the detection of DS26 is limited to a few epochs.

The bright source DS27 can be observed without confusion in the available data set covering the epochs between 2002 and 2018.

The source DS28 is at the northern tip of an apparent elongated L-band feature consisting of DS31 and DS33. We detect DS28 without confusion in several bands and epochs.

The source DS29 is on a north–south axis with DS24 and DS25. Like the former two sources, DS29 is at the edge of the IRS 13 cluster and north of X3 (Peißker et al. 2023b). We detect DS29 without confusion.

Like DS26, the source DS30 is close to the E star E1. Because of the brightness of DS30, we detect the source without confusion in various epochs.

The source DS31 suffers, like, for example, DS26, from the toxic imprint of the core stars of the IRS 13 cluster. This is reflected by a variation of the magnitude in various bands. The significance of the detection is lowered because the variation of the individual magnitude values is partially outside the range of the standard deviation.

The source DS32 is close to the brighter dusty sources of the IRS 13 cluster. Although the chance of confusion is increased by the amount of close-by stars, we detect DS32 in all epochs between 2002 and 2018.

As mentioned before, the location of DS33 can be associated with an elongated L-band feature (DS28). However, this feature is most likely a chance association because we identify the individual components as DS sources.