High-Resolution Infrared Spectroscopy of IRS 16CC and IRS 33N: Stellar Parameters and Implications for Star Formation Near Sgr A^*

Abstract

IRS 16CC and IRS 33N are among more than 100 young, massive stars identified within 0.5 pc from the Galactic central supermassive black hole Sgr A*, where conventional star formation processes are expected to be strongly suppressed. A subset of these stars, including IRS 16CC, has been confirmed to reside in a clockwise rotating stellar disk, and is thought to have formed in a massive, gaseous disk around Sgr A*. In contrast, other young massive stars, such as IRS 33N, exhibit dynamical behaviors that deviate significantly from those of the disk population, and their formation mechanism is still uncertain. To investigate their formation mechanism, we carried out near-infrared, high-resolution spectroscopic observations of IRS 16CC and IRS 33N using the Infrared Camera and Spectrograph on the Subaru telescope, equipped with an adaptive optics system. We compared the profiles of He I absorption lines with synthetic spectra generated from model atmospheres, and then compared derived stellar parameters with stellar evolutionary tracks to estimate their ages and initial masses. Our analysis yields their effective temperatures of ∼23,000 K, surface gravities of ∼2.8, and initial masses of $37\pm 6M_{\odot }$ and ${27}_{-3}^{+4}{M}_{\odot }$, consistent with spectral types of B0.5–1.5 supergiants. The ages of IRS 16CC and IRS 33N are estimated to be $4.4\pm 0.7$ Myr and $5.3_{-0.7}^{+1.1}$ Myr, respectively. These results suggest that, despite their different dynamical properties, the two stars are likely to share a common origin.

1. Introduction

The central parsec of our Galaxy contains the supermassive black hole (SMBH) Sagittarius A star (Sgr A*), e.g., [1,2,3], and 100–200 young massive stars, e.g., [4,5,6]. These facts make this region a unique laboratory for studying the star formation processes in the vicinity of an SMBH, as well as the interactions among young stars, the SMBH, the nuclear star cluster (NSC), and interstellar medium. Among the young stars, very massive stars such as Wolf–Rayet (WR) stars and OB supergiants exhibit distinct structures within this region. A subset of them forms a disk-like structure that has a clockwise (CW) sense of rotation, as projected onto the plane of the sky [7], and about 20 % of the massive stars lie in the CW disk, e.g., [5,6,8,9,10,11].

The mechanism that leads to the presence of young massive stars is not yet completely understood. Due to the tremendous tidal forces, standard star formation should be suppressed around the SMBH. The coherent motion of the disk stars may be indicative of “in situ” formation in a massive, gas disk around the SMBH, e.g., [12,13,14,15,16,17,18]. Gaseous accretion disks around an SMBH are expected to fragment under their own self-gravity. The fragments can collapse to form stars under conditions in which the timescales for star formation and cooling are shorter than the characteristic timescale of mass transport in the disk [19]. In this scenario, the steady build-up of the gas disk leads to stars on circular orbits, as the gas will have circularized prior to star formation. Several models have invoked the infall of giant molecular clouds or the collision of two clouds to produce initially eccentric stellar disks, e.g., [15,16,17,18,20].

Recent observations have provided growing evidence that multiple disc-like and filamentary young stellar structures may exist in this region, e.g., [21,22,23,24], although their formation mechanism is still uncertain. The existence of a second disk-like structure of counterclockwise (CCW) orbiting stars has been proposed [5,8,21]. Others are two filamentary structures at large projected distance from Sgr A* “Outer Filament 2” and “Outer Filament 3”; refs. [22,23], where Outer filament 2 is attributed to the outer part of the tilted and warped CW disk [21]; an edge-on plane-like structure oriented east–west on the sky “Plane 2” [24]. Plane 2 might be the same structure as Outer filament 3. Most young massive stars, as high as ∼75% may reside in these structures [22].

The coevality of the young massive stars is puzzling. The evolutionary phases of individual stars suggest that they have been formed $6\pm 2$ Myr ago [5,21,25], or $2.5$–$5.8$ Myr ago [26], indicating a short formation timescale of no more than 2–3 Myr. These young massive stars constitute multiple disc-like and filamentary structures, with at least two structures: one of them, the CW disk, is nearly retrograde with respect to the other, Outer filament 3/Plane 2 [22,24]. A simple formation scenario, such as the fragmentation of a single past gaseous accretion disk around the SMBH followed by dynamical evolution fails to account for the presence of such complex structures.

We have carried out high-resolution, near-infrared (NIR) spectroscopic observations of two young massive, B-type supergiants in this region: IRS 16CC (E27, S2-9) and IRS 33N (E33, S2-13). IRS 16CC has been confirmed to be a member of the CW disk even in the most recent studies by two independent groups [22,24]. In contrast, proper motion and radial velocity measurements have strongly suggested that the probability of IRS 33N being a member of the CW disk is very low. The detailed spectral analysis of blue supergiants allows for the precise determination of stellar parameters, including their ages. By comparing the stellar properties of two stars with distinct dynamical features, we aim to provide insights into the formation of stars around an SMBH.

2. Observations and Data Reduction

High-resolution spectra of IRS 16CC and IRS 33N (Figure 1) were obtained with the infrared camera and spectrograph (IRCS) [27] on the Subaru telescope [28] on 2017 May 6 (IRS 33N) and 2018 May 20 (IRS 16CC). The coordinates of the targets are [29]: 17:45:40.19, −29:00:27.53 (IRS 16CC), and 17:45:40.04, −29:00:30.30 (IRS 33N). We utilized the echelle K+ mode of IRCS with a slit width of $0_{·}^{″}$14, providing a spectral resolution of $R\sim 20,000$. The spectral coverage provided by the K+ mode is available on the IRCS website1. The slit was centered on the star S0-2/S2 and oriented at position angles of 178° and 67°, allowing IRS 33N and IRS 16CC, respectively, to be observed simultaneously with S0-2/S2. During these nights, we obtained 16 and 32 exposures for IRS 33N and IRS 16CC, respectively, each with an integration time of 300 s.

The spectra were reduced using standard IRAF2 routines, including dark subtraction, flat fielding, bad-pixel, and cosmic-ray corrections. We performed wavelength calibration using the atmospheric OH emission lines. Standard stars HD 152521 and 183997 were observed and used for the telluric correction. We performed continuum fitting over the entire wavelength range of order 27. The combined spectra of order 27 are shown in Figure 2. The signal-to-noise ratios for the combined spectra are $\approx 140$ for IRS 33N, and $\approx 85$ for IRS 16CC.

The most prominent feature in the spectra of typical B-type supergiants is the Br-$\gamma$ absorption line at 21,661 Å. In both stars, this feature appears as a strong absorption line in the order 26 spectra. However, we also detect emission lines within or adjacent to the Br-$\gamma$ absorption profiles. In addition, a distinct emission feature is present at ∼21,640 Å. Streams of ionized gas are present in the region surrounding Sgr A*, e.g., [30,31]. At the position of IRS 33N, two velocity components of H emission were detected [32]. These emission lines are likely associated with the “Bar” structure (≈ 21,660 Å) and the “Northern Arm” stream (≈ 21,640 Å). IRS 16CC is also located near the Northern Arm stream. In our observations, it is difficult to spatially resolve IRS 16CC and IRS 33N from the surrounding gas structures, making it challenging to use the Br-$\gamma$ line to determine stellar parameters.

In echelle order 27, we see two strong He I absorption features at 21,126 Å and 21,138 Å. These lines were detected in previous observations e.g., [9,33], and are known to be typical of OB Iab–II supergiants (Figure 2 of [5]). These supergiants show the limited number of prominent features in the K-band; apart from the features around Br-$\gamma$, the two He I lines constitute the only remaining features available for our analysis. Since rotational broadening dominates the He I line width, the doublet consisting of the 21,126 Å and 21,138 Å lines can be used to measure the projected rotational velocity ($vsini$) of the stars [34]. The lines are not resolved in medium-resolution spectra, and our study thus provides the first precise measurement of the rotational velocities of IRS 16CC and IRS 33N3. As shown in the following analysis, the shape and depth ratio of the two He I lines are also sensitive to both surface gravity ($logg$) and effective temperature ($T_{\mathrm{eff}}$). Therefore, we focus on the He I lines to determine the stellar parameters of IRS 16CC and IRS 33N in this study.

3. Modeling and Results

3.1. Synthetic Spectra

The aim of this study is to determine the stellar parameters of IRS 16CC and IRS 33N by comparing our observed spectra with synthetic spectra computed from model atmosphere and with theoretical evolutionary tracks. To compute the synthetic spectra, we used the codes TLUSTY [35], SYNSPEC [36], and Brewster [37]. TLUSTY solves basic equations for plane-parallel, horizontally homogeneous stellar atmosphere models in radiative and hydrostatic equilibrium. The basic input parameters are $T_{\mathrm{eff}}$, $logg$, and chemical composition. SYNSPEC is a spectral synthesis code that takes the model atmosphere computed by TLUSTY as input. Stellar rotation is not included at this stage. A code from the Brewster package rotBroadInt.py [36] was used to convolve the synthetic spectra with rotational broadening profiles corresponding to a given $vsini$.

Using the three codes, we generated stellar photospheric models of supergiants, and then constructed synthetic spectra with $T_{\mathrm{eff}}$ ranging from 22,000 K to 29,000 K in steps of 1000 K, $logg$ from 1.75 to 3.25 in steps of 0.25, and $vsini$ from 60 km s⁻¹ to 90 km s⁻¹ in steps of 5 km s⁻¹. Since the metallicity of young stars in the central region is approximately solar [38,39], we adopted a solar chemical composition in the SYNSPEC calculations. Finally, the wavelength resolution of the synthetic spectra was adjusted to match that of the observations. The observed and synthetic spectra in the wavelength range from 21,100 Å to 21,160 Å, covering the He I absorption features, are used for comparison.

In Figure 3, we compare the observed spectra of IRS 16CC and IRS 33N with synthetic spectra. To identify the synthetic spectrum that best matches the observed spectrum, we computed the ${\chi }^2$ values. The best-fit parameters are $T_{\mathrm{eff}}=24,000$ K, $logg=2.25$, and $vsini=70$ km s⁻¹ for IRS 16CC, and $T_{\mathrm{eff}}=24,000$ K, $logg=2.25$, and $vsini=85$ km s⁻¹ for IRS 33N (

Table 1. Preliminary stellar parameters.

Object	${\mathit{T}}_{\mathbf{eff}}$	$log\mathit{g}$	$log\mathbf{(}\mathit{L}\mathbf{/}{\mathit{L}}_{\odot }\mathbf{)}$	$\mathit{v}sin\mathit{i}$
	(K)	(dex)		(km s−1)
IRS 16CC	24,000 ± 2000	2.25 ± 0.50	5.61 ± 0.12	70 ± 10
IRS 33N	24,000 ± 2000	2.25 ± 0.50	5.38 ± 0.12	${85}_{-15}^{+10}$

).

When comparing the observed spectra with synthetic spectra, uncertainties in the continuum level could affect the results. Continuum determination is generally difficult for late-type stars because of their dense spectral features. In contrast, IRS 16CC and IRS 33N are early-type stars with relatively few strong lines, and their observed spectra (Figure 2) cover a sufficiently wide wavelength range to establish the continuum level on both the shorter- and longer-wavelength sides of the two He I features. Emission-like features adjacent to the He I features are also seen in the Keck/OSIRIS spectra of IRS 16CC (Figure 23 in Gautam et al. [40]) and in VLT/OSIRIS spectra of the averaged OB I/II spectra (Figure 2 in Paumard et al. [5]), indicating that they are likely to be real. Therefore, we conclude that uncertainties in the continuum determination do not significantly affect the comparison of the observed spectra with the synthetic ones.

3.2. Photometry and Luminosity

A comparison with theoretical evolutionary tracks requires photometric measurements. The photometric results of IRS 16CC and IRS 33N have been reported in many papers, e.g., [6,22,24,40,41,42,43,44]. Although IRS 33N shows variability, no periodic signal has been detected [43].

The photometric variability of IRS 16CC was reported by Gautam et al. [43], and its light curve is shown in Figure 9 of Haggard et al. [44]. As seen in the light curve, the variability is unlikely to be intrinsic to IRS 16CC, but is instead attributed to variable interstellar extinction along the line of sight. Therefore, we adopt an observed K-band magnitude $m_K=10.60\pm 0.05$ [45] to estimate the luminosity of IRS 16CC. This magnitude was measured from 1995 to 2005, prior to the dipping event reported by Haggard et al. [44], and is thus unaffected by it.

The luminosity is calculated by

$$log(L/L_{\odot })=-0.4(M_K+B{C}_K-M_{\odot }^{\mathrm{bol}}),$$

(1)

where $M_K$ and $B{C}_K$ are the absolute magnitude and the bolometric correction in the K-band, respectively. We use $M_{\odot }^{\mathrm{bol}}=4.74$ mag, the bolometric magnitude of the Sun. The absolute magnitude is calculated by

$$M_K=m_K-A_K-DM,$$

(2)

where $A_K$ and $DM$ are the amount of interstellar extinction in the K-band, and the distance modulus, respectively. Here, we adopt $A_K=2.46\pm 0.03$ [46], and $DM=14.5\pm 0.18$ [2]. For IRS 16CC ($m_K=10.60\pm 0.05$ [45]) and IRS 33N ($m_K=11.16\pm 0.06$ [43]), we obtain $M_K=-6.36\pm 0.19$ and $M_K=-5.80\pm 0.19$, respectively.

The bolometric correction is calculated by

$$B{C}_K=-7.24log\left(T_{\mathrm{eff}}\right)+28.80$$

(3)

from Martins and Plez [47]. When adopting $T_{\mathrm{eff}}=24,000\pm 2000$ K, we obtain $B{C}_K=$$-2.91$± 0.24. Finally, using Equation (1), we obtain $log(L/L_{\odot })=$ 5.61 ± 0.12 for IRS 16CC, and $log(L/L_{\odot })=$ 5.38 ± 0.12 for IRS 33N.

Although the K-band is most reliable and frequently used passband for GC observations, we also calculated $log(L/L_{\odot })$ using the H-band. Using $m_H=12.28\pm 0.11$ and $12.92\pm 0.10$ for IRS 16CC and IRS 33N [41], respectively, $A_H=4.35\pm 0.12$ [46], and the bolometric correction $B{C}_H=-7.24log\left(T_{\mathrm{eff}}\right)+28.89$ [47], we obtain $log(L/L_{\odot })=5.65\pm 0.14$ for IRS 16CC, and $log(L/L_{\odot })=5.40\pm 0.13$ for IRS 33N. These values are in very good agreement with those derived from the K-band. This indicates that the influence of uncertainties in the observational wavelengths and extinction is considered to be small.

The parameters obtained through the procedure described above are summarized in Table 1. We use these values as the “preliminary stellar parameters” of IRS 16CC and IRS 33N, derived from the comparison between the observed spectra and the synthetic spectra computed from model atmospheres.

3.3. BONNSAI

The refined stellar parameters were derived by fitting the evolutionary tracks using the BONN Stellar Astrophysics Interface (BONNSAI4) [48]. BONNSAI is a Bayesian framework that enables the testing of stellar evolution models and inferring stellar parameters from observational data. It employs the model grid of Brott et al. [49] and assumes that the star is undergoing normal single-star evolution. We used the preliminary parameters summarized in Table 1 as input to BONNSAI for each star. The priors are Gaussian distributions with the averages and standard deviations shown in Table 1.

The output of BONNSAI for IRS 16CC and IRS 33N are summarized in

Table 2. Output parameters of the BONNSAI simulations.

Object	SpT(a)	${\mathit{T}}_{\mathbf{eff}}$	$log\mathit{g}$	${\mathit{M}}_{\mathbf{ini}}^{\left(\mathbf{b}\right)}$	$log(\mathit{L}/{\mathit{L}}_{\odot })$	Age	$\mathit{v}sin\mathit{i}$
		(K)	(dex)	(${\mathbf{M}}_{\odot }$)		(Myr)	(km s−1)
IRS 16CC	B0.5–1I	$23,{600}_{-2500}^{+1300}$	$2.7\pm 0.2$	$37\pm 6$	$5.6_{-0.2}^{+0.1}$	$4.4\pm 0.7$	${70}_{-12}^{+11}$
IRS 33N	B0.7–1.5I	$22,500\pm 1900$	$2.9_{-0.2}^{+0.1}$	${27}_{-3}^{+4}$	$5.4\pm 0.1$	$5.3_{-0.7}^{+1.1}$	${80}_{-11}^{+16}$

(a) Spectral type. (b) Initial mass. The parameters and errors are from the BONNSAI analysis, where the median values of the full posterior probability distributions are employed.

. The input parameters, $T_{\mathrm{eff}}$, $logg$, $log(L/L_{\odot })$, and $vsini$ are refined by comparing the evolutionary tracks. Almost all input and refined parameters are matched within uncertainties. The refined $logg$ values are slightly larger than the preliminary ones.

BONSSAI provides the initial mass ($M_{\mathrm{ini}}$) and age for the stars. The derived values are $37\pm 6M_{\odot }$ and $4.4\pm 0.7$ Myr for IRS 16CC, and ${27}_{-3}^{+4}{M}_{\odot }$ and $5.3_{-0.7}^{+1.1}$ Myr for IRS 33N, respectively. Posterior probability distributions of the refined parameters are shown in Figure 4.

Note that there are methodological limitations in our study. We used only two He I absorption lines in the analysis. The prominent Br-$\gamma$ line cannot be used because of the interstellar emission at the similar wavelengths. Since metal lines were not available, our analysis is insensitive to the metal abundance of the two stars. We also computed synthetic spectra with twice the solar chemical abundance, but found no differences compared to those with solar abundance in the He I features. Hence, our study may include systematic uncertainties and/or parameter degeneracies, and further spectroscopy will be necessary to solve them.

4. Discussion and Conclusions

At least two distinct structures of stars have been found, and the presence of additional, more complex structures has been proposed in the central 0.5 pc region of our Galaxy, e.g., [22,24]. The origin of these complex structures is an intriguing subject of the GC studies. In this paper, we present the results of our NIR spectroscopic observations of two young massive stars, IRS 16CC and IRS 33N. IRS 16CC has been confirmed as a member of the well-established CW stellar disk, whereas IRS 33N is not. However, our analysis shows that their stellar parameters are remarkably similar (Table 2), suggesting that they share a common origin.

IRS 16CC was identified as an early-type star [9,50], and then classified as a O9.5–B0.5 supergiant [5]. Its early-type nature was also confirmed, e.g., [42,43]; however, detailed stellar parameters have not been determined for IRS 16CC. IRS 33N is slightly fainter than IRS 16CC in the K-band, and this could suggest a possible difference in their age. This star was spatially resolved for the first time by [51,52]. Paumard et al. [5] classified IRS 33N as B0.5-1 supergiant, and then the following observations have confirmed its early-type nature, e.g., [42].

IRS 16CC and IRS 33N are among the very bright B-type supergiants in this region, and exhibit distinct dynamical characteristics. Since the first detection of their proper motion [53], their three-dimensional motions have been precisely measured. IRS 16CC is a “founding member” of the CW stellar disk [7], and has been confirmed to be a member of the CW disk in all studies. Jia et al. [24] classified IRS 16CC as a member of the CW disk (their Table 11). IRS 16CC (E27) is also included in the list of the CW disk in Table 6 of von Fellenberg et al. [22].

The membership of IRS 33N is still uncertain, although its proper motions are as precisely measured as those of IRS 16CC. In Jia et al. [24], they concluded that the membership probabilities of IRS 33N for the CW disk and Plane 2 are zero, clearly indicating that IRS 33N is not a member of the CW disk at the very least. The lack of membership in the CW disk is also confirmed [22].

Meanwhile, IRS 33N might belong to a recently proposed structure, “Outer filament 2 (F2)” [22]. In their Figure 10, IRS 33N is assigned as a member of F2. They found that 37 stars are consistent in belonging to F2. This feature shows similarities with the CW disk, such as stellar brightness and low orbital eccentricities. By contrast, the stars in F2 show a larger projected distance of $7_{·}^{″}0$ from Sgr A*, and slightly higher median eccentricities than that for the CW disk. As a result, they classified IRS 33N as a star consistent with belonging on the outer warp of the CW disk Table 9 in [22].

In this study, we determined the detailed stellar parameters of IRS 16CC and IRS 33N (Table 2). The results suggest that the two stars exhibit very similar properties. The stellar parameters – $T_{\mathrm{eff}}$, $logg$, initial mass at the main-sequence stage $M_{\mathrm{ini}}$, $log(L/L_{\odot })$, age, $vsini$ – all agree well within the uncertainties, while IRS 16CC might be slightly younger and more massive than IRS 33N. IRS 16CC and IRS 33N were classified as O9.5–B0.5 and B0.5–1 supergiants, respectively, in a previous study [5]. Our results suggest that IRS 16CC is a B0.5–1 supergiant, and IRS 33N is a B0.7–1.5 supergiant (c.f. Table 10 in [54]).

To illustrate their similarity, we plot our results on the $log{T}_{\mathrm{eff}}$–$logg$ diagram (Figure 5) and the HR diagram (left panel in Figure 6). The stellar evolutionary tracks are also shown [49]. Note that the estimated masses and ages (Table 2) are not derived from a simple comparison with theoretical isochrones in a two-parameter space. We compute the posterior probability distribution of the stellar parameters using BONNSAI, which performs a multidimensional comparison between the observed results and stellar evolution models.

In the $log{T}_{\mathrm{eff}}$–$logg$ diagram, IRS 16CC and IRS 33N are located at nearly identical positions within the uncertainties. Both stars lie between the $20M_{\odot }$ and $50M_{\odot }$ evolutionary tracks. This diagram suggests that they are at least more massive stars than $20M_{\odot }$ given the uncertainties. The left panel in Figure 6 shows the location of the two stars on the HR diagram. IRS 33N is plotted between the $25M_{\odot }$ and the $30M_{\odot }$ evolutionary tracks and IRS 16CC is located close to the $40M_{\odot }$ track.

To our knowledge, this is the first study to determine $vsini$ of IRS 16CC and IRS 33N. However, it remains difficult to determine their true rotational velocities. The initial rotational velocities derived from BONNSAI have large uncertainties: ${140}_{-50}^{+190}$ km s⁻¹ and ${130}_{-40}^{+190}$ km s⁻¹ for IRS 16CC and IRS 33N, respectively. To investigate how these uncertainties in rotational velocity affect the derived stellar parameters, we show stellar evolutionary tracks in the right panel of Figure 6 for the initial rotational velocities of 0, ∼150, and ∼300 km s⁻¹ based on the Bonn stellar models [49]. As can be seen, the differences among them are very small, particularly at the temperatures of IRS 16CC and IRS 33N. Therefore, we have concluded that the uncertainties in stellar rotational velocities do not significantly affect our results.

The two stars are likely coeval. The derived initial masses and ages for IRS 16CC and IRS 33N are $37\pm 6M_{\odot }$ and $4.4\pm 0.7$ Myr, and ${27}_{-3}^{+4}{M}_{\odot }$ and $5.3_{-0.7}^{+1.1}$ Myr, respectively. Their initial masses may differ slightly, but their ages are nearly identical. Therefore, the two stars may have formed from the same progenitor environment. These results are consistent with the interpretation that the F2 feature proposed by [22] represents the outer warp of the CW disk.

The behavior of a stellar disk around SMBH has been studied since the discovery of the CW disk. A simple analytic approach and N-body simulations were performed considering the two-body relaxation and multi-stellar masses, e.g., [55]. The warp and the second disk-like structure due to the resonant relaxation could happen between the disc and the surrounding NSC, e.g., [56,57]. The ages of the IRS 16CC and IRS 33N are comparable to the vector-resonant relaxation timescale at their distance from Sgr A*, and such relaxation has been invoked to explain the observed distribution, e.g., [56,58]. Additional components such as stellar binaries and intermediate mass black holes, stellar cusp, gas rings such as the Circumnuclear Ring and mass segregation, stellar evolution, and binary heating have been included in N-body simulations, e.g., [59,60,61,62,63,64,65].

Since the stellar disk is rotating within the NSC, the gravity of the disk exerts a perturbation on the NSC, and in turn, a strong torque is exerted back on the disk from the NSC. Levin [66] carried out numerical simulations and analytical estimates for the CW disk and NSC. The numerical simulations demonstrate that the rotation of the NSC can scatter the stars in the outer part of the disk while aligning the stars at the inner part with the NSC’s rotational axis. In particular, when the NSC exhibits a high rotation rate, the disk is observed to become warped or split into multiple rings. The analytical estimates suggest that, in the case of the CW disk and Galactic NSC, the resonant friction timescale is found to be ∼2.5 Myr, which is consistent with the simulations. The timescale is also in line with the estimated age of IRS 16CC and IRS 33N. Therefore, the resonant friction between the stellar disk and the NSC may significantly influence the orbital evolution of the disk stars, and external massive perturbers may not necessarily need to be taken into account.