S62 and S4711: Indications of a Population of Faint Fast-moving Stars inside the S2 Orbit—S4711 on a 7.6 yr Orbit around Sgr A*

For this work, we used the SINFONI and NACO data sets that are already discussed, shown, and analyzed in (Peißker et al. 2019, 2020a, 2020b). For the K-band observations, we use the NAOS+CONICA (NACO) instrument with the adaptive optics (AO) guide star IRS7 located about 55 north of Sgr A*. The H+K observations are carried out with the Spectrograph for Integral Field Observations in the Near Infrared (SINFONI). The optical guide star for the SINFONI AO correction is located 1554 north and 885 east of Sgr A*. Both instruments were mounted at the Very Large Telescope (VLT) in Paranal/Chile and are now decommissioned. Standard data-reduction steps with the ESO pipeline were applied. For the SINFONI H+K data, we use DARK frames to correct for hot pixels. LINEARITY frames are taken to supervise the detector response. FLAT lamps measure the pixel-to-pixel response. DISTORTION frames are used to correct for optical distortions and to monitor the slitlet distances. Lastly, WAVE frames are taken in order to wavelength-calibrate the data. Since we also use NACO in the K-band imaging mode, the reduction steps are comparably short. We apply the FLAT field and bad pixel correction. For creating a mosaic, we shift the individual images in an 2048 × 2048 array to their related positions. Furthermore, the data from both instruments have been sky-corrected. The used data are listed in Appendix C.

For reducing the influence of overlapping point-spread function (PSF) wings, a low-pass filter is a suitable and efficient approach. We are subtracting a Gaussian flux density conserved smoothed image from the input image. For that, the size of the Gaussian filter should be close to the PSF size. In SINFONI, this is usually around 5–6 pixels corresponding to 62–75 mas and depends on the overall data quality. After the subtraction, we smooth the result again. In principle, the same Gaussian filter size is possible. However, we use different filter sizes of less than 6 pixel. The result that allows the best discrimination of densely packed stars from each other is then chosen manually. Since there is no loss in information, the process is stable against false positives (see also Peißker et al. 2020b).

Another method for analyzing the data is the high-pass filter, also known as the Lucy Richardson algorithm (Lucy 1974). Since noise can be associated with low frequencies, the high-pass filter helps to highlight image details that are above a self-defined threshold. It is known that the Galactic center and especially the S-cluster suffer from a spatially variable background. This leads, for example, to the creation of blended stars (Sabha et al. 2012). With this, a background subtraction is sufficient and needs to be adjusted for every data set because of different weather conditions and the varying number of high-quality observations. Cosmic rays, the influence of the detector cosmetics, readout errors, and the overall state of the data are noticeable error sources. The determination of the position of Sgr A* is based on the well-known and observed orbit of S2 (Parsa et al. 2017; Gravity Collaboration et al. 2019).

The close passage of S2 did not allow sensitive observations of the region covered by the S4711 orbit in 2017 until 2019. However, for every year from 2004 to 2016, we can confirm several detections of S4711 in the high-pass filtered NACO K-band images (Figures 1 and 2). Source positions are derived via Gaussian fits to the objects in the images of each epoch. Since the positional determinations in the high-resolution images are not necessarily Gaussian-distributed, we used the median in the years between 2006 and 2010 to avoid outliers (Figure 3). Consider also the detailed description of the analysis given in Peißker et al. (2020a). Based on the positions derived from these data sets we were able to fit the orbit of S4711 (indicated by red data points in Figure 2). The resulting orbital elements are presented in Table 1.

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The maximum distance of S4711 from Sgr A* is around 80 mas (≈6 pixel in the NACO images). Therefore, the star suffers blending and confusion with other objects in the crowded field. This effect is minimized because of the constant monitoring of the S-cluster in the last 25 yr but underlines the need for a sufficient number of high-quality observations.

Based on the NACO and SINFONI detection of S4711 (see Figures 1 and 4), we find a K-band magnitude of m_K = 18.43 ± 0.22 with

$$\begin{eqnarray}&&{m}_{{\rm{K}},{\rm{S}}4711}=-{m}_{{\rm{K}},{\rm{S}}2}+2.5\times \mathrm{log}(\mathrm{ratio}),\end{eqnarray} \tag{ 2 }$$

with aperture photometry and a S2 K-band magnitude of 14.15 (Schödel et al. 2010). We use this method to derive the apparent magnitude m_K for all newly discovered stars (see Table 2). To determine the mass of these faint S-cluster stars (FSS), we adapt from Cai et al. (2018):

$$\begin{eqnarray}&&\mathrm{lg}\displaystyle \frac{{M}_{{\rm{S}}}}{{M}_{\odot }}={\mathrm{km}}_{K}+b,\end{eqnarray} \tag{ 3 }$$

with k = −0.192 and b = 3.885. The authors of Cai et al. (2018) derive from a fit of the S-star properties presented in Habibi et al. (2017) the values for k and b. Using the same data from Habibi et al. (2017), we confirm b = 3.885 and use in the following k = −0.1925. Using Equation (3) with the values given in Habibi et al. (2017), we find an agreement with the stellar mass in the range of 5%–10% for the three discussed S-stars.⁴ We adapt an error of −1 M_⊙ and +2 M_⊙. With that, Equation (3) provides an accessible approach for deriving the mass for the S-stars when no spectroscopic information is available. Consult Table 2 for the stellar mass of S62 and S4711–S4715.

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In 2007, S4711 reaches it apoapse. Also, the distance between S4711 and S2 is sufficient enough to analyze the spectrum of the newly discovered star in the SINFONI data of the related year (Figure 5). We find an LOS velocity of v_Brγ = −291 ± −55 km s⁻¹. The depth of the HeI and Brγ⁵ absorption features are comparable with the analysis of the S-cluster stars presented in Habibi et al. (2017). Because of the apoapse position of S4711, the derived LOS velocity is a lower limit of the range of possible Doppler-shifted values. The observed HeI line at 2.161 μm is actually a doublet, namely 7³F − 4³D at 2.16137 μm and 7¹F − 4¹D at 2.16229 μm (Lumsden et al. 2001). This "shoulder" is clearly detectable in the spectrum (Figure 5) and shows an asymmetrical shape. This points toward a low rotational velocity ($v\,\sin i$) of the star. A singlet would be the result of a high $v\,\sin i$ value. The presence of a rotational velocity, however, prolongs the lifetime of the star (Clark et al. 2018) and therefore possible in-spiral events that will be discussed in Section 4. Considering the critical study of the rotational velocity by Zorec et al. (2017), we determine for S4711 $v\,\sin i$ = 239.60 ± 25.21 km s⁻¹ with the FWHM of the 2.161 μm HeI line. Even though Slettebak et al. (1975) finds somewhat lower values for the Brγ line, the derived rotational velocity here is in a comparable range with the findings of Clark & Steele (2000) and Abt et al. (2002).

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Furthermore, we derive from the shape of the Brγ line the spectral type of S4711. We use the NIR spectral atlas of Hanson et al. (1996) and follow the analysis presented in Eisenhauer et al. (2005) to determine the spectral type of S4711. For the Brγ line width (∼10 Å) and the spectrum, we find good agreement with the emission of a B8/9-V star with an effective temperature of about T_eff = 10,700–11,800K (Tokunaga 2000).

Because of the maximum distance to Sgr A* of around 0.1 arcsec, the data selection is limited due to blending events and overlapping orbits of close-by stars (Figure 6). This explains the data point density that is presented in Figure 2. We conclude that the observation of S4711 is hindered by the brighter close-by S-stars. Especially close to the pericenter passage of S2 in 2018 (Gravity Collaboration et al. 2018b), a detection of S4711 is not possible. From the orbit plot of the closest S-cluster members presented in Figure 6, we find an angle between the orbit of S4711 and S62 of about 45°. In comparison with the periapsis distance of about 2 mas for S62, we find for S4711 the pericentre distance of

$$\begin{eqnarray}&&{r}_{{\rm{p}}}=a(1-e)\simeq 0.7\,\mathrm{mpc},\end{eqnarray} \tag{ 4 }$$

and using 0.04 pc ≈ 1000 mas, we get r_p ≈ 12 mas = 144 au. Considering the periapsis distance of 120 au for S2 as obtained by Gravity Collaboration et al. (2019), S4711 has a comparable pericenter distance to Sgr A*. Its apocenter distance is closer than that for S2 by ∼900 au; see Table 3. Hence, given that the periods of S4711 and S62 are shorter than 10 yr, these may serve as better probes for relativistic effects than S2.

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Table 3.  Additional Orbital and Relativistic Parameters for S62, S4711, S4712, S4713, S4714, S4715 Stars in Comparison with S2 Star

Star	rp (au)	ra (au)	vp (km s−1) (% of c)	Γ (10−4)	zgrc (km s−1)	δϕ (arcmin)	${\dot{{\rm{\Omega }}}}_{\mathrm{LT}}$ (arcsec yr−1)
S62	17.8 ± 7.4	1462.4 ± 11.0	20124 ± 4244 (6.7 ± 1.4)	46	685.5 ± 288.6	74.7 ± 31.0	5.1 ± 3.2
S4711	143.7 ± 18.8	1094.7 ± 28.7	6693 ± 494 (2.2 ± 0.2)	5.6	84.5 ± 11.8	10.3 ± 1.3	0.34 ± 0.07
S4712	2366 ± 120	5075 ± 122	1449 ± 54 (0.48 ± 0.02)	0.34	5.1 ± 0.4	0.81 ± 0.05	(5.1 ± 0.5) × 10−4
S4713	1073 ± 110	2234 ± 144	2141 ± 153 (0.71 ± 0.05)	0.75	11.3 ± 1.3	1.8 ± 0.1	(5.8 ± 1.1) × 10−3
S4714	12.6 ± 9.3	1670 ± 10	23928 ± 8840 (8 ± 3)	64	966.1 ± 713.5	104.6 ± 76.3	7.0 ± 7.6
S4715	894 ± 83	1480 ± 122	2253 ± 129 (0.75 ± 0.04)	0.90	13.6 ± 1.4	2.4 ± 0.2	(1.4 ± 0.4) × 10−2
S2	119.3 ± 0.3	1949.9 ± 2.8	7582 ± 8 (2.527 ± 0.003)	6.8	101.7 ± 5.0	11.7 ± 0.6	0.19 ± 0.02

Note. From left to right, we list the star name, its pericenter distance (in au), its apocenter distance (in au), the pericenter velocity (in km s⁻¹ and % of light speed), the relativistic parameter defined as Γ = r_s/r_p, the gravitational redshift z_grc (in km s⁻¹), the Schwarzschild precession δϕ (in arcmin), and the Lense-Thirring precession rate of the ascending node ${\dot{{\rm{\Omega }}}}_{\mathrm{LT}}$ for the spin parameter of 0.5 (in arcsec per yer).

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In Peißker et al. (2020a), we used a variation of the position of S62 with respect to Sgr A* by ±1 px to derive the uncertainties for the orbital elements. However, the orbit of S4711 is even shorter compared to S62. A variation of ±1 px overestimates the range of possible orbital solutions compared to the extent of the orbit of S4711. Hence, we use the Markov chain Monte Carlo (MCMC) affine-invariant ensemble sampler (Foreman-Mackey et al. 2013) with PYTHON to derive the uncertainties for S4711, S4712, S4713, S4714, and S4715. For consistency, we also apply the MCMC-Metropolis-Hastings algorithm to the orbital elements of S62 (Figure 7). For the apriori distribution (prior), we use the results from the Keplerian fit model (Table 1). We then use iteration steps of 100 for the Bayesian updating. With this, we determine the mean of the posterior distribution of the Bayesian inference. For the mass and distance of Sgr A*, we adapt the values 4.15 × 10⁶ M_⊙ and 8.3 kpc from Parsa et al. (2017); Gillessen et al. (2017), and Gravity Collaboration et al. (2019). The 1σ uncertainties (68% confidence interval) for the S-stars investigated here are all in a comparable range (see Table 1). If the range of the uncertainties for an orbital parameter is not symmetrically distributed, we use the maximum value of the interval. We find that the MCMC sampler shows a satisfying compact probability for most parameters where the mean is almost identical with the prior (Figure 8). A broader posterior distribution would result in large uncertainties for the orbital parameters.

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To determine which of the newly identified faint S-stars are good probes of post-Newtonian effects, we first determine the relativistic parameter following Parsa et al. (2017):

$$\begin{eqnarray}&&{\rm{\Gamma }}=\displaystyle \frac{{r}_{{\rm{s}}}}{{r}_{{\rm{p}}}},\end{eqnarray} \tag{ 5 }$$

where r_s is the Schwarzschild radius of Sgr A*, r_s = 1.21 × 10¹²(M_•/4.1 × 10⁶ M_⊙) cm, and r_p = a(1−e) is the pericenter distance of the star. We list the values of Γ in Table 3. We see that S4714 and S62 have the largest values of Γ, followed by S4711, which has a Γ comparable to S2. Since the period of S4711 is less than half of the S2 period, its monitoring can reveal post-Newtonian effects twice as fast. The remaining stars, S4712, S4713, and S4715, have a Γ an order of magnitude smaller than S4711, hence they are weaker relativistic probes.

Following our analysis in Peißker et al. (2020a), we calculate the Schwarzschild periapsis shift (see Weinberg 1972) for S62, S4711–S4715 stars using

$$\begin{eqnarray}&&\delta \phi =\displaystyle \frac{6\pi G}{{c}^{2}}\,\displaystyle \frac{M}{a(1-{e}^{2})}=\displaystyle \frac{3\pi }{1+e}{\rm{\Gamma }}.\end{eqnarray} \tag{ 6 }$$

In Table 3, we list the values for all the stars. The largest reliable shift per period is for S62, δϕ = 74.7 ± 31.0 arcmin,⁶ and for S4714 δϕ = 104.6 ± 76.3 arcmin, albeit with a large uncertainty. S4711 has a comparable Schwarzschild precession, δϕ = 10.3 ± 1.3 arcmin, to the S-cluster star S2, δϕ = 11.7 ± 0.6 arcmin.

Since the first detection of the two stars in 2002 (S62) and 2004 (S4711), several periapse passages have been performed. Because of the periapse shift of S4711, a detectable orbit shift could be observed in the next 10–20 yr. In addition, the orbital trajectory of S62 should be shifted by almost 5° between 2023 and 2033. Since the bright star S2 is passing by the Sgr A* region every 15 yr, the observation of the periapse passages of S62 and S4711 may be challenging, in particular since one needs to measure orbital sections before and after their passage.

For the remaining faint stars, S4712, S4713, and S4715, we obtained an order of magnitude smaller shifts per period, δϕ = 0.81 ± 0.05, 1.8 ± 0.1, and 2.4 ± 0.2 arcmin, respectively, which follows from their values of Γ or in other words, from larger pericenter distances due to smaller eccentricities and larger semimajor axes. Another general relativistic parameter, which affects the observed wavelength of spectral lines, is the gravitational redshift, which can be expressed as

$$\begin{eqnarray}&&{z}_{\mathrm{gr}}c=c\left[{\left(1-\displaystyle \frac{{r}_{{\rm{s}}}}{r}\right)}^{-1/2}-1\right]\lesssim \displaystyle \frac{c{\rm{\Gamma }}}{2},\end{eqnarray} \tag{ 7 }$$

where the upper limit on the right is the approximate value at the pericenter (the approximation applies for Γ ≪ 1). In Figure 9, in the left panel, we show the total radial velocity of the stars, including the radial Doppler shift and the gravitational redshift. In the right panel, we depict the gravitational redshift alone, which is the largest at the pericenter for each star. The values of the gravitational redshift for all the stars are listed in Table 3. The largest gravitational redshift in the S-cluster so far appears to be for S4714 with z_grc = 966.1 ± 713.5 km s⁻¹, followed by S62 with z_grc = 685.5 ± 288.6 km s⁻¹. The gravitational redshift of S4711 z_grc = 84.5 ± 11.8 km s⁻¹ is within the uncertainty comparable to the value for S2. The remaining faint stars have a gravitational redshift of the order of 10 km s⁻¹.

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In addition, for S-stars with pericenter distances of the order of 1000 r_s and less, it is of great interest to measure the Lense-Thirring (LT) precession of the ascending node, since this would provide an independent probe of the black hole spin (Waisberg et al. 2018). For a star on an elliptical orbit around the SMBH, the LT precession of Ω can be calculated as follows (Merritt 2013a)

$$\begin{eqnarray}&&{\dot{{\rm{\Omega }}}}_{\mathrm{LT}}=\displaystyle \frac{2{G}^{2}{M}^{2}\chi }{{c}^{3}{a}^{3}{(1-{e}^{2})}^{3/2}}={{\rm{\Gamma }}}^{2}\displaystyle \frac{\chi c}{2{r}_{{\rm{a}}}}\sqrt{\tfrac{1-e}{1+e}},\end{eqnarray} \tag{ 8 }$$

where χ is the dimensionless spin of the black hole (0 < χ < 1). We list the values of ${\dot{{\rm{\Omega }}}}_{\mathrm{LT}}$ in arcseconds per year for all the sources in Table 3 for the assumed spin of χ = 0.5, which was chosen based on the spin constraints inferred from modeling the total and polarized flux density of NIR flares (χ ≥ 0.4, Meyer et al. 2006). The rate of the LT precession is generally larger than that for the S2 star; in particular we obtained the largest mean value for S4714, ${\dot{{\rm{\Omega }}}}_{\mathrm{LT}}=7.0\,\pm 7.6\,\mathrm{arcsec}\,{\mathrm{yr}}^{-1}$, followed by S62 with $5.1\,\pm 3.2\,\mathrm{arcsec}\,{\mathrm{yr}}^{-1}$. S4711 has the larger rate of the LT precession, ${\dot{{\rm{\Omega }}}}_{\mathrm{LT}}=0.34\,\pm 0.07\,\mathrm{arcsec}\,{\mathrm{yr}}^{-1}$ than the S2 star, which is expected to have ${\dot{{\rm{\Omega }}}}_{\mathrm{LT}}=0.19\pm 0.02\,\mathrm{arcsec}\,{\mathrm{yr}}^{-1}$. The remaining faint S-stars, namely S4712, S4713, and S4715, have values of ${\dot{{\rm{\Omega }}}}_{\mathrm{LT}}$ at least one order of magnitude smaller.

However, even for S62 and S4714, which have the best prospects for the Lense-Thirring precession, the monitoring will have to last for at least 20 yr to reliably measure the spin. The criterion of Waisberg et al. (2018), ${f}_{{\rm{w}}}=a{(1-{e}^{2})}^{3/4}$, is f_w ∼ 954 r_s for the star S62 and f_w ∼ 765 r_s for S4714. Following Waisberg et al. (2018), it would be necessary to monitor S4714 26 yr using 120 total observations with 10 μ as astrometric precision to detect the spin of χ = 0.9. For S62, the campaign would have to last ∼41 yr for the same parameters.

According to the Ramanujan approximation of an ellipse (see e.g., Almkvist & Berndt 1988), the orbital distance U of S4711 traveled during its 7.6 yr orbit can be calculated via

$$\begin{eqnarray}&&{U}_{{\rm{S}}4711}\approx (a+b)\pi \left(1+\displaystyle \frac{3{\lambda }^{2}}{10+\sqrt{4-3{\lambda }^{2}}}\right)\end{eqnarray} \tag{ 9 }$$

with $\lambda =\tfrac{a-b}{a+b}$ where a is taken from Table 1. The semiminor axis b can be calculated using the eccentricity e and the semimajor axis a with

$$\begin{eqnarray}&&b=\sqrt{{a}^{2}-{e}^{2}}.\end{eqnarray} \tag{ 10 }$$

For S4711, we derive a value of U_S4711 ≈ 18.29 mpc for the orbital length. In combination with its orbital time period, we derive a mean space velocity for S4711 to around 1540 km s⁻¹ which equals about 0.5%c. For S62, we derive with the values given in Table 1 a orbital distance of U_S62 ≈ 22.11 mpc with a mean 3d velocity of about 1370 km s⁻¹ = 0.3%c. Applying this analysis to S2 with the orbital elements from Gravity Collaboration et al. (2018a) and Gravity Collaboration et al. (2019), we get U_S2 ≈ 31.42 mpc and a mean 3D velocity of 1915.46 km s⁻¹ = 0.4%c.

The analysis of the NACO and SINFONI data reveals not only the existence of S4711, but also shows that there are several FSS candidates (Figure 10). The results of the observation of these FSS candidates are summarized in the following. For clarity, we follow the nomenclature introduced here and call them S4712, S4713, S4714, and S4715 to underline their uniqueness.

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S4712: this S-cluster member can be observed between 2008 and 2015. Because of S2, S19, and S13, a detection before 2008 and after 2015 is not free of confusion. The orbital elements are based on the Keplerian fit of the NACO data and are listed in Table 1.

S4713: compared to S4712, the observation of S4713 is limited to the years 2006 to 2010. Like for S4712, the stars S2, S19, S55, and S175 hinders a confusion-free observation of S4713 before and after 2006 and 2010.

S4714: the faint star S4714 can be observed for 4 consecutive years. In contrast to S4712 and S4713, the orbital time period is much smaller and is determined to be around 12 yr (see Table 1). The orbital time period is in line with S55 and S62. These two S-stars are also hindering the observation of S4714 because of blending effects.

S4715: S4715 has a longer orbital period than S2 star, which is 20.2 ± 2.4 yr. Together with S4712 and S4713, these are longer-period newly discovered faint S stars in comparison with S62, S4711, and S4714. Because of the crowded S-cluster, it should be noted that we do not observe a full orbit of S4712, S4713, S4714, and S4715. Because of the observation in several consecutive years, a blend star scenario (Sabha et al. 2012; Peißker et al. 2020a) can be excluded.

S4716: as shown in Figure 10, we find another S-cluster member between S19 and S38 that we name S4716 to underline the character of the source. However, we observe this object in the NACO data set of 2008 and 2009. Because of blending and the overlap of other nearby stars, an observation before 2008 and after 2009 is not satisfying.

As for S4712, S4713, S4714, and S4715, it is unlikely that these stars are blended background or foreground stars. This is underlined by the observation of more than 3 consecutive years (Sabha et al. 2012; Peißker et al. 2020a). When it comes to 20/a, 21/b, and S4716, it could be argued that these stars are foreground/background stars that are passing Sgr A* at small projected distances (see Eckart et al. 2002; Ghez et al. 2002).

Peißker et al. (2020a), Ali et al. (2020), and this work investigate members of the S-cluster. S62, S4711, and S4714 show highly eccentric orbits with a short semimajor axis (see Table 1). In Figure 11, we show the relation between the eccentricity as a function of the major axis. We want to point out an outlier not shown in Figure 11. This outlier is S85 and is 144 mpc away from the remaining stars. This is a significant distance relative to the extent of the S-cluster of around 40 mpc. Considering the large distance from the inner arcsecond, it raises doubt about the classification of S85 as a member of the S-cluster. In light of the Hills mechanism (Hills 1988) and the work of Zajaček et al. (2014) mentioned in the introduction, a detailed analysis of S85 could be fruitful. Besides the outlier, the trend of high eccentricity followed by a low major-axis is detected for the S-stars. We find for all stars with a larger major axis (>100 mpc) eccentricity values below 0.5. And vice versa, the density distribution of S-stars with a major axis <100 mpc shows a tendency toward eccentricity values higher than 0.5.

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Figure 12 shows the eccentricity distribution of known S-stars orbits, including the newly identified sources; by examining it we find that the more compact black disk (see Ali et al. 2020) exhibits a thermalized distribution (f(e) × de = 2e × de, Jeans 1919). Here, the term "thermalized" refers to reaching statistical equilibrium as a result of stellar interactions. The reason behind this may be the result of many Kozai–Lidov cycles that are triggered with the presence of a massive disturber (Chen & Amaro-Seoane 2014; see also Ali et al. 2020). Furthermore, it cannot be excluded that the Hills mechanism could also be a contributing process, especially for e > 0.9. It is worth noting that the short orbital timescale of these inner stars is probably the reason why they reached the thermalized arrangement in a short time. In contrast, the red disk displays a nearly flat distribution, peaking at e = 0.4, i.e., not thermalized. This could be due to the longer orbital periods and the on-average larger distances from Sgr A*. Therefore, the red disk stars might still need longer time to achieve the thermalized case. Nevertheless, they could also be subject to a disk-migration process that leaves them in a non-thermalized state.

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In addition to the previous possibilities, Merritt (2013b) proposed a plausible explanation for the current distribution of S-stars. Loss-cone dynamics describes the process in which the star suffers loss of angular momentum due to gravitational radiation at a very close distance to the SMBH. This leads to an orbit with high eccentricity. It is possible in this scenario that the star ends up being captured by the central mass. On the contrary, the star could evolve after some time and cross the Schwarzschild barrier, which defines the line of maximum eccentricity in the e − a diagram. As soon as this is achieved, resonant relaxation (RR) is then triggered, allowing the star to gain angular momentum and thus lowering its orbital eccentricity.

Based on this argument, we conclude that the red disk may be relaxed by RR, while the black disk is subject to an angular momentum loss process. However, Ali et al. (2020) found that the timescale of the scalar resonant relaxation that changes the value of angular momentum exceeds the current estimated age of the S-stars. Regarding this fact and using Newtonian simulations, Perets et al. (2007b) show that RR could already exhibit its dynamical effects in case the nucleus has a large density of compact disturbers (e.g., a population of black holes). Therefore, along with the previously mentioned possibilities, the proposed loss-cone justification could be considered as a valid scenario that describes the current eccentricity evolution.

Ali et al. (2020) present a detailed analysis of the kinematics of 112 stars that are present in the high velocity S-cluster and orbit the supermassive black hole Sgr A*. They found that the distribution of inclinations and flight directions deviate significantly from a uniform distribution that one would expect in the case of random orientation of the orbits. The S-cluster stars are arranged in two almost edge-on thick disks that are located at a position angle of about ±45° with respect to the Galactic plane. With 25°, the poles of this structure are close to the LOS. The reason for this arrangement is unclear. It may be due to a resonance process that started during the formation of the cluster of young B-dwarf stars about 6 Myr ago. Another possibility is the presence of a disturber at a distance of a few arcseconds from the S-cluster.

In relation to these two disks identified by Ali et al. (2020), we find that the stars S4711, S4712, and S4713 belong to the more compact (about <05 diameter) black disk, while S4714 and S4715 are members of the larger (∼1'' to 2'' diameter) red disk. More precisely and according to the 3D visual inspection, the orbit of S4715 seems to have approximately a 30° deviation from the plane of the red disk. As for the remaining newly identified stars, their orbits fit on average to within about 10° into the two-disk scheme. This implies that even the stars currently closest (both, physically and in projection) to SgrA* follow the kinematic structure of the S-cluster.