Spectroscopically Identified Intermediate Age Stars at 0.5 - 3 pc Distance from Sgr A*

Nuclear star clusters (NSCs) at the dynamical center of galaxies appear to have a complex star formation history. This suggests repeated star formation even in the influence of the strong tidal field from supermassive black holes.In our previous study, we have detected 31 so far unknown early-type star candidates throughout the Galactic NSC (at 0.5 - 3 pc from Sgr A*; Nishiyama and Schoedel 2013). The aim of this study is a confirmation of the spectral type for the candidates.We have carried out NIR spectroscopic observations of the candidates using Subaru/IRCS/AO188/LGS. K-band spectra for 20 out of the 31 candidates were obtained. By determining an equivalent width, EW(CO), of the 12CO absorption feature at 2.294 um, we have derived an effective temperature and a bolometric magnitude for each candidate, and then constructed an HR diagram.No young (~ Myr), massive stars are included in the 20 candidates we observed; however, 13 candidates are most likely intermediate-age giants (50 - 500 Myr). Two other sources have ages of ~1 Gyr, and the remaining five sources are old (>1 Gyr), late-type giants.Although none of the early-type star candidates from our previous narrow-band imaging observations can be confirmed as a young star, we find that the photometric technique is sensitive to distinguish old, late-type giants from young and intermediate-age populations. The intermediate-age stars could be so far unknown members of a population formed in a starburst ~100 Myr ago. Finding no young (~ a few Myr) stars at R = 0.5 - 3 pc favors the in-situ formation scenario for the presence of the young stars at R<0.5 pc. Furthermore, the different spatial distributions of the young and the intermediate-age stars imply that the Galactic NSC is an aggregate of stars born in different places and under different physical conditions.


Introduction
Most galaxies host luminous nuclear star clusters (NSCs; e.g., Carollo et al. 1998;Côté et al. 2006;Böker 2010;Georgiev & Böker 2014). Many of them have been found to coexist with supermassive black holes (SMBHs) at their center (Seth et al. 2008;Graham & Spitler 2009;Neumayer & Walcher 2012). Unlike SMBHs, NSCs are expected to provide a visible record of gas accretion and star formation at the center of galaxies; therefore studying stellar populations in NSCs can give us clues as to how stars are formed within the strong tidal field from SMBHs.
The NSC at the center of our Galaxy is the only one which can be resolved into individual stars with current instruments, making it an ideal target for studies of stellar populations and star formation history in NSCs. A concentration of young, massive stars at the center of the Milky Way's NSC, within a projected distance of about 0.5 pc of the SMBH Sagittarius A* (Sgr A*), was identified by spectroscopic observations and traces a starburst that occurred a few Myr ago (e.g., Paumard et al. 2006; Bartko et al. 2009;Lu et al. 2013;Yelda et al. 2014). However, due to the strong and patchy interstellar extinction toward the Galactic NSC, broad-band photometry can hardly be used to distinguish stellar populations (see, however, Schödel et al. 2010). The number of stars is too large to be surveyed with single or multi slit spectrographs. The apparent size of the NSC (half-light radius of ≈ 4.2 pc ≈ 1. ′ 8; Schödel et al. 2014) is too large to survey the entire region of the NSC using integral field spectrographs with a typical FoV of several arcsec, when operating with angular resolutions on the order of 0. ′′ 1, which is necessary in the crowded field of the Galactic center. Therefore most of the past observations of stellar populations in the Galactic NSC have been limited to a region within a pro-jected radius of R Sgr A * ∼ 0.5 pc from Sgr A* (e.g., Genzel et al. 2003;Paumard et al. 2006;Maness et al. 2007;Do et al. 2009; Bartko et al. 2010;Pfuhl et al. 2011;Do et al. 2013;Lu et al. 2013).
In our previous paper (Nishiyama & Schödel 2013), we aimed at overcoming these observational limitations by using near-infrared (NIR) imaging observations with narrow-band filters. CO band head absorption features starting at 2.29 µm can be used to distinguish between massive young stars and latetype giants (Buchholz et al. 2009). The absorption features are very strong for late-type (K and M) stars, become weaker for earlier spectral type, and are absent for stars earlier than early-F type (Wallace & Hinkle 1997). So we employed two narrow band filters, 2.34 µm at, and 2.25 µm just short-ward of, the CO feature, to derive a [2.25] − [2.34] 1 color as a proxy of stellar spectral type. In the magnitude range of 9.75 < [2.25] < 12.25, we thus found 31 so far unknown early-type [Wolf-Rayet (WR), supergiants or early O type] star candidates at R Sgr A * = 0.5−3 pc from the SMBH Sgr A* (Fig. 1).
To determine spectral types of the early-type star candidates, we have carried out adaptive-optics (AO) assisted spectroscopic observations with the Subaru telescope 2 and the infrared camera and spectrometer IRCS. In this work, we present the results of the observations for 20 of the above mentioned 31 early-type star candidates located outside the central 0.5 pc region.

Observations and Data Reduction
The spectroscopic targets were selected from the early-type star candidates found by Nishiyama & Schödel (2013). Fig. 2  color among the rest of the candidates, we have planned our observations to obtain spectra of as many targets as possible. It means that bright stars with a smaller separation angle from Sgr A* (i.e., observable without a change of natural tip-and-tilt guide stars) have a higher priority in our observations. As a result, we have observed 20 early-type star candidates (light green "×" in Fig. 2), and four red giants (red crosses) as a reference. As shown in Fig. 2 The spectroscopic observations were carried out in the nights of 12/13 June and 4/5 August 2012 with the Subaru telescope (Iye et al. 2004), and the infrared camera and spectrometer IRCS (Kobayashi et al. 2000). The 20 observed stars are indicated by green circles in Fig. 1. The exposure time was 300 sec for all the sources except # 57 (150 sec). The IRCS grism mode provides a spectral resolution of λ/∆λ ≈ 1, 900 in the K band with a slit width of 0. ′′ 1. 1 [λ] denotes a magnitude in a narrow-band filter with the central wavelength of λ.
2 Based on data collected at Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. ] 0.1) are already known early-type stars and dust embedded sources. Light green "×" represents the earlytype star candidates whose spectrum is obtained in this study, and red cross are observed red giants as a spectrum reference.
The reduction process included flat-fielding, sky subtraction, bad pixel correction, cosmic-ray removal, wavelength calibration with an arc lamp, spectrum extraction, and relative flux calibration. Flat field images were provided by obtaining spectra of continuum sources. Interspersed with the observations, we observed a dark cloud located at a few arcmin northwest of the Galactic center to obtain sky measurements. Argon arc frames were used to fit a dispersion solution.
Telluric correction was achieved by dividing each candidate's spectrum by that of one of the early-A main-sequence stars HD 126997 ( . Spectra for 20 of the candidates were obtained with Subaru/IRCS (green circles). The large cyan circle delimits a region within 0.5 pc (12. ′′ 9) in projection from Sgr A*. Spectra for five red giants were also obtained as a reference (red circles). Magenta arrows represent intermediate-age (50 Myr -500 Myr) stars (see §3 and 4).
(A0V), which were observed on the same night and at a similar airmass. Prior to division, the Br-γ line was removed from the standard star spectra by interpolating the stellar continua. The systematic influence of the SED of the A-stars was subsequently removed by multiplying with a blackbody spectrum of an appropriate effective temperature. Each spectrum was shifted to rest wavelength by using five or six of the 12 CO and 13 CO bandhead absorption features (vertical broken lines in Fig. 3). We removed the curvature of the stellar continua by dividing the spectra by a third or fourth polynomial function fitted to the line-free region of the stellar spectra. The resultant K-band spectra are shown in Fig. 3.
As a control sample, we also observed five stars located on the RGB in the color-magnitude diagram (Fig. 2). The same ob-servational settings were used as for the early-type star candidates.

Spectral Classification
K-band spectra provide prominent features which can be used for stellar classification. For early-type stars, the Br-γ absorption line is expected; however, no spectrum of our candidates shows the Br-γ absorption. Instead, all of the spectra show clear CO bandhead absorption features, indicative of a spectral type later than ∼ G4. So none of our 20 observed candidates is confirmed as an early-type star.
Many prominent features in the K-band, such as Na I, Ca I, and CO, have been widely used to investigate stellar parameters.
In particular the absorption strength of the 12 CO(2 −0) bandhead (≈ 2.294 µm) is a good indicator of a stellar effective temperature (T eff ). To measure the CO absorption depth, several index definitions have been proposed (see Mármol-Queraltó et al. 2008, and references therein); here we compute the CO index according to the recipe of Frogel et al. (2001). Pfuhl et al. (2011) used this definition to determine T eff of late-type stars in the Galactic NSC, and have found a smaller systematic uncertainty than other definitions used by Blum et al. (2003) and Maness et al. (2007).
The definition by Frogel et al. (2001) uses five narrow bandpasses, four at continuum, and one at the CO bandhead, to estimate the CO absorption depth (see Table 2 in Frogel et al. 2001). In our study, the continuum level ω C (λ) is determined with a linear fit to the flux levels in the continuum bandpasses, and the equivalent width EW(CO) is measured according to where ω C is the mean of continuum levels measured in the four bandpasses, and ω CO (λ) is the depth of CO absorption at wavelength λ. The uncertainty of EW(CO), σ CO , results from the uncertainty of the mean that is derived from the measurement in the four bandpasses. The resultant EW(CO) and σ CO for the early-type star candidates are shown in Table 1. Note that σ CO only includes the uncertainty in the continuum level and not any other systematic uncertainties from, e.g., correction of the spectral curvature. So the estimated σ CO shown here are lower limits. However, the expected systematic uncertainty is only on the order of a few percent when we use the definition by Frogel et al. (2001, see also §4).
For the effective temperature calibration, we use the following EW(CO)-T eff relation derived by Pfuhl et al. (2011): where T eff is in the unit of Kelvin. Pfuhl et al. (2011) used the definition of EW(CO) by Frogel et al. (2001), and derived the equation above using 33 red giants with known T eff , spectral type of G0 to M7, and metallicity of −0.3 < [Fe/H] < 0.2. This EW(CO)−T eff relation holds in the range 3.5 < EW(CO) < 24. Two early-type star candidates (# 54 and 62) and a reference red giant (RG46) have a larger EW(CO) than this range, so that we do not determine their T eff . It means that they are likely to be cooler than ≈ 2, 700 K.
To determine the amount of the interstellar extinction, we use the data sets of 1.71 µm and 2.25 µm narrow-band filters taken with VLT/ISAAC (Nishiyama & Schödel 2013 (Nishiyama et al. 2006). The typical uncertainty in A K determined by RMS of the colors the nearest stars is 0.68 mag. Note that the intrinsic color difference of K-M giants, ±0.1, is small enough to be safely ignored.
To determine bolometric magnitudes, a bolometric correction BC K is necessary. We follow the equation BC K = 2.6 − (T eff − 3800)/1500 from Blum et al. (2003). With BC K and A K , the bolometric magnitude can be calculated as M bol = K S − A K − DM + BC K , where K S is the observed K S -band magnitude and DM is a distance modulus of 14.5 at the distance of 8.0±0.15 kpc (Schödel et al. 2010). An uncertainty of DM of 0.04 mag is also quadratically added to the uncertainty of M bol . Note that we ignore the negligible magnitude difference between the K and K S bands. As a result, we obtain both T eff and M bol , and thus the observed stars can be plotted on a HR diagram (Fig. 4) Fig. 4. HR diagram for the early-type star candidates (green circles) and red giants as a reference (red circles). Overplotted are theoretical isochrones for ages of (from left to right) 50 Myr, 100 Myr, 500 Myr, 1 Gyr, 5 Gyr, and 10 Gyr with solar metallicity using the Padova code (Girardi et al. 2000;Marigo et al. 2008).
If supergiants are included in our targets, we need to use another EW(CO)−T eff relation for them; however, considering their rarity, and the observed magnitudes of our targets (K S > 10), it is safe to assume that no supergiant is included in our targets. In addition, the resultant bolometric magnitudes M bol of the early-type star candidates are fainter than −4.6 mag, even if we use the bolometric correction of BC K = 2.6 (Blum et al. 2003), and intrinsic colors of supergiants for the extinction correction; almost all of the supergiants in the central 5-pc region appear to be brighter than M bol ≈ −5.0 (Blum et al. 2003).
Without a proper motion measurement, it is still difficult to remove foreground/background sources completely. A less accurate but common way to remove such sources uses the interstellar extinction. We have constructed a narrow-band ([1.71] and [2.26]) color magnitude diagram for our targets, known earlytype stars and red giants, and other sources (Fig. 5) Fig. 2. We have confirmed that the color spread of stars observed in this work is almost the same as those of known earlytype stars and red giants in the NSC, suggesting that our targets are located in the NSC as well.

Narrow-band Photometry
The main goal of our work is a systematic search for young, massive stars throughout the Galactic NSC. To find candi-  Nishiyama & Schödel (2013). The observed early-type star candidates in this work are overplotted by light green "×". Dark green circles and red triangles represent spectroscopically identified early-type stars and late-type giants in the Galactic NSC, respectively.

Mag
dates of such young, massive stars in this region, we carried out NIR imaging observations using two narrow-band filters, 2.25 µm and 2.34 µm, with filter widths of ≈ 0.03 µm (Nishiyama & Schödel 2013). As shown in Fig. 3, the 2.34 µm filter is sensitive to the CO band head absorption at > ∼ 2.29 µm, a typical feature seen in late-type stars; on the other hand, the 2.25 µm filter is just short-ward of the CO absorption. When we measure magnitudes of stars in the two filters,  Nishiyama & Schödel 2013). The latter was adjusted such that the mean color of the RGB stars is 0 as described in the previous paragraph. As shown by green circles in Fig. 6 (2). The blue arrows represents spectral type in the case of giants (according to the Table 2 in Meyer et al. 1998). The horizontal dashed line represents the upper limit of EW(CO) to determine T eff with equation (2).

Results of Spectroscopic Follow-up Observations
In order to further investigate the nature of our target stars, we compared their position in the HR diagram ( Fig. 4) with the theoretical isochrones for solar metallicity (Girardi et al. 2000;Marigo et al. 2008). Some of our candidates are likely to be old (age 5 Gyr), late-type giants; on the other hand, most (13 out of 20) of them are located to the left of the 500-Myr isochrone. They are thus likely to be young giants with a mass in the range 2.5 M ⊙ < M < 6 M ⊙ , and are descendants of main-sequence B-type stars. No young (∼ Myr), massive star is included in the 20 candidates we observed. The data points in the HR diagram might have a systematic uncertainty. One of the candidates and three of the reference red giants are located clearly to the right and below of the old-est theoretical isochrone considering the uncertainties shown in the plot. Pfuhl et al. (2011) investigated systematic uncertainties in EW(CO) and T eff due to the differences of a spectral resolution and an amount of the interstellar extinction. They found no measurable impact in the EW(CO) index by Frogel et al. (2001) due to degrading the resolution from R ∼ 3, 000 to 2, 000, and the resolution in our observations is R ∼ 1, 900. Moreover, the Frogel et al. (2001) index is decreased by only less than a few percent due to the uncertainty in the extinction correction applied to the stars studied here, leading to the combined systematic uncertainty of less than 50 K in T eff .
Our source # 33 was observed and its stellar parameters were determined by Maness et al. (2007, source ID 300). Although they used a different definition for EW(CO) and EW(CO)-T eff relation, their resultant T eff and M bol are 4529 K and −3.58, respectively; both of them are in very good agreement with ours, T eff = 4638 ±169 and M bol = −3.6 ±0.2. This suggests no strong systematic offset in our determination of T eff and M bol , and that we have successfully found an intermediate-age population in the Galactic NSC. In any case, we do not think that the possible systematic uncertainties present in our HR diagram affect its main features; we can clearly distinguish two populations, an older, cooler one and a younger hotter one. Pfuhl et al. (2011) found a significant population of outliers which are distributed to the right and below of the oldest isochrone for solar metallicity. They ascribed the presence of the outliers to possible effects such as dust envelopes, variability, high metallicity, or uncertainty in stellar evolutionary models.
Several outliers, distributed to the right and below of the 10-Gyr isochrone, are also found in our HR diagram (Fig. 4). We have made a conservative estimate of the uncertainties in A K ( §3), leading to a typical σ M bol of 0.7 mag. Fig. 5 clearly demonstrates that the candidates must be located very close to the Galactic center; even if they are located at 1 kpc from the Galactic center, M bol would be changed only 0.3 mag, and they are thus still outliers.
The outliers can be potentially explained by their supersolar metallicity. In Fig. 7, we have constructed an HR diagram with isochrones of different metallicities. Here the PARSEC isochrones (Bressan et al. 2012) with Z = 0.3Z ⊙ (blue lines), Z ⊙ (black dotted lines), and 3Z ⊙ (magenta lines) are used. The diagram implies that most of the outliers are very old (∼ 10 Gyr) population with Z > ∼ 3Z ⊙ , and this has already been pointed out by Pfuhl et al. (2011). Observational constraints of the metallicity of the outliers are crucial to understand their true nature.
Stars in dense stellar cusps around SMBHs suffer much more close tidal encounters than in normal environments, and tidal spin-up of stars are expected in the Galactic center region (Alexander & Kumar 2001). The rotation of stars has an impact on the stellar evolution, and isochrones from Ekström et al. (2012) are thus used to understand the effect of the rotation. When the stellar rotation is considered, isochrones are shifted towards a higher luminosity. This cannot explain the existence of the outliers distributed to the right and below of the oldest isochrone in Fig. 4.
In the previous paper, we concluded that we found strong candidates for early-type stars (Nishiyama & Schödel 2013). However, as shown in Fig. 3 and 4, no young, massive star is included in our observed candidates; instead, most of them are an intermediate-age (50 Myr -500 Myr) population. We note that precision-photometry in our previous study was limited to the magnitude range of 9.75 < [2.25] < 12.25. Only WR stars, supergiants and early-O type stars are distributed in this range as early-type stars, and their expected number is rather small. B- . HR diagram as same as Fig. 4, but overplotted are theoretical isochrones for ages of (from left to right) 50 Myr, 100 Myr, 500 Myr, 1 Gyr, 5 Gyr, and 10 Gyr with Z = 0.3Z ⊙ (blue lines), Z = Z ⊙ (black dotted lines), and Z = 3Z ⊙ (magenta lines), using the PARSEC isochrones (Bressan et al. 2012). Note that the PARSEC isochrones do not include the tip of the AGB, but it can be used to compare isochrones for different metallicities.
type stars, which may be more frequent, have magnitudes around K ∼ 14 − 16 in the Galactic center. They could not have been found in our seeing-limited ISAAC observations, where the extreme crowding in the NSC severely limits completeness and photometric precision.
In our previous paper, we have shown an azimuthally averaged, projected stellar surface density plot as a function of the distance to Sgr A* for the early-type star candidates (Fig. 11 in Nishiyama & Schödel 2013). It shows a continuous profile in the range from 1. ′′ 5 to 60 ′′ with a power-law index of 1.60. However, again, no young, massive star is included in our observed candidates. It means that the profile we have made in the previous paper is not for the early-type, young and massive stars, but for stars younger than ∼ 500 Myr. Our results also indicate a lack of young, massive stars outside the central 0.5 pc region from Sgr A*; recently, Støstad et al. (2015) have found a break in the surface density profile of young stars (∼ 5 Myr) at 0.52 pc (∼ 13 ′′ ) from Sgr A*. This is consistent with the non-detection of genuine young, massive stars in our spectroscopic follow-up observations.
Although we have not found new young, massive (WR, supergiants or early O type) stars, it does not mean that there are no unknown young stars in the R Sgr A * = 0.5−3 pc region. As shown in Fig. 2, we have misidentified a few, already known early-type stars as RGB stars. In addition, we have not completed spectroscopic observations for the early-type star candidates we have found in the previous work. Therefore we do not exclude the possibility of the existence of unknown early-type stars at 0.5 − 3 pc from the SMBH.
The detection of the intermediate-age population shows that although the technique to measure the CO absorption depth with narrow-band filters cannot distinguish between young and intermediate-age stars, it works well to distinguish them from old, late-type giants. In our previous paper, we have estimated that the contamination rate of the early-type candidates by erroneous identification of late-type giants is about 20 % (Nishiyama & Schödel 2013). As shown in Fig. 6, 15 out of the 20 candidates show T eff > 3, 500 K, and they are clearly hotter than the late-type giants with T eff < ∼ 3, 000 K, leading to a contamination rate of 25 %. However, we note that we cannot distinguish the young (∼ Myr), massive stars from the intermediateage (< 500 Myr) stars in our imaging observations. As shown in Fig. 2, no clear difference is seen in the distributions of the spectroscopically confirmed massive, early-type stars and the intermediate-age population. Hence spectroscopic follow-up observation is necessary to discriminate genuine young, massive stars from the sample selected by our imaging observations with two narrow-band filters.
We present an HR diagram including results of previous works (Blum et al. 2003;Maness et al. 2007) in Fig. 8. Since the observations by Maness et al. (2007) were assisted by AO, their 50 % completeness limit is as deep as K S ∼ 15.5, about 4-mag deeper than ours; but note that the observations of Maness et al. (2007) were limited to eight relatively small fields (4. ′′ 2 × 4. ′′ 2 or 0.16 × 0.16 pc) within a projected distance of R Sgr A * = 1 pc from Sgr A*. On the other hand, the completeness of Blum et al. (2003), a magnitude-limited survey that encompassed the entire region of our ISAAC survey with a 4-m class telescope, appears to be slightly shallower than ours. This can probably be attributed to the excellent seeing during our ISAAC observations. Our findings also indicate that observations with higher angular resolutions, e.g., with AO, will allow us to reach a deeper limiting magnitude and search for late-O and B-type stars via narrow-band imaging.

Implications for Star Formation at the Galactic Center
Finding no WR, early-O main sequence and O supergiant stars at the R Sgr A * = 0.5 − 3 pc region disfavors the cluster infalling scenario for the presence of young stars in the central 0.5 pc region (e.g., Gerhard 2001;Kim & Morris 2003). This scenario proposed the formation of a massive cluster at more than several parsec distance from Sgr A*, where the tidal field from the SMBH is weak enough to form stars, followed by an infall of the cluster toward the central parsec. Since the star cluster migrates to the center via dynamical friction, a presence of some very massive stars at R Sgr A * > 0.5 pc, which escaped from the cluster is expected (e.g., Fujii et al. 2010), but no such stars have been found in our observations, and only two young, massive star candidates have been found in the recent HST Pa α survey [# 38 and # 133 in the list of Dong et al. (2011), but # 38 is likely to be a foreground O4-6I star (Mauerhan et al. 2010, star # 7)]. Considering the sensitivity for the Pa α emission (from evolved massive stars with strong wind) of the HST survey, and that for the CO absorption in our observations, the results described above provide further evidence to support the in-situ formation scenario.
However, we emphasize that we cannot exclude the cluster infall scenario in general. A migration of stellar clusters to the center is a natural consequence if clusters are formed in the Galactic center region. Massive stars tend to be carried very close to the center after migration, because massive stars sink to the cluster center due to the mass segregation, and stars at the  Blum et al. (2003) and Maness et al. (2007) are also plotted with black and blue circles, respectively. Overplotted are theoretical isochrones for ages (from left to right) 50 Myr, 100 Myr, 500 Myr, 1 Gyr, 5 Gyr, and 10 Gyr with solar metallicity using the Padova code (Girardi et al. 2000;Marigo et al. 2008).
outer region of the cluster easily become unbound (Fujii et al. 2010). The lifetime of the intermediate-age population stars we have found, more than 50 Myr, is long enough for clusters to migrate from a few tens parsec distance to the central a few parsec region (e.g., Gürkan & Rasio 2005). Hence the intermediate-age population we have found may be due to either in-situ formation or cluster infall. In the latter case, measuring the kinematics of the intermediate-age stars may give some clue as to their origin, given that the two-body relaxation time at their location is expected to be at least an order of magnitude longer than their lifetimes (Alexander 2005). A large part of our intermediate-age population might have been formed in a starburst about 100 Myr ago. From the detection of a fairly large number (∼ 10) of moderately luminous late-type stars, a starburst of 100 Myr ago was suggested within a projected distance of 0.5 pc of Sgr A* (Krabbe et al. 1995). Further spectroscopic observations confirmed the presence of such stars inside (Maness et al. 2007) and outside (Blum et al. 2003) of the central 0.5 pc region. The best-fit model for the star formation history of the Galactic NSC by Pfuhl et al. (2011, their Fig. 14) suggests that the star formation rate reached a minimum ∼ 1 Gyr ago, and then rose again ∼ 100 Myr ago. Hence the intermediate-age stars discovered by us may represent so far unknown members of the population formed ∼ 100 Myr ago.
The different spatial distribution between the young (a few Myr) and intermediate-age population stars is intriguing. Most of the young stars are concentrated in the central 0.5 pc region (e.g., Eckart et al. 1995;Genzel et al. 2000;Paumard et al. 2006;Do et al. 2013), while the intermediate-age stars are distributed throughout the NSC (Haller & Rieke 1989;Blum et al. 1996Blum et al. , 2003. Our observations further confirmed the widespread dis-tribution of the intermediate-age stars compared to the young massive stars. It is unlikely that the widespread distribution results from dynamical scattering of stars formed in the central 0.5 pc, because the intermediate-age stars are relatively heavy (M > ∼ 2.5 M ⊙ ). The two-body relaxation and mass segregation time scales in the NSC are on the order of 10 9 yr (Alexander 2005), i.e., we can expect that the kinematics and distribution of the intermediate-age stars still bears the fingerprint of their origin. As concerns the origin of these young stars, it is not difficult for star clusters to reach the central a few parsec region from a few tens parsec distance within ∼ 100 Myr via dynamical friction. Alternatively the stars might have been formed in the circumnuclear disk (Yusef-Zadeh et al. 2008). In any case, our results imply several paths of the star formation in the Galactic NSC, i.e., stars in the NSC have been formed in different places and under different physical conditions.

Summary
We have carried out spectroscopic observations of 20 out of 31 early-type star candidates in the nuclear star cluster at the center of our Galaxy, identified in the imaging survey by Nishiyama & Schödel (2013). We have found that 65 % of the candidates probably belong to an intermediate-age (50 Myr -500 Myr) population, and the rest of them are late-type giants older than ∼ 1 Gyr. The intermediate-age population stars are likely to have formed in a starburst about 100 Myr ago. None of the stars is as young as the few million year old stars within a projected radius of R Sgr A * = 0.5 pc of Sgr A*. We can thus conclude that the most recent star formation episode in the nuclear star cluster was confined to the immediate environment of Sgr A*, at least as concerns the most massive stars. Our findings thus also supports the in-situ formation of the O/WR stars near Sgr A* and speaks against the cluster-infall scenario. In the latter case, we would have expected to observe at least a few O/WR stars in the region beyond R Sgr A * = 0.5 pc. We show that narrowband imaging observations can be an efficient means to distinguish younger (< 500 Myr) stars from very old giants; however, our results also suggest that the kind of seeing-limited photometry with only two filters that we used in our previous work is not sufficient to discriminate young (< 10 Myr), massive stars from the intermediate-age (10 − 500 Myr) ones. Spectroscopic followup observations still play an important roll in the separation. The clearly different distribution of the young and intermediate-age stars in the Milky Way's nuclear star cluster may indicate different formation scenarios for the two populations.  Fig. 3. K-band spectra of the early-type star candidates (top) and RGB stars (bottom). Each star is identified above its spectrum with the ID assigned by Nishiyama & Schödel (2013) and Fig. 1. The position of the Br-γ, Na I doublet, Ca I triplet, four band heads of 12 CO, and two band heads of 13 CO are indicated by the vertical broken lines. The position and width of two narrow-band filters, 2.25 µm (NB2.25) and 2.34 µm (NB2.34), are also indicated by cyan hatched boxes. The spectra are sorted by the strength of the CO absorption feature at ≈ 2.294 µm from the top (weak) to the bottom (strong), in each panel.