MAPPING THE OUTER EDGE OF THE YOUNG STELLAR CLUSTER IN THE GALACTIC CENTER

Observations were obtained with Gemini-North's Near-Infrared Integral Field Spectrometer (NIFS) between 2012 May and 2014 May with natural guide star and laser guide star adaptive optics.⁶ NIFS provides a 2040 pixel wavelength spectrum in the K band (1.965–2.430 μm) for a continuous ${3}^{\prime\prime }$ × ${3}^{\prime\prime }$ spatial field (62 × 60 pixels). The spectral resolution is ∼5000 with a typical spatial resolution of 115–165 mas. The radial extent of the survey is from 75 to 23'' in projected distance from the Galactic center. The fields are separated into two regions, one north and one east of Sgr A*, for an approximate total surface area coverage of 99 arcsec².⁷ Each field was observed five or six times with an exposure time of 600 s per frame and a small (∼02) dither pattern. The fields are situated so as to avoid areas already examined by previous deep spectroscopic surveys and to examine either the projected location of the clockwise young stellar disk (eastern fields) or the region perpendicular to the clockwise young stellar disk (northern fields). The exception is the field NE1-1, which is between the two regions—for the purpose of this paper it will be considered as part of the northern regions. The locations of the fields, together with relevant observation regions from other papers, are indicated in Figure 1—information about each field is reported in Table 1.

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Table 1.  Summary of NIFS Observations

Name	Field Centera (arcsec)	Radius (arcsec)	Date (UT)	FWHM (mas)b	Nframesc	Guide Star	Avg Extinction (${A}_{{K}_{{\rm{s}}}}$)
E5-1	15.34, 0.43	15.34	2012 May 07	135	5	LGS	2.58
E5-2	14.62, −2.45	14.82	2013 May 23	140	5	LGS	2.75
E6-1	18.24, −0.45	18.25	2013 May 30	150	5	LGS	2.67
E6-2	17.65, −3.35	17.97	2012 May 05	115	5	LGS	2.73
E7-1	21.27, −1.35	21.31	2012 May 12	150	5	NGS	2.68
E7-2	20.57, −4.35	21.02	2012 May 12	145	6	NGS	2.66
N1-1	2.73, 8.67	9.09	2012 May 11	165	5	NGS	2.61
N1-2	5.36, 7.24	9.01	2012 May 11	165	5	NGS	2.75
NE1-1	10.08, 3.80	10.77	2014 May 14	135	5	LGS	2.41
N2-1d	4.23, 11.35	12.11	2012 May 13	225	5	NGS	2.63
N2-2d	6.84, 9.88	12.02	2012 May 13	350	5	NGS	2.76

Note.

^aR.A. and decl. offset in projected distance from Sgr A* (R.A. offset is positive to the east). ^bAverage FWHM found from two-dimensional Gaussian fits to the PSF used in StarFinder (PSF extracted from relatively isolated stars in the field). ^cEach frame has an integration time of 600 s. ^dDiscarded prior to analysis due to poor AO correction.

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We observe skies and two A-stars (HD 155379, HIP 96408) each night for calibration purposes. The Galactic center is densely populated with stars, and as such the science exposures could not be used for sky subtraction—separate sky observations from the region R.A. 17:45:50.558, decl. −29:00:01.30 were used for this purpose, while the science exposures themselves were used for annulus subtraction around each star (see Section 2.2). The A stars were used to correct for atmospheric absorption lines. We also use two tip-tilt stars, one for the northern regions (USNO 0609-0602733, R.A. 17:45:42.287, decl. −29:00:36.80) and one for the southern regions (USNO 0690-0602749, R.A. 17:45:40.720, decl. −29:00:11.20).

Data reduction of the raw science exposures was done using a modified version of the NIFS pipeline supplied by Gemini.⁸ The pipeline performs sky subtraction, dark subtraction, and flat-field correction and corrects for optical distortion on the detector. It also uses the spectra of the two A0V stars to correct for atmospheric absorption. The A-star spectra are featureless except for a strong Brγ absorption feature. To remove this feature, we divide the observed spectrum by a theoretical Vega spectrum from the Kurucz models⁹ (which has been convolved to match the A-star spectral resolution). After the pipeline, the resulting science frames were combined for each field, aligning individual data cubes by using the positions of bright sources in each frame.

To locate the stars, the point-spread function (PSF) fitting program StarFinder (Diolaiti et al. 2000) was used on collapsed versions of the science exposures. At times, StarFinder would fail to detect very obvious stars even when a very low correlation threshold was used in the detection algorithm. Due to this, we both used a very low correlation threshold (CT = 0.4) and checked visually for obvious false detections or omissions afterward. We find that StarFinder detects simulated stars (at their correct magnitude) with a 50% completeness down to ${K}_{{\rm{s}}}=16.2$. At fainter magnitudes false detections appear. We made an attempt to manually remove these, but detections fainter than ${K}_{{\rm{s}}}=16.2$ should still be approached with some caution (especially those not cross-referenced to a detection from Schödel et al. 2010). More details about the detection completeness can be found in Section 3 and in Appendix B . Specifically, it should be noted that these simulations lack the visual check for obvious omissions and false detections we make for the science exposures, and that this may lead to the simulations slightly underestimating photometric completeness (see Section 3.2). Absolute coordinates were then assigned to the sources by comparing pixel positions to known stellar positions from Hubble Space Telescope (HST) observations of the nuclear star cluster (GO-12182, PI Do), which were aligned to Two Micron All Sky Survey observations. The stellar coordinates are listed in Tables 2–apj513403t3 4 (Tables 3 and 4 can be found in Appendix A ). One of the final data cubes, with all star positions marked, can be seen in Figure 2. The rest of these data cube images can be found in the online supplementary material.

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Table 2.  NIFS Observations of Early-type Stars

			ΔR.A.a	ΔDecl.a	R		CO 2.2935	Err	CO 2.3227	Err	Brγ EW	Errb
Name	Date	${K}_{{\rm{s}}}$				S/N							${A}_{{K}_{{\rm{s}}}}$	Contam
			('')	('')	('')		EW (Å)	(Å)	EW (Å)	(Å)	(Å)	(Å)
N1-2-043	2012 May 11	12.8	3.73	7.15	8.07	67	0.0	0.3	1.1	0.2	1.4	0.4	2.60	N
N1-1-017	2012 May 11	16.0	4.08	8.37	9.31	16	1.4	1.1	1.4	0.6	2.5	2.0	2.61	N
NE1-1-035	2014 May 14	16.1	9.85	3.40	10.42	34	0.1	0.5	0.7	0.4	1.3	1.7	2.35	N
NE1-1-006	2014 May 14	13.0	9.67	4.36	10.61	141	0.4	0.1	2.3	0.1	0.7	0.3	2.45	N
NE1-1-004	2014 May 14	12.9	10.84	3.19	11.30	102	0.4	0.2	1.2	0.1	0.9	0.3	2.38	N
E5-1-013	2012 May 07	15.4	16.64	−0.27	16.64	34	1.4	0.5	2.7	0.4	0.7	1.4	2.60	N

Note.

^aR.A. and decl. offset in projected distance from Sgr A* (R.A. offset is positive to the east). ^bBrγ EW is difficult to determine due to, among other things, systematics stemming from the subtraction of local Brγ emission. We attempt to capture this uncertainty in our errors by combining the dispersion of Brγ EW for late-type stars at the same magnitude with the S/N-based random uncertainty.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 3.  NIFS Observations of Late-type Stars

			ΔR.A.a	ΔDecl.a	R		CO 2.2935	Err	CO 2.3227	Err	Na i	Err
Name	Date	${K}_{{\rm{s}}}$				S/N							${A}_{{K}_{{\rm{s}}}}$	Contam
			('')	('')	('')		EW (Å)	(Å)	EW (Å)	(Å)	EW (Å)	(Å)
N1-2-030	2012 May 11	15.8	4.27	6.48	7.76	20	10.1	0.9	11.1	0.6	4.1	0.5	2.67	Y
N1-1-022	2012 May 11	15.6	2.28	7.45	7.79	32	9.7	0.5	10.7	0.4	2.7	0.4	2.63	N
N1-2-019	2012 May 11	15.8	4.21	6.64	7.86	25	10.1	0.6	12.7	0.4	3.4	0.4	2.67	N
N1-2-010	2012 May 11	15.6	4.74	6.35	7.92	29	11.3	0.5	13.1	0.4	3.5	0.4	2.75	N
N1-1-045	2012 May 11	12.3	3.64	7.22	8.08	>40	6.8	0.2	5.6	0.2	0.5	0.1	2.56	N
N1-1-039	2012 May 11	15.9	3.44	7.33	8.10	16	4.3	1.0	5.7	0.7	1.4	0.8	2.50	N
N1-1-027	2012 May 11	15.8	0.95	8.11	8.16	13	7.4	1.1	12.3	0.6	0.4	0.8	2.62	N
N1-2-028	2012 May 11	15.9	4.91	6.58	8.21	25	9.5	0.6	10.4	0.5	0.7	0.5	2.78	N
N1-2-013	2012 May 11	15.2	5.57	6.04	8.21	24	10.7	0.6	12.3	0.5	1.9	0.5	2.80	N
N1-1-028	2012 May 11	15.7	2.62	7.80	8.22	19	8.3	0.8	9.7	0.6	1.4	0.6	2.64	N

Note.

^aR.A. and decl. offset in projected distance from Sgr A* (R.A. offset is positive to the east). ^bStar could not be cross-matched to Schödel et al. (2010). ${K}_{{\rm{s}}}$ magnitude estimated from the NIFS data.

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After obtaining the stellar positions, their spectra were extracted by way of aperture photometry on each spectral channel. The flux from a circular aperture with a radius of 1.8 pixels (∼90 mas) around the star was extracted. Furthermore, a median background spectrum with a 2 pixel annulus starting at 2 pixels from the center was subtracted from the spectrum of the star to remove the local background. Though this procedure may include very close stars in the background estimation, taking the median and manually checking stars for close companions helps to minimize this issue. Furthermore, for all close companions star-planting simulations were performed to check our performance in extracting the fainter spectrum. If a brighter star contaminated the spectrum (but not so much as to make the spectral type uncertain), it is noted in Tables 2 and 3. (See also Appendix B ).

The signal-to-noise ratio (S/N) per spectral channel was calculated with the region between 2.212 and 2.218 μm, which is relatively featureless in our spectra. We noted that spectrum quality of the brightest stars does not scale well with increasing flux at S/N > 40 due to intrinsic lines in the late-type stellar spectrum. We were unable to locate any regions with less features in our high-S/N late-type spectra, so the S/N of most bright stars is only constrained to be above 40. We still expect S/N to scale with the square root of star flux above this limit.

The ${K}_{{\rm{s}}}$-band magnitudes of the stars were found by matching detections to the photometry from Schödel et al. (2010).¹⁰ Location and estimated magnitudes were used to search for matching stars, after which the ${K}_{{\rm{s}}}$ values from the Schödel et al. (2010) measurements (if applicable) were used for further analysis. If no match could be found, an approximate magnitude calculated from the spectra intensity was used. Additionally, we use an extinction map of the Galactic center (again from Schödel et al. 2010) to shift all magnitude measurements to a mean extinction value of ${A}_{{K}_{{\rm{s}}}}=2.7$. The Schödel et al. (2010) extinction map shows average ${A}_{{K}_{{\rm{s}}}}$ values of between 2.41 and 2.75 between the different fields observed in this study (Table 1). These values are about average for the extinction in this region. Scoville et al. (2003) showed that the most eastern fields (near the circumnuclear disk) may have slightly higher extinction, though they use a different extinction law compared to Schödel et al. (2010). Regardless, the difference in extinction does not substantially affect our conclusions given the high completeness of this survey.

We extract a total of 375 spectra from the survey region. We utilize all 221 spectra from stars in the eastern fields for the analyses in this paper. In the northern fields, however, all data—26 spectra—from the fields N2-1 and N2-2 are discarded due to very low completeness (see Section 3). We are left with 128 usable spectra from the northern regions and 349 spectra in total.¹¹ The early-type stars are listed in Table 2, while the late-type stars are listed in Table 3. The stars that could not be spectral typed are listed in Table 4. Tables 3 and 4—listing the late-type and unknown stars—are in Appendix A .

Table 4.  NIFS Observations of Stars without Spectral Identification

Name	Date	${K}_{{\rm{s}}}$	ΔR.A.a	ΔDecl.a	R (arcsec)	S/N	${A}_{{K}_{{\rm{s}}}}$
N1-1-038	2012 May 11	17.3	1.98	7.50	7.76	2	2.65
N1-1-037	2012 May 11	17.7	2.34	7.63	7.98	3	2.63
N1-1-034	2012 May 11	17.1	2.15	7.82	8.11	7	2.60
N1-2-037	2012 May 11	17.2	5.78	6.42	8.64	6	2.79
N1-1-033	2012 May 11	16.2	1.23	8.68	8.76	3	2.60
N1-2-041	2012 May 11	17.5	5.80	7.61	9.57	4	2.79
N1-1-036	2012 May 11	...c	3.40	9.36	9.96	0	2.59
N1-2-038	2012 May 11	17.1	4.77	8.76	9.97	5	2.64
N1-2-034	2012 May 11	16.6	6.39	8.11	10.33	2	2.72
NE1-1-039	2014 May 14	16.5	10.16	2.86	10.55	14	2.34

Note.

^aR.A. and decl. offset in projected distance from Sgr A* (R.A. offset is positive to the east). ^bStar could not be cross-matched to Schödel et al. (2010). Approximate K' magnitude calculation used. ^cStar could not be cross-matched to Schödel et al. (2010) and was too faint for magnitude approximation.

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The identification of spectral types is primarily based on the presence or absence of the CO bandheads at 2.2935, 2.3227, 2.3525, and 2.3830 μm. Early-type stars are relatively featureless in the wavelength region observed, except for Brγ 2.1661 μm and possibly He i 2.0581 μm and He i 2.1126 μm. Detecting the Brγ absorption is difficult due to its low equivalent width in O and B stars (0–4 Å), combined with systematics from background subtraction (Brγ-emitting gas is pervasive through the Galactic center) and error induced from having to correct for the significant Brγ absorption in the A star we used to fix for atmospheric absorption. The He lines are also weak, but detectable for high-S/N spectra of early-type stars—especially He i 2.1126 μm. However, late-type stars have very strong CO bandheads, which make it an effective indicator of spectral type for almost all our sources, in addition to the Na i features at 2.2062 and 2.2090 μm. To illustrate the difference, Figure 3 shows five spectra: a faint young star, a bright young star, a faint old star, a bright old star, and a faint unclassified star. Notice that the CO bandheads are strong even in the faint late-type star.

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All stars were initially classified as either early-type, late-type, or unknown by visually examining their spectra. To further strengthen the spectral classifications, we measured EWs of CO $2.2935$, CO $2.3227\;\mu {\rm{m}}$ and the Na i lines. After correcting for velocities by shifting the spectra to rest wavelengths, the EWs for all spectra with S/N > 5 were found by normalizing the spectra and integrating over regions specified in Förster Schreiber (2000) for each line. Based on these equivalent width measurements, we re-evaluated a small (<5) number of the initial spectral classifications. As expected, we find a clear correlation between these EWs and the classification of stars as late-type or early-type—see the distributions in Figure 4. The EWs are shown in Tables 2 and 3.

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To study the projected surface-density profiles, we need to correct for both spectroscopic and photometric incompleteness. The spectroscopic completeness is, simply put, the success rate at which we are able to spectrally type stars. More precisely, it is defined as the number of stars spectrally classified over the total stars detected per magnitude bin, and it is a measure of how brightness impacts our ability to spectrally type stars. When there is too much noise, we can no longer classify the stars as early-type or late-type, which lowers the spectroscopic completeness.

Our spectral analysis relies heavily on the presence of the CO bandheads in late-type stars (and their absence in early-type stars). This naturally makes it more difficult for us to classify early-type stars than late-type stars. However, finding the spectroscopic completeness purely for early-type stars is challenging due to the low number of young stars, so we use the same spectroscopic completeness for both late-type and early-type stars. To minimize the negative effect of this in our analysis, and to increase the significance of our results, we introduce a magnitude threshold at ${K}_{{\rm{s}}}=15.5$. Any star fainter than this is not used for analysis. The spectroscopic completeness alone for such bright magnitudes is nearly 100%—we successfully spectral type all but one star brighter than the magnitude threshold. The one star that could not be spectral typed is too close to a very bright late-type star for reliable classification and was found when we performed star-planting simulations to confirm our ability to distinguish early- and late-type stars near bright sources (see Appendix B ). Hence, while the approximation that the early-type and late-type spectroscopic completenesses are equal is clearly not ideal, it is acceptable for the range of magnitudes used in the analysis. We also still have a high total completeness at this threshold (74%), and it is also the same magnitude threshold other publications have used, making comparisons easier (Bartko et al. 2010; Do et al. 2013a).

In total, 349 stars were detected, including those fainter than the magnitude threshold of ${K}_{{\rm{s}}}=15.5$.¹² Four stars were found to be foreground stars due to their very blue H–K band colors. Of the remaining 345, we found 6 early-type stars, 286 late-type stars, and 53 stars that could not be spectral typed due to low S/N.¹³ Of the 148 stars brighter than the magnitude threshold, 140 are late-type stars, 4 are early-type stars, 3 are foreground stars, and only 1 is spectrally unidentified. See Figure 5 for the average spectroscopic completeness over all fields. Note that all completeness correction is done before star magnitudes are extinction corrected.

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Photometric completeness is defined as the probability of detecting a star of a certain magnitude in the data cubes and is a measure of how well we are able to detect stars at any given magnitude. To measure this, we added artificial stars at random positions and proceeded to use the same StarFinder routine we used to initially detect stars to determine the probability of re-detecting the artifical stars. For every image (each one corresponding to a region in Figure 1) ∼750 stars were added per ${\rm{\Delta }}{K}_{{\rm{s}}}=0.5$ mag bin. The stars were re-detected by cross-referencing position and expected brightness of the added artificial star to the positions and brightnesses detected by StarFinder. Unlike the science exposures, we do not manually check these simulation cubes for obvious omissions and false detections. Because we match the detections with both positions and brightnesses, it is unlikely that any false detections match up exactly with the simulated stars (ensuring that we do not overestimate the photometric completeness). However, as obvious omissions are not added, it is possible that the simulations slightly underestimate the number of detected stars, and thus that the actual photometric completeness is slightly higher than what we calculate. To elaborate—for the science exposures some stars were manually added to the list of stars after the StarFinder routine, but due to the manual nature of this process, it could not be done for the automatic completeness calculation. This leads us to detect slightly fewer stars in the simulations, which leads to an artificially low completeness. However, the number of such obvious omissions manually added in the science exposures is low, particularly over the magnitude threshold (less than one per field). It follows that the number discrepancy of stars detected between the simulations and science data is low, and so is the effect on the completeness. This has negligible effect on our completeness analysis.

Having the photometric completeness for each field (Figure 6), we note that the observations with laser guide star adaptive optics correction obtained better results. The natural explanation to this is that the natural guide star is somewhat fainter and farther away than the laser. However, it should also be noted that most of the fields observed with laser guide star are situated farther from Sgr A*, so stellar density might be partly responsible for the observed completeness difference. A counter-argument to this is that a similar effect is observed in the spatial FWHM of the fields (see Table 1).

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Using the spectroscopic completeness and average photometric completeness, we can find an overall completeness curve. This total completeness curve measures the average likelihood of a detection and classification of any magnitude star in any our fields, i.e., the overall completeness over all fields. At the magnitude threshold ${K}_{{\rm{s}}}=15.5$ the total completeness varies between 59% and 92% for the analyzed fields. At any magnitude brighter than this threshold the total completeness is dominated by the photometric completeness rather than the spectroscopic completeness. In other words, if the star can be detected at all and is brighter than ${K}_{{\rm{s}}}=15.5$, then it can almost certainly be spectral typed. The major limiting factor on our completeness is source confusion due to low spatial resolution. Across all the fields, the average total, photometric, and spectroscopic completenesses at the magnitude threshold are 74%, 75%, and 98%, respectively. The total completeness curve, together with the spectroscopic and photometric completeness curves, can be seen in Figure 5.

With these completeness estimates we can approximate the total number of stars we could not detect or classify due to photometric or spectral incompleteness. Completeness correction over all regions adds 22.8 late-type stars and only 0.3 early-type stars. The total number count of stars with and without completeness correction is shown in Figure 7.

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Figure 8 shows the completeness-corrected projected surface-density profile for early- and late-type stars ${K}_{{\rm{s}}}\leqslant 15.5$. Four early-type stars brighter than the magnitude threshold were detected. Three of these four stars were detected in the northern regions: two in NE1-1 and one in N1-1. There is a significant dearth of early-type stars in the outer regions (see Sections 4.2 and 5). The most distant star from Sgr A* we detect is at a projected distance of 166, and it is also the only early-type star in the eastern fields. Its magnitude indicates that it is a B star, and it has a radial velocity opposite to what one would expect from a member of the clockwise young stellar disk.

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Other publications, most notably Bartko et al. (2010) and Do et al. (2013a), have also measured projected surface-density profiles for the Galactic center. Using the data from these publications, we again plot late-type and early-type density profiles in Figures 9 and 10.

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The late-type surface density can be seen in Figure 9 and is consistent with what we expect from previous surveys. This work finds evidence for a broken power-law late-type surface density profile, which is in agreement with the findings of Buchholz et al. (2009) and Do et al. (2013a). To fit the broken power law, we use the Bayesian parameter estimation method that does not require binning the data, introduced in Do et al. (2013b), and the following profile:

$$\begin{eqnarray}&&{\rho }_{\star }(R)=A{(\displaystyle \frac{R}{{R}_{{\rm{b}}}})}^{-\gamma }{(1+{(R/{R}_{{\rm{b}}})}^{\delta })}^{(\gamma -\alpha )/\delta }\end{eqnarray} \tag{ 1 }$$

where γ is the inner power-law slope, α is the outer slope, R is the projected radius from Sgr A*, R_b is the break radius, A is a normalization factor, and δ is the sharpness of the transition between the two slopes. We use the data from this publication and in Do et al. (2013a) to find the best fit, which has a break radius of ${10}^{\prime\prime }\pm {5}^{\prime\prime }$ and slopes $\gamma =-0.013\pm 0.170$ and $\alpha =1.15\pm 0.52$. The normalization factor is 3.27 ± 0.47 stars arcsec⁻², and δ is 5.44 ± 3.45. The fitted line is shown in cyan in Figure 9.

The early-type projected surface density can be seen in Figure 10. The data from this paper have been divided into two bins, one for the northern regions (at 96) and one for the eastern regions (at 180). It is compared first to the spectroscopic data from Do et al. (2013a) and Bartko et al. (2010), and second to the photometric data from Buchholz et al. (2009). There is a clear drop-off in stellar density below that predicted by the single power law from Do et al. (2013a) outside 13'', a drop-off that is observed in our data, the data from Bartko et al. (2010), and the photometric data from Buchholz et al. (2009). The data from Buchholz et al. (2009), despite being non-spectroscopic and prone to false detections, also seem to match the overall trend of the spectroscopic observations well. From Do et al. (2013a) we expect the early-type stars to follow a best-fit power law of ${\rm{\Gamma }}=0.90\pm 0.09$, which corresponds to an expected 9.1 young stars outside 12'' in our data. Only a single young star is detected in the region, with completeness correction adding 0.16 (or at most one) more. There is also a single non-classified star in the region, which could not be classified due to proximity to a brighter source. In contrast to sources with low-S/N spectra, it is no more likely to be early-type than any other star (see Appendix B ). Even so, if we assume that this star is actually early-type or that we missed one for a total of two early-type stars in the region, we observe at least seven less early-type stars than expected, which corresponds to a Poisson probability of 0.57% and a $2.5\sigma$ deficit. If we make the assumption that we detected all the young stars, our result corresponds to a 0.11% Poisson probability and a $3\sigma$ deficit. We conclude, based on the large area sampled, that there is a significant lack of young stars farther than 13'' away from Sgr A*, possibly indicating an edge in the young stellar cluster somewhere between 12'' and 14'' (∼0.50 pc). The last data point in the projected surface-density profile of young stars from Bartko et al. (2010) strengthens this conclusion. It also indicates that the edge has some azimuthal symmetry, as the Bartko data outside 12'' are mostly situated north of Sgr A* (compared to our fields situated east of Sgr A*), and both follow the general trend of Buchholz et al. (2009).

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The surface density in the northern fields—the data point at 96—is lower than the data from Bartko et al. (2010) and Do et al. (2013a). When comparing to overlapping regions from Bartko et al. (2010), we note that the low number of early-type stars in the northern fields is consistent for the overlapping sections. The northern fields only have half the area of the eastern fields, leading to a low statistical significance, and the results are consistent to within $1\sigma$ when compared to Do et al. (2013a).

Previous publications have shown that the observed density profile of the Galactic center young stellar cluster is consistent with a single power law inside 12'' (Paumard et al. 2006; Do et al. 2009, 2013a; Lu et al. 2009; Bartko et al. 2010; Yelda et al. 2014). Our observations demonstrate that extending this power law to larger radii overpredicts the number of young stars with a significance of at least $2.5\sigma$. We thus conclude that there is a drop in the surface density of the young stellar cluster, possibly indicating an outer edge to the young stellar cluster in the Galactic center, at ∼13'' (0.52 pc). This strengthens the validity of the results from Buchholz et al. (2009). The spectroscopic nature of our observations removes the bias from photometric surveys like that of Buchholz et al. (2009)—our result is thus more definite. The observed stellar density profile is consistent with a broken power law. N-body simulations have recently shown that relaxation times of disk stars can produce deviations from a single power law in times comparable to the estimated age of the disk (6 Myr; Šubr & Haas 2014), which makes such a broken power-law structure intriguing.

The detection of an outer edge to the young stellar cluster shows that the young stellar disk is unlikely to have been the result of an infalling high-density cluster core. Inward movement and subsequent tidal disruption of a cluster from a larger radius have previously been considered a possibility for the origin of the young stellar disk (Gerhard 2001). However, recent results have favored in situ formation in a massive accretion disk (Paumard et al. 2006; Lu et al. 2009; Bartko et al. 2010, among others). Our results add to the evidence against the infalling cluster hypothesis. Such a scenario would result in a shallow density profile, on the order of ${r}^{-0.75}$ (Berukoff & Hansen 2006). This comes with the caveat that mass segregation could cause the observed density profile for the massive O and B stars—the only stars that are bright enough to be detected with current instruments—to be steeper than the actual density profile for the cluster. However, the detection of an edge (or at least a significant decrease in the surface density) at around 12''–14'' is another strong argument for in situ star formation, as such an edge would simply mark the radius from Sgr A* at which stars could no longer form. An infalling cluster would leave a trail of stars, which we do not observe in this study.

It also follows that our results strengthen the hypothesis that the scale of the recent (4–6 Myr) star formation event in the Galactic center was within 0.5 pc of Sgr A* (Bartko et al. 2010). Recent publications have often more or less assumed a similar scale (Paumard et al. 2006; Šubr & Haas 2014); we provide evidence that this assumption is consistent with observed data.

Our results show an edge to the young stellar cluster in the eastern direction from Sgr A*, and combined with results from Bartko et al. (2010), they also imply a similar edge in the northern direction. It is currently unclear whether this cluster edge also represents the outer edge of the clockwise disk of young stars (Paumard et al. 2006; Bartko et al. 2009, 2010; Do et al. 2009, 2013a; Lu et al. 2009; Yelda et al. 2014). If the disk extends indefinitely with no warp, it is projected to lie on top of the regions we observed east of Sgr A*, i.e., our observations outside 13''. We do not detect any disk stars in this region, which strongly indicates that either (1) the disk has an outer edge closer to Sgr A* than 13'' or (2) the disk is warped. Several prior publications (Bartko et al. 2009; Kocsis & Tremaine 2011) have suggested such a warp of the disk, which could mean that our observations are off the disk plane. Regardless, a disk edge outside the cluster edge seems difficult to reconcile with observations and theory, particularly as results from Yelda et al. (2014) show a decreasing statistical significance of the disk with distance from Sgr A*. For now it seems likely that the young stellar disk—with or without warp—has an edge at ∼13'', or possibly closer to Sgr A*.

Here we explore the possibility that the truncation in the stellar disk may represent the radius of gravitational instability in the original gas disk, which would explain the observed edge to the young stellar disk and cluster. Star formation in a gaseous disk requires it to be gravitationally unstable in order to collapse. This instability will take place if the gas pressure and rotational support are less than the local self-gravity of the disk, and it is represented by the Toomre Q parameter (Toomre 1964):

$$\begin{eqnarray}&&Q=\displaystyle \frac{{v}_{\mathrm{Kep}}\sigma }{G\pi r{{\rm{\Sigma }}}_{\mathrm{gas}}},\end{eqnarray} \tag{ 2 }$$

where v_Kep is the local Keplerian velocity, σ is the velocity dispersion of the gas, r is the distance from the black hole, and ${{\rm{\Sigma }}}_{\mathrm{gas}}$ is the surface density of the gas. $Q\lt 1$ indicates that the gas is gravitationally unstable and will collapse. The disk is stable for $Q\gt 1$. Prior estimates of disk instabilities at the Galactic center disk have also used the Toomre Q parameter for analysis (e.g., Levin 2007; Nayakshin et al. 2007).

In order to estimate Q, we need to make a few assumptions about the original gas disk. We assume that the gas disk is in Keplerian orbit around the black hole, because the disk is well within its gravitational radius of influence. The gas velocity dispersion is unknown, but we can estimate it with two approaches: (1) using a fit to the observed velocity dispersion profile of young stars, or (2) using a velocity dispersion that is constant with disk radius. The first assumption yields ${\sigma }_{\mathrm{gas},r}(r)\propto 1/\sqrt{r}$ using data from Yelda et al. (2014), while the second assumption has ${\sigma }_{\mathrm{gas},k}(r)\;=\;$ constant. We assume that the gas disk surface density Σ follows the currently observed stellar surface-density profile ${{\rm{\Sigma }}}_{\mathrm{stars}}(r)\propto {r}^{-1.7}$ (Paumard et al. 2006; Lu et al. 2009; Bartko et al. 2010; Yelda et al. 2014). To obtain the absolute values of ${{\rm{\Sigma }}}_{\mathrm{gas}}$ requires knowledge of the star formation efficiency, as well as the current total disk mass. Because these parameters, especially the star formation efficiency, are poorly constrained, the absolute value of Q will also be highly uncertain. Here we take instead the approach of calculating the radial dependence of Q to determine whether the edge represents an increasing Q value with radius. For ${\sigma }_{\mathrm{gas},r}$ the radial dependence of Q is

$$\begin{eqnarray}&&Q(r)\propto \displaystyle \frac{{r}^{-0.5}{r}^{-0.5}}{{{rr}}^{-1.7}}\propto {r}^{-0.3},\end{eqnarray} \tag{ 3 }$$

while for a constant ${\sigma }_{\mathrm{gas},k}$

$$\begin{eqnarray}&&Q(r)\propto \displaystyle \frac{{r}^{-0.5}}{{{rr}}^{-1.7}}\propto {r}^{0.2}.\end{eqnarray} \tag{ 4 }$$

The two assumptions about ${\sigma }_{\mathrm{gas}}$ lead to different interpretations of the disk instability. For a radially dependent ${\sigma }_{\mathrm{gas}}$, Q decreases with radius, which would suggest that the disk instability criteria cannot explain the outer disk edge. For a constant ${\sigma }_{\mathrm{gas}}$, the interpretation would be the reverse. With Q increasing slightly with radius, this would be consistent with the disk having an outer edge because it is stable to gravitational collapse beyond a certain radius.

Our simple analysis of the disk instability criterion above shows that given the lack of knowledge of the initial conditions of the gas, it is inconclusive whether disk instability should lead to an observed edge to the currently observed stellar disk. The main emphasis of this section is to illuminate the need for more research on the initial conditions of the gas disk. Our calculations have large uncertainties, but with more precise initial parameters a similar procedure could lead to meaningful conclusions on both the history and the current state of the young stellar cluster.

Simulations of cloud–cloud collisions, such as those by Hobbs & Nayakshin (2009), show star formation that is qualitatively consistent with our results. These simulations result in an inner stellar disk of young stars along with streams of stars outside the plane of the disk. While the region where stars formed in Hobbs & Nayakshin (2009) is consistent with our present observations, the authors do not explore the different physical parameters of the initial clouds that would affect the size of the resulting cluster. More theoretical work is needed to constrain the radial range where cloud conditions were sufficient to form stars. Our observation of a scale radius of ∼0.5 pc may help constrain the radius at which the cloud–cloud collision occurred. In addition, this scale may provide tests for physical mechanisms that limit star formation in this region, such as feedback both from star formation and from accretion onto the supermassive black hole.