The Post-periapsis Evolution of Galactic Center Source G1: The Second Case of a Resolved Tidal Interaction with a Supermassive Black Hole

Our imaging analysis is divided into two parts: (i) astrometric analysis using the PSF fitting tool StarFinder and (ii) photometric and size calculations using a PSF convolved with a 2D elliptical Gaussian. Both measurements are described in detail below.

3.1.1. Astrometry

G1 is visually identified in every L' and Ms image (see Figure 1). Its astrometric properties in every image were obtained using the PSF fitting program StarFinder (Diolaiti et al. 2000) in a manner similar to what has been outlined in previous works (Yelda et al. 2014 and references therein). We initially ran StarFinder using a correlation threshold of 0.8 and 0.6 in the main image and subimages, respectively, to identify candidate sources in our images. This resulted in G1 detections in 2004, 2005, 2006, 2012, and 2013 in the L' data. In 2003, 2009, and all 2014 L' epochs and both the Ms data sets, a different approach was necessary to capture G1 due to poorer data quality, although G1 can be visually identified (Figure 1). We therefore altered the search criteria to seek a point source within a 3 pixel box centered at the point of the highest flux count, at the approximate position of G1 using a modified version of StarFinder that searches for additional sources at a lower correlation (Boehle et al. 2016). We did not use the 2016 L' data for astrometry, as we used the orbital model from 2003–2014 to predict the position of G1 in the 2016 data (see our photometric analysis, described in Section 3.1.2). With this modified procedure, G1 was detected in all epochs.

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While G1 is extended in the early epochs (Section 4.2), we still use the StarFinder astrometry that reliably determines G1's centroid, as the residuals in each epoch look symmetric. Two-dimensional Gaussian fits convolved with a point-spread function to G1 yielded peak positions consistent with the positions extracted from StarFinder.

The point sources identified in each epoch are matched across all epochs and transformed to a common coordinate system in which Sgr A* is at rest (see Yelda et al. 2010; Phifer et al. 2013; Yelda et al. 2014; for the application of our distortion solution to L'-band data, see Appendix A). Specifically, each L' list of stellar positions, or star list, is aligned to the K' star list that is nearest in time with the translation, rotation, and affine first-order transformation that is independent in x and y. The transformed G1 position is added to the K' star list, and the K' star lists from 1995 to 2014 are aligned as described in our earlier works (e.g., Ghez et al. 2008; Yelda et al. 2014) using measurements of infrared astrometric secondary standards taken through 2012 (Yelda et al. 2010, 2014; Boehle et al. 2016). Table 2 lists the astrometry for G1 in each epoch prior to 2016.

Table 2.  Data and Observed Properties of G1

Date	ΔR.A.a	ΔDecl.a	K'	L'	Ms	L' Semimajor Axis	PA of Gaussian
	(arcsec)	(arcsec)	(mag)	(mag)	(mag)	Intrinsic Size (au)	2D fit (deg)
2003.44	−0.077 ± 0.009	−0.059 ± 0.009	⋯	13.60 ± 0.54	⋯	⋯	⋯
2004.57	−0.073 ± 0.009	−0.068 ± 0.008	⋯	13.51 ± 0.23	⋯	460 ± 30	10.4 ± 4.0
2005.58	−0.069 ± 0.007	−0.860 ± 0.006	⋯	13.64 ± 0.05	12.71 ± 0.30	270 ± 30	27.4 ± 2.4
2006.39	−0.065 ± 0.006	−0.103 ± 0.006	⋯	13.87 ± 0.12	⋯	160 ± 50	16.0 ± 9.8
2009.56	−0.035 ± 0.006	−0.131 ± 0.010	⋯	14.38 ± 0.66	⋯	<170
2012.56	−0.029 ± 0.006	−0.162 ± 0.007	⋯	15.21 ± 0.12	⋯	<160
2013.55	−0.012 ± 0.006	−0.169 ± 0.006	>18.8	15.22 ± 0.19	⋯	<180
2014.22	0.002 ± 0.006	−0.183 ± 0.009	⋯	15.51 ± 0.15	⋯	<170
2014.36	0.003 ± 0.006	−0.196 ± 0.006	⋯	15.27 ± 0.21	⋯	⋯	⋯
2014.50	0.003 ± 0.006	−0.193 ± 0.007	⋯	15.53 ± 0.23	⋯	⋯	⋯
2014.59	0.006 ± 0.006	−0.185 ± 0.007	⋯	15.32 ± 0.19	⋯	⋯	⋯
2016.38	0.017 ± 0.004b	−0.202 ± 0.004b	>18.2c	15.50 ± 0.36c	14.81 ± 0.23c	⋯	⋯

Notes.

^aΔR.A. and ΔDecl. are given in a reference frame in which the location of the black hole is not at the origin (see Table 4). ^bThese positions come from our orbital solution derived from our L' data taken from 2003 through 2014. See Section 3.3 for more information on our orbital fit. ^cThe photometry in 2016 was derived using deconvolved images rather than StarFinder, as was done in previous epochs. See Section 3.1.2 for more information.

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3.1.2. Photometry and Size Measurement

The magnitudes of all point sources at K' were calculated using PSF fitting with the StarFinder procedure (see previous section). We chose IRS 16C, IRS 16NW, and IRS 16CC as our photometric calibrators; this is part of our standard K' calibration procedure (e.g., Yelda et al. 2014).

As G1 seems extended in 2004, 2005, and 2006 at L' and in the 2005 Ms data, we tested several photometric methods to obtain reliable photometry. To confirm whether the individual methods yielded reliable results during the epochs when G1 was visibly extended, we planted a 2D elliptical Gaussian model for the 2004 size (a Gaussian with a FWHM of ∼58 mas convolved with the PSF) in our data in three distinct regions: a high-background region, a low-background region, and near the position of G1. We planted sources with different brightnesses (mag_L' = 10–16) to determine whether we could recover its magnitude and physical extent.

We tested three different photometric procedures: (1) StarFinder with a PSF support array of 20 (200 pixels), following our standard K' analysis; (2) StarFinder with a PSF support array of 09 (90 pixels) to make the PSF more robust against background artifacts at larger distances from the core; and (3) a 2D fit with an intrinsic extended elliptical Gaussian source convolved with an empirical PSF model. The planting simulations returned significantly decreased fluxes with respect to their original planted magnitude in the case of StarFinder PSF fitting with both PSF sizes (methods 1 and 2). However, method 3 reliably recovered the fluxes and observed extent of the planted sources to within 20% at the faintest magnitude tested (${\mathrm{mag}}_{{{\rm{L}}}^{{\prime} }}$ = 16).

We applied method 3 to every single L' and Ms epoch (prior to 2016) using the IDL procedure mpfit2dfun. To prepare the images for model fitting, we first subtracted all L'-detected StarFinder sources. We then used the aligned L' and K' StarFinder star lists to find the position of K'-only detected sources and used the forced StarFinder algorithm from Boehle et al. (2016) to find the fluxes of these sources at L'. We subtracted these sources, as well as the StarFinder-generated backgrounds, from the original image. In our 2D elliptical Gaussian model, we allowed the position angle to vary and allowed for the FWHM to range between 0.3 and 10.0 pixels. If the FWHM of G1 fell below 0.3 pixels (∼3 mas) in an epoch, then a PSF without a Gaussian component was used instead. Our photometry is reported in Table 2. A comparison of the astrometry between the three methods yielded identical positions of G1 within 1σ errors.

To photometrically calibrate our L' and Ms data, we used S0-2, S0-12, S1-20, and S1-1 and their L' magnitudes from Schödel et al. (2010). These sources were chosen because they are all in the field of view for every epoch, including our subarrayed epochs (see Table 1). Similarly to Schödel et al. (2011), the Ms data were calibrated using the same magnitudes as L' because the relative colors of the calibrators are close to zero. The overall zero-point error from the Schödel et al. (2010) magnitudes is 0.15 mag at L' and is not taken into account in Table 2 or Figure 2 because it affects all photometric measurements in the same way.

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No K' counterpart was detected for G1, and star-planting simulations were performed to determine an upper magnitude limit. We used the L' position of G1 in the 2013 August image, where G1 is an isolated point source (see Figure 1) and transformed that into the 2013 July K' coordinate system. The star-planting simulations were carried out using our modified version of StarFinder (Phifer et al. 2013; Boehle et al. 2016). There is a K' source near G1 in 2013, S0-37, but it contributes at most 0.3 mJy to the overall L' flux of G1 (assuming the dereddening law outlined in Schödel et al. 2010 and that S0-37 has the same colors as S0-2). All photometry in each bandpass is reported in Table 2.

The recovered sizes of G1 from our model show that G1 is extended between 2004 and 2006 but is consistent with a point source from 2009 through 2014 (see Table 2). The magnitudes and sizes of G1 as a function of time are shown in Figures 2 and 3, respectively, while Figure 4 shows the elongation of G1 in the direction of orbital motion in 2004. The major axis angle of the 2D elliptical Gaussian is consistent with a tangential line to the orbit in 2004 and 2005 (10.4 ± 40 (tangent to orbit = 12.3 ± 2.8°) and 27.4 ± 4.8° (tangent to orbit = 21.0 ± 2.4°) west of north, respectively; see Figure 4).

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In order to be able to infer the blackbody properties of G1 in a later epoch when the source is compact, we utilize L' and Ms data from 2016. As G1 is in a confused region in this epoch, we adopt a different methodology to recover its K' upper limit and L' and Ms flux densities. The StarFinder-generated backgrounds are subtracted from each main map, and we subtract all StarFinder-identified point sources in the vicinity of our predicted position for G1. We then use the StarFinder-generated PSF to do an iterative Lucy–Richardson deconvolution (with 10,000 iterations). Aperture photometry is then performed after beam restoring at the predicted position of G1 based on its derived orbit from the 2003–2014 data. The photometry of the 2016 L' data matches well with the 2014 epochs.

The radial velocity for G1 was obtained using a similar approach to that developed by Phifer et al. (2013) for G2: a spectrum of G1 was extracted from our 2006 OSIRIS data at a location that was determined by transforming the high-quality 2005 L' star list to the OSIRIS coordinate system using a second-order polynomial transformation. The spectrum was extracted using an aperture radius of 1 pixel (corresponding to 35 mas) and applying a local sky subtraction in an area clear of known contaminating stars (e.g., Do et al. 2013). The extracted spectrum was calibrated using the standard techniques (Do et al. 2009b), and the peak in the resulting spectrum was fit with a Gaussian model to derive an observed radial velocity and its FWHM. The resulting heliocentric radial velocity was corrected by 3.64 km s⁻¹ to correspond to an local standard of rest (LSR) velocity of −1568 ± 60 km s⁻¹ on the date of the observation (see Table 3). The FWHM of the spectral line is 185 ± 41 km s⁻¹. The spectrum and the corresponding point source in the line emission map are shown in Figure 5.

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We compute the Brγ line luminosity similarly to Phifer et al. (2013) by comparing S0-2's flux density to G1's flux density. We estimate S0-2's dereddened flux density to be 14.1 ± 0.2 mJy (assuming the extinction prescription outlined in Schödel et al. 2010 and the flux density from Ghez et al. 2008) and compute an expected luminosity of S0-2 over the 2.15–2.159 μm bandpass to be 0.16 L_⊙. We then integrate over the same bandpass on the S0-2 and G1 spectra to get a final Brγ luminosity of G1 of (1.48 ± 0.17) × 10⁻³ L_⊙. To check for consistency, we followed this same procedure to integrate over the same bandwidth for G2 (2.17–2.179 μm), which yields a Brγ luminosity of (1.36 ± 0.25) × 10⁻³ L_⊙, consistent within 1σ with the 2006 G2 luminosity reported in Phifer et al. (2013).

Using this dereddened Brγ line luminosity from 2006 (in an epoch where G1 is resolved), we can estimate the Lyα emission luminosity. We used the relationship between the Brγ emission and the free–free emission given in Wynn-Williams et al. (1978) and solved for the Lyα luminosity using the formulae summarized in Genzel et al. (1982) and Becklin et al. (1994). We estimate that the Lyα luminosity is ∼2 L_⊙.

To derive the orbital properties of G1, we jointly fit for the Keplerian orbital parameters of S0-2, S0-38, and G1 (period, epoch of periapsis passage, eccentricity, position angle of the ascending node, argument of periapsis and inclination for each source) and the black hole parameters (the 2D position, the 3D velocity, and the mass of and distance to Sgr A*; see Table 4). S0-2 and S0-38 have complete orbital phase coverage and drive the black hole parameter fit. We use the same astrometry and radial velocities of S0-2 and S0-38 as reported in Boehle et al. (2016). Jointly fitting the three sources enables us to find an orbital solution for G1 and the black hole parameters. G1 alone does not have enough kinematic information to independently fit for the black hole parameters due to the lack of orbital phase coverage. We impose uniform, flat priors on each of the orbital parameters for G1 as follows: [0°, 360°] for the argument of periapsis (ω), [0°, 180°] for the position angle of the ascending node (Ω), [0°, 180°] for the inclination, [0, 1] for the eccentricity, [0, 6000] yr for the period, and [1990, 2010] for the time of periapsis passage. The G1 astrometry consists of 11 data points (see Section 3.1), including our newest astrometric measurements. For this orbital fit, we also used the three radial velocity measurements reported in Pfuhl et al. (2015) and our new measurement (Section 3.2; Table 3).

Table 4.  S0-2 and S0-38 Black Hole Parameter Values

Orbital Parameter	Peak Fita
X-position of Sgr A* (x0, mas)	${2.1}_{-0.3}^{+0.5}$± 1.90
Y-position of Sgr A* (y0, mas)	−4.4 ± 0.4 ± 1.23
ΔR.A. velocity of Sgr A* (Vx, mas yr−1)	−0.12${}_{-0.02}^{+0.03}$ ± 0.13
ΔDecl. velocity of Sgr A* (Vy, mas yr−1)	0.68 ± 0.05 ± 0.22
Radial velocity of Sgr A*(Vz, km s−1)	−20.4 ± 6.3 ± 4.28
Distance to Sgr A* (R0, kpc)	7.87 ± 0.11
Mass of Sgr A* (M, millions of M⊙)	${3.93}_{-0.13}^{+0.07}$
S0-2 Parameters
Time of closest approach (T0, yr)	2002.346 ± 0.003
Eccentricity (e)	${0.892}_{-0.001}^{+0.002}$
Period (P, yr)	${15.93}_{-0.05}^{+0.02}$
Angle to periapsis (ω, deg)	${66.8}_{-0.5}^{+0.3}$
Inclination (i, deg)	134.3 ± 0.3
Position angle of the ascending node (Ω, deg)	${228.0}_{-0.5}^{+0.4}$
S0-38 Parameters
Time of closest approach (T0, yr)	${2003.191}_{-0.017}^{+0.038}$
Eccentricity (e)	0.811 ± 0.003
Period (P, yr)	${19.22}_{-0.2}^{+0.1}$
Angle to periapsis (ω, deg)	${13}_{-21}^{+15}$
Inclination(i, deg)	169 ± 2
Position angle of the ascending node (Ω, deg)	${94}_{-14}^{+18}$

Note.

^aThe peak and corresponding 1σ errors are from the marginalized 1D distributions for the respective parameters. The first error term corresponds to the error determined by the orbital fit itself, while the second error term on the black hole parameters refers to uncertainty in the reference frame and was determined by Boehle et al. (2016).

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In this study, we include three sources of hypothetical systematics uncertainties: (i) source confusion, (ii) the presence of outliers, and (iii) uncertainty arising in the construction of the absolute reference frame.

Source confusion is a significant source of systematic error in our orbital fits, and the formal uncertainties are therefore underestimated. In order to account for this, we fit a second-order polynomial to our astrometric data points and add a single additive value in quadrature to the formal errors until the final reduced χ² of the second-order fit (that includes position, velocity, and acceleration) is equal to 1.0. The resulting additive value is 5.5 mas, which is roughly comparable to the formal uncertainties.

In order to assess the impact of hypothetical outliers, we use a jackknife resampling method, where we fit for G1's orbital parameters by dropping one epoch of observations at a time. This analysis, presented in Appendix B, shows results that are consistent with those reported in Table 4, and we conclude that no outlier significantly impacts our results.

Following the procedure described in the Appendix of Boehle et al. (2016), the systematic uncertainties due to the construction of the absolute reference frame have been assessed by using a jackknife resampling method. In this jackknife analysis, one of the seven masers used to construct the reference frame is dropped at a time. Boehle et al. (2016) showed that this systematic uncertainty is important for the SMBH position and velocity relative to the origin of the constructed reference frame but is negligible for all other fitted parameters, such as the SMBH mass and distance R₀ and the orbital parameters. We conclude that systematic effects arising from the construction of our absolute reference frame do not significantly impact the posterior probability distribution for stellar orbital parameters.

The orbit of G1 is consistent with Keplerian motion (see Figures 7 and 8). Based on our precise astrometry and radial velocity points, G1 lies on a highly eccentric orbit (e = ${0.99}_{-0.01}^{+0.001}$) and has recently passed through periapsis (T₀ = 2001.3 ± 0.4). The three orbital angles (position angle of the ascending node ${\rm{\Omega }}={87.1}_{-4.9}^{+5.0}$, argument of periapsis $\omega ={117.3}_{-2.9}^{+2.8}$, and inclination $i={109.0}_{-0.8}^{+0.9}$) are well constrained, but the orbital period is very poorly constrained due to a lack of orbital phase coverage. The 1D and 2D joint posterior distribution functions are shown in Figures 9 and 10. The best-fit orbit is shown in Figure 8, and the peak of the 1D marginalized probability distribution functions along with the maximum likelihood best fit are presented in Table 5. We only fit bound, closed orbits; G1 could be on a hyperbolic orbit, since the eccentricity distribution is artificially truncated. The period restriction of P < 6000 yr also constrains our orbital fits.

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Table 5.  Orbital Parameters for G1 and G2

Parameter	Best Fit, G1	Peak, G1a	Best Fit, G2b	Peak, G2b	G1 Fit
					Pfuhl et al. (2015)
Time of closest approach (T0, yr)	2001.0	${2001.3}_{-0.2}^{+0.4}$	2014.1	${2014.2}_{-0.05}^{+0.03}$	2001.6 ± 0.1
Eccentricity (e)	0.981	${0.992}_{-0.01}^{+0.002}$	0.962	${0.964}_{-0.073}^{+0.036}$	0.860 ± 0.050
Periapsis distance (Amin, au)	277	${298}_{-24}^{+32}$	193	201 ± 13	417 ± 239
Argument of periapsis (ω, deg)	118	117 ± 3	95	96 ± 2	109 ± 8
Inclination (i, deg)	109	109 ± 1	112	113 ± 2	108 ± 2
Position angle of the ascending node (Ω, deg)	89	${88}_{-4}^{+5}$	83	82 ± 2	69 ± 5

Notes.

^aThe errors reported here are the 1σ errors taken from the marginalized 1D distributions for the respective parameters. ^bG2 parameters are from performing an orbital fit on our available astrometric and spectroscopic points (those outlined in Meyer et al. 2014) in the fashion described in Section 3.3.

The clockwise disk parameters are i = 130° ± 15° and Ω = 96° ± 15°, where 15° reflects the half width at half maximum (HWHM) from the peak density of the clockwise disk, as reported in Yelda et al. (2014).

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Figure 6 shows our orbital plots, extracted G1 astrometry, and radial velocity measurements. Figure 8 presents our projection of the orbit onto the sky and compares it to the orbital solution from Pfuhl et al. (2015) while assuming the black hole parameters from Gillessen et al. (2009). The left panel of Figure 8 clearly shows that our optimal G1 solution is significantly different from the previously published solution of Pfuhl et al. (2015). As a consequence, the best-fit G1 orbit is no longer in agreement with G2's optimal solution (right panel of Figure 8; G2's orbit is thoroughly discussed in Gillessen et al. 2012, 2013b, Phifer et al. 2013, and Meyer et al. 2014). This can be understood because our data cover almost twice the time baseline presented in Pfuhl et al. (2015).

In the epochs closest to periapsis G1 is extended along the direction of orbital motion (the semimajor axis). Figure 3 shows the intrinsic extent of G1 corrected for the size of the PSF along both the semimajor and semiminor axes. The source shape is approximately elliptic, and the semimajor axis of an elliptical 2D Gaussian fit is aligned with the direction of linear motion (Figure 4). However, in the more recent epochs, G1 becomes more compact. Additionally, there is significant brightness variation of G1 at L' post-periapsis passage, which corresponds to its size evolution: when G1 is at its largest size, it is also brightest; when G1 is compact, it is ∼2 mag dimmer. The arrows in Figure 3 show the intrinsic (PSF-size-corrected) upper limits on the source size along the semimajor and semiminor axes, which is, on average, ∼170 au along the semimajor axis assuming R₀ = 8 kpc.

Figure 7 shows images of G1 with all of the neighboring point sources identified by StarFinder subtracted. The contours illustrate the size development of G1. The FWHM of the semimajor axis of G1 is as high as 463 ± 16 au in 2004.567 after correcting for the PSF contribution (see Figure 3) but decreases to the size of a point source after 2006. Figure 11 shows azimuthally averaged radial profiles of G1 from 2009 through 2014, showing that the size of G1 is indeed consistent with a point source.

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Our 2006 Brγ detection is quite shallow, and we are unable to determine whether G1 is resolved at Brγ. Due to the shallowness of the Brγ detection, we are unable to conclude if G1 is spatially resolved or has a velocity gradient.

There is a large photometric difference (∼2 mag) between the epochs when G1 is extended (2004, 2005, and 2006) and when it is pointlike. The brightness develops with size, as epochs when G1 is extended are brightest and epochs when G1 is pointlike are dimmer and remain at a constant magnitude from 2012 through 2016.

G1 is identified at L' and Ms (L' = 13.65 in 2005; Ms = 12.71 in 2005) but not at K' (K' > 18.8 in 2013). Assuming zero-point fluxes for L' from Tokunaga (2000) and the extinction law outlined in Schödel et al. (2010), we infer a dereddened L' flux of 2.7 ± 0.5 mJy in 2005.

In order to infer a temperature for G1 at a moment in time (2005) when it is extended enough to be resolved, we expect it to be optically thin, and therefore we use a modified blackbody,

$$\begin{eqnarray}&&{I}_{\nu }\propto {Q}_{0}{\left(\displaystyle \frac{\nu }{{\nu }_{0}}\right)}^{\beta }{B}_{\nu }({T}_{\mathrm{dust}}),\end{eqnarray} \tag{ 1 }$$

where ν₀ is the frequency at which the temperature is calculated, ${Q}_{0}/{\nu }_{0}^{\beta }$ is a constant, and B_ν is the Planck function. We take the power-law index β equal to 2, as in Lau et al. (2013) and consistent with extinction curves from Draine (2003). We separately do the same calculation assuming β = 0 (blackbody). The temperature is therefore calculated following the equation

$$\begin{eqnarray}&&{{\rm{L}}}^{{\prime} }-\mathrm{Ms}=-2.5{\rm{log}}\,\left[{\left(\displaystyle \frac{{\nu }_{{{\rm{L}}}^{{\prime} }}}{{\nu }_{\mathrm{Ms}}}\right)}^{\beta }\displaystyle \frac{{B}_{{{\rm{L}}}^{{\prime} }}({T}_{\mathrm{dust}})}{{B}_{\mathrm{Ms}}({T}_{\mathrm{dust}})}\right].\end{eqnarray} \tag{ 2 }$$

From our L' and Ms measurements, we are able to obtain a dereddened color (L'–Ms) of 0.706. Fitting a modified blackbody following Equation (2) with β = 2, the color temperature we obtain from our 2005 data is equal to 568 ± 44 K; assuming a blackbody (β = 0), we obtain a 2005 temperature of 426 ± 44 K, where our error bars are computed via a Monte Carlo simulation.

Using our L' and Ms photometric data in 2016 when G1 is observed to be pointlike and assuming that G1 behaves as a blackbody in this epoch (β = 0), we infer a blackbody temperature of 684 ± 75 K (where our error bars are again computed via a Monte Carlo simulation). Therefore, our inferred blackbody temperature has increased from 2005 to 2016.

Pfuhl et al. (2015) recently proposed that G1 and G2 are not only lying in the same orbital plane but follow the same trajectory. They speculate that the Keplerian orbits of G1 and G2 are closely related, and they postulate that the small deviations between the orbits of the two objects are due to the drag force from the ambient Galactic center medium. This additional drag force leads to an evolution of G2's orbit into G1's orbit over time. Similarly, McCourt & Madigan (2016) and Madigan et al. (2017) used G1 and G2 as probes to constrain the properties of the accretion flow surrounding Sgr A*. They modeled the orbital differences (as found by Pfuhl et al. 2015) between G1 and G2 in terms of an interaction with the background flow (McCourt & Madigan 2016) and in the accretion flow onto Sgr A* (Madigan et al. 2017). Based on their orbital analysis, they concluded that both sources could have originated from the clockwise young stellar disk (Paumard et al. 2006; Lu et al. 2009; Yelda et al. 2014).

However, the study we present here, which includes data taken several years beyond the last data point used in Pfuhl et al. (2015) (2014.6 versus 2010.5; true anomalies of 10.5° and 87, respectively), shows that despite the common orbital plane, G1 and G2 have distinct Keplerian orbits with a significant (>3σ) difference in their arguments of periapsis ∼3 times larger than the difference reported in Pfuhl et al. (2015). This is demonstrated in Figure 7 showing both the data and the best-fit orbits projected into the plane of the sky, as well as both best-fit orbits projected into the average orbital plane.

Our findings do not firmly exclude the models proposed by McCourt & Madigan (2016) and Madigan et al. (2017). However, while both models might be able to accommodate such a large change of the Keplerian orbit in the case of a compact gas cloud, the drag force scenario and a resulting common trajectory of G1 and G2 become increasingly unlikely in the context of a central star and thus larger object masses, as indicated by the compactness and brightness of both sources. The masses derived in the following sections and in Witzel et al. (2014) are 10⁵–10⁶ times larger than the originally proposed 3 Earth masses. The interpretation in Pfuhl et al. (2015) that G1 and G2 are two dense regions within the same extended gas streamer that fills one trajectory around the black hole and have an identical origin but are offset by ∼13 yr therefore seems unlikely.

The orbital planes of G1 and G2 are very similar, and they are fairly close to the plane defined by the clockwise disk (Yelda et al. 2014, and see Figure 10 of Pfuhl et al. 2015). G1 and G2 may have therefore originated the clockwise disk. We note, however, that there are other G2-like sources that do not lie on their common orbital plane (Sitarski et al. 2015).

Independent of whether G1 and G2 are related by a gas streamer, their physical natures are still not yet known. Recent results (e.g., Witzel et al. 2014; Valencia-S. et al. 2015, in contrast to Pfuhl et al. 2015) support the hypothesis that G2 has a stellar component due to its periapsis passage survival. This raises the question of whether there is similar evidence that G1 is stellar in nature.

In contrast to observations that G2 is unresolved at L', for G1 we are able to measure its size in 2005, and we can therefore put constraints on the optical depth, τ, of the dust envelope at this point in time. Based on several parameters calculated in Section 4.3 (T_β=2 = 568 K, T_β=0 = 426 K, r_G1,2005 = 137 au), we find that the optical depth of G1 is small in the epochs when it is resolved, and we can therefore conclude that the origin of the extended continuum emission is an optically thin medium in 2005. As calculated in Section 3.2, the ambient radiation field in the Galactic center is strong enough (with Lyα alone) to externally heat this optically thin shell. The profile of G1 in the epochs where it is extended is well constrained by a PSF convolved with a 2D Gaussian (see Section 3.1.2) and shows no evidence of two components (as could be modeled by a PSF + a 2D Gaussian). This indicates that we do not see a central, optically thick point source in 2005.

From 2009 onward, G1 is unresolved at L' and shows a significantly lower, roughly constant flux density of ∼0.6 mJy. Blackbody modeling of G1's L'–Ms color yields a temperature of 684 K, implying a blackbody radius of ∼1 au and a luminosity of ∼4.5 L_☉. This high luminosity and the fact that the object becomes more compact with time point to a substantially larger mass than 3 Earth masses. As indicated by the evolutionary tracks of main-sequence stars, this mass can be of the order of 1 M_⊙ (Figure 12). However, the large derived blackbody size for the unresolved G1 shows that it is not a main-sequence star, nor is G1 luminous enough to be a red giant.

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The material at the enormous radial distance from the center of G1 of r ∼ 230 au of the outer halo seen in the extended epochs certainly remains unbound from G1 for even much higher G1 masses than 1 M_⊙; in fact, this holds true for a central mass that is two orders of magnitude higher due to the weak M^1/3 dependence of the tidal radius. (Figure 13 shows the tidal radius (black lines) of a 2 M_⊙ source (solid line) and a 100 M_⊙ source (dashed line; see Witzel et al. 2014) plotted with the measured HWHMs of G1^*.) Therefore, this material is stripped, and its emission falls below the detection limit as its density decreases or grains are destroyed by X-rays and high-energy particles generated in the accretion flow (e.g., Lau et al. 2015 and references therein; Tielens et al. 1994). It is interesting to note that the minimal radius of material that remains bound throughout periapsis for a G1 mass of 1 M_⊙ and a periapsis passage distance of ∼300 au is 1 au (see Figure 14, which plots the tidal radius as a function of time since periapsis passage for G1 and G2). This corresponds nicely to the derived blackbody radius in 2016.

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The question remains how G1 has reached the enormous extent of d = 460 au in 2004. This likely requires that G1 was already large at periapsis passage. From an energy argument, we can determine the size of G1 at periapsis passage from the maximum shearing velocity, v_sh, of the object in the potential of the black hole according to the equation

$$\begin{eqnarray}&&{v}_{\mathrm{sh}}^{2}={\left(\displaystyle \frac{{r}_{\mathrm{obs}}-{r}_{\mathrm{per}}}{{\rm{\Delta }}t}\right)}^{2}\\ &&\quad =\,{\left[\sqrt{{v}_{* }^{2}-2{{GM}}_{\mathrm{BH}}\left[\displaystyle \frac{1}{{d}_{* }}-\displaystyle \frac{1}{{d}_{* }-{r}_{\mathrm{per}}}\right]}-{v}_{* }\right]}^{2}-\displaystyle \frac{2{Gm}}{{r}_{\mathrm{per}}},\end{eqnarray} \tag{ 3 }$$

where r_obs is the observed size in 2004; r_per is the half width along the Sgr A*-G1 line; v_* is the velocity of G1 at periapsis passage; m is the mass of G1; M_BH is the mass of the SMBH from Table 5; Δt is the difference between our observation date (2004.6) and periapsis passage time, the first epoch where we see a resolved G1; and d_* is the distance from the center of G1 to Sgr A*. Simultaneously solving for m and r_per, we find that r_per is larger than 21 au at the time of closest approach and that the solution is not strongly mass dependent.

Therefore, for G1 to have its measured size be so large in 2004, r_per must be ≥21.3 au at periapsis passage, and G1 was likely a large object even before it started interacting with the SMBH. If G1 began with a radius of 4, 3, or 2 au, it would have started interacting tidally with the SMBH 1.3, 0.9, or 0.4 yr before periapsis passage, respectively, giving it plenty of time to grow to be the large source we infer for periapsis passage.

While it is possible that G1 appears extended at L' because of confusion with background sources, we judge this to be unlikely. We have traced the orbits of all known stars close to G1 and Sgr A*, and G1 is certainly not confused with a bright (mag_L' < 16) source. But it is not fully excluded that, during the early epochs, there could be several dim stars whose images are overlapping that of nearby G1 for multiple epochs before separating and moving below the detection limit again. However, the symmetry in the extended residual after subtracting a point source makes this seem rather unlikely.

Our suggested model for G1's dust shell is as follows. G1 started tidally interacting with the SMBH with a rather large size several years prior to periapsis passage. The tidal radius penetrated deep into the dust shell (r ∼ 1 au), and the outer part of the optically thick shell became unbound from the source. This unbound shell became optically thin and externally heated by the surrounding radiation field in the Galactic center, which is what we observe starting in 2004. Over time, the tidally stripped dust expanded away and fell below the detection limit against the local background emission, and, by 2009, we see the optically thick surface of a massive, internally heated object as a point source that is 2 mag fainter than what is observed in 2004. Throughout all epochs, the source is also surrounded by an externally heated gas envelope that we observe as Brγ emission. As we discuss in Section 5.5, a possible physical explanation for G1's large size is that it could be an example of a black-hole-driven binary merger product (Phifer et al. 2013; Witzel et al. 2014; Prodan et al. 2015).

Several predictions have been made for the post-periapsis development of G2 in the case of a pure gas cloud. G1 and G2 have similar periapsis passage distances and blackbody sizes (as inferred in Section 4.3 for G1), and we expect them to tidally interact with the black hole in a comparable manner. Thus, in the following, we compare G1's post-periapsis observables to some of these predictions for G2.

Various models for G2 predict that if it were a pure gas cloud, it should undergo tidal shearing within 1 to 7 yr after periapsis. The Brγ flux of G2 was predicted to rapidly decrease over time (Anninos et al. 2012; Morsony et al. 2015), due to both the breakup of G2 and the heating of its gas. Observationally, the latest Brγ line detection of G1 occurred in 2008, 7 yr after periapsis passage (Pfuhl et al. 2015),⁷ not showing any indication of a strong decay or complete depletion. In fact, the post-periapsis luminosity of G1 is consistent with the pre-periapsis luminosity of G2 (see Section 3.2). We also note that G1's FWHM in 2006, 5 yr after periapsis passage, was 185 km s⁻¹, comparable to the line width of G2 5 yr before its periapsis passage in 2014 (Phifer et al. 2013). This provides strong constraints on future hydrodynamic modeling of the post-periapsis development of these objects.

Unlike G2, whose flux density stayed constant before and during periapsis (Witzel et al. 2014), G1's L' flux significantly decreased post-periapsis (Figure 2). The size of G1 at L' shows a similar decrease over time from a resolved, optically thin source 2 yr after periapsis to an unresolved, compact source 5 yr post-periapsis passage. Our calculation in the previous section indicates that G1 went through periapsis passage with a radius >21 au. These findings suggest that G1's smaller mass and larger size caused its dust envelope to have a stronger tidal interaction with Sgr A* than that of G2. While they have similar tidal radii close to periapsis passage, G1 interacts with the SMBH for a longer period of time than G2.

Several studies (e.g., Anninos et al. 2012; Gillessen et al. 2012, 2013a; Schartmann et al. 2012; Morsony et al. 2015) find that if G1 or G2 were a gas cloud, there should be a significant increase in the steady-state X-ray flux several months before and after periapsis passage due to shocks. The Chandra X-ray Observatory was launched in 1999, and the earliest observations of Sgr A* were conducted in late 1999 and 2000. Baganoff et al. (2001) and Ponti et al. (2015) showed no indication of an increase in the steady-state X-ray flux in the time around G1's periapsis passage (2001.3 ± 0.4; Figure 3 in Ponti et al. 2015), although they raised the possibility that there was an increase in the rate of bright flares.

The size evolution of G1 in L'; the fact that both sources are on distinct Keplerian orbits (which disfavors their origin in a common gas stream), as described in Section 5.1; the intact Brγ emission after 7 yr; the survival of G1 at L'; and the lack of an increased X-ray flux all support the hypothesis that G1 has a massive (∼1 M_⊙) central (stellar) component surrounded by an envelope of gas and dust, similar to our hypothesis for G2 (Witzel et al. 2014). Even if the mass of G1 is smaller than 1 M_⊙, it is still ∼10⁵ times larger than the masses suggested for a gas cloud (Gillessen et al. 2012; Pfuhl et al. 2015).

G1 shares some observed characteristics with known merged binaries. In this section, we qualitatively examine the plausibility of the hypothesis that G1 and G2 are binary merger products. Our inferred dust temperature of 430–570 K is within the ranges reported for other observed binary mergers, including V1309 Sco (Nicholls et al. 2013) and BLG-360 (Tylenda et al. 2013). The large size and luminosity inferred for G1 are similar to those for BLG-360. The high infrared flux density of G1 (2.7 mJy at L') shortly after periapsis passage (2005) is consistent with the high fluxes from other binary merger products after the merger has taken place. However, while binary mergers show similarities to the observed characteristics of G1, many aspects regarding merger processes and products remain unclear. Observationally, we know very little about the lifetime of merger products. We can only provide observational evidence for lower limits of a few years. For instance, V1309 Sco was originally discovered in 2008 September as a "red nova" (Nakano et al. 2008; Rudy et al. 2008a, 2008b; Tylenda et al. 2011) that had an evolving spectral type from F to M. Nicholls et al. (2013) showed that V1309 Sco was undetected in the mid-infrared regime prior to its outburst; ∼23 months afterward, the authors found a clear near- and mid-infrared excess. In 2012, 4 yr after its outburst, the infrared excess was still present (Tylenda & Kamiński 2016), stemming from a dust envelope reaching as far as a few thousand au from the object. Interpreting the G-sources as merger products would require that the duration of the dusty phase for G1 be at least 13 yr.

As the majority of stars in the field and in dense stellar clusters like the nuclear star cluster exist as multiple-component systems (e.g., Sana & Evans 2011; Duchêne & Kraus 2013; Prodan et al. 2015), it is not unreasonable that many of these could merge in the Galactic center and form extended envelopes of gas and dust. The probability of finding two merger products must also be considered, including the likelihood of finding two on highly eccentric orbits. Let us assume that the G1 and G2 binary systems formed in the most recent star formation event. Based on estimates of merger timescales that include the eccentric Kozai mechanism, Stephan et al. (2016) estimated that ≲20% of all binaries formed would merge within the first few million years. Thus, if 1000 binaries with a comparable luminosity to G1 have formed from the 10⁴ M_⊙ starburst event, then ∼200 mergers will occur. We estimate that the G1 and G2 systems crossed their individual Roche limits and merged between 10⁴–10⁶ yr after the last star formation episode. The duration of the dusty, red phase of the merger depends on the mass of the progenitors and the relaxation timescale and is not well constrained; it may be as long as a few Myr (Stephan et al. 2016), and, after core merger, the resulting star takes a Kelvin–Helmholtz time (a few Myr) to contract to a compact star. Thus, a significant number of the mergers may still be visible as dusty, red objects depending critically on the duration of the dusty, red phase. The similarity of the orbital planes and eccentricities is also not unexpected in the merger hypothesis, given that G1 and G2 may have a common origin in the disk of young stars and that observational bias favors the recognition of fast-moving objects near the SMBH.

The present high eccentricities of G1 and G2 in their respective orbits around Sgr A* are consistent with binary systems that have been affected by the eccentric Kozai–Lidov mechanism (Kozai 1962; Lidov 1962; Naoz 2016), because binary systems perturbed by a massive third body are more likely to merge on highly eccentric outer orbits (Naoz & Fabrycky 2014; Naoz 2016; Stephan et al. 2016). The detailed dynamics involved in the eccentric Kozai–Lidov mechanism that can yield merger products have been discussed in detail in the literature (see the review by Naoz 2016). The merger rate and merger-induced products have been discussed in Prodan et al. (2015) and Stephan et al. (2016).

Merged binary systems undergo many physical changes as the merger occurs. For example, there is usually an optical outburst immediately following the physical merging of the stars, along with an evolution of the spectral type (e.g., Tylenda et al. 2011, Nicholls et al. 2013). The very few examples that have been published thus far have been inferred to be merged binaries because of optical periodic variability from the binary system before the outburst and the absence of any periodicity from the system following the outburst (e.g., Tylenda et al. 2011). Searches are underway for bursting or periodic sources in the Galactic center that may be mergers at different stages (A. Gautam et al. 2017, in preparation).

Several other hypotheses exist that could describe the observables of G1, such as edge-on, protoplanetary disks around young, low-mass stars (Murray-Clay & Loeb 2012); disks around older stars (Miralda-Escudé 2012); or some other tidal disruption phenomenon involving a stellar object. Further observations, in particular of G2 after its periapsis transit, and more comprehensive statistics of infrared excess sources and intact binaries at the Galactic center will help to shed light on the nature of these objects.