# The Swansong of the Galactic Center Source X7: An Extreme Example of Tidal
Evolution near the Supermassive Black Hole

Anna Ciurlo Department of Physics and Astronomy, University of California, Los
Angeles, CA 90095, USA  Randall D. Campbell W. M. Keck Observatory, Waimea, HI
96743, US  Mark R. Morris Department of Physics and Astronomy, University of
California, Los Angeles, CA 90095, USA  Tuan Do Department of Physics and
Astronomy, University of California, Los Angeles, CA 90095, USA  Andrea M.
Ghez Department of Physics and Astronomy, University of California, Los
Angeles, CA 90095, USA  Eric E. Becklin  Department of Physics and Astronomy,
University of California, Los Angeles, CA 90095, USA  Rory O. Bentley
Department of Physics and Astronomy, University of California, Los Angeles, CA
90095, USA  Devin S. Chu Department of Physics and Astronomy, University of
California, Los Angeles, CA 90095, USA  Abhimat K. Gautam Department of
Physics and Astronomy, University of California, Los Angeles, CA 90095, USA
Yash A. Gursahani Department of Physics and Astronomy, University of
California, Los Angeles, CA 90095, USA  Aurélien Hees Sytemes de Reference
Temps Espace, Observatoire de Paris, Université Paris-Sciences-et-Lettres,
Centre National de la Recherche Scientifique, Sorbonne Universite,
Laboratoire National de métrologie et d’Essais, 61 avenue de l’Observatoire,
75014 Paris, France  Kelly Kosmo O’Neil Department of Physics and Astronomy,
University of California, Los Angeles, CA 90095, USA  Jessica R. Lu Astronomy
Department, University of California Berkeley, Berkeley, CA 94720, USA
Gregory D. Martinez  Department of Physics and Astronomy, University of
California, Los Angeles, CA 90095, USA  Smadar Naoz Department of Physics and
Astronomy, University of California, Los Angeles, CA 90095, USA  Mani L.
Bhaumik Institute for Theoretical Physics, Department of Physics and
Astronomy, UCLA, Los Angeles, CA 90095, USA  Shoko Sakai  Department of
Physics and Astronomy, University of California, Los Angeles, CA 90095, USA
Rainer Schödel  Instituto de Astrofísica de Andalucía, Consejo Superior de
Investigaciones Cientificas,
Glorieta de la Astronomia S/N, 18008 Granada, Spain

###### Abstract

We present two decades of new high-angular-resolution near-infrared data from
the W. M. Keck Observatory that reveal extreme evolution in X7, an elongated
dust and gas feature, presently located half an arcsecond from the Galactic
Center supermassive black hole. With both spectro-imaging observations of
Br-$\gamma$ line-emission and Lp (3.8 $\mu$m) imaging data, we provide the
first estimate of its orbital parameters and quantitative characterization of
the evolution of its morphology and mass. We find that the leading edge of X7
appears to be on a mildly eccentric (e$\sim$0.3), relatively short-period (170
years) orbit and is headed towards periapse passage, estimated to occur in
$\sim$2036\. Furthermore, our kinematic measurements rule out the earlier
suggestion that X7 is associated with the stellar source S0-73 or with any
other point source that has overlapped with X7 during our monitoring period.
Over the course of our observations, X7 has (1) become more elongated, with a
current length-to-width ratio of 9, (2) maintained a very consistent long-axis
orientation (position angle of 50∘), (3) inverted its radial velocity
differential from tip to tail from -50 to +80 km/sec, and (4) sustained its
total brightness (12.8 Lp magnitudes at the leading edge) and color
temperature (425 K), which suggest a constant mass of $\sim$50 MEarth. We
present a simple model showing that these results are compatible with the
expected effect of tidal forces exerted on it by the central black hole and we
propose that X7 is the gas and dust recently ejected from a grazing collision
in a binary system.

Galactic Center — near infrared — interstellar medium — black holes — tidal
interactions

##  1 Introduction

The immediate entourage of the supermassive black hole (SMBH) at the center of
the Milky Way Galaxy includes dense, co-spatial clusters of both young and old
stars (Paumard et al., 2006; Do et al., 2013; Lu et al., 2013), as well as
orbiting streams of gas and dust on scales from 0.1 to 1 pc (see reviews by
Morris & Serabyn 1996; Genzel et al. 2010). At smaller scales ($\sim$0.02 pc),
a collection of so-called G objects has been found (Gillessen et al., 2012;
Phifer et al., 2013; Pfuhl et al., 2015; Witzel et al., 2017; Ciurlo et al.,
2020): compact gas/dust features that have been interpreted as stellar objects
enshrouded by extended dust photospheres, possibly as a result of relatively
recent binary mergers (Witzel et al., 2014; Stephan et al., 2016; Ciurlo et
al., 2020). In at least two cases, the sizes of the G objects have apparently
exceeded their tidal radii as they passed through their orbital periapse near
the SMBH, causing them to shed an observable amount of their gas/dust
envelopes (Witzel et al., 2017; Gillessen et al., 2019), but thereafter, they
reverted to their compact form. One of the most intriguing objects found
within $\sim$0.02 pc of the SMBH is X7, the subject of this paper. The
position of X7 relative to other gas and dust constituents of the central
light-year of the Galaxy, including the electromagnetic counterpart of the
SMBH, Sgr A* (Ghez et al., 2005a; Genzel et al., 2003), is shown in Figure 1.

Figure 1: X7 in context: gas and dust structures in the Galactic Center.
Three-color image of the central $0.27\times 0.27$ parsecs of the Galactic
Center obtained with the NIRC2 imager at the W. M. Keck Observatory. Lp (3.8
$\mu$m) is shown in red, Ms (4.7 $\mu$m) in green, Kp (2.1 $\mu$m) in blue.
All three bands were observed in summer 2021 using adaptive optics (Section 2
provides details on these observations). Thermal emission from warm dust in X7
is well detected at Lp (3.8 $\mu$m). The source X3, originally thought to be
of the same nature as X7 (Mužić et al., 2007), is also visible in the
Southwest corner. Other prominent, larger-scale features include the tip of
the Northern Arm of the mini-spiral (Lo & Claussen, 1983) located to the south
of X7, the top part of the mini-cavity (Morris & Yusef-Zadeh, 1987; Yusef-
Zadeh et al., 1990) in the southwest, and the Epsilon source (Yusef-Zadeh et
al., 1990), immediately East of X7.

First noted by Clénet et al. (2004), then named by Mužić et al. (2007), X7 is
a filamentary dust/gas feature that, like the G objects, is observable in both
near-infrared thermal dust emission and in emission lines from ionized gas. As
it orbits the SMBH, X7 has been undergoing dramatic evolution over the past 20
years. X7’s early (mid-2000s) appearance resembled a cometary shape, which led
Mužić et al. (2007) to suggest that X7 results from a bow shock caused by
winds (either from nearby massive stars or from the supermassive black hole
itself). However, the bow shock appearance has not persisted in subsequent
years. More recently, Peißker et al. (2021) proposed instead that X7 is the
product of the interaction between the circumstellar envelope of an S-star (a
member of a group of early-type stars on tight, eccentric orbits around the
SMBH) and a wind emanating from the neighborhood of Sgr A*.

In this study we use the GCOI111Galactic Center Orbits Initiative (GCOI, PI:
Ghez), a growing 27-year database composed of data acquired at the W.M. Keck
Observatory. database from the long-term monitoring of this region with the W.
M. Keck Observatory, to characterize the morphological and dynamical evolution
of X7. We find that X7 is a complex feature with a rapidly evolving spatial-
velocity structure most likely due to tidal interactions with the SMBH.
Preliminary results of this analysis have previously been presented in
Campbell et al. (2021). With the GCOI database we have access to a set of
imaging data that is similar, but completely independent of, the one presented
by Peißker et al. (2021). Additionally, we present and analyze a much more
extensive set of spectroscopic data than what has previously been published,
which allows us to characterize the dynamical evolution of X7 over more than
15 years for the first time. These data, in combination with the imaging data,
provide comprehensive new insights into the characteristics and behavior of
this object. For the first time we compute the orbit of the leading edge of X7
and use it to model X7’s response to the gravity of the SMBH. We find here
that the evolution of X7’s shape can be well explained by the effect of the
gravity of the SMBH alone. We show that the initial bow-shock shape of X7 has
evolved to a more linear morphology and that it is starting to undergo
fragmentation. The orientation of X7’s elongation is inconsistent with its
direction of motion, with models of the collective stellar winds in the local
region and with a spherical outflow from the SMBH. The long-term monitoring
with integral field spectroscopy data reveal a clear positional and dynamical
separation of X7 from stellar sources, including the one proposed by Peißker
et al. (2021) and from nearby G object sources (G4 and G5, Ciurlo et al.
(2020)) due to distinct differences in both radial velocity and proper motion.
We do note and discuss an intriguing similarity in orbital motion with G3.

We describe the observations in Section 2 and in Section 3 the methodology we
employed to parameterize X7’s properties. In Section 4 we present our results
on X7’s morphology, orbit, length, brightness and mass. In Section 5 we model
X7’s tidal evolution. Several scenarios for the X7’s evolution and origin are
discussed in Section 6. The summary and conclusions of our study are reported
in Section 7.

##  2 Datasets

This study uses imaging (Section 2.1) and spectroscopic (Section 2.2) data
consisting of new data and existing data, taken as part of the GCOI. While the
majority of this dataset was acquired using the laser guide star adaptive
optics (AO) systems that operate with optical tip-tilt systems (Wizinowich et
al., 2006), using a guide star located $\sim$20 arcsec away from Sgr A*, some
of the latest datasets were taken with the newest AO systems. On Keck I, which
hosts the integral field unit OSIRIS (Larkin et al., 2006) used in this study,
the AO system has been upgraded to include an infrared tip-tilt system, TRICK,
enabling the use of IRS 7, a brighter and closer star for the tip-tilt
corrections for half of our 2020 and 2021 spectroscopic observations. On Keck
II, which hosts the imager NIRC2 (PI: K. Matthews), a near-infrared natural-
guide-star AO system that includes a pyramid wavefront sensor (Bond et al.,
2020), introduced the opportunity to use IRS 7 for both high- and low-order
wavefront corrections for all of our 2021 imaging observations. All three AO
systems deliver very near diffraction-limited performance.

###  2.1 Imaging data

Date | filter | itime [sec] | frames | FWHM
---|---|---|---|---
$\times$coadds | number | [mas]
2017-07-16 | Lp | 0.50$\times$30 | 368 | 96
2019-08-14 | Lp | 0.50$\times$60 | 294 | 90
2020-07-31 | Lp | 0.20$\times$30 | 29 | 98
2021-07-13 | Lp | 0.50$\times$60 | 40 | 102
2021-08-15 | Lp | 0.35$\times$85 | 43 | 93∗
2015-04-02 | Kp | 2.8$\times$10 | 18 | 72
2021-08-15 | Kp | 2.1$\times$14 | 36 | 49∗
2015-04-02 | Ms | 0.2$\times$600 | 32 | 122
2021-08-21 | Ms | 0.2$\times$200 | 34 | 103∗
Table 1:  Newly reported GCOI NIRC2 observations. All observations used a 10
mas pixel scale. The epochs marked with a ∗ have been observed in natural
guide star mode using an infrared wavefront sensor instead of the usual laser-
guide-star configuration.

A subset of the GCOI imaging data set used in this study, collected between
2002 and 2021, is primarily composed of NIRC2 observations taken through the
Lp band-pass filter (3.776 $\mu$m central wavelengths) during 22 nights, of
which the most recent 5 observations (post-2015) are newly reported. The
observations cover a field of view of roughly 10” x 10” around Sgr A*, with a
10 mas/pixel scale. For each night, the individual data frames are calibrated
and combined following the same procedure used for previously published data
(Ghez et al., 2004, 2005b; Phifer et al., 2013; Witzel et al., 2014). The
final images, which have an average resolution of 93 mas (FWHM), are placed in
an absolute coordinate system with Sgr A* at the center, using the known
positions and proper motions of 5 stars (IRS16 SW, IRS16 C, IRS16 NW, IRS29 N
and S1-23). The reference stars’ positions are measured by the GCOI pipeline
(see Sakai et al. 2019; Jia et al. 2019) and the alignment procedure is the
same as employed for the OSIRIS data in Ciurlo et al. (2020). Table 1 provides
details on the newly reported observations at Lp as well as two supplemental
epochs at Kp and Ms; Figure 1 shows a three-color image constructed from the
Kp, Lp, and Ms data taken in 2021.

###  2.2 Spectroscopic data

Date | scale | itime | frames | FWHM
---|---|---|---|---
[mas] | [sec] | number | [mas]
2019-05-11 | 35 | 900 | 7 | 88
2020-05-25 | 35 | 300 | 5 | 63∗
2020-07-23 | 35 | 900 | 8 | 63
2020-07-30 | 35 | 900 | 9 | 59
2020-08-03 | 35 | 900 | 10 | 63
2021-05-07 | 35 | 900 | 7 | 60∗
2020-08-13 | 20 | 900 | 7 | 46∗
Table 2:  Newly reported GCOI OSIRIS observations. Epochs marked with a ∗ have
been observed with TRICK, an infrared tip-tilt sensor used in conjunction with
the usual optical one.

Our spectroscopic data set, gathered between 2006 and 2021, consists of 33
nights of OSIRIS observations, of which the most recent 7 (post-2018) are
newly reported. We use 32 observations taken with a pixel scale of 35
mas/pixel. Additionally, we use one 20 mas/pixel observation to illustrate the
structure of X7 with slightly higher spatial resolution. The 35 mas/pixel
observations selected from the GCOI archive are those lacking substantial
residuals from telluric OH line subtraction (visible as extremely strong
absorption lines). All observations were taken at a position angle of 285
degrees with a spectral resolution of R$\sim$3800 and were obtained through
the Kn3 bandpass filter (2.121-2.220$\mu$m), which covers the hydrogen
recombination line Br-$\gamma$ (rest wavelength 2.1661 $\mu$m), forbidden
lines of iron [FeIII] (rest wavelengths 2.1457 and 2.2184 $\mu$m) and (near
the edge of the filter) the molecular hydrogen H2 1-0 S(1) line (rest
wavelength 2.1218 $\mu$m). The new data were calibrated in the same manner as
the existing GCOI OSIRIS data used for this study, which have been reported in
earlier GCOI publications (Ghez et al., 2008; Boehle et al., 2016; Chen et
al., 2018; Do et al., 2019). The selected observations consist of calibrated
and mosaicked data cubes from the GCOI Archive. For the 35 mas/pix
observations, this resulted in a final field of view of roughly to
3”$\times$2.5” centered on Sgr A* and a typical angular resolution of 78 mas
(evaluated on the star S0-2) while the 20 mas/pix observation has resolution
of 46 mas. The GCOI experimental design prioritized the observation of short
period stars close to Sgr A* rather than X7, resulting in X7 being only
partially within this smaller field of view. The GCOI data-cubes are
furthermore photometrically and astrometrically calibrated and stellar-
continuum-subtracted by the procedures described by Ciurlo et al. (2020).
Table 2 summarizes the newly reported spectroscopic observations.

##  3 Methodology

Precise proper motion measurements of an evolving resolved object cannot be
determined with a classical centroid method. Hence, we adopt an alternative
method and characterize the position, orientation, and length of X7 by taking
a series of nearly perpendicular line cuts, as shown in Figure 2 (top panels).
Through these cuts we define the northeast edge of X7’s ridge, closest to the
SMBH, as the ”tip” and the rest of the ridge as the ”tail”.

Figure 2:  Defining the position, orientation, and profile of X7. Top left:
NIRC2 2020 Lp image showing a series of cuts along X7 ridge. The central peak
of each cut (shown as a red dot) is determined with a Gaussian. A linear fit
to these peaks (green line) defines the ridge of X7 while the half-maximum
along ridge profile defines the location of the tip (shown as a blue dot).
Bottom left: 3D rendering of the NIRC2 cuts (the vertical axis represents the
intensity) in black, together with the corresponding the Gaussian fit over-
plotted in red and the tip measurement in blue. Top right: OSIRIS 2020
Br-$\gamma$ narrow-band image of X7 that highlights the series of cuts used to
measure the tip location. Bottom right: Comparison of X7’s ridge profile in
dust (NIRC2-Lp) and gas (OSIRIS Br-$\gamma$) emission (extracted along the
green lines shown in the top panels). A polynomial fit to each of the
profiles, along with the measured location of the tip, is shown in blue for
NIRC2 and in red for OSIRIS. The profiles are shifted along the direction of
the ridge to match the half-max points.

For the NIRC2 data, we take cuts every 14 mas and adapt the number of cuts to
the apparent lengthening of X7 in the plane of the sky: 15 cuts prior to 2011
and 21 cuts in 2011-2021. These cuts cover the leading northeast half of X7’s
ridge (Figure 2, top left panel). Small deviations of the inclination of the
cuts with respect to the ridge do not have a significant impact on our
measurements. At this stage, we avoid the southwest bottom half because the
early flared appearance of the tail and overlapping surrounding features bias
our measurements. The profile of each cut is fit by a Gaussian (red curves in
Figure 2, bottom left panel). In turn, the peaks obtained through the Gaussian
fit (5 of them pre-2011, 7 onward, represented as red dots in Figure 2, top
left panel) are fit with a straight line (green line in Figure 2, top left
panel). Then, the intensity profile of X7’s ridge is extracted along the line.
This ridge profile is fit to a fourth-order polynomial and the tip position is
defined as the point, along the leading edge of the ridge, where the intensity
is half of the ridge maximum. This definition is arbitrary but objective, as
it defines the location where X7’s intensity is rising rapidly, and is clearly
distinguished from the background. We estimate the positional error of the tip
as the variance of measurements obtained by changing the measurement
parameters: the lengths of the cuts, the number of cuts, starting location of
cuts, and order of the polynomial for the ridge profile fit. The line fit to
the peaks is also used to find the orientation of X7 with respect to Sgr A*
(Figure 2, left panel). Additionally, we define the total length of X7 as the
distance between the half power points of the polynomial fit (i.e between the
tip and the the half max point closest to the southwest corner where the ridge
intensity starts to decrease).

We measured the Lp surface brightness at the peak intensity (which is close to
the tip but encloses less background and is therefore a better determination
for the surface brightness) through aperture photometry. The flux was
extracted over a 0.09” aperture radius, subtracting the local background from
the median flux in an annulus of inner and outer radii 0.21 and 0.29”
respectively. We compare this measured flux to the one of nearby stars of know
magnitude. The variations in Lp magnitudes from year to year is only about 0.1
However, the absolute photometric error is larger, on the order of 0.5 mag
(Table LABEL:tab:res) due to high background, uncertainties in the Lp
magnitude of reference stars, variation in AO performances, and the fact that
we’re comparing an extended source to a point source.

To measure the astrometry of the tip and the orientation of the tail in the
OSIRIS data, we use a similar technique as that employed for NIRC2 data .
However, in the case of OSIRIS we also need to construct an intensity map by
selecting a slice of the cube in the wavelength dimension to isolate X7 from
the rest of the emission. The 2017 OSIRIS Kn3 spectrum of the tip of X7 is
shown in Figure 3: we focus on the Br-$\gamma$ line which is the most
prominent feature of X7’s spectrum (two emission lines of [Fe III] are also
associated with X7 but are less intense). We use an iterative process to
determine both the tip location and the tip’s radial velocity since they are
correlated measurements: first we do a qualitative assessment of the spatial
location of the peak emission, extract a spectrum over a 0.105” aperture
diameter and measure the radial velocity with a Gaussian fit to the
Br-$\gamma$ emission line (same procedure as described in Ciurlo et al. 2020).
Second we obtain a Br-$\gamma$ emission line map by collapsing the cube over 9
channels ($\sim$300 km/s) around the measured radial velocity. Third we use
the line map to measure the tip location as explained above for the NIRC2
measurement, with the only difference being the number of cuts used to cover
the same length of the ridge, due to the different spatial sampling in the two
instruments (0.01” per pixel for NIRC2 versus 0.035” for OSIRIS). For OSIRIS,
a total of 11 cuts were used for the orientation measurement. The position
uncertainty is determined as for NIRC2, with the addition of varying the
aperture size for the spectral extraction and the velocity width to use for
the slice of the OSIRIS data cube. The new tip location is used to remeasure
the radial velocity. The largest source of uncertainty to the radial velocity
measurement is the location at which the spectra is extracted. Therefore, we
characterize the uncertainties by varying the extraction position by 1-1.5
pixels. The standard deviation of these measurements it’s added in quadrature
to the statistical error which is quite small (1–2 km/s). Additionally, we
characterize the year-by-year evolution of the radial velocity gradient along
the ridge (from tip to tail). To do so we pick one epoch per year and extract
spectra (1.5 pixel aperture radius) on each pixel along the ridge (see Figure
6, third and sixth columns). The gradient, or slope, is determined from a
linear fit to the radial velocity distribution along the ridge.

Figure 3: Spectrum of the X7 tip in 2017 with the Kn3 filter. The rest
wavelengths of emission features of interest are highlighted with dotted lines
whereas the blue-shifted emission associated with X7 is highlighted with
arrows.

We measure the Br-$\gamma$ surface brightnesses evolution of X7 by measuring
it in every epoch at the peak of intensity (as discussed for the Lp data)
using a 0.0525” aperture radius, and an annulus of inner and outer radii of
0.0875 and 0.21”, respectively, for background correction. Additionally, the
total surface brightness of the Br-$\gamma$ line can be used to estimate the
density and the mass of X7 (see Section 4.5). We select the 2017 for this
derivation since it has the smallest difference between tip and tail radial
velocity. In order to maximize the signal-to-noise ratio, we combined all 2017
datasets (same procedure as in Ciurlo et al. 2020). This permits X7 emission
to be easily isolated from superimposed sources when slicing the cube (we
select the wavelength range 2.1594–2.1628 $\mu$m which corresponds to 14
spectral channels). We then create a mask to isolate X7 emission in the
spatial dimensions and extract its overall spectrum. The total flux of X7 is
then determined by fitting a Gaussian to the integrated Br-$\gamma$ line
profile to measure the total flux of X7.

All results of this analysis are reported in Table LABEL:tab:res.

Table 3: Summary of the measured X7 properties. RA and Dec are reported as offsets from Sgr A* (positive offsets Westward). Previously reported GCOI observations references: $a$) Ghez et al. 2004, $b$) Ghez et al. 2005b, $c$) Witzel et al. 2014, $d$) Ghez et al. 2008, $e$) Boehle et al. 2016, $f$) Phifer et al. 2013, $g$) Chu et al. 2018, $h$) Do et al. 2019. Date | Ref. | data | RA Dectip | RVtip | PA | length | RV slope | flux${}_{tip}(Br{\gamma})$ | flux${}_{tip}(Lp)$
---|---|---|---|---|---|---|---|---|---
type | [mas] | [km/s] | [deg] | [mas] | [km/s/”] | [mJy] | [mag]
2002-05-31 | a | Lp | 425$\pm$33 -523$\pm$29 | - | -132 | 225 | - | - | 12.64$\pm$0.37
2003-06-10 | a | Lp | 419$\pm$34 -531$\pm$36 | - | -127 | 243 | - | - | 12.58$\pm$0.40
2004-06-28 | b | Lp | 417$\pm$46 -485$\pm$43 | - | -129 | 242 | - | - | 12.77$\pm$0.44
2004-07-26 | b | Lp | 417$\pm$36 -508$\pm$36 | - | -129 | 201 | - | - | 12.72 $\pm$0.49
2005-07-31 | c | Lp | 412$\pm$26 -484$\pm$26 | - | -131 | 205 | - | - | 12.91 $\pm$0.50
2006-05-21 | c | Lp | 422$\pm$24 -450$\pm$23 | - | -132 | 247 | - | - | 12.98$\pm$0.49
2006-06-18 | d | Br-$\gamma$ | 364$\pm$36 -385$\pm$22 | -705$\pm$27 |  | - | +253 | 0.90$\pm$0.12 | -
2006-06-30 | d | Br-$\gamma$ | 418$\pm$24 -393$\pm$13 | -707$\pm$15 |  | - | - | 0.86$\pm$0.13 | -
2006-07-01 | e | Br-$\gamma$ | 391$\pm$45 -399$\pm$35 | -691$\pm$21 |  | - | - | 0.92$\pm$0.11 | -
2008-07-25 | e | Br-$\gamma$ | 372$\pm$21 -391$\pm$12 | -713$\pm$8 |  | - | +244 | 0.82$\pm$0.10 | -
2009-05-05 | e | Br-$\gamma$ | 397$\pm$45 -391$\pm$20 | -710$\pm$5 |  | - | +181 | 1.10$\pm$0.14 | -
2009-07-22 | f | Lp | 421$\pm$27 -428$\pm$26 | - | -131 | 273 | - | - | 12.76$\pm$0.48
2009-05-06 | e | Br-$\gamma$ | 393$\pm$55 -383$\pm$29 | -716$\pm$7 |  | - | - | 1.05$\pm$0.14 | -
2010-05-05 | e | Br-$\gamma$ | 389$\pm$52 -370$\pm$33 | -702$\pm$6 |  | - | - | 1.07$\pm$0.13 | -
2010-05-08 | e | Br-$\gamma$ | 404$\pm$64 -368$\pm$37 | -704$\pm$7 |  | - | +165 | 1.07$\pm$0.14 | -
2011-07-10 | e | Br-$\gamma$ | 377$\pm$54 -344$\pm$39 | -694$\pm$6 |  | - | +86 | 0.93$\pm$0.17 | -
2012-05-16 | f | Lp | 428$\pm$23 -380$\pm$23 | - | -133 | 313 | - | - | 12.96$\pm$0.49
2012-05-17 | f | Lp | 426$\pm$23 -377$\pm$24 | - | -134 | 285 | - | - | 13.02$\pm$0.48
2012-07-22 | e | Br-$\gamma$ | 381$\pm$55 -336$\pm$29 | -683$\pm$8 |  | - | 48 | 0.71$\pm$0.19 | -
2013-04-24 | f | Lp | 420$\pm$21 -367$\pm$21 | - | -132 | 256 | - | - | 12.83$\pm$0.47
2013-05-14 | e | Br-$\gamma$ | 397$\pm$46 -322$\pm$24 | -683$\pm$5 |  | - | - | 1.01$\pm$0.12 | -
2013-07-27 | e | Br-$\gamma$ | 385$\pm$55 -297$\pm$29 | -682$\pm$6 |  | - | +41 | 0.99$\pm$0.11 | -
2014-03-19 | c | Lp | 421$\pm$24 -347$\pm$24 | - | -128 | 240 | - | - | 12.59$\pm$0.43
2014-03-20 | c | Lp | 418$\pm$19 -355$\pm$19 | - | -132 | 243 | - | - | 12.88$\pm$0.49
2014-05-11 | c | Lp | 419$\pm$21 -341$\pm$22 | - | -131 | 284 | - | - | 12.86$\pm$0.49
2014-07-03 | g | Br-$\gamma$ | 385$\pm$53 -288$\pm$36 | -670$\pm$4 |  | - | +27 | 1.11$\pm$0.13 | -
2014-07-03 | c | Lp | 422$\pm$23 -347$\pm$23 | - | -128 | 246 | - | - | 12.67$\pm$0.48
2014-08-04 | c | Lp | 421$\pm$21 -335$\pm$22 | - | -131 | 260 | - | - | 12.92$\pm$0.49
2015-03-31 | c | Lp | 414$\pm$22 -327$\pm$23 | - | -131 | 276 | - | - | 12.89$\pm$0.49
2015-05-04 | g | Br-$\gamma$ | 418$\pm$69 -317$\pm$43 | -663$\pm$7 |  | - | - | 0.92$\pm$0.14 | -
2015-07-21 | g | Br-$\gamma$ | 362$\pm$55 -268$\pm$29 | -661$\pm$4 |  | - | -11 | 1.29$\pm$0.15 | -
2016-05-17 | c | Lp | 410$\pm$19 -293$\pm$20 | - | -129 | 309 | - | - | 12.95 $\pm$0.50
2017-05-17 | h | Br-$\gamma$ | 374$\pm$52 -238$\pm$33 | -626$\pm$3 |  | - | - | 1.09$\pm$0.13 | -
2017-05-18 | h | Br-$\gamma$ | 371$\pm$55 -225$\pm$29 | -624$\pm$3 |  | - | - | 1.06$\pm$0.12 | -
2017-05-19 | h | Br-$\gamma$ | 345$\pm$69 -226$\pm$43 | -624$\pm$6 |  | - | - | 0.88$\pm$0.18 | -
2017-07-16 | new | Lp | 401$\pm$19 -261$\pm$20 | - | -132 | 363 | - | - | 12.77$\pm$0.46
2017-07-19 | h | Br-$\gamma$ | 368$\pm$68 -222$\pm$36 | -622$\pm$4 |  | - | -55 | 1.02$\pm$0.12 | -
2017-07-27 | h | Br-$\gamma$ | 365$\pm$59 -204$\pm$31 | -623$\pm$5 |  | - | - | 0.65$\pm$0.21 | -
2017-08-14 | h | Br-$\gamma$ | 349$\pm$61 -219$\pm$38 | -621$\pm$3 |  | - | - | 1.45$\pm$0.11 | -
2018-04-24 | h | Br-$\gamma$ | 357$\pm$64 -193$\pm$37 | -611$\pm$7 |  | - | - | 0.82$\pm$0.11 | -
2018-05-23 | h | Br-$\gamma$ | 362$\pm$64 -211$\pm$37 | -609$\pm$4 |  | - | - | 0.89$\pm$0.10 | -
2018-07-22 | h | Br-$\gamma$ | 349$\pm$64 -200$\pm$37 | -607$\pm$5 |  | - | -83 | 1.00$\pm$0.12 | -
2018-07-31 | h | Br-$\gamma$ | 361$\pm$64 -209$\pm$37 | -605$\pm$4 |  | - | - | 0.77$\pm$0.18 | -
2018-08-11 | h | Br-$\gamma$ | 355$\pm$64 -202$\pm$37 | -606$\pm$5 |  | - | - | 1.25$\pm$0.10 | -
2019-05-11 | new | Br-$\gamma$ | 354$\pm$43 -183$\pm$25 | -593$\pm$4 |  | - | -109 | 1.42$\pm$0.09 | -
2019-08-14 | new | Lp | 395$\pm$21 -229$\pm$13 | - | -132 | 348 | - | - | 12.93$\pm$0.49
2020-05-25 | new | Br-$\gamma$ | 353$\pm$64 -178$\pm$37 | -556$\pm$8 |  | - | - | 1.44$\pm$0.10 | -
2020-07-23 | new | Br-$\gamma$ | 349$\pm$64 -169$\pm$37 | -560$\pm$3 |  | - | - | 1.76$\pm$0.14 | -
2020-07-30 | new | Br-$\gamma$ | 352$\pm$64 -167$\pm$37 | -555$\pm$13 |  | - | -183 | 1.36$\pm$0.15 | -
2020-07-31 | new | Lp | 365$\pm$20 -202$\pm$21 | - | -131 | 419 | - | - | 12.84$\pm$0.43
2020-08-03 | new | Br-$\gamma$ | 357$\pm$64 -167$\pm$37 | -558$\pm$4 |  | - | - | 1.34$\pm$0.16 | -
2021-05-07 | new | Br-$\gamma$ | 356$\pm$57 -159$\pm$36 | -546$\pm$8 |  | - | -174 | 0.84$\pm$0.12 | -
2021-07-13 | new | Lp | 362$\pm$16 -153$\pm$16 | - | -133 | 438 | - | - | 12.78$\pm$0.42
2021-08-15 | new | Lp | 358$\pm$21 -179$\pm$21 | - | -133 | 422 | - | - | 12.88$\pm$0.40
|  | average | 387 -306 | -641 | -131 | 288 | 30 | 1.05 | 12.8

##  4 Results

###  4.1 Morphology and dynamical evolution

Figure 4: Morphology evolution of X7’s thermal dust emission. NIRC2 Lp band
(3.8 $\mu$m) images between 2002 and 2021. The images are oriented with
equatorial north at the top, and with Sgr A* positioned in the upper left
corner of each panel.  Figure 5: Zoom-in of the structure of X7 showing
evidence for its fragmentation. The figure shows maps of Br-$\gamma$ emission
in 2020 using 35 and 20 mas (inset at left) pixel scales, obtained by
integrating over velocities in the data-cubes at which X7’s blueshifted
Br-$\gamma$ emission is present (corresponding to wavelengths of 2.1612 to
2.1628 $\mu$m). The line maps are cut out from the data cube at velocities
around that of X7. In the 20 mas map X7 is partially cropped owing to the
smaller field of view.

Over our $\sim$20 years of observations, X7 has undergone significant changes
in appearance, shape, velocity and position.

  * •

In the earlier epochs, X7 appeared to have a flared tail which, however, does
not persist after 2006, when the shape of X7 begins to become more linear
(Figure 4). More recently, the higher-resolution Br-$\gamma$ emission map,
obtained with a smaller OSIRIS platescale (20 mas), seems to indicate that the
ridge (or tail) of X7 is fragmenting (Figure 5).

  * •

The orientation of the ridge of X7 on the plane of the sky does not appear to
have changed significantly during the period of our observations: we find that
X7 maintains a constant position angle of -249∘ eastward from North with a
root-mean-square of 1.8∘.

  * •

X7 has nearly doubled its length in the plane of the sky over 18 years,
growing from 0.25” in 2003 to over 0.4” ($\sim$3300 AU) in 2021.

  * •

As X7 moves across the plane of the sky and stretches in length, its internal
radial velocity structure changes (see Figure 6). Over 15 years, the tip has
decelerated by approximately 200 km/sec. On the other hand, the tail does not
undergo such a dramatic change but still shows significant velocity evolution,
decelerating by $\sim$50 km/s.

In Appendix A we discuss additional fainter structures apparent in the
Br-$\gamma$ emission-line images.

Figure 6: Morphological and dynamical evolution of X7’s gas emission.
Br-$\gamma$ integrated intensity (left columns) and radial velocity for the
peak of the local profile (center columns) obtained between 2006 and 2021.
Br-$\gamma$ total intensity contours are overlaid on the color-coded velocity
maps. Both maps are constructed from a narrow wavelength band centered around
the blue-shifted Br-$\gamma$ emission extracted from the OSIRIS data-cubes
with stellar continua removed. The field shown is a 1.0$\times$1.0” area
southwest of Sgr A*, positioned so that Sgr A* is located at the upper left
corner of each panel. The intensity images illustrate proper motion and
morphology evolution of the X7 gas emission, similarly to what Figure 4 shows
for the dust emission. The velocity maps highlight the changes in velocity
structure, in particular the tip region as it becomes less blue-shifted going
from blue (-725 ${\pm}$ 15 km/sec) to reddish-green (-540 ${\pm}$ 15 km/sec)
in the color-coded maps over the 15 year time span. The dramatic changes in
the velocity structure of X7 are further demonstrated by the accompanying
plots (right) of the radial velocity along the X7 ridge as a function of
distance from the tip. The position angle of the ridge is highlighted as a
green line on the intensity maps and remains relatively constant at 52.4 ∘
${\pm}$ 6.7∘ .

###  4.2 Orbit of the tip

We determined that X7’s motion on the plane of the sky over a 19 year period
is approximately 0.35", mostly northward and arcing northeastward, with a
proper motion velocity of $\sim$135 km/s East and $\sim$690 km/s North. The
radial velocity measurements show that the tip decelerated from -725 to -550
km/sec over a 15 year time span (Figure 7, top-right panel). We can now
combine both the astrometric and radial velocity measurements and fit the
orbit of X7’s tip.

We have two sets of astrometric measurements: 1) the gas proper motion and
radial velocities measured from OSIRIS data, and 2) the dust proper motion
measured from NIRC2 data. Both measurements agree within the uncertainties,
but we observe a partial offset (more details in Appendix B). Given the
extended nature of X7, astrometric measurements are not straightforward,
especially across different instruments. Therefore, we opt for the most
conservative approach and use OSIRIS measurements only: OSIRIS astrometry data
is self-consistent with the radial velocity measurements.

Our analysis employs a new orbit-fitting software package developed by the
GCOI, NStarOrbits (Martinez et al., in prep.). We perform a Bayesian analysis
with a multi-modal nested sampling algorithm, MultiNest (Feroz et al., 2009) –
the same orbit-fitting methodology described in previous GCOI publications
(for example, see Do et al., 2019; Ciurlo et al., 2020), but implemented in a
much more efficient and modifiable way with NStarOrbits (further details on
the orbit-fitting procedure are described in Appendix D). In Table 4, we
present the weighted median and associated 68% confidence intervals
(statistical uncertainties only) for X7’s orbital parameters. The orbital fit
results are also illustrated in Figure 7. For the reported orbit fit, we use
observable-based priors (O’Neil et al., 2019), and fix the central potential
parameters to the average of the latest published estimates from Gravity
Collaboration et al. (2019, 2020) and Do et al. (2019). To confirm that this
orbit fitting strategy is robust, we also test several other orbit fitting
setups. For example, as described in Appendix D, we also fit X7 and S0-2
simultaneously. The resulting parameter estimates from the joint fit are
consistent with the case we report to within 1-$\sigma$. In Appendix E, we
show that including the NIRC2 astrometry in addition to the OSIRIS data
produces compatible results within the combined uncertainties.

Eccentricity | 0.34 $\pm$ 0.05
---|---
Period | 165 $\pm$ 19 years
Epoch of Periapse Passage | 2036 $\pm$ 2
Semi-major Axis | 4800 $\pm$ 1100 AU.
Inclination | 58 $\pm$ 2∘
Angle of Ascending Node | 43 $\pm$ 1∘
Argument of Periapse | -76 $\pm$ 9∘
Table 4: Keplerian orbital parameters of the X7 tip, based on OSIRIS data
only. The listed numbers are median values and 68% confidence intervals.
Uncertainties are statistical only.

Figure 7: Orbital motion of the leading tip of X7. Top left: Orbital fit (blue
line, with 1-$\sigma$ error envelope) superimposed on the astrometric
measurements of Br-$\gamma$ emission (empty circles, obtained with OSIRIS).
Top right: evolution of the radial velocity of the tip of X7, illustrated with
a sub-sample of one tip spectrum per year. The blue-shifted Br-$\gamma$
emission line is fitted with a Gaussian profile (red curve) to extract the
tip’s radial velocity. Bottom: astrometry (RA and Dec are reported as offsets
from Sgr A* with positive offsets Westward) and radial velocity fit for the
leading tip of X7. Measurements and their uncertainties (in black) are
compared to the resulting orbit model (with 1-$\sigma$ error envelopes in
light blue). All data points are consistent with the orbit model to within
2-sigma.

We find that X7’s tip is moving toward us, in front of the plane of the sky
containing Sgr A*, and orbiting Sgr A* with a period of nearly 200 years. It
is currently at a distance of $\sim$4000 AU from the SMBH and will reach its
closest point ($\sim$3200 AU) just before the year 2040.

###  4.3 Association with nearby objects

In Figure 8, we compare X7’s proper motion and shape evolution to the
trajectories of nearby objects, in order to investigate any possible
association with X7.

Figure 8:  X7 is not associated with any of the nearby, detectable stellar
sources that have crossed its path. The top panel shows contours of
Br-$\gamma$ emission over-plotted onto maps of stellar continuum emission for
all epochs. In this view, S0-73 and S0-30 show line-of-sight crossings with
X7. However, the proper motions of both of these stars have different
directions than that of X7, making them unlikely sources of the X7 gas
filament. The bottom left panel shows the proper motion measurements of the
tip of X7, contours of the whole feature (obtained from NIRC2-Lp for 2003,
2012 and 2020), and the proper motions of nearby stellar objects (stars as
triangles and the G object G5 as squares (Do et al., 2019; Ciurlo et al.,
2020)). The proper motion measurements of the tip have much larger
uncertainties than those of the stars because of the extended nature of X7.
The bottom right panel shows the modulo of the z position of X7 and S0-73,
according to their orbital models (one sigma uncertainties are shown) together
with S0-73 z position inferred from our acceleration measurement. It is
evident from the 3D orbits that S0-73 is not coincident with X7.

We find that S0-73 (S50 in Peißker et al. 2021), previously suggested to be
associated with X7 (Mužić et al., 2010; Peißker et al., 2021), is not
associated with X7. S0-73 does indeed overlap with X7 along the line of sight
in early observations, but appears to move towards the end of the tail and
lags behind the northern motion of X7 in recent years. X7’s motion and ridge
inclination are both at a significantly different position angle (to the
Northeast) compared to the proper motion of S0-73 (to the North-Northwest). To
confirm that the two sources do not only diverge on the plane of the sky, but
also have not been coincident in three-dimensional space, we fit a polynomial
to S0-73’s astrometry (reduced $\chi^{2}$ of 1.17). We find an 3-dimensional
radial acceleration of 1.35${}^{+0.17}_{-0.18}$ AU/yr2 and no significant
tangential acceleration (0.487${}^{+1.685}_{-1.687}$ arcsec/yr2). We also fit
a three-dimensional orbit to S0-73 astrometry (the faintness of S0-73 prevents
us from extracting its spectrum and measuring its radial velocity). For the
orbital fit, we adopt the same methodology as for X7 (Section 4.2): we fix the
black hole parameters and use an observable-based prior (but our choice of
prior does not impact our final conclusions, as demonstrated in Figure 8). We
find that the z position of S0-73 inferred from polynomial and the orbital fit
are compatible with each other and both constraints exclude S0-73 as being
directly connected to, or responsible for, the shape and motion of X7 (Figure
8, bottom-right panel).

S0-30 and S0-63 are also somewhat coincident with the ridge of X7 in some
epochs, but also are unlikely sources or associates of X7 since they show
different directions of motion and are not well aligned for the entire period
of observation.

G5 (Ciurlo et al., 2020) overlaps with X7 in the most recent observations, but
the two sources are completely unrelated since: 1) G5 is red-shifted (at +350
km/sec) while X7 is blue-shifted (at -600 km/sec) and 2) the two objects have
completely different trajectories. As we describe in detail in Appendix A, the
Br-$\gamma$ emission-line images show additional fainter structure, at least
partially co-moving with X7, that might be associated with X7 (albeit
difficult to trace systematically). This too is completely unrelated to G5,
contrary to what has been suggested by Peißker et al. (2021), for the same
reason stated above.

The area of sky that covers the central arcsecond near Sgr A* is extremely
crowded, with $\sim$30-50 detectable stars per arcsec2. Therefore X7, an
extended feature 0.3” in length with proper motion greater than 0.4” across
the plane of the sky over a nearly 20 year period during which it has been
observed, is very likely to have temporarily coincided on the plane of the sky
with several objects at various times.

However, there is one object that has an orbit and emission characteristics
(Lp, Br$\gamma$ and [Fe III]) that are remarkably similar to that of X7: the
dust-enshrouded object G3. Although G3’s proper motion does not coincide with
any portion of the ridge of X7 during the 20 years of our observations, its
orbit (Ciurlo et al., 2020) is strikingly similar to that of X7’s tip (Figure
9). This correspondence raises the interesting possibility that X7 and G3 are
dynamically linked, as we discuss in Section 6.2.1.

Additionally, we find that X7 orbit is not oriented in the same plane and
direction of clock-wise stellar disk (Paumard et al., 2006) nor other stellar
features in the region (von Fellenberg et al., 2022).

Figure 9:  Orbit comparison of X7 and G3. X7 (purple curve) and G3 (blue
curve) move in similar ways on the plane of the sky and have similar orbits.
We find that X7’s period, inclination, angle of ascending node and argument of
the periapse (respectively 165 years, 58∘, 43∘and -76∘) are similar to those
obtained in Ciurlo et al. (2020) for G3 (respectively 156 years, 52∘, 55∘and
-99 deg). The eccentricities are modest for X7 (0.34) and low for G3 (0.11).
Additionally, both objects are in the same phase of the orbits and are both
blueshifted (with a difference in radial velocity of 100 km/s in 2006).

###  4.4 Brightness variability

We find that, in both Br-$\gamma$ and Lp, the surface brightness remains
unchanged during our monitoring period, within an uncertainty of $\sim$35$\%$
for Br-$\gamma$ and $\sim$15$\%$ for Lp, with most of the uncertainty due to
AO performance variations.

This constant surface brightness in our 20 years of monitoring is somewhat
surprising given the substantial stretching that X7 has undergone. One might
expect the substantial stretching of X7 to be accompanied by a progressive
dimming of its surface brightness, even when one accounts for the secularly
changing projection of the tail of X7 on the plane of the sky during its
orbital evolution (see Section 5). Possible reasons for the constancy of the
surface brightnesses are discussed further in Appendix F.

###  4.5 Mass

The observed total Br-$\gamma$ line flux can be used to derive the density and
mass of X7 (we assume that the gas emission is optically thin.). In 2017, we
find a total flux of 3.68$\times$10-16 ergs s-1 cm-2 which, after correction
for extinction (Fritz et al., 2011), corresponds to $F_{\lambda}=3.55\times
10^{-15}$ ergs s-1 cm-2. The corresponding volume emissivity can then be
calculated as:

$\epsilon=\frac{F_{\lambda}\cdot 4\pi R_{0}^{2}}{V},$ (1)

where $R_{0}$ is the distance to the Galactic Center (Section 4.2) and $V$ is
the emitting volume. In 2017, the length of X7 was $\sim$0.36”, or 2891 AU.
The width of X7 is unresolved in the 2017 OSIRIS data with the 35 mas pixel
scale (measured width = 2.6$\pm$0.4 pixels), but we estimate the width of the
X7 ridge by appealing to the 2020 observation that used the 20 mas pixels.
There, we find a width of 68 mas for X7 which, corrected by the resolution
(the FWHM of the star S0-2, 50 mas), corresponds to an intrinsic width 48 mas,
or 390 AU. Assuming a cylindrical emitting volume, we find
$\epsilon\simeq$9.26$\times 10^{-18}$ ergs s-1 cm-3. To estimate the
corresponding density, we use the tabulations of Storey & Hummer (1995) for
emissivity as a function of density and temperature. For the temperature, we
adopt 7000 K, the typical gas temperature for Sgr A West derived by Roberts &
Goss (1993) from their radio recombination line data. The emissivity then
yields a hydrogen number density of $\sim$4.3$\times$104 cm-3. At this
density, the total hydrogen mass of X7 is 2.2$\times$1029 gm. Correcting for
an assumed 25$\%$ helium abundance by mass, this corresponds to $\sim$50 Earth
masses, or $\sim$3 Neptune masses. Given the assumptions made this estimates
is good to within about 30$\%$–50$\%$, but we underline that the order of
magnitude is what is relevant and it indicates a planetary mass rather than a
stellar mass.

##  5 Modeling the tidal evolution

We can gain insight on how X7 is expected to behave purely under the influence
of the gravity of the central black hole through a simple parsimonious
model222This model is similar to the one originally used in Gillessen et al.
(2012) for G2 under the assumption that G2 is a pure gas cloud, except that
our initial conditions have the points distributed along a line with a linear
velocity gradient, whereas the points in the Gillessen et al. model are
initially distributed in a spherically Gaussian fashion in phase space.

In this setup, we model X7 as a set of non-interacting test particles having
initial conditions provided by our observations. We assume that the ridge of
X7 is initially linear, and use its observed length and position angle in 2003
(the earliest epoch available with a good FWHM resolution), along with our
determined orbit of X7’s tip (Section 4.2), to calculate the subsequent
3-dimensional vector positions of 10 points equally spaced along X7’s length.
The orbit fit for the tip provides the tip’s initial 3-dimensional velocity
and, in order to assign initial velocities to the 10 points along X7, we
assume that the initial velocity gradient is directed along the ridge of X7,
and that it increases linearly from tip to tail. This assumption is consistent
with our observation of a radial velocity gradient along the tail of X7 in the
earliest epochs. Moreover, if X7 was created at some point in time by gas
being impulsively ejected in a particular direction, then it is natural to
expect that the points furthest from the tip would have the highest velocity.
In this setup, there are only two free parameters for the determination of the
position and velocity vectors in our model: the initial angle of the ridge
with respect to the line of sight, ($\theta_{z}$ in degrees), and the
coefficient of the linear increase ($m$ in AU/years/dx, where $dx$ is the
initial distance between points 175 AU) of the velocity along X7.

Given these prescriptions, we calculate the state vectors (3-dimensional
position and velocity) of 10 non-interacting points along X7 in 2003. Starting
from these state vectors we calculate, for each point along X7, the
corresponding orbital parameters (Grould et al., 2017). Given the orbital
parameters, we can then predict the position and velocity vectors of each
point along X7 at any given moment in time using purely Keplerian orbits. Our
method for assigning the initial state vectors of the points along X7’s ridge
leads to some of the points potentially following unbound orbits. Therefore,
we ensure that our orbital determinations can encompass hyperbolic orbits.

Provided with this model, we can vary our two free parameters ($\theta_{z}$
and $m$) to reproduce several of the observed properties of X7: the constant
position angle on the plane of the sky, the absence of an obvious curvature of
the ridge, the lengthening of the ridge with time and the observed evolution
of radial velocities along the ridge. These features are illustrated in Figure
6. Here, we characterize the evolution in radial velocities by extracting a
spectrum at each of the 10 reference points along X7 in every epoch. These
measured radial velocities approximately map to the modeled ones. There could
be some mismatch between the two because 1) in the model we start with 10
points equally spaced in 3 dimensions whereas our observations are from points
equally spaced in the plane of the sky, 2) in the model 10 points equally
spaced don’t necessarily maintain equal spacing and 3) given the extended and
evolving nature of X7 and the absence of resolved internal structure, there is
no assurance that any given point each point traces exactly the same gas from
epoch to epoch.

We have run the model on a grid of parameter values: angles between 0 and 90
degrees and $m$ between 1 and 10 AU/years/dx. The combination of free
parameters that most closely reproduces the observed motion of X7, its
orientation, its length on the plane of the sky, as well as its radial
velocity is $\theta_{z}$=20 degrees and $m$=0.02 AU/year/dx. The best model is
shown in Figure 10 along with our observations.

Figure 10: Model results best matching the dynamical and morphological
evolution of X7. In panels each point along X7 (modeled individually) is
identified by a different color (the tip is shown in black). $Left$: the
modeled orbital motion of X7 (sampled at 5 epochs during our observing period)
reproduce well the observed inclination and lengthening (all measurements are
represented, illustrated by gray, thick lines). The gray thin line shows the
orbital fit for the tip and the open circles the initial positions fed to the
model. $Right:$ the radial velocity structure and evolution is well reproduced
as well. The solid lines represent the model velocities (the colors match
those of the points in the left panel) and the dashed lines depict our
measurements of the radial velocities along the ridge of X7. The thick black
line represent the fit for the tip.

Even though this model is simple it illustrates quite well that gravity alone
can reproduce many of the observed properties quite well: (1) the position
angle of X7 on the plane of the sky is approximately constant, (2) the model
predicts a crossover of the radial velocities of the tail and tip, as
observed, (3) X7 undergoes tidal stretching by about the observed amount as it
approaches its orbital periapse near Sgr A* and (4) the ridge of X7 remains
linear and un-curved. This model also predicts that X7 was even more compact
in the years prior to our first observation in 2002, as we expect.

While this simplistic model is based on gravity alone, several other forces
can be at play in shaping X7 (magnetic drag, the drag caused by motion through
the accretion flow onto Sgr A*, local winds, etc.). The constraints on these
models are discussed in Section 6.3.

##  6 Discussion

What can be inferred about the nature of X7 depends fundamentally on whether
the observed gas and dust that compose it are associated with an object as
massive as a star. We have shown that X7 does not have a detectable stellar
counterpart (Section 4.3). Its observable manifestation consists entirely of
unbound gas and dust in orbit around the SMBH. For the past 20 years, the size
of X7 has far exceeded the tidal radius of any conceivable stellar object that
would not be easily detected. The 2002 projected distance of X7 from the SMBH
was $\sim 0.7^{\prime\prime}$ (Fig. 4). At this projected distance, the tidal
radius of an object of mass 1 M⊙ would be greater than 30 AU ($>$62 AU for a
10 M⊙ object). The tidal radius would be even larger at earlier times. Given
such required radii, it is unlikely that the gas and dust constituting X7
could consist of material that has been tidally removed from a stellar object
that has remained undetectable. Therefore, while we have previously
interpreted the G objects as being distended, dust-enshrouded stars having
outer radii that can, during their periapse passages near the SMBH, exceed
their tidal radii (Ciurlo et al. 2020, but see Gillessen et al. 2019 for
alternative scenarios), there is no evidence that the same is true for X7.

In the following, we first examine the constraints on the past and future
lifetime of X7, and then consider various possibilities for how it might have
formed.

###  6.1 When could X7 have formed?

If X7 consists only of gas and dust, then it is inevitable that tidal forces
will cause it to continue to stretch and ultimately dissipate as it passes
through periapse on a timescale of 15 to 20 years. Even if there is a massive,
undetected object within X7 that is somehow the source of the gas and dust
that we observe as X7, then as argued above, X7 cannot be bound to that
massive unseen object. Consequently, the gas and dust that constitute X7 will
dissipate in any case, and the feature that we now observe as X7 will not
survive periapse passage, even if it is associated with a putative massive
unseen object that does survive. The dissipated material might well be
observable for a relatively brief interval after the moment of periapse
passage of the tip, because different segments of the tail will reach periapse
at progressively later times.

The orbit that we have derived for the tip of X7 sets a limit on when X7 could
have formed. Since X7 cannot survive a passage through its orbital periapse,
its age as an unbound gas/dust feature is less than an orbital time, about 200
years. It is clearly a transient structure. Furthermore, the fact that X7 has
become increasingly elongated, by a factor of $\sim$2 since our first
observations in 2002, suggests that it was originally more compact. Indeed,
extrapolating backward in time from 2003, we do find that the model ridge
becomes more compact, but the extrapolation becomes unreliable beyond a few
years because our assumption of an initial linear velocity gradient along a
linear ridge in 2003 leads to possibly unrealistic non-linearities in the
velocity field at earlier times. Thus, at present, we are not able to derive a
precise date for the formation of X7.

###  6.2 How could X7 have formed?

####  6.2.1 Collisional Formation

The constraints on the age of X7 lead us to consider that X7 could have been
created by an impulsive event in the recent past. A promising possibility for
impulsively producing an unbound stream of gas is direct stellar collisions.
More generally, a collision responsible for the relatively small mass of X7
could have occurred not only between stars (e.g., Dale & Davies, 2006; Davies
et al., 2011; Rose et al., 2020), but also between stars and stellar remnants
(e.g., Rose et al., 2022), or between stars and massive planets or brown
dwarfs. Despite the large stellar density in the central light-year of the
Galaxy, direct stellar collisions are relatively rare except in two
circumstances: 1) the merger of a binary pair of stars in the presence of the
SMBH as a result of the eccentric Kozai-Lidov (EKL) effect (Naoz, 2016;
Stephan et al., 2019) and 2) the collision of a normal star or a compact
stellar remnant with a red giant.

#####  6.2.1.1 Gas ejection in an EKL-induced stellar merger

The EKL mechanism has been invoked to account for the G objects as products of
the induced merger of stars in binary systems. (Phifer et al., 2013; Witzel et
al., 2014; Prodan et al., 2015; Stephan et al., 2016; Witzel et al., 2017;
Ciurlo et al., 2020). However, there are major differences between X7 and the
G objects that lead us to conclude that X7 is not such a merged stellar
system:

  * •

G objects are observed to be much more compact (mostly point-like), in
contrast to the extended, roughly uniform-brightness, linear morphology of X7.
The spatial extents of the G objects, when they can be resolved, are also
smaller and fainter than the extended ridge of X7.

  * •

Extended material that has presumably been tidally removed from G objects is
apparently produced at or near their orbital periapse, whereas X7 has had a
very extended, linear morphology for the entire time that it has been
observed, and all of that long before its projected periapse passage in
$\sim$2036.

  * •

The material removed from G objects is spread out along their orbits (Witzel
et al., 2017; Gillessen et al., 2019), as expected for a tidal removal
process, in contrast to X7, for which the ridge of emission is oriented at a
large angle with respect to the orbital trajectory.

We also note that the star-centered model for G objects is not universally
accepted. The original notion that they are composed only of gas and dust
continues to be investigated (Gillessen et al., 2012, 2019), but the profound
structural and dynamical differences between X7 and the G objects mentioned
here indicate to us that different phenomena are at play in the two
circumstances.

When an EKL-induced direct stellar encounter takes place in a binary, it
happens as the eccentricity approaches unity, and because the encounter takes
place very near periapse, the orbital speeds are maximized (e.g., Naoz &
Fabrycky, 2014). As a consequence, such collisional encounters are likely to
unbind a considerable quantity of material even in the likely case in which
the initial encounter is a grazing collision (e.g., Salas et al., 2019). That
leads to two considerations relevant to X7: first, the two objects involved in
the collisional encounter (and ultimate merger) do not necessarily follow the
same subsequent orbit as the ejected, unbound gas, so a pure gas/dust feature
can be produced that is not physically co-located with the star or stars that
produced it (although their past orbits would have an intersection point).
Second, the gas ejected in such a collision would likely take the form of a
quasi-linear stream of unbound material. Note that such a dynamical situation
is consistent with the assumptions upon which the simple dynamical model
presented in section 5 is based. Depending on the binary mass ratio and the
stellar sizes, the amount of material ejected in an EKL-induced collisional
encounter, and the degree of collimation of the ejecta, can presumably be
quite variable, but this has not yet been investigated in detail.

In light of this EKL-induced collision scenario for producing X7, our finding
that G3 has a similar orbit to that of X7 is particularly interesting (Section
4.3). X7 and G3 can be regarded as a candidate pairing resulting from a recent
EKL-induced merger, with the resulting merger product being G3 and the ejecta
from the violent collisional encounter being X7.

Assuming that X7 was ejected from G3, one can ask whether the similarity of
their orbital parameters is plausible, given that there is no constraint on
the direction of the ejection (there need be no relationship between the
orientation of the pre-merger binary orbit and that of the orbit of the binary
around the black hole). The similarity of the semi-major axes of G3 and X7 can
be accommodated with a wide range of ejection velocities. Following the
equations outlined in Lu & Naoz (2019), we find that X7 could have been
ejected with a wide range of velocities, with an upper limit of two times the
Keplerian velocity of G3 about Sgr A* and the lower limit being at least the
escape velocity from G3. This wide range of allowable ejection velocities
yields a similarly wide range of differential orbital orientations between G3
and X7 (defined as the angle between the ejection velocity and G2 velocity Lu
& Naoz, 2019), for X7 to have been ejected in the merger process. The details
of the parameter space are beyond the scope of this paper, but we note that a
similarly wide range of the parameter space seems to exist for yielding an
eccentricity for X7 that is slightly higher than that of G3 (i.e., by $\sim
0.1$).

#####  6.2.1.2 Collisions of red giants with field objects

For ordinary collisions between isolated field objects, the most likely
targets would be red giants because of their large cross-section. Even a
Jupiter-mass object flying through the atmosphere of a red giant could unbind
a mass comparable to that of X7, depending on the relative velocity of the
collision partners (e.g., Sahai et al., 2003; Salas et al., 2019). The red
giant-compact object collision scenario has been investigated (Bailey &
Davies, 1999; Dale et al., 2009; Davies et al., 2011), and offers an
interesting possibility as a mechanism for producing X7. Because of the high
stellar density in the Galactic Center, red giants within 0.1 pc of the SMBH
can be expected to undergo multiple direct collisions with stars and stellar
remnants during their time on the red giant branch (Dale et al., 2009). At the
typical relative velocities found in the the central 0.1 pc of the GC (several
hundred km/s), main-sequence stars and stellar remnants will pass through the
atmosphere of the red giant, unbinding some quantity of gas and giving a
velocity impulse to the red giant core. If the collision partner is a main-
sequence star (less than a few solar masses, or a white dwarf or neutron
star), then the velocity impulse given to the stellar core is relatively
small, and most of the atmosphere remains bound to the core (Bailey & Davies,
1999). A more dramatic encounter occurs if the impactor is a $\sim 10$ M⊙
black hole. This is less frequent than collisions with main-sequence stars
(Dale et al., 2009), even if black hole remnants have been strongly
concentrated toward the center by dynamical mass segregation (Morris, 1993;
Miralda-Escudé & Gould, 2000; Freitag et al., 2006; Antonini, 2014; Rose et
al., 2022). In black hole-red giant collisions, almost all of the red giant
envelope could be removed and the core would receive a much larger kick
(Davies et al., 2011).

In any collision with a red giant, the amount of gas released depends on the
masses of the impactor and the red giant, their relative velocity, the impact
parameter, and the evolutionary stage of the giant. The relatively small
amount of mass that we infer for X7 ($\sim$50 Earth masses) can be attributed
to a collision with either kind of partner, but in the black hole case, the
collision parameters would be constrained to some combination of a relatively
large impact parameter and a relatively high relative velocity. Otherwise the
resulting mass of the unbound gas would be much larger.

Red giant collisions of the sort that might produce X7 would leave the red
giant in a distended and dynamically agitated state that would only settle
down on a Kelvin-Helmholtz timescale, so such stars could thereafter appear as
G objects for a timescale much longer than the observable lifetime of the
unbound ejecta. The production of an X7-like feature in this manner could
therefore be accompanied by the production of a G object. Consequently, we
again have a situation in which the similar orbits of X7 and G3 could
potentially be understood in terms of a single dynamical encounter.

However, we note that collisions between red giants and main-sequence stars
probably happen only about once every 105 yr in a flat stellar core such as
that found at the Galactic center (Rose et al., 2020, 2022), not frequently
enough for the recent production of X7 in this manner to be very likely.

####  6.2.2 Other Possible Formation Mechanisms

#####  6.2.2.1 Infalling gas cloud

The small semi-major axis (5000 AU) and modest eccentricity ($0.34$) of our
calculated orbit imply that X7 could not have been produced in a
straightforward manner from a distant gas reservoir. The closest reservoir
could be the broad northern arm gas stream of Sgr A West, lying to the south
of the X7 orbit. The northern edge of the northern arm is $\sim 10^{4}$ AU
from the nearest point of X7’s past orbital path (Fig. 11), so there is no
obvious intersection point. Furthermore, while the northern arm is strongly
blue-shifted at the point where it wraps around Sgr A* to the south of X7, its
radial velocity is far less extreme than that of X7 (up to -300 km/s compared
to -700 km/s for X7).

A number of small gas and dust clouds are located within a few arcseconds of
Sgr A* (see Figure 1). However, besides the much lower-mass G objects, no
gaseous structures are known to be present in the volume occupied by the orbit
of X7, although some might be found at larger radii. There are a few dust
features seen in projection near X7, but their velocity structure and
morphological evolution are inconsistent with being as close to Sgr A* as any
point in the orbit of X7.

Collisions of orbiting gas clouds are one way to produce low-angular-momentum
parcels of gas that can fall inward in the aftermath of the collision, but
such events are more likely to produce dynamically complex systems on
eccentric orbits rather than the isolated, relatively compact gas blob on a
mildly eccentric orbit that would have been the initial state of X7.

It remains possible that X7 is a piece of gaseous ”space-junk”, detached from
a local larger gas structure. Collisions between such structures and the
strong stellar winds from the WR stars in the region might create blobs of gas
with low angular momenta, but again, the expected eccentricities of such blobs
would likely be large, given the depth to which they would have to fall in the
black hole’s gravitational potential well.

#####  6.2.2.2 Colliding winds

One possible mechanism that has been suggested for producing the G objects,
based on the assumption that they are purely gaseous features, is the
formation of dense clumps in colliding stellar winds (e.g., Burkert et al.,
2012; Calderón et al., 2016). A similar mechanism might be considered for
producing X7. Indeed, Cuadra et al. (2006) had earlier argued that colliding
winds from massive stars can form cold clumps and filaments as they undergo
thermal instability after being shocked and compressed. Such clumps could have
a filamentary morphology with a velocity gradient along them (Pfuhl et al.,
2015; Plewa et al., 2017), which could possibly describe the initial stage of
X7. However, the requisite physical conditions for clump formation by this
process occur only rarely in the GC (Calderón et al., 2016), and when they are
produced, they are subject to quick evaporation by thermal conduction in the
hot medium of the GC (Calderón et al., 2018). Furthermore, a detailed
computational study by Calderón et al. (2020a) has shown that the maximum
masses of clumps formed in this way are too small to account for the G
objects, and that conclusion would hold even more strongly for X7. We
therefore conclude that the formation of X7 in stellar wind shocks is
unlikely.

###  6.3 Alternatives to determine X7’s tail orientation

The pure-gravity model presented in Section 5 reproduces well most of the
observed dynamical and morphological characteristics of X7. In the following,
we discuss several additional phenomena that could conceivably play a role in
producing the observed orientation of the tail. In particular, all scenarios
are constrained by the constant position angle of the tail, as well as the
fact that the tail is not aligned with the orbital direction of the tip’s
motion (Figure 11). However, we conclude from the success of our pure-gravity
model that the effect of these phenomena are likely to be secondary or
negligible.

Figure 11: Projected orbit of the X7 tip (white) overlaid on a 2020 gray-scale
Lp image. Contours show the X7 Lp emission at three different epochs,
illustrating that X7 is not elongating along its orbital trajectory. X7 orbit
is compact and does not overlap with nearby large-scale extended features,
such as the mini-spiral, whose Northern Arm is visible at lower-left of the
image.

####  6.3.1 A spherical wind from Sgr A*

Figure 12: The X7 tail does not point to Sgr A*. Red lines show the expected
tail orientation on the sky if it always points toward Sgr A* and is in the
plane of the feature’s orbit, while the thick gray lines show the observed
constant orientation.

X7 in early observations is roughly elongated toward Sgr A*, while the orbital
direction of the tip and the proper motion of X7’s overall structure are
oriented in a different direction. In earlier epochs X7’s elongation and
flared appearance were deemed consistent with the hypothesis that the
morphology of X7 results from a wind arising at or near Sgr A* (Mužić et al.,
2010). However, if that were the case, the tail would always lie in the plane
of the orbit and point toward Sgr A* in three dimensions. With our inferred
orbit of X7’s tip we can project the expected tail inclination onto the plane
of the sky on the assumption that the tail always points to Sgr A*. The result
is illustrated in Figure 12 along with the observed orientation of X7’s tail.
Given X7’s orbit, if it were always pointing toward Sgr A*, we would expect to
observe a variation in the tail orientation on the plane of the sky of greater
than 30 degrees during the course of our observations. Since the tail
orientation does not change by anywhere near that amount, we exclude a
spherical wind from Sgr A* as the cause of the orientation of X7’s tail.

####  6.3.2 Stellar winds

Another possibility is that X7 is shaped by the combined winds of the Wolf-
Rayet stars in the region. Recently Calderón et al. (2020b) and Ressler et al.
(2020) proposed two independent versions of such models. In both publications
the authors take into account the known motions and mass-loss characteristics
of the Wolf-Rayet stars to show how their winds evolve and interact, producing
3-dimensional maps of the wind vectors in the central parsec.

We use the orbit of X7’s tip to determine its line-of-sight distance relative
to Sgr A*. Given the 3-dimensional position and shape evolution implied by our
model, we can compare X7’s orientation to the modelled local wind direction at
X7’s location.

In the case of Calderón et al. (2020b) the direction of the winds at the
location of X7 is uncorrelated with the shape of X7: the winds are blowing
toward the East and therefore are oriented almost 45 degrees away from the sky
projection of X7’s tail (Calderon, private communication).

Ressler et al. (2020) additionally take into account the effect of the
strength and geometry of the magnetic field on the wind direction. Their
results indicate that, for stronger magnetic fields the direction of the
combined winds is toward the southwest (Ressler, personal communication),
consistent with X7’s shape. However, according to their model, over roughly a
decade during the period of our observations the wind turned significantly
(few tens of degrees) north whereas the X7 tail did not. Therefore, even
choosing a magnetic field strength that gives results that best match our
observations, we cannot reproduce the evolution of X7’s orientation.

Moreover, for both models, there is still substantial uncertainty in the wind
direction, since it depends strongly on the assumed parameters (magnetic field
strength, geometry, stellar mass loss rates and velocities). For example
Ressler et al. (2020) assume that the magnetic field is perpendicular to the
Galactic plane, which is justifiable at much larger scales, but in the
neighborhood of X7, the field is likely distorted by winds and by the Sgr A*
accretion flow. We conclude that there is no obvious correlation between the
orientation of X7 and the local wind direction, but the two very different
estimations of the local wind direction obtained in two independent
investigations illustrate the considerable uncertainty that presently exists.
Therefore, we cannot at present rule out the possibility that stellar winds
contribute to the shaping of X7.

####  6.3.3 Magnetic field

A sufficiently strong magnetic field could also be a direct cause of X7’s
morphology and orientation, as is the case for some other filamentary
structures in the Galactic center region. Roche et al. (2018) showed the
magnetic field direction averaged over the line of sight and projected onto
the plane of the sky using a relatively high-resolution polarization map of
the 12.5 $\mu$m dust emission in much of the Galaxy’s inner parsec. According
to this map, X7’s tail lies roughly perpendicular to the magnetic field lines.
Consequently, it appears unlikely that the magnetic field plays a role in
orienting X7. However, because the polarization measurement results from an
integral over all contributions along the line of sight, the possibility that
the magnetic field direction at the 3D location of X7 is aligned with X7
cannot be completely excluded.

##  7 Conclusions

Using two decades of imaging and spectroscopic data gathered with the Keck
Observatory, we analyze the morphological and dynamical evolution of the
extended, linear dust and gas structure, X7, presently located $\sim$0.5”
($\sim$4000 AU) from the Galactic black hole. We observe several properties of
this unique feature:

  * •

X7 exhibits relatively rapid proper motion, comparable to that typical of the
S-stars orbiting closely around the Galactic black hole, yet its orientation
remains remarkably constant even as it has moved through a substantial portion
of its orbit;

  * •

the internal spatio-velocity structure of X7 is changing with time: the tip
has decelerated (by approximately 200 km/sec from 2006 to 2021) whereas the
radial velocity of the tail remains relatively unchanged;

  * •

The 3D motion of X7’s leading tip is consistent with a tightly bound orbit
around Sgr A* having a period of only $\sim 200$ years;

  * •

the shape of X7 has changed with time, morphing from a bow-shock-like
structure to a more elongated, linear structure as it approaches the black
hole;

  * •

X7 has lengthened considerably as it has approached the central black hole,
but there is no evidence that this elongation has been accompanied by a
corresponding significant change in surface brightness with time;

  * •

higher-resolution data obtained in 2020 show that X7 might be fragmenting;

  * •

The proper motion of X7 is quite different from that of all detected stars in
its immediate environment, indicating that X7 is unlikely to be associated
with any of the known stellar sources that have coincided with it along the
line of sight during the period of our observations.

From these observations we draw the following conclusions.

  * •

The constant position angle of X7’s linear tail rules out shaping by a
spherical wind from Sgr A*. The observed orientation also appears to be
inconsistent with the local direction of the collective winds from nearby
Wolf-Rayet stars as well as with the projected magnetic field orientation in
this region given the current models and observations.

  * •

The rapidly decreasing radial velocity of X7’s tip is strong evidence of the
dominant gravitational influence of the SMBH. Indeed, we can reproduce the
observed properties of X7 (evolution of the radial velocity and its gradient
along the ridge, and the elongation and constant position angle of the ridge
on the plane of the sky) with a simple test-particle model in which the
particles respond only to the gravitational field of the black hole. Other
phenomena, including strong stellar winds, the accretion flow onto the SMBH,
and a potentially strong local magnetic field, therefore appear to have, at
most, a minor secondary effect on the dynamical evolution of X7.

While we are not able to definitively determine the origin of X7, we have
explored and emphasized the prospect that X7 was formed by an event such as a
stellar merger or a collision with a stellar or substellar object, or even
with a stellar remnant. In this light we note that the dust-enshrouded stellar
object, G3, has an orbit that is remarkably similar to that of X7, eliciting
the possibility that X7 could be the ejecta that resulted from the EKL-induced
binary merger that created G3. Further assessment of this intriguing scenario
will require both improved orbital determinations and detailed dynamical
modelling. Alternatively, we cannot rule out the possibility that X7 was
stripped or shed from one of the larger-scale interstellar structures in the
region, although we cannot trace its dynamics in a straightforward way to
those of nearby gas structures.

Regardless of its origin, the X7 wisp of gas and dust will continue to undergo
even more dramatic evolution in the next 10 or 20 years as it swings through
its closest approach to the black hole, becomes even more tidally stretched,
gets fragmented by instabilities, and interacts with the accretion flow,
potentially triggering enhanced accretion activity. Continued monitoring of X7
will allow us to closely witness these extreme changes, ending with the
ultimate tidal dissipation of the remnants of this intriguing structure.

The authors wish to acknowledge S. M. Ressler, D. Calderon and S. Rose for the
helpful insights provided by their theoretical models and A. Huddleston for
assisting with photometrical measurements. Support for this work was provided
by NSF AAG grant AST-1412615, Jim and Lori Keir, the W. M. Keck Observatory
Keck Visiting Scholar program, the Gordon and Betty Moore Foundation, the
Heising-Simons Foundation, and Howard and Astrid Preston. A. M. G.
acknowledges support from her Lauren B. Leichtman and Arthur E. Levine Endowed
Astronomy Chair. R. S. acknowledges financial support from the State Agency
for Research of the Spanish MCIU through the ”Center of Excellence Severo
Ochoa” award for the Istituto de Astrofísica de Andalucía (SEV-2017-0709) and
financial support from national project PGC2018-095049-B- C21 (MCIU/AEI/FEDER,
UE). S.N. acknowledges the partial support from NASA ATP 80NSSC20K0505, NSF
through grant No. 2206428, and thanks Howard and Astrid Preston for their
generous support. The W. M. Keck Observatory is operated as a scientific
partnership among the California Institute of Technology, the University of
California, and the National Aeronautics and Space Administration. The
Observatory was made possible by the generous financial support of the W. M.
Keck Foundation. The authors wish to recognize and acknowledge the very
significant cultural role and reverence that the summit of Maunakea has always
had within the indigenous Hawaiian community. We are most fortunate to have
the opportunity to conduct observations from this mountain.

##  Appendix A Extended structure

Figure 13: Illustration of X7’s complex morphology using OSIRIS Br-$\gamma$
emission as measured in 2013. The color scale illustrates the velocity
(km/sec), while the contours trace the intensity. The map is constructed using
a relatively narrow range of velocities between -540 and -730 km/sec. The X7
ridge (tip and tail) consists of the highest blue-shifted velocity gas.
Additionally, the X7 complex includes an arc of material to the northeast
labeled X7.1 and a clump of gas off of the tail to the south, labeled X7.2.
All of these blue-shifted Br-$\gamma$-emitting features are co-moving
northward. G4 is included in the slice because of its similar blueshifted
radial velocity but is unrelated to X7 as its proper motion is in a completely
different direction than that of X7 (Ciurlo et al., 2020). G5, which is also
unrelated to X7, is not included in this slice because of its redshifted
radial velocity.

Figure 13 shows a cut of the OSIRIS data around X7’s blueshifted Br-$\gamma$
emission. This cut includes G4, which is blueshifted at similar radial
velocities as its proper motion is in a completely different direction than
that of X7 (Ciurlo et al., 2020). The extended, lower-intensity gas emission
includes an arc-shaped feature to the Northwest of X7 which Peißker et al.
(2021) labeled as X7.1 and argued that it has a possible association with the
nearby compact G object, G5 (Ciurlo et al., 2020). However, our OSIRIS
integral field data indicate that G5 is red-shifted at +350 km/sec and X7.1 is
highly blue-shifted around -600 km/sec. Therefore G5 does not appear in the
slice and the two are clearly unrelated to each other. Moreover, X7.1 (Peißker
et al., 2021) seems to be moving in the same direction as the rest of X7
whereas G5 has a completely different trajectory, even though the two features
overlap in the most recent observations (see Figure 8, bottom-left panel).
Neither G5 or X7.1 are well detected in the NIRC2 Lp data.

The Br-$\gamma$ emission line map also reveals a knot-like feature to the
South of the X7 tail that we label X7.2. X7.2, like X7.1, has a proper motion
similar to that of X7 and is also similarly blue-shifted.

Even though X7.1 and X7.2 seem to be moving in the the same general direction
as X7, it is difficult to provide quantitative measurements consistently over
time, due to their extended nature and evolving morphology. Therefore, these
features are likely associated with X7; they might have a common origin with
X7 or might be evidence of material that is separating from X7. However, we
cannot determine their dynamical history in the same way we can for X7 and
thus cannot raw definitive conclusions about their relationship to X7.

The early cometary appearance of X7 in 2002–2006 that led Mužić et al. (2010)
to interpret X7 as a bow-shock might be attributable to the relative placement
of these fainter features (or alternatively to the presence of nearby sources
in this crowded environment, for example S0-73).

##  Appendix B Astrometry

The two sets of astrometric measurements of the X7 tip agree to within
estimated errors (see Figure 14), however, we observe that the NIRC2 points
tend to be systematically shifted West by less than 1-sigma uncertainty during
roughly half of the monitoring period.

Figure 14: X7 astrometry as measured in OSIRIS (white points) and NIRC2 (black
points).

This difference might be due to physical differences between the gas and dust
emission of the tip, given that the dust emissivity and the Br-$\gamma$
emissivity have different dependencies on density and temperature and that the
dust and gas temperatures can be quite different in this high-ionization
environment. However, we can’t rule out a systematic error in the
measurements. Such error might originate in the very different nature of the
two datasets (see for example Figure 2, bottom right panel). NIRC2 data have a
relatively high signal-to-noise ratio and are over-sampled at the pixel scale
of 0.010”. In contrast, OSIRIS data have lower signal-to-noise ratio and they
are slightly under-sampled at the 0.035” platescale, with an inherent PSF of
$\sim$0.050” FWHM. We also note that, because of the extended nature of X7,
given one set of measurements made over time with a particular instrument,
there is no guarantee that the tip location always follows the same parcel of
orbiting material in both datasets. Given these limitations, in the main text
we opt for using only OSIRIS astrometry and radial velocity measurements for
orbit fitting, which is self-consistent. We investigate the influence of NIRC2
measurements on the orbit in Appendix E.

##  Appendix C Dust Temperature

Using the NIRC2 observations made in three filters (Kp, Lp and Ms at 2.1, 3.8,
and 4.5 $\mu$m respectively), we can constrain the spectral energy
distribution (SED) using photometric measurements of the tip in these three
bands. We use differential aperture photometry between X7’s tip and the star
GCIRS 16C (L-mag = 8.2), assuming the absolute magnitude of GCIRS 16C is the
same for both Lp and Ms bands (similar to Schödel et al. 2011). To do so, we
used the same circular aperture for both the stellar source and X7’s tip: 9
pixel aperture radius for Lp and 11 pixel aperture radius for Ms. In both
cases, the background level was subtracted using the DAOphot (Stetson, 1987)
algorithm over an annulus of inner radius 30 pixels and outer radius 39
pixels. The DAOphot algorithm is designed to deal with crowded regions and it
eliminates outliers. We estimate the uncertainties in the photometry from the
variances of the measurements when changing background annular size,
photometry aperture size and the centering aperture size. Since X7 is not
detected in the Kp band, we use as upper detection limit of $\sim$18 mag in Kp
(Do et al., 2013). We adopt the extinction values AKs= 2.22, ALp=1.07 and
AM=0.94 (Gillessen et al., 2012) to estimate the dust color temperature at the
tip. This procedure of obtaining the SED is similar to what was previously
done for G2 by Gillessen et al. (2012). We then fit a Planck function to the
SED, yielding a color temperature of $425\pm 50$ K (Figure 15).

Figure 15: SED of X7’s tip. Fluxes measured at Kp (upper limit), Lp, and Ms,
plotted with an absolute magnitude scale. The overlaid curve is a 425 K black
body profile, which fits the measurements to within 50 K.

The temperature is comparable but somewhat lower than what was measured for G2
(Gillessen et al., 2012), possibly due to X7 not having a stellar core that
heats the dust. The relatively high Br-$\gamma$ surface brightness observed
for X7 is comparable to that of the G objects (Gillessen et al., 2012; Ciurlo
et al., 2020).

Performing photometric measurements along the ridge of X7, to look for
variations or a gradient in dust temperature, is compromised by the occasional
passage of background/foreground stellar sources. However, the 3-color image
in Figure 1 does not show any gradient, therefore we expect the dust
temperature to be nearly constant along the extent of the feature.

##  Appendix D Orbital fit with NStarOrbits

The orbit model assumes Keplerian motion dominated by a central SMBH point
potential. In this model, seven black hole parameters describe the mass,
3-dimensional position, and 3-dimensional linear motion of the central
potential in a common reference frame, and six Keplerian orbital elements
parameterize the orbit: eccentricity, orbital period, epoch of closest
approach to the SMBH, inclination, angle of the ascending node, and the
argument of periapse (e.g. Grould et al., 2017). While other stars closer to
the SMBH have been shown to be consistent with a post-Newtonian General
Relativistic model (Do et al., 2019; Gravity Collaboration et al., 2019,
2020), the Keplerian approximation is sufficient here to constrain the orbit
of X7.

Because the orbital period of X7 is relatively long compared to the time
baseline of observations, X7 alone cannot robustly constrain the black hole
parameters. As such, we fix the central potential parameters using information
from S0-2 – the brightest short-period star in the Galactic Center for which
more than one full orbit has been observed with both astrometric and radial
velocity measurements (for example, see Do et al., 2019; Gravity Collaboration
et al., 2019, 2020). We tested several sets of black hole parameters: an
average of the latest estimates reported in the literature (Gravity
Collaboration et al. (2020) and Do et al. (2019)), as well as the values from
each of these references independently. We find that the orbit of X7 is robust
to slight changes in the central potential parameters, as the fitted orbit
parameters are consistent to within 1-$\sigma$ for all of the above cases. For
completeness, we also fitted X7 simultaneously with S0-2, and again find that
the results are consistent with all fits described above. The results
presented in Table 4 and Figure 7 represent the case in which the mass of, and
distance to, the black hole are fixed to the average of the literature
measurements (4.07$\times$106 M⊙ and 8.1 kpc, respectively).

To ensure an unbiased orbital solution, we adopt an observable-based prior – a
prior that has been shown to mitigate biases in estimated parameters when the
orbital period is much longer than the time baseline of observations, as is
the case for X7 (O’Neil et al., 2019). Generally, orbits that are fit within
the Bayesian framework use priors that are uniform in the orbit model
parameters. However, standard uniform priors have been shown to cause biases
in the estimated orbit parameters for low-phase-coverage orbits. The
observable-based prior is designed to mitigate biases in such cases by
enabling all measurements to be equally likely before observations (O’Neil et
al., 2019). In this case, despite the relatively low orbital phase coverage of
X7, the radial velocity data provide enough constraining power that the
results do not appear biased by low phase coverage. In other words, uniform
priors and observable-based priors produce consistent results. While our
choice of prior does not impact the results for X7, it does make a substantial
difference in the inferred orbit of S0-73 (for which there is no radial
velocity data). Since the orbits of X7 and S0-73 are compared in Section 4.3,
we report the values from the observable-based prior case for consistency.

##  Appendix E Orbit fit including NIRC2 data

Figure 16: Orbital parameters for different datasets: OSIRIS-only orbit in
blue, OSIRIS plus NIRC2 orbit in magenta, NIRC2-only in red. Note that the
NIRC2-only orbit does not have any RV information and provides poor
constraints on several parameters.

As shown in Figure 14, and described in Appendix B, NIRC2 and OSIRIS
astrometric measurement are compatible but they have a residual offset that
could be systematic or physical. In the main body of the paper we opt for a
conservative approach and only use OSIRIS measurements. In Figure 16, we
report the orbital parameter obtained including NIRC astrometric points as
well as a pure-astrometry, NIRC2-only orbit fit for comparison. Adding NIRC2
astrometry leads to better constrained orbital parameters but might introduce
biased results because of a residual offset between the datasets. Fitting the
orbit using NIRC2 astrometry only we find less well constrained but mostly
compatible results.

##  Appendix F Expected brightness evolution

We observed no significant temporal change in the brightness of X7’s tip in
either the gas or dust emission (Section 4.5). There are several reasons to
expect the surface brightness of X7 to evolve as it orbits closer to Sgr A*.
First, our model indicates that the projection of the X7 tail along the line
of sight has been decreasing with time, which progressively increases the
column density through the tail, and thereby the surface brightness. On the
other hand, the stretching by the tidal force from Sgr A* reduces the linear
mass density along the ridge. Consequently, these are competing effects that
could together reduce the brightness evolution below our threshold for
detecting any significant changes. Tidal compression toward the central axis
of the ridge is also operating, but because the X7 ridge is unresolved in its
narrow dimension, such compression would not affect the optically thin Lp flux
density that we measure.

In contrast, the volume emissivity of the Br-$\gamma$ line depends on the
square of the gas density, so tidal compression in the narrow dimension of the
ridge can counteract tidal stretching to some extent in determining the
surface brightness of Br-$\gamma$ along the X7 ridge. The relative importance
of tidal stretching and tidal compression is a function of orbital phase,
orbital eccentricity, black hole mass, the ambient gas pressure, and the
distance to the black hole.

The other physical considerations affecting the evolution of the Lp and
Br-$\gamma$ surface brightness of X7 involve the environment through which X7
is orbiting. Given the orbit that we have determined (Section 4.2), we find
that the 3D distance of X7 from the black hole is comparable to or even inside
the Bondi radius, a region seen clearly in X-rays (Baganoff et al., 2003; Wang
et al., 2013), where the accretion flow encounters a shock that heats the
inflowing gas to temperatures exceeding $10^{7}$ K. The hot gas surrounding X7
and the X-rays emitted there are likely to raise the dust temperature, which
would counteract to some extent the decline of the surface brightness of the
Lp dust emission resulting from tidal stretching. In addition, the increased
pressure of the external medium as X7 gets closer to the black hole, owing to
both the higher temperature within and inside of the accretion shock and the
higher densities implied by the converging accretion flow, act to compress the
ridge of X7, adding to the tidal compression and therefore to the density-
dependent emissivity in the Br-$\gamma$ line. A quantitative investigation of
these environmental effects, as well as the net effects of tidal forces, is
outside the scope of this paper, but continued monitoring of both the line and
continuum surface brightness of X7 should provide important constraints on the
myriad physical processes at play.

The comments in this subsection have assumed that there is no source of dust
and gas continuously contributing to the mass of X7. We note, however, that if
such a source were present (and as discussed in Section 4.3, we have not
identified any luminous source that could serve as a candidate), then its
contributed material could add to the overall column density within X7, and
thereby be yet another factor contributing to the surface brightness.

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