Discovery of the Tadpole Molecular Cloud near the Galactic Nucleus

In this paper, we report the discovery of an isolated, peculiar compact cloud with a steep velocity gradient at 2.′6 northwest of Sgr A*. This “Tadpole” molecular cloud is unique owing to its characteristic head-tail structure in the position–velocity space. By tracing the CO J = 3–2 intensity peak in each velocity channel, we noticed that the kinematics of the Tadpole can be well reproduced by a Keplerian motion around a point-like object with a mass of 1 × 105 M ⊙. Changes in line intensity ratios along the orbit are consistent with the Keplerian orbit model. The spatial compactness of the Tadpole and absence of bright counterparts in other wavelengths indicate that the object could be an intermediate-mass black hole.


INTRODUCTION
It is widely accepted that large galaxies host a central supermassive black hole (SMBH) with millions to billions times the mass of the Sun (e.g., Kormendy & Richstone 1995;Kormendy & Ho 2013).A potential scenario for SMBH formation is based on intermediate-mass black holes (IMBHs), which have masses of 10 2-5 M ⊙ (e.g., Mezcua et al. 2017).Thus, detecting and studying IMBHs in detail are essential for understanding the formation and evolution of galactic nuclei.Numerous IMBH candidates have been identified in centers of globular clusters (e.g., Kızıltan et al. 2017), in nuclei of dwarf galaxies (e.g., Reines et al. 2013;Baldassare et al. 2015), or as ultraluminous X-ray sources in extragalaxies (e.g., Farrell et al. 2009).

DATA
We first discovered the Tadpole in the JCMT CO J=3-2 data, and confirmed it in the CO J=1-0 and CS J=2-1 line data obtained with the Nobeyama Radio Observatory (NRO) 45 m telescope.These data sets are briefly described below.

CO J=3-2 Line
The 12 CO J=3-2 line (345.795990GHz) observations of the CMZ were performed using the JCMT from 2013 July to 2014 July (Parsons et al. 2018).The Heterodyne Array Receiver Program (HARP; Buckle et al. 2009) and autocorrelation spectral imaging system (ACSIS) were used during these observations.The half-power beam width (HPBW) of the telescope was approximately 14 ′′ at 345 GHz.The ACSIS was operated in the 1 GHz bandwidth (976.56 kHz resolution) mode.During these observations, the system noise temperature (T sys ) ranged between 100-200 K.The rms noise level of the image cubes was between 0.4 K and 0.84 K.The details of the CO J=3-2 data and JCMT observations are presented in Parsons et al. (2018).We use the data after resampling onto a 7. ′′ 5×7.′′ 5×1 km s −1 grid.

CO J=1-0 Lines
The CO J=1-0 observations of the CMZ were performed using the Nobeyama Radio Observatory (NRO) 45 m telescope (Tokuyama et al. 2019).The 12 CO J=1-0 (115.27120GHz) line data were obtained from 2011 January 19 to 29 using the 25 beam array receiver system (BEARS; Sunada et al. 2000).As the receiver backend, the AC45 spectrometer system (Sorai et al. 2000) was employed in the 500 MHz bandwidth (0.5 MHz resolution) mode.The 13 CO J=1-0 (110.20135GHz) line data were obtained from 2016 February to March using the four-beam receiver system on the 45 m telescope (FOREST; Minamidani et al. 2016).The spectral analysis machine on the 45 m telescope (SAM45; Kuno et al. 2011;Kamazaki et al. 2012) was operated in the 1 GHz (244.14 kHz resolution) mode.The HPBW of the telescope was approximately 15 ′′ at 115 and 110 GHz.The typical T sys was ∼ 800 K and 150-300 K during the 12 CO and 13 CO observations, respectively.The data were resampled onto a 7. ′′ 5×7.′′ 5×2 km s −1 grid.The rms noise levels of the resultant 12 CO and 13 CO data cubes were 1.0 K and 0.2 K in main-beam temperature (T MB ), respectively.

CS J=2-1 Line
The CS J=2-1 (97.98096GHz) line observations of the CMZ were performed during the NRO 45 m Telescope Large Program through 2019 January-May and 2020 January-April.The mapping area was set to −1. • 5 ≤ l ≤ +1.• 5 and −0.• 25 ≤ b ≤ +0.• 25.The FOR-EST receiver and SAM45 spectrometer were used.The SAM45 was operated in the 1 GHz bandwidth (244.14 kHz resolution) mode.The HPBW of the telescope was ≃ 19 ′′ at 86 GHz.The T sys ranged from 150-300 K during the CS J=2-1 line observations.The data were resampled onto a 7. ′′ 5×7.′′ 5×2 km s −1 grid.The rms noise level of the resultant CS J=2-1 data cube was 0.14 K in T MB .The details of the CS data and NRO 45 m observations will be presented in the forthcoming paper (Takekawa et al. 2022, in preparation).• 091, -0 .

Spatial and Velocity Structure
Figure 2 shows the spatial and velocity structure of the Tadpole in various molecular lines.The Tadpole appears as a compact, well-defined clump in velocity-integrated maps (Figure 2a, c-e).In the CO J=3-2 integrated map (Figure 2a), the full width of half maximum (FWHM) angular diameter of the Tadpole is 28 ′′ .This angular diameter is 2 times the angular resolution (14 ′′ ), corresponding to a distance of 1.1 pc from the Galactic center.In the 13 CO J=1-0 and CS J=2-1 maps, the Tadpole has angular sizes similar to that depicted in the CO J=3-2 map, while the 12 CO J=1-0 map depicts an appearance that is larger by a factor of 2 compared with those depicted in the other maps.
The velocity extent of the Tadpole is from V LSR ≃ −135 km s −1 to −90 km s −1 (Figure 2b), indicating that it may be in the CMZ.The longitude-velocity behavior of the Tadpole is characterized by a "head-tail" structure, from which its name is derived.It depicts a steep velocity gradient of |∆V /∆l| ∼ 16 km s −1 pc −1 .The tail is obscure in the 13 CO J=1-0 and CS J=2-1 data sets.We show the spectra of CO and CS lines in Figure 3.
We learned that CO J=3-2 line can trace the kinematics of the Tadpole best because of its high intensity and well-defined appearance in the l-b-V space.Figure 4 shows the velocity channel maps of CO J=3-2 emission.The Tadpole appears with an elliptical shape in each velocity channel, changing its angular size with respect to velocity.It has the largest angular size of 36 ′′ ×24 ′′ in the V LSR = −130 to −125 km s −1 channel, while the smallest size of ∼ 20 ′′ is detected at both velocity ends.These angular sizes, which are comparable to the telescope's HPBWs, indicate that the spatial structure of the Tadpole is not well resolved using these single-dish observations; thus, the actual angular size must be far smaller than those observed.
The CO J=3-2 line emission shows a maximum intensity of 64 K km s −1 in the −130 to −125 km s −1 channel.We identified that the intensity maximum pixel in the Tadpole at each velocity channel continuously changes with respect to velocity.Note that these intensity maximum pixels trace an arc in the plane of the sky (Figure 4, bottom right panel).This behavior will be analyzed in more detail in the discussion section ( §4.1).
The virial theorem mass and molecular gas mass of the Tadpole yield a significantly high virial parameter, M VT /M gas ∼ 700.This indicates that the Tadpole is not in gravitational equilibrium.Following the method described in Stark et al. (1989), we estimated the selfgravity of the Tadpole and tidal force by the Galactic potential.The self-gravity of the cloud estimated here (∼ 10 −10 m s −2 ) is 2.5 orders of magnitude weaker than the tidal force (∼ 4 × 10 −8 m s −2 ).These assessments clearly demonstrate that the Tadpole cannot be bound by its self-gravity.This strongly indicates to the presence of an object with a mass comparable to the virial mass (4.7×10 5 M ⊙ ) inside the Tadpole.

Multiwavelength View
To search for the driving source behind the Tadpole, we referred to the 1.284 GHz data obtained using MeerKAT (Heywood et al. 2022), mid-infrared data obtained using the Spitzer Space Telescope (Ramírez et al. 2008;Churchwell et al. 2009), and X-ray data obtained at the Chandra X-ray Observatory (Muno et al. 2009).
No radio source brighter than 0.4 mJy beam −1 at 1.284 GHz was detected near the angular extent of the Tadpole, while a faint filament was seen in the Galactic south (Figure 5a).In the mid-infrared image (Figure 5b), we identified a faint triangular rim which may be the irradiated surface of the Tadpole.Considering the angular resolution of the Spitzer (∼ 2 ′′ ), the mid-infrared rim defines the angular extent of the Tadpole better than the CO J=3-2 appearance.We also checked the AT-LASGAL (870µm) and Hi-GAL (70, 160, 250, 350 and 500 µm) images (Contreras et al. 2013;Molinari et al. 2016), and found no separate feature toward the Tadpole above the sea of intense dust emission.A bright point-like source near the Galactic southwestern edge of the Tadpole is the long-period variable star V4872 Sgr (Matsunaga et al. 2009).In addition, we also identify dozens of point-like, mid-infrared sources toward the Tadpole.The X-ray image also shows numerous faint point-like sources toward the Tadpole (Figure 5c).Although the nature of these mid-infrared/X-ray point-like sources is unclear, we will refer to them in the discussion section ( §4.5).In short, the multiwavelength view confirms the absence of any energetic objects that can drive the Tadpole.

Tracing Molecular Gas Kinematics
The continuous change in the CO J=3-2 intensity maximum pixel along the arc with velocity ( §3.1) suggests that the bulk of warm molecular gas belongs to a certain trajectory, such as a closed orbit.To determine the orbit trajectory accurately, we constructed a CO J=3-2 data cube with a 2 ′′ ×2 ′′ ×1 km s −1 grid.Then, we calculated the accurate intensity peak position as the CO emission center of gravity using 5×5 pixels around the intensity maximum pixel in the Tadpole for each 1 km s −1 width velocity channel.
Figure 6 shows the l-b-V and l-b distributions of the intensity peak position in the Tadpole for each velocity channel.The arc-shape apparent in the l-b distribution became clearer than that depicted in Figure 4.The l-b-V distribution demonstrates the striking continuity of peak positions in the velocity direction, indicating that the bulk of warm molecular gas in the Tadpole may predominantly follow a certain closed orbit.

Keplerian Orbit Fitting
The arc-shaped spatial structure and continuous velocity change along the arc suggest that a rotational motion exists.Thus, we expect that the l-b-V behavior of warm molecular gas in the Tadpole can be reproduced by a Keplerian orbit around a point mass 1 .We performed the fitting of a Keplerian orbit to the intensity peak positions (Figure 6) following the method described in Zhao et al. (2009).We determined nine parameters.Five of these parameters are three-dimensional orbital parameters; namely, the semimajor axis (a), eccentricity (e), longitude of ascending node (Ω), argument of  1).The black and red filled circles denote the positions of the dynamical center and pericenter, respectively.The black arrow indicates the direction of rotation.The distance to the Tadpole is assumed to be same as that to the Galactic center.The χ 2 minimization approach was utilized in the l-b-V space.The χ 2 consists of two terms, namely, the spatial (χ 2 s ) and velocity terms (χ 2 v ).The spatial term is defined by the sum of the orthogonal distances between the peak position and the modeled orbit divided by the square of the positional uncertainty, which was set to 0.15 pc (3.′′ 6).The velocity term is, similarly, the sum of the velocity deviations between those of the peak positions and nearest posi-tions in the modeled orbit divided by a square of the velocity uncertainty, which was set to 1 km s −1 .
The best-fit parameters with 1σ uncertainties are listed in Table 1.The l-b-V locus of the orbit is presented in Figure 6.Note that the best-fit solution is bivalent because the orbits with i → (180 • − i) and Ω → (Ω + 180 • ) yield the same l-b-V locus.The fitting result indicates the presence of a point mass of 1.0×10 5 M ⊙ in the northwestern periphery of the Tadpole (Figure 6).

Tidal Stability of the Head
We examined the tidal stability of the head, assuming the Newtonian potential of a point mass, following the method described in Stark et al. (1989).The tidal force caused by the point mass and self-gravity doing work on the head were calculated as functions of the head diameter (Figure 7).A central mass of 1×10 5 M ⊙ and head mass of 660 M ⊙ were assumed.The curves of the two forces at the pericenter of the best-fit orbit (0.5 pc) intersect at d = 0.14 pc, while those at the apocenter intersect at d = 0.35 pc.Because the observed head diameter (∼ 1 pc) is larger than the critical value (0.14 pc) by a factor of seven, the Tadpole head is tidally unstable at the pericenter.If the head includes a selfgravitating core smaller than 0.14 pc, it may be able to survive several turns.It is possibly that the Tadpole has been trapped by the gravitational potential of the 10 5 M ⊙ point mass, being stretched by the strong tidal force to form the characteristic head-tail structure.This situation is similar to the simulation of a cloud tidally disrupted by a super massive black hole (Saitoh et al. 2014).Note that the Tadpole must have been lost its angular momentum to be captured during the encounter with the point mass.

Intensity Ratios along the Orbit
Here, we refer to the CO J=1-0, CO J=3-2, and CS J=2-1 line intensities, as well as CO J=3-2/CO J=1-0 (R 3-2/1-0 ) and CS J=2-1/CO J=1-0 (R CS/CO ) line intensity ratios to examine the Keplerian orbit scenario.The critical densities of the CO J=1-0, CO J=3-2, and CS J=2-1 transitions are approximately 10 2.5 , 10 4 , and 10 5 cm −3 , respectively, while their upper state energies are 5.6, 33, and 7.1 K, respectively.Thus, R CS/CO is sensitive to the variations in density while R 3-2/1-0 is affected by both the temperature and density.Figure 8 shows plots of line intensities and intensity ratios along the best-fit orbit.The motion along the orbit increases the orbital phase (φ) at all times, where the pericenter of the orbit corresponds to φ = 0 • .Both ratios exhibit higher values at the head, indicating that both the density and temperature are enhanced there.At the beginning of the tail, φ ∼ 170 • , R 3-2/1-0 demonstrates a prominent peak while R CS/CO does not.This suggest that the temperature is enhanced at the beginning of the tail.Then, both ratios decrease toward the tip of the tail.The higher temperature in the head may have been caused by the shock occurring at the first encounter with the point mass.This shock may be caused by collisions of gas clumps at the pericenter, where adjacent orbits are very close.In a fluid mechanical treatment, the same process is described as the "tidal compression" (Saitoh et al. 2014).The gas accumulation near the apocenter and/or the presence on a self-gravitating core can cause the higher density in the head.The tail may be really the low density, tidally stretched tail of the head.The temperature increase at the beginning of the tail could be caused by another shock at the congestion near the apocenter.Thus, the behaviors of intensity ratios are consistent with the Keplerian orbit scenario for the Tadpole.

What is a Point Mass?
The Keplerian orbit model requires the presence of a huge point mass at the dynamical center.What is this point-like massive object?The mass of 10 5 M ⊙ is larger than the Arches or Quintuplet clusters (∼ 10 4 M ⊙ Figer et al. 1999a,b).According to the best-fit model, a mass of 10 5 M ⊙ must be concentrated within a radius significantly smaller than 0.5 pc (the pericenter dis-tance), resulting in an average mass density higher than that of the Arches cluster (ρ ∼ 2×10 5 M ⊙ pc −3 Espinoza 2009).
Anyway, the absence of a bright infrared counterpart toward the Tadpole (Ramírez et al. 2008;Churchwell et al. 2009;Molinari et al. 2011) clearly rules out a stellar cluster from being a candidate for the point mass.
The most promising candidate for the point-like massive object in the Tadpole may be an IMBH.We searched for a counterpart for this point mass referring to X-ray images ( §3.3). Figure 9 shows the positions of point-like sources in the X-ray images superimposed on the composite mid-infrared images around (l, b) = (l 0 , b 0 ).The small statistical uncertainties in the l-b position of the dynamical center (Table 1) should be considered with some caution because the entire gas mass in the Tadpole is not confined within the single closed orbit.Notice that three point-like sources in the X-ray and mid-infrared reside within a 5 ′′ (∼ 10 times of the positional ambiguity of the dynamical center) angular distance from (l 0 , b 0 ) (Table 2).One source, SSTGC 489898, is apparent in both X-ray and mid-infrared images.The X-ray detected sources, SSTGC 489898 and CXOGC 174526.9-290124,exhibit hard spectra, indicating that they may be at the same distance to the Galactic center.No time variation has been detected from these sources (Zhu et al. 2018).If we assume the standard accretion disk model (L = Ṁ c 2 /12), their Xray luminosities correspond to Ṁ ∼ 1 × 10 −14 M ⊙ yr −1 .This very low mass accretion rate could be a challenge to our interpretation.Anyway, we suppose these three point-like sources are candidates for the luminous counterpart of the point mass.Although we currently have very little knowledge on these point-like sources, they should be considered as candidates for an IMBH in future studies.

CONCLUSIONS
We have discovered the so-called Tadpole, which is an isolated, peculiar compact cloud with an extraordinary velocity width and very high CO J=3-2/J=1-0 intensity ratio, at 2. ′ 6 northwest of Sgr A*.Our main conclusions can be summarized as follows: 1.The Tadpole molecular cloud has a size of ∼ 1 pc at the distance to the Galactic center and a velocity width of ∼ 50 km s −1 .
2. It demonstrates the characteristic "head-tail" structure in position-velocity space, having a steep velocity gradient of 16 km s −1 pc −1 .
b The source IDs and mid-infrared magnitudes are quoted from Ramírez et al. (2008).
c The source ID defined in Muno et al. (2009).
3. Its kinematics is well reproduced by a Keplerian motion around a point-like object with a mass of 1×10 5 M ⊙ .
4. It is plausible that the Tadpole has been trapped by the gravitational potential of the huge point mass, now being stretched by the strong tidal force.
5. The behaviors of line intensity ratios (R 3-2/1-0 and R CS/CO ) are consistent with the Keplerian orbit scenario.
6.The absence of bright objects near the putative point-like object suggests that the object is an inactive intermediate-mass black hole (IMBH).
These results are based on molecular line maps with 14 ′′ -19 ′′ resolutions obtained using single-dish telescopes.Future aperture synthesis observations of molecular lines with millimeter/submillimeter arrays will be able to delineate the orbit stream directly, increasing the reliability of the Keplerian orbit model for the Tadpole.

Figure 4 .
Figure 4. Velocity channel maps of the CO J=3-2 line from VLSR = −140 to −85 km s −1 near the Tadpole.The angular area is the same as that depicted in Figure 2a, c-e.The intensity unit is K km s −1 .The velocity range for integration is indicated at the bottom right corner of each panel.The magenta cross denotes the position of the maximum intensity pixel in each panel.The distribution of the maximum intensity pixels is shown in the bottom right panel.

Figure 5 .
Figure 5. Multiwavelength view near the Tadpole.White contours show the CO J=3-2 integrated intensity with a 50 K km s −1 interval.(a) Radio continuum image at 1.284 GHz obtained with the MeerKAT.(b) Composite mid-infrared image obtained with the Spitzer Space Telescope.The image depicts 8.0 µm band flux in red, 5.8 µm in green, and 4.5 µm in blue.(c) Composite X-ray image obtained with the Chandra X-ray Observatory.The image depicts 0.2-3.3keV count rate in red, 3.3-4.7 keV in green, and 4.7-8.0keV in blue.

Figure 6 .
Figure 6.The l-b-V distribution of CO J=3-2 intensity peak positions in the Tadpole in each 1 km s −1 width velocity channel.The head and tail of the Tadpole are denoted by blue and green, respectively.The l-b distribution is also shown in the base plane with CO J=3-2 contours.Grey lines represent the loci of the best-fit Keplerian orbit (Table1).The black and red filled circles denote the positions of the dynamical center and pericenter, respectively.The black arrow indicates the direction of rotation.

Figure 7 .
Figure 7. Plots of the tidal force due to the point mass (solid line) and self-gravity of the cloud (dashed lines) working on the head versus the head diameter.A central mass of 10 5 M⊙ and head mass of 660 M⊙ were assumed.The thick solid line indicates self-gravity at the pericenter distance (0.49 pc) while the thin solid line indicates that at the apocenter (1.01 pc).

Figure 8 .
Figure 8.(a) Plots of CO J=3-2 (filled circles), CO J=1-0 (crosses), and CS J=2-1 (open circles) main-beam temperatures at the CO J=3-2 intensity peaks versus orbital phase.(b) Plots of R 3-2/1-0 (filled circles) and R CS/CO (open circles) at the CO J=3-2 intensity peaks versus orbital phase.The phase ranges of the head and tail of the Tadpole are depicted in blue and green shades, respectively.

Figure 9 .
Figure 9. Distribution of X-ray point-like sources (open yellow circles: Muno et al. 2009, filled yellow circles: Zhu et al. 2018) superimposed on the composite mid-infrared image (color; same as Fig.5b).The red cross denotes the dynamical center of the best-fit Keplerian orbit, and the green dotted circle has a 5 ′′ radius.Black highlight the CO J=3-2 integrated intensity with a 50 K km s −1 interval.