Rotating Ionized Gas Ring around the Galactic Center IRS13E3

We detected a compact ionized gas associated physically with IRS13E3, an Intermediate Mass Black Hole (IMBH) candidate in the Galactic Center, in the continuum emission at 232 GHz and H30$\alpha$ recombination line using ALMA Cy.5 observation (2017.1.00503.S, P.I. M.Tsuboi). The continuum emission image shows that IRS13E3 is surrounded by an oval-like structure. The angular size is $0".093\pm0".006\times 0".061\pm0".004$ ( $1.14\times10^{16}$ cm $\times 0.74\times10^{16}$ cm). The structure is also identified in the H30$\alpha$ recombination line. This is seen as an inclined linear feature in the position-velocity diagram, which is usually a defining characteristic of a rotating gas ring around a large mass. The gas ring has a rotating velocity of $V_\mathrm{rot}\simeq230$ km s$^{-1}$ and an orbit radius of $r\simeq6\times10^{15}$ cm. From these orbit parameters, the enclosed mass is estimated to be $M_{\mathrm{IMBH}}\simeq2.4\times10^4$ $M_\odot$. The mass is within the astrometric upper limit mass of the object adjacent to Sgr A$^{\ast}$. Considering IRS13E3 has an X-ray counterpart, the large enclosed mass would be supporting evidence that IRS13E3 is an IMBH. Even if a dense cluster corresponds to IRS13E3, the cluster would collapse into an IMBH within $\tau<10^7$ years due to the very high mass density of $\rho \gtrsim8\times10^{11} M_\odot pc^{-3}$. Because the orbital period is estimated to be as short as $T=2\pi r/V_\mathrm{rot}\sim 50-100$ yr, the morphology of the observed ionized gas ring is expected to be changed in the next several decades. The mean electron temperature and density of the ionized gas are $\bar{T}_{\mathrm e}=6800\pm700$ K and $\bar{n}_{\mathrm e}=6\times10^5$ cm$^{-3}$, respectively. Then the mass of the ionized gas is estimated to be $M_{\mathrm{gas}}=4\times10^{-4} M_\odot$.


Introduction
Sagittarius A * (Sgr A * ) is the galactic nucleus of the nearest spiral galaxy, Milky Way, and harbors the Galactic Center black hole (GCBH) with M ∼ 4 × 10 6 M (e.g. Boehle et al. 2016, Abuter et al. 2018). This region is a precious laboratory for studying activities and structures of galactic nuclei because peculiar phenomena which will be found in the nuclei of external galaxies by future huge telescopes can be observed by Atacama Large Millimeter/Submillimeter Array (ALMA) here.
New ones have been discovered in succession since ALMA has started to observe Sgr A * and the surrounding region (e.g. Moser et al. 2017, Tsuboi et al. 2017b, Yusef-Zadeh et al. 2017a, Yusef-Zadeh et al. 2017b. Although the activity of Sgr A * must be supported by the gravitational energy release of the material accreting to the GCBH, it is an open question how the GCBH acquires the material up to the present huge mass. There are two possibilities about the growth history of the GCBH. The first one is that very dense and massive gas blobs had fallen to the GCBH. This is a simple scenario but it has several issues to grow the GCBH to the present mass. Even if gas blobs are accreting continuously to the GCBH within the Hubble time, the accretion rate is required to be up tȯ M ∼ 10 −4 − 10 −3 M year −1 . This is several orders of magnitude larger than the present estimated rate from observations (e.g. Agol 2000, Quataert & Gruzinov 2000. The very high accretion rate requires a quite low radiation efficiency of η ∼ 10 −9 − 10 −8 for Sgr A * . On the other hand, there is a possibility that the accretion rate may have been much higher in the past caused by any episodic large accretion event, for example, the formation of the Fermi Bubbles (Su, Slatyer,& Finkbeiner 2010) and it has decreased to the present rate.
The second one is that several heavy compact bodies, stellar-mass black holes and/or intermediate mass black holes (IMBHs), had fallen and merged into the GCBH. First of all, it is required that there are such objects in the surrounding region of Sgr A * . Recent X-ray observations have already revealed a dozen stellar-mass black holes around Sgr A * (Hailey et al. 2018). However, it is an open 2 question in the latter case (Cf. Schödel et al. 2005, Paumard et al. 2006, Genzel et al. 2010, Oka et al. 2016).
In our previous study, we detected a peculiar ionized gas flow associating with the Galactic Center IRS13E complex which is located to the southwest of Sgr A * by d = 4 × 10 17 cm (0.13 pc) in projection (Tsuboi et al. 2017b). The ionized gas flow has a very large velocity width (∆v FWZI ∼ 650 km s −1 ) and a very compact size (r ∼ 6 × 10 15 cm) in the complex. An extended ionized gas component connecting with the compact component has also been found. A hypothesis explains that this uncommon ionized gas system is a continuous gas flow orbiting on a high-eccentricity Keplerian orbit around IRS13E3 embedded in the complex. The enclosed mass is estimated to be 10 4 M by the analysis of the orbit, which is within the mass range of an IMBH. However, the Keplerian orbit parameters derived from the complicated trajectory in the position-velocity diagram should involve large ambiguity.
If IRS13E3 is an IMBH, an ionized gas ring would be rotating around it. ALMA is able to get the spatial and velocity resolved image of the disk. If the rotating ring is discovered, the enclosed mass derived with the simple structure must be reliable. This would be stronger evidence that the IMBH exists in the complex. We have searched such ionized gas with ALMA in order to prove our hypothesis that IRS13E3 is an IMBH. Throughout this paper, we adopt 8.0 kpc as the distance to the Galactic center (e.g. Ghez et al. 2008, Gillessen et al. 2009, Schödel, Merritt,& Eckart 2009, Boehle et al. 2016: 1 corresponds to 1.2 × 10 17 cm and 0.04 pc at the distance.

Observation and Data Reduction
We observed the area including Sgr A * and the IRS 13E complex at 230 GHz as an ALMA Cy. We performed the data analysis by Common Astronomy Software Applications (CASA) 3 (McMullin et al. 2007). Before imaging in the recombination line, the continuum emissions of Sgr A * and the Galactic Center Mini Spiral (GCMS) were subtracted from the data using CASA task, uvcontsub (fitorder=1) for the combined data in the ten-day observations. The imaging to obtain channel maps was done using CASA 5.4 with clean task. We also got the line-free continuum data using this task. This data was used for the continuum imaging shown below. We will show the full results including the resultant continuum maps of the other three spectral windows in another publication. The angular resolution using "natural weighting" is 0 .037 × 0 .024, P A = 87 • . The sensitivities of the original velocity width channels are 1σ = 90 µJy beam −1 or 2.3 K in T B in the emission-free areas. The sensitivity is slightly worse than the expected one by the ALMA sensitivity calculator because there are yet unavoidable sidelobes of Sgr A * in the channel maps. Jy. Such significant flux density change might make some artifacts including unavoidable sidelobe effects in the continuum map from the combined data. We used only the data of the first seven days to produce the resultant continuum map here. In addition, the data with the baselines over 11 km is removed because this seems to increase the sidelobe effects in the continuum map.The complex gain errors of the data were minimized using the "self-calibration" method in CASA.The "self-calibration" method give us to obtain a high dynamic range in the continuum map. The angular resolution using "natural weighting" is 0 .037 × 0 .025, P A = 85 • , which is almost the same as that of the channel maps. The sensitivity is 1σ = 50 µJy beam −1 or 1.3 K in T B in the emission-free areas. Although the sidelobe effects still remain around Sgr A * , the dynamic range reaches to > 40000 in the other areas of the map. Figure 1a shows the continuum map of the vicinity of Sgr A * at 340 GHz (Tsuboi et al. 2017b).     shown as the rectangle in Figure 1b. The angular resolution is 0 .037 × 0 .025, P A = 85 • in FWHM, which is shown as the oval at the lower left corner. IRS13E3 is clearly resolved into an inclined oval-like structure which is elongated in the direction of northeast to southwest. The angular source size of the structure is derived to be θ maj.obs. × θ min.obs. = 0. 093 ± 0. 006 × 0. 061 ± 0. 004, P A ∼ 64 • by the two-dimensional Gaussian fit including beamsize correction. These correspond to d maj.obs. × d min.obs. = 1.14 × 10 16 cm ×0.74 × 10 16 cm at the the Galactic center distance. The total flux density of the oval-like structure is S ν = 10.52 ± 0.90 mJy. The flat spectrum in mm wavelength suggests that the emission is an optically thin free-free emission (Tsuboi et al. 2017b). Moreover, finer structures are identified in the oval-like structure. The intensity peak of IRS13E3 at 232 GHz is located around the northeast side of the oval-like structure. The position is α ICRS = 17 h 45 m 39 s .7888(±0 s .00005), δ ICRS = −29 • 00 29 .7614(±0 .0003). The peak flux density is S ν = 1.712 ± 0.054 mJy beam −1 .

Results
A ridge-like structure extending from south to north crossing the oval-like structure is also identified in Figure 1c. This is probably a counter part of the ionized gas flow orbiting on a Keplerian orbit around IRS13E3, which has been identified in the previous observation (Tsuboi et al. 2017b).
The major axis of the oval-like structure is not parallel to the central axis of the extended gas flow and the crossing angle is about 45 • . The total flux density of the extended gas flow is S ν = 5.80 ± 0.59 mJy. There are also the components corresponding to the famous Wolf-Rayet stars, IRS13E2 and IRS13E4, which have no spread larger than the beam size.   Figure   3a). This is a counter part of the component extending to the south seen in the continuum map, Figure   1c. Many faint components are widely distributed in the panels with V c,LSR = −80, −59, and −39 km s −1 . These would belong to "Bar" of the GCMS which is extended widely (e.g. Figure 3 in Tsuboi et al. 2017b). The major part of "Bar" is probably resolved out at the high resolution in this and IRS13E4 are not clearly found. Figure 4b shows the position-velocity (PV) diagram in the H30α recombination line along the major axis of the oval-like structure of IRS13E3. The integration area is shown as the red rectangle in Figure 4a which is the continuum map at 232 GHz shown in figure 1c. The oval-like structure is seen as an inclined linear feature in Figure 4b. Generally, such a feature in a PV map indicates a ring like structure rotating around a massive object. The observed feature may be a part of an ionized gas ring rotating around IRS13E3. The rotating velocity of the structure is derived to be V rot ∼ 150/cosi km/s from the difference between the positive and negative ends of the linear feature after correction of thermal broadening. Here i is the inclination angle of the structure (i = 0 • for edgeon). The inclination angle is derived to be i ∼ 50 • from the aspect ratio of the Gaussian-fit angular size mentioned in Results. Then the rotating velocity is estimated to be V rot ∼ 230 km s −1 . While the radius of the orbit is derived to be r ∼ 6 × 10 15 cm from the semi-major axis of the angular size.

Enclosed Mass of IRS13E3
Assuming that the ionized gas obeys a single circular orbit simply, the enclosed mass is estimated to be M ∼ 2.4 × 10 4 M from the above parameters using the formula; M = mass is smaller than the enclosed mass based on the analysis for the Keplerian orbit of the larger extended gas flow (Tsuboi et al. 2017b), it is still in the mass range for IMBH. This mass is within the upper limit mass of the object adjacent to Sgr A * , which had been derived from the astrometry of Sgr A * using VLBA (Reid&Brunthaler 2004). Of course, massive compact objects do not uniquely imply BHs and the alternate may be a compact cluster of star or star remnant and so on. From the derived mass and orbit radius, the lower limit of the mass density is estimated to be ρ > ∼ 8 × 10 11 M pc −3 . According to the previous estimations (e.g. Maoz 1998), the cluster with such mass density and such mass would be collapsed within less than τ < 10 7 years and form a BH eventually.
Moreover, IRS13E3 is located within the 95% error circle (0 .3) of the X-ray point source detected by CHANDRA; CXOGCJ174539.7-290029 (Muno et al. 2009). The position and the error circle are shown in Figure 4a. The X-ray flux at 2 − 8 keV of the source is reported to F 2−8 = 1.12 × 10 −5 ph cm −2 s −1 , which is as large as about half that of SgrA * , F 2−8 = 2.44 × 10 −5 ph cm −2 s −1 . If a modest amount of gas accretes onto an IMBH, strong X-ray emission is expected to be produced. IRS13E3 has such a X-ray counterpart. Therefore this enclosed mass would be the convincing evidence that the IMBH exists in the complex.
On the other hand, figure 4c shows the PV diagram along the the south-extended gas flow. The integration area is shown as the white rectangle in figure 4a. The gas flow is seen as a curved feature in the PV diagram (a broken line curve), which is clearly distinguished from the gas ring mentioned above. This gas flow may correspond to a part of the Keplerian orbit around IRS13E3 identified by our previous observation (Tsuboi et al. 2017b). There is a faint component ∼ 0 .03 from the continuum peak in the PV diagram (an arrow), which is the positive velocity end of the curved feature. The physical distance is R ∼ 3.7 × 10 15 cm. The radial velocity of the component is V R ∼ 150 km s −1 .
Although, the north extension of the major axis of the gas flow does not coincide with the continuum peak position of IRS13E3 exactly (see figure 1c), we assume here that the gas flow is now falling toward IRS13E3 freely. We suppose that the gas flow had been nearly at rest in the far distance and the rest radial velocity was V ∞ ∼ −120 km s −1 from Figure 4c. Thus the gain in velocity during The mass is estimated to be M ∼ 1.0 × 10 4 /(cos j) 2 M using the formula; M = R∆V 2 2G . Here j is the angle between the moving direction of the gas flow and the line-of-sight (j = 0 • for the accord of the directions). This is roughly consistent with the enclosed mass mentioned above. The observed continuum image of IRS13E3 has inner structures as mentioned in the previous section (see figure 1c). These should show that the ionized gas does not occupy the orbit homogeneously. Because the orbital period is estimated to be T = 2πr/V rot ∼ 50 − 100 yr, the morphology of the observed ionized gas is expected to change significantly in the next several decades.

Physical Properties of the Rotating Ionized Gas Ring around IRS13E3
The LTE electron temperature, T * e , of the ionized gas ring around IRS13E3 is estimated from the ratio between the integrated recombination line intensity, S line (H30α)dV , and the continuum flux density, S cont (232GHz), assuming that the line and continuum emissions are optically thin. The well-known formula of the LTE electron temperature is given by ν GHz (1) The correction factor, a(ν, T * e ), at ν = 232 GHz is calculated to be a = 0.763 − 0.892 for T * e = 0.5 − 1.5 × 10 4 K (Mezger & Henderson 1967). We assume that the number ratio of He + to H + is N (He + ) N (H + ) = 0.09, a typical value in the Galactic center region (e.g. Tsuboi et al. 2017a). The LTE electron temperature is obtained by iteratively solving the formula for T * e . The total flux densities at 232 GHz of the ionized gas ring around IRS13E3 and the extended gas flow are S ν = 10.52±0.90 mJy and S ν = 5.80 ± 0.59 mJy, respectively. The integration areas are shown in Figure 4a as the two ovals.
Meanwhile the total integrated intensity of the H30α recombination line emission in these areas are S ν dv = 1.31 ± 0.13 Jy km s −1 and S ν dv = 0.68 ± 0.07 Jy km s −1 , respectively. The mean electron temperatures of the ionized gas ring and the extended gas flow are estimated to beT e = 6800 ± 700 K andT e = 7100 ± 700 K, respectively.
Using the observed brightness temperature of the continuum emission and the derived electron temperature, the electron density, n * e , of the ionized gas ring around IRS13E3 is estimated by the following well-known formula; (2) (Altenhoff et al. 1960). The mean electron density isn e = 6 × 10 5 cm −3 assuming that the ionized gas in IRS13E3 has a spherical shape with a diameter of d ∼ 1.14 × 10 16 cm or the path length is L ∼ 1.14×10 16 cm (see Results). The mass of the ionized gas ring is M = 4π 3 ( L 2 ) 3n e m H = 4×10 −4 M . velocity diagram. We consider that the ionized gas is a ring-like structure rotating around IRS13E3 with the rotating velocity of V rot 230 km s −1 and the orbit radius of r 6 × 10 15 cm. From these orbit parameters, the enclosed mass is estimated to be M 2.4 × 10 4 M . The mass is within the astrometric upper limit mass of the object adjacent to Sgr A * . Considering IRS13E3 has an X-ray counterpart, the large enclosed mass would be supporting evidence that IRS13E3 is an IMBH. Even if a dense cluster corresponds to IRS13E3, the cluster would collapse into an IMBH within τ < 10 7 years due to the very high mass density of ρ > ∼ 8×10 11 M pc −3 . Because the orbital period is estimated to be T = 2πr/V rot ∼ 50 − 100 yr, the morphology of the observed structure is expected to change in the next several decades. The mean electron temperature and density of the ionized gas ring arē T e = 6800 ± 700 K andn e = 6 × 10 5 cm −3 , respectively. Then the mass of the ionized gas ring is M = 4 × 10 −4 M .