On the Origin of High Energy Neutrinos from NGC 1068: the Role of Non-Thermal Coronal Activity

Draft version February 20, 2020 Typeset using LATEX twocolumn style in AASTeX63

On the Origin of High Energy Neutrinos from NGC 1068: The Role of Non-Thermal Coronal Activity

Yoshiyuki Inoue,1, 2 Dmitry Khangulyan,3 and Akihiro Doi4, 5

1Interdisciplinary Theoretical & Mathematical Science Program (iTHEMS), RIKEN, 2-1 Hirosawa, Saitama 351-0198, Japan 2Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan 3Department of Physics, Rikkyo University, Nishi-Ikebukuro 3-34-1, Toshima-ku, Tokyo 171-8501, Japan 4Institute of Space and Astronautical Science JAXA, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan 5Department of Space and Astronautical Science, The Graduate University for Advanced Studies (SOKENDAI),3-1-1 Yoshinodai, Chuou-ku, Sagamihara, Kanagawa 252-5210, Japan

(Dated: February 20, 2020)

ABSTRACT NGC 1068, a nearby type-2 Seyfert galaxy, is reported as the hottest neutrino spot in the 10-year survey data of IceCube. Although there are several different possibilities for the generation of high- energy neutrinos in astrophysical sources, feasible scenarios allowing such emission in NGC 1068 have not yet been firmly defined. We show that the flux level of GeV and neutrino emission observed from NGC 1068 implies that the neutrino emission can be produced only in the vicinity of the supermassive black hole in the center of the galaxy. The coronal parameters, such as magnetic field strength and corona size, making this emission possible are consistent with the spectral excess registered in the millimeter range. The suggested model and relevant physical parameters are similar to those revealed for several nearby Seyferts. Due to the internal gamma-ray attenuation, the suggested scenario cannot be verified by observations of NGC 1068 in the GeV and TeV gamma-ray energy bands. However, the optical depth is expected to become negligible for MeV gamma rays, thus future observations in this band will be able to prove our model.

Keywords: accretion, accretion disks — black hole physics — galaxies: active — galaxies: Seyfert — acceleration of particles — neutrinos

1. INTRODUCTION Production of very-high-energy (VHE) neutrinos is IceCube registered first astrophysical neutrinos with accompanied by emission of gamma-rays and the lu- energies of TeV–PeV several years ago (Aartsen et al. minosity of that component exceeds the neutrino one. 2013). However, their origin remains uncertain. Re- NGC 1068 is known as a gamma-ray emitter (Lenain cently, a nearby Seyfert galaxy NGC 1068, which ap- et al. 2010; Ajello et al. 2017; The Fermi-LAT collab- peared as the hottest spot in all-sky 10-year survey oration 2019). However, the reported neutrino flux is data of IceCube, was reported to be a neutrino source higher than the GeV gamma-ray flux (IceCube Collabo- with 2.9-σ confidence level (IceCube Collaboration et al. ration et al. 2019). Thus, it requires a significant attenuation of GeV gamma-rays. Unless one adopts a very arXiv:1909.02239v4 [astro-ph.HE] 19 Feb 2020 2019). Thus, studying possible neutrino production mechanisms in NGC 1068 is a timely task that may exotic spectrum of emitting particles, this implies a presence of enough dense X-ray target photons, X 1 keV. provide a key clue for unveiling the origin of the cos- ∼ mic diffuse neutrino background flux. The gamma-ray optical depth τ depends on the X-ray luminosity of this component LX and the size of the production regions R:

[email protected] −1 σγγ −1 −1 5 X LX Rs τ X LX R 10 , (1) [email protected] ≈ 4πc ' 1 keV LEdd R [email protected] where LEdd is the Eddington luminosity and Rs is the Schwarzschild radius. Although this estimate is not sen- sitive to the mass of the source, it suggests that such a 2 dense X-ray target can exist only in the vicinity of com- data (Antonucci & Barvainis 1988; Barvainis et al. 1996; pact objects. Doi & Inoue 2016; Behar et al. 2018). A large number, 103, of stellar-mass black hole Recently, Inoue & Doi(2018) reported the detection (or neutron star) systems,N ∼ i.e., X-ray binaries, can pro- of non-thermal coronal radio synchrotron emission from duce the neutrinos with the flux level required by the two nearby Seyferts, IC 4329A and NGC 985, utiliz- IceCube detection without violating the above crite- ing the Atacama Large Millimeter/submillimeter Array ria. Their typical luminosity distribution in a galaxy (ALMA), which enabled multi-band observations with −1.6 is represented by a power-law as dN/dLX LX high enough angular resolution to exclude the galactic (Swartz et al. 2011). This implies that the dominant∝ contamination. These observations provided the first contributor is the higher luminosity systems. How- determination of the key physical parameters of the ever, NGC 1068 hosts only three X-ray binaries with corona: magnetic field strength and its size. Given 39 −1 LX 10 erg s (Swartz et al. 2011), thus their num- the coronal parameters constrained by X-ray and ra- ber≥ is not sufficient at least by several orders of magni- dio observations, the non-thermal acceleration process tude. The only remaining candidate is the supermassive there should be capable of boosting particle energy to black holes (SMBHs) at the center of the galaxy. High the very-high-energy band resulting in the generation accretion rate, implied by the intrinsic X-ray luminosity of high-energy gamma-ray and neutrino emission (Inoue −2 of LX 10 LEdd (Bauer et al. 2015; Marinucci et al. et al. 2019). 2016),∼ does not allow an effective particle acceleration Very Long Baseline Array (VLBA) radio observations in the central black hole magnetosphere. Thus, Emis- detected a homogeneous emission at the cm-bands from sion of very-high-energy neutrinos from the vicinity of the central parsec of NGC 1068. The reported flux is SMBHs indicates the operation of efficient non-thermal attributed to the free-free emission (Gallimore et al. particle acceleration in the active galactic nuclei (AGNs) 2004). This spectrum is not consistent with the fluxes coronae. observed at higher frequencies, mm-bands, which shows NGC 1068 is a type-2 Seyfert galaxy, which is a class a spectral excess (see the Sec.“Observational Proper- of AGNs, emitting intense electromagnetic radiation in ties”). Because of the spectral shape the excess com- a broad range of frequencies. The intrinsic X-ray emis- ponent should be produced by non-thermal particles lo- sion is generated through Comptonization of accretion calized in a much more compact region, with the size disk photons in hot plasma above the disk, namely in similar to the one of the corona. corona (e.g., Katz 1976; Bisnovatyi-Kogan & Blinnikov In this Letter, we study the constraints on the non- 1977; Pozdniakov et al. 1977; Galeev et al. 1979; Taka- thermal particles in the corona of NGC 1068 imposed by hara 1979). Typical size of the AGN corona is about the observations in the radio and gamma-ray bands. We & 10Rs. If high-energy particles are accelerated in the check if the reported flux of VHE neutrino is consistent corona, the nucleus of NGC 1068 is a plausible candi- with the revealed properties of the corona non-thermal date for the observed neutrinos, which is consistent with particles. We also discuss the reason why NGC 1068 a number of previous studies (see e.g., Begelman et al. appears as the hottest spot among other Seyfert galaxies 1990; Stecker et al. 1992; Kalashev et al. 2015; Inoue based on the corona scenario. et al. 2019; Murase et al. 2019). There has been no clear observational evidence for the non-thermal coronal ac- 2. OBSERVATIONAL PROPERTIES tivity (Lin et al. 1993; Madejski et al. 1995). However, as NGC 1068 is one of the nearest and the best-studied several corona parameters, e.g., magnetic field strength Seyfert 2 galaxies in broadband (see, e.g., Pasetto et al. and corona size, remain highly uncertain, one cannot 2019, for details), where the central engine is supposed rule out the presence of high-energy particles in AGN to be blocked by the dusty torus. It locates at a distance corona. These parameters have a critical impact on the of 14 Mpc (100 70 pc, Tully 1988). expected non-thermal flux level. The∼ mass of the∼ central black hole is still uncertain. 7 The coronal synchrotron emission is a key for dissolv- It is estimated as 1 10 M from the measurement ing this problem as it reflects the non-thermal coronal of the rotational motion∼ × of a water maser disk (Green- activity directly and allows determining corona mag- hill et al. 1996; Huré 2002; Lodato & Bertin 2003). netic properties (e.g., Di Matteo et al. 1997; Inoue & However, the rotation curve is non-Keplerian (Lodato Doi 2014). By combining the radio and X-ray spectra, & Bertin 2003). The SMBH mass is also estimated as 7 8 one can also determine the size of coronae. A charac- 7 10 M and 1 10 M from the polarized broad teristic feature of the coronal synchrotron emission is ∼Balmer× emission line∼ and× the neutral FeKα line, respec- a spectral excess in the millimeter-band, so-called mm- tively (Minezaki & Matsushita 2015). In this study, we 7 excess. However, previous observations had presented adopt 5 10 M as the mass of the central SMBH of inconclusive evidence of such excess in the radio spectra NGC 1068.× of several Seyfert galaxies. A key observational chal- In centimeter radio observations, the jets are promi- lenge in registering the excess is the contamination by nent and extend for several kpcs in both directions. In extended galactic emission and a paucity of multi-band the central 100 region, the downstream jet emission ∼ On the Origin of High Energy Neutrinos from NGC 1068 3

102 Beam Size dominates in the centimeter regime. The jet changes Synchrotron, corona ALMA (Our work) 100 mas 00 Free-free, pc region VLBA its direction at 0.2 away from the nuclear region. 10 mas ∼ Total Archival Data 1 mas This change is presumed to be the result of an inter- ALMA action with a molecular cloud (Gallimore et al. 1996, 2004; Cotton et al. 2008). At long wavelengths, the

VLBA 1.4 GHz, 5 GHz, and 8.4 GHz (“cm-bands”) 1

[mJy] 10 observations reported the flux of 5.9 0.5 mJy with ν F a spectral index of 0.17 above 5 GHz± and nondetec- tion at 1.4 GHz, indicating− strong attenuation below 5 GHz (Gallimore et al. 2004). At 5 GHz, the bright- ness temperature is 2.5 106 K, which is too low ∼ × 100 for synchrotron self-absorption flux unless the magnetic 1 2 3 9 10 10 10 fields are order of 10 G(Gallimore et al. 1996, 2004). Frequency [GHz] As discussed in Gallimore et al.(2004), the free-free emission is the most likely origin of the 5 GHz and Figure 1. The cm-mm spectrum of NGC 1068. The 8.4 GHz flux. The emission region size is 0.8 pc with data points from VLBA (Gallimore et al. 2004) and ALMA a temperature of 106 K and the electron∼ density of (Garc´ıa-Burilloet al. 2016; Impellizzeri et al. 2019; Garc´ıa- 8 105 cm−3, which∼ is irrelevant to the central corona Burillo et al. 2019) are shown in green and orange, respec- ∼ × and much more extended. At short wavelengths (“mm- tively. The open points represent the newly analyzed ALMA bands”), the central compact region starts to dominate data. The size of circles corresponds to the beam sizes as in- the entire emission (Cotton et al. 2008; Imanishi et al. dicated in the figure. We also show the archival mm-cm data 2018). Together with multi-frequency observations, a having large beam sizes as upper limits in purple (Gallimore possible spectral excess was reported in the nucleus com- et al. 1996; Cotton et al. 2008; Pasetto et al. 2019). The er- ponent (Krips et al. 2006; Pasetto et al. 2019). Recently, ror bars correspond to 1-σ uncertainties, although those can high angular resolution observations with ALMA de- not be clearly seen because of their small errors. The blue- tected 6.6 0.3 mJy and 13.8 1.0 mJy flux from the dashed and green-dotted lines show the coronal synchrotron core at 256± GHz and 694 GHz,± respectively (Garc´ıa- and pc-scale free-free component, respectively. The black Burillo et al. 2016; Impellizzeri et al. 2019). As the solid line shows the sum of these two components. expected free-free component at the mm band based on the VLBA observations is only at 4 mJy, a new spectral component is emerging in the∼ mm band. In X-rays, NGC 1068 was first studied by Ginga upper limits (Gallimore et al. 1996; Cotton et al. 2008; (Koyama et al. 1989), where intense iron line was re- Pasetto et al. 2019). ported together with an estimate for the intrinsic X- NGC 1068 shows a mm-excess similar to those ob- ray luminosity of 1043−44 erg s−1. Later, it is reported served in previous objects (Inoue & Doi 2018). However, that the observed X-ray emission is due to the reflected we cannot claim a firm detection of this component in component (e.g., Ueno et al. 1994). Utilizing NuSTAR NGC 1068, because of a paucity of flux measurements, and other existing X-ray observatories, the reflected mixture of beam sizes, and the complex source structure. emission is revealed to be originated in multiple reflec- In this letter, motivated by the possible neutrino detection components (Bauer et al. 2015; Marinucci et al. tion (IceCube Collaboration et al. 2019) and detection 2016). The intrinsic 2-10 keV luminosity is estimated as of coronal synchrotron emission in other Seyferts (Inoue L = 7+7 1043 erg s−1 (Marinucci et al. 2016), while & Doi 2018), we consider specifically the possibility of X −4 coronal synchrotron emission to explain this mm-excess. according to× Bauer et al.(2015) it is 2 .2 1043 erg s−1. The coronal synchrotron self-absorption, breaking the In this Letter, we take the value of L = 7× 1043 erg s−1 X spectrum between 300 and 600 GHz, would imply a as the fiducial value. × firm relation between the corona magnetic field and size, putting constraints on the acceleration process at work 3. CORONAL SYNCHROTRON EMISSION in the corona. The excess of NGC 1068 can be reproduced with the Fig.1 shows the cm-mm spectrum of NGC 1068 based coronal synchrotron emission model with parameters of on measurements reported by Gallimore et al.(2004); the corona size R = 10 R , the magnetic field strength Garc´ıa-Burilloet al.(2016); Impellizzeri et al.(2019), c s B = 100 G, and the spectral index of non-thermal elec- where the beam size is 2, 50, 20 mas, respectively. trons p = 2.7 on top of free-free emission produced in pc- In addition, we obtain∼ the continuum∼ ∼ fluxes at 224, 345, size region (Gallimore et al. 2004). A much softer spec- and 356 GHz with beam sizes of 30 mas by analyzing tral index would violate either the ALMA measurements the latest ALMA band 6 and 7 data (2016.1.00232.S, or the flux upper limit at 351 GHz (Fig.1). The required Garc´ıa-Burilloet al. 2019). We also show the archival coronal size is consistent with optical–X-ray spectral fit- core region data sets having beam sizes > 50 mas as 4 ting studies (Jin et al. 2012) and micorolensing obser- The data is taken from Fig. 7 of IceCube Collaboration vation (Morgan et al. 2012) in other Seyferts. The pre- et al.(2019), and the 1, 2, and 3 σ regions are shown in viously reported coronal synchrotron objects IC 4329A the plot. For the comparison, we also show the expected 8 and NGC 985, whose black hole masses are 10 M , sensitivity curves of a future MeV gamma-ray mission, ∼ have Rc 40 Rs and B 10 G (Inoue & Doi 2018), GRAMS (Aramaki et al. 2019) and AMEGO (McEnery which are∼ similar to what∼ we required for the excess in et al. 2019). Gamma-ray model curve is the summa- NGC 1068 for the coronal synchrotron emission scenario. tion of leptonic and hadronic gamma-rays after internal Although we chose the coronal synchrotron emission (X-ray corona and UV accretion disk photons) and in- model as a possible explanation for the mm-excess, cur- tergalactic (on EBL photons) attenuation. For hadronic rent data sets do not allow us to give a clear evidence. processes, we consider both pp and pγ interactions. Future ALMA observations will be able to elucidate the We follow the assumptions on the coronal parame- origin of the excess. High angular resolution observa- ters as in Inoue et al.(2019) except for the gyrofactor tions will be able to precisely understand the contribu- and parameters determined by the coronal synchrotron tion of the free-free component. Multi-frequency and model explaining the mm-excess. Considering the mea- variability measurements in the mm-band will be also surement uncertainty, in the figure, we plot the model 4 able to determine the spectral shape and see the coro- curve region in the range of 30 ηg 3 10 for each ≤ ≤ × nal activity. curve. The darker region corresponds to lower ηg, in The coronal synchrotron emission is mostly deter- which models extend to higher energies. The injection mined by the following parameters: Rc, B, p, and the en- powers both in protons and electrons are set to equal as ergy fraction of non-thermal electrons (fnth). We fix the assumed in Inoue et al.(2019). energy fraction of non-thermal electrons as fnth = 0.03, The gyrofactor ηg = 30 was required in order to ex- which is required to explain the cosmic MeV gamma- plain the measured TeV diffuse neutrinos (Inoue et al. ray background radiation by the Comptonization coun- 2019). We note that the model curve with this ηg is still terpart (Inoue et al. 2019). We adopt standard coro- acceptable, given the measurement uncertainty (accord- nal temperature and Thomson scattering optical depth ing to the Fig.4 of IceCube Collaboration et al.(2019), value of 100 keV and 1.1, respectively (Inoue et al. 2019), the neutrino spectral index is constrained to a broad because both of them are not determined in Marinucci range above 2). Further detailed neutrino spectrum et al.(2016). will allow us to narrow down the range of ηg. If future data requires ηg 30, it will suggest that Seyferts 4. CORONAL GAMMA-RAY AND NEUTRINO are sub-dominant contributors to the diffuse neutrino EMISSION background fluxes. We investigate the properties of high energy emission As NGC 1068 is an AGN, it also features a bright ac- from the nucleus of NGC 1068 utilizing the derived coro- cretion disk and a hot corona. The disk and corona nal parameters based on the possible mm excess (See emission absorbs gamma rays via pair creation. For Fig.1). Observations of the electromagnetic emission the internal gamma-ray attenuation, we consider two constrain the parameters of the gamma-ray and neu- cases. One is the “uniform” emissivity case as assumed trino production model (Inoue et al. 2019) except for in (Inoue et al. 2019), while the other is the “screened” the energy injection ratio between protons and electrons case. In the uniform emissivity case, gamma-rays and and the gyro factor ηg, which is the mean free path of a target photons are uniformly distributed. Gamma rays particle in units of the gyroradius. are attenuated by a factor of 3u(τ)/τ, where u(τ) = Particles are expected to be accelerated by the dif- 1/2 + exp( τ)/τ [1 exp( τ)]/τ 2. Here τ is the − − − − fusive shock acceleration. Other mechanisms such as gamma-ray optical depth computed from the center of magnetosphere, turbulence, or reconnection can not ex- the corona. In the screened case, gamma-rays are as- plain the required electron distribution for the coronal sumed to be generated in the inner part of the corona, synchrotron emission because of high accretion rate and and the dominant attenuating photon field surrounds it. low magnetic field strength (See Sec. 8.3 in Inoue et al. Since the disk and corona temperature depends on the (2019) for details). Gamma-rays are generated through disk radius (Kawanaka et al. 2008), such configuration the Comptonization of disk photons and/or hadronic in- can be realized. Then, gamma-rays are attenuated by a teractions in coronae. Hadronic interactions generate factor of exp( τ). Gamma-rays are also attenuated by − neutrinos. Because of the intense X-ray and UV photon the intergalactic photons during the propagation to the field from the corona and the accretion disk, & 100 MeV Earth. In this Letter, we adopt Inoue et al.(2013) for gamma-rays are significantly attenuated. the intergalactic attenuation. Fig.2 shows the expected gamma-ray and neutrino In the screened case, the model can explain the pre- signals from NGC 1068 together with the observed liminary neutrino signals above several TeV without vio- gamma-ray data (The Fermi-LAT collaboration 2019; lating the gamma-ray data. On the other hand, the uni- Ajello et al. 2017; MAGIC Collaboration et al. 2019) and form emissivity model violates the low-energy gamma- the IceCube data (IceCube Collaboration et al. 2019). ray data. This implies a further detailed study of the On the Origin of High Energy Neutrinos from NGC 1068 5

8 10− ν : Corona tude fewer than requirement. The only feasible candi- γ: Corona (Screen) 9 GRAMS 10− γ: Corona (Uniform) date is the coronal activity of SMBHs at the center of (35 days) IceCube 4FGL the galaxy. 10 10− 3FHL s] MAGIC NGC 1068 is one of the best-studied type-2 Seyfert / 2

cm 11 galaxies. The nucleus ﬂux in the cm band comes from / 10−

[erg AMEGO the free-free emission component (Gallimore et al. 2004). (5 yrs) 12 10− However, at higher frequencies, an excess of core ﬂux GRAMS dN/dE 2 (3 yrs) is reported utilizing ALMA (Garc´ıa-Burilloet al. 2016; E 13 10− Impellizzeri et al. 2019). We found that the coronal

14 10− synchrotron emission model can reproduce the observed mm spectrum, which puts constraints on the accelera- 15 10− 106 107 108 109 1010 1011 1012 1013 1014 1015 1016 tion process in the corona. Energy [eV] Given the corona parameters revealed with ALMA Figure 2. The gamma-ray and neutrino spectrum of measurements, we studied the resulting gamma-ray and NGC 1068. The circle, square, and triangle data points neutrino emissions from the corona of NGC 1068. Al- though it is difficult to explain the gamma-ray flux are from The Fermi-LAT collaboration(2019), Ajello et al. above 100 MeV due to significant internal attenuation (2017), and MAGIC Collaboration et al.(2019), respectively. effect, the coronal emission can explain the reported Ice- The green shaded regions represent the 1, 2, and 3σ regions Cube neutrino flux with the gyro factor in the range of on the spectrum measured by IceCube (IceCube Collabora- 4 30 ηg 3 10 . Further neutrino data on NGC 1068 tion et al. 2019). The expected gamma-ray and neutrino will≤ narrow≤ down× the required range of η . It should be 4 g spectrum from the corona are shown for 30 ≤ ηg ≤ 3 × 10 . noted that ηg 30 is required for Seyferts to explain The darker region corresponds to lower ηg. The blue region the diffuse neutrino∼ fluxes up to 300 TeV (Inoue et al. shows the expected neutrino spectrum. The orange and ma- 2019). genta shaded region shows the gamma-ray spectrum for the In order not to violate the observed gamma-ray data, uniform case and the screened case, respectively. We also the corona can not be uniform. The dominant atten- overplot the sensitivity curves of GRAMS (Aramaki et al. uating photon field needs to surround the gamma-ray 2019) and AMEGO (McEnery et al. 2019) for for compari- emission region. Since the disk temperature depends on son. the disk radius, such a configuration can be realized. Future MeV gamma-ray observations will be the critical tool to test the corona scenario. coronal geometry is necessary. Future MeV gamma-ray An important question is what differs NGC 1068 from missions such as GRAMS (Aramaki et al. 2019) and other nearby Seyfert galaxies. NGC 1068 is not the AMEGO (McEnery et al. 2019) will verify our model brightest X-ray Seyfert (Oh et al. 2018). Its observed and help us to understand the coronal geometry, which hard X-ray flux is a factor of 16 fainter than the one is not well understood yet. of the brightest Seyfert, NGC 4151.∼ NGC 1068 is a type- Due to the internal attenuation, it is not easy for the 2 Seyfert galaxy, and obscured by the materials up to 25 −2 corona model to explain the entire observed gamma-ray the neutral hydrogen column density of NH 10 cm flux data up to 20 GeV, requiring another mechanism to (Bauer et al. 2015; Marinucci et al. 2016). If∼ we correct explain gamma-rays above 100 MeV such as star forma- this attenuation effect to understand the intrinsic X-ray tion activity (Ackermann et al. 2012), jet (Lenain et al. radiation power, NGC 1068 appears to be the intrin- 2010), or disk wind (Lamastra et al. 2016). sically brightest Seyfert. For example, intrinsically, it would be by a factor of 3.6 brighter than NGC 4151 5. DISCUSSIONS AND CONCLUSION in X-ray. As the dusty torus∼ does not obscure coronal The IceCube collaboration reported NGC 1068 as the neutrino emission, which can scale with accretion power, hottest spot in their 10-year survey (IceCube Collabora- NGC 1068 might be the brightest source of VHE neutri- tion et al. 2019). Surprisingly, the reported neutrino flux nos. This could be the reason why NGC 1068 appears as is higher than the GeV gamma-ray flux, which requires the hottest spot in the IceCube map rather than other different origins and a significant attenuation of GeV Seyfert galaxies. gamma-rays from the neutrino production site. This further implies a presence of enough dense X-ray target photons in the neutrino production region in order to attenuate gamma-rays & 100 MeV. Such a dense X-ray target can exist only in the vicinity of compact objects. However, stellar-mass objects such as X-ray binaries can not explain the whole neutrino flux because the number of such objects in NGC 1068 is several orders of magni- 6

ACKNOWLEDGMENTS The authors thank the anonymous referee for thought- ful and helpful comments. YI is supported by JSPS KAKENHI Grant Number JP16K13813, JP18H05458, JP19K14772, program of Leading Initiative for Excel- lent Young Researchers, MEXT, Japan, and RIKEN iTHEMS Program. DK is supported by JSPS KAK- ENHI Grant Numbers JP18H03722, JP24105007, and JP16H02170. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2016.1.00232.S. ALMA is a partnership of ESO (representing its mem- ber states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Re- public of Chile. The Joint ALMA Observatory is oper- ated by ESO, AUI/NRAO and NAOJ.

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