Star Formation Rates of Massive Molecular Clouds in the Central Molecular Zone
Xing Lu, Qizhou Zhang, Jens Kauffmann, Thushara Pillai, Adam Ginsburg, Elisabeth A. C. Mills, J. M. Diederik Kruijssen, Steven N. Longmore, Cara Battersby, Hauyu Baobab Liu, Qiusheng Gu
DD RAFT VERSION F EBRUARY
22, 2019Typeset using L A TEX twocolumn style in AASTeX62
Star Formation Rates of Massive Molecular Clouds in the Central Molecular Zone X ING L U ( 吕 行 ), Q IZHOU Z HANG , J ENS K AUFFMANN , T HUSHARA P ILLAI , A DAM G INSBURG , E LISABETH
A. C. M
ILLS , J. M. D
IEDERIK K RUIJSSEN , S TEVEN
N. L
ONGMORE , C ARA B ATTERSBY , H AUYU B AOBAB L IU , AND Q IUSHENG G U National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA Haystack Observatory, Massachusetts Institute of Technology, 99 Millstone Road, Westford, MA 01886, USA Boston University Astronomy Department, 725 Commonwealth Avenue, Boston, MA 02215, USA National Radio Astronomy Observatory, 1003 Lopezville Road, Socorro, NM 87801, USA Physics Department, Brandeis University, 415 South Street, Waltham, MA 02453, USA Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstraße 12-14, D-69120 Heidelberg, Germany Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK University of Connecticut, Department of Physics, 2152 Hillside Road, Storrs, CT 06269, USA European Southern Observatory, Karl-Schwarzschild-Straße 2, D-85748 Garching bei München, Germany School of Astronomy and Space Science, Nanjing University, Nanjing, Jiangsu 210093, China (Received - -, –; Revised - -, –; Accepted - -, –)
Submitted to ApJABSTRACTWe investigate star formation at very early evolutionary phases in five massive clouds in the inner 500 pc ofthe Galaxy, the Central Molecular Zone. Using interferometer observations of H O masers and ultra-compactH II regions, we find evidence of ongoing star formation embedded in cores of 0.2 pc scales and (cid:38) cm − densities. Among the five clouds, Sgr C possesses a high (9%) fraction of gas mass in gravitationally boundand/or protostellar cores, and follows the dense ( (cid:38) cm − ) gas star formation relation that is extrapolatedfrom nearby clouds. The other four clouds have less than 1% of their cloud masses in gravitationally boundand/or protostellar cores, and star formation rates 10 times lower than predicted by the dense gas star formationrelation. At the spatial scale of these cores, the star formation efficiency is comparable to that in Galactic disksources. We suggest that the overall inactive star formation in these Central Molecular Zone clouds could bebecause there is much less gas confined in gravitationally bound cores, which may be a result of the strongturbulence in this region and/or the very early evolutionary stage of the clouds when collapse has only recentlystarted. Keywords:
Galatic: center — stars: formation — ISM: clouds INTRODUCTIONThe classic Kennicutt-Schmidt relation (Schmidt 1959;Kennicutt 1998) describes a correlation between the star for-mation rate (SFR) per unit area and the total gas mass (in-cluding both molecular and atomic gases) in galaxies. One ofits variations is a linear correlation between the SFR (tracedby infrared luminosities or young stellar object counts) andthe amount of dense ( (cid:38) cm − ) molecular gas found inboth Galactic sources and external galaxies (Gao & Solomon Corresponding author: Xing [email protected], [email protected] dense gas star for-mation relation . This linear correlation is suggested to be aresult of constant star formation efficiency (SFE) in molecu-lar gas of densities (cid:38) cm − (Lada et al. 2012).The Central Molecular Zone (CMZ; Figure 1), the inner500 pc of our Galaxy, does not fit into this correlation. Itcontains molecular gas of several times 10 M (cid:12) with meandensities of ∼ cm − (Morris & Serabyn 1996; Ferrièreet al. 2007; potential multiple density components from 10 to 10 cm − , Walmsley et al. 1986; Mills et al. 2018), butthe SFR is lower by at least an order of magnitude than ex-pected from the dense gas star formation relation, both onthe scale of the entire CMZ (e.g., Yusef-Zadeh et al. 2009; An a r X i v : . [ a s t r o - ph . GA ] F e b L U ET AL . ◦ ◦ Galactic Longitude18 − ◦ G a l a c t i c La t i t ude
10 pc
20 km s −
50 km s − G0.253+0.016Sgr B1-off Sgr CSgr D Sgr B2 × × × × × N ( H )( c m − ) × Figure 1.
An overview of the CMZ and the six clouds in our observations. The background image shows column densities derived from
Herschel data (Battersby et al. 2011). The black boxes mark the same areas toward the six clouds in Figure 2. Sgr B2 is not included in ourobservations but is discussed in Sections 4.2 & 4.3, and is marked by a blue box. The orbital model for the gas streams in the CMZ proposedby Kruijssen et al. (2015) is shown by the green dashed curve, with two black arrows indicating the direction of the proposed orbital motion. et al. 2011; Immer et al. 2012; Longmore et al. 2013a; Barneset al. 2017) and of individual clouds (e.g., Kauffmann et al.2013, 2017a; Barnes et al. 2017). Kauffmann et al. (2017a,b)studied star formation and dense gas content of several rep-resentative massive clouds in the CMZ, and concluded thatstar formation in a time scale of 1.1 Myr in some of the CMZclouds is (cid:38)
10 times lower than expected from the linear cor-relation of Lada et al. (2010).A possible explanation for the low SFR in the CMZ cloudsis that these clouds are at very early evolutionary phases andactive star formation has not emerged yet (Kruijssen et al.2014; Krumholz & Kruijssen 2015; Krumholz et al. 2017),although this may not be able to account for individual cloudsthat already show signatures of late evolutionary phases (e.g.,H II regions in several clouds; Kauffmann et al. 2017a). Pre-vious studies using infrared luminosities (e.g., Barnes et al.2017) or free-free emission from H II regions (e.g., Long-more et al. 2013a; Kauffmann et al. 2017a) generally char-acterize star formation in a time scale of a few Myr. Avery young generation of star formation deeply embeddedin dense gas that is invisible in infrared or free-free emis-sion could have been missed. This young generation of starformation can be traced by masers, ultra-compact (UC) H II regions, and hot molecular cores that are usually associatedwith star formation that occurred in the last < (cid:38) II regions and a lack of dense and massive clumps has been noted for the 50 km s − cloud (Kauffmann et al. 2017b).If we only consider the protostellar population formed in thelast 0.3 Myr (i.e., those formed within a time scale compa-rable to the crossing time), then the derived SFR should bemore relevant to the observed gas, although the ratio betweenstar formation and gas is still time-dependent and evolution-ary cycling matters.To investigate star formation at very early evolutionaryphases in the CMZ clouds, we conducted observations us-ing the Submillimeter Array (SMA) at 1.3 mm and the KarlJ. Jansky Very Large Array (VLA) at the K -band toward asample of six massive clouds (Figures 1 & 2): the 20 km s − cloud, the 50 km s − cloud, G0.253+0.016, Sgr B1-off (alsoknown as Dust Ridge clouds e/f), Sgr C, and Sgr D. Thissample has been studied with the SMA at 280 GHz in Kauff-mann et al. (2017a,b). Five of them have high column densi-ties ( > cm − ; Figures 1 & 2) and therefore are potentialsites of star formation. One cloud, Sgr D, which is associ-ated with an H II region in projection, has been suggested toreside outside of the CMZ (e.g., Sawada et al. 2009; Sakaiet al. 2017). We include it here as a control object. In ad-dition, Sgr B2 is one of the most active star forming regionsin the Galaxy and one that we cannot overlook in the CMZ,therefore we compile published data from the literature andinclude it in the discussion of star formation. Throughoutthis paper, we adopt a distance of 8.1 kpc (the best-fit dis-tance to Sgr A* in Gravity Collaboration et al. 2018), exceptfor Sgr D, which we adopt 2.36 kpc (the parallax distancefrom Sakai et al. 2017).In Section 2, we introduce details of the SMA and VLAobservations and data reduction. In Section 3, we present theSMA 1.3 mm continuum emission, based on which we iden-tify cores at the 0.2 pc scale and estimate virial states of thecores. We also present VLA K -band radio continuum emis-sion and H O masers. Then in Section 4, we search for signa-tures of early phase star formation embedded in the cores us-ing H O masers and UC H II regions. We then estimate SFRs TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS h m s s s s s RA (J2000)07 − ◦ D e c ( J )
20 km s − cloud 1 pc h m s s s RA (J2000)01 − ◦ − ◦ D e c ( J )
50 km s − cloud 1 pc h m s s s s RA (J2000)45 − ◦ D e c ( J ) G0.253+0.016 1 pc h m s s s s RA (J2000)33 − ◦ D e c ( J ) Sgr B1 off 1 pc h m s s s s RA (J2000)29 − ◦ D e c ( J ) Sgr C 1 pc h m s s s s RA (J2000)03 − ◦ D e c ( J ) Sgr D 1 pc
Figure 2.
The six clouds in the sample. Background three-color images show
Spitzer µ m (blue), 4.5 µ m (green), and 8.0 µ m (red) emission.Contours show column densities derived from Herschel data (Battersby et al. 2011), starting from 10 cm − in steps of 0.5 × cm − . Theyellow dashed and green dotted loops in each panel show the mosaic fields of the SMA and VLA, respectively. of the clouds in Section 4.2, and compare with the dense gasstar formation relation in Section 4.3. The conclusions are inSection 5. All the scripts used in the analyses in this paperare available at https://github.com/xinglunju/CMZclouds. OBSERVATIONS AND DATA REDUCTION2.1.
SMA Observations
The six clouds were observed with the SMA (Ho et al.2004) in the compact and subcompact array configurationsto obtain the 1.3 mm continuum and spectral lines (expectG0.253+0.016 in the compact array configuration, for whichwe used the archival data). Each cloud was mosaiced withtwo to eight pointings to cover dense regions seen in the col-umn density maps (see dashed loops in Figure 2). The ASIC The SMA is a joint project between the Smithsonian Astrophysical Ob-servatory and the Academia Sinica Institute of Astronomy and Astrophysics,and is funded by the Smithsonian Institution and the Academia Sinica. correlator was configured to cover 217–221 GHz in the lowersideband and 229–233 GHz in the upper sideband, with a uni-form channel width of 0.812 MHz (1.1 km s − at 1.3 mm).Part of the SMA observations toward the 20 km s − cloudhas been published in Lu et al. (2015, 2017). Details of theobservations are listed in Table 1.In addition, we obtained the archival SMA 1.3 mm data inthe compact array configuration toward G0.253+0.016 (PI:K. G. Johnston), which have been published in Johnston et al.(2014).The data from the two array configurations were calibratedusing the IDL superset MIR . Continuum visibility modelswere fit using line-free channels with MIRIAD (Sault et al.1995). Then the two datasets were combined and imagedto produce continuum maps with CASA 4.2.0 (McMullinet al. 2007). Spectral lines were split from the continuum- L U ET AL . Table 1.
Summary of the SMA and VLA observations.
Project ID / PI Config. b antennas pointings a Bandpass Flux GainSMA 1.3 mm2012B-S097 / Q. Zhang SUBCOM 5 2013 May 21 20 km s − , Sgr C 8+3 Q1 Titan, Neptune Q2, Q3SUBCOM 5 2013 Aug 23 50 km s − , Sgr B1-off 4+6 Q1, Q4 Neptune Q2, Q32013A-S049 / X. Lu COM 6 2013 Jul 24 20 km s − − , Sgr C 4+3 Q1 Neptune Q2, Q3COM 6 2013 Aug 01 Sgr B1-off, Sgr D 6+2 Q1 Neptune Q2, Q3COM 6 2013 Aug 02 Sgr B1-off, Sgr D 6+2 Q1 MWC349A Q2, Q3COM 5 2013 Aug 03 20 km s − − − , 50 km s − − − − subtracted visibility data and were imaged separately with auniform channel width of 1.1 km s − . For all images, weused the Briggs weighting with a robustness of 0.5. We didnot use multiscale CLEAN or combine with single-dish data,as in our previous work (Lu et al. 2017), because in this pa-per we intended to study compact cores; therefore, we do notneed information on extended structures.The achieved rms and synthesized beam sizes are summa-rized in Table 2. The typical synthesized beam size (an-gular resolution) of continuum images is 5 (cid:48)(cid:48) × (cid:48)(cid:48) (equiva-lent to 0.2 pc × − . The continuum imagesand selected spectral line images are publicly available athttps://doi.org/10.5281/zenodo.1436909.The images presented in figures throughout this paper arewithout primary beam corrections. These images have uni-form rms levels across maps and are good for presentation,but the fluxes are attenuated toward the edge of the images.Therefore, when calculating densities and masses (e.g., inSection 3.1), we applied primary beam corrections to the im-ages to have correct fluxes.2.2. VLA Observations
The sample was observed with the NRAO Karl G. JanskyVLA in the DnC configuration, using a K -band setup thatcovers five metastable NH lines from ( J , K )=(1, 1) to (5, 5), The National Radio Astronomy Observatory is a facility of the NationalScience Foundation operated under cooperative agreement by AssociatedUniversities, Inc. an H O maser line at 22.235 GHz, and 1 GHz wide contin-uum centered at ∼
23 GHz. Part of the observations towardthe 20 km s − cloud has been published in Lu et al. (2015,2017), and details of the VLA observations can be found inTable 1.The data were calibrated using CASA 4.3.0. In the20 km s − cloud, Sgr C, and Sgr D, bright ( > Omasers are detected, so we performed self-calibration withthe channel where the peak H O maser emission is found.We tried two or three rounds of phase-only self-calibration,until the image rms stopped to improve, and did a final roundof phase and amplitude self-calibration. Then we appliedthe calibration tables to the data and produced images of theH O masers (see the next paragraph). We compared fluxes ofthe masers in the final image with those in the initial image tomake sure the amplitude is consistent. The rms of channelswith strong maser signals was significantly improved, and theachieved dynamic range is up to ∼ > O masers. The typical achieved
TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS Table 2.
Properties of the SMA/VLA images.
Continuum Spectral linesImages Bandwidth Beam size & PA RMS Channel width Beam size & PA RMS(GHz) ( (cid:48)(cid:48) × (cid:48)(cid:48) , ◦ ) (mJy beam − ) (km s − ) ( (cid:48)(cid:48) × (cid:48)(cid:48) , ◦ ) (mJy beam − )SMA 1.3 mm20 km s − × × − × × × × − × − × − × × × × − × × − × − × − × × × − × − × − × − × − × − OTE —Beams and rms of the SMA spectral line images are measured for line-free channels of SiO 5–4 images not corrected for primary beam response, but they slightly vary betweendifferent lines. Beams and rms of the VLA spectral line images are measured for line-free channels of H O maser images. The rms of the SMA and VLA continuum images aremeasured in emission-free regions away from the emission peaks not corrected for primary beam response. rms is 5 mJy beam − in 0.2 km s − for the H O maser, and35–200 µ Jy beam − for the continuum depending on the tar-get, with a beam size of 3 (cid:48)(cid:48) × (cid:48)(cid:48) , as summarized in Table 2.The continuum and maser images are publicly available athttps://doi.org/10.5281/zenodo.1436909. RESULTS3.1.
SMA Dust Emission
The SMA 1.3 mm continuum emission maps of the sixclouds are shown in Figure 3. We identified compact struc-tures with peak values above the 5 σ level and areas largerthan the synthesized beams, and within FWHM of the SMAprimary beams. Then we fit 2D Gaussians using the inter-active tool in CASAviewer to obtain their positions, decon-volved FWHM sizes, and fluxes. To have uniform noiselevels so that we can apply the same fitting criteria acrossthe maps, we performed the fit in the images without pri-mary beam corrections. We took the deconvolved FWHMof the 2D Gaussians as the sizes of the compact structures.The fluxes inside the deconvolved FWHM of the 2D Gaus-sians are half of the measured fluxes of the whole Gaussianprofiles, which we took as the fluxes of the compact struc-tures after applying the primary beam correction. In Sec-tion 3.1, we derived the mean densities inside the decon-volved FWHM sizes using these fluxes.The dendrogram algorithm is a widely used method forsource identification in radio astronomy (Rosolowsky et al.2008). We compared our result with the outcome of dendro-gram, shown in Appendix A, and found that they are gener-ally consistent. However, dendrogram is not able to separate closely packed structures (e.g., the two emission peaks in thesouthwestern end of Sgr C). It also misses several compactstructures that are slightly smaller than the synthesized beamsize but are spatially coincident with H O masers and there-fore are likely protostellar cores in nature (e.g., in the south-ern part of the 20 km s − cloud). In light of this, we chose torely on manual identification and added these structures forconsideration.In the end, we identified 58 structures, marked by ellipsesin Figure 3. They are named by the indices of ‘clumps’ theybelong to, plus the indices of peaks inside the clumps in de-creasing order of peak intensities. Here the clumps do nothave physical meanings but are for name tagging.We stress that the identification of compact structures isunlikely to be complete. Some features, especially those incrowded environments (e.g., the C4 clump in the 20 km s − cloud, the C2 clump in Sgr C), may have been missed. Nev-ertheless, we intended to study characteristic physical prop-erties of dense gas in these clouds, and structures identifiedusing this approach make up a good sample for our purpose.At the wavelength of 1.3 mm, the continuum emission inmolecular clouds is often attributed to thermal dust emissionassociated with dense gas (e.g., Beuther et al. 2002), but canalso be free-free emission from embedded H II regions (e.g.,Motte et al. 2003). To examine potential contribution fromfree-free emission, we compared the 1.3 mm continuum withthe radio continuum data in Section 3.4. Two compact struc-tures, C2P1 and C2P2 in the 50 km s − cloud, are associ-ated with radio continuum emission of similar or even higherfluxes than the 1.3 mm continuum emission. As discussed L U ET AL . Table 3.
Properties of cores.
Core ID R.A. & Decl. Deconvl. size & PA r c Flux a M core n (H ) σ totb α vir SF Indicators c (J2000) ( (cid:48)(cid:48) × (cid:48)(cid:48) , ◦ ) (pc) (mJy) ( M (cid:12) ) (10 cm − ) (km s − )20 km s − C1P1 17:45:37.58, − × − × − × − × − × − × − × − × − × − × − × − × − × − < × < > < − × − × − × − C1P1 17:45:52.08, − × − × − × − × − × − × − × − × − × − × − < × < > · · · · · · C3P1 17:46:10.63, − × − × − × − × − × − × − × − × − × − × − × − × − × · · · · · · C2P6 17:46:47.32, − × − × − × − × − × − × − × − × − × − × − × − × − × − × − × OH line. Otherwise they are derived from the SMA N H + line (Kauffmann et al.2017a).c W and H refer to H O masers and H II regions, respectively, with details in Sections 3.4 & 3.5.N OTE —Uncertainties of the core properties are discussed in Section 3.3.
TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS h m s s s RA (J2000)07 − ◦ D e c ( J )
20 km s − cloud H2 H10.05 0.10 0.15 17 h m s s s
2D Gaussians
C5P1 C5P2C4P1C4P2 C4P3C4P4C4P5C4P6C3P1C3P2C3P3 C2P1C2P2C2P3 C1P1C1P2C1P3 h m s s s RA (J2000) − ◦ − ◦ D e c ( J )
50 km s − cloud H1H2H3H40.02 0.03 17 h m s s s
2D Gaussians
C1P1C1P2C2P1 C2P2
Figure 3.
The SMA 1.3 mm continuum and VLA radio continuum emission in the six clouds. On the left side of each panel, both the backgroundimage and the grey contours show the SMA 1.3 mm continuum emission, with the scale bar attached to the top in the unit of Jy beam − . Thecontours start at the 5 σ level and increase in the step of 10 σ , where 1 σ is 4 mJy beam − for Sgr D, 2 mJy beam − for G0.253+0.016, and3 mJy beam − for the other four clouds. The green contours show the VLA radio continuum emission, starting at the 5 σ level in the step of10 σ (aside from Sgr D where the step is 20 σ ), where 1 σ values for each map can be found in Table 2. For both the SMA and VLA continuumemissions, dashed contours at the − σ level are plotted to show the level of imaging artifacts. (UC) H II regions identified in Section 3.4 aremarked by arrows and labeled. The dashed and dotted loops show the mosaic fields of the SMA and VLA, respectively. The synthesized beamsof the SMA and VLA are shown in the bottom left corner. On the right side of each panel, the background image is identical with that on theleft side, while the ellipses show the FWHM of 2D Gaussians fit to the cores. L U ET AL .in Section 3.4, the radio continuum in the 50 km s − cloudarises from several known H II regions. The 1.3 mm con-tinuum emission of the two compact structures therefore islikely dominated by free-free emission from the H II regions.These two structures are excluded from Table 3. A few com-pact structures in the 20 km s − cloud, Sgr B1-off, Sgr C,and Sgr D are also found to be associated with compact radiocontinuum emission, which is much weaker than the 1.3 mmcontinuum emission.We obtained dust emission fluxes of the compact structuresafter excluding the contribution from free-free emission inthe 1.3 mm continuum emission. We used a flat spectralindex from centimeter to 1.3 mm, assuming slightly opti-cally thick thermal free-free emission. If there is any op-tically thick free-free emission from hyper-compact H II re-gions, the spectral index between the frequencies of the VLAand SMA observations may be positive (rising), and the free-free contribution in the 1.3 mm continuum emission will begreater. However, hyper-compact H II regions are rare (theonly known cases in the CMZ are six hyper-compact H II re-gions in Sgr B2; De Pree et al. 2015), so we did not con-sider optically thick free-free emission in our assumption.Then we subtracted the radio continuum fluxes inside theFWHM of the compact structures from the corresponding1.3 mm continuum fluxes and obtained the dust emissionfluxes, which are listed in parentheses in Table 3. Follow-ing the nomenclature of Zhang et al. (2009), these structureswith typical radii of 0.1 pc are defined as cores. Excludingthe two compact structures in the 50 km s − cloud that aredominated by free-free emission, we identified 56 cores inthe six clouds, as listed in Table 3.We derived core masses following M core = R S ν d B ν ( T dust ) κ ν , (1)where R is the gas-to-dust mass ratio, S ν is the dust emissionflux, d is the distance, B ν ( T dust ) is the Planck function atthe dust temperature T dust , and κ ν is the dust opacity. Weassumed R =100, and κ ν =0.899 cm g − (MRN model withthin ice mantles, after 10 years of coagulation at 10 cm − ;Ossenkopf & Henning 1994). We assumed T dust = 20 K forthe cores, except for those in Sgr D where T dust is taken tobe 25 K, which are estimated from multi-band SED fittingof Herschel data (Kauffmann et al. 2017a). The masses ofthe cores are listed in Table 3. With a dust emission rms of3 mJy beam − , the 5 σ mass sensitivity is 22 M (cid:12) per beamfor the CMZ clouds.Assuming a spherical geometry with a radius r a that isequivalent to half of the geometric mean of the deconvolvedangular sizes of the cores, densities of molecular gas in the cores are derived with n ( H ) = 3 M core πr a d . m H = R S ν B ν ( T dust ) κ ν πr a d . m H , (2)where 2.8 is the molecular weight per H molecule (Kauff-mann et al. 2008) and m H is the mass of a hydrogen atom.We caution that these cores are defined in terms of theirspatial scales, but they are more massive than dense cores innearby molecular clouds at the same spatial scale (e.g., Alveset al. 2007), and their densities are an order of magnitudehigher ( (cid:38) cm − vs. ∼ cm − ). They may each forma cluster of stars instead of a single star or a multiple starsystem as assumed for those dense cores in nearby clouds.With higher angular resolutions, they may be further resolvedinto objects that map to individual protostars (e.g., Ginsburget al. 2018).Sgr B1-off is included in the SMA sample of Walker et al.(2018) with a similar observation setup. They identified twocores e1 and e2, corresponding to C2P1 and C2P2 in thiscloud in Figure 3 and Table 3. The masses we derived are40% to 50% smaller than their results, because we only con-sidered fluxes inside the deconvolved FWHM sizes thereforethe measured fluxes are smaller. They also estimated den-sities of these cores to be 10 –10 cm − , much higher thanthose of dense cores in nearby clouds.3.2. Virial States of the Cores
We studied virial states of the cores in these clouds. Thevirial parameter is defined as (Bertoldi & McKee 1992) α vir = 5 σ tot r a d G M core , (3)in which r a is the angular radius of the core as defined above,and σ tot is the total one-dimensional line width including boththermal and non-thermal components. The properties can befound in Table 3.The total line width σ tot was measured with the N H + (cid:38) cm − at a temperature of (cid:38)
50 K (Shirley 2015).In the starless core candidates where gas temperatures arelow (see Section 4.1.4), N H + may be chemically biased to-ward denser regions where CO is frozen out onto dust grains,therefore it may preferentially trace smaller line widths fromsmaller spatial scales (Caselli et al. 2002). When N H + is not detected, the CH OH line in our SMA 1.3 mm linedata (not combined with single-dish data) is used, which hasbeen shown to best spatially correlated with the dust emissionamong the 1.3 mm molecular lines (Lu et al. 2017). How-ever, CH OH is likely influenced by shocks, so we only usedit as a second choice. Two cores, C2P6 in G0.253+0.016 and
TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS h m s s s RA (J2000)44 − ◦ D e c ( J ) G0.253+0.016 h m s s s
2D Gaussians
C1P1 C1P2C1P3C2P1C2P2 C2P3C2P4C2P5 C2P6C3P1C3P2C3P3C3P4 C4P1 C4P2C4P3 h m s s s RA (J2000)32 − ◦ D e c ( J ) Sgr B1 off
H10.05 0.10 0.15 17 h m s s s
2D Gaussians
C1P1C2P1C2P2C2P3C2P4 C2P5C2P6
Figure 3. (Continued)
U ET AL ..
U ET AL .. h m s s s RA (J2000)29 − ◦ D e c ( J ) Sgr C
H1H2 H3H40.1 0.2 0.3 17 h m s s s
2D Gaussians
C1P1C2P1 C3P1C3P2C3P3 C4P1C4P2C5P1 C5P2 h m s s s RA (J2000)03 − ◦ D e c ( J ) Sgr D H1 h m s s s
2D Gaussians
C1P1C1P2C1P3C1P4C1P5
Figure 3. (Continued)
C2P5 in Sgr B1-off, are not detected in N H + or CH OHlines, therefore their virial parameters cannot be determined.We fit a single Gaussian to the mean spectrum of each core,shown in Appendix C, to obtain the intrinsic line width σ v that is deconvolved from the channel width. When both theN H + and CH OH lines are detected, the line widths mea-sured from them are usually consistent within a factor of 1.5.Our VLA observations cover five VLA NH lines, butwe did not use them to measure line widths of the coresfor three reasons. First, for the lower NH transitions, ( J , K )=(1, 1), (2, 2), and (3, 3), the hyperfine components tendto be blended together and strong absorption features are fre-quently seen toward the cores. Second, for the higher NH transitions, ( J , K )=(4, 4) and (5, 5), the signal-to-noise ratio is much lower (e.g., Figure 15 of Lu et al. 2017). Third, thecritical densities of the NH lines are of the order 10 cm − at a temperature of (cid:38)
50 K (Shirley 2015), therefore may notbe as good as N H + for tracing of gas in the cores. Nonethe-less, we attempted to fit the NH spectra when they are opti-cally thin and absorption is not significant (e.g., toward C1P1in the 20 km s − cloud), and the measured line widths agreewith those based on N H + within a factor of 1.5.We assume a gas temperature T gas of 100 K. This is thetypical temperature for cores at 0.2 pc scales based on non-LTE modeling of NH (2, 2) and (4, 4) lines (Lu et al. 2017),and it generally agrees with those in previous observations(Ao et al. 2013; Ginsburg et al. 2016; Krieger et al. 2017). TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS σ tot : σ tot = (cid:115) σ v − k B T gas µ m m p + k B T gas µ p m p , (4)in which the mean molecule weight µ p is 2.33, assuming90% H and 10% He, and µ m is 29 or 32 (i.e., the moleculeweight of N H + or CH OH, depending on which line is usedto measure the linewidth).The derived virial parameters α vir are listed in Table 3. Outof the 54 cores whose virial parameters can be determined, 17have α vir ≤ . These cores are likely gravitationally boundand unstable to collapse.3.3. Uncertainties of Core Properties
We reported uncertainties in the derived masses, densities,line widths, and virial parameters of the cores. The uncer-tainties are summarized in Table 4.The derived core masses depend on the dust opacity, thegas-to-dust mass ratio, dust temperatures, dust emissionfluxes, and distances. We followed Sanhueza et al. (2017) toadopt uncertainties of 28% and 15% for the dust opacity andmeasured dust emission fluxes at 1.3 mm. The uncertainty inthe distance to Sgr A* is small (0.4%; Gravity Collaborationet al. 2018). However, given that the clouds may be on anorbit of radius ∼
100 pc around Sgr A* (Molinari et al. 2011;Kruijssen et al. 2015), we adopt an uncertainty of ±
100 pc(1.2%) for the distance.The gas-to-dust mass ratio has a large uncertainty. Thevalue of 100 adopted for Equation 1 is characteristic fornearby clouds, although values up to 150 have been sug-gested (Draine 2011). On the other hand, the value for Galac-tic Center regions may be as low as ∼
50 (Giannetti et al.2017). Therefore, the uncertainty in the gas-to-dust ratio isadopted to be 50%.The dust temperature may have a large systematic errorfor the cores that are internally heated by protostars. Itcould reach 50 K around hot molecular cores at the radiusof 0.1 pc (Longmore et al. 2011), in which case the derivedcore masses using Equation 1 would decrease by a factor of3. This only affects cores with significant internal heating(potentially those with star formation indicators in Table 3),and may not be an issue for cores without signatures of starformation. Further discussion about the impact of the dusttemperature is in Section 4.1.4.We propagated uncertainties (random errors) in the dustopacity, the gas-to-dust ratio, dust emission fluxes, and thedistance, but excluded the systematic error in the dust tem-perature, and obtained an uncertainty of 59% for the masses.For cores with significant internal heating therefore poten-tially higher dust temperatures (e.g., assuming T dust = 50 K),the derived masses could systematically decrease by a factorof 3. The derived densities of the cores depend on the angularsizes and all the quantities that determine the masses. Themeasured angular sizes usually have uncertainties of 10%.We propagated these random errors but excluded the system-atic error in the dust temperature, and obtained an uncertaintyof 66% for the densities. Similar to the masses, for cores withsignificant internal heating with an assumed T dust = 50 K, thedensities could systematically decrease by a factor of 3.The fitting errors of the line widths, as shown in Ap-pendix C, are usually ∼ H + may be overestimated, when the lines are optically thick andthe hyperfine structure of N H + is considered (Caselli et al.2002). Second, absorption features are seen in several N H + spectra, probably due to missing flux of interferometers (seeAppendix C), which may lead to underestimated line widths.A third issue is the choice of the component to be fit whenthere are multiple velocity components, especially in the caseof G0.253+0.016 (Figure 16) where several components ofsimilar brightnesses are seen in the cores, making it ambigu-ous which component should be considered. In general, weadopted an uncertainty of 50% for all the line widths.Finally, the random errors of the masses, the line widths,and the angular sizes all propagate into that of the derivedvirial parameters. We estimated a large uncertainty of 120%(or a factor of 2.2) for the virial parameters without consider-ing the systematic error in the dust temperature, and an evenlarger uncertainty (a factor of >
4) for cores with significantinternal heating whose masses may be systematically overes-timated by a factor of 3. In addition to the uncertainties in thederived virial parameters, there are several factors that mayaffect the critical virial parameter. First, the magnetic fieldat 1 pc scales in G0.253+0.016 is suggested to be ∼ B = 5 mG, thecritical virial parameter would be as low as <
1, and most ofthe cores would be gravitationally unbound. Second, we haveignored rotation of the cores in the plane of the sky, whichmay be able to support them against collapse and make thecritical virial parameter smaller.3.4.
VLA Radio Continuum Emission
Radio continuum emission at 23 GHz obtained by the VLAis displayed as green contours in Figure 3. There are severalknown H II regions: one in the 20 km s − cloud (Ho et al.1985), four in the 50 km s − cloud (Goss et al. 1985; Millset al. 2011), and one in Sgr D (Liszt 1992). Our observa-tions confirmed radio continuum emission from them. Wealso detected several fainter compact sources that are associ-2 L U ET AL ..
Radio continuum emission at 23 GHz obtained by the VLAis displayed as green contours in Figure 3. There are severalknown H II regions: one in the 20 km s − cloud (Ho et al.1985), four in the 50 km s − cloud (Goss et al. 1985; Millset al. 2011), and one in Sgr D (Liszt 1992). Our observa-tions confirmed radio continuum emission from them. Wealso detected several fainter compact sources that are associ-2 L U ET AL .. Table 4.
Summary of uncertainties in derived core properties.
Core properties Related equations Considered quantities and random errors a Uncertainties b Mass ( M core ) Equation 1 κ ν (28%), S ν (15%), d (1.2%), R (50%) 59%Density ( n (H )) Equation 2 κ ν (28%), S ν (15%), d (1.2%), R (50%), r a (10%) 66%Virial parameter ( α vir ) Equation 3 κ ν (28%), S ν (15%), d (1.2%), R (50%), r a (10%), σ tot (50%) 120%a Details of the quantities can be found in Sections 3.1 & 3.2. κ ν – dust opaticy. S ν – dust emission flux. d – distance. R – gas-to-dust ratio. r a – angular size. σ tot – line width.b The dust temperature T dust has a large systematic error for the protostellar core candidates, and its effect on uncertainties of the derived properties is not considered here. We considerthe effect of T dust separately in Section 3.3. h m s s s s RA (J2000)07 D e c ( J )
20 km s cloud W0W1 W2W3 W4W5W6 W7W8W9W10W11-W13 W14W15W16W17 W18W19 h m s s s s RA (J2000) − ◦ − ◦ D e c ( J )
50 km s − cloud W1W2 W3W4
Figure 4.
VLA H O masers in the six clouds. The background images and contours show the SMA 1.3 mm continuum emission, and thedashed and dotted loops show the mosaic field of the SMA and VLA, which are identical to those in Figure 3. H O masers are marked bycrosses, among which red ones are those with AGB star counterparts. ated with dust emission, which may be embedded UC H II regions. Among them, the nature of the radio continuumin G0.253+0.016 has been discussed in Rodríguez & Zapata(2013) and Mills et al. (2015); one UC H II region in Sgr Chas been studied in Forster & Caswell (2000) and Kendrewet al. (2013); the UC H II region in the 20 km s − cloud hasbeen reported in Lu et al. (2017). In addition, we found onecompact radio continuum source in Sgr B1-off that is asso- ciated with a core, and several in Sgr C that have likely dustemission counterparts. Their nature will be discussed in Sec-tion 4.1.2. The detections are named with the letter ‘H’ plusa number by decreasing declinations in each cloud, and aremarked in Figure 3. In general, their morphologies are notellipse-like, so we did not fit 2D Gaussians to them, but mea-sured their fluxes above the 3 σ level contour and listed theresults in Table 5. TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS h m s s s RA (J2000)44 − ◦ D e c ( J ) G0.253+0.016
W1W2W3 h m s s s RA (J2000)32 − ◦ D e c ( J ) Sgr B1 off
W1W2W3W4 W5W6
Figure 4. (Continued)
Filamentary radio continuum emission of > − cloud and Sgr B1-off. Such structure in theCMZ has been suggested to have non-thermal origins (Hoet al. 1985; Lu et al. 2003; Zhao et al. 2016). As these arenot related to recent star formation, we do not consider themfurther in this paper. Several compact radio continuum emis-sion peaks without dust emission counterparts are also found(e.g., in Sgr C). They may be associated with more evolvedH II regions at late evolutionary phases, therefore are not con-sidered either. 3.5. VLA H O Masers
In our previous work (Lu et al. 2015), we reported the de-tection of 18 H O masers in the 20 km s − cloud. Here wesearched for H O masers in all the six clouds in our sample.All point sources with peak intensities above the 8 σ levelwere identified, where 1 σ is ∼ − in 0.2 km s − velocity bin (see Table 2), but we excluded those found indynamic-range limited channels, where the rms is signif-icantly higher than the theoretical sensitivity, as these are likely sidelobes of strong sources . Multiple velocity com-ponents along the same line of sight were counted as a singlemaser. In addition, several strong masers were found outsidethe FWHM of the VLA primary beams. For example, in the20 km s − cloud, we found two masers close to or outsideof the VLA primary beam boundaries in addition to the 18masers reported in Lu et al. (2015). Such masers are alsoseen in the 50 km s − cloud, Sgr C, and Sgr D. We took theminto account if their peak intensities are above the 10 σ level.A total of 56 H O masers were identified in the six clouds.We fit 2D Gaussians to the integrated intensity maps of themasers to determine their positions and integrated fluxes. Theresults are listed in Table 6, while the positions are marked inFigure 4 and the complete spectra shown in Appendix B. Themasers are named by decreasing declinations in each cloud.Note that in the 20 km s − cloud, we started with ‘W0’ that is This could leave out faint masers in such channels, but we note thatdynamic-range limited channels are only found within ± − ) of the brightest channels after self-calibration.This is a small fraction of the velocity ranges of the clouds, which are usually >
10 km s − , although it may become a problem if star formation is highlyclustered around the brightest masers in space and velocity. U ET AL ..
10 km s − , although it may become a problem if star formation is highlyclustered around the brightest masers in space and velocity. U ET AL .. h m s s s RA (J2000)29 − ◦ D e c ( J ) Sgr C
W1W2W3 W4W5 W6 W7 W8W9W10W11 W12W13W14 W15 W16 h m s s s RA (J2000)03 − ◦ D e c ( J ) Sgr D
W1 W2 W3W4 W5W6W7
Figure 4. (Continued)
Table 5.
Properties of H II regions. H II region ID R.A. & Decl. a F ν b log N c Spectral type c ZAMS mass c References & Alternative identifiers(J2000) (mJy) (s − ) ( M (cid:12) )20 km s − H1 17:45:37.59, − − − H1 17:45:52.23, − − − − − · · · Sgr C H1 17:44:41.20, − · · · H2 17:44:40.92, − · · · H3 17:44:40.19, − − − − II region.b Fluxes have been corrected for primary-beam response.c Spectral types and ZAMS masses of the (UC) H II regions are estimated following Panagia (1973) and Davies et al. (2011). outside of the VLA primary beams, in order to be consistentwith the catalog in Lu et al. (2015), while in the other cloudswe started with ‘W1’.The coordinates and fluxes of the masers in the 20 km s − cloud are slightly different from those reported in Lu et al.(2015), but are still within the pointing or flux calibrationuncertainties (position differences < (cid:48)(cid:48) , flux differences < O masers anddust emission is generally found in Figure 4, it is interestingto note that several H O masers in G0.253+0.016 (e.g., W1and W3) and Sgr B1-off (e.g., W1) do not seem to be asso-ciated with any dust emission. They may be unrelated to starformation and will be further discussed in Section 4.1.1.
TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS DISCUSSION4.1.
Signatures of Embedded Star Formation
We discuss signatures of star formation associated with thecores, and compare densities and virial states of the protostel-lar and starless core candidates.4.1.1. H O Masers H O masers have been detected in both low-mass ( ≤ M (cid:12) )and high-mass ( ≥ M (cid:12) ) star forming regions (Furuya et al.2003; Szymczak et al. 2005; Urquhart et al. 2011) and aresuggested to be associated with protostellar outflows (Elitzuret al. 1989; Codella et al. 2004). However, they may also bedetectable toward the atmosphere of AGB stars. We com-pare our maser detections with the AGB star catalogs ofLindqvist et al. (1992), Sevenster et al. (1997), Sjouwermanet al. (1998, 2002), and Messineo et al. (2002), which arebased on detections of OH/SiO masers, and with the catalogof Robitaille et al. (2008), which is based on infrared colorcriteria. Five of the H O masers have AGB star counterpartsand are marked as red crosses in Figure 4: W6 and W18 inthe 20 km s − cloud, W1 and W3 in the 50 km s − cloud,and W2 in Sgr B1-off. We thus excluded them in the follow-ing analysis. It is also possible that the AGB star catalogsare incomplete, therefore there may be more contaminationfrom uncataloged AGB stars.Another possibility is that the masers are created by pc-scale shocks, similar to the case of wide-spread class I CH OH masers found in the CMZ (Yusef-Zadeh et al. 2013).However, as we have argued in Lu et al. (2015), this is un-likely for most H O masers we detected, given their strongspatial correlation with the cores and their largely scat-tered velocities. For the eight H O masers not associatedwith detectable dust emission in the 50 km s − cloud (W4),G0.253+0.016 (W1, W3), Sgr B1-off (W1, W4, W6), andSgr C (W4, W15), however, this is a viable scenario. Al-ternatively, these masers may be associated with low-massprotostellar cores that are missed by our observations (e.g.,below the 5 σ mass sensitivity of 22 M (cid:12) ) or uncatalogedAGB stars.There are also six H O masers detected outside of theSMA mosaic fields and not associated with known AGB starsor other types of masers, including W0, W4, W7, and W19 inthe 20 km s − cloud, and W1 and W16 in Sgr C (but exclud-ing W1 in Sgr D that is associated with a class II CH OHmaser, see Section 4.1.3), therefore their association withdust emission is unknown and their nature cannot be deter-mined.Thus, we conclude that most (37 out of 56, a percentageof 66%) of the detected H O masers are likely associatedwith star formation activities. It is unclear whether they tracelow-mass or high-mass star formation. If we adopt the em-pirical correlation between the luminosities of H O masers and young stellar objects (e.g., Urquhart et al. 2011), thenthe more luminous H O masers ( (cid:38) − L (cid:12) ) would be as-sociated with high-mass young stellar objects. As listed inTable 6, there are 19 such masers in our observations, and wenote that some of them are associated with UC H II regions orclass II CH OH masers, which signify high-mass star forma-tion (see the next two sections). However, the scatter in thecorrelation of Urquhart et al. (2011) is large, and due to thetime variability of H O masers, their luminosities can changeby several orders of magnitude over several years (Felli et al.2007). We cannot rule out the possibility that some of thefainter masers are associated with high-mass star formation,or that some of the luminous H O masers trace low-mass starformation. 4.1.2. H II Regions H II regions are created by high-mass protostars of O orearly-B types (Churchwell 2002). As shown in Section 3.4,we confirm the existence of H II regions in the 20 km s − cloud, the 50 km s − cloud, and Sgr D using the VLA ra-dio continuum emission. In addition, several potential UCH II regions of < − cloud, Sgr B1-off, and Sgr C, and marked in Figure 3. We donot know their spectral indices, therefore are unable to ver-ify whether the radio continuum emission represents a ther-mal free-free component. However, the close spatial correla-tions with compact dust emission suggest that they are morelikely to be UC H II regions embedded in cores. Note that inG0.253+0.016 we detect radio continuum emission towardsthe core C2P1, but this emission has been suggested to be un-related to star formation (Mills et al. 2011, labeled as C3 intheir Figure 2). C2P1 is gravitationally unbound accordingto our virial analysis in Section 3.2 and is unlikely to formstars. Therefore, this emission is not identified as an UC H II region.The ionizing photon fluxes of H II regions N c are estimatedfrom their radio continuum emission, assuming optically thinfree-free emission and an electron temperature of 10 K, fol-lowing Mezger et al. (1974). Then assuming that each of theH II regions is powered by a single star, we determine spec-tral types of the ionizing sources by comparing to the fluxesof ZAMS stars in Panagia (1973) and Davies et al. (2011),and estimate their stellar masses. The results are listed inTable 5. 4.1.3. Other Types of Masers from Literature
Early evolutionary phases of star formation in these cloudsare also revealed by OH masers and CH OH masers. OHmasers have also been detected toward AGB stars, as dis-cussed in Section 4.1.1. Meanwhile, radiatively excitedclass II CH OH masers have been suggested to uniquelytrace high-mass star formation (Menten 1991; Ellingsen2006; Breen et al. 2013).6 L
U ET AL ..
U ET AL .. Table 6.
Properties of H O masers.
Maser ID R.A. & Decl. v peaka F peaka,b F integratedb L H O Cores/clumps Other masers(J2000) (km s − ) (mJy per channel) (mJy · km s − ) (10 − L (cid:12) )20 km s − W0 17:45:36.06, − − · · · W1 17:45:38.10, − − − − · · · W5 17:45:37.76, − − − · · · W8 17:45:37.68, − − − − − − − − − − − − − − − − − · · ·
50 km s − W1 17:45:49.41, − − − − − · · · G0.253+0.016 W1 17:46:08.90, − · · · W2 17:46:10.62, − − · · · Sgr B1-off W1 17:46:44.39, − · · · W2 17:46:43.41, − − − · · · W5 17:46:47.05, − II CH OHW6 17:46:46.73, − − · · · Sgr C W1 17:44:40.21, − − · · · W2 17:44:43.56, − − − − · · · W5 17:44:41.59, − − − − − − − − − − − − − − − − II CH OHW13 17:44:40.60, − − II CH OHW14 17:44:42.90, − − − − · · · W16 17:44:38.22, − − · · · Sgr D W1 17:48:48.55, − − · · · class II CH OHW2 17:48:42.96, − − − − − − − − − − − V lsr and flux of the strongest peak is listed, while the complete spectra can be found inAppendix B.b Peak fluxes and integrated fluxes have been corrected for primary-beam response. TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS O maser W13 and the core C4P1 in Sgr C.The class II CH OH maser catalog is taken from Caswellet al. (2010). Four masers are found, in Sgr B1-off towardsW5/C2P1, in Sgr C toward W12/C4P2 and W13/C4P1, andin Sgr D towards W1. Their H O maser counterparts arebright ( (cid:38) − L (cid:12) ), consistent with being associated withhigh-mass star formation (Section 4.1.1).Therefore, we conclude that our H O maser observationsrecover all previously detected star formation sites traced byOH and class II CH OH masers. Nevertheless, the detectionof class II CH OH masers helps to confirm high-mass starformation. We listed all these detections in the last columnof Table 6.4.1.4.
Densities and Virial States of Protostellar and StarlessCores
We classify the cores in a straightforward way as ‘pro-tostellar’, which are associated with H O masers and/or(UC) H II regions, and ‘starless’, where none of the star for-mation indicators is detected. Excluding Sgr D, we find 21protostellar core candidates and 28 starless core candidates inthe five CMZ clouds, as indicated in Table 3. With our classi-fication, the starless core sample may be contaminated (e.g.,some of the objects may already harbor protostars), while theprotostellar core sample is precise (i.e., all the cores in thissample are likely forming stars, minus potential contamina-tion by AGB stars) but is likely incomplete.One property that may be able to modulate star forma-tion in these cores is the density n (H ). A wide varietyof recent papers (Kruijssen et al. 2014; Rathborne et al.2014; Krumholz & Kruijssen 2015; Federrath et al. 2016;Krumholz et al. 2017; Ginsburg et al. 2018) have predicted ormeasured a density threshold for star formation in the CMZof 10 –10 cm − , which is much higher than the thresholdin the Galactic disk clouds, ∼ cm − (Lada et al. 2012).The other property significantly affecting star formation isthe virial parameter α vir (see Section 3.2), which determinesthe gravitational boundness of the cores. In Figure 5a, weplot these two properties of the protostellar and starless corecandidates.It is clear from Figure 5a that the protostellar core candi-dates tend to have higher densities and smaller virial parame- ters than the starless core candidates. We run a Kolmogorov-Smirnov (K-S) test to quantify how different the two samplesare in terms of densities and virial parameters. Usually whenthe p-value is much smaller than 0.05, the difference betweenthe two samples is significant, and when the p -value is muchlarger than 0.05, the difference is not significant and we can-not rule out the possibility that the two samples are drawnfrom the same distribution. The p -values from the K-S testof the densities or virial parameters of the two samples are < × − , suggesting the difference between the two sam-ples is statistically significant.However, we do not find a clear density or virial parame-ter threshold between the protostellar and starless core can-didates. The lowest density found in protostellar core can-didates is 1.0 × cm − , which is one order of magnitudelower than the highest density found in starless core candi-dates, 12.7 × cm − . On the other hand, 7 out of the 21protostellar core candidates have virial parameters >
2, whilesmall virial parameters of 1.1–1.3 are found in three star-less core candidates. In Figure 5a, we show these criteriaas shaded regions.If we consider the densities and virial parameters jointly,then the cores having both virial parameters < <
2) and densities above4.5 × cm − are all protostellar candidates. Likewise, thecore having both virial parameters > × cm − are all starless candidates (except C4P5 inthe 20 km s − cloud, which is protostellar but spatially unre-solved, so its density is a lower limit and its virial parameteris an upper limit). However, this does not suggest a clear cri-terion for separating the two samples, given the exceptionsdiscussed below.One protostellar core candidates, C2P1 in Sgr C, has a den-sity of 1.0 × cm − that is 10 times lower than the mediandensity of the protostellar core candidates and than most ofthe starless core candidates, even though its virial parameteris < >
2. If outflows already exist inthese cores, the line widths may be broadened therefore thevirial parameters may be overestimated. Another possibilityis that they further fragment into multiple substructures, eachof which is gravitationally bound but as a whole they are not.The starless core candidates, which may be contaminatedwith star forming cores, tend to have lower densities andlarger virial parameters than the protostellar core candidatesin Figure 5a. In particular, all the cores in G0.253+0.016show large virial parameters and may be unbound. In fact,8 L
U ET AL ..
U ET AL .. n (H ) (cm − )0.11.02.010.0 α v i r (a) ProtostellarStarless2468 2 4 610 n (H ) (cm − )0.11.02.010.0 α v i r (b) Protostellar with T dust =50 KStarless2468 2 4 6 Figure 5.
Densities and virial parameters of the protostellar andstarless core candidates in the five clouds. Horizontal error barsshow uncertainties in densities of 66%, while vertical error barsshow uncertainties in virial parameters of 120% (factor 2.2). (a)The vertical shaded area spans densities of 1.0 × cm − to12.7 × cm − , representing the sufficient and the necessary den-sity criteria for protostellar cores, respectively. Similarly, the hori-zontal shaded area spans between virial parameters of 20.9 and 1.12,representing the sufficient and the necessary virial parameter crite-ria for protostellar cores. (b) Same as the first panel but the densitiesand virial parameters of the protostellar core candidates are derivedassuming a dust temperature of 50 K. it is a question whether or not these substructures should becalled ‘cores’, because if they are indeed unbound, they willbe transient objects and likely disperse in a dynamical timescale. One potential bias of the analysis here is that dust tem-peratures in the protostellar core candidates may be higherthan the assumed 20 K because of internal heating, in whichcase the masses and the densities would be overestimated(see Section 3.3). Assuming a higher dust temperature of50 K for the protostellar core candidates, the densities willbe 3 times smaller while the virial parameters will be 3 timeslarger. As shown in Figure 5b, in this case the difference be-tween the protostellar and starless core candidates is not sig-nificant, with p -values of > M (cid:12) (corresponding to a density of0.7 × cm − assuming a typical radius of 0.1 pc). Al-though we detect several H O masers of lower luminosities(several times 10 − L (cid:12) ) that are usually found toward low-mass young stellar objects (Furuya et al. 2003), they are in-sufficient to account for the expected low-mass star forma-tion. Assuming a stellar initial mass function (IMF) fromKroupa (2001), about 100 low-mass ( ≤ M (cid:12) ) stars will formin company with each high-mass ( ≥ M (cid:12) ) star. Therefore,a large fraction of the low-mass star formation activity is notrevealed by our H O maser observations. Future interferom-eter observations with high angular resolution and sensitivitythat is able to resolve low-mass protostellar cores will help toaddress the issue of low-mass star formation in the CMZ.4.2.
SFRs of the Clouds
We attempt to estimate SFRs of the CMZ clouds based onthe H O masers and UC H II regions, which characterize starformation in deeply embedded phases. In this analysis, weexclude the more evolved H II regions that are not embed-ded in cores (e.g., H2 in the 20 km s − cloud and H1–H4in the 50 km s − cloud). We expect the resulting SFRs aremore closely related to the observed gas than the SFRs esti-mated in longer time scales based on H II regions or infraredluminosities, although evolutionary cycling between gas andstars still causes the ratio between both to evolve with time(Kruijssen & Longmore 2014).4.2.1. Derivation of the SFRs
First, we define the characteristic time scale. The typicallifetime of the UC H II region phase is ∼ O masers is estimated to be ∼ O masers andUC H II regions.Second, we estimate the stellar mass that will be formedbased on the observed star formation tracers. We assume a TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS Table 7.
SFRs of the five clouds in our sample plus Sgr B2 from the literature.
Cloud Mass a Bound Mass Bound Mass Fraction Masses of embedded high-mass protostars b M cluster SFR(10 M (cid:12) ) (10 M (cid:12) ) (%) ( M (cid:12) ) ( M (cid:12) ) (10 − M (cid:12) yr − )20 km s − ±
193 2.0 ± − · · · < < ±
82 0.3 ± ±
82 0.3 ± ±
223 2.7 ± ± × ±
3a The cloud masses in Kauffmann et al. (2017a), which adopted a distance of 8.34 kpc, have been scaled to the distance of 8.1 kpc.b Indicators of embedded high-mass protostars are noted in parentheses. For Sgr B2 we directly quote the number from Ginsburg et al. (2018). The stellar masses associated withUC H II regions are taken from Table 5. For H O masers, we first use the correlation between H O maser luminosities and bolometric luminosities in Urquhart et al. (2011) toestimate luminosities of the young stellar objects, then estimate the stellar masses assuming the luminosity comes from a single protostar following the mass-luminosity relationin Davies et al. (2011). These masses do not enter the calculation of SFRs. They only demonstrate the range of masses (all ≥ M (cid:12) , therefore in the high-mass regime). canonical multiple-power-law IMF following Kroupa (2001,Equation (2)), with stellar masses between 0.01 M (cid:12) and150 M (cid:12) .We estimate how massive clusters should be given the ob-served numbers of high-mass protostars. The numbers ofhigh-mass protostars are estimated by counting UC H II re-gions and luminous H O masers ( (cid:38) − L (cid:12) ) associatedwith cores. When both UC H II regions and H O masers aredetected, we count them as one. This approach alleviatesthe problem of Poisson noise associated with the detectionof H O masers. However, it still suffers from several uncer-tainties. As discussed in Section 4.1.1, using luminous H Omasers as indicators of high-mass star formation is highlyuncertain, and the multiplicity of protostars is also an issue.In Appendix D, we obtain a relation between clustermasses M cluster and numbers of high-mass protostars (seeFigure 20b) by running Monte-Carlo simulations. The frac-tional uncertainty in M cluster decreases when more high-massprotostars are detected (e.g., 86% for one detection and 25%for 10 detections).Stellar masses of the five clouds estimated using this rela-tion are listed in Table 7. Then divided by the characteristictime scale of 3 × yr, we obtain the SFRs of the cloudsas listed in Table 7 and plotted as blue dots in Figure 6.Note that the uncertainties in the SFRs of G0.253+0.016 andSgr B1-off are as large as the derived SFRs themselves, there-fore the SFRs of these two clouds should be treated as havingan upper limit of 0.6 × − M (cid:12) yr − .To validate our approach, we apply it to the whole CMZ,using the H O maser survey of Walsh et al. (2014). This sur-vey is a follow up of the HOPS survey (Walsh et al. 2011) thatcovers Galactic longitudes between 290 ◦ and 30 ◦ and Galac-tic latitudes between − . ◦ . ◦
5, and achieves a pointsource sensitivity of < − channel formost of the data. We only consider H O masers with peakfluxes ≥ (cid:38) − L (cid:12) at the distance of 8.1 kpc, and only count masers within | l | < ◦ . We find 112 such masers from the catalog of Walshet al. (2014), among which 49 are in Sgr B2. This num-ber should be a lower limit given the issues in detection rateand multiplicity, although the sample may be contaminatedby AGB stars. Assuming each of them is associated with ahigh-mass protostar, we use Equation D2, which agrees wellwith our simulations in Appendix D. The total stellar mass tobe formed is estimated to be 1.1 × M (cid:12) , then dividing bythe time scale of 0.3 Myr, we obtain a SFR of 0.04 M (cid:12) yr − .This is lower by a factor of 1.5–3 than those estimated frominfrared luminosities or free-free emission over the same area(0.06–0.12 M (cid:12) yr − ; Longmore et al. 2013a; Barnes et al.2017), which is reasonable given the limitations of our massmeasurements.4.2.2. Comparing with SFRs in Previous Studies
We compare the derived SFRs of the clouds with resultsin previous studies. Kauffmann et al. (2017a) has estimatedSFRs of these clouds based on (both compact and UC) H II regions and class II CH OH masers, which characterize starformation in a time scale of 1.1 Myr. Their results are markedas crosses in Figure 6a, and typical uncertainty in their esti-mate of SFRs is a factor of 2. The most significant differenceis that we find >
10 times lower SFR for the 50 km s − cloud( < × − M (cid:12) yr − vs. 3.2 × − M (cid:12) yr − ). Kauffmannet al. (2017a) took the four H II regions in this cloud into ac-count. Kauffmann et al. (2017b) noted the disconnection be-tween the active star formation traced by the four H II regionsand a lack of massive clumps in this cloud. Our result sug-gests inactive star formation in the 50 km s − cloud in the last0.3 Myr (one weak H O maser, no signatures of high-massstar formation), which is consistent with the observed dearthof cores.The SFR of Sgr C we derive is a factor of 3.4 higherthan Kauffmann et al. (2017a): (2.7 ± × − M (cid:12) yr − vs. 0.8 × − M (cid:12) yr − . Given the large uncertainties in ourestimate, this difference is not considered to be significant.0 L U ET AL .For the other three clouds, including the 20 km s − cloud,G0.253+0.016, and Sgr B1-off, the SFRs in this work andin Kauffmann et al. (2017a) generally agree within a factorof 3, and are ∼
10 times lower than expected by the linearcorrelation in Lada et al. (2010).In addition, Barnes et al. (2017) estimated embedded stel-lar population of G0.253+0.016 and Sgr B1-off (named asBrick and clouds e & f, respectively, in their Tables 4 & 5) us-ing infrared luminosities, and found >
10 times higher stellarmasses, which are upper limits, as the infrared luminositieshave non-negligible contributions from other sources (e.g.,external radiation, the diffuse infrared field at the Galacticcenter). 4.2.3.
The SFR of Sgr B2
We estimate the SFR of Sgr B2 using data from the lit-erature. The star formation at early evolutionary phases inSgr B2 was recently studied by Ginsburg et al. (2018), whodetected 271 compact continuum emission sources at 3 mmusing ALMA, which are argued to be a mix of hyper-compactH II regions and (high-mass) young stellar objects. Assumingthat these 271 compact sources represent similar evolutionaryphases as our H O maser and UC H II sample, we estimate atotal stellar mass of (2.6 ± × M (cid:12) using Equation D2,and obtain a SFR of 0.086 ± M (cid:12) yr − in a time scaleof 0.3 Myr.Our result is 40% larger than the result of 0.062 M (cid:12) yr − reported in Ginsburg et al. (2018). The difference comesfrom both the stellar masses and the assumed time scales.Ginsburg et al. (2018) obtained a stellar mass of 3.3 × M (cid:12) when only considering sources not associated with H II re-gions, which is 30% larger than our result, mostly because ofdifferent stellar masses attributed to each source. This indi-cates an additional uncertainty of 30% for the stellar massesin Sgr B2 from source classification. Ginsburg et al. (2018)also used a time scale of 0.74 Myr that is based on the dy-namical model of Kruijssen et al. (2015), which is longerthan our assumption of 0.3 Myr. Our result is also a factorof 2.4 larger than the result of 0.036 M (cid:12) yr − in Kauffmannet al. (2017a), which is based on the detection of 49 compactH II regions in a time scale of 1.1 Myr.Overall, we do not find significantly different SFRs forSgr B2 from different approaches, and the discrepancymostly comes from different assumed time scales. We sum-marize our estimate in Table 7.4.2.4. Comparing with the Orbital Model of the CMZ
We compare our results with the orbital model of Kruijs-sen et al. (2015). This model suggests that all major cloudsin the CMZ are subject to the gravitational potential aroundthe Galactic Center and move in several gas streams (see thegreen curve in Figure 1). It also suggests that star forma-tion in clouds could be triggered by tidal compression during a close passage to the bottom of the gravitational potentialwell near Sgr A*.In the model of Kruijssen et al. (2015), G0.253+0.016,Sgr B1-off, and Sgr B2 are moving along one gas stream andhave passed the pericenter to Sgr A*. Sgr C, the 20 km s − cloud, and the 50 km s − cloud are in the other gas stream,with Sgr C in the upstream, the 20 km s − cloud approach-ing the pericenter, and the 50 km s − cloud having passed thepericenter. As discussed previously and shown in Table 7,we find signatures of increasing SFRs from G0.253+0.016 toSgr B1-off to Sgr B2, which agree with the proposed mono-tonic increase of the star formation activity along the direc-tion of motion after passing by Sgr A* in this gas stream(Longmore et al. 2013b; Kruijssen et al. 2015). However, wedo not find a similar trend for Sgr C, the 20 km s − cloud,and the 50 km s − cloud. The derived SFRs of Sgr C andthe 20 km s − cloud are similar given the uncertainties, andare higher than that of the 50 km s − cloud. This may sug-gest that star formation in these clouds is not triggered bytidal compression when passing by the pericenter, but may beowing to self-gravity or impact of other sources (e.g., super-nova remnants: Lu et al. 2003; Mills et al. 2011; H II regions:Kendrew et al. 2013).4.3. Comparing with the Dense Gas Star FormationRelation
A quantitative comparison between star formation in thesefive CMZ clouds and that defined by the dense gas star for-mation relation has been done in Kauffmann et al. (2017a).Here we use the updated SFRs based on the H O masersand UC H II regions to carry out this analysis. As discussedin Section 4.2, these SFRs characterize embedded star for-mation at very early evolutionary phases therefore are moreclosely related to the observed gas.The cloud masses are taken from Kauffmann et al. (2017a),which are estimated using Herschel multi-wavelength data.The mean H densities of these clouds are (cid:38) cm − (Kauffmann et al. 2017a), therefore the dense gas fraction asdefined in Lada et al. (2010) is 100%—that is, all the gas inthese clouds are supposed to be ‘dense’ and will collapse andform stars (but see Mills et al. 2018 for potential multipledensity components in the 20 km s − cloud, the 50 km s − cloud, and G0.253+0.016, where ∼
85% of the gas has a den-sity of < cm − ). We then take the cloud masses to di-rectly compare with the SFRs in the clouds.The cloud masses and the SFRs of the five CMZ clouds(taken from Table 7) are plotted in Figure 6a. Given theirmasses, the SFR in Sgr C agrees with the linear correlationin Lada et al. (2010), while the SFRs in the other four cloudsare ∼
10 times lower than expected, around a linear relationwith a slope of 5 × − yr − . TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS Mass ( M (cid:12) )10 − − − − − − S F R ( M (cid:12) y r − ) nearby clouds(Lada et al. 2010) Sgr C 20 km s −
50 km s − G0.253+0.025Sgr B1 offSgr B2 (a)
Comparing different SFRs10 Mass ( M (cid:12) )10 − − − − − − S F R ( M (cid:12) y r − ) Sgr C 20 km s −
50 km s − G0.253+0.025Sgr B1 offSgr B2 (b)
Comparing different masses
Representative errorin the bound masses
Figure 6.
SFRs and masses of dense gas in the five CMZ clouds andin a sample of nearby clouds from Lada et al. (2010). Data of Sgr B2compiled from the literature are also shown. (a) The blue dots markthe masses and SFRs of the five CMZ clouds in our observationsplus Sgr B2. Errorbars, when presented, represent the errors listedin Table 7, and arrows suggest lower or upper limits. Each blue dotis connected to a magenta cross through a vertical line, which showsthe SFR derived in Kauffmann et al. (2017a). The black dasheddiagonal line marks the linear correlation in Lada et al. (2010), withred dots showing masses and SFRs of the nearby clouds based onwhich the correlation is derived. The blue dash-dotted diagonal linemarks the expected relation when the SFR is 10 times lower. (b) Theblue dots, errorbars, and the blue diagonal line are identical to thosein (a). In addition, each blue dot is connected to a cyan dot througha horizontal line, which marks the gravitationally bound masses inTable 7. The horizontal cyan error bar represents the uncertainty inthe gravitationally bound masses. The cyan dashed diagonal line is alinear fit to the cyan dots of the five CMZ clouds in our observations,with a slope of 10 − yr − . The big cyan dot for Sgr B2 denotes agravitationally bound mass of 4.5 × M (cid:12) , which is a lower limit. The linear relation between SFRs and gas masses can bewritten as (Lada et al. 2010)SFR = (cid:15)τ SF Mass , (5)in which (cid:15) is the SFE (the integrated efficiency of convert-ing gas to stars) in the gas under consideration, and τ SF isthe time scale of star formation. Then over a time scale of0.3 Myr, the SFE of the four clouds (the 20 km s − cloud, the50 km s − cloud, G0.253+0.016, and Sgr B1-off) is 0.15%.This is significantly lower than those found in Galactic diskclouds, which are usually a few percent (Lada et al. 2010;Louvet et al. 2014).In Section 4.1.4 we classify a sample of starless core can-didates with large virial parameters, which may not formstars. Especially for G0.253+0.016, most of the cloud massseems to be quiescent and irrelevant to high-mass star forma-tion (Rathborne et al. 2014). It might make more sense tocompare the masses in gravitationally bound cores, insteadof those of the whole clouds, with the SFRs.We attempt to estimate the gravitationally bound massesof the clouds by summing up masses of the protostellar corecandidates and the prestellar core candidates that are gravi-tationally bound ( α vir ≤
2, see Table 3). In the following, weconsider two systematic errors that significantly affect the es-timate of the gravitationally bound masses and show that theuncertainty in the derived masses is a factor of 3.First, the core identification in Section 3.1 is very likely in-complete, therefore the derived gravitationally bound massesare likely underestimated. To quantify how much mass maybe missed, we estimate upper limits of the core masses inthe 20 km s − cloud and Sgr C by taking the total dust emis-sion in the SMA maps into account. Most of the identifiedcores in these two clouds are protostellar and/or gravitation-ally bound, therefore we likely miss gravitationally boundgas in the core identification. We do not use the other threeclouds for this estimate, because the cores in them are mostlyunbound and the majority of the gas is clearly not involvedin star formation. Then we derive masses using the total dustemission fluxes in the 20 km s − cloud and Sgr C, whichare upper limits to the gravitationally bound masses. Thesemasses are 3 times higher than the derived bound masses.Second, the derived masses are likely affected by the sys-tematic error in the dust temperature owing to internal heat-ing, since we take all the protostellar core candidates intoaccount. As discussed in Section 3.3, the masses of coreswith significant internal heating may be overestimated by afactor of 3.We list the derived gravitationally bound masses in Table 7.In particular, Sgr C shows a high fraction of gravitationallybound mass (9%), while the other four clouds all have muchsmaller fractions ( < − cloud. This2 L U ET AL .has been noted in Kauffmann et al. (2017a) as a shallowermass-size slope in Sgr C than the other four clouds. It mayexplain the similar SFRs of Sgr C and the 20 km s − clouddespite the fact that the cloud mass of Sgr C is only 7.5% ofthat of the 20 km s − cloud.Then we plot the gravitationally bound masses against theSFRs in Figure 6b. The five clouds can be fit by a linear func-tion, with a slope of 10 − yr − , which indicates a gas con-sumption time of 1 Myr in these gravitationally bound cores.The linear relation is expected from a constant SFE. Follow-ing Equation 5, we obtain a SFE of 30% for the gas in thegravitationally bound/protostellar cores over a time scale of0.3 Myr. Given the systematic errors in the derived gravita-tionally bound masses as discussed previously, the SFE maybe as low as 10% and as high as 90%. This SFE is com-parable to the value of 30%–40% for dense cores in nearbyclouds (Alves et al. 2007; Könyves et al. 2015).In addition, we include Sgr B2 in the analysis, while thedata are compiled from the literature. The SFR at early evo-lutionary phases of 0.086 ± M (cid:12) yr − is based on thework of Ginsburg et al. (2018) (see Section 4.2.3). The cloudmass of Sgr B2 is taken to be 1.4 × M (cid:12) (Ginsburg et al.2018, scaled to the distance of 8.1 kpc). The gravitationallybound mass is difficult to characterize and similar analysis toours has not yet been published. As an approximate we usethe total gas mass of the four protoclusters (Sgr B2 NE, N,M, and S), 4.5 × M (cid:12) (Schmiedeke et al. 2016, scaled tothe distance of 8.1 kpc), which should be a lower limit giventhat the gas associated with the distributed protostellar popu-lation in Sgr B2 (Ginsburg et al. 2018) is not included. About200 among the 271 compact sources found by Ginsburg et al.(2018) are not associated with any of the four protoclusters,therefore the total bound gas mass might be as much as fourtimes larger than the mass in the four protoclusters if we as-sume the gas mass to be proportional to the number of com-pact sources. This results in a lower limit for the bound massfraction of 3.3% for Sgr B2 that is potentially several timeslarger.Comparing Sgr B2 with other clouds in Figure 6, we notethat its SFR agrees with the star formation dense gas relationin Lada et al. (2010), similar to the case of Sgr C. Its boundgas mass fraction, with a lower limit of 3.3%, is also similarto Sgr C but 5–40 times larger than those of the other fourclouds. When only considering the mass in the bound gas,Sgr B2 falls closely around the linear relation by fitting thefive clouds in our sample, as shown in Figure 6b.These results may suggest that star formation at the corescale in these CMZ clouds is not different from that in Galac-tic disk clouds in terms of the core to star-formation effi-ciency, but at the cloud scale, except for Sgr B2 and Sgr C,the star formation is ∼
10 times less efficient because lessthan 1% of gas is confined in gravitationally bound regions. This small fraction of gravitationally bound gas in the cloudsmay be because of the strong turbulence in these clouds(Oka et al. 2001; Shetty et al. 2012; Kruijssen & Longmore2013) as indicated by the large line widths in the cores (Ap-pendix C), or because the clouds have only recently con-densed, as expected if the CMZ as a whole is undergoingepisodic cycles of star formation activity (Kruijssen et al.2014; Krumholz & Kruijssen 2015; Krumholz et al. 2017). CONCLUSIONSWe use the SMA 1.3 mm continuum and the VLA K -bandcontinuum and H O maser observations to study star forma-tion in five massive molecular clouds in the CMZ and onecloud that is likely outside of the CMZ. The main results areas follows. • A total of 56 cores at the 0.2 pc scale are resolved bythe SMA continuum emission in the six clouds. Theirvirial parameters are derived using line widths mea-sured with the SMA N H + or CH OH lines. • In the five CMZ clouds, signatures of embedded starformation at very early evolutionary phases, as tracedby H O masers and compact free-free emission fromUC H II regions, are found toward the cores, based onwhich we classify the cores as protostellar or starless.The protostellar core candidates tend to have higherdensities and smaller virial parameters than the starlesscore candidates (Figure 5). • Based on the detection of bright H O masers (withluminosities (cid:38) − L (cid:12) ) and UC H II regions, SFRswithin a time scale of 0.3 Myr of the five CMZ cloudsare estimated. We also include Sgr B2 in the analysisafter compiling data from previous studies. The ob-served increasing SFRs from G0.253+0.016 to Sgr B1-off to Sgr B2 are expected by the CMZ orbital modelof Kruijssen et al. (2015), but the SFRs of the otherthree clouds do not show a monotonic change that ispredicted by this model. • Excluding Sgr B2 and Sgr C, SFRs of the other fourCMZ clouds are ∼
10 times lower than expected fromthe dense gas star formation relation extrapolated fromnearby clouds in Lada et al. (2010) (Figure 6a). Ifthe masses in protostellar and/or gravitationally boundcores are used instead, these clouds can be better fitwith a linear function, with a SFE of 30% over a timescale of 0.3 Myr (Figure 6b). Among the six CMZclouds (five in our sample plus Sgr B2 from the litera-ture), Sgr B2 and Sgr C stand out with larger fractionsof mass in gravitationally bound regions and higherSFRs per unit cloud mass.
TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS • We confirm that star formation in four of the CMZclouds is inactive with respect to the prediction of thedense gas star formation relation, even after taking starformation at very early evolutionary phases into ac-count. This is likely related to their low gravitationallybound gas fractions of < Facilities:
SMA, VLA,
Spitzer , Herschel
Software:
MIR, Miriad (Sault et al. 1995), CASA (Mc-Mullin et al. 2007), APLpy (Robitaille & Bressert 2012), As-tropy (Astropy Collaboration et al. 2013)APPENDIX A. IDENTIFICATION OF SUBSTRUCTURES USING DENDROGRAMWe identified compact structures (‘leaves’) in the SMA 1.3 mm continuum emission maps using the dendrogram algorithm(Rosolowsky et al. 2008) implemented with astrodendro . We adopted a minimum intensity of 4 σ where the σ values can befound in Table 2, below which the emission will not be considered, and a minimum significance of 1 σ , which characterizes thesignificance a local maxima has to reach to be considered as an independent structure. With this setup, the identified structureswill have peak intensities above the 5 σ level. We additionally specified that the number of pixels above the 5 σ level in onestructure must be larger than the pixel number within the FWHM of one synthesized beam. The results are presented in Figure 7,where the identified structures are marked by blue contours.This procedure occasionally misses obvious structures. For example, in the 20 km s − cloud several emission peaks arespatially coincident with H O masers therefore should be protostellar core candidates (see Figure 4), but are not identifiedbecause their areas are slightly smaller than the beam size. Another example is that in Sgr C two adjacent bright structures inthe southwestern end are identified as one because of their small projected spatial separation, but they should be two independentcores given that they are each associated with a UC H II region and a H O maser (see Figures 3 & 4). Therefore, in Section 3.1 weused the outcome of astrodendro as a reference but manually added or removed structures in consideration of the above situations. B. H O MASER SPECTRAWe present the spectra of all the detected H O masers in the six clouds in Figures 8–13. The x-axis is V lsr in unit of km s − ,while the y-axis is flux density in unit of mJy. Positions of the masers are marked in the maps in Figure 4. The labels of H Omasers with OH/IR star counterparts are marked by red. C. LINE WIDTHS IN CORESWe extract the mean spectra of N H + OH 4 –3 in ourSMA data, toward the identified cores. Then for each spectrum, a single Gaussian is fit to obtain the line width. The results areshown in Figures 14–19. https://dendrograms.readthedocs.io/en/stable/ U ET AL ..
MIR, Miriad (Sault et al. 1995), CASA (Mc-Mullin et al. 2007), APLpy (Robitaille & Bressert 2012), As-tropy (Astropy Collaboration et al. 2013)APPENDIX A. IDENTIFICATION OF SUBSTRUCTURES USING DENDROGRAMWe identified compact structures (‘leaves’) in the SMA 1.3 mm continuum emission maps using the dendrogram algorithm(Rosolowsky et al. 2008) implemented with astrodendro . We adopted a minimum intensity of 4 σ where the σ values can befound in Table 2, below which the emission will not be considered, and a minimum significance of 1 σ , which characterizes thesignificance a local maxima has to reach to be considered as an independent structure. With this setup, the identified structureswill have peak intensities above the 5 σ level. We additionally specified that the number of pixels above the 5 σ level in onestructure must be larger than the pixel number within the FWHM of one synthesized beam. The results are presented in Figure 7,where the identified structures are marked by blue contours.This procedure occasionally misses obvious structures. For example, in the 20 km s − cloud several emission peaks arespatially coincident with H O masers therefore should be protostellar core candidates (see Figure 4), but are not identifiedbecause their areas are slightly smaller than the beam size. Another example is that in Sgr C two adjacent bright structures inthe southwestern end are identified as one because of their small projected spatial separation, but they should be two independentcores given that they are each associated with a UC H II region and a H O maser (see Figures 3 & 4). Therefore, in Section 3.1 weused the outcome of astrodendro as a reference but manually added or removed structures in consideration of the above situations. B. H O MASER SPECTRAWe present the spectra of all the detected H O masers in the six clouds in Figures 8–13. The x-axis is V lsr in unit of km s − ,while the y-axis is flux density in unit of mJy. Positions of the masers are marked in the maps in Figure 4. The labels of H Omasers with OH/IR star counterparts are marked by red. C. LINE WIDTHS IN CORESWe extract the mean spectra of N H + OH 4 –3 in ourSMA data, toward the identified cores. Then for each spectrum, a single Gaussian is fit to obtain the line width. The results areshown in Figures 14–19. https://dendrograms.readthedocs.io/en/stable/ U ET AL .. h m s s s RA (J2000)07 − ◦ D e c ( J )
20 km s − Cloud h m s s s RA (J2000) − ◦ − ◦ D e c ( J )
50 km s − Cloud h m s s s RA (J2000)44 − ◦ D e c ( J ) G0.253+0.016 h m s s RA (J2000)32 − ◦ D e c ( J ) Sgr B1 off 0.2 pc h m s s s RA (J2000)29 − ◦ D e c ( J ) Sgr C h m s s RA (J2000)02 − ◦ D e c ( J ) Sgr D 0.2 pc
Figure 7.
Result of the dendrogram analysis. Background images and dashed loops show the SMA 1.3 mm continuum and the SMA mosaicfield, which are identical to those in Figure 3. Blue contours mark leaves identified using astrodendro .D.
ESTIMATE OF CLUSTER MASSES THROUGH MONTE-CARLO SIMULATIONSIn order to quantify the uncertainties in cluster masses stemming from the random sampling of stellar masses following theIMF as a probability distribution function, we run Monte-Carlo simulations to generate cluster masses, and find the relationbetween them and the number of high-mass ( ≥ M (cid:12) ) stars in the cluster. The scripts to run these simulations are available athttps://github.com/xinglunju/CMZclouds/tree/master/Mcluster.Following the Bayes theorem, the posterior probability of cluster masses M cluster given that there are N high-mass stars in thecluster is prob ( M cluster | N ) = prob ( M cluster ) prob ( N | M cluster ) prob ( N ) , (D1)in which prob ( M cluster ) is the prior probability of M cluster , prob ( N | M cluster ) is the likelihood of having N high-mass stars given acluster mass of M cluster , and prob ( N ) is the evidence and usually treated as a normalizing factor.We adopt a flat log-prior probability prob ( M cluster ) in a range of [10 , M (cid:12) , outside of which prob ( M cluster ) is set to 0. Toobtain the likelihood prob ( N | M cluster ) , we run Monte-Carlo simulations to generate stellar masses following the IMF (Equations 1& 2 of Kroupa 2001, with stellar masses between 0.01 M (cid:12) and 150 M (cid:12) ) as a probability distribution function until the total TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS W0 W1 W2 W3 W4 W5 W6 W7 W8 W9 W10
W11
W12
W13
W14
W15
W16
W17
W18 − −
20 0 20 400200
W19 F l u x D en s i t y ( m Jy ) V lsr (km s − ) Figure 8. H O maser spectra in the 20 km s − cloud detected by the VLA. mass reaches M cluster , and count the number of high-mass stars produced in this process. For each M cluster , we run the simulation10,000 times, and divide the number of the runs producing N high-mass stars by 10,000 to get the likelihood prob ( N | M cluster ) .Finally, the posterior probability prob ( M cluster | N ) is proportional to prob ( N | M cluster ) , and is shown in Figure 20a.The resulting posterior probability functions prob ( M cluster | N ) are skewed to the right side compared to a lognormal distribution.To better estimate peak locations, we fit Weibull distribution functions (Weibull 1951) to prob ( M cluster | N ) , shown in Figure 20a.We use the modes (peak locations) of the Weibull functions (therefore the most likely) as the final estimate of cluster masses, andthe rms of the simulated data to approximate the uncertainties in the estimated masses.In Figure 20b, we plot the cluster masses estimated above given N high-mass stars in the cluster. The result agrees well withthe analytical form directly derived from the IMF, M cluster = 95 . × N M (cid:12) , (D2)which is plotted as a dashed curve in Figure 20b. The simulations are able to give an estimate of uncertainties stemming from therandom sampling of stellar masses following the IMF as a probability distribution function. In Section 4.2, we rely on the datapoints in Figure 20b to estimate cluster masses.6 L U ET AL ..
W19 F l u x D en s i t y ( m Jy ) V lsr (km s − ) Figure 8. H O maser spectra in the 20 km s − cloud detected by the VLA. mass reaches M cluster , and count the number of high-mass stars produced in this process. For each M cluster , we run the simulation10,000 times, and divide the number of the runs producing N high-mass stars by 10,000 to get the likelihood prob ( N | M cluster ) .Finally, the posterior probability prob ( M cluster | N ) is proportional to prob ( N | M cluster ) , and is shown in Figure 20a.The resulting posterior probability functions prob ( M cluster | N ) are skewed to the right side compared to a lognormal distribution.To better estimate peak locations, we fit Weibull distribution functions (Weibull 1951) to prob ( M cluster | N ) , shown in Figure 20a.We use the modes (peak locations) of the Weibull functions (therefore the most likely) as the final estimate of cluster masses, andthe rms of the simulated data to approximate the uncertainties in the estimated masses.In Figure 20b, we plot the cluster masses estimated above given N high-mass stars in the cluster. The result agrees well withthe analytical form directly derived from the IMF, M cluster = 95 . × N M (cid:12) , (D2)which is plotted as a dashed curve in Figure 20b. The simulations are able to give an estimate of uncertainties stemming from therandom sampling of stellar masses following the IMF as a probability distribution function. In Section 4.2, we rely on the datapoints in Figure 20b to estimate cluster masses.6 L U ET AL .. W1 W2 W3 − −
20 0 20 40 60 80 100 120 1400204060 W4 F l u x D en s i t y ( m Jy ) V lsr (km s − ) Figure 9. H O maser spectra in the 50 km s − cloud detected by the VLA. W1 W2
20 40 60 800100200 W3 F l u x D en s i t y ( m Jy ) V lsr (km s − ) Figure 10. H O maser spectra in G0.253+0.016 detected by the VLA. W1 W2 W3 W4 W5 − −
20 0 20 40 60 80 100 120050 W6 F l u x D en s i t y ( m Jy ) V lsr (km s − ) Figure 11. H O maser spectra in Sgr B1-off detected by the VLA.
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U ET AL .. W1 W2 W3 W4 W5 W6 − − − −
10 0 100300 W7 F l u x D en s i t y ( m Jy ) V lsr (km s − ) Figure 13. H O maser spectra in Sgr D detected by the VLA. C1P1 N H + V lsr =28.0 km s − σ v =1.14 ± − C1P2 N H + V lsr =29.3 km s − σ v =1.16 ± − C1P3 N H + V lsr =12.9 km s − σ v =1.74 ± − C2P1 N H + V lsr =25.4 km s − σ v =2.44 ± − C2P2 N H + V lsr =20.5 km s − σ v =1.32 ± − C2P3 N H + V lsr =25.8 km s − σ v =0.98 ± − − C3P1 N H + V lsr =3.5 km s − σ v =1.84 ± − C3P2 CH OH V lsr =11.4 km s − σ v =1.27 ± − C3P3 N H + V lsr =3.7 km s − σ v =1.36 ± − C4P1 N H + V lsr =16.4 km s − σ v =1.45 ± − C4P2 CH OH V lsr =15.1 km s − σ v =1.31 ± − − C4P3 N H + V lsr = − − σ v =1.13 ± − −
20 0 20 4001
C4P4 N H + V lsr =13.9 km s − σ v =2.07 ± − −
20 0 20 40 − C4P5 N H + V lsr =13.8 km s − σ v =0.92 ± − −
20 0 20 4001
C4P6 N H + V lsr =14.5 km s − σ v =1.05 ± − −
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C5P1 N H + V lsr =14.8 km s − σ v =1.07 ± − −
20 0 20 40 − C5P2 N H + V lsr =15.0 km s − σ v =0.89 ± − T B ( K ) V lsr (km s − ) Figure 14.
The SMA N H + or CH OH spectra and best-fit models of cores in the 20 km s − cloud. The best-fit centroid velocities ( V lsr ) andline widths ( σ v , deconvolved from channel width) are noted in each panel.Davies, B., Hoare, M. G., Lumsden, S. L., et al. 2011, MNRAS,416, 972, doi: 10.1111/j.1365-2966.2011.19095.x De Pree, C. G., Peters, T., Mac Low, M. M., et al. 2015, ApJ, 815,123, doi: 10.1088/0004-637X/815/2/123 TAR F ORMATION R ATES OF C ENTRAL M OLECULAR Z ONE C LOUDS C1P1 N H + V lsr =50.1 km s − σ v =5.14 ± − C1P2 N H + V lsr =49.9 km s − σ v =5.18 ± − C2P1 N H + V lsr =54.5 km s − σ v =2.57 ± − − C2P2 N H + V lsr =45.2 km s − σ v =1.71 ± − T B ( K ) V lsr (km s − ) Figure 15.
The SMA N H + spectra and best-fit models of cores in the 50 km s − cloud. The best-fit line widths (deconvolved from channelwidth) are noted in each panel. − C1P1 N H + V lsr = − − σ v =2.28 ± − C1P2 N H + V lsr =9.1 km s − σ v =2.28 ± − C1P3 N H + V lsr =16.9 km s − σ v =1.27 ± − C2P1 N H + V lsr =11.0 km s − σ v =2.55 ± − C2P2 N H + V lsr =39.6 km s − σ v =1.10 ± − C2P3 N H + V lsr =40.5 km s − σ v =1.37 ± − C2P4 N H + V lsr =46.8 km s − σ v =2.56 ± − C2P5 N H + V lsr =4.5 km s − σ v =1.77 ± − C3P1 CH OH V lsr =31.9 km s − σ v =3.19 ± − C3P2 N H + V lsr =16.3 km s − σ v =2.13 ± − C3P3 N H + V lsr =14.4 km s − σ v =1.50 ± − C3P4 CH OH V lsr =16.5 km s − σ v =3.80 ± − C4P1 N H + V lsr =42.0 km s − σ v =1.87 ± − C4P2 N H + V lsr =49.9 km s − σ v =1.90 ± − C4P3 N H + V lsr =31.7 km s − σ v =2.36 ± − T B ( K ) V lsr (km s − ) Figure 16.
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U ET AL .. C1P1 CH OH V lsr =34.7 km s − σ v =3.14 ± − C2P1 N H + V lsr =33.3 km s − σ v =0.61 ± − C2P2 N H + V lsr =27.1 km s − σ v =1.75 ± − C2P3 N H + V lsr =26.4 km s − σ v =1.71 ± − − C2P4 N H + V lsr =38.0 km s − σ v =2.40 ± − C2P6 N H + V lsr =21.7 km s − σ v =1.37 ± − T B ( K ) V lsr (km s − ) Figure 17.
The SMA N H + or CH OH spectra and best-fit models of cores in Sgr B1-off. The best-fit line widths (deconvolved from channelwidth) are noted in each panel.
C1P1 CH OH V lsr = − − σ v =1.08 ± − − − − − C2P1 N H + V lsr = − − σ v =0.78 ± − − − − − C3P1 N H + V lsr = − − σ v =1.50 ± − − − − − C3P2 CH OH V lsr = − − σ v =1.76 ± − − − − − C3P3 N H + V lsr = − − σ v =1.27 ± − − − − − C4P1 N H + V lsr = − − σ v =1.71 ± − − − − − C4P2 N H + V lsr = − − σ v =1.60 ± − − − − − C5P1 N H + V lsr = − − σ v =2.11 ± − − − − − C5P2 N H + V lsr = − − σ v =2.24 ± − T B ( K ) V lsr (km s − ) Figure 18.
The SMA N H + or CH OH spectra and best-fit models of cores in Sgr C. The best-fit line widths (deconvolved from channelwidth) are noted in each panel. − −
20 0 2001
C1P1 N H + V lsr = − − σ v =0.68 ± − − −
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C1P2 N H + V lsr = − − σ v =1.59 ± − − −
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C1P3 N H + V lsr = − − σ v =2.47 ± − − −
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