Molecular Clouds in the Second Quadrant of the Milky Way Mid-plane from l=104.\!\!^{\circ}75 to l=119.\!\!^{\circ}75 and b=-5.\!\!^{\circ}25 to b=5.\!\!^{\circ}25
Yuehui Ma, Hongchi Wang, Chong Li, Lianghao Lin, Yan Sun, Ji Yang
DDraft version February 25, 2021
Typeset using L A TEX twocolumn style in AASTeX63
Molecular Clouds in the Second Quadrant of the Milky Way Mid-plane from l = . ◦
75 to l=119 . ◦ − . ◦
25 to b=5 . ◦ Yuehui Ma,
1, 2
Hongchi Wang,
1, 3
Chong Li,
1, 2
Lianghao Lin,
1, 3
Yan Sun, and Ji Yang Purple Mountain Observatory and Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing210033, China University of Chinese Academy of Sciences, 19A Yuquan Road, Shijingshan District, Beijing 100049, China School of Astronomy and Space Science, University of Science and Technology of China, Hefei, Anhui 230026, China (Accepted February 18, 2021)
Submitted to ApJSABSTRACTWe have studied the properties of molecular clouds in the second quadrant of the Milky Way Mid-plane from l=104 . ◦
75 to l=119 . ◦
75 and b= − . ◦
25 to b=5 . ◦
25 using the CO, CO, and C O J = 1 − CO and CO spectral cubes, respectively, using the DENDROGRAM +SCIMES algorithms. The distances of the molecular clouds are estimated and the physical propertieslike masses, sizes, and surface densities of the clouds are tabulated. The molecular clouds in thePerseus arm are about 30 −
50 times more massive and 4 − ∼
100 M (cid:12) pc − . We selected the 40most extended ( > ) molecular clouds from the CO catalog to build the H column densityprobability distribution function (N-PDF). About 78% of the N-PDFs of the selected molecular cloudsare well fitted with log-normal functions with only small deviations at high-densities which correspondto star-forming regions with scales of ∼ ∼ ∼ ∼ Keywords:
Galaxy: structure — ISM: clouds — radio lines: ISM — stars:formation — surveys —turbulence INTRODUCTIONMolecular clouds are the birthplace of stars. They arethe coldest and densest part of the turbulent and multi-phased interstellar medium (ISM). Since discovered byWilson et al. (1970), the CO molecule becomes the mostwidely used tracer of molecular clouds in the Milky Wayand the galaxies. Because of the high abundance of theCO molecule in the ISM, the low-J transitions of COare usually optically thick, whereas those of CO andC O are relatively more optically thin and therefore
Corresponding author: Yuehui Ma, Hongchi [email protected], [email protected] can be effectively used to trace the regions of molecularclouds at higher densities. The knowledge of the dis-tribution and physical properties of molecular clouds inthe Milky Way mainly comes from large-scale surveys ofthe rotational transitional emission from CO and its twoisotopologues CO and C O toward the Galactic plane(Burton et al. 1975; Scoville & Solomon 1975; Gordon& Burton 1976; Burton & Gordon 1978; Solomon et al.1987; Dame et al. 2001; Heyer et al. 2001; Roman-Duvalet al. 2010; Rice et al. 2016; Miville-Deschˆenes et al.2017). The masses of molecular clouds lie in the rangefrom a few tens of solar masses to about 10 M (cid:12) , whilethe sizes vary from ∼
10 to 150 pc. The typical veloc-ity dispersion of molecular clouds revealed by the sur-veys is ∼ − . The most massive molecular entities a r X i v : . [ a s t r o - ph . GA ] F e b Ma et al. ( > M (cid:12) ) are called giant molecular clouds (GMCs),which have complex and hierarchical structures that canbe further divided into clouds, clumps, and cores (Blitz& Williams 1999). The cloud mass function (CMF) isfound to follow a power-law distribution of exponents inthe range from ∼ − ∼ − M ∝ R h M , where h M depends on the inner density distribution of the molec-ular clouds (Kauffmann et al. 2010a,b).The hierarchical structure and the power-law behav-ior of the CMF and the σ v − r relation of molecularclouds are found to be the outcomes of large-scale tur-bulence in various numerical simulations ignoring self-gravitation (V´azquez-Semadeni & Garc´ıa 2001; Padoan& Nordlund 2002; Federrath et al. 2009). However, grav-ity is found to play an important role in the dynamicsof the molecular clouds on small scales ( < (Rosolowsky et al. 2008) and SCIMES (Colombo et al.2015) algorithms. Colombo et al. (2015) have madedetailed comparison of the performance between theDENDROGRAM+SCIMES algorithm and other algo-rithms such as CPROPS (Rosolowsky & Leroy 2006) https://dendrograms.readthedocs.io https://scimes.readthedocs.io and ClumpFind (Williams et al. 1994) frequently usedfor the automatic identification of extended structuresin spectrometric data. They found that CPROPS andClumpFind tend to overdivide the emission of moleculargas. Other traditional algorithms, like GAUSSCLUMPS(Stutzki & Guesten 1990) and FELLWALKER (Berry2015), are more suitable for the identification of clumpsor cores.The probability distribution function of H columndensity (N-PDF) of molecular clouds is a useful statisti-cal tool to investigate the underlying physics that influ-ence the structure of the molecular clouds. A log-normalbehavior of the N-PDF has been predicted in theoreti-cal studies (Vazquez-Semadeni 1994; Padoan et al. 1997;Klessen 2000) and is attributed to the supersonic turbu-lence in molecular clouds. Some following observationshave confirmed the existence of the log-normal N-PDFsin relatively quiescent molecular clouds (Goodman et al.2009; Kainulainen et al. 2014). Log-normal plus high-density power law tail or pure power-law distributions ofthe N-PDFs, have been observed in active star-formingregions with dust extinction or emission data (Kainu-lainen et al. 2009; Schneider et al. 2013; Tremblin et al.2014; Benedettini et al. 2015; Lombardi et al. 2015; Stutz& Kainulainen 2015). However, Alves et al. (2017) pro-pose that the completeness, i.e., the last closed contour,has a significant influence on the shape of N-PDFs andthey conclude that, above the completeness limit, thereis no observational evidence for log-normal N-PDFs inmolecular clouds. The results of Tassis et al. (2010)also challenge the one-to-one correspondence betweenthe shapes of the N-PDFs and the underlying physics inmolecular clouds, as log-normal N-PDFs are observed intheir modeled clouds without supersonic turbulence.In this work, we use the DENDROGRAM+SCIMESalgorithms to extract molecular clouds in the secondquadrant of the Milky Way mid-plane from l=104 . ◦
75 tol=119 . ◦
75 and b= − . ◦
25 to b=5 . ◦
25 using the CO and CO datasets from the MWISP project and study theirphysical properties. The observations are introduced inSection 2 and the results are presented in Section 3.We discuss the properties of the N-PDFs of a selectedsub-sample of molecular clouds in Section 4 and make asummary in Section 5. OBSERVATIONSWe have observed the CO , CO , and C O J =1 − ◦ × ◦ from l=104 . ◦
75 to l=119 . ◦
75 andb= − . ◦
25 to b=5 . ◦
25. The observation is part of theMWISP project, which is an unbiased simultaneous sur-vey of the J = 1 − olecular clouds in the second quadrant (cid:48)(cid:48) and 50 (cid:48)(cid:48) at 110 GHz and 115 GHz, respectively, and the point-ing of the telescope has an accuracy of about 5 (cid:48)(cid:48) duringall the observational epochs. The telescope is equippedwith a nine-beam Superconducting Spectroscopic ArrayReceiver (SSAR) (Shan et al. 2012). A two-sidebandSuperconductor-Insulator-Superconductor (SIS) mixerworks as the front end of the receiver. The CO , CO, and C O J = 1 − CO J = 1 − CO J = 1 − O J = 1 − − at 110 GHz. The antennatemperature is calibrated according to T mb = T ∗ A /η mb during observation, where the η mb is the main beam ef-ficiency and its value can be found in the annual statusreport of the PMO-13.7 m millimeter telescope.In the MWISP project, the survey area is divided intoindividual cells of size of 30 (cid:48) × (cid:48) . For each cell, the ob-servations were made in the position-switch on-the-fly(OTF) mode along the directions of Galactic longitudeand Galactic latitude. The scanning rate is 50 (cid:48)(cid:48) per sec-ond, and the dump time is 0.3 s. The data productsof the MWISP survey are automatically pre-processedafter observation. The pre-processing includes the rejec-tion of prominent bad channels, subtraction of a first-order baseline from every spectrum, and the combina-tion of the spectra obtained at different times for thesame sky position. The final data are regrided into30 (cid:48)(cid:48) × (cid:48)(cid:48) pixels in the directions of Galactic longitudeand latitude. The required standard for the medianRMS noise level in the MWISP project is below ∼ CO J = 1 − ∼ CO J = 1 − O J = 1 − http://english.dlh.pmo.cas.cn/fs/ RESULTS3.1.
Overall Distribution of Molecular Gas
The average spectra of the CO , CO , and theC O J = 1 − CO J = 1 − ∼ − ∼ −
35, and ∼ − − , respectively, while there are only two velocitycomponents, −
52 and −
10 km s − , in CO J = 1 − CO emission contained in thevelocity range from −
115 to −
75 km s − , not visiblein the total spectrum since it is confined in small re-gions. For clarity, we inserted in Figure 1 the averagespectrum of the CO line at the positions where the CO emission is detected in the velocity range from −
115 to −
75 km s − . The CO , CO , and C Oline emission is considered being detected at a positiononly when its spectrum show at least five, four, andthree contiguous channels, respectively, with intensitiesabove 2 σ RMS . The C O emission in the region is tooweak to be identified in the average spectrum. However,it clearly emerges in the average spectrum of the posi-tions where the C O J = 1 − ∼
34 and ∼
45 km s − in the CO spectrum andat ∼ −
75 and ∼
10 km s − in the CO spectrum areresidual bad channels not properly removed from theautomatic reduction pipeline, and so are the spikes at ∼ − ∼ − ∼ −
23, and ∼
60 km s − in the C Ospectrum. The bump in the velocity range from −
40 to −
17 km s − in the CO spectrum is caused by wavelikebaselines in the spectra.The spatial distribution of the molecular gas in dif-ferent velocity ranges in the region is shown in Figure2. The integrated intensity of CO emission in velocityranges from −
27 to 20, −
75 to −
27, and −
115 to − − are indicated with red, green, and blue colors, re-spectively. In the observed portion of the outer Galaxy,more negative local standard of rest (LSR) velocity cor-responds to farther distance. The nearby molecular gasshown in red color spreads over all the observed Galac-tic latitude range. The most distant gas, shown as theblue color, only distributes at positive Galactic latitudeswhich may be a result of the warp of the gas disk ofour galaxy (Westerhout 1957; Wouterloot et al. 1990).Several well known molecular clouds are located in thisregion, such as the nearby Cep GMC, shown in red inFigure 2, the GMC complex NGC 7538 and the CasGMC, shown in green. The Cep GMC is a low-massstar-forming region, while the NGC 7538 complex is thebirthplace of massive stars. The detailed analysis of the Ma et al.
Figure 1.
Average spectra of the CO , CO , and C O J = 1 − CO , CO , C O spectra, respectively. The spikes at ∼
34 and ∼
45 km s − in the CO spectrumand at ∼ −
75 and ∼
10 km s − in the CO spectrum are due to bad channels, and so are the spikes at ∼ − ∼ − ∼ −
23, and ∼
60 km s − in the C O spectrum. The left zoomed-in panel is the spectrum of the CO spectra averaged overthe spatial pixels that show emission in the velocity range from −
115 to −
75 km s − in at least five contiguous channels withintensities above 2 σ . The right zoomed-in panel is the average spectrum of C O line emission of all positions that have at leastthree contiguous channels with intensities above 2 σ . The green line represents the 3 σ noise level of the average spectrum. physical properties of Cas GMC was presented in ourprevious work Ma et al. (2019).Figure 3 shows the position velocity distribution of the CO emission along the directions of the Galactic longi-tude and latitude. Within the span of Galactic longitudecovered by this work, spiral arms of the Galaxy are iden-tified as continuous curves in the l-v diagram. The reddashed lines in Figure 3(a) shows the projected l-v po-sitions of the Local, Perseus, and the Outer arms thatare derived according to the fitted log-periodic spiralsof these arms in Reid et al. (2014), which are based onthe measured parallaxes of maser sources in high-massstar-forming regions and the Galactic rotation constantsfrom their model A5. The black dashed lines are the l-vlocations of the Local, Perseus, and Outer arms fromthe CfA CO observations (Cohen et al. 1980), which arepresented in figures 8 and 9 in Reid et al. (2016) and areused as the spiral arm traces in the Bayesian distanceestimator program in Reid et al. (2016). Therefore, thepreviously known kinematic anomaly, which can be in-ferred from the large discrepancy between the kinematicdistances and the luminosity/parallax distances of mas-sive star-forming regions (Xu et al. 2006), of the Perseusspiral arm, is shown in Figure 3(a) as the separation be-tween the red and black dashed “Perseus” lines. Thereexists a velocity shear between the east and west partsof the Perseus arm, divided by the shell-like structurelocated at l = 111 ◦ , v = −
45 km s − , which correspondsto the NGC 7538 complex. The molecular gas to the east of the NGC 7538 complex is mainly concentratedat −
37 km s − while the gas to the west of the complexmainly at −
52 km s − , which is the reason for the twopeaks observed at these velocities in the CO spectrumshown in Figure 1. The spiral arms in this region can beseen clearly in also the b-v diagram in Figure 3(b). Thevelocity dispersion of the molecular gas in the Local armis getting broader from south to north, which is causedby the fact that the majority of the gas in the Localarm is located at Galactic latitudes above b = 0 ◦ . Thevelocity of the molecular gas in the Perseus arm is grad-ually blue-shifted along the south to north direction, ascan be seen from Figure 3(b). Sun et al. (2015) and Duet al. (2016) identified hundreds of molecular clouds inthe “New” arm, which is the extension of the Scutum-Centaurus arm in the outer Galaxy (OSC arm), and theOuter arm using the MWISP data. The locations ofthose clouds that fall in the region observed in this workare shown with green circles and red squares, respec-tively. Some of the identified clouds are indiscernible inour position-velocity diagrams, which is caused by thebroad latitude range used in the integration.3.2. Statistics of CO , CO , and C O Emission inDifferent Spiral Arms
According to the l-v distribution of the CO emissionand the spiral arm traces, the molecular gas in the ob-served region can be divided into three layers, the Localarm layer (from −
27 to 20 km s − ), the Perseus arm olecular clouds in the second quadrant Figure 2.
Color-coded intensity maps of the CO emission in different velocity ranges. Red, green, and blue colors correspondto the CO integrated intensities in the velocity ranges from −
27 to 20, −
75 to −
27, and −
115 to −
75 km s − , respectively.The integrated intensity thresholds are 1.5 times √ Nσδv , where N is the number of velocity channels in the integrated velocityrange, σ is the RMS noise per velocity channel, and δv is the width of the velocity channel. The orange ellipses show the extentsof the supernova remnants (Green 2014, 2017) in the region. The H II regions and the H II region candidates in the WISEcatalog (Anderson et al. 2014) are indicated with blue and magenta circles, respectively. The corresponding names of the H II regions in the Sharpless’ catalog (Sharpless 1959) are shown with yellow letters, while the names of the supernova remnants areshown in red. Some active star-forming regions, like NGC 7822, are indicated with black letters. layer (from −
75 to −
27 km s − ), and the Outer+OSCarm layer (from −
115 to −
75 km s − ). Each layer canbe further divided into three kinds of masks based onthe detection of the CO , CO , and C O emission.Mask 1 is defined to be the regions where CO emissionis detected. Mask 2 is the regions where both CO and CO emission are detected, while Mask 3 is the regionwhere the emission from all three kinds of isotopologuesis detected. According to this definition, the Mask 1 re-gions contain the Masks 2 and 3 regions, while the Mask2 regions contain Mask 3 regions. The CO , CO ,and C O line emission is considered being detected at aposition only when their spectra show at least five, four,and three contiguous channels, respectively, with inten-sities above 2 σ RMS . Figure 4 presents the spatial distri-bution of Masks 1-3 in the three velocity layers. COand CO emission is detected in all the spiral arms,while the C O emission is only detected in very fewpixels of the first two layers, corresponding to the dens-est part of active star-forming regions like the Cep GMCand NGC 7538 complexes. The total numbers and thepercentages of the detection of CO , CO , and C O emission are presented in Table 1. The CO emission isdetected among 22.2% pixels with CO detection in theLocal arm, while this percentage is 24.1% in the Perseusarm and only 3.8% in the Outer+OSC arm. The C Oemission is detected among only about 0.31% pixels with CO detection in the Local and Perseus arms. We cal-culated the physical properties, such as the excitationtemperature, optical depth of the CO and C O emis-sion line, and the column density of the three isotopo-logues of the molecular gas for each pixel in Masks 1-3in the Local and Persues arms. Since the pixel numberwith good detection within the masks 2 and 3 regions inthe Outer+OSC arms are too small, their physical prop-erties are not calculated. The column density of COmolecule is directly converted from the H column den-sity using the abundance ratio [H / CO ] = 1.1 × (Frerking et al. 1982), while the H column density isobtained by multiplying the integrated intensity of the CO emission by a conversion factor X CO = 2 . × cm − (K km − ) − (Bolatto et al. 2013). The excitationtemperature of each pixel in each Mask and velocitylayer is calculated using the peak brightness tempera- Ma et al. (a)(b)
Figure 3. (a) L − v diagram of CO emission. The red dashed lines are the l − v curves of the Local, Perseus, and Outer spiralarms derived from model A5 from Reid et al. (2014). The black dashed lines are the location of the spiral arms derived from COand HI observations (Weaver 1970; Cohen et al. 1980), which are used as the arm traces in Reid et al. (2016). (b) B − v diagramof CO emission. The contours in the two panels start at 1.5 σ and then increase to 0.7 times the emission peak in seven stepswith the same intervals. The red squares and the green circles in the panels are the positions of the molecular clouds identifiedby (Du et al. 2016) and (Sun et al. 2015), representing the Outer arm and the New (OSC) arm, respectively. olecular clouds in the second quadrant CO in the corresponding velocity range of thatMask, using eq. 1 in Li et al. (2018). The optical depthof CO and C O in Masks 2 and 3 are derived us-ing the peak intensities of the CO and C O emissionin the corresponding Masks and velocity ranges, usingeqs. 2 and 3 of Li et al. (2018), respectively. The col-umn densities of CO and C O for the Local, Perseus,and Outer+OSC arms are calculated from the CO andC O integrated intensities in the corresponding velocityranges using eqs. 5 and 6 in Li et al. (2018). The statis-tics of the physical properties such as excitation temper-ature, optical depth, and column density of Masks 1-3are summarized in Figure 5 and Table 1.It can be seen from Table 1 that the median excitationtemperatures of Mask 1 in the four arms lie in the rangefrom 6 to 8 K, while those of the Mask 2 regions are rel-atively higher, lying in the range from 8 to 10 K, whichare typical for molecular clouds where the gas is self-shielded from the interstellar radiation field. The rangeof the excitation temperatures in the Local and Perseusarms is quite large, from about 4 K to 47 K, indicat-ing that large differences in the physical conditions andexcitation of the gas are present within the molecularclouds at the spatial scales resolved by the MWISP sur-vey. The densest regions, Mask 3, which correspond tothe active star-forming regions like the Cep GMC, NGC7822, L1188, and the NGC 7538 complex in the Localand Perseus arms, have much higher excitation temper-atures, with the median values from 15 to 19 K. This isexpected in regions where star formation is active sincethe new-born stars warm up their envelopes. Moreover,the radiation emitted by already formed stars, expeciallyif they are massive, can warm up their surrounding. Theoptical depth of CO emission, τ , is less than 1 inmost regions and has a median value in Mask 2 of about0.3 for both the Local and Perseus arms. However, itreaches as high as 1.5 in some pixels, which may be smallregions such as clumps or cores. The density in these re-gions can be much higher than that in the more diffusepart of the molecular clouds and consequently, the op-tical depth of the CO lines increases so that the linesbecome optically thick. The C O emission is opticallythin both in the Local and the Perseus arms, but, onaverage, the pixels in the local arm have a C O opticaldepth a factor of two higher than those in the Perseusarm. For the Local and Perseus arms, the distributionof N has a shape similar to that of N . How-ever, the median column densities of CO molecules isreduced by a factor of ∼ O molecule in the Perseus arm is greater than thatin the Local arm by a factor of ∼ Ma et al. (−27, 20)(−75, −27)
118 116 114 112 110 108 106Galactic Longitude ( o )−4−2024 G a l a c t i c La t i t ude ( o ) Mask 1Mask 2Mask 3 (−115, −75)
Figure 4.
Spatial distributions of molecular gas in different Masks in the three velocity layers. Blue, green, and red colorscorrespond to the regions where CO , CO , and C O emission is detected, respectively. Top, central and bottom panelscorrespond to the Local, Perseus, and Outer+OSC arms, respectively. The velocity ranges corresponding to each of the armsare given in the bottom right corner of each panel. The color compositions of the sky coverages of Masks 1-3 are shown in thelower-left corner of the bottom panel. olecular clouds in the second quadrant R e l a t i v e F r equen cy LocalPerseusOuter+OSC (a) τ R e l a t i v e F r equen cy LocalPerseus (b) τ C18O R e l a t i v e F r equen cy LocalPerseus (c) R e l a t i v e F r equen cy LocalPerseusOuter+OSC (d)
14 15 16 17 180.000.020.040.060.080.100.12 14 15 16 17 18lg N R e l a t i v e F r equen cy LocalPerseus (e)
C18O R e l a t i v e F r equen cy LocalPerseus (f)
Figure 5.
Histograms of (a) excitation temperature in Mask 1 regions, (b) optical depth of CO emission in Mask 2 regions,(c) optical depth of C O emission in Mask 3 regions, (d) column density of CO emission in Mask 1 regions, (e) column densityof CO emission in Mask 2 regions, and (f) column density of C O emission in Mask 3 regions in different arms. The colorsof the four arms are indicated in the upper-right corner of each panel. Ma et al. T a b l e . S t a t i s t i c a l p r o p e r t i e s o f m o l e c u l a r ga s i n t h e f o u r a r m s o f t h e G a l a xy A r m s M a s k P i x e l A r e a T e x τ C O τ C O l g ( N C O ) l g ( N C O ) l g ( N C O ) N a m e N a m e N u m ( P e r)( d e g2 )( K )( c m − )( c m − )( c m − ) ( )( )( )( )( )( )( )( )( )( ) L o c a l M a s k ( . % ) . . - . ( . ) ...... . - . ( . ) ...... M a s k ( . % ) . . - . ( . ) . - . ( . ) ...... . - . ( . ) ... M a s k ( . % ) . . - . ( . ) ... . - . ( . ) ...... . - . ( . ) P e r s e u s M a s k ( . % ) . . - . ( . ) ...... . - . ( . ) ...... M a s k ( . % ) . . - . ( . ) . - . ( . ) ...... . - . ( . ) ... M a s k ( . % ) . . - . ( . ) ... . - . ( . ) ...... . - . ( . ) O u t e r +O S C M a s k ( . % ) . . - . ( . ) ...... . - . ( . ) ...... M a s k ( . % ) . .................. M a s k ( . % ) ................... N o t e — C o l. : n a m e o f t h e a r m . C o l. : m a s k u s e d , t h e d e f i n i t i o n o f t h e m a s k s i s g i v e n i nS ec t . . . C o l. : nu m b e r o f p i x e l s w i t h goo dd e t ec t i o n f o ll o w i n g t h ec r i t e r i a e x p l a i n e d i nS ec t . . ,i np a r e n t h e s i s t h e p e r ce n t ag e o f t h e goo dp i x e l s w i t h r e s p ec tt o t h e t o t a l o b s e r v e dp i x e l s i s g i v e n . C o l. : t o t a l a n g u l a r s i ze o f p i x e l s w i t h goo dd e t ec t i o n . C o l. : r a n g e a nd m e d i a n v a l u e ( i np a r e n t h e s i s ) o f t h ee x c i t a t i o n t e m p e r a t u r e . C o l s . - : r a n g e s a nd m e d i a n v a l u e s ( i np a r e n t h e s i s ) o f t h e o p t i c a l d e p t h s o f C O a nd C O e m i ss i o n , r e s p ec t i v e l y . C o l s . - : r a n g e s a nd m e d i a n v a l u e s ( i np a r e n t h e s i s ) o f t h ec o l u m nd e n s i t y o f C O , C O , a nd C O , r e s p ec t i v e l y . olecular clouds in the second quadrant Catalogs of CO and CO Molecular Clouds
Decomposition of the CO and CO Emission intoIndividual Clouds
With the CO and CO line emission data, we iden-tify distinct CO and CO clouds in the surveyed re-gion using the DENDROGRAM plus the SCIMES algo-rithms.In practice, the dendrogram algorithm is memory con-suming when the dataset used is large. We smoothedthe width of the velocity channels of CO and COdata into 0.5 km s − , resulting in new CO and COdatacubes with median noise levels of 0.31 and 0.17 K,respectively. Before the implementation of the DEN-DROGRAM algorithm, only those voxels within at leasttwo consecutive velocity channels with intensities higherthan 2 σ are selected and all other velocity channels aremasked. The majority of the noise channels are removedunder this criterion, but some contiguous bad channelswere not removed. Nonetheless, if we set a higher noisethreshold or broader velocity coverage, real signal couldbe removed. The DENDROGRAM algorithm is thenimplemented to the noise-masked and velocity-smoothed CO and CO datacubes. The minimum difference be-tween two separate “leaves” in a dendrogram tree is setto be 3 σ , and the bottom threshold for detection is 2 σ .The minimum voxel number of an individual “leaf” is setto be 50, corresponding to 3.7 consecutive pixels alongeach of the l-b-v axes. The above settings correspondingto molecular cloud of size of 0.5 × × fordistances of 1.0 and 3.0 kpc, respectively, and velocityrange of 1.8 km s − . We use “volume” as the clusteringcriterion for the SCIMES algorithm. As a result, a maskcube that records the l-b-v positions and a catalog thatcontains the physical information of the output clustersare generated. The output “clusters” are taken to beindividual clouds in this work. Since some of the badchannels that produce spurious spikes in the spectra (seeFigure. 1) still exist in the masked and smoothed data,they may cause false identification of molecular clouds.Therefore, after the cloud identification, we performed amanual check for each identified cloud to further ensurethe identified molecular clouds are real structures andnot caused by bad channels. We carried out molecularcloud identification on CO and CO data separately,and cross-matched the two resulting catalogs. If morethan 85% voxels of a CO molecular cloud can be as-signed to a single CO cloud, then the CO cloud isconsidered to match to the CO cloud. As CO usuallytraces the denser part of a molecular cloud, we find thatone CO cloud usually contains several CO clouds.A total of 857 molecular clouds have been extractedfrom the CO J = 1 − CO J = 1 − −
115 to − −
75 to − −
27 to 20 km s − are assigned to the Outer+OSC,Perseus, and Local arms, respectively. The total num-bers of CO molecular clouds in the Local, Perseus,and Outer+OSC arms are 440, 399, and 18, respec-tively, while the corresponding numbers of CO molec-ular clouds are 176, 124, and 1. The CO cloud in theOuter+OSC arm is found to be artificial, which is causedby bad velocity channels, therefore, is removed in the fi-nal catalog. According to the result of cross-matching,279 CO molecular clouds have counterparts of COclouds. The name of the matching CO cloud for each CO cloud is given in the final catalog (see Table 3 inSection 3.4). Figures 6 and 7 present the demonstrationsof the outlines of the CO and CO molecular cloudsin the Local arm, respectively. The results of cloudsidentification in the Perseus and Outer+OSC arms areshown in the Appendix, Figures 20-22.3.3.2.
Distance estimation
Distance is critical for the calculation of the physicalparameters of molecular clouds. For the CO cloudswith centroid velocities less than −
27 km s − , whichare beyond the Local Arm, we adopted the kinematicdistances derived using a flat Galactic rotation curve,which is a good approximation for the outer Galaxy,with a solar galactocentric distance of R = 8.34 kpcand a rotation velocity of Θ = 240 km s − (Reid et al.2014). Since we are looking toward the outer Galaxy,our distance estimate is not affected by the near or farambiguity. For the nearby clouds, the peculiar motion ofthe gas and the internal velocity dispersion of molecularclouds may lead to large uncertainty in the estimationof the distances based on the kinematic method. There-fore for these clouds, we use an alternative method toestimate the distance. For molecular clouds within 2kpc, we looked for the position of sharp steepening inthe 3D reddening map within the projected area of eachcloud to determine their distances. We used the three-dimensional map of dust reddening up to 5 kpc pro-duced by Green et al. (2019) with the parallaxes fromGaia DR2 catalog and the stellar photometry from Pan-STARRS 1 and 2MASS.The public Python package “dustmaps” is used toquery the reddening map of Green et al. (2019). Wehave queried a region of the “median” dust reddeningcube with the same pixel size and spatial extent as ourCO datacube, which contains dust reddening along eachline-of-sight from distance modulus from 4 mag to 18.725mag in steps of 0.125 mag. For each CO cloud, we2
Ma et al.
118 116 114 112 110 108 106Galactic Longitude ( o )−4−2024 G a l a c t i c La t i t ude ( o ) ( K k m s − ) / (a)
118 116 114 112 110 108 106Galactic Longitude ( o )−40−30−20−1001020 V e l o c i t y ( k m s − ) ( K a r c deg ) / (b) Figure 6.
Demonstration of the outlines, as the output of the SCIMES algorithm, of the identified CO molecular clouds inthe Local arm in (a) l-b space and (b) l-v space. Different colors in the two panels correspond to different molecular clouds.The background image in panel (a) is the integrated intensity of CO in the velocity range from −
27 to 20 km s − , while thatof the panel (b) is the l-v diagram integrated along the Galactic latitude from b= − . ◦
25 to b=5 . ◦ derive the average dust reddening within the projectedboundary of the cloud at different distance modulus,such as panel (a) in Figure 8. The distance of the molec-ular cloud is considered to correspond to the distancemodulus where there is a sharp increase of the redden-ing curve, which also corresponds to a local maximum ofthe derivative of the reddening-distance modulus curve,defined as the dust reddening density. In practice, weuse two methods to determine the “step” in the aver-age reddening-modulus curve of each cloud. The firstmethod is to determine the distance modulus that cor-responds to the minimum of the second derivative ofthe reddening versus the distance modulus, as indicated by the blue dashed line in panel (b) in Figure 8. Thesecond method is to derive the modulus at which thecross-correlation between the integrated intensity mapand the reddening density map reaches the maximum,as indicated by the red dashed line in panel (c) in Figure8. For molecular clouds that have large angular sizes,such as the Cep GMC in Figure 8, the distances esti-mated by the two methods are consistent within 0.25mag distance modulus. In this case, the averaged valuefrom the two methods is adopted. For molecular cloudsof small angular size, the distances obtained by the twomethods are usually inconsistent. In this case, we choosethe modulus found by the first method. However, in olecular clouds in the second quadrant
118 116 114 112 110 108 106Galactic Longitude ( o )−4−2024 G a l a c t i c La t i t ude ( o ) ( K k m s − ) / (a)
118 116 114 112 110 108 106Galactic Longitude ( o )−40−30−20−1001020 V e l o c i t y ( k m s − ) ( K a r c deg ) / (b) Figure 7.
Same as Figure 6, but for CO clouds. practice, for some clouds there are multiple “steps” orno “step” in the reddening-modulus curves. When thereare multiple “steps” in the reddening-modulus curve, wecheck the average CO spectrum of the cloud and matcheach step with different velocity components with therule of more negative velocity corresponding to largerdistance. For those clouds that no obvious “step” in thereddening-modulus curve is found, the cloud distance isnot assigned. Figure 8 is given as an example of thedistance estimation. We have manually checked the fig-ures for each of the 440 CO clouds in the Local armto estimate their distances. Finally, there are 267 outof the 440 nearby CO molecular clouds with distanceassigned by using the extinction method.In summary, we estimated the distances of the molec-ular clouds of the Local arm with the 3D-extinction method, while for the clouds in the Perseus andOuter+OSC arms, we used the kinematic method. Thedistances of the CO clouds are taken to be that of theircounterpart CO clouds. For the CO clouds that donot have counterpart CO clouds, distances are not as-signed. The relationship of cloud distance with theircentroid velocity and the corresponding histograms aregiven in Figure 9. As shown in Figure 9, the molec-ular clouds in the Local arm are mainly concentratedat two distances, ∼
250 and ∼
750 pc with small dis-persions, while the distances of the molecular cloudsin the Perseus arm distributed in a wider range from ∼ ∼ ∼ Ma et al. the Outer+OSC arms are located in the distance rangefrom ∼ ∼ Physical Properties of the Identified MolecularClouds
The statistical properties of molecular clouds in ourGalaxy can provide insight into understanding theirformation, evolution, and environments (Dobbs et al.2014). In this section we derive the physical parametersof the identified CO and CO clouds.3.4.1.
Physical parameters
The centroid position and the velocity dispersion ofthe identified molecular cloud are given by the DEN-DROGRAM+SCIMES algorithms directly, which aredefined as the brightness temperature-weighted first andsecond moments within the p-p-v mask of the cloud, re-spectively (Colombo et al. 2015).The effective radius of a cloud is derived as the geo-metric mean of the major and minor axes of the cloudgiven by the algorithm, and then deconvoluted with theHPBW of the PMO-13.7 m telescope, R eff = 12 d ( θ a θ b − θ beam ) / (1)where θ a , θ b , are the fitted FWHM along the majorand minor axes of the cloud, and θ beam is the HPBWof the PMO-13.7 m telescope, and d is the distance tothe cloud. This method means that we approximatea molecular cloud to a Gaussian ellipsoid, and its pro-jected area is an ellipse.The total intensity and the exact area, in units ofsquare arcseconds, of each cloud are tabulated in theoutput table of the DENDROGRAM algorithm, whichcan be used to calculate the averaged column density ofa cloud as follows, N ( H ) = N tot /num p . (2)where N tot is the total column density of molecular hy-drogen, and num p is the total pixel number of a cloudthat can be obtained through dividing the exact area ofa cloud by the pixel size of the data.For the molecular clouds extracted from the CO J =1 − column density was derived inthe same way described in Section 3.2 using the formula N tot = X CO I CO , (3)where I CO is the CO intensity integrated over the to-tal area of the cloud and X CO = 2 . × cm − (Kkm − ) − (Bolatto et al. 2013) is the conversion factor. For the molecular clouds extracted from the CO data,we used a different method to derive the total H columndensity that takes into account the estimate of the gasexcitation temperature, the CO optical depth, and thevariation of the C/ C abundance ratio with the galac-tocentric distance. In particular, assuming the COmolecules are under the Local Thermodynamic Equilib-rium (LTE) condition, the total H column density ofthe CO clouds can be calculated according to N tot = A × . × τ ( CO )1 − e − τ ( CO ) . /T ex − e − . /T ex I CO , (4)where A is a constant related to the abundance ratio toconvert the CO column density to H column density, T ex is the excitation temperature, τ ( CO) is the op-tical depth at the peak intensity of the CO emissionwithin the boundary of a CO cloud, and I CO is thetotal CO integrated intensity. The constant A is theproduct of the abundance ratio [ C/ C] = 6.21 d GC +18.71 (Milam et al. 2005) and H / CO = 1 . × (Fr-erking et al. 1982), where d GC is the cloud distance fromthe Galactic center. The excitation temperature is cal-culated according to Eq. 1 in Li et al. (2018), using thepeak intensity of the CO emission within the bound-ary of the CO cloud, while the optical depth of the CO emission is according to Eq. 3 in Li et al. (2018).The cloud mass, either for the CO clouds or the CO clouds, is eventually obtained through M = N tot d Ω µm H , (5)where d is the cloud distance, Ω is the solid angle of eachpixel, and µ = 2.8 is the atomic weight per molecularhydrogen.The surface densities and number densities of theclouds are derived as follows,Σ = M/ ( πR eff ) (6) n ( H ) = 3 M/ (4 πR eff µm H ) . (7)The dynamical state of a molecular cloud is character-ized by the virial parameter, which measures the ratioof the internal kinetic energy to the gravitational en-ergy. In the literature, there are different forms of thevirial parameter. In this work we follow the definitionof Bertoldi & McKee (1992) α vir = 5 σ v R eff GM , (8)where G is the gravitational constant, σ v is the veloc-ity dispersion. Theoretically, the critical value of α vir for a non-magnetized isothermal hydrostatic equilibrium olecular clouds in the second quadrant E ( B − V ) (a) ∆ E ( B − V ) / ∆ d (b) C o rr e l a t i on (c)(d) (e) (f) −100 −50 0Velocity (km s −1 )−101234 T m b (g) Figure 8.
Example of distance estimate of molecular clouds using the 3D dust maps from Green et al. (2019). (a) Averagereddening versus distance modulus of the Cepheus GMC. The blue dashed line shows the distance of the Cepheus GMC. (b)Dust reddening density, ∆ E ( B − V ) / ∆ d , versus distance modulus. The blue dashed line marks the distance modulus thatcorresponds to the maximum of the ∆ E ( B − V ) / ∆ d value. (c) Variation of the cross-correlation between the reddening densitymap and the CO integrated intensity map of the cloud. The red dashed line shows the distance modulus that correspondsto the maximum of the cross-correlation. (d) CO intensity map of Cepheus GMC integrated within the PPV mask resultingfrom the SCIMES algorithm. (e) Dust reddening density map at the distance modulus indicated by the blue dashed line inpanel (b). (f) Dust reddening density map at the distance modulus as indicated by the red dashed line in panel (c). (g) Averagespectrum of CO emission within the projected boundary of Cepheus GMC. sphere is 2 (Kauffmann et al. 2013). A cloud with a virialparameter above or below the critical value will even-tually dissipate or collapse when not considering otherphysical mechanisms beside its self-gravity and internalpressure. We have derived the virial parameters for each CO and CO cloud.All above derived physical parameters of CO and CO clouds are tabulated in Tables 2 and 3, respec-tively. In Table 2 and Table 3, we have listed a totalof 857 CO molecular clouds and 300 CO molecu- lar clouds, respectively. However, the physical parame-ters, such as effective radius, mass, surface density, num-ber density, and virial parameter, are only presented forthe 684 CO molecular clouds and 274 CO molecularclouds that have assigned distances. The histograms ofthe physical parameters for the distance-assigned COand CO clouds are presented in Figures 11 and 12, re-spectively, and we also used the distance assigned cloudsas the sample to study the scaling relations in Section3.5.6
Ma et al. N u m be r −120−100−80 −60 −40 −20 0 20Velocity (km s −1 )0246810 D i s t an c e ( k p c ) Figure 9.
Relationship between the centroid velocities and the distances of the CO clouds. The upper and right panelsshow the statistics of the centroid velocity and the distance, respectively. We adopt the extinction distances for the clouds withvelocities v > −
27 km s − and the kinematic distances for the clouds with velocities v < −
27 km s − . olecular clouds in the second quadrant T a b l e . P r o p e r t i e s o f C O c l o ud s N a m e l b θ a θ b P A v l s r σ v d R e ff N ( H ) M a ss Σ n α v i r ◦◦ (cid:48)(cid:48)(cid:48)(cid:48) ◦ ( k m s − )( k m s − )( k p c )( p c )( c m − )( M (cid:12) )( M (cid:12) p c − )( c m − ) ( )( )( )( )( )( )( )( )( )( )( )( )( )( )( ) M W I S P G . - . - . . - . - . . . . . e + . . . M W I S P G . + . - . . . - . . ...... . e + ............ M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . + . - . . . - . . ...... . e + ............ M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . - . - . . - . - - . . . . . e + . . . M W I S P G . + . + . . . - . . ...... . e + ............ M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . + . - . . . - . . ...... . e + ............ M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . + . - . . . - . . ...... . e + ............ M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . + . - . . . - - . . ...... . e + ............ M W I S P G . - . - . . - . - . . . . . e + . . . M W I S P G . + . - . . . - - . . . . . e + . . . M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . + . - . . . - - . . ...... . e + ............ M W I S P G . + . - . . . - - . . . . . e + . . . M W I S P G . - . - . . - . - . . . . . e + . . . M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . + . - . . . - - . . . . . e + . . . M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . - . - . . - . - . . ...... . e + ............ M W I S P G . - . - . . - . - . . ...... . e + ............ M W I S P G . + . - . . . - . . ...... . e + ............ M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . - . - . . - . - - . . . . . e + . . . M W I S P G . + . - . . . - - . . . . . e + . . . M W I S P G . + . - . . . - . . . . . e + . . . M W I S P G . - . - . . - . - . . . . . e + . . . M W I S P G . + . - . . . - . . ...... . e + ............ M W I S P G . + . - . . . - . . ...... . e + ............ M W I S P G . - . - . . - . - . . . . . e + . . . N o t e — T h e s o u r ce n a m e i s d e f i n e dund e rt h e M W I S P s t a nd a r d . A cc o r d i n g t o t h e M W I S P s t a nd a r d f o r n o m e n c l a t u r e , m o l ec u l a r c l o ud s a r e n a m e d a f t e rt h e i r ce n tr o i dp o s i t i o n s a nd v e l o c i t i e s . Sp ec i f i c a ll y , t h e n a m e ss t a rt w i t h “ M W I S P ”a nd t h e n c o n t a i n t h e s p a t i a l c oo r d i n a t e s o f t h e m o l ec u l a r c l o ud s a cc u r a t e t o t h r ee d ec i m a l p l a ce s a nd t h ece n tr o i d v e l o c i t i e s a cc u r a t e t o t w o d ec i m a l p l a ce s . T h e a cc u r a c y i ss e t a cc o r d i n g t o t h e p o i n t i n ga cc u r a c y a nd t h e v e l o c i t y r e s o l u t i o n o f t h e P M O - . m t e l e s c o p e . C o l u m n s − i v e t h ece n tr o i dp o s i t i o n s , t h e i n t e n s i t y - w e i g h t e d m a j o r a nd m i n o r a x e s , a nd t h e p o s i t i o n a n g l e s o f t h ec l o ud s . T h ece n tr o i d v e l o c i t y , t h e v e l o c i t y d i s p e r s i o n , a nd t h e d i s t a n ce o f t h ec l o ud s a r e p r e s e n t e d i n c o l u m n s − . C o l u m n s − li s tt h ee ff ec t i v e r a d i u s , a v e r ag ec o l u m nd e n s i t y , m a ss , s u r f a ce d e n s i t y , nu m b e r d e n s i t y , a nd t h e v i r i a l p a r a m e t e r s o f t h ec l o ud s , r e s p ec t i v e l y . T h i s t a b l e i s a v a il a b l e i n i t s e n t i r e t y i n m a c h i n e − r e a d a b l e f o r m i n t h e o n li n e m a t e r i a l. Ma et al. T a b l e . P r o p e r t i e s o f C O c l o ud s N a m e l b θ a θ b P A v l s r σ v d R e ff T e x τ C O N ( H ) M a ss Σ n α v i r N a m e o f m a t c h i n g12 C O c l o ud ◦◦ (cid:48)(cid:48)(cid:48)(cid:48) ◦ ( k m s − )( k m s − )( k p c )( p c )( K ) c m − ( M (cid:12) )( M (cid:12) p c − ) c m − ( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( ) M W I S P G . + . - . . . - . . .............................. M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . .............................. M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . - . - . . - . - . . . . . . . e + . . . M W I S P G . - . - . M W I S P G . + . - . . . - - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . - . - . . - . - . . . . . . . e + . . . M W I S P G . - . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . - . - . . - . - . . . . . . . e + . . . M W I S P G . - . - . M W I S P G . - . - . . - . - - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . - . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . M W I S P G . + . - . . . - . . . . . . . e + . . . M W I S P G . + . - . N o t e — S a m e a s T a b l e bu t f o r C O c l o ud s . C o l u m n s − i v e t h ece n tr o i dp o s i t i o n s , t h e i n t e n s i t y - w e i g h t e d m a j o r a nd m i n o r a x e s , a nd t h e p o s i t i o n a n g l e s o f t h ec l o ud s . T h ece n tr o i d v e l o c i t y , t h e v e l o c i t y d i s p e r s i o n , a nd t h e d i s t a n ce o f t h ec l o ud s a r e p r e s e n t e d i n c o l u m n s − . C o l u m n s − li s tt h e d e r i v e dp a r a m e t e r s o f t h ec l o ud s ,i. e ., e ff ec t i v e r a d i u s , e x c i t a t i o n t e m p e r a t u r e , t h e o p t i c a l d e p t h o f C O e m i ss i o n , a v e r ag ec o l u m nd e n s i t y , m a ss , s u r f a ce d e n s i t y , nu m b e r d e n s i t y , a nd t h e v i r i a l p a r a m e t e r s o f t h ec l o ud s , r e s p ec t i v e l y . T h e l a s t c o l u m n g i v e s t h e n a m e o f t h e C O c l o ud t h a t m a t c h e s t h e C O c l o ud i n c o l u m n . T h i s t a b l e i s a v a il a b l e i n i t s e n t i r e t y i n m a c h i n e − r e a d a b l e f o r m i n t h e o n li n e m a t e r i a l. olecular clouds in the second quadrant Size and Mass of the Clouds
The histograms of the effective radius of the COand CO clouds are given in Figures 11(a) and 12(a),respectively. More than half of the CO and COclouds have sub-pc sizes. In the conventional classifi-cation scheme of molecular gas structures, these molec-ular entities should be classified as molecular clumps,but, for simplicity, we still refer to them as “clouds”in this work. The median radius of the CO molecu-lar clouds in the Local and Perseus arms are ∼ ∼ ∼ ∼ CO molecular clouds. The distributions ofthe mass of the CO and CO clouds are presentedin Figures 11(b) and 12(b). The median mass of COmolecular clouds in the Local, Perseus, and Outer+OSCarms is ∼
20 M (cid:12) , 1 × M (cid:12) , and 2 × M (cid:12) , re-spectively. The median mass of the CO clouds in theLocal and Perseus arms is 70 and 2 × M (cid:12) , respec-tively, which is moderately larger than that of the COclouds. Generally, the molecular clouds in the Perseusand Outer+OSC arms are much larger and more mas-sive than the molecular clouds in the Local arm. Thepossible reasons for the systematic difference betweenthe median radii and masses in the Local and Perseusarms are as follows.First, the distance selection effect, i.e., only the molec-ular clouds that are larger and more massive than thesensitivity limit can be detected, regardless of their dis-tance. The output molecular clouds of the SCIMES al-gorithm have similar minimum angular sizes, ∼ (cid:48)(cid:48) , andsimilar minimum total integrated-intensities, ∼
66 K kms − , at different distances, as shown in Figures 10(a)and 10(c). The minimum angular size and integrated-intensity correspond to the minimum effective radiusand mass that increase with distance, therefore causesthe non-detection of the smaller and less massive cloudsat the higher distances. Figures 10(b) and 10(d) showsthe variation of the effective radius and the mass of the CO clouds as a function of the cloud distance. Theminimum effective radius at 1 and 7.5 kpc, taken as thereference upper limit distances of the Local and Perseusarms, is ∼ ∼ ∼ ∼
349 M (cid:12) , respectively. The finitespatial resolution of our observations introduces an ad-ditional bias due to the fact that the minimum projectedangular distance on the sky between two clouds that al-lows us to identify them as separate structures increaseswith their distance. For this reason, clouds close to eachother are seen as one larger cloud at higher distances.Second, different methods are used in the distance esti-mation for the clouds in the two arms. We find that the distance estimated with the dust extinction map is usu-ally smaller than the kinematic distance. In addition,the distances of the molecular clouds in the Perseus armare also overestimated because of the kinematic abnor-mality of the Perseus arm. Third, same settings andcriteria are used with the SCIMES algorithm to identifyclouds in different spiral arms. It can be seen from Fig-ures 10(a) and 10(c) that the clouds identified by theSCIMES algorithm have similar angular sizes and to-tal integrated intensities in the Local and Perseus arms,therefore, the molecular clouds are inevitably less mas-sive in the Local arm than in the Perseus arm.In the concept that molecular clouds are overdensesub-structures of the turbulent, multi-phase fractal ISM(Scalo 1988), the distributions both of the size and themass of the clouds possess power-law forms, dN/dR ∝ R α R dN/dM ∝ M α M , where dN is the number of cloudsin the interval of dR or dM . Instead of fitting dN inequally separated radius bins, we fitted the linear rela-tionship between lg dN and lg R (and lg M ) taking ac-count of statistic errors, where dN , in this case, is thenumber in each logarithmic bin. The resulting exponentin the relation dN/d ( lgR ) ∝ R β is related to α R through β = 1 + α R , and the same for the mass. The minimumeffective radii (or mass) of the CO clouds at the refer-ence position of the Local and Pesrus arms are near thepeaks of their lg R (or lg M ) distributions. Therefore,we consider them as a reasonable estimate of the com-pleteness limit of the radius (or mass) distribution, andfitted the distribution from the center of the bin withthe peak values of dN to the center of the bin of thelargest lg R (or lg M ).As shown in Figure 11(a), the measured exponent, α R ,in the Local arm is − .
75, while in the Perseus arm is − .
42. The exponents for the radius distribution of the CO clouds are slightly smaller than the above values,which are − .
78 and − .
54 for the Local and Perseusarms, respectively. The best-fit of the power-law distri-bution dN/dM ∝ M αM is α M = − .
40 for the Local armand α M = − .
59 for the Perseus arm. The radius distri-butions derived in this work are shallower than those ofthe OGS and GRS survey, α R = − α R = − α R ∼ − . α M = − Ma et al. A ngu l a r s i z e ( a r cs e c ) (a) R e ff ( p c ) (b) I n t en s i t y ( K k m s − ) (c) -2 -2 M a ss ( M O • ) (d) Figure 10.
Variation versus distance of (a) the angular size, which is defined as the geometric mean of the intensity weightedsecond-moment of the spatial scale along the major and minor axes, (b) the effective radius, (c) the total integrated intensity, and(d) the mass of the CO clouds. The red dashed lines in panels (a) and (c) represent the minimum angular size and minimumtotal integrated-intensity that detected from nearby to a distance of 7.5 kpc. The red dashed lines in panels (b) and (d) arethe minimum effective radius and minimum mass corresponding to the minimum angular size and total integrated-intensity atdifferent distances. algorithm used by Roman-Duval et al. (2010) tends toseparate molecular clouds into several small-scale struc-tures (Li et al. 2020). On the contrary, in this work,we aim at identifying large structures that contain atleast 50 voxels in p-p-v space. Besides, the SCIMESalgorithm uses a clustering process to merge the con-necting “leaves” into a cloud, tending to connect smallstructures into a large one.3.4.3.
Surface Density and Number Density
Figures 11(c) and 11(d) present the distributions of Σand n H of the CO molecular clouds, and the corre-sponding distributions of the CO molecular clouds aregiven in Figure 12(c) and 12(d). The median mass sur-face densities of the CO clouds in the Local, Perseus,and Outer+OSC arms are ∼ ∼
45, and ∼
26 M (cid:12) pc − ,respectively, and the corresponding values of the COclouds in the Local and the Perseus arms are ∼
44 and ∼
89 M (cid:12) pc − . In the Local arm, about 63% of the to-tal mass of the CO clouds is contained in the cloudswith surface densities above the threshold for star forma-tion, ∼
140 M (cid:12) pc − (corresponds to N H2 ∼ . × cm − ) (Johnstone et al. 2004; Lada et al. 2010; Kain-ulainen et al. 2014), and the percentage is 88% in thePerseus arm.The maximum surface densities of the CO and COmolecular clouds are 431 and 1703 M (cid:12) pc − , whichcorrespond to H column densities of 1.9 × and7.7 × cm − , respectively. The maximum densitiesare located in the NGC 7538 GMC. Urquhart et al.(2013) suggested a lower limit of mass surface den-sity of 0.05 g cm − for massive star formation, whichcorresponds to H column density ∼ × cm − .The mass surface density of the NGC 7538 GMC ismuch higher than this limit, which is consistent withthe observed concentration of CH OH masers within it(Moscadelli & Goddi 2014), testifying the presence ofhigh-mass star formation activity in this region. Wealso checked the positions of other five CO molecularclouds with mass surface densities above 0.05 g cm − and found that these molecular clouds are all located inthe Perseus arm and that they are associated with H II regions or H II region candidates (Anderson et al. 2014). olecular clouds in the second quadrant −2 −1 0 1 2 3110100 Radius −2 −1 0 1 2 3lg R (pc)110100 N u m be r LocalPerseusOuter+OSCdN/dR ∝ R −1.75 ± dN/dR ∝ R −2.42 ± (a) -2 0 2 4 610 Mass -2 0 2 4 6lg M
Xco (M O • )10 N u m be r LocalPerseusOuter+OSCdN/dM ∝ M -1.40 ± dN/dM ∝ M -1.59 ± (b) Surface Density Σ (M O • pc -2 )020406080 N u m be r LocalPerseusOuter+OSC (c)
Number Density H2 (cm −3 )20406080100 N u m be r LocalPerseusOuter+OSC (d)
Velocity Dispersion σ v (km/s)020406080100 N u m be r LocalPerseusOuter+OSC (e)
Figure 11.
Distributions of (a) effective radii, (b) masses from the X CO method, (c) mass surface densities, (d) numberdensities, and (e) velocity dispersions, of the identified CO clouds. The red and the blue dashed lines in panels (a) and (b)give the power-law fitting of the distribution of the radius and the mass of the clouds respectively, with the blue dashed lines forthe clouds in the Local arm and the red dashed lines for the clouds in the Perseus arm. The blue and red dotted vertical linesin panel (a) and (b) indicate the minimum values of the radius and mass at the distances of the clouds in the Local and thePerseus arms, respectively. The green vertical line in panel (c) marks the surface density corresponding to the star formationthreshold of column density, i.e., 6 . × cm − (Johnstone et al. 2004; Lada et al. 2010; Kainulainen et al. 2014). The distributions of the number density of the COand CO molecular clouds in different spiral arms areshown in Figures 11(d) and 12(d), respectively. Themedian values of n H of CO molecular clouds in theLocal, Perseus, and Outer+OSC arms are 648, 157, and61 cm − , respectively, while the corresponding values of CO molecular clouds in the Local and Perseus armsare 786 and 326 cm − . The measured number densitiesof molecular clouds in the Local arm is systematicallyhigher than that in the Perseus and the Outer+OSCarms with both CO and CO as the tracer, whichmay indicate a bias and/or a systematic effect in theestimation of this parameter. This consideration is alsosupported by the fact that the median number densityof the distant (d > CO and CO J = 1 − ∼
700 cm − . One possible reason is that the num-ber density is a distance-dependent parameter. There-fore the same caveats listed in the previus subsection formass and distance are valid also for the number density.In particular, it scales with R eff as n ∼ R peff , where p isin the range from ∼ − ∼ − R eff , is overestimatedby a factor of two, which is the case for the massive star-forming region W3(OH) in the Perseus arm (Xu et al.2006), the number density could be underestimated for ∼
34% to ∼ CO critical density. Another possible factorto cause underestimation is that the volume filling factorof the CO and CO emission for the molecular cloudsin the Perseus arm is low. In other words, there are fineinternal structures in the molecular clouds that can notbe resolved by the beam of the PMO-13.7m telescope atthe distance of the Perseus arm. Metaphorically speak-ing, there could be “holes” in the molecular clouds thatcause dilution of the molecular line emission in the beamof the telescope.3.4.4.
Velocity Dispersion
The derived total velocity dispersion within theboundary of a given cloud includes the contributionsfrom the internal thermal motion and non-thermal tur-bulence. As shown in Figure 11(e), the median velocitydispersions of CO molecular clouds in the two spiral2
Ma et al. −1.0 −0.5 0.0 0.5 1.0 1.5110
Radius −1.0 −0.5 0.0 0.5 1.0 1.5lg R (pc)110 N u m be r LocalPerseusdN/dR ∝ R −1.78 ± dN/dM ∝ R −2.54 ± (a) Mass
LTE (M O • )10 N u m be r LocalPerseus (b)
Surface Density Σ (M O • pc -2 )051015202530 N u m be r LocalPerseus (c)
Number Density H2 (cm −3 )01020304050 N u m be r LocalPerseus (d)
Velocity Dispersion σ v (km/s)010203040 N u m be r LocalPerseus (e)
Figure 12.
Same as Figure 11, but for CO clouds. The mass of the CO clouds is calculated using the LTE method. arms are similar, ∼ . − . However the proportionof the molecular clouds with velocity dispersions greaterthan 1.5 km s − is larger in the Perseus arm than thatin the Local arm. Most of the molecular clouds in thePerseus arm with σ v > − are associated with orlocated in the vicinity of H II regions like S 163, S 157,and NGC 7538, indicating complex dynamics in theseregions. The median values of σ v of the CO molecularclouds in the Local and Perseus arms are 0.8 and 1.1km s − , respectively, similar to that of the CO molec-ular clouds. The distribution and median values of σ v from this work is consistent with that of the molecularclouds in the solar circle (Roman-Duval et al. 2010), andthe results from the OGS survey (Heyer et al. 2001).Miville-Deschˆenes et al. (2017) used a multi-Gaussiandecomposition method to re-analysis the dataset fromDame et al. (2001), and their results are nearly ∼ − ) ofthe CfA survey.3.4.5. Surface Density Variation Across the GalactocentricDistance
Heyer & Dame (2015) have made from the literaturea compilation of the cloud surface density Σ across theGalactocentric distance and found that the surface den-sities of the molecular clouds in the inner Galaxy aresignificantly higher than those in the outer Galaxy. Ob- servations have shown that Σ in the outer Galaxy de-creases exponentially as a function of the Galactocen-tric distance (Wouterloot et al. 1990). This kind of ra-dial distribution of Σ toward the outer Galaxy is con-firmed by the re-decomposition of the CO data from theCfA survey (Miville-Deschˆenes et al. 2017). The sur-face densities of the CO clouds toward the observedregion are shown as a function of the galactocentric dis-tance in Figure 13. The median surface density of theclouds in each 0.5 kpc bin first increases from ∼
30 to ∼ (cid:12) pc − from d GC =8.5 to 9 kpc, remains at around ∼
45 M (cid:12) pc − from 9 to 11 kpc, and then slightly de-creases to ∼
30 M (cid:12) pc − at 12.5 kpc. The scatter of Σ ineach d GC bin is significant. The median Σ obtained inthis work is comparable to the compiled results in Heyer& Dame (2015) and substantially lower than the surfacedensity in the inner galaxy, ∼
170 M (cid:12) pc − (Roman-Duval et al. 2010; Heyer & Dame 2015). The averagesurface density in galactocentric distance interval of 0.5kpc is calculated as the total mass of the clouds dividedby the total area of the clouds. We can see that theaverage surface density is higher than the median Σ inthe range of d GC < . d GC ∼ . − . kpc ). This differ-ence is reasonable as we can see in Figure 13 that thelarge and massive molecular clouds at these distancesalso have higher surface densities than the smaller andless massive ones. olecular clouds in the second quadrant GC (kpc)1101001000 Σ ( M O • p c - ) l g ( M / M O • ) Figure 13.
Variation of the surface densities of molecular clouds as a function of the galactocentric distances. The radii ofthe circles correspond to the sizes of the clouds and the color shades correspond to the masses of the clouds. The red diamondsare the average surface densities calculated through dividing the total mass with the total area of all the clouds in each intervalof galactocentric distance of 0.5 kpc. The black pluses show the medium surface density in each interval. The scatter of themedium surface density in each interval is indicated in the figure, which is defined as the square root of the mass-weighted meansquared deviation from the medium surface density in each interval. The lower-ends of the error bars of the first six medianvalues are negative and are not displayed.
Scaling Relations and Equilibrium States of themolecular clouds
In this section, we present the scaling relations be-tween the measured physical parameters of molecularclouds. 3.5.1.
Mass-radius relation
Larson’s third law (Larson 1981) states that molecu-lar clouds have a constant surface density which meansthat molecular clouds have a scaling relationship be-tween their masses and radii of the form of M ∝ R .However, the power-law exponent in the M-R relation isfound to be a probe of the internal density distributionof molecular fragments on the sub-pc to pc scales (Kauff-mann et al. 2010a,b). Observations of molecular cloudshave shown that the stellar cluster forming clumps aremore massive than those clumps devoid of stellar clus-ters although they have the same size (Rathborne et al.2006; Portegies Zwart et al. 2010; Walsh et al. 2011;Bressert et al. 2012). Kauffmann et al. (2010b) obtainedthe empirical relationship M ( R ) (cid:62) M (cid:12) ( R/pc ) . formolecular clouds capable to form massive stars.The M-R relations of the CO clouds in the Localand Perseus arms are presented in Figure 14(a). Theycan be well fitted with power-law functions of exponents ∼ ∼ .
06 to ∼
40 pc.None of the CO molecular clouds are distributed inthe region of the M-R parameter space capable of host- ing massive proto clusters following the prescription ofBressert et al. (2012). However, five molecular cloudshave surface mass densities above the lower limit of mas-sive star formation given by Urquhart et al. (2013) andthey are all associated with H II regions. The M-R rela-tions for the CO clouds are presented in Figure 15(a)and the fitted power-law exponents of the CO cloudsin the Local and Perseus arms are ∼ .
4, suggestingnon-uniform inner densities. Most of the CO molecu-lar clouds located above both the grey shaded area andthe 0.05 g cm − limit for possible massive star formation(Urquhart et al. 2013) in Figure 15(a) correspond to ac-tive star-forming regions in the Local arm, such as CepOB3 and L1188 GMCs, and the molecular clouds in thePerseus arm that are associated with H II regions. No-tably, the four molecular clouds that fall in the regionfor massive proto-cluster candidates are all associatedwith H II regions, namely NGC 7538, S157, and S152.These GMCs are candidate regions for massive clusterformation.3.5.2. Velocity Dispersion-Size relation
The resemblance of the exponent in the scaling re-lation σ v ∝ R . , found by Larson (1981), to that inthe velocity structure-function of incompressible turbu-lence (Kolmogorov 1941) reminds us of the importantrole of turbulence in molecular clouds. Observationally,Solomon et al. (1987) found that the scaling relation-4 Ma et al. -1 -1 R (pc)10 M X c o ( M O • ) Without High-mass Star FormationMassive Proto-cluster Candidates
LocalPerseusOuter+OSCM ∝ R ± M ∝ R ± (a) −1
110 10 −1 R (pc)110 σ v ( k m s − ) LocalPerseusOuter+OSC σ v ∝ R ± σ v ∝ R ± (b) −1 0 1 2 3020406080100120−1 0 1 2 3lg α vir N u m be r −1 0 1 2 3lg α vir N u m be r gravitationallybound Local 1.9%Perseus 29.1%Outer+OSC 33.3% (c) -2 -1 -2 M Xco (M O • )10 -1 α v i r LocalPerseusOuter+OSC α∝ M -0.41 ± α∝ M -0.53 ± (d) -2 -1 Σ (M O • pc -2 )10 -2 -1 σ / R ( k m s - p c - ) LocalPerseusOuter+OSC α vir = 1 α vir = 2 10 K cm -3 K cm -3 K cm -3 K cm -3 (e) Figure 14. (a) M − R relation of the CO clouds, (b) line-width − size relation, (c) distribution of the virial parameters, (d) therelationship between the virial parameters and the masses, and (e) the relationship between σ v /R and surface density of the CO clouds. The orange shaded area in panel (a) is the region defined by the M-R relations, found by Bressert et al. (2012),for the molecular clouds capable of forming massive proto clusters. The grey shaded area in panel (a) is the region where theclouds cannot form high-mass stars according to the relation M ( R ) (cid:54) M (cid:12) ( r/pc ) . of Kauffmann et al. (2010b). The greydashed lines in this panel indicate the empirical upper and lower bounds of the cloud surface density of 1 g cm − and 0.05 gcm − for massive star formation (Urquhart et al. 2013). The grey shaded area in panel (c) indicates α vir <
2. The fraction ofthe clouds with α vir less than 2 are shown in the top − right corner in panel (c). The fitted M − R, σ v − R, and M − α relations ofthe clouds in the Local and the Perseus arms are shown in blue and in red in panels (a), (b), and (d), respectively. ship between σ v and R is better confined with a steeperpower-law with an exponent of 0.5. This exponent hasbeen further confirmed by Heyer et al. (2009) using theGRS data with improved spatial and spectral resolu-tion. The interpretation of this relationship is attributedto the simple virial equilibrium state of the molecularcloud.The σ v − R relationship of the CO and CO cloudsare presented in Figures 14(b) and 15(b), respectively.The power-law exponents of the CO and CO cloudsin the Local arm are 0.27 and 0.29, respectively. Theexponents of the clouds in the Perseus arm are larger,0.44 and 0.43 for CO and CO clouds, respectively.The Pearson correlation coefficients of the fitted σ v − R relations for the two arms lie in the range from 0.42 to0.55. The Larson’s relation with the exponent of 0.38is also drawn in Figures 14(b) and 15(b) with grey dot-ted lines for comparison. The difference between thescaling exponents of the molecular clouds in the Localand Perseus arms possibly indicates different importanceof turbulence in molecular clouds at different Galacto- centric distances. Traficante et al. (2018) and Benedet-tini et al. (2020) suggested the presence of two differentregimes in the σ v − R relationship, with a quite flat powerlaw for the smaller clouds with radius below ∼ ∼ Equilibrium State of the Molecular Clouds
Figures 14(c) and 15(c) display the distribution of thevirial parameters of the CO and CO clouds, respec-tively, and also show the portion of the gravitationallybound ( α vir ≤
2) molecular clouds in each arm. A sub-critical ( α vir >
2) cloud will dissipate unless an externalpressure from the environment can help to confine thecloud, while a supercritical ( α vir (cid:28)
2) cloud will col-lapse within a few free fall time scales unless some otherphysical processes like the magnetic field are includedin supporting the cloud against gravity. The virial pa- olecular clouds in the second quadrant -1 -1 R (pc)10 M L T E ( M O • ) Without High-mass Star Formation
LocalPerseus
Massive Proto-cluster Candidates M ∝ R ± M ∝ R ± (a) −1 −1 R (pc)0.11.010.0 σ v ( k m s − ) LocalPerseus σ v ∝ R ± σ v ∝ R ± (b) −3 −2 −1 0 1 2 3010203040−3 −2 −1 0 1 2 3lg α vir N u m be r −3 −2 −1 0 1 2 3lg α vir N u m be r gravitationallybound Local 19.1%Perseus 58.2% (c) -2 -1 M LTE (M O • )10 -2 -1 α v i r LocalPerseus α∝ M -0.41 ± α∝ M -0.37 ± (d) -2 -1 Σ (M O • pc -2 )10 -2 -1 σ / R ( k m s - p c - ) LocalPerseus α vir = 1 α vir = 2 10 K cm -3 K cm -3 K cm -3 K cm -3 (e) Figure 15.
Same as Figure 14, but for CO clouds. rameters of the CO clouds in the Local arm span abroad range from ∼ ∼ COclouds in the Perseus arm lie in the range from ∼ ∼
60. However, the virial parameters of the COclouds are much smaller, from ∼ ∼
99 with an av-erage of ∼ ∼ ∼
25 with an average of ∼ CO cloudsin the Outer+OSC arm distributed within the range of α vir from ∼ ∼
10. The majority, ∼ CO clouds in the Local arm are gravitationally un-bound, whereas in the Local and Perseus arms, 19.1%and 58.2% of the CO clouds are gravitationally bound,respectively. The systematic difference of the virial pa-rameter between the clouds in the Local and the Perseusarms may indicate different dynamical states of molecu-lar clouds in the two arms. However, the percentage ofthe gravitationally bound clouds is distance-dependent,since the detection of small and less massive molecu-lar clouds is not complete in the Perseus arm. Besides,based on the scaling relation we have obtained in Figures14 and 15, the virial parameters of the molecular cloudsin the Perseus arm are proportional to R − . ∼− . eff . Ifthe distances of the molecular clouds in the Perseus armare overestimated by a factor of two, the virial param-eters would be underestimated by a factor of ∼
19% to ∼ α vir , the percentage of the gravitationally boundclouds in the Perseus arm is still higher than that inthe Local arm. The overall difference of the masses ofthe molecular clouds in the two spiral arms is anotherpotential cause for the difference in virial parameters.As discussed in the next paragraph, there is an anti-correlation between the masses of the clouds and theirvirial parameter. The molecular clouds in the Perseusarm usually have larger masses, therefore, tending tohave smaller virial parameters.Bertoldi & McKee (1992) have presented a theoret-ical argument that when self-gravity is unimportant,the virial parameter is expected to be correlated with M − / for the pressure-confined clumps. Kauffmannet al. (2013) have reevaluated virial parameters for densecores and clouds using data compiled from the literature.The power-law behavior α vir ∝ M h α is confirmed for allthe different samples of dense cores and clouds, and theexponents are tabulated in their table 2. We also findthe α vir ∝ M h α behaviour both for the CO and COclouds in our survey (Figures 14(d) and 15(d)). Thepower-law exponents of the α vir − M relation of COclouds in the Local and the Perseus arms are − .
41 and − .
53, respectively, within the mass range from ∼ (cid:12) to ∼ M (cid:12) . The exponents in α vir − M relationfor CO clouds in the Local and the Perseus arms are6
Ma et al. − .
41 and − .
37, respectively. The results obtained inthis work resemble those derived by Kauffmann et al.(2013) for the GRS survey (Heyer et al. 2009; Roman-Duval et al. 2010).Subcritical molecular clouds need other confiningsources to keep the equilibrium state. The virial the-orem for a uniform, isothermal, non-magnetized, spheri-cal cloud immersed in the interstellar environment withpressure P e can be written as (Spitzer 1978; Field et al.2011), σ R = 13 ( 3 πG Σ5 + 4 P e Σ ) (9)The solution for the pressure-confined virial equilibriumstate (PVE) is the V-shaped lines in Figures 14(e) and15(e) for different external pressures. The relation be-tween σ /R and Σ under the simple virial equilibriumcondition (SVE) (when the internal pressure balanceswith the self-gravity) with α vir = 1 and α vir = 2 arealso shown in Figures 14(e) and 15(e). In Figure 14(e),the subcritical CO molecular clouds in the Local andthe Perseus arms show poor correlation of σ /R with Σand they are clustered in the regime of external pres-sures from P e /k ∼ K cm − to P e /k ∼ K cm − ,with a trend that the CO clouds in the Local arm havehigher P e than the clouds in the Perseus arm. Some ofthe Perseus arm clouds are located below the α vir ∼ CO molecular clouds in the Localarm also show concentration in the σ /R versus Σ di-agram (Figure 15(e)). The external pressure needed toconfine the CO molecular clouds in the Local arm iscomparable to that of the CO clouds. DISCUSSION4.1.
Probability Distribution Functions of H ColumnDensity of Large molecular clouds
In this section, we investigate the N-PDFs of molecu-lar clouds in the surveyed region. Since the abundance of CO is much higher than CO in molecular clouds andthe CO emission is more extended than that of CO ,a CO cloud usually corresponds to several CO cloudsthat can be considered as the denser parts of the sameand more extend structure traced by the CO emission.Therefore, the boundary extracted from the CO emis-sion is more representative of the edge of a molecularcloud in the N-PDF analysis. To have sufficient pix-els to derive a robust N-PDF for a cloud, we selectedmolecular clouds of relatively large projected area. Ac-cording to the exact projected-area in the CO catalog,forty clouds with area greater than 0.35 arcdeg , i.e.,5000 pixels, are selected, among which 29 clouds be-long to the Local arm and 11 clouds to the Perseus arm. Since the CO emission has a lower optical depth thanthe CO emission, we used the CO emission within a CO cloud boundary to estimate the H column den-sity. The H column density is calculated as described inSection 3.4.1 at pixels where the peak brightness of the CO spectrum is at least above 4 σ RMS . An N-PDF issimply the histogram of the logarithm of the normalizedcolumn density, s = ln( N H / < N H > ). If the columndensity is log-normally distributed, the PDF of s followsthe formula p ( s ) = 1 √ πσ exp[ − ( s − µ ) σ ] , (10)where µ and σ are the mean and dispersion of the normaldistribution of s. If the column density is power-law-distributed, which means p ( s ) ∝ N αH , the PDF of s follows ln p ( s ) = αs + c, (11)where α is the power-law index and c is a constant re-lated to the probability of the starting location of thefitting. In the log-log space, the N-PDFs that have log-normal shapes show as parabolas, while those that havepower-law shapes show as straight lines.The derived N-PDFs for the selected clouds in the Lo-cal and the Perseus arms are presented in Figures 16 and17, respectively, in the order of the angular sizes of the CO boundaries. Because the names of the molecularclouds under the MWISP standard, like those in Table2, are too long to conveniently legend in Figures 16 and17, we use in this section the shortened names, whichstart with a letter “G” and followed by the spatial coor-dinates accurate to two decimal places. Except for Sec-tion 4.1, the identified molecular clouds are all namedaccording to the MWISP standard. The N-PDF of eachcloud is fitted with a log-normal function or a power-law,depending on the shape. For the N-PDFs that both alog-normal function and a power-law function can be fit,we use the reduced chi-squared of the fittings as the cri-terion to choose the better form of the fitting, with thefitting form of smaller reduced chi-squared being cho-sen. We fixed the upper limit of the fitting in the higherbin with at least ten counts. The lower limit for thepower-law fitting is fixed at the peak of the distribu-tion. For the log-normal fitting, ideally, the detectioncompleteness limit should be used as the lower limit inthe fitting. However, an accurate value of the detec-tion completeness limit for H column density is hard todetermine. In this work, we calculated the median un-certainty of H column density within the CO cloudand take three times the median uncertainty, which werefer to as reference detection completeness limit, as thelower limit in the log-normal fitting. By manual exami- olecular clouds in the second quadrant CO cloud (see, e.g., Figure18). Therefore, we believe that the reference complete-ness limit is a reasonable value for the lower limit in thelog-normal fitting. The mean column densities, statisti-cal, and fitted parameters of the N-PDFs of the selectedmolecular clouds are tabulated in Tables 4 and 5.Thirty-one (77.5%) of the forty selected clouds havelog-normal N-PDFs above the reference completenesslimit of column density without significant excesses atthe high density end, while seven of the selected cloudshave power-law N-PDFs and the N-PDFs of two cloudscan not be fitted with either log-normal or power-lawfunctions. Some molecular clouds have log-normal N-PDFs with minor excesses at the high column densityends. Most of the molecular clouds in our results havelog-normal N-PDFs, which is different from the resultsobtained by Alves et al. (2017). We note that the ref-erence detection completeness limit, which we used inthe fitting of log-normal N-PDF, is very close to thelast closed N(H ) isocontour of the cloud in Alves et al.(2017). Although the detailed shape of the N-PDF atthe low column density end may be affected by the se-lected different closed isocontours, the existence of theturn-over in the N-PDF, which is the important signa-ture of log-normal N-PDF, can not be altered by thesmall difference between the reference detection com-pleteness limit in this work and the last closed isocon-tour in Alves et al. (2017). The molecular clouds canbe divided into three categories according to the shapesof their N-PDFs, i.e., pure log-normal (LN), log-normalwith minor excess (LN*), and power-law (PL).Kainulainen et al. (2009) derived the N-PDFs for 23molecular clouds in the solar neighborhood, d ∼ column density. Their results suggest that molec-ular clouds that are active in star formation have log-normal forms of N-PDFs at low column density ends,but show significant excesses above log-normal distribu-tions or power-law distributions at high column densityends. Similar distributions have also been obtained inHerschel observations, such as the results of Schneideret al. (2013), Schneider et al. (2015), and Pokhrel et al.(2016). The σ parameters obtained by Kainulainen et al.(2009) from the fitting of the log-normal components ofthe N-PDFs lie between ∼ − s , σ fit (in order to distinguish from σ data inthe following text), in this work, however, lie between ∼ . ∼ . ∼ − −
1. Therefore, the high-density part of theN-PDF will significantly exceed the log-normal distri-bution and the resulting σ is then narrow. The fittingranges are much broader in this work, which may re-sult in broader log-normal N-PDFs. Nevertheless, thedispersion of s ( σ data ) calculated directly from the datafor the N-PDFs of active star-forming regions in Kain-ulainen et al. (2009) are all greater than 1. The σ data parameters in this work are similar to those of Kainu-lainen et al. (2009).4.2. Relation Between the Shapes of the N-PDFs andthe Star Forming Activities in the molecularclouds
We compare the spatial distribution of the H columndensities of the selected clouds with the infrared, WISE3/4 (12/22 µm ) band images, to examine the relationbetween the N-PDF forms and the star formation activ-ities in these molecular clouds. The WISE 3 and 4 bandsare good indicator of star formation since they containthe polycyclic aromatic hydrocarbon (PAH) emissionand the emission from the warm dust heated by starformation activities.8 Ma et al. −4 −2 0 2 4s = ln(N/
N-PDFs of the twenty-nine selected molecular clouds in the Local arm. The column densities of the clouds arenormalized by their mean, and the upper axes give the corresponding values of N H . The vertical black dash-dotted lines ineach panel indicate the reference detection completeness limit of the column density of each cloud. The horizontal dashed linesmark the p ( s ) at which the count in a bin is ten. The blue dashed curves are the Gaussian fittings of the N-PDFs, while themagenta curves are the power-law fittings. The corresponding fitting ranges are marked with purple (Gaussian fittings) or blue(power-law fittings) dotted lines in the panels of the fitted N-PDFs. The fitted parameters µ and σ of the Gaussian functionare indicated in blue, and the fitted exponents of the power-law function p ( s ) ∝ N αH are indicated in magenta. The red barsmark the statistical errors in each bin of s. olecular clouds in the second quadrant −4 −2 0 2 4s = ln(N/
Same as Figure 16, but for the eleven selected clouds in the Perseus arm. Ma et al.
Table 4.
Properties of the N-PDFs of the Clouds in the Local Arm
Name d M
LTE < NH > µdata σdata µfit σfit α Shapekpc (M (cid:12) ) (cm −
2) (LN/LN ∗ /PL)(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)G117.70+4.33 0.67 8.48 ×
103 1.15 × − − ×
104 2.86 × − − ∗ G106.53+4.08 0.87 1.31 ×
104 2.41 × − − ∗ G115.58 − ×
102 9.46 × − − − ×
101 5.43 × − − ×
103 1.34 × − − ×
103 1.39 × − − ×
104 2.18 × − − ∗ G106.12+0.58 0.41 6.36 ×
102 9.80 × − ×
101 6.48 × − − ×
103 1.91 × − − ×
103 9.66 × − − ×
101 7.35 × − − ×
103 1.25 × − − ×
102 7.20 × − − ×
101 5.40 × − − ×
101 8.62 × − − ×
102 8.30 × − − ×
102 8.54 × − − − ×
100 4.21 × − − ×
101 9.42 × − − − ×
100 3.64 × − ×
102 1.89 × − − ∗ G108.75+2.69 0.75 3.72 ×
103 4.18 × − − ∗ G111.11 − ×
100 3.68 × − − ×
102 8.07 × − − ×
103 1.11 × − − − ×
101 7.61 × − − ×
101 5.57 × − − Note —Columns 1 − H s = ln NH / < NH > of the clouds are presented in columns 5-6, while columns 7-8 give the corresponding fitted parameters.Column 9 presents the exponents, α , of the fitted power-law distributions. Column ten is the description of the shape of the fitted N-PDFs, where LN means log-normal,LN ∗ means log-normal distribution with slight excesses at the high-density end, and PL means power-law. Table 5.
Properties of the N-PDFs of the Clouds in the Perseus Arm
Name d M
LTE < NH > µdata σdata µfit σfit α Shapekpc (M (cid:12) ) (cm −
2) (LN/LN ∗ /PL)(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)G111.53 − ×
105 2.38 × − − − ×
105 4.02 × − − ×
105 7.96 × − − ∗ G113.29 − ×
104 1.55 × − − ×
104 1.85 × − − ∗ G116.80 − ×
103 9.79 × − − ∗ G115.67 − ×
104 2.90 × − − − ×
105 5.32 × − − ∗ G111.47+2.42 4.19 1.52 ×
104 1.51 × − − ×
103 6.72 × − − ×
104 1.36 × − − Note —Same as Table 4 but for the clouds in the Perseus arm. olecular clouds in the second quadrant G110.69+1.82 N H2
114 113 112 111 110 109Galactic Longitude ( o )0.51.01.52.02.53.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (a)
G118.05+3.15 N H2
119 118 117Galactic Longitude ( o )2.83.03.23.43.6 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (b)
G108.75+2.69 N H2 o )2.42.62.83.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (c)
G106.06+1.49 N H2 o )1.21.41.61.8 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (d)
Figure 18.
Column density distribution (left) and the WISE 3/4 band images (right) for the selected molecular clouds in theLocal arm. Panels (a) − (c) are three examples of the clouds that have log-normal N-PDFs with slight excesses at the high-densityend. The black contours in the left panels and the white contours in the right panels show the reference detection completenesslimit of the H column density of the clouds. The green contours in the left panels and the red contours in the right panels in(a)-(c) correspond to the column densities where the N-PDFs start to show excesses above log-normal distributions. Panel (d)is an example of the molecular clouds with power-law N-PDFs. The magenta contours in panel (d) show the column densitypeak occurrence. The orange circles in these figures mark the positions of the H II regions or H II region candidates in theWISE catalog. Ma et al.
G111.47+0.79 N H2 o )0.00.51.01.5 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (a)
G105.39+0.28 N H2 o )0.00.20.40.6 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (b)
G108.61−1.01 N H2 o )−1.4−1.2−1.0−0.8 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (c)
G113.29−0.73 N H2 o )−1.0−0.8−0.6−0.4 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (d)
Figure 19.
Same as Figure 18 but for the clouds in the Perseus arm. The first three panels are three examples of LN ∗ clouds,and the last panel is an example of PL clouds. olecular clouds in the second quadrant column density maps andthe WISE 3/4 images of three LN ∗ molecular clouds andone PL clouds in the Local arm and Figure 19 presentsthe example clouds in the Perseus arm. The H col-umn density maps and WISE 3/4 images of other se-lected molecular clouds are given in Figures 23-31 inthe Appendix. The green contours in the left paneland the red contours in the right panel of Figure 18(a)correspond to N ∼ × cm − , at which the cloudG110.69+1.82 (Cep GMC) has slight excesses above itslog-normal N-PDF. The contours coincide with three in-tensity peaks (Cep A, Cep B, and Cep F) in the columndensity map, of sizes of (cid:54) ∗ cloud G118.05+3.15 show excess above log-normal dis-tribution at two column densities, N H ∼ × cm − (within < H ∼ × cm − (within < II region.The N-PDF of LN ∗ molecular cloud G108.75+2.69 ex-hibits slight excesses above the log-normal distributionat the column density N H ∼ × cm − , shown asthe green and red contours in Figure 18(c). These con-tours coincide with a WISE H II region ( ∼ ∼ − ∗ molecular clouds inthe Perseus arm are mainly concentrated in regions ofsizes of ∼ −
10 pc that are associated with H II regions(Figure 19).The images for the cloud G106.06+1.49 which has thePL form of N-PDF are shown in Figure 18(d). We cansee that this cloud does not have signature of star for-mation activity. The other five molecular clouds withPL N-PDFs in our survey also do not exhibit star for-mation activity (see Figures 26(c), 26(d), 28(c), 29(a),and 31(a) in the Appendix). The power-law parts of theN-PDFs of the PL molecular clouds are concentrated inclumps or filaments of size or width of ∼ . − ∼ II regionS 163. The PL cloud G111.47+2.42 consists of a fewfilamentary structures with lengths of ∼ ∼ SUMMARYWe have conducted a comprehensive study of theproperties of molecular clouds in a 15 ◦ × ◦ region in the second quadrant of the Milky Way mid-plane us-ing the CO , CO , and C O data from the MWISPsurvey. The distribution and basic statistics of the phys-ical properties of the molecular gas are presented. Us-ing the DENDROGRAM based SCIMES algorithm, weused the CO and CO line emission to identify molec-ular clouds and studied the statistical properties of theseclouds. The scaling relations between the physical pa-rameters are investigated, and comparisons of the scal-ing relations between different spiral arms are discussed.Forty clouds are selected as a sub-sample to study theproperties of the N-PDFs using the CO emission lineas the tracer of H column density. The main resultsare presented as follows.1. Under the influence of the distance selection effect,we have identified molecular clouds in the Localarm above the size limit of ∼ ∼ (cid:12) , and large and massive molecular cloudsin the Perseus arm above the size limit of ∼ ∼
349 M (cid:12) . With this bias,the median mass of the identified CO and COmolecular clouds in the Perseus arm is ∼
50 and ∼
30 times that of the Local arm, respectively, andthe molecular clouds in the Perseus arm are ∼ CO emission, while ∼ CO emission. The surface densityof molecular clouds is significantly enhanced in thePerseus arm, up to ∼
100 M (cid:12) pc − .2. The exponent of the σ v − R relation is ∼ ∼ e /k ∼ − cm − is needed forthe molecular clouds in the Local arm to stay inequilibrium.4. The N-PDFs derived with the CO emission aredominated by log-normal distributions with few oronly minor excesses above the log-normal distribu-tion. The excesses at high-density correspond tostar-forming regions of scales ∼ − ∼ −
10 pc for the Perseusarm. The majority of the clouds that have power-law N-PDFs correspond to molecular clumps ofsizes of ∼ ∼ Ma et al.
ACKNOWLEDGMENTSWe thank the PMO-13.7 m telescope staffs for theirsupports during the observation and the staffs of theMWISP scientific group for their valuable suggestions.We thank the anonymous referee for his/her construc-tive suggestions that help to improve this manuscript.Y. M. thanks Fujun Du for his helpful discussion. Thiswork is supported by the National Key R&D Program ofChina (NO. 2017YFA0402701) and Key Research Pro-gram of Frontier Sciences of CAS under grant QYZDJ-SSW-SLH047. We acknowledge the support by NSFCgrant 11973091. Y.M. acknowledges financial supportsby the Natural Science Foundation of Jiangsu Provinceof China (Grant No. BK20181513) and by the Natu-ral Science Foundation of China (Grant No. 11973090).Y.S. acknowledges supports by NSFC grant 11773077.This work makes use of the SIMBAD database, operatedat CDS, Strasbourg, France. This research made use ofSCIMES, a Python package to find relevant structuresinto dendrograms of molecular gas emission using thespectral clustering approach.APPENDIXFigures 20-22 give the demonstration of the cloud identification using the DENDROGRAM+SCIMES algorithmsfor different tracers and different spiral arms. Figures 23-31 present the column density maps and the WISE 3/4 bandimages of the selected molecular clouds. olecular clouds in the second quadrant
118 116 114 112 110 108 106Galactic Longitude ( o )−4−2024 G a l a c t i c La t i t ude ( o ) ( K k m s − ) / (a)
118 116 114 112 110 108 106Galactic Longitude ( o )−90−80−70−60−50−40−30−20 V e l o c i t y ( k m s − ) ( K a r c deg ) / (b) Figure 20.
Demonstration of the outlines of the identified CO molecular clouds in the Perseus arm in the (a) l-b space andthe (b) l-v space. Different colors correspond to different molecular clouds. Ma et al.
118 116 114 112 110 108 106Galactic Longitude ( o )−4−2024 G a l a c t i c La t i t ude ( o ) ( K k m s − ) / (a)
118 116 114 112 110 108 106Galactic Longitude ( o )−110−100−90−80−70−60 V e l o c i t y ( k m s − ) ( K a r c deg ) / (b) Figure 21.
Same as Figure 20, but for the CO clouds in the Outer+OSC arm. olecular clouds in the second quadrant
118 116 114 112 110 108 106Galactic Longitude ( o )−4−2024 G a l a c t i c La t i t ude ( o ) ( K k m s − ) / (a)
118 116 114 112 110 108 106Galactic Longitude ( o )−80−70−60−50−40−30−20 V e l o c i t y ( k m s − ) ( K a r c deg ) / (b) Figure 22.
Same as Figure 20, but for CO clouds in the Perseus arm. Ma et al.
G117.70+4.33 N H2
119 118 117 116 115Galactic Longitude ( o )3.03.54.04.55.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (a)
G106.53+4.08 N H2
108 107 106 105Galactic Longitude ( o )2.53.03.54.04.55.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (b)
G115.58−2.72 N H2
117 116 115 114Galactic Longitude ( o )−5−4−3−2 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (c)
G112.22−2.38 N H2
114 113 112 111Galactic Longitude ( o )−3.0−2.5−2.0−1.5−1.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (d)
Figure 23.
Same as Figure 18, but for clouds G117.70+4.33 etc. olecular clouds in the second quadrant G115.50+1.84 N H2
116 115 114Galactic Longitude ( o )1.01.52.02.5 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (a)
G115.33+4.08 N H2
116 115 114Galactic Longitude ( o )3.54.04.55.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (b)
G106.12+0.58 N H2 o )−0.50.00.51.01.5 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (c)
G109.71+1.82 N H2 o )0.51.01.52.02.53.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (d)
Figure 24.
Same as Figure 18, but for clouds G115.50+1.84 etc. Ma et al.
G112.72+2.71 N H2 o )2.02.22.42.62.83.03.23.4 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (a)
G114.71+1.09 N H2 o )0.40.60.81.01.21.41.6 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (b)
G107.64+1.35 N H2 o )1.01.21.41.61.8 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (c)
G119.18+1.55 N H2 o )1.01.52.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (d)
Figure 25.
Same as Figure 18, but for clouds G112.72+2.71 etc. olecular clouds in the second quadrant G115.70+3.71 N H2 o )2.53.03.54.04.55.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (a)
G110.26+3.55 N H2 o )3.03.23.43.63.84.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (b)
G117.41+2.50 N H2 o )2.02.22.42.62.83.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (c)
G107.87+1.90 N H2 o )1.41.61.82.02.2 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (d)
Figure 26.
Same as Figure 18, but for clouds G115.70+3.71 etc. Ma et al.
G113.59+4.62 N H2 o )4.24.44.64.85.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (a)
G115.90−0.56 N H2 o )−1.0−0.8−0.6−0.4−0.2 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (b)
G110.78+3.86 N H2 o )3.63.84.04.24.4 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (c)
G113.31−1.22 N H2 o )−1.8−1.6−1.4−1.2−1.0−0.8 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (d)
Figure 27.
Same as Figure 18, but for clouds G113.59+4.62 etc. olecular clouds in the second quadrant G106.66+1.01 N H2 o )0.70.80.91.01.11.21.3 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (a)
G111.11−3.73 N H2 o )−4.2−4.0−3.8−3.6−3.4−3.2 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (b)
G114.78+0.82 N H2 o )0.40.60.81.01.21.4 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (c)
Figure 28.
Same as Figure 18, but for clouds G106.66+1.01 etc. Ma et al.
G117.54−0.57 N H2 o )−0.8−0.6−0.4−0.2 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (a)
G119.18+4.38 N H2 o )4.04.24.44.64.8 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (b)
Figure 29.
Same as Figure 18, but for clouds G117.54-0.57 etc. olecular clouds in the second quadrant G111.53−2.56 N H2 o )−3.5−3.0−2.5−2.0−1.5 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (a)
G109.97−0.21 N H2 o )−1.0−0.50.00.51.0 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (b)
G116.80−3.12 N H2 o )−3.6−3.4−3.2−3.0−2.8 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (c)
G115.67−1.61 N H2 o )−1.9−1.8−1.7−1.6−1.5−1.4−1.3 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (d)
Figure 30.
Same as Figure 18, but for clouds G111.53-2.56 etc. Ma et al.
G111.47+2.42 N H2 o )1.82.02.22.42.62.8 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (a)
G111.66+4.11 N H2 o )3.84.04.24.44.6 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (b)
G109.69+1.89 N H2 o )1.41.61.82.02.2 G a l a c t i c La t i t ude ( o ) W3 (green) & W4 (blue) (c)
Figure 31.
Same as Figure 18, but for clouds G108.61-1.01 etc. olecular clouds in the second quadrant