# The scaling relations and star formation laws of mini-starburst complexes

Quang Nguy$\tilde{\hat{\rm e}}$n-Lu’o’ng11affiliation: NAOJ Chile Observatory,
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan 22affiliation: Korea Astronomy and Space Science Institute,
776 Daedeok daero, Yuseoung, Daejeon 34055, Republic of Korea 33affiliation:
CITA, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada
††affiliation: EACOA Fellow at NAOJ, Japan & KASI, Korea, quang.nguyen-
luong<EMAIL_ADDRESS>, Hans V. V. Nguy$\tilde{\hat{\rm
e}}$n44affiliation: Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69,
D-53121 Bonn, Germany , Fredérique Motte55affiliation: Institut de
Planétologie et d’Astrophysique de Grenoble, LAOG (UMR 5571), Université de
Grenoble, BP 53, F-38041 Grenoble Cedex 09, France , Nicola
Schneider66affiliation: I. Physik. Institut, University of Cologne, 50937
Cologne, Germany , Michiko Fujii77affiliation: Theoretical Astronomy Division,
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan 88affiliation: Department of Astronomy, The University of
Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-0033, Japan , Fabien
Louvet99affiliation: Departamento de Astronomía, Universidad de Chile,
Santiago, Chile , Tracey Hill1010affiliation: Joint ALMA Observatory, 3107
Alonso de Cordova, Vitacura, Santiago, Chile , Patricio Sanhueza11affiliation:
NAOJ Chile Observatory, National Astronomical Observatory of Japan, 2-21-1
Osawa, Mitaka, Tokyo 181-8588, Japan , James O. Chibueze1111affiliation:
Department of Physics and Astronomy, Faculty of Physical Sciences, University
of Nigeria, Carver Building, 1 University Road, Nsukka, Nigeria , and Pierre
Didelon1212affiliation: Laboratoire AIM Paris-Saclay, CEA/IRFU - CNRS/INSU -
Université Paris Diderot, Service d’Astrophysique, Bât. 709, CEA-Saclay,
F-91191, Gif-sur-Yvette Cedex, France

###### Abstract

The scaling relations and the star formation laws for molecular cloud
complexes in the Milky Way is investigated using data from the 12CO 1–0 CfA
survey and from the literatures. We compare their masses $M_{\rm gas}$, mass
surface densities $\Sigma_{M_{\rm gas}}$, radii $R$, velocity dispersions
$\sigma$, star formation rates $SFR$, and SFR densities $\Sigma_{\rm SFR}$
with those of structures ranging from cores, clumps, Giant Molecular Clouds
(GMCs), to Molecular Cloud Complexes (MCCs), and to Galaxies, spanning 8
orders of magnitudes in size and 13 orders of magnitudes in mass. MCC are
mostly large ($R>50$ pc), massive ($\sim 10^{6}$ $\rm M_{\sun}$)
gravitationally unbound cloud structures. This results in the following
universal relations:

$\sigma\sim R^{0.5}$, $M_{\rm gas}\sim R^{2}$, $\Sigma_{\rm
SFR}\sim\Sigma_{M_{\rm gas}}^{1.5}$, ${SFR}\sim{M_{\rm gas}}^{0.9}$, and
${SFR}\sim{\sigma}^{2.7}$.

Variations in the slopes and the coefficients of these relations are found at
individual scales signifying different physics acting at different scales.
Additionally, there are breaks at the MCC scale in the $\sigma-R$ relation and
between the starburst and the normal star-forming objects in the $SFR-M_{\rm
gas}$ and $\Sigma_{\rm SFR}$-$\Sigma_{\rm M_{\rm gas}}$ relations. Therefore,
we propose to use the Schmidt-Kennicutt diagram to distinguish the starburst
from the normal star-forming structures by applying a $\Sigma_{M_{\rm gas}}$
threshold of $\sim 100$ $\rm M_{\sun}$pc-2 and a $\Sigma_{\rm SFR}$ threshold
of 1 $\rm M_{\sun}$yr-1 kpc-2. Mini-starburst complexes are gravitationally
unbound MCCs that have enhanced $\Sigma_{\rm SFR}$ ($>$1 $\rm M_{\sun}$yr-1
kpc-2), probably caused by dynamic events such as radiation pressure,
colliding flows, or spiral arm gravitational instability. Because of the
dynamical evolution, gravitational boundedness does not play a significant
role in characterizing the star formation activity of MCCs, especially the
mini-starburst complexes, which leads to the conclusion that the formation of
massive stars and clusters is dynamic. We emphasize the importance of
understanding mini-starburst in investigating the physics of starburst
galaxies.

###### Subject headings:

stars: formation, ISM: clouds, ISM: structure, (ISM:) evolution, methods:
observational, Galaxy: evolution
(Submitted on May 02, 2016; Accepted to publish on ApJ on Oct 09, 2016)

##  1\. Introduction

Molecular gas is an indispensable element of the galactic ecological system
and exists as coherent cloudy structures having different sizes: core ($<$0.1
pc), clump (0.1–1 pc), molecular cloud (GMC, 1–10 pc), and molecular cloud
complex (MCC, 10–100 pc) (Blitz & Williams, 1999). They are the stellar
nursery, therefore, large surveys of molecular clouds in the Milky Way are
necessary to understand their global star formation activities and connection
to the global properties of the Galaxy.

The birth of the millimeter-wave radio astronomy, and subsequently, of the
observations of Carbon Monoxide (CO) emission opened a new window into the
molecular gas (Wilson et al., 1970). Since then, molecular gas was discovered
progressively in star forming regions (Lada et al., 1974), in the Galaxy’s
diffuse interstellar medium (Cohen et al., 1980), and in other galaxies
(Elmegreen et al., 1980), thus revealed the ubiquity of molecular gas.

A milestone of the wide-field molecular gas observation is the CO 1–0 almost-
all-sky survey performed by the CfA 1.2 m telescopes (Dame et al., 1986,
2001). This survey formed a coherent and high spectral resolution basis for
subsequent follow-up surveys. Since then, surveys of different excitation
transitions or isotopologues were performed with larger telescopes to reach
higher angular resolutions, for example: CO 1–0 from the Three-mm Ultimate
Mopra Milky Way Survey (THRUMMS, Barnes et al. 2015), CO 3–2 from the CO 3–2
High-resolution Survey of the Galactic Plane (COHRS, Dempsey et al. 2013), or
the 13CO 1–0 from the Galactic Ring Survey (GRS, Jackson et al. 2006).
However, the CfA survey is still pertinent to create a large catalog of GMCs
and MCCs, and to study the mutual scaling relations between different physical
properties such as mass, size, velocity dispersion, and star formation rate
(SFR).

The existence of the universal relations between different physical properties
of star-forming structures is a suggestion that the basic physics governing
different objects are similar and only scale with their sizes. Confirmation or
refutation of this argument needs an investigation of these relations on
datasets that cover the entire physical scale range. Early on, Larson (1981)
pioneered in deriving the universal scaling relations between mass $M$, radius
$R$, and velocity dispersion $\sigma$ of molecular clouds; later, they are
named as the Larson’s relations. First, the linewidth-size relation
$\sigma\propto R^{\beta}$ with $\beta=0.38$ describes the structure of
molecular clouds as fragmentation due to Kolmogorow-like turbulent cascade.
Second, a linear correlation between the virial mass and total mass predicts
the virial equilibrium state of GMCs. Third, the inverse relationship between
the mean density and size implies a mass-size relation $M\propto R^{\alpha}$
with $\alpha=2$.

However, there are arguments against the universal scaling relations. Fore
instance, Lombardi et al. (2010) and Kauffmann et al. (2010) derived a
$M\propto R^{\alpha}$ relation with $\alpha\sim 1.2-1.6$ for substructures
inside individual GMC. Heyer et al. (2009) suggested that the coefficient of
the velocity dispersion-radius relation for Galaxy’s GMCs scales with the
surface density. Hughes et al. (2013) found no trivial scaling relations
between the three quantities: mass, size and velocity dispersion for GMCs and
MCCs in M51, M33, and the Large Magellanic Cloud. Utomo et al. (2015) and
Rebolledo et al. (2015) found similar results for GMCs with average radii of
20 pc in NGC 4526 and MCCs with averaged radii of $\sim 140-180$ pc in nearby
galaxies, respectively. Furthermore, Schneider & Brooks (2004) showed that the
coefficients of these relations strongly depend on the cloud structure
identification algorithm that was used.

Likewise, Schmidt (1959) and Kennicutt (1998) found a correlation between gas
surface density, $\sigma$, and Star Formation Rate density, $\Sigma_{\rm
SFR}$, in the form of ${\rm\Sigma_{SFR}}=A_{\rm KS}\times{\rm\sigma}^{N}$.
Galaxy types, spatial resolutions, SFR tracers, and gas tracers are among the
multiple factors that can change the power law index $N$ and the normalization
factor $A_{\rm KS}$ (Deharveng et al., 1994; Gao & Solomon, 2004; Bigiel et
al., 2008; Daddi et al., 2010).

The recent combinations of observations of Galactic clouds of $\sim$1–10 pc
and galaxy populations of $\sim$1–10 kpc revealed a large spread in the
$\Sigma_{SFR}-\sigma$ diagram (Heiderman et al., 2010; Evans et al., 2014;
Willis et al., 2015). For example, the $\Sigma_{SFR}-\sigma$ relation of low-
mass Galactic clouds derived by Heiderman et al. (2010) has a steeper slope
than the extragalactic one derived by Kennicutt (1998). Power law indexes
within the massive star forming complexes were found to scatter from 1.7 to
2.8 (Willis et al., 2015). Various modifications of the Schmidt-Kennicutt
relation were proposed: normalizing $\sigma$ by dynamical (Daddi et al., 2010)
or freefall timescales (Krumholz et al., 2012a), considering the SFR-dense gas
relation as $\Sigma_{\rm SFR}\propto\Sigma_{\rm dense~{}gas}$ (Lada et al.,
2012; Evans et al., 2014), or replacing the surface density by volume density
quantities to produce a linear relation between star formation rate volume-
density, $\rho_{SFR}$, and mass volume-density, $\rho_{\rm gas}$ (Evans et
al., 2014).

Studies trying to link these scaling relations across different spatial
scales, from local Galactic clouds to global galaxy, seem to miss the MCC
population, also called Giant Molecular Associations, having sizes and masses
of $>$ 50 pc and $\sim$ $10^{6}-10^{7}~{}\mbox{$\rm M_{\sun}$}$, respectively
(Nguyen Luong et al., 2011b). MCCs are important as they are the largest cloud
agglomeration in a galaxy and massive star formation is linked with a special
category of MCCs, the mini-starburst complexes (e.g., Motte et al., 2003;
Louvet et al., 2014). They are the birthplaces of massive OB stars and Young
Massive Clusters (YMCs), thus are important in maintaining the chemical,
energy, and mass balance of hosting galaxies (Bressert et al., 2012). This is
especially true for starburst galaxies such as the Antennae merger system,
which undergoes starburst events and contains many YMCs and mini-starburst
MCCs (Herrera et al., 2012; Whitmore et al., 2014).

Motivated by the needs of quantifying the scaling relations between different
physical quantities of MCCs in the Milky Way, we use the CfA CO survey to
catalog and characterize the physical properties of our MCCs and use radio
continuum data to measure their SFR. We discuss the data and the method of
identifying sources in Sections 2 and 3. In Section 4, we derive the physical
properties and SFR (density) of MCCs. Section 5 and Section 6 will examine the
scaling relations between different cloud properties and the star formation
laws for the all cloud structures ranging from GMCs to Galaxies. We elaborate
more the division of (mini)starburst and normal-star forming objects by using
the Schmidt-Kennicutt diagram and the possible sequence of forming mini-
starburst in Section 7.

##  2\. Data

###  2.1. 12CO Data from the CfA Survey

The 12CO 1–0 data from the CO all-sky survey is used to catalog and
characterize MCCs in the Galaxy. This survey was made with the CfA 1.2 m
telescopes located in both northern and southern hemispheres. The observations
are sub-Nyquist sampled with an effective angular resolution of 8′.8. The
spectral cube contains data obtained from various independent observations
starting in 1986 (Dame et al., 1986; Bronfman et al., 1989) and ending in 2001
(Dame et al., 2001), stored in the CO survey archive111
http://www.cfa.harvard.edu/rtdc/CO/. The combined data cube is provided in
main beam antenna temperature and has a sensitivity of $\sim$ 1.5 K per 0.65
km s-1 , although individual surveys have sensitivity $\sim$ 0.12–1 K per
0.65- km s-1channel. We use the “whole galaxy cube” covering the entire 360°
longitude range and -40° to 40° latitude range. The integrated map of the
Galactic Plane, where MCCs reside, is shown in Figure 1.

###  2.2. Radio continuum

To derive the SFRs of MCCs, we use the 21 cm radio continuum data from the VLA
Galactic Plane Survey (VGPS, Stil et al. 2006), the Canadian Galactic Plane
Survey (CGPS, Taylor et al. 2003), and the Southern Galactic Plane Survey
(SGPS, Haverkorn et al. 2006). VGPS has a FWHM beam of 1′ and covers the
Galactic longitude 18–67°, CGPS has a FWHM beam of 1′ and covers the Galactic
longitude 63–175°, and SGPS has a FWHM of 2.2′ covering the Galactic longitude
253–358°.

$\begin{array}[]{c}\hskip-28.45274pt\includegraphics[angle={0},width=512.1496pt]{NLQfg1.eps}\\\
\hskip-28.45274pt\includegraphics[angle={0},width=512.1496pt]{NLQfg2.eps}\\\
\hskip-28.45274pt\includegraphics[angle={0},width=512.1496pt]{NLQfg3.eps}\end{array}$

Figure 1.— The integrated 12CO 1–0 map of the CO CfA all sky survey, over
which mini-starburst MCCs are indicated by circles. Names of well-known MCCs
are labelled. Young Massive Clusters and OB Associations from Portegies Zwart
et al. (2010) are marked as squares, respectively.

###  2.3. Complementary data

We complement our data with literature data to increase the dynamical ranges
of all parameters. For the Larson relations (Section 5), we add cloud
properties data from the following sources:

  * •

clumps/GMCs: Maruta et al. (2010), Onishi et al. (2002), Shimajiri et al.
(2015), Heyer et al. (2009), Roman-Duval et al. (2010), Evans et al. (2014).

  * •

MCCs: García et al. (2014), Murray (2011), Donovan Meyer et al. (2013),
Rosolowsky (2007), Miura et al. (2012, 2014), Wei et al. (2012).

  * •

Galaxies: Leroy et al. (2013), Tacconi et al. (2013), Genzel et al. (2010).

For the Schmidt-Kennicutt scaling relation (Section 6), we add SFR data from
the following sources:

  * •

GMCs: Heiderman et al. (2010), Lada et al. (2010), Evans et al. (2014).

  * •

MCCs: García et al. (2014), Bolatto et al. (2008), Murray (2011), Donovan
Meyer et al. (2013), Rosolowsky (2007), Miura et al. (2012, 2014), Wei et al.
(2012).

  * •

Galaxies: Leroy et al. (2013), Tacconi et al. (2013), Genzel et al. (2010).

For the galaxies sample, we calculate the velocity dispersion assuming that
the entire galaxy is a dynamical system, thus we do not distinguish between
elliptical and disk galaxies or starburst and normal galaxies. We convert the
orbital time from Leroy et al. (2013) sample or the dynamical time from Genzel
et al. (2010) and Tacconi et al. (2013) samples to a rotation velocity as
$V_{\rm rot}=\frac{2\pi R}{t_{\rm dyn,orb}}$. Then, the velocity dispersion is
written as $\sigma=\frac{2\pi^{2}GR\sigma}{1.5V_{\rm rot}}$. The radi used
here are either the optical B-band 25th magnitude isophote (Leroy et al.,
2013) or the half-light radii (Genzel et al., 2010; Tacconi et al., 2013). The
local galaxies in Leroy et al. (2013) have velocity dispersions smaller than
their rotation velocity, but the high-z galaxies in Genzel et al. (2010);
Tacconi et al. (2013) have velocity dispersion larger than rotation velocity.
This is probably, because the high-z galaxies are highly turbulent than the
local galaxies.

Beside that, we also add data from individual mini-starburst regions in a
galaxy at $z=1.987$ (Zanella et al., 2015), in SDP81 galaxy at $z=3.042$
(Hatsukade et al., 2015), and in Arp 220 (Scoville, 2013).

Systematic errors caused by different measurements are unavoidable but we
assume that these errors have little affect on our analysis. For example,
errors caused by mass determinations from different tracers such as 12CO,
13CO, or dust emission; or errors caused by the variation of the abundances
for the CO/H2 conversion as a function of position in the galaxy; or errors
caused by the exclusion of the CO-dark gas, are not taken into account. So,
the mass estimates are the lower limits of the true values. We are aware of
these error sources, but due to our large statistical sample, and assuming an
uncertainty of typically 50%, we are still able to derive robust scaling
relations. Actually, these errors can be safely ignored because they typically
vary around about 30%-100% of the measured values and all relations that we
will discuss are presented in log-log space.

##  3\. Source identification and Distances

Initially, we use the
Duchamp222http://www.atnf.csiro.au/people/Matthew.Whiting/Duchamp algorithm to
decompose the 3D spectral cube. This program is designed to extract sources in
large H I surveys and is the main extraction tool of the Australian Square
Kilometre Array Pathfinder (Whiting & Humphreys, 2012). Although it is
optimized for H I source extraction, its utility towards molecular clouds and
maser extraction has been proven (Carlhoff et al., 2013; Walsh et al., 2016).
For our extraction, Duchamp detected successfully GMCs outside and inside the
Galactic Plane. However, in the Galactic Plane, Duchamp tends to either break
down the emission into too many individual clouds if we set a weak merging
condition or merge to too large structures. This is likely the same problem
occured for other detection alogrithms (Gaussclumps, Stutzki & Guesten 1989;
Clumpfind, Williams et al. 1994; Dendogram, Rosolowsky et al. 2008 ). Finally,
we decided for a conservative approach to select MCCs by eye inspection.

We identify strong CO peaks in the integrated intensity and position-velocity
maps of Dame et al. (2001) and then average CO spectra over $0.5\arcdeg\times
0.5\arcdeg$ areas surrounding the CO peaks that correspond to $\sim$13–52 pc
boxes at 1.5–6 kpc distances. The global velocity extent measured from these
first-guess integrated spectra are used to integrate CO lines and create
first-guess integrated maps of the MCC. For each MCC, we then iteratively
refine its associated area, $A$, and velocity extent until they are properly
distinguished both in velocity and space from a background of three times the
local rms. By setting the local rms as threshold, we can trace all material
down to the observational sensitivity level, but not having homogeneous column
density threshold across all MCCs. We fit Gaussian profiles to the average
spectrum of each MCC to derive its velocity dispersion, $\sigma_{\rm CO}$, and
its velocity-integrated intensity, $W_{\rm CO}$. To summarize, the main
criteria to include a cloud in MCC are that their velocity range is not more
than 15  km s-1 far from the bulk velocity of the cloud and it is connected to
the main and other clouds by diffuse gas features. This method was proven to
be more suited to identify MCCs than automatic detection, as in the cases of
the W43 (Nguyen Luong et al., 2011a) and the RCW 106 (Nguyen et al., 2015).

After identifying a sample of 44 MCCs (Table 1), we estimate their distances
to the Sun following this sequential scheme: (1) assigning a parallax distance
if it is available from the Bar and Spiral Structure Legacy (BeSSeL, Reid et
al. 2014)333http://bessel.vlbi-astrometry.org and the VLBI Exploration of
Radio Astrometry (VERA, Honma et al. 2007)444http://veraserver.mtk.nao.ac.jp
projects or other individual parallax measurements from the literature; (2)
assigning a photometric distance if it is available from the literature; (3)
assigning an averaged ambiguity-resolved kinematic distance if it is available
from the literature; (4) calculating our own kinematic distance as $d_{\rm
kin}=R_{\rm 0}{\rm cos}\left(l\right)\pm\sqrt{r^{2}-R_{\rm 0}^{2}{\rm
sin}^{2}\left(l\right)}$ where $R_{\rm 0}$ is the Galactocentric radius of the
Sun, $V_{\rm 0}$ is the orbital velocity of the Sun around the Galactic
center, $V\left(r\right)$ is the rotation curve and $V_{\rm r}$ is the radial
velocity of the cloud. The result is 11 out of 44 have parallax distances, 1
has photometric distance, 8 have kinematic distances with ambiguity resolved
by HI absorption, and 24 have near kinematic distances.

##  4\. Physical properties

Complex | l | b | $V_{\rm LSR}$ | $\sigma$ | $d$ | $A$ | $R$ | $L_{\rm CO}$ | $M_{\rm gas}$ | $\Sigma_{\rm gas}$ | $S_{\rm 21cm}^{\rm int}$ | SFR | $\Sigma_{\rm SFR}$ | $\alpha_{\rm vir}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
name |  |  |  |  |  | $\times 10^{-2}$ |  | $\times 10^{3}$ | $\times 10^{6}$ |  |  |  |  |
| (°) | (°) |  ( km s-1) |  ( km s-1) | (kpc) |  (kpc2) | (pc) |  (L⊙) |  (M⊙) |  (M⊙ pc-2) | (Jy) |  (M⊙ yr-1) | (M⊙ yr-1kpc-2) |
G111 | 111.0 | -1.0 | -49 | 7.9 |  3.34 | 5.7 | 134 | 7.2 | 2.2 | 38.7 | 1860 | 0.014 | 0.25 | 4.4
G80-CygnusX | 80.0 | 0.0 | 2 | 6.6 |  1.5 | 3.7 | 108 | 40.7 | 2.2 | 59.9 | 45759 | 0.062 | 1.68 | 2.5
G52…… | 52.1 | -0.4 | 55 | 6.9 |  6.9 | 2.0 | 79 | 1.8 | 1.9 | 95.6 | 2818 | 0.0725 | 3.6 | 2.3
G49-W51…. | 49.5 | -0.5 | 57 | 9.8 |  5.41 | 1.8 | 76 | 3.6 | 2.5 | 139.9 | 10237 | 0.184 | 10.2 2 | 3.4
G44.4…… | 44.4 | -0.2 | 61 | 7.2 |  9.3 | 1.8 | 75 | 2.7 | 1.5 | 82.7 | 5272 | 0.070 | 3.89 | 3.1
G42-W49…. | 42.0 | -0.5 | 63 | 9.5 |  11.1 | 2.8 | 93 | 1.5 | 4.9 | 179.2 | 6069 | 0.51 | 17.86 | 2.0
G40…….. | 40.0 | 0.0 | 32 | 6.1 | 2.2 | 3.4 | 104 | 13.0 | 1.8 | 52.1 | 7783 | 0.026 | 0.77 | 2.5
G39…….. | 39.0 | -0.4 | 65 | 27.3 |  12.1 | 13.1 | 204 | 33.1 | 15.7 | 120.2 | 6447 | 0.079 | 0.60 | 11.3
G35-W48…. | 35.0 | -1.0 | 46 | 14.0 |  3.27 | 3.3 | 101 | 15.3 | 4.5 | 138.0 | 8379 | 0.075 | 2.27 | 5.2
G30-W43…. | 30.5 | -0.5 | 93 | 16.3 |  5.5 | 2.8 | 94 | 11.1 | 9.3 | 329.5 | 15282 | 0.320 | 11.40 | 3.1
G25.9…… | 25.9 | -0.5 | 100 | 10.0 | 5.4 | 2.5 | 88 | 4.5 | 3.7 | 148.5 | 12688 | 0.255 | 10.24 | 2.8
G25.5+52 km s-1 | 25.5 | -0.2 | 52 | 11.1 | 3.4 | 1.1 | 58 | 5.2 | 1.7 | 154.0 | 15012 | 0.120 | 10.91 | 5.0
G25.5+102 km s-1 | 25.5 | -0.1 | 102 | 11.8 | 5.5 | 2.7 | 93 | 5.6 | 4.6 | 169.8 | 15164 | 0.317 | 11.75 | 3.2
G23.7+60 km s-1 | 23.7 | -0.5 | 60 | 9.9 |  6.21 | 2.0 | 80 | 4.4 | 4.7 | 230.9 | 15342 | 0.407 | 20.40 | 2.0
G24+100 km s-1 | 23.5 | -0.2 | 93 | 21.1 | 5.9 | 3.2 | 101 | 13.9 | 13.2 | 411.9 | 17171 | 0.413 | 12.91 | 4.0
G21…….. | 21.0 | -0.7 | 51 | 13.2 | 3.6 | 1.2 | 61 | 7.3 | 2.6 | 216.8 | 11690 | 0.1048 | 6.10 | 4.8
G20.9….. | 20.9 | 0.0 | 32 | 14.7 | 2.6 | 0.6 | 44 | 5.1 | 1.0 | 151.3 | 12909 | 0.060 | 10.0 0 | 11.8
G18.2…… | 18.2 | -0.3 | 47 | 10.3 | 3.6 | 1.2 | 61 | 7.3 | 2.6 | 217.7 | 5044 | 0.045 | 3.75 | 3.0
G16.8-M16/M17…. | 16.8 | 0.4 | 23 | 5.9 |  1.98 | 0.5 | 39 | 4.7 | 0.7 | 140.7 | 8560 | 0.031 | 6.20 | 2.3
G13.5-W33.. | 13.5 | -0.5 | 24 | 36.1 |  2.92 | 1.2 | 61 | 29.8 | 4.7 | 393.2 | 439 | 0.00175 | 0.149 | 19.8
G10-W31…. | 9.7 | -0.5 | 22 | 15.7 |  4.95 | 2.3 | 85 | 14.0 | 9.5 | 416.2 | - | - | 1.0 | 2.6
G8.2……. | 8.2 | 0.2 | 17 | 8.4 | 2.9 | 0.8 | 49 | 6.3 | 1.5 | 188.4 | - | - | 1.0 | 2.8
G7.5……. | 7.5 | -1.0 | 17 | 8.7 | 3.0 | 0.8 | 51 | 7.9 | 2.0 | 234.4 | - | - | 1.0 | 2.3
G3.5……. | 5.7 | -0.5 | 13 | 8.6 | 3.1 | 2.8 | 93 | 19.0 | 5.0 | 179.7 | - | - | 0.9 | 1.6
G0-CMZ….. | 0.5 | 0.0 | -6 | 23.1 |  7.9 | 51.6 | 405 | 74.8 | 128.5 | 249.1 | - | - | 0.9 | 2.0
G355……. | 355.0 | 0.0 | 95 | 20.0 | 6.1 | 0.8 | 50 | 2.7 | 2.8 | 344.2 | 824 | 0.0212 | 2.50 | 8.4
G344……. | 344.3 | -0.3 | -71 | 8.1 | 4.8 | 2.6 | 91 | 3.3 | 2.1 | 80.4 | 703 | 0.0112 | 0.423 | 3.3
G343……. | 343.0 | 0.0 | -28 | 8.0 | 2.7 | 2.6 | 91 | 17.5 | 3.4 | 129.7 | 426 | 0.00214 | 0.077 | 2.0
G342-127 km s-1 | 342.5 | 0.0 | -127 | 8.1 |  8.10 | 3.5 | 105 | 2.2 | 2.5 | 71.3 | 245 | 0.007 | 0.17 | 3.2
G342-79 km s-1 | 342.5 | 0.0 | -79 | 7.8 |  4.74 | 2.3 | 85 | 3.4 | 2.4 | 102.8 | 245 | 0.004 | 0.173 | 2.5
G340……. | 340.3 | -0.5 | -37 | 14.1 |  3.41 | 0.8 | 51 | 10.4 | 2.6 | 309.4 | 684 | 0.00426 | 0.50 | 4.6
G337……. | 337.0 | -0.5 | -118 | 8.9 |  7.85 | 3.8 | 109 | 2.3 | 2.9 | 76.5 | 2385 | 0.074 | 1.95 | 3.5
G334……. | 334.0 | 0.0 | -87 | 9.4 | 4.9 | 2.2 | 84 | 4.1 | 2.7 | 122.4 | 2312 | 0.0384 | 1.77 | 3.2
G330-RCW106 | 333.1 | -0.4 | -46 | 13.9 | 3.5 | 0.9 | 53 | 11.7 | 3.2 | 348.4 | 3111 | 0.0278 | 3.22 | 3.8
G331-90 km s-1 | 331.6 | -0.1 | -93 | 10.4 |  7.44 | 2.5 | 88 | 5.5 | 4.0 | 162.0 | 1863 | 0.0348 | 1.40 | 2.8
G329-75 km s-1.. | 328.5 | 0.0 | -75 | 30.2 | 4.4 | 4.1 | 114 | 28.0 | 15.1 | 369.5 | 714 | 0.0095 | 0.244 | 8.0
G329-25 km s-1.. | 329.0 | 0.0 | -45 | 7.7 | 3.0 | 3.3 | 103 | 14.3 | 3.5 | 104.6 | 917 | 0.00571 | 0.18 | 2.0
G327……. | 327.0 | 0.0 | -45 | 7.8 | 2.9 | 1.8 | 75 | 11.3 | 2.7 4 | 149.4 | 2563 | 0.0149 | 0.83 | 2.0
G320……. | 320.8 | -0.3 | -62 | 12.3 | 4.0 | 1.5 | 69 | 4.2 | 1.9 | 124.1 | 811 | 0.00897 | 0.67 | 6.5
G318……. | 318.0 | -0.3 | -44 | 8.1 | 3.0 | 0.8 | 51 | 5.5 | 1.4 | 163.6 | 833 | 0.00518 | 0.625 | 2.9
G316.5….. | 316.5 | -0.3 | -48 | 9.1 | 3.3 | 1.0 | 57 | 6.1 | 1.9 | 180.0 | 1224 | 0.0092 | 0.1 | 3.0
G314……. | 314.5 | -0.3 | -49 | 8.9 | 3.6 | 1.2 | 61 | 7.4 | 2.6 | 219.3 | 280 | 0.0025 | 0.25 | 2.1
G311……. | 311.8 | -0.2 | -49 | 8.9 | 4.0 | 2.4 | 86 | 11.7 | 5.1 | 214.4 | 1099 | 0.0121 | 0.5 | 1.6
G309……. | 309.5 | -0.4 | -44 | 11.2 | 3.8 | 1.8 | 75 | 9.0 | 3.7 | 205.9 | 528 | 0.0053 | 0.28 | 3.0
Table 1 Cloud and SFR characteristics of the massive molecular cloud complexes
(MCCs) in the Milky Way. The distances quoted in red rectangles are parallax
distances, in black rectangles are photometric distances, in green rectangles
are ambiguity resolved kinematic distances, and the rests are near-kinematic
distances. References of parallax distances to several well-known MCCs: G111
(Choi et al., 2014), Cygnus X (Rygl et al., 2012), W51 (Sato et al., 2010),
W49 (Zhang et al., 2013), G35-W48 (Zhang et al., 2009), W43 (Zhang et al.,
2014), G23.7+60 (Sanna et al., 2014), M16/M17 (Xu et al., 2011), W33 (Immer et
al., 2013), W31 (Sanna et al., 2014), CMZ (Reid et al., 2009), CMZ (Reid et
al., 2009), NGC6334/NGC6357 (Chibueze et al., 2014). For ambiguity resolved
kinematic distances, we obtain them from Jones & Dickey (2012) and Anderson &
Bania (2009). The SFRS of G10, G8.2, G7.5, G3.5, and CMZ MCCs are not
calculated because the lack of radio continuum data toward the central
molecular zone.

###  4.1. Cloud properties

We use the CO 1–0 emission as a proxy to estimate the total gas mass content
of molecular cloud structure. For this purpose, using the CO 1–0 alone is
subjected to two major problems. First, CO may not trace all molecular
hydrogen in molecular clouds and it miss the ’CO-dark’ gas (Langer et al.,
2014). Second, the CO 1–0 emission becomes optically thick quickly in the
dense parts of the molecular clouds. Moreover, Barnes et al. (2015) proposed
that the linear conversion from CO integrated intensity to H2 gas column
density might underestimate the true column density. However, for the first-
order global mass estimate, this is acceptable. The X factor $X=2\times
10^{20}~{}{\rm cm}^{-2}$ ${\rm K}^{-1}\,(\rm\mbox{\,km$\,$s${}^{-1}$})^{-1}$
is used to convert the CO integrated intensity to H2 gas column density as
recommended by Bolatto et al. (2013), which was established after an exhausted
investigation of all possible measurements. The mean hydrogen molecular mass
$m_{\rm H_{2}}=\mu m_{\rm H}=2.8m_{\rm H}$ which also accounts for helium
contained in the gas is used to convert from number to mass column density. We
note that additionally intrinsic uncertainties on the $X$ factor can also
contribute to the error of the estimated column density and mass (see, e.g.,
Shetty et al., 2011).

Eventually, we derived the following physical parameters:

  * •

Velocity-integrated intensity $W_{\mbox{CO}}$ (K  km s-1) by integrating the
channel maps within the velocity range derived from the Gaussian fit of the
integrated spectrum,

  * •

Equivalent radius $R=\sqrt{A/\pi}$ (pc) from the surface area $A$ (pc2)
measured in the integrated map,

  * •

Velocity dispersion $\sigma=\frac{\Delta v_{\rm,FWHM}}{\sqrt{\rm 8ln2}}$ ( km
s-1) from the FWHM linewidth ${\Delta v_{\rm,FWHM}}$ resulted from Gaussian
fitting of the integrated spectra,

  * •

CO luminosity $L_{\rm CO}=AW_{\mbox{CO}}$
$\rm\left(K\mbox{\,km$\,$s${}^{-1}$}pc^{2}\right)$,

  * •

Total gas mass $M=L_{\rm CO}X_{\rm CO}m_{\mbox{\tiny H2}}\left(\mbox{$\rm
M_{\sun}$}\right)$,

  * •

Gas surface density $\Sigma_{\rm gas}=\frac{M}{A}$ ${\rm\left(\mbox{$\rm
M_{\sun}$}pc^{-2}\right)}$,

  * •

Virial parameter $\alpha_{\rm vir}=5\sigma_{\rm 1D}^{2}R/GM$ with the
gravitational constant G.

Our focus is on the 44 MCCs that are more massive than $10^{6}~{}\mbox{$\rm
M_{\sun}$}$ (Table 1). All of them lie in the Galactic Plane within the
longitude ranging from 0°to 90° or 310°to 355° and the latitude ranging from
-1°to +1°, thus, mainly in the first and fourth quadrants (see Figure 1). Our
MCCs coincide spatially with all massive GMCs having mass larger than
$10^{6}~{}\mbox{$\rm M_{\sun}$}$ in the other CO surveys (Heyer et al., 2009;
Roman-Duval et al., 2010; García et al., 2014). All MCCs hosting massive star
clusters characterized by Murray (2011) are associated with MCCs in our
catalog. We also cover well-known MCCs such as W43 (Nguyen Luong et al.,
2011a), Cygnus X (Schneider et al., 2006), W49 (Galván-Madrid et al., 2013),
and W51 (Ginsburg et al., 2015). Therefore, we can conclude that our MCCs
catalog is a robust catalog of nearby MCCs. Table 1 lists, for each MCC the
location (l, b, $V_{\rm VLSR}$), extent ($A$, $R$, $\sigma$), CO luminosity
($L_{\rm CO}$) along with its associated mass ($M_{\rm gas}$), gas surface
density ($\Sigma_{\rm gas}$) and viral parameter ($\alpha_{\rm vir}$). Their
typical sizes and masses range from 40 pc to 100 pc and from $1\times
10^{6}~{}\mbox{$\rm M_{\sun}$}$ to $5\times 10^{7}~{}\mbox{$\rm M_{\sun}$}$.
One exception is the Central Molecular Zone which has a mass of $1.3\times
10^{8}~{}\mbox{$\rm M_{\sun}$}$ over a area with equivalent radius of 406 pc.

To assess the detection completeness, we compare the number of MCCs in our
catalog (44) with the total expected number of MCCs in the Milky Way from
power-law mass distribution, $\frac{dN}{dm}\propto m_{\rm GMC}^{\gamma}$ with
$\gamma=-1.5$ (e.g. Simon et al. 2001). Assuming that the Galactic molecular
mass ranges from the minimum mass $M_{\rm L}=10^{2}~{}\mbox{$\rm M_{\sun}$}$
to the maximum mass $M_{\rm U}=10^{7}~{}\mbox{$\rm M_{\sun}$}$, we calculate
the number of GMCs above a certain mass $m$ by integrating the mass
distribution function over the mass range $[M_{\rm L}-m]$. This yields:

$N(>m)=\frac{2-\gamma}{\gamma-1}\times\left(\frac{\left(\frac{M_{\rm
U}}{m}\right)^{\gamma-1}-1}{1-\left(\frac{M_{\rm L}}{M_{\rm
U}}\right)^{2-\gamma}}\right)\times\frac{M_{\rm Tot}}{M_{\rm U}}\,\,\,,$ (1)

where $M_{\rm Tot}=10^{9}~{}\mbox{$\rm M_{\sun}$}$ is the total gas mass in
the Milky Way (Dame et al., 2001). A total number of $\sim$300 MCCs with
masses larger than $10^{6}~{}\mbox{$\rm M_{\sun}$}$ is expected in the entire
Galaxy, about six times the number of detected MCCs. Our detection scheme
mostly focuses on the near side of the Milky Way, covering only $\sim$1/5 of
the Galactic plane, the part in the first and fourth quadrants (see Figure 2)
therefore the total number of 44 MCCs is complete within this Galactic region.

MCCs scatter along the Galactic plane and follow closely the spiral arms
structure (see Figures 1 and 2). Most (70%) of the MCCs lie along the Scutum-
Centaurus or Sagittarius arms, the two most prominent spiral arms in the Milky
Way (Dame et al., 2001), and a few other lie along the Norma arm, Perseus
arms, and interarm regions. We note that YMCs, the potential descendant of
mini-starburst clouds, also lie along the spiral arms (Portegies Zwart et al.,
2010) (see also Figure 2). This is in line with extragalactic observations and
numerical simulations, which find that the most massive, most turbulent, and
most actively star-forming regions are located in the spiral arms rather than
in the inter-arm zones (Koda et al., 2012; Dobbs et al., 2006; Fujimoto et
al., 2014). MCCs are concentrated to the midplane, they distribute within the
latitude range $\pm 1\arcdeg$ or approximately $\sim$200 pc from the Galactic
plane equator (see Figure 1).

Figure 2.— Location of the mini-starburst MCCs over the spiral-arm structure
of the Milky Way as modelled by Vallée (2014). Mini-starburst MCCs are
indicated by circles. Well-known MCCs are labelled. Young Massive Clusters and
OB Asscotiation from Portegies Zwart et al. (2010) are marked as squares,
respectively.

###  4.2. SFRs from radio continuum emission

To calculate the immediate past (last $5\times 10^{6}$ yr, or the timescale of
one OB star generation) SFR of MCCs, we follow the same approach as in Nguyen
et al. (2015). Following Mezger & Henderson (1967), we use the 21 cm continuum
emission to calculate the total Ly$\alpha$ continuum photons emitted by young
massive stars that drive HII regions as

$\frac{N_{\rm Ly\alpha}}{8.9\times
10^{46}\,\text{s}^{-1}}=\frac{S_{\nu}}{\text{Jy}}\left(\frac{\phantom{N}\nu\phantom{N}}{\text{GHz}}\right)^{0.1}\left(\frac{T_{e}}{10^{4}\,\text{K}}\right)^{-0.45}\left(\frac{d}{\text{kpc}}\right)^{2}\,.$
(2)

where $T_{e}=8000$ K (Wilson et al., 2012) is the electron temperature,
$\nu=1.42$ GHz is the observing frequency, and $d$ is the distance to the
region.

Assuming that an O7 star with mass larger than 25 $\rm M_{\sun}$ emits on
average $N_{\rm Ly\alpha}={5\times 10^{48}\,\text{s}^{-1}}$ (Martins et al.,
2005), we calculate the SFR of the MCCs based on the SFR calibration for a
full typical mass spectrum derived by (Murray & Rahman, 2010) as

$\frac{{\rm SFR}}{\rm\mbox{$\rm M_{\sun}$}yr^{-1}}=4.1\times
10^{-54}\frac{{N_{\rm Ly\alpha}}}{\rm s^{-1}}\,.$ (3)

The SFR is then calculated for the entire MCCs using the area derived from CO
emission (see Table 1). The SFR density of our MCCs range from 1 to 10
$\rm~{}\mbox{$\rm M_{\sun}$}\,yr^{-1}\,kpc^{-2}$, which are in the high range
of the Gould Belt dense cores (Heiderman et al., 2010), although the sizes of
MCCs are hundreds times as large. SFR densities of MCCs are comparable with
the SFR of super giant H II regions in M33 (Miura et al., 2014). The fact that
these high SFR densities fill up the missing part in the SFR-Mass diagram
derived by Lada et al. (2010) suggests that MCCs are good candidates to link
the SFRs from local GMC scale to global galaxy scale (see Figure 7).

When using the radio continuum flux to estimate the SFR of MCCs, a few
assumptions have to be made, such as the mass spectrum over which the total
stellar mass is calculated, the maximum cut-off mass of the mass spectrum, the
non-dispersal property of the gas clouds, or the independence of the mass
spectrum on the total gas mass. These assumption might add up uncertainties to
our SFR measurements.

##  5\. Global Larson’s scaling relations and break at MCC scales

$\begin{array}[]{ll}\includegraphics[angle={0},width=256.0748pt]{NLQfg5.eps}&\end{array}$

Figure 3.— The Larson’s scaling relation of velocity dispersion-radius. All
objects are divided into three categories: GMCs (size $<$ 10 pc), MCC (10 $<$
size $<$ 1000 pc), and Galaxy (size $>$ 1000 pc). The continuous lines are
linear fits to the velocity dispersion-radius relations of GMC (pink), MCC
(green), and all (black).

$\begin{array}[]{l}\includegraphics[angle={0},width=256.0748pt]{NLQfg6.eps}\\\
\end{array}$

Figure 4.— The histogram of the virial parameters $\alpha_{\rm vir}$ of all
objects which are divided into three categories: GMCs (size $<$ 10 pc), MCC
(10 $<$ size $<$ 1000 pc), and Galaxy (size $>$ 1000 pc). The dotted line
divides the gravitaionally bound ($\alpha_{\rm vir}<1$) and unbound
($\alpha_{\rm vir}>1$) regimes.

$\begin{array}[]{ll}\includegraphics[angle={0},width=256.0748pt]{NLQfg7.eps}\end{array}$

Figure 5.— The Larson’s scaling relation of mass-radius. Symbols are as in
Figure 3. All objects are divided into three categories: GMCs (size $<$ 10
pc), MCC (10 $<$ size $<$ 1000 pc), and Galaxy (size $>$ 1000 pc). The
continuous lines are linear fits to the mass-radius relations of GMC (pink),
MCC (green), and all (black).

We analyse the scaling relations between different physical properties (mass,
radius, gas mass density, and velocity dispersion) of cloud structures across
8 orders of magnitude in size and 13 orders of magnitude in mass using the
most complete compilation of molecular cloud structures discussed in Section
2.3. To investigate the scale dependency of the scaling relations, we divide
the dataset into three populations: GMCs ($R<10$ pc), MCCs ($10<R<100$ pc),
galaxies ($R>100$ pc). These sub-divisions contain literature data and our
MCCs data. We then plot the velocity dispersion versus radius diagram to
describe the first Larson’s relation (Figure 3), the histogram of virial
parameters to describe the second Larson’s relation (Figure 4), the mass
versus radius to present the third Larson’s relation (Figure 5). Subsequently,
we fit linear functions in log-log space to the $\sigma-R$ and $M-R$ to derive
their power-laws relations.

As an independent check of the correlation between two parameters, we also
calculate the Pearson correlation coefficient $r_{\rm p}$, which is the
covariance of the two parameters divided by the product of their standard
deviation. An $r_{\rm p}>0.7$ describes a strong correlated parameter pair, an
$<0.3<r_{\rm p}<0.7$ describes a moderate correlated parameter pair, and an
$r_{\rm p}<0.3$ describes an uncorrelated parameter pair. The positive sign
indicates the positive correlation and vice versa.

###  5.1. The $\sigma-R$ relation

For the line width-size relation (Figure 3), we obtain the following results:

$\displaystyle{\rm GMC:}\,\,\,{\sigma}$
$\displaystyle=10^{-0.2}{R}^{0.4},r_{p}=0.9$ (4) $\displaystyle{\rm
MCC:}\,\,\,{\sigma}$ $\displaystyle=10^{-0.6}{R}^{0.7},r_{p}=0.6$ (5)
$\displaystyle{\rm All:}\,\,\,{\sigma}$
$\displaystyle=10^{-0.2}{R}^{0.5},r_{p}=0.9$ (6)

The slope 0.4 of the power law fitted to GMCs is close to $\beta\sim 0.38$
measured by Larson (1981). This is in between the range of the slopes of the
pure Kolmogorov turbulent structure ($\sigma\propto R^{0.33}$) and the Burger
shock-generated one ($\sigma\propto R^{0.5}$) cases. Simulations of cloud
formation through turbulent shocks, for examples those of Bonnell et al.
(2006) or Dobbs & Bonnell (2007), also produce a $\sigma\propto R^{0.4}$
relation. However, the slope 0.7 of the fit to the MCC population is much
higher than the GMC’s one, even higher than the slope of the Burger shock-
generated fractals.

As for the Pearson correlation coefficient, while the GMC and entire
populations produce a good correlation between $\sigma$ and $R$ ($r_{\rm
p}=0.9$ and $r_{\rm p}=0.9$, respectively), the MCC population has weaker
correlation ($r_{\rm p}=0.6$) and the galaxy population has no correlation
($r_{\rm p}=-0.2$). Similarly, no relation between line-width and size is
found for MCCs in nearby galaxies (Hughes et al., 2013; Utomo et al., 2015;
Rebolledo et al., 2015). Together with our MCC data, we suggest that there is
a break at the MCCs scale in addition to an apparent universal $\sigma-R$
relation. However, this break may be artificial due to different measurements
such as tracers, methods, resolution and thresholds for the mass determination
were used, or due to the intrinsic different properties of the samples. A more
homogeneous investigation is therefore needed to confirm this break.

###  5.2. The virial parameter histogram

The second Larson relation describes the tendency of the molecular clouds to
reach the virial equilibrium state. We check this hypothesis by examing the
virial parameter $\sigma=5\sigma_{\rm 1D}^{2}R/GM$. A cloud structure is
dominated by gravitational energy if $\sigma\leq 1$, otherwise external
pressure takes control. In Figure 4, we plot the histogram of virial
parameters for different populations. The mean virial parameter of the GMCs is
1.0, of MCCs is 1.8, and of the entire sample is 1.2. Since $\sigma$ of GMCs
is closer to 1, the internal gravitational energy is stronger than kinetic
energy as oppose to MCCs which are dominated by kinetic energy as their
$\sigma$ is larger than 1. In other words, GMCs are closer to be
gravitationally bound than MCCs which are super virial and unbound. Similar
results were found for MCCs in other galaxies (Hughes et al., 2013). For the
case of our MCCs listed in Table 1, their virial parameters are even larger.
This picture is also seen in simulations where most of the large structures
are unbound and the small structure are bound (Dobbs et al., 2011; Fujimoto et
al., 2014). The large velocity dispersion may be caused by the fact that MCC
is a more dynamic system that can form a compressive environment. Susequently,
this results in a higher specific star formation rate or star formation
density as we discussed later on.

###  5.3. The $M_{\rm gas}-R$ relation

The third Larson relation implies that the mass and size obey a power relation
$M_{\rm gas}\propto R^{\alpha}$ with $\alpha\sim 2$, or all molecular cloud
structures have similar mass surface density, which we examine in Figure 5.
The best fits to the GMCs, MCCs, galaxies and entire samples yield slopes of
1.9, 2.2, and 2.0, respectively:

$\displaystyle{\rm GMC:}\,\,\,{M_{\rm gas}}$
$\displaystyle=10^{2.6}{R}^{1.9},r_{p}=1.0$ (7) $\displaystyle{\rm
MCC:}\,\,\,{M_{\rm gas}}$ $\displaystyle=10^{2.1}{R}^{2.2},r_{p}=0.7$ (8)
$\displaystyle{\rm All:}\,\,\,{M_{\rm gas}}$
$\displaystyle=10^{2.6}{R}^{2.0},r_{p}=1.0$ (9)

All three slopes are very close to $M_{\rm gas}\propto R^{2}$ although that of
MCCs slightly deviates from 2. They are in between the value of $\sim~{}1.6$
for substructures within individual clouds (Lombardi et al., 2010; Kauffmann
et al., 2010) and the value of $\sim 2.4$ derived for GMCs in the Galactic
Plane GRS survey (Roman-Duval et al., 2010). The good correlation between mass
and size are also present in the large Pearson coefficients: 1.0 for GMCs, 0.7
for MCCs, and 1.0 for the entire population.

The result of this Section is that there is an apparent universal relation
between velocity dispersion and size, mass and size of cloud structures across
8 orders of magnitude in size and 13 orders of magnitude in mass. However,
there is a break at the MCC scale in the $\sigma-R$ relation and the slopes of
individual populations are slightly different. The virial parameters of GMCs
and Galaxies are close to 1 while those of MCCs are larger than 1, thus
signifies the importance of the kinetic energy contribution in regulating the
MCC structures.

##  6\. The star formation rates - gas properties relation

Similar as in Section 5, we construct the scaling relations and their best-
fitted power law models between the $SFR$ surface density $\Sigma_{\rm SFR}$
and mass surface density $\Sigma_{\rm gas}$, between the SFR and the total
mass $M_{\rm gas}$. In addition, we also calculate the Pearson correlation
coefficients for different pairs of parameters.

###  6.1. The Schmidt-Kennicutt $\Sigma_{\rm SFR}-\Sigma_{M_{\rm gas}}$
relation

The $\Sigma_{\rm SFR}-\Sigma_{M_{\rm gas}}$ relation was first constructed by
Kennicutt (1998) for the integrated SFR density $\Sigma_{\rm SFR}$ and the
total gas mass density $\Sigma_{M_{\rm gas}}$ of normal star-forming and
starburst galaxies. Since then, it was generated as one of the most applicable
tool to explain the universal role of gravity in forming stars. Recently, the
relation has been extended to GMCs scale (Heiderman et al., 2010; Krumholz et
al., 2012b) in an endeavour to establish a universal star formation law that
connects local to global scales. We re-investigate this relation for our
combined dataset by constructing the SFR density and gas mass density relation
in Figure 6 and deriving their best linear fits to the $\Sigma_{\rm
SFR}$-$\sigma$ relations in the log-log space as:

$\displaystyle{\rm GMC:}\,\,\,{\rm\Sigma_{SFR}}$
$\displaystyle=10^{-4.9}{\rm\Sigma_{M_{\rm gas}}}^{2.4},r_{p}=0.8$ (10)
$\displaystyle{\rm MCC:}\,\,\,{\rm\Sigma_{SFR}}$
$\displaystyle=10^{-3.0}{\rm\Sigma_{M_{\rm gas}}}^{1.3},r_{p}=0.5$ (11)
$\displaystyle{\rm GALAXY:}\,\,\,{\rm\Sigma_{SFR}}$
$\displaystyle=10^{-3.8}{\rm\Sigma_{M_{\rm gas}}}^{1.4},r_{p}=1.0$ (12)
$\displaystyle{\rm ALL:}\,\,\,{\rm\Sigma_{SFR}}$
$\displaystyle=10^{-3.4}{\rm\Sigma_{M_{\rm gas}}}^{1.5},r_{p}=0.7$ (13)

The slopes of the $\Sigma_{\rm SFR}$-$\Sigma_{M_{\rm gas}}$ relations are
different among different populations. While GMCs have the steepest slope of
2.4, MCCs have the most shallow slope of 1.3, Galaxies have a slope that is
closest to the original value of 1.4 derived by Kennicutt (1998). The steeper
slope of the GMC population is consistent with that of the star-forming clump
population (Heiderman et al., 2010) and of the resolved individual MCCs
(Willis et al., 2015). From a global view of our data, we derive a universal
Schmidt-Kennicutt scaling relation with a slope of 1.5 and large scatters in
the GMC and MCC populations. The Pearson coefficients show that $\Sigma_{\rm
SFR}$ and $\Sigma_{M_{\rm gas}}$ correlate strongly ($r_{p}=0.9$) in the
galaxy population while they correlate least in the MCC population
($r_{p}=0.5$).

###  6.2. The ${\rm SFR}-M_{\rm gas}$ relation

$\begin{array}[]{cc}\includegraphics[angle={0},width=256.0748pt]{NLQfg8}&\includegraphics[angle={0},width=256.0748pt]{NLQfg9}\\\
\includegraphics[angle={0},width=256.0748pt]{NLQfg10}&\includegraphics[angle={0},width=256.0748pt]{NLQfg11}\\\
\end{array}$

Figure 6.— The Schmidt-Kennicutt relation of $\Sigma_{\rm
SFR}$-$\Sigma_{M_{\rm gas}}$ for objects ranging from Milky Way clouds to
unresolved galaxies and the best fits. The white and grey regions are divided
by the gas surface density of 100 $\rm M_{\sun}$ pc-2 and the SFR density of 1
$\rm M_{\sun}$ yr-1 kpc-2. Top-Left diagram includes only literature data,
Top-Right diagram includes literature data and our MCCs from this study,
Bottom-Left diagram includes literature data, our MCCs and mini-starburst MCCs
from this study, and Top-Right diagram includes all data and different linear
fits as discussed in Equations 10-13 in Section 6.1. We note that the dense
cores samples ($R<$ 1 pc) from Maruta et al. (2010), Onishi et al. (2002), and
Shimajiri et al. (2015) are not included in the SFR analysis due to the lack
of SFR measurements.

Instead of comparing the surface density quantities of SFR and mass, we
examine the integrated SFR and the integrated gas mass relation in Figure 7.
Our literature and new data of MCCs fill the $SFR-M_{\rm gas}$ plane and
connect the smallest cloud scale to galaxy scale. We plot in Figure 7 the
relation between SFR and $M_{\rm gas}$ in the log-log space and fits linear
functions to them to obtain the following results for different populations:

$\displaystyle{\rm GMC:}\,\,\,{\rm{SFR}}$ $\displaystyle=10^{-7.4}{\rm
M_{gas}}^{0.8},r_{p}=0.7$ (14) $\displaystyle{\rm MCC:}\,\,\,{\rm{SFR}}$
$\displaystyle=10^{-6.2}{\rm M_{gas}}^{0.6},r_{p}=0.4$ (15) $\displaystyle{\rm
GALAXY:}\,\,\,{\rm{SFR}}$ $\displaystyle=10^{-11.7}{\rm
M_{gas}}^{1.3},r_{p}=0.9$ (16) $\displaystyle{\rm ALL:}\,\,\,{\rm{SFR}}$
$\displaystyle=10^{-7.6}{\rm M_{gas}}^{0.9},r_{p}=1.0~{}~{}~{}.$ (17)

The slopes of our fits are super-linear for the Galaxy population and sub-
linear for all other cases. The slope of the fit to the combined data, is sub-
linear with a slope of 0.87, which does not quite agree with the unity slopes
derived by Wu et al. (2005) or Lada et al. (2010). Thus to the first order,
this universal scaling relation is useful to establish a common relation
between SFR and the total gas mass for all star-forming objects. However, at
the individual scales, this relation has strong scatter and the linear fits to
the data vary strongly. The strong correlation between SFR and $M_{\rm gas}$
of the entire dataset can also be seen in the large Pearson coefficient
($r_{p}=0.95$). Similar as in the $\Sigma_{\rm SFR}$-$\Sigma_{\rm gas}$
relation, the MCC has very low Pearson coefficient ($r_{p}=0.37$), indicating
the low correlation between $SFR$ and $M_{\rm gas}$. For example, the total
SFR of MCCs vary almost over 4 orders of magnitude. However, they are
consistent with the recent numerical simulation of star formation activities
in MCCs, these simulation show large SFR spreads in the $SFR$-$M_{\rm gas}$
diagram (Howard et al., 2016). Lada et al. (2012) suggested that the spread in
$SFR$-$M$ diagram is the effect of the dense gas fraction which we could not
address with the current data. While we would expect that the slopes of the
$SFR$-$M$ relations are super-linear as similar as those of $\Sigma_{\rm
SFR}$-$\Sigma_{M_{\rm gas}}$ relations, they are however sub-linear. The
reasons is that the gas surface density also scales with Area as
$A\sim\Sigma_{M_{\rm gas}}^{-q}$. Therefore, if there is $SFR\propto M_{\rm
gas}^{p}$, we should get $\Sigma_{\rm SFR}\propto A^{-1}\Sigma_{M_{\rm
gas}}^{p}=A^{p-1}\Sigma_{M_{\rm gas}}^{p}$. The dependency of gas surface
density on area has been investigated by Burkert & Hartmann (2013), who showed
that $\Sigma_{M_{\rm gas}}$ scales with Area as $A\sim\Sigma_{M_{\rm
gas}}^{-3}$ for low-mass star forming regions and $A\sim\Sigma_{M_{\rm
gas}}^{-1}$ for massive cores .

$\begin{array}[]{cc}\includegraphics[angle={0},width=256.0748pt]{NLQfg12.eps}\end{array}$

Figure 7.— The SFR$-M_{\rm gas}$ relation for objects ranging from Milky Way
clouds to unresolved galaxies and the best fits.

###  6.3. The ${\rm SFR}$-$\sigma$ relation

Ideally, if all of the scaling relations in Section 5.1, 5.3, and 6.2 hold
together, we can deduce a relation between $\Sigma_{\rm SFR}$-$\sigma$ from
the other relations. Because $\sigma\propto R^{0.3-0.5}$ and ${\rm
M_{gas}}\propto R^{2}$, we have the relation ${\rm
M_{gas}}\propto\sigma^{4-7}$. As a consequence of the relation
${\rm{SFR}}\propto{\rm M_{gas}}^{\left({0.8-1.3}\right)}$, we should have a
relation ${\rm{SFR}}\propto{\sigma}^{\left({3.1-8.8}\right)}$. However, as
shown in Figure 8, we obtain different slopes from fitting power laws to the
individual populations and also combined dataset:

$\begin{array}[]{c}\includegraphics[angle={0},width=256.0748pt]{NLQfg13.eps}\end{array}$

Figure 8.— The SFR$-\sigma$ (SFR - velocity dispersion) relation for objects
ranging from Milky Way clouds to unresolved galaxies and their best fits.
There are less GMC data points because there are less GMCs that have both SFR
and velocity dispersion measurements.

$\displaystyle{\rm MCC:}\,\,\,{\rm{SFR}}$
$\displaystyle=10^{-2.9}{\rm\sigma}^{0.9},r_{p}=0.3$ (18) $\displaystyle{\rm
GALAXY:}\,\,\,{\rm{SFR}}$ $\displaystyle=10^{-1.8}{\rm\sigma}^{1.9},r_{p}=0.8$
(19) $\displaystyle{\rm ALL:}\,\,\,{\rm{SFR}}$
$\displaystyle=10^{-3.8}{\rm\sigma}^{2.7},r_{p}=0.8$ (20)

The empirical fits show that SFR increases with the velocity dispersion but
the slopes are much shallower than the theoretical prediction from other
scaling laws. A global fit with a slope of 2.7 fits well to the entire
dataset. But fits to GMC and MCC populations are uncertain because their
velocity dispersion ranges are less than an order of magnitude.

Krumholz & Burkhart (2016) created feedback-driven models and gravity-driven
models to explain the SFR$-\sigma$ relations in the galaxy interstellar media
and found that the former model produces a steeper relation SFR$-\sigma^{2}$
while the later model produces a shallower and dense-gas-mass-fraction
dependence relation SFR$-f_{\rm DG}\sigma$. These slopes are close to the
slope of our galaxy population data, however, they are not applicable to MCCs
and GMCs, which seem to be fitted with steeper slopes. Similarly at the
previous cases, MCCs have smallest Pearson coefficient ($r_{p}=0.3$) or their
$SFR$ and $\sigma$ are not correlated well.

##  7\. Discussion & Conclusion

###  7.1. Four quadrants of the Schmidt-Kennicutt diagram

One of the application of the $\Sigma_{\rm SFR}-\Sigma_{\rm gas}$ diagram is
to distinguish the starburst from the normal galaxies. Daddi et al. (2010),
for example, argued that the two different regimes of star formation in
galaxies are caused by the longer depletion time of normal galaxies than that
of the starburst. For the same gas surface density, the starburst galaxies and
mini-starburst MCCs have higher SFR density than the normal star forming
galaxies and normal star-forming MCCs, therefore lie at a higher location in
the Schmidt-Kennicutt diagram. However, the scatter in the $\Sigma_{\rm
SFR}-\Sigma_{\rm gas}$ are getting larger as there are better observations,
both in galactic and extragalactic scales, which make the recognition of small
deviation from the universal law unnoticeable. Using our combined data, we
propose an alternative way to distinguish starburst from normal star-forming
objects by applying the $\Sigma_{\rm SFR}$ and $\sigma$ thresholds to the
Schmidt-Kennicutt diagram.

A $\Sigma_{\rm gas}$ threshold of $\sim 100-120~{}\mbox{$\rm M_{\sun}$}{\rm
pc}^{-2}$ was suggested as the borderline between star-forming and non star-
forming clouds or between normal spiral galaxies and starburst galaxies (Lada
et al., 2010; Heiderman et al., 2010). As we can already see in the Schmidt-
Kennicutt diagram in Figure 6, som MCCs or galaxies, and even some GMCs have
star formation at $\Sigma_{\rm gas}<100~{}\mbox{$\rm M_{\sun}$}{\rm pc}^{-2}$.
However, this threshold can be safely used as a threshold dividing different
star formation modes: isolated versus clustered, normal versus starburst,
while the later ones always require more gas with $\Sigma_{\rm
gas}>100-120~{}\mbox{$\rm M_{\sun}$}{\rm pc}^{-2}$ (Wu et al., 2005;
Kennicutt, 1998). There is exception such as the central molecular zone in the
Milky Way, which has high gas mass surface density but low SFR density.
Additionally, we use the $\Sigma_{\rm SFR}\sim 1~{}\mbox{$\rm M_{\sun}$}{\rm
yr}^{-1}{\rm kpc}^{-2}$ as the threshold between starburst and non-starburst
objects. This SFR threshold was originally used to distinguish between
starburst and normal-star forming galaxies (Kennicutt, 1998).

Putting these two thresholds into the Schmidt-Kennicut diagram, as in Figure
6, the four quadrants are divided and named clockwise as: low-density
starburst quadrant, normal star-forming quadrant, inefficient-star forming
quadrant, and starburst quadrant. Structures in the starburst quadrant have
high gas density and high star formation efficiency such as starburst galaxy
and ministarburst complex. Structures in the inefficient star-formation
quadrant also have high gas density, however their star formation is impeded.
The Central Molecular Zone is a good example of the exception case (Immer et
al., 2012). The majority of structures in the normal-star formation quadrant
are galaxies and they follow well the Schmitt-Kennicutt fit with much less
scatter than objects in the starburst quadrant. In the low-density starburst
quadrant, the low gas density inhibit high SFR density higher than
$1~{}\mbox{$\rm M_{\sun}$}{\rm yr}^{-1}{\rm kpc}^{-2}$. Nevertheless, there
are maybe a few candidates that have $\Sigma_{\rm SFR}>1~{}\mbox{$\rm
M_{\sun}$}{\rm yr}^{-1}{\rm kpc}^{-2}$, or they might be the outliers.

###  7.2. Definition of mini-starburst complexes

The starburst phenomenon was first suggested by observations of the excess
star formation activity in galaxy nuclei (Arp & O’Connell, 1975; Huchra,
1977). More recently, Elbaz et al. (2011) proposed that a galaxy experiences a
starburst phase if its ‘current SFR’ is twice higher than its SFR averaged
over time and used to define its ‘main sequence SFR’. With a total gas mass of
$1\times 10^{9}~{}\mbox{$\rm M_{\sun}$}$ (Dame et al., 1993), the Milky Way
becomes a starburst galaxy only if its SFR is as high as 20 times of the
current rate of $\sim 0.7-2~{}\mbox{$\rm M_{\sun}$}$ yr-1 (Robitaille &
Whitney, 2010). The Milky Way as a whole, is therefore far from experiencing a
starburst phase. However, SFR is not uniformly distributed across the Milky
Way but excess star formation activity exist in MCC that forms massive star
clusters (Nguyen Luong et al., 2011a; Murray, 2011).

We define the mini-starburst MCCs as objects having these properties:

  * •

total gas mass is larger than $10^{6}\,\,\mbox{$\rm M_{\sun}$}$,

  * •

gravitationally unbound,

  * •

Star formation rate density is larger than 1 $\mbox{$\rm M_{\sun}$}{\rm
yr}^{-1}{\rm kpc}^{-2}$ or its location is on the starburst quadrant in the
Schmidt-Kennicutt diagram (see Figure 6).

From the 44 massive MCCs detected in Section 3, we obtain 21 mini-starburst
MCCs. Most of them are the famous mini-starburt MCCs studied extensively in
the literatures, for example:

  * •

RCW 106 is the second brightest MCC in our survey, resides in the Scutum-
Centaurus arm and surrounds the bright giant H II region RCW 106 hosting a
rich OB cluster (Rodgers et al., 1960; Nguyen et al., 2015).

  * •

W43 lies at the meeting point of the Scutum-Centaurus (or Scutum-Crux) arm and
the Bar. This mini-starburst is a prototypical example of a mini-starburst MCC
(Nguyen Luong et al., 2011b; Carlhoff et al., 2013).

  * •

W49 lies on the Perseus arm and hosts ongoing starburst event and forms a very
massive star with mass from 100–190 $\rm M_{\sun}$ (Galván-Madrid et al.,
2013).

  * •

Cygnus X is one of the most massive mini-starburst MCC and is located in the
Cygnus arm (Schneider et al., 2006).

  * •

W51 is near the tangent point of the Sagittarius arm, has a high dense gas
fraction and host massive star formation events (Ginsburg et al., 2015).

We compare the Galactic mini-starburst with the extragalactic mini-starburst
which are resolved to a comparable scale. First, we use data from Arp 220, a
relatively nearby (d$\sim 75$ Mpc) ultraluminous infrared galaxy (Soifer et
al., 1984), which contains two nuclei that are powered by extreme starburst
activity. Sakamoto et al. (2008); Wilson et al. (2014); Scoville et al. (2015)
used ALMA to resolve the Arp 220 down to a spatial scale of $\sim 100~{}$pc
and obtain gas mass densities of $5.4\times 10^{4}$ and $\rm 14\times
10^{4}~{}\mbox{$\rm M_{\sun}$}pc^{-2}$ for the Eastern and Western nucleus.
Taking into account the SFR of $\rm 100-200~{}\mbox{$\rm M_{\sun}$}yr^{-1}$
(Scoville et al., 2015), we obtain a SFR density $\rm
10{{}^{4}}-10{{}^{4.5}}~{}\mbox{$\rm M_{\sun}$}yr^{-1}kpc^{-2}$, the highest
SFR density at the MCC scale. Second, we use data of 14 starburst MCC clumps
in SDP.81 galaxy derived from ALMA observations. SDP.81 is one of the bright
galaxy at a redshift $z=3.042$ (or a luminosity distance of $\sim 25\times
10^{3}$ Mpc) and is gravitationally lensed by a foreground galaxy at z =
0.2999, therefore it allows us to resolve the gas properties down the scale of
$\sim 200$ pc by ALMA (Hatsukade et al., 2015). Finally, we also include in
our comparison the data from the first direct measurement of a MCC clump at z
= 1.987 down to the scale of $\sim 500$ pc (Zanella et al., 2015). Although
they are larger than our mini-starburst, we still compare them with our data
keeping in mind that their $\sigma$ and $\Sigma_{\rm SFR}$ can be higher if we
resolve them at a smaller scale.

The SFR and SFR density of the extragalactic mini-starburst are ten to hundred
times higher than the Galactic counterparts that they are located in the upper
part of the starburst quadrant and the upper part of the SFR$-M_{\rm gas}$
diagram. Highly-compressed gas in these extragalactic mini-starbursts may be
the origin of their active star formation activities.

###  7.3. Dynamical Evolution of mini-starburst MCCs

We advocate that the high $\Sigma_{\rm SFR}$ and high $\sigma$ of a mini-
starburst MCC is caused by dynamical processes happen during the MCCs
evolution. These processes are supported by externally induced pressure such
as shocks, galactic disk gravitational instability or colliding flow (Vazquez-
Semadeni et al., 1996; Bonnell et al., 2013). Therefore, mini-starburst MCCs
are often found at highly dynamics regions such as the overlapping regions in
Antennae galaxy (Herrera et al., 2012; Fukui et al., 2014) or at the end of
the Galactic Bar (Nguyen Luong et al., 2011b). Simulation of molecular cloud
evolution in a galaxy also agrees with this view by showing that MCCs are
concentrated mostly in the Bar or spiral arms, and have high SFR (Fujimoto et
al., 2014).

$\begin{array}[]{c}\includegraphics[angle={0},width=256.0748pt]{NLQfg14.eps}\end{array}$

Figure 9.— The SFR$-\alpha_{vir}$ (SFR - virial parameter) relation for
objects ranging from Milky Way clouds to unresolved galaxies. It shows that
there is no particular relation between SFR and $\sigma$ but the mini-
starburst MCCs are mostly gravitationally unbound. There are less GMC data
points because there are less GMCs that have both SFR and velocity dispersion
measurements.

In all cases, continuous gas flows agglomerate clouds, compress material and
develop active star formation sites (e.g., Koyama & Inutsuka, 2000; Bergin et
al., 2004), which explains why mini-starburst MCCs have high SFR (see Sect.
7.2). This framework is also called cloud-cloud collision, advocated as the
main formation mechanism of massive star and stellar cluster (Inoue & Fukui,
2013). For example, in W43, one of the most active massive star-forming
regions, both large-scale and small-scale gas flows were observed as a mean of
forming dense gas and massive stars (Motte et al., 2014; Nguyen-Luong et al.,
2013; Louvet et al., 2014).

In addition, a super-linear relation between $SFR-\sigma$ (Figure 8)
indicating that SFR increases with the turbulence or compression degrees of
the gas supports the dynamical view of MCC evolution. The steep slope of the
$SFR-\sigma$ relation, especially that of MCC, disagrees with the slope
produced by the gravity-driven models or feedback-driven model (Krumholz &
Burkhart, 2016). Therefore, cloud compression plays a stronger role in
controlling the structure and the star formation activity, beyond gravity and
feedback. As a consequence, the majority of MCCs are gravitational unbound and
form stars efficiently as shown in Figure 9, especially th mini-starburst
MCCs.

##  8\. conclusions

We investigated the connection between the local and global star formation by
comparing the mass, size, line width, and star formation rate of cloud
structures across 8 orders of magnitude in size and 13 orders of magnitude in
mass. Our focus is on molecular cloud complexes (MCCs), which have radii of
$\sim$50–70 pc and masses $>10^{6}~{}\mbox{$\rm M_{\sun}$}$. We use the 12CO
1–0 CfA survey to identify and characterize a sample of 44 MCCs in the Milky
Way (see Table 1). This sample is complete up to a distance of 6 kpc from the
Sun. Their distribution follows the spiral arms, especially the Scutum-
Centaurus and Sagittarius arms (see Figures 1-2).

Together with data from the literature, we reproduced the scaling relations
and the star formation laws: $\sigma-R$, $M_{\rm gas}-R$, $\Sigma_{\rm
SFR}-\Sigma_{M_{\rm gas}}$, ${\rm SFR}-M_{\rm gas}$, and ${\rm SFR}-\sigma$.
Apart from being apparently universal, the slopes and the coefficients are
different for individual scales: GMC, MCC, and galaxy. Second, there is a
break at the MCC scale in the $\sigma-R$ relation and a break between the
starburst objects such as mini-starburst, star-forming clumps from the normal
star-forming objects in the SFR-$M_{\rm gas}$ and $\Sigma_{\rm
SFR}$-$\Sigma_{M_{\rm gas}}$ relations.

These breaks enable us using the Schmidt-Kennicutt diagram to distinguish the
starburst from the normal star-forming objects by using the $\Sigma_{M_{\rm
gas}}$ threshold of 100 $\rm M_{\sun}$pc-2 and the $\Sigma_{\rm SFR}$
threshold of 1 $\rm M_{\sun}$yr-1 kpc-2. These two thresholds divide the
$\Sigma_{\rm SFR}-\Sigma_{M_{\rm gas}}$ diagram into four quadrants: Q1 as
low-density starburst quadrant, Q2 as normal star-forming quadrant, Q3 as
inefficient-star forming quadrant, and Q4 as starburst quadrant. Mini-starburt
MCC are gravitationally unbound MCCs that have enhanced SFR density that is
larger than $1\,\mbox{$\rm M_{\sun}$}$ yr-1 kpc-2.

We propose that mini-starburst MCC is formed through a dynamical process,
which enhance the compression of clouds and induce intense star formation as
bursts and eventually form young massive star cluster. Because of the
dynamical evolution, gravitational boundedness does not play a significant
role in characterizing the star formation activity of mini-starburst MCCs.
Therefore, there is no particular relation between SFR and the virial
parameter (see Figures 8-9).

QNL acknowledges the financial support from the East Asian Core Observatories
Association (EACOA) through the EACOA fellow program and the support from
Canadian Institute for Theoretical Astrophysics during his visit at CITA. N.S.
acknowledges support through the DFG project numbers 0s 177/2-1 and 177/2-2,
and central funds of the DFG-priority program ISM-SPP. We thank the anonymous
referee and Neal J. Evans for giving constructive comments which improve the
quality of the paper.

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