11institutetext: Institut de Recherche en Astrophysique et Planétologie
(IRAP), Université Paul Sabatier, Toulouse cedex 4, France 22institutetext:
IRAM, 300 rue de la Piscine, 38406 Saint Martin d’Hères, France.
22email<EMAIL_ADDRESS>33institutetext: LERMA, Observatoire de Paris, PSL
Research University, CNRS, Sorbonne Universités, 75014 Paris, France.
44institutetext: Institut Laue-Langevin, 71 avenue des Martyrs - CS 20156,
38042 cedex 9 Grenoble, France 55institutetext: Department of Physics,
University of Connecticut, Storrs, CT, 06269, USA 66institutetext: Department
of Astronomy & Astrophysics, University of Chicago, 5640 South Ellis Avenue,
Chicago, IL 60637, USA 77institutetext: Astronomisches Rechen-Institut,
Zentrum für Astronomie der Universität Heidelberg, Mönchhofstraße 12-14,
D-69120 Heidelberg, Germany 88institutetext: Universität Heidelberg, Zentrum
für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Str 2,
D-69120 Heidelberg, Germany 99institutetext: International Centre for Radio
Astronomy Research, University of Western Australia, 7 Fairway, Crawley, 6009,
WA, Australia 1010institutetext: Universität Heidelberg, Interdisziplinäres
Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, 69120
Heidelberg, Germany 1111institutetext: Sterrenkundig Observatorium,
Universiteit Gent, Krijgslaan 281 S9, B-9000 Gent, Belgium 1212institutetext:
Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121,
Bonn, Germany 1313institutetext: The Observatories of the Carnegie Institution
for Science, 813 Santa Barbara Street, Pasadena, CA 91101, USA
1414institutetext: INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi
5, I-50157 Firenze, Italy 1515institutetext: Departamento de Astronomía,
Universidad de Chile, Casilla 36-D, Santiago, Chile 1616institutetext:
Department of Physics & Astronomy, University of Wyoming, Laramie, WY 82071
USA 1717institutetext: European Southern Observatory, Karl-Schwarzschild
Straße 2, D-85748 Garching bei München, Germany 1818institutetext: Univ Lyon,
Univ Lyon 1, ENS de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon
UMR5574,
F-69230 Saint-Genis-Laval, France 1919institutetext: Research School of
Astronomy and Astrophysics, Australian National University, Canberra, ACT
2611, Australia 2020institutetext: ARC Centre of Excellence for All Sky
Astrophysics in 3 Dimensions (ASTRO 3D), Australia 2121institutetext: Center
for Astrophysics $\mid$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA
02138, USA 2222institutetext: Department of Astronomy, The Ohio State
University, 140 West 18th Avenue, Columbus, Ohio 43210, USA 2323institutetext:
Max-Planck-Institut für extraterrestrische Physik, Giessenbachstraße 1,
D-85748 Garching, Germany 2424institutetext: School of Mathematics and
Physics, University of Queensland, St Lucia 4067, Australia 2525institutetext:
Department of Physics, Tamkang University, No.151, Yingzhuan Road, Tamsui
District, New Taipei City 251301, Taiwan 2626institutetext: Observatorio
Astronómico Nacional (IGN), C/Alfonso XII, 3, E-28014 Madrid, Spain
2727institutetext: Department of Physics, University of Alberta, Edmonton, AB
T6G 2E1, Canada 2828institutetext: Max-Planck-Institut für Astronomie,
Königstuhl 17, D-69117, Heidelberg, Germany 2929institutetext: Department of
Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton,
ON L8S 4M1, Canada 3030institutetext: Canadian Institute for Theoretical
Astrophysics (CITA), University of Toronto, 60 St George Street, Toronto, ON
M5S 3H8, Canada 3131institutetext: Sub-department of Astrophysics, Department
of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK

# The impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSE

Antoine Zakardjian The impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSE Jérôme Pety The impact of H II regions on Giant Molecular
Cloud properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact
of H II regions on Giant Molecular Cloud properties in nearby galaxies sampled
by PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSE Cinthya N. Herrera The impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSEThe impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSEThe impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSE Annie Hughes The impact of H II
regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSE Elias Oakes The
impact of H II regions on Giant Molecular Cloud properties in nearby galaxies
sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular
Cloud properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact
of H II regions on Giant Molecular Cloud properties in nearby galaxies sampled
by PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSE Kathryn Kreckel
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galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and MUSE
Chris Faesi The impact of H II regions on Giant Molecular Cloud properties in
nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on
Giant Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSE Simon C. O. Glover The impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSE Brent Groves The impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSEThe impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSE Ralf S. Klessen The impact of H II
regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSE Sharon Meidt The
impact of H II regions on Giant Molecular Cloud properties in nearby galaxies
sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular
Cloud properties in nearby galaxies sampled by PHANGS ALMA and MUSE Ashley
Barnes The impact of H II regions on Giant Molecular Cloud properties in
nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on
Giant Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSE Francesco Belfiore The impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSE Ivana Bešlić The impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSEThe impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSE Frank Bigiel The impact of H II
regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSE Guillermo A.
Blanc The impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSEThe impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and MUSE
Mélanie Chevance The impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSE Daniel A. Dale The impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSEThe impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSE Jakob den Brok The impact of H II
regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSE Cosima
Eibensteiner The impact of H II regions on Giant Molecular Cloud properties in
nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on
Giant Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSE Eric Emsellem The impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSE Axel García-Rodríguez The impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSEThe impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSE Kathryn Grasha The impact of H II
regions on Giant Molecular Cloud properties in nearby galaxies sampled by
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II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSE Eric W. Koch The
impact of H II regions on Giant Molecular Cloud properties in nearby galaxies
sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular
Cloud properties in nearby galaxies sampled by PHANGS ALMA and MUSE Adam K.
Leroy The impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant
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Daizhong Liu The impact of H II regions on Giant Molecular Cloud properties in
nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on
Giant Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSE Rebecca Mc Elroy The impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSE Lukas Neumann The impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSEThe impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSE Hsi-An Pan The impact of H II regions
on Giant Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA
and MUSEThe impact of H II regions on Giant Molecular Cloud properties in
nearby galaxies sampled by PHANGS ALMA and MUSE Miguel Querejeta The impact of
H II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSE Alessandro Razza
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galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and MUSE
Erik Rosolowsky The impact of H II regions on Giant Molecular Cloud properties
in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions
on Giant Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA
and MUSE Toshiki Saito The impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSE Francesco Santoro The impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSEThe impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSE Eva Schinnerer The impact of H II
regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSE Jiyai Sun The
impact of H II regions on Giant Molecular Cloud properties in nearby galaxies
sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular
Cloud properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact
of H II regions on Giant Molecular Cloud properties in nearby galaxies sampled
by PHANGS ALMA and MUSEThe impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSE Antonio Usero
The impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and MUSE
Elizabeth J. Watkins The impact of H II regions on Giant Molecular Cloud
properties in nearby galaxies sampled by PHANGS ALMA and MUSEThe impact of H
II regions on Giant Molecular Cloud properties in nearby galaxies sampled by
PHANGS ALMA and MUSE Thomas Williams The impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSEThe impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSEThe impact of H II regions on Giant
Molecular Cloud properties in nearby galaxies sampled by PHANGS ALMA and
MUSEThe impact of H II regions on Giant Molecular Cloud properties in nearby
galaxies sampled by PHANGS ALMA and MUSE

(Received ; accepted )

###### Abstract

Context. The final stages of molecular cloud evolution involve cloud
disruption due to feedback by massive stars, with recent literature suggesting
the importance of early (i.e. pre-supernova) feedback mechanisms.

Aims. We aim to determine whether feedback from massive stars in H II regions
has a measurable impact on the physical properties of molecular clouds at a
characteristic scale of $\sim$100 pc, and whether the imprint of feedback on
the molecular gas depends on the local galactic environment.

Methods. We identify giant molecular clouds (GMCs) associated with H II
regions for a sample of 19 nearby galaxies using catalogs of GMCs and H II
regions released by the PHANGS-ALMA and PHANGS-MUSE surveys, using the overlap
of the CO and $\mathrm{H\alpha}$ emission as the key criterion for physical
association. We compare the distributions of GMC and H II region properties
for paired and non-paired objects. We investigate correlations between GMC and
H II region properties among galaxies and across different galactic
environments to determine whether GMCs that are associated with H II regions
have significantly distinct physical properties to the parent GMC population.

Results. We identify trends between the $\mathrm{H\alpha}$ luminosity of an H
II region and the CO peak brightness and the molecular mass of GMCs that we
tentatively attribute to a direct physical connection between the matched
objects, and which arise independently of underlying environmental variations
of GMC and H II region properties within galaxies. The study of the full
sample nevertheless hides a large variability galaxy by galaxy.

Conclusions. At the $\sim$100 pc scales accessed by the PHANGS-ALMA and
PHANGS-MUSE data, pre-supernova feedback mechanisms in H II regions have a
subtle but measurable impact on the properties of the surrounding molecular
gas, as inferred from CO observations.

##  1 Introduction

Stellar feedback is a key process in galaxy evolution. Simulated galaxies
without feedback cannot reproduce the observed properties of galaxies: they
cool too rapidly, exhausting their gas supply through the rapid transformation
of gas into stars (e.g. Schaye et al., 2015). On cloud scales, stellar
feedback is often invoked to explain the low observed efficiency of star
formation in Giant Molecular Clouds (GMCs), which convert only $\sim 1\%$ of
their mass into stars per cloud free-fall time (Krumholz, 2014; Fujimoto et
al., 2016; Utomo et al., 2018; Grudić et al., 2019; Kim et al., 2021b). On
larger scales, stellar feedback contributes to driving galactic winds and
outflows (Hopkins et al., 2012; Bolatto et al., 2013). Stellar feedback
processes include protostellar jets and outflows, stellar winds, direct
radiation from stars that can ionize the gas, re-processed radiation from
interstellar dust, and supernovae (Krumholz et al., 2019; Chevance et al.,
2022b). While there is consensus about the overall importance of stellar
feedback, much work remains to be done to quantify the timescales,
efficiencies and relative importance of the various forms of feedback across
the diversity of galactic environments that host star formation.

The impact of stellar feedback on the surrounding molecular gas has been
investigated on $\sim$parsec scales in individual Galactic star-forming
regions (Pabst et al., 2019; Watkins et al., 2019; Barnes et al., 2020;
Großschedl et al., 2021; Luisi et al., 2021; Olivier et al., 2021) and in
Local Group targets (Lopez et al., 2011, 2014; McLeod et al., 2018, 2019,
2020, 2021). These studies underline the importance of pre-supernovae
feedback. Further afield, studies of star formation and feedback in the nearby
galaxy population have investigated the properties of H II regions and GMCs in
their galactic context (Barnes et al., 2021; Rosolowsky et al., 2021), the
efficiency of star formation within the molecular gas reservoir (Utomo et al.,
2018), the relative spatial configuration and intensity of the CO and
$\mathrm{H\alpha}$ emission (Schinnerer et al., 2019; Chevance et al., 2020;
Pan et al., 2022) and the inferred timescales for various phases of the star
formation process.

One outstanding question is whether feedback from star formation significantly
modifies the properties of their natal clouds, not only at the immediate
working surface, but also on the $\sim 50-100\,$pc scales on which global
cloud properties are typically measured. In this paper, we study the impact of
the H II regions on the surrounding molecular gas by exploring the properties
of molecular clouds that are spatially coincident with H II regions identified
in 19 nearby galaxies. This study leverages recent data from the PHANGS-ALMA
and PHANGS-MUSE surveys111http://www.phangs.org (Leroy et al., 2021a, b;
Emsellem et al., 2022), which have characterized several $10^{4}$ GMCs in 88
galaxies (Rosolowsky et al., 2021) and a similar number of H II regions in a
subset of 19 galaxies (Santoro et al., 2022). Our study is complementary to
the detailed, parsec-scale studies of individual star-forming regions that can
obtain estimates of individual feedback terms (Barnes et al., 2021, 2022),
since it provides an overview of how stellar feedback impacts the molecular
gas reservoir across a wide range of galactic environments and interstellar
conditions. By analysing the properties of neighbouring clouds and H II
regions, it likewise offers a complementary view to previous pixel-based
analyses that have robustly characterised the statistical relationship between
the molecular gas reservoir and star formation activity (most notably to
obtain evolutionary timescales of the star formation process, e.g. Chevance et
al., 2020, 2022a; Kim et al., 2022) but have so far been less focused on the
physical properties of the star-forming gas.

Table 1: Properties of our galaxy sample

Galaxy | Distance | Incl. | Morph. | Stellar Mass | Linear Res. | Linear Res.
---|---|---|---|---|---|---
|  $[$Mpc$]$ |  $[$deg$]$ |  | $[\log_{10}{M_{\sun}}]$ |  $[$ALMA, pc$]$ |  $[$MUSE, pc$]$
IC 5332 | 9.0 | 27 | SABc | 9.7 | 32 | 38
NGC 0628 | 9.8 | 9 | Sc | 10.3 | 53 | 44
NGC 1087 | 15.8 | 43 | Sc | 9.9 | 123 | 71
NGC 1300 | 19.0 | 32 | Sbc | 10.6 | 112 | 82
NGC 1365 | 19.6 | 55 | Sb | 11.0 | 131 | 109
NGC 1385 | 17.2 | 44 | Sc | 10.0 | 106 | 56
NGC 1433 | 18.6 | 29 | SBa | 10.9 | 98 | 82
NGC 1512 | 18.8 | 42 | Sa | 10.7 | 115 | 114
NGC 1566 | 17.7 | 30 | SABb | 10.8 | 95 | 69
NGC 1672 | 19.4 | 43 | Sb | 10.7 | 182 | 90
NGC 2835 | 12.2 | 41 | Sc | 10.0 | 50 | 68
NGC 3351 | 10.0 | 45 | Sb | 10.4 | 70 | 51
NGC 3627 | 11.3 | 57 | Sb | 10.8 | 89 | 58
NGC 4254 | 13.1 | 34 | Sc | 10.4 | 113 | 57
NGC 4303 | 17.0 | 24 | Sbc | 10.5 | 152 | 64
NGC 4321 | 15.2 | 38 | SABb | 10.7 | 126 | 86
NGC 4535 | 15.8 | 45 | Sc | 10.5 | 119 | 43
NGC 5068 | 5.2 | 36 | Sc | 9.4 | 26 | 26
NGC 7496 | 18.7 | 36 | Sb | 10.0 | 152 | 81

Table references: (Anand et al., 2021), (Emsellem et al., 2022), (Lang et al.,
2020), (Leroy et al., 2021a).

Section 2 summarizes the properties of the PHANGS-ALMA and PHANGS-MUSE data,
and of the GMC and H II region catalogs derived from those data. Section 3
presents the method that we use to match GMCs with H II regions. Section 4
compares the properties of matched GMC/H II-regions to the general population
of GMCs and H II regions in our sample galaxies. In Section 5, we investigate
the correlations between GMC properties and H II region luminosity for the
matched GMC/H II-regions. In Section 6, we investigate whether the effects of
local radiative feedback can be robustly distinguished from co-variations of
GMC and H II region properties within different galactic environments. Section
8 discusses the results and Section 9 summarizes our findings. Appendices A to
E present supplemental figures and tests of our methodology that complement
the main content of the article. For instance, Appendix D examines the
correlations between GMC properties and H II region luminosity in individual
galaxies.

##  2 Data and catalogs

In this paper, we compare the GMC and H II region populations of 19 galaxies
in the PHANGS sample with both ALMA CO(2$-$1) (Leroy et al., 2021a, b) and
MUSE $\mathrm{H\alpha}$ imaging (Emsellem et al., 2022). Table 1 summarizes
the properties of our 19 target galaxies, which are adopted from the PHANGS
Sample Table v1.6 (Leroy et al., 2021b). For the analysis in Section 6, we use
estimates for the local stellar surface density presented by Sun et al.
(2022). In this section, we summarize the key properties of the PHANGS-ALMA
and PHANGS-MUSE data and of the GMCs and H II-region catalogs derived from
those data.

###  2.1 PHANGS-ALMA CO (2-1) data

We analyze GMCs that are identified in the PHANGS-ALMA survey of nearby
galaxies (Leroy et al., 2021a, b). The GMC catalogs that we use are derived
from the combined 12m+7m+TP PHANGS-ALMA CO(2$-$1) data cubes, which have a
spectral resolution of $2.5\mathrm{\,km\,s^{-1}}$ and a typical angular
resolution of ${\sim}1^{\prime\prime}$ to $1.5^{\prime\prime}$, corresponding
to linear resolutions between $\sim 30$ and $\sim 180$ pc at the distance of
our target galaxies. These combined cubes are sensitive to emission from all
spatial scales. The PHANGS-ALMA observations were designed to target the
region of active star formation in each galaxy, with a field of view that
typically extends to $R\sim 0.3R_{25}$. The mean $1\sigma$ sensitivity of the
cubes is $\sim 0.2$ K per spectral channel. An overview of the PHANGS-ALMA
survey science goals, observing strategy, and data products is presented in
Leroy et al. (2021b). A detailed description of the PHANGS-ALMA data
processing, including calibration, imaging and combination steps, is presented
in Leroy et al. (2021a). The PHANGS-ALMA CO(2$-$1) data cubes are available
from the PHANGS team website 222http://www.phangs.org, the ALMA archive
333https://almascience.eso.org/alma-data/lp/PHANGS/ and the Canadian Astronomy
Data Center (CADC)444
https://www.canfar.net/storage/list/phangs/RELEASES/PHANGS-ALMA/.

###  2.2 PHANGS-ALMA GMC catalogs

We use the public GMC catalogs released by PHANGS-ALMA on the PHANGS team
website. These catalogs were generated using
pycprops555https://github.com/phangsteam/pycprops/, which is a python
implementation of the cprops algorithm originally presented in Rosolowsky &
Leroy (2006). A detailed description of the pycprops methodology, including
its application to a subsample of 10 PHANGS-ALMA CO(2$-$1) data cubes, is
presented in Rosolowsky et al. (2021). The full set of GMC catalogs for 88
galaxies in the PHANGS-ALMA survey is presented in a companion paper by Hughes
et al (in prep). We refer the reader to those papers for a complete
description of the PHANGS-ALMA GMC catalogs, but briefly summarize here the
catalog generation process and the derivation of the key quantities that we
use in our analysis.

Catalog generation by pycprops proceeds in two main stages. First, significant
emission in the data cube is identified. The emission is then segmented into
distinct structures (‘clouds’ for simplicity) by identifying significant local
maxima and uniquely assigning all the emission to each of these maxima. The
criteria used to identify and segment the significant emission in the PHANGS-
ALMA CO(2$-$1) data cubes are explained in detail by Rosolowsky et al. (2021).
In short, the decomposition for the PHANGS-ALMA GMC catalogs proceeds by
searching for regions larger than the telescope beam with intensities
$>2\sigma$ that are contiguous in position and velocity with $>4\sigma$ peaks.
Compactness is strongly preferred, such that local maxima are rarely merged
into larger structures.

In a second step, the emission associated with each cloud is characterized,
and physical properties of the cloud are determined. pycprops uses moments of
the emission to estimate cloud properties. The moment-based quantities are
corrected for the effects of sensitivity and the finite resolution of the data
before translating them into estimates of physical quantities. In this paper,
we investigate correlations involving the following GMC properties:

  * •

The CO peak temperature, $T_{\mathrm{peak}}$. This is the CO brightness
temperature, measured at the brightest voxel within the cloud boundary.

  * •

Cloud molecular mass, $M_{\mathrm{CO}}$. We use the CO-based GMC mass
estimate, which is obtained by multiplying the cloud luminosity
$L_{\mathrm{CO}}$ by a CO-to-H2 conversion factor, $\alpha_{\mathrm{CO}}$. The
cloud luminosity is the sum of the intensity within the cloud boundary, and is
related to the mass via $M_{\mathrm{CO}}=\alpha_{\mathrm{CO}}L_{\mathrm{CO}}$.
The PHANGS-ALMA GMC catalogs implement the $\alpha_{\mathrm{CO}}$ calibration
of Sun et al. (2020), with an adopted CO($2-1$) to CO($1-0$) line ratio
$R_{21}=0.65$. The $\alpha_{\mathrm{CO}}$ adopted for each cloud depends only
on the local metallicity, which is estimated according to the global mass-
metallicity scaling relation of Sánchez et al. (2019) and the universal
metallicity gradient of Sánchez et al. (2014). We refer the reader to Sun et
al. (2020) for a more complete discussion. Due to the restricted range of
metallicities of our sample galaxies, $L_{\mathrm{CO}}$ and $M_{\mathrm{CO}}$
are effectively interchangeable for our analysis in this paper.

  * •

Cloud surface density, $\Sigma_{\mathrm{mol}}$. We estimate the typical
molecular gas surface density within the cloud as
$\Sigma_{\mathrm{mol}}=M_{\mathrm{CO}}/(2{\pi R^{2}})$.

  * •

Cloud radius at FWHM, $R$. The cloud size is estimated from the intensity-
weighted second moments over the two spatial axes of the cube (i.e. the
spatial variances $\sigma_{x}^{2}$ and $\sigma_{y}^{2}$), and an intensity-
weighted covariance term $\sigma_{xy}$. These measurements are used to
determine the major and minor axes of the emission distribution and the
cloud’s position angle. The major and minor axis measurements are corrected
for the finite sensitivity and angular resolution of the data,
$\sigma_{\mathrm{maj,corr}}$ and $\sigma_{\mathrm{min,corr}}$. The cloud
radius is then calculated as
$R=\eta\sqrt{\sigma_{\mathrm{maj,corr}}\sigma_{\mathrm{min,corr}}}$, with
$\eta=\sqrt{2\ln 2}=1.18$.

  * •

The characteristic turbulent linewidth at a fiducial scale of 1 pc,
$\sigma_{0}$. To estimate $\sigma_{0}$, we assume that the turbulent structure
function within all clouds has an index of 0.5 (e.g., Heyer & Brunt, 2004). It
is related to the observed cloud-scale velocity dispersion $\sigma_{v}$
according to
$\sigma_{0}=\sigma_{v}/\sqrt{R_{\mathrm{3D}}/\mathrm{1\leavevmode\nobreak\
pc}}.$ Here, $\sigma_{v}$ is the square root of the intensity-weighted
variance of the emission along the spectral axis within the cloud boundary,
and $R_{\mathrm{3D}}$ is an estimate for the three-dimensional mean radius of
the cloud. $R_{\mathrm{3D}}$ differs from the projected FWHM size $R$. In
practice,

$R_{\mathrm{3D}}=\left\\{\begin{array}[]{rl}R&;\quad R\leq H/2\\\
\sqrt[3]{\frac{R^{2}H}{2}}&;\quad R>H/2\leavevmode\nobreak\
,\end{array}\right.$ (1)

where $H=100$ pc is the assumed scale-height of the molecular gas in a
galactic disk (Malhotra, 1994).

  * •

Virial parameter of the whole cloud, $\alpha_{\rm vir}$. This provides an
estimate of the relative strength of the gravitational binding energy versus
the kinetic energy of a molecular cloud. The PHANGS-GMC catalogs adopt
$\alpha_{\rm vir}=10\times\sigma_{v}^{2}R_{3D}/(GM_{\rm CO})$.

  * •

Free-fall collapse time, $\tau_{\mathrm{ff}}$, which is derived from a
combination of the above quantities, as

$\tau_{\mathrm{ff}}=\sqrt{\frac{3\pi}{32G\rho}}=\sqrt{\frac{\pi^{2}R_{\mathrm{3D}}^{3}}{4GM_{\rm
CO}}}\leavevmode\nobreak\ .$ (2)

The factor of 4 in the denominator arises from the adopted two dimensional
Gaussian cloud model, which measures the density assuming half the mass is
contained within the FWHM cloud size.

###  2.3 PHANGS-MUSE Data Description

We use observations from the Very Large Telescope/Multi Unit Spectroscopic
Explorer (VLT/MUSE; Bacon et al. 2010), which is ideally suited for surveying
nearby galaxies given its wide $\sim$1 arcmin field-of-view and broad
wavelength coverage (4800-9300 Å) at moderate (R$\sim$2000) spectral
resolution. The PHANGS-MUSE survey (PI: Schinnerer; Emsellem et al. 2022)
provides optical integral field unit maps across the central star-forming
disks of 19 nearby (D$<$19 Mpc, 1″$<$100 pc) spiral galaxies with low to
moderate inclination (¡60∘). The region surveyed in each galaxy is matched to
the PHANGS-ALMA coverage, requiring several MUSE pointings per galaxy.

The typical seeing during our observations was 0.8″ in R-band, which
corresponds to a typical physical scale of $\sim$70 pc for our galaxies. This
is well-matched to the PHANGS-ALMA observations, and is adequately sampled by
the 0.2″ pixel size. To create a datacube corresponding to the full observed
field of view for each galaxy, the data for individual pointings were first
convolved such that the PSF is uniform for each galaxy before combination. We
fit all stellar continuum emission (spatially binned to a S/N¿35)
simultaneously with the emission lines (where we fit each individual pixel) on
the resulting combined cube. The resulting maps of the H$\alpha$ line emission
are then used to identify the individual H II regions which are used in this
work. Full details of the data reduction and production of emission line maps
for PHANGS-MUSE are presented in Emsellem et al. (2022).

###  2.4 PHANGS-MUSE H II region catalogs

To locate and characterize the H II regions, we use the nebular catalogs
compiled by Santoro et al. (2022) and described fully in Groves et al. (2023),
which are constructed by applying the HIIphot algorithm (Thilker et al., 2000)
to the PHANGS-MUSE H$\alpha$ line maps.

The key physical properties of the identified objects in the catalogs are
derived using integrated spectra within the footprint of each region, assuming
Gaussian line profiles and correcting for the instrumental dispersion along
the spectral axis at location of the $\mathrm{H\alpha}$ line ($\sim$49 km s-1,
Bacon et al., 2017). To select the H II regions from the nebular catalogs, we
select regions that have properties consistent with photo-ionization by
massive stars by applying the [O iii]/H$\beta$ vs [N ii]/H$\alpha$ (Kauffmann
et al., 2003) and [O iii]/H$\beta$ vs [S ii]/H$\alpha$ (Kewley et al., 2001)
demarcations, excluding any nebulae where any of these lines has a signal-to-
noise ratio of less than 3\. We further exclude nebulae that overlap with
foreground stars or overlap with the edge of our fields.

In this paper, we work primarily with the total H$\alpha$ luminosity,
$L(\mathrm{H\alpha})$ and size of the H II regions. The H II region size is
defined as the circularized radius equivalent to the pixel area found in each
H II region footprint. The total H$\alpha$ luminosity is obtained from the sum
of the H$\alpha$ within the H II region footprint. The $L(\mathrm{H\alpha})$
measurements that we use are corrected for dust extinction: a global
extinction correction for each galaxy is applied to account for foreground
extinction in the Milky Way (Schlafly & Finkbeiner, 2011), and an individual
extinction correction for each H II region that accounts for the dust within
the target galaxy is determined using the observed Balmer decrement
(H$\alpha$/H$\beta$). The latter assumes a Milky Way extinction curve
(O’Donnell, 1994) with $R_{\mathrm{V}}=3.1$. We refer the reader to Groves et
al. (2023) for a more detailed explanation of the H II region property
definitions and of the corrections that are applied for, e.g., extinction and
instrumental resolution. As described in the catalog paper, derived physical
quantities including metallicity (Pilyugin & Grebel, 2016), H$\alpha$ line
width, and $\Sigma SFR$, are briefly considered in our analysis, but not
explored in depth.

##  3 A method to match GMCs and H II regions

Figure 1: Example results of the algorithm used to match GMCs (blue) and H II
regions (red) for the same field-of-view. The background image is
$\mathrm{H\alpha}$ line emission from a spiral arm segment in NGC 4254. The
right and left panels show the matches obtained when the area of the GMC/H II
overlap region is at least 10% and 70%, respectively, of projected area of a
GMC. Imposing a higher overlap percentage leads to fewer identifications of
matched GMC/H II-regions. Table 2: The fraction of GMCs and H II regions that
are identified as matched objects across our sample.

| GMCs | H II regions
---|---|---
MOP | By Number | By Mass | By Number | By Luminosity
% | % | % | % | %
10 | 38.8 | 41.4 | 19.5 | 48.0
40 | 10.4 | 11.6 | 3.8 | 27.8
70 | 2.8 | 2.6 | 1.0 | 10.9
666The fractions are indicated by number relative to the total number of GMCs
(10866) and H II regions (29904), and their contribution to the combined
molecular gas mass ($5.1\times 10^{10}M_{\odot}$) and $\mathrm{H\alpha}$
luminosity ($5.4\times 10^{42}$erg s-1) of the galaxies in our sample. Results
are reported for a MOP of 10, 40 and 70% (see main text).

Our science goal is to determine whether H II regions influence the physical
properties of GMCs. In this section, we describe the method that we use to
determine whether a GMC and H II region are physically associated.
Specifically, we work with catalogued measurements of the radial velocity of
each GMC and H II region, and the pixel masks that are generated during the
cataloging process to identify the boundaries and projected area of each
region. The key criterion in our matching method is the spatial overlap
between the projected areas of the GMCs and H II regions. We use the pixel
masks of the GMC and H II regions to identify and measure regions of overlap.
The H II region masks are reprojected using nearest-neighbour interpolation to
match the astrometry and pixelization scheme of the GMC masks. We superpose
the binary masks of each galaxy to identify pixels that are common to both
GMCs and H II region masks. We construct a list of the GMCs that are members
of regions with common pixels and calculate the percentage of the projected
area of each GMC that is also present within an H II region footprint. We
consider an H II region to be paired with a GMC when it occupies more than a
minimal overlap percentage, MOP, of the GMC’s projected area. We do not,
however, consider the percentage of the H II region covered by the GMC. This
makes our pairing method asymmetric. This is physically motivated in the sense
that we are searching for potential signatures of H II region feedback on GMC
properties at a scale of $\sim 100\,$pc. We thus prioritise the detection of
pairs where the H II region covers a significant fraction of the GMC area.
From our initial list of paired regions, we exclude candidate pairs where the
difference between the radial velocity of the GMC and H II region is larger
than 10$\mathrm{\,km\,s^{-1}}$.

We found it necessary to refine our basic approach for the relatively common
situation where a single GMC has pixels that overlap multiple H II regions (or
vice versa). Of the total number of GMCs that share common pixels with H II
regions, approximately half (47%) overlap with more than one H II region. For
H II regions, the fraction is smaller (19%). We decided to allow each GMC to
have more than one associated H II region, but require that H II regions be
uniquely identified with a GMC, in practice assigning it to the GMC that is
most covered by the H II region’s projected area. We discuss the rationale for
this approach and compare it to other possible choices, e.g., using only
exclusive GMCs-H II region pairs, in Appendix A.1.

Our matching approach is illustrated in Fig. 1. This figure shows the GMCs and
H II regions within a spiral arm region of NGC 4254. The left panel
illustrates the results for a MOP of 10%: here, GMC B is uniquely matched with
H II region 3, while GMC A is matched with both H II regions 1 and 2. The
right panel illustrates a MOP of 70%: here, only GMCs A and B remain, and now
GMC A is uniquely matched with H II region 2\. For most of the analysis in
this paper, we set MOP=40%. Using a higher MOP value would allow us to
pinpoint the GMCs where H II region feedback is likely to be the most
pronounced, potentially making it easier to identify any signatures of
feedback on the cloud properties. However, imposing higher MOP values would
also reduce the number of identified pairs, making any conclusions less
general. Our adopted MOP of 40% is thus a compromise, based on both physical
and practical considerations. We present several tests of our method, and
justify our choice for several user-defined parameters in Appendix A.3.

##  4 Properties of matched GMC-H II regions

Figure 2: Probability density functions of key physical properties of H II
regions and of GMCs. Top, from left to right: extinction-corrected
$\mathrm{H\alpha}$ luminosity and size. Bottom, from top left to bottom right:
CO luminosity, size, peak temperature, velocity dispersion, surface density,
characteristic turbulent linewidth, free-fall time and virial parameter. The
distribution for the full GMC (H II region) population is shown in red, while
the matched GMCs/H II regions adopting a MOP of 10, 40 and 70% are shown in
blue, green and gold respectively.

We applied our GMC-H II region matching algorithm to the 19 galaxies that are
common to the PHANGS-ALMA and PHANGS-MUSE surveys. In NGC 7496 and IC5332, our
matching strategy failed to identity any matched GMC and H II region for some
or all of the minimum overlap percentage thresholds that we used. For the rest
of this paper, we therefore present results for the remaining 17 galaxies. In
this section, we compare the properties of matched GMC-H II regions with the
typical properties of their parent distributions, as well as the impact of the
adopted MOP on the detection statistics of matched regions and the property
distribution shapes.

###  4.1 Detection of matched GMC-H II regions

Table 2 summarizes the overall results of our matching strategy, i.e. the
number of identified GMC-H II region pairs for MOP thresholds of 10, 40 and
70%, and the fraction of CO and $\mathrm{H\alpha}$ luminosity that the paired
objects represent in each case. Not surprisingly, fewer matched GMC-H II
regions are identified at higher MOP thresholds. Matched GMC-H II regions
barely exceed 50% of their parent populations, even using a low MOP threshold
of 10%. This is qualitatively consistent with previous studies that found a
significant reservoir of quiescent CO-bright gas in galaxies and a relatively
short timescale for its disruption by stellar feedback (e.g. Schinnerer et
al., 2019; Chevance et al., 2022a). Measured across our full sample, for a MOP
threshold of 10%, the CO luminosity associated with GMCs in matched GMC-H II
regions is $41$%, which roughly corresponds to the number of clouds identified
within these regions $39$%. While relatively fewer in number, the H II regions
associated with matched GMC-H II regions make a more significant contribution
to the total $\mathrm{H\alpha}$ luminosity (19.5% in number vs 48% in flux for
a MOP threshold of 10%). Table 4 in Appendix B presents the detection
statistics and contribution to total CO and $\mathrm{H\alpha}$ luminosity of
the matched GMC-H II regions for individual galaxies.

###  4.2 Properties of matched GMC-H II regions compared to their parent
distributions

Figure 2 presents the empirical probability density functions (PDF) of the
size and luminosity of the H II regions and of several physical properties of
GMCs (size, luminosity, peak temperature, velocity dispersion, surface
density, characteristic turbulence linewidth, virial parameter, and free-fall
time). The PDFs were computed using a kernel density estimation method. In
each panel, the distribution of the parent population is shown in red, while
the distribution for matched objects using MOP criteria of $10$, $40$ and
$70$% are shown in blue, green and gold respectively.

We conducted Kolmogorov-Smirnov tests (scipy.stats.kstest) and Anderson-
Darling tests (scipy.stats.anderson_ksamp) to assess whether the differences
in the distributions in Fig. 2 are statistically significant. If the influence
of H II regions on GMCs is localized, then we expect that the trends in Fig. 2
will become more pronounced as we increase the adopted MOP. If the trends
instead result from the covariation of GMC and H II region properties that are
themselves due to larger scale effects (e.g., the co-location of clouds and H
II regions in spiral arms), then we would expect the distributions to be less
sensitive to the adopted minimum overlap percentage.

Figure 2d shows that matched GMCs are on average smaller than the parent
population (mean radius of 45 pc vs 69 pc for a MOP threshold of 70%), whereas
Fig. 2b shows that matched H II regions are on average bigger than the parent
population. This difference is more pronounced for higher MOP thresholds and
is mostly due to the asymmetry of our matching criteria. The effect is larger
for the H II region sizes than for the GMC sizes. This is because our input
GMC catalogs only contain resolved sources, while the H II region catalogs
contain a large fraction (80%) of point sources.

GMCs in the matched populations exhibit a larger fraction of clouds with high
CO peak brightness than the overall GMC population, as shown in Fig. 2e. This
cannot be due to our matching strategy, since GMCs generally show a marginally
positive or no trend between their size and CO peak brightness. The
luminosities of the GMCs and H II regions follow the size trends since these
properties are correlated to first order. A population of luminous GMCs is
still evident in the matched populations, however, even though there are
relatively fewer large GMCs: In Fig. 2c the $MOP=70$% (gold) population lies
clearly above the parent GMC population (red) at high CO luminosity, even
though there are more large GMCs in the parent population. These trends in
size and brightness reinforce each other to yield a clear progression in the
typical surface density and inferred free-fall time (Figs. 2g and 2i) of the
matched GMCs, such that GMCs in the matched population identified with
$MOP=70$% have roughly twice the surface density of the average GMC in the
parent population, while the inferred typical free-fall time (which varies
inversely with the surface density) of the matched GMCs is correspondingly
shorter.

The distributions of cloud properties that involve the GMC velocity dispersion
are more difficult to distinguish. In Fig. 2f and j, the average velocity
dispersion and virial parameter of the matched GMCs are slightly smaller than
those of the parent population, which is to be expected from their smaller
typical size and slightly higher brightness. If the variation in the velocity
dispersion was due purely to the cloud’s smaller size and the Larson size-
linewidth relation, then we would expect the distributions of the
characteristic turbulent linewidth at a fiducial scale of 1 pc to be the same
for the matched and parent GMC populations. For the higher MOP thresholds, we
instead see in Fig. 2h a slight shift towards a larger average characteristic
turbulent linewidth, and a larger fraction of clouds with higher
characteristic turbulent linewidths, suggesting we may statistically detect a
contribution to the cloud linewidth in the GMCs with matched H II regions
above and beyond the effect of cloud size. Potentially, this could reflect a
slight increase of the turbulence within GMCs that closely associated with H
II regions. The difference is small however (a shift of
$<0.1$$\mathrm{\,km\,s^{-1}}$ pc-0.5 in the mean value).

The results of the tests that we conducted to determine whether the observed
differences in the distributions are statistically are listed in Table 5 and
Table 6. While the Anderson-Darling test is less sensitive to outliers
compared to the Kolmogorov-Smirnov test, both tests give similar results. For
a minimum overlap percentage of 40% or above, all the distributions of the
matched GMCs properties are statistically different from their parent
distributions. This is also true for the characteristic turbulent linewidth,
which shows only a small variation in the distribution mean for different
adopted values of the MOP.

###  4.3 Intermediate summary

  * •

Matched GMC/H II-regions represent a non-negligible fraction of the overall
GMC population in our sample galaxies. For a 10% minimum overlap percentage,
40% of the GMCs and one fifth of the H II regions are matched, and these
matched pairs represent about 50% of the total CO and $\mathrm{H\alpha}$
luminosity that arises from the catalogued objects.

  * •

All observed trends in the GMC property distributions are significant
according to standard statistical tests.

  * •

Matched GMCs have a smaller size and higher typical CO peak temperature than a
GMC from the overall population. The relative small size of the matched GMCs
likely derives from the asymmetry of our adopted matching strategy.

  * •

The observed distributions suggest that the GMCs matched with H II regions are
denser than a typical GMC. The larger typical surface density is at least
partly due to their higher intrinsic brightness at the pixel-level, as
reflected in their higher typical peak CO brightness values.

  * •

The virial parameter and free-fall time of matched GMCs have lower average
values than the overall GMC population, which follows from the observed trends
of their luminosity, size and velocity dispersion.

  * •

The characteristic turbulent linewidth of matched GMCs is slightly higher than
for a typical GMC when a high ($\geq 40$%) MOP threshold is used.

For the rest of the paper, we focus on the mass, the peak brightness, the
characteristic turbulent linewidth and the molecular gas surface density of
the GMCs. The three latter ones are intensive cloud properties that are often
invoked by theories to explain the star formation rate and feedback, and do
not scale directly with the GMC size by construction.

##  5 Correlations between matched GMC properties and the $\mathrm{H\alpha}$
luminosity of the H II regions

Figure 3: Correlation matrix of the different GMC and H II region properties
investigated. The top left blue square shows the correlations between GMC
properties considering the entire sample. The bottom right red square shows
the correlations between the properties of H II regions considering the entire
sample. The bottom left black rectangle shows the strengths of the
correlations between matched GMC and H II regions for a MOP of 70%. Figure 4:
Scatter plots of various GMC properties as a function of the
$\mathrm{H\alpha}$ luminosity for three different MOP of the H II/GMC pairs:
10% for the left column, 40% for the middle one, and 70% for the right one.
The GMC properties are from top to bottom: the molecular mass, the
characteristic turbulent linewidth, the surface density and the peak
temperature. The black solid lines show a power law fit and its uncertainty
for each scatter plot. The dashed lines show the $\pm 3\sigma$ levels from the
fitted line. The solid red line represents the linear regressions obtained in
the leftmost column, for comparison. The fitted line properties are displayed
on the bottom right corner of each panel.

In this section, we investigate whether there are significant correlations
between the properties of the matched GMCs and H II regions for our maximum
MOP threshold (70%). We then investigate how the adopted MOP threshold
influences the observed correlations between GMC and H II region properties,
focusing on the $\mathrm{H\alpha}$ luminosity of the H II region as our
primary independent variable, and describe two simple randomization tests that
we used to determine whether the observed correlations could arise by chance.
We characterize any observed correlations using a simple power-law fit and a
goodness-of-fit statistic, which we present immediately below.

###  5.1 Characterizing a power law fit

We characterize correlations by computing an ordinary least square power-law
fit to the observed trends and the associated $\pm 3\sigma$ levels from the
fitted line. To assess the quality of the correlation, we compute the $R^{2}$
coefficient, defined as

$R^{2}=1-\frac{\sum_{i}(Y_{i}-\langle
Y\rangle)^{2}}{\sum_{i}(Y_{i}-F_{i})^{2}},$ (3)

where $Y_{i}$ represents the logarithm of the studied property for GMC $i$,
$\langle Y\rangle$ is the mean of the logarithm of this property over the
studied sample, and $F_{i}$ represents the values predicted by our fit. The
numerator is proportional to the variance of the logarithm of the studied GMC
property, while the denominator is proportional to the variance of the
logarithm of the property about the power law fit of $\mathrm{H\alpha}$
luminosity of the H II region. A $R^{2}$ value of $1$ indicates that the
correlation is exactly linear in log-log space. A $R^{2}$ value of $0$
indicates that the predicted properties $Y$ are independent of the value of
the X axis variable. In other words, the higher the $R^{2}$ value, the better
the GMC property is predicted by a power law model from the $\mathrm{H\alpha}$
luminosity of the H II region.

We also compute confidence intervals on the $R^{2}$ coefficients through a
standard bootstrap approach. We refit a power law using data samples that were
constructed by selecting $N$ pairs from the original data with replacement
where $N$ was the number of original pairs: On average, 36% of the pairs are
different, implying that pairs are typically duplicated $\sim 2$ to 3 times.
We repeat this operation 10 000 times, each time computing the $R^{2}$
coefficient between the two quantities of interest. We then compute the 95%
confidence interval associated with the distribution obtained from these 10
000 trials.

###  5.2 Correlations between GMC and H II region properties

We first explore the correlations between the properties of matched GMC and H
II regions. We compute the $R^{2}$ coefficient between 1) GMC properties, 2) H
II region properties, and 3) properties of GMCs and H II regions for matched
pairs. Figure 3 presents the correlation matrices, which are sorted to display
the strongest correlations in the top left corner of each matrix as far as
possible. It shows that the virial parameter and free-fall time of GMCs are
essentially uncorrelated with any of the H II region properties. In contrast,
all other properties of the matched GMCs exhibit some degree of correlation
with the properties of their associated H II regions. The $\mathrm{H\alpha}$
luminosity and star formation rate are highly correlated with the GMC
luminosity and mass. Moderate correlations with these H II region properties
are observed for the GMC size and velocity dispersion, with weaker
correlations obtained for the GMC surface density, characteristics turbulent
linewidth and CO peak temperature. The H II region velocity dispersion,
metallicity, and stellar surface density exhibit correlations with the CO
luminosity, molecular mass, size and velocity dispersion of the associated
GMCs, but are mostly uncorrelated with the molecular surface density,
characteristic turbulent width and CO peak temperature.

The CO luminosity and mass are tightly correlated, justifying that we use them
interchangeably in the following. The GMC size and velocity dispersion are
also well-correlated with the molecular mass. These correlations reflect the
well-known Larson’s scaling relations (Larson, 1981). The characteristic
turbulent linewidth shows a strong positive correlation with the velocity
dispersion. As expected from their definitions, the free-fall time follows the
molecular gas surface density.

The $\mathrm{H\alpha}$ luminosity is correlated with all the other H II region
properties that we consider, albeit only weakly with the metallicity and local
stellar surface density. Due to the additional strong covariance between the
$\mathrm{H\alpha}$ luminosity and the size, star formation rate and velocity
dispersion of the H II regions that we observe in Fig. 3, we restrict our
comparison to studying GMC properties as a function of the H II region
$\mathrm{H\alpha}$ luminosity for the remainder of the paper.

###  5.3 Evolution with the minimum overlap percentage

Figure 4 presents scatter plots of the GMC properties as a function of the
$\mathrm{H\alpha}$ luminosity for three different MOP used to identify the
GMC/H II-region pairs: 10, 40, and 70%. To help visualize how the correlation
changes with the MOP that we adopt, the solid red lines indicate the power-law
fit for a minimum overlap percentage of 10% in all panels.

The $\mathrm{H\alpha}$ luminosities of the catalogued H II regions in our
sample cover about five orders of magnitude, while the properties of matched
GMCs cover a smaller dynamic range: $\sim 1.5$ dex for peak temperature, $\sim
2$ dex for the characteristic turbulent linewidth, up to $\sim 3$ dex for the
surface density and molecular mass. The plots illustrate the correlations
indicated by the matrix in Fig. 3: a good correlation between the GMC mass and
the $\mathrm{H\alpha}$ luminosity of its associated H II region at all MOP
thresholds, but weaker and more scattered relationships for the intensive
cloud properties, especially at high MOP values. For a MOP threshold of 40%,
the $R^{2}$ values range from 0.12 for the peak brightness to 0.55 for the GMC
molecular mass, indicating that GMC properties do indeed show a positive
correlation with the $\mathrm{H\alpha}$ luminosity of the H II region. The
power-law indices that we obtain range from 0.20 for the GMC surface density
to 0.58 for the molecular mass. The GMC peak brightness and characteristic
turbulent linewidth show intermediate power-law indices of 0.12 and 0.14,
respectively. There is, however, structure in the plots in Fig. 4 that is not
completely captured by a simple power-law fit, and which is most evident for
the correlations involving intensive GMCs properties when the GMC-H II-region
pairs are identified using higher ($\geq 40\%$) MOP thresholds. Some of this
structure in the correlation may be due to galactic environment, as we discuss
in Section 6.

Figure 5: $R^{2}$ (top) and power law index (bottom) of the fits of various
GMC properties (as a function of the $\mathrm{H\alpha}$ luminosity of the
matched H II region) against the MOP. The fitted GMC properties are from left
to right: the molecular mass, the peak temperature, the surface density, and
the characteristic turbulent linewidth. Blue (resp. red) lines show an
increase (resp. decrease) of the $R^{2}$ coefficient with the minimal overlap
percentage. The uncertainty intervals are computed using a standard bootstrap
method.

In Fig. 5 we plot how the $R^{2}$ coefficients and the power-law slope of the
observed correlations depend on the adopted MOP. When increasing the minimum
overlap percentage from 10 to 70%, we find that the correlation between GMC
molecular mass and the $\mathrm{H\alpha}$ luminosity of the matched H II
regions clearly exhibits a higher $R^{2}$ coefficient and a steeper power-law
slope. The correlation with the CO peak temperature on the other hand
marginally weakens with increasing MOP. The correlation of the GMC surface
density and the characteristic turbulent linewidth with $\mathrm{H\alpha}$
luminosity of the matched H II regions show no dependence (within the
confidence interval) on the adopted MOP.

###  5.4 Randomization tests to check whether the observed correlations are
genuine

We conducted two tests to investigate whether the observed correlations
reflect a potential physical influence of the H II regions on the GMCs. First,
we randomized the $\mathrm{H\alpha}$ luminosities of the H II regions in the
PHANGS-MUSE catalog, holding their positions and sizes constant. The
properties and positions of the GMCs were also left unchanged. We then
computed the $R^{2}$ coefficients for the same set of correlations described
above. We performed this randomization test 10 000 times in order to gauge the
typical range of $R^{2}$ values that might arise randomly. We obtained $R^{2}$
values of 0 to 0.04 for all the properties, i.e., lower than the lowest
$R^{2}$ value (0.15) that we obtained for the actual correlations (see Fig.
14).

To assess whether the observed correlations are an artifact of our matching
strategy, we next randomized both the sizes and the $\mathrm{H\alpha}$
luminosities of the H II regions, regenerated the list of matched GMC/H II
regions, and constructed the same set of correlations as described above. This
yields typical $R^{2}$ values of 0 to 0.003, much lower than 0.15 (see Fig.
15). We note that completely randomizing the positions of the H II regions is
unfeasible, since the projected area occupied by H II regions and GMCs
represents only 11.2% and 10.6% of the observed field-of-view. Assigning
random positions to the GMCs or H II regions would thus result in no GMC/H II-
region pairs being detected.

Table 3: Number and luminosity of GMCs and H II regions per galactic
environment of the studied sample, for a MOP of 40%.

Galactic Environment | GMC | H II regions | CO Luminosity |  $\mathrm{H\alpha}$ Luminosity
---|---|---|---|---
# | %aa$a$Proportion of the matched GMC/H II region pairs that are in a specific region with respect to the total number of pairs. | # | %aa$a$Proportion of the matched GMC/H II region pairs that are in a specific region with respect to the total number of pairs. | %bb$b$Proportion of the luminosity for the matched GMC/H II region pairs that are in a specific region with respect to the total luminosity of the matched GMG/H II regions. | %bb$b$Proportion of the luminosity for the matched GMC/H II region pairs that are in a specific region with respect to the total luminosity of the matched GMG/H II regions.
Nucleus & Bars | 113 | 10.1 | 115 | 10.2 | 17.6 | 19.7
Arms | 605 | 53.4 | 610 | 53.4 | 60.2 | 54.7
Inter-arms & Outer Disk | 414 | 36.5 | 417 | 36.4 | 22.3 | 25.6
All environments | 1121 | 100.0 | 1142 | 100.0 | 100.0 | 100.0

777

Galactic Environment | GMC | H II regions | CO Luminosity |  $\mathrm{H\alpha}$ Luminosity
---|---|---|---|---
Matched | Total | Matched | Matched | Total | Matched | Matched | Matched
| # | # | %aa$a$Proportion of the matched GMC/H II region pairs that are in a specific environment with respect to the total number of GMCs or H II regions in this environment. | # | # | %aa$a$Proportion of the matched GMC/H II region pairs that are in a specific environment with respect to the total number of GMCs or H II regions in this environment. | %bb$b$Proportion of the luminosity for the matched GMC/H II region pairs that are in a specific environment with respect to the total luminosity of the GMCs or H II regions in this environment. | %bb$b$Proportion of the luminosity for the matched GMC/H II region pairs that are in a specific environment with respect to the total luminosity of the GMCs or H II regions in this environment.
Nucleus & Bars | 113 | 2509 | 4.5 | 115 | 2710 | 4.2 | 5.2 | 12.8
Arms | 605 | 4405 | 13.6 | 610 | 12033 | 5.1 | 19.6 | 41.4
Inter-arms & Outer Disk | 414 | 3951 | 10.3 | 417 | 15161 | 2.7 | 10.0 | 34.7

888

###  5.5 Intermediate summary

  * •

A positive correlation between GMC properties (mass, surface density, CO peak
brightness temperature, and characteristic turbulent linewidth) and the
$\mathrm{H\alpha}$ luminosity of the matched H II regions exists for a MOP of
10%. The relationship between GMC properties and $\mathrm{H\alpha}$ luminosity
of the matched H II region can be represented by a power law to first order.

  * •

The dependence of GMC properties on the $\mathrm{H\alpha}$ luminosity of the
matched H II region varies as a function of the minimum overlap percentage in
diverse ways. On one hand, the strength of the correlation between the
$\mathrm{H\alpha}$ luminosity and the molecular mass significantly improves as
we increase the MOP. The correlations with the GMC surface density and the
characteristic turbulent linewidth remain unchanged, and the correlation with
the CO peak brightness temperature weakens for higher MOP thresholds.

  * •

The observed correlations cannot be reproduced in tests that randomize the
$\mathrm{H\alpha}$ luminosity and/or sizes of the H II regions before and
after identifying the matched GMC-H II region pairs.

##  6 Correlations within different galactic environments

Figure 6: Probability density functions of the stellar mass surface density
within 500 pc of the matched GMC/H II-regions. Global population in red and
matched population, with a MOP of 40%, in black. The vertical dashed lines
show the limits used to define the three stellar density environments in
Section 6. Figure 7: Fraction of GMC/H II-region pairs with low, medium or
high density environments in the galaxies center (nucleus and bar), arms, and
disk (interarms and outer disk), for a MOP of 40%. Figure 8: Scatter plots of
various GMC properties as a function of the $\mathrm{H\alpha}$ luminosity for
different environmental stellar surface densities measured at a scale of 500
pc, in a similar fashion to Fig 4. Each column represents a bin of
environmental stellar surface density, as defined in Section 6. From left to
right; low density, average density and high density environments. The red
line shows the global correlation from Section 5 with a MOP of 40%.

Both the distributions of the GMC properties and their correlation with the H
II region luminosity vary with the minimum overlap percentage that we use to
identify a GMC/H II region pair. A possible explanation of these results is
that GMC properties hosting H II regions are modified by local radiative
feedback. Another possibility is that correlations between GMC and H II region
properties arise from their co-variation with the local galactic environment.
It is thus important to consider whether the matched GMC/H II regions are
preferentially located in certain galactic environments, and whether the
galactic environment has an influence on the observed correlations. In this
section, we investigate the correlations as a function of the kpc-scale
environment surrounding the GMC/H II-region pairs. Specifically, we focus on
the stellar surface density. We explored a number of other large-scale
properties of the galactic environment, such as the star formation rate
surface density and molecular gas surface density, but found that they closely
track the stellar surface density and give similar results as those presented
below.

###  6.1 Method

To investigate whether there is a dependence on galactic environment, we
sorted the GMC/H II region pairs into three equally-populated bins of the
local stellar surface density, which we measured within an aperture of radius
500 pc around each GMC/H II region pair using the stellar surface density maps
of PHANGS galaxies presented by Sun et al. (2022). We used the GMC/H II region
pairs identified using a MOP of 40 %, yielding 380 pairs per bin. For the sake
of simplicity, we refer to the first bin as “low density environments” (0
$\leq$ log($\Sigma_{\star}$ / 1 M⊙ pc-2) $\leq$ 2.0), the second bin as
“average density environments” (2.0 $\leq$ log($\Sigma_{\star}$) $\leq$ 2.9)
and the last bin as “high density environments” (2.9 $\leq$
log($\Sigma_{\star}$) $\leq$ 3.7).

Figure 6 shows the empirical probability density function of the stellar
surface density surrounding the GMC/H II region pairs. The vertical dashed
lines represent the bin limits. There is an observable difference between the
distributions of the parent GMC population and of the GMCs that have an
interface with an H II region (MOP of 40%). The number of GMCs that are
matched with an H II region appears to decrease at the highest stellar surface
densities. This effect is naturally explained if the timescale of significant
interaction between GMCs and H II regions is shorter in regions of high
stellar surface density.

###  6.2 Results

To illustrate how the stellar surface density bins relate to the commonly used
dynamical environments, Fig. 7 presents the relative proportion of low,
average and high stellar surface density environments that are present in the
nuclear and bar regions of galaxies (henceforth referred to collectively as
the center environment), in spiral arms, and in interarm regions and galaxy
outer disks (henceforth referred to as the disk environment). Galaxy centers
are almost exclusively composed of high stellar surface density environments.
Low, average and high stellar surface density environments are present in
roughly equal proportions within spiral arms. Galaxy disks are charcterized by
low stellar surface density environments.

Figure 8 shows the correlations between $\mathrm{H\alpha}$ luminosity and GMC
properties for GMC/H II-region pairs for each stellar surface density bin. The
correlations between the $\mathrm{H\alpha}$ luminosity and the GMC properties
are clearly different from one environment to the other: the correlations are
stronger and steeper in the high stellar surface density environments, and
less pronounced in the low stellar surface density environments.

The correlations involving the different GMC properties exhibit different
trends with stellar surface density. A correlation between GMC mass and H II
region luminosity persists across all bins, although it steepens with
increasing stellar surface density. Correlations between the H II region
luminosity and other intensive GMC properties, on the other hand, are weak to
non-existent in low stellar surface density environments, and only clearly
emerge for $\log\Sigma_{\star}>2$

###  6.3 Intermediate summary

  * •

The correlations between GMC properties and the $\mathrm{H\alpha}$ luminosity
improve with increasing kpc-scale stellar surface density. The correlations
are the strongest in high stellar surface density environments, and either
weaker (for the molecular mass) or non-existent in lower stellar surface
density environments.

  * •

There is a strong correlation between the GMC mass and the H II region
luminosity across the full range of kpc-scale stellar surface densities in our
sample (Fig. 8 top row). In contrast, the GMC surface density or peak
temperature are uncorrelated with the H II region luminosity in low stellar
surface density environments, while they become clearly correlated in high
stellar surface density environments.

  * •

The overall correlations between the CO peak temperature, molecular gas
surface density and the H II region $\mathrm{H\alpha}$ luminosity seen in Fig.
4 are much weaker than the same correlations in the “dense” kpc-environments
seen in the right column of Fig. 8. This difference may partly be due to a
dilution effect. GMC/H II-region pairs in the low density environments
accounts for a large fraction of the overall population of GMC/H II-region
pairs. The fact that they show a weaker correlation than average thus dilutes
the correlation signature.

  * •

Comparing Fig. 4 and 8 shows that the correlations of the intensive GMC
properties with the H II region luminosity are much more sensitive to the kpc-
scale stellar density than to the MOP. This effect is weaker for the
characteristic turbulent linewidth than for the peak temperature and surface
density of GMCs. In contrast, the correlation of the GMC mass with the H II
region luminosity is about as sensitive to the stellar density as it is to the
MOP. This difference of behavior suggests that correlations involving the
intensive properties may stem from co-variations of GMC and H II regions
properties with galactic-scale environment, while the correlation of the GMC
mass with the stellar surface density is influenced by the local (i.e. cloud-
scale) effects.

##  7 Correlations within individual galaxies

Our combined sample of H II regions and GMCs is drawn from 17 galaxies. Among
their global properties, the inclination and distance of the host galaxies
could have an impact on our matching procedure, and by extension on the
correlations that we observe. In this section, we investigate whether the
correlations described in Section 5 exist within individual galaxies by
considering galaxies separately, where presumably observational effects such
as inclination, distance and resolution do not play a role. For completeness,
we also explored whether the correlations could be related to other galaxy
properties, namely the total CO luminosity, total $\mathrm{H\alpha}$
luminosity, metallicity, stellar mass and distance from the star-forming main
sequence. For this analysis, we use the list of matched GMC/H II region pairs
identified using a MOP of 40%. We identify between 29 (for NGC 2835) and 227
(for NGC 1566) pairs in each galaxy in our sample, with a mean of 114 pairs
per galaxy. This is sufficient to consider the correlations between GMC
properties and H II region luminosity within individual galaxies, but
prohibits exploring trends with stellar density within them.

We examined the correlations between GMC properties and the H II region
luminosity using the same procedure as in Section 5, measuring the power law
slope and $R^{2}$ statistic for each. A full list of our per-galaxy results is
presented in Table 7 of Appendix D. For each of the GMC properties that we
consider, we find significant variability among galaxies in terms of the slope
and quality of a power law fit. Consistent with the global trend in Section 5,
the GMC mass tends to be well correlated with the $\mathrm{H\alpha}$
luminosity within individual galaxies, with moderate ($R^{2}$¿0.3) to strong
($R^{2}$¿0.5) correlations obtained for 13 galaxies. Few individual galaxies
reveal a significant correlation between the H II region luminosity and the
GMC surface density or characteristic turbulent linewidth, again consistent
with the global trends. It is striking, however, that individual galaxies
reveal a much stronger correlation between the CO peak brightness and H II
region luminosity than can be discerned from the global trends, with $R^{2}$
values that are comparable to those obtained for the correlations with GMC
mass (i.e. $R^{2}$¿0.3 for 13 galaxies, and three galaxies with $R^{2}$¿0.5).

We explored whether there were any systematic trends between these correlation
results and properties of the host galaxies by plotting the derived power law
slopes and $R^{2}$ statistics against galaxy distance, inclination, stellar
mass, total CO and $\mathrm{H\alpha}$ luminosity, mean $\log\Sigma_{\star}$,
offset from the star-forming main sequence, and number of pairs identified.
These results are presented in Appendix D. We find no dependence of the
strength and slope of the observed correlations on the inclination or distance
to the galaxy, suggesting that the correlations are not driven by geometric
effects (e.g. viewing angle) or resolution. In general, lower mass systems in
our sample tend to exhibit poorer correlations between the GMC properties and
the H II region luminosity. Since the typical stellar surface density in
galaxy disks tends to scale with the galaxy total mass and luminosity, this
result is consistent with the weaker correlations observed for low stellar
surface density galactic environments that we described in Section 6.

##  8 Discussion

Figure 9: Joint PDFs and their marginalized PDFs of the GMCs peak temperature
(left) and molecular mass (right) with the matched H II region
$\mathrm{H\alpha}$ luminosity for two MOP: 1% in red, and 70% in blue. The
joint PDFs are shown as contour plots. The medians of the marginalized PDFs
and the power laws fitted on the joint PDFs are overlaid as straight lines.

In this paper, we searched for evidence for a potential impact of H II regions
on GMC properties as measured on spatial scales between 30 and 180 pc. We
presented a method to match H II regions to a GMC based on their relative
overlap region.

We studied 1) the distributions of characteristic cloud properties (molecular
mass, surface density, CO peak temperature, and characteristic turbulent
linewidth) of GMCs that are associated with H II regions, and how these
distributions vary as a function of the MOP that we adopt to identify matched
objects, and 2) correlations between GMC properties and the $\mathrm{H\alpha}$
luminosity of their associated H II regions, again as a function of the MOP.
To establish whether our results are consistent with the observed correlations
having a local origin (i.e. a direct physical link between the cloud’s
physical state and the H II region), we investigated whether the correlations
vary with the kpc-scale stellar surface density, and global properties of the
host galaxy, including observational properties such as distance and
inclination.

In this section, we briefly summarize the trends that we observe and outline
three potential physical scenarios that could explain them. To conclude, we
summarize the lessons learnt during this exercise.

###  8.1 Two families of behaviors experienced by the properties of the GMC/H
II-region pairs with increasing overlap

Figure 9 presents the joint and marginalized PDFs of the GMC molecular mass
and CO peak temperature and the $\mathrm{H\alpha}$ luminosity of its
associated H II region for two minimum overlap percentage thresholds: 1% in
red, and 70% in blue. A MOP threshold of 1% yields a good approximation for
all the GMCs that are contiguous or overlapping with at least one H II region.
We used a kernel method to compute all the PDFs. Figure 9 illustrates that
increasing the MOP causes two distinct effects on the correlations between GMC
properties and the $\mathrm{H\alpha}$ luminosity.

First, the CO peak temperature (and the other intensive properties)
demonstrate one behavior when we vary the overlap criterion: as we impose a
higher MOP increases, the median value of the GMC property also significantly
increases. This behavior reduces the dynamic range of the x and y axis values,
reducing the $R^{2}$ value of the correlations.

Second, the GMC mass shows a different behavior: its correlation with the
$\mathrm{H\alpha}$ luminosity strengthens and steepens. Additionally the
median shifts towards lower masses. The latter effect is mostly due to the
asymmetry of the matching criterion.

###  8.2 Potential Physical Origin

The physical properties of GMCs follow Larson-type scaling relations, such
that larger GMCs also tend to be more massive and more turbulent. Appendix E
confirms that these relationships exist for the GMCs that we identify with H
II regions using any MOP. However, these relationships fail to explain either
why the CO peak temperature increases with the MOP or why the correlation of
the GMC mass with the $\mathrm{H\alpha}$ luminosity strengthens when
increasing the minimum overlap percentage. We consider three possible
scenarios to explain these two observed behaviors.

The environmental/coincidence scenario

The galactic environment induces covariation of GMCs and H II region
properties without a direct causal connection between them.

The epigenetic scenario

Parent GMCs transmit some of the properties from their environment to their
child H II regions.

The radiative feedback scenario

The child H II regions disrupt and alter the intrinsic properties of their
parent molecular cloud.

The trends identified in our analysis are likely due to a combination of these
scenarios. For instance, there could be a “background” co-variation of matched
GMCs and H II regions due to a common environment or to the heritage of some
of the GMC properties to the associated H II regions, and local effects (e.g.,
stellar radiative feedback) could become the predominant driver of the GMC/H
II-region correlations only observed for highly overlapping pairs.

####  8.2.1 Environmental / coincidence scenario

Section 6 first shows that the correlations between the GMC properties and the
$\mathrm{H\alpha}$ luminosity are sensitive to the kpc-scale stellar surface
density, when considering all the matched GMC/H II-region pairs. For instance,
there is no correlation of the CO peak brightness and surface density with the
$\mathrm{H\alpha}$ luminosity in low density kpc-scale environments, but these
correlations appear and improve systematically as a function of the kpc-scale
stellar density. This means that the kpc environment plays a role in setting
the correlations of the GMCs properties with the luminosity of the matched H
II regions.

However, Sections 5 and 6 also show that the correlation between the
$\mathrm{H\alpha}$ luminosity and the molecular mass is much more sensitive to
the MOP than to the kpc environment. This argues in favor of a local origin of
this behavior.

####  8.2.2 Epigenetic scenario

Section 5 shows a strong positive correlation between the H II region
$\mathrm{H\alpha}$ luminosity and the molecular cloud mass. Moreover, this
correlation increases in steepness and strength when increasing the MOP.
Section 6 also showed that this correlation persists even in low density
environments, where crowding is less of an issue. This suggests that this
correlation is not driven by coincidental co-variation of the GMC and H II
region properties, but has a local origin. An evolutionary link offers a
natural local origin: a high-mass GMC is needed to make a large and thus
luminous H II region. In this scenario, GMC properties are partly regulated by
their kpc-scale environment. This information is transmitted to their child H
II regions. This is similar to epigenetics (i.e. the study of how the
environment can cause changes that affect the way genes work).

####  8.2.3 Stellar feedback scenario

The observed spatial de-correlation on small ($<$100pc) scales between
molecular gas and young star forming regions (Schruba et al., 2010; Onodera et
al., 2010; Grasha et al., 2018; Kreckel et al., 2018; Kruijssen et al., 2018;
Grasha et al., 2019; Kruijssen et al., 2019; Schinnerer et al., 2019; Chevance
et al., 2020) indicates that within the star formation cycle the clearing and
dissolution of the natal molecular birth cloud must occur on relatively short
timescales. Recent results indicate that pre-supernova feedback processes are
essential contributors to this process (Barnes et al., 2021; McLeod et al.,
2021; Olivier et al., 2021; Barnes et al., 2022), with clearing times
estimated to be only a few Myr (Kim et al., 2021a; Chevance et al., 2022a; Kim
et al., 2022). By isolating the sub-set of GMCs that overlaps with H II
regions, it is possible that we are catching this process in the act. If this
is the case, we expect to see some imprint on these feedback processes onto
the parent GMC. Some tentative evidence for this was identified in the
‘Headlight cloud’ in NGC 0628 (Herrera et al., 2020), where CO emission
associated with this cloud was suggested to be overluminous due to heating by
the associated H II region.

With our matched GMC and H II region sample, we identify a weak positive
correlation between CO peak brightness and H$\alpha$ luminosity (Fig. 4). This
correlation is strongest within dense kpc scale environments, with $R^{2}$ =
0.32. It clearly decreases with increasing overlap percentage (Fig. 5), and is
essentially absent at minimum overlap percentages of 70%. Looking in low
density kpc scale environments, where the cleanest matches are possible and
there should be less contribution from neighboring or clustered star-forming
regions, the correlation is absent ($R^{2}$ = 0.00). Analysis of individual
galaxies (Section 7), on the other hand, tends to confirm a trend between CO
peak brightness and H$\alpha$ luminosity, suggesting the scatter in Figures 4
and 8 is at least partly due to galaxy-to-galaxy variation.

The CO peak temperature significantly shifts to higher values when the MOP
increases (see Fig. 2 in Sect. 4). This shift effect happens even in low
density environments, and thus probably has a local origin. Moreover, the
origin of this local effect is completely independent from the strength of the
correlation of the GMC mass with the $\mathrm{H\alpha}$ luminosity (see
Appendix E). This independent effect could be explained by the fact that
massive young stars naturally heat the Photon-Dominated Regions at the
interface between H II regions and GMCs. The larger the MOP, the larger the
interface and thus the more efficient heating. This effect would saturate the
line peak brightness of the low-$J$ CO lines and would enhance higher-$J$ CO
brightness.

We also look for a positive correlation between H$\alpha$ luminosity and
characteristic turbulent linewidth, and find a weak trend for any MOP. We
identify a peak correlation at moderate 40% overlap percentage ($R^{2}$ =
0.14). Nevertheless, the characteristic turbulent linewidth of matched GMCs
shifts systematically towards higher values when we adopt a higher MOP
(Section 4), the opposite behaviour to $\sigma_{v}$ that decreases in similar
conditions. This could hint to a slight increase of the turbulent motion in
GMCs by nearby H II regions.

###  8.3 Studying the impact of H II regions on GMCs: Lessons learnt

Studying the impact of H II regions on GMCs in nearby galaxies on 30 to 180 pc
scales is a difficult challenge for several reasons.

  * •

The PHANGS GMC and H II region catalogs present a large number of physical
properties for each of these objects. This is a high-dimensional parameter
space to be explored.

  * •

Some of the catalog properties are dependent by construction (e.g. the mass
and size of GMCs). Even among physical properties that are in principle
independent, there are well-established empirical correlations between GMC
properties (e.g. Larson-type scaling relations) and between H II region
properties.

  * •

The co-variation among properties of GMCs and H II regions in different
galactic environments can be larger than the impact of physical processes on
cloud-scales and below that regulate the co-evolution of GMC and H II regions.

In summary, we are searching for subtle signatures in a high-dimensional space
among properties that demonstrate pre-existing correlations due to diverse
physical origins. This implies we need to devise methods that maximize the
probability of detecting a signature of H II region feedback on their natal
GMC, without misinterpreting or biasing the results.

The timescale for disrupting GMCs via H II region feedback is relatively short
compared to the cloud lifetime (Kim et al., 2021a; Chevance et al., 2022a). We
thus need to search for a transient state. This, as well as the considerations
outlined above, tends to favour using a high MOP to pinpoint the GMCs where H
II region feedback is most pronounced. The drawback of such a choice is that
pairs with a large overlap percentage are rare, leading us to combine regions
from different galaxies. This complicates the interpretation due to the
different characteristic environments within galaxies of different types.

In this paper, we compromised by adopting a fiducial minimum overlap
percentage of 40% and studying how the joint PDFs and correlations vary as a
function of MOP thresholds between 10 and 70%. We also used an asymmetric
matching criterion to focus on the H II regions that are most likely to impact
GMC properties on the spatial scales that are accessible to PHANGS-ALMA (i.e.
$\sim 100\,$pc). Increasing the angular resolution of nearby galaxy imaging
surveys would allow us to better locate the interfaces between matched GMCs
and H II regions, while maintaining good statistics. A less time-consuming
alternative would be to increase the angular resolution of the observations
towards selected pairs to validate the scenarios envisaged here.

The covariation of GMC properties and H II regions properties is a further
complication, since the signature of feedback can be mistakenly considered as
scatter around pre-existing correlations, while it actually is a hidden
control variable. In other words, it is important to reveal how this
(previously hidden) variable impacts pre-existing correlations of GMC
properties. Once again, much higher resolution observations of extragalactic
high-mass star-forming regions would be useful to understand how feedback
signatures might manifest themselves in lower resolution observations over a
much larger sample.

##  9 Conclusions

In this paper, we studied the physical properties of GMCs associated with H II
regions for 17 galaxies in the PHANGS-ALMA survey. Our primary goal was to
determine whether GMC properties on cloud scales (here $30$ to 180 pc) are
modified by star formation feedback. We studied the distribution of four cloud
properties (GMC mass, surface density, CO peak temperature, and characteristic
turbulent linewidth) and the correlations between these properties with the
$\mathrm{H\alpha}$ luminosity of the associated H II regions. The main
conclusions of our study are:

  1. 1.

Matched GMC/H II-regions represent a non-negligible fraction of the overall
population of GMCs and H II regions in galaxies. GMCs have a higher detection
rate by number in matched regions than H II regions. When considering the
detected flux rather than the number of detected objects, H II regions in
matched pairs represent a larger fraction of their host galaxy’s
$\mathrm{H\alpha}$ luminosity than the contribution of GMCs in matched pairs
to the galaxy’s CO luminosity.

  2. 2.

Matched GMCs tend to be denser than a typical GMC.

  3. 3.

In all galaxies and environments, the GMC mass (as inferred from its CO
luminosity) is well-correlated with the $\mathrm{H\alpha}$ luminosity of its
associated H II region. The GMC surface density, CO peak temperature, and
characteristic turbulent linewidth exhibit weaker correlations with the
$\mathrm{H\alpha}$ luminosity.

  4. 4.

The galactic environment has an impact on the observed correlation between GMC
mass and the $\mathrm{H\alpha}$ luminosity. The correlation is generally
stronger and steeper in the dense kpc-scale environments (typified by the
centers and bars of galaxies), and weaker in the low density kpc-scale
enviroments (e.g., outer disks and interarms).

  5. 5.

The correlations observed using the combined sample of matched GMC-H II
regions from 17 galaxies obscures some variability galaxy by galaxy. In
particular, individual galaxies often exhibit significant correlations between
the molecular mass, the CO peak temperature and the $\mathrm{H\alpha}$
luminosity. The correlation with GMC mass persists when the combined sample is
considered, but the correlation between CO peak temperature and
$\mathrm{H\alpha}$ luminosity is highly scattered when the matched regions in
all galaxies are combined.

  6. 6.

GMC properties exhibit different behaviours when we adjust the MOP that we use
to identify matched GMC-H II regions. The median value of intensive cloud
properties, i.e., the molecular surface density, CO peak temperature, and
characteristic turbulent width, shifts towards higher values when a higher
value of MOP is adopted. But the power law index of their correlation with the
$\mathrm{H\alpha}$ luminosity remains constant. In contrast, the molecular
mass decreases with increasing overlap percentage, while its correlation with
the $\mathrm{H\alpha}$ luminosity strengthens.

We propose a scenario where the kpc-scale galactic environment regulates the
typical properties of GMCs, and massive GMCs are required to produce the most
luminous H II regions. Focussing on the matched GMC-H II regions that we
identify using a high overlap percentage, we identify variations in the CO
peak brightness and (more tentatively) characteristic turbulent linewidth that
may be a signature of H II region feedback on the molecular gas. Generally,
however, it is difficult to unambiguously identify variations in the physical
properties of GMCs with the impact of feedback at the spatial scales
accessible to PHANGS-ALMA.

One way to confirm our results would be to observe a sample of extragalactic
high mass star-forming regions at much better angular resolution in order to
fully disentangle the effects of galactic environment and H II region
feedback. Examining the relative strengths of the different $J$ CO lines as a
function of the MOP would be another useful independent test of the proposed
link between feedback and CO peak brightness, since we expect that higher $J$
CO lines would have further enhanced brightness. For future investigations, we
also propose to refine the criteria used to identify associated GMC-H II
regions to take better account of physical quantities that are relevant to
cloud disruption by stellar feedback. One such approach would be to compare
the fraction of $\mathrm{H\alpha}$ luminosity in the overlapping region with
the fraction of molecular gas available in the interaction region, i.e. the
number of ionizing photons per molecule of hydrogen, rather than the simpler
projected area criterion used here.

###### Acknowledgements.

This work was carried out as part of the PHANGS collaboration. Based on
observations collected at the European Southern Observatory under ESO
programmes 1100.B-0651, 095.C-0473, and 094.C-0623 (PHANGS–MUSE; PI
Schinnerer), as well as 094.B-0321 (MAGNUM; PI Marconi), 099.B-0242,
0100.B-0116, 098.B-0551 (MAD; PI Carollo) and 097.B-0640 (TIMER; PI Gadotti).
This work was supported in part by the French Agence Nationale de la Recherche
through the DAOISM grant ANR-21-CE31-0010 and by the Programme National
“Physique et Chimie du Milieu Interstellaire” (PCMI) of CNRS/INSU with
INC/INP, co-funded by CEA and CNES. KK gratefully acknowledges funding from
the German Research Foundation (DFG) in the form of an Emmy Noether Research
Group (grant number KR4598/2-1, PI Kreckel). HAP acknowledges support by the
Ministry of Science and Technology of Taiwan under grant
110-2112-M-032-020-MY3. ATB, FB, IB, JdB would like to acknowledge funding
from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (grant agreement No.726384/Empire). CE
acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG)
Sachbeihilfe, grant No. BI1546/3-1. KG is supported by the Australian Research
Council through the Discovery Early Career Researcher Award (DECRA) Fellowship
DE220100766 funded by the Australian Government. KG is supported by the
Australian Research Council Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D), through project number CE170100013. SCOG, RSK and EJW
acknowledge financial support from DFG via the Collaborative Research Center
(SFB 881, Project-ID 138713538) ’The Milky Way System’ (subprojects A1, B1,
B2, B8, P2), and they thank for funding from the European Research Council in
the ERC synergy grant ‘ECOGAL – Understanding our Galactic ecosystem: From the
disk of the Milky Way to the formation sites of stars and planets’ (project ID
855130) as well as from the Heidelberg Cluster of Excellence (EXC 2181 -
390900948) ‘STRUCTURES: A unifying approach to emergent phenomena in the
physical world, mathematics, and complex data’. MC gratefully acknowledges
funding from the DFG through an Emmy Noether Research Group (grant numbers
CH2137/1-1 and KR4801/1-1), as well as from the European Research Council
(ERC) under the European Union’s Horizon 2020 re- search and innovation
programme via the ERC Starting Grant MUSTANG (grant agreement number 714907).
The work of JS is partially supported by the Natural Sciences and Engineering
Research Council of Canada (NSERC) through the Canadian Institute for
Theoretical Astrophysics (CITA) National Fellowship. ES and TGW acknowledge
funding from the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (grant agreement No. 694343).

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##  Appendix A Supplemental information about the matching method

###  A.1 Single matching vs multiple matching

For the spatial overlap matching method used in this paper, particular care
must be taken when dealing with GMCs that overlap multiple H II regions (and
vice versa). One option would be to require that GMCs and H II regions form
exclusive pairs, i.e. ensuring that each H II region is uniquely identified to
a GMC, which itself is only identified with a single H II region. This
approach is simple to implement, but physically unrealistic: GMCs and H II
regions are not randomly distributed, but instead preferentially located
within larger-scale coherent spatial structures, such as spiral arms and
inter-arm feathers (Schinnerer et al. 2017), where star-forming complexes are
often crowded together. Star formation in a GMC may result in multiple H II
regions (see, e.g., Williams & McKee 1997). The probability of hosting
multiple H II regions is more likely for GMCs more massive than a few
$10^{5}\mathrm{\,M_{\odot}}$, which is true for most of the clouds in the
PHANGS GMC catalog. Overall, the fraction of associations involving multiple
GMCs and H II regions is significant. The number of GMCs overlapping with
multiple H II regions represents 47% of the total number of overlapping GMCs,
while the percentage of H II regions that overlap with multiple GMCs is 19% of
the total number of overlapping H II regions. This approximately holds for any
MOP. We therefore decided to allow each GMC to have more than one associated H
II region, but require that H II regions are uniquely identified with a GMC,
in practice assigning it to the GMC that overlaps the largest percentage of
the H II region’s projected area.

###  A.2 Asymmetry of the matching criterion

Figure 10: Probability Distribution Functions of the size of GMCs in blue and
H II regions in red. Means, medians, and standard deviations of the two
distributions are listed on the left.

We are specifically looking for H II regions that may significantly modify the
properties of their natal GMC clouds, not only at the immediate working
surface, but also on the $\sim 50-100\,$pc scales on which global cloud
properties are typically measured. This implies that we are searching for H II
regions whose energy content is a significant fraction of the GMC one. In
particular, we will explicitly try to avoid selecting all the small H II
regions associated to large GMCs because their feedback would have negligible
impact and they would dilute the searched signatures on the GMC properties.

For completeness, Fig. 10 presents the probability density functions (PDFs) of
the radii of H II regions and GMCs across our sample. The size of resolved
GMCs or H II regions are corrected for the size of ALMA and MUSE point spread
function. But this plot should not be over-interpreted because the GMC and H
II-region catalogs treat differently unresolved sources. The unresolved GMCs,
on one hand, are filtered out from the PHANGS-ALMA catalog of GMCs, which
rejects objects when their size cannot be deconvolved from the beam size
(Rosolowsky et al. 2021). On the other hand, the majority ($\sim 80$%) of the
catalogued H II regions are point sources, for which we only have an upper
limit of their projected area, corresponding to the point spread function of
the VLT/MUSE instrument (Santoro et al. 2022). That is why the distribution of
H II region size exhibits shallow peaks at the resolution of the observations,
namely $\sim$50 pc, $\sim$60 pc and $\sim$80 pc. Using these definitions, the
10 to 90 percentile range is $32-109$ pc for the GMC radius, and $33-87$ pc
for the H II region radius. And there exist H II regions as large as the
largest identified GMCs.

###  A.3 Overlap parameter choices

Figure 11: Histogram of the relative velocity (left) and number of pairs as a
function of the MOP (right) between associated GMCs and H II regions for all
galaxies in the sample. One GMC/H II-region pair is present in this histogram
when at least one pixel is overlapping. The mean, median, and standard
deviation of the overlap distribution are listed on the top right corner. The
vertical dashed lines in the right panel represent the 10%, 40% and 70% MOP.

When matching GMCs and H II regions with the overlap matching method coupled
with the velocity offset, two parameters are left to the user: the MOP and the
velocity offset threshold. The left panel of Fig. 11 presents the histogram of
the number of GMC/H II region pairs as a function of their velocity offsets.
Limiting the velocity offset between a spatially overlapping GMC and H II
region ensures that the two objects are at least contiguous in position-
position-velocity space. The uncertainty on the velocity of H II regions is
$\sim 49\mathrm{\,km\,s^{-1}}$, larger than the uncertainty on GMC velocity,
and thus the limiting factor on the velocity offset threshold. We thus chose a
velocity offset threshold of 10$\mathrm{\,km\,s^{-1}}$. We note that limiting
the velocity offset to a value lower than 10$\mathrm{\,km\,s^{-1}}$, e.g.,
5$\mathrm{\,km\,s^{-1}}$, does not alter our results. As for the minimal
overlap percentage, using a 40% MOP as a fiducial value allows us to filter
out matched H II regions and GMCs that are potentially physically unrelated,
while keeping a large enough sample of GMC/H II region pairs to compute
reliable statistics. The right panel of Fig. 11 presents the histogram of the
number of GMC/H II region pairs according to the projected area of overlap.
The distribution of overlap percentages between H II regions and GMCs has a
mean of 17%, a median of 10%, and a standard deviation of 18%.

##  Appendix B Properties of the matched GMC/H II regions in individual
galaxies

Figure 12: Comparison of the footprints of the matched GMCs/H II regions (left panel) with the footprints of all the GMCs (center panel) and of all the H II regions (right panel) for the NGC 4254 galaxy. The background image shows the $\mathrm{H\alpha}$ line emission in grey and the environmental masks: the center in yellow, the spiral arms in white, and the inter-arms and disk violet. In this case, regions are matched when the overlap area represents at least 40% of the GMC region area. Table 4: Number and luminosity of GMCs and H II regions per galaxy of the studied sample as a function of the MOP. Galaxy | % | GMC | H II regions | CO mass | H$\alpha$ luminosity
---|---|---|---|---|---
Total | Matched | Total | Matched | Total | Matched | Total | Matched
# | % | # | % | $\mathrm{\,M_{\odot}}$ | % | $\mathrm{\,erg\,s^{-1}}$ | %
NGC 0628 | 10 | 809 | 56.7 | 2869 | 23.5 | 9.69$\times 10^{8}$ | 69.0 | 9.58$\times 10^{40}$ | 81.1
| 40 |  | 15.0 |  | 4.3 | 9.69$\times 10^{8}$ | 18.7 | 9.58$\times 10^{40}$ | 51.0
| 70 |  | 3.5 |  | 1.0 | 9.69$\times 10^{8}$ | 4.1 | 9.58$\times 10^{40}$ | 21.5
NGC 1087 | 10 | 308 | 60.4 | 1011 | 27.7 | 1.07$\times 10^{9}$ | 64.7 | 1.76$\times 10^{41}$ | 58.5
| 40 |  | 14.3 |  | 4.4 | 1.07$\times 10^{9}$ | 14.2 | 1.76$\times 10^{41}$ | 32.7
| 70 |  | 2.6 |  | 0.8 | 1.07$\times 10^{9}$ | 3.3 | 1.76$\times 10^{41}$ | 15.4
NGC 1300 | 10 | 434 | 37.6 | 1478 | 15.0 | 1.21$\times 10^{9}$ | 39.7 | 9.16$\times 10^{40}$ | 52.1
| 40 |  | 14.3 |  | 4.2 | 1.21$\times 10^{9}$ | 16.9 | 9.16$\times 10^{40}$ | 32.1
| 70 |  | 2.8 |  | 0.8 | 1.21$\times 10^{9}$ | 2.1 | 9.16$\times 10^{40}$ | 10.2
NGC 1365 | 10 | 1092 | 7.1 | 1455 | 6.0 | 1.62$\times 10^{10}$ | 10.5 | 1.38$\times 10^{42}$ | 7.6
| 40 |  | 3.7 |  | 2.7 | 1.62$\times 10^{10}$ | 4.5 | 1.38$\times 10^{42}$ | 5.6
| 70 |  | 1.4 |  | 1.0 | 1.62$\times 10^{10}$ | 1.5 | 1.38$\times 10^{42}$ | 3.2
NGC 1385 | 10 | 407 | 49.4 | 1029 | 26.1 | 1.16$\times 10^{9}$ | 65.3 | 2.97$\times 10^{41}$ | 66.4
| 40 |  | 20.1 |  | 8.0 | 1.16$\times 10^{9}$ | 28.5 | 2.97$\times 10^{41}$ | 50.2
| 70 |  | 5.4 |  | 2.1 | 1.16$\times 10^{9}$ | 9.1 | 2.97$\times 10^{41}$ | 27.1
NGC 1433 | 10 | 355 | 25.1 | 1736 | 6.0 | 1.03$\times 10^{9}$ | 20.2 | 6.70$\times 10^{40}$ | 26.4
| 40 |  | 12.4 |  | 2.5 | 1.03$\times 10^{9}$ | 10.5 | 6.70$\times 10^{40}$ | 21.6
| 70 |  | 3.9 |  | 0.8 | 1.03$\times 10^{9}$ | 2.4 | 6.70$\times 10^{40}$ | 11.5
NGC 1512 | 10 | 317 | 20.2 | 632 | 10.8 | 6.36$\times 10^{8}$ | 21.7 | 6.04$\times 10^{40}$ | 42.9
| 40 |  | 13.2 |  | 6.8 | 6.36$\times 10^{8}$ | 14.2 | 6.04$\times 10^{40}$ | 38.7
| 70 |  | 5.4 |  | 2.7 | 6.36$\times 10^{8}$ | 7.0 | 6.04$\times 10^{40}$ | 32.7
NGC 1566 | 10 | 1127 | 38.9 | 2404 | 24.1 | 5.30$\times 10^{9}$ | 48.9 | 4.20$\times 10^{41}$ | 63.5
| 40 |  | 12.8 |  | 6.1 | 5.30$\times 10^{9}$ | 20.2 | 4.20$\times 10^{41}$ | 49.0
| 70 |  | 2.7 |  | 1.2 | 5.30$\times 10^{9}$ | 4.1 | 4.20$\times 10^{41}$ | 22.0
NGC 1672 | 10 | 517 | 31.5 | 1581 | 13.9 | 6.14$\times 10^{9}$ | 43.4 | 6.77$\times 10^{41}$ | 52.3
| 40 |  | 7.9 |  | 2.6 | 6.14$\times 10^{9}$ | 14.9 | 6.77$\times 10^{41}$ | 33.5
| 70 |  | 1.4 |  | 0.4 | 6.14$\times 10^{9}$ | 3.5 | 6.77$\times 10^{41}$ | 9.3
NGC 2835 | 10 | 211 | 26.5 | 1121 | 5.4 | 1.05$\times 10^{8}$ | 44.5 | 5.78$\times 10^{40}$ | 32.0
| 40 |  | 22.3 |  | 4.3 | 1.05$\times 10^{8}$ | 37.6 | 5.78$\times 10^{40}$ | 28.8
| 70 |  | 17.1 |  | 3.3 | 1.05$\times 10^{8}$ | 26.9 | 5.78$\times 10^{40}$ | 26.5
NGC 3351 | 10 | 370 | 42.2 | 1284 | 14.8 | 5.64$\times 10^{8}$ | 34.3 | 6.35$\times 10^{40}$ | 18.4
| 40 |  | 8.9 |  | 2.6 | 5.64$\times 10^{8}$ | 11.2 | 6.35$\times 10^{40}$ | 13.4
| 70 |  | 1.9 |  | 0.5 | 5.64$\times 10^{8}$ | 1.1 | 6.35$\times 10^{40}$ | 2.0
NGC 3627 | 10 | 983 | 35.2 | 1635 | 27.6 | 5.56$\times 10^{9}$ | 41.1 | 3.77$\times 10^{41}$ | 59.2
| 40 |  | 7.0 |  | 4.3 | 5.56$\times 10^{9}$ | 10.0 | 3.77$\times 10^{41}$ | 34.2
| 70 |  | 2.4 |  | 1.5 | 5.56$\times 10^{9}$ | 2.7 | 3.77$\times 10^{41}$ | 15.0
NGC 4254 | 10 | 918 | 61.8 | 2960 | 29.4 | 5.86$\times 10^{9}$ | 76.2 | 4.44$\times 10^{41}$ | 78.0
| 40 |  | 10.1 |  | 3.2 | 5.86$\times 10^{9}$ | 13.0 | 4.44$\times 10^{41}$ | 26.8
| 70 |  | 0.9 |  | 0.3 | 5.86$\times 10^{9}$ | 1.5 | 4.44$\times 10^{41}$ | 5.0
NGC 4303 | 10 | 874 | 49.7 | 3067 | 21.6 | 5.98$\times 10^{9}$ | 63.6 | 6.22$\times 10^{41}$ | 73.2
| 40 |  | 10.1 |  | 2.9 | 5.98$\times 10^{9}$ | 14.1 | 6.22$\times 10^{41}$ | 35.1
| 70 |  | 1.7 |  | 0.5 | 5.98$\times 10^{9}$ | 1.7 | 6.22$\times 10^{41}$ | 8.6
NGC 4321 | 10 | 1214 | 40.4 | 1847 | 34.4 | 4.94$\times 10^{9}$ | 54.5 | 3.03$\times 10^{41}$ | 66.2
| 40 |  | 6.6 |  | 4.3 | 4.94$\times 10^{9}$ | 11.7 | 3.03$\times 10^{41}$ | 34.8
| 70 |  | 1.2 |  | 0.8 | 4.94$\times 10^{9}$ | 2.9 | 3.03$\times 10^{41}$ | 12.8
NGC 4535 | 10 | 638 | 32.9 | 1938 | 15.3 | 1.78$\times 10^{9}$ | 46.8 | 1.26$\times 10^{41}$ | 57.3
| 40 |  | 5.5 |  | 1.8 | 1.78$\times 10^{9}$ | 8.2 | 1.26$\times 10^{41}$ | 24.7
| 70 |  | 0.9 |  | 0.3 | 1.78$\times 10^{9}$ | 2.8 | 1.26$\times 10^{41}$ | 11.0
NGC 5068 | 10 | 292 | 39.4 | 1857 | 8.6 | 1.01$\times 10^{8}$ | 56.8 | 2.76$\times 10^{40}$ | 50.3
| 40 |  | 22.3 |  | 3.6 | 1.01$\times 10^{8}$ | 27.8 | 2.76$\times 10^{40}$ | 35.7
| 70 |  | 13.4 |  | 2.1 | 1.01$\times 10^{8}$ | 15.0 | 2.76$\times 10^{40}$ | 29.4

As an example, Fig. 12 compares the spatial distribution of matched GMC/H II-
regions in NGC 4254 for a MOP of 40% with the spatial footprints of the full
distributions of GMCs and H II regions, and the environment masks.

Table 4 presents the statistics of matched GMC-H II regions for each galaxy in
our sample. For three different MOP thresholds, we list total number of H II
regions and GMCs in each galaxy, the percentage of H II regions and GMCs that
are located in matched regions, and their absolute and relative contributions
to each galaxy’s H$\alpha$ and CO luminosities. Fig. 13 shows the correlation
between CO peak temperature and $\mathrm{H\alpha}$ luminosity considering H II
region/GMC pairs from NGC 1672, NGC 4535, and NGC 4321 separately. These 3
galaxies harbor the highest correlation coefficient between CO peak
temperature and $\mathrm{H\alpha}$ luminosity $(R^{2}\geq 0.5)$.

|  |
---|---|---
Figure 13: Scatter plots of the CO peak temperature as a function of the
$\mathrm{H\alpha}$ luminosity for the 3 galaxies in our sample (NGC 1672, NGC
4535, NGC 4321) where these two properties are the most correlated. In this
figure, the MOP is 40%.

##  Appendix C Supplemental information to assess the robustness of the
results

Table 5: Kolmogorov-Smirnov tests performed to assess whether the
distributions are significantly different. Top: Comparison of the
distributions of matched GMC/H II-regions with their parent distributions.
Bottom: Comparison of the distributions of matched GMC/H II-regions for
different minimum overlap percentages.

Parent distribution vs matched GMC/H II-regions
---
Minimum Overlap | GMC properties
Percentage |  | Size | $L_{\mathrm{CO}}$ | $\sigma_{v}$ | $\Sigma_{\mathrm{mol}}$ | $\sigma_{0}$ | $\alpha_{\mathrm{vir}}$ | $T_{\mathrm{peak}}$ | $\tau_{\mathrm{ff}}$
10% | s value | 1.00 | 1.00 | 0.73 | 1.00 | 0.98 | 0.78 | 0.92 | 0.99
| p value |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3
| Different ? | yes | yes | yes | yes | yes | yes | yes | yes
40% | s value | 1.00 | 1.00 | 0.73 | 1.00 | 0.98 | 0.80 | 0.88 | 0.99
| p value |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3
| Different ? | yes | yes | yes | yes | yes | yes | yes | yes
70% | s value | 1.00 | 1.00 | 0.73 | 1.00 | 0.98 | 0.83 | 0.86 | 0.99
| p value |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3
| Different ? | yes | yes | yes | yes | yes | yes | yes | yes

Matched GMC/H II-regions vs Matched GMC/H II-regions
---
Minimum Overlap | GMC properties
Percentage |  | Size | $L_{\mathrm{CO}}$ | $\sigma_{v}$ | $\Sigma_{\mathrm{mol}}$ | $\sigma_{0}$ | $\alpha_{\mathrm{vir}}$ | $T_{\mathrm{peak}}$ | $\tau_{\mathrm{ff}}$
10% vs 40% | s value | 0.20 | 0.09 | 0.05 | 0.13 | 0.06 | 0.07 | 0.11 | 0.17
| p value |  $\ll$1e-3 |  $\ll$1e-3 | 1.60e-02 |  $\ll$1e-3 | 5.20e-03 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3
| Different ? | yes | yes | yes | yes | yes | yes | yes | yes
10% vs 70% | s value | 0.35 | 0.22 | 0.13 | 0.24 | 0.10 | 0.11 | 0.20 | 0.32
| p value |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 | 3.94e-03 | 2.05e-03 |  $\ll$1e-3 |  $\ll$1e-3
| Different ? | yes | yes | yes | yes | yes | yes | yes | yes
40% vs 70% | s value | 0.20 | 0.14 | 0.09 | 0.12 | 0.05 | 0.04 | 0.10 | 0.17
| p value |  $\ll$1e-3 |  $\ll$1e-3 | 3.98e-02 | 3.05e-03 | 4.86e-01 | 8.18e-01 | 1.40e-02 |  $\ll$1e-3
| Different ? | yes | yes | yes | yes | yes | no | yes | yes

Table 6: Anderson-Darling tests performed to assess whether the distributions
are significantly different. Top: Comparison of the distributions of matched
GMC/H II-regions with their parent distributions. Bottom: Comparison of the
distributions of matched GMC/H II-regions for different minimum overlap
percentages.

Parent distribution vs matched GMC/H II-regions
---
Minimum Overlap | GMC properties
Percentage |  | Size | $L_{\mathrm{CO}}$ | $\sigma_{v}$ | $\Sigma_{\mathrm{mol}}$ | $\sigma_{0}$ | $\alpha_{\mathrm{vir}}$ | $T_{\mathrm{peak}}$ | $\tau_{\mathrm{ff}}$
10% | s value |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2
| c value | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96
| p value |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3
| Different ? | yes | yes | no | yes | yes | yes | yes | yes
40% | s value |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2
| c value | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96
| p value |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3
| Different ? | yes | yes | yes | yes | yes | yes | yes | yes
70% | s value |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2 |  $\gg$1e2
| c value | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96
| p value |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3
| Different ? | yes | yes | yes | yes | yes | yes | yes | yes

Matched GMC/H II-regions vs Matched GMC/H II-regions
---
Minimum Overlap | GMC properties
Percentage |  | Size | $L_{\mathrm{CO}}$ | $\sigma_{v}$ | $\Sigma_{\mathrm{mol}}$ | $\sigma_{0}$ | $\alpha_{\mathrm{vir}}$ | $T_{\mathrm{peak}}$ | $\tau_{\mathrm{ff}}$
10% vs 40% | s value |  $\gg$1e2 | 21.72 | 6.79 | 63.95 | 7.13 | 14.61 | 35.91 | 97.71
| c value | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96
| p value |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3
| Different ? | yes | yes | yes | yes | yes | yes | yes | yes
10% vs 70% | s value |  $\gg$1e2 | 48.69 | 13.61 | 55.43 | 8.62 | 8.24 | 37.88 |  $\gg$1e2
| c value | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96
| p value |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3 |  $\ll$1e-3
| Different ? | yes | yes | yes | yes | yes | yes | yes | yes
40% vs 70% | s value | 30.20 | 12.92 | 2.85 | 7.35 | 0.74 | -0.50 | 6.15 | 20.06
| c value | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | 1.96
| p value |  $\ll$1e-3 |  $\ll$1e-3 | 2.22e-02 |  $\ll$1e-3 | 1.63e-01 | 2.50e-01 | 1.38e-03 |  $\ll$1e-3
| Different ? | yes | yes | yes | yes | no | no | yes | yes

Figure 14: Histograms of the $R^{2}$ coefficient between the different GMC
properties and the $\mathrm{H\alpha}$ luminosity, after shuffling the
$\mathrm{H\alpha}$ luminosity values, for three different minimum overlap
percentage of the H II/GMC pairs: 10% for the left column, 40% for the middle
one, and 70% for the right one. The solid lines show the mean of the
distribution and the dotted lines the 1 standard deviation interval around the
mean. Figure 15: Histograms of the $R^{2}$ coefficient between the different
GMC properties and the $\mathrm{H\alpha}$ luminosity, after shuffling the
$\mathrm{H\alpha}$ luminosity values while keeping the relationship between
$\mathrm{H\alpha}$ luminosity and H II region radius values, for three
different MOP of the H II/GMC pairs: 10% for the left column, 40% for the
middle one, and 70% for the right one. The solid lines show the mean of the
distribution and the dotted lines the 1 standard deviation interval around the
mean. Figure 16: Bootstrap tests of the significance of the power law index
change with the MOP. The red line represents the power law index obtained
after matching with a 70% overlap, and the dashed lines its confidence
interval. The blue distribution represents the power law indices obtained
after randomly sampling N pairs from the parent distribution (10% overlap),
where N is the size of the 70% minimal overlap distribution. This random
sampling has been performed 10000 times in order to obtain the distribution.
This figure shows that the change in power law index with the MOP cannot arise
from a random sampling of the parent population, except for the surface
density.

##  Appendix D Supplemental figures about the variability of the properties of
the matched GMC/H II-regions as a function of the galaxy

Table 7: Correlation properties ($R^{2}$ coefficient and power law index) for
various GMC properties as a function of the $\mathrm{H\alpha}$ luminosity for
each galaxy in the sample. The minimum overlap percentage used for the
matching is 40%. The galaxies are sorted by decreasing $R^{2}$ coefficient for
each individual sub-table.

Molecular Mass
---
Galaxy | $R^{2}$ | slope
NGC 4535 | 0.65 | 0.51
NGC 1672 | 0.60 | 0.59
NGC 4321 | 0.54 | 0.55
NGC 3351 | 0.51 | 0.47
NGC 1566 | 0.48 | 0.57
NGC 0628 | 0.43 | 0.46
NGC 3627 | 0.43 | 0.46
NGC 4254 | 0.42 | 0.59
NGC 1385 | 0.42 | 0.38
NGC 4303 | 0.38 | 0.47
NGC 1300 | 0.37 | 0.37
NGC 1512 | 0.36 | 0.24
NGC 1365 | 0.35 | 0.33
NGC 2835 | 0.25 | 0.21
NGC 1087 | 0.17 | 0.21
NGC 5068 | 0.15 | 0.18
NGC 1433 | 0.10 | 0.13

Surface density
---
Galaxy | $R^{2}$ | slope
NGC 3627 | 0.37 | 0.34
NGC 4535 | 0.35 | 0.34
NGC 4321 | 0.25 | 0.30
NGC 1566 | 0.23 | 0.32
NGC 0628 | 0.15 | 0.20
NGC 1672 | 0.13 | 0.21
NGC 3351 | 0.11 | 0.22
NGC 4254 | 0.11 | 0.24
NGC 5068 | 0.10 | 0.18
NGC 1512 | 0.09 | 0.15
NGC 1300 | 0.06 | 0.14
NGC 1385 | 0.05 | 0.13
NGC 4303 | 0.05 | 0.17
NGC 2835 | 0.04 | 0.11
NGC 1087 | 0.04 | 0.12
NGC 1365 | 0.02 | 0.08
NGC 1433 | 0.00 | -0.03

Peak Temperature
---
Galaxy | $R^{2}$ | slope
NGC 1672 | 0.71 | 0.43
NGC 4535 | 0.69 | 0.30
NGC 4321 | 0.57 | 0.34
NGC 3627 | 0.45 | 0.26
NGC 3351 | 0.44 | 0.28
NGC 1566 | 0.41 | 0.31
NGC 1385 | 0.38 | 0.24
NGC 1365 | 0.34 | 0.16
NGC 1512 | 0.34 | 0.15
NGC 4303 | 0.33 | 0.29
NGC 0628 | 0.32 | 0.19
NGC 4254 | 0.32 | 0.38
NGC 1300 | 0.31 | 0.16
NGC 1087 | 0.16 | 0.14
NGC 2835 | 0.15 | 0.08
NGC 5068 | 0.06 | 0.07
NGC 1433 | 0.06 | 0.05

Characteristic Turbulent Linewidth
---
Galaxy | $R^{2}$ | slope
NGC 3627 | 0.26 | 0.10
NGC 4321 | 0.23 | 0.15
NGC 1566 | 0.23 | 0.15
NGC 4254 | 0.17 | 0.15
NGC 1433 | 0.12 | 0.10
NGC 1300 | 0.12 | 0.10
NGC 1512 | 0.11 | 0.16
NGC 4535 | 0.10 | 0.09
NGC 1672 | 0.09 | 0.07
NGC 1365 | 0.08 | 0.07
NGC 0628 | 0.07 | 0.11
NGC 4303 | 0.05 | 0.07
NGC 2835 | 0.05 | 0.08
NGC 1385 | 0.04 | 0.08
NGC 5068 | 0.03 | 0.08
NGC 1087 | 0.01 | 0.04
NGC 3351 | 0.00 | 0.02

Figure 17: $R^{2}$ coefficients of the temperature at peak with the
$\mathrm{H\alpha}$ luminosity considering H II region/GMC pairs from each
galaxy in the sample separately. Top from left to right: $R^{2}$ coefficients
versus the number of matched H II regions and GMCs, distance, inclination and
total stellar mass of the host galaxy. Bottom from left to right: $R^{2}$
coefficients versus the galaxy’s CO luminosity, total $\mathrm{H\alpha}$
luminosity, average stellar surface density within a 500 pc radius around each
of the H II region/GMC pairs and the galaxy’s offset from the main sequence.
The red dashed line shows the global $R^{2}$ coefficient from Section 5.
Figure 18: Same as figure 17 but the $R^{2}$ values are replaced by the power
law indices.

Figures 17 and 18 present respectively the correlations coefficients and power
law indices of the correlation between the GMC peak brightness and the H II
region $\mathrm{H\alpha}$ luminosity, as a function of different galaxy-wide
properties. The properties in question are: the total number of matched GMC/H
II regions, the galaxy’s distance, inclination, stellar mass, total CO
luminosity, total $\mathrm{H\alpha}$ luminosity, mean stellar density
environment and distance from the main sequence. For these figures the MOP is
40%. Reassuringly, the galaxy’s distance, inclination or number of matched
GMC/H II regions doesn’t have any impact on the found correlations.

To be more quantitative about the effect of inclination and metallicity, we
computed a linear regression of the correlation coefficient $R^{2}$ (of the
peak temperature correlation with $\mathrm{H\alpha}$ luminosity) against the
galaxies inclinations, total CO luminosities and metallicities. This will
allow us to check whether a galactic property has a significant impact on the
correlations or not.

For the linear regression between $R^{2}$ and the galaxy inclination, the
resulting correlation coefficient and slope are respectively $0.07\pm 0.08$
and $0.004\pm 0.009$. These numbers are consistent with 0, so the galaxy
inclination has no impact on the correlations. For the linear regression
between $R^{2}$ and the galaxy metallicity, the resulting correlation
coefficient and slope are respectively $0.15\pm 0.18$ and $0.89\pm 1.15$.
These numbers are also consistent with 0, so the galaxy metallicity has no
impact on the correlations. For comparison, the linear regression between
$R^{2}$ and the galaxy’s total CO luminosity yields a correlation coefficient
and a slope of respectively $0.32\pm 0.13$ and $0.16\pm 0.06$.

##  Appendix E Supplemental information about the co-variations of GMC
properties

Figure 19: Evolution of Larson’s, Heyer’s, and peak temperature vs surface
density correlations for all the GMCs in the sample first columns, and three
different minimum overlap percentage of the H II/GMC pairs: 10% for the second
column, 40% for the third one, and 70% for the fourth one. The black solid and
dotted lines show the power law fits and their uncertainty, respectively. The
dashed lines show the $\pm 3\sigma$ levels from the fitted line. The power law
parameters are displayed on the bottom right corner of each panel. The red
solid lines show the power law fit for the parent population (all GMCs in the
sample). Figure 20: Evolution of joint PDF between the peak temperature (top),
characteristic turbulent linewidth (bottom) and the molecular mass for all the
GMCs in the sample first columns, and three different MOP of the H II/GMC
pairs: 10% for the second column, 40% for the third one, and 70% for the
fourth. The reminder of the layout is similar to Fig. 19.

The evolution of the correlations of the GMC properties with the
$\mathrm{H\alpha}$ luminosity of the associated H II regions show two
different trends. It is well known that GMC properties co-vary through
Larson’s and Heyer’s relationships (Heyer & Brunt 2004; Larson 1981). We ask
here which part of the uncovered trends are controlled by these co-variations
of the GMC properties.

Figure 19 shows the joint PDFs of the quantities that are known to co-vary in