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Kathryn Kreckel

Publications and source records attributed to Kathryn Kreckel.

At least 91 records · Page 5Linked to original sources

The Two-Dimensional Metallicity Distribution and Mixing Scales of Nearby Galaxies

Understanding the spatial distribution of metals within galaxies allows us to study the processes of chemical enrichment and mixing in the interstellar medium (ISM). In this work, we map the two-dimensional distribution of metals using a Gaussian Process Regression (GPR) for 19 star-forming galaxies observed with the Very Large Telescope/Multi Unit Spectroscopic Explorer (VLT-MUSE) as part of the PHANGS-MUSE survey. We find that 12 of our 19 galaxies show significant two-dimensional metallicity variation. Those without significant variations typically have fewer metallicity measurements, indicating this is due to the dearth of HII regions in these galaxies, rather than a lack of higher-order variation. After subtracting a linear radial gradient, we see no enrichment in the spiral arms versus the disc. We measure the 50 per cent correlation scale from the two-point correlation function of these radially-subtracted maps, finding it to typically be an order of magnitude smaller than the fitted GPR kernel scale length. We study the dependence of the two-point correlation scale length with a number of global galaxy properties. We find no relationship between the 50 per cent correlation scale and the overall gas turbulence, in tension with existing theoretical models. We also find more actively star forming galaxies, and earlier type galaxies have a larger 50 per cent correlation scale. The size and stellar mass surface density do not appear to correlate with the 50 per cent correlation scale, indicating that perhaps the evolutionary state of the galaxy and its current star formation activity is the strongest indicator of the homogeneity of the metal distribution.

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PHANGS-MUSE: the HII region luminosity function of local star-forming galaxies

We use an unprecedented sample of about 23,000 HII regions detected at an average physical resolution of 67pc in the PHANGS-MUSE sample to study the extragalactic HII region Ha luminosity function (LF). Our observations probe the star-forming disk of 19 nearby spiral galaxies with low inclination and located close to the star formation main sequence at z=0. The mean LF slope $α$ in our sample is =1.73 with a $σ$ of 0.15. We find that $α$ decreases with the galaxy's star formation rate surface density and argue that this is driven by an enhanced clustering of young stars at high gas surface densities. Looking at the HII regions within single galaxies we find that no significant variations occur between the LF of the inner and outer part of the star-forming disk, whereas the LF in the spiral arm areas is shallower than in the inter-arm areas for six out of the 13 galaxies with clearly visible spiral arms. We attribute these variations to the spiral arms increasing the molecular clouds arm--inter-arm mass contrast and find suggestive evidence that they are more evident for galaxies with stronger spiral arms. Furthermore, we find systematic variations in $α$ between samples of HII regions with high and low ionization parameter q and argue that they are driven by the aging of HII regions.

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The PHANGS-HST Survey: Physics at High Angular resolution in Nearby GalaxieS with the Hubble Space Telescope

The PHANGS program is building the first dataset to enable the multi-phase, multi-scale study of star formation across the nearby spiral galaxy population. This effort is enabled by large survey programs with ALMA, VLT/MUSE, and HST, with which we have obtained CO(2-1) imaging, optical spectroscopic mapping, and high resolution UV-optical imaging, respectively. Here, we present PHANGS-HST, which has obtained five band NUV-U-B-V-I imaging of the disks of 38 spiral galaxies at distances of 4-23 Mpc, and parallel V and I band imaging of their halos, to provide a census of tens of thousands of compact star clusters, and multi-scale stellar associations. The combination of HST, ALMA, and VLT/MUSE observations will yield an unprecedented joint catalog of the observed and physical properties of ~100,000 star clusters, associations, HII regions, and molecular clouds. With these basic units of star formation, PHANGS will systematically chart the evolutionary cycling between gas and stars, across a diversity of galactic environments found in nearby galaxies. We discuss the design of the PHANGS-HST survey, and provide an overview of the HST data processing pipeline and first results, highlighting new methods for selecting star cluster candidates, morphological classification of candidates with convolutional neural networks, and identification of stellar associations over a range of physical scales with a watershed algorithm. We describe the cross-observatory imaging, catalogs, and software products to be released. These high-level science products will seed a broad range of investigations, in particular, the study of embedded stellar populations and dust with JWST, for which a PHANGS Cycle 1 Treasury program to obtain eight band 2-21 $μ$m imaging has been approved.

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Star formation in the nearby dwarf galaxy DDO 53: interplay between gas accretion and stellar feedback

We present the results of a multiwavelength study of the nearby dwarf galaxy DDO 53 - a relatively isolated member of the M 81 group. We analyse the atomic and ionised gas kinematics (based on the observations with Fabry-Perot interferometer in H$α$ line and archival data in HI 21 cm line), distribution, excitation and oxygen abundance of the ionised gas (based on the long-slit and integral-field spectroscopy and on imaging with narrow-band filters), and their relation with the young massive stars (based on archival HST data). We detect a faint 2-kpc sized supershell of ionised gas surrounding the galaxy. Most probably, this structure represents a large-scale gas outflow, however it could be also created by the ionising quanta leaking from star-forming regions to the marginally detected atomic hydrogen surrounding the galactic disc. We analyse the properties of the anomalous HI in the north part of the galaxy and find that its peculiar kinematics is also traced by ionised gas. We argue that this HI feature is related to the accreting gas cloud captured from the intergalactic medium or remaining after the merger event occurred >1 Gyr ago. The infalling gas produces shocks in the interstellar medium and could support the star formation activity in the brightest region in DDO 53.

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PHANGS-ALMA: Arcsecond CO(2-1) Imaging of Nearby Star-Forming Galaxies

We present PHANGS-ALMA, the first survey to map CO J=2-1 line emission at ~1" ~ 100pc spatial resolution from a representative sample of 90 nearby (d<~20 Mpc) galaxies that lie on or near the z=0 "main sequence" of star-forming galaxies. CO line emission traces the bulk distribution of molecular gas, which is the cold, star-forming phase of the interstellar medium. At the resolution achieved by PHANGS-ALMA, each beam reaches the size of a typical individual giant molecular cloud (GMC), so that these data can be used to measure the demographics, life-cycle, and physical state of molecular clouds across the population of galaxies where the majority of stars form at z=0. This paper describes the scientific motivation and background for the survey, sample selection, global properties of the targets, ALMA observations, and characteristics of the delivered ALMA data and derived data products. As the ALMA sample serves as the parent sample for parallel surveys with VLT/MUSE, HST, AstroSat, VLA, and other facilities, we include a detailed discussion of the sample selection. We detail the estimation of galaxy mass, size, star formation rate, CO luminosity, and other properties, compare estimates using different systems and provide best-estimate integrated measurements for each target. We also report the design and execution of the ALMA observations, which combine a Cycle~5 Large Program, a series of smaller programs, and archival observations. Finally, we present the first 1" resolution atlas of CO emission from nearby galaxies and describe the properties and contents of the first PHANGS-ALMA public data release.

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PHANGS-ALMA Data Processing and Pipeline

We describe the processing of the PHANGS-ALMA survey and present the PHANGS-ALMA pipeline, a public software package that processes calibrated interferometric and total power data into science-ready data products. PHANGS-ALMA is a large, high-resolution survey of CO J=2-1 emission from nearby galaxies. The observations combine ALMA's main 12-m array, the 7-m array, and total power observations and use mosaics of dozens to hundreds of individual pointings. We describe the processing of the u-v data, imaging and deconvolution, linear mosaicking, combining interferometer and total power data, noise estimation, masking, data product creation, and quality assurance. Our pipeline has a general design and can also be applied to VLA and ALMA observations of other spectral lines and continuum emission. We highlight our recipe for deconvolution of complex spectral line observations, which combines multiscale clean, single scale clean, and automatic mask generation in a way that appears robust and effective. We also emphasize our two-track approach to masking and data product creation. We construct one set of "broadly masked" data products, which have high completeness but significant contamination by noise, and another set of "strictly masked" data products, which have high confidence but exclude faint, low signal-to-noise emission. Our quality assurance tests, supported by simulations, demonstrate that 12-m+7-m deconvolved data recover a total flux that is significantly closer to the total power flux than the 7-m deconvolved data alone. In the appendices, we measure the stability of the ALMA total power calibration in PHANGS--ALMA and test the performance of popular short-spacing correction algorithms.

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On the duration of the embedded phase of star formation

Feedback from massive stars plays a key role in molecular cloud evolution. After the onset of star formation, the young stellar population is exposed by photoionization, winds, supernovae, and radiation pressure from massive stars. Recent observations of nearby galaxies have provided the evolutionary timeline between molecular clouds and exposed young stars, but the duration of the embedded phase of massive star formation is still ill-constrained. We measure how long massive stellar populations remain embedded within their natal cloud, by applying a statistical method to six nearby galaxies at 20-100 pc resolution, using CO, Spitzer 24$\rm\,μm$, and H$α$ emission as tracers of molecular clouds, embedded star formation, and exposed star formation, respectively. We find that the embedded phase (with CO and 24$\rm\,μm$ emission) lasts for $2{-}7$ Myr and constitutes $17{-}47\%$ of the cloud lifetime. During approximately the first half of this phase, the region is invisible in H$α$, making it heavily obscured. For the second half of this phase, the region also emits in H$α$ and is partially exposed. Once the cloud has been dispersed by feedback, 24$\rm\,μm$ emission no longer traces ongoing star formation, but remains detectable for another $2{-}9$ Myr through the emission from ambient CO-dark gas, tracing star formation that recently ended. The short duration of massive star formation suggests that pre-supernova feedback (photoionization and winds) is important in disrupting molecular clouds. The measured timescales do not show significant correlations with environmental properties (e.g. metallicity). Future JWST observations will enable these measurements routinely across the nearby galaxy population.

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The organization of cloud-scale gas density structure: high resolution CO vs. 3.6 $μ$m brightness contrasts in nearby galaxies

In this paper we examine the factors that shape the distribution of molecular gas surface densities on the 150 pc scale across 67 morphologically diverse star-forming galaxies in the PHANGS-ALMA CO (2-1) survey. Dividing each galaxy into radial bins, we measure molecular gas surface density contrasts, defined here as the ratio between a fixed high percentile of the CO distribution and a fixed reference level in each bin. This reference level captures the level of the faint CO floor that extends between bright filamentary features, while the intensity level of the higher percentile probes the structures visually associated with bright, dense ISM features like spiral arms, bars, and filaments. We compare these contrasts to matched percentile-based measurements of the 3.6 $μ$m emission measured using Spitzer/IRAC imaging, which trace the underlying stellar mass density. We find that the logarithms of CO contrasts on 150 pc scales are 3-4 times larger than, and positively correlated with, the logarithms of 3.6 $μ$m contrasts probing smooth non-axisymmetric stellar bar and spiral structures. The correlation appears steeper than linear, consistent with the compression of gas as it flows supersonically in response to large-scale stellar structures, even in the presence of weak or flocculent spiral arms. Stellar dynamical features appear to play an important role in setting the cloud-scale gas density in our galaxies, with gas self-gravity perhaps playing a weaker role in setting the 150 pc-scale distribution of gas densities.

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Resolving the Dust-to-Metals Ratio and CO-to-H$_2$ Conversion Factor in the Nearby Universe

We investigate the relationship between the dust-to-metals ratio (D/M) and the local interstellar medium environment at ~2 kpc resolution in five nearby galaxies: IC342, M31, M33, M101, and NGC628. A modified blackbody model with a broken power-law emissivity is used to model the dust emission from 100 to 500 um observed by Herschel. We utilize the metallicity gradient derived from auroral line measurements in HII regions whenever possible. Both archival and new CO rotational line and HI 21 cm maps are adopted to calculate gas surface density, including new wide field CO and HI maps for IC342 from IRAM and the VLA, respectively. We experiment with several prescriptions of CO-to-H$_2$ conversion factor, and compare the resulting D/M-metallicity and D/M-density correlations, both of which are expected to be non-negative from depletion studies. The D/M is sensitive to the choice of the conversion factor. The conversion factor prescriptions based on metallicity only yield too much molecular gas in the center of IC342 to obtain the expected correlations. Among the prescriptions tested, the one that yields the expected correlations depends on both metallicity and surface density. The 1-$σ$ range of the derived D/M spans 0.40-0.58. Compared to chemical evolution models, our measurements suggest that the dust growth time scale is much shorter than the dust destruction time scale. The measured D/M is consistent with D/M in galaxy-integrated studies derived from infrared dust emission. Meanwhile, the measured D/M is systematically higher than the D/M derived from absorption, which likely indicates a systematic offset between the two methods.

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PHANGS-HST: Star Cluster Spectral Energy Distribution Fitting with CIGALE

The sensitivity and angular resolution of photometric surveys executed by the Hubble Space Telescope (HST) enable studies of individual star clusters in galaxies out to a few tens of megaparsecs. The fitting of spectral energy distributions (SEDs) of star clusters is essential for measuring their physical properties and studying their evolution. We report on the use of the publicly available Code Investigating GALaxy Emission (CIGALE) SED fitting package to derive ages, stellar masses, and reddenings for star clusters identified in the Physics at High Angular resolution in Nearby GalaxieS-HST (PHANGS-HST) survey. Using samples of star clusters in the galaxy NGC 3351, we present results of benchmark analyses performed to validate the code and a comparison to SED fitting results from the Legacy ExtraGalactic Ultraviolet Survey (LEGUS). We consider procedures for the PHANGS-HST SED fitting pipeline, e.g., the choice of single stellar population models, the treatment of nebular emission and dust, and the use of fluxes versus magnitudes for the SED fitting. We report on the properties of clusters in NGC 3351 and find, on average, the clusters residing in the inner star-forming ring of NGC 3351 are young ($< 10$ Myr) and massive ($10^{5} M_{\odot}$) while clusters in the stellar bulge are significantly older. Cluster mass function fits yield $β$ values around -2, consistent with prior results with a tendency to be shallower at the youngest ages. Finally, we explore a Bayesian analysis with additional physically-motivated priors for the distribution of ages and masses and analyze the resulting cluster distributions.

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Distances to PHANGS Galaxies: New Tip of the Red Giant Branch Measurements and Adopted Distances

PHANGS-HST is an ultraviolet-optical imaging survey of 38 spiral galaxies within ~20 Mpc. Combined with the PHANGS-ALMA, PHANGS-MUSE surveys and other multiwavelength data, the dataset will provide an unprecedented look into the connections between young stars, HII regions, and cold molecular gas in these nearby star-forming galaxies. Accurate distances are needed to transform measured observables into physical parameters (e.g., brightness to luminosity, angular to physical sizes of molecular clouds, star clusters and associations). PHANGS-HST has obtained parallel ACS imaging of the galaxy halos in the F606W and F814W bands. Where possible, we use these parallel fields to derive tip of the red giant branch (TRGB) distances to these galaxies. In this paper, we present TRGB distances for 11 galaxies from ~4 to ~15 Mpc, based on the first year of PHANGS-HST observations. Five of these represent the first published TRGB distance measurements (IC 5332, NGC 2835, NGC 4298, NGC 4321, and NGC 4328), and eight of which are the best available distances to these targets. We also provide a compilation of distances for the 118 galaxies in the full PHANGS sample, which have been adopted for the first PHANGS-ALMA public data release.

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Pre-supernova feedback mechanisms drive the destruction of molecular clouds in nearby star-forming disc galaxies

It is a major open question which physical processes stop the accretion of gas onto giant molecular clouds (GMCs) and limit the efficiency at which gas is converted into stars within these GMCs. While feedback from supernova explosions has been the popular feedback mechanism included in simulations of galaxy formation and evolution, `early' feedback mechanisms such as stellar winds, photoionisation and radiation pressure are expected to play an important role in dispersing the gas after the onset of star formation. These feedback processes typically take place on small scales ($\sim 10-100$ pc) and their effects have therefore been difficult to constrain in environments other than the Milky Way. We apply a novel statistical method to $\sim 1$" resolution maps of CO and Ha emission across a sample of nine nearby disc galaxies, in order to measure the time over which GMCs are dispersed by feedback from young, high-mass stars, as a function of the galactic environment. We find that GMCs are typically dispersed within $\sim$ 3 Myr after the emergence of unembedded high-mass stars, showing no significant trend with galactocentric radius. Comparison with analytical predictions demonstrates that, independently of the environment, early feedback mechanisms (particularly photoionisation and stellar winds) play a crucial role in dispersing GMCs and limiting their star formation efficiency in nearby galaxies. Finally, we show that the efficiency at which the energy injected by these early feedback mechanisms couples with the parent GMC is relatively low (a few tens of per cent), such that the vast majority of momentum and energy emitted by the young stellar populations escapes the parent GMC.

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Measuring the mixing scale of the ISM within nearby spiral galaxies

The spatial distribution of metals reflects, and can be used to constrain, the processes of chemical enrichment and mixing. Using PHANGS-MUSE optical integral field spectroscopy, we measure the gas phase oxygen abundances (metallicities) across 7,138 HII regions in a sample of eight nearby disc galaxies. In Paper I (Kreckel et al. 2019) we measure and report linear radial gradients in the metallicities of each galaxy, and qualitatively searched for azimuthal abundance variations. Here, we examine the two-dimensional variation in abundances once the radial gradient is subtracted, Delta(O/H), in order to quantify the homogeneity of the metal distribution and to measure the mixing scale over which HII region metallicities are correlated. We observe low (0.03--0.05 dex) scatter in Delta(O/H) globally in all galaxies, with significantly lower (0.02--0.03 dex) scatter on small (<600 pc) spatial scales. This is consistent with the measurement uncertainties, and implies the two-dimensional metallicity distribution is highly correlated on scales of <600 pc. We compute the two point correlation function for metals in the disc in order to quantify the scale lengths associated with the observed homogeneity. This mixing scale is observed to correlate better with the local gas velocity dispersion (of both cold and ionized gas) than with the star formation rate. Selecting only HII regions with enhanced abundances relative to a linear radial gradient, we do not observe increased homogeneity on small scales. This suggests that the observed homogeneity is driven by the mixing introducing material from large scales rather than by pollution from recent and on-going star formation.

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Molecular Gas Properties on Cloud Scales Across the Local Star-forming Galaxy Population

Using the PHANGS-ALMA CO (2-1) survey, we characterize molecular gas properties on ${\sim}$100 pc scales across 102,778 independent sightlines in 70 nearby galaxies. This yields the best synthetic view of molecular gas properties on cloud scales across the local star-forming galaxy population obtained to date. Consistent with previous studies, we observe a wide range of molecular gas surface densities (3.4 dex), velocity dispersions (1.7 dex), and turbulent pressures (6.5 dex) across the galaxies in our sample. Under simplifying assumptions about sub-resolution gas structure, the inferred virial parameters suggest that the kinetic energy of the molecular gas typically exceeds its self-gravitational binding energy at ${\sim}$100 pc scales by a modest factor (1.3 on average). We find that the cloud-scale surface density, velocity dispersion, and turbulent pressure (1) increase towards the inner parts of galaxies, (2) are exceptionally high in the centers of barred galaxies (where the gas also appears less gravitationally bound), and (3) are moderately higher in spiral arms than in inter-arm regions. The galaxy-wide averages of these gas properties also correlate with the integrated stellar mass, star formation rate, and offset from the star-forming main sequence of the host galaxies. These correlations persist even when we exclude regions with extraordinary gas properties in galaxy centers, which contribute significantly to the inter-galaxy variations. Our results provide key empirical constraints on the physical link between molecular cloud populations and their galactic environment.

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The lifecycle of molecular clouds in nearby star-forming disc galaxies

It remains a major challenge to derive a theory of cloud-scale ($\lesssim100$ pc) star formation and feedback, describing how galaxies convert gas into stars as a function of the galactic environment. Progress has been hampered by a lack of robust empirical constraints on the giant molecular cloud (GMC) lifecycle. We address this problem by systematically applying a new statistical method for measuring the evolutionary timeline of the GMC lifecycle, star formation, and feedback to a sample of nine nearby disc galaxies, observed as part of the PHANGS-ALMA survey. We measure the spatially-resolved ($\sim100$ pc) CO-to-H$α$ flux ratio and find a universal de-correlation between molecular gas and young stars on GMC scales, allowing us to quantify the underlying evolutionary timeline. GMC lifetimes are short, typically 10-30 Myr, and exhibit environmental variation, between and within galaxies. At kpc-scale molecular gas surface densities $Σ_{\rm H_2}\geqslant8$M$_{\odot}$pc$^{-2}$, the GMC lifetime correlates with time-scales for galactic dynamical processes, whereas at $Σ_{\rm H_2}\leqslant8$M$_{\odot}$pc$^{-2}$ GMCs decouple from galactic dynamics and live for an internal dynamical time-scale. After a long inert phase without massive star formation traced by H$α$ (75-90% of the cloud lifetime), GMCs disperse within just 1-5 Myr once massive stars emerge. The dispersal is most likely due to early stellar feedback, causing GMCs to achieve integrated star formation efficiencies of 4-10% These results show that galactic star formation is governed by cloud-scale, environmentally-dependent, dynamical processes driving rapid evolutionary cycling. GMCs and HII regions are the fundamental units undergoing these lifecycles, with mean separations of 100-300 pc in star-forming discs. Future work should characterise the multi-scale physics and mass flows driving these lifecycles.

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The headlight cloud in NGC 628: An extreme giant molecular cloud in a typical galaxy disk

Cloud-scale surveys of molecular gas reveal the link between molecular clouds properties and star formation (SF) across a range of galactic environments. Cloud populations in galaxy disks are considered to be representative of the `normal' SF. At high resolution, however, clouds with exceptional gas properties and SF activity may also be observed in normal disk environments. In this paper, we study the brightest cloud traced in CO emission in the disk of NGC628. The cloud is spatially coincident with an extremely bright HII region. We characterize its molecular gas properties and investigate how feedback and large-scale processes influence the properties of the molecular gas. High resolution CO ALMA observations are used to characterize its mass and dynamical state, which are compared to other clouds in NGC628. A LVG analysis is used to constrain the beam-diluted density and temperature of the molecular gas. We analyze the MUSE spectrum using Starburst99 to characterize the young stellar population associated with the HII region. The cloud is massive ($1-2\times10^7$M$_{\odot}$), with a beam-diluted density of $n_{\rm H_2}=5\times10^4$ cm$^{-3}$. It has a low virial parameter, suggesting that its CO emission may be overluminous due to heating by the HII region. A young ($2-4$ Myr), massive $3\times10^{5}$ M$_{\odot}$ stellar population is associated. We argue that the cloud is currently being destroyed by feedback from young massive stars. Due to the cloud's large mass, this phase of the cloud's evolution is long enough for the impact of feedback on the excitation of the gas to be observed. Its high mass may be related to its location at a spiral co-rotation radius, where gas experiences reduced galactic shear compared to other regions of the disk, and receives a sustained inflow of gas that can promote the cloud's mass growth.

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The Gas-Star Formation Cycle in Nearby Star-Forming Galaxies I. Assessment of Multi-scale Variations

The processes regulating star formation in galaxies are thought to act across a hierarchy of spatial scales. To connect extragalactic star formation relations from global and kpc-scale measurements to recent cloud-scale resolution studies, we have developed a simple, robust method that quantifies the scale dependence of the relative spatial distributions of molecular gas and recent star formation. In this paper, we apply this method to eight galaxies with roughly 1 arcsec resolution molecular gas imaging from the PHANGS-ALMA and PAWS surveys that have matched resolution, high quality narrowband Halpha imaging. At a common scale of 140pc, our massive (log(Mstar/Msun)=9.3-10.7), normally star-forming (SFR/Msun/yr=0.3-5.9) galaxies exhibit a significant reservoir of quiescent molecular gas not associated with star formation as traced by Halpha emission. Galactic structures act as backbones for both molecular and HII region distributions. As we degrade the spatial resolution, the quiescent molecular gas disappears, with the most rapid changes occurring for resolutions up to about 0.5kpc. As the resolution becomes poorer, the morphological features become indistinct for spatial scales larger than about 1kpc. The method is a promising tool to search for relationships between the quiescent or star-forming molecular reservoir and galaxy properties, but requires a larger sample size to identify robust correlations between the star-forming molecular gas fraction and global galaxy parameters.

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Mapping electron temperature variations across a spiral arm in NGC 1672

We report one of the first extragalactic observations of electron temperature variations across a spiral arm. Using MUSE mosaic observations of the nearby galaxy NGC 1672, we measure the [N II]5755 auroral line in a sample of 80 HII regions in the eastern spiral arm of NGC1672. We discover systematic temperature variations as a function of distance perpendicular to the spiral arm. The electron temperature is lowest on the spiral arm itself and highest on the downstream side. Photoionization models of different metallicity, pressure, and age of the ionizing source are explored to understand what properties of the interstellar medium drive the observed temperature variations. An azimuthally varying metallicity appears to be the most likely cause of the temperature variations. The electron temperature measurements solidify recent discoveries of azimuthal variations of oxygen abundance based on strong lines, and rule out the possibility that the abundance variations are artefacts of the strong-line calibrations.

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