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Brent Groves

Publications and source records attributed to Brent Groves.

At least 109 records · Page 6Linked to original sources

SH$α$DE: Survey description and mass-kinematics scaling relations for dwarf galaxies

The Study of H$α$ from Dwarf Emissions (SH$α$DE) is a high spectral resolution (R=13500) H$α$ integral field survey of 69 dwarf galaxies with stellar masses $10^6<M_\star<10^9 \,\rm{M_\odot}$. The survey used FLAMES on the ESO Very Large Telescope. SH$α$DE is designed to study the kinematics and stellar populations of dwarf galaxies using consistent methods applied to massive galaxies and at matching level of detail, connecting these mass ranges in an unbiased way. In this paper we set out the science goals of SH$α$DE, describe the sample properties, outline the data reduction and analysis processes. We investigate the $\log{M_{\star}}-\log{S_{0.5}}$ mass-kinematics scaling relation, which have previously shown potential for combining galaxies of all morphologies in a single scaling relation. We extend the scaling relation from massive galaxies to dwarf galaxies, demonstrating this relation is linear down to a stellar mass of $M_{\star}\sim10^{8.6}\,\rm{M_\odot}$. Below this limit, the kinematics of galaxies inside one effective radius appear to be dominated by the internal velocity dispersion limit of the H$α$-emitting gas, giving a bend in the $\log{M_{\star}}-\log{S_{0.5}}$ relation. Replacing stellar mass with total baryonic mass using gas mass estimate reduces the severity but does not remove the linearity limit of the scaling relation. An extrapolation to estimate the galaxies' dark matter halo masses, yields a $\log{M_{h}}-\log{S_{0.5}}$ scaling relation that is free of any bend, has reduced curvature over the whole mass range, and brings galaxies of all masses and morphologies onto the virial relation.

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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 VLA-COSMOS 3 GHz Large Project: Evolution of specific star formation rates out to $z\sim5$

We provide a coherent, uniform measurement of the evolution of the logarithmic star formation rate (SFR) - stellar mass ($M_*$) relation, called the main sequence of star-forming galaxies (MS), for galaxies out to $z\sim5$. We measure the MS using mean stacks of 3 GHz radio continuum images to derive average SFRs for $\sim$200,000 mass-selected galaxies at $z>0.3$ in the COSMOS field. We describe the MS relation adopting a new model that incorporates a linear relation at low stellar mass (log($M_*$/M$_\odot$)$<$10) and a flattening at high stellar mass that becomes more prominent at low redshift ($z<1.5$). We find that the SFR density peaks at $1.5<z<2$ and at each epoch there is a characteristic stellar mass ($M_* = 1 - 4 \times 10^{10}\mathrm{M}_\odot$) that contributes the most to the overall SFR density. This characteristic mass increases with redshift, at least to $z\sim2.5$. We find no significant evidence for variations in the MS relation for galaxies in different environments traced by the galaxy number density at $0.3<z<3$, nor for galaxies in X-ray groups at $z\sim0.75$. We confirm that massive bulge-dominated galaxies have lower SFRs than disk-dominated galaxies at a fixed stellar mass at $z<1.2$. As a consequence, the increase in bulge-dominated galaxies in the local star-forming population leads to a flattening of the MS at high stellar masses. This indicates that "mass-quenching" is linked with changes in the morphological composition of galaxies at a fixed stellar mass.

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PHANGS CO kinematics: disk orientations and rotation curves at 150 pc resolution

We present kinematic orientations and high resolution (150 pc) rotation curves for 67 main sequence star-forming galaxies surveyed in CO (2-1) emission by PHANGS-ALMA. Our measurements are based on the application of a new fitting method tailored to CO velocity fields. Our approach identifies an optimal global orientation as a way to reduce the impact of non-axisymmetric (bar and spiral) features and the uneven spatial sampling characteristic of CO emission in the inner regions of nearby galaxies. The method performs especially well when applied to the large number of independent lines-of-sight contained in the PHANGS CO velocity fields mapped at 1'' resolution. The high resolution rotation curves fitted to these data are sensitive probes of mass distribution in the inner regions of these galaxies. We use the inner slope as well as the amplitude of our fitted rotation curves to demonstrate that CO is a reliable global dynamical mass tracer. From the consistency between photometric orientations from the literature and kinematic orientations determined with our method, we infer that the shapes of stellar disks in the mass range of log($\rm M_{\star}(M_{\odot})$)=9.0-10.9 probed by our sample are very close to circular and have uniform thickness.

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The SAMI Galaxy Survey: Gas velocity dispersions in low-$z$ star-forming galaxies and the drivers of turbulence

We infer the intrinsic ionised gas kinematics for 383 star-forming galaxies across a range of integrated star-formation rates (SFR $\in [10^{-3}, 10^2]$ M$_\odot$ yr$^{-1}$) at $z \lesssim 0.1$ using a consistent 3D forward-modelling technique. The total sample is a combination of galaxies from the SAMI Galaxy Survey and DYNAMO survey. For typical low-$z$ galaxies taken from the SAMI Galaxy Survey, we find the vertical velocity dispersion ($σ_{v, z}$) to be positively correlated with measures of star-formation rate, stellar mass, HI gas mass, and rotational velocity. The greatest correlation is with star-formation rate surface density ($Σ_\text{SFR}$). Using the total sample, we find $σ_{v, z}$ increases slowly as a function of integrated star-formation rate in the range SFR $\in$ [$10^{-3}$, 1] M$_\odot$ yr$^{-1}$ from $17\pm3$ km s$^{-1}$ to $24\pm5$ km s$^{-1}$ followed by a steeper increase up to $σ_{v, z}$ $\sim 80$ km s$^{-1}$ for SFR $\gtrsim 1$ M$_\odot$ yr$^{-1}$. This is consistent with recent theoretical models that suggest a $σ_{v, z}$ floor driven by star-formation feedback processes with an upturn in $σ_{v, z}$ at higher SFR driven by gravitational transport of gas through the disc.

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The SAMI Galaxy Survey: Decomposed Stellar Kinematics of Galaxy Bulges and Disks

We investigate the stellar kinematics of the bulge and disk components in 826 galaxies with a wide range of morphology from the Sydney-AAO Multi-object Integral-field spectroscopy (SAMI) Galaxy Survey. The spatially-resolved rotation velocity (V) and velocity dispersion ($σ$) of bulge and disk components have been simultaneously estimated using the penalized pixel fitting (pPXF) method with photometrically defined weights for the two components. We introduce a new subroutine of pPXF for dealing with degeneracy in the solutions. We show that the V and $σ$ distributions in each galaxy can be reconstructed using the kinematics and weights of the bulge and disk components. The combination of two distinct components provides a consistent description of the major kinematic features of galaxies over a wide range of morphological types. We present Tully-Fisher and Faber-Jackson relations showing that the galaxy stellar mass scales with both V and $σ$ for both components of all galaxy types. We find a tight Faber-Jackson relation even for the disk component. We show that the bulge and disk components are kinematically distinct: (1) the two components show scaling relations with similar slopes, but different intercepts; (2) the spin parameter $λ_R$ indicates bulges are pressure-dominated systems and disks are supported by rotation; (3) the bulge and disk components have, respectively, low and high values in intrinsic ellipticity. Our findings suggest that the relative contributions of the two components explain, at least to first order, the complex kinematic behaviour of galaxies.

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Spinning Bar and a Star-formation Inefficient Repertoire: Turbulence in Hickson Compact Group NGC7674

The physics regulating star formation (SF) in Hickson Compact Groups (HCG) has thus far been difficult to describe, due to their unique kinematic properties. In this study we expand upon previous works to devise a more physically meaningful SF relation able to better encompass the physics of these unique systems. We combine CO(1--0) data from the Combined Array from Research in Millimeter Astronomy (CARMA) to trace the column density of molecular gas $Σ_\mathrm{gas}$ and deep H$α$ imaging taken on the Southern Astrophysical Research (SOAR) Telescope tracing $Σ_\mathrm{SFR}$ to investigate star formation efficiency across face-on HCG, NGC7674. We find a lack of universality in star formation, with two distinct sequences present in the $Σ_\mathrm{gas}-Σ_\mathrm{SFR}$ plane; one for inside and one for outside the nucleus. We devise a SF relation based on the multi-freefall nature of gas and the critical density, which itself is dependent on the virial parameter $α_{\mathrm{vir}}$, the ratio of turbulent to gravitational energy. We find that our modified SF relation fits the data and describes the physics of this system well with the introduction of a virial parameter of about 5--10 across the galaxy. This $α_{\mathrm{vir}}$ leads to an order-of-magnitude reduction in SFR compared to $α_{\mathrm{vir}}\approx 1$ systems.

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ALMA reveals the molecular gas properties of 5 star-forming galaxies across the main sequence at 3 < z < 3.5

We present the detection of CO(5-4) with S/N> 7 - 13 and a lower CO transition with S/N > 3 (CO(4-3) for 4 galaxies, and CO(3-2) for one) with ALMA in band 3 and 4 in five main sequence star-forming galaxies with stellar masses 3-6x10^10 M/M_sun at 3 < z < 3.5. We find a good correlation between the total far-infrared luminosity LFIR and the luminosity of the CO(5-4) transition L'CO(5-4), where L'CO(5-4) increases with SFR, indicating that CO(5-4) is a good tracer of the obscured SFR in these galaxies. The two galaxies that lie closer to the star-forming main sequence have CO SLED slopes that are comparable to other star-forming populations, such as local SMGs and BzK star-forming galaxies; the three objects with higher specific star formation rates (sSFR) have far steeper CO SLEDs, which possibly indicates a more concentrated episode of star formation. By exploiting the CO SLED slopes to extrapolate the luminosity of the CO(1-0) transition, and using a classical conversion factor for main sequence galaxies of alpha_CO = 3.8 M_sun(K km s^-1 pc^-2)^-1, we find that these galaxies are very gas rich, with molecular gas fractions between 60 and 80%, and quite long depletion times, between 0.2 and 1 Gyr. Finally, we obtain dynamical masses that are comparable with the sum of stellar and gas mass (at least for four out of five galaxies), allowing us to put a first constraint on the alpha_CO parameter for main sequence galaxies at an unprecedented redshift.

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What Drives the Redshift Evolution of Strong Emission Line Ratios?

We study the physical mechanisms that cause the offset between low-redshift and high-redshift galaxies on the [OIII]/H$β$ versus [NII]/H$α$ ``Baldwin, Phillips & Terlevich'' (BPT) diagram using a sample of local analogues of high-redshift galaxies. These high-redshift analogue galaxies are selected from the Sloan Digital Sky Survey. Located in the same region on the BPT diagram as the ultra-violet selected galaxies at $z\sim2$, these high-redshift analogue galaxies provide an ideal local benchmark to study the offset between the local and high-redshift galaxies on the BPT diagram. We compare the nitrogen-to-oxygen ratio (N/O), the shape of the ionising radiation field, and ionisation parameters between the high-redshift analogues and a sample of local reference galaxies. The higher ionisation parameter in the high-redshift analogues is the dominant physical mechanism driving the BPT offset from low- to high-redshift, particularly at high {\nii/\ha}. Furthermore, the N/O ratio enhancement also plays a minor role to cause the BPT offset. However, the shape of the ionising radiation field is unlikely to cause the BPT offset because the high-redshift analogues have a similar hard ionising radiation field as local reference galaxies. This hard radiation field cannot be produced by the current standard stellar synthesis models. The stellar rotation and binarity may help solve the discrepancy.

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[CI](1-0) and [CI](2-1) in resolved local galaxies

We present resolved [CI] line intensities of 18 nearby galaxies observed with the SPIRE FTS spectrometer on the Herschel Space Observatory. We use these data along with resolved CO line intensities from $J_\mathrm{up} = 1$ to 7 to interpret what phase of the interstellar medium the [CI] lines trace within typical local galaxies. A tight, linear relation is found between the intensities of the CO(4-3) and [CI](2-1) lines; we hypothesize this is due to the similar upper level temperature of these two lines. We modeled the [CI] and CO line emission using large velocity gradient models combined with an empirical template. According to this modeling, the [CI](1-0) line is clearly dominated by the low-excitation component. We determine [CI] to molecular mass conversion factors for both the [CI](1-0) and [CI](2-1) lines, with mean values of $α_{\mathrm{[CI](1-0)}} = 7.3$ M$_{\mathrm{sun}}$ K$^{-1}$ km$^{-1}$ s pc$^{-2}$ and $α_{\mathrm{[CI](2-1)}} = 34 $ M$_{\mathrm{sun}}$ K$^{-1}$ km$^{-1}$ s pc$^{-2}$ with logarithmic root-mean-square spreads of 0.20 and 0.32 dex, respectively. The similar spread of $α_{\mathrm{[CI](1-0)}}$ to $α_{\mathrm{CO}}$ (derived using the CO(2-1) line) suggests that [CI](1-0) may be just as good a tracer of cold molecular gas as CO(2-1) in galaxies of this type. On the other hand, the wider spread of $α_{\mathrm{[CI](2-1)}}$ and the tight relation found between [CI](2-1) and CO(4-3) suggest that much of the [CI](2-1) emission may originate in warmer molecular gas.

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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 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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The large-scale ionization cones in the Galaxy

There is compelling evidence for a highly energetic Seyfert explosion (10^{56-57} erg) that occurred in the Galactic Centre a few million years ago. The clearest indications are the x-ray/gamma-ray "10 kpc bubbles" identified by the Rosat and Fermi satellites. In an earlier paper, we suggested another manifestation of this nuclear activity, i.e. elevated H-alpha emission along a section of the Magellanic Stream due to a burst (or flare) of ionizing radiation from Sgr A*. We now provide further evidence for a powerful flare event: UV absorption line ratios (in particular CIV/CII, SiIV/SiII) observed by the Hubble Space Telescope reveal that some Stream clouds towards both galactic poles are highly ionized by a source capable of producing ionization energies up to at least 50 eV. We show how these are clouds caught in a beam of bipolar, radiative "ionization cones" from a Seyfert nucleus associated with Sgr A*. In our model, the biconic axis is tilted by about 15 deg from the South Galactic Pole with an opening angle of roughly 60 deg. For the Stream at such large Galactic distances (D > 75 kpc), nuclear activity is a plausible explanation for all of the observed signatures: elevated H-alpha emission and H ionization fraction (X_e > 0.5), enhanced CIV/CII and SiIV/SiII ratios, and high CIV and SiIV column densities. Wind-driven "shock cones" are ruled out because the Fermi bubbles lose their momentum and energy to the Galactic corona long before reaching the Stream. The nuclear flare event must have had a radiative UV luminosity close to the Eddington limit (f_E ~ 0.1-1). Our time-dependent Seyfert flare models adequately explain the observations and indicate the Seyfert flare event took place T_o = 3.5 +/- 1 Myr ago. The timing estimates are consistent with the mechanical timescales needed to explain the x-ray/gamma-ray bubbles in leptonic jet/wind models (2-8 Myr).

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Searching for signs of jet-driven negative feedback in the nearby radio galaxy UGC 05771

Hydrodynamical simulations predict that the jets of young radio sources can inhibit star formation in their host galaxies by injecting heat and turbulence into the interstellar medium (ISM). To investigate jet-ISM interactions in a galaxy with a young radio source, we have carried out a multi-wavelength study of the $z = 0.025$ Compact Steep Spectrum radio source hosted by the early-type galaxy UGC 05771. Using Keck/OSIRIS observations, we detected H\textsubscript{2} 1--0 S(1) and [Fe \textsc{ii}] emission at radii of 100s of pc, which traces shocked molecular and ionised gas being accelerated outwards by the jets to low velocities, creating a `stalling wind'. At kpc radii, we detected shocked ionised gas using observations from the CALIFA survey, covering an area much larger than the pc-scale radio source. We found that existing interferometric radio observations fail to recover a large fraction of the source's total flux, indicating the likely existence of jet plasma on kpc scales, which is consistent with the extent of shocked gas in the host galaxy. To investigate the star formation efficiency in UGC 05771, we obtained IRAM CO observations to analyse the molecular gas properties. We found that UGC 05771 sits below the Kennicutt-Schmidt relation, although we were unable to definitively conclude if direct interactions from the jets are inhibiting star formation. This result shows that jets may be important in regulating star formation in the host galaxies of compact radio sources.

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Comparison of Theoretical Starburst Photoionisation Models for Optical Diagnostics

We study and compare different examples of stellar evolutionary synthesis input parameters used to produce photoionisation model grids using the MAPPINGS V modelling code. The aim of this study is to (a) explore the systematic effects of various stellar evolutionary synthesis model parameters on the interpretation of emission lines in optical strong-line diagnostic diagrams, (b) characterise the combination of parameters able to reproduce the spread of local galaxies located in the star-forming region in the Sloan Digital Sky Survey, and (c) investigate the emission from extremely metal-poor galaxies using photoionisation models. We explore and compare the stellar input ionising spectrum (stellar population synthesis code [Starburst99, SLUG, BPASS], stellar evolutionary tracks, stellar atmospheres, star-formation history, sampling of the initial mass function) as well as parameters intrinsic to the H II region (metallicity, ionisation parameter, pressure, H II region boundedness). We also perform a comparison of the photoionisation codes MAPPINGS and CLOUDY. On the variations in the ionising spectrum model parameters, we find that the differences in strong emission-line ratios between varying models for a given input model parameter are small, on average ~0.1 dex. An average difference of ~0.1 dex in emission-line ratio is also found between models produced with MAPPINGS and CLOUDY. Large differences between the emission-line ratios are found when comparing intrinsic H II region parameters. We find that low-metallicity galaxies are better explained by a density-bounded H II region and higher pressures better encompass the spread of galaxies at high redshift.

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The SAMI Galaxy Survey: mass-kinematics scaling relations

We use data from the Sydney-AAO Multi-object Integral-field spectroscopy (SAMI) Galaxy Survey to study the dynamical scaling relation between galaxy stellar mass $M_*$ and the general kinematic parameter $S_K = \sqrt{K V_{rot}^2 + σ^2}$ that combines rotation velocity $V_{rot}$ and velocity dispersion $σ$. We show that the $\log M_* - \log S_K$ relation: (1)~is linear above limits set by properties of the samples and observations; (2)~has slightly different slope when derived from stellar or gas kinematic measurements; (3)~applies to both early-type and late-type galaxies and has smaller scatter than either the Tully-Fisher relation ($\log M_* - \log V_{rot}$) for late types or the Faber-Jackson relation ($\log M_* - \logσ$) for early types; and (4)~has scatter that is only weakly sensitive to the value of $K$, with minimum scatter for $K$ in the range 0.4 and 0.7. We compare $S_K$ to the aperture second moment (the `aperture velocity dispersion') measured from the integrated spectrum within a 3-arcsecond radius aperture ($σ_{3^{\prime\prime}}$). We find that while $S_{K}$ and $σ_{3^{\prime\prime}}$ are in general tightly correlated, the $\log M_* - \log S_K$ relation has less scatter than the $\log M_* - \log σ_{3^{\prime\prime}}$ relation.

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