arXiv subjects

S. Brough

Publications and source records attributed to S. Brough.

At least 73 records · Page 4Linked to original sources

arXiv2017

The SAMI Galaxy Survey: the intrinsic shape of kinematically selected galaxies

Using the stellar kinematic maps and ancillary imaging data from the Sydney AAO Multi Integral field (SAMI) Galaxy Survey, the intrinsic shape of kinematically-selected samples of galaxies is inferred. We implement an efficient and optimised algorithm to fit the intrinsic shape of galaxies using an established method to simultaneously invert the distributions of apparent ellipticities and kinematic misalignments. The algorithm output compares favourably with previous studies of the intrinsic shape of galaxies based on imaging alone and our re-analysis of the ATLAS3D data. Our results indicate that most galaxies are oblate axisymmetric. We show empirically that the intrinsic shape of galaxies varies as a function of their rotational support as measured by the "spin" parameter proxy Lambda_Re. In particular, low spin systems have a higher occurrence of triaxiality, while high spin systems are more intrinsically flattened and axisymmetric. The intrinsic shape of galaxies is linked to their formation and merger histories. Galaxies with high spin values have intrinsic shapes consistent with dissipational minor mergers, while the intrinsic shape of low-spin systems is consistent with dissipationless multi-merger assembly histories. This range in assembly histories inferred from intrinsic shapes is broadly consistent with expectations from cosmological simulations.

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arXiv2017

The SAMI Galaxy Survey: understanding observations of large-scale outflows at low redshift with EAGLE simulations

This work presents a study of galactic outflows driven by stellar feedback. We extract main sequence disc galaxies with stellar mass $10^9\le$ M$_{\star}/$M$_{\odot} \le 5.7\times10^{10}$ at redshift $z=0$ from the highest resolution cosmological simulation of the Evolution and Assembly of GaLaxies and their Environments (EAGLE) set. Synthetic gas rotation velocity and velocity dispersion ($σ$) maps are created and compared to observations of disc galaxies obtained with the Sydney-AAO Multi-object Integral field spectrograph (SAMI), where $σ$-values greater than $150$ km s$^{-1}$ are most naturally explained by bipolar outflows powered by starburst activity. We find that the extension of the simulated edge-on (pixelated) velocity dispersion probability distribution depends on stellar mass and star formation rate surface density ($Σ_{\rm SFR}$), with low-M$_{\star}/$low-$Σ_{\rm SFR}$ galaxies showing a narrow peak at low $σ$ ($\sim30$ km s$^{-1}$) and more active, high-M$_{\star}/$high-$Σ_{\rm SFR}$ galaxies reaching $σ>150$ km s$^{-1}$. Although supernova-driven galactic winds in the EAGLE simulations may not entrain enough gas with T $<10^5$ K compared to observed galaxies, we find that gas temperature is a good proxy for the presence of outflows. There is a direct correlation between the thermal state of the gas and its state of motion as described by the $σ$-distribution. The following equivalence relations hold in EAGLE: $i)$ low-$σ$ peak $\,\Leftrightarrow\,$ disc of the galaxy $\,\Leftrightarrow\,$ gas with T $<10^5$ K; $ii)$ high-$σ$ tail $\,\Leftrightarrow\,$ galactic winds $\,\Leftrightarrow\,$ gas with T $\ge 10^5$ K.

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arXiv2017

The SAMI Galaxy Survey: Global stellar populations on the size-mass plane

We present an analysis of the global stellar populations of galaxies in the SAMI Galaxy Survey. Our sample consists of 1319 galaxies spanning four orders of magnitude in stellar mass and includes all morphologies and environments. We derive luminosity-weighted, single stellar population equivalent stellar ages, metallicities and alpha enhancements from spectra integrated within one effective radius apertures. Variations in galaxy size explain the majority of the scatter in the age--mass and metallicity--mass relations. Stellar populations vary systematically in the plane of galaxy size and stellar mass, such that galaxies with high stellar surface mass density are older, more metal-rich and alpha-enhanced than less dense galaxies. Galaxies with high surface mass densities have a very narrow range of metallicities, however, at fixed mass, the spread in metallicity increases substantially with increasing galaxy size (decreasing density). We identify residual correlations with morphology and environment. At fixed mass and size, galaxies with late-type morphologies, small bulges and low Sersic n are younger than early-type, high n, high bulge-to-total galaxies. Age and metallicity both show small residual correlations with environment; at fixed mass and size, galaxies in denser environments or more massive halos are older and somewhat more metal rich than those in less dense environments. We connect these trends to evolutionary tracks within the size--mass plane.

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arXiv2017

The SAMI Galaxy Survey: Data Release One with Emission-line Physics Value-Added Products

We present the first major release of data from the SAMI Galaxy Survey. This data release focuses on the emission-line physics of galaxies. Data Release One includes data for 772 galaxies, about 20% of the full survey. Galaxies included have the redshift range 0.004 < z < 0.092, a large mass range (7.6 < log(Mstellar/M$_\odot$) < 11.6), and star-formation rates of 10^-4 to 10^1\ M$_\odot$/yr. For each galaxy, we include two spectral cubes and a set of spatially resolved 2D maps: single- and multi-component emission-line fits (with dust extinction corrections for strong lines), local dust extinction and star-formation rate. Calibration of the fibre throughputs, fluxes and differential-atmospheric-refraction has been improved over the Early Data Release. The data have average spatial resolution of 2.16 arcsec (FWHM) over the 15~arcsec diameter field of view and spectral (kinematic) resolution R=4263 (sigma=30km/s) around Halpha. The relative flux calibration is better than 5\% and absolute flux calibration better than $\pm0.22$~mag, with the latter estimate limited by galaxy photometry. The data are presented online through the Australian Astronomical Observatory's Data Central.

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arXiv2017

The SAMI Galaxy Survey: Disk-halo interactions in radio-selected star-forming galaxies

In this paper, we compare the radio emission at 1.4 GHz with optical outflow signatures of edge-on galaxies. We report observations of six edge-on star-forming galaxies in the Sydney-AAO Multi-object Integral-field spectrograph (SAMI) Galaxy Survey with 1.4 GHz luminosities $> 1\times10^{21}$ W Hz$^{-1}$. Extended minor axis optical emission is detected with enhanced \nii/H$α$ line ratios and velocity dispersions consistent with galactic winds in three of six galaxies. These galaxies may host outflows driven by a combination of thermal and cosmic ray processes. We find that galaxies with the strongest wind signatures have extended radio morphologies. Our results form a baseline for understanding the driving mechanisms of galactic winds.

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arXiv2017

The SAMI Galaxy Survey: energy sources of the turbulent velocity dispersion in spatially-resolved local star-forming galaxies

We investigate the energy sources of random turbulent motions of ionised gas from H$α$ emission in eight local star-forming galaxies from the Sydney-AAO Multi-object Integral field spectrograph (SAMI) Galaxy Survey. These galaxies satisfy strict pure star-forming selection criteria to avoid contamination from active galactic nuclei (AGN) or strong shocks/outflows. Using the relatively high spatial and spectral resolution of SAMI, we find that -- on sub-kpc scales our galaxies display a flat distribution of ionised gas velocity dispersion as a function of star formation rate (SFR) surface density. A major fraction of our SAMI galaxies shows higher velocity dispersion than predictions by feedback-driven models, especially at the low SFR surface density end. Our results suggest that additional sources beyond star formation feedback contribute to driving random motions of the interstellar medium (ISM) in star-forming galaxies. We speculate that gravity, galactic shear, and/or magnetorotational instability (MRI) may be additional driving sources of turbulence in these galaxies.

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arXiv2017

Galaxy And Mass Assembly (GAMA): The environments of high- and low- excitation radio galaxies

We study the environments of low- and high- excitation radio galaxies (LERGs and HERGs respectively) in the redshift range $0.01 < z < 0.4$, using a sample of 399 radio galaxies and environmental measurements from the Galaxy And Mass Assembly (GAMA) survey. In our analysis we use the fifth nearest neighbour density ($Σ_{5}$) and the GAMA galaxy groups catalogue (G3Cv6) and construct control samples of galaxies matched in {\update stellar mass and colour} to the radio-detected sample. We find that LERGs and HERGs exist in different environments and that this difference is dependent on radio luminosity. High-luminosity LERGs ($L_{\rm NVSS} \gtrsim 10^{24}$ W Hz$^{-1}$) lie in much denser environments than a matched radio-quiet control sample (about three times as dense, as measured by $Σ_{5}$), and are more likely to be members of galaxy groups ($82^{+5}_{-7}$ percent of LERGs are in GAMA groups, compared to $58^{+3}_{-3}$ percent of the control sample). In contrast, the environments of the HERGs and lower luminosity LERGs are indistinguishable from that of a matched control sample. Our results imply that high-luminosity LERGs lie in more massive haloes than non-radio galaxies of similar stellar mass and colour, in agreement with earlier studies (Wake et al. 2008; Donoso et al. 2010). When we control for the preference of LERGs to be found in groups, both high- and low- luminosity LERGs are found in higher-mass haloes ($\sim 0.2$ dex; at least 97 percent significant) than the non-radio control sample.

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arXiv2017

The SAMI Galaxy Survey: Kinematics of Dusty Early-Type Galaxies

Recently, large samples of visually classified early-type galaxies (ETGs) containing dust have been identified using space-based infrared observations with the Herschel Space Telescope. The presence of large quantities of dust in massive ETGs is peculiar as X-ray halos of these galaxies are expected to destroy dust in 10 Myr (or less). This has sparked a debate regarding the origin of the dust: is it internally produced by asymptotic giant branch (AGB) stars, or is it accreted externally through mergers? We examine the 2D stellar and ionised gas kinematics of dusty ETGs using IFS observations from the SAMI galaxy survey, and integrated star-formation rates, stellar masses, and dust masses from the GAMA survey. Only 8% (4/49) of visually-classified ETGs are kinematically consistent with being dispersion-supported systems. These "dispersion-dominated galaxies" exhibit discrepancies between stellar and ionised gas kinematics, either offsets in the kinematic position angle or large differences in the rotational velocity, and are outliers in star-formation rate at a fixed dust mass compared to normal star-forming galaxies. These properties are suggestive of recent merger activity. The remaining 90% of dusty ETGs have low velocity dispersions and/or large circular velocities, typical of "rotation-dominated galaxies". These results, along with the general evidence of published works on X-ray emission in ETGs, suggest that they are unlikely to host hot, X-ray gas consistent with their low stellar mass when compared to dispersion-dominated galaxies. This means dust will be long lived and thus these galaxies do not require external scenarios for the origin of their dust content.

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arXiv2017

The SAMI Galaxy Survey: The cluster redshift survey, target selection and cluster properties

We describe the selection of galaxies targeted in eight low redshift clusters (APMCC0917, A168, A4038, EDCC442, A3880, A2399, A119 and A85; $0.029 < z < 0.058$) as part of the Sydney-AAO Multi-Object integral field Spectrograph Galaxy Survey (SAMI-GS). We have conducted a redshift survey of these clusters using the AAOmega multi-object spectrograph on the 3.9m Anglo-Australian Telescope. The redshift survey is used to determine cluster membership and to characterise the dynamical properties of the clusters. In combination with existing data, the survey resulted in 21,257 reliable redshift measurements and 2899 confirmed cluster member galaxies. Our redshift catalogue has a high spectroscopic completeness ($\sim 94\%$) for $r_{\rm petro} \leq 19.4$ and clustercentric distances $R< 2\rm{R}_{200}$. We use the confirmed cluster member positions and redshifts to determine cluster velocity dispersion, $\rm{R}_{200}$, virial and caustic masses, as well as cluster structure. The clusters have virial masses $14.25 \leq {\rm log }({\rm M}_{200}/\rm{M}_{\odot}) \leq 15.19$. The cluster sample exhibits a range of dynamical states, from relatively relaxed-appearing systems, to clusters with strong indications of merger-related substructure. Aperture- and PSF-matched photometry are derived from SDSS and VST/ATLAS imaging and used to estimate stellar masses. These estimates, in combination with the redshifts, are used to define the input target catalogue for the cluster portion of the SAMI-GS. The primary SAMI-GS cluster targets have $R< \rm{R}_{200}$, velocities $|v_{\rm pec}| < 3.5σ_{200}$ and stellar masses $9.5 \leq {\rm log(M}^*_{approx}/\rm{M}_{\odot}) \leq 12$. Finally, we give an update on the SAMI-GS progress for the cluster regions.

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arXiv2017

Galaxy and Mass Assembly (GAMA): Probing the merger histories of massive galaxies via stellar populations

The merging history of galaxies can be traced with studies of dynamically close pairs. These consist of a massive primary galaxy and a less massive secondary (or satellite) galaxy. The study of the stellar populations of secondary (lower mass) galaxies in close pairs provides a way to understand galaxy growth by mergers. Here we focus on systems involving at least one massive galaxy - with stellar mass above $10^{11}M_\odot$ in the highly complete GAMA survey. Our working sample comprises 2,692 satellite galaxy spectra (0.1<z<0.3). These spectra are combined into high S/N stacks, and binned according to both an "internal" parameter, the stellar mass of the satellite galaxy (i.e. the secondary), and an "external" parameter, selecting either the mass of the primary in the pair, or the mass of the corresponding dark matter halo. We find significant variations in the age of the populations with respect to environment. At fixed mass, satellites around the most massive galaxies are older and possibly more metal rich, with age differences ~1-2Gyr within the subset of lower mass satellites ($\sim 10^{10}M_\odot$). These variations are similar when stacking with respect to the halo mass of the group where the pair is embedded. The population trends in the lower-mass satellites are consistent with the old stellar ages found in the outer regions of massive galaxies.

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arXiv2017

Galaxy And Mass Assembly: The 1.4GHz SFR indicator, SFR-M* relation and predictions for ASKAP-GAMA

We present a robust calibration of the 1.4GHz radio continuum star formation rate (SFR) using a combination of the Galaxy And Mass Assembly (GAMA) survey and the Faint Images of the Radio Sky at Twenty-cm (FIRST) survey. We identify individually detected 1.4GHz GAMA-FIRST sources and use a late-type, non-AGN, volume-limited sample from GAMA to produce stellar mass-selected samples. The latter are then combined to produce FIRST-stacked images. This extends the robust parametrisation of the 1.4GHz-SFR relation to faint luminosities. For both the individually detected galaxies and our stacked samples, we compare 1.4GHz luminosity to SFRs derived from GAMA to determine a new 1.4GHz luminosity-to-SFR relation with well constrained slope and normalisation. For the first time, we produce the radio SFR-M* relation over 2 decades in stellar mass, and find that our new calibration is robust, and produces a SFR-M* relation which is consistent with all other GAMA SFR methods. Finally, using our new 1.4GHz luminosity-to-SFR calibration we make predictions for the number of star-forming GAMA sources which are likely to be detected in the upcoming ASKAP surveys, EMU and DINGO.

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arXiv2017

Galaxy and Mass Assembly (GAMA): Exploring the WISE Cosmic Web in G12

We present an analysis of the mid-infrared WISE sources seen within the equatorial GAMA G12 field, located in the North Galactic Cap. Our motivation is to study and characterize the behavior of WISE source populations in anticipation of the deep multi-wavelength surveys that will define the next decade, with the principal science goal of mapping the 3D large scale structures and determining the global physical attributes of the host galaxies. In combination with cosmological redshifts, we identify galaxies from their WISE W1 3.4um resolved emission, and by performing a star-galaxy separation using apparent magnitude, colors and statistical modeling of star-counts. The resultant galaxy catalog has ~590,000 sources in 60 deg^2, reaching a W1 5-sigma depth of 31 uJy. At the faint end, where redshifts are not available, we employ a luminosity function analysis to show that approximately 27% of all WISE extragalactic sources to a limit of 17.5 mag (31 uJy) are at high redshift, z > 1. The spatial distribution is investigated using two-point correlation functions and a 3D source density characterization at 5 Mpc and 20 Mpc scales. For angular distributions, we find brighter and more massive sources are strongly clustered relative to fainter and lower mass source; likewise, based on WISE colors, spheroidal galaxies have the strongest clustering, while late-type disk galaxies have the lowest clustering amplitudes. Along the radial direction, the strongest clustering is in the largest redshift shell, while the weakest is in the nearest redshift shell, consistent with the stellar mass and morphological type dependency results. In three dimensions, we find a number of distinct groupings, often bridged by filaments and super-structures. Using special visualization tools, we map these structures, exploring how clustering may play a role with stellar mass and galaxy type.

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arXiv2016

The SAMI Galaxy Survey: Asymmetry in Gas Kinematics and its links to Stellar Mass and Star Formation

We study the properties of kinematically disturbed galaxies in the SAMI Galaxy Survey using a quantitative criterion, based on kinemetry (Krajnovic et al.). The approach, similar to the application of kinemetry by Shapiro et al. uses ionised gas kinematics, probed by Hα emission. By this method 23+/-7% of our 360-galaxy sub-sample of the SAMI Galaxy Survey are kinematically asymmetric. Visual classifications agree with our kinemetric results for 90% of asymmetric and 95% of normal galaxies. We find stellar mass and kinematic asymmetry are inversely correlated and that kinematic asymmetry is both more frequent and stronger in low-mass galaxies. This builds on previous studies that found high fractions of kinematic asymmetry in low mass galaxies using a variety of different methods. Concentration of star forma- tion and kinematic disturbance are found to be correlated, confirming results found in previous work. This effect is stronger for high mass galaxies (log(M*) > 10) and indicates that kinematic disturbance is linked to centrally concentrated star formation. Comparison of the inner (within 0.5Re) and outer Hα equivalent widths of asymmetric and normal galaxies shows a small but significant increase in inner equivalent width for asymmetric galaxies.

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arXiv2016

The SAMI Galaxy Survey: Spatially resolving the environmental quenching of star formation in GAMA galaxies

We use data from the Sydney-AAO Multi-Object Integral Field Spectrograph (SAMI) Galaxy Survey and the Galaxy And Mass Assembly (GAMA) survey to investigate the spatially-resolved signatures of the environmental quenching of star formation in galaxies. Using dust-corrected measurements of the distribution of H$α$ emission we measure the radial profiles of star formation in a sample of 201 star-forming galaxies covering three orders of magnitude in stellar mass (M$_{*}$; $10^{8.1}$-$10^{10.95}\, $M$_{\odot}$) and in $5^{th}$ nearest neighbour local environment density ($Σ_{5}$; $10^{-1.3}$-$10^{2.1}\,$Mpc$^{-2}$). We show that star formation rate gradients in galaxies are steeper in dense ($\log_{10}(Σ_{5}/$Mpc$^{2})>0.5$) environments by $0.58\pm 0.29\, dex\, $r$_{e}^{-1}$ in galaxies with stellar masses in the range $10^{10}<$M$_{*}/$M$_{\odot}<10^{11}$ and that this steepening is accompanied by a reduction in the integrated star formation rate. However, for any given stellar mass or environment density the star-formation morphology of galaxies shows large scatter. We also measure the degree to which the star formation is centrally concentrated using the unitless scale-radius ratio ($r_{50,Hα}/r_{50,cont}$), which compares the extent of ongoing star formation to previous star formation. With this metric we find that the fraction of galaxies with centrally concentrated star formation increases with environment density, from $\sim 5\pm 4\%$ in low-density environments ($\log_{10}(Σ_{5}/$Mpc$^{2})<0.0$) to $30\pm 15\%$ in the highest density environments ($\log_{10}(Σ_{5}/$Mpc$^{2})>1.0$). These lines of evidence strongly suggest that with increasing local environment density the star formation in galaxies is suppressed, and that this starts in their outskirts such that quenching occurs in an outside-in fashion in dense environments and is not instantaneous.

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arXiv2016

Galaxy And Mass Assembly (GAMA): The absence of stellar mass segregation in galaxy groups and consistent predictions from GALFORM and EAGLE simulations

We investigate the contentious issue of the presence, or lack thereof, of satellites mass segregation in galaxy groups using the Galaxy And Mass Assembly (GAMA) survey, the GALFORM semi-analytic and the EAGLE cosmological hydrodynamical simulation catalogues of galaxy groups. We select groups with halo mass $12 \leqslant \log(M_{\text{halo}}/h^{-1}M_\odot) <14.5$ and redshift $z \leqslant 0.32$ and probe the radial distribution of stellar mass out to twice the group virial radius. All the samples are carefully constructed to be complete in stellar mass at each redshift range and efforts are made to regularise the analysis for all the data. Our study shows negligible mass segregation in galaxy group environments with absolute gradients of $\lesssim0.08$ dex and also shows a lack of any redshift evolution. Moreover, we find that our results at least for the GAMA data are robust to different halo mass and group centre estimates. Furthermore, the EAGLE data allows us to probe much fainter luminosities ($r$-band magnitude of 22) as well as investigate the three-dimensional spatial distribution with intrinsic halo properties, beyond what the current observational data can offer. In both cases we find that the fainter EAGLE data show a very mild spatial mass segregation at $z \leqslant 0.22$, which is again not apparent at higher redshift. Interestingly, our results are in contrast to some earlier findings using the Sloan Digital Sky Survey. We investigate the source of the disagreement and suggest that subtle differences between the group finding algorithms could be the root cause.

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arXiv2016

Galaxy And Mass Assembly (GAMA): detection of low-surface-brightness galaxies from SDSS data

We report on a search for new low-surface-brightness galaxies (LSBGs) using Sloan Digital Sky Survey (SDSS) data within the GAMA equatorial fields. The search method consisted of masking objects detected with SDSS photo, combining gri images weighted to maximise the expected signal-to-noise ratio (SNR), and smoothing the images. The processed images were then run through a detection algorithm that finds all pixels above a set threshold and groups them based on their proximity to one another. The list of detections was cleaned of contaminants such as diffraction spikes and the faint wings of masked objects. From these, selecting potentially the brightest in terms of total flux, a list of 343 LSBGs was produced having been confirmed using VISTA Kilo-degree Infrared Galaxy Survey (VIKING) imaging. The photometry of this sample was refined using the deeper VIKING Z band as the aperture-defining band. Measuring their $g-i$ and $J-K$ colours shows that most are consistent with being at redshifts less than 0.2. The photometry is carried out using an AUTO aperture for each detection giving surface brightnesses of $μ_{r} \ge 25 \, \mathrm{mag} \, \mathrm{arcsec}^{-2}$ and magnitudes of $r > 19.8$ mag. None of these galaxies are bright enough to be within the GAMA main survey limit but could be part of future deeper surveys to measure the low-mass end of the galaxy stellar mass function.

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arXiv2016

The SAMI Galaxy Survey: the link between angular momentum and optical morphology

We investigate the relationship between stellar and gas specific angular momentum $j$, stellar mass $M_{*}$ and optical morphology for a sample of 488 galaxies extracted from the SAMI Galaxy Survey. We find that $j$, measured within one effective radius, monotonically increases with $M_{*}$ and that, for $M_{*}>$10$^{9.5}$ M$_{\odot}$, the scatter in this relation strongly correlates with optical morphology (i.e., visual classification and Sérsic index). These findings confirm that massive galaxies of all types lie on a plane relating mass, angular momentum and stellar light distribution, and suggest that the large-scale morphology of a galaxy is regulated by its mass and dynamical state. We show that the significant scatter in the $M_{*}-j$ relation is accounted for by the fact that, at fixed stellar mass, the contribution of ordered motions to the dynamical support of galaxies varies by at least a factor of three. Indeed, the stellar spin parameter (quantified via $λ_R$) correlates strongly with Sérsic and concentration indices. This correlation is particularly strong once slow-rotators are removed from the sample, showing that late-type galaxies and early-type fast rotators form a continuous class of objects in terms of their kinematic properties.

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arXiv2016

GAMA/H-ATLAS: Common star-formation rate indicators and their dependence on galaxy physical parameters

We compare common star-formation rate (SFR) indicators in the local Universe in the GAMA equatorial fields (around 160 sq. deg.), using ultraviolet (UV) photometry from GALEX, far-infrared (FIR) and sub-millimetre (sub-mm) photometry from H-ATLAS, and Halpha spectroscopy from the GAMA survey. With a high-quality sample of 745 galaxies (median redshift 0.08), we consider three SFR tracers: UV luminosity corrected for dust attenuation using the UV spectral slope beta (SFRUV,corr), Halpha line luminosity corrected for dust using the Balmer decrement (BD) (SFRHalpha,corr), and the combination of UV and IR emission (SFRUV+IR). We demonstrate that SFRUV,corr can be reconciled with the other two tracers after applying attenuation corrections by calibrating IRX (i.e. the IR to UV luminosity ratio) and attenuation in the Halpha (derived from BD) against beta. However, beta on its own is very unlikely to be a reliable attenuation indicator. We find that attenuation correction factors depend on parameters such as stellar mass, z and dust temperature (Tdust), but not on Halpha equivalent width (EW) or Sersic index. Due to the large scatter in the IRX vs beta correlation, when compared to SFRUV+IR, the beta-corrected SFRUV,corr exhibits systematic deviations as a function of IRX, BD and Tdust.

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