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Sarah Brough

Publications and source records attributed to Sarah Brough.

At least 109 records · Page 6Linked to original sources

The SAMI Galaxy Survey: Revisiting Galaxy Classification Through High-Order Stellar Kinematics

Recent cosmological hydrodynamical simulations suggest that integral field spectroscopy can connect the high-order stellar kinematic moments h3 (~skewness) and h4 (~kurtosis) in galaxies to their cosmological assembly history. Here, we assess these results by measuring the stellar kinematics on a sample of 315 galaxies, without a morphological selection, using 2D integral field data from the SAMI Galaxy Survey. A proxy for the spin parameter ($λ_{R_e}$) and ellipticity ($ε_e$) are used to separate fast and slow rotators; there exists a good correspondence to regular and non-regular rotators, respectively, as also seen in earlier studies. We confirm that regular rotators show a strong h3 versus $V/σ$ anti-correlation, whereas quasi-regular and non-regular rotators show a more vertical relation in h3 and $V/σ$. Motivated by recent cosmological simulations, we develop an alternative approach to kinematically classify galaxies from their individual h3 versus $V/σ$ signatures. We identify five classes of high-order stellar kinematic signatures using Gaussian mixture models. Class 1 corresponds to slow rotators, whereas Classes 2-5 correspond to fast rotators. We find that galaxies with similar $λ_{R_e}-ε_e$ values can show distinctly different h3-$V/σ$ signatures. Class 5 objects are previously unidentified fast rotators that show a weak h3 versus $V/σ$ anti-correlation. These objects are predicted to be disk-less galaxies formed by gas-poor mergers. From morphological examination, however, there is evidence for large stellar disks. Instead, Class 5 objects are more likely disturbed galaxies, have counter-rotating bulges, or bars in edge-on galaxies. Finally, we interpret the strong anti-correlation in h3 versus $V/σ$ as evidence for disks in most fast rotators, suggesting a dearth of gas-poor mergers among fast rotators.

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A Study of Central Galaxy Rotation with Stellar Mass and Environment

We present a pilot analysis of the influence of galaxy stellar mass and cluster environment on the probability of slow rotation in 22 central galaxies at mean redshift $z=0.07$. This includes new integral-field observations of 5 central galaxies selected from the Sloan Digital Sky Survey, observed with the SPIRAL integral-field spectrograph on the Anglo-Australian Telescope. The composite sample presented here spans a wide range of stellar masses, $10.9<$log(M$_{*}/$M$_{\odot})<12.0$, and are embedded in halos ranging from groups to clusters, $12.9<$log(M$_{200}/$M$_{\odot})<15.6$. We find a mean probability of slow rotation in our sample of P(SR)$=54\pm7$percent. Our results show an increasing probability of slow rotation in central galaxies with increasing stellar mass. However, when we examine the dependence of slow rotation on host cluster halo mass we do not see a significant relationship. We also explore the influence of cluster dominance on slow rotation in central galaxies. Clusters with low dominance are associated with dynamically younger systems. We find that cluster dominance has no significant effect on the probability of slow rotation in central galaxies. These results conflict with a paradigm in which halo mass alone predetermines central galaxy properties.

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Galaxy And Mass Assembly (GAMA): Active Galactic Nuclei in Pairs of Galaxies

There exist conflicting observations on whether or not the environment of broad and narrow line AGN differ and this consequently questions the validity of the AGN unification model. The high spectroscopic completeness of the GAMA survey makes it ideal for a comprehensive analysis of the close environment of galaxies. To exploit this, and conduct a comparative analysis of the environment of broad and narrow line AGN within GAMA, we use a double-Gaussian emission line fitting method to model the more complex line profiles associated with broad line AGN. We select 209 type 1 (i.e., unobscured), 464 type 1.5-1.9 (partially obscured), and 281 type 2 (obscured) AGN within the GAMA II database. Comparing the fractions of these with neighbouring galaxies out to a pair separation of $350\,\text{kpc }h^{-1}$ and $Δz < 0.012$ shows no difference between AGN of different type, except at separations less than $20\,\text{kpc }h^{-1}$ where our observations suggest an excess of type 2 AGN in close pairs. We analyse the properties of the galaxies neighbouring our AGN and find no significant differences in colour or the star formation activity of these galaxies. Further to this we find that $Σ_5$ is also consistent between broad and narrow line AGN. We conclude that the observations presented here are consistent with AGN unification.

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The SAMI galaxy survey: Galaxy Interactions and Kinematic Anomalies in Abell 119

Galaxy mergers are important events that can determine the fate of a galaxy by changing its morphology, star-formation activity and mass growth. Merger systems have commonly been identified from their disturbed morphologies, and we now can employ Integral Field Spectroscopy to detect and analyze the impact of mergers on stellar kinematics as well. We visually classified galaxy morphology using deep images ($μ_{\rm r} = 28\,\rm mag\,\, arcsec^{-2}$) taken by the Blanco 4-m telescope at the Cerro Tololo Inter-American Observatory. In this paper we investigate 63 bright ($M_{\rm r}<-19.3$) spectroscopically-selected galaxies in Abell 119; of which 53 are early type and 20 galaxies show a disturbed morphology by visual inspection. A misalignment between the major axes in the photometric image and the kinematic map is conspicuous in morphologically-disturbed galaxies. Our sample is dominated by early-type galaxies, yet it shows a surprisingly tight Tully-Fisher relation except for the morphologically-disturbed galaxies which show large deviations. Three out of the eight slow rotators in our sample are morphology disturbed. The visually-selected morphologically-disturbed galaxies are generally more asymmetric, visually as well as kinematically. Our findings suggest that galaxy interactions, including mergers and perhaps fly-bys, play an important role in determining the orientation and magnitude of galaxy's angular momentum.

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Galaxy And Mass Assembly (GAMA): the Stellar Mass Budget of Galaxy Spheroids and Disks

We build on a recent photometric decomposition analysis of 7506 Galaxy and Mass Assembly (GAMA) survey galaxies to derive stellar mass function fits to individual spheroid and disk component populations down to a lower mass limit of log(M_*/M_sun)= 8. We find that the spheroid/disk mass distributions for individual galaxy morphological types are well described by single Schechter function forms. We derive estimates of the total stellar mass densities in spheroids (rho_spheroid = 1.24+/-0.49 * 10^8 M_sun Mpc^-3 h_0.7) and disks (rho_disk = 1.20+/-0.45 * 10^8 M_sun Mpc^-3 h_0.7), which translates to approximately 50% of the local stellar mass density in spheroids and 48% in disks. The remaining stellar mass is found in the dwarf "little blue spheroid" class, which is not obviously similar in structure to either classical spheroid or disk populations. We also examine the variation of component mass ratios across galaxy mass and group halo mass regimes, finding the transition from spheroid to disk mass dominance occurs near galaxy stellar mass ~10^11 M_sun and group halo mass ~10^12.5 M_sun/h. We further quantify the variation in spheroid-to-total mass ratio with group halo mass for central and satellite populations as well as the radial variation of this ratio within groups.

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Galaxy And Mass Assembly (GAMA): Galaxy colour gradients versus colour, structure and luminosity

Using single-component fits to SDSS/UKIDSS images of galaxies in the G09 region of the GAMA survey we study radial colour gradients across the galaxy population. We use the multiwavelength information provided by MegaMorph analysis of galaxy light profiles to calculate intrinsic colour gradients, and divide into six subsamples split by overall Sérsic index ($n$) and galaxy colour. We find a bimodality in the colour gradients of high- and low-$n$ galaxies in all wavebands, which varies with overall galaxy luminosity. Global trends in colour gradients therefore result from combining the contrasting behaviour of a number of different galaxy populations. The ubiquity of strong negative colour gradients supports the picture of inside-out growth through gas accretion for blue, low-$n$ galaxies, and through dry minor mergers for red, high-$n$ galaxies. An exception is the blue high-n population, with properties indicative of dissipative major mergers.

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Galaxy And Mass Assembly (GAMA): $\mathcal{M_\star}-R_{\rm e}$ relations of $z=0$ bulges, discs and spheroids

We perform automated bulge + disc decomposition on a sample of $\sim$7500 galaxies from the Galaxy And Mass Assembly (GAMA) survey in the redshift range of 0.002$<$z$<$0.06 using SIGMA, a wrapper around GALFIT3. To achieve robust profile measurements we use a novel approach of repeatedly fitting the galaxies, varying the input parameters to sample a large fraction of the input parameter space. Using this method we reduce the catastrophic failure rate significantly and verify the confidence in the fit independently of $χ^2$. Additionally, using the median of the final fitting values and the 16$^{th}$ and 84$^{th}$ percentile produces more realistic error estimates than those provided by GALFIT, which are known to be underestimated. We use the results of our decompositions to analyse the stellar mass - half-light radius relations of bulges, discs and spheroids. We further investigate the association of components with a parent disc or elliptical relation to provide definite $z=0$ disc and spheroid $\mathcal{M_\star}-R_{\rm e}$ relations. We conclude by comparing our local disc and spheroid $\mathcal{M_\star}-R_{\rm e}$ to simulated data from EAGLE and high redshift data from CANDELS-UDS. We show the potential of using the mass-size relation to study galaxy evolution in both cases but caution that for a fair comparison all data sets need to be processed and analysed in the same manner.

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Spatial Correlation Between Dust and H$α$ Emission in Dwarf Irregular Galaxies

Using a sample of dwarf irregular galaxies selected from the ALFALFA blind HI-survey and observed using the VIMOS IFU, we investigate the relationship between H$α$ emission and Balmer optical depth ($τ_{\text{b}}$). We find a positive correlation between H$α$ luminosity surface density and Balmer optical depth in 8 of 11 at $\geq$ 0.8$σ$ significance (6 of 11 at $\geq$ 1.0$σ$) galaxies. Our spaxels have physical scales ranging from 30 to 80 pc, demonstrating that the correlation between these two variables continues to hold down to spatial scales as low as 30 pc. Using the Spearman's rank correlation coefficient to test for correlation between $Σ_{\text{H}α}$ and $τ_{\text{b}}$ in all the galaxies combined, we find $ρ= 0.39$, indicating a positive correlation at 4$σ$ significance. Our low stellar-mass galaxy results are in agreement with observations of emission line regions in larger spiral galaxies, indicating that this relationship is independent of the size of the galaxy hosting the emission line region. The positive correlation between H$α$ luminosity and Balmer optical depth within spaxels is consistent with the hypothesis that young star-forming regions are surrounded by dusty birth-clouds.

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Galaxy And Mass Assembly (GAMA): Understanding the wavelength dependence of galaxy structure with bulge-disc decompositions

With a large sample of bright, low-redshift galaxies with optical$-$near-IR imaging from the GAMA survey we use bulge-disc decompositions to understand the wavelength-dependent behavior of single-Sérsic structural measurements. We denote the variation in single-Sérsic index with wavelength as $\mathcal{N}$, likewise for effective radius we use $\mathcal{R}$. We find that most galaxies with a substantial disc, even those with no discernable bulge, display a high value of $\mathcal{N}$. The increase in Sérsic index to longer wavelengths is therefore intrinsic to discs, apparently resulting from radial variations in stellar population and/or dust reddening. Similarly, low values of $\mathcal{R}$ ($<$ 1) are found to be ubiquitous, implying an element of universality in galaxy colour gradients. We also study how bulge and disc colour distributions vary with galaxy type. We find that, rather than all bulges being red and all discs being blue in absolute terms, both components become redder for galaxies with redder total colours. We even observe that bulges in bluer galaxies are typically bluer than discs in red galaxies, and that bulges and discs are closer in colour for fainter galaxies. Trends in total colour are therefore not solely due to the colour or flux dominance of the bulge or disc.

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Dependence of GAMA galaxy halo masses on the cosmic web environment from 100 square degrees of KiDS weak lensing data

Galaxies and their dark matter haloes are part of a complex network of mass structures, collectively called the cosmic web. Using the tidal tensor prescription these structures can be classified into four cosmic environments: voids, sheets, filaments and knots. As the cosmic web may influence the formation and evolution of dark matter haloes and the galaxies they host, we aim to study the effect of these cosmic environments on the average mass of galactic haloes. To this end we measure the galaxy-galaxy lensing profile of 91,195 galaxies, within 0.039 < z < 0.263, from the spectroscopic Galaxy And Mass Assembly (GAMA) survey, using ~100 square degrees of overlapping data from the Kilo-Degree Survey (KiDS). In each of the four cosmic environments we model the contributions from group centrals, satellites and neighbouring groups to the stacked galaxy-galaxy lensing profiles. After correcting the lens samples for differences in the stellar mass distribution, we find no dependence of the average halo mass of central galaxies on their cosmic environment. We do find a significant increase in the average contribution of neighbouring groups to the lensing profile in increasingly dense cosmic environments. We show, however, that the observed effect can be entirely attributed to the galaxy density at much smaller scales (within 4 Mpc/h), which is correlated with the density of the cosmic environments. Within our current uncertainties we find no direct dependence of galaxy halo mass on their cosmic environment.

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GAMA/WiggleZ: The 1.4GHz radio luminosity functions of high- and low-excitation radio galaxies and their redshift evolution to z=0.75

We present radio Active Galactic Nuclei (AGN) luminosity functions over the redshift range 0.005 < z < 0.75. The sample from which the luminosity functions are constructed is an optical spectroscopic survey of radio galaxies, identified from matched Faint Images of the Radio Sky at Twenty-cm survey (FIRST) sources and Sloan Digital Sky Survey (SDSS) images.The radio AGN are separated into Low Excitation Radio Galaxies (LERGs) and High Excitation Radio Galaxies (HERGs) using the optical spectra. We derive radio luminosity functions for LERGs and HERGs separately in the three redshift bins (0.005 < z < 0.3, 0.3 < z < 0.5 and 0.5 < z <0.75). The radio luminosity functions can be well described by a double power-law. Assuming this double power-law shape the LERG population displays little or no evolution over this redshift range evolving as ~$(1+z)^{0.06}$ assuming pure density evolution or ~ $(1+z)^{0.46}$ assuming pure luminosity evolution. In contrast, the HERG population evolves more rapidly, best fitted by ~$(1+z)^{2.93}$ assuming a double power-law shape and pure density evolution. If a pure luminosity model is assumed the best fitting HERG evolution is parameterised by ~$(1+z)^{7.41}$. The characteristic break in the radio luminosity function occurs at a significantly higher power (~1 dex) for the HERG population in comparison to the LERGs. This is consistent with the two populations representing fundamentally different accretion modes.

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Galaxy And Mass Assembly (GAMA): Stellar mass growth of spiral galaxies in the cosmic web

We look for correlated changes in stellar mass and star formation rate along filaments in the cosmic web by examining the stellar masses and UV-derived star formation rates (SFR) of 1,799 ungrouped and unpaired spiral galaxies that reside in filaments. We devise multiple distance metrics to characterise the complex geometry of filaments, and find that galaxies closer to the cylindrical centre of a filament have higher stellar masses than their counterparts near the periphery of filaments, on the edges of voids. In addition, these peripheral spiral galaxies have higher specific star formation rates (SSFR) at a given mass. Complementing our sample of filament spiral galaxies with spiral galaxies in tendrils and voids, we find that the average SFR of these objects in different large scale environments are similar to each other with the primary discriminant in SFR being stellar mass, in line with previous works. However, the distributions of SFRs are found to vary with large-scale environment. Our results thus suggest a model in which in addition to stellar mass as the primary discriminant, the large-scale environment is imprinted in the SFR as a second order effect. Furthermore, our detailed results for filament galaxies suggest a model in which gas accretion from voids onto filaments is primarily in an orthogonal direction. Overall, we find our results to be in line with theoretical expectations of the thermodynamic properties of the intergalactic medium in different large-scale environments.

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Galaxy And Mass Assembly (GAMA): the Stellar Mass Budget by Galaxy Type

We report an expanded sample of visual morphological classifications from the Galaxy and Mass Assembly (GAMA) survey phase two, which now includes 7,556 objects (previously 3,727 in phase one). We define a local (z <0.06) sample and classify galaxies into E, S0-Sa, SB0-SBa, Sab-Scd, SBab-SBcd, Sd-Irr, and "little blue spheroid" types. Using these updated classifications, we derive stellar mass function fits to individual galaxy populations divided both by morphological class and more general spheroid- or disk-dominated categories with a lower mass limit of log(Mstar/Msun) = 8 (one dex below earlier morphological mass function determinations). We find that all individual morphological classes and the combined spheroid-/bulge-dominated classes are well described by single Schechter stellar mass function forms. We find that the total stellar mass densities for individual galaxy populations and for the entire galaxy population are bounded within our stellar mass limits and derive an estimated total stellar mass density of rho_star = 2.5 x 10^8 Msun Mpc^-3 h_0.7, which corresponds to an approximately 4% fraction of baryons found in stars. The mass contributions to this total stellar mass density by galaxies that are dominated by spheroidal components (E and S0-Sa classes) and by disk components (Sab-Scd and Sd-Irr classes) are approximately 70% and 30%, respectively.

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Galaxy And Mass Assembly (GAMA): Panchromatic Data Release (far-UV --- far-IR) and the low-z energy budget

We present the GAMA Panchromatic Data Release (PDR) constituting over 230deg$^2$ of imaging with photometry in 21 bands extending from the far-UV to the far-IR. These data complement our spectroscopic campaign of over 300k galaxies, and are compiled from observations with a variety of facilities including: GALEX, SDSS, VISTA, WISE, and Herschel, with the GAMA regions currently being surveyed by VST and scheduled for observations by ASKAP. These data are processed to a common astrometric solution, from which photometry is derived for 221,373 galaxies with r<19.8 mag. Online tools are provided to access and download data cutouts, or the full mosaics of the GAMA regions in each band. We focus, in particular, on the reduction and analysis of the VISTA VIKING data, and compare to earlier datasets (i.e., 2MASS and UKIDSS) before combining the data and examining its integrity. Having derived the 21-band photometric catalogue we proceed to fit the data using the energy balance code MAGPHYS. These measurements are then used to obtain the first fully empirical measurement of the 0.1-500$μ$m energy output of the Universe. Exploring the Cosmic Spectral Energy Distribution (CSED) across three time-intervals (0.3-1.1Gyr, 1.1-1.8~Gyr and 1.8---2.4~Gyr), we find that the Universe is currently generating $(1.5 \pm 0.3) \times 10^{35}$ h$_{70}$ W Mpc$^{-3}$, down from $(2.5 \pm 0.2) \times 10^{35}$ h$_{70}$ W Mpc$^{-3}$ 2.3~Gyr ago. More importantly, we identify significant and smooth evolution in the integrated photon escape fraction at all wavelengths, with the UV escape fraction increasing from 27(18)% at z=0.18 in NUV(FUV) to 34(23)% at z=0.06. The GAMA PDR will allow for detailed studies of the energy production and outputs of individual systems, sub-populations, and representative galaxy samples at $z<0.5$. The GAMA PDR can be found at: http://gama-psi.icrar.org/

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The WiggleZ Dark Energy Survey: Probing the Epoch of Radiation Domination using Large Scale Structure

We place the most robust constraint to date on the scale of the turnover in the cosmological matter power spectrum using data from the WiggleZ Dark Energy Survey. We find this feature to lie at a scale of $k_0=0.0160^{+0.0041}_{-0.0035}$ [h/Mpc] (68% confidence) for an effective redshift of 0.62 and obtain from this the first-ever turnover-derived distance and cosmology constraints: a measure of the cosmic distance-redshift relation in units of the horizon scale at the redshift of radiation-matter equality (r_H) of D_V(z=0.62)/r_H=18.3 (+6.3/-3.3) and, assuming a prior on the number of extra relativistic degrees of freedom $N_{eff}=3$, constraints on the matter density parameter $Ω_Mh^2=0.136^{+0.026}_{-0.052}$ and on the redshift of matter-radiation equality $z_{eq}=3274^{+631}_{-1260}$. All results are in excellent agreement with the predictions of standard LCDM models. Our constraints on the logarithmic slope of the power spectrum on scales larger than the turnover is bounded in the lower limit with values only as low as -1 allowed, with the prediction of standard LCDM models easily accommodated by our results. Lastly, we generate forecasts for the achievable precision of future surveys at constraining $k_0$, $Ω_Mh^2$, $z_{eq}$ and $N_{eff}$. We find that BOSS should substantially improve upon the WiggleZ turnover constraint, reaching a precision on $k_0$ of $\pm$9% (68% confidence), translating to precisions on $Ω_Mh^2$ and $z_{eq}$ of $\pm$10% (assuming a prior $N_{eff}=3$) and on $N_{eff}$ of (+78/-56)% (assuming a prior $Ω_Mh^2=0.135$). This is sufficient precision to sharpen the constraints on $N_{eff}$ from WMAP, particularly in its upper limit. For Euclid, we find corresponding attainable precisions on $(k_0, Ω_Mh^2, N_eff)$ of (3,4,+17/-21)%. This represents a precision approaching our forecasts for the Planck Surveyor.

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The SAMI Galaxy Survey: Can we trust aperture corrections to predict star formation?

In the low redshift Universe (z<0.3), our view of galaxy evolution is primarily based on fibre optic spectroscopy surveys. Elaborate methods have been developed to address aperture effects when fixed aperture sizes only probe the inner regions for galaxies of ever decreasing redshift or increasing physical size. These aperture corrections rely on assumptions about the physical properties of galaxies. The adequacy of these aperture corrections can be tested with integral-field spectroscopic data. We use integral-field spectra drawn from 1212 galaxies observed as part of the SAMI Galaxy Survey to investigate the validity of two aperture correction methods that attempt to estimate a galaxy's total instantaneous star formation rate. We show that biases arise when assuming that instantaneous star formation is traced by broadband imaging, and when the aperture correction is built only from spectra of the nuclear region of galaxies. These biases may be significant depending on the selection criteria of a survey sample. Understanding the sensitivities of these aperture corrections is essential for correct handling of systematic errors in galaxy evolution studies.

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The Gas Phase Mass Metallicity Relation for Dwarf Galaxies: Dependence on Star Formation Rate and HI Gas Mass

Using a sample of dwarf galaxies observed using the VIMOS IFU on the VLT, we investigate the mass-metallicity relation (MZR) as a function of star formation rate (FMR$_{\text{SFR}}$) as well as HI-gas mass (FMR$_{\text{HI}}$). We combine our IFU data with a subsample of galaxies from the ALFALFA HI survey crossmatched to the Sloan Digital Sky Survey to study the FMR$_{\text{SFR}}$ and FMR$_{\text{HI}}$ across the stellar mass range 10$^{6.6}$ to 10$^{8.8}$ M$_\odot$, with metallicities as low as 12+log(O/H) = 7.67. We find the 1$σ$ mean scatter in the MZR to be 0.05 dex. The 1$σ$ mean scatter in the FMR$_{\text{SFR}}$ (0.02 dex) is significantly lower than that of the MZR. The FMR$_{\text{SFR}}$ is not consistent between the IFU observed galaxies and the ALFALFA/SDSS galaxies for SFRs lower than 10$^{-2.4}$ M$_\odot$ yr$^{-1}$, however this could be the result of limitations of our measurements in that regime. The lowest mean scatter (0.01 dex) is found in the FMR$_{\text{HI}}$. We also find that the FMR$_{\text{HI}}$ is consistent between the IFU observed dwarf galaxies and the ALFALFA/SDSS crossmatched sample. We introduce the fundamental metallicity luminosity counterpart to the FMR, again characterized in terms of SFR (FML$_{\text{SFR}}$) and HI-gas mass (FML$_{\text{HI}}$). We find that the FML$_{\text{HI}}$ relation is consistent between the IFU observed dwarf galaxy sample and the larger ALFALFA/SDSS sample. However the 1$σ$ scatter for the FML$_{\text{HI}}$ relation is not improved over the FMR$_{\text{HI}}$ scenario. This leads us to conclude that the FMR$_{\text{HI}}$ is the best candidate for a physically motivated fundamental metallicity relation.

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The masses of satellites in GAMA galaxy groups from 100 square degrees of KiDS weak lensing data

We use the first 100 sq. deg. of overlap between the Kilo-Degree Survey (KiDS) and the Galaxy And Mass Assembly (GAMA) survey to determine the galaxy halo mass of ~10,000 spectroscopically-confirmed satellite galaxies in massive ($M > 10^{13}h^{-1}{\rm M}_\odot$) galaxy groups. Separating the sample as a function of projected distance to the group centre, we jointly model the satellites and their host groups with Navarro-Frenk-White (NFW) density profiles, fully accounting for the data covariance. The probed satellite galaxies in these groups have total masses $\log M_{\rm sub} /(h^{-1}{\rm M}_\odot) \approx 11.7 - 12.2$ consistent across group-centric distance within the errorbars. Given their typical stellar masses, $\log M_{\rm \star,sat}/(h^{-2}{\rm M}_\odot) \sim 10.5$, such total masses imply stellar mass fractions of $M_{\rm \star,sat} /M_{\rm sub} \approx 0.04 h^{-1}$ . The average subhalo hosting these satellite galaxies has a mass $M_{\rm sub} \sim 0.015M_{\rm host}$ independent of host halo mass, in broad agreement with the expectations of structure formation in a $Λ$CDM universe.

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