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Register a new userThe SAMI Galaxy Survey: Bayesian Inference for Gas Disk Kinematics using a Hierarchical Gaussian Mixture Model
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We present a novel Bayesian method, referred to as Blobby3D, to infer gas kinematics that mitigates the effects of beam smearing for observations using Integral Field Spectroscopy (IFS). The method is robust for regularly rotating galaxies despite substructure in the gas distribution. Modelling the gas substructure within the disk is achieved by using a hierarchical Gaussian mixture model. To account for beam smearing effects, we construct a modelled cube that is then convolved per wavelength slice by the seeing, before calculating the likelihood function. We show that our method can model complex gas substructure including clumps and spiral arms. We also show that kinematic asymmetries can be observed after beam smearing for regularly rotating galaxies with asymmetries only introduced in the spatial distribution of the gas. We present findings for our method applied to a sample of 20 star-forming galaxies from the SAMI Galaxy Survey. We estimate the global H$alpha$ gas velocity dispersion for our sample to be in the range $bar{sigma}_v sim $[7, 30] km s$^{-1}$. The relative difference between our approach and estimates using the single Gaussian component fits per spaxel is $Delta bar{sigma}_v / bar{sigma}_v = - 0.29 pm 0.18$ for the H$alpha$ flux-weighted mean velocity dispersion.
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Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on mixture model which is known as the EM algorithm where the parameters of the mixture model are usually estimated into a maximum likelihood estimation framework. Bayesian approach for finite and infinite Gaussian mixture model generates point estimates for all variables as well as associated uncertainty in the form of the whole estimates posterior distribution. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in Bayesian inference for finite and infinite Gaussian mixture model in order to seamlessly introduce their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning this field and given the paucity of scope to present this discussion, e.g., the separated analysis of the generation of Dirichlet samples by stick-breaking and Polyas Urn approaches. We refer the reader to literature in the field of the Dirichlet process mixture model for a much detailed introduction to the related fields. Some excellent examples include (Frigyik et al., 2010; Murphy, 2012; Gelman et al., 2014; Hoff, 2009). This survey is primarily a summary of purpose, significance of important background and techniques for Gaussian mixture model, e.g., Dirichlet prior, Chinese restaurant process, and most importantly the origin and complexity of the methods which shed light on their modern applications. The mathematical prerequisite is a first course in probability. Other than this modest background, the development is self-contained, with rigorous proofs provided throughout.
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.
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 ($sigma$) 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 $sigma$ 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 $sigma$ 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 $lambda_R$ 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.
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 ($lambda_{R_e}$) and ellipticity ($epsilon_e$) 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 $V/sigma$ anti-correlation, whereas quasi-regular and non-regular rotators show a more vertical relation in h3 and $V/sigma$. Motivated by recent cosmological simulations, we develop an alternative approach to kinematically classify galaxies from their individual h3 versus $V/sigma$ 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 $lambda_{R_e}-epsilon_e$ values can show distinctly different h3-$V/sigma$ signatures. Class 5 objects are previously unidentified fast rotators that show a weak h3 versus $V/sigma$ 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 $V/sigma$ as evidence for disks in most fast rotators, suggesting a dearth of gas-poor mergers among fast rotators.
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 H{alpha} 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 H{alpha} equivalent widths of asymmetric and normal galaxies shows a small but significant increase in inner equivalent width for asymmetric galaxies.
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