Galaxy 3D Shape Recovery using Mixture Density Network

Abstract

Since the turn of the century, astronomers have been exploiting the rich information afforded by combining stellar kinematic maps and imaging in an attempt to recover the intrinsic, three-dimensional (3D) shape of a galaxy. A common intrinsic shape recovery method relies on an expected monotonic relationship between the intrinsic misalignment of the kinematic and morphological axes and the triaxiality parameter. Recent studies have, however, cast doubt about underlying assumptions relating shape and intrinsic kinematic misalignment. In this work, we aim to recover the 3D shape of individual galaxies using their projected stellar kinematic and flux distributions using a supervised machine learning approach with mixture density network (MDN). Using a mock dataset of the EAGLE hydrodynamical cosmological simulation, we train the MDN model for a carefully selected set of common kinematic and photometric parameters. Compared to previous methods, we demonstrate potential improvements achieved with the MDN model to retrieve the 3D galaxy shape along with the uncertainties, especially for prolate and triaxial systems. We make specific recommendations for recovering galaxy intrinsic shapes relevant for current and future integral field spectroscopic galaxy surveys.

Figures (12)

• Figure 1: Flowchart of the intrinsic shape determination pipeline. For each simulated galaxy, mock IFS images are constructed from which the kinematic and photometric features are extracted. Principal component analysis is applied for feature selection to choose a number of important features (those not selected are in grey). These are then fed to the mixture density network with 3 dense hidden layers of 128 nodes each. In the last layer, the MDN outputs a linear combination of Gaussian mixture parameters given by the weights $\alpha_{i}$, standard deviations $\sigma_{i}$, and means $\mu_{i}$ to predict the $p$ and $q$ distributions.
• Figure 2: The distribution of galaxy shapes measured from the RefL0100N1504 box of the EAGLE simulation. In dark grey squares we show galaxies that have undergone a major or minor merger within the last 5 Gyr, which we class as "disturbed". Light gray outline triangles show systems with significant bar structures. The histograms show the distribution of these barred and merger systems in $p$ and $q$ in light and dark grey respectively. Coloured circles represent galaxies that we have selected for our investigation. Each colour demonstrates the shape of the system, with spherical objects in yellow, prolate objects in orange, triaxial objects in pink and oblate objects in blue.
• Figure 3: Demonstrating the equal sampling of $p-q$ space within the training set. Each point shows an individual EAGLE galaxy within the full sample. Coloured points show galaxies selected for the training and validation sets, while grey points demonstrate galaxies that have been left for the testing phase. The colour of each point denotes the number of times that galaxy is observed in order to keep that $p-q$ region equally sampled. The number in the corner of each $p-q$ region demonstrates the total number of observations within that region.
• Figure 4: (Top left) Considering the raw distributions of tuneable observation properties controlled in each mock observation using a corner plot. The relationship between each property is demonstrated in purple. By "raw" we mean the values modified per observation i.e. viewing angle, size of the PSF and projected distance to the object. (Bottom right) Considering the relative distributions of the important tuneable observation properties to ensure mock observations are uniform in the important ratios, as shown in the blue corner plot. These ratios, i.e. the size of the PSF relative to the size of the object, and the number of pixels within the measurement radius, are important for measuring observable kinematics to produce an unbiased training set. The approximately uniform distribution shown in blue demonstrates that our sample selection is not biasing our algorithm results.
• Figure 5: Histograms showing how different intrinsic shapes of EAGLE galaxies within our training data populate each observable parameter. In each case, the spherical systems are shown in yellow, prolate systems in orange, triaxial systems in purple and oblate systems in blue. The overall height of the bar shows the distribution of each kinematic parameter within the full training set. The coloured regions then demonstrate the percentage of each bar that is made up of each intrinstic shape. Starred (*) axis labels have been divided into equally-sized log10 bins to more clearly delineate between the groups, though bar labels are shown as the raw values for clarity. This plot demonstrates that, in none of the single measurements can we cleanly distinguish between the intrinsic shapes directly. This justifies the machine learning approach.