Galaxy stellar and total mass estimation using machine learning

Conventional galaxy mass estimation methods suffer from model assumptions and degeneracies. Machine learning, which reduces the reliance on such assumptions, can be used to determine how well present-day observations can yield predictionsfor the distributions of stellar and dark matter. In this work, we use a general sample of galaxies from the TNG100 simulation to investigate the ability of multi-branch convolutional neural network (CNN) based machine learning methods to predict the central (i.e., within 1 − 2 effective radii) stellar and total masses, and the stellar mass-to-light ratio M∗ /L. These models take galaxy images and spatially-resolved mean velocity and velocity dispersion maps as inputs. Such CNN-based models can in general break the degeneracy between baryonic and dark matter in the sense that the model can make reliable predictions onthe individual contributions of each component. For example, with r-band images and two galaxy kinematic maps as inputs, our model predicting M∗ /L has a prediction uncertainty of 0.04 dex. Moreover, to investigate which (global) features significantly contribute to the correct predictions of the properties above, we utilize a gradient boosting machine. We find that galaxy luminosity dominates the prediction of all masses in the central regions, with stellar velocity dispersion coming next. We also investigate the main contributing features when predicting stellar and dark matter mass fractions ( f∗ , fDM ) and the dark mattermass MDM , and discuss the underlying astrophysics

SDSS-IV MaNGA: Stellar M/L gradients and the M/L-colour relation in galaxies

The stellar mass-to-light ratio gradient in SDSS r-band ∇(M*/Lr) of a galaxy depends on its mass assembly history, which is imprinted in its morphology and gradients of age, metallicity, and stellar initial mass function (IMF). Taking a MaNGA sample of 2051 galaxies with stellar masses ranging from 109 to 1012M⊙ released in SDSS DR15, we focus on face-on galaxies, without merger and bar signatures, and investigate the dependence of the 2D ∇(M*/Lr) on other galaxy properties, including M*/Lr-colour relationships by assuming a fixed Salpeter IMF as the mass normalization reference. The median gradient is ∇M*/Lr ∼ −0.1 (i.e. the M*/Lr is larger at the centre) for massive galaxies, becomes flat around M* ∼ 1010M⊙ and change sign to ∇M*/Lr ∼ 0.1 at the lowest masses. The M*/Lr inside a half-light radius increases with increasing galaxy stellar mass; in each mass bin, early-type galaxies have the highest value, while pure-disc late-type galaxies have the smallest. Correlation analyses suggest that the mass-weighted stellar age is the dominant parameter influencing the M*/Lr profile, since a luminosity-weighted age is easily affected by star formation when the specific star formation rate (sSFR) inside the half-light radius is higher than 10−3 Gyr−1. With increased sSFR gradient, one can obtain a steeper negative ∇(M*/Lr). The scatter in the slopes of M*/L-colour relations increases with increasing sSFR, for example, the slope for post-starburst galaxies can be flattened to 0.45 from the global value 0.87 in the M*/L versus g − r diagram. Hence converting galaxy colours to M*/L should be done carefully, especially for those galaxies with young luminosity-weighted stellar ages, which can have quite different star formation histories

Tibetan sheep are better able to cope with low energy intake than Small-tailed Han sheep due to lower maintenance energy requirements and higher nutrient digestibilities

Tibetan sheep are indigenous to the Qinghai-Tibetan Plateau (QTP) and are well-adapted to and even thrive under the harsh alpine conditions. Small-tailed Han sheep were introduced to the plateau because of their high prolificacy and are maintained mainly in feedlots. Because of their different backgrounds, we hypothesised that Tibetan and Small-tailed Han sheep would differ in their utilization of energy intake and predicted that Tibetan sheep would cope better with low energy intake than Small-tailed Han sheep. To test this prediction, we determined nutrient digestibilities, energy requirements for maintenance and blood metabolite and hormone concentrations involved in energy metabolism in these breeds. Sheep of each breed (n = 24 of each, all wethers and 1.5 years of age) were distributed randomly into one of four groups and offered ad libitum diets of different digestible energy (DE) densities: 8.21, 9.33, 10.45 and 11.57 MJ DE/kg Dry matter (DM). Following 42 d of measuring feed intake, a 1-week digestion and metabolism experiment was done. DM intakes did not differ between breeds nor among treatments but, by design, DE intake increased linearly in both breeds as dietary energy level increased (P < 0.001). The average daily gain (ADG) was significantly greater in the Tibetan than Small-tailed Han sheep (P = 0.003) and increased linearly in both breeds (P < 0.001). In addition, from the regression analysis of ADG on DE intake, daily DE maintenance requirements were lower for Tibetan than for Small-tailed Han sheep (0.41 vs 0.50 MJ/BW0.75, P < 0.05). The DE and metabolizable energy (ME) digestibilities were higher in the Tibetan than Small-tailed Han sheep (P < 0.001) and increased linearly as the energy level increased in the diet (P < 0.001). At the lowest energy treatment, Tibetan sheep when compared with Small-tailed Han sheep, had: 1) higher serum glucose and glucagon, but lower insulin concentrations (P < 0.05), which indicated a higher capacity for gluconeogenesis and ability to regulate glucose metabolism; and 2) higher non-esterified fatty acids (NEFA) and lower very low density lipoprotein (VLDL) and triglyceride (TG) concentrations (P < 0.05), which indicated a higher capacity for NEFA oxidation but lower ability for triglyceride (TG) synthesis. We concluded that our prediction was supported as these differences between breeds conferred an advantage for Tibetan over Small-tailed Han sheep to cope better with low energy diets

Eta invariants for flat manifolds

Using H. Donnelly result from the article "Eta Invariants for G-Spaces" we calculate the eta invariants of the signature operator for almost all 7-dimensional flat manifolds with cyclic holonomy group. In all cases this eta invariants are an integer numbers. The article was motivated by D. D. Long and A. Reid article "On the geometric boundaries of hyperbolic 4-manifolds, Geom. Topology 4, 2000, 171-178Comment: 18 pages, a new version with referees comment