In a ΛCDM Universe, the specific stellar angular momentum ( j * ) and stellar mass (M * ) of a galaxy are correlated as a consequence of the scaling existing for dark matter haloes ( j h ∝ M 2/3 h ). The shape of this law is crucial to test galaxy formation models, which are currently discrepant especially at the lowest masses, allowing to constrain fundamental parameters, e.g. the retained fraction of angular momentum. In this study, we accurately determine the empirical j * − M * relation (Fall relation) for 92 nearby spiral galaxies (from S0 to Irr) selected from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample in the unprecedented mass range 7 log M * /M 11.5. We significantly improve all previous estimates of the Fall relation by determining j * profiles homogeneously for all galaxies, using extended Hi rotation curves, and selecting only galaxies for which a robust j * could be measured (converged j * (< R) radial profile). We find the relation to be well described by a single, unbroken power-law j * ∝ M α * over the entire mass range, with α = 0.55 ± 0.02 and orthogonal intrinsic scatter of 0.17 ± 0.01 dex. We finally discuss some implications for galaxy formation models of this fundamental scaling law and, in particular, the fact that it excludes models in which discs of all masses retain the same fraction of the halo angular momentum.
Aims. We estimate the mass of the inner (< 20 kpc) Milky Way and the axis ratio of its inner dark matter halo using globular clusters as tracers. At the same time, we constrain the distribution in phase-space of the globular cluster system around the Galaxy. Methods. We use the Gaia Data Release 2 catalogue of 75 globular clusters' proper motions and recent measurements of the proper motions of another 20 distant clusters obtained with the Hubble Space Telescope. We describe the globular cluster system with a distribution function (DF) with two components: a flat, rotating disc-like one and a rounder, more extended halo-like one. While fixing the Milky Way's disc and bulge, we let the mass and shape of the dark matter halo and we fit these two parameters, together with six others describing the DF, with a Bayesian method. Results. We find the mass of the Galaxy within 20 kpc to be M(< 20 kpc) = 1.91 +0.18 −0.17 × 10 11 M , of which M DM (< 20 kpc) = 1.37 +0.18 −0.17 × 10 11 M is in dark matter, and the density axis ratio of the dark matter halo to be q = 1.30 ± 0.25. Assuming a concentrationmass relation, this implies a virial mass M vir = 1.3 ± 0.3 × 10 12 M . Our analysis rules out oblate (q < 0.8) and strongly prolate halos (q > 1.9) with 99% probability. Our preferred model reproduces well the observed phase-space distribution of globular clusters and has a disc component that closely resembles that of the Galactic thick disc. The halo component follows a power-law density profile ρ ∝ r −3.3 , has a mean rotational velocity of V rot −14 km s −1 at 20 kpc, and has a mildly radially biased velocity distribution (β 0.2 ± 0.07, which varies significantly with radius only within the inner 15 kpc). We also find that our distinction between disc and halo clusters resembles, although not fully, the observed distinction in metal-rich ([Fe/H]> −0.8) and metal-poor ([Fe/H]≤ −0.8) cluster populations.
It is commonly believed that galaxies use, throughout the Hubble time, a very small fraction of the baryons associated to their dark matter halos to form stars. This so-called low "star formation/Ω c is the cosmological baryon fraction, is expected to reach its peak at nearly L * (at efficiency ≈ 20%) and decline steeply at lower and higher masses. We have tested this using a sample of nearby star-forming galaxies, from dwarfs (M 10 7 M ) to high-mass spirals (M 10 11 M ) with Hi rotation curves and 3.6µm photometry. We fit the observed rotation curves with a Bayesian approach by varying three parameters, stellar mass-to-light ratio Υ , halo concentration c and mass M halo . We found two surprising results: 1) the star formation efficiency is a monotonically increasing function of M with no sign of a decline at high masses, and 2) the most massive spirals (M 1 − 3 × 10 11 M ) have f ≈ 0.3 − 1, i.e. they have turned nearly all the baryons associated to their haloes into stars. These results imply that the most efficient galaxies at forming stars are massive spirals (not L * galaxies), they reach nearly 100% efficiency and thus, once both their cold and hot gas is considered into the baryon budget, they have virtually no missing baryons. Moreover, there is no evidence of mass quenching of the star formation occurring in galaxies up to halo masses of M halo ≈ a few × 10 12 M .
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