Local points on Shimura coverings of Shimura curves at bad reduction primes

Let XD be the Shimura curve associated with an indefinite rational quaternion algebra of reduced discriminant D>1. For each prime l|D, there is a natural cyclic Galois covering of Shimura curves XD,l → XD constructed by adding certain level structure at l. The main goal of this note is to study the existence of local points at primes p≠l of bad reduction on the intermediate curves of these coverings and their Atkin–Lehner quotients.Peer ReviewedPostprint (author's final draft

Constraints on the shape of the Milky Way dark matter halo from the Sagittarius stream

We propose a new model for the dark matter halo of the Milky Way that fits the properties of the stellar stream associated with the Sagittarius dwarf galaxy. Our dark halo is oblate with q_z = 0.9 for r < 10 kpc, and can be made to follow the Law & Majewski model at larger radii. However, we find that the dynamical perturbations induced by the Large Magellanic Cloud on the orbit of Sgr cannot be neglected when modeling its streams. When taken into account, this leads us to constrain the Galaxy's outer halo shape to have minor-to-major axis ratio (c/a)_\Phi = 0.8 and intermediate-to-major axis ratio (b/a)_\Phi = 0.9, in good agreement with cosmological expectations.Comment: 5 pages, 5 figures. Accepted for publication in ApJ Letters. Minor changes to match published versio

Pullbacks of Saito-Kurokawa lifts and a central value formula for degree 6 L-series

We prove an explicit central value formula for a family of complex L-series of degree 6 for GL2 × GL3 which arise as factors of certain Garret–Rankin triple product L-series associated with modular forms. Our result generalizes a previous formula of Ichino involving Saito–Kurokawa lifts, and as an application we prove Deligne’s conjecture stating the algebraicity of the central values of the considered L-series up to the relevant periods.Peer ReviewedPostprint (author's final draft

Matching the dark matter profiles of dSph galaxies with those of simulated satellites: a two parameter comparison

We compare the dark matter halos' structural parameters derived for four Milky Way dwarf spheroidal galaxies to those of subhalos found in cosmological $N$-body simulations. We confirm that estimates of the mass at a single fixed radius are fully consistent with the observations. However, when a second structural parameter such as the logarithmic slope of the dark halo density profile measured close to the half-light radius is included in the comparison, we find little to no overlap between the satellites and the subhalos. Typically the right mass subhalos have steeper profiles at these radii than measurements of the dSph suggest. Using energy arguments we explore if it is possible to solve this discrepancy by invoking baryonic effects. Assuming that feedback from supernovae can lead to a reshaping of the halos, we compute the required efficiency and find entirely plausible values for a significant fraction of the subhalos and even as low as 0.1%. This implies that care must be taken not to exaggerate the effect of supernovae feedback as this could make the halos too shallow. These results could be used to calibrate and possibly constrain feedback recipes in hydrodynamical simulations.Comment: 6 pages, 3 figures, submitted to ApJ

The effect of radial migration on galactic disks

We study the radial migration of stars driven by recurring multi-arm spiral features in an exponential disk embedded in a dark matter halo. The spiral perturbations redistribute angular momentum within the disk and lead to substantial radial displacements of individual stars, in a manner that largely preserves the circularity of their orbits and that results, after 5 Gyr (~40 full rotations at the disk scalelength), in little radial heating and no appreciable changes to the vertical or radial structure of the disk. Our results clarify a number of issues related to the spatial distribution and kinematics of migrators. In particular, we find that migrators are a heavily biased subset of stars with preferentially low vertical velocity dispersions. This "provenance bias" for migrators is not surprising in hindsight, for stars with small vertical excursions spend more time near the disk plane and thus respond more readily to non-axisymmetric perturbations. We also find that the vertical velocity dispersion of outward migrators always decreases, whereas the opposite holds for inward migrators. To first order, newly arrived migrators simply replace stars that have migrated off to other radii, thus inheriting the vertical bias of the latter. Extreme migrators might therefore be recognized, if present, by the unexpectedly small amplitude of their vertical excursions. Our results show that migration, understood as changes in angular momentum that preserve circularity, can affect strongly the thin disk, but cast doubts on models that envision the Galactic thick disk as a relic of radial migration.Comment: 10 pages, 12 figures. ApJ in pres