The group of strong Galois objects associated to a cocommutative Hopf quasigroup

Let H be a cocommutative faithfully flat Hopf quasigroup in a strict symmetric monoidal category with equalizers. In this paper we introduce the notion of (strong) Galois H-object and we prove that the set of isomorphism classes of (strong) Galois H-objects is a (group) monoid which coincides, in the Hopf algebra setting, with the Galois group of H-Galois objects introduced by Chase and Sweedler

OTELO survey: optimal emission-line flux determination with OSIRIS/GTC

Emission-line galaxies are important targets for understanding the chemical evolution of galaxies in the universe. Deep, narrow-band imaging surveys allow to detect and study the flux and the equivalent widths (EW) of the emission line studied. The present work has been developed within the context of the OTELO project, an emission line survey using the Tunable Filters (TF) of OSIRIS, the first generation instrument on the GTC 10.4m telescope located in La Palma, Spain, that will observe through selected atmospheric windows relatively free of sky emission lines. With a total survey area of 0.1 square degrees distributed in different fields, reaching a 5 \sigma depth of 10^-18 erg/cm^2/s and detecting objects of EW < 0.3 A, OTELO will be the deepest emission line survey to date. As part of the OTELO preparatory activities, the objective of this study is to determine the best combination of sampling and full width at half maximum (FWHM) for the OSIRIS tunable filters for deblending H\alpha from [NII] lines by analyzing the flux errors obtained. We simulated the OTELO data by convolving a complete set of synthetic HII galaxies in EW with different widths of the OSIRIS TFs. We estimated relative flux errors of the recovered H\alpha and [NII]6583 lines. We found that, for the red TF, a FWHM of 12 A and a sampling of 5 A is an optimal combination that allow deblending H\alpha from the [NII]6583 line with a flux error lower than 20%. This combination will allow estimating SFRs and metallicities using the H\alpha flux and the N2 method, respectively.Comment: 16 pages, 9 figures. Some authors added. Accepted for publication in PAS

Frustration free gapless Hamiltonians for Matrix Product States

For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate ground state (the so-called non-injective case), we construct another 'uncle' Hamiltonian which is local and frustration free but gapless, and its spectrum is $\R^+$. The construction is obtained by linearly perturbing the matrices building up the state in a random direction, and then taking the limit where the perturbation goes to zero. For MPS where the parent Hamiltonian has a unique ground state (the so-called injective case) we also build such uncle Hamiltonian with the same properties in the thermodynamic limit.Comment: 36 pages, new version with some contents rearranged, and a correction in the injective cas

The central parsecs of M87: jet emission and an elusive accretion disc

We present the first simultaneous spectral energy distribution (SED) of M87 core at a scale of 0.4 arcsec ($\sim 32\, \rm{pc}$) across the electromagnetic spectrum. Two separate, quiescent, and active states are sampled that are characterized by a similar featureless SED of power-law form, and that are thus remarkably different from that of a canonical active galactic nuclei (AGN) or a radiatively inefficient accretion source. We show that the emission from a jet gives an excellent representation of the core of M87 core covering ten orders of magnitude in frequency for both the active and the quiescent phases. The inferred total jet power is, however, one to two orders of magnitude lower than the jet mechanical power reported in the literature. The maximum luminosity of a thin accretion disc allowed by the data yields an accretion rate of $< 6 \times 10^{-5}\, \rm{M_\odot \, yr^{-1}}$, assuming 10% efficiency. This power suffices to explain M87 radiative luminosity at the jet-frame, it is however two to three order of magnitude below that required to account for the jet's kinetic power. The simplest explanation is variability, which requires the core power of M87 to have been two to three orders of magnitude higher in the last 200 yr. Alternatively, an extra source of power may derive from black hole spin. Based on the strict upper limit on the accretion rate, such spin power extraction requires an efficiency an order of magnitude higher than predicted from magnetohydrodynamic simulations, currently in the few hundred per cent range.Comment: 18 pages, 6 figures. Accepted for publication in MNRA