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We present observational evidence of late-time interaction between the ejecta of the hydrogen-poor Type Ib supernova (SN) 2019yvr and hydrogen-rich circumstellar material (CSM), similar to the Type Ib SN 2014C. A narrow H{\alpha} emission line appears simultaneously with a break in the light-curve decline rate at around 80-100 d after explosion. From the interaction delay and the ejecta velocity, under the assumption that the CSM is detached from the progenitor, we estimate the CSM inner radius to be located at ~6.5-9.1 {\times} 10^{15} cm. The H{\alpha} emission line persists throughout the nebular phase at least up to +420 d post-explosion, with a full width at half maximum of ~2000 km/s. Assuming a steady mass-loss, the estimated mass-loss rate from the luminosity of the H{\alpha} line is ~3-7 {\times} 10^{-5} M_\odot yr^{-1}. From hydrodynamical modelling and analysis of the nebular spectra, we find a progenitor He-core mass of 3-4 M{_\odot}, which would imply an initial mass of 13-15 M{_\odot}. Our result supports the case of a relatively low-mass progenitor possibly in a binary system as opposed to a higher mass single star undergoing a luminous blue variable phase., Comment: 8 pages, 5 figures, published in MNRAS

Abstract: The interaction of dark matter particles (WIMPs) with the odd-mass $^{73}$Ge and $^{131}$Xe target nuclei ,{ {that is the recoil rates corresponding to the elastic scattering of WIMPs by these nuclei}}, is analysed in the context of the minimal extensions of the SUSY model. The BCS+QRPA technique plus the quasiparticle-phonon coupling scheme is used to describe the nuclear structure part of the calculations. The resulting values for the nuclear spin content of both nuclei are compared to values previously reported in the literature.

Dark Matter particles can be detected directly via their elastic scattering with nuclei. Next generation experiments can eventually find physical evidences about dark matter candidates. With this motivation in mind, we have calculated the expected signals of dark matter particles in xenon detectors. The calculations were performed by considering different masses and parameters within the minimal supersymmetric standard model. Since the detectors can also detect neutrinos, we have analyzed the supernova neutrino signal including a sterile neutrino in the formalism. Using this 3+1 scheme, we make predictions for both the normal and inverse mass hierarchy. In order to perform a study of the response of planned direct-detection experiments, to be located in ANDES (Agua Negra Deep Experimental Site), we have calculated the neutrino contributions to the background by taken into account reactor's neutrinos and geoneutrinos at the site of the lab. As a test detector, we take a Xenon1T-like array., Comment: 23 pages,11 figures

Neutrinos play an important role in core-collapse supernova events since they are a key piece to understand the explosion mechanisms. The analysis of the neutrino fluxes can bring answers to neutrino's related problems e.g.: mass hierarchy, spectral splitting, sterile neutrinos, etc. In this work we study the impact of neutrino oscillations and the possible existence of eV sterile neutrinos upon the supernova neutrino flux $F_\nu(E)$. We have calculated the energy distribution of the neutrino flux from a supernova and the total number of events which would be detected in a liquid scintillator. We also present an analysis for the conversion probabilities as a function of the active-sterile neutrino mixing parameters. Finally, we have carried out a statistical analysis to extract values for the mixing parameters of the model., Comment: 20 pages, 11 figures, 74 references

We analyze the characteristic polynomial associated to an ellipsoid and another quadric in the context of the contact detection problem. We obtain a necessary and sufficient condition for an efficient method to detect contact. This condition is a feature on the size and the shape of the quadrics and can be checked directly from their parameters. Under this hypothesis, contact can be noticed by means of discriminants of the characteristic polynomial. Furthermore, relative positions can be classified through the sign of the coefficients of this polynomial.

We prove that the homotopic distance between two maps defined on a manifold is bounded above by the sum of their subspace distances on the critical submanifol of any Morse-Bott function. This generalizes the Lusternik-Schnirelmann theorem (for Morse functions), and a similar result by Farber for the topological complexity. Analogously, we prove that, for analytic manifolds, the homotopic distance is bounded by the sum of the subspace distances on any submanifold and its cut locus. As an application, we show how navigation functions can be used to solve a generalized motion planning problem., Comment: 19 pages

The production of heavy-mass elements due to the rapid neutron-capture mechanism (r-process) is associated with astrophysical scenarios, such as supernovae and neutron-star mergers. In the r-process the capture of neutrons is followed by $\beta$-decays until nuclear stability is reached. A key element in the chain of nuclear weak-decays leading to the production of isotopes may be the change of the parameters controlling the neutrino sector, due to the mixing of active and sterile species. In this work we have addressed this question and calculated $\beta$-decay rates for the nuclei involved in the r-process chains as a function of the neutrino mixing parameters. These rates were then used in the calculation of the abundance of the heavy elements produced in core-collapse supernova and in neutron-star mergers, starting from different initial mass-fraction distributions. The analysis shows that the core-collapse supernova environment contributes with approximately $30\%$ of the total heavy nuclei abundance while the neutron-star merger contributes with about $70\%$ of it. Using available experimental data we have performed a statistical analysis to set limits on the active-sterile neutrino mixing angle and found a best-fit value $\sin^2 2\theta_{14}=0.22$, a value comparable with those found in other studies reported in the literature.

We study the Rayleigh quotient of a Hermitian matrix with quaternionic coefficients and prove its main properties. As an application, we give some relationships between left and right eigenvalues of Hermitian and symplectic matrices., Comment: 14 pages

A possible mechanism for the formation of heavy-mass elements in supernovae is the rapid neutron-capture-mechanism (r-process). It depends upon the electron-fraction $Y_e$, a quantity which is determined by beta-decay-rates. In this paper, we focus on the calculation of electroweak decay-rates in presence of massive neutrinos. The resulting expressions are then used to calculate nuclear reactions entering the rapid-neutron capture. We fix the astrophysical parameters to the case of a core-collapse supernova. The neutrino sector includes a mass scheme and mixing angles for active neutrinos, and also by including the mixing between active and sterile neutrinos. The results of the calculations show that the predicted abundances of heavy-mass nuclei are indeed affected by the neutrino mixing., Comment: 13 pages, 5 figures

Let $Sp(n)$ be the symplectic group of quaternionic $(n\times n)$-matrices. For any $1\leq k\leq n$, an element $A$ of $Sp(n)$ can be decomposed in $A= \begin{bmatrix} \alpha&T\cr \beta&P \end{bmatrix}$ with $P$ a $(k\times k)$-matrix. In this work, starting from a singular value decomposition of $P$, we obtain what we call a relative singular value decomposition of $A$. This feature is well adapted for the study of the quaternionic Stiefel manifold $X_{n,k}$, and we apply it to the determination of the Lusternik-Schnirelmann category of $Sp(k)$ in $X_{2k-j,k}$, for $j= 0,\,1,\,2$, Comment: 18 pages

The inclusion of massive neutrinos affects the cross sections involved in the formation of heavy nuclei, modifying their abundances. Rapid neutron capture processes (r-process) are often associated with explosive events such as core-collapse supernovae. In this work we study the effects of active and sterile neutrino oscillations and interactions, upon the calculation of neutrino fluxes, the baryonic density and the electron fraction of the material. We have considered two different initial distribution functions of the neutrinos and different combinations of mixing parameters (including {\theta} 34 = 0). We use the formalism of density matrices for the calculations and included the effects of neutrino oscillations, interactions with matter and self-neutrino interactions. We found that the interactions of the neutrinos with matter and with themselves change the electron fraction, affecting the onset of the r-process.

Neutrino induced reactions are a basic ingredient in astrophysical processes like star evolution. The existence of neutrino oscillations affects the rate of nuclear electroweak decays which participates in the chain of events that determines the fate of the star. Among the processes of interest, the production of heavy elements in core-collapse supernovae is strongly dependent upon neutrino properties, like the mixing between different species of neutrinos. In this work we study the effects of neutrino oscillations upon the electron fraction as a function of the neutrino mixing parameters, for two schemes: the $1+1$ scheme (one active neutrino and one sterile neutrino) and the $2+1$ scheme (two active neutrinos and one sterile neutrino). We have performed this analysis considering a core-collapse supernovae and determined the physical conditions needed to activate the nuclear reaction chains involved in the r-process. We found that the interactions of the neutrinos with matter and among themselves and the initial amount of sterile neutrinos in the neutrino-sphere might change the electron fraction, therefore affecting the onset of the r-process. We have set constrains on the active-sterile neutrino mixing parameters. They are the square-mass-difference $\Delta m^2_{14} $, the mixing angle $\sin^2 2\theta_{14}$, and the hindrance factor $\xi_s $ for the occupation of sterile neutrinos. The calculations have been performed for different values of $X_{\alpha}$, which is the fraction of $\alpha$-particles. For $X_{\alpha}=0$ the r-process is taking place if $\Delta m^2_{14} \geq 2 \, {\rm eV}^2 $, $\sin^2 2\theta_{14} < 0.8 $ and $\xi_s < 0.5$. For larger values of $X_{\alpha}$ the region of parameters is strongly reduced. The present results are compared to results available in the literature.

We characterize all possible relative positions between a hyperboloid of one sheet and a sphere through the roots of a characteristic polynomial associated to these quadrics. The classification is also suitable for a hyperboloid and a ellipsoid in some situations. As an application, this provides a method to detect contact between the two surfaces by a simple calculation in many real world applications., Comment: 21 pages

We consider height functions on symmetric spaces $M\cong G/K$ embedded in the associated matrix Lie group $G$. In particular we study the relationship between the critical sets of the height function on $G$ and its restriction to $M$. Also we prove that the gradient flow on $M$ can be integrated by means of a generalized Cayley transform. This allows to obtain explicit local charts for the critical submanifolds. Finally, we discuss how to reduce the generic case to a height function whose ground hyperplane is orhogonal to a real diagonal matrix. This result requires to prove the existence of a polar decomposition adapted to the automorphism defining $M$. Detailed examples are given., Comment: 24 pags

It is known that a $2\times 2$ quaternionic matrix has one, two or an infinite number of left eigenvalues, but the available algebraic proofs are difficult to generalize to higher orders. In this paper a different point of view is adopted by computing the topological degree of a characteristic map associated to the matrix and discussing the rank of the differential. The same techniques are extended to $3\times 3$ matrices, which are still lacking a complete classification., Comment: 21 pages

We prove that the LS category of the symplectic group $Sp(n)$ is bounded above by $\binom{n+1}{2}$. This is achieved by computing the number of critical levels of a height function., Comment: 6 pages. Corrected version with only minor changes

We introduce the notion of characteristic function of a quaternionic matrix, whose roots are the left eigenvalues. We prove that for all $2\times 2$ matrices and for $3\times 3$ matrices having some zero entry outside the diagonal there is a characteristic function which is a polynomial. For the other $3\times 3$ matrices the characteristic function is a rational function with one point of discontinuity. We prove that Hamilton-Cayley theorem holds in all cases., Comment: 14 pages, new version with a complete proof of Hamilton-Cayley theorem for all 3x3 matrices

We prove that given four arbitrary quaternion numbers of norm 1 there always exists a $2\times 2$ symplectic matrix for which those numbers are left eigenvalues. The proof is constructive. An application to the LS category of Lie groups is given., Comment: 7 pages

The aim of this paper is to use the so-called Cayley transform to compute the LS category of Lie groups and homogeneous spaces by giving explicit categorical open coverings. When applied to U(n), $U(2n)/Sp(n)$ and $U(n)/O(n)$ this method is simpler than those formerly known. We also show that the Cayley transform is related to height functions in Lie groups, allowing to give a local linear model of the set of critical points. As an application we give an explicit covering of $Sp(2)$ by categorical open sets. The obstacles to generalize these results to $Sp(n)$ are discussed., Comment: 14 pages

We obtain a complete characterization of the $2\times 2$ symplectic matrices having an infinite number of left eigenvalues. Previously, we give a new proof of a result from Huang and So about the number of eigenvalues of a quaternionic matrix. This is achieved by applying an algorithm for the resolution of equations due to De Leo et al., Comment: 7 pages