Dark matter searches with asteroseismology

High-precision asteroseismic data provides an excellent opportunity to test theories of stellar evolution and new physics, such as the properties of the dark matter (DM) of the Universe. Here we will show that some models of DM lead to changes in the classical scenario of stellar evolution. The accumulation of DM in the core of low-mass stars reduces their central temperatures and inhibits the formation of small convective cores in 1.1-1.3 Ms stars. We review the asteroseismic constraints that have been set to the characteristics of the DM particles, obtained comparing the oscillations of the star Alpha Cen B with modified stellar models. To conclude, we discuss the prospects to use CoRoT and Kepler data on main-sequence stars and red giants to further constrain the nature of DM.Comment: Proceedings of "The Space Photometry Revolution, CoRoT3-KASC7 joint meeting", Toulouse 201

First asteroseismic limits on the nature of dark matter

We report the first constraints on the properties of weakly interacting low-mass dark matter (DM) particles using asteroseismology. The additional energy transport mechanism due to accumulated asymmetric DM particles modifies the central temperature and density of low-mass stars and suppresses the convective core expected in 1.1-1.3 Ms stars even for an environmental DM density as low as the expected in the solar neighborhood. An asteroseismic modeling of the stars KIC 8006161, HD 52265 and Alpha Cen B revealed small frequency separations significantly deviated from the observations, leading to the exclusion of a region of the DM parameter space mass versus spin-dependent DM-proton scattering cross section comparable with present experimental constraints.Comment: 5 pages, 3 figures. v2 matches version to be published in ApJ

Stellar convective cores as dark matter probes

The recent detection of a convective core in a main-sequence solar-type star is used here to test particular models of dark matter (DM) particles, those with masses and scattering cross sections in the range of interest for the DM interpretation of the positive results in several DM direct detection experiments. If DM particles do not effectively self-annihilate after accumulating inside low-mass stars (e.g. in the asymmetric DM scenario) their conduction provides an efficient mechanism of energy transport in the stellar core. For main-sequence stars with masses between 1.1 and 1.3 Msun, this mechanism may lead to the suppression of the inner convective region expected to be present in standard stellar evolution theory. The asteroseismic analysis of the acoustic oscillations of a star can prove the presence/absence of such a convective core, as it was demonstrated for the first time with the Kepler field main-sequence solar-like pulsator, KIC 2009505. Studying this star we found that the asymmetric DM interpretation of the results in the CoGeNT experiment is incompatible with the confirmed presence of a small convective core in KIC 2009505.Comment: to appear on Physical Review

Embeddability and rate identifiability of Kimura 2-parameter matrices

Deciding whether a Markov matrix is embeddable (i.e. can be written as the exponential of a rate matrix) is an open problem even for $4\times 4$ matrices. We study the embedding problem and rate identifiability for the K80 model of nucleotide substitution. For these $4\times 4$ matrices, we fully characterize the set of embeddable K80 Markov matrices and the set of embeddable matrices for which rates are identifiable. In particular, we describe an open subset of embeddable matrices with non-identifiable rates. This set contains matrices with positive eigenvalues and also diagonal largest in column matrices, which might lead to consequences in parameter estimation in phylogenetics. Finally, we compute the relative volumes of embeddable K80 matrices and of embeddable matrices with identifiable rates. This study concludes the embedding problem for the more general model K81 and its submodels, which had been initiated by the last two authors in a separate work.Comment: 20 pages; 10 figure

The Sun and stars: Giving light to dark matter

During the last century, with the development of modern physics in such diverse fields as thermodynamics, statistical physics, and nuclear and particle physics, the basic principles of the evolution of stars have been successfully well understood. Nowadays, a precise diagnostic of the stellar interiors is possible with the new fields of helioseismology and astroseismology. Even the measurement of solar neutrino fluxes, once a problem in particle physics, is now a powerful probe of the core of the Sun. These tools have allowed the use of stars to test new physics, in particular the properties of the hypothetical particles that constitute the dark matter of the Universe. Here we present recent results obtained using this approach.Comment: 12 pages, 3 figure

Signatures of Dark Matter Burning in Nuclear Star Clusters

In order to characterize how dark matter (DM) annihilation inside stars changes the aspect of a stellar cluster, we computed the evolution until the ignition of the He burning of stars from 0.7 M sun to 3.5 M sun within halos of DM with different characteristics. We found that, when a cluster is surrounded by a dense DM halo, the positions of the cluster' stars in the H-R diagram have a brighter and hotter turnoff point than in the classical scenario without DM, therefore giving the cluster a younger appearance. The high DM densities required to produce these effects are expected only in very specific locations, such as near the center of our Galaxy. In particular, if DM is formed by the 8 GeV weakly interacting massive particles recently invoked to reconcile the results from direct detection experiments, then this signature is predicted for halos of DM with a density ρχ = 3 × 105 GeV cm-3. A DM density gradient inside the stellar cluster would result in a broader main sequence, turnoff, and red giant branch regions. Moreover, we found that for very high DM halo densities the bottom of the isochrones in the H-R diagram rises to higher luminosities, leading to a characteristic signature on the stellar cluster. We argue that this signature could be used to indirectly probe the presence of DM particles in the location of a cluster

Using interior point solvers for optimizing progressive lens models with spherical coordinates

Research Report UPC-DEIO DR 2019Designing progressive lenses is a complex problem that has beenpreviously solved by formulating an optimization model based on Cartesiancoordinates. In this work a new progressive lens model using spherical co-ordinates is presented, and interior point solvers are used to solve this newoptimization model. Although this results in a highly nonlinear, nonconvex,continuous optimization problem, the new spherical coordinates model exhibitsbetter convexity properties compared to previous ones based on Cartesian co-ordinates. The real-world instances considered gave rise to nonlinear optimiza-tion problems of about 900 variables and 15000 constraints. Each constraintcorresponds to a point of the grid used to define the lens surface. The numberof variables depends on the precision of a B-spline basis used for the repre-sentation of the surface, and the number of constraints depends on the shapeand quality of the design. We present results of progressive lenses obtainedusing the AMPL modeling language and the nonlinear interior point solversIPOPT, LOQO and KNITRO. Computational results are reported, as wellas some examples of real-world progressive lenses calculated using this newmodel. Progressive lenses obtained are competitive in terms of quality withthose resulting from previous models that are used in commercial glasses.Peer ReviewedPreprin