Quantum Phase Transitions in the Interacting Boson Model: Integrability, level repulsion and level crossing

We study the quantum phase transition mechanisms that arise in the Interacting Boson Model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.Comment: Accepted in PR

High-precision acoustic helium signatures in 18 low-mass low-luminosity red giants. Analysis from more than four years of Kepler observations

High-precision frequencies of acoustic modes in red giant stars are now available thanks to the long observing length and high-quality of the light curves provided by the NASA Kepler mission, thus allowing to probe the interior of evolved cool low-mass stars with unprecedented level of detail. We characterize the acoustic signature of the helium second ionization zone in a sample of 18 low-mass low-luminosity red giants by exploiting new mode frequency measurements derived from more than four years of Kepler observations. We analyze the second frequency differences of radial acoustic modes in all the stars of the sample by using the Bayesian code Diamonds. We find clear acoustic glitches due to the signature of helium second ionization in all the stars of the sample. We measure the acoustic depth and the characteristic width of the acoustic glitches with a precision level on average around $\sim$2% and $\sim$8%, respectively. We find good agreement with theoretical predictions and existing measurements from the literature. Lastly, we derive the amplitude of the glitch signal at $\nu_\mathrm{max}$ for the second differences and for the frequencies with an average precision of $\sim$6%, obtaining values in the range 0.14-0.24 $\mu$Hz, and 0.08-0.33 $\mu$Hz, respectively, which can be used to investigate the helium abundance in the stars.Comment: 12 pages, 19 figures, 3 tables. Accepted for publication in A&

Bayesian peak bagging analysis of 19 low-mass low-luminosity red giants observed with Kepler

The currently available Kepler light curves contain an outstanding amount of information but a detailed analysis of the individual oscillation modes in the observed power spectra, also known as peak bagging, is computationally demanding and challenging to perform on a large number of targets. Our intent is to perform for the first time a peak bagging analysis on a sample of 19 low-mass low-luminosity red giants observed by Kepler for more than four years. This allows us to provide high-quality asteroseismic measurements that can be exploited for an intensive testing of the physics used in stellar structure models, stellar evolution and pulsation codes, as well as for refining existing asteroseismic scaling relations in the red giant branch regime. For this purpose, powerful and sophisticated analysis tools are needed. We exploit the Bayesian code Diamonds, using an efficient nested sampling Monte Carlo algorithm, to perform both a fast fitting of the individual oscillation modes and a peak detection test based on the Bayesian evidence. We find good agreement for the parameters estimated in the background fitting phase with those given in the literature. We extract and characterize a total of 1618 oscillation modes, providing the largest set of detailed asteroseismic mode measurements ever published. We report on the evidence of a change in regime observed in the relation between linewidths and effective temperatures of the stars occurring at the bottom of the RGB. We show the presence of a linewidth depression or plateau around $\nu_\mathrm{max}$ for all the red giants of the sample. Lastly, we show a good agreement between our measurements of maximum mode amplitudes and existing maximum amplitudes from global analyses provided in the literature, useful as empirical tools to improve and simplify the future peak bagging analysis on a larger sample of evolved stars.Comment: 78 pages, 46 figures, 22 tables. Accepted for publication in A&

A population synthesis study of the luminosity function of hot white dwarfs

We present a coherent and detailed Monte Carlo simulation of the population of hot white dwarfs. We assess the statistical significance of the hot end of the white dwarf luminosity function and the role played by the bolometric corrections of hydrogen-rich white dwarfs at high effective temperatures. We use the most up-to-date stellar evolutionary models and implement a full description of the observational selection biases to obtain realistic simulations of the observed white dwarf population. Our theoretical results are compared with the luminosity function of hot white dwarfs obtained from the Sloan Digital Sky Survey (SDSS), for both DA and non-DA white dwarfs. We find that the theoretical results are in excellent agreement with the observational data for the population of white dwarfs with hydrogen deficient atmospheres (non-DA white dwarfs). For the population of white dwarfs with hydrogen-rich atmospheres (white dwarfs of the DA class), our simulations show some discrepancies with the observations for the brightest luminosity bins. These discrepancies can be attributed to the way in which the masses of the white dwarfs contributing to this luminosity bin have been computed, as most of them have masses smaller than the theoretical lower limit for carbon-oxygen white dwarfs. We conclude that the way in which the observational luminosity function of hot white dwarfs is obtained is very sensitive to the particular implementation of the method used to derive the masses of the sample. We also provide a revised luminosity function for hot white dwarfs with hydrogen-rich atmospheres.Comment: 6 pages, 5 figures, accepted for publication in A&

Routh reduction and the class of magnetic Lagrangian systems

In this paper, some new aspects related to Routh reduction of Lagrangian systems with symmetry are discussed. The main result of this paper is the introduction of a new concept of transformation that is applicable to systems obtained after Routh reduction of Lagrangian systems with symmetry, so-called magnetic Lagrangian systems. We use these transformations in order to show that, under suitable conditions, the reduction with respect to a (full) semi-direct product group is equivalent to the reduction with respect to an Abelian normal subgroup. The results in this paper are closely related to the more general theory of Routh reduction by stages.Comment: 23 page

Time-dependent Photoionization of Gaseous Nebulae: the Pure Hydrogen Case

We study the problem of time-dependent photoionization of low density gaseous nebulae subjected to sudden changes in the intensity of ionizing radiation. To this end, we write a computer code that solves the full time-dependent energy balance, ionization balance, and radiation transfer equations in a self-consistent fashion for a simplified pure hydrogen case. It is shown that changes in the ionizing radiation yield ionization/thermal fronts that propagate through the cloud, but the propagation times and response times to such fronts vary widely and non-linearly from the illuminated face of the cloud to the ionization front (IF). Ionization/thermal fronts are often supersonic, and in slabs initially in pressure equilibrium such fronts yield large pressure imbalances that are likely to produce important dynamical effects in the cloud. Further, we studied the case of periodic variations in the ionizing flux. It is found that the physical conditions of the plasma have complex behaviors that differ from any steady-state solutions. Moreover, even the time average ionization and temperature is different from any steady-state case. This time average is characterized by over-ionization and a broader IF with respect to the steady-state solution for a mean value of the radiation flux. Around the time average of physical conditions there is large dispersion in instantaneous conditions, particularly across the IF, which increases with the period of radiation flux variations. Moreover, the variations in physical conditions are asynchronous along the slab due to the combination of non-linear propagation times for thermal/ionization fronts and equilibration times.Comment: Accepted for publication in ApJ. 36 pages, 12 figure