Cooling of quark stars in the colour superconductive phase: effect of photons from glueball decay

The cooling history of a quark star in the colour superconductive phase is investigated. Here we specifically focus on the two-flavour colour (2SC) phase where the novel process of photon generation via glueball (GLB) decay has already been investigated. The picture we present here can, in principle, be generalized to quark stars entering a superconductive phase where similar photon generation mechanisms are at play. As much as 10⁴⁵–10⁴⁷ erg of energy is provided by the GLB decay in the 2SC phase. The generated photons slowly diffuse out of the quark star, keeping it hot and radiating as a blackbody (with possibly a Wien spectrum in gamma-rays) for millions of years. We discuss hot radio-quiet isolated neutron stars in our picture (such as RX J185635–3754 and RX J0720.4–3125) and argue that their nearly blackbody spectra (with a few broad features) and their remarkably tiny hydrogen atmosphere are indications that these might be quark stars in the colour superconductive phase where some sort of photon generation mechanism (reminiscent of the GLB decay) has taken place. Fits to observed data of cooling compact stars favour models with superconductive gaps of  Δ_2SC∼ 15–35 MeV  and densities  ρ_2SC= (2.5–3.0) ×ρ_N  (ρ_N being the nuclear matter saturation density) for quark matter in the 2SC phase. If correct, our model combined with more observations of isolated compact stars could provide vital information to studies of quark matter and its exotic phases.     

Gravity modes and mixed modes as probes of stellar cores in main‐sequence stars: From solar‐like to β Cep stars

We investigate how the frequencies of gravity modes depend on the detailed properties of the chemical composition gradient that develops near the core of main‐sequence stars and, therefore, on the transport processes that are able to modify the μ profile in the central regions. We show that in main‐sequence models, similarly to the case of white dwarfs, the periods of high‐order gravity modes are accurately described by a uniform period spacing superposed to an oscillatory component. The periodicity and amplitude of such a component are related, respectively, to the location and sharpness of the μ gradient. We briefly discuss and interpret, by means of this simple approximation, the effect of turbulent mixing near the core on the periods of both high‐order and low‐order g modes, as well as of modes of mixed pressure‐gravity character. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Seismic study of stellar convective regions: the base of the convective envelope in low-mass stars

The possibility of observing solar-type oscillations on other stars is of great relevance to investigating the uncertain aspects of the internal structure of stars. One of these aspects is the convective overshoot that takes place at the borders of the envelopes of stars of mass similar to, or lower than, the Sun. It affects the temperature stratification, mixing, rotation and magnetic-field generation. Asteroseismology can provide an observational test for the studies of the structure of such overshoot regions.
The seismic study of the transition in the Sun, located at the base of the convection zone, has been successful in determining the characteristics of this layer in the Sun. In this work we consider the extension of the analysis to other solar-type stars (of mass between 0.85 and 1.2 M_⊙) in order to establish a method for determining the characteristics of their convective envelopes. In particular, we hope to be able to establish seismologically that a star does indeed possess a convective envelope, to measure the size of the convective region and also to constrain the properties of an overshoot layer at the bottom of the envelope. The limitations in terms of observational uncertainties and stellar characteristics, and the detectability of an overshoot layer, are discussed.     

Seismic signatures of strange stars with crust

We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l , the fundamental mode (without radial nodes) has a frequency of ∼300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies ≳20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (having approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.     

Chromothermal oscillations and collapse of strange stars to black holes: astrophysical implications

We study the effects of temperature on strange stars. It is found that the maximum mass of the star decreases with the increase of temperature, as at high temperatures the equations of state become softer. Moreover, if the temperature of a strange star increases, keeping its baryon number fixed, its gravitational mass increases and its radius decreases. This leads to a limiting temperature, where it turns into a black hole. These features are the result of a combined effect of the change of gluon mass and the quark distribution with temperature. We report on a new type of radial oscillation of strange stars, driven by what we call 'chromothermal' instability. We also discuss the relevance of our findings in the astrophysics of core collapse supernovae and gamma-ray bursts.     

Lessons for asteroseismology from white dwarf stars

The interpretation of pulsation data for sun-like stars is currently facing challenges quite similar to those faced by white dwarf modelers ten years ago. The observational requirements for uninterrupted long-term monitoring are beginning to be satisfied by successful multi-site campaigns and dedicated satellite missions. But exploration of the most important physical parameters in theoretical models has been fairly limited, making it difficult to establish a detailed best-fit model for a particular set of oscillation frequencies. I review the past development and the current state of white dwarf asteroseismology, with an emphasis on what this can tell us about the road to success for asteroseismology of other types of stars.     

Pair emission from bare magnetized strange stars

The dominant emission from bare strange stars is thought to be electron–positron pairs, produced through spontaneous pair creation (SPC) in a surface layer of electrons tied to the star by a superstrong electric field. The positrons escape freely, but the electrons are directed towards the star and quickly fill all available states, such that their degeneracy suppresses further SPC. An electron must be reflected and gain energy in order to escape, along with the positron. Each escaping electron leaves a hole that is immediately filled by another electron through SPC. We discuss the collisional processes that produce escaping electrons. When the Landau quantization of the motion perpendicular to the magnetic field is taken into account, electron–electron collisions can lead to an escaping electron only through a multistage process involving higher Landau levels. Although the available estimates of the collision rate are deficient in several ways, it appears that the rate is too low for electron–electron collisions to be effective. A simple kinetic model for electron–quark collisions leads to an estimate of the rate of pair production that is analogous to thermionic emission, but the work function is poorly determined.     

Bulk viscosity of mixed nucleon–hyperon–quark matter in neutron stars

We calculate the coefficient of bulk viscosity by considering the non-leptonic weak interactions in the cores of hybrid stars with both hyperons and quarks. We first determine the dependence of the production rate of neutrons on the reaction rate of quarks in the non-leptonic processes, that is,  Γ _n = K _s Γ _s +Γ_Λ+ 2Γ_Σ−  . The conversion rate,   K _s   , in our scenario is a complicated function of baryon number density. We also consider the medium effect of quark matter on bulk viscosity. Using these results, we estimate the limiting rotation of the hybrid stars, which may suppress the r-mode instability more effectively. Hybrid stars should be the candidates for the extremely rapid rotators.     

Seismology of stellar envelopes: probing the outer layers of a star through the scattering of acoustic waves

The outer layers of Sun-like stars are regions of rapid spatial variation which modulate the p-mode frequencies by partially reflecting the constituent acoustic waves. With the accuracy that has been achieved by current solar observations, and that is expected from imminent stellar observations, this modulation can be observed from the spectra of the low-degree modes. We present a new and simple theoretical calculation to determine the leading terms in an asymptotic expansion of the outer phase of these modes, which is determined by the structure of the surface layers of the star. Our procedure is to compare the stellar envelope with a plane-parallel polytropic envelope, which we regard as a smooth reference background state. Then we can isolate a seismic signature of the acoustic phase and relate it to the stratification of the outer layers of the convection zone. One can thereby constrain theories of convection that are used to construct the convection zones of the Sun and Sun-like stars. The accuracy of the diagnostic is tested in the solar case by comparing the predicted outer phase with an exact numerical calculation.     

Crust–core coupling and r-mode damping in neutron stars: a toy model

r-modes in neutron stars with crusts are damped by viscous friction at the crust–core boundary. The magnitude of this damping, evaluated by Bildsten & Ushomirsky (BU) under the assumption of a perfectly rigid crust, sets the maximum spin frequency for neutron stars spun up by accretion in low-mass X-ray binaries (LMXBs). In this paper we explore the mechanical coupling between the core r-modes and the elastic crust, using a toy model of a constant-density neutron star having a crust with a constant shear modulus. We find that, at spin frequencies in excess of ≈50 Hz, the r-modes strongly penetrate the crust. This reduces the relative motion (slippage) between the crust and the core compared with the rigid-crust limit. We therefore revise down, by as much as a factor of 10²–10³ , the damping rate computed by BU, significantly reducing the maximal possible spin frequency of neutron stars with solid crusts. The dependence of the crust–core slippage on the spin frequency is complicated, and is very sensitive to the physical thickness of the crust. If the crust is sufficiently thick, the curve of the critical spin frequency for the onset of the r-mode instability becomes multivalued for some temperatures; this is related to avoided crossings between the r-mode and higher-order torsional modes in the crust. The critical frequencies are comparable to the observed spins of neutron stars in LMXBs and millisecond pulsars.     

Time-dependent convection seismic study of five γ Doradus stars

We apply for the first time the time-dependent convection (TDC) treatment of Gabriel and Grigahcène et al. to the photometric mode identification in γ Doradus (γ Dor) stars. We consider the influence of this treatment on the theoretical amplitude ratios and phase differences. Comparison with the observed amplitudes and phases of the stars γ Dor, 9 Aurigae, HD 207223 = HR 8330, HD 12901 and 48501 is presented and enables us to identify the degree ℓ of the pulsation modes for four of them. We also determine the mode stability for different models of these stars. We show that our TDC models agree better with observations than with frozen convection models. Finally, we compare the results obtained with different values of the mixing-length parameter α.     

The effect of turbulent mixing on the g‐mode spectrum of MS stars

Understanding transport processes inside stars is one of the main goals of asteroseismology. Chemical turbulent mixing can affect the internal distribution of μ near the energy generating core, having an effect on the evolutionary tracks similar to that of overshooting. This mixing leads to a smoother chemical composition profile near the edge of the convective core, which is reflected in the behavior of the buoyancy frequency and, therefore, in the frequencies of gravity modes. We describe the effects of convective overshooting and turbulent mixing on the frequencies of gravity modes in B‐type main sequence stars. In particular, the cases of p‐g mixed modes in β Cep stars and high‐order modes in SPBs are considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal evolution of rotating hybrid stars

As a neutron star spins down, the nuclear matter is continuously converted into quark matter due to the core density increase, and then latent heat is released. We have investigated the thermal evolution of neutron stars undergoing such deconfinement phase transition. We have taken into account the conversion in the frame of the general theory of relativity. The released energy has been estimated as a function of changed rate of deconfinement baryon number. The numerical solutions to the cooling equation are seen to be very different from those without the heating effect. The results show that neutron stars may be heated to higher temperatures which is well matched with pulsar's data despite the onset of fast cooling in neutron stars with quark matter cores. It is also found that the heating effect has a magnetic field strength dependence. This feature could be particularly interesting for high temperatures of low-field millisecond pulsars at a later stage. The high temperature could fit the observed temperature for PSR J0437−4715.