Radial pulsations of neutron stars: computing alternative polytropic models regarding density and adiabatic index (original) (raw)
Related papers
In this paper we compute general-relativistic polytropic models simulating rigidly rotating, pulsating neutron stars. These relativistic compact objects, with a radius of ~10 km and mass between ~1.4 and 3.2 solar masses, are closely related to pulsars. We emphasize on computing the change in the pulsation eigenfrequencies owing to a rigid rotation, which, in turn, is a decisive issue for studying stability of such objects. In our computations, we keep rotational perturbation terms of up to second order in the angular velocity.
Radial pulsation frequencies of slowly rotating neutron stars
We study the radial pulsation frequencies of slowly rotating neutron stars in general relativistic formalism using realistic equations of state. It is found that the pulsation frequencies are always an increasing function of rotation rate. The increasing rate of frequency depends on the nature of equations of state. Cameron [1] suggested that the vibration of neutron stars might excite motions that might have interesting astrophysical applications, which lead to a series of investigations of the vibrational properties of neutron stars. The earliest detailed calculations were done by Meltzer and Thorne [2] and Thorne [3], where they investigated the radial as well as nonradial oscillations using available equation of state, such as the Harrison-Walker-Wheeler equation of state. These and other early studies by Wheeler [4], Chau [5] and Occhionero [6] indicated that the majority
Radial oscillations of relativistic stars
We present a new survey of the radial oscillation modes of neutron stars. This study complements and corrects earlier studies of radial oscillations. We present an extensive list of frequencies for the most common equations of state and some more recent ones. In order to check the accuracy, we use two different numerical schemes which yield the same results. The stimulation for this work comes from the need of the groups that evolve the full nonlinear Einstein equation to have reliable results from perturbation theory for comparison.
Avoided crossings in radial pulsations of neutron and strange stars
Astronomy and Astrophysics, 1999
Radial pulsations of neutron stars and strange quark stars with nuclear crust are studied. The avoided crossing phenomenon occurring for the radial modes is found and discussed. Neutron star models are constructed using a realistic equation of state of dense matter and strange star models using a phenomenological bag model of quark matter. The eigenfrequencies of the three lowest modes of linear, adiabatic pulsations are calculated, using the relativistic equations for the radial oscillations.
Fundamental oscillation modes of neutron stars: Validity of universal relations
Physical Review D, 2015
We study the f-mode frequencies and damping times of nonrotating neutron stars (NS) in general relativity (GR) by solving the linearized perturbation equations, with the aim to establish "universal" relations that depend only weakly on the equations of state (EOS). Using a more comprehensive set of EOSs, we reexamine some proposed empirical relations that describe the f-mode parameters in terms of mass and radius of the neutron star (NS), and we test a more recent proposal for expressing the f-mode parameters as quadratic functions of the effective compactness. Our extensive results for each equation of state considered allow us to study the accuracy of each proposal. In particular, the empirical relation proposed in the literature for the damping time in terms of the mass and radius deviates considerably from our results. We introduce a new universal relation for the product of the f-mode frequency and damping time as a function of the (ordinary) compactness, which proved to be more accurate. The more recently proposed relations using the effective compactness, on the other hand, also fit our data accurately. Our results show that the maximum oscillation frequency depends strongly on the EOS, such that the measurement of a high oscillation frequency would rule out several EOSs. Lastly, we compare the exact mode frequencies to those obtained in the Cowling approximation, and also to results obtained with a nonlinear evolution code, validating the implementations of the different approaches.
On the r-mode spectrum of relativistic stars: the inclusion of the radiation reaction
Monthly Notices of the Royal Astronomical Society, 2002
We consider both mode calculations and time evolutions of axial r-modes for relativistic uniformly rotating non-barotropic neutron stars, using the slow-rotation formalism, in which rotational corrections are considered up to linear order in the angular velocity Ω. We study various stellar models, such as uniform density models, polytropic models with different polytropic indices n, and some models based on realistic equations of state. For weakly relativistic uniform density models, and polytropes with small values of n, we can recover the growth times predicted from Newtonian theory when standard multipole formulae for the gravitational radiation are used. However, for more compact models, we find that relativistic linear perturbation theory predicts a weakening of the instability compared to the Newtonian results. When turning to polytropic equations of state, we find that for certain ranges of the polytropic index n, the r-mode disappears, and instead of a growth, the time evolutions show a rapid decay of the amplitude. This is clearly at variance with the Newtonian predictions. It is, however, fully consistent with our previous results obtained in the low-frequency approximation.
Radial pulsations and stability of protoneutron stars
Astron Astrophys, 1997
Radial pulsations of newborn neutron stars (protoneutron stars) are studied for a range of internal temperatures and entropies per baryon predicted by the existing numerical simulations. Protoneutron star models are constructed using a realistic equation of state of hot dense matter, and under various assumptions concerning stellar interior (large trapped lepton number, zero trapped lepton number, isentropic, isothermal). Under prevailing conditions, linear oscillations of a protoneutron star can be treated as adiabatic, and evolutionary effects can be neglected on dynamic timescale. The dynamic behavior is governed by the adiabatic index, which in turn depends on the physical state of the stellar interior. The eigenfrequencies of the lowest radial modes of linear, adiabatic pulsations are calculated. Stability of protoneutron stars with respect to small radial perturbations is studied, and the validity of the static stability criteria is discussed.
Adiabatic Survey of Subdwarf B Star Oscillations. II. Effects of Model Parameters on Pulsation Modes
Astrophysical Journal Supplement Series, 2002
We present the Ðrst results of a large, systematic adiabatic survey of the pulsation properties of models of subdwarf B (sdB) stars. This survey is aimed at providing the most basic theoretical data with which to analyze the asteroseismological properties of the recently discovered class of pulsating sdB stars (the EC 14026 stars). Such a theoretical framework has been lacking up to now. In this paper, the Ðrst of a series of three, an adiabatic pulsation code is used to compute, in the 80È1500 s period window, the radial (l \ 0) and nonradial (from l \ 1 up to l \ 3) oscillation modes for a representative evolutionary model of subdwarf B stars. Quantities such as the periods, kinetic energies, Ðrst-order rotational splitting coefficients, eigenfunctions, and weight functions are given by the code, providing a complete set of very useful diagnostic tools with which to study the mode properties. The main goal is to determine how these quantities relate to the internal structure of B subdwarfs, a crucial and necessary step if one wants to eventually apply the tools of asteroseismology to EC 14026 stars. All modes (p, f, and g) were considered in order to build the most complete picture we can have on pulsations in these stars. In that context, we show that g-modes are essentially deep interior modes oscillating mainly in the radiative helium-rich core (but not in the convective nucleus), while p-modes are shallower envelope modes. We demonstrate that g-modes respond to a trapping/conÐnement phenomenon induced mainly by the He/H chemical transition between the H-rich envelope and the He-rich core of subdwarf B stars. This phenomenon is very similar in nature to the g-mode trapping and conÐnement mechanisms observed in pulsating white dwarf models. We emphasize that p-modes may also experience distortions of their period distribution due to this He/H transition, although these are not as pronounced as in the g-mode case. These phenomena are of great interest as they can potentially provide powerful tools for probing the internal structure of these objects, in particular, with respect to constraining the mass of their H-rich envelope. The results given in this Ðrst paper form the minimal background on pulsation mode characteristics in sdB stars. Upcoming discussions on additional mode properties in subdwarf B star models (Paper II and Paper III of this series) will strongly rely on these basic results since they provide essential guidance in understanding mode period behaviors as functions of B subdwarf stellar parameters and/or evolution.
Non-adiabatic linear pulsation models for low-mass helium stars
Monthly Notices of the Royal Astronomical Society, 1999
Non-adiabatic linear pulsation models have been calculated for low-mass stars with effective temperatures between 16 000 and 35 000 K, and with surface gravities in the range 3 , log g , 5X The radial pulsation models assume a homogeneous stellar envelope which is deficient in hydrogen and display the well-known Z-bump instability to radial pulsations. The aim of this paper has been to explore the behaviour of the Z-bump instability as a function of mass and composition around a reference model with M 0X5 M (Y X 0X00Y Z 0X02. It is shown that the Z-bump instability persists to low masses (M , 0X4 M () but is suppressed either by a reduction in metallicity Z or by a selective enhancement of the carbon abundance. An unexpected result is the discovery that Z-bump instability persists at hydrogen abundances X. 0X3, although the position of the red edge is sensitive to X. We have found that non-radial pulsations are also excited in the same instability region as radial pulsations. The implications of these results for individual low-mass helium stars are discussed. It is concluded that Z-bump driven pulsations (radial and/or non-radial) may be excited in some helium-rich subdwarf B stars, representing a possible major extension to the class of variable stars represented by the prototype V652 Her.