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Umin Lee

Publications and source records attributed to Umin Lee.

36 records · Page 2Linked to original sources
arXiv2013

Viscous decretion discs around rapidly rotating stars

We discuss steady viscous Keplerian decretion discs around rapidly rotating stars. We assume that low frequency modes, which may be excited by the opacity bump mechanism, convective motion in the core, or tidal force if the star is in a binary system, can transport an enough amount of angular momentum to the region close to the stellar surface. Under this assumption, we construct a star-disc system, in which there forms a viscous decretion disc around a rapidly rotating star because of the angular momentum supply. We find a series of solutions of steady viscous decretion discs around a rapidly rotating star that extend to $R_{\rm disc}\gtsim~10R_*$ with $R_*$ being the equatorial radius of the star, depending on the amount of angular momentum supply.

astro-ph.SR↗
arXiv2011

Amplitudes of low frequency modes in rotating B type stars

Using weakly non-linear theory of oscillation, we estimate the amplitudes of low frequency modes in a slowly pulsating B (SPB) star, taking account of the effects of rotation on the modes. Applying the formulation by Schenk et al (2002), we compute non-linear coupling coefficient between the low frequency modes and estimate the equilibrium amplitudes of the modes excited in the star, assuming the amplitudes of the unstable modes are saturated as a result of non-linear coupling with stable modes, that is, as a result of parametric instability expected between one unstable mode and two stable modes. We use the traditional approximation to calculate adiabatic and non-adiabatic oscillations in a rotating star. We find $r$-modes in a rapidly rotating star play a significant role in the amplitude determination through non-linear coupling. We also find that for low $m$ modes, the fractional amplitudes of the radiative luminosity caused by the low frequency modes are of order $10^{-4}$ to $10^{-3}$ at the surface.

astro-ph.SR↗
arXiv2010

Stability of g-modes in rotating B-type stars

We have studied the stability of low degree $g$-modes in uniformly rotating B-type stars, taking into account the effects of the Coriolis force and the rotational deformation. From an analysis treating rotation frequency as a small parameter it is found that slow rotation tends to $destabilize$ high radial-order $retrograde$ $g$-modes, although the effect is very small or absent for relatively low order modes. Calculating eigenfrequencies at selected rotation rates, we find, on the other hand, that rapid rotation tends to $stabilize$ $retrograde$ $g$-modes. The stabilizing effect appears stronger for less massive B-type stars having low effective temperatures. If we change rotation rate continuously, the frequency of a $g$-mode belonging to ($l', m$) crosses frequencies of other $g$-modes belonging to ($l', m$). If the parity of the two encountering modes are the same, they interact each other and the stability (i.e., imaginary part of eigenfrequency) of each mode is modified. Using an asymptotic method we discuss the property of such mode crossings and couplings. For rapidly rotating stars mode couplings are important for the stability of low degree $g$-modes. In particular, we find that the stabilization of retrograde $g$-modes in rapidly rotating stars is due to many strong mode couplings, while %prograde sectoral% modes are exceptionally immune to the damping effects from the mode couplings.

astro-ph.SR↗
arXiv2010

Light curves from rapidly rotating neutron stars

We calculate light curves produced by a hot spot of a rapidly rotating neutron star, assuming that the spot is perturbed by a core $r$-mode, which is destabilized by emitting gravitational waves. To calculate light curves, we take account of relativistic effects such as the Doppler boost due to the rapid rotation and light bending assuming the Schwarzschild metric around the neutron star. We assume that the core $r$-modes penetrate to the surface fluid ocean to have sufficiently large amplitudes to disturb the spot. For a $l'=m$ core $r$-mode, the oscillation frequency $ω\approx2mΩ/[l'(l'+1)]$ defined in the co-rotating frame of the star will be detected by a distant observer, where $l'$ and $m$ are respectively the spherical harmonic degree and the azimuthal wave number of the mode, and $Ω$ is the spin frequency of the star. In a linear theory of oscillation, using a parameter $A$ we parametrize the mode amplitudes such that ${\rm max}\left(|ξ_θ|,|ξ_ϕ|\right)/R=A$ at the surface, where $ξ_θ$ and $ξ_ϕ$ are the $θ$ and $ϕ$ components of the displacement vector of the mode and $R$ is the radius of the star. For the $l'=m=2$ $r$-mode with $ω=2Ω/3$, we find that the fractional Fourier amplitudes at $ω=2Ω/3$ in light curves depend on the angular distance $θ_s$ of the spot centre measured from the rotation axis and become comparable to or even larger than $A\sim0.001$ for small values of $θ_s$.

astro-ph.HE↗
arXiv2009

Non-axisymmetric low frequency oscillations of rotating and magnetized neutron stars

We investigate non-axisymmetric low frequency modes of a rotating and magnetized neutron star, assuming that the star is threaded by a dipole magnetic field whose strength at the stellar surface, $B_0$, is less than $\sim 10^{12}$G, and whose magnetic axis is aligned with the rotation axis. For modal analysis, we use a neutron star model composed of a fluid ocean, a solid crust, and a fluid core, where we treat the core as being non-magnetic assuming that the magnetic pressure is much smaller than the gas pressure in the core. Here, we are interested in low frequency modes of a rotating and magnetized neutron star whose oscillation frequencies are similar to those of toroidal crust modes of low spherical harmonic degree and low radial order. For a magnetic field of $B_0\sim 10^7$G, we find Alfvén waves in the ocean have similar frequencies to the toroidal crust modes, and we find no $r$-modes confined in the ocean for this strength of the field. We calculate the toroidal crustal modes, the interfacial modes peaking at the crust/core interface, and the core inertial modes and $r$-modes, and all these modes are found to be insensitive to the magnetic field of strength $B_0\ltsim10^{12}$G. We find the displacement vector of the core $l^\prime=|m|$ $r$-modes have large amplitudes around the rotation axis at the stellar surface even in the presence of a surface magnetic field $B_0\sim10^{10}$G, where $l^\prime$ and $m$ are the spherical harmonic degree and the azimuthal wave number of the $r$-modes, respectively. We suggest that millisecond X-ray variations of accretion powered X-ray millisecond pulsars can be used as a probe into the core $r$-modes destabilized by gravitational wave radiation.

astro-ph.SR↗
arXiv2006

Axisymmetric oscillations of magnetic neutron stars

We calculate axisymmetric oscillations of rotating neutron stars composed of the surface fluid ocean, solid crust, and fluid core, taking account of a dipole magnetic field as strong as $B_S\sim 10^{15}$G at the surface. The adiabatic oscillation equations for the solid crust threaded by a dipole magnetic field are derived in Newtonian dynamics, on the assumption that the axis of rotation is aligned with the magnetic axis so that perturbations on the equilibrium can be represented by series expansions in terms of spherical harmonic functions $Y_l^m(θ,ϕ)$ with different degrees $l$ for a given azimuthal wave number $m$ around the the magnetic axis. Although the three component models can support a rich variety of oscillation modes, axisymmetric ($m=0$) toroidal $_{l}t_n$ and spheroidal $_ls_n$ shear waves propagating in the solid crust are our main concerns, where $l$ and $n$ denote the harmonic degree and the radial order of the modes, respectively. In the absence of rotation, axisymmetric spheroidal and toroidal modes are completely decoupled, and we consider the effects of rotation on the oscillation modes only in the limit of slow rotation. We find that the oscillation frequencies of the fundamental toroidal torsional modes $_{l}t_n$ in the crust are hardly affected by the magnetic field as strong as $B_S\sim 10^{15}$G at the surface. As the radial order $n$ of the shear modes in the crust becomes higher, however, both spheroidal and toroidal modes become susceptible to the magnetic field and their frequencies in general get higher with increasing $B_S$. We also find that the surface $g$ modes and the crust/ocean interfacial modes are suppressed by a strong magnetic field, and that there appear magnetic modes in the presence of a strong magnetic field.

astro-ph↗
arXiv2005

R modes of slowly pulsating B stars

We examine pulsational stability of low $m$ $r$ modes in SPB stars by calculating fully nonadiabatic oscillations of uniformly rotating stars, where $m$ is an integer representing the azimuthal wave number around the rotation axis. $R$ modes are rotationally induced, non-axisymmetric, oscillation modes, whose oscillation frequency strongly depends on the rotation frequency $Ω$ of the star. They are conveniently classified by using two integer indices $m$ and $l^\prime\ge |m|$ that define the asymptotic oscillation frequency $2mΩ/[l^\prime(l^\prime+1)]$ in the limit of $Ω\to 0$. We find low $m$, high radial order, odd $r$ modes with $l^\prime=m$ in SPB stars are excited by the same iron opacity bump mechanism that excites low frequency $g$ modes of the variables, when the rotation frequency $Ω$ is sufficiently high. No even $r$ modes with low $m$ are found to be pulsationally unstable. Since the surface pattern of the temperature perturbation of odd modes is antisymmetric about the equator of the star, observed photometric amplitudes caused by the unstable odd $r$ modes with $l^\prime=m$ are strongly dependent on the inclination angle between the axis of rotation and the line of sight. Applying the wave-meanflow interaction formalism to nonadiabatic $r$ modes in rapidly rotating SPB models, we find that because of the $rϕ$ component of the Reynolds stress and the radial transport of the eddy fluctuation of density in the rotating star, the surface rotation is accelerated by the forcing due to the low $l^\prime=m$ unstable $r$ modes.

astro-ph↗
arXiv2005

Light curves of oscillating neutron stars

We calculate light curves produced by $r$-modes with small azimuthal wavenumbers, $m$, propagating in the surface fluid ocean of rotating neutron stars. We include relativistic effects due to rapid rotation, and propagate photons from the stellar surface to a distant observer using the Schwarzschild metric. The wave motions of the surface $r$-modes are confined to the equatorial region of the star, and the surface pattern of the temperature variation can be either symmetric (for even modes) or anti-symmetric (for odd modes) with respect to the equator. Since for the surface $r$-modes the oscillation frequency in the corotating frame of the star is much smaller than the rotation frequency, $Ω$, we employ the approximation in which the oscillation frequency in the inertial frame, $σ$, is given by $σ= -mΩ$. We find that the $even$, $m = 1$ $r$-mode produces the largest light variations. The dominant Fourier component in the light curves of these modes is the fundamental having $σ=-Ω$, and the first harmonic component having $σ=-2Ω$ is always negligible in comparison. The dominant Fourier component of the even, $m=2$ $r$-modes is the first harmonic. Although the $odd$ $r$-modes produce smaller amplitude light variations compared with the $even$ modes, the light curves of the former have a stronger first harmonic component. If both $m=1$ and 2 $r$-modes are excited simultaneously, a rich variety of light curves is possible, including those having an appreciable first harmonic component. We show that the phase difference, $δ-δ_E$, between the bolometric light curve and that at a particular photon energy can possibly be used as a probe of the stellar compactness, $R/M$, where $R$ and $M$ are the radius and mass of the star.

astro-ph↗
arXiv2004

R-modes of a neutron star with a magnetic dipole field

We study $r$-modes of a rotating magnetized neutron star, assuming a magnetic dipole field whose axis is aligned with the axis of rotation. We approach the problem by applying a singular perturbation theory to the oscillations of rotating stars. In this treatment, we divide the star into a thin surface magnetic layer and a non-magnetic core. We integrate linearized ideal MHD equations in the surface magnetic layer and non-magnetic oscillation equations in the core, and match the two integrations at the interface to obtain a complete solution. For a polytropic neutron star model of mass $M=1.4M_\odot$ and radius $R=10^6$cm, the magnetic dipole field becomes effective on the modal properties of the $r$-modes only when the field strength $B_S$ is much greater than $10^{14}$G. We also find that the damping effects caused by very short magnetic perturbations in the surface layer are not important for the $r$-mode instability of rapidly rotating neutron stars if the field strength $B_S$ is smaller than $10^{12}$G.

astro-ph↗
arXiv2003

Inertial modes of neutron stars with the superfluid core

We investigate the modal properties of inertial modes of rotating neutron stars with the core filled with neutron and proton superfluids, taking account of entrainment effects between the superfluids. In this paper, the entrainment effects are modeled by introducing a parameter $η$ so that no entrainment state is realized at $η=0$. We find that inertial modes of rotating neutron stars with the superfluid core are split into two families, which we call ordinary fluid inertial modes ($i^o$-mode) and superfluid inertial modes ($i^s$-mode). The two superfluids in the core counter-move for the $i^s$-modes. For the $i^o$-modes, $κ_0=\lim_{Ω\to 0}ω/Ω$ is only weakly dependent on the entrainment parameter $η$, where $Ω$ and $ω$ are the angular frequency of rotation and the oscillation frequency observed in the corotating frame of the star, respectively. For the $i^s$-modes, on the other hand, $|κ_0|$ almost linearly increases as $η$ increases. Avoided crossings as functions of $η$ are therefore quite common between $i^o$- and $i^s$-modes. We find that some of the $i^s$-modes that are unstable against the gravitational radiation reaction at $η=0$ become stable when $η$ is larger than $η_{crit}$, the value of which depends on the mode. Since the radiation driven instability associated with the current multipole radiation is quite weak for the inertial modes and the mutual friction damping in the superfluid core is strong, the instability caused by the inertial modes will be easily suppressed unless the entrainment parameter $η$ is extremely small and the mutual friction damping is sufficiently weak.

astro-ph↗
arXiv2003

r-modes in Relativistic Superfluid Stars

We discuss the modal properties of the $r$-modes of relativistic superfluid neutron stars, taking account of the entrainment effects between superfluids. In this paper, the neutron stars are assumed to be filled with neutron and proton superfluids and the strength of the entrainment effects between the superfluids are represented by a single parameter $η$. We find that the basic properties of the $r$-modes in a relativistic superfluid star are very similar to those found for a Newtonian superfluid star. The $r$-modes of a relativistic superfluid star are split into two families, ordinary fluid-like $r$-modes ($r^o$-mode) and superfluid-like $r$-modes ($r^s$-mode). The two superfluids counter-move for the $r^s$-modes, while they co-move for the $r^o$-modes. For the $r^o$-modes, the quantity $κ\equivσ/Ω+m$ is almost independent of the entrainment parameter $η$, where $m$ and $σ$ are the azimuthal wave number and the oscillation frequency observed by an inertial observer at spatial infinity, respectively. For the $r^s$-modes, on the other hand, $κ$ almost linearly increases with increasing $η$. It is also found that the radiation driven instability due to the $r^s$-modes is much weaker than that of the $r^o$-modes because the matter current associated with the axial parity perturbations almost completely vanishes.

gr-qc↗
arXiv2002

R-modes of neutron stars with the superfluid core

We investigate the modal properties of the $r$-modes of rotating neutron stars with the core filled with neutron and proton superfluids, taking account of entrainment effects between the superfluids. The stability of the $r$-modes against gravitational radiation reaction is also examined considering viscous dissipation due to shear and a damping mechanism called mutual friction between the superfluids in the core. We find the $r$-modes in the superfluid core are split into ordinary $r$-modes and superfluid $r$-modes, which we call, respectively, $r^o$- and $r^s$-modes. The two superfluids in the core flow together for the $r^o$-modes, while they counter-move for the $r^s$-modes. For the $r^o$-modes, the coefficient $κ_0\equiv\lim_{Ω\to 0}ω/Ω$ is equal to $2m/[l^\prime(l^\prime+1)]$, almost independent of the parameter $η$ that parameterizes the entrainment effects between the superfluids, where $Ω$ is the angular frequency of rotation, $ω$ the oscillation frequency observed in the corotating frame of the star, and $l^\prime$ and $m$ are the indices of the spherical harmonic function representing the angular dependence of the $r$-modes. For the $r^s$-modes, on the other hand, $κ_0$ is equal to $2m/[l^\prime(l^\prime+1)]$ at $η=0$ (no entrainment), and it almost linearly increases as $η$ is increased from $η=0$. The mutual friction in the superfluid core is found ineffective to stabilize the $r$-mode instability caused by the $r^o$-mode except in a few narrow regions of $η$. The $r$-mode instability caused by the $r^s$-modes, on the other hand, is extremely weak and easily damped by dissipative processes in the star.

astro-ph↗
arXiv2002

Nonradial Oscillations of Neutron Stars with a Solid Crust -- Analysis in the Relativistic Cowling Approximation--

Nonradial oscillations of relativistic neutron stars with a solid crust are computed in the relativistic Cowling approximation, in which all metric perturbations are ignored. For the modal analysis, we employ three-component relativistic neutron star models with a solid crust, a fluid core, and a fluid ocean. As a measure for the relativistic effects on the oscillation modes, we calculate the relative frequency difference defined as $δσ/σ\equiv(σ_{GR}-σ_N)/σ_{GR}$, where $σ_{GR}$ and $σ_R$ are, respectively, the relativistic and the Newtonian oscillation frequencies. The relative difference $δσ/σ$ takes various values for different oscillation modes of the neutron star model, and the value of $δσ/σ$ for a given mode depends on the physical properties of the models. We find that $|δσ/σ|$ is less than $\sim0.1$ for most of the oscillation modes we calculate, although there are a few exceptions such as the fundamental (nodeless) toroidal torsional modes in the crust, the surface gravity modes confined in the surface ocean, and the core gravity modes trapped in the fluid core. We also find that the modal properties, represented by the eigenfunctions, are not strongly affected by introducing general relativity. It is however shown that the mode characters of the two interfacial modes, associated with the core/crust and crust/ocean interfaces, have been interchanged between the two through an avoided crossing when we move from Newtonian dynamics to general relativistic dynamics.

astro-ph↗
arXiv2001

Relativistic r-modes in Slowly Rotating Neutron Stars: Numerical Analysis in the Cowling Approximation

We investigate the properties of relativistic $r$-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the influence of the Coriolis like force on the stellar oscillations, but ignore the effects of the centrifugal like force. For three neutron star models, we calculated the fundamental $r$-modes with $l'=m=2$ and 3. We found that the oscillation frequency $\barσ$ of the fundamental $r$-mode is in a good approximation given by $\barσ\approx κ_0 Ω$, where $\barσ$ is defined in the corotating frame at the spatial infinity, and $Ω$ is the angular frequency of rotation of the star. The proportional coefficient $κ_0$ is only weakly dependent on $Ω$, but it strongly depends on the relativistic parameter $GM/c^2R$, where $M$ and $R$ are the mass and the radius of the star. All the fundamental $r$-modes with $l'=m$ computed in this study are discrete modes with distinct regular eigenfunctions, and they all fall in the continuous part of the frequency spectrum associated with Kojima's equation (Kojima 1998). These relativistic $r$-modes are obtained by including the effects of rotation higher than the first order of $Ω$ so that the buoyant force plays a role, the situation of which is quite similar to that for the Newtonian $r$-modes.

gr-qc↗
arXiv2000

R-modes of neutron stars with a solid crust

We investigate the properties of $r$-mode oscillations of a slowly rotating neutron star with a solid crust, by taking account of the effects of the Coriolis force. For the modal analysis we employ three-component neutron star models that are composed of a fluid core, a solid crust and a surface fluid ocean. For the three-component models, we find that there exist two kinds of $r$-modes, that is, those confined in the surface fluid ocean and those confined in the fluid core, which are most important for the $r$-mode instability. The $r$-modes do not have any appreciable amplitudes in the solid crust if rotation rate of the star is sufficiently small. We find that the core $r$-modes are strongly affected by mode coupling with the crustal torsional (toroidal) modes and lose their simple properties of the eigenfunction and eigenfrequency as functions of the angular rotation velocity $Ω$. This indicates that the extrapolation formula, which is obtained in the limit of $Ω\to 0$, cannot be used to examine the $r$-mode instability of rapidly rotating neutron stars with a solid crust unless the effects of mode coupling with the crustal torsional modes are correctly taken into account.

astro-ph↗
arXiv2000

Rotational modes of non-isentropic stars and the gravitational radiation driven instability

We investigate the properties of r-mode and inertial mode of slowly rotating, non-isentropic, Newtonian stars, by taking account of the effects of the Coriolis force and the centrifugal force. For the non-isentropic models we consider only two cases, that is, the models with the stable fluid stratification in the whole interior and the models that are fully convective. For simplicity we call these two kinds of models "radiative" and "convective" models in this paper. For both cases, we assume the deviation of the models from isentropic structure is small. Examining the dissipation timescales due to the gravitational radiation and several viscous processes for the polytropic neutron star models, we find that the gravitational radiation driven instability of the r-modes remains strong even in the non-isentropic models. Calculating the rotational modes of the radiative models as functions of the angular rotation frequency $Ω$, we find that the inertial modes are strongly modified by the buoyant force at small $Ω$, where the buoyant force as a dominant restoring force becomes comparable with or stronger than the Coriolis force. Because of this property we obtain the mode sequences in which the inertial modes at large $Ω$ are identified as g-modes or the r-modes with l=|m| at small $Ω$. We also note that as $Ω$ increases from $Ω=0$ the retrograde g-modes become retrograde inertial modes, which are unstable against the gravitational radiation reaction.

astro-ph↗
arXiv1999

Inertial modes of slowly rotating isentropic stars

We investigate inertial mode oscillations of slowly and uniformly rotating, isentropic, Newtonian stars. Inertial mode oscillations are induced by the Coriolis force due to the star's rotation, and their characteristic frequencies are comparable with the rotation frequency $Ω$ of the star. So called r-mode oscillations form a sub-class of the inertial modes. In this paper, we use the term ``r-modes'' to denote the inertial modes for which the toroidal motion dominates the spheroidal motion, and the term ``inertial modes'' to denote the inertial modes for which the toroidal and spheroidal motions have comparable amplitude to each other. Using the slow rotation approximation consistent up to the order of $Ω^3$, we study the properties of the inertial modes and r-modes, by taking account of the effect of the rotational deformation of the equilibrium on the eigenfrequencies and eigenfunctions. The eigenfrequencies of the r-modes and inertial modes calculated in this paper are in excellent agreement with those obtained by Lindblom et al (1999) and Lockitch & Friedman (1998). We also estimate the dissipation timescales due to the gravitational radiation and several viscous processes for polytropic neutron star models. We find that for the inertial modes, the mass multipole gravitational radiation dominates the current multipole radiation, which is dominating in the case of the r-modes. It is also found that the inertial mode instability is more unstable than previously reported by Lockitch & Friedman (1998), and survives the viscous damping processes relevant in neutron stars.

astro-ph↗