arXiv subjects

Lee Lindblom

Publications and source records attributed to Lee Lindblom.

69 records · Page 4Linked to original sources

arXiv2001

Gravitational radiation from the r-mode instability

The instability in the r-modes of rotating neutron stars can (in principle) emit substantial amounts of gravitational radiation (GR) which might be detectable by LIGO and similar detectors. Estimates are given here of the detectability of this GR based the non-linear simulations of the r-mode instability by Lindblom, Tohline and Vallisneri. The burst of GR produced by the instability in the rapidly rotating 1.4 solar mass neutron star in this simulation is fairly monochromatic with frequency near 960 Hz and duration about 100 s. A simple analytical expression is derived here for the optimal S/N for detecting the GR from this type of source. For an object located at a distance of 20 Mpc we estimate the optimal S/N to be in the range 1.2 to about 12.0 depending on the LIGO II configuration.

gr-qc↗

arXiv2001

Models of Rapidly Rotating Neutron Stars: Remnants of Accretion Induced Collapse

Equilibrium models of differentially rotating nascent neutron stars are constructed, which represent the result of the accretion induced collapse of rapidly rotating white dwarfs. The models are built in a two-step procedure: (1) a rapidly rotating pre-collapse white dwarf model is constructed; (2) a stationary axisymmetric neutron star having the same total mass and angular momentum distribution as the white dwarf is constructed. The resulting collapsed objects consist of a high density central core of size roughly 20 km, surrounded by a massive accretion torus extending over 1000 km from the rotation axis. The ratio of the rotational kinetic energy to the gravitational potential energy of these neutron stars ranges from 0.13 to 0.26, suggesting that some of these objects may have a non-axisymmetric dynamical instability that could emit a significant amount of gravitational radiation.

astro-ph↗

arXiv2001

Non-Linear Evolution of the r-Modes in Neutron Stars

The evolution of a neutron-star r-mode driven unstable by gravitational radiation (GR) is studied here using numerical solutions of the full non-linear fluid equations. The amplitude of the mode grows to order unity before strong shocks develop which quickly damp the mode. In this simulation the star loses about 40% of its initial angular momentum and 50% of its rotational kinetic energy before the mode is damped. The non-linear evolution causes the fluid to develop strong differential rotation which is concentrated near the surface and especially near the poles of the star.

astro-ph↗

arXiv2001

Neutron Star Pulsations and Instabilities

Gravitational radiation (GR) drives an instability in certain modes of rotating stars. This instability is strong enough in the case of the r-modes to cause their amplitudes to grow on a timescale of tens of seconds in rapidly rotating neutron stars. GR emitted by these modes removes angular momentum from the star at a rate which would spin it down to a relatively small angular velocity within about one year, if the dimensionless amplitude of the mode grows to order unity. A pedagogical level discussion is given here on the mechanism of GR instability in rotating stars, on the relevant properties of the r-modes, and on our present understanding of the dissipation mechanisms that tend to suppress this instability in neutron stars. The astrophysical implications of this GR driven instability are discussed for young neutron stars, and for older systems such as low mass x-ray binaries. Recent work on the non-linear evolution of the r-modes is also presented.

astro-ph↗

arXiv2000

Effect of a neutron-star crust on the r-mode instability

The presence of a viscous boundary layer under the solid crust of a neutron star dramatically increases the viscous damping rate of the fluid r-modes. We improve previous estimates of this damping rate by including the effect of the Coriolis force on the boundary-layer eigenfunction and by using more realistic neutron-star models. If the crust is assumed to be perfectly rigid, the gravitational radiation driven instability in the r-modes is completely suppressed in neutron stars colder than about 1.5 x 10^8 K. Energy generation in the boundary layer will heat the star, and will even melt the crust if the amplitude of the r-mode is large enough. We solve the heat equation explicitly (including the effects of thermal conduction and neutrino emission) and find that the r-mode amplitude needed to melt the crust is approximately a_c = 5 x 10^{-3} for maximally rotating neutron stars. If the r-mode saturates at an amplitude larger than a_c, the heat generated is sufficient to maintain the outer layers of the star in a mixed fluid-solid state analogous to the pack ice on the fringes of the Arctic Ocean. We argue that in young, rapidly rotating neutron stars this effect considerably delays the formation of the crust. By considering the dissipation in the ice flow, we show that the final spin frequency of stars with r-mode amplitude of order unity is close to the value estimated for fluid stars without a crust.

astro-ph↗

arXiv1999

R-Modes in Superfluid Neutron Stars

The analogs of r-modes in superfluid neutron stars are studied here. These modes, which are governed primarily by the Coriolis force, are identical to their ordinary-fluid counterparts at the lowest order in the small angular-velocity expansion used here. The equations that determine the next order terms are derived and solved numerically for fairly realistic superfluid neutron-star models. The damping of these modes by superfluid ``mutual friction'' (which vanishes at the lowest order in this expansion) is found to have a characteristic time-scale of about 10^4 s for the m=2 r-mode in a ``typical'' superfluid neutron-star model. This time-scale is far too long to allow mutual friction to suppress the recently discovered gravitational radiation driven instability in the r-modes. However, the strength of the mutual friction damping depends very sensitively on the details of the neutron-star core superfluid. A small fraction of the presently acceptable range of superfluid models have characteristic mutual friction damping times that are short enough (i.e. shorter than about 5 s) to suppress the gravitational radiation driven instability completely.

gr-qc↗

arXiv1999

Stability of the r-modes in white dwarf stars

Stability of the r-modes in rapidly rotating white dwarf stars is investigated. Improved estimates of the growth times of the gravitational-radiation driven instability in the r-modes of the observed DQ Her objects are found to be longer (probably considerably longer) than 6x10^9y. This rules out the possibility that the r-modes in these objects are emitting gravitational radiation at levels that could be detectable by LISA. More generally it is shown that the r-mode instability can only be excited in a very small subset of very hot (T>10^6K), rather massive (M>0.9M_sun) and very rapidly rotating (P_min 10^9y) to allow the amplitude to grow to a dynamically significant level. This makes it extremely unlikely that the r-mode instability plays a significant role in any real white dwarf stars.

gr-qc↗

arXiv1999

Second-order rotational effects on the r-modes of neutron stars

Techniques are developed here for evaluating the r-modes of rotating neutron stars through second order in the angular velocity of the star. Second-order corrections to the frequencies and eigenfunctions for these modes are evaluated for neutron star models. The second-order eigenfunctions for these modes are determined here by solving an unusual inhomogeneous hyperbolic boundary-value problem. The numerical techniques developed to solve this unusual problem are somewhat non-standard and may well be of interest beyond the particular application here. The bulk-viscosity coupling to the r-modes, which appears first at second order, is evaluated. The bulk-viscosity timescales are found here to be longer than previous estimates for normal neutron stars, but shorter than previous estimates for strange stars. These new timescales do not substantially affect the current picture of the gravitational radiation driven instability of the r-modes either for neutron stars or for strange stars.

gr-qc↗

arXiv1998

Generalized r-Modes of the Maclaurin Spheroids

Analytical solutions are presented for a class of generalized r-modes of rigidly rotating uniform density stars---the Maclaurin spheroids---with arbitrary values of the angular velocity. Our analysis is based on the work of Bryan; however, we derive the solutions using slightly different coordinates that give purely real representations of the r-modes. The class of generalized r-modes is much larger than the previously studied `classical' r-modes. In particular, for each l and m we find l-m (or l-1 for the m=0 case) distinct r-modes. Many of these previously unstudied r-modes (about 30% of those examined) are subject to a secular instability driven by gravitational radiation. The eigenfunctions of the `classical' r-modes, the l=m+1 case here, are found to have particularly simple analytical representations. These r-modes provide an interesting mathematical example of solutions to a hyperbolic eigenvalue problem.

gr-qc↗

arXiv1998

Gravitational waves from hot young rapidly rotating neutron stars

Gravitational radiation drives an instability in the r-modes of young rapidly rotating neutron stars. This instability is expected to carry away most of the angular momentum of the star by gravitational radiation emission, leaving a star rotating at about 100 Hz. In this paper we model in a simple way the development of the instability and evolution of the neutron star during the year-long spindown phase. This allows us to predict the general features of the resulting gravitational waveform. We show that a neutron star formed in the Virgo cluster could be detected by the LIGO and VIRGO gravitational wave detectors when they reach their ``enhanced'' level of sensitivity, with an amplitude signal-to-noise ratio that could be as large as about 8 if near-optimal data analysis techniques are developed. We also analyze the stochastic background of gravitational waves produced by the r-mode radiation from neutron-star formation throughout the universe. Assuming a substantial fraction of neutron stars are born with spin frequencies near their maximum values, this stochastic background is shown to have an energy density of about 10^-9 of the cosmological closure density, in the range 20 Hz to 1 kHz. This radiation should be detectable by ``advanced'' LIGO as well.

gr-qc↗

arXiv1998

Gravitational Radiation Instability in Hot Young Neutron Stars

We show that gravitational radiation drives an instability in hot young rapidly rotating neutron stars. This instability occurs primarily in the l=2 r-mode and will carry away most of the angular momentum of a rapidly rotating star by gravitational radiation. On the timescale needed to cool a young neutron star to about T=10^9 K (about one year) this instability can reduce the rotation rate of a rapidly rotating star to about 0.076Ω_K, where Ω_K is the Keplerian angular velocity where mass shedding occurs. In older colder neutron stars this instability is suppressed by viscous effects, allowing older stars to be spun up by accretion to larger angular velocities.

gr-qc↗

arXiv1998

Phase Transitions and the Mass-Radius Curves of Relativistic Stars

The properties of the mass-radius curves of relativistic stellar models constructed from an equation of state with a first-order phase transition are examined. It is shown that the slope of the mass-radius curve is continuous unless the discontinuity in the density at the phase transition point has a certain special value. The curve has a cusp if the discontinuity is larger than this value. The curvature of the mass-radius curve becomes singular at the point where the high density phase material first appears. This singularity makes the mass-radius curve appear on large scales to have a discontinuity in its slope at this point, even though the slope is in fact continuous on microscopic scales. Analytical formulae describing the behavior of these curves are found for the simple case of models with two-zone uniform-density equations of state.

gr-qc↗

arXiv1997

Relativistic Stellar Pulsations With Near-Zone Boundary Conditions

A new method is presented here for evaluating approximately the pulsation modes of relativistic stellar models. This approximation relies on the fact that gravitational radiation influences these modes only on timescales that are much longer than the basic hydrodynamic timescale of the system. This makes it possible to impose the boundary conditions on the gravitational potentials at the surface of the star rather than in the asymptotic wave zone of the gravitational field. This approximation is tested here by predicting the frequencies of the outgoing non-radial hydrodynamic modes of non-rotating stars. The real parts of the frequencies are determined with an accuracy that is better than our knowledge of the exact frequencies (about 0.01%) except in the most relativistic models where it decreases to about 0.1%. The imaginary parts of the frequencies are determined with an accuracy of approximately M/R, where M is the mass and R is the radius of the star in question.

gr-qc↗

arXiv1996

Gravitational Helioseismology?

The magnitudes of the external gravitational perturbations associated with the normal modes of the Sun are evaluated to determine whether these solar oscillations could be observed with the proposed Laser Interferometer Space Antenna (LISA), a network of satellites designed to detect gravitational radiation. The modes of relevance to LISA---the $l=2$, low-order $p$, $f$ and $g$-modes---have not been conclusively observed to date. We find that the energy in these modes must be greater than about $10^{30} \rm{ergs}$ in order to be observable above the LISA detector noise. These mode energies are larger than generally expected, but are much smaller than the current observational upper limits. LISA may be confusion-limited at the relevant frequencies due to the galactic background from short-period white dwarf binaries. Present estimates of the number of these binaries would require the solar modes to have energies above about $10^{33} \rm{ergs}$ to be observable by LISA.

gr-qc↗

arXiv1995

The Relaxation Effect in Dissipative Relativistic Fluid Theories

The dynamics of the fluid fields in a large class of causal dissipative fluid theories is studied. It is shown that the physical fluid states in these theories must relax (on a time scale that is characteristic of the microscopic particle interactions) to ones that are essentially indistinguishable from the simple relativistic Navier-Stokes descriptions of these states. Thus, for example, in the relaxed form of a physical fluid state the stress energy tensor is in effect indistinguishable from a perfect fluid stress tensor plus small dissipative corrections proportional to the shear of the fluid velocity, the gradient of the temperature, etc.

gr-qc↗