2,934 research outputs found
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.Comment: 12 pages, 3 figures; minor changes and additions as will appear in
the version to be published in Physical Review D, January 199
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.Comment: 13 pages, 5 figures, revte
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.Comment: 10 pages (REVTeX 3.1), 5 figs., 1 table, fixed minor typos, published
in Phys. Rev. D 56, 2118 (1997
Toward stable 3D numerical evolutions of black-hole spacetimes
Three dimensional (3D) numerical evolutions of static black holes with
excision are presented. These evolutions extend to about 8000M, where M is the
mass of the black hole. This degree of stability is achieved by using
growth-rate estimates to guide the fine tuning of the parameters in a
multi-parameter family of symmetric hyperbolic representations of the Einstein
evolution equations. These evolutions were performed using a fixed gauge in
order to separate the intrinsic stability of the evolution equations from the
effects of stability-enhancing gauge choices.Comment: 4 pages, 5 figures. To appear in Phys. Rev. D. Minor additions to
text for clarification. Added short paragraph about inner boundary dependenc
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<P<1.2P_min) white dwarf stars. Further, the growth
times of this instability are so long that these conditions must persist for a
very long time (t>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.Comment: 5 Pages, 5 Figures, revte
The metaphysics of Machian frame-dragging
The paper investigates the kind of dependence relation that best portrays Machian frame-dragging in general relativity. The question is tricky because frame-dragging relates local inertial frames to distant distributions of matter in a time-independent way, thus establishing some sort of non-local link between the two. For this reason, a plain causal interpretation of frame-dragging faces huge challenges. The paper will shed light on the issue by using a generalized structural equation model analysis in terms of manipulationist counterfactuals recently applied in the context of metaphysical enquiry by Schaffer (2016) and Wilson (2017). The verdict of the analysis will be that frame-dragging is best understood in terms of a novel type of dependence relation that is half-way between causation and grounding
The genus Xanthomendoza in Norway
We distinguish five Xanthomendoza species in Norway, viz., X. borealis, X. fallax, X. fulva, X. oregana, and X. ulophyllodes, based on morphology and molecular evidence. This paper gives an updated taxonomy of the Norwegian species of Xanthomendoza, and addresses previous misconceptions. Xanthomendoza ulophyllodes is reported as occurring in Norway. The species was previously misunderstood in Norway and removed fromthe Nordic checklist. We show that the nuclear internal transcribed spacer (nrITS) is a useful barcode marker for the treated species. We provide a key and short descriptions of the species, with notes on specific issues, ecology, geographic distribution, illustrations, maps, and a DNA reference library (DNA barcoding).publishedVersio
A Spectral Approach to the Relativistic Inverse Stellar Structure Problem
A new method for solving the relativistic inverse stellar structure problem
is presented. This method determines a spectral representation of the unknown
high density portion of the stellar equation of state from a knowledge of the
total masses M and radii R of the stars. Spectral representations of the
equation of state are very efficient, generally requiring only a few spectral
parameters to achieve good accuracy. This new method is able, therefore, to
determine the high density equation of state quite accurately from only a few
accurately measured [M,R] data points. This method is tested here by
determining the equations of state from mock [M,R] data computed from tabulated
"realistic" neutron-star equations of state. The spectral equations of state
obtained from these mock data are shown to agree on average with the originals
to within a few percent (over the entire high density range of the neutron-star
interior) using only two [M,R] data points. Higher accuracies are achieved when
more data are used. The accuracies of the equations of state determined in
these examples are shown to be nearly optimal, in the sense that their errors
are comparable to the errors of the best-fit spectral representations of these
realistic equations of state.Comment: 12 pages; 1 table; v2 minor changes to version accepted in Phys. Rev.
Differential rotation of the unstable nonlinear r-modes
At second order in perturbation theory, the r-modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation reaction, the differential rotation is constant in time and has been computed by Sá. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance ϖ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the r-mode instability removes this gauge freedom; the exponentially growing differential rotation of the unstable second-order r-mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for slowly rotating models with polytropic equations of state
Differential rotation of nonlinear r-modes
Differential rotation of r-modes is investigated within the nonlinear theory
up to second order in the mode amplitude in the case of a slowly-rotating,
Newtonian, barotropic, perfect-fluid star. We find a nonlinear extension of the
linear r-mode, which represents differential rotation that produces large scale
drifts of fluid elements along stellar latitudes. This solution includes a
piece induced by first-order quantities and another one which is a pure
second-order effect. Since the latter is stratified on cylinders, it cannot
cancel differential rotation induced by first-order quantities, which is not
stratified on cylinders. It is shown that, unlikely the situation in the
linearized theory, r-modes do not preserve vorticity of fluid elements at
second-order. It is also shown that the physical angular momentum and energy of
the perturbation are, in general, different from the corresponding canonical
quantities.Comment: 9 pages, revtex4; section III revised, comments added in Introduction
and Conclusions, references updated; to appear in Phys. Rev.
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