1,254 research outputs found
A Pedagogical Discussion Concerning the Gravitational Energy Radiated by Keplerian Systems
We first discuss the use of dimensional arguments (and of the quadrupolar
emission hypothesis) in the derivation of the gravitational power radiated on a
circular orbit. Then, we show how to simply obtain the instantaneous power
radiated on a general Keplerian orbit by approximating it locally by a circle.
This allows recovering with a good precision, in the case of an ellipse, the
highly non trivial dependence on the eccentricity of the average power given by
general relativity. The whole approach is understandable by undergraduate
students.Comment: A simpler method has been used in the calculations, which requires
now only standard knowledge (the radius of curvature is defined by the normal
acceleration). Two figures have been added. Concerning the dimensional
analysis, the comparison with electromagnetism has been detaile
How to adapt broad-band gravitational-wave searches for r-modes
Up to now there has been no search for gravitational waves from the r-modes
of neutron stars in spite of the theoretical interest in the subject. Several
oddities of r-modes must be addressed to obtain an observational result: The
gravitational radiation field is dominated by the mass current
(gravitomagnetic) quadrupole rather than the usual mass quadrupole, and the
consequent difference in polarization affects detection statistics and
parameter estimation. To astrophysically interpret a detection or upper limit
it is necessary to convert the wave amplitude to an r-mode amplitude. Also, it
is helpful to know indirect limits on gravitational-wave emission to gauge the
interest of various searches. Here I address these issues, thereby providing
the ingredients to adapt broad-band searches for continuous gravitational waves
to obtain r-mode results. I also show that searches of existing data can
already have interesting sensitivities to r-modes.Comment: 8 pages, no figure
Had the planet mars not existed: Kepler's equant model and its physical consequences
We examine the equant model for the motion of planets, which has been the
starting point of Kepler's investigations before he modified it because of Mars
observations. We show that, up to first order in eccentricity, this model
implies for each orbit a velocity which satisfies Kepler's second law and
Hamilton's hodograph, and a centripetal acceleration with an inverse square
dependence on the distance to the sun. If this dependence is assumed to be
universal, Kepler's third law follows immediately. This elementary execice in
kinematics for undergraduates emphasizes the proximity of the equant model
coming from Ancient Greece with our present knowledge. It adds to its
historical interest a didactical relevance concerning, in particular, the
discussion of the Aristotelian or Newtonian conception of motion
R-Mode Oscillations and Spindown of Young Rotating Magnetic Neutron Stars
Recent work has shown that a young, rapidly rotating neutron star loses
angular momentum to gravitational waves generated by unstable r-mode
oscillations. We study the spin evolution of a young, magnetic neutron star
including both the effects of gravitational radiation and magnetic braking
(modeled as magnetic dipole radiation). Our phenomenological description of
nonlinear r-modes is similar to, but distinct from, that of Owen et al. (1998)
in that our treatment is consistent with the principle of adiabatic invariance
in the limit when direct driving and damping of the mode are absent. We show
that, while magnetic braking tends to increase the r-mode amplitude by spinning
down the neutron star, it nevertheless reduces the efficiency of gravitational
wave emission from the star. For B >= 10^14 (\nus/300 Hz)^2 G, where \nus is
the spin frequency, the spindown rate and the gravitational waveforms are
significantly modified by the effect of magnetic braking. We also estimate the
growth rate of the r-mode due to electromagnetic (fast magnetosonic) wave
emission and due to Alfven wave emission in the neutron star magnetosphere. The
Alfven wave driving of the r-mode becomes more important than the gravitational
radiation driving when B >= 10^13 (\nus/150 Hz)^3 G; the electromagnetic wave
driving of the r-mode is much weaker. Finally, we study the properties of local
Rossby-Alfven waves inside the neutron star and show that the fractional change
of the r-mode frequency due to the magnetic field is of order 0.5 (B/10^16 G)^2
(\nus/100 Hz)^-2.Comment: 18 pages, 4 figures; ApJ, accepted (v544: Nov 20, 2000); added two
footnotes and more discussion of mode driving by Alfven wave
A simple derivation of Kepler's laws without solving differential equations
Proceeding like Newton with a discrete time approach of motion and a
geometrical representation of velocity and acceleration, we obtain Kepler's
laws without solving differential equations. The difficult part of Newton's
work, when it calls for non trivial properties of ellipses, is avoided by the
introduction of polar coordinates. Then a simple reconsideration of Newton's
figure naturally leads to en explicit expression of the velocity and to the
equation of the trajectory. This derivation, which can be fully apprehended by
beginners at university (or even before) can be considered as a first
application of mechanical concepts to a physical problem of great historical
and pedagogical interest
Signatures of Classical Periodic Orbits on a Smooth Quantum System
Gutzwiller's trace formula and Bogomolny's formula are applied to a
non--specific, non--scalable Hamiltonian system, a two--dimensional anharmonic
oscillator. These semiclassical theories reproduce well the exact quantal
results over a large spatial and energy range.Comment: 12 pages, uuencoded postscript file (1526 kb
Asymptotic and measured large frequency separations
With the space-borne missions CoRoT and Kepler, a large amount of
asteroseismic data is now available. So-called global oscillation parameters
are inferred to characterize the large sets of stars, to perform ensemble
asteroseismology, and to derive scaling relations. The mean large separation is
such a key parameter. It is therefore crucial to measure it with the highest
accuracy. As the conditions of measurement of the large separation do not
coincide with its theoretical definition, we revisit the asymptotic expressions
used for analysing the observed oscillation spectra. Then, we examine the
consequence of the difference between the observed and asymptotic values of the
mean large separation. The analysis is focused on radial modes. We use series
of radial-mode frequencies to compare the asymptotic and observational values
of the large separation. We propose a simple formulation to correct the
observed value of the large separation and then derive its asymptotic
counterpart. We prove that, apart from glitches due to stellar structure
discontinuities, the asymptotic expansion is valid from main-sequence stars to
red giants. Our model shows that the asymptotic offset is close to 1/4, as in
the theoretical development. High-quality solar-like oscillation spectra
derived from precise photometric measurements are definitely better described
with the second-order asymptotic expansion. The second-order term is
responsible for the curvature observed in the \'echelle diagrams used for
analysing the oscillation spectra and this curvature is responsible for the
difference between the observed and asymptotic values of the large separation.
Taking it into account yields a revision of the scaling relations providing
more accurate asteroseismic estimates of the stellar mass and radius.Comment: accepted in A&
R-Mode Oscillations in Rotating Magnetic Neutron Stars
We show that r-mode oscillations distort the magnetic fields of neutron stars
and that their occurrence is likely to be limited by this interaction. If the
field is gtrsim 10^{16} (Omega/Omega_B) G, where Omega and Omega_B are the
angular velocities of the star and at which mass shedding occurs, r-mode
oscillations cannot occur. Much weaker fields will prevent gravitational
radiation from exciting r-mode oscillations or damp them on a relatively short
timescale by extracting energy from the modes faster than gravitational wave
emission can pump energy into them. For example, a 10^{10} G poloidal magnetic
field that threads the star's superconducting core is likely to prevent the
ell=2 mode from being excited unless Omega exceeds 0.35 Omega_B. If Omega is
larger than 0.35 Omega_B initially, the ell=2 mode may be excited but is likely
to decay rapidly once Omega falls below 0.35 Omega_B, which happens in lesssim
15^d if the saturation amplitude is gtrsim 0.1. The r-mode oscillations may
play an important role in determining the structure of neutron star magnetic
fields.Comment: 4 pages, 1 postscript figure, uses emulateapj; submitted to ApJ
Letters 1999 Nov 8; accepted 2000 Jan 25; this version is essentially
identical to the original version except that Figure 2 was deleted in order
to fit within the ApJ Letters page limi
An indole alkaloid from Strychnos erichsonii
Le premier alcaloïde indolique de type vobasine rencontré dans les #Loganiaceae a été isolé des écorces de #Strychnos erichsonii, récoltées en Guyane Française. Sa structure confirmée par cristallographie Rx. (Résumé d'auteur
The r-mode instability: Analytical solution with gravitational radiation reaction
Analytical r-mode solutions are investigated within the linearized theory in
the case of a slowly rotating, Newtonian, barotropic, non-magnetized,
perfect-fluid star in which the gravitational radiation (GR) reaction force is
present. For the GR reaction term we use the 3.5 post-Newtonian order expansion
of the GR force, in order to include the contribution of the current quadrupole
moment. We find the explicit expression for the r-mode velocity perturbations
and we conclude that they are sinusoidal with the same frequency as the
well-known GR force-free linear r-mode solution, and that the GR force drives
the r-modes unstable with a growth timescale that agrees with the expression
first found by Lindblom, Owen and Morsink. We also show that the amplitude of
these velocity perturbations is corrected, relatively to the GR force-free
case, by a term of order W^6, where W is the angular velocity of the star.Comment: 11 pages, RevTeX4. Discussion on the nonlinear theory removed.
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