221 research outputs found
Gravitational waves from binaries on unbound orbits
A generalized true anomaly-type parametrization, convenient to describe both
bound and open orbits of a two-body system in general relativity is introduced.
A complete description of the time evolution of both the radial and of the
angular equations of a binary system taking into account the first order
post-newtonian (1PN) is given. The gravitational radiation field emitted by the
system is computed in the 1PN approximation including higher multipole moments
beyond the standard quadrupole term. The gravitational waveforms in the time
domain are explicitly given up to the 1PN order for unbound orbits, but the
results are also illustrated on binaries on elliptic orbits with special
attention given to the effects of eccentricity.Comment: 27 pages, 10 figures, to appear in Phys. Rev.
A BABCOCK-LEIGHTON SOLAR DYNAMO MODEL WITH MULTI-CELLULAR MERIDIONAL CIRCULATION IN ADVECTION- AND DIFFUSION-DOMINATED REGIMES
Babcock-Leighton type solar dynamo models with single-celled meridional
circulation are successful in reproducing many solar cycle features. Recent
observations and theoretical models of meridional circulation do not indicate a
single-celled flow pattern. We examine the role of complex multi-cellular
circulation patterns in a Babcock-Leighton solar dynamo in advection- and
diffusion-dominated regimes. We show from simulations that presence of a weak,
second, high-latitude reverse cell speeds up the cycle and slightly enhances
the poleward branch in butterfly diagram, whereas the presence of a second cell
in depth reverses the tilt of butterfly wing to an anti-solar type. A butterfly
diagram constructed from middle of convection zone yields a solar-like pattern,
but this may be difficult to realize in the Sun because of magnetic buoyancy
effects. Each of the above cases behaves similarly in higher and lower magnetic
diffusivity regimes. However, our dynamo with a meridional circulation
containing four cells in latitude behaves distinctly differently in the two
regimes, producing solar-like butterfly diagrams with fast cycles in the higher
diffusivity regime, and complex branches in butterfly diagrams in the lower
diffusivity regime. We also find that dynamo solutions for a four-celled
pattern, two in radius and two in latitude, prefer to quickly relax to
quadrupolar parity if the bottom flow-speed is strong enough, of similar order
of magnitude as the surface flow-speed.Comment: 40 pages, 19 figures, accepted in Ap
Mass loss and longevity of gravitationally bound oscillating scalar lumps (oscillatons) in D-dimensions
Spherically symmetric oscillatons (also referred to as oscillating soliton
stars) i.e. gravitationally bound oscillating scalar lumps are considered in
theories containing a massive self-interacting real scalar field coupled to
Einstein's gravity in 1+D dimensional spacetimes. Oscillations are known to
decay by emitting scalar radiation with a characteristic time scale which is,
however, extremely long, it can be comparable even to the lifetime of our
universe. In the limit when the central density (or amplitude) of the
oscillaton tends to zero (small-amplitude limit) a method is introduced to
compute the transcendentally small amplitude of the outgoing waves. The results
are illustrated in detail on the simplest case, a single massive free scalar
field coupled to gravity.Comment: 23 pages, 2 figures, references on oscillons added, version to appear
in Phys. Rev.
Negative radiation pressure exerted on kinks
The interaction of a kink and a monochromatic plane wave in one dimensional
scalar field theories is studied. It is shown that in a large class of models
the radiation pressure exerted on the kink is negative, i.e. the kink is {\sl
pulled} towards the source of the radiation. This effect has been observed by
numerical simulations in the model, and it is explained by a
perturbative calculation assuming that the amplitude of the incoming wave is
small. Quite importantly the effect is shown to be robust against small
perturbations of the model. In the sine-Gordon (sG) model the time
averaged radiation pressure acting on the kink turns out to be zero. The
results of the perturbative computations in the sG model are shown to be in
full agreement with an analytical solution corresponding to the superposition
of a sG kink with a cnoidal wave. It is also demonstrated that the acceleration
of the kink satisfies Newton's law.Comment: 23 pages, 8 figures, LaTeX/RevTe
What does a strongly excited 't Hooft-Polyakov magnetic monopole do?
The time evolution of strongly exited SU(2) Bogomolny-Prasad-Sommerfield
(BPS) magnetic monopoles in Minkowski spacetime is investigated by means of
numerical simulations based on the technique of conformal compactification and
on the use of hyperboloidal initial value problem. It is found that an
initially static monopole does not radiate the entire energy of the exciting
pulse toward future null infinity. Rather, a long-lasting quasi-stable
`breathing state' develops in the central region and certain expanding shell
structures -- built up by very high frequency oscillations -- are formed in the
far away region.Comment: 4 pages, 6 figure
Instabilities of Twisted Strings
A linear stability analysis of twisted flux-tubes (strings) in an SU(2)
semilocal theory -- an Abelian-Higgs model with two charged scalar fields with
a global SU(2) symmetry -- is carried out. Here the twist refers to a relative
phase between the two complex scalars (with linear dependence on, say, the
coordinate), and importantly it leads to a global current flowing along the the
string. Such twisted strings bifurcate with the Abrikosov-Nielsen-Olesen (ANO)
solution embedded in the semilocal theory. Our numerical investigations of the
small fluctuation spectrum confirm previous results that twisted strings
exhibit instabilities whose amplitudes grow exponentially in time. More
precisely twisted strings with a single magnetic flux quantum admit a
continuous family of unstable eigenmodes with harmonic dependence, indexed
by a wavenumber . Carrying out a perturbative
semi-analytic analysis of the bifurcation, it is found that the purely
numerical results are very well reproduced. This way one obtains not only a
good qualitative description of the twisted solutions themselves as well as of
their instabilities, but also a quantitative description of the numerical
results. Our semi-analytic results indicate that in close analogy to the known
instability of the embedded ANO vortex a twisted string is also likely to
expand in size caused by the spreading out of its magnetic flux.Comment: 27 pages, 18 figures. Typos corrected, references adde
On the compatibility of a flux transport dynamo with a fast tachocline scenario
The compatibility of the fast tachocline scenario with a flux transport
dynamo model is explored. We employ a flux transport dynamo model coupled with
simple feedback formulae relating the thickness of the tachocline to the
amplitude of the magnetic field or to the Maxwell stress. The dynamo model is
found to be robust against the nonlinearity introduced by this simplified fast
tachocline mechanism. Solar-like butterfly diagrams are found to persist and,
even without any parameter fitting, the overall thickness of the tachocline is
well within the range admitted by helioseismic constraints. In the most
realistic case of a time and latitude dependent tachocline thickness linked to
the value of the Maxwell stress, both the thickness and its latitude dependence
are in excellent agreement with seismic results. In the nonparametric models,
cycle related temporal variations in tachocline thickness are somewhat larger
than admitted by helioseismic constraints; we find, however, that introducing a
further parameter into our feedback formula readily allows further fine tuning
of the thickness variations.Comment: Accepted in Solar Physic
Resonant excitations of the 't Hooft-Polyakov monopole
The spherically symmetric magnetic monopole in an SU(2) gauge theory coupled
to a massless Higgs field is shown to possess an infinite number of resonances
or quasinormal modes. These modes are eigenfunctions of the isospin 1
perturbation equations with complex eigenvalues, ,
satisfying the outgoing radiation condition. For , their
frequencies approach the mass of the vector boson, , while
their lifetimes tend to infinity. The response of the monopole to
an arbitrary initial perturbation is largely determined by these resonant
modes, whose collective effect leads to the formation of a long living
breather-like excitation characterized by pulsations with a frequency
approaching and with an amplitude decaying at late times as .Comment: 4 page
An analytical approximation scheme to two point boundary value problems of ordinary differential equations
A new (algebraic) approximation scheme to find {\sl global} solutions of two
point boundary value problems of ordinary differential equations (ODE's) is
presented. The method is applicable for both linear and nonlinear (coupled)
ODE's whose solutions are analytic near one of the boundary points. It is based
on replacing the original ODE's by a sequence of auxiliary first order
polynomial ODE's with constant coefficients. The coefficients in the auxiliary
ODE's are uniquely determined from the local behaviour of the solution in the
neighbourhood of one of the boundary points. To obtain the parameters of the
global (connecting) solutions analytic at one of the boundary points, reduces
to find the appropriate zeros of algebraic equations. The power of the method
is illustrated by computing the approximate values of the ``connecting
parameters'' for a number of nonlinear ODE's arising in various problems in
field theory. We treat in particular the static and rotationally symmetric
global vortex, the skyrmion, the Nielsen-Olesen vortex, as well as the 't
Hooft-Polyakov magnetic monopole. The total energy of the skyrmion and of the
monopole is also computed by the new method. We also consider some ODE's coming
from the exact renormalization group. The ground state energy level of the
anharmonic oscillator is also computed for arbitrary coupling strengths with
good precision.Comment: 5 pages, 3 tables, Late
Small amplitude quasi-breathers and oscillons
Quasi-breathers (QB) are time-periodic solutions with weak spatial
localization introduced in G. Fodor et al. in Phys. Rev. D. 74, 124003 (2006).
QB's provide a simple description of oscillons (very long-living spatially
localized time dependent solutions). The small amplitude limit of QB's is
worked out in a large class of scalar theories with a general self-interaction
potential, in spatial dimensions. It is shown that the problem of small
amplitude QB's is reduced to a universal elliptic partial differential
equation. It is also found that there is the critical dimension, ,
above which no small amplitude QB's exist. The QB's obtained this way are shown
to provide very good initial data for oscillons. Thus these QB's provide the
solution of the complicated, nonlinear time dependent problem of small
amplitude oscillons in scalar theories.Comment: 24 pages, 19 figure
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