230 research outputs found
Atomic Spectral Features During Thermonuclear Flashes on Neutron Stars
The gravitational redshift measured by Cottam, Paerels and Mendez for the
neutron star (NS) in the low-mass X-ray binary EXO 0748-676 depends on the
identification of an absorption line during a type I burst as the H
line from hydrogenic Fe. We show that Fe is present above the photosphere as
long as during the burst. In
this limit, the total Fe column is for incident material of solar abundances and only depends on the
nuclear physics of the proton spallation. The Fe destruction creates many heavy
elements with which may imprint photo-ionization edges on the NS spectra
during a radius expansion event or in a burst cooling tail. Detecting these
features in concert with those from Fe would confirm a redshift measurement. We
also begin to address the radiative transfer problem, and find that a
concentrated Fe layer with and column (depending on the line depth) above the hotter
continuum photosphere is required to create the H line of the observed
strength. This estimate must be refined by considerations of non-LTE effects as
well as resonant line transport. Until these are carried out, we cannot say
whether the Fe column from accretion and spallation is in conflict with the
observations. We also show that hydrogenic Fe might remain in the photosphere
due to radiative levitation from the high burst flux.Comment: Substantially revised version, to appear in Ap J Letter
Classification of integrable hydrodynamic chains and generating functions of conservation laws
New approach to classification of integrable hydrodynamic chains is
established. Generating functions of conservation laws are classified by the
method of hydrodynamic reductions. N parametric family of explicit hydrodynamic
reductions allows to reconstruct corresponding hydrodynamic chains. Plenty new
hydrodynamic chains are found
Whitham systems and deformations
We consider the deformations of Whitham systems including the "dispersion
terms" and having the form of Dubrovin-Zhang deformations of Frobenius
manifolds. The procedure is connected with B.A. Dubrovin problem of
deformations of Frobenius manifolds corresponding to the Whitham systems of
integrable hierarchies. Under some non-degeneracy requirements we suggest a
general scheme of the deformation of the hyperbolic Whitham systems using the
initial non-linear system. The general form of the deformed Whitham system
coincides with the form of the "low-dispersion" asymptotic expansions used by
B.A. Dubrovin and Y. Zhang in the theory of deformations of Frobenius
manifolds.Comment: 27 pages, Late
Gurevich-Zybin system
We present three different linearizable extensions of the Gurevich-Zybin
system. Their general solutions are found by reciprocal transformations. In
this paper we rewrite the Gurevich-Zybin system as a Monge-Ampere equation. By
application of reciprocal transformation this equation is linearized.
Infinitely many local Hamiltonian structures, local Lagrangian representations,
local conservation laws and local commuting flows are found. Moreover, all
commuting flows can be written as Monge-Ampere equations similar to the
Gurevich-Zybin system. The Gurevich-Zybin system describes the formation of a
large scale structures in the Universe. The second harmonic wave generation is
known in nonlinear optics. In this paper we prove that the Gurevich-Zybin
system is equivalent to a degenerate case of the second harmonic generation.
Thus, the Gurevich-Zybin system is recognized as a degenerate first negative
flow of two-component Harry Dym hierarchy up to two Miura type transformations.
A reciprocal transformation between the Gurevich-Zybin system and degenerate
case of the second harmonic generation system is found. A new solution for the
second harmonic generation is presented in implicit form.Comment: Corrected typos and misprint
Reciprocal transformations of Hamiltonian operators of hydrodynamic type: nonlocal Hamiltonian formalism for linearly degenerate systems
Reciprocal transformations of Hamiltonian operators of hydrodynamic type are
investigated. The transformed operators are generally nonlocal, possessing a
number of remarkable algebraic and differential-geometric properties. We apply
our results to linearly degenerate semi-Hamiltonian systems in Riemann
invariants. Since all such systems are linearizable by appropriate
(generalized) reciprocal transformations, our formulae provide an infinity of
mutually compatible nonlocal Hamiltonian structures, explicitly parametrized by
arbitrary functions of one variable.Comment: 26 page
Transmission of a Symmetric Light Pulse through a Wide QW
The reflection, transmission and absorption of a symmetric electromagnetic
pulse, which carrying frequency is close to the frequency of an interband
transition in a QW (QW), are obtained. The energy levels of a QW are assumed
discrete, one exited level is taken into account. The case of a wide QW is
considered when a length of the pulse wave, appropriate to the carrying
frequency, is comparable to the QW's width. In figures the time dependencies of
the dimensionless reflection, absorption are transmission are represented. It
is shown, that the spatial dispersion and a distinction in refraction indexes
influence stronger reflection.Comment: 8 pages,8 figures with caption
Weakly-nonlocal Symplectic Structures, Whitham method, and weakly-nonlocal Symplectic Structures of Hydrodynamic Type
We consider the special type of the field-theoretical Symplectic structures
called weakly nonlocal. The structures of this type are in particular very
common for the integrable systems like KdV or NLS. We introduce here the
special class of the weakly nonlocal Symplectic structures which we call the
weakly nonlocal Symplectic structures of Hydrodynamic Type. We investigate then
the connection of such structures with the Whitham averaging method and propose
the procedure of "averaging" of the weakly nonlocal Symplectic structures. The
averaging procedure gives the weakly nonlocal Symplectic Structure of
Hydrodynamic Type for the corresponding Whitham system. The procedure gives
also the "action variables" corresponding to the wave numbers of -phase
solutions of initial system which give the additional conservation laws for the
Whitham system.Comment: 64 pages, Late
Formation of Resonant Atomic Lines during Thermonuclear Flashes on Neutron Stars
Motivated by the measurement of redshifted Fe H lines during type I
X-ray bursts on EXO 0748-676 (Cottam, Paerels & Mendez), we study the formation
of atomic Fe lines above the photosphere of a bursting neutron star (). We discuss the effects of Stark broadening,
resonant scattering and NLTE (level population) on the formation of hydrogenic
Fe H, Ly and P lines. From the observed equivalent
width of the Fe H line, we find an implied Fe column of , which is 3-10 times larger than the Fe column
calculated from the accretion/spallation model of Bildsten, Chang & Paerels. We
also estimate that the implied Fe column is about a factor of 2-3 larger than a
uniform solar metallicity atmosphere. We discuss the effects of rotational
broadening and find that the rotation rate of \EXO must be slow, as confirmed
by the recent measurement of a 45 Hz burst oscillation by Villarreal &
Strohmayer. We also show that the Fe Ly EW 15-20 eV
(redshifted 11-15 eV) and the P EW 4-7 eV (redshifted 3-5 eV)
when the H EW is 10 eV (redshifted 8 eV). The Ly line is
rotationally broadened to a depth of , making it difficult to
observe with {\it Chandra}. We also show that radiative levitation can likely
support the Fe column needed to explain the line.Comment: 10 pages, 8 figures, to be published in Ap
Hydrogen Phases on the Surface of a Strongly Magnetized Neutron Star
The outermost layers of some neutron stars are likely to be dominated by
hydrogen, as a result of fast gravitational settling of heavier elements. These
layers directly mediate thermal radiation from the stars, and determine the
characteristics of X-ray/EUV spectra. For a neutron star with surface
temperature T\lo 10^6 K and magnetic field B\go 10^{12} G, various forms of
hydrogen can be present in the envelope, including atom, poly-molecules, and
condensed metal. We study the physical properties of different hydrogen phases
on the surface of a strongly magnetized neutron star for a wide range of field
strength and surface temperature . Depending on the values of and
, the outer envelope can be either in a nondegenerate gaseous phase or in a
degenerate metallic phase. For T\go 10^5 K and moderately strong magnetic
field, B\lo 10^{13} G, the envelope is nondegenerate and the surface material
gradually transforms into a degenerate Coulomb plasma as density increases. For
higher field strength, G, there exists a first-order phase
transition from the nondegenerate gaseous phase to the condensed metallic
phase. The column density of saturated vapor above the metallic hydrogen
decreases rapidly as the magnetic field increases or/and temperature decreases.
Thus the thermal radiation can directly emerge from the degenerate metallic
hydrogen surface. The characteristics of surface X-ray/EUV emission for
different phases are discussed. A separate study concerning the possibility of
magnetic field induced nuclear fusion of hydrogen on the neutron star surface
is also presented.Comment: TeX, 35 pages including 6 postscript figures. To be published in Ap
Global entrainment of transcriptional systems to periodic inputs
This paper addresses the problem of giving conditions for transcriptional
systems to be globally entrained to external periodic inputs. By using
contraction theory, a powerful tool from dynamical systems theory, it is shown
that certain systems driven by external periodic signals have the property that
all solutions converge to a fixed limit cycle. General results are proved, and
the properties are verified in the specific case of some models of
transcriptional systems. The basic mathematical results needed from contraction
theory are proved in the paper, making it self-contained
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