82,893 research outputs found
Tuning in on Cepheids: Radial velocity amplitude modulations. A source of systematic uncertainty for Baade-Wesselink distances
[Abridged] I report the discovery of modulations in radial velocity (RV)
curves of four Galactic classical Cepheids and investigate their impact as a
systematic uncertainty for Baade-Wesselink distances. Highly precise Doppler
measurements were obtained using the Coralie high-resolution spectrograph since
2011. Particular care was taken to sample all phase points in order to very
accurately trace the RV curve during multiple epochs and to search for
differences in linear radius variations derived from observations obtained at
different epochs. Different timescales are sampled, ranging from cycle-to-cycle
to months and years. The unprecedented combination of excellent phase coverage
obtained during multiple epochs and high precision enabled the discovery of
significant modulation in the RV curves of the short-period s-Cepheids QZ
Normae and V335 Puppis, as well as the long-period fundamental mode Cepheids l
Carinae and RS Puppis. The modulations manifest as shape and amplitude
variations that vary smoothly on timescales of years for short-period Cepheids
and from one pulsation cycle to the next in the long-period Cepheids. The order
of magnitude of the effect ranges from several hundred m/s to a few km/s. The
resulting difference among linear radius variations derived using data from
different epochs can lead to systematic errors of up to 15% for
Baade-Wesselink-type distances, if the employed angular and linear radius
variations are not determined contemporaneously. The different natures of the
Cepheids exhibiting modulation in their RV curves suggests that this phenomenon
is common. The observational baseline is not yet sufficient to conclude whether
these modulations are periodic. To ensure the accuracy of Baade-Wesselink
distances, angular and linear radius variations should always be determined
contemporaneously.Comment: 7 pages, 5 figures, 1 table. Accepted for publication in A&A letter
Some z<sub>n-1</sub> terraces from z<sub>n</sub> power-sequences, n being an odd prime power
A terrace for Zm is a particular type of sequence formed from the m elements of Zm. For m
odd, many procedures are available for constructing power-sequence terraces for Zm; each terrace of this
sort may be partitioned into segments, of which one contains merely the zero element of Zm, whereas
every other segment is either a sequence of successive powers of an element of Zm or such a sequence
multiplied throughout by a constant. We now refine this idea to show that, for m=n−1, where n is an odd prime power, there are many ways in which power-sequences in Zn can be used to arrange the elements of Zn \ {0} in a sequence of distinct entries i, 1 ≤ i ≤ m, usually in two or more segments, which becomes a terrace for Zm when interpreted modulo m instead of modulo n. Our constructions provide terraces for Zn-1 for all prime powers n satisfying 0 < n < 300 except for n = 125, 127 and 257
Special functions from quantum canonical transformations
Quantum canonical transformations are used to derive the integral
representations and Kummer solutions of the confluent hypergeometric and
hypergeometric equations. Integral representations of the solutions of the
non-periodic three body Toda equation are also found. The derivation of these
representations motivate the form of a two-dimensional generalized
hypergeometric equation which contains the non-periodic Toda equation as a
special case and whose solutions may be obtained by quantum canonical
transformation.Comment: LaTeX, 24 pp., Imperial-TP-93-94-5 (revision: two sections added on
the three-body Toda problem and a two-dimensional generalization of the
hypergeometric equation
New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory
DifferentialGeometry is a Maple software package which symbolically performs
fundamental operations of calculus on manifolds, differential geometry, tensor
calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the
variational calculus. These capabilities, combined with dramatic recent
improvements in symbolic approaches to solving algebraic and differential
equations, have allowed for development of powerful new tools for solving
research problems in gravitation and field theory. The purpose of this paper is
to describe some of these new tools and present some advanced applications
involving: Killing vector fields and isometry groups, Killing tensors and other
tensorial invariants, algebraic classification of curvature, and symmetry
reduction of field equations.Comment: 42 page
Symmetries of the Einstein Equations
Generalized symmetries of the Einstein equations are infinitesimal
transformations of the spacetime metric that formally map solutions of the
Einstein equations to other solutions. The infinitesimal generators of these
symmetries are assumed to be local, \ie at a given spacetime point they are
functions of the metric and an arbitrary but finite number of derivatives of
the metric at the point. We classify all generalized symmetries of the vacuum
Einstein equations in four spacetime dimensions and find that the only
generalized symmetry transformations consist of: (i) constant scalings of the
metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms.
Our results rule out a large class of possible ``observables'' for the
gravitational field, and suggest that the vacuum Einstein equations are not
integrable.Comment: 15 pages, FTG-114-USU, Plain Te
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