35,451 research outputs found
Stellar Over-densities in the Outer Halo of the Milky Way
This study presents a tomographic survey of a subset of the outer halo (10-40
kpc) drawn from the Sloan Digital Sky Survey Data Release 6. Halo substructure
on spatial scales of degrees is revealed as an excess in the local density
of sub-giant stars. With an appropriate assumption of a model stellar isochrone
it is possible for us to then derive distances to the sub-giant population. We
describe three new candidate halo substructures; the 160- and 180-degree
over-densities (at distances of 17 and 19 kpc respectively and radii of 1.3 and
1.5 kpc respectively) and an extended feature at 28 kpc that covers at least
162 square degrees, the Virgo Equatorial Stream. In addition, we recover the
Sagittarius dwarf galaxy (Sgr) leading arm material and the Virgo Over-density.
The derived distances, together with the number of sub-giant stars associated
with each substructure, enables us to derive the integrated luminosity for the
features. The tenuous, low surface brightness of the features strongly suggests
an origin from the tidal disruption of an accreted galaxy or galaxies. Given
the dominance of the tidal debris of Sgr in this region of the sky we
investigate if our observations can be accommodated by tidal disruption models
for Sgr. The clear discordance between observations and model predictions for
known Sgr features means it is difficult to tell unambiguously if the new
substructures are related to Sgr or not. Radial velocities in the stellar
over-densities will be critical in establishing their origins.Comment: 14 pages, 7 figures, PASA accepte
Integrable Abel equations and Vein's Abel equation
We first reformulate and expand with several novel findings some of the basic
results in the integrability of Abel equations. Next, these results are applied
to Vein's Abel equation whose solutions are expressed in terms of the third
order hyperbolic functions and a phase space analysis of the corresponding
nonlinear oscillator is also providedComment: 12 pages, 4 figures, 17 references, online at Math. Meth. Appl. Sci.
since 7/28/2015, published 4/201
Ermakov-Lewis Invariants and Reid Systems
Reid's m'th-order generalized Ermakov systems of nonlinear coupling constant
alpha are equivalent to an integrable Emden-Fowler equation. The standard
Ermakov-Lewis invariant is discussed from this perspective, and a closed
formula for the invariant is obtained for the higher-order Reid systems (m\geq
3). We also discuss the parametric solutions of these systems of equations
through the integration of the Emden-Fowler equation and present an example of
a dynamical system for which the invariant is equivalent to the total energyComment: 8 pages, published versio
Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations
We emphasize two connections, one well known and another less known, between
the dissipative nonlinear second order differential equations and the Abel
equations which in its first kind form have only cubic and quadratic terms.
Then, employing an old integrability criterion due to Chiellini, we introduce
the corresponding integrable dissipative equations. For illustration, we
present the cases of some integrable dissipative Fisher, nonlinear pendulum,
and Burgers-Huxley type equations which are obtained in this way and can be of
interest in applications. We also show how to obtain Abel solutions directly
from the factorization of second-order nonlinear equationsComment: 6 pages, 7 figures, published versio
Integrable equations with Ermakov-Pinney nonlinearities and Chiellini damping
We introduce a special type of dissipative Ermakov-Pinney equations of the
form v_{\zeta \zeta}+g(v)v_{\zeta}+h(v)=0, where h(v)=h_0(v)+cv^{-3} and the
nonlinear dissipation g(v) is based on the corresponding Chiellini integrable
Abel equation. When h_0(v) is a linear function, h_0(v)=\lambda^2v, general
solutions are obtained following the Abel equation route. Based on particular
solutions, we also provide general solutions containing a factor with the phase
of the Milne type. In addition, the same kinds of general solutions are
constructed for the cases of higher-order Reid nonlinearities. The Chiellini
dissipative function is actually a dissipation-gain function because it can be
negative on some intervals. We also examine the nonlinear case
h_0(v)=\Omega_0^2(v-v^2) and show that it leads to an integrable hyperelliptic
caseComment: 15 pages, 5 figures, 1 appendix, 21 references, published versio
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